ITU-Rpy documentation¶

ITU-Rpy is a python implementation of the ITU-R P. Recommendations to compute atmospheric attenuation in slant and horizontal paths.

A complete overview of the contents of this documentation can be found in the Table of Contents at the bottom of this page.
Instructions on how to install ITU-Rpy are located at the Installation page.
Results of running ITU-Rpy against the validation examples provided by the ITU (where available) are available at the Validation page.

Citation¶

If you use ITU-Rpy in one of your research projects, please cite it as:

@misc{iturpy-2017,
      title={ITU-Rpy: A python implementation of the ITU-R P. Recommendations to compute
         atmospheric attenuation in slant and horizontal paths.},
      author={Inigo del Portillo},
      year={2017},
      publisher={GitHub},
      howpublished={\url{https://github.com/inigodelportillo/ITU-Rpy/}}
}

Usage and examples¶

The Quick Start guide provides different examples on how to use ITUR-py.

Additional examples can be found in the examples folder, and the snippet of code below.

import itur

f = 22.5 * itur.u.GHz    # Link frequency
D = 1 * itur.u.m         # Size of the receiver antenna
el = 60                  # Elevation angle constant of 60 degrees
p = 3                    # Percentage of time that attenuation values are exceeded.

# Generate a regular grid latitude and longitude points with 1 degrees resolution
lat, lon = itur.utils.regular_lat_lon_grid()

# Comute the atmospheric attenuation
Att = itur.atmospheric_attenuation_slant_path(lat, lon, f, el, p, D)
itur.plotting.plot_in_map(Att.value, lat, lon,
                       cbar_text='Atmospheric attenuation [dB]')

which produces

Atmospheric attenuation worldmap @ 22.5 GHz.

Table of Contents¶

Installation¶

Installation from pypi¶

To install ITU-Rpy from pypi, please use the following command on the command line:

pip install itur

Manual Installation¶

To install the development version of ITU-Rpy, please type the following commands on the command line:

git clone https://github.com/inigodelportillo/ITU-Rpy
cd ITU-Rpy
pip install -U -r requirements.txt
python setup.py install

Installing Cartopy¶

Cartopy can be used to plot results in maps. Installation of Cartopy is optional, and ITU-Rpy will still work without it. However, some plotting capabilities will be deactivated. A quick overview of Cartopy if provided below:

Cartopy is a Python package designed for geospatial data processing in order to produce maps and other geospatial data analyses. Cartopy has the ability to transform points, lines, vectors, polygons and images between different projections, and it can be combined with Matplotlib to plot contours, images, vectors, lines or points in the transformed coordinates.

To install Cartopy from pypi, please use the following command on the command line:

pip install cartopy

If that does not work, you can try to download it using conda:

conda -c conda-forge install cartopy

If you are using Windows, you can also install cartopy using the appropriate pre-compiled wheels file from this webpage. After downloading the .whl file, cartopy can be installed running:

pip install name_of_whl_file.whl

Quick Start¶

If you have not installed ITU-Rpy yet take a look at the installation instructions and make sure that all the requirements are fulfilled. Examples to illustrate the usage of ITU-Rpy are provided in the examples-folder. In order to understand the models used, check the models section .

To get started, we will walk you through a few examples that show the most illustrative case studies for

First, we explain the basic usage of ITU-Rpy by computing the attenuation at a single location.
Second, we explain the usage of ITU-Rpy using vectorized operations.
Finally, we summarize other useful atmospheric functions in the library. The complete API description can be accessed through the API section .

Single location attenuation¶

Here we will compute the link attenuation vs. at a frequency of 22.5 GHz for a link between a satellite in GEO at the orbital slot 77 W and a ground station in Boston.

In addition, we will show how to compute other parameters of interest such as 0 degree isotherm, rainfall intensity exceeded during 0.01 % of the time, total columnar content liquid water or temperature.

First, let’s define the coordinates of our ground station and compute the elevation angle of the link

import itur
import astropy.units as u

# Ground station coordinates (Boston)
lat_GS = 42.3601
lon_GS = -71.0942

# Satellite coordinates (GEO, 77 W)
lat_sat = 0
lon_sat = -77
h_sat = 35786 * u.km

# Compute the elevation angle between satellite and ground station
el = itur.utils.elevation_angle(h_sat, lat_sat, lon_sat, lat_GS, lon_GS)

Next, we define the link parameters

f = 22.5 * u.GHz    # Link frequency
D = 1.2 * u.m       # Antenna diameters

Finally, we compute the total atmospheric attenuation as well as the different contributions for a set of unavailability values and plot the results. Note the flag return_contributions = True when calling function itur.atmospheric_attenuation_slant_path.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import ScalarFormatter

# Define unavailabilities vector
unavailabilities = np.logspace(-1.5, 1.5, 100)

# Compute the
A_g, A_c, A_r, A_s, A_t = [], [], [], [], []
for p in unavailabilities:
        a_g, a_c, a_r, a_s, a_t = itur.atmospheric_attenuation_slant_path(lat_GS, lon_GS,
                                                                          f, el, p, D,
                                                                          return_contributions=True)
        A_g.append(a_g.value)
        A_c.append(a_c.value)
        A_r.append(a_r.value)
        A_s.append(a_s.value)
        A_t.append(a_t.value)

# Plot the results
ax = plt.subplot(1,1,1)
ax.semilogx(unavailabilities, A_g, label='Gaseous attenuation')
ax.semilogx(unavailabilities, A_c, label='Cloud attenuation')
ax.semilogx(unavailabilities, A_r, label='Rain attenuation')
ax.semilogx(unavailabilities, A_s, label='Scintillation attenuation')
ax.semilogx(unavailabilities, A_t, label='Total atmospheric attenuation')

ax.xaxis.set_major_formatter(ScalarFormatter())
ax.set_xlabel('Percentage of time attenuation value is exceeded [%]')
ax.set_ylabel('Attenuation [dB]')
ax.grid(which='both', linestyle=':')
plt.legend()

which results in the following plot image:

Atmospheric attenuation at Boston for a link to GEO - 77 W.

Note the by default, ITU-Rpy returns Quantity type objects, which are based on astropy.units module. Quantity objects are special objects that contain a value and unit attributes. Conversion among units is possible using the .to() method.

Atmospheric parameters such as temperature, pressure, or water-vapor density can be passed to function itur.atmospheric_attenuation_slant_path manually if known, otherwise ITU-Rpy will compute them automatically using the appropriate ITU Recommendation models. Similarly, if the ground station height above mean sea level is known, it can also be introduced manually.

Vectorial operations¶

One of the main characteristics of ITU-Rpy is that it allows for broadcasting of operations when using vectors. This allows for several use cases.

Multiple cities¶

First, we might be interested in computing the atmospheric attenuation values exceeded for 0.1 % of the time for a bunch of locations. This can be done as:

import itur
cities = {'Boston': (42.36, -71.06),
          'New York': (40.71, -74.01),
          'Los Angeles': (34.05, -118.24),
          'Denver': (39.74, -104.99),
          'Las Vegas': (36.20, -115.14),
          'Seattle': (47.61, -122.33),
          'Washington DC': (38.91, -77.04)}

lat = [coords[0] for coords in cities.values()]
lon = [coords[1] for coords in cities.values()]

# Satellite coordinates (GEO, 4 E)
lat_sat = 0
lon_sat = -77
h_sat = 35786 * itur.u.km

# Compute the elevation angle between satellite and ground stations
el = itur.utils.elevation_angle(h_sat, lat_sat, lon_sat, lat, lon)

# Set the link parameters
f = 22.5 * itur.u.GHz    # Link frequency
D = 1.2 * itur.u.m       # Antenna diameters
p = 0.1                  # Unavailability (Values exceeded 0.1% of time)

# Compute the atmospheric attenuation
Ag, Ac, Ar, As, Att = itur.atmospheric_attenuation_slant_path(
        lat, lon, f, el, p, D, return_contributions=True)

and we can plot the results

# Plot the results
city_idx = np.arange(len(cities))
width = 0.15

fig, ax = plt.subplots(1, 1)
ax.bar(city_idx, Att.value, 0.6, label='Total atmospheric Attenuation')

ax.bar(city_idx - 1.5 * width, Ar.value, width, label='Rain attenuation')
ax.bar(city_idx - 0.5 * width, Ag.value, width, label='Gaseous attenuation')
ax.bar(city_idx + 0.5 * width, Ac.value, width, label='Clouds attenuation')
ax.bar(city_idx + 1.5 * width, As.value, width,
           label='Scintillation attenuation')

# Set the labels
ticks = ax.set_xticklabels([''] + list(cities.keys()))
for t in ticks:
        t.set_rotation(45)
ax.set_ylabel('Atmospheric attenuation exceeded for 0.1% [dB]')

# Format image
ax.yaxis.grid(which='both', linestyle=':')
ax.legend(loc='upper center', bbox_to_anchor=(0.5, 1.3), ncol=2)
plt.tight_layout(rect=(0, 0, 1, 0.85))

Atmospheric attenuation exceeded for 0.1 % of the average year in different cities of the US.

Attenuation over regions of the Earth¶

A second use case for vectorization is computation of the atmospheric attenuation (and other parameters) over large geographical regions. Let’s say that we want to compute the attenuation over Africa of a new Ka-band satellite located in GEO at slot 4 E.

import itur
import astropy.units as u

# Generate regular grid of latitude and longitudes with 1 degree resolution
lat, lon = itur.utils.regular_lat_lon_grid(lat_max=60,
                                           lat_min=-60,
                                           lon_max=65,
                                           lon_min=-35)

# Satellite coordinates (GEO, 4 E)
lat_sat = 0
lon_sat = 4
h_sat = 35786 * u.km

# Compute the elevation angle between satellite and ground station
el = itur.utils.elevation_angle(h_sat, lat_sat, lon_sat, lat, lon)

f = 22.5 * u.GHz    # Link frequency
D = 1.2 * u.m       # Antenna diameters
p = 1               # Unavailability (Values exceeded 1% of time)
Att = itur.atmospheric_attenuation_slant_path(lat, lon, f, el, p, D)

If you have installed Basemap (see installation instructions ), you can use function itur.plotting.plot_in_map() to display the results as an image:

# Plot the results
m = itur.plotting.plot_in_map(Att.value, lat, lon,
                           cbar_text='Atmospheric attenuation [dB]',
                           cmap='magma')

# Plot the satellite location
m.scatter(lon_sat, lat_sat, c='white', s=20)

Atmospheric attenuation over Africa @ 22.5 GHz.

Dependency with link parameters¶

Vectorization works in a lot of different ways. For example, let’s say that we want to compute the dependency of the attenuation with the elevation angle for a the example presented in the `Single location attenuation example <>`_. We can just do it using the code below

import itur
import astropy.units as u

itur.deactivate_output_quantity()

# Ground station coordinates (Boston)
lat_GS = 42.3601
lon_GS = -71.0942

# Vectorize the elevation angle
el = np.linspace(10, 90, 50)

f = 22.5 * u.GHz    # Link frequency
D = 1.2 * u.m       # Antenna diameters
p = 1               # Unavailability (Values exceeded 1% of time)
Att = itur.atmospheric_attenuation_slant_path(lat_GS, lon_GS, f, el, p, D)

plt.figure()
plt.plot(el, Att.value)
plt.xlabel('Elevation angle [deg]')
plt.ylabel('Attenuation [dB]')
plt.grid(which='major', linestyle=':')

Atmospheric attenuation at Boston vs. elevation angle.

Another example of vectorization can be found below in the code to plot the atmospheric attenuation due to gases vs. frequency.

import itur
import astropy.units as u
import numpy as np

el = 90
rho = 7.5 * u.g / u.m**3
P = 1013 * u.hPa
T = 25 * u.deg_C
f = np.linspace(1, 350, 1000)

Att = itur.gaseous_attenuation_slant_path(f, el, rho, P, T)
plt.semilogy(f, Att)
plt.xlabel('Frequency [GHz]')
plt.ylabel('Gaseous Attenuation [dB]')
plt.grid(which='both', linestyle=':')

Gaseous attenuation vs. frequency.

The only parameter that cannot be vectorized is the unavailability - percentage of time that values are exceeded. A for loop needs always to be used to compute attenuation values for different unavailabilities (p), as was shown in the `Single location attenuation example <>`_.

Other atmospheric functions¶

We conclude the quickstart with a summary of other functions included in ITU-Rpy that might be useful to compute atmospheric attenuation related parameters. The complete API description can be accessed through the API section .

import itur

# Location of the receiver ground stations
lat = 41.39
lon = -71.05

# Link parameters
el = 60                # Elevation angle equal to 60 degrees
f = 22.5 * itur.u.GHz  # Frequency equal to 22.5 GHz
D = 1 * itur.u.m       # Receiver antenna diameter of 1 m
p = 0.1                # We compute values exceeded during 0.1 % of the average
                                           # year

# Compute atmospheric parameters
hs = itur.topographic_altitude(lat, lon)
T = itur.surface_mean_temperature(lat, lon)
P = itur.standard_pressure(lat, hs)
rho_p = itur.surface_water_vapour_density(lat, lon, p, hs)
rho_sa = itur.models.itu835.water_vapour_density(lat, hs)
T_sa = itur.models.itu835.temperature(lat, hs)
V = itur.models.itu836.total_water_vapour_content(lat, lon, p, hs)

# Compute rain and cloud-related parameters
R_prob = itur.models.itu618.rain_attenuation_probability(lat, lon, el, hs)
R_pct_prob = itur.models.itu837.rainfall_probability(lat, lon)
R001 = itur.models.itu837.rainfall_rate(lat, lon, p)
h_0 = itur.models.itu839.isoterm_0(lat, lon)
h_rain = itur.models.itu839.rain_height(lat, lon)
L_red = itur.models.itu840.columnar_content_reduced_liquid(lat, lon, p)
A_w = itur.models.itu676.zenit_water_vapour_attenuation(lat, lon, p, f, alt=hs)

# Compute attenuation values
A_g = itur.gaseous_attenuation_slant_path(f, el, rho_p, P, T)
A_r = itur.rain_attenuation(lat, lon, f, el, hs=hs, p=p)
A_c = itur.cloud_attenuation(lat, lon, el, f, p)
A_s = itur.scintillation_attenuation(lat, lon, f, el, p, D)
A_t = itur.atmospheric_attenuation_slant_path(lat, lon, f, el, p, D)

Running the code above produces the following results. The ITU Recommendation where the variable or the procedure to compute it is referred appears in square brackets.

The ITU recommendations predict the following values for the point located
at coordinates (41.39, -71.05)
  - Height above the sea level                  [ITU-R P.1511]      22.9 m
  - Surface mean temperature                    [ITU-R P.1510]      9.4 deg_C
  - Surface pressure                            [ITU-R P.835]       1005.4 hPa
  - Standard surface temperature                [ITU-R P.835]       13.6 deg_C
  - Standard water vapour density               [ITU-R P.835]       8.9 g / m3
  - Water vapor density (p=0.1%)                [ITU-R P.836]       20.3 g / m3
  - Total water vapour content (p=0.1%)         [ITU-R P.836]       54.6 kg / m2
  - Rain attenuation probability                [ITU-R P.618]       9.6 %
  - Rain percentage probability                 [ITU-R P.837]       7.8 %
  - Rainfall rate exceeded for p=0.1%           [ITU-R P.837]       12.9 mm / h
  - 0 degree C isotherm height                  [ITU-R P.839]       3.2 km
  - Rain height                                 [ITU-R P.839]       3.5 km
  - Columnar content of reduced liquid (p=0.1%) [ITU-R P.840]       3.0 kg / m2
  - Zenit water vapour attenuation (p=0.1%)     [ITU-R P.676]       1.5 dB


Attenuation values exceeded for p=0.1% of the average year for a link with el=60 deg, f=22.5 GHz,
D=1.0 m and receiver ground station located at coordinates (41.39, -71.05)
  - Rain attenuation                            [ITU-R P.618]       8.2 dB
  - Gaseous attenuation                         [ITU-R P.676]       1.5 dB
  - Clouds attenuation                          [ITU-R P.840]       1.6 dB
  - Scintillation attenuation                   [ITU-R P.618]       0.3 dB
  - Total atmospheric attenuation               [ITU-R P.618]       10.8 dB

API Documentation¶

ITU-Rpy

Contents¶

itur package¶

Package contents¶

ITU-RPy is a python implementation of the ITU-P R Recommendations.

ITU-Rpy can be used to compute atmospheric attenuation for Earth-to-space and horizontal paths, for frequencies in the GHz range.

The propagation loss on an Earth-space path and a horizontal-path, relative to the free-space loss, is the sum of different contributions, namely:

attenuation by atmospheric gases;

attenuation by rain, other precipitation and clouds;

scintillation and multipath effects;

attenuation by sand and dust storms.

Each of these contributions has its own characteristics as a function of frequency, geographic location and elevation angle. ITU-Rpy allows for fast, vectorial computation of the different contributions to the atmospheric attenuation.

itur.atmospheric_attenuation_slant_path(lat, lon, f, el, p, D, hs=None, rho=None, R001=None, eta=0.5, T=None, H=None, P=None, hL=1000.0, Ls=None, tau=45, V_t=None, mode='approx', return_contributions=False, include_rain=True, include_gas=True, include_scintillation=True, include_clouds=True)[source]¶

Calculate long-term atmospheric attenuation statistics for slant paths.

This function provides estimates of the long-term statistics of the slant-path atmospheric attenuation at a given location, for frequencies up to 55 GHz and percentages of time 0.001% < p < 50%.

The model used is based on the guidelines provided in Section 2 of ITU-R P.618. If optional values are not provided they will be automatically computed using the procedures described in other ITU-R P. recommendations.

Parameters:

lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points
lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
f (number or Quantity) – Frequency (GHz)
el (sequence, number or Quantity) – Elevation angle (degrees)
p (number) – Percentage of the time the rain attenuation value is exceeded.
D (number or Quantity) – Physical diameter of the earth-station antenna (m)
hs (number, sequence, or numpy.ndarray, optional) – Height above mean sea level of the earth station (km). If local data for the earth station height above mean sea level is not available, an estimate is obtained from the maps of topographic altitude given in Recommendation ITU-R P.1511.
rho (number or Quantity, optional) – Water vapor density (g/m3). If not provided, an estimate is obtained from Recommendation Recommendation ITU-R P.836.
R001 (number or Quantity, optional) –
Point rainfall rate for the location for 0.01% of an average year (mm/h). If not provided, an estimate is obtained from Recommendation ITU-R P.837. Some useful values:
- 0.25 mm/h : Drizzle
- 2.5 mm/h : Light rain
- 12.5 mm/h : Medium rain
- 25.0 mm/h : Heavy rain
- 50.0 mm/h : Downpour
- 100 mm/h : Tropical
- 150 mm/h : Monsoon
eta (number, optional) – Antenna efficiency. Default value 0.5 (conservative estimate)
T (number, sequence, or numpy.ndarray, optional) – Average surface ambient temperature (°C) at the site. If None, uses the ITU-R P.1510 to estimate the surface ambient temperature.
H (number, sequence, or numpy.ndarray, optional) – Average surface relative humidity (%) at the site. If None, uses the ITU-R P.836 to estimate the wet term of the surface relative humidity.
P (number, sequence, or numpy.ndarray, optional) – Average surface pressure (hPa) at the site. If None, uses the ITU-R P.835 to estimate the average surface pressure.
hL (number, optional) – Height of the turbulent layer (m). Default value 1000 m
Ls (number, optional) – Slant path length (km). If not provided, it will be computed using the rain height and the elevation angle. The ITU model does not require this parameter as an input.
tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45
V_t (number or Quantity, optional) – Integrated water vapour content along the path (kg/m2 or mm). If not provided this value is estimated using Recommendation ITU-R P.836. Default value None
mode (string, optional) – Mode for the calculation of gaseous attenuation. Valid values are ‘approx’, ‘exact’. If ‘approx’ Uses the method in Annex 2 of Recommendation ITU-R P.676, else uses the method described in Section 1. Default, ‘approx’
return_contributions (bool, optional) – Determines whether individual contributions from gases, rain, clouds and scintillation are returned in addition to the total attenuation (True), or just the total atmospheric attenuation (False). Default is False
include_rain (bool, optional) – Determines whether to include the rain contribution in the total atmospheric attenuation calculation or not. Default is True
include_gas (bool, optional) – Determines whether to include the gaseous contribution in the total atmospheric attenuation calculation or not. Default is True
include_scintillation (bool, optional) – Determines whether to include the scintillation contribution in the total atmospheric attenuation calculation or not. Default is True
include_clouds (bool, optional) – Determines whether to include the clouds contribution in the total atmospheric attenuation calculation or not. Default is True

Returns:

A (Quantity) – Total atmospheric attenuation (dB)
Ag, Ac, Ar, As, A (tuple) – Gaseous, Cloud, Rain, Scintillation contributions to total attenuation, and total attenuation (dB)

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.utils package¶

itur.utils is a utilities library for ITU-Rpy.

This utility library for ITU-Rpy contains methods to: * Load data and build an interpolator object. * Prepare the input and output arrays, and handle unit transformations. * Compute distances and elevation angles between two points on Earth and or space.

itur.utils.load_data_interpolator(path_lat, path_lon, path_data, interp_fcn, flip_ud=True)[source]¶

Load a lat-lon tabulated dataset and build an interpolator.

Parameters:	path_lat (string) – Path for the file containing the latitude values path_lon (string) – Path for the file containing the longitude values path_data (string) – Path for the file containing the data values interp_fcn (string) – The interpolation function to be used flip_ud (boolean) – Whether to flip the latitude and data arrays along the first axis. This is an artifact of the format that the ITU uses to encode its data, which is inconsistent across recommendations (in some recommendations, latitude are sorted in ascending order, in others they are sorted in descending order).
Returns:	interp – An interpolator that given a latitude-longitude pair, returns the data value
Return type:	interp_fcn

itur.utils.load_data(path, is_text=False, **kwargs)[source]¶

Load data files from ./itur/data/.

Loads data from a comma-separated values file. The contents of the file can be numeric or text-based.

Parameters:	path (string) – Path of the data to load is_text (bool) – Indicates whether the data is text (True) or numerical (False). Default value is False.
Returns:	data – Numpy-array with the data. Numerical data is returned as a float
Return type:	numpy.ndarray

itur.utils.get_input_type(inpt)[source]¶

Return the type of the input.

If the input is an object of type Quantity, it returns the type of the associated value

Parameters:	inpt (object) – The input object.
Returns:	type – The type of the input.
Return type:	type

itur.utils.prepare_input_array(input_array)[source]¶

Format an array to be a 2-D numpy-array.

If the contents of input_array are 0-D or 1-D, it converts is to an array with at least two dimensions.

Parameters:	input_array (numpy.ndarray, sequence, or number) – The input value. It can be a scalar, 1-D array, or 2-D array.
Returns:	output_array – An 2-D numpy array with the input values
Return type:	numpy.ndarray

itur.utils.prepare_output_array(output_array, type_input=None)[source]¶

Format the output to have the same shape and type as the input.

This function is a generic wrapper to format the output of a function to have the same type as the input. ITU-Rpy makes extensive use of numpy arrays, but uses this function to return outputs having the same type that was provided in the input of the function.

itur.utils.prepare_quantity(value, units=None, name_val=None)[source]¶

Convert the input to the required units.

The function verifies that the input has the right units and converts it to the desired units. For example, if a value is introduced in km but posterior frequencies require this value to be in meters, this function would be called with units=u.m

Parameters:	value (astropy.units.Quantity, number, sequence, or np.ndarry) – The input value units (astropy.units) – Desired units of the output name_val (string) – Name of the variable (for debugging purposes)
Returns:	q – An numpy array with the values converted to the desired units.
Return type:	numpy.ndarray

itur.utils.compute_distance_earth_to_earth(lat_p, lon_p, lat_grid, lon_grid, method=None)[source]¶

Compute the distance between a point and a matrix of (lat, lons).

If the number of elements in lat_grid is smaller than 100,000, uses the WGS84 method, otherwise, uses the Haversine formula.

Parameters:	lat_p (number) – Latitude projection of the point P (degrees) lon_p (number) – Longitude projection of the point P (degrees) lat_grid (number, sequence of np.ndarray) – Grid of latitude points to which compute the distance (degrees) lon_grid (number, sequence of np.ndarray) – Grid of longitude points to which compute the distance (degrees)
Returns:	d – Distance between the point P and each point in (lat_grid, lon_grid) (km)
Return type:	numpy.ndarray

itur.utils.compute_distance_earth_to_earth_wgs84(lat_p, lon_p, lat_grid, lon_grid)[source]¶

Compute the distance between points using the WGS84 inverse method.

Compute the distance between a point (P) in (lat_p, lon_p) and a matrix of latitude and longitudes (lat_grid, lon_grid) using the WGS84 inverse method.

Parameters:	lat_p (number) – Latitude projection of the point P (degrees) lon_p (number) – Longitude projection of the point P (degrees) lat_grid (number, sequence of np.ndarray) – Grid of latitude points to which compute the distance (degrees) lon_grid (number, sequence of np.ndarray) – Grid of longitude points to which compute the distance (degrees)
Returns:	d – Distance between the point P and each point in (lat_grid, lon_grid) (km)
Return type:	numpy.ndarray

itur.utils.compute_distance_earth_to_earth_haversine(lat_p, lon_p, lat_grid, lon_grid)[source]¶

Compute the distance between points using the Haversine formula.

Compute the distance between a point (P) in (lat_s, lon_s) and a matrix of latitude and longitudes (lat_grid, lon_grid) using the Haversine formula.

Parameters:	lat_p (number) – Latitude projection of the point P (degrees) lon_p (number) – Longitude projection of the point P (degrees) lat_grid (number, sequence of np.ndarray) – Grid of latitude points to which compute the distance (degrees) lon_grid (number, sequence of np.ndarray) – Grid of longitude points to which compute the distance (degrees)
Returns:	d – Distance between the point P and each point in (lat_grid, lon_grid) (km)
Return type:	numpy.ndarray

References

This is based on the Haversine formula

itur.utils.regular_lat_lon_grid(resolution_lat=1, resolution_lon=1, lon_start_0=False, lat_min=-90, lat_max=90, lon_min=-180, lon_max=180)[source]¶

Build regular latitude and longitude matrices.

Builds a latitude and longitude coordinate matrix with resolution resolution_lat, resolution_lon.

Parameters:

resolution_lat (number) – Resolution for the latitude axis (deg)
resolution_lon (number) – Resolution for the longitude axis (deg)
lon_start_0 (boolean) – Indicates whether the longitude is indexed using a 0 - 360 scale (True) or using -180 - 180 scale (False). Default value is False

Returns:

lat (numpy.ndarray) – Grid of coordinates of the latitude point
lon (numpy.ndarray) – Grid of coordinates of the longitude point

itur.utils.elevation_angle(h, lat_s, lon_s, lat_grid, lon_grid)[source]¶

Compute the elevation angle between a satellite and a point on Earth.

Compute the elevation angle between a satellite located in an orbit at height h and located above coordinates (lat_s, lon_s) and a matrix of latitude and longitudes (lat_grid, lon_grid).

Parameters:	h (float) – Orbital altitude of the satellite (km) lat_s (float) – Latitude of the projection of the satellite (degrees) lon_s (float) – Longitude of the projection of the satellite (degrees) lat_grid (number, sequence of np.ndarray) – Grid of latitude points to which compute the elevation angle (degrees) lon_grid (number, sequence of np.ndarray) – Grid of longitude points to which compute the elevation angle (degrees)
Returns:	elevation – Elevation angle between the satellite and each point in (lat_grid, lon_grid) (degrees)
Return type:	numpy.ndarray

References

[1] http://www.propagation.gatech.edu/ECE6390/notes/ASD5.pdf - Slides 3, 4

itur.plotting package¶

itur.plotting provides convenient function to plot maps in ITU-Rpy.

This submodule uses matplotlib and cartopy as the default library to plot maps. Alternatively, the user can use basemap (if installed).

The example below shows the use of plot_in_map to display the mean surface temperature on the Earth.

import itur

# Generate a regular grid of latitude and longitudes with 0.1 degree
#  resolution.
lat, lon = itur.utils.regular_lat_lon_grid(resolution_lat=0.1,
                                           resolution_lon=0.1)

# Compute the surface mean temperature
T = itur.models.itu1510.surface_mean_temperature(lat, lon)

# Display the results in a map (using cartopy)
ax = itur.plotting.plot_in_map(
        T, lat, lon, cmap='jet', vmin=230, vmax=310,
        cbar_text='Annual mean surface temperature [K]')

# Display the results in a map (using basemap)
ax = itur.plotting.plot_in_map_basemap(
        T, lat, lon, cmap='jet', vmin=230, vmax=310,
        cbar_text='Annual mean surface temperature [K]')

itur.plotting.plot_in_map(data, lat=None, lon=None, lat_min=None, lat_max=None, lon_min=None, lon_max=None, cbar_text='', ax=None, figsize=(6, 4), **kwargs)[source]¶

Plot the values in data in a map using cartopy.

The map uses an PlateCarree projection. Either {lat, lon} or {lat_min, lat_max, lon_min, lon_max} need to be provided as inputs. This function requires that cartopy and matplotlib are installed.

Parameters:	data (np.ndarray) – Data values to be plotted. lat (np.ndarray) – Matrix with the latitudes for each point in data (deg N) lon (np.ndarray) – Matrix with the longitudes for each point in data (deg E) lat_min (float) – Minimum latitude of the data (deg N) lat_max (float) – Maximum latitude of the data (deg N) lon_min (float) – Minimum longitude of the data (deg E) lat_max – Maximum longitude of the data (deg E) cbar_text (string) – Colorbar text caption. ax (Axes) – matplotlib axes where the data will be plotted. figsize (tuple) – Dimensions of the Figure *kwargs (dict*) – Key-value arguments that will be passed to the contourf function.
Returns:	ax – The matploltib axes object
Return type:	Axes

itur.plotting.plot_in_map_basemap(data, lat=None, lon=None, lat_min=None, lat_max=None, lon_min=None, lon_max=None, cbar_text='', ax=None, figsize=(6, 4), **kwargs)[source]¶

Plot the values in data in a map using basemap.

The map uses an equidistant cylindrical projection. Either {lat, lon} or {lat_min, lat_max, lon_min, lon_max} to be provided as inputs. This function requires that basemap and matplotlib are installed.

Parameters:	data (np.ndarray) – Data values to be plotted. lat (np.ndarray) – Matrix with the latitudes for each point in data (deg N) lon (np.ndarray) – Matrix with the longitudes for each point in data (deg E) lat_min (float) – Minimum latitude of the data (deg N) lat_max (float) – Maximum latitude of the data (deg N) lon_min (float) – Minimum longitude of the data (deg E) lat_max – Maximum longitude of the data (deg E) cbar_text (string) – Colorbar text caption. ax (Axes) – matplotlib axes where the data will be plotted. figsize (tuple) – Dimensions of the Figure *kwargs (dict*) – Key-value arguments that will be passed to the imshow function.
Returns:	m – The map object generated by Basemap
Return type:	Basemap

itur.models package¶

The itur.models package contains the implementation of the models described in the different ITU-R P. recommendations.

Individual modules can be imported from itur.models using itu<recomendation_number>, as shown below:

import itur.models.itu618

Each module contains two functions, get_version() and change_version(), that allow to obtain or change the version currently being used. The script below provides an example for the module that implements Recommendation ITU-R P.618.

import itur.models.itu618 as itu618

print('Current version of ITU-R P.618: ', itu618.get_version())
itu618.change_version(12)  # Change to version ITU-R P.618-12

By default, each module contains a __model object that acts as a singleton instance for the recommendation model. For most use cases, it is recommended that the developers interact with the model using the publicly documented functions. This way, it is ensured that all functions called belong to the same recommendation version, and that the parameters passed to the functions have the right units and format.

However, if a developer wants to instantiate a new model object (i.e., to compare results from different version, for development purposes), a new object can be instantiated as shown in the example below:

import itur.models.itu618 as itu618

model_618_12 = itu618._ITU618(12)
model_618_13 = itu618._ITU618(13)

Package contents¶

Recommendation ITU-R P.453¶

This Recommendation provides a method to estimate the radio refractive index and its behaviour for locations worldwide; describes both surface and vertical profile characteristics; and provides global maps for the distribution of refractivity parameters and their statistical variation.

Title	PDF	Latest approved in
Recommendation ITU-R P.453	[PDF]	2019-08
its formula and refractivity data
Current recommendation version (In force)		Date
Recommendation ITU-R P.453-14	[PDF]	08/2019
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.453-13	[PDF]	12/2017
Recommendation ITU-R P.453-12	[PDF]	09/2016
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.453-14	[PDF]	08/2019
Recommendation ITU-R P.453-11	[PDF]	07/2015
Recommendation ITU-R P.453-10	[PDF]	02/2012
Recommendation ITU-R P.453-9	[PDF]	04/2003
Recommendation ITU-R P.453-8	[PDF]	02/2001
Recommendation ITU-R P.453-7	[PDF]	10/1999
Recommendation ITU-R P.453-6	[PDF]	05/1997
Recommendation ITU-R P.453-5	[PDF]	10/1995
Recommendation ITU-R P.453-4	[PDF]	08/1994

Introduction¶

The atmospheric radio refractive index, n, can be computed by the following formula:

\[ \begin{align}\begin{aligned}n &= 1 + N\cdot 10^{-6}\\N &= 77.6 \frac{P_d}{T} + 72\frac{e}{T} +3.75\cdot10^{5}\frac{e}{T^2}\end{aligned}\end{align} \]

where

\(P_d\) : dry atmospheric pressure (hPa)
\(P\) : total atmospheric pressure (hPa)
\(e\) : water vapour pressure (hPa)
\(T\) : absolute temperature (K)

Furthermore, in the absence of reliable local data, data on refractivity and refractivity gradients all over the world can be computed using global numerical maps provided in this recommendation.

Module description¶

itur.models.itu453.change_version(new_version)[source]¶

Change the version of the ITU-R P.453 recommendation currently being used.

This function changes the model used for the ITU-R P.453 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

13: Activates recommendation ITU-R P.453-13 (12/17)

12: Activates recommendation ITU-R P.453-12 (07/15)

itur.models.itu453.get_version()[source]¶

Obtain the version of the ITU-R P.453 recommendation currently being used.

Returns:	version – The version of the ITU-R P.453 recommendation being used.
Return type:	int

itur.models.itu453.wet_term_radio_refractivity(e, T)[source]¶

Determine the wet term of the radio refractivity.

Parameters:	e (number or Quantity) – Water vapour pressure (hPa) T (number or Quantity) – Absolute temperature (K)
Returns:	N_wet – Wet term of the radio refractivity (-)
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.dry_term_radio_refractivity(Pd, T)[source]¶

Determine the dry term of the radio refractivity.

Parameters:	Pd (number or Quantity) – Dry atmospheric pressure (hPa) T (number or Quantity) – Absolute temperature (K)
Returns:	N_dry – Dry term of the radio refractivity (-)
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.radio_refractive_index(Pd, e, T)[source]¶

Compute the radio refractive index.

Parameters:	Pd (number or Quantity) – Dry atmospheric pressure (hPa) e (number or Quantity) – Water vapour pressure (hPa) T (number or Quantity) – Absolute temperature (K)
Returns:	n – Radio refractive index (-)
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.water_vapour_pressure(T, P, H, type_hydrometeor='water')[source]¶

Determine the water vapour pressure.

Parameters:	T (number or Quantity) – Absolute temperature (C) P (number or Quantity) – Total atmospheric pressure (hPa) H (number or Quantity) – Relative humidity (%) type_hydrometeor (string) – Type of hydrometeor. Valid strings are ‘water’ and ‘ice’
Returns:	e – Water vapour pressure (hPa)
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.saturation_vapour_pressure(T, P, type_hydrometeor='water')[source]¶

Determine the saturation water vapour pressure.

Parameters:	T (number or Quantity) – Absolute temperature (C) P (number or Quantity) – Total atmospheric pressure (hPa) type_hydrometeor (string) – Type of hydrometeor. Valid strings are ‘water’ and ‘ice’
Returns:	e_s – Saturation water vapour pressure (hPa)
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.map_wet_term_radio_refractivity(lat, lon, p=50)[source]¶

Determine the wet term of the radio refractivity.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
Returns:	N_wet – Wet term of the radio refractivity (-)
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.DN65(lat, lon, p)[source]¶

Determine the statistics of the vertical gradient of radio: refractivity in the lower 65 m from the surface of the Earth.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of time exceeded for p% of the average year
Returns:	DN65_p – Vertical gradient of radio refractivity in the lowest 65 m from the surface of the Earth exceeded for p% of the average year
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

itur.models.itu453.DN1(lat, lon, p)[source]¶

Determine the statistics of the vertical gradient of radio: refractivity over 1 km layer from the surface.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of time exceeded for p% of the average year
Returns:	DN1_p – Vertical gradient of radio refractivity over a 1 km layer from the surface exceeded for p% of the average year
Return type:	Quantity

References

[1] The radio refractive index: its formula and refractivity data https://www.itu.int/rec/R-REC-P.453/en

Recommendation ITU-R P.530¶

This Recommendation provides prediction methods for the propagation effects that should be taken into account in the design of digital fixed line-of-sight links, both in clear-air and rainfall conditions. It also provides link design guidance in clear step-by-step procedures including the use of mitigation techniques to minimize propagation impairments. The final outage predicted is the base for other Recommendations addressing error performance and availability.

Title	PDF	Latest approved in
Recommendation ITU-R P.530	[PDF]	2021-09
Propagation data and prediction methods required for the design of terrestrial line-of-sight systems
Current recommendation version (In force)		Date
Recommendation ITU-R P.530-18	[PDF]	09/2021
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.530-17	[PDF]	12/2017
Recommendation ITU-R P.530-16	[PDF]	07/2015
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.530-18	[PDF]	09/2021
Recommendation ITU-R P.530-15	[PDF]	09/2013
Recommendation ITU-R P.530-14	[PDF]	02/2012
Recommendation ITU-R P.530-13	[PDF]	10/2009
Recommendation ITU-R P.530-12	[PDF]	02/2007
Recommendation ITU-R P.530-11	[PDF]	03/2005
Recommendation ITU-R P.530-10	[PDF]	11/2001
Recommendation ITU-R P.530-9	[PDF]	02/2001
Recommendation ITU-R P.530-8	[PDF]	10/1999
Recommendation ITU-R P.530-7	[PDF]	08/1997
Recommendation ITU-R P.530-6	[PDF]	10/1995
Recommendation ITU-R P.530-5	[PDF]	08/1994

Introduction¶

The propagation loss on a terrestrial line-of-sight path relative to the free-space loss (see Recommendation ITU-R P.525) is the sum of different contributions as follows:

attenuation due to atmospheric gases;

diffraction fading due to obstruction or partial obstruction of the path;

fading due to multipath, beam spreading and scintillation;

attenuation due to variation of the angle-of-arrival/launch;

attenuation due to precipitation;

attenuation due to sand and dust storms.

Each of these contributions has its own characteristics as a function of frequency, path length and geographic location. These are described in the paragraphs that follow.

Module description¶

itur.models.itu530.change_version(new_version)[source]¶

Change the version of the ITU-R P.530 recommendation currently being used.

This function changes the model used for the ITU-R P.530 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

16: Activates recommendation ITU-R P.530-16 (07/15) (Current version)

itur.models.itu530.get_version()[source]¶

Obtain the version of the ITU-R P.530 recommendation currently being used.

Returns:	version – The version of the ITU-R P.530 recommendation being used.
Return type:	int

itur.models.itu530.fresnel_ellipse_radius(d1, d2, f)[source]¶

Compute the radius of the first Fresnel ellipsoid.

Parameters:	d1 (number, sequence, or numpy.ndarray) – Distances from the first terminal to the path obstruction. [km] d2 (number, sequence, or numpy.ndarray) – Distances from the second terminal to the path obstruction. [km] f (number) – Frequency of the link [GHz]
Returns:	F1 – Radius of the first Fresnel ellipsoid [m]
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.diffraction_loss(d1, d2, h, f)[source]¶

Estimate the diffraction loss over average terrain.

Diffraction loss over average terrain. This value is valid for losses greater than 15 dB.

Parameters:	d1 (number, sequence, or numpy.ndarray) – Distances from the first terminal to the path obstruction. [km] d2 (number, sequence, or numpy.ndarray) – Distances from the second terminal to the path obstruction. [km] h (number, sequence, or numpy.ndarray) – Height difference between most significant path blockage and the path trajectory. h is negative if the top of the obstruction of interest is above the virtual line-of-sight. [m] f (number) – Frequency of the link [GHz]
Returns:	A_d – Diffraction loss over average terrain [dB]
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.multipath_loss_for_A(lat, lon, h_e, h_r, d, f, A)[source]¶

Estimate the single-frequency (or narrow-band) fading distribution.

Method for predicting the single-frequency (or narrow-band) fading distribution at large fade depths in the average worst month in any part of the world. Given a fade depth value ‘A’, determines the amount of time it will be exceeded during a year

This method does not make use of the path profile and can be used for initial planning, licensing, or design purposes.

This method is only valid for small percentages of time.

Multi-path fading and enhancement only need to be calculated for path lengths longer than 5 km, and can be set to zero for shorter paths.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points h_e (number) – Emitter antenna height (above the sea level) [m] h_r (number) – Receiver antenna height (above the sea level) [m] d (number, sequence, or numpy.ndarray) – Distances between antennas [km] f (number) – Frequency of the link [GHz] A (number) – Fade depth [dB]
Returns:	p_w – percentage of time that fade depth A is exceeded in the average worst month [%]
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.multipath_loss(lat, lon, h_e, h_r, d, f, A)[source]¶

Estimate the percentage of time that any fade depth is exceeded.

Method for predicting the percentage of time that any fade depth is exceeded. This method combines the deep fading distribution given in the multipath_loss_for_A’ and an empirical interpolation procedure for shallow fading down to 0 dB.

This method does not make use of the path profile and can be used for initial planning, licensing, or design purposes.

Multi-path fading and enhancement only need to be calculated for path lengths longer than 5 km, and can be set to zero for shorter paths.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points h_e (number) – Emitter antenna height (above the sea level) [m] h_r (number) – Receiver antenna height (above the sea level) [m] d (number, sequence, or numpy.ndarray) – Distances between antennas [km] f (number) – Frequency of the link [GHz] A (number) – Fade depth [dB]
Returns:	p_w – percentage of time that fade depth A is exceeded in the average worst month [%]
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.rain_attenuation(lat, lon, d, f, el, p, tau=45, R001=None)[source]¶

Estimate long-term statistics of rain attenuation.

Attenuation can also occur as a result of absorption and scattering by such hydro-meteors as rain, snow, hail and fog. Although rain attenuation can be ignored at frequencies below about 5 GHz, it must be included in design calculations at higher frequencies, where its importance increases rapidly.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points d (number, sequence, or numpy.ndarray) – Path length [km] f (number) – Frequency of the link [GHz] el (sequence, or number) – Elevation angle (degrees) p (number) – Percentage of the time the rain attenuation value is exceeded. R001 (number, optional) – Point rainfall rate for the location for 0.01% of an average year (mm/h). If not provided, an estimate is obtained from Recommendation Recommendation ITU-R P.837. Some useful values: 0.25 mm/h : Drizzle 2.5 mm/h : Light rain 12.5 mm/h : Medium rain 25.0 mm/h : Heavy rain 50.0 mm/h : Downpour 100 mm/h : Tropical 150 mm/h : Monsoon tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45
Returns:	A_r – Attenuation exceeded during p percent of the time [dB]
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.inverse_rain_attenuation(lat, lon, d, f, el, Ap, tau=45, R001=None)[source]¶

Estimate the percentage of time a given attenuation is exceeded.

Estimate the percentage of time a given attenuation is exceeded due to rain events.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points d (number, sequence, or numpy.ndarray) – Path length [km] f (number) – Frequency of the link [GHz] el (sequence, or number) – Elevation angle (degrees) Ap (number) – Fade depth R001 (number, optional) – Point rainfall rate for the location for 0.01% of an average year (mm/h). If not provided, an estimate is obtained from Recommendation Recommendation ITU-R P.837. Some useful values: 0.25 mm/h : Drizzle 2.5 mm/h : Light rain 12.5 mm/h : Medium rain 25.0 mm/h : Heavy rain 50.0 mm/h : Downpour 100 mm/h : Tropical 150 mm/h : Monsoon tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45
Returns:	p – Percentage of time that the attenuation A is exceeded.
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.rain_event_count(lat, lon, d, f, el, A, tau=45, R001=None)[source]¶

Estimate the number of fade events exceeding attenuation ‘A’.

Estimate the number of fade events exceeding attenuation ‘A’ for 10 seconds or longer.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points d (number, sequence, or numpy.ndarray) – Path length [km] f (number) – Frequency of the link [GHz] el (sequence, or number) – Elevation angle (degrees) A (number) – Fade depth R001 (number, optional) – Point rainfall rate for the location for 0.01% of an average year (mm/h). If not provided, an estimate is obtained from Recommendation Recommendation ITU-R P.837. Some useful values: 0.25 mm/h : Drizzle 2.5 mm/h : Light rain 12.5 mm/h : Medium rain 25.0 mm/h : Heavy rain 50.0 mm/h : Downpour 100 mm/h : Tropical 150 mm/h : Monsoon tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45
Returns:	p – Percentage of time that the attenuation A is exceeded.
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.XPD_outage_clear_air(lat, lon, h_e, h_r, d, f, XPD_g, C0_I, XPIF=0)[source]¶

Estimate the probability of outage due to cross-polar discrimination.

Estimate the probability of outage due to cross-polar discrimination reduction due to clear-air effects, assuming that a target C0_I is required.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points h_e (number) – Emitter antenna height (above the sea level) [m] h_r (number) – Receiver antenna height (above the sea level) [m] d (number, sequence, or numpy.ndarray) – Distances between antennas [km] f (number) – Frequency of the link [GHz] XPD_g (number) – Manufacturer’s guaranteed minimum XPD at boresight for both the transmitting and receiving antennas [dB] C0_I (number) – Carrier-to-interference ratio for a reference BER [dB] XPIF (number, optional) – Laboratory-measured cross-polarization improvement factor that gives the difference in cross-polar isolation (XPI) at sufficiently large carrier-to-noise ratio (typically 35 dB) and at a specific BER for systems with and without cross polar interference canceler (XPIC). A typical value of XPIF is about 20 dB. Default value 0 dB (no XPIC) [dB]
Returns:	p_XP – Probability of outage due to clear-air cross-polarization
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

itur.models.itu530.XPD_outage_precipitation(lat, lon, d, f, el, C0_I, tau=45, U0=15, XPIF=0)[source]¶

Estimate the probability of outage due to cross-polar discrimination.

Estimate the probability of outage due to cross-polar discrimination reduction due to precipitation effects, assuming that a target C0_I is required.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points d (number, sequence, or numpy.ndarray) – Distances between antennas [km] f (number) – Frequency of the link [GHz] el (sequence, or number) – Elevation angle (degrees) C0_I (number) – Carrier-to-interference ratio for a reference BER [dB] tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45 U0 (number, optional) – Coefficient for the cumulative distribution of the co-polar attenuation (CPA) for rain. Default 15 dB. XPIF (number, optional) – Laboratory-measured cross-polarization improvement factor that gives the difference in cross-polar isolation (XPI) at sufficiently large carrier-to-noise ratio (typically 35 dB) and at a specific BER for systems with and without cross polar interference canceler (XPIC). A typical value of XPIF is about 20 dB. Default value 0 dB (no XPIC) [dB]
Returns:	p_XP – Probability of outage due to precipitation cross-polarization
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of terrestrial line-of-sight systems: https://www.itu.int/rec/R-REC-P.530/en

Recommendation ITU-R P.618¶

This Recommendation provides methods to predict the various propagation parameters needed in planning Earth-space systems operating in either the Earth-to-space or space-to-Earth direction.

Title	PDF	Latest approved in
Recommendation ITU-R P.618	[PDF]	2017-12
Propagation data and prediction methods required for the design of Earth-space telecommunication systems
Current recommendation version (In force)		Date
Recommendation ITU-R P.618-13	[PDF]	12/2017
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.618-13	[PDF]	12/2017
Recommendation ITU-R P.618-12	[PDF]	07/2015
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.618-11	[PDF]	09/2013
Recommendation ITU-R P.618-10	[PDF]	10/2009
Recommendation ITU-R P.618-9	[PDF]	08/2007
Recommendation ITU-R P.618-8	[PDF]	04/2003
Recommendation ITU-R P.618-7	[PDF]	02/2001
Recommendation ITU-R P.618-6	[PDF]	10/1999
Recommendation ITU-R P.618-5	[PDF]	05/1997
Recommendation ITU-R P.618-4	[PDF]	10/1995
Recommendation ITU-R P.618-3	[PDF]	08/1994

Introduction¶

The propagation loss on an Earth-space path, relative to the free-space loss, is the sum of different contributions as follows:

attenuation by atmospheric gases;

attenuation by rain, other precipitation and clouds;

focusing and defocusing;

decrease in antenna gain due to wave-front incoherence;

scintillation and multipath effects;

attenuation by sand and dust storms.

Each of these contributions has its own characteristics as a function of frequency, geographic location and elevation angle. As a rule, at elevation angles above 10 degrees, only gaseous attenuation, rain and cloud attenuation and possibly scintillation will be significant, depending on propagation conditions.

Module description¶

itur.models.itu618.change_version(new_version)[source]¶

Change the version of the ITU-R P.618 recommendation currently being used.

This function changes the model used for the ITU-R P.618 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

13: Activates recommendation ITU-R P.618-13 (12/17) (Current version)

12: Activates recommendation ITU-R P.618-12 (07/15) (Superseded)

itur.models.itu618.get_version()[source]¶

The version of the current model for the ITU-R P.618 recommendation.

Obtain the version of the ITU-R P.618 recommendation currently being used.

Returns:	version – The version of the ITU-R P.618 recommendation being used.
Return type:	int

itur.models.itu618.rain_attenuation(lat, lon, f, el, hs=None, p=0.01, R001=None, tau=45, Ls=None)[source]¶

Calculation of long-term rain attenuation statistics from point rainfall rate. The following procedure provides estimates of the long-term statistics of the slant-path rain attenuation at a given location for frequencies up to 55 GHz.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points f (number) – Frequency (GHz) el (sequence, or number) – Elevation angle (degrees) hs (number, sequence, or numpy.ndarray, optional) – Heigh above mean sea level of the earth station (km). If local data for the earth station height above mean sea level is not available, an estimate is obtained from the maps of topographic altitude given in Recommendation ITU-R P.1511. p (number, optional) – Percentage of the time the rain attenuation value is exceeded. R001 (number, optional) – Point rainfall rate for the location for 0.01% of an average year (mm/h). If not provided, an estimate is obtained from Recommendation Recommendation ITU-R P.837. Some useful values: 0.25 mm/h : Drizzle 2.5 mm/h : Light rain 12.5 mm/h : Medium rain 25.0 mm/h : Heavy rain 50.0 mm/h : Downpour 100 mm/h : Tropical 150 mm/h : Monsoon tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45 Ls (number, optional) – Slant path length (km). If not provided, it will be computed using the rain height and the elevation angle. The ITU model does not require this parameter as an input.
Returns:	attenuation – Attenuation due to rain (dB)
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.models.itu618.rain_attenuation_probability(lat, lon, el, hs=None, Ls=None, P0=None)[source]¶

The following procedure computes the probability of non-zero rain attenuation on a given slant path Pr(Ar > 0).

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points el (sequence, or number) – Elevation angle (degrees) hs (number, sequence, or numpy.ndarray, optional) – Heigh above mean sea level of the earth station (km). If local data for the earth station height above mean sea level is not available, an estimate is obtained from the maps of topographic altitude given in Recommendation ITU-R P.1511. Ls (number, sequence, or numpy.ndarray, optional) – Slant path length from the earth station to the rain height (km). If data about the rain height is not available, this value is estimated automatically using Recommendation ITU-R P.838 P0 (number, sequence, or numpy.ndarray, optional) – Probability of rain at the earth station, (0 ≤ P0 ≤ 1)
Returns:	p – Probability of rain attenuation on the slant path (%)
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.models.itu618.site_diversity_rain_outage_probability(lat1, lon1, a1, el1, lat2, lon2, a2, el2, f, tau=45, hs1=None, hs2=None)[source]¶

Calculate the link outage probability in a diversity based scenario (two ground stations) due to rain attenuation. This method is valid for frequencies below 20 GHz, as at higher frequencies other impairments might affect affect site diversity performance.

This method predicts Pr(A1 > a1, A2 > a2), the joint probability (%) that the attenuation on the path to the first site is greater than a1 and the attenuation on the path to the second site is greater than a2.

Parameters:	lat1 (number or Quantity) – Latitude of the first ground station (deg) lon1 (number or Quantity) – Longitude of the first ground station (deg) a1 (number or Quantity) – Maximum admissible attenuation of the first ground station (dB) el1 (number or Quantity) – Elevation angle to the first ground station (deg) lat2 (number or Quantity) – Latitude of the second ground station (deg) lon2 (number or Quantity) – Longitude of the second ground station (deg) a2 (number or Quantity) – Maximum admissible attenuation of the second ground station (dB) el2 (number or Quantity) – Elevation angle to the second ground station (deg) f (number or Quantity) – Frequency (GHz) tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45 hs1 (number or Quantity, optional) – Altitude over the sea level of the first ground station (km). If not provided, uses Recommendation ITU-R P.1511 to compute the toporgraphic altitude hs2 (number or Quantity, optional) – Altitude over the sea level of the first ground station (km). If not provided, uses Recommendation ITU-R P.1511 to compute the toporgraphic altitude
Returns:	probability – Joint probability (%) that the attenuation on the path to the first site is greater than a1 and the attenuation on the path to the second site is greater than a2
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.models.itu618.scintillation_attenuation(lat, lon, f, el, p, D, eta=0.5, T=None, H=None, P=None, hL=1000)[source]¶

Calculation of monthly and long-term statistics of amplitude scintillations at elevation angles greater than 5° and frequencies up to 20 GHz.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points f (number or Quantity) – Frequency (GHz) el (sequence, or number) – Elevation angle (degrees) p (number) – Percentage of the time the scintillation attenuation value is exceeded. D (number) – Physical diameter of the earth-station antenna (m) eta (number, optional) – Antenna efficiency. Default value 0.5 (conservative estimate) T (number, sequence, or numpy.ndarray, optional) – Average surface ambient temperature (°C) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity. H (number, sequence, or numpy.ndarray, optional) – Average surface relative humidity (%) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity. P (number, sequence, or numpy.ndarray, optional) – Average surface pressure (hPa) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity. hL (number, optional) – Height of the turbulent layer (m). Default value 1000 m
Returns:	attenuation – Attenuation due to scintillation (dB)
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.models.itu618.scintillation_attenuation_sigma(lat, lon, f, el, p, D, eta=0.5, T=None, H=None, P=None, hL=1000)[source]¶

Calculation of the standard deviation of the amplitude of the scintillations attenuation at elevation angles greater than 5° and frequencies up to 20 GHz.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points f (number or Quantity) – Frequency (GHz) el (sequence, or number) – Elevation angle (degrees) p (number) – Percentage of the time the scintillation attenuation value is exceeded. D (number) – Physical diameter of the earth-station antenna (m) eta (number, optional) – Antenna efficiency. Default value 0.5 (conservative estimate) T (number, sequence, or numpy.ndarray, optional) – Average surface ambient temperature (°C) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity. H (number, sequence, or numpy.ndarray, optional) – Average surface relative humidity (%) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity. P (number, sequence, or numpy.ndarray, optional) – Average surface pressure (hPa) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity. hL (number, optional) – Height of the turbulent layer (m). Default value 1000 m
Returns:	attenuation – Attenuation due to scintillation (dB)
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.models.itu618.rain_cross_polarization_discrimination(Ap, f, el, p, tau=45)[source]¶

Calculation of the cross-polarization discrimination (XPD) statistics from rain attenuation statistics. The following procedure provides estimates of the long-term statistics of the cross-polarization discrimination (XPD) statistics for frequencies up to 55 GHz and elevation angles lower than 60 deg.

Parameters:	Ap (number, sequence, or numpy.ndarray) – Rain attenuation (dB) exceeded for the required percentage of time, p, for the path in question, commonly called co-polar attenuation (CPA) f (number) – Frequency el (number, sequence, or numpy.ndarray) – Elevation angle (degrees) p (number) – Percentage of the time the XPD is exceeded. tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45
Returns:	attenuation – Cross-polarization discrimination (dB)
Return type:	Quantity

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

itur.models.itu618.fit_rain_attenuation_to_lognormal(lat, lon, f, el, hs, P_k, tau)[source]¶

Compute the log-normal fit of rain attenuation vs. probability of occurrence.

Parameters:

lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points
lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
f (number or Quantity) – Frequency (GHz)
el (sequence, or number) – Elevation angle (degrees)
hs (number, sequence, or numpy.ndarray, optional) – Heigh above mean sea level of the earth station (km). If local data for the earth station height above mean sea level is not available, an estimate is obtained from the maps of topographic altitude given in Recommendation ITU-R P.1511.
P_k (number) – Rain probability
tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45

Returns:

sigma_lna – Standar deviation of the lognormal distribution
m_lna – Mean of the lognormal distribution

References

[1] Propagation data and prediction methods required for the design of Earth-space telecommunication systems: https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.618-12-201507-I!!PDF-E.pdf

Recommendation ITU-R P.676¶

This Recommendation provides methods to estimate the attenuation of atmospheric gases on terrestrial and slant paths

Title	PDF	Latest approved in
Recommendation ITU-R P.676	[PDF]	2022-08
Attenuation by atmospheric gases and related effects
Current recommendation version (In force)		Date
Recommendation ITU-R P.676-13	[PDF]	08/2022
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.676-12	[PDF]	08/2019
Recommendation ITU-R P.676-11	[PDF]	09/2016
Recommendation ITU-R P.676-10	[PDF]	09/2013
Recommendation ITU-R P.676-9	[PDF]	02/2012
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.676-13	[PDF]	08/2022
Recommendation ITU-R P.676-8	[PDF]	10/2009
Recommendation ITU-R P.676-7	[PDF]	02/0207
Recommendation ITU-R P.676-6	[PDF]	03/2005
Recommendation ITU-R P.676-5	[PDF]	02/2001
Recommendation ITU-R P.676-4	[PDF]	10/1999
Recommendation ITU-R P.676-3	[PDF]	08/1997
Recommendation ITU-R P.676-2	[PDF]	10/1995
Recommendation ITU-R P.676-1	[PDF]	03/1992

Introduction¶

This Recommendation provides the following three methods of predicting the specific and path gaseous attenuation due to oxygen and water vapour:

Calculation of specific and path gaseous attenuation using the line-by-line summation assuming the atmospheric pressure, temperature, and water vapour density vs. height;

An approximate estimate of specific and path gaseous attenuation assuming the water vapour density at the surface of the Earth;

An approximate estimate of path attenuation assuming the integrated water vapour content along the path.

These prediction methods can use local meteorological data, or reference atmospheres or meteorological maps corresponding to a desired probability of exceedance that are provided in other ITU-R P-series Recommendations. In the absence of local data, a combination of: a) the reference atmospheric profiles given in Recommendation ITU-R P.835 may be used, b) the mean annual global reference atmosphere given in Recommendation ITU-R P.835, c) the map of mean annual surface temperature in Recommendation ITU-R P.1510 and d) the maps of surface water vapour density vs. exceedance probability given in Recommendation ITU-R P.836 may be used in lieu of the standard ground-level surface water vapour density of 7.5 g/m3.

The method to compute an estimate of gaseous attenuation computed by a summation of individual absorption lines that is valid for the frequency range 1-1 000 GHz, and the method to compute a simplified approximate method to estimate gaseous attenuation that is applicable in the frequency range 1-350 GHz.

Module description¶

itur.models.itu676.change_version(new_version)[source]¶

Change the version of the ITU-R P.676 recommendation currently being used.

This function changes the model used for the ITU-R P.676 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

12: Activates recommendation ITU-R P.676-12 (08/19) (Current version)

11: Activates recommendation ITU-R P.676-11 (09/16) (Superseded)

10: Activates recommendation ITU-R P.676-10 (09/13) (Superseded)

9: Activates recommendation ITU-R P.676-9 (02/12) (Superseded)

itur.models.itu676.get_version()[source]¶

Obtain the version of the ITU-R P.676 recommendation currently being used.

Returns:	version – The version of the ITU-R P.530 recommendation being used.
Return type:	int

itur.models.itu676.gaseous_attenuation_terrestrial_path(r, f, el, rho, P, T, mode)[source]¶

Estimate the attenuation of atmospheric gases on terrestrial paths. This function operates in two modes, ‘approx’, and ‘exact’:

‘approx’: a simplified approximate method to estimate gaseous attenuation that is applicable in the frequency range 1-350 GHz.

‘exact’: an estimate of gaseous attenuation computed by summation of individual absorption lines that is valid for the frequency range 1-1,000 GHz

Parameters:	r (number or Quantity) – Path length (km) f (number or Quantity) – Frequency (GHz) el (sequence, number or Quantity) – Elevation angle (degrees) rho (number or Quantity) – Water vapor density (g/m*3) P (number* or Quantity) – Atmospheric pressure (hPa) T (number or Quantity) – Absolute temperature (K) mode (string, optional) – Mode for the calculation. Valid values are ‘approx’, ‘exact’. If ‘approx’ Uses the method in Annex 2 of the recommendation (if any), else uses the method described in Section 1. Default, ‘approx’
Returns:	attenuation – Terrestrial path attenuation (dB)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gaseous_attenuation_slant_path(f, el, rho, P, T, V_t=None, h=None, mode='approx')[source]¶

Estimate the attenuation of atmospheric gases on slant paths. This function operates in two modes, ‘approx’, and ‘exact’:

‘approx’: a simplified approximate method to estimate gaseous attenuation that is applicable in the frequency range 1-350 GHz.

‘exact’: an estimate of gaseous attenuation computed by summation of individual absorption lines that is valid for the frequency range 1-1,000 GHz

Parameters:	f (number or Quantity) – Frequency (GHz) el (sequence, number or Quantity) – Elevation angle (degrees) rho (number or Quantity) – Water vapor density (g/m3) P (number or Quantity) – Atmospheric pressure (hPa) T (number or Quantity) – Absolute temperature (K) V_t (number or Quantity (kg/m2)) – Integrated water vapour content from: a) local radiosonde or radiometric data or b) at the required percentage of time (kg/m2) obtained from the digital maps in Recommendation ITU-R P.836 (kg/m2). If None, use general method to compute the wet-component of the gaseous attenuation. If provided, ‘h’ must be also provided. Default is None. h (number, sequence, or numpy.ndarray) – Altitude of the receivers. If None, use the topographical altitude as described in recommendation ITU-R P.1511. If provided, ‘V_t’ needs to be also provided. Default is None. mode (string, optional) – Mode for the calculation. Valid values are ‘approx’, ‘exact’. If ‘approx’ Uses the method in Annex 2 of the recommendation (if any), else uses the method described in Section 1. Default, ‘approx’
Returns:	attenuation – Slant path attenuation (dB)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gaseous_attenuation_inclined_path(f, el, rho, P, T, h1, h2, mode='approx')[source]¶

Estimate the attenuation of atmospheric gases on inclined paths between two ground stations at heights h1 and h2. This function operates in two modes, ‘approx’, and ‘exact’:

‘approx’: a simplified approximate method to estimate gaseous attenuation that is applicable in the frequency range 1-350 GHz.

‘exact’: an estimate of gaseous attenuation computed by summation of individual absorption lines that is valid for the frequency range 1-1,000 GHz

Parameters:	f (number or Quantity) – Frequency (GHz) el (sequence, number or Quantity) – Elevation angle (degrees) rho (number or Quantity) – Water vapor density (g/m3) P (number or Quantity) – Atmospheric pressure (hPa) T (number or Quantity) – Absolute temperature (K) h1 (number or Quantity) – Height of ground station 1 (km) h2 (number or Quantity) – Height of ground station 2 (km) mode (string, optional) – Mode for the calculation. Valid values are ‘approx’, ‘exact’. If ‘approx’ Uses the method in Annex 2 of the recommendation (if any), else uses the method described in Section 1. Default, ‘approx’
Returns:	attenuation – Inclined path attenuation (dB)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.slant_inclined_path_equivalent_height(f, P, rho=7.5, T=298.15)[source]¶

Computes the equivalent height to be used for oxygen and water vapour gaseous attenuation computations.

Parameters:	f (number or Quantity) – Frequency (GHz) P (number or Quantity) – Atmospheric pressure (hPa) rho (number or Quantity) – Water vapor density (g/m3) T (number or Quantity) – Absolute temperature (K)
Returns:	ho, hw – Equivalent height for oxygen and water vapour (km)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.zenit_water_vapour_attenuation(lat, lon, p, f, V_t=None, h=None)[source]¶

An alternative method may be used to compute the slant path attenuation by water vapour, in cases where the integrated water vapour content along the path, V_t, is known.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of the time the zenit water vapour attenuation value is exceeded. f (number or Quantity) – Frequency (GHz) V_t (number or Quantity, optional) – Integrated water vapour content along the path (kg/m2 or mm). If not provided this value is estimated using Recommendation ITU-R P.836. Default value None h (number, sequence, or numpy.ndarray) – Altitude of the receivers. If None, use the topographical altitude as described in recommendation ITU-R P.1511
Returns:	A_w – Water vapour attenuation along the slant path (dB)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gammaw_approx(f, P, rho, T)[source]¶

Method to estimate the specific attenuation due to water vapour using the approximate method descibed in Annex 2.

Parameters:	f (number or Quantity) – Frequency (GHz) P (number or Quantity) – Atmospheric pressure (hPa) rho (number or Quantity) – Water vapor density (g/m3) T (number or Quantity) – Absolute temperature (K)
Returns:	gamma_w – Water vapour specific attenuation (dB/km)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gamma0_approx(f, P, rho, T)[source]¶

Method to estimate the specific attenuation due to dry atmosphere using the approximate method descibed in Annex 2.

Parameters:	f (number or Quantity) – Frequency (GHz) P (number or Quantity) – Atmospheric pressure (hPa) rho (number or Quantity) – Water vapor density (g/m3) T (number or Quantity) – Absolute temperature (K)
Returns:	gamma_w – Dry atmosphere specific attenuation (dB/km)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gammaw_exact(f, P, rho, T)[source]¶

Method to estimate the specific attenuation due to water vapour using the line-by-line method described in Annex 1 of the recommendation.

Parameters:	f (number or Quantity) – Frequency (GHz) P (number or Quantity) – Atmospheric pressure (hPa) rho (number or Quantity) – Water vapor density (g/m3) T (number or Quantity) – Absolute temperature (K)
Returns:	gamma_w – Water vapour specific attenuation (dB/km)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gamma0_exact(f, P, rho, T)[source]¶

Method to estimate the specific attenuation due to dry atmosphere using the line-by-line method described in Annex 1 of the recommendation.

Parameters:	f (number or Quantity) – Frequency (GHz) P (number or Quantity) – Atmospheric pressure (hPa) rho (number or Quantity) – Water vapor density (g/m3) T (number or Quantity) – Absolute temperature (K)
Returns:	gamma_w – Dry atmosphere specific attenuation (dB/km)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

itur.models.itu676.gamma_exact(f, P, rho, T)[source]¶

Method to estimate the specific attenuation using the line-by-line method described in Annex 1 of the recommendation.

Parameters:	f (number or Quantity) – Frequency (GHz) P (number or Quantity) – Atmospheric pressure (hPa) rho (number or Quantity) – Water vapor density (g/m3) T (number or Quantity) – Absolute temperature (K)
Returns:	gamma – Specific attenuation (dB/km)
Return type:	Quantity

References

[1] Attenuation by atmospheric gases: https://www.itu.int/rec/R-REC-P.676/en

Recommendation ITU-R P.835¶

This Recommendation provides expressions and data for reference standard atmospheres required for the calculation of gaseous attenuation on Earth-space paths.

Title	PDF	Latest approved in
Recommendation ITU-R P.835	[PDF]	2017-12
Reference standard atmospheres
Current recommendation version (In force)		Date
Recommendation ITU-R P.835-6	[PDF]	12/2017
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.835-6	[PDF]	12/2017
Recommendation ITU-R P.835-5	[PDF]	02/2012
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.835-4	[PDF]	03/2005
Recommendation ITU-R P.835-3	[PDF]	10/1999
Recommendation ITU-R P.835-2	[PDF]	08/1997
Recommendation ITU-R P.835-1	[PDF]	08/1994

Introduction¶

This recommendation provides the equations to determine the temperature, pressure and water-vapour pressure as a function of altitude, as described in the U.S. Standard Atmosphere 1976. These values should be used for calculating gaseous attenuation when more reliable local data are not available.

Module description¶

itur.models.itu835.change_version(new_version)[source]¶

Change the version of the ITU-R P.835 recommendation currently being used.

This function changes the model used for the ITU-R P.835 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

6: Activates recommendation ITU-R P.835-6 (12/17) (Current version)

5: Activates recommendation ITU-R P.835-5 (02/12) (Superseded)

itur.models.itu835.get_version()[source]¶

The version of the model currently in use for the ITU-R P.835 recommendation.

Obtain the version of the ITU-R P.835 recommendation currently being used.

Returns:	version – The version of the ITU-R P.835 recommendation being used.
Return type:	int

itur.models.itu835.temperature(lat, h, season='summer')[source]¶

Determine the temperature at a given latitude and height.

Method to determine the temperature as a function of altitude and latitude, for calculating gaseous attenuation along an Earth-space path. This method is recommended when more reliable local data are not available.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points h (number or Quantity) – Height (km) season (string) – Season of the year (available values, ‘summer’, and ‘winter’). Default ‘summer’
Returns:	T – Temperature (K)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

itur.models.itu835.pressure(lat, h, season='summer')[source]¶

Determine the atmospheric pressure at a given latitude and height.

Method to determine the pressure as a function of altitude and latitude, for calculating gaseous attenuation along an Earth-space path. This method is recommended when more reliable local data are not available.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points h (number or Quantity) – Height (km) season (string) – Season of the year (available values, ‘summer’, and ‘winter’). Default ‘summer’
Returns:	P – Pressure (hPa)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

itur.models.itu835.water_vapour_density(lat, h, season='summer')[source]¶

Determine the water vapour density at a given latitude and height.

Method to determine the water-vapour density as a function of altitude and latitude, for calculating gaseous attenuation along an Earth-space path. This method is recommended when more reliable local data are not available.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points h (number or Quantity) – Height (km) season (string) – Season of the year (available values, ‘summer’, and ‘winter’). Default ‘summer’
Returns:	rho – Water vapour density (g/m^3)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

itur.models.itu835.standard_temperature(h, T_0=288.15)[source]¶

Determine the standard temperature at a given height.

Method to compute the temperature of an standard atmosphere at a given height. The reference standard atmosphere is based on the United States Standard Atmosphere, 1976, in which the atmosphere is divided into seven successive layers showing linear variation with temperature.

Parameters:	h (number or Quantity) – Height (km) T_0 (number or Quantity) – Surface temperature (K)
Returns:	T – Temperature (K)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

itur.models.itu835.standard_pressure(h, T_0=288.15, P_0=1013.25)[source]¶

Determine the standard pressure at a given height.

Method to compute the total atmopsheric pressure of an standard atmosphere at a given height.

The reference standard atmosphere is based on the United States Standard Atmosphere, 1976, in which the atmosphere is divided into seven successive layers showing linear variation with temperature.

Parameters:	h (number or Quantity) – Height (km) T_0 (number or Quantity) – Surface temperature (K) P_0 (number or Quantity) – Surface pressure (hPa)
Returns:	P – Pressure (hPa)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

itur.models.itu835.standard_water_vapour_density(h, h_0=2, rho_0=7.5)[source]¶

Determine the standard water vapour density at a given height.

The reference standard atmosphere is based on the United States Standard Atmosphere, 1976, in which the atmosphere is divided into seven successive layers showing linear variation with temperature.

Parameters:	h (number or Quantity) – Height (km) h_0 (number or Quantity) – Scale height (km) rho_0 (number or Quantity) – Surface water vapour density (g/m^3)
Returns:	rho – Water vapour density (g/m^3)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

itur.models.itu835.standard_water_vapour_pressure(h, h_0=2, rho_0=7.5)[source]¶

Determine the standard water vapour pressure at a given height.

The reference standard atmosphere is based on the United States Standard Atmosphere, 1976, in which the atmosphere is divided into seven successive layers showing linear variation with temperature.

Parameters:	h (number or Quantity) – Height (km) h_0 (number or Quantity) – Scale height (km) rho_0 (number or Quantity) – Surface water vapour density (g/m^3)
Returns:	e – Water vapour pressure (hPa)
Return type:	Quantity

References

[1] Reference Standard Atmospheres https://www.itu.int/rec/R-REC-P.835/en

Recommendation ITU-R P.836¶

This Recommendation provides methods to predict the surface water vapour density and total columnar water vapour content on Earth-space paths.

Title	PDF	Latest approved in
Recommendation ITU-R P.836	[PDF]	2017-12
surface density and total columnar content
Current recommendation version (In force)		Date
Recommendation ITU-R P.836-6	[PDF]	12/2017
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.836-6	[PDF]	12/2017
Recommendation ITU-R P.836-5	[PDF]	09/2013
Recommendation ITU-R P.836-4	[PDF]	10/2009
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.836-3	[PDF]	11/2001
Recommendation ITU-R P.836-2	[PDF]	02/2001
Recommendation ITU-R P.836-1	[PDF]	08/1997
Recommendation ITU-R P.836-0	[PDF]	03/1992

Introduction¶

Atmospheric water vapour and oxygen cause absorption at millimetre wavelengths especially in the proximity of absorption lines (see Recommendation ITU-R P.676). The concentration of atmospheric oxygen is relatively constant; however, the concentration of water vapour varies both geographically and with time.

For some applications, the total water vapour content along a path can be used for the calculation of excess path length and for the attenuation due to atmospheric water vapour, where the attenuation due to atmospheric water vapour is assumed to be proportional to the total water vapour content through its specific mass absorption coefficient.

This Recommendation provides method used for global calculations of propagation effects that require an estimate of surface water vapour density or total columnar content of water vapour and its seasonal variation, when more accurate local data are not available.

Module description¶

itur.models.itu836.change_version(new_version)[source]¶

Change the version of the ITU-R P.836 recommendation currently being used.

This function changes the model used for the ITU-R P.836 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

6: Activates recommendation ITU-R P.836-6 (12/17) (Current version)

5: Activates recommendation ITU-R P.836-5 (09/13) (Superseded)

4: Activates recommendation ITU-R P.836-4 (10/09) (Superseded)

itur.models.itu836.get_version()[source]¶

Obtain the version of the ITU-R P.836 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu836.surface_water_vapour_density(lat, lon, p, alt=None)[source]¶

Compute the surface water vapour density along a path.

This method computes the surface water vapour density along a path at a desired location on the surface of the Earth.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of time exceeded for p% of the average year alt (number, sequence, or numpy.ndarray) – Altitude of the receivers. If None, use the topographical altitude as described in recommendation ITU-R P.1511
Returns:	rho – Surface water vapour density (g/m3)
Return type:	Quantity

References

[1] Water vapour: surface density and total columnar content https://www.itu.int/rec/R-REC-P.836/en

itur.models.itu836.total_water_vapour_content(lat, lon, p, alt=None)[source]¶

Compute the total water vapour content along a path.

This method computes the total water vapour content along a path at a desired location on the surface of the Earth.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of time exceeded for p% of the average year alt (number, sequence, or numpy.ndarray) – Altitude of the receivers. If None, use the topographical altitude as described in recommendation ITU-R P.1511
Returns:	V – Total water vapour content (kg/m2)
Return type:	Quantity

References

[1] Water vapour: surface density and total columnar content https://www.itu.int/rec/R-REC-P.836/en

Recommendation ITU-R P.837¶

This Recommendation provides a method to compute the characteristics of precipitation for propagation modelling

Title	PDF	Latest approved in
Recommendation ITU-R P.837	[PDF]	2017-06
Characteristics of precipitation for propagation modelling
Current recommendation version (In force)		Date
Recommendation ITU-R P.837-7	[PDF]	06/2017
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.837-7	[PDF]	06/2017
Recommendation ITU-R P.837-6	[PDF]	02/2012
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.837-5	[PDF]	08/2007
Recommendation ITU-R P.837-4	[PDF]	04/2003
Recommendation ITU-R P.837-3	[PDF]	02/2001
Recommendation ITU-R P.837-2	[PDF]	10/1999
Recommendation ITU-R P.837-1	[PDF]	08/1994

Introduction¶

Rainfall rate statistics with a 1-min integration time are required for the prediction of rain attenuation in terrestrial and satellite links. Data of long-term measurements of rainfall rate may be available from local sources, but only with higher integration times. This Recommendation provides maps of meteorological parameters that have been obtained using the European Centre for Medium-Range Weather Forecast (ECMWF) ERA-40 re-analysis database, which are recommended for the prediction of rainfall rate statistics with a 1-min integration time, when local measurements are missing.

Module description¶

itur.models.itu837.change_version(new_version)[source]¶

Change the version of the ITU-R P.837 recommendation currently being used.

This function changes the model used for the ITU-R P.837 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

7: Activates recommendation ITU-R P.837-7 (12/17) (Current version)

6: Activates recommendation ITU-R P.837-6 (02/12) (Superseded)

itur.models.itu837.get_version()[source]¶

Obtain the version of the ITU-R P.837 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu837.rainfall_probability(lat, lon)[source]¶

Compute the percentage probability of rain in an average year, P0, at a given location.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
Returns:	P0 – Percentage probability of rain in an average year (%)
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.837/en

itur.models.itu837.rainfall_rate(lat, lon, p)[source]¶

Compute the rainfall rate exceeded for p% of the average year at a given location.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of time exceeded for p% of the average year
Returns:	R001 – Rainfall rate exceeded for p% of the average year
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.837/en

itur.models.itu837.unavailability_from_rainfall_rate(lat, lon, R)[source]¶

Compute the percentage of time of the average year that a given rainfall rate (R) is exceeded at a given location

This method calls successively to rainfall_rate (sing bisection) with different values of p.

Note: This method cannot operate in a vectorized manner.

Parameters:	lat (number) – Latitude of the receiver point lon (number) – Longitude of the receiver point R (number, sequence, or numpy.ndarray) – Rainfall rate (mm/h)
Returns:	p – Rainfall rate exceeded for p% of the average year
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.837/en

Recommendation ITU-R P.838¶

This Recommendation provides a method to compute the specific attenuation for rain for use in prediction methods.

Title	PDF	Latest approved in
Recommendation ITU-R P.838	[PDF]	2005-03
Specific attenuation model for rain for use in prediction methods
Current recommendation version (In force)		Date
Recommendation ITU-R P.838-3	[PDF]	03/2005
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.838-3	[PDF]	03/2005
Recommendation ITU-R P.838-2	[PDF]	04/2003
Recommendation ITU-R P.838-1	[PDF]	10/1999
Recommendation ITU-R P.838-0	[PDF]	03/1992

Introduction¶

The specific attenuation \(\gamma_R\) (dB/km) is obtained from the rain rate \(R:math:\) (mm/h) using the power-law relationship:

\[\gamma_R = k R^{\alpha}\]

Values for the coefficients \(k\) and \(\alpha\) are determined as functions of frequency, f (GHz), and this recommendation provides value valid in the range from 1 to 1 000 GHz. The models from Recommendation ITU-R P.838 have been developed from curve-fitting to power-law coefficients derived from scattering calculations:

Module description¶

itur.models.itu838.change_version(new_version)[source]¶

Change the version of the ITU-R P.838 recommendation currently being used.

This function changes the model used for the ITU-R P.838 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

3: Activates recommendation ITU-R P.838-3 (03/05) (Current version)

2: Activates recommendation ITU-R P.838-2 (04/03) (Superseded)

1: Activates recommendation ITU-R P.838-1 (10/99) (Superseded)

0: Activates recommendation ITU-R P.838-0 (03/92) (Superseded)

itur.models.itu838.get_version()[source]¶

Obtain the version of the ITU-R P.838 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu838.rain_specific_attenuation_coefficients(f, el, tau)[source]¶

Compute the values for the coefficients k and α.

A method to compute the values for the coefficients k and α to compute the rain specific attenuation \(\gamma_R\) (dB/km) (dB/km)

Parameters:

f (number or Quantity) – Frequency (GHz)
el (number, sequence, or numpy.ndarray) – Elevation angle of the receiver points
tau (number, sequence, or numpy.ndarray) – Polarization tilt angle relative to the horizontal (degrees). Tau = 45 deg for circular polarization)

Returns:

k (number) – Coefficient k (non-dimensional)
α (number) – Coefficient α (non-dimensional)

References

[1] Rain height model for prediction methods: https://www.itu.int/rec/R-REC-P.838/en

itur.models.itu838.rain_specific_attenuation(R, f, el, tau)[source]¶

Compute the specific attenuation γ_R (dB/km) given the rainfall rate.

A method to compute the specific attenuation γ_R (dB/km) from rain. The value is obtained from the rainfall rate R (mm/h) using a power law relationship.

\[\gamma_R = k R^\alpha\]

Parameters:	R (number, sequence, numpy.ndarray or Quantity) – Rain rate (mm/h) f (number or Quantity) – Frequency (GHz) el (number, sequence, or numpy.ndarray) – Elevation angle of the receiver points tau (number, sequence, or numpy.ndarray) – Polarization tilt angle relative to the horizontal (degrees). Tau = 45 deg for circular polarization)
Returns:	γ_R – Specific attenuation from rain (dB/km)
Return type:	numpy.ndarray

References

[1] Rain height model for prediction methods: https://www.itu.int/rec/R-REC-P.838/en

Recommendation ITU-R P.839¶

This Recommendation provides a method to predict the rain height for propagation prediction.

Title	PDF	Latest approved in
Recommendation ITU-R P.839	[PDF]	2013-09
Rain height model for prediction methods
Current recommendation version (In force)		Date
Recommendation ITU-R P.839-4	[PDF]	09/2013
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.839-4	[PDF]	09/2013
Recommendation ITU-R P.839-3	[PDF]	02/2001
Recommendation ITU-R P.839-2	[PDF]	10/1999
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.839-1	[PDF]	08/1997
Recommendation ITU-R P.839-0	[PDF]	03/1992

Introduction¶

The mean annual rain height above mean sea level, hR, may be obtained from the 0° C isotherm as:

\[h_R = h_0 + 0.36 \qquad \text{km}\]

for areas of the world where no specific information is available, the mean annual 0° C isotherm height above mean sea level, h0, is an integral part of this Recommendation. The data is provided from 0° to 360° in longitude and from +90° to –90° in latitude. For a location different from the grid-points, the mean annual 0° C isotherm height above mean sea level at the desired location can be derived by performing a bilinear interpolation on the values at the four closest gridpoints.

Module description¶

itur.models.itu839.change_version(new_version)[source]¶

Change the version of the ITU-R P.839 recommendation currently being used.

This function changes the model used for the ITU-R P.839 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

4: Activates recommendation ITU-R P.839-4 (09/2013) (Current version)

3: Activates recommendation ITU-R P.839-3 (02/01) (Superseded)

2: Activates recommendation ITU-R P.839-2 (10/99) (Superseded)

itur.models.itu839.get_version()[source]¶

Obtain the version of the ITU-R P.839 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu839.isoterm_0(lat, lon)[source]¶

Estimate the zero degree Celsius isoterm height for propagation prediction.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
Returns:	h0 – Zero degree Celsius isoterm height (km)
Return type:	numpy.ndarray

References

[1] Rain height model for prediction methods: https://www.itu.int/rec/R-REC-P.839/en

itur.models.itu839.rain_height(lat, lon)[source]¶

Estimate the annual mean rain height for propagation prediction.

The mean annual rain height above mean sea level, \(h_R\), may be obtained from the 0° C isotherm as:

\[h_R = h_0 + 0.36 \qquad \text{km}\]

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
Returns:	hR – Annual mean rain height (km)
Return type:	numpy.ndarray

References

[1] Rain height model for prediction methods: https://www.itu.int/rec/R-REC-P.839/en

Recommendation ITU-R P.840¶

This Recommendation provides methods to predict the attenuation due to clouds and fog on Earth-space paths.

Title	PDF	Latest approved in
Recommendation ITU-R P.840	[PDF]	2019-08
Attenuation due to clouds and fog
Current recommendation version (In force)		Date
Recommendation ITU-R P.840-8	[PDF]	08/2019
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.840-8	[PDF]	08/2019
Recommendation ITU-R P.840-7	[PDF]	12/2017
Recommendation ITU-R P.840-6	[PDF]	09/2013
Recommendation ITU-R P.840-5	[PDF]	02/2012
Recommendation ITU-R P.840-4	[PDF]	10/2009
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.840-3	[PDF]	10/1999
Recommendation ITU-R P.840-2	[PDF]	08/1997
Recommendation ITU-R P.840-1	[PDF]	08/1994

Introduction¶

For clouds or fog consisting entirely of small droplets, generally less than 0.01 cm, the Rayleigh approximation is valid for frequencies below 200 GHz and it is possible to express the attenuation in terms of the total water content per unit volume. Thus the specific attenuation within a cloud or fog can be written as:

\[\gamma_c(f, T) = M \cdot K_l(f, T) \qquad \text{[dB/km]}\]

where:

\(\gamma_c\) : specific attenuation (dB/km) within the cloud;
\(K_l\) : specific attenuation coefficient ((dB/km)/(g/m3));
\(M\) : liquid water density in the cloud or fog (g/m3).
\(f\) : frequency (GHz).
\(T\) : cloud liquid water temperature (K).

At frequencies of the order of 100 GHz and above, attenuation due to fog may be significant. The liquid water density in fog is typically about 0.05 g/m3 for medium fog (visibility of the order of 300 m) and 0.5 g/m3 for thick fog (visibility of the order of 50 m).

Module description¶

itur.models.itu840.change_version(new_version)[source]¶

Change the version of the ITU-R P.840 recommendation currently being used.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

8: Activates recommendation ITU-R P.840-8 (08/19) (Current version)

7: Activates recommendation ITU-R P.840-7 (12/17) (Superseded)

6: Activates recommendation ITU-R P.840-6 (09/13) (Superseded)

5: Activates recommendation ITU-R P.840-5 (02/12) (Superseded)

4: Activates recommendation ITU-R P.840-4 (10/09) (Superseded)

itur.models.itu840.get_version()[source]¶

Obtain the version of the ITU-R P.840 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu840.specific_attenuation_coefficients(f, T)[source]¶

Compute the specific attenuation coefficient for cloud attenuation.

A method to compute the specific attenuation coefficient. The method is based on Rayleigh scattering, which uses a double-Debye model for the dielectric permittivity of water.

This model can be used to calculate the value of the specific attenuation coefficient for frequencies up to 1000 GHz:

Parameters:	f (number) – Frequency (GHz) T (number) – Temperature (degrees C)
Returns:	Kl – Specific attenuation coefficient (dB/km)
Return type:	numpy.ndarray

References

[1] Attenuation due to clouds and fog: https://www.itu.int/rec/R-REC-P.840/en

itur.models.itu840.columnar_content_reduced_liquid(lat, lon, p)[source]¶

Compute the total columnar contents of reduced cloud liquid water.

A method to compute the total columnar content of reduced cloud liquid water, Lred (kg/m2), exceeded for p% of the average year

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points p (number) – Percentage of time exceeded for p% of the average year
Returns:	Lred – Total columnar content of reduced cloud liquid water, Lred (kg/m2), exceeded for p% of the average year
Return type:	numpy.ndarray

References

[1] Attenuation due to clouds and fog: https://www.itu.int/rec/R-REC-P.840/en

itur.models.itu840.cloud_attenuation(lat, lon, el, f, p, Lred=None)[source]¶

Compute the cloud attenuation in a slant path.

A method to estimate the attenuation due to clouds along slant paths for a given probability. If local measured data of the total columnar content of cloud liquid water reduced to a temperature of 273.15 K, Lred, is available from other sources, (e.g., from ground radiometric measurements, Earth observation products, or meteorological numerical products), the value should be used directly.

The value of the cloud attenuation is computed as:

\[A=\frac{L_{red}(\text{lat}, \text{lon}, p, T) \cdot K_l(f, T)}{\sin(\text{el})}\]

where:

\(L_{red}\) : total columnar content of liquid water reduced to a temperature of 273.15 K (kg/m2);
\(K_l\) : specific attenuation coefficient ((dB/km)/(g/m3));
\(el\) : path elevation angle (deg).
\(f\) : frequency (GHz).
\(p\) : Percentage of time exceeded for p% of the average year (%).
\(T\) : temperature (K). Equal to 273.15 K.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points el (number, sequence, or numpy.ndarray) – Elevation angle of the receiver points (deg) f (number) – Frequency (GHz) p (number) – Percentage of time exceeded for p% of the average year Lred (number) – Total columnar contents of reduced cloud liquid water. (kg/m2)
Returns:	A – Cloud attenuation, A (dB), exceeded for p% of the average year
Return type:	numpy.ndarray

References

[1] Attenuation due to clouds and fog: https://www.itu.int/rec/R-REC-P.840/en

itur.models.itu840.lognormal_approximation_coefficient(lat, lon)[source]¶

Total columnar contents of cloud liquid water distribution coefficients.

The annual statistics of the total columnar content of reduced cloud liquid water content can be approximated by a log-normal distribution. This function computes the coefficients for the mean, \(m\), standard deviation, \(\sigma\), and probability of non-zero reduced total columnar content of cloud liquid water, \(Pclw\), for such the log-normal distribution.

Parameters:

lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points
lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points

Returns:

m (numpy.ndarray) – Mean of the lognormal distribution
σ (numpy.ndarray) – Standard deviation of the lognormal distribution
Pclw (numpy.ndarray) – Probability of cloud liquid water of the lognormal distribution

References

[1] Attenuation due to clouds and fog: https://www.itu.int/rec/R-REC-P.840/en

Recommendation ITU-R P.1144¶

This Recommendation provides a guide to the Recommendations of Radiocommunication Study Group 3 which contain propagation prediction methods. It advises users on the most appropriate methods for particular applications as well as the limits, required input information, and output for each of these methods.

Title	PDF	Approved in
Recommendation ITU-R P.1144	[PDF]	2019-08
Guide to the application of the propagation methods of Radiocommunication Study Group 3
Latest Recommendation		Date
Recommendation ITU-R P.1144-10	[PDF]	08/2019

Introduction¶

Recommendation ITU-R P.1144 provides . In particular, the recommendation describes how to perform bi-linear and bi-cubic interpolation over the geophysical maps included in other recommendations.

Module description¶

Interpolation methods for the geophysical properties used to compute propagation effects. These methods are based on those in Recommendation ITU-R P.1144-7.

References

[1] Guide to the application of the propagation methods of Radiocommunication Study Group 3: https://www.itu.int/rec/R-REC-P.1144/en

itur.models.itu1144.is_regular_grid(lats_o, lons_o)[source]¶

Determinere whether the grids in lats_o and lons_o are both regular grids or not.

A grid is regular if the difference (column-wise or row-wise) between consecutive values is constant across the grid.

Parameters:	lats_o (numpy.ndarray) – Grid of latitude coordinates lons_o (numpy.ndarray) – Grid of longitude coordinates
Returns:	is_regular
Return type:	boolean

itur.models.itu1144.nearest_2D_interpolator(lats_o, lons_o, values)[source]¶

Produces a 2D interpolator function using the nearest value interpolation method. If the grids are regular grids, uses the scipy.interpolate.RegularGridInterpolator, otherwise, scipy.intepolate.griddata

Values can be interpolated from the returned function as follows:

f = nearest_2D_interpolator(lat_origin, lon_origin, values_origin)
interp_values = f(lat_interp, lon_interp)

Parameters:	lats_o (numpy.ndarray) – Latitude coordinates of the values usde by the interpolator lons_o (numpy.ndarray) – Longitude coordinates of the values usde by the interpolator values (numpy.ndarray) – Values usde by the interpolator
Returns:	interpolator – Nearest neighbour interpolator function
Return type:	function

itur.models.itu1144.bilinear_2D_interpolator(lats_o, lons_o, values)[source]¶

Produces a 2D interpolator function using the bilinear interpolation method. If the grids are regular grids, uses the scipy.interpolate.RegularGridInterpolator, otherwise, scipy.intepolate.griddata

Values can be interpolated from the returned function as follows:

f = nearest_2D_interpolator(lat_origin, lon_origin, values_origin)
interp_values = f(lat_interp, lon_interp)

Parameters:	lats_o (numpy.ndarray) – Latitude coordinates of the values usde by the interpolator lons_o (numpy.ndarray) – Longitude coordinates of the values usde by the interpolator values (numpy.ndarray) – Values usde by the interpolator
Returns:	interpolator – Bilinear interpolator function
Return type:	function

itur.models.itu1144.bicubic_2D_interpolator(lats_o, lons_o, values)[source]¶

Produces a 2D interpolator function using the bicubic interpolation method. Uses the scipy.intepolate.griddata method.

Values can be interpolated from the returned function as follows:

f = nearest_2D_interpolator(lat_origin, lon_origin, values_origin)
interp_values = f(lat_interp, lon_interp)

Parameters:	lats_o (numpy.ndarray) – Latitude coordinates of the values usde by the interpolator lons_o (numpy.ndarray) – Longitude coordinates of the values usde by the interpolator values (numpy.ndarray) – Values usde by the interpolator
Returns:	interpolator – Bicubic interpolator function
Return type:	function

Recommendation ITU-R P.1510¶

This Recommendation contains monthly and annual maps of mean surface temperature that are recommended for the prediction of statistics of different propagation effects such as rainfall rate, rain attenuation and gaseous attenuation due to water vapour and oxygen.

Title	PDF	Latest approved in
Recommendation ITU-R P.1510	[PDF]	2017-06
Mean surface temperature
Current recommendation version (In force)		Date
Recommendation ITU-R P.1510-1	[PDF]	06/2017
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.1510-1	[PDF]	06/2017
Recommendation ITU-R P.1510-0	[PDF]	02/2001

Introduction¶

Recommendation ITU-R P.1510 contains monthly and annual maps of mean surface temperature that are recommended for the prediction of statistics of different propagation effects such as rainfall rate, rain attenuation and gaseous attenuation due to water vapour and oxygen.

The monthly and annual mean surface temperature data (K) at 2 m above the surface of the Earth is an integral part of this Recommendation, and is provided as a grid. The latitude grid is from −90° N to +90° N in 0.75° steps, and the longitude grid is from −180° E to +180° E in 0.75° steps.

The monthly mean surface temperature maps have been derived from 36 years (1979-2014) of European Centre of Medium-range Weather Forecast (ECMWF) ERA Interim data, and the annual mean surface temperature map is the average of the monthly mean surface temperature maps weighted by the relative number of days in each calendar month.

Module description¶

itur.models.itu1510.change_version(new_version)[source]¶

Change the version of the ITU-R P.1510 recommendation currently being used.

This function changes the model used for the ITU-R P.1510 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

1: Activates recommendation ITU-R P.1510-1 (06/17) (Current version)
0: Activates recommendation ITU-R P.1510-0 (02/01) (Current version)

itur.models.itu1510.get_version()[source]¶

Obtain the version of the ITU-R P.1510 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu1510.surface_mean_temperature(lat, lon)[source]¶

Annual mean surface temperature (K) at 2 m above the surface of the Earth.

A method to estimate the annual mean surface temperature (K) at 2 m above the surface of the Earth

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
Returns:	annual_temperature – Annual mean surface temperature (K). Same dimensions as lat and lon.
Return type:	numpy.ndarray

References

[1] Annual mean surface temperature: https://www.itu.int/rec/R-REC-P.1510/en

itur.models.itu1510.surface_month_mean_temperature(lat, lon, m)[source]¶

Monthly mean surface temperature (K) at 2 m above the surface of the Earth.

A method to estimate the monthly mean surface temperature (K) at 2 m above the surface of the Earth

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points m (integer) – Index of the month (1=Jan, 2=Feb, 3=Mar, 4=Apr, …)
Returns:	monthly_temperature – Monthly mean surface temperature (K). Same dimensions as lat and lon.
Return type:	numpy.ndarray

References

[1] Annual mean surface temperature: https://www.itu.int/rec/R-REC-P.1510/en

Recommendation ITU-R P.1511¶

This Recommendation provides global topographical data, information on geographic coordinates, and height data for the prediction of propagation effects for Earth-space paths in ITU-R recommendations.

Title	PDF	Latest approved in
Recommendation ITU-R P.1511	[PDF]	2019-08
Topography for Earth-space propagation modelling
Current recommendation version (In force)		Date
Recommendation ITU-R P.1511-2	[PDF]	08/2019
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.1511-2	[PDF]	08/2019
Recommendation ITU-R P.1511-1	[PDF]	07/2015
Recommendation ITU-R P.1511-0	[PDF]	02/2001

Introduction¶

This model shall be used to obtain the height above mean sea level when no local data are available or when no data with a better spatial resolution is available.

The values of topographic height of the surface of the Earth above mean sea level (km) are an integral part of this Recommendation. The data is provided on a 1/12° grid in both latitude and longitude. For a location different from the grid points, the height above mean sea level at the desired location can be obtained by performing a bi-cubic interpolation on the values at the sixteen closest grid points

Module description¶

itur.models.itu1511.change_version(new_version)[source]¶

Change the version of the ITU-R P.1511 recommendation currently being used.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

1: Activates recommendation ITU-R P.1511-1 (07/15) (Current version)

0: Activates recommendation ITU-R P.1511-0 (02/01) (Superseded)

itur.models.itu1511.get_version()[source]¶

Obtain the version of the ITU-R P.1511 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu1511.topographic_altitude(lat, lon)[source]¶

Topographical height (km) above mean sea level of the surface of the Earth.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points
Returns:	altitude – Topographic altitude (km)
Return type:	numpy.ndarray

References

[1] Topography for Earth-to-space propagation modelling: https://www.itu.int/rec/R-REC-P.1511/en

Recommendation ITU-R P.1623¶

This Recommendation provides prediction methods of fade dynamics on Earth-space paths.

Title	PDF	Latest approved in
Recommendation ITU-R P.1623	[PDF]	2005-03
Prediction method of fade dynamics on Earth-space paths
Current recommendation version (In force)		Date
Recommendation ITU-R P.1623-1	[PDF]	03/2005
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.1623-1	[PDF]	03/2005
Recommendation ITU-R P.1623-0	[PDF]	04/2003

Introduction¶

In the design of a variety of telecommunication systems, the dynamic characteristics of fading due to atmospheric propagation are of concern to optimize system capacity and meet quality and reliability criteria. Examples are fixed networks that include a space segment and systems that apply fade mitigation or resource sharing techniques.

Several temporal scales can be defined, and it is useful to have information on fade slope, fade duration and interfade duration statistics for a given attenuation level. Fade duration is defined as the time interval between two crossings above the same attenuation threshold whereas interfade duration is defined as the time interval between two crossings below the same attenuation threshold. Fade slope is defined as the rate of change of attenuation with time.

Of particular interest in the context of availability criteria is the distinction between fades of shorter and longer duration than 10 s. Knowledge of the distribution of fade duration as a function of fade depth is also a prerequisite for the application of risk concepts in the provision of telecommunication services.

In addition, information about the expected fade slope is essential to assess the required minimum tracking rate of a fade mitigation system.

Module description¶

itur.models.itu1623.Qfunc(z)[source]¶

Tail distribution function of the standard normal distribution.

Q(z) is the probability that a normal (Gaussian) random variable will a value larger than z standard deviations

The Q-function can be expressed in terms of the error function as

\[Q(z) = \frac{1}{2} \left(1 - erf\left(\frac{z}{\sqrt{2}}\right)\right)\]

Parameters:	z (float) – Value to evaluate Q at.
Returns:	q – Value of the Q function evaluated at z.
Return type:	float

itur.models.itu1623.change_version(new_version)[source]¶

Change the version of the ITU-R P.1623 recommendation currently being used.

This function changes the model used for the ITU-R P.1623 recommendation to a different version.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

1: Activates recommendation ITU-R P.1623-1 (03/2005) (Current version)

0: Activates recommendation ITU-R P.1623-0 (04/2003) (Superseded)

itur.models.itu1623.get_version()[source]¶

Obtain the version of the ITU-R P.1623 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu1623.fade_duration_probability(D, A, el, f)[source]¶

Compute the probability of occurrence of fades of duration longer than D.

Compute the probability of occurrence of fades of duration d longer than D (s), given that the attenuation a is greater than A (dB).

This probability can be estimated from the ratio of the number of fades of duration longer than D to the total number of fades observed, given that the threshold A is exceeded.

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz)
Returns:	p – Probability of occurence of fade events of duration d longer than D given a>A, P(d > D\|a > A)
Return type:	number, sequence, or numpy.ndarray

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration_cummulative_probability(D, A, el, f)[source]¶

Compute the cumulative probability of exceedance of fades of duration longer than D.

Compute the cummulative exceedance probability F(d > D|a > A), the total fraction (between 0 and 1) of fade time due to fades of duration d longer than D (s), given that the attenuation a is greater than A (dB).

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz)
Returns:	F – Cumulative probability of exceedance, total fraction of fade time due to fades of d > D
Return type:	number, sequence, or numpy.ndarray

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration_number_fades(D, A, el, f, T_tot)[source]¶

Compute the number of fades of duration longer than D.

For a given reference period, the number of fades of duration longer D is estimated by multiplying the probability of occurrence P(d > D|a > A) by the total number of fades exceeding the threshold, Ntot(A).

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz) T_tot (number) – Total fade time from cumulative distribution (P(A)/100)Reference time period. T_tot should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.618. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time T_tot for the reference period considered. For a reference period of a year, T_tot = ((100-availability_in_pctg)/100)365.25243600 [s]
Returns:	N – threshold A
Return type:	Total number of fades of duration d longer than D, for a given

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration_total_exceedance_time(D, A, el, f, T_tot)[source]¶

Compute the total exceedance time of fades of duration longer than D.

The total exceedance time due to fade events of duration longer than D is obtained by multiplying the fraction of time F(d > D|a > A) by the total time that the threshold is exceeded, Ttot(A).

Parameters:	D (number, sequence, or numpy.ndarray) – Event durations, array, (s) A (number) – Attenuation threshold, scalar, (dB) el (number) – Elevation angle towards the satellite, deg (5 - 60) f (number) – Frequency, GHz (between 10 and 50 GHz) T_tot (number) – Total fade time from cumulative distribution (P(A)/100)Reference time period. T_tot should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.618. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time T_tot for the reference period considered. For a reference period of a year, T_tot = ((100-availability_in_pctg)/100)365.25243600 [s]
Returns:	T
Return type:	Total fading time due to fades of d > D for A threshold.

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_duration(D, A, el, f, T_tot)[source]¶

Compute the probability of occurrence of fades of duration longer than D.

Compute the probability of occurrence of fades of duration d longer than D (s), given that the attenuation a is greater than A (dB) and F(d > D|a > A), the cumulative exceedance probability, or, equivalently, the total fraction (between 0 and 1) of fade time due to fades of duration d longer than D (s), given that the attenuation a is greater than A (dB).

The function also returns other parameters associated to the fade duration prediction method. See ITU-R P.1623 Annex 1 Section 2.2

Parameters:

D (number, sequence, or numpy.ndarray) – Event durations, array, (s)
A (number) – Attenuation threshold, scalar, (dB)
el (number) – Elevation angle towards the satellite, deg (5 - 60)
f (number) – Frequency, GHz (between 10 and 50 GHz)
T_tot (number) –
Total fade time from cumulative distribution (P(A)/100)*Reference time period. T_tot should be obtained from local data. If this long-term statistic is not available, an estimate can be calculated from Recommendation ITU-R P.618. In this case the procedure consists in calculating the CDF of total attenuation, deriving the percentage of time the considered attenuation threshold A is exceeded and then the associated total exceedance time T_tot for the reference period considered.

For a reference period of a year, T_tot = ((100-availability_in_pctg)/100)*365.25*24*3600 [s]

Returns:

p (probability of occurence of fade events of) – duration d longer than D given a>A, P(d > D|a > A)
F (cumulative probability of exceedance, total) – fraction of fade time due to fades of d > D
N (total number of fades of duration d longer than D, for a given) – threshold A
T (total fading time due to fades of d > D for A threshold)

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_slope(z, A, f_B, delta_t)[source]¶

Compute the probability of exceeding a valueo f fade slope.

Fade slope is defined as the rate of change of attenuation with time information about the expected fade slope is essential to assess the required minimum tracking rate of a fade mitigation system. The model is valid for the following ranges of parameters:

frequencies from 10 to 30 GHz

elevation angles from 10° to 50°.

See ITU-R P.1623 Annex 1 Section 3.2

Parameters:

z (number, sequence, or numpy.ndarray) – array of fade slope values (dB/s)
A (number) – attenuation threshold, scalar, dB (range 0 - 20 dB)
f_B (number) – 3 dB cut-off frequency of the low pass filter (Hz, range 0.001 - 1) used to remove tropospheric scintillation and rapid variations of rain attenuation from the signal. Experimental results show that a 3 dB cut-off frequency of 0.02 Hz allows scintillation and rapid variations of rain attenuation to be filtered out adequately.
delta_t (number) – Time interval length over which fade slope is calculated (s), 2-200 s

Returns:

p (conditional probability (probability density function)) – that the fade slope is equal to the fade slope for a given attenuation value, A
P (conditional probability (complementary cumulative) – distribution function)that the fade slope is exceeded for a given attenuation value, A
P2 (conditional probability that the absolute value of) – the fade slope is exceeded for a given attenuation value, A
sigma_z (standard deviation of the conditional fade slope)
Remark
——
The output is an array of 4 elements.

Example

import itur.models.itu1623 as itu1623

z = np.linspace(-2,2,100)
A = 10
f_B = 0.02
delta_t = 1
p, P, P2, sigma_z = itu1623.fade_slope(z, A, f_B, delta_t)

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

itur.models.itu1623.fade_depth(N_target, D_target, A, PofA, el, f)[source]¶

Compute the maximum fade a link must tolerate given a target outage intensity value (number of events) and a target duration of event.

The fade depth is computed by numerical solution of the fade_duration problem.

See ITU-R P.1623 Annex 1 Section 3.2

Parameters:

N_target (int) – Target outage intensity (scalar)
D_target (int) – Event duration (scalar)
A (number, sequence, or numpy.ndarray) – Attenuation distribution (CDF, A) for the link under analysis
PofA (number, sequence, or numpy.ndarray) – Probability that A is exceeded (CDF, probability)
el (number) – Elevation angle (deg)
f (number) – Frequency (GHz)

Returns:

a_min (number) – Minimum attenuation the link must tolerate to meet the OI target
Remark
——
This function uses scipy’s fsolve as optimizer.

Example

import itur.models.itu1623 as itu1623

N_target = 25
D_target = 60
PofA = np.array([50, 30, 20, 10, 5, 3, 2, 1, .5, .3, .2, .1, .05, .03,
                 .02, .01, .005, .003, .002, .001])
A = np.array([0.4, 0.6, 0.8, 1.8, 2.70, 3.5, 4.20, 5.7, 7.4, 9, 10.60,
              14, 18.3, 22.3, 25.8, 32.6, 40.1, 46.1, 50.8, 58.8])
el = 38.5
f = 28
itu1623.fade_depth(N_target, D_target, A, PofA, el, f) # 21.6922280

References

[1] Prediction method of fade dynamics on Earth-space paths: https://www.itu.int/rec/R-REC-P.1623/en

Recommendation ITU-R P.1853¶

This Recommendation provides methods to synthesize rain attenuation and scintillation for terrestrial and Earth-space paths and total attenuation and tropospheric scintillation for Earth-space paths.

Title	PDF	Latest approved in
Recommendation ITU-R P.1853	[PDF]	2019-08
Time series synthesis of tropospheric impairments
Current recommendation version (In force)		Date
Recommendation ITU-R P.1853-2	[PDF]	08/2019
Recommendations implemented in ITU-Rpy		Date
Recommendation ITU-R P.1853-1	[PDF]	02/2012
Recommendation ITU-R P.1853-0	[PDF]	10/2009
Recommendations not implemented in ITU-Rpy		Date
Recommendation ITU-R P.1853-2	[PDF]	08/2019

Introduction¶

The planning and design of terrestrial and Earth-space radiocommunication systems requires the ability to synthesize the time dynamics of the propagation channel. For example, this information may be required to design various fade mitigation techniques such as, inter alia, adaptive coding and modulation, and transmit power control.

The methodology presented in this Recommendation provides a technique to synthesize rain attenuation and scintillation time series for terrestrial and Earth-space paths and total attenuation and tropospheric scintillation for Earth-space paths that approximate the rain attenuation statistics at a particular location.

Module description¶

itur.models.itu1853.change_version(new_version)[source]¶

Change the version of the ITU-R P.1853 recommendation currently being used.

Parameters:

new_version (int) –

Number of the version to use. Valid values are:

1: Activates recommendation ITU-R P.1853-1 (02/12) (Current version)

0: Activates recommendation ITU-R P.1853-0 (10/09) (Superseded)

itur.models.itu1853.get_version()[source]¶

Obtain the version of the ITU-R P.1853 recommendation currently being used.

Returns:	version – Version currently being used.
Return type:	int

itur.models.itu1853.set_seed(seed)[source]¶

Set the seed used to generate random numbers.

Parameters:	seed (int) – Seed used to generate random numbers

itur.models.itu1853.rain_attenuation_synthesis(lat, lon, f, el, hs, Ns, Ts=1, tau=45, n=None)[source]¶

A method to generate a synthetic time series of rain attenuation values.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points f (number or Quantity) – Frequency (GHz) el (sequence, or number) – Elevation angle (degrees) hs (number, sequence, or numpy.ndarray, optional) – Heigh above mean sea level of the earth station (km). If local data for the earth station height above mean sea level is not available, an estimate is obtained from the maps of topographic altitude given in Recommendation ITU-R P.1511. Ns (int) – Number of samples Ts (int) – Time step between consecutive samples (seconds) tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45 n (list, np.array, optional) – Additive White Gaussian Noise used as input for the
Returns:	rain_att – Synthesized rain attenuation time series (dB)
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.1853/en

itur.models.itu1853.scintillation_attenuation_synthesis(Ns, f_c=0.1, Ts=1)[source]¶

A method to generate a synthetic time series of scintillation attenuation values.

Parameters:	Ns (int) – Number of samples f_c (float) – Cut-off frequency for the low pass filter Ts (int) – Time step between consecutive samples (seconds)
Returns:	sci_att – Synthesized scintilation attenuation time series (dB)
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.1853/en

itur.models.itu1853.integrated_water_vapour_synthesis(lat, lon, Ns, Ts=1, n=None)[source]¶

The time series synthesis method generates a time series that reproduces the spectral characteristics and the distribution of water vapour content.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points Ns (int) – Number of samples Ts (int) – Time step between consecutive samples (seconds) n (list, np.array, optional) – Additive White Gaussian Noise used as input for the
Returns:	L – Synthesized water vapour content time series (kg/m2)
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.1853/en

itur.models.itu1853.cloud_liquid_water_synthesis(lat, lon, Ns, Ts=1, n=None)[source]¶

The time series synthesis method generates a time series that reproduces the spectral characteristics, rate of change and duration statistics of cloud liquid content events.

Parameters:	lat (number, sequence, or numpy.ndarray) – Latitudes of the receiver points lon (number, sequence, or numpy.ndarray) – Longitudes of the receiver points Ns (int) – Number of samples Ts (int) – Time step between consecutive samples (seconds) n (list, np.array, optional) – Additive White Gaussian Noise used as input for the
Returns:	V – Synthesized cloud liquid water time series (mm)
Return type:	numpy.ndarray

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.1853/en

itur.models.itu1853.total_attenuation_synthesis(lat, lon, f, el, p, D, Ns, Ts=1, hs=None, tau=45, eta=0.65, rho=None, H=None, P=None, hL=1000, return_contributions=False)[source]¶

The time series synthesis method generates a time series that reproduces the spectral characteristics, rate of change and duration statistics of the total atmospheric attenuation events.

The time series is obtained considering the contributions of gaseous, cloud, rain, and scintillation attenuation.

Parameters:

lat (number) – Latitudes of the receiver points
lon (number) – Longitudes of the receiver points
f (number or Quantity) – Frequency (GHz)
el (number) – Elevation angle (degrees)
p (number) – Percentage of the time the rain attenuation value is exceeded.
D (number or Quantity) – Physical diameter of the earth-station antenna (m)
Ns (int) – Number of samples
Ts (int) – Time step between consecutive samples (seconds)
tau (number, optional) – Polarization tilt angle relative to the horizontal (degrees) (tau = 45 deg for circular polarization). Default value is 45
hs (number, sequence, or numpy.ndarray, optional) – Heigh above mean sea level of the earth station (km). If local data for the earth station height above mean sea level is not available, an estimate is obtained from the maps of topographic altitude given in Recommendation ITU-R P.1511.
eta (number, optional) – Antenna efficiency. Default value 0.5 (conservative estimate)
rho (number or Quantity, optional) – Water vapor density (g/m3). If not provided, an estimate is obtained from Recommendation Recommendation ITU-R P.836.
H (number, sequence, or numpy.ndarray, optional) – Average surface relative humidity (%) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity.
P (number, sequence, or numpy.ndarray, optional) – Average surface pressure (hPa) at the site. If None, uses the ITU-R P.453 to estimate the wet term of the radio refractivity.
hL (number, optional) – Height of the turbulent layer (m). Default value 1000 m
return_contributions (bool, optional) – Determines whether individual contributions from gases, rain, clouds and scintillation are returned in addition ot the total attenuation (True), or just the total atmospheric attenuation (False). Default is False

Returns:

A (Quantity) – Synthesized total atmospheric attenuation time series (dB)
Ag, Ac, Ar, As, A (tuple) – Synthesized Gaseous, Cloud, Rain, Scintillation contributions to total attenuation time series, and synthesized total attenuation time seires (dB).

References

[1] Characteristics of precipitation for propagation modelling https://www.itu.int/rec/R-REC-P.1853/en

It is also advisable that developers use the index, module index, and search page below for quick access to specific functions:

Validation¶

ITU-Rpy has been validated using the ITU Validation examples (rev 5.1) , which provides test cases for parts of Recommendations ITU-R P.453-14, P.618-13, P.676-12, P.836-6, P.837-7, P.838-3, P.839-4, P.840-8, P.1511-2, P.1623-1.

For each part of the recommendation that has a counterpart function in ITU-Rpy, the results of the executing the ITUR-py function are compared against the values provided in the ITU Validation examples. The absolute and relative errors between these two quantities are computed, and each test case is color-coded (green = pass, errors are negligible, red = fail, errors are above 0.01%).

The links below show the validation results for each of the recommendations:

Validation results ITU-R P.453-14 ¶

This page contains the validation examples for Recommendation ITU-R P.453-14: TBD.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.453-14
- Function map_wet_term_radio_refractivity

Function map_wet_term_radio_refractivity ¶

The table below contains the results of testing function map_wet_term_radio_refractivity. The test cases were extracted from spreadsheet ITURP453-14_Nwet.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)
p = 50.0  # (%)

# Make call to test-function map_wet_term_radio_refractivity
itur_val = itur.models.itu453.map_wet_term_radio_refractivity(lat=lat, lon=lon, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 128.1408003  # nan
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu453.map_wet_term_radio_refractivity

ITU-Rpy Function	lat (°N)	lon (°E)	p (%)	ITU Validation nan	ITU-Rpy Result nan	Absolute Error	Relative Error
models.itu453.map_wet_term_radio_refractivity	3.133	101.70	50.0	128.140800	128.140800	3.33e-08	0.000
models.itu453.map_wet_term_radio_refractivity	22.900	-43.23	50.0	104.358475	104.358475	3.33e-08	0.000
models.itu453.map_wet_term_radio_refractivity	23.000	30.00	50.0	36.471667	36.471667	3.33e-09	0.000
models.itu453.map_wet_term_radio_refractivity	25.780	-80.22	50.0	113.273867	113.273867	4.26e-14	0.000
models.itu453.map_wet_term_radio_refractivity	28.717	77.30	50.0	75.660135	75.660135	3.33e-09	0.000
models.itu453.map_wet_term_radio_refractivity	33.940	18.43	50.0	80.140160	80.140160	-4.44e-09	-0.000
models.itu453.map_wet_term_radio_refractivity	41.900	12.49	50.0	61.218900	61.218900	-4.44e-09	-0.000
models.itu453.map_wet_term_radio_refractivity	51.500	-0.14	50.0	50.389262	50.389262	-2.22e-09	-0.000

Validation results ITU-R P.618-13 ¶

This page contains the validation examples for Recommendation ITU-R P.618-13: Propagation data and prediction methods required for the design of Earth-space telecommunication systems.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.618-13

Function rain_cross_polarization_discrimination ¶

The table below contains the results of testing function rain_cross_polarization_discrimination. The test cases were extracted from spreadsheet ITURP618-13_A_xpd.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
f = 14.25  # (GHz)
el = 31.07699124  # (°)
p = 1.0  # (%)
tau = 0.0  # (°)
Ap = 0.49531707  # (dB)

# Make call to test-function rain_cross_polarization_discrimination
itur_val = itur.models.itu618.rain_cross_polarization_discrimination(f=f, el=el, p=p, tau=tau, Ap=Ap)

# Compute error with respect to value in ITU example file
ITU_example_val = 49.47769944  # (dB)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu618.rain_cross_polarization_discrimination

ITU-Rpy Function	f (GHz)	el (°)	p (%)	tau (°)	Ap (dB)	ITU Validation (dB)	ITU-Rpy Result (dB)	Absolute Error	Relative Error
models.itu618.rain_cross_polarization_discrimination	14.25	31.076991	1.000	0.0	0.495317	49.477699	49.477699	-5.20e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	40.232036	1.000	0.0	0.623263	49.377149	49.377149	2.78e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	46.359693	1.000	0.0	0.421017	53.938571	53.938571	-3.09e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	31.076991	0.100	0.0	2.185847	40.203026	40.203026	8.35e-10	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	40.232036	0.100	0.0	2.696765	40.260014	40.260014	-5.62e-10	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	46.359693	0.100	0.0	1.913388	44.682657	44.682657	-2.50e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	31.076991	0.010	0.0	6.798072	32.887586	32.887586	3.19e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	40.232036	0.010	0.0	8.223265	33.120273	33.120273	2.67e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	46.359693	0.010	0.0	5.941806	37.629187	37.629187	-3.61e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	31.076991	0.001	0.0	14.899822	28.054505	28.054505	-4.09e-10	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	40.232036	0.001	0.0	17.671558	28.481053	28.481053	1.58e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	46.359693	0.001	0.0	12.981517	33.075103	33.075103	1.53e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	31.076991	1.000	0.0	2.207786	44.190517	44.190517	-2.90e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	40.232036	1.000	0.0	2.823466	43.836439	43.836439	-3.21e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	46.359693	1.000	0.0	1.960636	48.369649	48.369649	8.79e-10	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	31.076991	0.100	0.0	8.570058	34.928405	34.928405	-2.71e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	40.232036	0.100	0.0	10.731008	34.739991	34.739991	2.65e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	46.359693	0.100	0.0	7.808323	39.126903	39.126903	5.30e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	31.076991	0.010	0.0	23.444445	27.862900	27.862900	-5.74e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	40.232036	0.010	0.0	28.742722	27.860873	27.860873	-5.37e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	46.359693	0.010	0.0	21.248620	32.343669	32.343669	2.66e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	31.076991	0.001	0.0	45.198656	23.548935	23.548935	2.97e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	40.232036	0.001	0.0	54.255612	23.754016	23.754016	2.84e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	46.359693	0.001	0.0	40.681330	28.333811	28.333811	-1.58e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	22.278335	1.000	0.0	1.706901	38.650730	38.650730	2.63e-10	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	52.678985	1.000	0.0	1.437313	46.239921	46.239921	-4.91e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	22.278335	0.100	0.0	8.271647	27.963454	27.963454	4.38e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	52.678985	0.100	0.0	6.297247	36.834658	36.834658	3.48e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	22.278335	0.010	0.0	18.944104	22.644928	22.644928	-3.59e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	52.678985	0.010	0.0	16.429807	30.868800	30.868800	-2.72e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	22.278335	0.001	0.0	29.911713	20.292923	20.292923	4.44e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	52.678985	0.001	0.0	29.930948	27.632370	27.632370	-3.24e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	22.278335	1.000	0.0	6.813368	33.646885	33.646885	-4.56e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	52.678985	1.000	0.0	6.654856	40.086834	40.086834	3.63e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	22.278335	0.100	0.0	29.318968	22.854139	22.854139	4.86e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	52.678985	0.100	0.0	25.562955	30.675965	30.675965	3.41e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	22.278335	0.010	0.0	59.625764	17.882554	17.882554	-1.53e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	52.678985	0.010	0.0	58.474383	25.042467	25.042467	-2.07e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	22.278335	0.001	0.0	83.599639	16.169229	16.169229	-7.31e-10	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	52.678985	0.001	0.0	93.395625	22.427035	22.427035	4.53e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	48.241171	1.000	90.0	1.274464	45.794052	45.794052	-2.26e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	85.804596	1.000	90.0	2.001027	74.875777	74.875777	-7.07e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	20.143358	1.000	90.0	1.012354	42.526404	42.526404	1.79e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	48.241171	0.100	90.0	5.486347	36.508437	36.508437	4.77e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	85.804596	0.100	90.0	11.001455	65.273303	65.273304	-1.24e-08	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	20.143358	0.100	90.0	5.881071	30.564398	30.564398	3.68e-09	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	48.241171	0.010	90.0	14.872137	30.189886	30.189886	3.08e-10	0.000
models.itu618.rain_cross_polarization_discrimination	14.25	85.804596	0.010	90.0	21.610579	63.370502	63.370502	-1.42e-08	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	20.143358	0.010	90.0	12.289760	26.192025	26.192025	-1.47e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	48.241171	0.001	90.0	28.236031	26.537261	26.537261	-2.07e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	85.804596	0.001	90.0	28.819504	64.717261	64.717261	-8.39e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	14.25	20.143358	0.001	90.0	17.441993	25.008801	25.008801	-2.79e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	48.241171	1.000	90.0	5.887822	39.721343	39.721343	4.54e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	85.804596	1.000	90.0	10.213148	67.739322	67.739322	-4.96e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	20.143358	1.000	90.0	3.701584	38.523477	38.523477	3.83e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	48.241171	0.100	90.0	22.226229	30.442770	30.442770	-3.46e-10	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	85.804596	0.100	90.0	48.819968	58.023471	58.023471	-6.32e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	20.143358	0.100	90.0	19.239104	26.349498	26.349498	4.11e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	48.241171	0.010	90.0	52.833721	24.437965	24.437965	-1.17e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	85.804596	0.010	90.0	83.378562	56.633773	56.633773	-1.08e-08	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	20.143358	0.010	90.0	35.970377	22.356294	22.356294	-2.06e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	48.241171	0.001	90.0	87.962337	21.383360	21.383360	5.13e-09	0.000
models.itu618.rain_cross_polarization_discrimination	29.00	85.804596	0.001	90.0	96.675211	58.824705	58.824705	-6.98e-09	-0.000
models.itu618.rain_cross_polarization_discrimination	29.00	20.143358	0.001	90.0	45.674191	21.851236	21.851236	3.93e-09	0.000

Function rain_attenuation ¶

The table below contains the results of testing function rain_attenuation. The test cases were extracted from spreadsheet ITURP618-13_A_rain.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 51.5  #  (°N)
lon = -0.14  # (°E)
hs = 0.031382984  #  (km)
el = 31.07699124  # (°)
f = 14.25  # (GHz)
tau = 0.0  # (°)
p = 1.0  # (%)
R001 = 26.48052  # (mm/h)

# Make call to test-function rain_attenuation
itur_val = itur.models.itu618.rain_attenuation(lat=lat, lon=lon, hs=hs, el=el, f=f, tau=tau, p=p, R001=R001)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.495317069  # (dB)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu618.rain_attenuation

ITU-Rpy Function	lat (°N)	lon (°E)	hs (km)	el (°)	f (GHz)	tau (°)	p (%)	R001 (mm/h)	ITU Validation (dB)	ITU-Rpy Result (dB)	Absolute Error	Relative Error
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	14.25	0.0	1.000	26.480520	0.495317	0.495317	2.17e-11	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	14.25	0.0	1.000	33.936232	0.623263	0.623263	2.06e-10	0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	14.25	0.0	1.000	27.135868	0.421017	0.421017	1.40e-10	0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	14.25	0.0	0.100	26.480520	2.185847	2.185847	1.28e-10	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	14.25	0.0	0.100	33.936232	2.696765	2.696765	4.37e-10	0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	14.25	0.0	0.100	27.135868	1.913388	1.913388	5.49e-11	0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	14.25	0.0	0.010	26.480520	6.798072	6.798072	9.61e-10	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	14.25	0.0	0.010	33.936232	8.223265	8.223265	7.29e-10	0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	14.25	0.0	0.010	27.135868	5.941806	5.941806	-2.64e-10	-0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	14.25	0.0	0.001	26.480520	14.899822	14.899822	1.91e-09	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	14.25	0.0	0.001	33.936232	17.671558	17.671558	-1.92e-09	-0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	14.25	0.0	0.001	27.135868	12.981517	12.981517	2.47e-09	0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	29.00	0.0	1.000	26.480520	2.207786	2.207786	3.84e-11	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	29.00	0.0	1.000	33.936232	2.823466	2.823466	2.25e-10	0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	29.00	0.0	1.000	27.135868	1.960636	1.960636	1.28e-11	0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	29.00	0.0	0.100	26.480520	8.570058	8.570058	5.85e-10	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	29.00	0.0	0.100	33.936232	10.731008	10.731008	-1.49e-09	-0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	29.00	0.0	0.100	27.135868	7.808323	7.808323	-2.67e-10	-0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	29.00	0.0	0.010	26.480520	23.444445	23.444445	-1.91e-09	-0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	29.00	0.0	0.010	33.936232	28.742722	28.742722	-1.98e-09	-0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	29.00	0.0	0.010	27.135868	21.248620	21.248620	6.22e-10	0.000
models.itu618.rain_attenuation	51.500	-0.14	0.031383	31.076991	29.00	0.0	0.001	26.480520	45.198656	45.198656	3.56e-09	0.000
models.itu618.rain_attenuation	41.900	12.49	0.046123	40.232036	29.00	0.0	0.001	33.936232	54.255612	54.255612	-3.29e-09	-0.000
models.itu618.rain_attenuation	33.940	18.43	0.000000	46.359693	29.00	0.0	0.001	27.135868	40.681330	40.681330	4.43e-09	0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	14.25	0.0	1.000	50.639304	1.706901	1.706901	-4.20e-10	-0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	14.25	0.0	1.000	78.299499	1.437313	1.437313	1.97e-10	0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	14.25	0.0	0.100	50.639304	8.271647	8.271647	-2.71e-09	-0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	14.25	0.0	0.100	78.299499	6.297247	6.297247	2.20e-10	0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	14.25	0.0	0.010	50.639304	18.944104	18.944104	4.59e-10	0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	14.25	0.0	0.010	78.299499	16.429807	16.429807	1.59e-10	0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	14.25	0.0	0.001	50.639304	29.911713	29.911713	5.32e-09	0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	14.25	0.0	0.001	78.299499	29.930948	29.930948	3.99e-09	0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	29.00	0.0	1.000	50.639304	6.813368	6.813368	-3.45e-10	-0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	29.00	0.0	1.000	78.299499	6.654856	6.654856	1.76e-10	0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	29.00	0.0	0.100	50.639304	29.318968	29.318968	-7.76e-09	-0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	29.00	0.0	0.100	78.299499	25.562955	25.562955	-9.96e-11	-0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	29.00	0.0	0.010	50.639304	59.625764	59.625764	-3.59e-09	-0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	29.00	0.0	0.010	78.299499	58.474383	58.474383	-1.82e-09	-0.000
models.itu618.rain_attenuation	22.900	-43.23	0.000000	22.278335	29.00	0.0	0.001	50.639304	83.599639	83.599639	6.90e-09	0.000
models.itu618.rain_attenuation	25.780	-80.22	0.008617	52.678985	29.00	0.0	0.001	78.299499	93.395625	93.395625	-8.98e-10	-0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	14.25	90.0	1.000	63.618888	1.274464	1.274464	-6.19e-11	-0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	14.25	90.0	1.000	99.151172	2.001027	2.001027	3.34e-10	0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	14.25	90.0	1.000	42.910072	1.012354	1.012354	6.18e-10	0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	14.25	90.0	0.100	63.618888	5.486347	5.486347	4.37e-10	0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	14.25	90.0	0.100	99.151172	11.001455	11.001455	3.78e-09	0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	14.25	90.0	0.100	42.910072	5.881071	5.881071	2.82e-09	0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	14.25	90.0	0.010	63.618888	14.872137	14.872137	4.25e-09	0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	14.25	90.0	0.010	99.151172	21.610579	21.610579	-2.07e-09	-0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	14.25	90.0	0.010	42.910072	12.289760	12.289760	4.58e-09	0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	14.25	90.0	0.001	63.618888	28.236031	28.236031	-3.08e-09	-0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	14.25	90.0	0.001	99.151172	28.819504	28.819504	3.40e-09	0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	14.25	90.0	0.001	42.910072	17.441993	17.441993	-2.61e-09	-0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	29.00	90.0	1.000	63.618888	5.887822	5.887822	1.95e-10	0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	29.00	90.0	1.000	99.151172	10.213148	10.213148	-3.36e-09	-0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	29.00	90.0	1.000	42.910072	3.701584	3.701584	1.41e-09	0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	29.00	90.0	0.100	63.618888	22.226229	22.226229	7.10e-10	0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	29.00	90.0	0.100	99.151172	48.819968	48.819968	1.86e-09	0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	29.00	90.0	0.100	42.910072	19.239104	19.239104	7.05e-09	0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	29.00	90.0	0.010	63.618888	52.833721	52.833721	4.50e-09	0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	29.00	90.0	0.010	99.151172	83.378562	83.378562	2.28e-09	0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	29.00	90.0	0.010	42.910072	35.970377	35.970377	6.23e-09	0.000
models.itu618.rain_attenuation	28.717	77.30	0.209384	48.241171	29.00	90.0	0.001	63.618888	87.962337	87.962337	2.93e-09	0.000
models.itu618.rain_attenuation	3.133	101.70	0.051251	85.804596	29.00	90.0	0.001	99.151172	96.675211	96.675211	4.49e-09	0.000
models.itu618.rain_attenuation	9.050	38.70	2.539862	20.143358	29.00	90.0	0.001	42.910072	45.674191	45.674191	8.68e-09	0.000

Function rain_attenuation_probability ¶

The table below contains the results of testing function rain_attenuation_probability. The test cases were extracted from spreadsheet ITURP618-13_A_rain.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 51.5  #  (°N)
lon = -0.14  # (°E)
hs = 0.031382984  #  (km)
el = 31.07699124  # (°)
Ls = 4.690817392  # (km)
P0 = 0.053615096  # (0-1)

# Make call to test-function rain_attenuation_probability
itur_val = itur.models.itu618.rain_attenuation_probability(lat=lat, lon=lon, hs=hs, el=el, Ls=Ls, P0=P0)

# Compute error with respect to value in ITU example file
ITU_example_val = 7.341941569  # (%)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu618.rain_attenuation_probability

ITU-Rpy Function	lat (°N)	lon (°E)	hs (km)	el (°)	Ls (km)	P0 (0-1)	ITU Validation (%)	ITU-Rpy Result (%)	Absolute Error	Relative Error
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	51.500	-0.14	0.031383	31.076991	4.690817	0.053615	7.341942	7.341942	1.13e-08	0.000
models.itu618.rain_attenuation_probability	41.900	12.49	0.046123	40.232036	4.646914	0.052697	7.093501	7.093501	-3.29e-08	-0.000
models.itu618.rain_attenuation_probability	33.940	18.43	0.000000	46.359693	3.542007	0.012757	1.744680	1.744680	2.20e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	22.900	-43.23	0.000000	22.278335	10.969955	0.014177	2.582901	2.582901	4.63e-08	0.000
models.itu618.rain_attenuation_probability	25.780	-80.22	0.008617	52.678985	5.735099	0.029079	4.038043	4.038043	5.94e-08	0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000
models.itu618.rain_attenuation_probability	28.717	77.30	0.209384	48.241171	6.768266	0.010709	1.644749	1.644749	4.24e-08	0.000
models.itu618.rain_attenuation_probability	3.133	101.70	0.051251	85.804596	4.919907	0.045365	5.010168	5.010183	-1.46e-05	-0.000
models.itu618.rain_attenuation_probability	9.050	38.70	2.539862	20.143358	6.516372	0.047125	6.984766	6.984766	-5.45e-08	-0.000

Function scintillation_attenuation ¶

The table below contains the results of testing function scintillation_attenuation. The test cases were extracted from spreadsheet ITURP618-13_A_sci.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 51.5  #  (°N)
lon = -0.14  # (°E)
f = 14.25  # (GHz)
el = 31.07699124  # (°)
p = 1.0  # (%)
D = 1.0  # (m)
eta = 0.65  # (0-1)

# Make call to test-function scintillation_attenuation
itur_val = itur.models.itu618.scintillation_attenuation(lat=lat, lon=lon, f=f, el=el, p=p, D=D, eta=eta)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.261931889  # (dB)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu618.scintillation_attenuation

ITU-Rpy Function	lat (°N)	lon (°E)	f (GHz)	el (°)	p (%)	D (m)	eta (0-1)	ITU Validation (dB)	ITU-Rpy Result (dB)	Absolute Error	Relative Error
models.itu618.scintillation_attenuation	51.500	-0.14	14.25	31.076991	1.000	1.0	0.65	0.261932	0.261932	6.92e-11	0.000
models.itu618.scintillation_attenuation	41.900	12.49	14.25	40.232036	1.000	1.0	0.65	0.224052	0.224052	2.16e-10	0.000
models.itu618.scintillation_attenuation	33.940	18.43	14.25	46.359693	1.000	1.0	0.65	0.232799	0.232799	2.71e-10	0.000
models.itu618.scintillation_attenuation	51.500	-0.14	14.25	31.076991	0.100	1.0	0.65	0.422845	0.422845	-3.64e-10	-0.000
models.itu618.scintillation_attenuation	41.900	12.49	14.25	40.232036	0.100	1.0	0.65	0.361695	0.361695	-4.47e-10	-0.000
models.itu618.scintillation_attenuation	33.940	18.43	14.25	46.359693	0.100	1.0	0.65	0.375816	0.375816	-2.50e-10	-0.000
models.itu618.scintillation_attenuation	51.500	-0.14	14.25	31.076991	0.010	1.0	0.65	0.628287	0.628287	8.48e-11	0.000
models.itu618.scintillation_attenuation	41.900	12.49	14.25	40.232036	0.010	1.0	0.65	0.537427	0.537427	-2.22e-10	-0.000
models.itu618.scintillation_attenuation	33.940	18.43	14.25	46.359693	0.010	1.0	0.65	0.558408	0.558408	-1.24e-10	-0.000
models.itu618.scintillation_attenuation	51.500	-0.14	14.25	31.076991	0.001	1.0	0.65	0.910213	0.910213	-3.44e-11	-0.000
models.itu618.scintillation_attenuation	41.900	12.49	14.25	40.232036	0.001	1.0	0.65	0.778581	0.778581	1.25e-10	0.000
models.itu618.scintillation_attenuation	33.940	18.43	14.25	46.359693	0.001	1.0	0.65	0.808978	0.808978	4.40e-10	0.000
models.itu618.scintillation_attenuation	51.500	-0.14	20.00	31.076991	1.000	1.0	0.65	0.316526	0.316526	3.95e-10	0.000
models.itu618.scintillation_attenuation	41.900	12.49	20.00	40.232036	1.000	1.0	0.65	0.270358	0.270358	-3.40e-10	-0.000
models.itu618.scintillation_attenuation	33.940	18.43	20.00	46.359693	1.000	1.0	0.65	0.280680	0.280680	2.25e-10	0.000
models.itu618.scintillation_attenuation	51.500	-0.14	20.00	31.076991	0.100	1.0	0.65	0.510979	0.510979	3.27e-10	0.000
models.itu618.scintillation_attenuation	41.900	12.49	20.00	40.232036	0.100	1.0	0.65	0.436447	0.436447	-2.18e-10	-0.000
models.itu618.scintillation_attenuation	33.940	18.43	20.00	46.359693	0.100	1.0	0.65	0.453111	0.453111	2.81e-10	0.000
models.itu618.scintillation_attenuation	51.500	-0.14	20.00	31.076991	0.010	1.0	0.65	0.759241	0.759241	-1.35e-10	-0.000
models.itu618.scintillation_attenuation	41.900	12.49	20.00	40.232036	0.010	1.0	0.65	0.648498	0.648498	-1.03e-10	-0.000
models.itu618.scintillation_attenuation	33.940	18.43	20.00	46.359693	0.010	1.0	0.65	0.673258	0.673258	-3.64e-10	-0.000
models.itu618.scintillation_attenuation	51.500	-0.14	20.00	31.076991	0.001	1.0	0.65	1.099929	1.099929	-1.76e-10	-0.000
models.itu618.scintillation_attenuation	41.900	12.49	20.00	40.232036	0.001	1.0	0.65	0.939492	0.939492	-3.07e-10	-0.000
models.itu618.scintillation_attenuation	33.940	18.43	20.00	46.359693	0.001	1.0	0.65	0.975363	0.975363	-1.68e-10	-0.000
models.itu618.scintillation_attenuation	22.900	-43.23	14.25	22.278335	1.000	1.0	0.65	0.620097	0.620097	-2.05e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	14.25	52.678985	1.000	1.0	0.65	0.266475	0.266475	3.59e-10	0.000
models.itu618.scintillation_attenuation	22.900	-43.23	14.25	22.278335	0.100	1.0	0.65	1.001044	1.001044	-1.80e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	14.25	52.678985	0.100	1.0	0.65	0.430179	0.430179	1.25e-10	0.000
models.itu618.scintillation_attenuation	22.900	-43.23	14.25	22.278335	0.010	1.0	0.65	1.487407	1.487407	-3.10e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	14.25	52.678985	0.010	1.0	0.65	0.639185	0.639185	1.73e-10	0.000
models.itu618.scintillation_attenuation	22.900	-43.23	14.25	22.278335	0.001	1.0	0.65	2.154839	2.154839	-8.12e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	14.25	52.678985	0.001	1.0	0.65	0.926000	0.926000	-4.03e-10	-0.000
models.itu618.scintillation_attenuation	22.900	-43.23	20.00	22.278335	1.000	1.0	0.65	0.750597	0.750597	-2.69e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	20.00	52.678985	1.000	1.0	0.65	0.321045	0.321045	-2.79e-11	-0.000
models.itu618.scintillation_attenuation	22.900	-43.23	20.00	22.278335	0.100	1.0	0.65	1.211713	1.211713	-9.65e-11	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	20.00	52.678985	0.100	1.0	0.65	0.518273	0.518273	3.66e-11	0.000
models.itu618.scintillation_attenuation	22.900	-43.23	20.00	22.278335	0.010	1.0	0.65	1.800432	1.800432	-5.00e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	20.00	52.678985	0.010	1.0	0.65	0.770079	0.770079	-3.54e-10	-0.000
models.itu618.scintillation_attenuation	22.900	-43.23	20.00	22.278335	0.001	1.0	0.65	2.608324	2.608324	-2.10e-10	-0.000
models.itu618.scintillation_attenuation	25.780	-80.22	20.00	52.678985	0.001	1.0	0.65	1.115631	1.115631	2.81e-11	0.000
models.itu618.scintillation_attenuation	28.717	77.30	14.25	48.241171	1.000	1.0	0.65	0.215641	0.215641	-4.71e-10	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	14.25	85.804596	1.000	1.0	0.65	0.221671	0.221671	-2.26e-10	-0.000
models.itu618.scintillation_attenuation	9.050	38.70	14.25	20.143358	1.000	1.0	0.65	0.485340	0.485340	-2.90e-10	-0.000
models.itu618.scintillation_attenuation	28.717	77.30	14.25	48.241171	0.100	1.0	0.65	0.348117	0.348117	1.80e-10	0.000
models.itu618.scintillation_attenuation	3.133	101.70	14.25	85.804596	0.100	1.0	0.65	0.357851	0.357851	2.18e-10	0.000
models.itu618.scintillation_attenuation	9.050	38.70	14.25	20.143358	0.100	1.0	0.65	0.783500	0.783500	-4.79e-11	-0.000
models.itu618.scintillation_attenuation	28.717	77.30	14.25	48.241171	0.010	1.0	0.65	0.517252	0.517252	-4.49e-10	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	14.25	85.804596	0.010	1.0	0.65	0.531716	0.531716	1.72e-10	0.000
models.itu618.scintillation_attenuation	9.050	38.70	14.25	20.143358	0.010	1.0	0.65	1.164169	1.164169	3.55e-10	0.000
models.itu618.scintillation_attenuation	28.717	77.30	14.25	48.241171	0.001	1.0	0.65	0.749353	0.749353	-1.35e-10	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	14.25	85.804596	0.001	1.0	0.65	0.770308	0.770308	-1.59e-10	-0.000
models.itu618.scintillation_attenuation	9.050	38.70	14.25	20.143358	0.001	1.0	0.65	1.686556	1.686556	6.69e-10	0.000
models.itu618.scintillation_attenuation	28.717	77.30	20.00	48.241171	1.000	1.0	0.65	0.259933	0.259933	-3.98e-10	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	20.00	85.804596	1.000	1.0	0.65	0.266539	0.266539	-2.69e-10	-0.000
models.itu618.scintillation_attenuation	9.050	38.70	20.00	20.143358	1.000	1.0	0.65	0.587745	0.587745	2.58e-11	0.000
models.itu618.scintillation_attenuation	28.717	77.30	20.00	48.241171	0.100	1.0	0.65	0.419618	0.419618	-4.68e-10	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	20.00	85.804596	0.100	1.0	0.65	0.430283	0.430283	1.27e-10	0.000
models.itu618.scintillation_attenuation	9.050	38.70	20.00	20.143358	0.100	1.0	0.65	0.948816	0.948816	5.16e-10	0.000
models.itu618.scintillation_attenuation	28.717	77.30	20.00	48.241171	0.010	1.0	0.65	0.623492	0.623492	-4.51e-11	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	20.00	85.804596	0.010	1.0	0.65	0.639339	0.639339	2.46e-10	0.000
models.itu618.scintillation_attenuation	9.050	38.70	20.00	20.143358	0.010	1.0	0.65	1.409803	1.409803	1.90e-10	0.000
models.itu618.scintillation_attenuation	28.717	77.30	20.00	48.241171	0.001	1.0	0.65	0.903266	0.903266	-8.27e-11	-0.000
models.itu618.scintillation_attenuation	3.133	101.70	20.00	85.804596	0.001	1.0	0.65	0.926223	0.926223	-4.60e-10	-0.000
models.itu618.scintillation_attenuation	9.050	38.70	20.00	20.143358	0.001	1.0	0.65	2.042413	2.042413	2.39e-10	0.000

Function atmospheric_attenuation_slant_path ¶

The table below contains the results of testing function atmospheric_attenuation_slant_path. The test cases were extracted from spreadsheet ITURP618-13_A_total.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 51.5  #  (°N)
lon = -0.14  # (°E)
f = 14.25  # (GHz)
el = 31.07699124  # (°)
p = 1.0  # (%)
D = 1.0  # (m)
eta = 0.65  # h
tau = 0.0  # (°)
hs = 0.031382984  # (km)

# Make call to test-function atmospheric_attenuation_slant_path
itur_val = itur.atmospheric_attenuation_slant_path(lat=lat, lon=lon, f=f, el=el, p=p, D=D, eta=eta, tau=tau, hs=hs)

# Compute error with respect to value in ITU example file
ITU_example_val = 1.212790721  # (dB)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results atmospheric_attenuation_slant_path

ITU-Rpy Function	lat (°N)	lon (°E)	f (GHz)	el (°)	p (%)	D (m)	eta h	tau (°)	hs (km)	ITU Validation (dB)	ITU-Rpy Result (dB)	Absolute Error	Relative Error
atmospheric_attenuation_slant_path	51.500	-0.14	14.25	31.076991	1.000	1.0	0.65	0.0	0.031383	1.212791	1.212792	-9.85e-07	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	14.25	40.232036	1.000	1.0	0.65	0.0	0.046123	1.104002	1.103999	2.08e-06	0.000
atmospheric_attenuation_slant_path	33.940	18.43	14.25	46.359693	1.000	1.0	0.65	0.0	0.000000	0.827813	0.827802	1.03e-05	0.001
atmospheric_attenuation_slant_path	51.500	-0.14	14.25	31.076991	0.100	1.0	0.65	0.0	0.031383	2.901523	2.901527	-4.07e-06	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	14.25	40.232036	0.100	1.0	0.65	0.0	0.046123	3.171655	3.171647	8.43e-06	0.000
atmospheric_attenuation_slant_path	33.940	18.43	14.25	46.359693	0.100	1.0	0.65	0.0	0.000000	2.310531	2.310486	4.51e-05	0.002
atmospheric_attenuation_slant_path	51.500	-0.14	14.25	31.076991	0.010	1.0	0.65	0.0	0.031383	7.507265	7.507277	-1.16e-05	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	14.25	40.232036	0.010	1.0	0.65	0.0	0.046123	8.693154	8.693131	2.34e-05	0.000
atmospheric_attenuation_slant_path	33.940	18.43	14.25	46.359693	0.010	1.0	0.65	0.0	0.000000	6.330976	6.330848	1.29e-04	0.002
atmospheric_attenuation_slant_path	51.500	-0.14	14.25	31.076991	0.001	1.0	0.65	0.0	0.031383	15.608798	15.608820	-2.28e-05	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	14.25	40.232036	0.001	1.0	0.65	0.0	0.046123	18.141360	18.141315	4.52e-05	0.000
atmospheric_attenuation_slant_path	33.940	18.43	14.25	46.359693	0.001	1.0	0.65	0.0	0.000000	13.370111	13.369858	2.52e-04	0.002
atmospheric_attenuation_slant_path	51.500	-0.14	29.00	31.076991	1.000	1.0	0.65	0.0	0.031383	4.836825	4.836830	-4.03e-06	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	29.00	40.232036	1.000	1.0	0.65	0.0	0.046123	4.570303	4.570294	8.81e-06	0.000
atmospheric_attenuation_slant_path	33.940	18.43	29.00	46.359693	1.000	1.0	0.65	0.0	0.000000	3.379708	3.379662	4.60e-05	0.001
atmospheric_attenuation_slant_path	51.500	-0.14	29.00	31.076991	0.100	1.0	0.65	0.0	0.031383	11.199171	11.199185	-1.43e-05	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	29.00	40.232036	0.100	1.0	0.65	0.0	0.046123	12.475796	12.475765	3.07e-05	0.000
atmospheric_attenuation_slant_path	33.940	18.43	29.00	46.359693	0.100	1.0	0.65	0.0	0.000000	9.223537	9.223368	1.69e-04	0.002
atmospheric_attenuation_slant_path	51.500	-0.14	29.00	31.076991	0.010	1.0	0.65	0.0	0.031383	26.071751	26.071786	-3.56e-05	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	29.00	40.232036	0.010	1.0	0.65	0.0	0.046123	30.486002	30.485927	7.45e-05	0.000
atmospheric_attenuation_slant_path	33.940	18.43	29.00	46.359693	0.010	1.0	0.65	0.0	0.000000	22.661253	22.660836	4.16e-04	0.002
atmospheric_attenuation_slant_path	51.500	-0.14	29.00	31.076991	0.001	1.0	0.65	0.0	0.031383	47.828120	47.828182	-6.15e-05	-0.000
atmospheric_attenuation_slant_path	41.900	12.49	29.00	40.232036	0.001	1.0	0.65	0.0	0.046123	56.000323	56.000197	1.26e-04	0.000
atmospheric_attenuation_slant_path	33.940	18.43	29.00	46.359693	0.001	1.0	0.65	0.0	0.000000	42.095681	42.094967	7.15e-04	0.002
atmospheric_attenuation_slant_path	22.900	-43.23	14.25	22.278335	1.000	1.0	0.65	0.0	0.000000	2.744155	2.744149	5.42e-06	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	14.25	52.678985	1.000	1.0	0.65	0.0	0.008617	2.211657	2.211641	1.64e-05	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	14.25	22.278335	0.100	1.0	0.65	0.0	0.000000	9.281657	9.281632	2.48e-05	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	14.25	52.678985	0.100	1.0	0.65	0.0	0.008617	7.067191	7.067125	6.63e-05	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	14.25	22.278335	0.010	1.0	0.65	0.0	0.000000	19.954158	19.954107	5.16e-05	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	14.25	52.678985	0.010	1.0	0.65	0.0	0.008617	17.198261	17.198104	1.57e-04	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	14.25	22.278335	0.001	1.0	0.65	0.0	0.000000	30.941244	30.941171	7.30e-05	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	14.25	52.678985	0.001	1.0	0.65	0.0	0.008617	30.701438	30.701182	2.56e-04	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	29.00	22.278335	1.000	1.0	0.65	0.0	0.000000	10.598519	10.598499	2.02e-05	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	29.00	52.678985	1.000	1.0	0.65	0.0	0.008617	9.640183	9.640109	7.36e-05	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	29.00	22.278335	0.100	1.0	0.65	0.0	0.000000	33.091860	33.091780	7.97e-05	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	29.00	52.678985	0.100	1.0	0.65	0.0	0.008617	28.546737	28.546478	2.59e-04	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	29.00	22.278335	0.010	1.0	0.65	0.0	0.000000	63.403111	63.402964	1.47e-04	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	29.00	52.678985	0.010	1.0	0.65	0.0	0.008617	61.458236	61.457700	5.36e-04	0.001
atmospheric_attenuation_slant_path	22.900	-43.23	29.00	22.278335	0.001	1.0	0.65	0.0	0.000000	87.397350	87.397165	1.85e-04	0.000
atmospheric_attenuation_slant_path	25.780	-80.22	29.00	52.678985	0.001	1.0	0.65	0.0	0.008617	96.381911	96.381144	7.67e-04	0.001
atmospheric_attenuation_slant_path	28.717	77.30	14.25	48.241171	1.000	1.0	0.65	90.0	0.209384	2.257937	2.257627	3.09e-04	0.014
atmospheric_attenuation_slant_path	3.133	101.70	14.25	85.804596	1.000	1.0	0.65	90.0	0.051251	2.824233	2.824188	4.54e-05	0.002
atmospheric_attenuation_slant_path	9.050	38.70	14.25	20.143358	1.000	1.0	0.65	90.0	2.539862	1.961326	1.961309	1.77e-05	0.001
atmospheric_attenuation_slant_path	28.717	77.30	14.25	48.241171	0.100	1.0	0.65	90.0	0.209384	6.467817	6.466594	1.22e-03	0.019
atmospheric_attenuation_slant_path	3.133	101.70	14.25	85.804596	0.100	1.0	0.65	90.0	0.051251	11.820801	11.820572	2.29e-04	0.002
atmospheric_attenuation_slant_path	9.050	38.70	14.25	20.143358	0.100	1.0	0.65	90.0	2.539862	6.807726	6.807629	9.70e-05	0.001
atmospheric_attenuation_slant_path	28.717	77.30	14.25	48.241171	0.010	1.0	0.65	90.0	0.209384	15.852418	15.849412	3.01e-03	0.019
atmospheric_attenuation_slant_path	3.133	101.70	14.25	85.804596	0.010	1.0	0.65	90.0	0.051251	22.430758	22.430350	4.08e-04	0.002
atmospheric_attenuation_slant_path	9.050	38.70	14.25	20.143358	0.010	1.0	0.65	90.0	2.539862	13.221879	13.221694	1.84e-04	0.001
atmospheric_attenuation_slant_path	28.717	77.30	14.25	48.241171	0.001	1.0	0.65	90.0	0.209384	29.217451	29.212334	5.12e-03	0.018
atmospheric_attenuation_slant_path	3.133	101.70	14.25	85.804596	0.001	1.0	0.65	90.0	0.051251	29.643393	29.642906	4.87e-04	0.002
atmospheric_attenuation_slant_path	9.050	38.70	14.25	20.143358	0.001	1.0	0.65	90.0	2.539862	18.400290	18.400055	2.34e-04	0.001
atmospheric_attenuation_slant_path	28.717	77.30	29.00	48.241171	1.000	1.0	0.65	90.0	0.209384	9.723246	9.721866	1.38e-03	0.014
atmospheric_attenuation_slant_path	3.133	101.70	29.00	85.804596	1.000	1.0	0.65	90.0	0.051251	13.417997	13.417768	2.29e-04	0.002
atmospheric_attenuation_slant_path	9.050	38.70	29.00	20.143358	1.000	1.0	0.65	90.0	2.539862	7.008331	7.008272	5.92e-05	0.001
atmospheric_attenuation_slant_path	28.717	77.30	29.00	48.241171	0.100	1.0	0.65	90.0	0.209384	26.061086	26.056323	4.76e-03	0.018
atmospheric_attenuation_slant_path	3.133	101.70	29.00	85.804596	0.100	1.0	0.65	90.0	0.051251	52.023250	52.022248	1.00e-03	0.002
atmospheric_attenuation_slant_path	9.050	38.70	29.00	20.143358	0.100	1.0	0.65	90.0	2.539862	22.535474	22.535192	2.83e-04	0.001
atmospheric_attenuation_slant_path	28.717	77.30	29.00	48.241171	0.010	1.0	0.65	90.0	0.209384	56.668601	56.658341	1.03e-02	0.018
atmospheric_attenuation_slant_path	3.133	101.70	29.00	85.804596	0.010	1.0	0.65	90.0	0.051251	86.582645	86.581095	1.55e-03	0.002
atmospheric_attenuation_slant_path	9.050	38.70	29.00	20.143358	0.010	1.0	0.65	90.0	2.539862	39.274555	39.274076	4.79e-04	0.001
atmospheric_attenuation_slant_path	28.717	77.30	29.00	48.241171	0.001	1.0	0.65	90.0	0.209384	91.798780	91.783468	1.53e-02	0.017
atmospheric_attenuation_slant_path	3.133	101.70	29.00	85.804596	0.001	1.0	0.65	90.0	0.051251	99.882180	99.880568	1.61e-03	0.002
atmospheric_attenuation_slant_path	9.050	38.70	29.00	20.143358	0.001	1.0	0.65	90.0	2.539862	49.004791	49.004245	5.46e-04	0.001

Validation results ITU-R P.676-12 ¶

This page contains the validation examples for Recommendation ITU-R P.676-12: Attenuation by atmospheric gases and related effects.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.676-12

Function gaseous_attenuation_slant_path ¶

The table below contains the results of testing function gaseous_attenuation_slant_path. The test cases were extracted from spreadsheet ITURP676-12_A_gas.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
f = 14.25  # (GHz)
el = 31.07699124  # (°)
rho = 13.79653679  # (g/m3)
P = 1009.485612  # (hPA)
T = 283.6108756  #  (C)
h = 0.031382984  # (km)
V_t = 33.72946527  #  (kg/m2)

# Make call to test-function gaseous_attenuation_slant_path
itur_val = itur.models.itu676.gaseous_attenuation_slant_path(f=f, el=el, rho=rho, P=P, T=T, h=h, V_t=V_t)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.226874038  # (dB)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu676.gaseous_attenuation_slant_path

ITU-Rpy Function	f (GHz)	el (°)	rho (g/m3)	P (hPA)	T (C)	h (km)	V_t (kg/m2)	ITU Validation (dB)	ITU-Rpy Result (dB)	Absolute Error	Relative Error
models.itu676.gaseous_attenuation_slant_path	14.25	31.076991	13.796537	1009.485612	283.610876	0.031383	33.729465	0.226874	0.226874	3.20e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	40.232036	18.262420	1007.721474	288.089737	0.046123	36.048109	0.189481	0.189481	-1.29e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	46.359693	22.730002	1013.250000	293.369680	0.000000	37.955600	0.176011	0.176011	-2.98e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	31.076991	14.412531	1009.485612	283.610876	0.031383	35.725554	0.236085	0.236085	3.32e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	40.232036	18.749209	1007.721474	288.089737	0.046123	37.513014	0.194969	0.194969	-2.48e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	46.359693	23.199501	1013.250000	293.369680	0.000000	40.511906	0.184676	0.184676	-3.89e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	31.076991	14.783593	1009.485612	283.610876	0.031383	37.295953	0.243411	0.243411	7.32e-11	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	40.232036	19.092542	1007.721474	288.089737	0.046123	38.329647	0.198062	0.198062	6.92e-11	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	46.359693	23.514645	1013.250000	293.369680	0.000000	42.210224	0.190521	0.190521	-3.61e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	31.076991	15.041048	1009.485612	283.610876	0.031383	38.244078	0.247880	0.247880	2.88e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	40.232036	19.346819	1007.721474	288.089737	0.046123	39.051281	0.200805	0.200805	5.58e-11	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	46.359693	23.759345	1013.250000	293.369680	0.000000	43.410461	0.194697	0.194697	-2.08e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	31.076991	13.796537	1009.485612	283.610876	0.031383	33.729465	0.837660	0.837660	-1.39e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	40.232036	18.262420	1007.721474	288.089737	0.046123	36.048109	0.706966	0.706966	3.09e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	46.359693	22.730002	1013.250000	293.369680	0.000000	37.955600	0.665978	0.665978	-5.62e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	31.076991	14.412531	1009.485612	283.610876	0.031383	35.725554	0.880473	0.880473	6.19e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	40.232036	18.749209	1007.721474	288.089737	0.046123	37.513014	0.732381	0.732381	2.27e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	46.359693	23.199501	1013.250000	293.369680	0.000000	40.511906	0.706485	0.706485	-1.84e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	31.076991	14.783593	1009.485612	283.610876	0.031383	37.295953	0.914534	0.914534	5.43e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	40.232036	19.092542	1007.721474	288.089737	0.046123	38.329647	0.746677	0.746677	4.67e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	46.359693	23.514645	1013.250000	293.369680	0.000000	42.210224	0.733784	0.733784	1.27e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	31.076991	15.041048	1009.485612	283.610876	0.031383	38.244078	0.935286	0.935286	-1.04e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	40.232036	19.346819	1007.721474	288.089737	0.046123	39.051281	0.759364	0.759364	5.10e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	46.359693	23.759345	1013.250000	293.369680	0.000000	43.410461	0.753268	0.753268	2.05e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	22.278335	20.739431	1013.250000	297.453541	0.000000	49.513184	0.411484	0.411484	-4.83e-11	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	52.678985	22.466488	1012.215224	297.574654	0.008617	57.497546	0.223232	0.223232	-1.07e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	22.278335	21.046143	1013.250000	297.453541	0.000000	52.007390	0.428947	0.428947	-1.01e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	52.678985	22.792038	1012.215224	297.574654	0.008617	59.222332	0.229296	0.229296	3.46e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	22.278335	21.247533	1013.250000	297.453541	0.000000	53.485111	0.439437	0.439437	-8.09e-11	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	52.678985	23.000809	1012.215224	297.574654	0.008617	60.314611	0.233171	0.233171	1.81e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	22.278335	21.369403	1013.250000	297.453541	0.000000	54.631809	0.447641	0.447641	3.39e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	52.678985	23.163948	1012.215224	297.574654	0.008617	61.161560	0.236195	0.236195	-4.61e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	22.278335	20.739431	1013.250000	297.453541	0.000000	49.513184	1.627537	1.627537	-3.62e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	52.678985	22.466488	1012.215224	297.574654	0.008617	57.497546	0.900283	0.900283	-5.50e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	22.278335	21.046143	1013.250000	297.453541	0.000000	52.007390	1.708828	1.708828	-3.79e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	52.678985	22.792038	1012.215224	297.574654	0.008617	59.222332	0.928337	0.928337	1.10e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	22.278335	21.247533	1013.250000	297.453541	0.000000	53.485111	1.757604	1.757604	-6.95e-11	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	52.678985	23.000809	1012.215224	297.574654	0.008617	60.314611	0.946255	0.946255	-2.25e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	22.278335	21.369403	1013.250000	297.453541	0.000000	54.631809	1.795751	1.795751	-5.24e-11	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	52.678985	23.163948	1012.215224	297.574654	0.008617	61.161560	0.960229	0.960229	1.51e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	48.241171	24.710531	988.348774	298.058499	0.209384	70.591345	0.285722	0.285722	-2.52e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	85.804596	23.474627	1007.108268	299.605408	0.051251	62.584697	0.191743	0.191743	-4.92e-11	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	20.143358	11.723170	743.187216	290.210093	2.539862	25.925669	0.222224	0.222224	-7.43e-11	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	48.241171	25.120009	988.348774	298.058499	0.209384	72.477248	0.293396	0.293396	-3.05e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	85.804596	23.756613	1007.108268	299.605408	0.051251	63.593435	0.194664	0.194664	-4.53e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	20.143358	12.085274	743.187216	290.210093	2.539862	26.641637	0.226881	0.226881	2.16e-10	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	48.241171	25.398943	988.348774	298.058499	0.209384	73.574292	0.297904	0.297904	-4.60e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	85.804596	23.952441	1007.108268	299.605408	0.051251	64.336356	0.196825	0.196825	3.20e-11	0.000
models.itu676.gaseous_attenuation_slant_path	14.25	20.143358	12.348773	743.187216	290.210093	2.539862	27.087127	0.229798	0.229798	-1.92e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	48.241171	25.599327	988.348774	298.058499	0.209384	74.502008	0.301735	0.301735	-1.03e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	85.804596	24.105412	1007.108268	299.605408	0.051251	64.946376	0.198608	0.198608	-4.24e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	14.25	20.143358	12.547214	743.187216	290.210093	2.539862	27.511871	0.232580	0.232580	4.88e-11	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	48.241171	24.710531	988.348774	298.058499	0.209384	70.591345	1.158466	1.158466	5.10e-11	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	85.804596	23.474627	1007.108268	299.605408	0.051251	62.584697	0.778114	0.778114	4.38e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	20.143358	11.723170	743.187216	290.210093	2.539862	25.925669	0.704136	0.704136	4.69e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	48.241171	25.120009	988.348774	298.058499	0.209384	72.477248	1.192810	1.192810	2.16e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	85.804596	23.756613	1007.108268	299.605408	0.051251	63.593435	0.791490	0.791490	1.34e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	20.143358	12.085274	743.187216	290.210093	2.539862	26.641637	0.720856	0.720856	3.93e-13	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	48.241171	25.398943	988.348774	298.058499	0.209384	73.574292	1.212963	1.212963	5.56e-11	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	85.804596	23.952441	1007.108268	299.605408	0.051251	64.336356	0.801390	0.801390	-2.23e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	20.143358	12.348773	743.187216	290.210093	2.539862	27.087127	0.731314	0.731314	2.23e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	48.241171	25.599327	988.348774	298.058499	0.209384	74.502008	1.230094	1.230094	-2.70e-10	-0.000
models.itu676.gaseous_attenuation_slant_path	29.00	85.804596	24.105412	1007.108268	299.605408	0.051251	64.946376	0.809550	0.809550	4.12e-10	0.000
models.itu676.gaseous_attenuation_slant_path	29.00	20.143358	12.547214	743.187216	290.210093	2.539862	27.511871	0.741298	0.741298	6.94e-12	0.000

Function gamma_exact ¶

The table below contains the results of testing function gamma_exact. The test cases were extracted from spreadsheet ITURP676-12_gamma.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
f = 12.0  # (GHz)
P = 1013.25  # (hPA)
rho = 7.5  # (g/cm3)
T = 288.15  # (K)

# Make call to test-function gamma_exact
itur_val = itur.models.itu676.gamma_exact(f=f, P=P, rho=rho, T=T)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.018233652  # (dB/km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu676.gamma_exact

ITU-Rpy Function	f (GHz)	P (hPA)	rho (g/cm3)	T (K)	ITU Validation (dB/km)	ITU-Rpy Result (dB/km)	Absolute Error	Relative Error
models.itu676.gamma_exact	12.0	1013.25	7.5	288.15	0.018234	0.018234	-2.89e-10	-0.000
models.itu676.gamma_exact	20.0	1013.25	7.5	288.15	0.108931	0.108931	-2.93e-10	-0.000
models.itu676.gamma_exact	60.0	1013.25	7.5	288.15	14.778317	14.778317	2.88e-09	0.000
models.itu676.gamma_exact	90.0	1013.25	7.5	288.15	0.380843	0.380843	-4.95e-10	-0.000
models.itu676.gamma_exact	130.0	1013.25	7.5	288.15	0.793354	0.793354	-2.46e-10	-0.000
models.itu676.gamma_exact	1.0	1013.25	7.5	288.15	0.005440	0.005440	2.15e-10	0.000
models.itu676.gamma_exact	2.0	1013.25	7.5	288.15	0.006920	0.006920	1.47e-10	0.000
models.itu676.gamma_exact	3.0	1013.25	7.5	288.15	0.007539	0.007539	1.08e-11	0.000
models.itu676.gamma_exact	4.0	1013.25	7.5	288.15	0.008089	0.008089	-2.01e-10	-0.000
models.itu676.gamma_exact	5.0	1013.25	7.5	288.15	0.008714	0.008714	-1.77e-10	-0.000
models.itu676.gamma_exact	6.0	1013.25	7.5	288.15	0.009459	0.009459	1.13e-10	0.000
models.itu676.gamma_exact	7.0	1013.25	7.5	288.15	0.010351	0.010351	3.42e-10	0.000
models.itu676.gamma_exact	8.0	1013.25	7.5	288.15	0.011416	0.011416	-2.99e-10	-0.000
models.itu676.gamma_exact	9.0	1013.25	7.5	288.15	0.012684	0.012684	-1.82e-10	-0.000
models.itu676.gamma_exact	10.0	1013.25	7.5	288.15	0.014199	0.014199	5.18e-11	0.000
models.itu676.gamma_exact	11.0	1013.25	7.5	288.15	0.016019	0.016019	-1.24e-10	-0.000
models.itu676.gamma_exact	12.0	1013.25	7.5	288.15	0.018234	0.018234	-2.89e-10	-0.000
models.itu676.gamma_exact	13.0	1013.25	7.5	288.15	0.020980	0.020980	-1.02e-10	-0.000
models.itu676.gamma_exact	14.0	1013.25	7.5	288.15	0.024473	0.024473	-1.31e-10	-0.000
models.itu676.gamma_exact	15.0	1013.25	7.5	288.15	0.029058	0.029058	-5.96e-11	-0.000
models.itu676.gamma_exact	16.0	1013.25	7.5	288.15	0.035316	0.035316	-9.40e-11	-0.000
models.itu676.gamma_exact	17.0	1013.25	7.5	288.15	0.044234	0.044234	-8.23e-11	-0.000
models.itu676.gamma_exact	18.0	1013.25	7.5	288.15	0.057513	0.057513	1.20e-10	0.000
models.itu676.gamma_exact	19.0	1013.25	7.5	288.15	0.077918	0.077918	-1.87e-10	-0.000
models.itu676.gamma_exact	20.0	1013.25	7.5	288.15	0.108931	0.108931	-2.93e-10	-0.000
models.itu676.gamma_exact	21.0	1013.25	7.5	288.15	0.150432	0.150432	1.94e-10	0.000
models.itu676.gamma_exact	22.0	1013.25	7.5	288.15	0.187337	0.187337	-3.02e-10	-0.000
models.itu676.gamma_exact	23.0	1013.25	7.5	288.15	0.194289	0.194289	4.49e-11	0.000
models.itu676.gamma_exact	24.0	1013.25	7.5	288.15	0.173161	0.173161	-1.46e-10	-0.000
models.itu676.gamma_exact	25.0	1013.25	7.5	288.15	0.146235	0.146235	2.06e-10	0.000
models.itu676.gamma_exact	26.0	1013.25	7.5	288.15	0.125028	0.125028	1.32e-10	0.000
models.itu676.gamma_exact	27.0	1013.25	7.5	288.15	0.110735	0.110735	-2.58e-10	-0.000
models.itu676.gamma_exact	28.0	1013.25	7.5	288.15	0.101756	0.101756	-2.07e-10	-0.000
models.itu676.gamma_exact	29.0	1013.25	7.5	288.15	0.096494	0.096494	3.25e-10	0.000
models.itu676.gamma_exact	30.0	1013.25	7.5	288.15	0.093825	0.093825	-2.65e-10	-0.000
models.itu676.gamma_exact	31.0	1013.25	7.5	288.15	0.093020	0.093020	-1.86e-10	-0.000
models.itu676.gamma_exact	32.0	1013.25	7.5	288.15	0.093619	0.093619	-2.43e-10	-0.000
models.itu676.gamma_exact	33.0	1013.25	7.5	288.15	0.095332	0.095332	-4.62e-10	-0.000
models.itu676.gamma_exact	34.0	1013.25	7.5	288.15	0.097979	0.097979	-1.93e-10	-0.000
models.itu676.gamma_exact	35.0	1013.25	7.5	288.15	0.101457	0.101457	-4.89e-10	-0.000
models.itu676.gamma_exact	36.0	1013.25	7.5	288.15	0.105720	0.105720	4.54e-10	0.000
models.itu676.gamma_exact	37.0	1013.25	7.5	288.15	0.110762	0.110762	2.84e-10	0.000
models.itu676.gamma_exact	38.0	1013.25	7.5	288.15	0.116615	0.116615	1.65e-10	0.000
models.itu676.gamma_exact	39.0	1013.25	7.5	288.15	0.123352	0.123352	2.33e-10	0.000
models.itu676.gamma_exact	40.0	1013.25	7.5	288.15	0.131086	0.131086	2.80e-10	0.000
models.itu676.gamma_exact	41.0	1013.25	7.5	288.15	0.139981	0.139981	2.68e-10	0.000
models.itu676.gamma_exact	42.0	1013.25	7.5	288.15	0.150269	0.150269	3.31e-10	0.000
models.itu676.gamma_exact	43.0	1013.25	7.5	288.15	0.162276	0.162276	-4.90e-12	-0.000
models.itu676.gamma_exact	44.0	1013.25	7.5	288.15	0.176460	0.176460	1.26e-10	0.000
models.itu676.gamma_exact	45.0	1013.25	7.5	288.15	0.193481	0.193481	3.81e-10	0.000
models.itu676.gamma_exact	46.0	1013.25	7.5	288.15	0.214318	0.214318	-1.86e-10	-0.000
models.itu676.gamma_exact	47.0	1013.25	7.5	288.15	0.240480	0.240480	4.84e-10	0.000
models.itu676.gamma_exact	48.0	1013.25	7.5	288.15	0.274425	0.274425	-4.91e-10	-0.000
models.itu676.gamma_exact	49.0	1013.25	7.5	288.15	0.320551	0.320551	-1.99e-10	-0.000
models.itu676.gamma_exact	50.0	1013.25	7.5	288.15	0.388427	0.388427	1.99e-10	0.000
models.itu676.gamma_exact	51.0	1013.25	7.5	288.15	0.504721	0.504721	-3.93e-10	-0.000
models.itu676.gamma_exact	52.0	1013.25	7.5	288.15	0.737479	0.737479	1.71e-10	0.000
models.itu676.gamma_exact	53.0	1013.25	7.5	288.15	1.249765	1.249765	4.17e-10	0.000
models.itu676.gamma_exact	54.0	1013.25	7.5	288.15	2.338904	2.338904	-1.21e-10	-0.000
models.itu676.gamma_exact	55.0	1013.25	7.5	288.15	4.324956	4.324956	3.08e-10	0.000
models.itu676.gamma_exact	56.0	1013.25	7.5	288.15	7.191136	7.191136	4.19e-11	0.000
models.itu676.gamma_exact	57.0	1013.25	7.5	288.15	10.205851	10.205852	-3.39e-09	-0.000
models.itu676.gamma_exact	58.0	1013.25	7.5	288.15	12.498391	12.498391	-3.72e-09	-0.000
models.itu676.gamma_exact	59.0	1013.25	7.5	288.15	13.785280	13.785280	-2.11e-09	-0.000
models.itu676.gamma_exact	60.0	1013.25	7.5	288.15	14.778317	14.778317	2.88e-09	0.000
models.itu676.gamma_exact	61.0	1013.25	7.5	288.15	15.166986	15.166986	-2.31e-09	-0.000
models.itu676.gamma_exact	62.0	1013.25	7.5	288.15	14.161167	14.161167	-4.44e-09	-0.000
models.itu676.gamma_exact	63.0	1013.25	7.5	288.15	11.001342	11.001342	-2.97e-09	-0.000
models.itu676.gamma_exact	64.0	1013.25	7.5	288.15	7.020353	7.020353	-6.92e-11	-0.000
models.itu676.gamma_exact	65.0	1013.25	7.5	288.15	3.990338	3.990338	-1.21e-10	-0.000
models.itu676.gamma_exact	66.0	1013.25	7.5	288.15	2.154196	2.154196	7.42e-11	0.000
models.itu676.gamma_exact	67.0	1013.25	7.5	288.15	1.227115	1.227115	4.67e-10	0.000
models.itu676.gamma_exact	68.0	1013.25	7.5	288.15	0.805021	0.805021	1.83e-10	0.000
models.itu676.gamma_exact	69.0	1013.25	7.5	288.15	0.611819	0.611819	-4.54e-10	-0.000
models.itu676.gamma_exact	70.0	1013.25	7.5	288.15	0.513993	0.513993	4.88e-10	0.000
models.itu676.gamma_exact	71.0	1013.25	7.5	288.15	0.456680	0.456680	-3.64e-10	-0.000
models.itu676.gamma_exact	72.0	1013.25	7.5	288.15	0.419049	0.419049	3.12e-10	0.000
models.itu676.gamma_exact	73.0	1013.25	7.5	288.15	0.393232	0.393232	-1.70e-10	-0.000
models.itu676.gamma_exact	74.0	1013.25	7.5	288.15	0.375190	0.375190	-4.12e-10	-0.000
models.itu676.gamma_exact	75.0	1013.25	7.5	288.15	0.362554	0.362554	8.17e-11	0.000
models.itu676.gamma_exact	76.0	1013.25	7.5	288.15	0.353835	0.353835	4.18e-10	0.000
models.itu676.gamma_exact	77.0	1013.25	7.5	288.15	0.348044	0.348044	-2.67e-10	-0.000
models.itu676.gamma_exact	78.0	1013.25	7.5	288.15	0.344501	0.344501	-4.78e-10	-0.000
models.itu676.gamma_exact	79.0	1013.25	7.5	288.15	0.342726	0.342726	-1.19e-10	-0.000
models.itu676.gamma_exact	80.0	1013.25	7.5	288.15	0.342368	0.342368	9.74e-11	0.000
models.itu676.gamma_exact	81.0	1013.25	7.5	288.15	0.343167	0.343167	-1.40e-10	-0.000
models.itu676.gamma_exact	82.0	1013.25	7.5	288.15	0.344926	0.344926	-1.13e-10	-0.000
models.itu676.gamma_exact	83.0	1013.25	7.5	288.15	0.347495	0.347495	-4.10e-10	-0.000
models.itu676.gamma_exact	84.0	1013.25	7.5	288.15	0.350757	0.350757	1.18e-10	0.000
models.itu676.gamma_exact	85.0	1013.25	7.5	288.15	0.354619	0.354619	-4.94e-10	-0.000
models.itu676.gamma_exact	86.0	1013.25	7.5	288.15	0.359008	0.359008	2.15e-10	0.000
models.itu676.gamma_exact	87.0	1013.25	7.5	288.15	0.363867	0.363867	-4.80e-10	-0.000
models.itu676.gamma_exact	88.0	1013.25	7.5	288.15	0.369150	0.369150	-4.01e-10	-0.000
models.itu676.gamma_exact	89.0	1013.25	7.5	288.15	0.374818	0.374818	3.30e-10	0.000
models.itu676.gamma_exact	90.0	1013.25	7.5	288.15	0.380843	0.380843	-4.95e-10	-0.000
models.itu676.gamma_exact	91.0	1013.25	7.5	288.15	0.387202	0.387202	-1.20e-10	-0.000
models.itu676.gamma_exact	92.0	1013.25	7.5	288.15	0.393877	0.393877	2.12e-10	0.000
models.itu676.gamma_exact	93.0	1013.25	7.5	288.15	0.400855	0.400855	-3.37e-10	-0.000
models.itu676.gamma_exact	94.0	1013.25	7.5	288.15	0.408129	0.408129	-3.90e-11	-0.000
models.itu676.gamma_exact	95.0	1013.25	7.5	288.15	0.415693	0.415693	-1.90e-10	-0.000
models.itu676.gamma_exact	96.0	1013.25	7.5	288.15	0.423549	0.423549	2.48e-10	0.000
models.itu676.gamma_exact	97.0	1013.25	7.5	288.15	0.431701	0.431701	3.52e-10	0.000
models.itu676.gamma_exact	98.0	1013.25	7.5	288.15	0.440158	0.440158	1.15e-10	0.000
models.itu676.gamma_exact	99.0	1013.25	7.5	288.15	0.448936	0.448936	-3.11e-10	-0.000
models.itu676.gamma_exact	100.0	1013.25	7.5	288.15	0.458059	0.458059	2.49e-10	0.000
models.itu676.gamma_exact	101.0	1013.25	7.5	288.15	0.467558	0.467558	-2.27e-10	-0.000
models.itu676.gamma_exact	102.0	1013.25	7.5	288.15	0.477477	0.477477	-1.65e-10	-0.000
models.itu676.gamma_exact	103.0	1013.25	7.5	288.15	0.487876	0.487876	1.86e-10	0.000
models.itu676.gamma_exact	104.0	1013.25	7.5	288.15	0.498836	0.498836	9.17e-12	0.000
models.itu676.gamma_exact	105.0	1013.25	7.5	288.15	0.510473	0.510473	3.16e-10	0.000
models.itu676.gamma_exact	106.0	1013.25	7.5	288.15	0.522944	0.522944	1.69e-10	0.000
models.itu676.gamma_exact	107.0	1013.25	7.5	288.15	0.536477	0.536477	3.96e-10	0.000
models.itu676.gamma_exact	108.0	1013.25	7.5	288.15	0.551407	0.551407	-2.42e-10	-0.000
models.itu676.gamma_exact	109.0	1013.25	7.5	288.15	0.568236	0.568236	-2.64e-11	-0.000
models.itu676.gamma_exact	110.0	1013.25	7.5	288.15	0.587749	0.587749	2.53e-10	0.000
models.itu676.gamma_exact	111.0	1013.25	7.5	288.15	0.611222	0.611222	4.85e-10	0.000
models.itu676.gamma_exact	112.0	1013.25	7.5	288.15	0.640824	0.640824	-1.98e-10	-0.000
models.itu676.gamma_exact	113.0	1013.25	7.5	288.15	0.680468	0.680468	1.71e-10	0.000
models.itu676.gamma_exact	114.0	1013.25	7.5	288.15	0.737669	0.737669	1.32e-11	0.000
models.itu676.gamma_exact	115.0	1013.25	7.5	288.15	0.827930	0.827930	-4.62e-10	-0.000
models.itu676.gamma_exact	116.0	1013.25	7.5	288.15	0.984980	0.984980	4.85e-10	0.000
models.itu676.gamma_exact	117.0	1013.25	7.5	288.15	1.277069	1.277069	2.73e-10	0.000
models.itu676.gamma_exact	118.0	1013.25	7.5	288.15	1.740788	1.740788	-4.65e-10	-0.000
models.itu676.gamma_exact	119.0	1013.25	7.5	288.15	1.924373	1.924373	2.69e-10	0.000
models.itu676.gamma_exact	120.0	1013.25	7.5	288.15	1.515969	1.515969	8.54e-11	0.000
models.itu676.gamma_exact	121.0	1013.25	7.5	288.15	1.150394	1.150394	6.17e-11	0.000
models.itu676.gamma_exact	122.0	1013.25	7.5	288.15	0.960113	0.960113	-3.17e-10	-0.000
models.itu676.gamma_exact	123.0	1013.25	7.5	288.15	0.865748	0.865748	-2.29e-12	-0.000
models.itu676.gamma_exact	124.0	1013.25	7.5	288.15	0.817871	0.817871	-4.18e-10	-0.000
models.itu676.gamma_exact	125.0	1013.25	7.5	288.15	0.793758	0.793758	1.82e-10	0.000
models.itu676.gamma_exact	126.0	1013.25	7.5	288.15	0.782753	0.782753	-1.29e-10	-0.000
models.itu676.gamma_exact	127.0	1013.25	7.5	288.15	0.779515	0.779515	-1.12e-11	-0.000
models.itu676.gamma_exact	128.0	1013.25	7.5	288.15	0.781178	0.781178	1.29e-10	0.000
models.itu676.gamma_exact	129.0	1013.25	7.5	288.15	0.786116	0.786116	-2.43e-10	-0.000
models.itu676.gamma_exact	130.0	1013.25	7.5	288.15	0.793354	0.793354	-2.46e-10	-0.000
models.itu676.gamma_exact	131.0	1013.25	7.5	288.15	0.802287	0.802287	2.44e-10	0.000
models.itu676.gamma_exact	132.0	1013.25	7.5	288.15	0.812525	0.812525	6.00e-11	0.000
models.itu676.gamma_exact	133.0	1013.25	7.5	288.15	0.823814	0.823814	-1.49e-10	-0.000
models.itu676.gamma_exact	134.0	1013.25	7.5	288.15	0.835981	0.835981	-4.23e-10	-0.000
models.itu676.gamma_exact	135.0	1013.25	7.5	288.15	0.848912	0.848912	-4.39e-10	-0.000
models.itu676.gamma_exact	136.0	1013.25	7.5	288.15	0.862531	0.862531	-3.39e-10	-0.000
models.itu676.gamma_exact	137.0	1013.25	7.5	288.15	0.876789	0.876789	7.94e-11	0.000
models.itu676.gamma_exact	138.0	1013.25	7.5	288.15	0.891658	0.891658	2.07e-10	0.000
models.itu676.gamma_exact	139.0	1013.25	7.5	288.15	0.907125	0.907125	5.72e-11	0.000
models.itu676.gamma_exact	140.0	1013.25	7.5	288.15	0.923189	0.923189	-3.51e-10	-0.000
models.itu676.gamma_exact	141.0	1013.25	7.5	288.15	0.939861	0.939861	-1.21e-10	-0.000
models.itu676.gamma_exact	142.0	1013.25	7.5	288.15	0.957161	0.957161	1.48e-10	0.000
models.itu676.gamma_exact	143.0	1013.25	7.5	288.15	0.975117	0.975117	2.49e-10	0.000
models.itu676.gamma_exact	144.0	1013.25	7.5	288.15	0.993767	0.993767	-3.37e-10	-0.000
models.itu676.gamma_exact	145.0	1013.25	7.5	288.15	1.013156	1.013156	-1.90e-10	-0.000
models.itu676.gamma_exact	146.0	1013.25	7.5	288.15	1.033342	1.033342	-1.45e-10	-0.000
models.itu676.gamma_exact	147.0	1013.25	7.5	288.15	1.054390	1.054390	-3.04e-10	-0.000
models.itu676.gamma_exact	148.0	1013.25	7.5	288.15	1.076380	1.076380	4.38e-10	0.000
models.itu676.gamma_exact	149.0	1013.25	7.5	288.15	1.099402	1.099402	-1.43e-10	-0.000
models.itu676.gamma_exact	150.0	1013.25	7.5	288.15	1.123565	1.123565	-1.98e-10	-0.000
models.itu676.gamma_exact	151.0	1013.25	7.5	288.15	1.148992	1.148992	-1.71e-10	-0.000
models.itu676.gamma_exact	152.0	1013.25	7.5	288.15	1.175832	1.175832	4.13e-10	0.000
models.itu676.gamma_exact	153.0	1013.25	7.5	288.15	1.204257	1.204257	-6.22e-11	-0.000
models.itu676.gamma_exact	154.0	1013.25	7.5	288.15	1.234469	1.234469	-1.30e-10	-0.000
models.itu676.gamma_exact	155.0	1013.25	7.5	288.15	1.266709	1.266709	2.64e-11	0.000
models.itu676.gamma_exact	156.0	1013.25	7.5	288.15	1.301261	1.301261	3.28e-11	0.000
models.itu676.gamma_exact	157.0	1013.25	7.5	288.15	1.338466	1.338466	1.11e-10	0.000
models.itu676.gamma_exact	158.0	1013.25	7.5	288.15	1.378730	1.378730	1.79e-10	0.000
models.itu676.gamma_exact	159.0	1013.25	7.5	288.15	1.422548	1.422548	3.02e-10	0.000
models.itu676.gamma_exact	160.0	1013.25	7.5	288.15	1.470518	1.470518	-1.56e-11	-0.000
models.itu676.gamma_exact	161.0	1013.25	7.5	288.15	1.523374	1.523374	3.33e-10	0.000
models.itu676.gamma_exact	162.0	1013.25	7.5	288.15	1.582021	1.582021	-2.02e-10	-0.000
models.itu676.gamma_exact	163.0	1013.25	7.5	288.15	1.647586	1.647586	2.83e-10	0.000
models.itu676.gamma_exact	164.0	1013.25	7.5	288.15	1.721486	1.721486	-1.83e-10	-0.000
models.itu676.gamma_exact	165.0	1013.25	7.5	288.15	1.805518	1.805518	-3.18e-10	-0.000
models.itu676.gamma_exact	166.0	1013.25	7.5	288.15	1.901988	1.901988	5.04e-11	0.000
models.itu676.gamma_exact	167.0	1013.25	7.5	288.15	2.013888	2.013888	3.77e-10	0.000
models.itu676.gamma_exact	168.0	1013.25	7.5	288.15	2.145157	2.145157	1.30e-10	0.000
models.itu676.gamma_exact	169.0	1013.25	7.5	288.15	2.301047	2.301047	3.02e-10	0.000
models.itu676.gamma_exact	170.0	1013.25	7.5	288.15	2.488677	2.488677	-9.00e-11	-0.000
models.itu676.gamma_exact	171.0	1013.25	7.5	288.15	2.717859	2.717859	-4.51e-10	-0.000
models.itu676.gamma_exact	172.0	1013.25	7.5	288.15	3.002369	3.002369	1.18e-11	0.000
models.itu676.gamma_exact	173.0	1013.25	7.5	288.15	3.361946	3.361946	-3.52e-10	-0.000
models.itu676.gamma_exact	174.0	1013.25	7.5	288.15	3.825481	3.825481	1.16e-10	0.000
models.itu676.gamma_exact	175.0	1013.25	7.5	288.15	4.436214	4.436214	8.38e-11	0.000
models.itu676.gamma_exact	176.0	1013.25	7.5	288.15	5.260269	5.260269	-4.04e-10	-0.000
models.itu676.gamma_exact	177.0	1013.25	7.5	288.15	6.400521	6.400521	-4.44e-10	-0.000
models.itu676.gamma_exact	178.0	1013.25	7.5	288.15	8.017786	8.017786	1.23e-10	0.000
models.itu676.gamma_exact	179.0	1013.25	7.5	288.15	10.356174	10.356174	-2.11e-10	-0.000
models.itu676.gamma_exact	180.0	1013.25	7.5	288.15	13.741083	13.741083	1.92e-09	0.000
models.itu676.gamma_exact	181.0	1013.25	7.5	288.15	18.411761	18.411761	4.05e-09	0.000
models.itu676.gamma_exact	182.0	1013.25	7.5	288.15	23.843154	23.843154	-4.24e-09	-0.000
models.itu676.gamma_exact	183.0	1013.25	7.5	288.15	27.677742	27.677742	-3.00e-09	-0.000
models.itu676.gamma_exact	184.0	1013.25	7.5	288.15	27.037613	27.037613	-3.92e-09	-0.000
models.itu676.gamma_exact	185.0	1013.25	7.5	288.15	22.616532	22.616532	-2.71e-09	-0.000
models.itu676.gamma_exact	186.0	1013.25	7.5	288.15	17.493731	17.493731	4.00e-09	0.000
models.itu676.gamma_exact	187.0	1013.25	7.5	288.15	13.352922	13.352922	5.21e-09	0.000
models.itu676.gamma_exact	188.0	1013.25	7.5	288.15	10.385526	10.385526	-1.44e-09	-0.000
models.itu676.gamma_exact	189.0	1013.25	7.5	288.15	8.319332	8.319332	-3.17e-10	-0.000
models.itu676.gamma_exact	190.0	1013.25	7.5	288.15	6.871215	6.871215	1.14e-10	0.000
models.itu676.gamma_exact	191.0	1013.25	7.5	288.15	5.837000	5.837000	-3.69e-10	-0.000
models.itu676.gamma_exact	192.0	1013.25	7.5	288.15	5.082089	5.082089	-4.70e-10	-0.000
models.itu676.gamma_exact	193.0	1013.25	7.5	288.15	4.519256	4.519256	-4.58e-10	-0.000
models.itu676.gamma_exact	194.0	1013.25	7.5	288.15	4.091497	4.091497	-3.04e-10	-0.000
models.itu676.gamma_exact	195.0	1013.25	7.5	288.15	3.760872	3.760872	-4.51e-10	-0.000
models.itu676.gamma_exact	196.0	1013.25	7.5	288.15	3.501597	3.501597	-2.17e-11	-0.000
models.itu676.gamma_exact	197.0	1013.25	7.5	288.15	3.295767	3.295767	-1.65e-10	-0.000
models.itu676.gamma_exact	198.0	1013.25	7.5	288.15	3.130691	3.130691	-5.55e-12	-0.000
models.itu676.gamma_exact	199.0	1013.25	7.5	288.15	2.997199	2.997199	-4.00e-11	-0.000
models.itu676.gamma_exact	200.0	1013.25	7.5	288.15	2.888548	2.888548	-5.17e-11	-0.000
models.itu676.gamma_exact	201.0	1013.25	7.5	288.15	2.799698	2.799698	2.36e-10	0.000
models.itu676.gamma_exact	202.0	1013.25	7.5	288.15	2.726826	2.726826	-4.59e-10	-0.000
models.itu676.gamma_exact	203.0	1013.25	7.5	288.15	2.666990	2.666990	-2.84e-10	-0.000
models.itu676.gamma_exact	204.0	1013.25	7.5	288.15	2.617902	2.617902	-1.26e-10	-0.000
models.itu676.gamma_exact	205.0	1013.25	7.5	288.15	2.577758	2.577758	3.54e-10	0.000
models.itu676.gamma_exact	206.0	1013.25	7.5	288.15	2.545124	2.545124	-1.81e-10	-0.000
models.itu676.gamma_exact	207.0	1013.25	7.5	288.15	2.518846	2.518846	-2.31e-10	-0.000
models.itu676.gamma_exact	208.0	1013.25	7.5	288.15	2.497989	2.497989	-3.72e-10	-0.000
models.itu676.gamma_exact	209.0	1013.25	7.5	288.15	2.481788	2.481788	-3.87e-10	-0.000
models.itu676.gamma_exact	210.0	1013.25	7.5	288.15	2.469615	2.469615	-1.71e-10	-0.000
models.itu676.gamma_exact	211.0	1013.25	7.5	288.15	2.460947	2.460947	-4.40e-11	-0.000
models.itu676.gamma_exact	212.0	1013.25	7.5	288.15	2.455348	2.455348	4.72e-10	0.000
models.itu676.gamma_exact	213.0	1013.25	7.5	288.15	2.452451	2.452451	8.93e-11	0.000
models.itu676.gamma_exact	214.0	1013.25	7.5	288.15	2.451947	2.451947	-2.71e-10	-0.000
models.itu676.gamma_exact	215.0	1013.25	7.5	288.15	2.453573	2.453573	-2.32e-10	-0.000
models.itu676.gamma_exact	216.0	1013.25	7.5	288.15	2.457105	2.457105	-2.24e-11	-0.000
models.itu676.gamma_exact	217.0	1013.25	7.5	288.15	2.462350	2.462350	-4.17e-10	-0.000
models.itu676.gamma_exact	218.0	1013.25	7.5	288.15	2.469142	2.469142	-1.30e-10	-0.000
models.itu676.gamma_exact	219.0	1013.25	7.5	288.15	2.477338	2.477338	3.03e-10	0.000
models.itu676.gamma_exact	220.0	1013.25	7.5	288.15	2.486814	2.486814	-4.93e-10	-0.000
models.itu676.gamma_exact	221.0	1013.25	7.5	288.15	2.497462	2.497462	-3.36e-10	-0.000
models.itu676.gamma_exact	222.0	1013.25	7.5	288.15	2.509186	2.509186	-3.94e-10	-0.000
models.itu676.gamma_exact	223.0	1013.25	7.5	288.15	2.521903	2.521903	1.21e-10	0.000
models.itu676.gamma_exact	224.0	1013.25	7.5	288.15	2.535542	2.535542	4.92e-10	0.000
models.itu676.gamma_exact	225.0	1013.25	7.5	288.15	2.550037	2.550037	-4.50e-10	-0.000
models.itu676.gamma_exact	226.0	1013.25	7.5	288.15	2.565332	2.565332	2.67e-10	0.000
models.itu676.gamma_exact	227.0	1013.25	7.5	288.15	2.581377	2.581377	4.10e-10	0.000
models.itu676.gamma_exact	228.0	1013.25	7.5	288.15	2.598127	2.598127	2.78e-10	0.000
models.itu676.gamma_exact	229.0	1013.25	7.5	288.15	2.615543	2.615543	-3.37e-10	-0.000
models.itu676.gamma_exact	230.0	1013.25	7.5	288.15	2.633589	2.633589	4.63e-10	0.000
models.itu676.gamma_exact	231.0	1013.25	7.5	288.15	2.652236	2.652236	-3.24e-10	-0.000
models.itu676.gamma_exact	232.0	1013.25	7.5	288.15	2.671454	2.671454	4.86e-10	0.000
models.itu676.gamma_exact	233.0	1013.25	7.5	288.15	2.691219	2.691219	-2.53e-10	-0.000
models.itu676.gamma_exact	234.0	1013.25	7.5	288.15	2.711509	2.711509	2.25e-10	0.000
models.itu676.gamma_exact	235.0	1013.25	7.5	288.15	2.732304	2.732304	3.76e-10	0.000
models.itu676.gamma_exact	236.0	1013.25	7.5	288.15	2.753588	2.753588	1.16e-10	0.000
models.itu676.gamma_exact	237.0	1013.25	7.5	288.15	2.775343	2.775343	3.22e-11	0.000
models.itu676.gamma_exact	238.0	1013.25	7.5	288.15	2.797558	2.797558	-4.52e-10	-0.000
models.itu676.gamma_exact	239.0	1013.25	7.5	288.15	2.820219	2.820219	-1.17e-10	-0.000
models.itu676.gamma_exact	240.0	1013.25	7.5	288.15	2.843316	2.843316	2.11e-11	0.000
models.itu676.gamma_exact	241.0	1013.25	7.5	288.15	2.866840	2.866840	4.19e-10	0.000
models.itu676.gamma_exact	242.0	1013.25	7.5	288.15	2.890782	2.890782	-2.46e-10	-0.000
models.itu676.gamma_exact	243.0	1013.25	7.5	288.15	2.915135	2.915135	-3.25e-10	-0.000
models.itu676.gamma_exact	244.0	1013.25	7.5	288.15	2.939894	2.939894	2.11e-10	0.000
models.itu676.gamma_exact	245.0	1013.25	7.5	288.15	2.965054	2.965054	2.56e-10	0.000
models.itu676.gamma_exact	246.0	1013.25	7.5	288.15	2.990610	2.990610	3.24e-10	0.000
models.itu676.gamma_exact	247.0	1013.25	7.5	288.15	3.016559	3.016559	-4.15e-10	-0.000
models.itu676.gamma_exact	248.0	1013.25	7.5	288.15	3.042898	3.042898	5.60e-11	0.000
models.itu676.gamma_exact	249.0	1013.25	7.5	288.15	3.069627	3.069627	-3.56e-10	-0.000
models.itu676.gamma_exact	250.0	1013.25	7.5	288.15	3.096744	3.096744	-3.29e-10	-0.000
models.itu676.gamma_exact	251.0	1013.25	7.5	288.15	3.124248	3.124248	3.68e-10	0.000
models.itu676.gamma_exact	252.0	1013.25	7.5	288.15	3.152141	3.152141	-2.69e-10	-0.000
models.itu676.gamma_exact	253.0	1013.25	7.5	288.15	3.180423	3.180423	8.10e-11	0.000
models.itu676.gamma_exact	254.0	1013.25	7.5	288.15	3.209097	3.209097	-4.40e-10	-0.000
models.itu676.gamma_exact	255.0	1013.25	7.5	288.15	3.238164	3.238164	-2.72e-10	-0.000
models.itu676.gamma_exact	256.0	1013.25	7.5	288.15	3.267628	3.267628	3.82e-10	0.000
models.itu676.gamma_exact	257.0	1013.25	7.5	288.15	3.297492	3.297492	-3.92e-10	-0.000
models.itu676.gamma_exact	258.0	1013.25	7.5	288.15	3.327761	3.327761	6.93e-11	0.000
models.itu676.gamma_exact	259.0	1013.25	7.5	288.15	3.358440	3.358440	4.02e-10	0.000
models.itu676.gamma_exact	260.0	1013.25	7.5	288.15	3.389535	3.389535	-4.13e-10	-0.000
models.itu676.gamma_exact	261.0	1013.25	7.5	288.15	3.421052	3.421052	4.66e-11	0.000
models.itu676.gamma_exact	262.0	1013.25	7.5	288.15	3.452998	3.452998	1.63e-10	0.000
models.itu676.gamma_exact	263.0	1013.25	7.5	288.15	3.485382	3.485382	-1.77e-10	-0.000
models.itu676.gamma_exact	264.0	1013.25	7.5	288.15	3.518213	3.518213	-4.94e-10	-0.000
models.itu676.gamma_exact	265.0	1013.25	7.5	288.15	3.551499	3.551499	3.37e-10	0.000
models.itu676.gamma_exact	266.0	1013.25	7.5	288.15	3.585252	3.585252	3.80e-10	0.000
models.itu676.gamma_exact	267.0	1013.25	7.5	288.15	3.619484	3.619484	3.57e-10	0.000
models.itu676.gamma_exact	268.0	1013.25	7.5	288.15	3.654207	3.654207	-2.07e-10	-0.000
models.itu676.gamma_exact	269.0	1013.25	7.5	288.15	3.689435	3.689435	4.13e-10	0.000
models.itu676.gamma_exact	270.0	1013.25	7.5	288.15	3.725184	3.725184	4.29e-10	0.000
models.itu676.gamma_exact	271.0	1013.25	7.5	288.15	3.761470	3.761470	8.06e-11	0.000
models.itu676.gamma_exact	272.0	1013.25	7.5	288.15	3.798310	3.798310	-4.66e-10	-0.000
models.itu676.gamma_exact	273.0	1013.25	7.5	288.15	3.835725	3.835725	-1.25e-10	-0.000
models.itu676.gamma_exact	274.0	1013.25	7.5	288.15	3.873736	3.873736	-4.56e-10	-0.000
models.itu676.gamma_exact	275.0	1013.25	7.5	288.15	3.912367	3.912367	7.15e-11	0.000
models.itu676.gamma_exact	276.0	1013.25	7.5	288.15	3.951643	3.951643	3.65e-10	0.000
models.itu676.gamma_exact	277.0	1013.25	7.5	288.15	3.991592	3.991592	1.24e-10	0.000
models.itu676.gamma_exact	278.0	1013.25	7.5	288.15	4.032246	4.032246	8.69e-11	0.000
models.itu676.gamma_exact	279.0	1013.25	7.5	288.15	4.073638	4.073638	-2.35e-10	-0.000
models.itu676.gamma_exact	280.0	1013.25	7.5	288.15	4.115805	4.115805	7.53e-11	0.000
models.itu676.gamma_exact	281.0	1013.25	7.5	288.15	4.158790	4.158790	-2.97e-10	-0.000
models.itu676.gamma_exact	282.0	1013.25	7.5	288.15	4.202638	4.202638	1.22e-10	0.000
models.itu676.gamma_exact	283.0	1013.25	7.5	288.15	4.247399	4.247399	-1.71e-10	-0.000
models.itu676.gamma_exact	284.0	1013.25	7.5	288.15	4.293130	4.293130	3.96e-10	0.000
models.itu676.gamma_exact	285.0	1013.25	7.5	288.15	4.339894	4.339894	2.71e-10	0.000
models.itu676.gamma_exact	286.0	1013.25	7.5	288.15	4.387762	4.387762	-3.64e-10	-0.000
models.itu676.gamma_exact	287.0	1013.25	7.5	288.15	4.436812	4.436812	-1.82e-10	-0.000
models.itu676.gamma_exact	288.0	1013.25	7.5	288.15	4.487133	4.487133	3.26e-10	0.000
models.itu676.gamma_exact	289.0	1013.25	7.5	288.15	4.538827	4.538827	1.83e-10	0.000
models.itu676.gamma_exact	290.0	1013.25	7.5	288.15	4.592008	4.592008	9.68e-11	0.000
models.itu676.gamma_exact	291.0	1013.25	7.5	288.15	4.646805	4.646805	3.68e-10	0.000
models.itu676.gamma_exact	292.0	1013.25	7.5	288.15	4.703368	4.703368	7.39e-11	0.000
models.itu676.gamma_exact	293.0	1013.25	7.5	288.15	4.761867	4.761867	4.35e-10	0.000
models.itu676.gamma_exact	294.0	1013.25	7.5	288.15	4.822499	4.822499	7.84e-11	0.000
models.itu676.gamma_exact	295.0	1013.25	7.5	288.15	4.885495	4.885495	1.83e-10	0.000
models.itu676.gamma_exact	296.0	1013.25	7.5	288.15	4.951119	4.951119	-2.10e-10	-0.000
models.itu676.gamma_exact	297.0	1013.25	7.5	288.15	5.019686	5.019686	-1.72e-10	-0.000
models.itu676.gamma_exact	298.0	1013.25	7.5	288.15	5.091564	5.091564	-2.90e-10	-0.000
models.itu676.gamma_exact	299.0	1013.25	7.5	288.15	5.167190	5.167190	-9.81e-12	-0.000
models.itu676.gamma_exact	300.0	1013.25	7.5	288.15	5.247089	5.247089	-3.87e-10	-0.000
models.itu676.gamma_exact	301.0	1013.25	7.5	288.15	5.331888	5.331888	-1.70e-10	-0.000
models.itu676.gamma_exact	302.0	1013.25	7.5	288.15	5.422350	5.422350	-2.41e-10	-0.000
models.itu676.gamma_exact	303.0	1013.25	7.5	288.15	5.519407	5.519407	-4.98e-10	-0.000
models.itu676.gamma_exact	304.0	1013.25	7.5	288.15	5.624209	5.624209	-5.51e-11	-0.000
models.itu676.gamma_exact	305.0	1013.25	7.5	288.15	5.738183	5.738183	-1.26e-10	-0.000
models.itu676.gamma_exact	306.0	1013.25	7.5	288.15	5.863128	5.863128	7.16e-11	0.000
models.itu676.gamma_exact	307.0	1013.25	7.5	288.15	6.001328	6.001328	1.73e-10	0.000
models.itu676.gamma_exact	308.0	1013.25	7.5	288.15	6.155723	6.155723	2.83e-10	0.000
models.itu676.gamma_exact	309.0	1013.25	7.5	288.15	6.330146	6.330146	2.30e-10	0.000
models.itu676.gamma_exact	310.0	1013.25	7.5	288.15	6.529669	6.529669	-2.21e-10	-0.000
models.itu676.gamma_exact	311.0	1013.25	7.5	288.15	6.761108	6.761108	4.60e-10	0.000
models.itu676.gamma_exact	312.0	1013.25	7.5	288.15	7.033795	7.033795	1.90e-10	0.000
models.itu676.gamma_exact	313.0	1013.25	7.5	288.15	7.360752	7.360752	-1.27e-10	-0.000
models.itu676.gamma_exact	314.0	1013.25	7.5	288.15	7.760560	7.760560	-3.14e-10	-0.000
models.itu676.gamma_exact	315.0	1013.25	7.5	288.15	8.260373	8.260373	4.20e-10	0.000
models.itu676.gamma_exact	316.0	1013.25	7.5	288.15	8.900903	8.900903	-4.79e-10	-0.000
models.itu676.gamma_exact	317.0	1013.25	7.5	288.15	9.744688	9.744688	2.60e-10	0.000
models.itu676.gamma_exact	318.0	1013.25	7.5	288.15	10.889185	10.889185	-3.27e-09	-0.000
models.itu676.gamma_exact	319.0	1013.25	7.5	288.15	12.482780	12.482780	-4.83e-10	-0.000
models.itu676.gamma_exact	320.0	1013.25	7.5	288.15	14.723576	14.723576	-2.88e-09	-0.000
models.itu676.gamma_exact	321.0	1013.25	7.5	288.15	17.809242	17.809242	-4.34e-09	-0.000
models.itu676.gamma_exact	322.0	1013.25	7.5	288.15	21.987923	21.987923	3.10e-09	0.000
models.itu676.gamma_exact	323.0	1013.25	7.5	288.15	27.614013	27.614013	-1.58e-09	-0.000
models.itu676.gamma_exact	324.0	1013.25	7.5	288.15	34.010735	34.010735	3.77e-09	0.000
models.itu676.gamma_exact	325.0	1013.25	7.5	288.15	37.892209	37.892209	2.59e-10	0.000
models.itu676.gamma_exact	326.0	1013.25	7.5	288.15	35.935051	35.935051	-3.16e-09	-0.000
models.itu676.gamma_exact	327.0	1013.25	7.5	288.15	29.978411	29.978411	5.21e-09	0.000
models.itu676.gamma_exact	328.0	1013.25	7.5	288.15	23.903133	23.903133	3.35e-09	0.000
models.itu676.gamma_exact	329.0	1013.25	7.5	288.15	19.295446	19.295446	-1.62e-09	-0.000
models.itu676.gamma_exact	330.0	1013.25	7.5	288.15	16.115428	16.115428	5.62e-10	0.000
models.itu676.gamma_exact	331.0	1013.25	7.5	288.15	13.960793	13.960793	2.97e-09	0.000
models.itu676.gamma_exact	332.0	1013.25	7.5	288.15	12.488934	12.488934	4.08e-09	0.000
models.itu676.gamma_exact	333.0	1013.25	7.5	288.15	11.468502	11.468502	1.91e-10	0.000
models.itu676.gamma_exact	334.0	1013.25	7.5	288.15	10.751700	10.751700	-8.71e-10	-0.000
models.itu676.gamma_exact	335.0	1013.25	7.5	288.15	10.243974	10.243974	-4.13e-09	-0.000
models.itu676.gamma_exact	336.0	1013.25	7.5	288.15	9.882698	9.882698	-4.29e-10	-0.000
models.itu676.gamma_exact	337.0	1013.25	7.5	288.15	9.625634	9.625634	1.37e-10	0.000
models.itu676.gamma_exact	338.0	1013.25	7.5	288.15	9.446598	9.446598	2.47e-10	0.000
models.itu676.gamma_exact	339.0	1013.25	7.5	288.15	9.329258	9.329258	5.55e-11	0.000
models.itu676.gamma_exact	340.0	1013.25	7.5	288.15	9.261534	9.261534	-4.24e-10	-0.000
models.itu676.gamma_exact	341.0	1013.25	7.5	288.15	9.234207	9.234207	3.01e-10	0.000
models.itu676.gamma_exact	342.0	1013.25	7.5	288.15	9.240521	9.240521	3.05e-10	0.000
models.itu676.gamma_exact	343.0	1013.25	7.5	288.15	9.275658	9.275658	-3.72e-10	-0.000
models.itu676.gamma_exact	344.0	1013.25	7.5	288.15	9.336250	9.336250	1.72e-10	0.000
models.itu676.gamma_exact	345.0	1013.25	7.5	288.15	9.420030	9.420030	-2.90e-10	-0.000
models.itu676.gamma_exact	346.0	1013.25	7.5	288.15	9.525579	9.525579	-1.13e-12	-0.000
models.itu676.gamma_exact	347.0	1013.25	7.5	288.15	9.652172	9.652172	4.61e-10	0.000
models.itu676.gamma_exact	348.0	1013.25	7.5	288.15	9.799673	9.799673	4.90e-10	0.000
models.itu676.gamma_exact	349.0	1013.25	7.5	288.15	9.968476	9.968476	-3.37e-10	-0.000
models.itu676.gamma_exact	350.0	1013.25	7.5	288.15	10.159479	10.159479	3.44e-09	0.000

Function gamma0_exact ¶

The table below contains the results of testing function gamma0_exact. The test cases were extracted from spreadsheet ITURP676-12_gamma.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
f = 12.0  # (GHz)
P = 1013.25  # (hPA)
rho = 7.5  # (g/cm3)
T = 288.15  # (K)

# Make call to test-function gamma0_exact
itur_val = itur.models.itu676.gamma0_exact(f=f, P=P, rho=rho, T=T)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.008698264  # (dB/km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu676.gamma0_exact

ITU-Rpy Function	f (GHz)	P (hPA)	rho (g/cm3)	T (K)	ITU Validation (dB/km)	ITU-Rpy Result (dB/km)	Absolute Error	Relative Error
models.itu676.gamma0_exact	12.0	1013.25	7.5	288.15	0.008698	0.008698	-6.88e-11	-0.000
models.itu676.gamma0_exact	20.0	1013.25	7.5	288.15	0.011884	0.011884	-4.78e-10	-0.000
models.itu676.gamma0_exact	60.0	1013.25	7.5	288.15	14.623475	14.623475	3.51e-09	0.000
models.itu676.gamma0_exact	90.0	1013.25	7.5	288.15	0.038870	0.038870	-7.24e-11	-0.000
models.itu676.gamma0_exact	130.0	1013.25	7.5	288.15	0.041509	0.041509	4.00e-10	0.000
models.itu676.gamma0_exact	1.0	1013.25	7.5	288.15	0.005389	0.005389	-1.68e-10	-0.000
models.itu676.gamma0_exact	2.0	1013.25	7.5	288.15	0.006716	0.006716	-4.74e-10	-0.000
models.itu676.gamma0_exact	3.0	1013.25	7.5	288.15	0.007076	0.007076	-1.33e-10	-0.000
models.itu676.gamma0_exact	4.0	1013.25	7.5	288.15	0.007259	0.007259	-2.78e-10	-0.000
models.itu676.gamma0_exact	5.0	1013.25	7.5	288.15	0.007400	0.007400	-2.56e-10	-0.000
models.itu676.gamma0_exact	6.0	1013.25	7.5	288.15	0.007537	0.007537	-8.29e-11	-0.000
models.itu676.gamma0_exact	7.0	1013.25	7.5	288.15	0.007683	0.007683	-1.65e-10	-0.000
models.itu676.gamma0_exact	8.0	1013.25	7.5	288.15	0.007844	0.007844	-2.52e-10	-0.000
models.itu676.gamma0_exact	9.0	1013.25	7.5	288.15	0.008023	0.008023	-4.46e-10	-0.000
models.itu676.gamma0_exact	10.0	1013.25	7.5	288.15	0.008224	0.008224	2.97e-10	0.000
models.itu676.gamma0_exact	11.0	1013.25	7.5	288.15	0.008449	0.008449	-3.94e-10	-0.000
models.itu676.gamma0_exact	12.0	1013.25	7.5	288.15	0.008698	0.008698	-6.88e-11	-0.000
models.itu676.gamma0_exact	13.0	1013.25	7.5	288.15	0.008975	0.008975	1.24e-10	0.000
models.itu676.gamma0_exact	14.0	1013.25	7.5	288.15	0.009281	0.009281	3.96e-10	0.000
models.itu676.gamma0_exact	15.0	1013.25	7.5	288.15	0.009619	0.009619	-3.01e-10	-0.000
models.itu676.gamma0_exact	16.0	1013.25	7.5	288.15	0.009991	0.009991	-5.30e-11	-0.000
models.itu676.gamma0_exact	17.0	1013.25	7.5	288.15	0.010400	0.010400	3.53e-10	0.000
models.itu676.gamma0_exact	18.0	1013.25	7.5	288.15	0.010849	0.010849	-3.41e-10	-0.000
models.itu676.gamma0_exact	19.0	1013.25	7.5	288.15	0.011342	0.011342	-4.01e-10	-0.000
models.itu676.gamma0_exact	20.0	1013.25	7.5	288.15	0.011884	0.011884	-4.78e-10	-0.000
models.itu676.gamma0_exact	21.0	1013.25	7.5	288.15	0.012478	0.012478	1.33e-10	0.000
models.itu676.gamma0_exact	22.0	1013.25	7.5	288.15	0.013130	0.013130	3.46e-11	0.000
models.itu676.gamma0_exact	23.0	1013.25	7.5	288.15	0.013847	0.013847	1.44e-10	0.000
models.itu676.gamma0_exact	24.0	1013.25	7.5	288.15	0.014636	0.014636	1.79e-10	0.000
models.itu676.gamma0_exact	25.0	1013.25	7.5	288.15	0.015505	0.015505	1.77e-10	0.000
models.itu676.gamma0_exact	26.0	1013.25	7.5	288.15	0.016463	0.016463	3.86e-10	0.000
models.itu676.gamma0_exact	27.0	1013.25	7.5	288.15	0.017523	0.017523	-4.01e-10	-0.000
models.itu676.gamma0_exact	28.0	1013.25	7.5	288.15	0.018696	0.018696	4.76e-11	0.000
models.itu676.gamma0_exact	29.0	1013.25	7.5	288.15	0.019999	0.019999	-1.10e-10	-0.000
models.itu676.gamma0_exact	30.0	1013.25	7.5	288.15	0.021450	0.021450	-2.40e-10	-0.000
models.itu676.gamma0_exact	31.0	1013.25	7.5	288.15	0.023069	0.023069	1.71e-10	0.000
models.itu676.gamma0_exact	32.0	1013.25	7.5	288.15	0.024884	0.024884	-2.24e-10	-0.000
models.itu676.gamma0_exact	33.0	1013.25	7.5	288.15	0.026925	0.026925	3.04e-10	0.000
models.itu676.gamma0_exact	34.0	1013.25	7.5	288.15	0.029229	0.029229	7.06e-11	0.000
models.itu676.gamma0_exact	35.0	1013.25	7.5	288.15	0.031843	0.031843	1.36e-10	0.000
models.itu676.gamma0_exact	36.0	1013.25	7.5	288.15	0.034823	0.034823	1.43e-11	0.000
models.itu676.gamma0_exact	37.0	1013.25	7.5	288.15	0.038239	0.038239	-2.90e-10	-0.000
models.itu676.gamma0_exact	38.0	1013.25	7.5	288.15	0.042180	0.042180	-4.91e-10	-0.000
models.itu676.gamma0_exact	39.0	1013.25	7.5	288.15	0.046758	0.046758	4.58e-11	0.000
models.itu676.gamma0_exact	40.0	1013.25	7.5	288.15	0.052117	0.052117	6.41e-11	0.000
models.itu676.gamma0_exact	41.0	1013.25	7.5	288.15	0.058445	0.058445	-1.02e-10	-0.000
models.itu676.gamma0_exact	42.0	1013.25	7.5	288.15	0.065994	0.065994	-1.75e-10	-0.000
models.itu676.gamma0_exact	43.0	1013.25	7.5	288.15	0.075103	0.075103	-4.57e-10	-0.000
models.itu676.gamma0_exact	44.0	1013.25	7.5	288.15	0.086242	0.086242	5.34e-11	0.000
models.itu676.gamma0_exact	45.0	1013.25	7.5	288.15	0.100081	0.100081	-1.54e-10	-0.000
models.itu676.gamma0_exact	46.0	1013.25	7.5	288.15	0.117605	0.117605	2.27e-10	0.000
models.itu676.gamma0_exact	47.0	1013.25	7.5	288.15	0.140330	0.140330	-3.76e-10	-0.000
models.itu676.gamma0_exact	48.0	1013.25	7.5	288.15	0.170720	0.170720	1.56e-10	0.000
models.itu676.gamma0_exact	49.0	1013.25	7.5	288.15	0.213175	0.213175	1.36e-11	0.000
models.itu676.gamma0_exact	50.0	1013.25	7.5	288.15	0.277269	0.277269	4.69e-10	0.000
models.itu676.gamma0_exact	51.0	1013.25	7.5	288.15	0.389671	0.389671	-7.01e-11	-0.000
models.itu676.gamma0_exact	52.0	1013.25	7.5	288.15	0.618430	0.618430	3.45e-10	0.000
models.itu676.gamma0_exact	53.0	1013.25	7.5	288.15	1.126612	1.126612	1.46e-11	0.000
models.itu676.gamma0_exact	54.0	1013.25	7.5	288.15	2.211542	2.211542	-3.72e-10	-0.000
models.itu676.gamma0_exact	55.0	1013.25	7.5	288.15	4.193282	4.193282	6.19e-12	0.000
models.itu676.gamma0_exact	56.0	1013.25	7.5	288.15	7.055044	7.055044	1.49e-10	0.000
models.itu676.gamma0_exact	57.0	1013.25	7.5	288.15	10.065238	10.065238	-2.14e-09	-0.000
models.itu676.gamma0_exact	58.0	1013.25	7.5	288.15	12.353147	12.353147	-1.29e-09	-0.000
models.itu676.gamma0_exact	59.0	1013.25	7.5	288.15	13.635296	13.635296	-4.04e-09	-0.000
models.itu676.gamma0_exact	60.0	1013.25	7.5	288.15	14.623475	14.623475	3.51e-09	0.000
models.itu676.gamma0_exact	61.0	1013.25	7.5	288.15	15.007159	15.007159	4.00e-09	0.000
models.itu676.gamma0_exact	62.0	1013.25	7.5	288.15	13.996211	13.996211	-2.27e-09	-0.000
models.itu676.gamma0_exact	63.0	1013.25	7.5	288.15	10.831088	10.831088	-1.43e-09	-0.000
models.itu676.gamma0_exact	64.0	1013.25	7.5	288.15	6.844589	6.844589	-4.91e-10	-0.000
models.itu676.gamma0_exact	65.0	1013.25	7.5	288.15	3.808804	3.808804	-3.44e-10	-0.000
models.itu676.gamma0_exact	66.0	1013.25	7.5	288.15	1.966618	1.966618	2.29e-10	0.000
models.itu676.gamma0_exact	67.0	1013.25	7.5	288.15	1.033389	1.033389	-6.65e-11	-0.000
models.itu676.gamma0_exact	68.0	1013.25	7.5	288.15	0.605466	0.605466	4.26e-10	0.000
models.itu676.gamma0_exact	69.0	1013.25	7.5	288.15	0.406986	0.406986	-1.98e-10	-0.000
models.itu676.gamma0_exact	70.0	1013.25	7.5	288.15	0.304105	0.304105	-1.47e-10	-0.000
models.itu676.gamma0_exact	71.0	1013.25	7.5	288.15	0.241601	0.241601	-1.64e-11	-0.000
models.itu676.gamma0_exact	72.0	1013.25	7.5	288.15	0.198532	0.198532	3.84e-10	0.000
models.itu676.gamma0_exact	73.0	1013.25	7.5	288.15	0.167046	0.167046	3.21e-10	0.000
models.itu676.gamma0_exact	74.0	1013.25	7.5	288.15	0.143142	0.143142	-4.86e-10	-0.000
models.itu676.gamma0_exact	75.0	1013.25	7.5	288.15	0.124485	0.124485	4.08e-12	0.000
models.itu676.gamma0_exact	76.0	1013.25	7.5	288.15	0.109604	0.109604	4.89e-10	0.000
models.itu676.gamma0_exact	77.0	1013.25	7.5	288.15	0.097526	0.097526	3.75e-10	0.000
models.itu676.gamma0_exact	78.0	1013.25	7.5	288.15	0.087579	0.087579	-4.72e-10	-0.000
models.itu676.gamma0_exact	79.0	1013.25	7.5	288.15	0.079289	0.079289	-3.24e-10	-0.000
models.itu676.gamma0_exact	80.0	1013.25	7.5	288.15	0.072307	0.072307	-3.27e-10	-0.000
models.itu676.gamma0_exact	81.0	1013.25	7.5	288.15	0.066378	0.066378	-3.25e-10	-0.000
models.itu676.gamma0_exact	82.0	1013.25	7.5	288.15	0.061305	0.061305	3.09e-10	0.000
models.itu676.gamma0_exact	83.0	1013.25	7.5	288.15	0.056939	0.056939	-1.84e-10	-0.000
models.itu676.gamma0_exact	84.0	1013.25	7.5	288.15	0.053163	0.053163	-1.40e-10	-0.000
models.itu676.gamma0_exact	85.0	1013.25	7.5	288.15	0.049886	0.049886	3.78e-10	0.000
models.itu676.gamma0_exact	86.0	1013.25	7.5	288.15	0.047033	0.047033	3.41e-10	0.000
models.itu676.gamma0_exact	87.0	1013.25	7.5	288.15	0.044547	0.044547	2.33e-10	0.000
models.itu676.gamma0_exact	88.0	1013.25	7.5	288.15	0.042382	0.042382	-4.06e-10	-0.000
models.itu676.gamma0_exact	89.0	1013.25	7.5	288.15	0.040500	0.040500	3.08e-10	0.000
models.itu676.gamma0_exact	90.0	1013.25	7.5	288.15	0.038870	0.038870	-7.24e-11	-0.000
models.itu676.gamma0_exact	91.0	1013.25	7.5	288.15	0.037469	0.037469	2.13e-10	0.000
models.itu676.gamma0_exact	92.0	1013.25	7.5	288.15	0.036279	0.036279	-3.94e-10	-0.000
models.itu676.gamma0_exact	93.0	1013.25	7.5	288.15	0.035286	0.035286	4.99e-11	0.000
models.itu676.gamma0_exact	94.0	1013.25	7.5	288.15	0.034481	0.034481	-5.00e-11	-0.000
models.itu676.gamma0_exact	95.0	1013.25	7.5	288.15	0.033858	0.033858	4.01e-10	0.000
models.itu676.gamma0_exact	96.0	1013.25	7.5	288.15	0.033418	0.033418	1.96e-10	0.000
models.itu676.gamma0_exact	97.0	1013.25	7.5	288.15	0.033163	0.033163	-1.08e-12	-0.000
models.itu676.gamma0_exact	98.0	1013.25	7.5	288.15	0.033102	0.033102	-3.81e-10	-0.000
models.itu676.gamma0_exact	99.0	1013.25	7.5	288.15	0.033249	0.033249	-1.05e-10	-0.000
models.itu676.gamma0_exact	100.0	1013.25	7.5	288.15	0.033625	0.033625	-7.81e-11	-0.000
models.itu676.gamma0_exact	101.0	1013.25	7.5	288.15	0.034262	0.034262	-2.89e-10	-0.000
models.itu676.gamma0_exact	102.0	1013.25	7.5	288.15	0.035201	0.035201	-4.37e-10	-0.000
models.itu676.gamma0_exact	103.0	1013.25	7.5	288.15	0.036499	0.036499	-2.76e-10	-0.000
models.itu676.gamma0_exact	104.0	1013.25	7.5	288.15	0.038238	0.038238	-4.76e-11	-0.000
models.itu676.gamma0_exact	105.0	1013.25	7.5	288.15	0.040527	0.040527	-3.01e-10	-0.000
models.itu676.gamma0_exact	106.0	1013.25	7.5	288.15	0.043524	0.043524	2.19e-10	0.000
models.itu676.gamma0_exact	107.0	1013.25	7.5	288.15	0.047453	0.047453	-9.53e-11	-0.000
models.itu676.gamma0_exact	108.0	1013.25	7.5	288.15	0.052644	0.052644	9.67e-11	0.000
models.itu676.gamma0_exact	109.0	1013.25	7.5	288.15	0.059596	0.059596	4.41e-10	0.000
models.itu676.gamma0_exact	110.0	1013.25	7.5	288.15	0.069088	0.069088	-2.25e-10	-0.000
models.itu676.gamma0_exact	111.0	1013.25	7.5	288.15	0.082387	0.082387	-2.34e-10	-0.000
models.itu676.gamma0_exact	112.0	1013.25	7.5	288.15	0.101655	0.101655	-2.43e-10	-0.000
models.itu676.gamma0_exact	113.0	1013.25	7.5	288.15	0.130787	0.130787	-9.19e-12	-0.000
models.itu676.gamma0_exact	114.0	1013.25	7.5	288.15	0.177281	0.177281	-2.16e-10	-0.000
models.itu676.gamma0_exact	115.0	1013.25	7.5	288.15	0.256608	0.256608	1.28e-10	0.000
models.itu676.gamma0_exact	116.0	1013.25	7.5	288.15	0.402454	0.402454	-1.58e-10	-0.000
models.itu676.gamma0_exact	117.0	1013.25	7.5	288.15	0.683016	0.683016	3.01e-10	0.000
models.itu676.gamma0_exact	118.0	1013.25	7.5	288.15	1.134866	1.134866	1.29e-10	0.000
models.itu676.gamma0_exact	119.0	1013.25	7.5	288.15	1.306379	1.306379	2.15e-10	0.000
models.itu676.gamma0_exact	120.0	1013.25	7.5	288.15	0.886109	0.886109	5.60e-12	0.000
models.itu676.gamma0_exact	121.0	1013.25	7.5	288.15	0.509172	0.509172	3.69e-10	0.000
models.itu676.gamma0_exact	122.0	1013.25	7.5	288.15	0.307769	0.307769	-3.83e-10	-0.000
models.itu676.gamma0_exact	123.0	1013.25	7.5	288.15	0.202101	0.202101	-2.01e-10	-0.000
models.itu676.gamma0_exact	124.0	1013.25	7.5	288.15	0.142570	0.142570	-5.33e-11	-0.000
models.itu676.gamma0_exact	125.0	1013.25	7.5	288.15	0.106446	0.106446	-3.96e-10	-0.000
models.itu676.gamma0_exact	126.0	1013.25	7.5	288.15	0.083104	0.083104	2.67e-10	0.000
models.itu676.gamma0_exact	127.0	1013.25	7.5	288.15	0.067232	0.067232	-4.38e-10	-0.000
models.itu676.gamma0_exact	128.0	1013.25	7.5	288.15	0.055982	0.055982	-2.29e-10	-0.000
models.itu676.gamma0_exact	129.0	1013.25	7.5	288.15	0.047732	0.047732	-4.15e-10	-0.000
models.itu676.gamma0_exact	130.0	1013.25	7.5	288.15	0.041509	0.041509	4.00e-10	0.000
models.itu676.gamma0_exact	131.0	1013.25	7.5	288.15	0.036702	0.036702	-2.17e-11	-0.000
models.itu676.gamma0_exact	132.0	1013.25	7.5	288.15	0.032912	0.032912	-6.43e-11	-0.000
models.itu676.gamma0_exact	133.0	1013.25	7.5	288.15	0.029873	0.029873	2.67e-10	0.000
models.itu676.gamma0_exact	134.0	1013.25	7.5	288.15	0.027400	0.027400	1.83e-10	0.000
models.itu676.gamma0_exact	135.0	1013.25	7.5	288.15	0.025359	0.025359	-1.72e-10	-0.000
models.itu676.gamma0_exact	136.0	1013.25	7.5	288.15	0.023658	0.023658	-1.46e-10	-0.000
models.itu676.gamma0_exact	137.0	1013.25	7.5	288.15	0.022224	0.022224	3.75e-10	0.000
models.itu676.gamma0_exact	138.0	1013.25	7.5	288.15	0.021005	0.021005	8.12e-11	0.000
models.itu676.gamma0_exact	139.0	1013.25	7.5	288.15	0.019961	0.019961	-4.96e-10	-0.000
models.itu676.gamma0_exact	140.0	1013.25	7.5	288.15	0.019060	0.019060	2.75e-10	0.000
models.itu676.gamma0_exact	141.0	1013.25	7.5	288.15	0.018278	0.018278	1.62e-10	0.000
models.itu676.gamma0_exact	142.0	1013.25	7.5	288.15	0.017596	0.017596	1.66e-10	0.000
models.itu676.gamma0_exact	143.0	1013.25	7.5	288.15	0.016998	0.016998	-3.73e-10	-0.000
models.itu676.gamma0_exact	144.0	1013.25	7.5	288.15	0.016471	0.016471	-3.81e-10	-0.000
models.itu676.gamma0_exact	145.0	1013.25	7.5	288.15	0.016006	0.016006	-4.46e-10	-0.000
models.itu676.gamma0_exact	146.0	1013.25	7.5	288.15	0.015593	0.015593	3.39e-10	0.000
models.itu676.gamma0_exact	147.0	1013.25	7.5	288.15	0.015226	0.015226	2.54e-10	0.000
models.itu676.gamma0_exact	148.0	1013.25	7.5	288.15	0.014900	0.014900	2.64e-10	0.000
models.itu676.gamma0_exact	149.0	1013.25	7.5	288.15	0.014608	0.014608	2.97e-10	0.000
models.itu676.gamma0_exact	150.0	1013.25	7.5	288.15	0.014347	0.014347	-2.74e-10	-0.000
models.itu676.gamma0_exact	151.0	1013.25	7.5	288.15	0.014113	0.014113	-1.57e-10	-0.000
models.itu676.gamma0_exact	152.0	1013.25	7.5	288.15	0.013904	0.013904	5.37e-11	0.000
models.itu676.gamma0_exact	153.0	1013.25	7.5	288.15	0.013717	0.013717	2.29e-10	0.000
models.itu676.gamma0_exact	154.0	1013.25	7.5	288.15	0.013550	0.013550	7.46e-11	0.000
models.itu676.gamma0_exact	155.0	1013.25	7.5	288.15	0.013400	0.013400	1.89e-10	0.000
models.itu676.gamma0_exact	156.0	1013.25	7.5	288.15	0.013266	0.013266	-3.84e-10	-0.000
models.itu676.gamma0_exact	157.0	1013.25	7.5	288.15	0.013146	0.013146	3.91e-11	0.000
models.itu676.gamma0_exact	158.0	1013.25	7.5	288.15	0.013040	0.013040	3.00e-10	0.000
models.itu676.gamma0_exact	159.0	1013.25	7.5	288.15	0.012946	0.012946	-4.64e-10	-0.000
models.itu676.gamma0_exact	160.0	1013.25	7.5	288.15	0.012863	0.012863	-3.19e-11	-0.000
models.itu676.gamma0_exact	161.0	1013.25	7.5	288.15	0.012790	0.012790	1.45e-10	0.000
models.itu676.gamma0_exact	162.0	1013.25	7.5	288.15	0.012726	0.012726	2.91e-10	0.000
models.itu676.gamma0_exact	163.0	1013.25	7.5	288.15	0.012671	0.012671	2.71e-10	0.000
models.itu676.gamma0_exact	164.0	1013.25	7.5	288.15	0.012624	0.012624	-4.16e-10	-0.000
models.itu676.gamma0_exact	165.0	1013.25	7.5	288.15	0.012585	0.012585	-2.65e-10	-0.000
models.itu676.gamma0_exact	166.0	1013.25	7.5	288.15	0.012552	0.012552	2.31e-10	0.000
models.itu676.gamma0_exact	167.0	1013.25	7.5	288.15	0.012526	0.012526	4.50e-10	0.000
models.itu676.gamma0_exact	168.0	1013.25	7.5	288.15	0.012506	0.012506	-4.50e-10	-0.000
models.itu676.gamma0_exact	169.0	1013.25	7.5	288.15	0.012492	0.012492	-4.30e-10	-0.000
models.itu676.gamma0_exact	170.0	1013.25	7.5	288.15	0.012483	0.012483	-1.51e-10	-0.000
models.itu676.gamma0_exact	171.0	1013.25	7.5	288.15	0.012479	0.012479	-1.31e-10	-0.000
models.itu676.gamma0_exact	172.0	1013.25	7.5	288.15	0.012479	0.012479	-4.00e-10	-0.000
models.itu676.gamma0_exact	173.0	1013.25	7.5	288.15	0.012484	0.012484	4.23e-10	0.000
models.itu676.gamma0_exact	174.0	1013.25	7.5	288.15	0.012493	0.012493	-3.06e-10	-0.000
models.itu676.gamma0_exact	175.0	1013.25	7.5	288.15	0.012507	0.012507	-5.33e-12	-0.000
models.itu676.gamma0_exact	176.0	1013.25	7.5	288.15	0.012524	0.012524	1.12e-10	0.000
models.itu676.gamma0_exact	177.0	1013.25	7.5	288.15	0.012544	0.012544	-2.07e-10	-0.000
models.itu676.gamma0_exact	178.0	1013.25	7.5	288.15	0.012568	0.012568	2.89e-10	0.000
models.itu676.gamma0_exact	179.0	1013.25	7.5	288.15	0.012595	0.012595	-2.68e-10	-0.000
models.itu676.gamma0_exact	180.0	1013.25	7.5	288.15	0.012626	0.012626	3.54e-10	0.000
models.itu676.gamma0_exact	181.0	1013.25	7.5	288.15	0.012659	0.012659	-4.23e-10	-0.000
models.itu676.gamma0_exact	182.0	1013.25	7.5	288.15	0.012695	0.012695	-2.21e-11	-0.000
models.itu676.gamma0_exact	183.0	1013.25	7.5	288.15	0.012734	0.012734	1.64e-10	0.000
models.itu676.gamma0_exact	184.0	1013.25	7.5	288.15	0.012775	0.012775	-4.54e-10	-0.000
models.itu676.gamma0_exact	185.0	1013.25	7.5	288.15	0.012819	0.012819	3.75e-11	0.000
models.itu676.gamma0_exact	186.0	1013.25	7.5	288.15	0.012866	0.012866	-3.17e-10	-0.000
models.itu676.gamma0_exact	187.0	1013.25	7.5	288.15	0.012914	0.012914	2.26e-10	0.000
models.itu676.gamma0_exact	188.0	1013.25	7.5	288.15	0.012965	0.012965	-3.86e-10	-0.000
models.itu676.gamma0_exact	189.0	1013.25	7.5	288.15	0.013018	0.013018	4.68e-10	0.000
models.itu676.gamma0_exact	190.0	1013.25	7.5	288.15	0.013073	0.013073	4.93e-10	0.000
models.itu676.gamma0_exact	191.0	1013.25	7.5	288.15	0.013130	0.013130	-1.38e-10	-0.000
models.itu676.gamma0_exact	192.0	1013.25	7.5	288.15	0.013189	0.013189	-4.40e-10	-0.000
models.itu676.gamma0_exact	193.0	1013.25	7.5	288.15	0.013250	0.013250	-3.07e-10	-0.000
models.itu676.gamma0_exact	194.0	1013.25	7.5	288.15	0.013312	0.013312	-2.21e-10	-0.000
models.itu676.gamma0_exact	195.0	1013.25	7.5	288.15	0.013377	0.013377	2.33e-12	0.000
models.itu676.gamma0_exact	196.0	1013.25	7.5	288.15	0.013443	0.013443	4.57e-10	0.000
models.itu676.gamma0_exact	197.0	1013.25	7.5	288.15	0.013511	0.013511	3.61e-10	0.000
models.itu676.gamma0_exact	198.0	1013.25	7.5	288.15	0.013580	0.013580	2.54e-10	0.000
models.itu676.gamma0_exact	199.0	1013.25	7.5	288.15	0.013651	0.013651	1.83e-10	0.000
models.itu676.gamma0_exact	200.0	1013.25	7.5	288.15	0.013724	0.013724	-1.33e-10	-0.000
models.itu676.gamma0_exact	201.0	1013.25	7.5	288.15	0.013798	0.013798	-1.45e-10	-0.000
models.itu676.gamma0_exact	202.0	1013.25	7.5	288.15	0.013873	0.013873	-3.38e-10	-0.000
models.itu676.gamma0_exact	203.0	1013.25	7.5	288.15	0.013950	0.013950	-9.59e-11	-0.000
models.itu676.gamma0_exact	204.0	1013.25	7.5	288.15	0.014028	0.014028	4.18e-10	0.000
models.itu676.gamma0_exact	205.0	1013.25	7.5	288.15	0.014107	0.014107	3.71e-10	0.000
models.itu676.gamma0_exact	206.0	1013.25	7.5	288.15	0.014188	0.014188	3.64e-10	0.000
models.itu676.gamma0_exact	207.0	1013.25	7.5	288.15	0.014270	0.014270	-4.75e-10	-0.000
models.itu676.gamma0_exact	208.0	1013.25	7.5	288.15	0.014354	0.014354	-3.98e-10	-0.000
models.itu676.gamma0_exact	209.0	1013.25	7.5	288.15	0.014438	0.014438	3.90e-11	0.000
models.itu676.gamma0_exact	210.0	1013.25	7.5	288.15	0.014524	0.014524	5.38e-11	0.000
models.itu676.gamma0_exact	211.0	1013.25	7.5	288.15	0.014611	0.014611	-2.91e-10	-0.000
models.itu676.gamma0_exact	212.0	1013.25	7.5	288.15	0.014699	0.014699	-2.47e-11	-0.000
models.itu676.gamma0_exact	213.0	1013.25	7.5	288.15	0.014789	0.014789	-2.06e-10	-0.000
models.itu676.gamma0_exact	214.0	1013.25	7.5	288.15	0.014879	0.014879	1.33e-10	0.000
models.itu676.gamma0_exact	215.0	1013.25	7.5	288.15	0.014970	0.014970	3.83e-11	0.000
models.itu676.gamma0_exact	216.0	1013.25	7.5	288.15	0.015063	0.015063	-3.17e-10	-0.000
models.itu676.gamma0_exact	217.0	1013.25	7.5	288.15	0.015157	0.015157	4.16e-10	0.000
models.itu676.gamma0_exact	218.0	1013.25	7.5	288.15	0.015251	0.015251	-2.00e-10	-0.000
models.itu676.gamma0_exact	219.0	1013.25	7.5	288.15	0.015347	0.015347	-3.46e-10	-0.000
models.itu676.gamma0_exact	220.0	1013.25	7.5	288.15	0.015444	0.015444	9.23e-11	0.000
models.itu676.gamma0_exact	221.0	1013.25	7.5	288.15	0.015541	0.015541	-4.45e-10	-0.000
models.itu676.gamma0_exact	222.0	1013.25	7.5	288.15	0.015640	0.015640	-1.57e-10	-0.000
models.itu676.gamma0_exact	223.0	1013.25	7.5	288.15	0.015740	0.015740	1.49e-10	0.000
models.itu676.gamma0_exact	224.0	1013.25	7.5	288.15	0.015840	0.015840	8.53e-11	0.000
models.itu676.gamma0_exact	225.0	1013.25	7.5	288.15	0.015942	0.015942	-2.90e-10	-0.000
models.itu676.gamma0_exact	226.0	1013.25	7.5	288.15	0.016044	0.016044	-4.48e-10	-0.000
models.itu676.gamma0_exact	227.0	1013.25	7.5	288.15	0.016147	0.016147	-3.64e-10	-0.000
models.itu676.gamma0_exact	228.0	1013.25	7.5	288.15	0.016252	0.016252	-4.97e-10	-0.000
models.itu676.gamma0_exact	229.0	1013.25	7.5	288.15	0.016357	0.016357	2.32e-10	0.000
models.itu676.gamma0_exact	230.0	1013.25	7.5	288.15	0.016463	0.016463	4.57e-10	0.000
models.itu676.gamma0_exact	231.0	1013.25	7.5	288.15	0.016570	0.016570	3.89e-10	0.000
models.itu676.gamma0_exact	232.0	1013.25	7.5	288.15	0.016677	0.016677	-1.70e-10	-0.000
models.itu676.gamma0_exact	233.0	1013.25	7.5	288.15	0.016786	0.016786	1.89e-10	0.000
models.itu676.gamma0_exact	234.0	1013.25	7.5	288.15	0.016895	0.016895	4.99e-10	0.000
models.itu676.gamma0_exact	235.0	1013.25	7.5	288.15	0.017006	0.017006	4.30e-10	0.000
models.itu676.gamma0_exact	236.0	1013.25	7.5	288.15	0.017117	0.017117	3.00e-10	0.000
models.itu676.gamma0_exact	237.0	1013.25	7.5	288.15	0.017228	0.017228	9.10e-11	0.000
models.itu676.gamma0_exact	238.0	1013.25	7.5	288.15	0.017341	0.017341	4.59e-10	0.000
models.itu676.gamma0_exact	239.0	1013.25	7.5	288.15	0.017455	0.017455	-2.57e-10	-0.000
models.itu676.gamma0_exact	240.0	1013.25	7.5	288.15	0.017569	0.017569	-2.29e-11	-0.000
models.itu676.gamma0_exact	241.0	1013.25	7.5	288.15	0.017684	0.017684	-1.00e-10	-0.000
models.itu676.gamma0_exact	242.0	1013.25	7.5	288.15	0.017800	0.017800	-3.80e-11	-0.000
models.itu676.gamma0_exact	243.0	1013.25	7.5	288.15	0.017916	0.017916	3.34e-10	0.000
models.itu676.gamma0_exact	244.0	1013.25	7.5	288.15	0.018034	0.018034	-8.39e-11	-0.000
models.itu676.gamma0_exact	245.0	1013.25	7.5	288.15	0.018152	0.018152	3.42e-10	0.000
models.itu676.gamma0_exact	246.0	1013.25	7.5	288.15	0.018271	0.018271	-1.20e-11	-0.000
models.itu676.gamma0_exact	247.0	1013.25	7.5	288.15	0.018390	0.018390	-2.32e-11	-0.000
models.itu676.gamma0_exact	248.0	1013.25	7.5	288.15	0.018511	0.018511	1.84e-10	0.000
models.itu676.gamma0_exact	249.0	1013.25	7.5	288.15	0.018632	0.018632	2.44e-10	0.000
models.itu676.gamma0_exact	250.0	1013.25	7.5	288.15	0.018754	0.018754	-4.50e-10	-0.000
models.itu676.gamma0_exact	251.0	1013.25	7.5	288.15	0.018876	0.018876	2.64e-10	0.000
models.itu676.gamma0_exact	252.0	1013.25	7.5	288.15	0.019000	0.019000	3.15e-10	0.000
models.itu676.gamma0_exact	253.0	1013.25	7.5	288.15	0.019124	0.019124	4.06e-10	0.000
models.itu676.gamma0_exact	254.0	1013.25	7.5	288.15	0.019249	0.019249	1.31e-11	0.000
models.itu676.gamma0_exact	255.0	1013.25	7.5	288.15	0.019374	0.019374	3.89e-10	0.000
models.itu676.gamma0_exact	256.0	1013.25	7.5	288.15	0.019500	0.019500	-4.33e-10	-0.000
models.itu676.gamma0_exact	257.0	1013.25	7.5	288.15	0.019627	0.019627	3.58e-10	0.000
models.itu676.gamma0_exact	258.0	1013.25	7.5	288.15	0.019755	0.019755	3.53e-10	0.000
models.itu676.gamma0_exact	259.0	1013.25	7.5	288.15	0.019883	0.019883	-7.52e-11	-0.000
models.itu676.gamma0_exact	260.0	1013.25	7.5	288.15	0.020012	0.020012	2.27e-10	0.000
models.itu676.gamma0_exact	261.0	1013.25	7.5	288.15	0.020142	0.020142	1.93e-10	0.000
models.itu676.gamma0_exact	262.0	1013.25	7.5	288.15	0.020273	0.020273	-4.65e-10	-0.000
models.itu676.gamma0_exact	263.0	1013.25	7.5	288.15	0.020404	0.020404	-2.57e-10	-0.000
models.itu676.gamma0_exact	264.0	1013.25	7.5	288.15	0.020536	0.020536	8.07e-11	0.000
models.itu676.gamma0_exact	265.0	1013.25	7.5	288.15	0.020668	0.020668	-4.12e-10	-0.000
models.itu676.gamma0_exact	266.0	1013.25	7.5	288.15	0.020801	0.020801	7.32e-11	0.000
models.itu676.gamma0_exact	267.0	1013.25	7.5	288.15	0.020935	0.020935	1.11e-10	0.000
models.itu676.gamma0_exact	268.0	1013.25	7.5	288.15	0.021070	0.021070	3.87e-11	0.000
models.itu676.gamma0_exact	269.0	1013.25	7.5	288.15	0.021205	0.021205	-4.82e-11	-0.000
models.itu676.gamma0_exact	270.0	1013.25	7.5	288.15	0.021341	0.021341	-3.02e-10	-0.000
models.itu676.gamma0_exact	271.0	1013.25	7.5	288.15	0.021478	0.021478	-1.28e-10	-0.000
models.itu676.gamma0_exact	272.0	1013.25	7.5	288.15	0.021615	0.021615	-1.93e-10	-0.000
models.itu676.gamma0_exact	273.0	1013.25	7.5	288.15	0.021754	0.021754	-4.28e-10	-0.000
models.itu676.gamma0_exact	274.0	1013.25	7.5	288.15	0.021892	0.021892	-4.17e-11	-0.000
models.itu676.gamma0_exact	275.0	1013.25	7.5	288.15	0.022032	0.022032	4.73e-10	0.000
models.itu676.gamma0_exact	276.0	1013.25	7.5	288.15	0.022172	0.022172	3.30e-10	0.000
models.itu676.gamma0_exact	277.0	1013.25	7.5	288.15	0.022313	0.022313	4.40e-10	0.000
models.itu676.gamma0_exact	278.0	1013.25	7.5	288.15	0.022455	0.022455	3.95e-10	0.000
models.itu676.gamma0_exact	279.0	1013.25	7.5	288.15	0.022597	0.022597	4.60e-10	0.000
models.itu676.gamma0_exact	280.0	1013.25	7.5	288.15	0.022740	0.022740	-4.44e-10	-0.000
models.itu676.gamma0_exact	281.0	1013.25	7.5	288.15	0.022884	0.022884	2.50e-10	0.000
models.itu676.gamma0_exact	282.0	1013.25	7.5	288.15	0.023028	0.023028	-2.69e-10	-0.000
models.itu676.gamma0_exact	283.0	1013.25	7.5	288.15	0.023174	0.023174	-2.01e-10	-0.000
models.itu676.gamma0_exact	284.0	1013.25	7.5	288.15	0.023319	0.023319	-1.58e-10	-0.000
models.itu676.gamma0_exact	285.0	1013.25	7.5	288.15	0.023466	0.023466	-1.83e-10	-0.000
models.itu676.gamma0_exact	286.0	1013.25	7.5	288.15	0.023614	0.023614	2.28e-10	0.000
models.itu676.gamma0_exact	287.0	1013.25	7.5	288.15	0.023762	0.023762	9.60e-11	0.000
models.itu676.gamma0_exact	288.0	1013.25	7.5	288.15	0.023911	0.023911	-5.99e-11	-0.000
models.itu676.gamma0_exact	289.0	1013.25	7.5	288.15	0.024060	0.024060	-2.58e-10	-0.000
models.itu676.gamma0_exact	290.0	1013.25	7.5	288.15	0.024211	0.024211	-8.18e-11	-0.000
models.itu676.gamma0_exact	291.0	1013.25	7.5	288.15	0.024362	0.024362	2.82e-10	0.000
models.itu676.gamma0_exact	292.0	1013.25	7.5	288.15	0.024514	0.024514	8.49e-12	0.000
models.itu676.gamma0_exact	293.0	1013.25	7.5	288.15	0.024667	0.024667	-4.07e-10	-0.000
models.itu676.gamma0_exact	294.0	1013.25	7.5	288.15	0.024820	0.024820	-1.94e-10	-0.000
models.itu676.gamma0_exact	295.0	1013.25	7.5	288.15	0.024975	0.024975	-3.58e-10	-0.000
models.itu676.gamma0_exact	296.0	1013.25	7.5	288.15	0.025130	0.025130	2.73e-10	0.000
models.itu676.gamma0_exact	297.0	1013.25	7.5	288.15	0.025286	0.025286	-2.06e-11	-0.000
models.itu676.gamma0_exact	298.0	1013.25	7.5	288.15	0.025443	0.025443	9.65e-11	0.000
models.itu676.gamma0_exact	299.0	1013.25	7.5	288.15	0.025601	0.025601	-6.27e-11	-0.000
models.itu676.gamma0_exact	300.0	1013.25	7.5	288.15	0.025760	0.025760	-2.82e-10	-0.000
models.itu676.gamma0_exact	301.0	1013.25	7.5	288.15	0.025919	0.025919	4.73e-10	0.000
models.itu676.gamma0_exact	302.0	1013.25	7.5	288.15	0.026080	0.026080	-4.02e-11	-0.000
models.itu676.gamma0_exact	303.0	1013.25	7.5	288.15	0.026241	0.026241	-4.41e-10	-0.000
models.itu676.gamma0_exact	304.0	1013.25	7.5	288.15	0.026403	0.026403	1.59e-10	0.000
models.itu676.gamma0_exact	305.0	1013.25	7.5	288.15	0.026567	0.026567	2.86e-11	0.000
models.itu676.gamma0_exact	306.0	1013.25	7.5	288.15	0.026731	0.026731	-3.21e-10	-0.000
models.itu676.gamma0_exact	307.0	1013.25	7.5	288.15	0.026897	0.026897	-2.89e-10	-0.000
models.itu676.gamma0_exact	308.0	1013.25	7.5	288.15	0.027063	0.027063	-3.60e-10	-0.000
models.itu676.gamma0_exact	309.0	1013.25	7.5	288.15	0.027231	0.027231	-2.96e-10	-0.000
models.itu676.gamma0_exact	310.0	1013.25	7.5	288.15	0.027399	0.027399	-3.46e-10	-0.000
models.itu676.gamma0_exact	311.0	1013.25	7.5	288.15	0.027569	0.027569	-4.87e-10	-0.000
models.itu676.gamma0_exact	312.0	1013.25	7.5	288.15	0.027740	0.027740	3.05e-10	0.000
models.itu676.gamma0_exact	313.0	1013.25	7.5	288.15	0.027913	0.027913	-2.39e-10	-0.000
models.itu676.gamma0_exact	314.0	1013.25	7.5	288.15	0.028086	0.028086	-2.38e-11	-0.000
models.itu676.gamma0_exact	315.0	1013.25	7.5	288.15	0.028261	0.028261	2.95e-11	0.000
models.itu676.gamma0_exact	316.0	1013.25	7.5	288.15	0.028437	0.028437	-4.45e-10	-0.000
models.itu676.gamma0_exact	317.0	1013.25	7.5	288.15	0.028615	0.028615	2.53e-10	0.000
models.itu676.gamma0_exact	318.0	1013.25	7.5	288.15	0.028795	0.028795	3.35e-10	0.000
models.itu676.gamma0_exact	319.0	1013.25	7.5	288.15	0.028975	0.028975	-1.08e-10	-0.000
models.itu676.gamma0_exact	320.0	1013.25	7.5	288.15	0.029158	0.029158	1.76e-10	0.000
models.itu676.gamma0_exact	321.0	1013.25	7.5	288.15	0.029342	0.029342	-2.26e-10	-0.000
models.itu676.gamma0_exact	322.0	1013.25	7.5	288.15	0.029528	0.029528	-3.42e-10	-0.000
models.itu676.gamma0_exact	323.0	1013.25	7.5	288.15	0.029716	0.029716	9.63e-11	0.000
models.itu676.gamma0_exact	324.0	1013.25	7.5	288.15	0.029907	0.029907	3.89e-10	0.000
models.itu676.gamma0_exact	325.0	1013.25	7.5	288.15	0.030099	0.030099	4.06e-10	0.000
models.itu676.gamma0_exact	326.0	1013.25	7.5	288.15	0.030294	0.030294	-1.14e-10	-0.000
models.itu676.gamma0_exact	327.0	1013.25	7.5	288.15	0.030491	0.030491	4.47e-10	0.000
models.itu676.gamma0_exact	328.0	1013.25	7.5	288.15	0.030691	0.030691	2.57e-10	0.000
models.itu676.gamma0_exact	329.0	1013.25	7.5	288.15	0.030893	0.030893	2.97e-10	0.000
models.itu676.gamma0_exact	330.0	1013.25	7.5	288.15	0.031099	0.031099	1.19e-10	0.000
models.itu676.gamma0_exact	331.0	1013.25	7.5	288.15	0.031308	0.031308	4.33e-12	0.000
models.itu676.gamma0_exact	332.0	1013.25	7.5	288.15	0.031521	0.031521	3.89e-10	0.000
models.itu676.gamma0_exact	333.0	1013.25	7.5	288.15	0.031738	0.031738	3.79e-10	0.000
models.itu676.gamma0_exact	334.0	1013.25	7.5	288.15	0.031958	0.031958	1.55e-10	0.000
models.itu676.gamma0_exact	335.0	1013.25	7.5	288.15	0.032184	0.032184	-1.20e-11	-0.000
models.itu676.gamma0_exact	336.0	1013.25	7.5	288.15	0.032415	0.032415	-4.58e-10	-0.000
models.itu676.gamma0_exact	337.0	1013.25	7.5	288.15	0.032652	0.032652	-6.69e-12	-0.000
models.itu676.gamma0_exact	338.0	1013.25	7.5	288.15	0.032895	0.032895	4.23e-10	0.000
models.itu676.gamma0_exact	339.0	1013.25	7.5	288.15	0.033145	0.033145	-2.88e-10	-0.000
models.itu676.gamma0_exact	340.0	1013.25	7.5	288.15	0.033403	0.033403	-3.78e-11	-0.000
models.itu676.gamma0_exact	341.0	1013.25	7.5	288.15	0.033670	0.033670	1.26e-10	0.000
models.itu676.gamma0_exact	342.0	1013.25	7.5	288.15	0.033948	0.033948	8.57e-11	0.000
models.itu676.gamma0_exact	343.0	1013.25	7.5	288.15	0.034237	0.034237	-2.13e-10	-0.000
models.itu676.gamma0_exact	344.0	1013.25	7.5	288.15	0.034540	0.034540	1.61e-10	0.000
models.itu676.gamma0_exact	345.0	1013.25	7.5	288.15	0.034859	0.034859	2.94e-10	0.000
models.itu676.gamma0_exact	346.0	1013.25	7.5	288.15	0.035196	0.035196	4.89e-10	0.000
models.itu676.gamma0_exact	347.0	1013.25	7.5	288.15	0.035555	0.035555	1.91e-10	0.000
models.itu676.gamma0_exact	348.0	1013.25	7.5	288.15	0.035939	0.035939	-2.64e-10	-0.000
models.itu676.gamma0_exact	349.0	1013.25	7.5	288.15	0.036354	0.036354	-8.97e-11	-0.000
models.itu676.gamma0_exact	350.0	1013.25	7.5	288.15	0.036806	0.036806	-5.05e-11	-0.000

Function gammaw_exact ¶

The table below contains the results of testing function gammaw_exact. The test cases were extracted from spreadsheet ITURP676-12_gamma.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
f = 12.0  # (GHz)
P = 1013.25  # (hPA)
rho = 7.5  # (g/cm3)
T = 288.15  # (K)

# Make call to test-function gammaw_exact
itur_val = itur.models.itu676.gammaw_exact(f=f, P=P, rho=rho, T=T)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.009535388  # (dB/km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu676.gammaw_exact

ITU-Rpy Function	f (GHz)	P (hPA)	rho (g/cm3)	T (K)	ITU Validation (dB/km)	ITU-Rpy Result (dB/km)	Absolute Error	Relative Error
models.itu676.gammaw_exact	12.0	1013.25	7.5	288.15	0.009535	0.009535	-2.20e-10	-0.000
models.itu676.gammaw_exact	20.0	1013.25	7.5	288.15	0.097047	0.097047	1.85e-10	0.000
models.itu676.gammaw_exact	60.0	1013.25	7.5	288.15	0.154842	0.154842	3.64e-10	0.000
models.itu676.gammaw_exact	90.0	1013.25	7.5	288.15	0.341973	0.341973	-4.22e-10	-0.000
models.itu676.gammaw_exact	130.0	1013.25	7.5	288.15	0.751845	0.751845	3.54e-10	0.000
models.itu676.gammaw_exact	1.0	1013.25	7.5	288.15	0.000051	0.000051	-4.62e-09	-0.009
models.itu676.gammaw_exact	2.0	1013.25	7.5	288.15	0.000204	0.000204	-3.79e-10	-0.000
models.itu676.gammaw_exact	3.0	1013.25	7.5	288.15	0.000463	0.000463	1.44e-10	0.000
models.itu676.gammaw_exact	4.0	1013.25	7.5	288.15	0.000830	0.000830	7.72e-11	0.000
models.itu676.gammaw_exact	5.0	1013.25	7.5	288.15	0.001313	0.001313	7.88e-11	0.000
models.itu676.gammaw_exact	6.0	1013.25	7.5	288.15	0.001922	0.001922	1.96e-10	0.000
models.itu676.gammaw_exact	7.0	1013.25	7.5	288.15	0.002668	0.002668	-4.93e-10	-0.000
models.itu676.gammaw_exact	8.0	1013.25	7.5	288.15	0.003572	0.003572	-4.72e-11	-0.000
models.itu676.gammaw_exact	9.0	1013.25	7.5	288.15	0.004661	0.004661	2.64e-10	0.000
models.itu676.gammaw_exact	10.0	1013.25	7.5	288.15	0.005974	0.005974	-2.45e-10	-0.000
models.itu676.gammaw_exact	11.0	1013.25	7.5	288.15	0.007570	0.007570	2.70e-10	0.000
models.itu676.gammaw_exact	12.0	1013.25	7.5	288.15	0.009535	0.009535	-2.20e-10	-0.000
models.itu676.gammaw_exact	13.0	1013.25	7.5	288.15	0.012005	0.012005	-2.26e-10	-0.000
models.itu676.gammaw_exact	14.0	1013.25	7.5	288.15	0.015192	0.015192	4.73e-10	0.000
models.itu676.gammaw_exact	15.0	1013.25	7.5	288.15	0.019439	0.019439	2.42e-10	0.000
models.itu676.gammaw_exact	16.0	1013.25	7.5	288.15	0.025325	0.025325	-4.09e-11	-0.000
models.itu676.gammaw_exact	17.0	1013.25	7.5	288.15	0.033835	0.033835	-4.35e-10	-0.000
models.itu676.gammaw_exact	18.0	1013.25	7.5	288.15	0.046664	0.046664	4.61e-10	0.000
models.itu676.gammaw_exact	19.0	1013.25	7.5	288.15	0.066575	0.066575	2.14e-10	0.000
models.itu676.gammaw_exact	20.0	1013.25	7.5	288.15	0.097047	0.097047	1.85e-10	0.000
models.itu676.gammaw_exact	21.0	1013.25	7.5	288.15	0.137954	0.137954	6.13e-11	0.000
models.itu676.gammaw_exact	22.0	1013.25	7.5	288.15	0.174207	0.174207	-3.37e-10	-0.000
models.itu676.gammaw_exact	23.0	1013.25	7.5	288.15	0.180442	0.180442	-9.96e-11	-0.000
models.itu676.gammaw_exact	24.0	1013.25	7.5	288.15	0.158525	0.158525	-3.25e-10	-0.000
models.itu676.gammaw_exact	25.0	1013.25	7.5	288.15	0.130730	0.130730	2.96e-11	0.000
models.itu676.gammaw_exact	26.0	1013.25	7.5	288.15	0.108565	0.108565	-2.54e-10	-0.000
models.itu676.gammaw_exact	27.0	1013.25	7.5	288.15	0.093212	0.093212	1.43e-10	0.000
models.itu676.gammaw_exact	28.0	1013.25	7.5	288.15	0.083060	0.083060	-2.54e-10	-0.000
models.itu676.gammaw_exact	29.0	1013.25	7.5	288.15	0.076494	0.076494	4.35e-10	0.000
models.itu676.gammaw_exact	30.0	1013.25	7.5	288.15	0.072375	0.072375	-2.52e-11	-0.000
models.itu676.gammaw_exact	31.0	1013.25	7.5	288.15	0.069951	0.069951	-3.56e-10	-0.000
models.itu676.gammaw_exact	32.0	1013.25	7.5	288.15	0.068735	0.068735	-1.86e-11	-0.000
models.itu676.gammaw_exact	33.0	1013.25	7.5	288.15	0.068407	0.068407	2.34e-10	0.000
models.itu676.gammaw_exact	34.0	1013.25	7.5	288.15	0.068749	0.068749	-2.64e-10	-0.000
models.itu676.gammaw_exact	35.0	1013.25	7.5	288.15	0.069614	0.069614	3.75e-10	0.000
models.itu676.gammaw_exact	36.0	1013.25	7.5	288.15	0.070897	0.070897	4.40e-10	0.000
models.itu676.gammaw_exact	37.0	1013.25	7.5	288.15	0.072522	0.072522	-4.26e-10	-0.000
models.itu676.gammaw_exact	38.0	1013.25	7.5	288.15	0.074435	0.074435	-3.44e-10	-0.000
models.itu676.gammaw_exact	39.0	1013.25	7.5	288.15	0.076594	0.076594	1.88e-10	0.000
models.itu676.gammaw_exact	40.0	1013.25	7.5	288.15	0.078969	0.078969	2.16e-10	0.000
models.itu676.gammaw_exact	41.0	1013.25	7.5	288.15	0.081535	0.081535	3.69e-10	0.000
models.itu676.gammaw_exact	42.0	1013.25	7.5	288.15	0.084275	0.084275	-4.94e-10	-0.000
models.itu676.gammaw_exact	43.0	1013.25	7.5	288.15	0.087173	0.087173	4.52e-10	0.000
models.itu676.gammaw_exact	44.0	1013.25	7.5	288.15	0.090218	0.090218	7.22e-11	0.000
models.itu676.gammaw_exact	45.0	1013.25	7.5	288.15	0.093400	0.093400	-4.64e-10	-0.000
models.itu676.gammaw_exact	46.0	1013.25	7.5	288.15	0.096713	0.096713	-4.14e-10	-0.000
models.itu676.gammaw_exact	47.0	1013.25	7.5	288.15	0.100150	0.100150	-1.40e-10	-0.000
models.itu676.gammaw_exact	48.0	1013.25	7.5	288.15	0.103705	0.103705	3.53e-10	0.000
models.itu676.gammaw_exact	49.0	1013.25	7.5	288.15	0.107376	0.107376	-2.13e-10	-0.000
models.itu676.gammaw_exact	50.0	1013.25	7.5	288.15	0.111159	0.111159	-2.70e-10	-0.000
models.itu676.gammaw_exact	51.0	1013.25	7.5	288.15	0.115050	0.115050	-3.23e-10	-0.000
models.itu676.gammaw_exact	52.0	1013.25	7.5	288.15	0.119049	0.119049	-1.74e-10	-0.000
models.itu676.gammaw_exact	53.0	1013.25	7.5	288.15	0.123153	0.123153	4.02e-10	0.000
models.itu676.gammaw_exact	54.0	1013.25	7.5	288.15	0.127362	0.127362	2.51e-10	0.000
models.itu676.gammaw_exact	55.0	1013.25	7.5	288.15	0.131674	0.131674	3.02e-10	0.000
models.itu676.gammaw_exact	56.0	1013.25	7.5	288.15	0.136092	0.136092	-1.08e-10	-0.000
models.itu676.gammaw_exact	57.0	1013.25	7.5	288.15	0.140614	0.140614	-2.54e-10	-0.000
models.itu676.gammaw_exact	58.0	1013.25	7.5	288.15	0.145243	0.145243	-4.27e-10	-0.000
models.itu676.gammaw_exact	59.0	1013.25	7.5	288.15	0.149984	0.149984	-6.93e-11	-0.000
models.itu676.gammaw_exact	60.0	1013.25	7.5	288.15	0.154842	0.154842	3.64e-10	0.000
models.itu676.gammaw_exact	61.0	1013.25	7.5	288.15	0.159827	0.159827	-3.12e-10	-0.000
models.itu676.gammaw_exact	62.0	1013.25	7.5	288.15	0.164956	0.164956	-1.69e-10	-0.000
models.itu676.gammaw_exact	63.0	1013.25	7.5	288.15	0.170255	0.170255	4.55e-10	0.000
models.itu676.gammaw_exact	64.0	1013.25	7.5	288.15	0.175765	0.175765	4.22e-10	0.000
models.itu676.gammaw_exact	65.0	1013.25	7.5	288.15	0.181535	0.181535	2.23e-10	0.000
models.itu676.gammaw_exact	66.0	1013.25	7.5	288.15	0.187578	0.187578	-1.55e-10	-0.000
models.itu676.gammaw_exact	67.0	1013.25	7.5	288.15	0.193727	0.193727	-4.67e-10	-0.000
models.itu676.gammaw_exact	68.0	1013.25	7.5	288.15	0.199555	0.199555	-2.42e-10	-0.000
models.itu676.gammaw_exact	69.0	1013.25	7.5	288.15	0.204833	0.204833	-2.56e-10	-0.000
models.itu676.gammaw_exact	70.0	1013.25	7.5	288.15	0.209888	0.209888	-3.64e-10	-0.000
models.itu676.gammaw_exact	71.0	1013.25	7.5	288.15	0.215079	0.215079	-3.48e-10	-0.000
models.itu676.gammaw_exact	72.0	1013.25	7.5	288.15	0.220517	0.220517	-7.24e-11	-0.000
models.itu676.gammaw_exact	73.0	1013.25	7.5	288.15	0.226186	0.226186	-4.90e-10	-0.000
models.itu676.gammaw_exact	74.0	1013.25	7.5	288.15	0.232047	0.232047	7.45e-11	0.000
models.itu676.gammaw_exact	75.0	1013.25	7.5	288.15	0.238069	0.238069	7.76e-11	0.000
models.itu676.gammaw_exact	76.0	1013.25	7.5	288.15	0.244231	0.244231	-7.08e-11	-0.000
models.itu676.gammaw_exact	77.0	1013.25	7.5	288.15	0.250518	0.250518	3.58e-10	0.000
models.itu676.gammaw_exact	78.0	1013.25	7.5	288.15	0.256922	0.256922	-6.14e-12	-0.000
models.itu676.gammaw_exact	79.0	1013.25	7.5	288.15	0.263437	0.263437	2.05e-10	0.000
models.itu676.gammaw_exact	80.0	1013.25	7.5	288.15	0.270060	0.270060	4.24e-10	0.000
models.itu676.gammaw_exact	81.0	1013.25	7.5	288.15	0.276788	0.276788	1.85e-10	0.000
models.itu676.gammaw_exact	82.0	1013.25	7.5	288.15	0.283621	0.283621	-4.21e-10	-0.000
models.itu676.gammaw_exact	83.0	1013.25	7.5	288.15	0.290556	0.290556	-2.26e-10	-0.000
models.itu676.gammaw_exact	84.0	1013.25	7.5	288.15	0.297593	0.297593	2.57e-10	0.000
models.itu676.gammaw_exact	85.0	1013.25	7.5	288.15	0.304733	0.304733	1.28e-10	0.000
models.itu676.gammaw_exact	86.0	1013.25	7.5	288.15	0.311975	0.311975	-1.26e-10	-0.000
models.itu676.gammaw_exact	87.0	1013.25	7.5	288.15	0.319320	0.319320	2.86e-10	0.000
models.itu676.gammaw_exact	88.0	1013.25	7.5	288.15	0.326767	0.326767	4.60e-12	0.000
models.itu676.gammaw_exact	89.0	1013.25	7.5	288.15	0.334318	0.334318	2.17e-11	0.000
models.itu676.gammaw_exact	90.0	1013.25	7.5	288.15	0.341973	0.341973	-4.22e-10	-0.000
models.itu676.gammaw_exact	91.0	1013.25	7.5	288.15	0.349733	0.349733	-3.33e-10	-0.000
models.itu676.gammaw_exact	92.0	1013.25	7.5	288.15	0.357598	0.357598	-3.94e-10	-0.000
models.itu676.gammaw_exact	93.0	1013.25	7.5	288.15	0.365570	0.365570	-3.87e-10	-0.000
models.itu676.gammaw_exact	94.0	1013.25	7.5	288.15	0.373648	0.373648	1.10e-11	0.000
models.itu676.gammaw_exact	95.0	1013.25	7.5	288.15	0.381835	0.381835	4.09e-10	0.000
models.itu676.gammaw_exact	96.0	1013.25	7.5	288.15	0.390131	0.390131	5.12e-11	0.000
models.itu676.gammaw_exact	97.0	1013.25	7.5	288.15	0.398538	0.398538	3.53e-10	0.000
models.itu676.gammaw_exact	98.0	1013.25	7.5	288.15	0.407056	0.407056	4.96e-10	0.000
models.itu676.gammaw_exact	99.0	1013.25	7.5	288.15	0.415687	0.415687	-2.06e-10	-0.000
models.itu676.gammaw_exact	100.0	1013.25	7.5	288.15	0.424434	0.424434	3.27e-10	0.000
models.itu676.gammaw_exact	101.0	1013.25	7.5	288.15	0.433296	0.433296	6.22e-11	0.000
models.itu676.gammaw_exact	102.0	1013.25	7.5	288.15	0.442276	0.442276	2.72e-10	0.000
models.itu676.gammaw_exact	103.0	1013.25	7.5	288.15	0.451376	0.451376	4.62e-10	0.000
models.itu676.gammaw_exact	104.0	1013.25	7.5	288.15	0.460599	0.460599	5.67e-11	0.000
models.itu676.gammaw_exact	105.0	1013.25	7.5	288.15	0.469945	0.469945	-3.83e-10	-0.000
models.itu676.gammaw_exact	106.0	1013.25	7.5	288.15	0.479419	0.479419	-5.01e-11	-0.000
models.itu676.gammaw_exact	107.0	1013.25	7.5	288.15	0.489024	0.489024	4.91e-10	0.000
models.itu676.gammaw_exact	108.0	1013.25	7.5	288.15	0.498762	0.498762	-3.38e-10	-0.000
models.itu676.gammaw_exact	109.0	1013.25	7.5	288.15	0.508640	0.508640	-4.67e-10	-0.000
models.itu676.gammaw_exact	110.0	1013.25	7.5	288.15	0.518661	0.518661	4.78e-10	0.000
models.itu676.gammaw_exact	111.0	1013.25	7.5	288.15	0.528835	0.528835	-2.82e-10	-0.000
models.itu676.gammaw_exact	112.0	1013.25	7.5	288.15	0.539170	0.539170	4.53e-11	0.000
models.itu676.gammaw_exact	113.0	1013.25	7.5	288.15	0.549681	0.549681	1.80e-10	0.000
models.itu676.gammaw_exact	114.0	1013.25	7.5	288.15	0.560388	0.560388	2.29e-10	0.000
models.itu676.gammaw_exact	115.0	1013.25	7.5	288.15	0.571322	0.571322	4.10e-10	0.000
models.itu676.gammaw_exact	116.0	1013.25	7.5	288.15	0.582526	0.582526	-3.57e-10	-0.000
models.itu676.gammaw_exact	117.0	1013.25	7.5	288.15	0.594053	0.594053	-2.83e-11	-0.000
models.itu676.gammaw_exact	118.0	1013.25	7.5	288.15	0.605922	0.605922	4.06e-10	0.000
models.itu676.gammaw_exact	119.0	1013.25	7.5	288.15	0.617993	0.617993	5.33e-11	0.000
models.itu676.gammaw_exact	120.0	1013.25	7.5	288.15	0.629861	0.629861	7.98e-11	0.000
models.itu676.gammaw_exact	121.0	1013.25	7.5	288.15	0.641222	0.641222	-3.07e-10	-0.000
models.itu676.gammaw_exact	122.0	1013.25	7.5	288.15	0.652345	0.652345	6.55e-11	0.000
models.itu676.gammaw_exact	123.0	1013.25	7.5	288.15	0.663647	0.663647	1.99e-10	0.000
models.itu676.gammaw_exact	124.0	1013.25	7.5	288.15	0.675301	0.675301	-3.65e-10	-0.000
models.itu676.gammaw_exact	125.0	1013.25	7.5	288.15	0.687313	0.687313	-4.22e-10	-0.000
models.itu676.gammaw_exact	126.0	1013.25	7.5	288.15	0.699649	0.699649	-3.95e-10	-0.000
models.itu676.gammaw_exact	127.0	1013.25	7.5	288.15	0.712282	0.712282	4.27e-10	0.000
models.itu676.gammaw_exact	128.0	1013.25	7.5	288.15	0.725196	0.725196	3.58e-10	0.000
models.itu676.gammaw_exact	129.0	1013.25	7.5	288.15	0.738383	0.738383	1.72e-10	0.000
models.itu676.gammaw_exact	130.0	1013.25	7.5	288.15	0.751845	0.751845	3.54e-10	0.000
models.itu676.gammaw_exact	131.0	1013.25	7.5	288.15	0.765585	0.765585	2.65e-10	0.000
models.itu676.gammaw_exact	132.0	1013.25	7.5	288.15	0.779613	0.779613	1.24e-10	0.000
models.itu676.gammaw_exact	133.0	1013.25	7.5	288.15	0.793940	0.793940	-4.15e-10	-0.000
models.itu676.gammaw_exact	134.0	1013.25	7.5	288.15	0.808581	0.808581	3.94e-10	0.000
models.itu676.gammaw_exact	135.0	1013.25	7.5	288.15	0.823553	0.823553	-2.68e-10	-0.000
models.itu676.gammaw_exact	136.0	1013.25	7.5	288.15	0.838874	0.838874	-1.93e-10	-0.000
models.itu676.gammaw_exact	137.0	1013.25	7.5	288.15	0.854566	0.854566	-2.96e-10	-0.000
models.itu676.gammaw_exact	138.0	1013.25	7.5	288.15	0.870653	0.870653	1.26e-10	0.000
models.itu676.gammaw_exact	139.0	1013.25	7.5	288.15	0.887164	0.887164	-4.46e-10	-0.000
models.itu676.gammaw_exact	140.0	1013.25	7.5	288.15	0.904129	0.904129	3.74e-10	0.000
models.itu676.gammaw_exact	141.0	1013.25	7.5	288.15	0.921583	0.921583	-2.84e-10	-0.000
models.itu676.gammaw_exact	142.0	1013.25	7.5	288.15	0.939565	0.939565	-1.83e-11	-0.000
models.itu676.gammaw_exact	143.0	1013.25	7.5	288.15	0.958119	0.958119	-3.78e-10	-0.000
models.itu676.gammaw_exact	144.0	1013.25	7.5	288.15	0.977295	0.977295	4.40e-11	0.000
models.itu676.gammaw_exact	145.0	1013.25	7.5	288.15	0.997150	0.997150	2.56e-10	0.000
models.itu676.gammaw_exact	146.0	1013.25	7.5	288.15	1.017749	1.017749	-4.84e-10	-0.000
models.itu676.gammaw_exact	147.0	1013.25	7.5	288.15	1.039164	1.039164	4.42e-10	0.000
models.itu676.gammaw_exact	148.0	1013.25	7.5	288.15	1.061480	1.061480	1.75e-10	0.000
models.itu676.gammaw_exact	149.0	1013.25	7.5	288.15	1.084794	1.084794	-4.40e-10	-0.000
models.itu676.gammaw_exact	150.0	1013.25	7.5	288.15	1.109218	1.109218	7.61e-11	0.000
models.itu676.gammaw_exact	151.0	1013.25	7.5	288.15	1.134879	1.134879	-1.31e-11	-0.000
models.itu676.gammaw_exact	152.0	1013.25	7.5	288.15	1.161928	1.161928	3.59e-10	0.000
models.itu676.gammaw_exact	153.0	1013.25	7.5	288.15	1.190540	1.190540	-2.91e-10	-0.000
models.itu676.gammaw_exact	154.0	1013.25	7.5	288.15	1.220920	1.220920	-2.04e-10	-0.000
models.itu676.gammaw_exact	155.0	1013.25	7.5	288.15	1.253309	1.253309	-1.63e-10	-0.000
models.itu676.gammaw_exact	156.0	1013.25	7.5	288.15	1.287995	1.287995	4.17e-10	0.000
models.itu676.gammaw_exact	157.0	1013.25	7.5	288.15	1.325319	1.325319	7.23e-11	0.000
models.itu676.gammaw_exact	158.0	1013.25	7.5	288.15	1.365690	1.365690	-1.20e-10	-0.000
models.itu676.gammaw_exact	159.0	1013.25	7.5	288.15	1.409602	1.409602	-2.34e-10	-0.000
models.itu676.gammaw_exact	160.0	1013.25	7.5	288.15	1.457655	1.457655	1.63e-11	0.000
models.itu676.gammaw_exact	161.0	1013.25	7.5	288.15	1.510584	1.510584	1.88e-10	0.000
models.itu676.gammaw_exact	162.0	1013.25	7.5	288.15	1.569294	1.569294	-4.93e-10	-0.000
models.itu676.gammaw_exact	163.0	1013.25	7.5	288.15	1.634915	1.634915	1.21e-11	0.000
models.itu676.gammaw_exact	164.0	1013.25	7.5	288.15	1.708862	1.708862	2.32e-10	0.000
models.itu676.gammaw_exact	165.0	1013.25	7.5	288.15	1.792933	1.792933	-5.35e-11	-0.000
models.itu676.gammaw_exact	166.0	1013.25	7.5	288.15	1.889435	1.889435	-1.80e-10	-0.000
models.itu676.gammaw_exact	167.0	1013.25	7.5	288.15	2.001362	2.001362	-7.31e-11	-0.000
models.itu676.gammaw_exact	168.0	1013.25	7.5	288.15	2.132651	2.132651	-4.20e-10	-0.000
models.itu676.gammaw_exact	169.0	1013.25	7.5	288.15	2.288555	2.288555	-2.68e-10	-0.000
models.itu676.gammaw_exact	170.0	1013.25	7.5	288.15	2.476195	2.476195	6.14e-11	0.000
models.itu676.gammaw_exact	171.0	1013.25	7.5	288.15	2.705381	2.705381	-3.20e-10	-0.000
models.itu676.gammaw_exact	172.0	1013.25	7.5	288.15	2.989890	2.989890	4.12e-10	0.000
models.itu676.gammaw_exact	173.0	1013.25	7.5	288.15	3.349462	3.349462	2.25e-10	0.000
models.itu676.gammaw_exact	174.0	1013.25	7.5	288.15	3.812987	3.812987	4.21e-10	0.000
models.itu676.gammaw_exact	175.0	1013.25	7.5	288.15	4.423707	4.423707	8.91e-11	0.000
models.itu676.gammaw_exact	176.0	1013.25	7.5	288.15	5.247745	5.247745	4.84e-10	0.000
models.itu676.gammaw_exact	177.0	1013.25	7.5	288.15	6.387977	6.387977	-2.37e-10	-0.000
models.itu676.gammaw_exact	178.0	1013.25	7.5	288.15	8.005218	8.005218	-1.66e-10	-0.000
models.itu676.gammaw_exact	179.0	1013.25	7.5	288.15	10.343578	10.343578	5.71e-11	0.000
models.itu676.gammaw_exact	180.0	1013.25	7.5	288.15	13.728458	13.728458	-4.43e-09	-0.000
models.itu676.gammaw_exact	181.0	1013.25	7.5	288.15	18.399102	18.399102	-5.25e-10	-0.000
models.itu676.gammaw_exact	182.0	1013.25	7.5	288.15	23.830459	23.830459	2.78e-09	0.000
models.itu676.gammaw_exact	183.0	1013.25	7.5	288.15	27.665008	27.665008	-4.17e-09	-0.000
models.itu676.gammaw_exact	184.0	1013.25	7.5	288.15	27.024838	27.024838	-4.47e-09	-0.000
models.itu676.gammaw_exact	185.0	1013.25	7.5	288.15	22.603713	22.603713	2.25e-09	0.000
models.itu676.gammaw_exact	186.0	1013.25	7.5	288.15	17.480866	17.480866	2.32e-09	0.000
models.itu676.gammaw_exact	187.0	1013.25	7.5	288.15	13.340008	13.340008	3.99e-09	0.000
models.itu676.gammaw_exact	188.0	1013.25	7.5	288.15	10.372561	10.372561	-5.48e-11	-0.000
models.itu676.gammaw_exact	189.0	1013.25	7.5	288.15	8.306314	8.306314	2.15e-10	0.000
models.itu676.gammaw_exact	190.0	1013.25	7.5	288.15	6.858142	6.858142	-3.79e-10	-0.000
models.itu676.gammaw_exact	191.0	1013.25	7.5	288.15	5.823870	5.823870	-2.31e-10	-0.000
models.itu676.gammaw_exact	192.0	1013.25	7.5	288.15	5.068900	5.068900	-3.02e-11	-0.000
models.itu676.gammaw_exact	193.0	1013.25	7.5	288.15	4.506007	4.506007	-1.51e-10	-0.000
models.itu676.gammaw_exact	194.0	1013.25	7.5	288.15	4.078184	4.078184	-8.23e-11	-0.000
models.itu676.gammaw_exact	195.0	1013.25	7.5	288.15	3.747495	3.747495	-4.54e-10	-0.000
models.itu676.gammaw_exact	196.0	1013.25	7.5	288.15	3.488154	3.488154	-4.79e-10	-0.000
models.itu676.gammaw_exact	197.0	1013.25	7.5	288.15	3.282257	3.282257	4.74e-10	0.000
models.itu676.gammaw_exact	198.0	1013.25	7.5	288.15	3.117111	3.117111	-2.60e-10	-0.000
models.itu676.gammaw_exact	199.0	1013.25	7.5	288.15	2.983548	2.983548	-2.23e-10	-0.000
models.itu676.gammaw_exact	200.0	1013.25	7.5	288.15	2.874824	2.874824	8.12e-11	0.000
models.itu676.gammaw_exact	201.0	1013.25	7.5	288.15	2.785901	2.785901	3.81e-10	0.000
models.itu676.gammaw_exact	202.0	1013.25	7.5	288.15	2.712953	2.712953	-1.21e-10	-0.000
models.itu676.gammaw_exact	203.0	1013.25	7.5	288.15	2.653040	2.653040	-1.88e-10	-0.000
models.itu676.gammaw_exact	204.0	1013.25	7.5	288.15	2.603874	2.603874	4.56e-10	0.000
models.itu676.gammaw_exact	205.0	1013.25	7.5	288.15	2.563651	2.563651	-1.71e-11	-0.000
models.itu676.gammaw_exact	206.0	1013.25	7.5	288.15	2.530936	2.530936	4.55e-10	0.000
models.itu676.gammaw_exact	207.0	1013.25	7.5	288.15	2.504575	2.504575	2.43e-10	0.000
models.itu676.gammaw_exact	208.0	1013.25	7.5	288.15	2.483635	2.483635	2.58e-11	0.000
models.itu676.gammaw_exact	209.0	1013.25	7.5	288.15	2.467350	2.467350	-4.26e-10	-0.000
models.itu676.gammaw_exact	210.0	1013.25	7.5	288.15	2.455091	2.455091	-2.25e-10	-0.000
models.itu676.gammaw_exact	211.0	1013.25	7.5	288.15	2.446336	2.446336	2.47e-10	0.000
models.itu676.gammaw_exact	212.0	1013.25	7.5	288.15	2.440648	2.440648	4.97e-10	0.000
models.itu676.gammaw_exact	213.0	1013.25	7.5	288.15	2.437662	2.437662	2.95e-10	0.000
models.itu676.gammaw_exact	214.0	1013.25	7.5	288.15	2.437068	2.437068	-4.04e-10	-0.000
models.itu676.gammaw_exact	215.0	1013.25	7.5	288.15	2.438603	2.438603	-2.70e-10	-0.000
models.itu676.gammaw_exact	216.0	1013.25	7.5	288.15	2.442042	2.442042	2.94e-10	0.000
models.itu676.gammaw_exact	217.0	1013.25	7.5	288.15	2.447193	2.447193	1.67e-10	0.000
models.itu676.gammaw_exact	218.0	1013.25	7.5	288.15	2.453891	2.453891	7.04e-11	0.000
models.itu676.gammaw_exact	219.0	1013.25	7.5	288.15	2.461991	2.461991	-3.51e-10	-0.000
models.itu676.gammaw_exact	220.0	1013.25	7.5	288.15	2.471371	2.471371	4.15e-10	0.000
models.itu676.gammaw_exact	221.0	1013.25	7.5	288.15	2.481920	2.481920	1.09e-10	0.000
models.itu676.gammaw_exact	222.0	1013.25	7.5	288.15	2.493546	2.493546	-2.36e-10	-0.000
models.itu676.gammaw_exact	223.0	1013.25	7.5	288.15	2.506164	2.506164	-2.80e-11	-0.000
models.itu676.gammaw_exact	224.0	1013.25	7.5	288.15	2.519702	2.519702	4.07e-10	0.000
models.itu676.gammaw_exact	225.0	1013.25	7.5	288.15	2.534095	2.534095	-1.60e-10	-0.000
models.itu676.gammaw_exact	226.0	1013.25	7.5	288.15	2.549288	2.549288	-2.85e-10	-0.000
models.itu676.gammaw_exact	227.0	1013.25	7.5	288.15	2.565229	2.565229	-2.27e-10	-0.000
models.itu676.gammaw_exact	228.0	1013.25	7.5	288.15	2.581875	2.581875	-2.25e-10	-0.000
models.itu676.gammaw_exact	229.0	1013.25	7.5	288.15	2.599186	2.599186	4.31e-10	0.000
models.itu676.gammaw_exact	230.0	1013.25	7.5	288.15	2.617127	2.617127	5.74e-12	0.000
models.itu676.gammaw_exact	231.0	1013.25	7.5	288.15	2.635666	2.635666	2.87e-10	0.000
models.itu676.gammaw_exact	232.0	1013.25	7.5	288.15	2.654776	2.654776	-3.44e-10	-0.000
models.itu676.gammaw_exact	233.0	1013.25	7.5	288.15	2.674433	2.674433	-4.42e-10	-0.000
models.itu676.gammaw_exact	234.0	1013.25	7.5	288.15	2.694613	2.694613	-2.74e-10	-0.000
models.itu676.gammaw_exact	235.0	1013.25	7.5	288.15	2.715299	2.715299	-5.39e-11	-0.000
models.itu676.gammaw_exact	236.0	1013.25	7.5	288.15	2.736471	2.736471	-1.84e-10	-0.000
models.itu676.gammaw_exact	237.0	1013.25	7.5	288.15	2.758115	2.758115	-5.87e-11	-0.000
models.itu676.gammaw_exact	238.0	1013.25	7.5	288.15	2.780217	2.780217	8.95e-11	0.000
models.itu676.gammaw_exact	239.0	1013.25	7.5	288.15	2.802764	2.802764	1.40e-10	0.000
models.itu676.gammaw_exact	240.0	1013.25	7.5	288.15	2.825747	2.825747	4.40e-11	0.000
models.itu676.gammaw_exact	241.0	1013.25	7.5	288.15	2.849156	2.849156	-4.81e-10	-0.000
models.itu676.gammaw_exact	242.0	1013.25	7.5	288.15	2.872982	2.872982	-2.08e-10	-0.000
models.itu676.gammaw_exact	243.0	1013.25	7.5	288.15	2.897219	2.897219	3.41e-10	0.000
models.itu676.gammaw_exact	244.0	1013.25	7.5	288.15	2.921860	2.921860	2.94e-10	0.000
models.itu676.gammaw_exact	245.0	1013.25	7.5	288.15	2.946902	2.946902	-8.64e-11	-0.000
models.itu676.gammaw_exact	246.0	1013.25	7.5	288.15	2.972339	2.972339	3.36e-10	0.000
models.itu676.gammaw_exact	247.0	1013.25	7.5	288.15	2.998168	2.998168	-3.91e-10	-0.000
models.itu676.gammaw_exact	248.0	1013.25	7.5	288.15	3.024387	3.024387	-1.28e-10	-0.000
models.itu676.gammaw_exact	249.0	1013.25	7.5	288.15	3.050995	3.050995	4.00e-10	0.000
models.itu676.gammaw_exact	250.0	1013.25	7.5	288.15	3.077990	3.077990	1.21e-10	0.000
models.itu676.gammaw_exact	251.0	1013.25	7.5	288.15	3.105372	3.105372	1.04e-10	0.000
models.itu676.gammaw_exact	252.0	1013.25	7.5	288.15	3.133141	3.133141	4.16e-10	0.000
models.itu676.gammaw_exact	253.0	1013.25	7.5	288.15	3.161300	3.161300	-3.25e-10	-0.000
models.itu676.gammaw_exact	254.0	1013.25	7.5	288.15	3.189848	3.189848	-4.54e-10	-0.000
models.itu676.gammaw_exact	255.0	1013.25	7.5	288.15	3.218790	3.218790	3.39e-10	0.000
models.itu676.gammaw_exact	256.0	1013.25	7.5	288.15	3.248127	3.248127	-1.86e-10	-0.000
models.itu676.gammaw_exact	257.0	1013.25	7.5	288.15	3.277865	3.277865	2.51e-10	0.000
models.itu676.gammaw_exact	258.0	1013.25	7.5	288.15	3.308006	3.308006	-2.83e-10	-0.000
models.itu676.gammaw_exact	259.0	1013.25	7.5	288.15	3.338557	3.338557	4.77e-10	0.000
models.itu676.gammaw_exact	260.0	1013.25	7.5	288.15	3.369523	3.369523	3.59e-10	0.000
models.itu676.gammaw_exact	261.0	1013.25	7.5	288.15	3.400910	3.400910	-1.47e-10	-0.000
models.itu676.gammaw_exact	262.0	1013.25	7.5	288.15	3.432726	3.432726	-3.72e-10	-0.000
models.itu676.gammaw_exact	263.0	1013.25	7.5	288.15	3.464979	3.464979	8.01e-11	0.000
models.itu676.gammaw_exact	264.0	1013.25	7.5	288.15	3.497677	3.497677	4.26e-10	0.000
models.itu676.gammaw_exact	265.0	1013.25	7.5	288.15	3.530831	3.530831	-2.51e-10	-0.000
models.itu676.gammaw_exact	266.0	1013.25	7.5	288.15	3.564451	3.564451	3.07e-10	0.000
models.itu676.gammaw_exact	267.0	1013.25	7.5	288.15	3.598549	3.598549	2.46e-10	0.000
models.itu676.gammaw_exact	268.0	1013.25	7.5	288.15	3.633137	3.633137	-2.46e-10	-0.000
models.itu676.gammaw_exact	269.0	1013.25	7.5	288.15	3.668230	3.668230	4.61e-10	0.000
models.itu676.gammaw_exact	270.0	1013.25	7.5	288.15	3.703843	3.703843	-2.70e-10	-0.000
models.itu676.gammaw_exact	271.0	1013.25	7.5	288.15	3.739992	3.739992	2.09e-10	0.000
models.itu676.gammaw_exact	272.0	1013.25	7.5	288.15	3.776695	3.776695	-2.73e-10	-0.000
models.itu676.gammaw_exact	273.0	1013.25	7.5	288.15	3.813971	3.813971	3.02e-10	0.000
models.itu676.gammaw_exact	274.0	1013.25	7.5	288.15	3.851844	3.851844	-4.14e-10	-0.000
models.itu676.gammaw_exact	275.0	1013.25	7.5	288.15	3.890335	3.890335	-4.01e-10	-0.000
models.itu676.gammaw_exact	276.0	1013.25	7.5	288.15	3.929471	3.929471	3.41e-11	0.000
models.itu676.gammaw_exact	277.0	1013.25	7.5	288.15	3.969279	3.969279	-3.16e-10	-0.000
models.itu676.gammaw_exact	278.0	1013.25	7.5	288.15	4.009791	4.009791	-3.08e-10	-0.000
models.itu676.gammaw_exact	279.0	1013.25	7.5	288.15	4.051041	4.051041	3.06e-10	0.000
models.itu676.gammaw_exact	280.0	1013.25	7.5	288.15	4.093065	4.093065	-4.81e-10	-0.000
models.itu676.gammaw_exact	281.0	1013.25	7.5	288.15	4.135906	4.135906	4.53e-10	0.000
models.itu676.gammaw_exact	282.0	1013.25	7.5	288.15	4.179609	4.179609	3.91e-10	0.000
models.itu676.gammaw_exact	283.0	1013.25	7.5	288.15	4.224225	4.224225	3.01e-11	0.000
models.itu676.gammaw_exact	284.0	1013.25	7.5	288.15	4.269810	4.269810	-4.46e-10	-0.000
models.itu676.gammaw_exact	285.0	1013.25	7.5	288.15	4.316428	4.316428	4.53e-10	0.000
models.itu676.gammaw_exact	286.0	1013.25	7.5	288.15	4.364148	4.364148	4.08e-10	0.000
models.itu676.gammaw_exact	287.0	1013.25	7.5	288.15	4.413050	4.413050	-2.78e-10	-0.000
models.itu676.gammaw_exact	288.0	1013.25	7.5	288.15	4.463223	4.463223	3.86e-10	0.000
models.itu676.gammaw_exact	289.0	1013.25	7.5	288.15	4.514767	4.514767	4.41e-10	0.000
models.itu676.gammaw_exact	290.0	1013.25	7.5	288.15	4.567797	4.567797	1.79e-10	0.000
models.itu676.gammaw_exact	291.0	1013.25	7.5	288.15	4.622443	4.622443	8.59e-11	0.000
models.itu676.gammaw_exact	292.0	1013.25	7.5	288.15	4.678854	4.678854	6.54e-11	0.000
models.itu676.gammaw_exact	293.0	1013.25	7.5	288.15	4.737200	4.737200	-1.58e-10	-0.000
models.itu676.gammaw_exact	294.0	1013.25	7.5	288.15	4.797679	4.797679	2.73e-10	0.000
models.itu676.gammaw_exact	295.0	1013.25	7.5	288.15	4.860520	4.860520	-4.60e-10	-0.000
models.itu676.gammaw_exact	296.0	1013.25	7.5	288.15	4.925989	4.925989	-4.83e-10	-0.000
models.itu676.gammaw_exact	297.0	1013.25	7.5	288.15	4.994400	4.994400	-1.51e-10	-0.000
models.itu676.gammaw_exact	298.0	1013.25	7.5	288.15	5.066121	5.066121	-3.86e-10	-0.000
models.itu676.gammaw_exact	299.0	1013.25	7.5	288.15	5.141589	5.141589	5.29e-11	0.000
models.itu676.gammaw_exact	300.0	1013.25	7.5	288.15	5.221329	5.221329	-1.05e-10	-0.000
models.itu676.gammaw_exact	301.0	1013.25	7.5	288.15	5.305969	5.305969	3.57e-10	0.000
models.itu676.gammaw_exact	302.0	1013.25	7.5	288.15	5.396270	5.396270	-2.00e-10	-0.000
models.itu676.gammaw_exact	303.0	1013.25	7.5	288.15	5.493166	5.493166	-5.73e-11	-0.000
models.itu676.gammaw_exact	304.0	1013.25	7.5	288.15	5.597805	5.597805	-2.14e-10	-0.000
models.itu676.gammaw_exact	305.0	1013.25	7.5	288.15	5.711616	5.711616	-1.55e-10	-0.000
models.itu676.gammaw_exact	306.0	1013.25	7.5	288.15	5.836397	5.836397	3.92e-10	0.000
models.itu676.gammaw_exact	307.0	1013.25	7.5	288.15	5.974431	5.974431	4.62e-10	0.000
models.itu676.gammaw_exact	308.0	1013.25	7.5	288.15	6.128660	6.128660	-3.56e-10	-0.000
models.itu676.gammaw_exact	309.0	1013.25	7.5	288.15	6.302915	6.302915	-4.74e-10	-0.000
models.itu676.gammaw_exact	310.0	1013.25	7.5	288.15	6.502269	6.502269	1.25e-10	0.000
models.itu676.gammaw_exact	311.0	1013.25	7.5	288.15	6.733539	6.733539	-5.26e-11	-0.000
models.itu676.gammaw_exact	312.0	1013.25	7.5	288.15	7.006054	7.006054	-1.15e-10	-0.000
models.itu676.gammaw_exact	313.0	1013.25	7.5	288.15	7.332839	7.332839	1.12e-10	0.000
models.itu676.gammaw_exact	314.0	1013.25	7.5	288.15	7.732474	7.732474	-2.90e-10	-0.000
models.itu676.gammaw_exact	315.0	1013.25	7.5	288.15	8.232112	8.232112	3.91e-10	0.000
models.itu676.gammaw_exact	316.0	1013.25	7.5	288.15	8.872465	8.872465	-3.46e-11	-0.000
models.itu676.gammaw_exact	317.0	1013.25	7.5	288.15	9.716073	9.716073	7.11e-12	0.000
models.itu676.gammaw_exact	318.0	1013.25	7.5	288.15	10.860390	10.860390	1.40e-09	0.000
models.itu676.gammaw_exact	319.0	1013.25	7.5	288.15	12.453804	12.453804	-3.75e-10	-0.000
models.itu676.gammaw_exact	320.0	1013.25	7.5	288.15	14.694418	14.694418	-2.06e-09	-0.000
models.itu676.gammaw_exact	321.0	1013.25	7.5	288.15	17.779900	17.779900	-2.11e-09	-0.000
models.itu676.gammaw_exact	322.0	1013.25	7.5	288.15	21.958394	21.958394	1.44e-09	0.000
models.itu676.gammaw_exact	323.0	1013.25	7.5	288.15	27.584296	27.584296	1.32e-09	0.000
models.itu676.gammaw_exact	324.0	1013.25	7.5	288.15	33.980828	33.980828	4.39e-09	0.000
models.itu676.gammaw_exact	325.0	1013.25	7.5	288.15	37.862111	37.862111	-1.15e-09	-0.000
models.itu676.gammaw_exact	326.0	1013.25	7.5	288.15	35.904757	35.904757	4.96e-09	0.000
models.itu676.gammaw_exact	327.0	1013.25	7.5	288.15	29.947920	29.947920	1.76e-09	0.000
models.itu676.gammaw_exact	328.0	1013.25	7.5	288.15	23.872443	23.872443	3.09e-09	0.000
models.itu676.gammaw_exact	329.0	1013.25	7.5	288.15	19.264553	19.264553	3.08e-09	0.000
models.itu676.gammaw_exact	330.0	1013.25	7.5	288.15	16.084329	16.084329	3.44e-09	0.000
models.itu676.gammaw_exact	331.0	1013.25	7.5	288.15	13.929485	13.929485	-3.04e-09	-0.000
models.itu676.gammaw_exact	332.0	1013.25	7.5	288.15	12.457413	12.457413	4.69e-09	0.000
models.itu676.gammaw_exact	333.0	1013.25	7.5	288.15	11.436764	11.436764	3.81e-09	0.000
models.itu676.gammaw_exact	334.0	1013.25	7.5	288.15	10.719742	10.719742	-2.03e-09	-0.000
models.itu676.gammaw_exact	335.0	1013.25	7.5	288.15	10.211790	10.211790	8.85e-10	0.000
models.itu676.gammaw_exact	336.0	1013.25	7.5	288.15	9.850283	9.850283	2.91e-11	0.000
models.itu676.gammaw_exact	337.0	1013.25	7.5	288.15	9.592983	9.592983	1.44e-10	0.000
models.itu676.gammaw_exact	338.0	1013.25	7.5	288.15	9.413703	9.413703	-1.76e-10	-0.000
models.itu676.gammaw_exact	339.0	1013.25	7.5	288.15	9.296113	9.296113	3.43e-10	0.000
models.itu676.gammaw_exact	340.0	1013.25	7.5	288.15	9.228131	9.228131	-3.86e-10	-0.000
models.itu676.gammaw_exact	341.0	1013.25	7.5	288.15	9.200536	9.200536	1.75e-10	0.000
models.itu676.gammaw_exact	342.0	1013.25	7.5	288.15	9.206573	9.206573	2.20e-10	0.000
models.itu676.gammaw_exact	343.0	1013.25	7.5	288.15	9.241420	9.241420	-1.59e-10	-0.000
models.itu676.gammaw_exact	344.0	1013.25	7.5	288.15	9.301710	9.301710	1.14e-11	0.000
models.itu676.gammaw_exact	345.0	1013.25	7.5	288.15	9.385171	9.385171	4.16e-10	0.000
models.itu676.gammaw_exact	346.0	1013.25	7.5	288.15	9.490383	9.490383	-4.91e-10	-0.000
models.itu676.gammaw_exact	347.0	1013.25	7.5	288.15	9.616617	9.616617	2.70e-10	0.000
models.itu676.gammaw_exact	348.0	1013.25	7.5	288.15	9.763734	9.763734	-2.46e-10	-0.000
models.itu676.gammaw_exact	349.0	1013.25	7.5	288.15	9.932122	9.932122	-2.47e-10	-0.000
models.itu676.gammaw_exact	350.0	1013.25	7.5	288.15	10.122673	10.122673	4.87e-10	0.000

Function zenit_water_vapour_attenuation ¶

The table below contains the results of testing function zenit_water_vapour_attenuation. The test cases were extracted from spreadsheet ITURP676-12_zenith_attenuation.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 0.0  #  (°N)
lon = 0.0  # (°E)
p = 0.0  # (hPa)
f = 14.25  # (GHz)
h = 0.031382984  # (km)
V_t = 33.72946527  #  (kg/m2)

# Make call to test-function zenit_water_vapour_attenuation
itur_val = itur.models.itu676.zenit_water_vapour_attenuation(lat=lat, lon=lon, p=p, f=f, h=h, V_t=V_t)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.070935174  # (dB/km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu676.zenit_water_vapour_attenuation

ITU-Rpy Function	f (GHz)	h (km)	V_t (kg/m2)	ITU Validation (dB/km)	ITU-Rpy Result (dB/km)	Absolute Error	Relative Error
models.itu676.zenit_water_vapour_attenuation	14.25	0.031383	33.729465	0.070935	0.070935	1.14e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.046123	36.048109	0.076415	0.076415	4.43e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	37.955600	0.080993	0.080993	2.82e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.031383	35.725554	0.075647	0.075647	9.46e-11	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.046123	37.513014	0.079925	0.079925	-1.76e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	40.511906	0.087230	0.087230	-4.29e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.031383	37.295953	0.079403	0.079403	-3.61e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.046123	38.329647	0.081899	0.081899	4.16e-11	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	42.210224	0.091438	0.091438	-3.44e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.031383	38.244078	0.081691	0.081691	-3.08e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.046123	39.051281	0.083652	0.083652	4.58e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	43.410461	0.094442	0.094442	4.65e-11	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.031383	33.729465	0.334146	0.334146	-1.16e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.046123	36.048109	0.358893	0.358893	1.68e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	37.955600	0.383457	0.383457	-2.03e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.031383	35.725554	0.356150	0.356150	2.66e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.046123	37.513014	0.375233	0.375233	-2.68e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	40.511906	0.412697	0.412697	-4.18e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.031383	37.295953	0.373674	0.373674	-3.85e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.046123	38.329647	0.384412	0.384412	-3.14e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	42.210224	0.432403	0.432403	3.39e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.031383	38.244078	0.384346	0.384346	2.10e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.046123	39.051281	0.392567	0.392567	2.46e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	43.410461	0.446465	0.446465	3.82e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	49.513184	0.110117	0.110117	-6.24e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.008617	57.497546	0.131634	0.131634	4.11e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	52.007390	0.116716	0.116716	9.22e-11	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.008617	59.222332	0.136433	0.136433	1.12e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	53.485111	0.120678	0.120678	2.87e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.008617	60.314611	0.139500	0.139500	1.37e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.000000	54.631809	0.123780	0.123780	-3.43e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.008617	61.161560	0.141893	0.141893	-3.81e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	49.513184	0.519700	0.519700	-2.51e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.008617	57.497546	0.618607	0.618607	-4.10e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	52.007390	0.550470	0.550470	-1.29e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.008617	59.222332	0.640866	0.640866	4.06e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	53.485111	0.568929	0.568929	-8.01e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.008617	60.314611	0.655082	0.655082	1.67e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.000000	54.631809	0.583371	0.583371	-2.92e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.008617	61.161560	0.666170	0.666170	-2.41e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.209384	70.591345	0.169409	0.169409	-5.27e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.051251	62.584697	0.145943	0.145943	2.77e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	2.539862	25.925669	0.053180	0.053180	-2.29e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.209384	72.477248	0.175105	0.175105	-1.35e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.051251	63.593435	0.148835	0.148835	-2.53e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	2.539862	26.641637	0.054765	0.054765	-3.49e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.209384	73.574292	0.178448	0.178448	4.80e-10	0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.051251	64.336356	0.150977	0.150977	-1.79e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	2.539862	27.087127	0.055756	0.055756	-2.94e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.209384	74.502008	0.181291	0.181291	-2.89e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	0.051251	64.946376	0.152744	0.152744	-1.11e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	14.25	2.539862	27.511871	0.056704	0.056704	-2.94e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.209384	70.591345	0.771408	0.771408	3.93e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.051251	62.584697	0.680016	0.680016	4.93e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	2.539862	25.925669	0.192886	0.192886	2.83e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.209384	72.477248	0.796963	0.796963	-4.93e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.051251	63.593435	0.693311	0.693311	3.27e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	2.539862	26.641637	0.198603	0.198603	8.58e-11	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.209384	73.574292	0.811954	0.811954	4.39e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.051251	64.336356	0.703154	0.703154	1.90e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	2.539862	27.087127	0.202174	0.202174	3.83e-10	0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.209384	74.502008	0.824702	0.824702	-2.21e-10	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	0.051251	64.946376	0.711268	0.711268	-7.39e-11	-0.000
models.itu676.zenit_water_vapour_attenuation	29.00	2.539862	27.511871	0.205590	0.205590	1.52e-10	0.000

Validation results ITU-R P.836-6 ¶

This page contains the validation examples for Recommendation ITU-R P.836-6: Water vapour: surface density and total columnar content.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.836-6
- Function surface_water_vapour_density
- Function total_water_vapour_content

Function surface_water_vapour_density ¶

The table below contains the results of testing function surface_water_vapour_density. The test cases were extracted from spreadsheet ITURP836-6_surface_water_vapour_density_annual.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)
alt = 0.05125146  # (km)
p = 0.1  # (%)

# Make call to test-function surface_water_vapour_density
itur_val = itur.models.itu836.surface_water_vapour_density(lat=lat, lon=lon, alt=alt, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 24.32302408  # (g/m3)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu836.surface_water_vapour_density

ITU-Rpy Function	lat (°N)	lon (°E)	alt (km)	p (%)	ITU Validation (g/m3)	ITU-Rpy Result (g/m3)	Absolute Error	Relative Error
models.itu836.surface_water_vapour_density	3.133	101.70	0.051251	0.10	24.323024	24.323024	3.06e-08	0.000
models.itu836.surface_water_vapour_density	3.133	101.70	0.051251	0.15	24.195729	24.195729	3.52e-08	0.000
models.itu836.surface_water_vapour_density	3.133	101.70	0.051251	0.30	23.952441	23.952441	3.28e-08	0.000
models.itu836.surface_water_vapour_density	3.133	101.70	0.051251	0.35	23.893346	23.893346	2.71e-08	0.000
models.itu836.surface_water_vapour_density	22.900	-43.23	0.000000	0.10	21.591649	21.591649	-2.67e-09	-0.000
models.itu836.surface_water_vapour_density	22.900	-43.23	0.000000	0.15	21.461644	21.461644	6.24e-10	0.000
models.itu836.surface_water_vapour_density	22.900	-43.23	0.000000	0.30	21.247533	21.247533	4.81e-09	0.000
models.itu836.surface_water_vapour_density	22.900	-43.23	0.000000	0.35	21.186760	21.186760	-1.08e-09	-0.000
models.itu836.surface_water_vapour_density	23.000	30.00	0.187594	0.10	11.983147	11.983148	-2.61e-09	-0.000
models.itu836.surface_water_vapour_density	23.000	30.00	0.187594	0.15	11.721333	11.721333	2.28e-09	0.000
models.itu836.surface_water_vapour_density	23.000	30.00	0.187594	0.30	11.229887	11.229887	-6.12e-10	-0.000
models.itu836.surface_water_vapour_density	23.000	30.00	0.187594	0.35	11.117501	11.117501	-4.93e-09	-0.000
models.itu836.surface_water_vapour_density	25.780	-80.22	0.008617	0.10	23.448289	23.448289	-4.73e-09	-0.000
models.itu836.surface_water_vapour_density	25.780	-80.22	0.008617	0.15	23.281960	23.281960	-4.93e-09	-0.000
models.itu836.surface_water_vapour_density	25.780	-80.22	0.008617	0.30	23.000809	23.000809	-1.48e-09	-0.000
models.itu836.surface_water_vapour_density	25.780	-80.22	0.008617	0.35	22.937809	22.937809	-3.99e-09	-0.000
models.itu836.surface_water_vapour_density	28.717	77.30	0.209384	0.10	26.009841	26.009841	1.07e-08	0.000
models.itu836.surface_water_vapour_density	28.717	77.30	0.209384	0.15	25.769706	25.769706	3.15e-09	0.000
models.itu836.surface_water_vapour_density	28.717	77.30	0.209384	0.30	25.398943	25.398943	8.78e-09	0.000
models.itu836.surface_water_vapour_density	28.717	77.30	0.209384	0.35	25.314770	25.314770	9.35e-09	0.000
models.itu836.surface_water_vapour_density	33.940	18.43	0.000000	0.10	24.001565	24.001565	-3.08e-09	-0.000
models.itu836.surface_water_vapour_density	33.940	18.43	0.000000	0.15	23.859876	23.859876	-4.09e-09	-0.000
models.itu836.surface_water_vapour_density	33.940	18.43	0.000000	0.30	23.514645	23.514645	3.03e-09	0.000
models.itu836.surface_water_vapour_density	33.940	18.43	0.000000	0.35	23.419545	23.419545	-3.93e-09	-0.000
models.itu836.surface_water_vapour_density	41.900	12.49	0.046123	0.10	19.851665	19.851665	1.54e-08	0.000
models.itu836.surface_water_vapour_density	41.900	12.49	0.046123	0.15	19.556349	19.556349	1.09e-08	0.000
models.itu836.surface_water_vapour_density	41.900	12.49	0.046123	0.30	19.092542	19.092542	1.56e-08	0.000
models.itu836.surface_water_vapour_density	41.900	12.49	0.046123	0.35	18.988935	18.988935	1.70e-08	0.000
models.itu836.surface_water_vapour_density	51.500	-0.14	0.031383	0.10	15.370307	15.370307	-1.86e-08	-0.000
models.itu836.surface_water_vapour_density	51.500	-0.14	0.031383	0.15	15.177703	15.177703	-1.26e-08	-0.000
models.itu836.surface_water_vapour_density	51.500	-0.14	0.031383	0.30	14.783593	14.783593	-1.66e-08	-0.000
models.itu836.surface_water_vapour_density	51.500	-0.14	0.031383	0.35	14.671618	14.671618	-1.81e-08	-0.000

Function total_water_vapour_content ¶

The table below contains the results of testing function total_water_vapour_content. The test cases were extracted from spreadsheet ITURP836-6_total_water_vapour_content_annual.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)
alt = 0.05125146  # (km)
p = 0.1  # (%)

# Make call to test-function total_water_vapour_content
itur_val = itur.models.itu836.total_water_vapour_content(lat=lat, lon=lon, alt=alt, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 65.92042976  # (kg/m2)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu836.total_water_vapour_content

ITU-Rpy Function	lat (°N)	lon (°E)	alt (km)	p (%)	ITU Validation (kg/m2)	ITU-Rpy Result (kg/m2)	Absolute Error	Relative Error
models.itu836.total_water_vapour_content	3.133	101.70	0.051251	0.10	65.920430	65.920430	8.01e-08	0.000
models.itu836.total_water_vapour_content	3.133	101.70	0.051251	0.15	65.350645	65.350645	8.86e-08	0.000
models.itu836.total_water_vapour_content	3.133	101.70	0.051251	0.30	64.336356	64.336356	8.42e-08	0.000
models.itu836.total_water_vapour_content	3.133	101.70	0.051251	0.35	64.112166	64.112166	8.34e-08	0.000
models.itu836.total_water_vapour_content	22.900	-43.23	0.000000	0.10	56.387886	56.387886	2.81e-09	0.000
models.itu836.total_water_vapour_content	22.900	-43.23	0.000000	0.15	55.360647	55.360647	3.97e-09	0.000
models.itu836.total_water_vapour_content	22.900	-43.23	0.000000	0.30	53.485111	53.485111	-7.41e-10	-0.000
models.itu836.total_water_vapour_content	22.900	-43.23	0.000000	0.35	53.039183	53.039183	-1.65e-09	-0.000
models.itu836.total_water_vapour_content	23.000	30.00	0.187594	0.10	38.801076	38.801076	3.39e-09	0.000
models.itu836.total_water_vapour_content	23.000	30.00	0.187594	0.15	37.545803	37.545803	1.80e-09	0.000
models.itu836.total_water_vapour_content	23.000	30.00	0.187594	0.30	34.965412	34.965412	2.92e-09	0.000
models.itu836.total_water_vapour_content	23.000	30.00	0.187594	0.35	34.401687	34.401687	-4.85e-09	-0.000
models.itu836.total_water_vapour_content	25.780	-80.22	0.008617	0.10	62.684831	62.684831	-3.05e-09	-0.000
models.itu836.total_water_vapour_content	25.780	-80.22	0.008617	0.15	61.793775	61.793775	4.01e-09	0.000
models.itu836.total_water_vapour_content	25.780	-80.22	0.008617	0.30	60.314611	60.314611	-7.41e-10	-0.000
models.itu836.total_water_vapour_content	25.780	-80.22	0.008617	0.35	59.984996	59.984996	3.17e-09	0.000
models.itu836.total_water_vapour_content	28.717	77.30	0.209384	0.10	75.614529	75.614529	2.00e-08	0.000
models.itu836.total_water_vapour_content	28.717	77.30	0.209384	0.15	74.963746	74.963746	2.42e-08	0.000
models.itu836.total_water_vapour_content	28.717	77.30	0.209384	0.30	73.574292	73.574292	2.03e-08	0.000
models.itu836.total_water_vapour_content	28.717	77.30	0.209384	0.35	73.243239	73.243239	2.15e-08	0.000
models.itu836.total_water_vapour_content	33.940	18.43	0.000000	0.10	45.198952	45.198952	-4.96e-09	-0.000
models.itu836.total_water_vapour_content	33.940	18.43	0.000000	0.15	44.152752	44.152752	2.59e-10	0.000
models.itu836.total_water_vapour_content	33.940	18.43	0.000000	0.30	42.210224	42.210224	-1.94e-09	-0.000
models.itu836.total_water_vapour_content	33.940	18.43	0.000000	0.35	41.697726	41.697726	-3.38e-09	-0.000
models.itu836.total_water_vapour_content	41.900	12.49	0.046123	0.10	40.071283	40.071283	2.20e-08	0.000
models.itu836.total_water_vapour_content	41.900	12.49	0.046123	0.15	39.474620	39.474620	2.39e-08	0.000
models.itu836.total_water_vapour_content	41.900	12.49	0.046123	0.30	38.329647	38.329647	2.46e-08	0.000
models.itu836.total_water_vapour_content	41.900	12.49	0.046123	0.35	38.083213	38.083213	2.15e-08	0.000
models.itu836.total_water_vapour_content	51.500	-0.14	0.031383	0.10	39.642498	39.642498	-4.76e-08	-0.000
models.itu836.total_water_vapour_content	51.500	-0.14	0.031383	0.15	38.824475	38.824475	-4.33e-08	-0.000
models.itu836.total_water_vapour_content	51.500	-0.14	0.031383	0.30	37.295953	37.295953	-4.50e-08	-0.000
models.itu836.total_water_vapour_content	51.500	-0.14	0.031383	0.35	36.822058	36.822058	-4.19e-08	-0.000

Validation results ITU-R P.837-7 ¶

This page contains the validation examples for Recommendation ITU-R P.837-7: Characteristics of precipitation for propagation modelling.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.837-7

Function rainfall_rate ¶

The table below contains the results of testing function rainfall_rate. The test cases were extracted from spreadsheet ITURP837-7_rainfall_rate.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)
p = 0.01  # (%)

# Make call to test-function rainfall_rate
itur_val = itur.models.itu837.rainfall_rate(lat=lat, lon=lon, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 99.15117186  # (mm/hr)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu837.rainfall_rate

ITU-Rpy Function	lat (°N)	lon (°E)	p (%)	ITU Validation (mm/hr)	ITU-Rpy Result (mm/hr)	Absolute Error	Relative Error
models.itu837.rainfall_rate	3.133	101.70	0.01	99.151172	99.148114	3.06e-03	0.003
models.itu837.rainfall_rate	3.133	101.70	0.10	34.647981	34.648009	-2.74e-05	-0.000
models.itu837.rainfall_rate	3.133	101.70	0.15	27.763620	27.763657	-3.72e-05	-0.000
models.itu837.rainfall_rate	3.133	101.70	0.30	18.262544	18.262543	8.56e-07	0.000
models.itu837.rainfall_rate	3.133	101.70	0.35	16.494932	16.494967	-3.48e-05	-0.000
models.itu837.rainfall_rate	22.900	-43.23	0.01	50.639304	50.639304	-2.13e-14	-0.000
models.itu837.rainfall_rate	22.900	-43.23	0.10	14.589630	14.589645	-1.46e-05	-0.000
models.itu837.rainfall_rate	22.900	-43.23	0.15	11.005101	11.005096	4.68e-06	0.000
models.itu837.rainfall_rate	22.900	-43.23	0.30	6.237962	6.238021	-5.86e-05	-0.001
models.itu837.rainfall_rate	22.900	-43.23	0.35	5.382396	5.382411	-1.48e-05	-0.000
models.itu837.rainfall_rate	23.000	30.00	0.01	0.000000	0.000000	0.00e+00	0.000
models.itu837.rainfall_rate	23.000	30.00	0.10	0.000000	0.000000	0.00e+00	0.000
models.itu837.rainfall_rate	23.000	30.00	0.15	0.000000	0.000000	0.00e+00	0.000
models.itu837.rainfall_rate	23.000	30.00	0.30	0.000000	0.000000	0.00e+00	0.000
models.itu837.rainfall_rate	23.000	30.00	0.35	0.000000	0.000000	0.00e+00	0.000
models.itu837.rainfall_rate	25.780	-80.22	0.01	78.299499	78.298293	1.21e-03	0.002
models.itu837.rainfall_rate	25.780	-80.22	0.10	25.338881	25.338747	1.35e-04	0.001
models.itu837.rainfall_rate	25.780	-80.22	0.15	19.866836	19.866847	-1.07e-05	-0.000
models.itu837.rainfall_rate	25.780	-80.22	0.30	12.436766	12.436785	-1.93e-05	-0.000
models.itu837.rainfall_rate	25.780	-80.22	0.35	11.075661	11.075653	8.12e-06	0.000
models.itu837.rainfall_rate	28.717	77.30	0.01	63.618888	63.597246	2.16e-02	0.034
models.itu837.rainfall_rate	28.717	77.30	0.10	16.538574	16.538493	8.04e-05	0.000
models.itu837.rainfall_rate	28.717	77.30	0.15	12.046514	12.046479	3.49e-05	0.000
models.itu837.rainfall_rate	28.717	77.30	0.30	6.216006	6.215967	3.87e-05	0.001
models.itu837.rainfall_rate	28.717	77.30	0.35	5.196098	5.196132	-3.41e-05	-0.001
models.itu837.rainfall_rate	33.940	18.43	0.01	27.135868	27.134966	9.02e-04	0.003
models.itu837.rainfall_rate	33.940	18.43	0.10	7.431932	7.431947	-1.49e-05	-0.000
models.itu837.rainfall_rate	33.940	18.43	0.15	5.530319	5.530275	4.32e-05	0.001
models.itu837.rainfall_rate	33.940	18.43	0.30	3.035066	3.035061	4.97e-06	0.000
models.itu837.rainfall_rate	33.940	18.43	0.35	2.592761	2.592780	-1.91e-05	-0.001
models.itu837.rainfall_rate	41.900	12.49	0.01	33.936232	33.936232	-7.11e-15	-0.000
models.itu837.rainfall_rate	41.900	12.49	0.10	11.197983	11.197917	6.59e-05	0.001
models.itu837.rainfall_rate	41.900	12.49	0.15	8.884726	8.884735	-9.69e-06	-0.000
models.itu837.rainfall_rate	41.900	12.49	0.30	5.753563	5.753540	2.30e-05	0.000
models.itu837.rainfall_rate	41.900	12.49	0.35	5.180588	5.180605	-1.65e-05	-0.000
models.itu837.rainfall_rate	51.500	-0.14	0.01	26.480520	26.480520	-3.55e-15	-0.000
models.itu837.rainfall_rate	51.500	-0.14	0.10	8.992471	8.992486	-1.45e-05	-0.000
models.itu837.rainfall_rate	51.500	-0.14	0.15	7.173693	7.173695	-1.55e-06	-0.000
models.itu837.rainfall_rate	51.500	-0.14	0.30	4.690336	4.690312	2.44e-05	0.001
models.itu837.rainfall_rate	51.500	-0.14	0.35	4.232586	4.232578	8.03e-06	0.000

Function rainfall_rate ¶

The table below contains the results of testing function rainfall_rate. The test cases were extracted from spreadsheet ITURP837-7_rainfall_rate_R001.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)
p = 0.01  # (%)

# Make call to test-function rainfall_rate
itur_val = itur.models.itu837.rainfall_rate(lat=lat, lon=lon, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 99.1481136  # (mm/hr)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu837.rainfall_rate

ITU-Rpy Function	lat (°N)	lon (°E)	p (%)	ITU Validation (mm/hr)	ITU-Rpy Result (mm/hr)	Absolute Error	Relative Error
models.itu837.rainfall_rate	3.133	101.70	0.01	99.148114	99.148114	2.84e-14	0.000
models.itu837.rainfall_rate	22.900	-43.23	0.01	50.639304	50.639304	-2.13e-14	-0.000
models.itu837.rainfall_rate	23.000	30.00	0.01	0.000000	0.000000	0.00e+00	0.000
models.itu837.rainfall_rate	25.780	-80.22	0.01	78.298293	78.298293	-1.42e-13	-0.000
models.itu837.rainfall_rate	28.717	77.30	0.01	63.597246	63.597246	7.11e-14	0.000
models.itu837.rainfall_rate	33.940	18.43	0.01	27.134966	27.134966	3.55e-15	0.000
models.itu837.rainfall_rate	41.900	12.49	0.01	33.936232	33.936232	-7.11e-15	-0.000
models.itu837.rainfall_rate	51.500	-0.14	0.01	26.480520	26.480520	-3.55e-15	-0.000

Function rainfall_probability ¶

The table below contains the results of testing function rainfall_probability. The test cases were extracted from spreadsheet ITURP837-7_rainfall_rate_probability.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)

# Make call to test-function rainfall_probability
itur_val = itur.models.itu837.rainfall_probability(lat=lat, lon=lon)

# Compute error with respect to value in ITU example file
ITU_example_val = 4.53654368  # (%)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu837.rainfall_probability

ITU-Rpy Function	lat (°N)	lon (°E)	ITU Validation (%)	ITU-Rpy Result (%)	Absolute Error	Relative Error
models.itu837.rainfall_probability	3.133	101.70	4.536544	4.536544	-4.98e-09	-0.000
models.itu837.rainfall_probability	22.900	-43.23	1.417734	1.417734	1.05e-09	0.000
models.itu837.rainfall_probability	23.000	30.00	0.000519	0.000519	-1.14e-09	-0.000
models.itu837.rainfall_probability	25.780	-80.22	2.907852	2.907852	-4.20e-10	-0.000
models.itu837.rainfall_probability	28.717	77.30	1.070894	1.070894	-3.49e-09	-0.000
models.itu837.rainfall_probability	33.940	18.43	1.275674	1.275674	9.22e-10	0.000
models.itu837.rainfall_probability	41.900	12.49	5.269719	5.269719	-1.87e-09	-0.000
models.itu837.rainfall_probability	51.500	-0.14	5.361510	5.361510	-3.71e-09	-0.000

Validation results ITU-R P.838-3 ¶

This page contains the validation examples for Recommendation ITU-R P.838-3: Specific attenuation model for rain for use in prediction methods.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.838-3
- Function rain_specific_attenuation

Function rain_specific_attenuation ¶

The table below contains the results of testing function rain_specific_attenuation. The test cases were extracted from spreadsheet ITURP838-3_rain_specific_attenuation.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
el = 31.07699124  # (°)
f = 14.25  # (GHz)
R = 26.48052  # (mm/h)
tau = 0.0  #  t(°)

# Make call to test-function rain_specific_attenuation
itur_val = itur.models.itu838.rain_specific_attenuation(el=el, f=f, R=R, tau=tau)

# Compute error with respect to value in ITU example file
ITU_example_val = 1.58130839  # (dB/km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu838.rain_specific_attenuation

ITU-Rpy Function	el (°)	f (GHz)	R (mm/h)	tau t(°)	ITU Validation (dB/km)	ITU-Rpy Result (dB/km)	Absolute Error	Relative Error
models.itu838.rain_specific_attenuation	31.076991	14.25	26.480520	0.0	1.581308	1.581308	-3.66e-09	-0.000
models.itu838.rain_specific_attenuation	40.232036	14.25	33.936232	0.0	2.061732	2.061732	-1.25e-09	-0.000
models.itu838.rain_specific_attenuation	46.359693	14.25	27.135868	0.0	1.592084	1.592084	6.90e-10	0.000
models.itu838.rain_specific_attenuation	31.076991	14.25	26.480520	0.0	1.581308	1.581308	-3.66e-09	-0.000
models.itu838.rain_specific_attenuation	40.232036	14.25	33.936232	0.0	2.061732	2.061732	-1.25e-09	-0.000
models.itu838.rain_specific_attenuation	46.359693	14.25	27.135868	0.0	1.592084	1.592084	6.90e-10	0.000
models.itu838.rain_specific_attenuation	31.076991	14.25	26.480520	0.0	1.581308	1.581308	-3.66e-09	-0.000
models.itu838.rain_specific_attenuation	40.232036	14.25	33.936232	0.0	2.061732	2.061732	-1.25e-09	-0.000
models.itu838.rain_specific_attenuation	46.359693	14.25	27.135868	0.0	1.592084	1.592084	6.90e-10	0.000
models.itu838.rain_specific_attenuation	31.076991	14.25	26.480520	0.0	1.581308	1.581308	-3.66e-09	-0.000
models.itu838.rain_specific_attenuation	40.232036	14.25	33.936232	0.0	2.061732	2.061732	-1.25e-09	-0.000
models.itu838.rain_specific_attenuation	46.359693	14.25	27.135868	0.0	1.592084	1.592084	6.90e-10	0.000
models.itu838.rain_specific_attenuation	31.076991	29.00	26.480520	0.0	5.021802	5.021802	9.37e-10	0.000
models.itu838.rain_specific_attenuation	40.232036	29.00	33.936232	0.0	6.278460	6.278460	3.08e-10	0.000
models.itu838.rain_specific_attenuation	46.359693	29.00	27.135868	0.0	5.031355	5.031355	-3.63e-09	-0.000
models.itu838.rain_specific_attenuation	31.076991	29.00	26.480520	0.0	5.021802	5.021802	9.37e-10	0.000
models.itu838.rain_specific_attenuation	40.232036	29.00	33.936232	0.0	6.278460	6.278460	3.08e-10	0.000
models.itu838.rain_specific_attenuation	46.359693	29.00	27.135868	0.0	5.031355	5.031355	-3.63e-09	-0.000
models.itu838.rain_specific_attenuation	31.076991	29.00	26.480520	0.0	5.021802	5.021802	9.37e-10	0.000
models.itu838.rain_specific_attenuation	40.232036	29.00	33.936232	0.0	6.278460	6.278460	3.08e-10	0.000
models.itu838.rain_specific_attenuation	46.359693	29.00	27.135868	0.0	5.031355	5.031355	-3.63e-09	-0.000
models.itu838.rain_specific_attenuation	31.076991	29.00	26.480520	0.0	5.021802	5.021802	9.37e-10	0.000
models.itu838.rain_specific_attenuation	40.232036	29.00	33.936232	0.0	6.278460	6.278460	3.08e-10	0.000
models.itu838.rain_specific_attenuation	46.359693	29.00	27.135868	0.0	5.031355	5.031355	-3.63e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	14.25	50.639304	0.0	3.321396	3.321396	2.32e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	14.25	78.299499	0.0	5.115035	5.115035	-3.10e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	14.25	50.639304	0.0	3.321396	3.321396	2.32e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	14.25	78.299499	0.0	5.115035	5.115035	-3.10e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	14.25	50.639304	0.0	3.321396	3.321396	2.32e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	14.25	78.299499	0.0	5.115035	5.115035	-3.10e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	14.25	50.639304	0.0	3.321396	3.321396	2.32e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	14.25	78.299499	0.0	5.115035	5.115035	-3.10e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	29.00	50.639304	0.0	9.424302	9.424302	1.87e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	29.00	78.299499	0.0	13.592901	13.592901	-3.74e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	29.00	50.639304	0.0	9.424302	9.424302	1.87e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	29.00	78.299499	0.0	13.592901	13.592901	-3.74e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	29.00	50.639304	0.0	9.424302	9.424302	1.87e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	29.00	78.299499	0.0	13.592901	13.592901	-3.74e-09	-0.000
models.itu838.rain_specific_attenuation	22.278335	29.00	50.639304	0.0	9.424302	9.424302	1.87e-09	0.000
models.itu838.rain_specific_attenuation	52.678985	29.00	78.299499	0.0	13.592901	13.592901	-3.74e-09	-0.000
models.itu838.rain_specific_attenuation	48.241171	14.25	63.626681	90.0	3.729013	3.729013	4.82e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	14.25	99.135590	90.0	6.340646	6.340646	-2.31e-10	-0.000
models.itu838.rain_specific_attenuation	20.143358	14.25	42.910072	90.0	2.350323	2.350323	-3.09e-09	-0.000
models.itu838.rain_specific_attenuation	48.241171	14.25	63.626681	90.0	3.729013	3.729013	4.82e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	14.25	99.135590	90.0	6.340646	6.340646	-2.31e-10	-0.000
models.itu838.rain_specific_attenuation	20.143358	14.25	42.910072	90.0	2.350323	2.350323	-3.09e-09	-0.000
models.itu838.rain_specific_attenuation	48.241171	14.25	63.626681	90.0	3.729013	3.729013	4.82e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	14.25	99.135590	90.0	6.340646	6.340646	-2.31e-10	-0.000
models.itu838.rain_specific_attenuation	20.143358	14.25	42.910072	90.0	2.350323	2.350323	-3.09e-09	-0.000
models.itu838.rain_specific_attenuation	48.241171	14.25	63.626681	90.0	3.729013	3.729013	4.82e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	14.25	99.135590	90.0	6.340646	6.340646	-2.31e-10	-0.000
models.itu838.rain_specific_attenuation	20.143358	14.25	42.910072	90.0	2.350323	2.350323	-3.09e-09	-0.000
models.itu838.rain_specific_attenuation	48.241171	29.00	63.626681	90.0	10.286992	10.286992	3.92e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	29.00	99.135590	90.0	16.318369	16.318369	-2.17e-09	-0.000
models.itu838.rain_specific_attenuation	20.143358	29.00	42.910072	90.0	6.833646	6.833646	2.75e-09	0.000
models.itu838.rain_specific_attenuation	48.241171	29.00	63.626681	90.0	10.286992	10.286992	3.92e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	29.00	99.135590	90.0	16.318369	16.318369	-2.17e-09	-0.000
models.itu838.rain_specific_attenuation	20.143358	29.00	42.910072	90.0	6.833646	6.833646	2.75e-09	0.000
models.itu838.rain_specific_attenuation	48.241171	29.00	63.626681	90.0	10.286992	10.286992	3.92e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	29.00	99.135590	90.0	16.318369	16.318369	-2.17e-09	-0.000
models.itu838.rain_specific_attenuation	20.143358	29.00	42.910072	90.0	6.833646	6.833646	2.75e-09	0.000
models.itu838.rain_specific_attenuation	48.241171	29.00	63.626681	90.0	10.286992	10.286992	3.92e-09	0.000
models.itu838.rain_specific_attenuation	85.804596	29.00	99.135590	90.0	16.318369	16.318369	-2.17e-09	-0.000
models.itu838.rain_specific_attenuation	20.143358	29.00	42.910072	90.0	6.833646	6.833646	2.75e-09	0.000

Validation results ITU-R P.839-4 ¶

This page contains the validation examples for Recommendation ITU-R P.839-4: Rain height model for prediction methods.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.839-4
- Function isoterm_0
- Function rain_height

Function isoterm_0 ¶

The table below contains the results of testing function isoterm_0. The test cases were extracted from spreadsheet ITURP839-4_rain_height.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)

# Make call to test-function isoterm_0
itur_val = itur.models.itu839.isoterm_0(lat=lat, lon=lon)

# Compute error with respect to value in ITU example file
ITU_example_val = 4.5979744  # (km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu839.isoterm_0

ITU-Rpy Function	lat (°N)	lon (°E)	ITU Validation (km)	ITU-Rpy Result (km)	Absolute Error	Relative Error
models.itu839.isoterm_0	3.133	101.70	4.597974	4.597974	8.88e-16	0.000
models.itu839.isoterm_0	22.900	-43.23	3.798779	3.798779	3.33e-09	0.000
models.itu839.isoterm_0	23.000	30.00	4.168000	4.168000	0.00e+00	0.000
models.itu839.isoterm_0	25.780	-80.22	4.209461	4.209461	-3.33e-09	-0.000
models.itu839.isoterm_0	28.717	77.30	4.898204	4.898204	-4.44e-09	-0.000
models.itu839.isoterm_0	33.940	18.43	2.203303	2.203303	4.44e-09	0.000
models.itu839.isoterm_0	41.900	12.49	2.687493	2.687493	-3.33e-09	-0.000
models.itu839.isoterm_0	51.500	-0.14	2.092733	2.092733	-3.33e-09	-0.000

Function rain_height ¶

The table below contains the results of testing function rain_height. The test cases were extracted from spreadsheet ITURP839-4_rain_height.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)

# Make call to test-function rain_height
itur_val = itur.models.itu839.rain_height(lat=lat, lon=lon)

# Compute error with respect to value in ITU example file
ITU_example_val = 4.9579744  # (km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu839.rain_height

ITU-Rpy Function	lat (°N)	lon (°E)	ITU Validation (km)	ITU-Rpy Result (km)	Absolute Error	Relative Error
models.itu839.rain_height	3.133	101.70	4.957974	4.957974	8.88e-16	0.000
models.itu839.rain_height	22.900	-43.23	4.158779	4.158779	3.33e-09	0.000
models.itu839.rain_height	23.000	30.00	4.528000	4.528000	-8.88e-16	-0.000
models.itu839.rain_height	25.780	-80.22	4.569461	4.569461	-3.33e-09	-0.000
models.itu839.rain_height	28.717	77.30	5.258204	5.258204	-4.44e-09	-0.000
models.itu839.rain_height	33.940	18.43	2.563303	2.563303	4.44e-09	0.000
models.itu839.rain_height	41.900	12.49	3.047493	3.047493	-3.33e-09	-0.000
models.itu839.rain_height	51.500	-0.14	2.452733	2.452733	-3.33e-09	-0.000

Validation results ITU-R P.840-8 ¶

This page contains the validation examples for Recommendation ITU-R P.840-8: Attenuation due to clouds and fog.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.840-8
- Function cloud_attenuation
- Function columnar_content_reduced_liquid

Function cloud_attenuation ¶

The table below contains the results of testing function cloud_attenuation. The test cases were extracted from spreadsheet ITURP840-8_cloud_attenuation.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 51.5  #  (°N)
lon = -0.14  # (°E)
f = 14.25  # (GHz)
el = 31.07699124  # (°)
p = 1.0  # (%)

# Make call to test-function cloud_attenuation
itur_val = itur.models.itu840.cloud_attenuation(lat=lat, lon=lon, f=f, el=el, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.45516982  # (dB)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu840.cloud_attenuation

ITU-Rpy Function	lat (°N)	lon (°E)	f (GHz)	el (°)	p (%)	ITU Validation (dB)	ITU-Rpy Result (dB)	Absolute Error	Relative Error
models.itu840.cloud_attenuation	51.50	-0.14	14.25	31.076991	1.0	0.455170	0.455170	-4.40e-09	-0.000
models.itu840.cloud_attenuation	41.90	12.49	14.25	40.232036	1.0	0.263385	0.263385	-1.16e-09	-0.000
models.itu840.cloud_attenuation	33.94	18.43	14.25	46.359693	1.0	0.187794	0.187794	1.50e-09	0.000
models.itu840.cloud_attenuation	51.50	-0.14	14.25	31.076991	0.5	0.534571	0.534571	1.78e-09	0.000
models.itu840.cloud_attenuation	41.90	12.49	14.25	40.232036	0.5	0.323039	0.323039	4.83e-09	0.000
models.itu840.cloud_attenuation	33.94	18.43	14.25	46.359693	0.5	0.239238	0.239238	3.21e-09	0.000
models.itu840.cloud_attenuation	51.50	-0.14	14.25	31.076991	0.3	0.591367	0.591367	-4.62e-10	-0.000
models.itu840.cloud_attenuation	41.90	12.49	14.25	40.232036	0.3	0.361147	0.361147	-3.25e-09	-0.000
models.itu840.cloud_attenuation	33.94	18.43	14.25	46.359693	0.3	0.287229	0.287229	-2.87e-09	-0.000
models.itu840.cloud_attenuation	51.50	-0.14	14.25	31.076991	0.2	0.624487	0.624487	1.33e-09	0.000
models.itu840.cloud_attenuation	41.90	12.49	14.25	40.232036	0.2	0.388640	0.388640	-3.95e-09	-0.000
models.itu840.cloud_attenuation	33.94	18.43	14.25	46.359693	0.2	0.320697	0.320697	1.84e-09	0.000
models.itu840.cloud_attenuation	51.50	-0.14	29.00	31.076991	1.0	1.772469	1.772469	-2.75e-09	-0.000
models.itu840.cloud_attenuation	41.90	12.49	29.00	40.232036	1.0	1.025643	1.025643	-3.42e-09	-0.000
models.itu840.cloud_attenuation	33.94	18.43	29.00	46.359693	1.0	0.731286	0.731286	3.54e-09	0.000
models.itu840.cloud_attenuation	51.50	-0.14	29.00	31.076991	0.5	2.081665	2.081665	1.03e-09	0.000
models.itu840.cloud_attenuation	41.90	12.49	29.00	40.232036	0.5	1.257939	1.257939	2.14e-09	0.000
models.itu840.cloud_attenuation	33.94	18.43	29.00	46.359693	0.5	0.931612	0.931612	1.90e-09	0.000
models.itu840.cloud_attenuation	51.50	-0.14	29.00	31.076991	0.3	2.302831	2.302831	-2.05e-10	-0.000
models.itu840.cloud_attenuation	41.90	12.49	29.00	40.232036	0.3	1.406338	1.406338	4.26e-11	0.000
models.itu840.cloud_attenuation	33.94	18.43	29.00	46.359693	0.3	1.118494	1.118494	-4.99e-09	-0.000
models.itu840.cloud_attenuation	51.50	-0.14	29.00	31.076991	0.2	2.431803	2.431803	-3.04e-09	-0.000
models.itu840.cloud_attenuation	41.90	12.49	29.00	40.232036	0.2	1.513395	1.513395	4.73e-09	0.000
models.itu840.cloud_attenuation	33.94	18.43	29.00	46.359693	0.2	1.248820	1.248820	-1.27e-09	-0.000
models.itu840.cloud_attenuation	22.90	-43.23	14.25	22.278335	1.0	0.541833	0.541833	-1.26e-09	-0.000
models.itu840.cloud_attenuation	25.78	-80.22	14.25	52.678985	1.0	0.533175	0.533175	-2.16e-09	-0.000
models.itu840.cloud_attenuation	22.90	-43.23	14.25	22.278335	0.5	0.857468	0.857468	-4.54e-09	-0.000
models.itu840.cloud_attenuation	25.78	-80.22	14.25	52.678985	0.5	0.639566	0.639566	-3.07e-09	-0.000
models.itu840.cloud_attenuation	22.90	-43.23	14.25	22.278335	0.3	1.056028	1.056028	-2.62e-09	-0.000
models.itu840.cloud_attenuation	25.78	-80.22	14.25	52.678985	0.3	0.722669	0.722669	1.78e-09	0.000
models.itu840.cloud_attenuation	22.90	-43.23	14.25	22.278335	0.2	1.208442	1.208442	5.78e-10	0.000
models.itu840.cloud_attenuation	25.78	-80.22	14.25	52.678985	0.2	0.760938	0.760938	3.84e-09	0.000
models.itu840.cloud_attenuation	22.90	-43.23	29.00	22.278335	1.0	2.109942	2.109942	-3.44e-09	-0.000
models.itu840.cloud_attenuation	25.78	-80.22	29.00	52.678985	1.0	2.076228	2.076228	2.71e-09	0.000
models.itu840.cloud_attenuation	22.90	-43.23	29.00	22.278335	0.5	3.339051	3.339051	-3.20e-09	-0.000
models.itu840.cloud_attenuation	25.78	-80.22	29.00	52.678985	0.5	2.490524	2.490524	-2.60e-09	-0.000
models.itu840.cloud_attenuation	22.90	-43.23	29.00	22.278335	0.3	4.112259	4.112259	5.50e-10	0.000
models.itu840.cloud_attenuation	25.78	-80.22	29.00	52.678985	0.3	2.814133	2.814133	-3.98e-09	-0.000
models.itu840.cloud_attenuation	22.90	-43.23	29.00	22.278335	0.2	4.705774	4.705774	-1.21e-09	-0.000
models.itu840.cloud_attenuation	25.78	-80.22	29.00	52.678985	0.2	2.963156	2.963156	-2.75e-09	-0.000
models.itu840.cloud_attenuation	28.72	77.30	14.25	48.241171	1.0	0.685601	0.685601	-4.38e-09	-0.000
models.itu840.cloud_attenuation	3.13	101.70	14.25	85.804596	1.0	0.622148	0.622148	4.81e-09	0.000
models.itu840.cloud_attenuation	9.05	38.70	14.25	20.143358	1.0	0.657652	0.657652	2.05e-09	0.000
models.itu840.cloud_attenuation	28.72	77.30	14.25	48.241171	0.5	0.831794	0.831794	2.57e-09	0.000
models.itu840.cloud_attenuation	3.13	101.70	14.25	85.804596	0.5	0.654899	0.654899	-2.35e-09	-0.000
models.itu840.cloud_attenuation	9.05	38.70	14.25	20.143358	0.5	0.718165	0.718165	-1.13e-09	-0.000
models.itu840.cloud_attenuation	28.72	77.30	14.25	48.241171	0.3	0.907731	0.907731	-3.08e-09	-0.000
models.itu840.cloud_attenuation	3.13	101.70	14.25	85.804596	0.3	0.677159	0.677159	-3.75e-09	-0.000
models.itu840.cloud_attenuation	9.05	38.70	14.25	20.143358	0.3	0.752449	0.752449	2.71e-09	0.000
models.itu840.cloud_attenuation	28.72	77.30	14.25	48.241171	0.2	0.958302	0.958302	2.14e-09	0.000
models.itu840.cloud_attenuation	3.13	101.70	14.25	85.804596	0.2	0.690306	0.690306	-1.60e-09	-0.000
models.itu840.cloud_attenuation	9.05	38.70	14.25	20.143358	0.2	0.771120	0.771120	1.80e-09	0.000
models.itu840.cloud_attenuation	28.72	77.30	29.00	48.241171	1.0	2.669786	2.669786	-4.93e-09	-0.000
models.itu840.cloud_attenuation	3.13	101.70	29.00	85.804596	1.0	2.422697	2.422697	-1.13e-09	-0.000
models.itu840.cloud_attenuation	9.05	38.70	29.00	20.143358	1.0	2.560952	2.560952	3.84e-09	0.000
models.itu840.cloud_attenuation	28.72	77.30	29.00	48.241171	0.5	3.239076	3.239076	-3.17e-09	-0.000
models.itu840.cloud_attenuation	3.13	101.70	29.00	85.804596	0.5	2.550232	2.550232	3.09e-09	0.000
models.itu840.cloud_attenuation	9.05	38.70	29.00	20.143358	0.5	2.796592	2.796592	-2.58e-09	-0.000
models.itu840.cloud_attenuation	28.72	77.30	29.00	48.241171	0.3	3.534779	3.534779	3.05e-09	0.000
models.itu840.cloud_attenuation	3.13	101.70	29.00	85.804596	0.3	2.636914	2.636914	-1.37e-09	-0.000
models.itu840.cloud_attenuation	9.05	38.70	29.00	20.143358	0.3	2.930099	2.930099	-2.97e-09	-0.000
models.itu840.cloud_attenuation	28.72	77.30	29.00	48.241171	0.2	3.731709	3.731709	-1.49e-09	-0.000
models.itu840.cloud_attenuation	3.13	101.70	29.00	85.804596	0.2	2.688109	2.688109	3.06e-09	0.000
models.itu840.cloud_attenuation	9.05	38.70	29.00	20.143358	0.2	3.002805	3.002805	-3.77e-09	-0.000

Function columnar_content_reduced_liquid ¶

The table below contains the results of testing function columnar_content_reduced_liquid. The test cases were extracted from spreadsheet ITURP840-8_columnar_content_reduced_liquid.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.13  #  (°N)
lon = 101.7  # (°E)
p = 0.2  # (%)

# Make call to test-function columnar_content_reduced_liquid
itur_val = itur.models.itu840.columnar_content_reduced_liquid(lat=lat, lon=lon, p=p)

# Compute error with respect to value in ITU example file
ITU_example_val = 3.70165196  # (kg/m2)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu840.columnar_content_reduced_liquid

ITU-Rpy Function	lat (°N)	lon (°E)	p (%)	ITU Validation (kg/m2)	ITU-Rpy Result (kg/m2)	Absolute Error	Relative Error
models.itu840.columnar_content_reduced_liquid	3.130	101.70	0.20	3.701652	3.701652	-4.09e-09	-0.000
models.itu840.columnar_content_reduced_liquid	3.130	101.70	0.30	3.631154	3.631154	-3.73e-09	-0.000
models.itu840.columnar_content_reduced_liquid	3.130	101.70	0.50	3.511788	3.511788	3.47e-09	0.000
models.itu840.columnar_content_reduced_liquid	3.130	101.70	1.00	3.336166	3.336166	1.02e-09	0.000
models.itu840.columnar_content_reduced_liquid	3.133	101.70	0.10	3.805251	3.805251	3.56e-11	0.000
models.itu840.columnar_content_reduced_liquid	3.133	101.70	0.15	3.744512	3.744512	3.95e-10	0.000
models.itu840.columnar_content_reduced_liquid	3.133	101.70	0.30	3.630958	3.630958	2.67e-11	0.000
models.itu840.columnar_content_reduced_liquid	3.133	101.70	0.35	3.594946	3.594946	2.16e-11	0.000
models.itu840.columnar_content_reduced_liquid	9.050	38.70	0.20	1.427798	1.427798	4.00e-09	0.000
models.itu840.columnar_content_reduced_liquid	9.050	38.70	0.30	1.393227	1.393227	6.67e-10	0.000
models.itu840.columnar_content_reduced_liquid	9.050	38.70	0.50	1.329746	1.329746	-8.89e-10	-0.000
models.itu840.columnar_content_reduced_liquid	9.050	38.70	1.00	1.217702	1.217702	6.67e-10	0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.10	2.829932	2.829932	-1.85e-10	-0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.15	2.615428	2.615428	3.33e-10	0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.20	2.463236	2.463236	4.44e-11	0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.30	2.152561	2.152561	-1.08e-09	-0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.30	2.152561	2.152561	-8.15e-11	-0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.35	2.030425	2.030425	2.60e-10	0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	0.50	1.747825	1.747825	-3.48e-09	-0.000
models.itu840.columnar_content_reduced_liquid	22.900	-43.23	1.00	1.104449	1.104449	2.56e-09	0.000
models.itu840.columnar_content_reduced_liquid	23.000	30.00	0.10	0.443821	0.443821	-3.33e-10	-0.000
models.itu840.columnar_content_reduced_liquid	23.000	30.00	0.15	0.367759	0.367759	2.17e-10	0.000
models.itu840.columnar_content_reduced_liquid	23.000	30.00	0.30	0.252496	0.252496	-3.70e-10	-0.000
models.itu840.columnar_content_reduced_liquid	23.000	30.00	0.35	0.230477	0.230477	3.46e-10	0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.10	3.529275	3.529275	-2.79e-10	-0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.15	3.368053	3.368053	-4.33e-10	-0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.20	3.253664	3.253664	1.87e-09	0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.30	3.090031	3.090031	3.33e-09	0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.30	3.090031	3.090031	3.33e-10	0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.35	2.982802	2.982802	3.91e-10	0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	0.50	2.734695	2.734695	1.38e-09	0.000
models.itu840.columnar_content_reduced_liquid	25.780	-80.22	1.00	2.279782	2.279782	2.55e-09	0.000
models.itu840.columnar_content_reduced_liquid	28.717	77.30	0.10	4.230726	4.230726	3.11e-10	0.000
models.itu840.columnar_content_reduced_liquid	28.717	77.30	0.15	4.004952	4.004952	4.59e-10	0.000
models.itu840.columnar_content_reduced_liquid	28.717	77.30	0.30	3.641943	3.641943	-2.65e-10	-0.000
models.itu840.columnar_content_reduced_liquid	28.717	77.30	0.35	3.550068	3.550068	-3.85e-10	-0.000
models.itu840.columnar_content_reduced_liquid	28.720	77.30	0.20	3.843565	3.843565	-6.32e-10	-0.000
models.itu840.columnar_content_reduced_liquid	28.720	77.30	0.30	3.640732	3.640732	3.95e-09	0.000
models.itu840.columnar_content_reduced_liquid	28.720	77.30	0.50	3.336166	3.336166	1.80e-09	0.000
models.itu840.columnar_content_reduced_liquid	28.720	77.30	1.00	2.749811	2.749811	-4.63e-09	-0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.10	1.476286	1.476286	3.88e-10	0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.15	1.342662	1.342662	-2.59e-11	-0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.20	1.247855	1.247855	-2.32e-09	-0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.30	1.117630	1.117630	6.43e-10	0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.30	1.117630	1.117630	-3.57e-10	-0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.35	1.061279	1.061279	-4.82e-10	-0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	0.50	0.930893	0.930893	-4.82e-09	-0.000
models.itu840.columnar_content_reduced_liquid	33.940	18.43	1.00	0.730721	0.730721	4.04e-10	0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.10	1.498460	1.498460	-1.43e-10	-0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.15	1.411412	1.411412	4.24e-11	0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.20	1.349650	1.349650	-2.55e-09	-0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.30	1.254176	1.254176	2.37e-09	0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.30	1.254176	1.254176	3.65e-10	0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.35	1.214240	1.214240	-1.65e-10	-0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	0.50	1.121834	1.121834	4.17e-09	0.000
models.itu840.columnar_content_reduced_liquid	41.900	12.49	1.00	0.914672	0.914672	-4.23e-09	-0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.10	1.903298	1.903298	3.83e-10	0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.15	1.803804	1.803804	9.72e-11	0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.20	1.733211	1.733211	-1.19e-09	-0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.30	1.641289	1.641289	3.01e-09	0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.30	1.641289	1.641289	1.23e-11	0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.35	1.593721	1.593721	1.46e-10	0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	0.50	1.483659	1.483659	2.96e-09	0.000
models.itu840.columnar_content_reduced_liquid	51.500	-0.14	1.00	1.263286	1.263286	4.20e-10	0.000

Validation results ITU-R P.1510-1 ¶

This page contains the validation examples for Recommendation ITU-R P.1510-1: Mean surface temperature.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.1510-1
- Function surface_mean_temperature

Function surface_mean_temperature ¶

The table below contains the results of testing function surface_mean_temperature. The test cases were extracted from spreadsheet ITURP1510-1_temperature.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 51.5  #  (°N)
lon = -0.14  # (°E)

# Make call to test-function surface_mean_temperature
itur_val = itur.models.itu1510.surface_mean_temperature(lat=lat, lon=lon)

# Compute error with respect to value in ITU example file
ITU_example_val = 283.6108756  # (K)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1510.surface_mean_temperature

ITU-Rpy Function	lat (°N)	lon (°E)	ITU Validation (K)	ITU-Rpy Result (K)	Absolute Error	Relative Error
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	51.500	-0.14	283.610876	283.610876	4.44e-08	0.000
models.itu1510.surface_mean_temperature	41.900	12.49	288.089737	288.089737	1.11e-08	0.000
models.itu1510.surface_mean_temperature	33.940	18.43	293.369680	293.369679	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	22.900	-43.23	297.453541	297.453541	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	25.780	-80.22	297.574654	297.574654	3.33e-08	0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	28.717	77.30	298.058499	298.058499	-3.33e-08	-0.000
models.itu1510.surface_mean_temperature	3.133	101.70	299.605408	299.605407	3.33e-08	0.000
models.itu1510.surface_mean_temperature	9.050	38.70	290.210093	290.210093	-3.33e-08	-0.000

Validation results ITU-R P.1511-1 ¶

This page contains the validation examples for Recommendation ITU-R P.1511-1: Topography for Earth-to-space propagation modelling.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.1511-1
- Function topographic_altitude

Function topographic_altitude ¶

The table below contains the results of testing function topographic_altitude. The test cases were extracted from spreadsheet ITURP1511-1_topographic_altitude.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)

# Make call to test-function topographic_altitude
itur_val = itur.models.itu1511.topographic_altitude(lat=lat, lon=lon)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.23610446  # (km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1511.topographic_altitude

ITU-Rpy Function	lat (°N)	lon (°E)	ITU Validation (km)	ITU-Rpy Result (km)	Absolute Error	Relative Error
models.itu1511.topographic_altitude	3.133	101.70	0.051251	0.051246	5.67e-06	0.011
models.itu1511.topographic_altitude	22.900	-43.23	0.000000	0.000000	-1.00e-09	0.000
models.itu1511.topographic_altitude	23.000	30.00	0.187594	0.187595	-1.35e-06	-0.001
models.itu1511.topographic_altitude	25.780	-80.22	0.008617	0.008617	4.57e-07	0.005
models.itu1511.topographic_altitude	28.717	77.30	0.209384	0.209383	4.70e-07	0.000
models.itu1511.topographic_altitude	33.940	18.43	0.000000	0.000000	-1.00e-09	0.000
models.itu1511.topographic_altitude	41.900	12.49	0.046123	0.046124	-1.17e-06	-0.003
models.itu1511.topographic_altitude	51.500	-0.14	0.031383	0.031380	2.67e-06	0.009
models.itu1511.topographic_altitude	9.050	38.70	2.539862	2.539859	2.45e-06	0.000

Validation results ITU-R P.1511-2 ¶

This page contains the validation examples for Recommendation ITU-R P.1511-2: Topography for Earth-to-space propagation modelling.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.1511-2
- Function topographic_altitude

Function topographic_altitude ¶

The table below contains the results of testing function topographic_altitude. The test cases were extracted from spreadsheet ITURP1511-2_topographic_altitude.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
lat = 3.133  #  (°N)
lon = 101.7  # (°E)

# Make call to test-function topographic_altitude
itur_val = itur.models.itu1511.topographic_altitude(lat=lat, lon=lon)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.05125146  # (km)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1511.topographic_altitude

ITU-Rpy Function	lat (°N)	lon (°E)	ITU Validation (km)	ITU-Rpy Result (km)	Absolute Error	Relative Error
models.itu1511.topographic_altitude	3.133	101.70	0.051251	0.051246	5.67e-06	0.011
models.itu1511.topographic_altitude	22.900	-43.23	0.000000	0.000000	-1.00e-09	0.000
models.itu1511.topographic_altitude	23.000	30.00	0.187594	0.187595	-1.35e-06	-0.001
models.itu1511.topographic_altitude	25.780	-80.22	0.008617	0.008617	4.57e-07	0.005
models.itu1511.topographic_altitude	28.717	77.30	0.209384	0.209383	4.70e-07	0.000
models.itu1511.topographic_altitude	33.940	18.43	0.000000	0.000000	-1.00e-09	0.000
models.itu1511.topographic_altitude	41.900	12.49	0.046123	0.046124	-1.17e-06	-0.003
models.itu1511.topographic_altitude	51.500	-0.14	0.031383	0.031380	2.67e-06	0.009
models.itu1511.topographic_altitude	9.050	38.70	2.539862	2.539859	2.45e-06	0.000

Validation results ITU-R P.1623-1 ¶

This page contains the validation examples for Recommendation ITU-R P.1623-1: Prediction method of fade dynamics on Earth-space paths.

All test cases were extracted from the ITU Validation examples file (rev 5.1).

Functions tested

Validation results ITU-R P.1623-1

Function fade_duration_cummulative_probability ¶

The table below contains the results of testing function fade_duration_cummulative_probability. The test cases were extracted from spreadsheet ITURP1623-1_fade_duration_params.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
D = 30.0  # (s)
A = 12.51  # (dB)
el = 20.33  # (°)
f = 30.0  # (GHz)

# Make call to test-function fade_duration_cummulative_probability
itur_val = itur.models.itu1623.fade_duration_cummulative_probability(D=D, A=A, el=el, f=f)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.923603873  #
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1623.fade_duration_cummulative_probability

ITU-Rpy Function	D (s)	A (dB)	el (°)	f (GHz)	ITU Validation	ITU-Rpy Result	Absolute Error	Relative Error
models.itu1623.fade_duration_cummulative_probability	30.0	12.51	20.33	30.0	0.923604	0.923604	-4.27e-10	-0.000
models.itu1623.fade_duration_cummulative_probability	30.0	19.03	20.33	30.0	0.917391	0.917391	-2.54e-10	-0.000
models.itu1623.fade_duration_cummulative_probability	10.0	7.64	20.33	14.5	0.973161	0.973161	-4.50e-11	-0.000
models.itu1623.fade_duration_cummulative_probability	10.0	12.47	20.33	14.5	0.969723	0.969723	-3.27e-10	-0.000
models.itu1623.fade_duration_cummulative_probability	1.0	11.59	37.63	39.6	0.971179	0.971179	2.26e-10	0.000
models.itu1623.fade_duration_cummulative_probability	60.0	11.59	37.63	39.6	0.849674	0.849674	-4.01e-10	-0.000
models.itu1623.fade_duration_cummulative_probability	300.0	11.59	37.63	39.6	0.705296	0.705296	6.77e-11	0.000
models.itu1623.fade_duration_cummulative_probability	600.0	11.59	37.63	39.6	0.583576	0.583576	1.26e-10	0.000
models.itu1623.fade_duration_cummulative_probability	1200.0	11.59	37.63	39.6	0.429033	0.429033	3.49e-10	0.000
models.itu1623.fade_duration_cummulative_probability	1800.0	11.59	37.63	39.6	0.335491	0.335491	3.21e-10	0.000
models.itu1623.fade_duration_cummulative_probability	3600.0	11.59	37.63	39.6	0.193791	0.193791	1.20e-11	0.000

Function fade_duration_number_fades ¶

The table below contains the results of testing function fade_duration_number_fades. The test cases were extracted from spreadsheet ITURP1623-1_number_of_fades.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
D = 30.0  # (s)
A = 12.51  # (dB)
el = 20.33  # (°)
f = 30.0  # (GHz)
T_tot = 315576.0  # (s)

# Make call to test-function fade_duration_number_fades
itur_val = itur.models.itu1623.fade_duration_number_fades(D=D, A=A, el=el, f=f, T_tot=T_tot)

# Compute error with respect to value in ITU example file
ITU_example_val = 810.1909872  #
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1623.fade_duration_number_fades

ITU-Rpy Function	D (s)	A (dB)	el (°)	f (GHz)	T_tot (s)	ITU Validation	ITU-Rpy Result	Absolute Error	Relative Error
models.itu1623.fade_duration_number_fades	30.0	12.51	20.33	30.0	315576.000000	810.190987	810.190987	-1.74e-08	-0.000
models.itu1623.fade_duration_number_fades	30.0	19.03	20.33	30.0	94672.800000	263.482270	263.482270	2.50e-08	0.000
models.itu1623.fade_duration_number_fades	10.0	7.64	20.33	14.5	31557.600000	187.739006	187.739006	-2.75e-09	-0.000
models.itu1623.fade_duration_number_fades	10.0	12.47	20.33	14.5	9467.280000	63.671567	63.671567	4.49e-09	0.000
models.itu1623.fade_duration_number_fades	1.0	11.59	37.63	39.6	157788.000000	3075.079280	3075.079280	-3.93e-07	-0.000
models.itu1623.fade_duration_number_fades	60.0	11.59	37.63	39.6	157788.000000	267.324031	267.324031	7.27e-09	0.000
models.itu1623.fade_duration_number_fades	300.0	11.59	37.63	39.6	157788.000000	97.965854	97.965854	3.98e-09	0.000
models.itu1623.fade_duration_number_fades	600.0	11.59	37.63	39.6	157788.000000	52.729218	52.729218	-4.59e-09	-0.000
models.itu1623.fade_duration_number_fades	1200.0	11.59	37.63	39.6	157788.000000	23.629371	23.629371	-1.14e-09	-0.000
models.itu1623.fade_duration_number_fades	1800.0	11.59	37.63	39.6	157788.000000	13.506736	13.506736	3.38e-09	0.000
models.itu1623.fade_duration_number_fades	3600.0	11.59	37.63	39.6	157788.000000	4.425827	4.425827	-2.96e-10	-0.000
models.itu1623.fade_duration_number_fades	10.0	1.10	30.00	14.0	395486.300000	1668.160083	1668.160083	-4.01e-07	-0.000
models.itu1623.fade_duration_number_fades	20.0	1.10	30.00	14.0	395486.300000	1349.672725	1349.672725	-2.26e-08	-0.000
models.itu1623.fade_duration_number_fades	30.0	1.10	30.00	14.0	395486.300000	1187.975446	1187.975446	-2.57e-07	-0.000
models.itu1623.fade_duration_number_fades	50.0	1.10	30.00	14.0	395486.300000	968.757536	968.757536	-3.67e-09	-0.000
models.itu1623.fade_duration_number_fades	70.0	1.10	30.00	14.0	395486.300000	819.405465	819.405465	3.02e-08	0.000
models.itu1623.fade_duration_number_fades	100.0	1.10	30.00	14.0	395486.300000	665.033744	665.033744	4.85e-08	0.000
models.itu1623.fade_duration_number_fades	200.0	1.10	30.00	14.0	395486.300000	401.326405	401.326405	4.08e-08	0.000
models.itu1623.fade_duration_number_fades	300.0	1.10	30.00	14.0	395486.300000	279.908154	279.908153	4.92e-08	0.000
models.itu1623.fade_duration_number_fades	500.0	1.10	30.00	14.0	395486.300000	165.425843	165.425843	8.01e-10	0.000
models.itu1623.fade_duration_number_fades	1000.0	1.10	30.00	14.0	395486.300000	70.889868	70.889868	2.78e-09	0.000
models.itu1623.fade_duration_number_fades	2000.0	1.10	30.00	14.0	395486.300000	25.893644	25.893644	1.10e-09	0.000
models.itu1623.fade_duration_number_fades	3000.0	1.10	30.00	14.0	395486.300000	13.314322	13.314322	-3.24e-09	-0.000
models.itu1623.fade_duration_number_fades	5000.0	1.10	30.00	14.0	395486.300000	5.309439	5.309439	2.62e-11	0.000
models.itu1623.fade_duration_number_fades	10.0	3.00	30.00	14.0	41152.940740	222.892169	222.892169	6.80e-09	0.000
models.itu1623.fade_duration_number_fades	20.0	3.00	30.00	14.0	41152.940740	180.377199	180.377199	-1.94e-08	-0.000
models.itu1623.fade_duration_number_fades	30.0	3.00	30.00	14.0	41152.940740	155.798554	155.798554	8.48e-09	0.000
models.itu1623.fade_duration_number_fades	50.0	3.00	30.00	14.0	41152.940740	122.626410	122.626410	-1.76e-08	-0.000
models.itu1623.fade_duration_number_fades	70.0	3.00	30.00	14.0	41152.940740	100.937752	100.937752	-4.38e-08	-0.000
models.itu1623.fade_duration_number_fades	100.0	3.00	30.00	14.0	41152.940740	79.327733	79.327733	-3.61e-09	-0.000
models.itu1623.fade_duration_number_fades	200.0	3.00	30.00	14.0	41152.940740	44.537187	44.537187	-4.29e-09	-0.000
models.itu1623.fade_duration_number_fades	300.0	3.00	30.00	14.0	41152.940740	29.606190	29.606190	9.51e-10	0.000
models.itu1623.fade_duration_number_fades	500.0	3.00	30.00	14.0	41152.940740	16.372608	16.372608	-6.17e-09	-0.000
models.itu1623.fade_duration_number_fades	1000.0	3.00	30.00	14.0	41152.940740	6.345620	6.345620	-2.44e-10	-0.000
models.itu1623.fade_duration_number_fades	2000.0	3.00	30.00	14.0	41152.940740	2.072255	2.072255	-2.60e-10	-0.000
models.itu1623.fade_duration_number_fades	3000.0	3.00	30.00	14.0	41152.940740	0.992754	0.992754	2.88e-10	0.000
models.itu1623.fade_duration_number_fades	5000.0	3.00	30.00	14.0	41152.940740	0.360170	0.360170	-5.10e-10	-0.000
models.itu1623.fade_duration_number_fades	10.0	6.00	30.00	14.0	8439.016398	54.389922	54.389922	-2.32e-09	-0.000
models.itu1623.fade_duration_number_fades	20.0	6.00	30.00	14.0	8439.016398	43.742582	43.742582	-4.12e-09	-0.000
models.itu1623.fade_duration_number_fades	30.0	6.00	30.00	14.0	8439.016398	37.083143	37.083143	-1.06e-09	-0.000
models.itu1623.fade_duration_number_fades	50.0	6.00	30.00	14.0	8439.016398	28.375238	28.375238	-2.50e-09	-0.000
models.itu1623.fade_duration_number_fades	70.0	6.00	30.00	14.0	8439.016398	22.860953	22.860953	1.48e-09	0.000
models.itu1623.fade_duration_number_fades	100.0	6.00	30.00	14.0	8439.016398	17.519794	17.519794	-4.73e-09	-0.000
models.itu1623.fade_duration_number_fades	200.0	6.00	30.00	14.0	8439.016398	9.300675	9.300675	-2.05e-10	-0.000
models.itu1623.fade_duration_number_fades	300.0	6.00	30.00	14.0	8439.016398	5.958399	5.958399	-4.47e-10	-0.000
models.itu1623.fade_duration_number_fades	500.0	6.00	30.00	14.0	8439.016398	3.131783	3.131783	3.96e-10	0.000
models.itu1623.fade_duration_number_fades	1000.0	6.00	30.00	14.0	8439.016398	1.124527	1.124527	2.15e-10	0.000
models.itu1623.fade_duration_number_fades	2000.0	6.00	30.00	14.0	8439.016398	0.337402	0.337402	-3.45e-10	-0.000
models.itu1623.fade_duration_number_fades	3000.0	6.00	30.00	14.0	8439.016398	0.153244	0.153244	-2.99e-10	-0.000
models.itu1623.fade_duration_number_fades	5000.0	6.00	30.00	14.0	8439.016398	0.051782	0.051782	-1.41e-10	-0.000
models.itu1623.fade_duration_number_fades	10.0	9.00	30.00	14.0	3073.432203	21.939310	21.939310	-2.27e-09	-0.000
models.itu1623.fade_duration_number_fades	20.0	9.00	30.00	14.0	3073.432203	17.506532	17.506532	-2.88e-09	-0.000
models.itu1623.fade_duration_number_fades	30.0	9.00	30.00	14.0	3073.432203	14.663494	14.663494	-4.45e-11	-0.000
models.itu1623.fade_duration_number_fades	50.0	9.00	30.00	14.0	3073.432203	11.019315	11.019315	2.95e-09	0.000
models.itu1623.fade_duration_number_fades	70.0	9.00	30.00	14.0	3073.432203	8.757618	8.757618	4.85e-10	0.000
models.itu1623.fade_duration_number_fades	100.0	9.00	30.00	14.0	3073.432203	6.605381	6.605381	-6.27e-11	-0.000
models.itu1623.fade_duration_number_fades	200.0	9.00	30.00	14.0	3073.432203	3.385196	3.385196	6.00e-10	0.000
models.itu1623.fade_duration_number_fades	300.0	9.00	30.00	14.0	3073.432203	2.119102	2.119102	1.39e-11	0.000
models.itu1623.fade_duration_number_fades	500.0	9.00	30.00	14.0	3073.432203	1.079042	1.079042	-2.46e-10	-0.000
models.itu1623.fade_duration_number_fades	1000.0	9.00	30.00	14.0	3073.432203	0.369475	0.369475	3.28e-10	0.000
models.itu1623.fade_duration_number_fades	2000.0	9.00	30.00	14.0	3073.432203	0.105187	0.105187	-4.43e-10	-0.000
models.itu1623.fade_duration_number_fades	3000.0	9.00	30.00	14.0	3073.432203	0.046225	0.046225	4.17e-10	0.000
models.itu1623.fade_duration_number_fades	5000.0	9.00	30.00	14.0	3073.432203	0.014949	0.014949	2.93e-10	0.000
models.itu1623.fade_duration_number_fades	10.0	12.00	30.00	14.0	1401.370018	10.757668	10.757668	1.22e-09	0.000
models.itu1623.fade_duration_number_fades	20.0	12.00	30.00	14.0	1401.370018	8.518435	8.518435	1.50e-09	0.000
models.itu1623.fade_duration_number_fades	30.0	12.00	30.00	14.0	1401.370018	7.070472	7.070472	1.35e-09	0.000
models.itu1623.fade_duration_number_fades	50.0	12.00	30.00	14.0	1401.370018	5.241774	5.241774	1.25e-09	0.000
models.itu1623.fade_duration_number_fades	70.0	12.00	30.00	14.0	1401.370018	4.123662	4.123662	3.04e-10	0.000
models.itu1623.fade_duration_number_fades	100.0	12.00	30.00	14.0	1401.370018	3.073520	3.073520	2.43e-10	0.000
models.itu1623.fade_duration_number_fades	200.0	12.00	30.00	14.0	1401.370018	1.534482	1.534482	4.00e-10	0.000
models.itu1623.fade_duration_number_fades	300.0	12.00	30.00	14.0	1401.370018	0.944261	0.944261	8.10e-11	0.000
models.itu1623.fade_duration_number_fades	500.0	12.00	30.00	14.0	1401.370018	0.469680	0.469680	-2.05e-10	-0.000
models.itu1623.fade_duration_number_fades	1000.0	12.00	30.00	14.0	1401.370018	0.155289	0.155289	3.79e-10	0.000
models.itu1623.fade_duration_number_fades	2000.0	12.00	30.00	14.0	1401.370018	0.042535	0.042535	2.64e-10	0.000
models.itu1623.fade_duration_number_fades	3000.0	12.00	30.00	14.0	1401.370018	0.018245	0.018245	3.68e-11	0.000
models.itu1623.fade_duration_number_fades	5000.0	12.00	30.00	14.0	1401.370018	0.005713	0.005713	2.17e-11	0.000
models.itu1623.fade_duration_number_fades	10.0	15.00	30.00	14.0	680.678272	5.528898	5.528898	-1.85e-10	-0.000
models.itu1623.fade_duration_number_fades	20.0	15.00	30.00	14.0	680.678272	4.346392	4.346392	1.30e-10	0.000
models.itu1623.fade_duration_number_fades	30.0	15.00	30.00	14.0	680.678272	3.581086	3.581086	-4.88e-10	-0.000
models.itu1623.fade_duration_number_fades	50.0	15.00	30.00	14.0	680.678272	2.625959	2.625959	-1.87e-10	-0.000
models.itu1623.fade_duration_number_fades	70.0	15.00	30.00	14.0	680.678272	2.048928	2.048928	-3.90e-10	-0.000
models.itu1623.fade_duration_number_fades	100.0	15.00	30.00	14.0	680.678272	1.512629	1.512629	4.59e-11	0.000
models.itu1623.fade_duration_number_fades	200.0	15.00	30.00	14.0	680.678272	0.739519	0.739519	-2.21e-11	-0.000
models.itu1623.fade_duration_number_fades	300.0	15.00	30.00	14.0	680.678272	0.448879	0.448879	-1.85e-10	-0.000
models.itu1623.fade_duration_number_fades	500.0	15.00	30.00	14.0	680.678272	0.219133	0.219133	2.98e-11	0.000
models.itu1623.fade_duration_number_fades	1000.0	15.00	30.00	14.0	680.678272	0.070456	0.070456	-2.13e-10	-0.000
models.itu1623.fade_duration_number_fades	2000.0	15.00	30.00	14.0	680.678272	0.018714	0.018714	-2.19e-10	-0.000
models.itu1623.fade_duration_number_fades	3000.0	15.00	30.00	14.0	680.678272	0.007874	0.007874	2.37e-10	0.000
models.itu1623.fade_duration_number_fades	5000.0	15.00	30.00	14.0	680.678272	0.002403	0.002403	-2.25e-10	-0.000

Function fade_duration_probability ¶

The table below contains the results of testing function fade_duration_probability. The test cases were extracted from spreadsheet ITURP1623-1_fade_duration_params.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
D = 30.0  # (s)
A = 12.51  # (dB)
el = 20.33  # (°)
f = 30.0  # (GHz)

# Make call to test-function fade_duration_probability
itur_val = itur.models.itu1623.fade_duration_probability(D=D, A=A, el=el, f=f)

# Compute error with respect to value in ITU example file
ITU_example_val = 0.183841589  #
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1623.fade_duration_probability

ITU-Rpy Function	D (s)	A (dB)	el (°)	f (GHz)	ITU Validation	ITU-Rpy Result	Absolute Error	Relative Error
models.itu1623.fade_duration_probability	30.0	12.51	20.33	30.0	0.183842	0.183842	-4.29e-10	-0.000
models.itu1623.fade_duration_probability	30.0	19.03	20.33	30.0	0.184234	0.184234	-3.17e-10	-0.000
models.itu1623.fade_duration_probability	10.0	7.64	20.33	14.5	0.488779	0.488779	-3.19e-11	-0.000
models.itu1623.fade_duration_probability	10.0	12.47	20.33	14.5	0.489294	0.489294	-9.73e-11	-0.000
models.itu1623.fade_duration_probability	1.0	11.59	37.63	39.6	1.000000	1.000000	0.00e+00	0.000
models.itu1623.fade_duration_probability	60.0	11.59	37.63	39.6	0.086932	0.086932	8.69e-11	0.000
models.itu1623.fade_duration_probability	300.0	11.59	37.63	39.6	0.031858	0.031858	2.19e-10	0.000
models.itu1623.fade_duration_probability	600.0	11.59	37.63	39.6	0.017147	0.017147	-2.10e-10	-0.000
models.itu1623.fade_duration_probability	1200.0	11.59	37.63	39.6	0.007684	0.007684	-3.02e-10	-0.000
models.itu1623.fade_duration_probability	1800.0	11.59	37.63	39.6	0.004392	0.004392	-3.47e-10	-0.000
models.itu1623.fade_duration_probability	3600.0	11.59	37.63	39.6	0.001439	0.001439	-8.83e-11	-0.000

Function fade_duration_total_exceedance_time ¶

The table below contains the results of testing function fade_duration_total_exceedance_time. The test cases were extracted from spreadsheet ITURP1623-1_fade_duration_params.csv from the ITU Validation examples file (rev 5.1). In addition to the input-arguments, expected result (ITU Validation), and ITU-Rpy computed result (ITUR-py Result), the absolute and relative errors are shown. Each test case is color-coded depending on the magnitude of the errors (green = pass, errors are negligible, red = fail, relative error is above 0.01%).

In addition, the code snippet below shows an example of how to generate the first row of the results in the table:

import itur

# Define input attributes
D = 30.0  # (s)
A = 12.51  # (dB)
el = 20.33  # (°)
f = 30.0  # (GHz)
T_tot = 315576.0  # (s)

# Make call to test-function fade_duration_total_exceedance_time
itur_val = itur.models.itu1623.fade_duration_total_exceedance_time(D=D, A=A, el=el, f=f, T_tot=T_tot)

# Compute error with respect to value in ITU example file
ITU_example_val = 291467.215960567  # (s)
error = ITU_example_val - itur_val.value
error_rel = error / ITU_example_val * 100  # (%)

Validation results models.itu1623.fade_duration_total_exceedance_time

ITU-Rpy Function	D (s)	A (dB)	el (°)	f (GHz)	T_tot (s)	ITU Validation (s)	ITU-Rpy Result (s)	Absolute Error	Relative Error
models.itu1623.fade_duration_total_exceedance_time	30.0	12.51	20.33	30.0	315576.00	291467.215961	291467.215961	-3.49e-10	-0.000
models.itu1623.fade_duration_total_exceedance_time	30.0	19.03	20.33	30.0	94672.80	86851.997600	86851.997600	3.78e-10	0.000
models.itu1623.fade_duration_total_exceedance_time	10.0	7.64	20.33	14.5	31557.60	30710.632581	30710.632581	-4.37e-11	-0.000
models.itu1623.fade_duration_total_exceedance_time	10.0	12.47	20.33	14.5	9467.28	9180.643332	9180.643332	4.17e-10	0.000
models.itu1623.fade_duration_total_exceedance_time	1.0	11.59	37.63	39.6	157788.00	153240.459707	153240.459707	-2.91e-10	-0.000
models.itu1623.fade_duration_total_exceedance_time	60.0	11.59	37.63	39.6	157788.00	134068.283701	134068.283701	-2.91e-11	-0.000
models.itu1623.fade_duration_total_exceedance_time	300.0	11.59	37.63	39.6	157788.00	111287.301883	111287.301883	3.06e-10	0.000
models.itu1623.fade_duration_total_exceedance_time	600.0	11.59	37.63	39.6	157788.00	92081.221388	92081.221388	3.93e-10	0.000
models.itu1623.fade_duration_total_exceedance_time	1200.0	11.59	37.63	39.6	157788.00	67696.250744	67696.250744	2.91e-11	0.000
models.itu1623.fade_duration_total_exceedance_time	1800.0	11.59	37.63	39.6	157788.00	52936.430347	52936.430347	-4.44e-10	-0.000
models.itu1623.fade_duration_total_exceedance_time	3600.0	11.59	37.63	39.6	157788.00	30577.895884	30577.895884	5.31e-10	0.000

F.A.Q.¶

I cannot install Basemap¶

This happens most likely because you are using python version > 3.X. You can try to install from conda-forge conda install -c conda-forge cartopy or, if you are using Windows, using the appropriate pre-compiled wheels file from this webpage. Once you download the .whl file you can install it using pip install name_of_whl_file.whl.

The first time I run ITU-Rpy is considerable slower¶

ITU-Rpy loads in memory several datasets upon first execution. This process might take up to 30 seconds. Once that datasets are loaded into memory ITU-Rpy uses cached versions to reduce execution time.

I cannot operate with the values returned by ITU-Rpy¶

ITU-Rpy returns Quantity objects, which consist of a value and a unit. Only quantities with compatible dimensions can be added / subtracted.

import itur
d1 = 300 * itur.u.m
d2 = 0.2 * itur.u.km

print(d1 + d2)     # prints 500.0 m

p1 = 1013 * itur.u.hPa
print(d1 + p1)     # Generates an error.

The user can transform between compatible units using the .to() method.

print(d1.to(itur.u.km))    # prints 0.3 km

One can access to the values and units using the .value and .unit methods respectively. Some matplotlib functions accept Quantities as inputs (plt.plot, plt.scatter), whereas others require plain values (plt.bar).

I discovered a bug/have criticism or ideas on ITU-Rpy. Where should I report to?¶

ITU-Rpy uses the GitHub issue-tracker to take care of bugs and questions. If you experience problems with ITU-Rpy, try to provide a full error report with all the typical information (OS, version, console-output, minimum working example, …). This makes it a lot easier to reproduce the error and locate the problem.

Contributing to ITU-Rpy¶

We welcome all contributions to grow and improve ITU-Rpy. There are many ways you can contribute, be it filing bug reports, writing new documentation or submitting patches for new or fixed behavior. This guide provides everything you need to get started.

Writing code¶

The ITU-Rpy source code is managed using Git and is hosted on GitHub. The recommended way for new contributors to submit code to ` ITU-Rpy <https://github.com/inigodelportillo/ITU-Rpy/>`_ is to fork this repository and submit a pull request after committing changes to their fork. The pull request will then need to be approved by one of the core developers before it is merged into the main repository.

Coding style¶

Please follow these guidelines when writing code for ITU-Rpy:

Follow the PEP 8 Python style guide.

Try to use the same code style as used in the rest of the project.

New features and recommendations should be documented. Include examples and use cases where appropriate.

If possible, add appropriate unit tests for validation.

Bug Reports and Feature Requests¶

If you have encountered a problem with ITU-Rpy or have an idea for a new feature, please submit it to the GitHub issue-tracker.

Including or providing a link to the source files involved may help us fix the issue. If possible, try to create a minimal project that produces the error and post that instead.

Improving Documentation¶

ITU-Rpy welcomes documentation contributions. Documentation on ITU-Rpy falls into the following categories:

API reference: The API reference docs are generated from docstrings in the ITU-Rpy source code.

Narrative documentation: These are tutorials and other writing that’s not part of the ITU-Rpy source code. This documentation is in the ITU-Rpy/docs folder of the GitHub repository.

License¶

This program is free software: you can redistribute it and/or modify it under the terms of the MIT license (see below).

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

If you use ITU-Rpy in one of your research projects, please use the citation provided below.

MIT¶

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Citation¶

If you use ITU-Rpy in one of your research projects, please cite it as:

@misc{iturpy-2017,
      title={ITU-Rpy: A python implementation of the ITU-R P. Recommendations to compute
         atmospheric attenuation in slant and horizontal paths.},
      author={Inigo del Portillo},
      year={2017},
      publisher={GitHub},
      howpublished={\url{https://github.com/inigodelportillo/ITU-Rpy/}}
}

Contact¶

ITU-Rpy is developed and maintained by Inigo del Portillo (inigo.del.portillo@gmail.com).

ITU-Rpy uses the GitHub issue-tracker to take care of bugs and questions. If you experience problems with ITU-Rpy, try to provide a full error report with all the typical information (OS, version, console-output, minimum working example, …). This makes it a lot easier to reproduce the error and locate the problem.

Citation¶

If you use ITU-Rpy in one of your research projects, please cite it as:

@misc{iturpy-2017,
      title={ITU-Rpy: A python implementation of the ITU-R P. Recommendations to compute
         atmospheric attenuation in slant and horizontal paths.},
      author={Inigo del Portillo},
      year={2017},
      publisher={GitHub},
      howpublished={\url{https://github.com/inigodelportillo/ITU-Rpy/}}
}

Indices and tables¶

Other¶

ITU-Rpy is mainly written in Python 3 and continuously tested with Python 3.5-3.9.

ITU-Rpy has the following dependencies: numpy, scipy, pyproj, and astropy. Installing cartopy and matplotlib is recommended to display results in a map.