# -*- coding: utf-8 -*-
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from astropy import units as u
from itur.utils import (prepare_input_array,
prepare_output_array,
get_input_type,
prepare_quantity)
class __ITU835__():
"""Class to model the ITU-R P.835 recommendation.
The procedures to compute the reference standard atmosphere parameters
pressented in these versions are identical to those included in version
ITU_T P.835.
Available versions:
* P.835-6 (12/17) (Current version)
* P.835-5 (02/12) (Superseded)
Not available versions:
* P.835-1 (08/94) (Superseded)
* P.835-2 (08/97) (Superseded)
* P.835-3 (10/99) (Superseded)
* P.835-4 (03/05) (Superseded)
"""
# This is an abstract class that contains an instance to a version of the
# ITU-R P.835 recommendation.
def __init__(self, version=6):
if version == 6:
self.instance = _ITU835_6()
elif version == 5:
self.instance = _ITU835_5()
else:
raise ValueError(
'Version ' +
str(version) +
' is not implemented' +
' for the ITU-R P.835 model.')
@property
def __version__(self):
return self.instance.__version__
def temperature(self, lat, h, season='summer'):
#
return self.instance.temperature(lat, h, season)
def pressure(self, lat, h, season='summer'):
return self.instance.pressure(lat, h, season)
def water_vapour_density(self, lat, h, season='summer'):
return self.instance.water_vapour_density(lat, h, season)
def standard_temperature(self, h, T_0):
return self.instance.standard_temperature(h, T_0)
def standard_pressure(self, h, T_0, P_0):
return self.instance.standard_pressure(h, T_0, P_0)
def standard_water_vapour_density(self, h, h_0, rho_0):
return self.instance.standard_water_vapour_density(h, h_0, rho_0)
def standard_water_vapour_pressure(self, h, h_0=2, rho_0=7.5):
return self.instance.standard_water_vapour_pressure(h, h_0, rho_0)
class _ITU835_6():
def __init__(self):
self.__version__ = 6
self.year = 2017
self.month = 12
self.link = 'https://www.itu.int/rec/R-REC-P.835-6-201712-I/en'
@staticmethod
def standard_temperature(h, T_0=288.15):
"""
"""
h_p = 6356.766 * h / (6356.766 + h)
# Warnings because of sqrt are expected
with np.errstate(invalid='ignore'):
T = np.where(h_p <= 11, 288.15 - 6.5 * h_p,
np.where(np.logical_and(11 < h_p, h_p <= 20),
216.65,
np.where(np.logical_and(20 < h_p, h_p <= 32),
216.65 + (h_p - 20),
np.where(np.logical_and(32 < h_p, h_p <= 47),
228.65 + 2.8 * (h_p - 32),
np.where(np.logical_and(47 < h_p, h_p <= 51),
270.65,
np.where(np.logical_and(51 < h_p, h_p <= 71),
270.65 - 2.8 * (h_p - 51),
np.where(np.logical_and(71 < h_p, h_p <= 84.852),
214.65 - 2.0 * (h_p - 71),
np.where(np.logical_and(86 <= h, h <= 91),
186.8673,
np.where(np.logical_and(91 < h, h <= 100),
263.1905 - 76.3232 * np.sqrt((1 - ((h - 91)/19.9429)**2)),
195.08134)))))))))
return T
@staticmethod
def standard_pressure(h, T_0=None, P_0=None):
"""
"""
h_p = 6356.766 * h / (6356.766 + h)
with np.errstate(invalid='ignore'):
P = np.where(h_p <= 11,
1013.25 * (288.15 / (288.15 - 6.5 * h_p))**(-34.1632 / 6.5),
np.where(np.logical_and(11 < h_p, h_p <= 20),
226.3226 * np.exp(-34.1632 * (h_p - 11) / 216.65),
np.where(np.logical_and(20 < h_p, h_p <= 32),
54.74980 * (216.65 / (216.65 + (h_p - 20))) ** 34.1632,
np.where(np.logical_and(32 < h_p, h_p <= 47),
8.680422 * (228.65 / (228.65 + 2.8 * (h_p - 32))) **
(34.1632 / 2.8),
np.where(np.logical_and(47 < h_p, h_p <= 51),
1.109106 * np.exp(-34.1632 * (h_p - 47) / 270.65),
np.where(np.logical_and(51 < h_p, h_p <= 71),
0.6694167 * (270.65 / (270.65 - 2.8 * (h_p - 51)))**(-34.1632 / 2.8),
np.where(np.logical_and(71 < h_p, h_p <= 84.852),
0.03956649 *(214.65 / (214.65 - 2.0 * (h_p - 71)))**(-34.1632 / 2.0),
np.where(np.logical_and(86 <= h, h <= 100),
np.exp(95.571899 -4.011801 * h + 6.424731e-2 * h**2 -
4.789660e-4 * h**3 + 1.340543e-6 * h**4),
1e-62)))))))).astype(float)
return P
@staticmethod
def standard_water_vapour_density(h, h_0=2, rho_0=7.5):
"""
"""
return rho_0 * np.exp(-h / h_0)
def standard_water_vapour_pressure(self, h, h_0=2, rho_0=7.5):
"""
"""
rho_h = self.standard_water_vapour_density(h, h_0, rho_0)
T_h = self.standard_temperature(h)
return rho_h * T_h / 216.7
# Low latitude standard atmosphere functions (Section ITU-R P.835-6 2) #
@staticmethod
def low_latitude_temperature(h):
"""Section 2 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h < 17)),
300.4222 - 6.3533 * h + 0.005886 * h**2,
np.where(np.logical_and((17 <= h), (h < 47)),
194 + (h - 17) * 2.533,
np.where(np.logical_and((47 <= h), (h < 52)), 270,
np.where(np.logical_and((52 <= h), (h < 80)),
270 - (h - 52) * 3.0714,
np.where(np.logical_and((80 <= h), (h <= 100)), 184, 184)))))
def low_latitude_pressure(self, h):
"""Section 2 of Recommendation ITU-R P.835-6."""
P10 = 284.8526 # Pressure at 10 km using the equation below
P72 = 0.0313660 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1012.0306 - 109.0338 * h + 3.6316 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.165 * (h - 72)), np.nan)))
@staticmethod
def low_latitude_water_vapour(h):
"""Section 3.1 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h <= 15)), 19.6542 *
np.exp(- 0.2313 * h - 0.1122 * h**2 + 0.01351 * h**3 -
0.0005923 * h**4), 0)
# Mid latitude standard atmosphere functions (Section ITU-R P.835-6 3)
@staticmethod
def mid_latitude_temperature_summer(h):
"""Section 3.1 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h < 13)),
294.9838 - 5.2159 * h - 0.07109 * h**2,
np.where(np.logical_and((13 <= h), (h < 17)), 215.15,
np.where(np.logical_and((17 <= h), (h < 47)),
215.15 * np.exp((h - 17) * 0.008128),
np.where(np.logical_and((47 <= h), (h < 53)), 275,
np.where(np.logical_and((53 <= h), (h < 80)),
275 + 20 * (1 - np.exp((h - 53) * 0.06)),
np.where(np.logical_and((80 <= h), (h <= 100)),
175, np.nan))))))
def mid_latitude_pressure_summer(self, h):
"""Section 3.1 of Recommendation ITU-R P.835-6."""
P10 = 283.7096 # Pressure at 10 km using the equation below
P72 = 0.03124022 # Pressure at 72 km using the equation below
return np.where(
np.logical_and((0 <= h), (h <= 10)),
1012.8186 - 111.5569 * h + 3.8646 * h**2, np.where(
np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(
np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.165 * (h - 72)),
np.nan)))
@staticmethod
def mid_latitude_water_vapour_summer(h):
"""Section 3.1 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h <= 15)),
14.3542 * np.exp(- 0.4174 * h - 0.02290 * h**2 +
0.001007 * h**3), 0)
@staticmethod
def mid_latitude_temperature_winter(h):
"""Section 3.2 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h < 10)),
272.7241 - 3.6217 * h - 0.1759 * h**2,
np.where(np.logical_and((10 <= h), (h < 33)), 218,
np.where(np.logical_and((33 <= h), (h < 47)),
218 + (h - 33) * 3.3571,
np.where(np.logical_and((47 <= h), (h < 53)), 265,
np.where(np.logical_and((53 <= h), (h < 80)),
265 - (h - 53) * 2.0370,
np.where(np.logical_and((80 <= h), (h <= 100)),
210, np.nan))))))
def mid_latitude_pressure_winter(self, h):
"""Section 3.2 of Recommendation ITU-R P.835-6."""
P10 = 258.9787 # Pressure at 10 km using the equation below
P72 = 0.02851702 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1018.8627 - 124.2954 * h + 4.8307 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.155 * (h - 72)), np.nan)))
@staticmethod
def mid_latitude_water_vapour_winter(h):
"""Section 3.2 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and(0 <= h, h <= 10),
3.4742 * np.exp(- 0.2697 * h - 0.03604 * h**2 +
0.0004489 * h**3), 0)
# High latitude standard atmosphere functions (Section ITU-R P.835-6 4) #
@staticmethod
def high_latitude_temperature_summer(h):
"""Section 4.1 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h < 10)),
286.8374 - 4.7805 * h - 0.1402 * h**2,
np.where(np.logical_and((10 <= h), (h < 23)), 225,
np.where(np.logical_and((23 <= h), (h < 48)),
225 * np.exp((h - 23) * 0.008317),
np.where(np.logical_and((48 <= h), (h < 53)), 277,
np.where(np.logical_and((53 <= h), (h < 79)),
277 - (h - 53) * 4.0769,
np.where(np.logical_and((79 <= h), (h <= 100)),
171, np.nan))))))
def high_latitude_pressure_summer(self, h):
"""Section 4.1 of Recommendation ITU-R P.835-6."""
P10 = 269.6138 # Pressure at 10 km using the equation below
P72 = 0.04582115 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1008.0278 - 113.2494 * h + 3.9408 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.140 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.165 * (h - 72)), np.nan)))
@staticmethod
def high_latitude_water_vapour_summer(h):
"""Section 4.1 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h <= 15)),
8.988 * np.exp(- 0.3614 * h - 0.005402 * h**2 -
0.001955 * h**3), 0)
@staticmethod
def high_latitude_temperature_winter(h):
"""Section 4.2 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h < 8.5)),
257.4345 + 2.3474 * h - 1.5479 * h**2 +
0.08473 * h**3,
np.where(np.logical_and((8.5 <= h), (h < 30)), 217.5,
np.where(np.logical_and((30 <= h), (h < 50)),
217.5 + (h - 30) * 2.125,
np.where(np.logical_and((50 <= h), (h < 54)), 260,
np.where(np.logical_and((54 <= h), (h <= 100)),
260 - (h - 54) * 1.667, np.nan)))))
def high_latitude_pressure_winter(self, h):
"""Section 4.2 of Recommendation ITU-R P.835-6."""
P10 = 243.8718 # Pressure at 10 km using the equation below
P72 = 0.02685355 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1010.8828 - 122.2411 * h + 4.554 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.150 * (h - 72)), np.nan)))
@staticmethod
def high_latitude_water_vapour_winter(h):
"""Section 4.2 of Recommendation ITU-R P.835-6."""
return np.where(np.logical_and((0 <= h), (h <= 10)),
1.2319 * np.exp(0.07481 * h - 0.0981 * h**2 +
0.00281 * h**3), 0)
def temperature(self, lat, h, season='summer'):
""" Section 2 of Recommendation ITU-R P.835-6."""
if season == 'summer':
return np.where(
np.abs(lat) < 22, self.low_latitude_temperature(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_temperature_summer(h),
self.high_latitude_temperature_summer(h)))
elif season == 'winter':
return np.where(
np.abs(lat) < 22, self.low_latitude_temperature(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_temperature_winter(h),
self.high_latitude_temperature_winter(h)))
else:
raise ValueError("The value for argument 'season' is not correct."
"Valid values are 'summer' and 'winter'.")
def pressure(self, lat, h, season='summer'):
""" Section 2 of Recommendation ITU-R P.835-6."""
if season == 'summer':
return np.where(
np.abs(lat) < 22, self.low_latitude_pressure(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_pressure_summer(h),
self.high_latitude_pressure_summer(h)))
elif season == 'winter':
return np.where(
np.abs(lat) < 22, self.low_latitude_pressure(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_pressure_winter(h),
self.high_latitude_pressure_winter(h)))
else:
raise ValueError("The value for argument 'season' is not correct."
"Valid values are 'summer' and 'winter'")
def water_vapour_density(self, lat, h, season='summer'):
""" Section 2 of Recommendation ITU-R P.835-6."""
if season == 'summer':
return np.where(
np.abs(lat) < 22, self.low_latitude_water_vapour(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_water_vapour_summer(h),
self.high_latitude_water_vapour_summer(h)))
elif season == 'winter':
return np.where(
np.abs(lat) < 22, self.low_latitude_water_vapour(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_water_vapour_winter(h),
self.high_latitude_water_vapour_winter(h)))
else:
raise ValueError("The value for argument 'season' is not correct."
"Valid values are 'summer' and 'winter'")
class _ITU835_5():
def __init__(self):
self.__version__ = 5
self.year = 2012
self.month = 2
self.link = 'https://www.itu.int/rec/R-REC-P.835-5-201202-I/en'
@staticmethod
def standard_temperature(h, T_0=288.15):
"""
"""
H = np.array([0, 11, 20, 32, 47, 51, 71, 85])
T = np.array([0, -65, -65, -53, -11, -11, -67, -95]) + T_0
return np.interp(h, H, T)
@staticmethod
def standard_pressure(h, T_0=288.15, P_0=1013.25):
"""
"""
H = [0, 11, 20, 32, 47, 51, 71, 85]
L = [-6.5, 0, 1, 2.8, 0, -2.8, -2]
T = np.array([0, -65, -65, -53, -11, -11, -67, -95]) + T_0
num_splits = np.minimum(np.searchsorted(H, h), 7)
if not hasattr(num_splits, '__iter__'):
num_splits = list([num_splits])
ret = np.ones_like(h) * P_0
for ret_i, n in enumerate(num_splits):
n = n.squeeze()
P = np.zeros((n + 1))
P[0] = P_0
for i in range(n):
h_p = h[ret_i] if i == (n - 1) else H[i + 1]
if L[i] != 0:
P[i + 1] = P[i] * \
(T[i] / (T[i] + L[i] * (h_p - H[i])))**(34.163 / L[i])
else:
P[i + 1] = P[i] * np.exp(-34.162 * (h_p - H[i]) / T[i])
ret[ret_i] = P[-1]
return ret
@staticmethod
def standard_water_vapour_density(h, h_0=2, rho_0=7.5):
"""
"""
return rho_0 * np.exp(-h / h_0)
def standard_water_vapour_pressure(self, h, h_0=2, rho_0=7.5):
"""
"""
rho_h = self.standard_water_vapour_density(h, h_0, rho_0)
T_h = self.standard_temperature(h)
return rho_h * T_h / 216.7
# Low latitude standard atmosphere functions (Section ITU-R P.835 5-2) #
@staticmethod
def low_latitude_temperature(h):
"""Section 2 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h < 17)),
300.4222 - 6.3533 * h + 0.005886 * h**2,
np.where(np.logical_and((17 <= h), (h < 47)),
194 + (h - 17) * 2.533,
np.where(np.logical_and((47 <= h), (h < 52)), 270,
np.where(np.logical_and((52 <= h), (h < 80)),
270 - (h - 52) * 3.0714,
np.where(np.logical_and((80 <= h), (h <= 100)), 184, np.nan)))))
def low_latitude_pressure(self, h):
"""Section 2 of Recommendation ITU-R P.835-5."""
P10 = 284.8526 # Pressure at 10 km using the equation below
P72 = 0.03136608 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1012.0306 - 109.0338 * h + 3.6316 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.165 * (h - 72)), np.nan)))
@staticmethod
def low_latitude_water_vapour(h):
"""Section 3.1 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h <= 15)), 19.6542 *
np.exp(- 0.2313 * h - 0.1122 * h**2 + 0.01351 * h**3 -
0.0005923 * h**4), 0)
# Mid latitude standard atmosphere functions (Section ITU-R P.835-6 3)
@staticmethod
def mid_latitude_temperature_summer(h):
"""Section 3.1 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h < 13)),
294.9838 - 5.2159 * h - 0.07109 * h**2,
np.where(np.logical_and((13 <= h), (h < 17)), 215.15,
np.where(np.logical_and((17 <= h), (h < 47)),
215.15 * np.exp((h - 17) * 0.008128),
np.where(np.logical_and((47 <= h), (h < 53)), 275,
np.where(np.logical_and((53 <= h), (h < 80)),
275 + 20 * (1 - np.exp((h - 53) * 0.06)),
np.where(np.logical_and((80 <= h), (h <= 100)),
175, np.nan))))))
def mid_latitude_pressure_summer(self, h):
"""Section 3.1 of Recommendation ITU-R P.835-5."""
P10 = 283.7096 # Pressure at 10 km using the equation below
P72 = 0.031240222 # Pressure at 72 km using the equation below
return np.where(
np.logical_and((0 <= h), (h <= 10)),
1012.8186 - 111.5569 * h + 3.8646 * h**2, np.where(
np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(
np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.165 * (h - 72)),
np.nan)))
@staticmethod
def mid_latitude_water_vapour_summer(h):
"""Section 3.1 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h <= 15)),
14.3542 * np.exp(- 0.4174 * h - 0.02290 * h**2 +
0.001007 * h**3), 0)
@staticmethod
def mid_latitude_temperature_winter(h):
"""Section 3.2 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h < 10)),
272.7241 - 3.6217 * h - 0.1759 * h**2,
np.where(np.logical_and((10 <= h), (h < 33)), 218,
np.where(np.logical_and((33 <= h), (h < 47)),
218 + (h - 33) * 3.3571,
np.where(np.logical_and((47 <= h), (h < 53)), 265,
np.where(np.logical_and((53 <= h), (h < 80)),
265 - (h - 53) * 2.0370,
np.where(np.logical_and((80 <= h), (h <= 100)),
210, np.nan))))))
def mid_latitude_pressure_winter(self, h):
"""Section 3.2 of Recommendation ITU-R P.835-5."""
P10 = 258.9787 # Pressure at 10 km using the equation below
P72 = 0.02851702 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1018.8627 - 124.2954 * h + 4.8307 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.155 * (h - 72)), np.nan)))
@staticmethod
def mid_latitude_water_vapour_winter(h):
"""Section 3.2 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and(0 <= h, h <= 10),
3.4742 * np.exp(- 0.2697 * h - 0.03604 * h**2 +
0.0004489 * h**3), 0)
# High latitude standard atmosphere functions (Section ITU-R P.835-5 4) #
@staticmethod
def high_latitude_temperature_summer(h):
"""Section 4.1 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h < 10)),
286.8374 - 4.7805 * h - 0.1402 * h**2,
np.where(np.logical_and((10 <= h), (h < 23)), 225,
np.where(np.logical_and((23 <= h), (h < 48)),
225 * np.exp((h - 23) * 0.008317),
np.where(np.logical_and((48 <= h), (h < 53)), 277,
np.where(np.logical_and((53 <= h), (h < 79)),
277 - (h - 53) * 4.0769,
np.where(np.logical_and((79 <= h), (h <= 100)),
171, np.nan))))))
def high_latitude_pressure_summer(self, h):
"""Section 4.1 of Recommendation ITU-R P.835-5."""
P10 = 269.6138 # Pressure at 10 km using the equation below
P72 = 0.04582115 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1008.0278 - 113.2494 * h + 3.9408 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.140 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.165 * (h - 72)), np.nan)))
@staticmethod
def high_latitude_water_vapour_summer(h):
"""Section 4.1 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h <= 15)),
8.988 * np.exp(- 0.3614 * h - 0.005402 * h**2 -
0.001955 * h**3), 0)
@staticmethod
def high_latitude_temperature_winter(h):
"""Section 4.2 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h < 8.5)),
257.4345 + 2.3474 * h - 1.5479 * h**2 +
0.08473 * h**3,
np.where(np.logical_and((8.5 <= h), (h < 30)), 217.5,
np.where(np.logical_and((30 <= h), (h < 50)),
217.5 + (h - 30) * 2.125,
np.where(np.logical_and((50 <= h), (h < 54)), 260,
np.where(np.logical_and((54 <= h), (h <= 100)),
260 - (h - 54) * 1.667, np.nan)))))
def high_latitude_pressure_winter(self, h):
"""Section 4.2 of Recommendation ITU-R P.835-5."""
P10 = 243.8718 # Pressure at 10 km using the equation below
P72 = 0.02685355 # Pressure at 72 km using the equation below
return np.where(np.logical_and((0 <= h), (h <= 10)),
1010.8828 - 122.2411 * h + 4.554 * h**2,
np.where(np.logical_and((10 < h), (h <= 72)),
P10 * np.exp(-0.147 * (h - 10)),
np.where(np.logical_and((72 < h), (h <= 100)),
P72 * np.exp(-0.150 * (h - 72)), np.nan)))
@staticmethod
def high_latitude_water_vapour_winter(h):
"""Section 4.2 of Recommendation ITU-R P.835-5."""
return np.where(np.logical_and((0 <= h), (h <= 10)),
1.2319 * np.exp(0.07481 * h - 0.0981 * h**2 +
0.00281 * h**3), 0)
def temperature(self, lat, h, season='summer'):
""" Section 2 of Recommendation ITU-R P.835-5."""
if season == 'summer':
return np.where(
np.abs(lat) < 22, self.low_latitude_temperature(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_temperature_summer(h),
self.high_latitude_temperature_summer(h)))
else:
return np.where(
np.abs(lat) < 22, self.low_latitude_temperature(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_temperature_winter(h),
self.high_latitude_temperature_winter(h)))
def pressure(self, lat, h, season='summer'):
""" Section 2, 3, 4 of Recommendation ITU-R P.835-5."""
if season == 'summer':
return np.where(
np.abs(lat) < 22, self.low_latitude_pressure(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_pressure_summer(h),
self.high_latitude_pressure_summer(h)))
else:
return np.where(
np.abs(lat) < 22, self.low_latitude_pressure(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_pressure_winter(h),
self.high_latitude_pressure_winter(h)))
def water_vapour_density(self, lat, h, season='summer'):
""" Section 2 of Recommendation ITU-R P.835-5."""
if season == 'summer':
return np.where(
np.abs(lat) < 22, self.low_latitude_water_vapour(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_water_vapour_summer(h),
self.high_latitude_water_vapour_summer(h)))
else:
return np.where(
np.abs(lat) < 22, self.low_latitude_water_vapour(h),
np.where(
np.abs(lat) < 45, self.mid_latitude_water_vapour_winter(h),
self.high_latitude_water_vapour_winter(h)))
__model = __ITU835__()
[docs]def change_version(new_version):
"""
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)
"""
global __model
__model = __ITU835__(new_version)
[docs]def get_version():
"""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: int
The version of the ITU-R P.835 recommendation being used.
"""
global __model
return __model.__version__
[docs]def temperature(lat, h, season='summer'):
""" 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: Quantity
Temperature (K)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
type_output = get_input_type(lat)
lat = prepare_input_array(lat)
h = prepare_quantity(h, u.km, 'Height')
val = __model.temperature(lat, h, season)
return prepare_output_array(val, type_output) * u.Kelvin
[docs]def pressure(lat, h, season='summer'):
""" 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: Quantity
Pressure (hPa)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
type_output = get_input_type(lat)
lat = prepare_input_array(lat)
h = prepare_quantity(h, u.km, 'Height')
val = __model.pressure(lat, h, season)
return prepare_output_array(val, type_output) * u.hPa
[docs]def water_vapour_density(lat, h, season='summer'):
""" 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: Quantity
Water vapour density (g/m^3)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
type_output = get_input_type(lat)
lat = prepare_input_array(lat)
h = prepare_quantity(h, u.km, 'Height')
val = __model.water_vapour_density(lat, h, season)
return prepare_output_array(val, type_output) * u.g / u.m**3
[docs]def standard_temperature(h, T_0=288.15):
""" 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: Quantity
Temperature (K)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
h = prepare_quantity(h, u.km, 'Height')
T_0 = prepare_quantity(T_0, u.Kelvin, 'Surface temperature')
return __model.standard_temperature(h, T_0) * u.Kelvin
[docs]def standard_pressure(h, T_0=288.15, P_0=1013.25):
""" 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: Quantity
Pressure (hPa)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
type_output = get_input_type(h)
h = prepare_quantity(h, u.km, 'Height')
h = np.atleast_1d(h)
T_0 = prepare_quantity(T_0, u.Kelvin, 'Surface temperature')
P_0 = prepare_quantity(P_0, u.hPa, 'Surface pressure')
val = __model.standard_pressure(h, T_0, P_0)
return prepare_output_array(val, type_output) * u.hPa
[docs]def standard_water_vapour_density(h, h_0=2, rho_0=7.5):
""" 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: Quantity
Water vapour density (g/m^3)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
h = prepare_quantity(h, u.km, 'Height')
h_0 = prepare_quantity(h_0, u.km, 'Scale height')
rho_0 = prepare_quantity(
rho_0,
u.g / u.m**3,
'Surface water vapour density')
return __model.standard_water_vapour_density(h, h_0, rho_0) * u.g / u.m**3
[docs]def standard_water_vapour_pressure(h, h_0=2, rho_0=7.5):
"""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: Quantity
Water vapour pressure (hPa)
References
----------
[1] Reference Standard Atmospheres
https://www.itu.int/rec/R-REC-P.835/en
"""
global __model
h = prepare_quantity(h, u.km, 'Height')
h_0 = prepare_quantity(h_0, u.km, 'Scale height')
rho_0 = prepare_quantity(
rho_0,
u.g / u.m**3,
'Surface water vapour density')
return __model.standard_water_vapour_pressure(h, h_0, rho_0) * u.hPa