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