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7: Activates recommendation ITU-R P.840-7 (12/17) (Superseded)

6: Activates recommendation ITU-R P.840-6 (09/13) (Superseded)

5: Activates recommendation ITU-R P.840-5 (02/12) (Superseded)

4: Activates recommendation ITU-R P.840-4 (10/09) (Superseded)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