Rec. ITU-R P.840-3
1
RECOMMENDATION ITU-R P.840-3
ATTENUATION DUE TO CLOUDS AND FOG
(Question ITU-R 201/3)
(1992-1994-1997-1999)
Rec. ITU-R P.840-3
The ITU Radiocommunication Assembly,
considering
a)
that there is a need to give guidance to engineers in the design of Earth-space telecommunication systems for
frequencies higher than 10 GHz;
b)
that attenuation due to clouds may be a factor of importance especially for microwave systems well above
10 GHz or low-availability systems,
recommends
1
that the curves, models and maps given in Annex 1 should be used for the calculation of attenuation due to
clouds and fog.
ANNEX 1
1
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:
c  Kl M
dB/km
(1)
where:

c :
specific attenuation (dB/km) within the cloud
Kl : specific attenuation coefficient ((dB/km)/(g/m3))
M:
liquid water density in the cloud or fog (g/m3).
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).
2
Specific attenuation coefficient
A mathematical model based on Rayleigh scattering, which uses a double-Debye model for the dielectric permittivity
 ( f ) of water, can be used to calculate the value of Kl for frequencies up to 1 000 GHz:
Kl 
0.819 f
(dB/km)/(g/m3)
" (1  2 )
(2)
where f is the frequency (GHz), and:
 
2 + '
"
(3)
2
Rec. ITU-R P.840-3
The complex dielectric permittivity of water is given by:
"( f ) 
'( f ) 
f (0 – 1)
fp 1 + (f / fp)2
0 – 1
1 + (f / f )2
p 



f (1 – 2)
(4)
fs 1 + (f / fs)2
1 – 2
1 + (f / f )2
s 

+ 2
(5)
where:
0  77.6  103.3 ( – 1)
(6)
1  5.48
(7)
2  3.51
(8)
  300 / T
(9)
with T the temperature (K).
The principal and secondary relaxation frequencies are:
fp  20.09 – 142 ( – 1)  294 ( – 1)2
GHz
(10)
fs  590 – 1 500 ( – 1)
GHz
(11)
Figure 1 shows the values of Kl at frequencies from 5 to 200 GHz and temperatures between –8° C and 20° C. For cloud
attenuations, the curve corresponding to 0° C should be used.
Rec. ITU-R P.840-3
3
FIGURE 1
Specific attenuation by water droplets at various
temperatures as function of frequency
Specific attenuation coefficient, Kl ((dB/km) / (g/m³))
10
5
20° C
10° C
0° C
– 8° C
2
1
0.5
0.2
0.1
0.05
0.02
0.01
5
10
20
50
100
200
Frequency (GHz)
0840-01
FIGURE 0840-01 = 12 cm
4
3
Rec. ITU-R P.840-3
Cloud attenuation
To obtain the attenuation due to clouds for a given probability value, the statistics of the total columnar content of liquid
water L (kg/m2) or, equivalently, mm of precipitable water for a given site must be known yielding:
A 
L Kl
sin 
dB
for 90    5
(12)
where  is the elevation angle and Kl is read from Fig. 1. Note that Kl is identical to the mass absorption coefficient aL
introduced in Recommendation ITU-R P.836, equation (1).
Statistics of the total columnar content of liquid water may be obtained from radiometric measurements or from
radiosonde launches.
In the absence of local measurements, the total columnar content of cloud liquid water (normalized to 0 C) values shown
in Figs. 2 to 5 should be used to derive cloud attenuation.
The values shown in the Figures are in kg/m2 for four different yearly exceedance probability levels. The maps were
derived from two years of data with a spatial resolution of 1.5 in latitude and longitude. Data files containing these data
as well as data for additional probability levels can be obtained from the ITU Radiocommunication Bureau. The latitude
grid of the data files is from 90 N to –90 S in 1.5 steps; the longitude grid is from 0 to 360 in 1.5 steps.
For a location different from the gridpoints, obtain the total columnar content at the desired location by performing a bilinear interpolation on the values at the four closest grid points.
To obtain the value exceeded for a probability different from those in the data files, use a semi-logarithmic interpolation
(logarithmic on the probability in per cent and linear on the total columnar content).
FIGURE 0840-02 = 21 cm
–80
–60
–40
–20
0
20
40
60
80
0.3
0.3
–150
0.1
0.1
0.3
0.1
0.1
0.1
0.1
0.1
FIGURE 2
–100
0.1
0.1
0.3
0.1
–50
0.1
0.5
0.1
0.1
0.1
0
0.5
0.1
0.1
0.3
0.1
0.1
Longitude (degrees)
0.1
0.1
0.5
0.1
0.1
50
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
100
0.5
0.1
Normalized total columnar content of cloud liquid water (kg/m2) exceeded for 20% of the year
0.3
0840-02
0.1
0.5
0.5
0.1
0.1
0.3
0.3
150
0.3
0.1
Rec. ITU-R P.840-3
5
Latitude (degrees)
FIGURE 0840-03 = 21 cm
–80
–60
–40
–20
0
20
40
60
80
0.2
–150
0.2
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.2
0.2
–100
0.2
0.6
0.4
–50
0.8
0.2
0.2
0.2
0
0.2
0.6
Longitude (degrees)
0.4
0.4
0.2
0.4
50
0.2
0.2
0.2
0.2
0.2
0.4
0.2
100
0.8
0.8
Normalized total columnar content of cloud liquid water (kg/m2) exceeded for 10% of the year
FIGURE 3
0.2
0.4
0.8
0.2
0840-03
0.4
0.4
0.2
150
0.4
0.2
0.2
0.8
0.6
0.6
0.4
0.6
6
Rec. ITU-R P.840-3
Latitude (degrees)
FIGURE 0840-04 = 21 cm
–80
–60
–40
–20
0
20
40
60
80
1
0.6
0.6
0.6
–150
1
0.2
0.2
1
1
0.2
0.2
0.6
0.2
0.6
0.2
0.2
–100
0.2
0.6
0.6
1
0.2
0.2
0.6
–50
0.6
1
0.2
1
0.2
0.2
0.6
0.2
0
Longitude (degrees)
0.2
0.6
0.6
0.2
0.2
0.2
0.2
50
0.2
0.6
0.6
0.6
0.2
0.6
0.2
0.2
1
0.2
0.2
0.2
0.6
100
1
1
0.2
0.2
0.6
0.6
0.2
1
0.2
Normalized total columnar content of cloud liquid water (kg/m2) exceeded for 5% of the year
FIGURE 4
0.2
150
0.6
0.6
0840-04
0.6
1
0.6
1
1
0.6
0.2
Rec. ITU-R P.840-3
7
Latitude (degrees)
FIGURE 0840-05 = 21 cm
–80
–60
–40
–20
0
20
40
60
80
–150
1.6
1.2
0.8
1.6
0.4
1.6
0.8
0.8
1.2
0.4
–100
0.4
1.6
0.4
1.2
0.4
0.8
0.4
1.2
0.8
0.4
0.8
2
1.2
–50
0.8
1.6
1.2
0.8
0.4
0.4
0.8
0.4
0.4
0.4
1.2
0.8
0.4
0
Longitude (degrees)
1.6
0.4
2
0.4
0.8
1.2
1.2
0.8
1.2
0.8
0.4
0.8
0.4
50
1.2
0.8
1.2
0.8
0.8
2
100
2
2
2
0.4
0.8
2
Normalized total columnar content of cloud liquid water (kg/m2) exceeded for 1% of the year
FIGURE 5
0.8
2
2
1.6
0.8
0.4
2
150
1.2
1.6
1.2
0840-05
0.4
0.8
1.2
2
1.2
0.8
1.6
1.6
1.2
0.4
8
Rec. ITU-R P.840-3
Latitude (degrees)