Rec. ITU-R P.837-4
1
RECOMMENDATION ITU-R P.837-4
Characteristics of precipitation for propagation modelling
(Question ITU-R 201/3)
(1992-1994-1999-2001-2003)
The ITU Radiocommunication Assembly,
considering
a)
that information on the statistics of precipitation intensity is needed for the prediction of
attenuation and scattering caused by precipitation;
b)
that the information is needed for all locations on the globe and a wide range of
probabilities,
recommends
1
that the model in Annex 1 be used to obtain the rainfall rate, Rp, exceeded for any given
percentage of the average year, p, and for any location (with an integration time of 1 min). This
model is to be applied to the data supplied in the digital files ESARAINxxx.TXT; (the data files
may be obtained from that part of the ITU-R website dealing with Radiocommunication
Study Group 3);
2
that, for easy reference, Figs. 1 to 6 in Annex 2 be used to select the rainfall rate exceeded
for 0.01% of the average year. These Figures were also derived from the model and data described
in Annex 1.
Annex 1
Model to derive the rainfall rate exceeded for a given
probability of the average year and a given location
The data files ESARAINPR6.TXT, ESARAIN_MC.TXT and ESARAIN_MS.TXT contain
respectively the numerical values for the variables Pr6, Mc and Ms while data files
ESARAINLAT.TXT and ESARAINLON.TXT contain the latitude and longitude of each of the
data entries in all other files. These data files were derived from 15 years of data of the European
Centre of Medium-range Weather Forecast (ECMWF).
2
Rec. ITU-R P.837-4
Step 1: Extract the variables Pr6, Mc and Ms for the four points closest in latitude (Lat) and
longitude (Lon) to the geographical coordinates of the desired location. The latitude grid is from
90 N to –90 S in 1.5° steps; the longitude grid is from 0 to 360 in 1.5 steps.
Step 2: From the values of Pr6, Mc and Ms at the four grid points obtain the values Pr6(Lat,Lon),
Mc(Lat,Lon) and Ms(Lat,Lon) at the desired location by performing a bi-linear interpolation, as
described in Recommendation ITU-R P.1144.
Step 3: Derive the percentage probability of rain in an average year, P0, from:

P0 ( Lat , Lon)  Pr 6 ( Lat , Lon) 1  e  0.0117 ( Ms ( Lat , Lon ) / Pr 6 ( Lat , Lon )

(1)
If Pr6 is equal to zero, the percentage probability of rain in an average year and the rainfall rate
exceeded for any percentage of an average year are equal to zero. In this case, the following steps
are unnecessary.
Step 4: Derive the rainfall rate, Rp, exceeded for p % of the average year, where p  P0, from:
 B  B 2  4 AC
R p ( Lat , Lon) 
2A
mm/h
(2)
where:
Aab
(2a)
B  a  c ln( p / P0(Lat,Lon))
(2b)
C  ln( p / P0(Lat,Lon))
(2c)
a  1.11
(2d)
and
b
( Mc ( Lat , Lon)  Ms ( Lat , Lon))
22 932 P0
c  31.5b
(2e)
(2f)
NOTE 1 – An implementation of this model and the associated data in MATLAB is also available from
the ITU-R website dealing with Radiocommunication Study Group 3.
Latitude
180
0
10
20
30
40
50
60
70
80
90
50
80
40
30
120
120
100
35
25
15
10
60
40
40
35
120
100
50
200
20
100
30
25
80
35
10
220
25
30
20
FIGURE 1
20
30
60
15
40
20
120
240
10
15
50
120
80
20
100
20
Longitude
20
15
260
50
50
20
40
30
25
10
50
80
60
80
120
80
15
10
100
100
40
35
10
280
120
100
30
25
15
Rain rate (mm/h) exceeded for 0.01% of the average year
30
20
35
100
100
100
35
100
300
120
100
35
80
80
100
25
15
5
120
60
15
30
100
0837-01
20
40
100
120
50
50
320
120
50
60
25
Rec. ITU-R P.837-4
3
Annex 2
Latitude
0
10
20
30
40
50
60
70
80
90
300
25
100
80
35
120
20
80
100
15
10
120
100
30
25
15
25
50
120
100
320
60
5
30
120
25
5
80
15
35
35
100
20
20
10
5
30
40
60
120
100
20
15
30
25
10
340
10
15
FIGURE 2
25
10
20
30
30
0
100
5
30
25
30
20
80
80
100
25
5
25
25
20
40
40
100
5
20
20
20
20
Longitude
35
30
30
50
40
30
10
100
100
35
25
120
15
30
5
25
25
10
25
40
10
15
Rain rate (mm/h) exceeded for 0.01% of the average year
100
25
80
10
25
15
100
10
10
15
20
10
10
60
10
10
10
10
20
120
120
10
15
15
10
100
100
80
10
5
10
25
120
0837-02
80
120
120
60
15
15
20
20
10
4
Rec. ITU-R P.837-4
Latitude
0
10
20
30
40
50
60
70
80
90
20
60
10
10
10
10
20
15
15
10
15
20
20
15
100
120
80
10
15
10
50
80
15
80
120
60
20
10
80
20
15
5
10
100
120
80
10
10
25
20
120
120
15
25
20
15
FIGURE 3
100
120
120
5
120
120
100
60
30
25
20
80
30
10
20
10
20
15
25
50
100
35
100
50
30
30
120
Longitude
100
120
60
20
40
15
35
35
100
120
80
30
100
35
20
140
120
25
15
10
120
80
15
Rain rate (mm/h) exceeded for 0.01% of the average year
120
100
60
60
20
15
160
80
50
40
25
100
30
35
20
50
15
10
0837-03
120
Rec. ITU-R P.837-4
5
Latitude
180
–70
–60
–50
–40
–30
–20
–10
0
80
100
10
15
20
35
40
50
60
120
25
30
200
30
120
100
100
220
80
80
FIGURE 4
60
40
60
240
30
35
50
25
60
50
10
15
20
15
Longitude
20
50
260
50
30
10
40
15
25
10
280
20
Rain rate (mm/h) exceeded for 0.01% of the average year
5
10
80
100
15
100
300
5
20
60
80
60
100
100
10
40
20
15
50
25
30
60
30
0837-04
320
35
40
60
60
60
100
6
Rec. ITU-R P.837-4
Latitude
–70
–60
–50
–40
–30
–20
–10
0
300
20
80
30
40
60
320
60
60
60
100
80
40
50
340
20
25
35
FIGURE 5
30
80
15
15
5
10
30
60
0
25
10
10
20
35
20
Longitude
80
100
35
50
25
30
50
50
100
60
60
80
80
40
40
80
5
35
100
10
40
60
Rain rate mm/h) exceeded for 0.01% of the average year
15
25
100
20
60
60
35
80
40
50
120
30
30
0837-05
80
25
Rec. ITU-R P.837-4
7
Latitude
–70
–60
–50
–40
–30
–20
–10
0
60
35
40
50
60
80
100
120
120
5
10
30
25
15
20
80
25
25
25
80
100
120
120
30
20
5
60
FIGURE 6
20
100
15
10
120
15
100
30
30
30
20
50
60
80
20
120
Longitude
20
100
30
100
100
25
20
50
80
25
20
25
100
30
40
100
20
140
30
100
120
Rain rate (mm/h) exceeded for 0.01% of the average year
15
30
40
50
80
120
35
60
10
50
100
160
30
35
60
5
50
40
60
0837-06
120
25
50
120
8
Rec. ITU-R P.837-4