UK Study Group 3
CP 72
February 2002
Element for Inclusion in Handbook on Interference
Some material for the Handbook on Interference has already been developed in previous
submissions to ITU-R Working Party 3M and has been incorporated into Annex 26 of
Document 3M/7. This material will be updated in the light of the new version of the rain
scatter model presented in CP???.
It is intended also to include some example calculations with the model, to facilitate users in
checking their own implementations of the model, and this document contains a possible
example calculation, for an earth station located at Bercenay, France.
Details of each step in the calculation of transmission loss are given for three particular steps,
at 150, 200 and 250 km ranges, where each of the components has contributions, to provide a
guide. Also given is an example of the iteration procedure, in which the transmission loss is
calculated, starting at a maximum distance of 400 km and decrementing by 1 km steps. For
each step, the transmission loss is given, with the coordination distance given by the range
immediately preceding the step at which the calculated transmission loss is just less than the
criterion to be used, i.e. the minimum permissible basic transmission loss.
Example Calculation
Set coordinates for Bercenay:
48 13 N, 3 53 E
Set time percentage:
0.005%
Obtain rainfall rate for 0.005% of time from P.837-3:
40.74 mm/h
Obtain rain height from P.839-3:
2.718 km
Obtain average surface water vapour density from P.836-3:
7.07 g/m3.
Set frequency:
f = 14.0 GHz
Set gain of terrestrial station:
GT = 42 dB
Set elevation of earth station:
 = 20
Figures 1 to 4 show the variation of some key parameters in the calculation of the
transmission loss due to rain scatter.
2
6
2.0
5
1.5
Value
Value, km
4
3
1.0
2
hm
hc
1
0
100
150
200
250
1
0.5
2
0.0
100
300
150
Range, km
FIGURE 1
Variation of hm and hc with range
250
300
FIGURE 2
Variation of 1 and 2 with range
1.2
1.50
1.0
1.25
0.8
1.00
Value
Value
200
Range, km
0.6
0.4
Cb
Ca
0.75
0.50
a
b
0.2
0.0
100
150
200
250
Range, km
FIGURE 3
Variation of a and b with range
0.25
300
0.00
100
150
200
250
300
Range, km
FIGURE 4
Variation of Ca and Cb with range
To facilitate development of software implementations of the model, Table 1 lists values for
the key parameters in the model for determining transmission loss due to rain scatter, at three
ranges, 150, 200 and 250 km. Table 2 then lists the transmission loss as a function of range,
decreasing in 1 km steps from an initial range of 400 km.
3
TABLE 1
Values of key parameters in the determination of transmission loss due to rain scatter
Parameter
Range, km
Dry air specific attenuation, o
Water vapour specific attenuation, w
Radius of rain cell, dc
Specific rain attenuation, R
Rain attenuation scaling distance, rm
Angle between terrestrial station and rain cell, 
Height of beam intersection, hm
Pathlength from terrestrial station to rain cell, rt
Pathlength from rain cell to earth station, rr
Distance from rain cell to earth station, de
Limit of integration, hc
Attenuation outside common volume to ES, 1
Attenuation outside common volume to TS, 2
Attenuation outside common volume below hR, b
Attenuation outside common volume above hR, a
Scatter transfer function below hR, Cb
Scatter transfer function above hR, Ca
Calculation of transmission loss
20 log r
20 log f
14 log R
10 log C
Terrestrial antenna gain, GT
10 log S
Gaseous attenuation, Ag
Transmission loss,
L = 173 + a – b – c – d – e + f + g
150
0.0176
1.324
150.016
3.868
3.634
2.217
1.723
1.756
0.438
0.207
1.039
0
a
b
c
d
e
f
g
43.522
200
0.008002
0.01558
2.453
1.925
0.912
0.0235
2.353
200.037
6.874
6.458
2.718
1.754
1.756
0.435
0.406
0.698
1.072
250
0.0294
3.678
250.072
10.736
10.084
3.678
0
1.756
0.668
1.0
0
0.3425
47.959
0.233
3.121
46.021
22.923
22.541
-1.317
42.0
0.233
4.187
135.831
137.294
143.061
-3.419
-4.653
0
4.913
4
TABLE 2
Transmission loss versus range
Range
km
Loss
dB
Range
km
Loss
dB
Range
km
Loss
dB
Range
km
Loss
dB
400
399
398
397
396
395
394
393
392
391
390
389
388
387
386
385
384
383
382
381
380
379
378
377
376
375
374
373
372
371
370
369
368
367
366
365
364
363
362
361
360
359
358
185.59
185.25
184.92
184.58
184.25
183.92
183.59
183.25
182.92
182.59
182.27
181.94
181.61
181.28
180.96
180.63
180.31
179.98
179.66
179.34
179.02
178.70
178.38
178.06
177.74
177.42
177.10
176.79
176.47
176.16
175.84
175.53
175.22
174.90
174.59
174.28
173.97
173.66
173.35
173.04
172.74
172.43
172.12
357
356
355
354
353
352
351
350
349
348
347
346
345
344
343
342
341
340
339
338
337
336
335
334
333
332
331
330
329
328
327
326
325
324
323
322
321
320
319
318
317
316
315
171.82
171.51
171.21
170.91
170.61
170.30
170.00
169.70
169.40
169.10
168.81
168.51
168.21
167.92
167.62
167.33
167.03
166.74
166.45
166.15
165.86
165.57
165.28
164.99
164.71
164.42
164.13
163.84
163.56
163.27
162.99
162.71
162.42
162.14
161.86
161.58
161.30
161.02
160.74
160.46
160.19
159.91
159.63
314
313
312
311
310
309
308
307
306
305
304
303
302
301
300
299
298
297
296
295
294
293
292
291
290
289
288
287
286
285
284
283
282
281
280
279
278
277
276
275
274
273
272
159.36
159.08
158.81
158.54
158.26
157.99
157.72
157.45
157.18
156.91
156.64
156.38
156.11
155.84
155.58
155.31
155.05
154.78
154.52
154.26
154.00
153.74
153.48
153.22
152.96
152.70
152.44
152.18
151.93
151.67
151.42
151.16
150.91
150.66
150.40
150.15
149.90
149.65
149.40
149.15
148.91
148.66
148.41
271
270
269
268
267
266
265
264
263
262
261
260
259
258
257
256
255
254
253
252
251
250
249
248
247
246
245
244
243
242
241
240
239
238
237
236
235
234
233
232
231
230
229
148.16
147.92
147.67
147.42
147.17
146.93
146.68
146.43
146.19
145.95
145.70
145.46
145.22
144.97
144.73
144.49
144.25
144.01
143.77
143.54
143.30
143.06
142.83
142.59
142.35
142.12
141.89
141.65
141.42
141.19
140.96
140.73
140.50
140.27
140.04
139.81
139.59
139.36
139.13
138.91
138.68
138.46
138.23
5
From this table, for a required transmission loss of 160 dB, a coordination distance of 317 km
would be indicated, and for a loss of 145 dB, a coordination distance of 259 km is shown.
For a required transmission loss of 160 dB, the coordination area is then a circle of radius 317
km, located at a distance of de = 16.2 km from the earth station, in the direction of the antenna
main beam, while for a required transmission loss of 145 dB, the coordination area is a circle
of radius 259 km at a distance of de = 10.8 km from the earth station.