INTERNATIONAL TELECOMMUNICATION
UNION
RADIOCOMMUNICATION
STUDY GROUPS
UK SG3
CP 73
Document 3M/UK-AB
February 2002
English only
Received:
Subject: Recommendation ITU-R P.620-4, WRC 2000 Resolution 74
United Kingdom
PROPOSED REVISIONS TO RECOMMENDATION ITU-R P.620-4
Summary
Resolution 74 from the World Radio Conference in 2000 requested the ITU-R to continue
studying refinements to propagation mode (2) for the coordination of earth stations, to address
(a) the elevation angle dependence of the coordinating earth station and (b) to investigate
methods to address the propagation mode (2) water vapour density for both radio climate
zones B and C.
The United Kingdom has developed a new method for determining propagation mode (2) rain
scatter interference, closely based on the model in Recommendation ITU-R P.452-9, in which
the elevation angle of the earth station is an input parameter. The new method is based on an
analytical integration of the rain scatter transfer function for scattering from both below and
above the rain height (melting layer). The coupling losses due to scattering from above the
melting layer, which, in many cases, is what determines the required coordination distance,
are thus derived from an expression analagous to that in Recommendation P.452-9, rather
than an emprical correction factor, as in the current model in Recommendation P.620-4.
The new model takes input radiometeorological data from the ITU-R digital world maps now
incorporated in Recommendations ITU-R P.837-3, for rainfall rate, P.839-3, for rain height,
and P.836-3, for surface water vapour density, and thus addresses the second request in
Resolution 74.
This document proposes a revision to the mode (2) method in Recommendation P.620-4
based on this model. A companion document contains full details of the development and
testing of the model and gives examples of the coordination distances which result from the
new model, comparing these with those which result from the current method in
Recommendation P.620-4.
Proposal:
Replace the current Appendix 3 to Annex 1 in Recommendation ITU-R
P.620-4 with the following text.
2
APPENDIX 3 TO ANNEX 1
Calculation of the coordination distance for propagation mode (2)
1
Overview
The methodology to determine the coordination distance for propagation mode (2) rain scatter
interference is based on the bistatic radar equation, with the so-called “narrow-beam”
approximation for the earth station antenna, in which the spreading loss from the scattering
volume to the earth station antenna is cancelled by the antenna gain. The method thus
depends primarily on the pathlength from the terrestrial station to the scattering volume, i.e.
the rain cell.
The algorithm given below allows transmission loss, Lr(p2) (dB), to be obtained as a function
of rainfall rate, R(p2) (mm/h), and with the separation distance between the edge of the rain
cell and the possible location of the terrestrial station, ri (km), as a parameter. The geometry
of the rain scatter process is illustrated in Figure 1.
FIGURE 1
Geometry of the rain scatter process
ES is the earth station with antenna elevation ; TS is the terrestrial station.
The procedure to determine the hydrometeor scatter contour is as follows:
3
The value of R(p2), should be found from Recommendation ITU-R P.837-3 for the required
average annual time percentage, p2 (0.001% to 10%), and the latitude and longitude
appropriate to the earth station location.
Values of Lr(p2) are then calculated for decrementing values of ri, starting at the maximum
coordination distance dmax2 for propagation mode (2), given in Table 2. The recommended
distance decrement, s (km), is 1 km. The value of ri is decremented until the corresponding
value of Lr(p2 is just less than the required transmission loss L(p2). Thus, decrement ri until
either of the following conditions are true:
Lr  p2   L p2 
(50a)
ri  d min
(50b)
or
where this latter condition represents the minimum coordiantion distance.
The coordination distance dr is then given by the immediately preceding value of ri:
d r  ri 1  d max2  s  i  1
(51)
The resulting coordination distance, dr, is the propagation pathlength between the transmitting
terrestrial station and the edge of the rain cell that will provide the required transmission path
loss. Assuming that scattering from the rain cell is isotropic in azimuth, the coordination
contour is defined as a circle, centred at the edge of the rain cell, with radius dr.
The coordination contour is then drawn as a circle diameter dr centred at a distance de from
the earth station along the earth-station azimuthal direction, where de is the distance from the
earth station to the edge of the rain cell, as indicated in Figure 1; determination of the distance
de is defined in the following procedure.
2
Maximum calculation distance
As discussed in §5.2 of Annex 1, it is necessary to set upper limits to the maximum distance
used in the iterative calculation of coordination distance, from which the iterative calculations
begin. The maximum calculation distance to be used for propagation mode (2) (dmax2) is
latitude dependent and is given in Table 2.
TABLE 2
Propagation mode (2) maximum calculation distances (dmax2) (km)
Latitude (degrees)
0-30
30-40
40-50
50-60
> 60
Distance (km)
350
360
340
310
280
4
3
Calculation of the propagation mode (2) coordination contour
Determine the rainfall rate exceeded for p2 % of time, R(p2), from Recommendation ITU-R
P.837-3, for the latitude and longitude of the earth station. Note that p2 % is the average
annual percentage time applicable to propagation mode (2).
Note also that the rainfall rate and rain height will not vary significantly between the location
of the earth station and the location of the rain cell along the azimuthal direction of the earth
station, since the distance between these two points will typically be less than ~30 km, for
earth-station elevation angles down to 10.
Determine the specific attenuation, R, (dB/km) due to rain using Recommendation ITU-R
P.838-1.
Set the diameter of the rain cell, dc (km):
d c  3.3R p2 
0.08
(52)
Determine the mean rain height above ground, hR (km) from Recommendation ITU-R P.839-3
for the latitude and longitude of the earth station.
Calculate an intermediate parameter, :
  R  p2   10.19
(53)
Calculate the scaling distance, rm (km) for the attenuation outside the common scattering
volume:
rm  600R p2 
0.5
10
(54)
The specific attenuation due to dry air, in dB/km, is evaluated from the following expression:

6.09
4.81

2
3
 o  7.19 10 3  2

 f 10
2
f

0
.
227
 f  57  1.5 

(55)
From Recommendation ITU-R P.836-3, determine the surface water-vapour density,  (g/m3),
exceeded for [50]% of time at the latitude and longitude corresponding to the earth station.
Note that, for simplicity in determining propagation mode(2) contours, the water-vapour
density is assumed constant over the path. The water-vapour specific attenuation is then
given in dB/km by:
5

 wv  0.050  0.0021 

 2
3.6
4
 f  10
2
 f  22.2  8.5 
(56)
Set the gain of the terrestrial station antenna (assumed to be 42 dBi):
GT  42
(57)
Iterative calculations
Beginning with the maximum coordination distance, obtained from Table 2, evaluate
equations (58) to (77) inclusive, for decreasing values of ri, where ri is the current separation
distance (km) between the earth station and the possible location of a terrestrial station and i =
0, 1, 2,…etc.:
ri  d max 2  i  s
(58)
Continue this process until the condition given in inequality (50) is true. At this point, the
rain-scatter coordination distance, dr, has the preceding value of ri, i.e.:
d r  d max 2  i  1  s
(59)
If an iteration results in d r  d min , then d r  d min and the iteration terminates.
Determine the height above ground of the point of intersection between the antenna beams
from the terrestrial station and the earth station:
 1

hm  rE 
 1
 cos

where
(60)
 is the angular separation between the earth station and the point on the Earth’s
surface at the current distance, ri:

ri
rE
radians
rE is the effective radius of the Earth, rE = 8 500 km.
Determine the pathlength from the terrestrial station to the beam intersection point:
(61)
6
rt  hm 1 2
rE
hm
(62)
Determine the pathlength from the beam intersection to the earth station:
rr  re2 sin 2   hm2  2hm rE  rE sin 
where
(63)
 is the elevation angle of the earth station antenna.
Determine the horizontal distance from the earth station to the edge of the rain cell:
 r

d e  rr arcsin  E cos  
 hm  rE

(64)
Calculate the parameter hc which depends on the region within the rain cell where the beam
intersection occurs:
hm

hc  hR
h  d tan 
c
 m
for hR  hm
for hm  hR  hm  d c tan 
(65)
for hR  hm  d c tan 
Calculate the attenuation from the point at the current distance to the beam intersection:

 r
2   R rm 1  exp   t
 rm




(66)
and the attenuation from the beam intersection to the earth station:


 d e 
 R rm 1  exp   
 rm 


1  
  d e  hR cot  
 d

  exp   e
 R rm exp  
rm

 rm
 

for hm  hR



(67)
for hm  hR
From these, evaluate the total path attenuation for scattering by rain below the rain height:

 

b  exp  0.23 1  2 
 cos 


(68)
7
and the total path attenuation for scattering from the melting layer and ice above the rain
height:
h  hm

 
a  exp  0.23 1   R c
sin 
 cos 




(69)
Calculate the effective scatter transfer function for scattering by rain below the rain height:
Cb 
4.34
sin  


1  exp  0.23 R hc  hm 


 R 1  cos   
1  cos  

(70)
and for scattering by ice above the rain height:
Ca 
0.67
exp 1.5hc  hm  exp 1.5hm  hR  d c tan  
sin  s
(71)
The total effective scatter transfer function is then given by:
C  b Cb  a Ca
(72)
Determine the deviation from Rayleigh scattering for frequencies above 10 GHz:
0.005 f  10 R  p2 
10 log S  
0
1.7
0.4
for 10  f  40
for f  10 or when Cb  0
(73)
Note that this deviation from Rayleigh scattering applies only to scattering from rain, below
the rain height.
The attenuation by atmospheric gases is now evaluated from the following expressions. First,
determine the equivalent path lengths, to take account of the decrease in gaseous specific
attenuation with height. For the path from the terrestrial station to the rain cell:
0.9rt
d to  
243  0.4rt  270
0.85rt
d tv  
187  0.4rt  220
for rt  270 km
for rt  270 km
for rt  220 km
for rt  220 km
(74a)
(74b)
and for the path from the rain cell to the earth station:
d ro  0.8rr
(75a)
d rv  0.5rr
(75b)
8
The gaesous attenuation is then determined from:
Ag   o d to  d ro    wv d tv  d rv 
(76)
Finally, the transmission loss is determined from:
Lr  p2   173  20 log ri  20 log f  14 log R  p2   10 log C  10 log S  GT  Ag
(77)
The distance dr which results from this iteration is the distance from the terrestrial station to
the edge of the rain cell, and the coordination contour then given by a circle of diameter dr,
centred at a distance de from the earth station, along its azimuthal direction, as indicated in
Figure 2.
FIGURE 2
Location of coordination contour
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