RAIN FADE CALCULATIONS

Introduction

Rain fade is the dominant factor in path loss variation above 10GHz, and can have an

effect below that frequency at low elevations. This short note describes on of the

ITU-R methods for calculating rain fade. It can also be use to relate the required

availability of satellite circuits to the fade margin that must be included in the link

budget.

Fain fades vary with frequency, location, polarisation and rainfall rate. The depth of

fade in dB can be calculated from:

LRAIN = γR DRAIN

Where: LRAIN is the rain loss in dB

γR is the specific attenuation (dB/Km)

DRAIN is the path length through the troposphere in Km,

To calculate the rain attenuation we need to know:

• Latitude and longitude of the earth station to within a degree.

• Altitude of the station in Km.

• The frequency of operation

• The polarisation of the signal.

• The required availability of the satellite circuit.

Determining DRAIN

DRAIN is effectively the slant range of the portion of the signal that lies below the

freezing point (zero degree isotherm) in the atmosphere. The assumption is that all

rain originates at this level.

hANTENNA

hRAIN

Rain height

(zero degree isotherm)

elevation

anglee Antenna

height

Datum

DRAIN

DRAIN can be calculated from simple trigonometry from the above diagram.

)(

)(

eSin

hhD

ANTENNARAIN

RAIN

−=

This implies knowledge of the rain height hRAIN. ITU-R Recommendation P.839

relates rain height to location. It is reproduced at table 1.

Latitude ϕϕϕϕ hRAIN Region

ϕ > 23 N 5 - 0.075 (ϕ - 23) N hemisphere (except N America &

Europe)

0 ≤ ϕ ≤ 23N 5 N hemisphere (except N America &

Europe)

3.2-0.075 (ϕ - 35) N hemisphere N America & Europe

west of 60E Longitude

0 ≥ ϕ ≥ 21S 5 S hemisphere

21S > ϕ ≥ 71S 5 + 0.1(ϕ +21) S hemisphere

71S > ϕ S hemisphere

Table 1

From this we can calculate hRAIN, and through that DRAIN.

Determining γγγγR

In order to determine γR it is first necessary to identify the rainfall region from the

attached maps (Appendix 1). Table 2 links the rainfall rate to the percentage of the

time it is exceeded in any year by rainfall region.

Zone Percentage

of time R

exceeded A B C D E F G H J K L M N P Q

1.0 <0.1 0.5 0.7 2.1 0.6 1.7 3 2 8 1.5 2 4 5 12 24

0.3 0.8 2 2.8 4.5 2.4 4.5 7 4 13 4.2 7 11 15 34 49

0.1 2 3 5 8 6 8 12 10 20 12 15 22 35 65 72

0.03 5 6 9 13 12 15 20 18 28 23 33 40 65 105 96

0.01 8 12 15 19 22 28 30 32 35 42 60 63 95 145 115

0.003 14 21 26 29 41 54 45 55 45 70 105 95 140 200 142

0.001 22 32 42 42 70 78 65 83 55 100 150 120 180 250 170

Table 2

This gives the value of the rainfall rate R, which can be used to determine γR. The

two methods for determining γR are empirical. They methods are:

Method 1: Calculation (ITU-R Recommendation P.838)

Method 2: Nomogram (CCIR Report 721 – no longer available)

If circular polarisation is to be used then calculate the average value of γR for vertical

and horizontal polarisation should be used.

Method 1

Specific attenuation can be found from: αγ kR

R=

The values of K and α can be found from ITU-R Recommendation P.838. The table

is attached at Appendix 2.

Method 2

The CCIR used to publish a very useful nomogram in Report 721 (no longer

available). This links specific attenuation directly to frequency and rainfall rate. The

Nomogram is at Appendix 3.

Example

What fade depth should be allowed for an X-band (8GHz) terminal operating in

Denmark if an availability of 99.9% is required? The terminal is looking at a satellite

with an elevation angle of 25 degrees, using horizontal polarisation, and is located at

sea level.

Find DRAIN

Denmark lies in W Europe at around 52 degrees N. Thus ϕ-=52, and from table 1

hRAIN=3.2-0.075 (ϕ - 35)= 1.925 Km. Since e= 25 degrees, and hANTENNA=0 Km:

555.4)25(

0925.1

)(

)(=

−=

−=

SineSin

hhD

ANTENNARAIN

RAINKm

Find γγγγR

Find the rainfall rate that will only be exceeded 0.1% of the time for a satellite

terminal in Denmark (i.e. the rainfall rate that will give 99.9% availability). From the

map Denmark is in region E. From table 2, the value of R that will only be exceeded

for 0.1% of the time is 6mm/hr.

Method 1: 0489.0600454.0 327.1=×==

αγ kRR

dB/Km

Method 2: γR = 0.048 dB/Km

Calculate LRAIN

LRAIN = γR DRAIN

Since DRAIN = 4.555 Km and γR = 0.048 dB/Km:

LRAIN = 0.0489 x 4.555

LRAIN =0.22 dB

Appendix 1 – Rainfall Rate Maps

Appendix 2 – Table of Coefficients

Horizontal polarisation Vertical polarisation Frequency

GHz K α K α

1 0.0000387 0.912 0.0000352 0.880

2 0.000154 0.963 0.000138 0.923

4 0.000650 1.121 0.000591 1.075

6 0.00175 1.308 0.00155 1.265

7 0.00301 1.332 0.00265 1.312

8 0.00454 1.327 0.00395 1.310

10 0.0101 1.276 0.00887 1.264

12 0.0188 1.217 0.0168 1.200

15 0.0367 1.154 0.0335 1.128

20 0.0751 1.099 0.0601 1.065

25 0.124 1.061 0.113 1.030

30 0.187 1.021 0.167 1.000

35 0.263 0.979 0.233 0.963

40 0.350 0.939 0.310 0.929

Appendix 3 – Nomogram