Indian Journal of Radio & Space Physics

Vol. 36, August 2007, pp. 325-344

Variability of millimetrewave rain attenuation and rain rate prediction: A survey

R Bhattacharya, R Das, R Guha & S Deb Barman

Department of Environmental Science, University of Kalyani, Kalyani 741 235, India

and

A B Bhattacharya

Department of Physics, University of Kalyani, Kalyani 741 235, India

Received 24 May 2006; revised 31 January 2007; accepted 3 May 2007

This paper reviews the literature on attenuation of mm-wave due to rain and rain rate prediction methods to analyze the

performance of the various systems proposed by different workers at different parts of the globe under varying

meteorological and topographical conditions with an emphasis on the observational reports made in the tropics, particularly

in the Indian subcontinent. In this comprehensive review, besides considering the various features related to rain rate, the

various methods proposed for prediction of rain attenuation have been examined and thereby a comparison of those

prediction methods is made. Finally, scopes for future investigation have been critically focused.

Key words: Rain attenuation, rain rate, millimetrewave

PACS No.: 92.60. Ta

1 Introduction

Radio wave propagation is a complex

phenomenon. The international regulations for

tropospheric radio wave communication are based on

set of propagation models. Such models are

developed by making physical and statistical

analyses of collected data. The more we become

rich in the understanding of different phenomena

involved, the more we can improve our models.

Several propagation models through the troposphere

for frequencies above 1 GHz can be thought of.

Existing models may be improved for rain attenuation

and for trans-horizon tropospheric scatter

(troposcatter) propagation. Rain plays a significant

role in the undesired absorption of microwave,

millimetre and centimetre wave propagation in the

lower atmosphere. Besides rain, other major

contributors are water vapour, liquid water clouds and

fog. Such absorptions cause variations in the signal

strengths.

Attenuation value exceeded less than 2% of the

year is due to rain or cloud except at 22 GHz water

vapour absorption line and 60 GHz oxygen line. The

model cloud gives attenuation comparable to rain at

2% of the year. At smaller percentages, rain is

considered as the sole cause of attenuation to the

communication system designer.

In the past, several theoretical and experimental

studies were made in respect of rain attenuation to

obtain better service reliability in communication.

Crane1 theoretically calculated attenuation for a

known rainfall intensity along a path. During 1980

and onwards, prediction techniques for statistical

estimation of attenuation probability for a particular

path have been studied. Two approaches are made −

one based on the use of large number of attenuation

statistics at different frequencies, locations and path

geometries and the other based on the synthesis of

attenuation values from meteorological data. Latter

approach is of great interest in modelling since a large

number of data are available.

There is no established theory of statistical

variations of rainfall intensity, specific attenuation

and attenuation along a path which are linked with

each other in a complex manner. Rice and Holmberg2,

Lee3 and Dutton and Dougherty

4 carried out statistical

analysis of U.S. National Weather Service rain

accumulation data and provided an estimate of year-

to-year variations of rain rate distribution.

Rain shows prominent spatial and temporal

variation along a horizontal path, which prompts

statistical estimation of instantaneous rain rate profile

along the path. Several workers have proposed

different models for calculation of attenuation along a

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

326

path. Most of the models were developed using point

rain rate and path attenuation measurements. Model

rainstorms have also been developed from weather

radar data analysis to convert point rainfall statistics

to path attenuation estimates5.

A very useful new technique, viz., ‘observation of

phase delay from GPS satellites’ has emerged; it

allows continuous monitoring of atmospheric water

vapour content along a slant path using

millimetrewave radio propagation6-11

. Water vapour,

rain, cloud and oxygen attenuate radiowaves very

significantly. Attenuation due to water vapour along

earth-space radio links increase prominently above 50

GHz and becomes higher than the peak absorption

found at 22.235 GHz water vapour resonance line12

.

Moreover, oxygen, cloud and rain (especially, light

rain) play a very important role on propagation above

50 GHz. Water vapour contributes to both attenuation

and tropospheric scintillation on earth-space paths13

;

also a relation has been established between the

occurrence of water vapour and cloud attenuation14

.

Due to continuous presence of water vapour in the

atmosphere and a greater occurrence rate of cloud

than rain, these two factors need to be properly

assessed. Using GPS technique, a comparison of

attenuation has been made between the radiosonde

and radiometer data15

to support millimetrewave

propagation in the study of attenuation.

Lastly, a suitable model is needed for predicting

the attenuation on a slant path with the variation of

rain intensity. Below 60 GHz, the attenuation due to

snow or ice is very small and hence neglected16

.

Liquid rain drop is the only cause of attenuation.

Studies on the variation of attenuation with height

show that major attenuation occurs below the height

of the bright band17

(0C isotherm); this fact is also

supported from comparisons between radar based

attenuation prediction and simultaneous path

attenuation measurements18,19

. The rain intensity, on

the average, does not vary with height between the

surface and the base of the bright band as evident

from weather radar data20,21

. This leads one to model

the specific attenuation as constant from the surface

up to a height near 0C isotherm level which also

needs to be estimated statistically.

An attenuation prediction model should contain

estimates of expected year-to-year and station-to-

station variation and also expected attenuation at the

same exceedence probability. A model on such

estimates has been developed by Crane16

. The

attenuation was compared between predictions from

model and available attenuation observations made on

a number of propagation paths and obtained

agreement within expected uncertainty.

The growing demand of communication services

has congested the currently available radio spectrum

to such an extent that a need has been felt for larger

bandwidth and new frequency band above 20 GHz is

being explored. However, the rain attenuates the

upper spectrum and frequencies suffer strong

impairment as the rain drop diameter approaches the

size of operating wavelength. In tropical countries

like India, a great diversity of climatic conditions has

been witnessed in the recent past and a search is on to

find out a prediction model, useful for all ranges of

rain fall rate.

2 Troposcatter propagation

Rain scatter is considered to be partly due to

interference. However, it is unlikely that there would

be interference due to rain. At frequencies slightly

below 10 GHz, rain scatter prediction technique gives

an excellent estimate of the strength of scattered

signal. Rain scatter model suffers a problem above 10

GHz when rain attenuation along signal path and from

scattering volume reduces signal level, whereas

simultaneous scattering within the volume boosts up

the signal level. Attenuation and scattering need not

be modelled together, since the former is much more

important, and troposcatter link systems should be

designed at lower frequencies. In fact, modelling of

transhorizon scatter propagation is undergoing a rapid

change due to lot of research work and in the coming

days revised models are likely to revolutionize our

knowledge of troposcatter processes.

2.1 Rain attenuation

Another part of rain scatter process is the

attenuation of signal by rain along the scatter path.

Way back in 1947 Ryde22

presented a rain attenuation

model. After two decades Medhurst23

published a

revised model of Ryde & Ryde and he concluded that

“… (the) agreement is not entirely satisfactory; there

is a tendency for the measured attenuations to exceed

the maximum possible levels predicted by the

theory”. A decade later, Crane24

looked afresh at the

model predictions and compared them with the

measured values taking the data available to Medhurst

and new data published after that. He found an

average matching between model predictions and

measurements.

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

327

A rain attenuation model should predict both the

median distribution for a number of yearly attenuation

distributions as well as the amount of expected

deviations of distribution of attenuation for any single

year of observation from the long term median

distribution. Old and early models considered

raindrop sizes, shapes, uniform rain rates along a path,

etc. For uniformity in rain rate, the time average of

rain rate at a point was considered by Bussey25

to

approximate the path average rain rate along a link.

Considering the specific attenuation to be propor-

tional to rain rate, such a model works well, but the

physics involved in the process was very much

complicated. Earlier models give estimation of point

rain rate statistics and the statistics of variation of rain

along a path. Statistics of path length through rain has

also been modelled with the advent of satellite

communication.

Initially, the models were physical observation

based, but with the availability of attenuation statistics

such models were adjusted. Today, enough data are

available for a standard model. However, the practical

methods, which are adopted to measure the

attenuation statistics do not give a reliable model and

compels one to turn back to the models that are

physical in nature. Development and evaluation of

models require a method to control the quality of data

observation in the model26-28

. The ITUR (formerly

known as CCIR) gathers round the clock global data,

which measures attenuation. Crane29

used such data

and noticed that the statistical deviations of

attenuation from model predictions were log-normal

and the parameters used in log-normal process

practically did not change significantly for different

models. The ITUR (CCIR) recommended models did

show the smallest deviations.

The deviations of observations from USA in the

CCIR database were analyzed for a physically based

model by Crane30

. Figure 1 shows the cumulative

distribution function (CDF) for log ratio of measured

and modelled attenuation at 0.01% of a year. As the

statistical distribution for path-to-path variation is log-

normal, the log ratios were plotted on a normal

probability paper. The CDF must lie on a straight line

provided the log-normal hypothesis is correct. In

order to display all the observations on a single graph,

the attenuation prediction model was used to

normalize the data. The same general result is valid

for a different prediction model. Only the bias value

(intercept with zero value for reduced variate)

changes, but the slopes of best fit curve to the

deviations remain unaltered.

2.2 Analysis of moderate and intense rainfall rates

With the increasing demand in recent years, there

is greater congestion of communication spectrum

which leads to allocation of greater bandwidth and

hence the increasing need for short wave lengths

(centimetre and millimetre) in terrestrial and satellite

links. Rain has been established to be the principal

cause for attenuation in the microwave radio links. In

recent years, for frequencies above 10 GHz in single

Fig. 1 — Cumulative distribution of attenuation prediction errors for all observations in the CCIR data bank from USA (after Crane, 1996)

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

328

and dual polarization techniques, especially in

satellite communications, various aspects of

precipitation is being studied in a great detail31

.

2.2.1 Study of rainfall rate over Indian locations

In tropical countries communication for higher

frequencies are disturbed due to high rain rate. Rain

strongly attenuates the radio waves above 10 GHz,

which is a main impediment to satellite link

performance32

. Studies of the variations of rainfall

pattern are helpful for predicting propagation

conditions. The drop size distribution varied widely in

the tropics. Distribution of rain attenuation at 11.7

GHz has been compared with prediction models33

by

utilizing INSAT-2C satellite signals. Theoretically

estimated attenuation of radio waves using the

concept of decay of rain path profile at 11 GHz and

13.4 GHz for 56° elevation angle over Delhi27

showed

that CCIR model underestimates the attenuation over

India. Average altitude of 0°C isotherm varies from

4.7 km at 40° latitude to 3.1 km at 60° latitude34

. The

vertical structure of attenuation assumes a constant

value up to 0°C isotherm based on the drop size

distribution analysis35,36

. It is found that excess

attenuation due to rainfall above a certain threshold

frequency limits the LOS links37

.

2.3 Study of rain structure using X-band radar reflectivity

To assess the interference between terrestrial and

earth-space satellite links, it is important to study the

effect of scattered radio signals from transmitters.

Advent of wind profiler38

and MST radar39

has

generated a considerable interest in the study of radar

bright band. A study of rain structure for both

horizontal and vertical extensions has been made with

X-band radar40

at 9.375 GHz. Reflected radiowaves

from rain cells are used to find horizontal and vertical

extension of rain for which measurements are made

from radar plan position indicator (PPI) and range

height indicator (RHI). Results of such extension are

shown to depend upon radar reflectivity factor (dBz),

which is essentially a measure of strength of

scattering cross-section (which causes interference in

radio signals) of raincells41

.

2.4 Vegetation biomass and microwave emissivity

For better understanding and protection of our

environment and good management of natural

resources we need to keep vigil on soil and plant

biomass. Presently, remote sensing technology is not

much in use; rather, use of active and passive

microwave sensors are of great demand. They are

used to find moisture content of open and vegetation

covered soil to have a knowledge of the physical

principle involved and to find observation parameters

together with its accuracy. Study of plant biomass and

its water content has been done by many

researchers42,43

. Biomass is one of the most important

parameters for evaluation of crop type and its yield, as

it contains water, which attenuates microwave.

Vegetation biomass changes with growth of crop and

its dielectric is found to be related with microwave

emissivity, which is used in remote sensing. From the

study by Singh and Sharan44

, microwave emissivity at

X-band is found to increase with biomass.

3 Surface point rain rate prediction In absence of any theory, estimations of surface

point rain rate are done empirically from available

long term rain accumulation data of two types – one is

long duration hourly, daily and annual accumulation

data for a large number of geographical locations and

the other is the excessive precipitation data available

from a limited number of locations3. Instantaneous

data are taken together with attenuation values to

compare evaluation of model; but such data are not

suitable to give expected rain rate distribution. In

order to estimate attenuation along a path, the specific

attenuation at each point of the path is needed. For

prediction of attenuation, instantaneous rain rate

distribution is regarded as very useful, but its

measurements fluctuate due to atmospheric

turbulence. To remove turbulence, rain rate averages

are taken. Amount of averaging required for

estimation of rain rate distribution depends upon its

application. There is equivalence between temporal

and spatial averaging for translating rain cells and

Bussey25

recommended the use of hourly averages for

attenuation estimation on 50 km terrestrial paths.

Radar study shows that rain cells present in the high

rain rate region cause significant attenuation. Rice and

Holmberg2 and Lee

3 devised models for instantaneous

rain rate estimation. The Rice-Holmberg model

provides a good estimate of rain rate distribution in

0.1-1 % range.

3.1 Vertical variation of specific attenuation and

its prediction

The point-to-path model predicts rain rate variation

along a horizontal path and is used in the design of

terrestrial communication systems. But, for slant

paths, vertical variation of specific attenuation is also

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

329

required. Although ice, snow, etc. do not produce

attenuation, but raindrops, raindrop sizes and melting

ice particles give significant attenuation.

Radar studies show that rain can be represented, on

the average, by a constant reflectivity from surface up

to the height of 0οC isotherm

21. Depending upon the

raindrop size distribution, a constant reflectivity value

means a constancy in the value of specific attenuation.

This fact leads to model a vertical profile of specific

attenuation, which gives a constant value from ground

up to the height of 0C isotherm.

To estimate the vertical attenuation the required

measurement is the rain height. Some investigations

on the variation of rain height at different locations

are reported by Mondal et al.26

taking the 0°C

isotherm as the rain height.

3.2 Variation of attenuation about its estimated value

Specific attenuation is calculated from point rain

rate value using a power law and employing Laws and

Parsons raindrop size distribution35,45,46

. Differences

in specific attenuation obtained from above

distribution as well as from a large number of

observed drop size distributions are statistically very

small for frequencies up to 50 GHz. But at higher

frequencies, errors in the measurement of drop size

distribution for small drop size range affect the

accuracy of specific attenuation and rain rate

relationship. Additional uncertainties linked with

sampling of drop size distribution are small and

ignorable16

. The physical limit of attenuating zone is

defined without any uncertainty for a terrestrial path,

but it depends upon the vertical extent of rain region

for a slant path.

Thus, the several steps of attenuation prediction

model use the median values of statistically variable

quantities. The statistical processes linked with each

step are assumed to be independent of each other and

the variances combined on that basis.

A new model for easy application for prediction of

rain attenuation in case of terrestrial or slant path

propagation has been prepared by Crane. This model

was extended globally on the basis of zonal averages.

It was successfully applied for stations in low

mountains near the coast, but not considered for

modification of vertical temperature profile due to

large regions of high terrain. Further studies on

understanding of the local variations in rain

rate climate are essential. The model can also be

extended to accommodate seasonal and monthly

predictions.

3.3 Prediction of attenuation on earth-space links

Modification of refractive condition of atmosphere

depending upon the moisture content has been

investigated in India by many workers. It is found that

LOS links are affected around the coastal regions up

to a few kilometres due to land-sea breeze. The

change of refractive profile, in turn, reduces the

microwave signal47

. Deterioration of a communication

link at 13 GHz in monsoon month revealed that the

communication link did not serve the purpose 5% of

time48

. Full communication link can be achieved

during monsoon months if an extra gain of 12-15 dB

is provided to the transmitting system. The

attenuation is found to be 0.5 dB/km at 22.235 GHz

during monsoon months (Fig. 2). Ground-based

zenith looking radiometer has a window49

and

the signal suffers no change with respect to the

total attenuation within 1% height limit. Radar

reflectivity is an important tool to estimate the

microstructure of rain cell40

. Rain rate is calculated

using Z-R relation. A detail of precipitation structure

is also calculated by Gairola et al.50

using combined

microwave and IR rain algorithm during a Bay

cyclone. The simultaneous measurements of

precipitation by passive radiometry and radar

reflectivity can be utilized to calculate rain attenuation

for earth-space paths.

According to ITU-R (formerly CCIR) rain climatic

zones have been designed following the

characteristics of precipitation for propagation

modelling51

. Prediction of path attenuation by ITU-R

underestimates the radiometrically derived cumulative

distributions (CDs) of path attenuation, in general.

Furthermore, the ITU-R procedure may not match

well with the rainfall rate characteristics. The model

only predicts rain induced attenuation. Figure 3 shows

total attenuation statistics for measured annual, worst

month and predicted (ITU-R method) cumulative

statistics. The ITU-R prediction model52

needs

knowledge of the rain rate exceeded 0.01% of the

time as measured using a gauge with one minute

integration time. This factor contributes to the

overestimation of attenuation by the ITU-R model.

The standard ITU-R “H” zone rain profile has a

rainfall rate exceeding 32 mm/hr for 0.01% of the

time. Other factors may also be responsible for the

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

330

difference between the measured and predicted

attenuations.

3.4 Equiprobable point-to-path average models for different

types of rain

Here one is to rely on dual polarization radar data.

The Chilbolton dual polarization radar is, perhaps, the

best instrument in Europe and USA53

, which offers

the most accurate calibration of dual polarization

facilities with high volumetric resolution. Dual

polarization technique is able to characterize drop size

distributions (for a given form) for every radar range

gate. Hence, it enables us to retain systematic drop

size rain-structure dependence in the model. A study

of horizontal variation in rain intensity is done for

characterization of spatial rain intensity. Widespread

(stratiform) and showery (convective) are

differentiated by the presence of bright band or its

absence. For this purpose, an automatic edge

detection technique is successfully applied to obtain

Fig 2 — Electromagnetic wave attenuation profile due to water vapour and oxygen as a function of frequency in the millimetre wave

band (after Karmakar et al. 2002)

Fig 3 — Cumulative attenuation statistics (after ITUR Recommendation, 1992)

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

331

precise rain height in widespread rain. Leitao and

Watson54

analyzed 40 distinct rain events, out of

which 17 were in showery rain category. They

employed edge detection technique very successfully

and placed all the stormy convective structures in the

widespread rain category. Such categorization was

essential for development of the model, which could

well be applied over UK and beyond. Showery

(convective) rain data can also be applied to almost all

regions in UK in order to make prediction of

attenuation in 11-14 GHz band. However, a

knowledge of relative occurrence of widespread-to-

showery rain is essential for making prediction of

attenuation over the European region. The spatial

distribution data of rainfall intensity are, thus, related

to the type of rainfall in this point-to-path average

model. This strongly supports the approach of the said

model.

4 Slant path attenuation statistics

Terrestrial and satellite communication systems

mainly operate at centimetre and millimetre

wavelengths. Signal degradations in such links occur

mainly due to rain. This poses a major problem in

electromagnetic wave propagation through raindrops.

Studies on microwave precipitation are based mainly

on three steps: (i) to calculate scattered amplitude

when a plane electromagnetic wave is incident on a

rain drop, (ii) to evaluate the far-field intensities of a

plane wave which penetrates through a thin layer of

rain cloud and (iii) to assess the overall degradation of

signal in presence of thick precipitation. On the basis

of simple assumptions, rigorous mathematical

analyses have been done. However, meteorological

uncertainties of rainfall are very much complex and

they greatly limit the necessity of the results obtained

from theoretical studies for practical applications.

4.1 Drop size distribution for microwave link modelling

Radiowave propagation depends on the physical

characteristics of rain. Rain attenuation characteristics

at 11 GHz reveals that it has significant contribution

within 10° elevation angle28

and cause degradation of

the communication link. The drop size also plays an

important role. It is found that the link suffers

attenuation in April, May and June when the rain rate

is not so high. High attenuation not always coincides

with high rainfall. Study of drop size reveals that

attenuation increased from 1.4 dB/mm to 3.2 dB/mm

when the drop size increased from 3.4 mm to 4.5 mm

diameter55

. The rain drop size distribution depends

upon the climatic conditions and varies from region to

region, and also on rain types such as drizzle,

widespread, shower, thunderstorm and convective,

within the same region. Many experiments carried out

using distrometer for developing rain drop size

distribution reveals that the drop size distribution

(DSD) would be log-normal for tropical region

compared to exponential distribution for temperate

region. The DSD experiments carried out in Nigeria,

Brazil, Malaysia and India confirm the log-normal

drop size distribution model to be suitable for tropical

region. The coefficients of distribution would change

with the region. Rain drop size distribution

experiment conducted in India also shows the distinct

difference in the presence of rain drop sizes during

shower and thunderstorm rain at the same rain rate in

different rain events, which is very important for

evaluating the microwave and millimetre wave

attenuation model for radio link engineering. The

presence of small raindrops gives the absorption of

radio signals at millimetre waves compared to the

scattering effect, which is prevalent for larger drops56

.

4.2 Power law

For engineering applications, the specific

attenuation and phase shift are expressed by a power

law relationship35

given by aRb (values of parameters

a and b are available for widespread rain35,36

for a

wide range of frequencies). Mie calculations of

spherical raindrops were applied to get the values of a

and b and hence do not differentiate between vertical

and horizontal polarizations. Harden et al.57

and

Fedi58

used log-normal drop size distribution to obtain

the values of a and b for spherical raindrops. The

specific rain attenuation has been evaluated based on

rain drop size data collected from India during 1989

by Verma and Jha59

. All such calculations give the

value of specific attenuation only. In case of

depolarization effect, values of parameters a and b for

both specific attenuation and specific phase-shift are

required.

The relationship between the rain-rates for two

different integration times can be obtained by using

power law35

,

Rt = aRTb …(1)

where R is the rain intensity in mm/h, t the integration

time at which rain rate is calculated, T the integration

time at which rain rate is available and a, b are

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

332

parameters which depend on the frequency and

microphysical properties of rain. Using 10s and 15

min integration times Sarkar et al.60

empirically tested

the power low which comes out as:

0.852

10 15 min2.567sR R= …(2)

Simple power law and two segment power law fit

for a particular phase-shift. In case of shower and

thunderstorms, such phase-shift is significant for

communication studies over a limited range of rain

and hence a simple power law shift is enough. Olsen

et al.35

calculated specific attenuation using Laws and

Parsons distributions for spherical drops at 0оC and

10оC. They observed the horizontal and vertical

polarization results averaged at 10оC. Moreover, with

the increase in frequency, parameters a and b may

become insensitive to the temperature.

4.3 Prediction of slant path rain attenuation statistics

Prediction of rain attenuation along a slant path can

be done by measuring radar reflectivity data. Uses of

a dual polarized data make our prediction of rain

parameters more precise and accurate.

To predict slant path attenuation successfully from

radar reflectivity data, one needs to use the radar to

find out slant path attenuation for any path. This

necessitates for satellite beacon or radiometric studies.

Radars have not been widely used so far to collect

attenuation statistics data. Reasons are two fold:

(a) one needs to handle a large number of data to be

collected and analyzed and (b) a reliable dual

polarized radar is to be used. However, a radar can be

used to scan an area in space during rain to give us a

database. Effects of elevation angle, frequency of

operation, rain height and site diversity can be studied

from such database.

4.4 Prediction of attenuation from reflectivity (Z) and

differential reflectivity (ZDR)

Rain can be described by a gamma drop size

distribution (DSD) as given below:

N(D) = Nµ Dµ

exp(–ΩµD) …(3)

Here, we encounter three parameters (µ, N and Ω),

but in radar measurements only two variables are

required. Stutzman et al.61

made an extensive study to

match predicted attenuation with the measured value

on slant path and noticed that a value of µ = 2 gave

the best matching and it was used in their subsequent

work. In respect of other rain parameters, viz., drop

shape and its distribution, canting angle and its

distribution, they used Morrison-Cross drop shapes

assuming all drops to be oblate; also canting angle for

all drops was taken to be zero as it does not affect

very much the attenuation prediction for a circularly

polarized wave.

The DSD was estimated in a radar range cell by

generating a large number of Tables relating Z and

ZDR to a wide range of DSDs with µ = 2 together

with a range of Ω and N. Although the process is

rigorous, it is more accurate compared to empirical

relationships for reflectivity and attenuation.

For a known value of DSD, forward attenuation

can be predicted at any frequency. Here, the

transmission matrix for each rain cell is calculated

and then summed over the entire path to get total path

attenuation. The RHI data were used to eliminate

melting layer effect and to obtain the layer height, if it

was present. It also enabled not to carry out

attenuation calculation at the lower edge.

In case of low ZDR, radar signals undergo random

fluctuations and lead to attenuation prediction

unreliable. When attenuation is calculated from Z and

ZDR, the approximate relationship gives attenuation

to be proportional to 1/(ZDR)1.5

. From this, it is

evident that attenuation goes to infinity when ZDR

approaches zero and the finite value of ZDR is

obtained with appreciable reflectivity. To avoid

fluctuation of ZDR due to raindrop reflection, all

range cells, for which reflectivity Z<22 dBz, are

neglected. For Z >22 dBz and ZDR less than 1dB,

Stutzman et al.61

used an approximate relationship to

get the value of attenuation. The relationship is:

Ω = aRb with R = (10

z/10/200)

0.625 …(4)

Values of a and b are given by Olsen et al35

.

Attenuation prediction for many events from radar

data shows good agreement with beacon attenuation

measurements for every slant path. Over and

underprediction of attenuation occurred in other

events. The predicted attenuation was in very good

agreement with the measured one.

4.5 Rain attenuation in the tropics

In tropical latitudes where rain rate is high,

communication link at higher frequencies is a major

problem. Severe attenuation and depolarization32

of

radio waves occur above 10 GHz. For setting up of

links above 10 GHz at places where rain plays havoc,

study of meteorological variations of humidity and

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

333

rainfall is essential for reliable communication. Most

of the attenuation studies so far for earth-space links

were confined mostly to the temperate zones of the

world. However, very few measurements have been

carried out in tropical region like India, Singapore,

Brazil, where rain characteristics (both horizontal and

vertical rain structure) are different from those of

temperate climate. In India, experiment were

conducted at 20/30 GHz for LOS link distance of 6

km for prediction of horizontal characteristics of rain

attenuation62

. Similarly radiometer were used at the

same frequency for vertical characteristics of rain and

rain height for prediction of slant path attenuation.

Tremendous use of satellites in telecommunication

demands further study of attenuation in the tropics

where rain plays major role compared to other

hydrometeors63

. Since the nature of precipitation in

the temperate regions varies widely from that at

the tropics, the system design of one place will

not be suitable for the other. The causes which make

system design different at the two places are: (i) rain

drop size distribution which is usually larger in the

tropics, (ii) 0C isotherm height at the tropics is

greater than that at temperate regions and (iii) the lack

of reliable rain study at the tropics; even the recent

ITU-R recommendations for rain attenuation

measurement at the tropics failed to give satisfactory

result64

.

For a reliable prediction of rain attenuation, rainfall

characteristics of a particular region is to be

investigated properly for system design. Two

constraints are there for such investigation – one is the

lack of availability of geographical rain rate

probability in the tropics, and the other is the lack of a

valid model for estimation of rain attenuation in the

tropics. Hence, attenuation is directly measured from

satellites and margins for future satellite systems are

estimated. Prediction models of rain attenuation are

available, but those are based upon the results

obtained mainly in temperate climates. The prediction

model of rain attenuation developed by Verma and

Jha56

based on the experiment conducted in India are

available for communication system designer for

providing appropriate fade margin for reliable

communication above 10 GHz; otherwise the

communication system designed, based on rain

attenuation data of temperate climate, can provide

outage of radio signals leading to link failure for

higher rain rate as experienced in Singapore by

Singapore Telecommunications, which lead to the

detailed study of rain attenuation. Raina and Uppal65

have also collected some data from radiometric

studies over New Delhi, although these are not

enough for a good understanding of propagation

mechanism in the tropics33

.

5 Attenuation and brightness temperature

Gaseous absorption and emission of

communication waves by the atmosphere were

calculated by CCIR (International Radio Consultative

Committee) employing radioactive transfer

programme as described by Waters66

. The role of

atmospheric emission in communications and the

relationship between absorption and emission have

been given by Smith67

. The atmospheric emission (i.e.

brightness temperature) and attenuation model were

discussed and comparisons with respect to

measurements and other models were made67

.

At radio frequencies, scattering is insignificant and

hence attenuation in the gaseous atmosphere will be

due to absorption only.

For frequencies up to 340 GHz, the gaseous

atmospheric emission is a major source of external

noise in the earth-space communication system68

.

Since NASA was interested in low noise receivers,

attention was given on noise sources also.

Earth’s atmosphere (dry state) consisting of oxygen

(20.946%), nitrogen (78.084%) and argon (0.934%)

all by volume and totaling to 99.964% is well mixed

at nearly 80 km height where dissociation of O2

molecules to atomic oxygen takes place. Carbon

dioxide accounts for the rest and mixes well in the

atmosphere. However, water vapour is the main

variable component in the atmosphere. The saturation

vapour pressure is directly proportional to

temperature. Centimetre and millimetre waves are

absorbed chiefly by oxygen and water vapour. In fact,

water vapour lines occur at 22.235 GHz, 183.31 GHz

and 325. 152 GHz. Tails at higher frequencies

need also to be considered; informations on these

lines are given by McClatchey et al.69

, Rothman

and McClatchey70

and Rothman71,72

. Oxygen and

water vapour absorption in the window region

has a remarkable effect. Ozone has spectral lines

in the microwave region, which are neglected to a

first approximation. Waters66

has discussed about

stronger O3 lines and those of other minor

constituents.

The absorption coefficient which is a function of

pressure, temperature and frequency can also be a

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

334

function of the earth’s magnetic field in the upper

atmosphere. Total absorption for a path through the

atmosphere is given by:

0

dii

A lγ∞

= ∑∫ …(5)

where γi is the absorption co-efficient for the i-th

gaseous constituent. In almost all communication

purposes, two gaseous absorbers are taken — one for

water vapour and the other for molecular oxygen.

Thus, A is rewritten as,

0 ω 0,ω

0 0

( + )d dA l lγ γ γ∞ ∞

= =∫ ∫ …(6)

where γ0 and γω are the absorption coefficients for

oxygen and water vapour, respectively, and γo,ω is

their joint absorption coefficient. According to

Kirchoff’s law, while in local thermodynamic

equilibrium (LTE), the emission from a gas must be

equal to its absorption at each frequency. This leads to

the earth’s atmosphere to be LTE. Rayleigh-Jeans law

states that brightness is proportional to temperature at

radio frequencies. The brightness temperature, TB, is

used here to refer to the temperature of sky in a

particular direction as seen by an antenna of very

narrow beam width.

5.1 Model of absorption and brightness temperature

The JPL (Jet Propulsion Laboratory) model uses

expression given by Waters66

, but Rosenkranz73

expression is used for oxygen absorption coefficient.

Oxygen (O2) spectrum between 48 and 67 GHz shows

about 28 discrete lines, which are broadened to a

single broad maximum at one atmosphere pressure.

Above 30 km, these lines are well separated and

exhibit marked Zeeman splitting. Since the earth’s

magnetic field changes from 0.6 G at poles to

0.3 G at the equator, the zenith absorption

between 48 GHz and 67 GHz depends on the

magnetic latitude change.

5.2 Wet antenna attenuation

Besides attenuation of radio waves by rain,

moisture, clouds, etc. along its propagation path,

another major cause of attenuation occurs when the

receiving antenna surface is wet74-78

. Investigations on

the type and amount of attenuation by several

researchers78-80

led to the following results:

(i) Wet surface of antenna can attenuate signals of

the order of 10 dB at Ka-band.

(ii) Deep and rapid fluctuations in antenna gain may

occur due to the nature of rain type and other

meteorological factors.

(iii) Compared to wet reflectors, attenuation due to

wet radome surface is higher.

(iv) Whatever be the rain rate, the attenuation caused

by a wet antenna is mainly due to quantity of

water deposited on the antenna surface at that

instant.

Moreover, the antenna attenuation depends on

several other factors, viz., type of antenna and its

elevation angle, type of rain and drop size, wind speed

and direction and nature of antenna surface. If all

these factors and wetness of antenna are not

considered, we cannot get actual attenuation. Signal

degradation for a wet antenna surface is two-fold:

(a) Fall in antenna gain gives rise to signal loss, and

(b) Deep and rapid fluctuations in antenna gain at

any instant due to water accumulated on the

antenna surface at that time has an adverse effect

on the signal strength.

The design and cost of a link at Ka-band are

severely affected for above two reasons. Since signal

degradation depends upon the type of antenna used in

a link81

, the measured attenuation data are of very

limited use. However, Kharadly and Ross82

estimated

total path attenuation on a statistical basis considering

all the factors on the Vancouver-ACTS path, and

suitable models are developed for proper assessment

of attenuation.

5.3 Microwave and infrared (IR) study of cyclones

Studies of visible and IR band from geostationary

satellites provide us information of immense value to

monitor cyclonic storms. There is a relation between

the radiation at the cloud top and rain received by

land and ocean; rain measurements from IR is done

from this relation. Microwave radiation and

brightness temperature have got a direct relation with

precipitation; hence microwave radiation can be

considered to obtain the amount of latent heat

released in a tropical cyclone’s rain regions. Charles

and Doswell83

obtained microwave brightness

temperature and mapped rainfall regions in the

Hurricane and tropical disturbances. Retrieval of rain

rate and warm core structure during tropical cyclone

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

335

were done by Brueske and Velden84

using Advanced

Microwave Sounding Unit (AMSU) radiometer.

Some satellite-derived parameters are: precipitable

water, liquid water, rainfall rate, sea surface

temperature and wind speed which were considered

by Elsberry and Velden85

. They developed a linear

regression relationship from the estimation of surface

intensity and cloud cover associated with the tropical

cyclones based upon hydrostatic assumptions. Gairola

and Krishnamurti86

used Special Sensor

Microwave/Imager (SSM/I), Nimbus and Sea-sat

SMMR data to locate the position of deep depression,

cyclones, etc. Microwave data were used successfully

by Rao and MacArthur87

, and Rodgers and Pierce88

to

determine the intensity of a tropical cyclone and its

change. Stress was also given on hybrid techniques by

several workers who used geostationary satellite and

polar passive microwave radiometer in order to cover

a vast area to prepare a global map of tropical rainfall.

The algorithm developed by Gairola and Krishna-

murti86

is well tested for entire global tropics to

predict medium range cyclones. Gairola et al.50

have

used this algorithm to get precipitation regionally

during a very heavy cyclonic storm over Bay of

Bengal. Knowledge of rainfall at a place can help

planning and design of water resources project.

Although the algorithm was prepared initially for

global scale, it is capable of predicting rain properly

in the regional scale phenomena like cyclone.

6 Water vapour attenuation In the study of earth-space communication links,

role of oxygen and water vapour need special

treatment as they play a dominant role in such links.

They attenuate signals to a large extent leading to

unreliability of the links. The attenuation due to

oxygen molecule remains almost constant over the

entire world, whereas water vapour density changes to

a large extent from place to place. As a result,

attenuation due to water vapour will be of main

interest89-92

.

6.1 Measurement of attenuation

In clear air, both water vapour and oxygen

attenuate signals to an extent depending upon its

frequency; they also cause delay in propagation,

bending of ray and produce noise in receivers. Most

important gaseous element in the lower atmosphere is

water vapour, which absorbs ultra short waves at

22.235, 183.3 and 325.152 GHz. The liquid water in

the atmosphere absorbs strongly above radio waves

due to heavy displacement current. As temperature is

strongly connected with saturation water vapour

pressure, so the attenuation of signals due to water

vapour will vary as its concentration always change

with place and time.

Distribution of water vapour is obtained by using

radiosonde data. The change in distribution of water

vapour content over the Indian subcontinent is largely

due to its geographical and seasonal pattern. Along

the south-west coast the moisture content is maximum

whilst the minimum value is obtained over Srinagar.

The attenuation due to water vapour for small angle of

elevation becomes high due to dominance of the

tropospheric effects.

At radio frequencies, scattering effect can be

neglected in a gaseous atmosphere; hence attenuation

measurement due to absorption is of major concern.

Total gaseous absorption in the atmosphere for a path

of length γg (in km) is:

0

0

(in dB) ( )da a

A r r

γ

γ= ∫ …(7)

where,

γa(r) = γ0(r) + γω(r)

γa = Specific attenuation (dB/km)

γo, γω = Oxygen and water vapour attenuations.

To facilitate computer calculations use of Van

Vleck-Weisskoff line approximation was done.

Hence, γω can be written as:

ω 2 2

24 7.330.067

( 22.3) 6.6 ( 183.5) 5f fγ

= + +

− + − +

2 4

2

4.4( ρ10 )

( 323.8) 10f

f

−+

− + …(8)

here, f is the signal frequency and ρ the water vapour

density (g/m3). This Eq. (8) is found to be valid up to

350 GHz.

Upon integration of Eq. (8), one gets total

attenuation over earth-space link through the

atmosphere. The troposphere is largely responsible for

attenuation in the slant path communication for

elevation angle less than 10o. Introducing the concept

of equivalent path by replacing actual length in the

atmosphere we get the total path attenuation as:

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

336

ω

2 1/2

4

4(sin θ + sinθ)

A

R

γ=

+

…(9)

where, R = Effective radius of the earth.

Sarkar et al.93

calculated attenuation for different

frequencies between 5 and 350 GHz for different

elevation angle (θ) by using water vapour

concentration (ρ) and observations over the Indian

subcontinent.

7 Comparison of rain attenuation prediction

methods Terrestrial and slant communication systems,

which operate above 7 GHz are affected by rain, snow

and hail (also called hydrometeors). Above threshold

value (7 GHz), it depends chiefly on the rain rate

intensity and its drop size distribution. Among the

above hydrometeors, rain is of primary concern whilst

others occur very rare in tropical countries. Hence,

rain attenuation, particularly in tropical countries,

affects performance and faithfulness of communi-

cation systems.

At WAR conference (World Administrative Radio

conference), India was allotted two geosynchronous

satellite positions at 56οE and 68

οE longitudes at

12 GHz broadcasting frequency. This prompted

Indian workers to study rain attenuation at 12 GHz.

Prasad et al.94

have compared several prediction

methods of rain attenuation. They observed

attenuation by using radiometers operating at 11 and

13.4 GHz in order to find a suitable prediction

technique. They used Dicke type radiometers, both

consisting of horn-fed paraboloidal reflector type

antenna one of whose diameter is 1.2 m with a gain of

17 dB (for 11 GHz) and the other was of diameter 1.5

m with a noise figure of 5 dB and brightness

temperature 10-300 K (for 13.4 GHz).

7.1 Rain height

In order to calculate rain height and specific

attenuation (which is needed to obtain effective path

length), all prediction techniques of slant path rain

attenuation need point rainfall statistics. The physical

rain height up to which rain occurs (hFR) is taken to be

equal to 0οC isotherm height. This fact is very

important in slant path attenuation. Data from

temperate zone countries (tropical) are mainly used to

obtain rain height. Hence, prediction techniques

overestimate attenuation in equatorial and tropical

zones. As a result, one is to consider a small effective

rain height than the actual physical height in the new

CCIR prediction method. Here we take into account

the non-uniform vertical rain profile at low latitudes

mainly in tropical and equatorial regions. By

analyzing equiprobable measured attenuation and also

the point rainfall intensity data, one can get effective

rain height (hR). Rain height of 0οC isotherm is valid

for widespread rain, but fails for warm convective

type rain and thunderstorms. Prasad et al.94

deduced

effective rain heights using 11 and 13.4 GHz zenith

looking radiometers. Rain rates were measured

simultaneously using raingauge over Delhi. In order

to deduce effective rain height, vertical attenuation

and corresponding rain rates were considered. The 11

GHz data were taken for 1988-89 period, whereas

13.4 GHz data correspond to the period 1984-86.

Some deviations were observed in two sets of plots

for height above 60 mm/h rain rate. Principal cause of

such variation might be due to year-to-year variations

in the microstructure of rain, as the measurements

were made at different times. Also slight deviations in

the two radiometers specifications can cause above

variations.

7.2 Methods of prediction of rain attenuation

For any communication system, statistical

estimation of rain attenuation is necessary. A

prediction technique which can be applied widely

should have the following criteria: (i) it is easy to

apply and should agree well with experimental values

for different rain zones, (ii) it should be very less

dependent on methods of finding rainfall intensity and

(iii) the technique must bear a physical meaning.

Proper prediction method leads to right site location

through the analysis of climatic variation of

attenuation95,96

. Some prediction methods of wide use

are: (i) CCIR97

, (ii) Garcia-Lopez’s method,

(iii) Moupfouma’s method and (iv) Crane’s method.

7.2.1 Garcia-Lopez’s method

This is a simple method which has been developed

by using a good data base. Here, values of the

coefficients that occur during calculation of

attenuation are supplied separately for tropical

countries.

The method gives attenuation formula as:

s ss

( )a L bR CL dA kR L a

e

+ + = +

…(10)

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

337

Values of the constants k and a depend on

frequency, temperature and drop-size distribution.The

CCIR Tables prepared on the basis of vertical and

horizontal polarizations (between 1 and 400 GHz)

provide values of the constants. Prasad et al.94

considered only vertical polarization.

Here, R = rain rate in mm/h and Ls = Equivalent

path length (in km), where,

Ls = (hFR − hS)/sinθ …(11)

Here, hS = ground elevation in km; θ = elevation

angle; hFR = 0οC isotherm height and a, b, c, d, e are

constants and their values are given by Garcia-Lopez

et al.98

. Two sets of values are given–one is for

worldwide use, while the other is for Australia.

Second set of values can be used in tropical countries

like India as Australia gives tropical climatic

variations. For tropical climates: a = 0.72, b = 76,

c =–4.75, d = 2408 and e = 10,000.

7.2.2 CCIR method

In CCIR method (now known as ITU-R), the rain

height hFR is given by

hFR = 3 + 0.028φ, 0 < φ < 36

= 4 – 0.075 (φ – 36), φ > 36

…(12)

where φ = latitude angle. Equation (11) provides slant

path length. Horizontal projection (LG) of slant path

length is given by

LG = LS cos θ …(12a)

The reduction factor r0.01 for 0.01% of the time and

for rain rate R0.01 < 100 mm/h is given by:

0.01

G O

1

1 ( / )r

L L=

+ …(13)

where,

L0 = 35 exp (– 0.015 R0.01) …(14)

When, R0.01 > 100 mm/h, the accepted value of

R0.01 in Eq. (13) is 100 mm/h. Considering the

frequency dependent coefficients the value of specific

attenuation (γ) is obtained from:

γ = kRa …(15)

The predicted value of attenuation which exceeded

0.01% of time on an annual average is given by

A0.01 = γLs r0.01 (in dB) …(16)

whereas for other percentage of time the predicted

attenuation value is derived from:

Ap /A0.01 = 0.12p–(0.546 + 0.043 log p)

…(17)

where p is the percentage.

It should be noted that in recent ITU-R methods,

the rain heights are given by a worldwide map rather

than a function of a latitude (φ). This is an important

modification done in expressing the rain height in rain

attenuation prediction models.

7.2.3 Moupfouma’s method

The method has been developed99

by using mainly

tropical data. The method needs elevation angle of the

slant path, site height from sea level, etc. Here, the

rain rate for 0.01% of time and also for other

percentage of time is needed to introduce the concept

of correction factor. Predicted attenuation is given by

s0.38/ 0.25

0.01

s0.36

s

( )( / )(dB)

1 η( / 0.01)

La

pu

m

kR u p R RA L

p L

−

−= ×

+ …(18)

where,

m = 1 + 1.4 × 10-4

f 1.76

loge(Ls)

f = Frequency in GHz

Ls = Slant path length (km)

η = 0, if l < 5 km and f < 25 GHz and η = 0.03 for

all other cases.

k,a = Those constants mentioned in Garcia-Lopez’s

method95

.

p = Percentage of time

R0.01= Rain rate for 0.01% of time

Rp = Rain rate for p % of time

Moupfouma99

has provided the values of a for

different locations throughout the world. Slant path

formula is given by,

R 0s 1/ 2

2 R 0

,

sin θ 2 sinθ8500

H HL

H H

−= −

+ +

for θ ≥ 50

…(19)

Here, θ is the angle of elevation; H0 is the location

height from mean sea level; HR is 0οC isotherm

height.

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

338

It should be pointed out that Crane100

has proposed

a method using revised two-component model.

However, the method is valid for slant paths only.

7.3 Prediction of microwave rain attenuation in the tropics

Attenuation of microwave signal by rain is a major

problem to designers and service providers all over

the world. Since 1940, researchers in Europe and

USA are conducting work on microwave attenuation

due to moisture, rain, clouds and other factors. It is

now well known that different models on rain

attenuation and drop size distribution are valid for

different regions, i.e., a model which is valid in one

region can give much different result in another

region. So people gave serious thought on developing

attenuation and rain drop size distribution models for

different climatic regions.

In Singapore, work on microwave attenuation

started in 1988 with a 21 GHz link and a link path of

7 km. With the success achieved in the result, the link

path was reduced to 1.1 km, which is within the

average rain cell diameter (~ 2 km). Yeo et al.101,102

and Li et al.103

worked on rain attenuation and rain

drop size models which were successfully employed

in the climate of Singapore. Following earlier success,

Yeo et al.104

extended their work on attenuation for

horizontally and vertically polarized microwaves in

10-40 GHz band. Their model of attenuation and drop

size distribution is well valid for use in tropical

climates. In India, work on the rain drop size

distribution data started during 1989, and 1100 rain

events of 1 min duration’s DSD data were used to

develop rain drop size distribution model and

compared with MP (Moupfouma) and LP (Lopez)

DSD model of attenuation coefficients. Specific

attenuation shows a significant difference in

attenuation in 60 and 100 GHz due to presence of

different types of rain drop sizes above a certain

higher rain rate105

.

7.4 Fading of radio signals

Besides water vapour, cloud and rainfall, various

other atmospheric constituents are responsible for

fading of radio signals in millimetre waveband.

Amount of these fading components in the

atmosphere always vary with time. Basic problem in

radio propagation is the calibration of background

signal fluctuations from surrounding atmospheric

gases. A renewed interest has grown to find out

causes of such fluctuations and to develop separate

models for each cause, which, in turn, might be

frequency dependent. A signal will fade when rain

and cloud as well as water vapour and oxygen are

present. Davies and Watson15

have devised a method,

which shows that phase delay from clouds and rain

drops are negligible. Tranquilla and Alrizzo106

have

shown that clouds accompanied by heavy rain

introduce measurable phase delay. Davies et al.107

have shown that, in a non-rain event, cloud effect can

be separated from water vapour effect which makes

one possible to develop a theoretical model for cloud

attenuation. Attenuation due to water vapour and

oxygen (gases) is eliminated from total attenuation

measured from radiometer, which ultimately gives us

attenuation due to rain and cloud only. Physical

models for prediction of radiowave propagation

should combine all rain and non-rain time events

(cloud, rain and scintillation effects); the technique of

Davies and Watson15

has become acceptable from this

standpoint.

8 Discussion and conclusions

Sometimes, measurement and model development

run simultaneously. Any departure from model

prediction lead to a new thought about the process and

consequent refinement of the experiment. When

several propagation mechanisms are present in the

iterative model, each one need to be iterated

separately. After a model matures, the development

process must continue to explore the estimation of

variability and maintenance of data quality. Prasad

et al.94

observed radiometric attenuation at 10 and

90 angles of elevation and compared their results

with the attenuation predicted by other methods. They

deduced rain heights using the empirical relation of

CCIR97

which is latitude dependent. They tested four

cdfs and of these only one showed good agreement

with the CCIR technique. In case of 10 elevation

angle, CCIR method gave more deviation. Garcia-

Lopez’s method was in well agreement for all the four

cdfs followed by Moupfouma’s technique. Moreover,

Garcia-Lopez’s method showed minimum r.m.s.

variation (0.3834). Although the cdfs’ tested were few

in number, but still the study reveals that Garcia-

Lopez’s method is very much useful in predicting rain

attenuation over the northern India. Calculation of

attenuation by this method follows the pattern of rain

rate. This method is very much useful for calculation

of attenuation with a great accuracy provided the cdfs

of rain rate are available. The plus points of this

method are that, it is simple, easily computable and

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

339

with large number of data the coefficients can be

suitably changed according to regional needs. For

calculation of attenuation at other percentage of time

(0.01% and onwards), the scaling equation of CCIR97

model is re-adjusted depending upon the attenuation

values, which are observed experimentally. From the

above study, one gets a choice for picking up rain

attenuation prediction technique over northern part of

India and can carry out analysis with whatever

database is available.

Smith67

has presented a unified set of absorption

and brightness curves from measurements and other

models. Agreement was within 15% for absorption

co-efficient (7.5 g/m3 water vapour at 290 K) and for

total zenithal attenuation (for 7.5 g/m3 surface water

vapour and for standard U.S atmosphere of 1976).

Above unified set can be safely used for obtaining a

consistent set of attenuation and emission curves.

Water vapour attenuation of short radiowaves is found

to decrease with the increase in angle of elevation. It

is revealed from the studies that satellite

communications with limited availability of

transmitted power can be very much unreliable when

water vapour concentration becomes high.

Performance of a dual polarized satellite system

degrades above 10 GHz due to rain attenuation and

ice depolarization. Although rain attenuation is

common to both single and dual polarized systems by

reducing the received signal power, but ice-

depolarization is unique to the latter. Depolarization is

defined as the change in the state of polarization of

transmitted signal108,109

. Performance prediction of a

DPSC system at and above Ku-band including digital

systems has been done quite successfully by

Vasseur110

. Link availability degradation by a dual

polarized system compared to single polarized system

has also been calculated. In a digital system,

prediction of link availability is connected with

transmission quality. Link availability prediction

method has been applied to Ku-and Ka-band satellite

links and performances of single and dual polarized

systems are compared. In the tropical regions,

however, link availability of both single and dual

polarized systems become remarkably low. Needless

to mention here that if a dual polarized system is

hampered by depolarization then one can consider

depolarization compensation method given by

Stutzman108

.

Demand for satellite communication has grown

remarkably in recent times thereby increasing the

need for higher and higher operating frequencies. Use

of digital systems at higher frequencies makes our

technology more sophisticated. At frequencies above

5 GHz, particularly in the micro-and millimeterwave

range, performance degradation in the earth-satellite

link occurs due to attenuation of signal by

atmospheric hydrometeors111,112

(viz., rain, hail, fog,

snow, ice crystal, etc). Lin and Chen113

have

considered attenuation (which include both absorption

and scattering) due to rain as primary cause;

attenuation due to other hydrometeors are considered

as secondary which affect RF propagation. Many rain

attenuation models have been developed for last few

decades. Shape of raindrop is considered either as

sphere or an oblate spheroid to obtain rain attenuation.

In this respect experimental results were provided by

Medhurst23

, Yeo et al.102

and Crane and Sheih114

. Out

of all available models, Pruppacher and Pitter (P-P)

model115

is widely accepted which has been further

simplified by Li et al.116

. Lin and Chen113

used this

modified P-P model to investigate extinction cross-

sections of raindrops with mean radii between 0.25

and 3.5 mm and in the frequency band 0.6 GHz-100

GHz. In India 20/30 GHz radiometric measurements

were done by Jassal et al117

. Results of extinction

cross-sections for horizontal and vertical polarizations

can very well the predict rain attenuation in wireless

communications113

. In the optical region, water

vapour, aerosols, ozone and, in particular, clouds

impede monitoring of crops during monsoon. This

necessitates the use of microwave remote sensing or

temporal composting of optical data117,118

.

Passive microwave radiometer can globally assess

surface temperature, its wetness and snow cover119

.

Moisture content of soil and evapo-transpiration

fluxes were estimated by Lakshmi et al.120

by using

special sensor microwave imager (SSMI) data. So far

combined use of optical and microwave data for crop

study has been less. Singh and Dadhwal121

used SSMI

radiometer data for regional assessment of crop

growth and developed temporal profiles of MPDI for

different class of land cover which are very useful for

crop growth monitoring.

9 Scopes for future investigations

Capability of the wireless communication systems

has reached its zenith today. It has brought the whole

world at the fingertips of the mankind, yet the

communication systems have many shortcomings to

overcome. There are lot of impediments which

INDIAN J RADIO & SPACE PHYS, AUGUST 2007

340

radiowaves suffer in its journey and thereby

hampering reliable communication. Researchers have

solved several problems to obtain a faithful link but

much more work need to be done.

The lines for further investigation are indicated

below:

(i) It has been observed that fog attenuation

dominates in the infrared and optical bands,

whereas rain attenuation plays havoc at

millimetre wavebands; hence a combined dual

waveband link or use of a compromise

propagation frequency can be thought of.

Absorption bands at 60 GHz and 183 GHz have

many civil and defence applications for a short

path-length of a few kilometres and even less

since absorption at these bands beyond a few

kilometres is very high. Amount of attenuation

may vary from place to place; in cities or

industrial belts pollution may play a big role; in

forests vegetation may have a different role,

whereas in villages or deserts attenuation will be

different. A similar study may, therefore, be

carried out for obtaining a proper path-length.

(ii) For propagation along vertical and horizontal

paths at 22.235 GHz and 94 GHz, absorption

values are often found to be not correlated. It is

suggested to look for correlation of attenuation,

if any, for 22.235 GHz along horizontal and 94

GHz along vertical paths, since attenuation will

be less at 22.235 GHz. At lower rain rates,

attenuation becomes large and increases with

frequency above a critical value. Due to growing

need of millimetrewave frequencies, it is

proposed to look afresh at the low rain rate

attenuation statistics at higher frequencies.

(iii) Post rain attenuation modelling has been done at

22.235 GHz (λ=1.35 cm); the same modelling

can be considered at other window frequencies

in the millimetre waveband. Again the amount

of residual post-rain attenuation was found to be

higher at lower rain rates, which indicates that

such rain rates are associated with smaller

raindrops and low velocity of fall. A study of

post-rain attenuation with rain rate or a relation

between rain drop size and velocity of fall may

be carried out.

(iv) Scattering of radio waves is another major cause

of concern to the communication people.

Electromagnetic waves are scattered mainly by

raindrops, water vapour and oxygen molecules.

Scattered waves cause interference which

degrades signal. Hence a thorough study of

radioscatter in the microwave and millimeter

wavebands will be vital for planning and

designing of radiosystems. A major cause of

attenuation is the effect of wet antenna during

rain. Studies of antenna attenuation and

development of antenna design which does not

attenuate signal during rain can be undertaken.

(v) Multipath fading is an important cause of signal

deterioration in the clear sky condition and

during rain events in the microwave and

millimetrewave ranges. Further researches can

be carried out on multipath fading. With the ever

increasing demand for radio wave

communications, more frequencies above 10

GHz need to be considered for terrestrial and

satellite communications. But signal attenuation

beyond 10 GHz due to rain, water vapour and

other atmospheric constituents is of major

concern. Accurate prediction of attenuation is a

great challenge to the communication people.

Usually, rain data are collected for intervals of

1 h or more; but correct prediction of attenuation

generally requires 1 min or less interval of rain

rate data. Statistical conversion of 1h rain rate

data into 1 min or less rain rate data for proper

prediction of attenuation over tropical and non-

tropical zones may be explored globally.

(vi) Rain drop size distribution models and

attenuation models are established to be highly

regionalized. Studies can be undertaken on such

models at different propagation frequencies and

a global map for prediction of attenuation can be

thought of. Microwave and millimetrewave

remote sensing of various land, soil and

environment at various frequencies are now in

great demand because such a study can provide

a lot of inputs to the agriculture and meteorology

in association with modern satellites. Hence, a

vivid investigation of such remote sensing

technique needs to be probed further. Effects of

sea breeze and breeze in hilly terrains on

propagation factors over a LOS link in India and

elsewhere can be investigated at different

frequencies.

BHATTACHARYA et al.: MILLIMETREWAVE RAIN ATTENUATION & RAIN RATE PREDICTION

341

(vii) Remote sensing of microwave and

milimetrewave radiometry is of paramount

importance to monitor soil and vegetation status

on a regional and global scale. It can also help us

to study the moisture content of soil and its

fertility to investigate vegetation biomass for

estimation of crop yield and its type and many

such agricultural needs may be explored in a

great detail. Radio refractivity largely controls

the quality and reliability of radars and

communication systems. Hence, a thorough

study of radio refractivity in the coastal regions,

hilly places, forests and deserts can be

undertaken at various frequencies in different

seasons. Such a study can be of immense help

for prediction of radar and other communication

system performances.

There are many questions still unanswered,

hopefully, awaits for the improvement of the existing

instruments and techniques and development of the

new ones.

Acknowledgements

The authors are extremely grateful to the

Reviewers of this paper for the valuable comments

and suggestions. We are also thankful to the research

workers whose work published in different

journals/proceedings, etc. have been used in this

paper.

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