NTIA Report 84-148

Microwave Terrestrial LinkRain Attenuation Prediction

Parameter Analysis

E. J. Dutton

u.s. DEPARTMENT OF COMMERCEMalcolm Baldrige, Secretary ,

David J. Markey, Assistant Secretaryfor Communications and Information

April 1984

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PREFACEThis report and the associat@ct project work have been part of an effort

sponsored by the Propagation gngineering Branch of the United States Army Communi­cations Electronics EnginQering·lnstallation Agency (USACEEIA). Their contributionsand guidance are gratefully acknowledged.

Appreciation is also expressed to R. Hassler, C. E. Lewis, J. Spiegel, and

C. Timmons--employees and students at the University of Colorado in Boulder, Colorado,

who have contributed to the results in this repQrt~ as well as to F. K. Steele ofthe Institute for Telecommunication Scienc~§~ NTtA. The drafting work of C. M. Millerand consultation efforts of Dr. H. T. OQygherty, both private contractors, are alsoacknowledged.

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TABLE OF CONTENTSPAGE

LIST OF FIGURESLIST OF TABLESPREfACEABSTRACT1~ RAIN RAT[ DISTRIBUTION MODEL-DATA COMPARISONS

1.1 ThUnderstorm Ratios1. 2~1ethod§ of Cornparison and Data Summary1. 3 Resul ts

2. PREDICTION OF MICROWAVE TERRESTRIAL LINK RAIN ATTENUATION2.1 Rai.n Att@nuation Distribution Prediction t·1odels

2.1.1 Older MOdels2.1.~ MadQrate~y New Models2.1.3 Very Recent Models2.1.4 A Proposed New Model

2.1.5 r~bde'1ng Year-to-Year Variability2.2 Comparison of Models with Data

2.3 Conclusions fram th~ Comparisons3. WORLDWIDE RAINFALL cONtOUR MAPS

3.1 The Federal Republic of Germany and Vicinity

3.2 Okinawa

3.3 Republic of Korea and Vicinity3.4 Southwest Asia

3.5 Central America

3.6 The United States of America3.7 Southeast Asia

4. SYNOPSIS5. REFERENCES

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APPENDIX: IDENTIFICATION Of SITES USED IN THE PREPARATION OF CONTOUR MAPS 149

in SECTION 3

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FIGURE1

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LIST OF FIGURES

Rice-Holmberg rain rate distribution mOd~l ~rediction5 uSing

thunderstorm ratio, Stat Miam1~ Fl, compared with one year l 5

distribution of observed data.Rice-Holmberg rainrated'·stri1:Yution model predictions using the

thunderstorm ratio; O'fO ' .01' at Miami, FL, compared with oneyear's distrlbUt1onof observed data.

Comparison of observed data, distributions at Wallops Island, VA,

with the Rice-Holmberg rain rate distribution prediction model

using the'S and U'jD 1 .01 thunderstorm ratios. The first columnshows three data-regres~'i'On s\iffiffiary techni ques. The resul tantregress i on and ttre ~ @f\tl 95 percent confidence limi ts are comparedwith sand U'/D I

• 01 modeling results in the second and thirdcolumns, respectively.Comparison of observed data and pr~dlGted dlstr1but1ons atMiami, FL, in the format of ~i~Ure 3.

Comparison of observed data and predicted distributions at Rio de

Janeiro, Brazil, in the format of Figure 3.Map of the world showing 13 worldwide locations with usablerain rate distribution data.Illustration of ray-path geometry used in the PROMOD terrestrial­link attenuation distribution pr@dlction model.Comparison of the PROMOD attenuation distribution prediction modelwith data over a 5.1 km, 17.7 GHz link between Rico and Palmetto, GA.Comparison of the Barsis et ale (-1973) attenuation distribution modelwith data over a 5.1km, 17.7 GHz link between Rico and Palmetto, GA.

Comparison of the Battesti et ale (1971) attenuation distribution

prediction model with data over a 5.1 km, 17.7 GHz link between

Rico and Palmetto, GA.Comparison of the GLOBAL {Crane, 1980) attenuation distributionprediction model with data over a 5.1 km, 17.7 GHz link betweenRico and Palmetto, GA.Comparison of the TWO-COMPONENT (erane, 1982) attenuation dis­tribution prediction model with data over a 5.1 km, 17.7 GHz

link between Rico and Palmetto, GA.

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FIGURE

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Comparison of the Lin (1977) attenuation distribution prediction

model with data over a 5.1 km, 17.7 GHz link between Rico and

Palmetto, GA.

Comparison of the r~orita and Higuti (1976) attenuation diistribu­

tion prediction model with data over a 5.1 km, 17.7GHz link

between Rico and Palmetto, GA.

Comparison of the Misme and Fimbel (1975) attenuation distributionprediction model with data over a 5.1 km, 17.7 GHz link betweenRico and Palmetto, GA.

Comparison of the modified Lin (Kanellopoulos, 1983) attenuation

distribution prediction model with data over a 5.1 km~ 17.7 GHz

link between Rico and Palmetto, GA.

Comparison of the CCIR (1982) attenuation distribution prediction

model with data over a 5.1 km, 17.7 GHz link between Rico and

Palmetto, GA.

Map of data locations in the Federal Republic of Germany and

vicinity.

Contour map of the average annual precipitation, M, in milli­

meters for the .Federal Republic of Germany and vicinity.

Contour map of the average annual number of days, O.Ol,withprecipitation great.er than .01 in. for. the Federal Republic of

Germany and vicinity.

Contour map of the average annual number of days, U, with thunder­storms for the Federal Republic of Germany and vicinity.

Contour map of the greatest monthly precipitation, Mm, in 30 con­

secutive years, in millimeters, for the Federal Republic ofGermany and vicinity.Contour map of the thunderstorm ratio, B, for the Federal Republic

of Germany and vicinity.

Contour map of the thunderstorm ratio, UfO.Ol' for the FederalRepublic of Germany and vicinity.

Contour map of the year-to-year standard deviation, styl' in milli­

meters, of total annual precipitation for the Federal Republic of

Germany and vicinity.

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FIGURE26

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Contour map of the year-to-year standard deviation, sC' of theannual number of days with precipitation greater than .01 in.for the Federal Republic of Germany and vicinity.Contour map of the year-to-year standard deviation, su' of theannual number of days with thunderstorms for the Federal Republicof Germany and vicinity.

Contour map of the rain rate, Rl(S), in millimeters per hour,expected to be exceeded 1 percent of an average year and derivedusing the thunderstorm ratio, S, for the Federal Republic ofGermany and vicinity.

Contour map of the rain rate, R.l(S), in millimeters per hour,expected to be exceeded O. 1 percent of an average yea r a.nd deri vedusing the thunderstorm ratio, S, for the Federal Republic ofGermany and vicinity.

Contour map of the rain rate, R.Ol(S), in millimeters per hour,expected to be exceeded 0.01 percent of an average yeaF and derivedusing the thunderstorm ratio, S, for the Federal Republic ofGermany and vicinity.

Contour map of the rain rate, Rl(U/D), in millimeters per hour,expected to be exceeded 1 percent of an average year and derived

using the thunderstorm ratio, U/O. Ol ' for the federal Republic ofGermany and vicinity.Contour map of the rain rate, R.l(U/D), in millimeters per hour,expected to be exceeded 0.1 percent of an average year and derived

using the thunderstorm ratio, U/O. Ol ' for the Federal Republic ofGermany and vicinity.

Contour map of the rain rate, R.Ol(U/D), in millimeters per hour,expected to be exceeded 0.01 percent of an average year and

derived using the thunderstorm ratio, U/O. 01 ' for the FederalRepublic of Germany and vicinity.

Contour map of the estimated year-to-year standard deviation, sR 'in millimeters per hour, of rain rate expected at the 1 percent 1exceedance level for the Federal Republic of Germany and Vicinity.

Contour map of the estimated year-to-year standard deviation, sR '

in millimeters per hour, of rain rate expected at the 0.1 percentl

exceedance level for the Federal Republic of Germany and vicinity.

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Contour map of the estimated year-to-year standard deviation, SR 'in millimeters per hour, of rain rate expected at the 0.01 percen2l

exceedance level for the Federal Republic of Germany and vicinity.Map of data locations in the Republic of Korea and vicinity.Contour map of the average annual precipitation, M, in millimeters,for the Republic of Korea and vicinity.Contour map of the average annual number of days, 0. 01 , with pre­cipitation greater than .01 in., for the Republic of Korea andvicinity.Contour map of the average annual number of days, U, withthunderstorms for the Republic of "Korea and vicinity.

Contour map of the thunderstorm ratio, U/D. Ol ' for the Republicof Korea and vicinity.Contour map of the year-to-year standard deviation, sM' in milli­meters, of total annual precipitation for the Republic of Koreaand vicinity.

Contour map of the year-to-yearstandard deviation, sO' of theannual number of days with precipitation greater than .01 in.,for the Republic of Korea and vicinity.

Contour map of theyear-to-year standard deviation, su' 6f theannual number of days with thunderstorms for the Republic ofKorea and vicinity.

Contour map of the rain rate, Rl(U/D), in millimeters per hour~

expected to be exceeded 1 percent of an average year and derived

using the thunderstorm ratio, U/D. Ol ' for the Republic of Koreaand vicinity.Contour map of the rain irate, R.1(U/D), in millimeters per hour,expected to be exceeded 0.1 percent of an average year and derived

using th~ thunderstorm ratio, U/D. Ol ' of the Republic of Koreaand vicinity.Contour map of the rain rate, R.01(U/O), in millimeters per hour,expected to be exceeded 0.01 percent of an average year and derived

using the thunderstorm ratio, U/D. Ol ' for the Republic of Koreaand vicinity.

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PAGE73Contour map of the estimated year ... to-year standard deviation, sR'

in millimeters per hour, of rain rate expected at the I percent 1

exceedance level for the Republic of Korea and vicinity.

Contour map of the estimated year-to-year standard deviation, sR '

in millimeters per hour, of rain rate expected at the O.lexceeda~ce

level for the Republic of Korea and vicinity.

Contour map of the estimatedyear-to-year standard deviation,

sR ,in millimeters per hour, of rain rate expected at the.01

0.01 percentexceedance level for the Republic of Korea and vicinity.

Map of data locations in Southwest Asia.

Contour map of the average annual precipitation, i~1, in millimeters,

for Southwest Asia.

Contour map of the average annual number of days, 0. 01 , with pre­

cipitation greater than .01 in., for Southwest Asia.

Contour map of the average annual number of days,U, with thunder­

storms for Southwest Asia.

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FIGURE48

55 Contouf .. map of the greatest monthly precipitation, ~1m' in 30 con- 81

secutiveyears, in millimeters, for Southwest Asia.

56 Contour map of the thunderstorm ratio, B, for Southwest Asia. 82

57 Contour map of the thunderstorm ratio,.U/O. Ol ' for Southwest Asia. 83

58 Contour map of the year-to-year standard deviation, sM' inmilli- 84

meters, of total annual precipitation for Southwest Asia~

59 Contour map of the year-to-year standard deviation, sO' of the 85annual number of days with precipitation greater than .01 in., for

Southwest Asia.

60 Contour map of the year-to-year _standard deviation, su' of the 86

annual number of days with thunderstorms for Southwest 'Asia.

61 Contour map of the rain rate, Rl (S), in mill imetersper hour, 87

expected to be exceeded 1 percent of an average year and derived

using the thunderstorm ratio, B, for Southwest Asia.

62 Contour map of the rain rate, R.l(S), in millimeters per hour, 88

expected to be exceeded 0.1 percent of an average year and

derived using the thunderstorm ratio, B, for Southwest Asia.

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Contour map of the rain rate, R.Ol(S), in millimeters per hour,

expected to be exceeded 0.01 perceht of an average year and derivedusing the thunderstorm ratio, S, for Southwest Asia.Contour map of the rain rate, Rl(U/O), in millimeters pet" hour,expected to be exceeded 1 percent of an average year and derived

using the thunderstorm ratio, U/O. Ol ' for Southwest Asia~

Contour map of the rain rate, R.l(U/O), in millimeters per hour,expected to be exceeded 0.1 percent of an average year andderived using the thunderstorm ratio, U/O. Ol ' for Southwest Asia.Contour map of the rain rate, R.Ol(U/O), in millimeters per hour,expected to be exceeded 0.01 percent of an average year and

derived using the thunderstorm ratio, U/O. Ol ' for Southwest Asia.Contour map of the estimated year-to-year standard deviation, sR 'in millimeters per hour, of rain rate expected at the 1 percent 1

exceedance level for Southwest Asia.Contour map of the estimated year-to-year standard deviation, sR 'in millimeters per hour, of the rain rate expected at the 0.1 .1

percent exceedance level for Southwest Asia.Contour map of the estimated year-to-year standard deviation,sR ,in millimeters per hour, of rain rate expected at the 0.01

.01percent exceedance level for Southwest Asia.Map of data locations in Central Ame·~ica.

Contour map of the average annual precipitation, M, in millimeters,

for Central America.Contour map of the average annual number of days, 0. 01 , with pre­cipitation greater than .01 in., for Central America.Contour map of the average annual number of days, U, with thunder­storms for Central America.Contour map of the thunderstorm ratio, U/O. Ol ' for Central America.

Contour map of the year-to-year standard deviation, sr~' in milli­meters, of total annual precipitation for Central America.

Contour map of the year-to-year standard deviation, sO' of the

annual number of days with precipitation greater than .01 inch,for Central America.

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deviation, sR ,109.01

in millimeters per hour, of rain rate expected at the 0.01 percentexceedance level for Central America.Map of data locations in the United States of America. 111Contour map of the average annual precipitation, M, in millimeters, 112

for the United States of America.86 Contour map of the average annual number of days, 0. 01 , with pre- 113

cipitation greater than .01 in., for the United States of America.87 Contour map of the average annual number of days, U, with thunder- 114

storms for the United States of America.88 Contour map of the greatest monthly precipitation, Mm, in 30 con- 115

secutive years, in millimeters, for the United States of America.89 Contour map of the thunderstorm ratio, S, for the United States of 116

America.

90 Contour map of the thunderstorm ratio, U/D. Ol ' for the United 117States of America.

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FI~URE

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Ggntour maR qf the year~to~year standard deviation, sM' in milli­m~ter§, of tQtal ~nnual precipitation for the United States ofAmerica.

Contour map of the year-to~year standard deviation, sO' of theannyal nymb~r of d&ys with precipitation greater than .01 in., forthe United States of America.Contour map of th~ year-to-year standard deviation, $U' of the

annual num~er gf ~ay§ with thunderstorms for the United States ofAmerica.Contour map of the rain rate, Rl(S), in millimeters per hour,expected to be exceeded 1 percent" of an average year and derivedfrom the thunderstorm ratio, S, for the United Stat~s of America.

~pnto~r map of th~ rain rate" R.l(S), ill millimet~r$ per hour,expected to b~ §){~e~dedO~J' p~rcent pf (in av~ra~e year andderived from the thunderstorm ratio, B, for the United States ofAmerica.Contour ma~ of the rain rate, R.Ol(S), in millimeters per hour,~~pected to be exceeded 0.01 percent of an average year Cindderived from the thunderstorm ratio, S, for the United States ofAmerica.Contour map of the rain rate, Rl(U/D), in millimeters per hour,

e~pected to be exc~edeq 1 perc~nt qf an avergg~ y~ar anq d~rived

from the thunderstorm ratio, U/D.Ol~ for the United StCit~s ofAmerica.

Contour map ~f the rain rate, R.l(U/D), in millimeters per hour,expected to be exceeded 0.1 percent of an average year and derived

from the thunderstorm ratio, U/D. Ol ' for the United States ofAmerica.

Contour map of the rain rate, R.Ol(U/D), in millimeters per hqur,expected to beexc~eded 0.01 percent of an av~rage year Cind ~~ri¥ed

from the thunderstorm ratio, U/D. Ol ' for the United States of

America.Contour map of the estimatedyear-to-year standard deviation,

sR {S), in millimeters per hour, of rain rate expected at the 1 per~

ce~t exceedance level, derived from the thunderstorm ratio, S, for

the United States of America.

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FIGURE101

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Contour map of the estimated year-to-year standard deviation,

sR . (6), in millimeters per hour, of rain rate expected at the. 1

0.1 percent exceedance level, derived from the thunderstorm ratio,

S, for the United States of America.

Contour map of the estimated year-to-year standard deviation,

sR . (S), in millimeters per hour, of rain rate expected at the.01

0.01 percent exceedance level, derived from the thunderstorm ratio,S, for the United States of America.

Contour map of the estimated year-to-year standard deviation,

sR (U/O), in millimeters per hour, of rain rate expected at the1

1 percent exceedance level, derived from the thunderstorm ratio,

U/O. Ol ' for the United States of America.Contour map of the estimated year-to-year standard deviation,

sR (U/O), in millimeters per hour, of rain rate expected at the. 1

0.1 percent exceedancelevel, derived from the thunderstorm ratio,U/O. 01 ' for the United States of America.Contour map of the estimated year-to-year standard deviation,

sR (U/O), in millimeters per hour, of rain rate expected at the.01

0.01 percent exceedance level, derived from the thunderstorm ratio,

U/O. Ol ' for the United States of America.Map of data locations in Southeast Asia.

Contour map of the average annual precipitation, M, in millimeters,

for Southeast Asia.

Contour map of the average annual number of days, 0. 01 , with pre­

cipitation greater than .01 in., for Southeast Asia.Contour map of the average annual number of days, U, with thunder­

storms for Southeast Asia.

Contour map of the thunderstorm ratio, U/O. Ol ' for Southeast Asia.Contour map of the year-to-year standard deviation, sM' in mill,,...

meters, of total annual precipitation for Southeast Asia.

Contour map of the year-to-year standard deviation, sO' of the

annual number of days with precipitation greater than .01 in.,

for Southeast Asia.

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Contour map of the YE~ar-to-year standard deviation, su' of theannual number of days with thunderstorms for Southeast Asia.Contour map of the rain rate, Rl(U/D), in millimeters per hour,expected to be exceeded 1 percent of an average year and derived

from the thunderstorm ratio, U/D. Ol ' for Southeast Asia.

Contour map of the rain rate, R.l(U/D), in millimeters per hour,expected to be exceeded 0.1 percent of an average year andderived from the thunderstorm ratio, U/D. Ol ' for Southeast Asia.Contour map of the rain rate, R.Ol(U/D), in millimeters per hour,expected to be exceeded 0.01 percent of an average year and

derived from the thunderstorm ratio, U/D. Ol ' for Southeast Asia.Contour map of the estimated year-to-year standard deviation, sR 'in millimeters per hour, of rain rate expected at the 1 percent 1exceedance level for Southeast Asia.

Contour map of the estimated year-to-year standard deviation, sR '. 1

in millimeters per hour, of rain rate expected at the 0.1 exceedancelevel for Southeast Asia.Contour map of the estimated year-to-year standard deviation,sR ,in millimeters per hour, of rain rate expected at the

.010.01 exceedance level for Southeast Asia.

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LIST OF TABLES

TABLE PAGE

Absolute Value of Observed Rain Rate Deviation, 6R, Outside Pre- 13dieted 0.5 and 99.5 Percent Confidence Limits Using the TwoThunderstorm Ratio Estimation Procedures in the RH Model

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Summary of Departures of Yearly Microwave Attenuation Data Distri­butions Above the Modeled 99.5 Percent Confidence Limit "at the0.01 Percentile Exceedance Level for 10 Prediction Models

Summary of Absolute Values of Departures of Yearly MicrowaveAttenuation Data Outside the 99 Percent Confidence Interval atthe 0.01 Percentile Exceedance Level for 10 Prediction Models

Rain Rate and Rain Attenuation Prediction Parameters for Okinawa

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Microwave Terrestrial LinkRain Attenuation Prediction Parameter Analysis

E. J. Dutton*

Because rain attenuation continues to be a problem for the operationof microwave links worldwide, this report examines the behavior and theprediction of rain rate and rain attenuation·distributions on a worldwidebasis. Particular emphasis is placed' on seven areas of the world ofspecial interest. to the Uo S. Army Communications Electronics andEngineering~Installation Agency (USACEEIA).

The first part of the report discusses the need for, and provides,an alternative thunderstorm ratio in the Rice-Holmberg rain rate distri­bution prediction model. This new thunderstorm ratio is more readilyobtained in regions of thE~ world with s..parse, and less historical,meteorological data. Comparisons of rain rate distributions predictedfrom the Rice-Holmberg model with observed distributions are thenpresented.

The second part of the report discusses rain attenuation predictionon terrestrial microwave links .. Ten models, including a newly~derived

model for this report, are presented for this purpose. Of these 10models, however, only 3 contain a year-to-year variability pred"ictionfeature--a feature usua ll.y necessary to the annua 1 di stri buti on predi c­tion process. An lI ad hocl! annual variability is attached to thE~

remaining 7 models. All 10 models are then intercompared withobserved rain attenuation distribution data.

The third, and largest, part of the report presents contour mapsof the parameters necessary for annual rain rate distribution predic­tions. Also presented are contour maps of rain rate distributionprediction results at the 1, 0.1, and 0.01 percentile exceedancelevels, for use to the reader in predicting annual rain attenuationdistributions at those levels. Seven specific regions of the world havebeen contoured in this report:

1. the Federal Republic of Germany and vicinity,2. Okinawa,3. the Republic of Korea and vicinity,4. Southwest Asia,5. Central America,6. the United States of America,7. Southeast Asia.

Key Words: attenuation distributions; contour maps; microwave links; model-datacomparisons; rain attenuation

*The author is with the Institute for Telecommunication Sciences, National Telecom­munications and Information Administration, U. S. Department of Commerce,Boulder, Colorado 80303.

1. RAIN RATE DISTRIBUTION MODEL-DATA COMPARISONSThe ra"in rate distribution prediction model used throughout this report is

the Rice-Holmberg (RH) model developed by Rice and Holmberg (1973) and modified

by Dutton (1977a). The modification consists of year-to-year variability "wings"around the median prediction originally given by the RH model. Most of the detailsof the development of the RH model are given in Dutton (1977a), so that in this

report it suffices to indicate the inputs to and outputs from the RH model. Theinputs are:

1. M,the average annual precipitation in millimeters, and its year-to-year

standard deviation, sM'2. 0. 01 , the average annual number of days with precipitation greater

than 0~01 inches (0.25mm), and its year-to~year standard deviation, sO'3. U, the average annual number of days with thunderstorms, and its

year-to-year standard deviation, su' and4. Mm, the maximum monthly precipitation of 30 consecutive years of record,

in millimeters.

The outputs are the rainrates, R, in millimeters per hour, at given percentile levels,

P(R), at which Ris expected to be exceeded, and the year-to-year standarddevia­

tions, sR' at P(R).

1.1. ThunderstormRatios

The RH model as developed in the references above makes use of an intermediateparameter known as the "thunderstorm ratio," S. The basic purp6se of this parameter

is distinction between convective. and stratiform types of rainfall. The thunder­storm ratio was originally defined as

where

B Bo

jo.25+2exp [-0.35(1 ~0.125M)]!

S = 0.03 + O.97exp [-5 exp(-0.004 M )Jo' '.' . .., m

(1)

(2)

The exact orlgln of these formulations is not known, but they are most likely the

result of curve-fitting to data in the original RH model of Rice and Holmberg (1973).

Formulas (1) and (2) have two unfortunate aspects, however. First, they are cumber­

some to use, except on a computer. Second, and more important, they require the only

2

use of r-~m in the RH model calculations. The value Mm is very difficult to obtain on

a worldwide data basis because so many years of data are required to obtain it.

This often greatly reduces (sometimes to none) the number of RH model results thatcan be calculated in a given part of the world. This fact would have severelyhampered the production of worldwide rain rate results were it not for an alterna­tive "thunderstorm ratio" development.

This alternative is a straightforward one, defining the thunderstorm ratio as

the ratio of U', the annual number of days with the thunderstorms to 0: 01 , the annualnumber of days with precipitation >.01 inches. The statistical measures of U' are

U and su' while the statistical measures of 0: 01 , are 0. 01 and So . In order to.01

obtain statistical variation of S, it is. necessary to redefine S in (1) as S' with

U' and an M' , the annual precipitation in millimeters, measured by Mand sM' so thatwe now have

S' = Sol 0.25 + 2 exp [ -0.35(1 ~10.125 M')] ! (3)

where So' a quantity without much annual variability, is still given by (2).As a consequence, not only will rain rate predictions made with the thunderstorm

ratio U'/O: Ol have a different average annual value than predictions made with S',but they will have different confidence bands as well. This will be illustrated inthe next subsection of this report, where comparisons of the two thunderstorm ratio

definitions are made.

1.2 Methods of Comparison and Data Summary

The simplest method of comparison of rain rate data distributions and rain rate

prediction distributions is exemplified in Figures 1 and 2. There, an observedyearly distribution of rain rate at Miami, Florida, is compared first (in Figure l)with the prediction procedure using the B thunderstorm ratio, and then (in Figure 2)

with the U'/O:Ol thunderstorm ratio prediction procedure. In these figures, thefive prediction (dotted) curves represent, from left to right, the 0.5, 5, 50(median), 95, and 99.5 percent prediction confidence limits. About all that can besaid regarding the successor failure of a given prediction method is that if the

data curve tends to be bounded by the prediction curves, it is a more reasonableprediction than if the curve lies outside the bounds. For example, the 0.5 and 99.5

percent curves bound a region in which all but one extreme year out of 100 should

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50% \\\\\_ 99.5~

S%-\~~\\\\\ \-\\-95%\\ \\\

.5~~\\\\\\

• 1

.fJl

• PJ2Jl L.--- L-.----L.----------~-----.............I2'J

to(/J

(/J

.~

.,....

(J.)

E

+>c:Q.)

ULQ)

0...

u(IJ

..Q.

a:

Rain rate Cmm/hr)

Figure 1. Rice-Holmberg rain rate distribution model predictions using thethunderstorm ratio, S, at Miami, FL, compared with one year1sdistribution of observed data.

4

-0Q.)

-0(J.l

Q.)

uX

W

.r--

uCIJ

.Qa:

cuE

.,....

~ 1

."1

M i am i, Flo rid a

l)/D

-...ll--- 9S~

.5~ ---

15eJleJf?JSf)• fJfJ 1 '---__...-.....-__----I....__~.........---l------...a...-.l~---'

~

Rain rate (mm/hr)Figure 2. Rice-Holmberg rain rate distribution model predictions using the

thunderstorm ratio, U1/D 1• Ol ' at Miami, FL, compared with one

year1s distribution of observed data.

5

lie. It cannot be determined, a priori, what kind of year the data represent; hence;

proximity to anyone prediction curve has no inherent significance.

The difficulty with this simple metho'd of comparison is that as more and moredata-years become available, comparison graphs such as Figure 1 and 2 tend tobecome so replete with curves that confusion can result. To' avoid this difficulty,

a data summary procedure, resulting in fewer distribution curves, is highly desirable.

However, there are more data summary procedures than one, and we shall now investi­gate the use of three of them.

All three of the data-summary procedures involve statistical regression. It

should be noted that statistical regression using the method of least squares isnot strictly applicable to distribution data, but should be a reasonable approxima­

tion (Crow et al., 1960, p. 150). The most reasonable starting point in the useof statistical regression is the use of the canonical, two-variable least-squaresregression procedure. Although linear regression would normally be the first pro­cedure investigated, because of the curvilinear shape of most rain rate distribu­tion data, parabolic regression was used instead. This procedure will be referredto as "unwe ighted data-distribution summary," for reasons that we shall explainshortly. At this point it should be noted that the authors intend to avoid as muchof the sometimes-formidable detail of the statistical mathematics and discussion aspossible herein. A report by Dougherty and Dutton (1934) contains much of the

necessary detail of applying regression techniques to data distributions.

Because rain rate data distributions tend to have greateryear-to-year varia­bility at lower percentiles of time than at higher percentiles, a procedure that wehave termed "we ighted data-distribution summary" has also been developed. The

weighting refers to the mathematical weighting of the variances at each percentileused in a parabolic regression procedure (Dougherty and Dutton, 1984).

The third procedure has been termed "mean-scaled, data-distribution summary."This procedure is accomplished by taking data at any given (jth) percentile level,

p. and obtaining the average rain rate, ~(p.) at that level. Then each individualJ . J

rain rate, R(Pj)' at that level is normalized by dividing it by R(Pj)' This processis repeated at all percentile levels of interest. Since rain rate at larger exceed­

ance percentiles is ipso facto smaller than rain rate at smaller exceedance percen­tiles, the rain rate variability at the larger percentiles also will be correspond-

inglyless than at the smaller percentiles. Therefore, the normalized data distri­bution should show more even variability (homoscedasticity) across all percentiles,

and thus be amenable to an unweighted linear regression analysis. Such a regression

6

is performed, and the rain rate distribution is then recovered by multiplying

regressed results by the appropriate R(Pj)'Figures 3, 4, and 5 are examples of the three distribution data-summarizing

procedures applied to three different geographical locations that show some of

the advantages and disadvantages of the three procedures. Figure 3 is an analysisfor Wallops Island, Virginia, a location with five observed annual distributions ofrain rate (Goldhirsh, 1982), shown as dashed curves in the left-hand three panels ofFigure 3. The left-hand panels (top to bottom) of Figure 3 show the weighted-regres­sion, unweighted-regression, and mean-scaled summaries, respectively, of these dis­tributions as solid lines, representing the regression line itself (50 percent) andits 5 and 95 percent prediction limits. The middle {top to bottom) three panels of

Figure 3 show the comparison of the data-summa~ curves with the rainfall predictioncurves for Wallops Island (dash-dotted) from the RH model using the thunderstormratio, S. The right-hand three panels of Figure 3 show the comparison of the data­summary curves with the rainfall prediction curves for Wallops Island (dash-dotted)from the RH model using the thunderstorm ratio U1/O: Ol . In all cases, t~e pred~c­

tion curves from the RH model are the median (50 percent) distribution predictionand the 5 and 95 percent confidence limit curves, as indicated in the upper middleand upper right-hand panels of Figure 3. Figures 4 and 5 are identical in formatto Figure 3 except that they represent Miami, Florida, with two observed annualdistributions of rain rate (Jones and Sims, 1971), and Rio de Janeiro, Brazil, with

three observed annual distributions of rain rate (CCIR, 1981).

It is apparent from Figures 3, 4, and 5 that they tell more about the data-sum­

marization procedures than they do about comparison of the two rain rate predictionmethods. In Figure 3 all three data-summary procedures work fairly well, givingreasonably smooth results. In Figure 4, however, weighted regression summary looks

almost comical. In Figure 5, no summary procedure is attractive. Weighted regres­sion looks nearly as bad as in Figure 4, unweightedregression doesn1t enclose allthe data points it is supposed to summarize, and mean-scaling has a ridiculously

large 95 percent confidence limit. One requirement for the use of weighted regres­

sion seems to be that at least 4 or 5 distributions are needed before it can bereasonably used. Otherwise, when you have, say, only two. distributions, as forMiami in Figure 4, the data distributions can intersect, resulting in percentile

levels with zero variability. Thus, the summary prediction limits can oscillate aboutthe median, with a very nondistribution-like behavior.

7

~ .211

+'CllJU

llJ0...

Nall a psIs 1 an d Va

Weighted

~

u(,J

..Qcr:

llJE

r-

+'CG.JU

llJ0...

-Util

..Qcr:llJE

r-

+'CllJU

llJ0...

\\

\

Nal1aps Island Va

U/DWeighted

LlllJLl

llJllJU)<

W

~

Util

.n-cr:

llJE

r-

+'CllJU

llJ0...

Ral" Rate Cm~/hr)

Nall a psI s 1 an d Va

Un",elghted

Pa' ~ Rat.e (mm/hr)

LlllJLl

llJllJU)<

W

-Util

...Q

cr:

+->CllJU

llJ0...

R a i n Rat e Cmm / h r )

Nal1aps Island Va

Bet aUn",elghted

Ra i n Rate Cmm/hr)

LlllJ

LlllJllJU)<

W

~

Util

...Q

cr:

~ .211

+'CQ.lU

Q.l0...

Ra 1 (1 ,~a tern'll / ~ .- )

Na 11 aps Is 1 and Va

U/DUn",etghted

Pain Rate Cmm!hr)

Ll LlllJ llJLl Ll

llJNallaps Isl and Va

llJllJ llJU U)< )<

w W

til.~

(0

tiltil

-~

u Util til

.n- ...Q

cr: cr:llJ .211 llJE E

r= r=+' +'c CllJ llJU U

llJ llJ0... 0...

Pa 1 n Rate Cmm/hr)

Nallaps Island Va

Beta

Rain Rate Cmm/hr)

LlllJ

LlllJllJU)<

W

.~

u(I)

...Q

cr:

+'CQ.lU

Q.l0...

Nallaps Island Va

U/DMean-:scaled

~ ~,

, '~~''''-'",- '",- '",-

'",- '",- '",-'", '",- '",-

''\ '",- '",­'",- '",-

'~ '",- '",-\\. '",- '",-

'",- "\. '",­'",- '",- '",-

, , '\.

Pain Rate Cmm/hr)

Figure 3. Comparison of observed data distributions at Wallops Island, VA,with the Rice-Holmberg rain rate distribution prediction modelusing the Sand U1/D 1. 01 thunderstorm ratios. The first columnshows three data-regression summary techniques. The resultantregression and the 5 and 95 percent confidence limits are comparedwith the Sand U1/D 1. 01 modeling results in the second and thirdcolumns, respectively.

8

R a 1 n I;:) ate Cmm/h r )

5'}'o 95'}'o

~-~~,,,i,

-0-0

-0(l.l

(l.l -0(l.l

-0 (l.l-0

(l.l

Miami (l.l Miami (l.l

(l.l u (l.l

u )< Bet a u)< W

)<

WWeighted

Weighted W

I"l(,1

(,1

(,1 U(,1

~(,1

J2

~cr: J2

cr: cr:

'\"(l.l

E

~ \\ r-+J

\ c 50'7'0cc

3:(l.l

(l.l

\ u 95'}'o (l.l

u u

(l.l 5....'7'0 \ ~O'}'o(l.l

(l.l

0....0.... 0....

\250 300 350

Ra 1 n Rate Cmm/n r) Ra i n Rate Cmm/hr)

\,\

-0\'

-0 .\ -0eu (l.l eu

-0 -0 -0eu

Miami(l.l \,\ Miami

(l.l

Mi amieu (l.l (l.l

u u \\\ Betau

U/D)< )< )<W

Un",.,tght.,dW

~\' Un",.,tght.,dW

Un",elghted

\,~,I':l \\\ I':l \,~, I':l(,1 (,1 \,~, (,1

(,1

~~(,1 (,1

u u \,~, u(,1

~(,1

, ,\ (,1

J2

'"J2

\~\J2

cr: cr: cr:eu ~~ \'~\E

~ '\r- ~ \'~\ ~

+J +J \\\ +Jc c

\'~\c

(l.l (l.l euu u \ \~ \ u

(l.l (l.l (l.l

0.... 0.... \\~,\ 0..

~

50I

100

Ra 1 n Rate (mr-:/h r) Ra in Rate Cmm/hr) Ra i n F~ ate (mm/hr)

-0 -0 -0eu eu eu

-0 -0 -0eu

Miamieu

Miamieu

Miamieu eu euu u

Betau

U/D)< )< )<

w w W

I':l ~ I':l I':ltil

~(,1 (,1

til (,1 (,1

u ~ u Util (,1 (,1

J2~~

J2 J2cr: cr: cr:eu \0-E

\ \r- ~ ~

+J \ +J +JC \ c ceu eu euu \ u UL f....

eu (l) (l)

0.... 0.... 0....

.001

Ra in Rate Cmm/hr) Ra i n Rate (mm/hr) Ra i n F~ ate Cmm/hr)

Figure 4. Comparison of observed data and predicted distributions atMiami, FL, in the format of Figure 3.

9

""0 ""0 ""0Q.l Q.l Q.l

""0 ""0 ""0Q.l

Rio de JaneiroQ.l Q.l

Q.l Q.l Rio de Jane ira Q.l Rio de Jane i rou u u:x :x Bet a :x U/O

w w .1 WWetghhd Weighted W.lghhd

(17.~

~ ~ ~

(17 (17 (17

(17 (17 (17

.~

.~ .~

U U U(17 (17 (17

-'2 -'2 -'2a: a: a:

Q.l .81Q.l .81 Ql .81

E E E

l- I- l-

+>....., +>

C C CQl Ql Ql

U u 50% uL 95"10

L L

llJ Q.l 95% Ql

a.... a.... a....

.001 .8al .aal

P'lin Rate (mrn/hr) R;i in Rate (mm/hr) I~a in Rate Cmm/h r )

""0Q.l

""0Q.lQ.lU:x

w .1

I':l(17

(17.~

u(17

-'2a:

Q.l .81E

l-

+>CQlUL

Q.la....

Rio de Janeiro

Unwetghted

\

""0Q.l

""CQ.lQ.lU:xw

I':l(17

(17

u(17

..aa:

Q.l .81E

l-

+>CQlULQ.l

G.-

.881

Rio de JaneiroBeta

Unw.I ghted

uW

..J:Ja:~ .81

I-

Rio de JaneiroU/O

Ra 1 n Pc.+. e (m rr. 'h r' ) Rain Rate (mm/hr) Rain Rate (mm/hr)

""C ""C ""0

cu cu Q.l

""C ""0 ""Ccu

Rio de Janeirocu

Rio de Janeiro Q.l

cu cu Ql

U U U)( :x Beta :x

W .1 !'tean-.caledW W

l'1.an-:lIcal.d

'"(17 (17.- .~ .~

td lU I':l

'" (17 (17

'" w (17.-u u u

'" w w..a ..J:J -'2a: a: a:I) .11 cu .81 CU .81e E E

~ l- I-

+' +> +>C C CI) CU Ql

U U U

'- L L

I) CU Q.l

a.. a.. a..

••1 .881 .a81

·Rain Ra':.e (mm/hr) Rain Rate (mm/hr)

Rio de JaneiroU/O

l'1ean-:lIcal.d

Rain Rate (mm/hr)

Figure 5. Comparison of observed data and predicted distributions atRio de Janeiro, Brazil, in the format of Figure 3.

10

In general, the performance of the various data-summarization techniques shouldbe such that when numerous years of annual distributions become available, weighte~

regression should perform rather well. At this point, however, rain rate distribu­tions, at the locations for which we have them, are available for no more than fiveyears and usually only fora single year (or less). Thus, we shall use the simple

method of comparison of data and predicted distributions, discussed earlier, tofurther analyze the twoRH model prediction methods.

1.3 ResultsOn the map of the world, given as Figure 6, 13 worldwide locations from which

usable rain rate distribution data are available are shown. There are some rainrate distribution data from other locations around the world, but these data aregenerally not sufficiently extensive, are discontinuous, or are taken from measur- ,ing instruments with overly large integration times. In order to be used in theanalysis given in this subsection, data were required to be taken continuously overat least a year in time, and the rain gauge integration time was required to befive minutes or less. This, in turn, contains the implicit requirement that therain-measuring instrument had to be a recording rain gauge.

There are actually 20 locations worldwide that satisfied these requirements,but some of them were practically coincident geographically with others, resulting I

in only 13 locations that are distinct on the map of Figure 6. In the process ofsatisfying the stated location requirements, all available German data were elimi­nated. Because, however, Germany is an important location in the context of thisreport, the best example of German data--10 continuous months from Darmstadt--wasretained and used in the anal.ysis. Data from the other important locations, con­sidered in the contour mapping in Section 3 of this report, were~ with the exceptionof the U. S. A. (United States of America), unavailable to our know"ledge. This isevident from the map of Figure 6, as well. In a few cases, mostly in Japan, inte­gration times were unknown, but since the data were measured by recording rain gauges,it is most likely that the integration time is <5 minutes in all these cases. Hence,these data were included.

Table 1 shows an analysis and summary of the comparison of obsE~rved rain ratedistributions from the 20 data locations versus predicted results from the RH model

using the standard S and the U1/D: Ol thunderstorm ratios. As noted earlier, theonly likely significant comparison of data distributions with the prediction distri­

butions is based upon whether the-data distribution lies inside or outside the 0.5

and 99.5 percent prediction levels. This is the type of comparison made in Table 1.

11

1800

180°150°90°

60°

60°

30°

30°

0°

0°30°

30°60°

60°90°

90°120°

120°

150°

150°

180°

180°

75°

700L~~~~&~-l~ ~~L-~~ ((l(]~ Loo

60°~ I (J I~ II:

145°:lL30°1 I I~~';' ,~. L. .......... -r- CL.,",v",",cun" I -/ ~ 'r\.. '? ~ TOKYO; 130°___ ,~ I ,

I 150I I I ~~ ~-~ V+--\{+~~\ MA~RO 15°N

~ 6;1 ATOLL

~- ~ 0015° I I I '- { I I ( )--0-1 1-~-:-4~ I 1150

30°1 I 1_( )RIODEI~+--\) I I \ _ ) 1300

-\1J, 0 JJ45° I d- 45°

60°~I

60°I

Figure 6. Map of the world showing 13 worldwide locations with usable rain ratedistribution data.

Table 1Absolute Value of Observed Rain Rate Deviation, 6R, Outside 0.5 and 99.5 Percent Confidence limits

Using the Two Thunderstorm Ratio Estimation Procedures in the RH Model

ObservingStation

i

Data Gauge

Period IntegrationTime

(years) (min.)

Il1R i lat 1% Exceedance

Level(mm/hr)

S U1/0 1~ 01

Il1R i lat 0.1% Exceedance

Level(mm/hr)

SU1/01.01

Il1R i Iat 0.01~ Exceedance

Level(mm/hr)

f3 UI/O I.01

Il1R i Iat 0.001% Exceedance

Level(mm/hr)

S U1 /0 I.01

AssignedWeight,

Wi

3

2 5

131

2.83

10

2

J

13

1

3

2

20

1

2

2.83

10

0.83

3.67

1

1

1

1.25

4

3

a4

4

21

21

aa

21

43

56

37

12

30

4

a

a

3

a aa 2

59

49

13

19

1

a

32

a

15

a

a

aa

a

a

a9

a

a24

33

a

aa

a

aa

a

aa

a

8

14

a aa aa 20

13 a14 7

a aa aa 15

a

aa

3

a

o

a

a

a

a

a

a

aa

a

a aa aa aa a

a aa a2 9

3 a

() ()v v

a

a

a

a

2

a

a

a

a

a aa aa a

a aa aa aa ao 0

5

1 1

1 1

1 .25 1

A 0.03

2

2 1

20 5

1 1

3.67

1

0.83

Miami, FLIsland Beach, NJFrankl in, NCWallops Island, VAStockholm, SwedenStockholm, SwedenAtlanta, GAMajuro Atoll,Marshall Islands

Palmetto, GA(near Atlanta)

Paris, FranceTokyo (Takematsu),Japan

Tokyo (Ka shi rna ) ,Japan

Woody Is., Alaska

Paris(Montsouris),France

Paris(Gometz),France

Rio de Janeiro,Brazil

Blacksburg, VA

Tokyo(Shakuji i),Japan

Tokyo (Saka i) ,Japan

Oarmstadt,FRG

w

Averagedeparture,Il1RI 0.10 0.05 0.. 13 0.17 1.62 1.65 6.. 02 6.94

In order to put these comparisons on a quanti.tative basis, the absolute value of the

departure, 6R i , outside either the 0.5 or 99.5 percent prediction value (largest of

the two used, if both outside), for a given observing station, i, was assessed.Zero departures were assigned if the observed distribution lies inside the predictedconfidence limits. Four exceedancepercentiles, 1, 0.1, 0.01, and 0.001 percent,were checked in the analysis, as shown in Table 1.

Because some of the 20 locations observed annual rain rate distributions for alonger period of time than others, it was necessary to assign a weight, wi' to eachlocation. Nonunity weights represent situations where the data were 1I1umpedll

into a single distribution, longer (or shorte~in the case of Darmstadt) than anannual distribution. The average departure 16RI is then given by

16RI =

20

.I l w·16R.\1= 1 1

20) w.

1i=l

(4)

The results of the averaging process of Equation (4) are shown at the bottom ofTable 1, which show a slight worsening of the deviation for the U'/D: Ol thunderstormratio method as contrasted with the standard S method. The dashes in Table 1 indi­cate a lack of data that therefore could not be included in the average values at

the bottom of Table 1.The apparent slight increase in error by using the U1/D:Olmethod is, in the

author1s opinion, hardly sufficient to gainsay its use as an alternative to thestandard S method. So much more data can be processed, with more meaningful contour­ing* as in Section 3, that U1/D: Ol seems to be a significant and often desirable

alternative to, and even replacement for, the standard S thunderstorm ratio usagein the RH model.

2. PREDICTION OF MICROWAVE TERRESTRIAL LINK RAIN ATTENUATIONThe classical relationship between specific attenuation (attenuation per unit

length), aCf), and rain rate, R,is

a(f) = a(f)Rb(f) (5)

*The U'(D ' . Ol method appears to give a more reasonable estimate of low percentile

rain rates in mountainous regions.

14

where f is frequency, and a(f) and b(f) are frequency-dependent coefficients, was

d~veloped nearly 40 years ago, and has been steadily refined since (Ryde, 1946;Medhurst, 1965; Olsen et al., 1978). This relationship can be regarded as

\.

reasonably well established for frequencies less than about 15 GHz. What is not so

well established, however, is the behavior of total attenuation, T(f), along a path

of length L, versus a given point rain rate, R. We can establish a relationship,

from (5) without difficulty, where R is now a II pa th-average rain rate. 11 We can also

establish a relationship equivalent to (6),

T(f) = a(f)Rb(f)D (7)e

where De is an "effective path length. 1I

Determining ~, D , or whatever other parameter can be defined to explain raine

inhomogeneity along a microwave path is the real impediment. Numerous models have

been developed to account for path rain inhomogeneity in predicting the distribution

of rain attenuation over a year1s time. A number of these models will be discussed

next.

2.1 Rain Attenuation Distribution Prediction Models

Rain attenuation distribution prediction models have been available for about

10 years. Some of the earlier ones were not initially presented in the distribution

prediction format, but are easily adapted. Chronologically, these models can be

subdivided into three categories: older models, moderately new models, and very

recent models. This is the context in which they are presented in this report.

2.1.1 Older Models

Barsis et ale (1973) present a set of curves for conversion of R to R. There

is not a tabular presentation of R/R given with this model, but rathE~r a graph to

which we fit curves for computer interpolation and extrapolation. This model intro­

duces an effective djstance maximum of 22 km. The model uses (5) to evaluate

specific attenuation, but with no suggested a(f) and b(f) values, we have chosen to

use the values of Olsen et ale (1978) in connection with this model.

Battesti et ale (1971) have presented a procedure for the reduction of rain

intensity, presumably analogous to R/R. It is not entirely clear that the II reduction

15

factor ll in their paper is directly applicable to attenuation or to probability, but

we have assumed it applies to attenuation. Little information is given on how the

reduction factor was obtained. Therefore, again, we have taken the liberty ofincorporating it into computer software by means of curvefitting. Rain rate,R, canbe chosen at some percentile, P, of a year, permitting evaluation of T(f) at P, also.

2.1.2 Moderately New Models

Lin (1975) presented a formidable model for the assessment of R/R. Then Lin

(1977) developed a much simpler version, which is, because of its relative simplicity,in widespread use today. The model can be described by,

T(f) = a(f)Rb{f)L K (R,L)r

where Kr{R,L), the path reduction coefficient, is given by

(8)

R - 6.21 + L 2636

(9)

provided R > 10 mm/hr. In (9), L is in kilometers and R is in millimeters per hour.This model has been verified at locations referred by Lin (1977) as IIcity A,H II city

8,·· etc. The rain rate, R, then, as in the older models, can be obtained for some

percentile, P, of a year, so that T(f) also applies to that percentile. The con­stants in (9) were evaluated from 11 GHz data taken at Palmetto, Georgia.

Morita and Higuti (1976) introduce a gamma distribution for point rain rates,then develop a ··spatial correlation function ll to extend the concept (implicitly) topath rain rates and then (explicitly) to rain attenuation distributions, still usinga gamma distribution. They use the specific attenuation relation (5) to derive

these results. However, rain rate is not needed as an input to this model, sincewe solve the inverse gamma function to obtain T(f), given the exceedance percentile,

P(A>T(f)), where A is a random-variable attenuation. The gamma distribution for

rain rate, R, can be written as

P(r>R) (10)

In (10), v and c are parameters of the distribution, r(v) is a gamma function,

x is a dummy variable, and r is a random-variable attenuation. It is necessary to

evaluate v and c in order to use the Morita-Higuti model, and they do not provide a

16

procedure. However, regression can be used to relate v and c to total annual pre­cipitation, M, in millimeters and the thunderstorm ratio, S, (see Section 1). Thisyields

1.1 = 2.90 x lO-4(SM)O.926 mm/hr (lla)2 5.41 x 10-3( sr~) "I. 024 (mm/hr)2 (llb)0 =

where2/ 2 (llc)v = 1.1 0

and2 (11 d)c = 1.1/0

Misme and Fimbel (1975) developed a terrestrial link rain attenuation distribu­

tion prediction model that was later expanded by Misme and Waldtenfel (1980) intoan earth/space attenuation model. The latter paper is brought to the attention ofthe reader because it is a direct extension of the terrestrial link model, and itis written in English, whereas the 1975 paper is written in French. This is asomewhat abstract model, the greatest abstraction surrounding the definition of an"area of storm centers," S.. From this parameter the authors developed a ratio of Sto the area of a precipitation cell from which they ~onclude that lithe probabilityfor intensity R to be observed at any point of the link is, of course, greater thanthat of R being observed at a given point by a factor found equal to ... 11 the ratio.

A computer algorithm is included with the methodology that calculates P(A>T(f)).This algorithm has proven helpful, but has had to be somewhat rewritten for our

purposes to obtain the inverse of P(A>T(f)).Crane (1980) has developed a model that has become more commonly known as the

"g1obal model." It is a straightforward and readily usable model, thE~ basis of

which isa tri-exponential expression that accounts for point-to-path rain rateconversion. The model has some abrupt changes depending upon the path length used.The model requires input of a rain rate R, observed for a percentile P. These R1smust be obtained on a zonal basis, with eight zones worldwide, and an expanded

zonal version for the U. S. A.

2.1.3 Very Recent ModelsCrane (1982) published another model that shall be referred to as the Iitwo-compo~

nent" model. This model divides rainfall into a core "ce lll! (heavier rain) sur­rounded by "debris" (lighter rain). Then abi-exponential distribution is used torepresent the rain rate distribution, with one exponential term representing the

17

cellular rain and the other exponential term representing the debris rain. This

concept, and the appearance of the resultant rain rate distribution, is very similar

to the Rice-Holmberg procedure (see Section 1). The bi-exponential concept is then

extended to attenuation distributions. The parameters of the distributions areevaluated on a rain-zone basis, as in the global model, and are tabulated.

As a consequence, the "two-component" model can only be evaluated on the zonal

basis, whereas other approaches (e.g., contour maps) can be interfaced with theglobal model.

Kanellopoulos (1983) has presented an interesting modification to the

Lin (1977) model, described earlier. The Lin model is based on the use of rain

rates observed fro~ gauges having 5-minute integration times. Since smaller inte­

gration times (e.g., l-minute times) are considered more representative of instane­ous rates, Kanellopoulos (1983) introduces a factor in (8) that permits use of

rain rates observed at any integration time.eonsideringthe worldwide proliferation of microwave terrestrial link rain

attenuation distribution prediction models, the eeIR (1982) has developed its own

model. They assume that the attenuation TO.Ol(f), expected to be exceeded 0.01 per­cent of an average year is given by (8) for the corresponding R at the 0.01 per­

centile. The T(f) at any percentile, P, is then given ~y

where

{

0.03,c =

0.41 ,

0.001 < P < 0.01%,

0.01 < P < 0.1% .

(12 )

The factor Kr(R,L) in (8) is taken to be independent of R, and is given by

9090+ 4L

(13)

2.1.4 A Proposed New ModelDutton et ale (1982) discuss the concept of a "probability modification

factor" (PMF) as a procedure for correcting for finite storm sizes on satellite/

ground communication links. The PMF multiplies the percent of time, Po' during an

average year that homogeneous rainfall-caused attenuation is expected at a given

location. The resultant value represents the percent of time, P (P.5?o)' that the

18

actual attenuation is expected to be exceeded along the path to the satellite. As

such, it is not directly interpretable as the Kr(R,L) in (8).The idea behind this model is the establishment of a PMf for use on terrestrial

links. The first consideration is that the PMF should likely be larger than thesatellite/earth PMF. This is because the total effective path length through rain

is likely to be much smaller; hence, it should encounter more homogeneous rainfallconditions, as illustrated in Figure 7. In Figure 7 the ground-projection length,~TOP' of the satellite/earth path through all possible rain is given by

LTOP ~ 130.33 IFiTOP (14 )

where hTOP is the expected storm-top height. In (14), hTOP and LTOP are in kilo­meters, and hTOP is obtainable from the surface rain rate R. Note that the"satellite/earth path" in FiguY"e 7 is assumed to have an elevation angle of 0° atthe earth station*. In this case, the PMF of Dutton et ale (1982) becomes, for

frequency, f, in gigahertz,

PMF (15 )

If we now introduce a factor,

LG(L) = ~OP ,

to (usually) increase the PMF for terrestrial-link application, (15) becomes

2PMF = 0.987 (~~~il- G(L)

( 16)

(17 )

Hence, the Dutton-Dougherty rain attenuation model for satellite/earth links(Dutton et al., 1982) can be adapted for use as a terrestrial link model, which

we shall call PROMOD.

*It is recognized that not all terrestrial links have 0° elevation angles, but

accounting for other angles has little impact on the modeling.

19

No

Surface

Figure 7. Illustration of ray-path geometry used in the PROr·10D terrestrial-linkattenuation distribution prediction model.

2.1.5 i~odeling Year-to-Year Variability

The PROMOD model, since it is a direct modification of the Dutton et ale (1982)

satellite/earth model, inherently contains an allowance for the often large year-to~

year variability in the prediction of annual rain attenuation distributions. Most

of the other models discussed in this section do not contain such a feature, being

instead restricted to predicting an average or median annual distribution. Moreoften, the modelers derive a single distribution, but do not indicatE~ its statisticalmeaning; hen~e, we have chosen to interpret such models as median annual distribu~

tions.It is necessary to accommodate year-to-year variability in thesE~ other models

since it will be required for comparison of the various mbdels, and the ultimate

choice of one of them as "best ll for a given area. The global model (Crane, 1980)

and the two-component model (Crane, 1982) contain a recommendation that theyear-to-year standard deviation be 36 percent of the expected (median) attenuation

distribution at the 1 and 0.001 perce~tile levels, while at the 0.1 and 0.01 percen­

tiles, it is 28 percent of the expected distribution. We have taken the liberty offitting a quadratic to the four percentages (36, 28,28, 36) to obtain percentagevalues for intermediate percentiles (e.g., we get 27.0 percent of the expected

distribution at the 0.03 perce~tile). The remaining models do not consider year-to­year variability; therefore, we have chosen an ad hoc procedure to obtain year-to­year variability for each model. Whenever possible, we have tried to apply the

Dutton et ale (1982) variability techniques to such models. This is because thevariability can be based on local meteorological data rather than the universalpercentage values of Crane (1980).

Thus, the Crane (1980) result is used with the CCIR (1982) and Misme andFimbel (1975) methods. This is because the CCIR (1982) model i~ a zonal model,similar to the global model, and the Misme and Fimbel (1975) mOd~l 15 not amenableto the other variability t,echnique. Otherwise, the Barsis (1973), Battesti et ale(1971), Lin (1977), Morita and Higuti (1976), and modified Lin (Kanellopoulas, 1983)t

models can be used in connection with the Dutton et ale (1982) year-to-year attenu­ation variability technique. Note, however, that the modifications (lla) and (llb)must be made in the r~1orita and Higuti (1976) model before the variability techniqueis usable.

It is not necessarily fair to many of these models to attach an arbitrary vari­

ability technique and then compare the models with data, as is done in the next

section. Therefore, in addition to comparing all the models in the next section,

a com~arison is made limited to the PROMOD model, the global model, and the

21

two-component model (see Section 2.3. These are the three models that directly con­

tain an allowance for year-to-year variability in the prediction of annual rain-rateattenuation distributions.

2.2 Comparison of Models with DataThe 10 models discussed in the last section must somehow be compared with one

another using available data in a manner that has some physical meaning. An approachthat has very little meaning is the comparison of a predicted m~dian or average

annual distribution of rain attenuation with one given yearly data distribution.Unless one knows where the observed annual distribution lies with respect to allother possible annual distributions in the historical sample space, one has nobusiness comparing with the median, or any other such individual predicted distribu­tion. This kind of comparison has been common in the past, but the conclusions tobe drawn from such comparisons are generally nugatory.

Hence, another, more meaningful comparison approach must be sought. This

approach undoubtedly must use the concept of predicted year-to-year variability inrain attenuation distributions, since this variability is usually significantlylarge for percentages below 0.1 percent of a year. The approach that seems best for

the moment, although it is not as quantitative as might be desirable, determineswhether a given yearly data distribution lies inside or outside a desired confi­dence interval about the median predicted rain attenuation distribution. This con­fidence interval is determined from the predicted year-to-year variability of thedistribution.

We now must consider an appropriate confidence interval to use in this test.

At first glance, a 90 percent confidence interval might seem sufficient, but thenthere is still a prediction of 1 chance in 10 that the inside/outside comparisontest has no significance. If we extend to a 99 percent confidence interval, there

is now a prediction of 1 chance in lob that the test has no significance~ and we

shall deem that an appropriate risk to run.As for the test itself, all we have discussed to this point is a very unquanti­

tative binary (yes,no) test of simply whether or not a given annual data distribu­tion lies inside or outside certain predicted confidence limits on a predictedmedian distribution. We can improve the quantitative aspect somewhat by determining

the magnitude of the departure outside the confidence interval. This departureshould tend to have more meaning the larger the confidence interval. Because

system designers and users are often interested in the highest attenuation, the

departure above the upper confidence limit only (99.5 percent) can be tabulated.

22

Since users are generally interested in a given availability requirement (percent

of the time a given attenuation is exceeded--often 0.01 percent), the departure is

probably more meaningful if tabulated in decibels at that level.Figures 8 through 17 illustrate the comparison technique for a 17.7 GHz, 5.1 km

link between Rico and Palmetto, Georgia. There is one figure for each of the 10

modeled distributions discussed earlier, as identified in the legend 'in the upperright-hand corner of each figure. On each of Figures 8 through 17 are five predicteddistributions. The inner curve is the median (50 percent) year rain attenuationdistribution, the region between the inner two curves surrounding the median-yearcurve is the 90 percent confidence interval of year-to-yearvariability (i.e., thetwo· curves, from left to right are the 5 percent and 95 percent confidence limits).The region between the outer two curves surrounding the median-year distribution isthe 99 percent confidence interval of year-to-year attenuation variability (i;e.,

the two curves, from left to right are the 0.5 percent and 99.5 percent confidencelimits). We shall choose the 0.01 percent exceedance level as the ordinate ~alue

at which we shall make our inside/outside comparison for the 99 percent cpnfidenceinterval. Furthermore, we shall use the same percentage values in the comparisonof all data that follow, for reasons stated earlier. In Figures 8 through 17 thereis no case where the data curve, represented by the dot-dashed line, lis outside the99 percent confidence interval. It is notable in Figures 8 throughl? that the con­

fidence intervals range from very wide, as with the Battesti et ale (1971) model

used in Figure 10, to very narrow, as with the Morita and Higuti (1976) model used

in Figure 14. This inconsistency no doubt results from the amalgamation of differ­ent models in order to produce comparison results, and thereby to some unknown degree

will prejudice the results. As will be seen, when all models are compared, theBattesti et ale (1971) modified model yields the best comparison with data, and theMorita and Higuti (1976) modified model yields the poorest comparison with data.

The 10 analyzed models generally use rain rate as an input, with the notedexception of the Morita and Higuti (1976) model. The Morita and Higuti (1976)

modified model uses expressions (lla) and (llb) which require the thunderstorm

ratio, S, and average annual precipitation, M, as inputs. Although the other ninemodels use rain rate as an input, no consistent choice of a value of rain rate ata specific' location for a given percentage of time (e.g., 0.01 percent) exists

among the models. Most of the models simply require rain rate, without specifyingits choice, whereas the Crane (1980), the two-component (Crane, 1982), and the

CCIR (1982) models require a tabulated zonal rain rate input. The PROMOD model

23

150

Rico-PalmettoPromodFrequency= 17.7 GHzDistance= 5.1 km

50• 2J2J 1 L...-_--L.--..\..-J-..---~-..L----~--.A.-----------'

~

-0Q.)

-0Q)

(1J(J

xw

(/J• 1

or--

(d

(;)

(/)

or--

U(/)

.Q([

Q.)

Eor--

.fJlt-

~

c(J..)

ULQ.)

0.-

RttenlJation (dB)Figure 8. Comparison of the PROMOD attenuation distribution prediction

model with data over a 5.1 km, 17.7GHz link between Rico andPalmetto, GA.

24

Rico-PalmettoBar-sis

Frequency= 17_7 GHzDis t an c e = 5 . 1 k m

• ~e! 1 L-....-_--L_--L....J- -l-.._--..L._.J....--_-....-_""-- ...

~ SeJ leJ0 15~ 2~0

Rttenuat; on (dB)

Figure 9. Comparison of the Barsis et ale (1973) attenuation distributionmodel with data over a 5.1 km, 17.7 GHz link between Rico andPalmetto, GA.

25

15eJ

Rico-PalmettoBattestiFrequency= 17.7 GHzIJ i s t a nc e= 5 . 1 k m

• ·eJeJ 1 .. L...----l -...L..-L-__---~~----~""'---~----I

~

LS(J.)

LS(l)

(l)

U)<

W

(/J• 1

.,.-..

(t1

(IJ

(/)

.,....

U(I)

.Q([

Q)

E.~l

t-

-t->CQ.)

UL

CU0...

Rttenuation (dB)

Figure 10. Comp rison of the Battesti et al. (1971) attenuation,distributionpred ction model with data over a 5.1 km, 17.7 GHz link betweenRico and Palmetto, GA.

26

Rico-PalmettoGlobalFrequency= 17.7 GHzDistance= 5.1 km

50

• ~eJ 1 a.a....-..&--__---...L.-I--__----L._--a.4-- ~ ......

eJ

-0III

-0Q.)

Q.)

Ux

W

C/) • 1

or--

(d

(/)

CIJor--

U(/)

-'2IT:

(].)

E

t-.eJl

+>CQ)

ULQ.)

(L

Rt ten u a t ion (d B )Figure 11. Comparison of the GLOBAL (Crane, 1980) attenuation distribution

prediction model with data over a 5.1 km, 17.7 GHz link betweenRico and Palmetto, GA.

27

15fJ

Rico-Palmetto

2 componentFrequency= 17.7 GHzDistance= 5.1 km

50• ~2Jl I---..L--_---L---J.------J....----J---~---~-----.....

eJ

Rttenuation (dE)Figure 12. Comparison of the TWO-COMPONENT (Crane, 1982} attenuation dis­

tribution prediction model with data over a 5.1 km, 17.7 GHzlink between Rico and Palmetto, GA.

28

-0(J.)

-0(l)

lJ.)

uxw

(,/)• 1

or-

(t1

(I)

(IJ

or--

U(I)

..Q([

lJ.)

E.01 bor--

t-

+-'c(J.)

UL

U.l0...

Ric 0 _. Pal me·t t 0

Lin

Frequency= 17.7 GHzDistance= 5.1 km

lSet

Rttenuation (dB)Figure 13. Comparison of the Lin (1977) attenuation distribution prediction

model with data over a 5.1 km, 17.7 GHz link between Rico andPalmetto, GA.

29

150

Ri co-Fa 1met-to

Mo r ; t a

Frequency= 17.7 GHzDistance= 5.1 km

50• eJeJ 1 "--- --L-......LI.o--oI--......--a-------------.-"'--------.....

eJ

Rttenuation (dB)Figure 14. Comparison of the f10rita and Higuti (1976) attenuation distri­

bution prediction model with data over a5.1 km, 17.7 GHz linkbetween Rico and Palmetto, GA.

30

15~

Rico-PalmettoMisme

Frequency= 17.7 GHzDis t an c e = 5 . 1 k m

• ~ell U----L._---.;.---L--L.--.__..L..-_""--I. -A--__•__-t

~

-0(J.)

-0Q.)

Q.)

u)<

W

(I) • 1

.,......

(t1

(I)

(/)

UV')

.QIT:

Q.)

E

l-e ~ 1

-+JCQ.)

UL

QJ0....

Rttenuation (dB)Figure 15. Comparison of the ~1isme and Fimbel (1975) attenuation distri­

bution prediction model with data over a 5.1 km, 17.7 GHz linkbetween Rico and Palmetto, GA.

31

150IfJfJ

R ; C 0 -,p a 1met t 0

modified LinFrequency~ 17.7 GHzDistance= 5.1 km

SeJ• &lei 1 ~----'I--..a---_~_,--_",,---_..-... L-_-----'

e

-aQ)

-a(l)

IIIUX

W

V?• 1

.,...

(tJ

C/)

CI).,...

UCI?

.S2a:

Q.)

E.,...

.ellf-

+->cQ.)

ULQ.)

0-.

Rttenuation (dB)Figure 16. Comparison of the modified Lin (Kanellopoulos, 1983) attenua­

tion distribution prediction model with data over a 5.1 km,17.7 GHz link between Rico and Palmetto, GA.

32

lSi'

17.7 GHz5 . 1 km

Frequenc:y=Distance=

Rico-PalmettoCCIR

•eel I ......_a...-__~..&.-.o_--'-_~....... ....... --'

fJ

-0Q.)

-0QlQ)

Uxw

V? • 1

.r--

ttl(.1,1

(f).,.....

U(I)

..Q

a:Q)

E.,..

.elll-

+>cQ.)

u'-Q.)

a..

Rttenuation (dB)Figure 17. Comparison of the CCIR (1982) attenuation distribution

prediction model with data over a 5.1 km, 17.7 GHz linkbetween Rico and Palmetto, GA.

33

(see Section 2.1.4) prefers the use of a rain rate derived from the Rice-Holmberg(RH) model, using the U'/O: Ol thunderstorm ratio (see Sections 1.0 and 1.1). For

the other models that need rain rate input to predict the median annual attenuation

distribution, we have arbitrarily chosen to use the U'/O: Ol version of the RH model

to obtain those rain rates. Year-to-year variability was discussed in Section 2.1.5,

but it should be noted that the U1/O: Ol thunderstorm ratio is also used in connection

with obtaining year-to-year attenuation variability for the PRor~oo model, and in

those other models where the PROMOO-type year-to-year variability is also used.

Table 2 summarizes 56 individual attenuation comparisons made at the 0.01 per­

cent level. Each of the 10 prediction models are compared with at least one year's

worth of data distribution at several worldwide locations. There are not nearly asmany locations as comparisons because each distribution represents results from a

specific link, having a given path length and operating frequency, and there are

often several links at one geographic location. Table 2 shows the average and max­

imum departures of the data above the 99.5 percent confidence limit at the 0.01 per­cent exceedance level for these 56 comparisons. In addition, Table 2 shows the

"overall prediction efficiencY,1I E, in percent, where

N - nOE = ---.X

N 100 (18 )

In (18), nO is the number of comparisons with departures and N{=56} is the total

number of comparisons. AnE is also shown by climatic zone. Koppen (1918) subdi­vided the world into five major climatic zones, specified as zones A~ B, C, D, E.Without going into further detail, zone A is a wet, tropical zone; zone B is a dry,

arid zone; zone C is a warm, temperate zone; zone 0 is a cold,temperate zone; and

zone E is a polar-region zone. Most major industrial nations are located in zone C;

hence, therein occ~rred most of the data (50 out of 56 distributions) used in

Table 2. Zones A and 0 accounted for three distributions apiece in Table 2, and

zones Band E are not represented.Table 3 is analogous to Table 2, except that it summarizes departures from the

99 percent confidence interval at the 0.01 percent exceedance level for the 56

comparisons. In other words, it summarizes departures (as absolute values) above

the 99.5 percent confidence limit and below the 0.05 percent confidence limit. Asmentioned earlier, there is more meaning for the system designer to Table 2 as

34

Table 2Summary of Departures of Yearly Microwqve Attenuation Data Distributions Above the i~odeled

99.5 Percent Confidence Limit at the 0.01 Percentile Exceedance Level for 10 Prediction Models

Two t·1ori ta Nisme Kanel-Barsis Battesti Gl oba1 Component Lin and and lopoulos CCIR

Promod et a1. et ale (Crane, (Crane, (1977 ) Hi gu t i Fimbel (1983) (1982 )(1973) (1-971 ) 1980) 1982) (1976) (1975)

OverallPredictionEfficiency,s(percent) 100. a 94.6 100 98.2 98.2 92.9 82.1 92.9 89.3 78.6

Averageoutsidedeparture

(dB) 0 0.247 0 O. 131 0.160 0.118 0.674 0.128 0.597 0.639wU1

r~aximum

OutsideDeparture

(dB) 0 12.50 0 7.36 8.94 3.34 7.33 5.89 9.26 9.48

PredictionEfficiencyin Koppen

ZoneA 100.0 lOO.O 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0C 100.0 94.0 100.0 98.0 98.0 92.0 80.0 92.0 88.0 76.0D 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

Table 3

Summary of Absolute Values of Departures of Yearly l~icrowave Attenuation Data Outside the99 Percent Confidence Interval* at the 0.01 Percentile Exceedance Level for 10 Prediction Models

Two r~ori ta r,1i sme Kane1-Barsis Battesti Global Component Lin and and lopoulos CeIR

Promod et ale et ale (Crane, (Crane, (1977 ) Higuti Fimbe1 (1983) (1982 )(1973) (1971 ) 1980) 1982) (1976) (1975)

OverallPredictionEfficiencys(percent) 98.2 94.6 100.0 98.2 92.9 91 .1 66.1 92.9 87.5 80.4

AverageOutsideDeparture

w (dB) 0.115 0.247 0 0.131 0.327 0.226 2.139 0.128 0.658 0.578(j)

MaximumOutsideDeparture

(dB) 6.46 12.50 0 7.36 8.94 6.02 19.66 5.89 9.26 9.48

PredictionEff; cfencyin Koppen

ZoneA 100.0 100.0 100.0 100.0 0 100.0 100.0 100.0 100.0 100.0C 100.0 94.0 100.0 98.0 98.0 90.0 64.0 92.0 86.0 78.00 67.0 100.0 100.0 100.0 100.0 100. a 67.0 100.0 100.0 100.0

*i.e., outside either the 0.5% or 99.5% confidence limit

opposed to Table 3, but Table 3 represents the truer test of 99 percent significance(i.e., that t~ere is only 1 chance in 100 that the data curve really should lieoutside the 99 percent confidence interval).

2.3 Conclusions from the ComparisonsTables 2 and 3 indicate that the poorest comparisons occur with those models

for which a year-to-year variability estimate had to be arbitrarily added. Thisperhaps has biased the comparison against these models, but since, as we have alsodiscussed, m'odels without any year-to-year variability estimates are also not par­ticularly valuable, we dec"ided to make this type of comparison.

If we restrict comparison to the IIcompl~tell models (i.e., those VJith year-to­

year variability estimates); narTlely, thePROMOD, global (Crane, 1980) and two-compo­nent (Crane, 1982) models, results from Tables 2 and 3 really indicate no clearlysuperior approach. It should be noted that the global model is the simplest

approach of the three to apply, which, under some circumstances, might make itpreferable to the others.

Of the five KBppen (1918) major worldwide climatic zones, only zoneC containsenough data to convey any meaning from the results of Tables 2 and 3. At least asmuch data would have to be acquired in zones A, B, D, and E befori much significancecoul dbe attached to conclusions about comparisons made for these cl inla te types.

Hence, while these comparisons have been interesting an~ useful in delineatingproblem areas ranging from modeling inadequacies to the meaning of distributiondata/model comparisons, they have not particularly shed any light on the question

of which models work best in given regions of the world. Thus, we have not under­taken such a worldwide subdivision. It can be said that probably no more than3 bf the 10 models analyzed should be used under any circumstar.ces. These arethe three IIcompletell rnodels just discussed.

3. WORLDWIDE RAINFALL CONTOUR MAPSIn this section, contour maps of specific areas of the world that are of

especial interest to, USACEEIA are presented. The data locations and their co-or­dinates from which these maps were drawn are given in the Appendix. These maps

contain (a) the rainfall pa~ameters that are useful in predicting rain rates from

the RH model, and (b) some of these selected predicted rain rates and theiryear-to-year variability that can be used in prediction of rainfall effects onmicrowave links. Generally, the maps present the following parameters (unlessdata are insufficient to represent them):

37

1. M, the average annual precipitation in millimeters,

2. 0. 01 , the average annual number of days with precipitation greaterthan 0.01 inches (0.25 mm),

3. U, the average annual number of days with thunderstorms,4. Mm, the maximum monthly precipitation of 30 consecutive years (360

months) of record, in millimeters,5. So, the thunderstorm ratio associated with the original RH model

(see Se~tion 1),

6. U/O. Ol ' an average annual thunderstorm ratio, generally obtained bydividing item 3 by item 2 at a given location* (see Section 1),

7. sM' the year-to~year standard deviation of M,in millimeters,8. sO' theyear-to-year standard deviation of 0. 01 , in days,9. su' the year-to-year standard.deviationof U,in days,

10. Rl(S), the median annual rain rate expected to be exceeded 1 percent ofa year, obtained using S, in millimeters per hour,

11. R.l(S), the median annual rain rate expected to be ~xceeded O~l percent ofa year, obtained using S, in millimeters per hour,

12. R.Ol(S), the median annual rain rate expected to be exceeded 0.01 percentof a year, obtained using S~ in millimeters per hour,

13. Rl(U/D), the median annual rain rate expected to be exceeded 1 percent

of a year, obtained using U/O. Ol ' in millimeters per hour~

14. R.1(U/D), the median ~nnual rain rate expected t~ be exceeded 0.1 percentof a year,obtained using U/O.Ol,inmillimeters per hour,

15. R.Ol(U/D), the median annual rain rate expected to be exceeded 0.01 per­cent of a year, obtained using U/O. Ol ' in millimeters per hour,

16. sR' the predicted year-to-year standard deviation of Rl , obtained from1

items 10 or 13, in millimeters per hour,

17. sR' the predicted year-to-year standard deviation of R. l , obtained. 1

from items 11 or 14 above~ in millimeters per hour,and

18. sR ,the predicted year-to-year standard deviation of R. Ol ' obtained.01

from items 12 or 15 above, in millimeters per hour.

* Although this is not a strictly correct procedure for obtaining the averagevalue, it is usually necessitated by lack of data.

38

Data from which to draw the contour maps contained herein were obtained frompublished compilations of summarized data. Usually the amount of data available foranalysis of one parameter (e.g., M) was not equal to the amount of data availablefor analysis of another parameter in the same area (e.g., U). Some parameters in I

I

certain parts of the world were totally unavailable (e.g., S) forcing already-dis- :cussed alternative procedures to be developed for their estimation. The maps pre­sented in this section appear to be about as thoroughly detailed as is possible fromcurrent data sources. Each global area discussed in this section contains a mapshowing the data locations used, but the reader should recognize that, often as not,some basic data were missing at these locations, and maps were often contoured onthe basis of fewer locations. The following publications were the sources of thebasic data used herein:

o Monthly Climatic Data for the World, 1950-1980, Volumes 3-33, Nos. 1-12,sponsored by the World Meteorological Organization (WMO) , availablethrough the Na ti onal Ocea ni c and Atmospheric Admi ni stra ti on, En.v i ronmenta 1Data Center, Asheville, North Carolina 28801, U.S.A.

D Climatological Data, National Summary, Annual Summary, 1950-1980,Volumes 1-31, No. 13, available through the National Oceanic and Atmos­pheric Administration, Environmental Data Center, Asheville, NorthCarolina 28801, U.S.A.

o U. S. Naval Weather Service World-Wide Airfield Summaries, Volumes I-X,

available through the National Technical Information Service, 5285 PortRoyal Road, Springfield, VA 22161, U.S.A., May, 1970-April, 1971

o Climatological Normals (CLINO) for Climat and Climat Ship Stations forthe Period 1931-1960, World Meteorological Organization PublicationWMO/OMM No. 117, TP.52, 1971

o World Distribution of Thunderstorm Days, Parts I and II, World Meteoro­logical Organization Publication WMO/O~1~1 No. 21, TP.6

o Tables of TemperaturE~,Relative Humidity, and Precipitation for the

World, Parts I-VI, Publication M.O.617a-f, Air Ministry MeteorologicalOffice, printed by HE~r ~1ajesty's Stationery Office, London, U.K., 1961.

Now, let us consider the individual global areas that have been contour mapped.

39

3.1 The Fed.era 1 Repub1i c of Germany and Vi ci ni tyFigure 18 shows the 131 data locations* used' for contouring maps in the

vicinity of the Federal Republic of Germany (FRG/"West Germanyll). Data locations

are also located in the Gernlan Dem~cratic Republic (1lEast Germany"), The Netherlands,

Belgium, France, Switzerland, Austria, and Czechoslovakia. Figures 19-36 show M,

D.0l' U, Mm, f3 , U/ D.0l' SW SD'sU' R1(f3), R. 1(f3), R. 01(f3), R1(U/ D), R. 1(U / D) ,

R. 01 (U/D), sR ' sR ' and sR ' in that order. The values of sR ' sR ' and sR1 .1 .01 1 . 1 .01

were obtained using S. Values of these parameters were also available using U/D. Ol '

but are not presented since they are nearly identical.. Some of the basic param­

eters--namely 0. 01 , sO' and sU--were estimated.

The only values of precipitation days that were available, to the author1s

knowledge, were values of 0. 1, the number of days with precipitation greater than

0.1 inches. Therefore, simple linear extrapolation is used to obtain 0. 01 ; viz,

0. 01 ( ~ :~1) U. S. D. 1(19 )

In (19), the ratio (D. 01 /D. 1)U.S. is obtained from data in the U.S.A. for 102 loca­tions for which 0. 1 and 0. 01 are both available (Dutton et al., 1974). The averagevalue of the ratio, denoted by the bar in (19), is then used on the Koppen (1918)

zone climatic basis (see Section 2.2) to obtain a relational factor between 0. 01from 0. 1 in the FRG vicinity, as well as in other global areas yet to be discussed.

The FRG and vicinity are in zone' C; hence, U.S.A. zone Cdata only were used to

obtain the mean ratio in (19). Thtsprocedure for determining D. 01 from D. 1 is adeparture from the regression procedures of Dutton et ale (1974) used in Europe,

but it appears nearly as effective and is a good dealsilnpler.

As noted earlier, So and Su were also estimated. Once again, the U.S.A. data

sources provided 304 points from which we could establish the relations

(20)

*Data were not always available from all locations for any given mapped parameter.Sometimes only one parameter (usually M) was available at a given data location.

40

/(

l"-

"­')

(•••

(

\ ~~~)\ C'''''· I...,-,~,I ~ l",iJ \

'-1' .\It;it"

CZECHOSLOlvAKIA

•

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12°AUSTRIA

GERMAN

DEMOCRATIC

•

••

•

••

•

•

••

•

• •

•

•

••

••

•

•

•FEDERAL

• REPUBLIC OF

GERMANY

• •

•

••

.'.-"' ../,. ,·,····_-~t..<~><>j·, j~

•

C"'SWITZERLAND

NETH.

FRANCE

Scaleskm E:3:, F3 I

o 20 40 60 80Mi ~"=:F===C~

o 20 40 60 80

••

•

•(. ..(·.LUX.•'.

••

BELG.

Figure 18. r,1ap of data locations in the Federal Republ ic of Germanyand vicinity.

41

Figure 19. Contour map of the average annual precipitation, N, inmillimeters for the Federal RepUblic of Germany and vicinity.

42

190

--..............---..160

IIII

160-- ,.--1~~~~~~---~..... 160~ I~~~- -' Ii

II!

't

f""h) ! <

i

Figure 20. Contour map of th~ average annual number of days, 0 Dl' withprecipitation greater than ~Ol in, for the Federal'Republic of Germany and vicini~,

43

2015

15---- ..-JI

20~--""

25---__.......:.-

25---

,II

Figure 21. Contour map of the average annual number of days, U, withthunderstorms for the Federal Republic of Germany andvicinity.

44

Scales '2°km FA ........... I

0 20 40 60 80Mi.CI Ii ::::J

0 20 40 60 80

/ 210 230

210

Figure 22. Contour map of the greatest monthly precipitation, ~, in30 consecutive years, in millimeters, for theFederal Rep~blic of Germany and vicinity.

45

Figure 23. Contour map of the thunderstorm ratio, B,for the FederalRepublic ~f Germany and vicinity.

.10

Scales

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km E3 Ed:Jo 20 40 60 80

Mi. E==3 E++3::Jo 20 40 60 80

.08

Scoleskm E3 F3 :::J

o 20 40 60 80ML~ ~ ::J

o 20 40 60 80

.10~ __

.15

Figure 24. Contour map of the thundersto~ r~t!o~U/D.Ol' for theFederal Republic of Germany and Vlclnlty.

47

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Scoles

140

km FA c:::::::a Io 20 40 60 80

Mi. F=3 F=3o 20 40 60

I80

160

100

160

Figure 25. Contour map nf the year-to-year standard deviation, ~r inmillimeters, of total annual precipitation for theFederal Republic of G'ermany and vicinity.

48

Figure 26. Contour map of the year-to-year standard deviation, sO' of theannual numbe~ of days with precipitation greater than .01 in.for the Federal Republic of Germany and vicini~.

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",,48° N

~--,._- 50°

..,/

/.......,_-/

/"'('\1

.....---.......... \ J

" -------.:.......;,.--:::::;;,;;;;;::--t-y-,_.....

17

4-9

Scaleskm E3 F3:::J

o 20 40 60 80Mi E:::::+3 F d

o 20 40 60

6°E

T-----.:..-----J--~::L-__+____<_;~_+_-----..J~( vIi

i

16

15

14

15

Scales

km E3 F3 Io 20 40 60 80

Mi F=3 F=3 Io 20 40 60 80

5 . ,

6--7{~

4--......._.....

5--------..4

4

12°

,I

Figure 27. Contour map of the year-to-year standard deviation, 511 , of theannual number of days with thunderstorms for the FederalRepublic of Germany and vicinity.

bO

2.5

Scales

km FA Fa Io 20 40 60 80

Mi. F"'F3 F+3o 20 40 60

II

2.5

80

\\\

>(

/(

l." \ ...,

I\')

~----t~52°

(

"{'-\\

JI

l.~ 1....,-.......,..J '\.\.,.).,5 ,

Figure 28. Contour map of rain rate, 21(S), in millimeters per hour, expected tobe exceeded 1 percent of an average year and derived using the thunder­storm ratio, S, for the Republic of ?ermany and vicinity.

51

Scoles

km E3 c::::::::a Io 20 40 60 80

ML f++3 &=3 Io 20 40 60 80

8.5

8.0

7.58.0

8.5 /9.0 9.5

,­J

Figure 29. Contour mao of the rain rate, R 1(6), in millimeters per hour, expectedto be exceeded 0.1 percent of a~ average year and derived using thethunderstorm ratio, S, for the Federal Republic of Germany and vicinity.

52

N

\\\)

(

/ll

"" "-

""I\

")

--...-....--------r ...~ 520

t\('-\

\J

Jl~ 1...,-,

,..,~ \'l..)J ,

25

.....___---- 3S

~'--+-__-- 30

-----__-40

".

.-//",

45/,. -:,.J

\ /\ J

...~ ~" - _-'-+._..,,_..,..~--_.__ ~_~-::#--_ .__~_._.0.._..__,__,•.__,,_••---_.

))\..,

\50 )

Scaleskm E3 t==::a I

o 20 40 60 80Mi F"==3 E=3 ]

o 20 40 60 80

Figure 30. Contour map of the rain rate, R 01(S), in millimeters per hour,expected to be exceeded 0.01 pettent of an average year and derivedusing the thunderstorm ratio~ S, for the Federal Republic of Germanyand vicinity.

53

"')

(~.....)

Scales

I/

Ir,-Jl .........

I <

t~=~----t-------"-----'-----'---+------"'-::'I::",f-<----+-----~, I )I ; I ,.)"

I

km Mo lt10 ioMi. F'"3 F'"3 I

o 20 40 60 80

i

~/

2.0

Figure 31.

3.0

Contour map of the rain rate, R (U/O), in millimeters per hour,expected to be exceeded 1 perce~t of ~n average year and derivedusing the thunderstorm ratiD, UfO 01' for the federal Republic ofSermany and vicintty~ •

54

Scales

km Mo lt10 ioMi. F=3 e=+3 I

o 20 40 60 80

8

_~_...,.-.,,... 7......__....------ \...,

7

N

7

11

Figure 32. Contour ma~ of the rain rate, R.l(U/D), in millimeters per hour,expected to be exceeded 8.1 percent of an average year and derivedusing the thunde~storm ratio, UfO 01' for the Federal Republic ofSermany and vicinity. ·

Scoleskm E====:I=~~~

o 20Mi. E::=d

o 20

40

50

r-1

60

Figure 33. Contour map of the rain rate, R.Ol(U/O), in mitlimeters per hour,

expected to be exceeded 0.01 percent of an average year and derivedusing the thunderstorm ratio, U/O. Ol ' for the Federal Republic of3ermany and vicinity.

56

Scaleskm E3 F3 I

o 20 40 60 80Mi. F"+3 F*3

o 20

\\\)(

/(

l" '\.

')

I\')\~

..... -,-r--·~r 520

l"

{

"""\II

l""'"" 1,\--,,; -' 1',jJ ,

rI

0.40

Figure 34. Contour map of the estimated year-to-year standard deviation, sR 'in millimeters per hour, of rain rate expected at the 1 percent 1exceedance level for the Federal Republic of iSermany and vicinity.

57

Scaleskm E3 F'"'3 I

o 20 40 60 80Mi ..~ h""d J

o 20 40 60 80

\\\)

{

/(

l" '\.

')

(

~_-.._1.4 '-,

-----__".,.1 .~~ 520

(

"( """"\

\)

Il""'" 1..,-,

/~ l\...)J ,

2.5Figure 35. Contour map of the estimated year-to-year standard deviation, sR '

in millimeters per hour, o~ rain rate expected at the 0.1 .1percent exceedance level for the Federal Republic of Germany andvicinity.

58

Scoleskm E3 F3 I

o 20 40 60 80ML f++3 f++3 I

o 20 40 60 80

~~-5.5

\'II

'"--+----r 52°(~\

('-\

"tI

4.0

4.0

6.5

Figure 36. Contour map of the estimated year~to-year.standard deviation, sR 'in millimeters per hour, of rain rate expected at the 0.01 per- .01cent exceedance level for the Federal Republic of Germany andvicinity.

59

and

sU= (:y) U.S. U (21 )

The mean ratios in (20) and (21) were obtained from the U.S.A. data base, again onthe Koppen (1918) zonal basis.

At this time it should be noted that values of Mm often cannot be obtained as

well, although for the FRG and vicinity they are available. In this case we havechosen not to use a method such as (19), (20), or (21) to obtain ~1 , but rather just

mdenote missing data on maps. This is because in the case of M , however, partialmmaps (except in the case of Okinawa, which is an unusual case, anyway, as discussedin Section 3.2) were often able to be drawn.

3.2 Okinawa

Table 4 summarizes results from Okinawa, in the one departure from contour

mapping. There were only four data locations, as shawn in Table 4, on Okinawa, all

of which were military installations. Furthermore, all four locations are very close

to one another on the west side of Okinawa. As a consequence, a meaningful map

of all of Okinawa could simply not be drawn. The values of Rl(B), R.l(B), and R.Ol(S)could not be obtained because of unavailable M information. As was the case for

mthe FRG and vicinity, 0. 01 , sO' andsU were estimated using the approach of (19),(20), and (21), respectively. Okinawa was determined as lying in Koppen (1918) zone

C for purposes of this analysis.

3.3 Republic of Korea and Vicinity

Figure 37 shows the 33 data locations used for contouring maps in the Republic

of Korea (ROK/South Korea) and vicinity. With the exception afone location,located in the People1s Democratic Republic of Korea (North Korea), all data~ame

from the ROK. Figures 38 to 50 show M, 0. 01 , U, U/D. 01 ' sM,sD' sU' R1(U/D),

R. 1(U/D), R. 01 (U/D), sR1

' sR. l' and sR. 01' in tha t order.

There were only four values of M available for the ROK; hence, it was decidedmthat this constituted an insufficient data base from which to draw a contour map.

With no Mm map, there are correspondingly, then, no maps of S or the rain rates

predicted from the thunderstorm ratio, S. Thus we were once again obliged to rely

upon U/D. Ol for rain rate predictions, which also, once again, shows its value as an

alternative thunderstorm ratio. As in previous areas analyzed, the parameters

60

Table 4Rain Rate and Rain Attenuation Prediction Parameters for Okinawa

LOCATION r~1 0. 01 U U/O. Ol'(mm) (days) (days)

Naha 21 03. 1 171 .8 18.6 0.3 1 0.108

Futema 2037.1 136.2 17.3 0.3 0.127

Kadena 2039.6 140.3 18.6 0.3 0.133

Hamby 2037.1 136.2 17.3 0.3 0.127

LOCATION SM So Su(mm) (days) (days)

Naha 581.8 18.55 3.24

Futema 581.8 14.71 3.01

Kadena 581.8 15.15 3.24

Hamby 581.8 14.71 3.01

LOCATION R1(UfD) R. 1(U/0) R.01(U/D)(mm/hr) (mm/hr) (mm/hr)

Naha 5.776 28.320 99.945

Futema 5.703 29.567 99.066

Kadena 5.705 29.284 99.100

Hamby 5.703 29.567 99.066

LOCATION s sR sR1 . 1 R. 01(mm/hr) (mm/hr) (mm/hr)

Naha 1.934 7.627 7.266

Futema 1.978 8.418 7.777

Kadena 1.998 8.118 7.227

Hamby 1.978 8.418 7.777

61

iP.D.R.

OF

KOREA

•• ,••

REPUBLIC

•

•

•

•

•

Figure 37. nap of data locations in the Republic of Korea and vicinity.

G2

o 20 60 100statute miles Ll I I I !

kilometers n'll' Io 50 tOO

200...J.,

300

40 0 N ­ I----------+-w----~~~-L---------+--

700

1300

32 °l ~-------

Figure 38. Contour map of the average annual precipitation, M, in milli­meters, for the Republic of Korea and vicinity.

G3

I300

95-r-~__~

o 20 60 lOastatute miles l I I I i I

kifometersilliil 'Io 50 100

703 8° ---T----4~~~~__.~~,_L~

---------f-..:-- _

Figure 39. Contour map of the average annual number of days, 0 01' withprecipitation greater than .01 in. for the Republic of _Koreaand vicinity.

64

8~-8

200..J

1300

6

126 0

10

o 20 60 100statute miles l' I I' \

kilometers Illllt Io 50 roo

'--0.

." .3 6 0 - --~--- -=-10:=--if":;;:~--iiiiiiiiii;;i--~~~~~r-- -----------t-

40 0 N-.-r----------J---- __

I32°-T/-- ,-+- ---L _+_

Figure 40. Contour map of the average annual number of days, U, withthunderstorms for the Republic of Korea and vicinity.

u5

o 20 60 faastatute miles I I I I I l

kilometers IIIII1 Io 50 roo

2(JOI=- .-,

300

.06

32

Figure 41. Contour map of ~he thunderstorm ratio, U/D.01

, for the Republicof Korea and vicinity:

06

o 20 '30 100 Isto tute mil es L.1...L.1..l.1-l--ll_l~.!__~--._'W~

~.....-300

,,----...... 350

Figure 42. Contour map of the year-to-year standard deviation, sM' inmillimeters, of total annual precipitation for the Republic ofKorea and vicinity.

G7

o

8

E

o 20 ,l

e mt iesUL..l...J.\.......J.....,...L.........,;L--~~_~l_."lre~.-.:~

k i i0 meters -IT-''-'',\..,..,---l~~['~jl~"'"__'~Ui"'''''-r---

o 50 tOC)

3

32

Figure 43. Contour map of the year-to-year standard deviation, sO' of theannual number of days with precipitation greater than .01 in.,for the Republic of Korea and vicinity.

o 20 60 100statute miles Lt I 1 I

kilometers fllill Io 5C) 100

200l.1 J

I30C;

32

Figure 44. Contour map of the year-to-year standard deviation, su' of theannual number of days with thunderstorms for theRe~pub1i c ofKorea and vicinity.

69

200a 20 60 100 .,.j" I I I I I I

sto tute m I es _I_".........--,--.,--I-r-I'kilometers 111111 I 300

.0 50 100

32°-+------------JL +T

_

Figure 45. Contour map of the rain rate, Rl

(UfO), in millimeters per hour,expected to be exceeded 1 percent of an average year and derivedusing the thunderstorm ratio, UfO 01' for the Republic of Koreaand vicinity. .

70

o 20 60 2statute miles l I I I I !~_=_ 1m••J

kilometerslllill ! ! TmrI4il~'

o 50 roo

o

"..0

32

Figure 46. Contour map of the rain rate, R. 1(U/O), in millimeters per hour,

expected to be exceeded 0.1 percent of an average ~ear and derivedu~i~g.the thunderstorm ratio, U/O 01' of the Republic of Korea andV1Clnlty. ."

71

o 20tute miles II I

kilometers 11111' I

o 50 roo

f')L

r~ 1 1M I~3

Figure 47. Contour map of the rain rate, R.Ol(U/O), in millimeters per hour,

expected to be exceeded 0.01 percent of an average year and derivedusing the thunderstorm ratio, U/O ~l,for the Republic of f~orea andvicinity. .v

72

o 20 60s!OTute nliJes I I I ....L L~~~,,~

kilometers ,.,..11...'....,.1i...,..I--...,.....-~-·'"T......,,··""""""...~o SCI 100

o

Figure 4B. Contour map of the estimated year~to-year standard deviation,sR ,in millimeters per hour, of rain rate expected at the 1 per-

l cent exceedance level for the Republic of Korea and vicinity.

73

2C)Oi ~..m~....~~

3

32

o 20 60 100L I I I 1 Itute mil es l.- -.-..---J...~.--............-

k i !0 mete rs "'rt I II...,.I-....,...1-.....,---r--1!1---1

,0 50 !OO~30C)

3.0~_~

<1

Figure 49. Contour map of the estimated year-to-year standard deviation,sR ,in millimeters per hour, of rain rate expected at the 0.1

'.1 percent exceedance level for the Republic of Korea and vicinity.

74

o 20 60 roostatute miles LI I i .j

k i iometerso 50 100 3

126 0

75

Figure 50. Contour map of the estimated year-to-year standard deviatfon,sR ,in millimeters per hour~ of rain rate expected at t~e

.01 0.01 percent exceedance level for the Republic of Koreaand vicinity.,

0. 01 , sO' and sU were estimated from (19), (20), and (21), by determining that theROK and vicinity are in Koppen (1918) zone C.

3.4 Southwest Asia

Figure 51 shows the 185 data locations used for contouring maps in the South­

west Asia area, including the Middle East. Locations appear to be spread relatively

uniformly over the area, encompassing a variety of climatic types. In spite of

this, many locations did not contain complete data sets, as can be seen from

Figures 52 to 69. Figures 52 to 69 show M, D. Ol ' U, Mm, S, U/D. Ol ' sM' sD' su'

Rl(S), R.l(S), R.Ol(S), Rl(U/D), R.l(U/D), R.Ol(U/D), SR1

' SR.l

' and SR.Ol

' in that

order. Figure 55 shows that a discontinuity, marked liND OATA,II exists in the con­

touring of Mm in the Iran-Afghanistan region~ This lack of data for Mm also carries

over to any parameters derived from Mm; namely, S, Rl(S), R.l(S), and R.Ol(S). Hence,Figures 56, 61, 62, and 63 have the same liND DATA" region indicated thereon. Values

of sR' sR ,and sR were derived from UfO. Ol rather than from B because of the.1 .01

more complete data base.

As in earlier cases, 0. 01 , sO' and Su were estimated using (19), (20), and (21),

respectively, in southwest Asia. In this situation, however, southwest Asia

encompasses .Koppen (1918) zones A, B, C, andO. This required the calculation and

use of four different ratios in the U.S.A. for use with (19) through (21), insteadof only one ratio as has been the case in previously mapped areas. While the pre­

vailing perception of southwest Asia and the r1iddle East is that of a dry, hot

climate, many parts of the region can be quite cold, and others, such as western

India, extremely wet.

3.5 Central America

Figure 70 shows the 47 data locations used for contouring maps in CentralAmerica. There are few data stations just above the isthmus region in Costa Ricaand Nicaragua. As a consequence, there is often a total void of data in that

region, resulting in a liND OATA II indication on many of the contour maps for Central

America . Fig ures 71 to 83 show ~1, D. 01' U, U/ D. 01' S1-1' SD' SU' R1(U/ D), R. 1(U/ D) ,R.Ol(U/D), sR ,sR ,and sR ,in that order.

1 . 1 .01As in some earlier cases, there were insufficiently few (five) values of Mm

available; whence, it was decided not to base any contour maps of M , or any of the. mparameters dependent upon it (S, Rl(S}, etc.) on such a limited sample. It was,

however, possible once again to substitute the "thunderstormratio," UfO"Ol' for

76

o 50 100 200 300 400 500 600 MILESE3 e---3 e---3 e---3E3E+3IE+311o 100200 400 600 800 1000 KILOMETERS

70°I

65°I

60°

~r-. /--.TUR-KE-v--~l-'- _..--- ,--;:;---. T---. ._..r-"qr--- .~..--kn-.. r f I I (\ 1

~~'T .,~,-/ ).lJ/ "I I

I" '''~ ~". '-. ( ! )! U.S.S.R. "I ~.~" ..... I • ) i f JI , ,'- . ~ " I ' ; J

135.. o~~~~'_"" 1./ L/·. t •..•, '., ) 1/"1 t·'_r/~"'\. J-1{;~.,. I I

"'/~.Jl. '~-:?' it- t.....~(.... "- .' "~'. ~~"-'-+-..1 '.. /' Y \ I . ...._-~ I' !~"'--. ' I'\..... I • •

VLEBAN~;fj.sY;~~/ --t'1--~--I l~ I ~--·li-ISRA E, L., I.. ,'/..f,.:~! ~,,/•./'~.,- \ •• ..•.1 t. ~ •... J () .,' I't..· I • j. J... " J" I '~, •. -/ I ..1-... / •

~" ,.f..',? r 'IRAQ )''1-, I IRAN , - - ,

f..•:~/J. ORO.." . I " '. ,.~~)I ~~\.,,,..'", • /1 • ,'. IL ' J IIvv·t- ~!:.~ 5 \, \1 ... \~ i . 01

I r. -=ul-.----.f- j'!l.""",~~ql,,).l\ :... .', ./.... • I(//I'~~ -- -I .~"..;. -I- '\. • I '.' -' ".' _ ' .. _, !'P. J. I l

\ViA. , f ~.•. ·.·l.~·;';·.,·~:,··-.,.·..---:-. -&- J-I.\ /~~~ \" I • ,

I -- • II I. 1·• --- · -:-l\ /. ' INDIA

"'-!'-.J

Figure 51. Map of data locations in Southwest Asia.

70°65°60 0

o 50 100 200 300 400 500 600 NILESE3 E3 ...---=3 E3E3 E*3 I E+3 I I I 1000o 100200 400 600 800 1000 KILOMETERS

'-JC';.-

Figure 52. Contour map of the average annual precipitation~ M, in millimeters, for SouthwestAsia.

o 50.100 200 300 400 500 600 MiLESE=f:=E?3 E-3 E-3............,-~- r--~:r==t-==f--~T---l

o 100200 400 600 800 1000 KILOMETERS

-.......:\D

30(\ ~-.::::: ' f t .....

f \ 20/-.1\\;~\ / \

\

l \I l

25~ k_". \Ir "\/ \ \/" (-"t~ ~

\

50°I

.. 0 ~550 60° 65° 70°

Figure 53. Contour map of the average annual number of days, 0 01' with precipitationgreater than .01 in., for Southwest Asia. ·

c:a

----.~--- Ie.

65° 10°

Figure 54. Contour map of the average annual number of days, U, with thunderstorms forSouthwest Asia.

o 50 100 200 300 400 500 600 MILESEC e--3 E=3 E=3

10°I

65°I

60°

E3-- mE=E'=-"-J [- F=±-=3 I ..... _,

o 100 200 400 600 800 1000 KILOMETE RS

-- 0~ 550

CkJ

Figure 55. Contour map of the greatest monthly precipitation, ~1m' in 30 consecutive years, inmillimeters, for Southwest Asia.

10065 060 0

o 50 100 200 300 400 500 600 MILESE3 . E-3 E=3 E-3E=C E+3 I EF3 ! Io 100200 400 600 800 1000 KILOMETERS

... 0 ~550

ex..N

Figure 56. Contour map of the thunderstorm ratio, S, for Southwest Asia.

10°65°-60 0

f,o 50 100 200 300 400 500 600 .. MILESE3 E=3 E=3 t====1E3 E+"'3 I E+3 I- .)

o 100200 400 600 800 1000 KILOMETERS

Figure 57. Contour map of the thunderstorm ratio, U/D.Ol' for Southwest Asia.

C-:2I)~135°__I /! IIIV

1.4

..._~~.I .2.•~.__ . -- .....,_ .4~t\.' \.

12 ,'i' 1/ \ / '" .I~o~ 4-..--'---~..J1___ \---t-...- ~

i n." %--::::1 , .I \~ 1(' II \v~ II 'j' \ II ~ I

1

250

-+---~-· ) /-I '~/I \ J

I

C"W

70°65°60°

I q

~'100j

2001

~300 I

o 50 100 200 300 400 500 600 MILESE3 e----3 E=3 E=3E3 E+3 I e-+=£:::J::Jo 100200 400 600 800 1000 KILOMETERS

Figure 58. Contour map of the year-to-year standard deviation, sM' in millimeters, of totalannual precipitation for Southwest Asia.

70°

I;tr----.....\.r...,

I

I65°

I60°

o 50 100 200 300 400 500 600 MILESE3 F""""F3 E-3 E-3E3 ESE3 I EF3 I J

o 100200 400 600 800 1000 KILOMETERS

l~~ I

I~~;

c'")U1

Figure 59. Contour.map of the year-to-year standard deviation, sO' of the annual number ofdays with precipitation greater than .01 in., for Southwest Asia.

o 50 100 200 300 400 500 600 MILESE3 E=3 t==3 t===tE3 E=E3 I E+S3 I Io 100200 400 600 800 1000 KILOMETE RS

co<:'\

I60° 65° 10°

Figure 60. Contour fua~of ~he year-to-year standard deviation, sU' of the annual number ofdays with thunderstorms for Southwest Asia.

~ I ~.8I' y--.I_J~I \)

r--T.\-~ 1.-,..,-,~",-". ,._._.._--L..,--~..I{' I \ 1I I ~I

I (I /_ \.... .4 I I i J).2 .. I _~

~---~+~~ ~

I'-.-..~ ------

~ I

I. I

o 50 100 200 300 400 500 600 MILESEI e---3 t==3 t==3E3 E+=3 I EF3 I to 100200 400 600 800 1000 KILOMETERS

NODATA

I

I--

o

I I I I I I 1.2lOoN 400 E 50° - 0~ 55° 60° ~5° ~Oo I~ I 1.-_.

Figure 61. Contour map of the rain rate, R1(S), in ~illimeters per hour, expected to

be exceeded 1 percent of an average year and derived using the thunder­storm ratio, S, for Southwest Asia.

o 50 100 200 300 400 500 600 MILESE3 e--3 e---3 E-3E3 t=+=I I E+3 I Io 100200 400 600 800 1000 KILOMETERS

45° . . 50° ... 0~ 55° 60° 650 700I---~ I I I I

Contour map of the rain rate, Rl(S}, in millimeters per hour, expected tobe exceeded 0.1 percent of an average year and derived using the thunder­storm ratio, S, for Southwest Asia.

100N~E

Figure 62.

---7

Mills

fro-....

I HI13~°-r ~i '-"'. ,,;

VV~iIILs.:tI "',

!300

-: - . \ Ii [.1. 2 -:t 2.-~--LI \ 1/ ....~ ---'

.

1.. \. t J'/ /.I )\ /..'

I. ) /f\. ./ ;1 ~~.I.I JI- \ I

1

250

- \ / '. .\'I "~._--;-----+---~ 1'"1"

I Ir \. I I If ~ I II J '-- \ II I I I

CDCJ

0:'~

o 50 100 200 300 400 500 600 MILESE3 e---3 E---=3 E---=3

. "\ rfo02Mo I 6~O I

lOON~~~~ - O~i50 6!OO 6!50 ~OoFigure 63. Contour mar of the rain rate, R.O,(S), in millimeters per hour, expected to

~e exceeded 0.01 percent of an average year and derived using the thunder­storm ratio, S, for Southwest Asia.

'8

1.0

1.5

2.0 ; 3.0. 5.0

o 50 100 200 300 400 500 600 MILESE3 E=3 E=3 E=3E3 ESE3 I E+3 I·.]o 100 200 400 600 800 1000 KILOMETE RS

... 0~ 55° 60° 65° 70°I I I I

Figure 64. Contour map of the rain rate, Rl(~/D), in millimeters per hour, expected to

be exceeded 1 percent of an average ..year and derived using the thunderstormratio, U/D. Ol ' for Southwest Asia

70°I

o 50 100 200 300 400 500 600 MILESE3 e---3 t==3 t==3E3 EF3 I E"3S3 I:Jo 100200 400 600 800 1000 KILOMETERS

, I} 1:::;:::;r J v L i

I ~.~ I ... / I IlooN 40 0 E ~ ~5° 5.Q/[ - 0~~5° 6,0° ~5°

Figure 65. Contour map of the rain rate, R. l (U/D), in millimeters per hour, expected to

be exceeded 0.1 percent of an average y~ar and derived using the thunderstormratio, U/D. Ol ' for Southwest Asia.

1350

V!'.....>-...-.,.I '\ •

130G~! "1I ) \ '/I \ ( II! ~ ILlI \) /\I I \I I '",I '\. f .I j \

125 0

, I '_ \r-r--I I ~ ~"\f-AI20°1------.1

I

I

~--'

~

N

-'--------1 I II i. I i

o 50 100 200 300 400 500 600 MILESE3..---=3 t====I ES3E3. E±3 I E'±"3 I .Jo 100200 400 600 800 1000 KILOMETERS

lOON . it40vo. tE l.---Y...\ . 45° . . 50° - 0 ~55° 60 0 65° 100.~("'~ I I I r

Figure 6b"":- Contour map of the rain rate, R.cn(U/D), in millimeters per hour, expected to

be exceeded 0.01 percent of an average year and derived using the thunderstormratio, U/D. Ol ' for Southwest Asia.

"-0LV

:'. . rl_ _ I

10oN -40oE. r0T 5tO - o~550----- L.:f\ I ~ I

Figure 67. Contour map of the estimated year-to-yearmeters per hour, of rain rate expected atSouthwest Asia.

o 50 100 200 300 400 500 600 MILESE3 E=3 E-3 E-3E3 F-F3 I E+3 I Io 100200 400 600 800 1000 KILOMETERS

I60° 65° 70°

• I f

standard deviation, SD , in milli-the 1 percent exceeda~~e level for

70°65°60°

o 50 100 200 300 400 500 600 MILESE3 E---a E=3 E=3E3 E+3 I E+3 1.1o 100200 400 600 800 1000 KILOMETE RS

I \ ~I I'r,~'" I i \../1 v-J I\~ r~! \ 1 I~ _, ,...--,,\,.f /J~I I .,.~, I,/~-

__ i L ,/ I \ l://L . I

-------1-+::\/ l ~. (I r=r""\1f'f -----I----~ ., ,I l II \ i1 t !

I l iI "'., I

~ 1/~._+- /. -k-..-

- 0 ~550

'-D~

Figure 63. Contour map of the estimated year-to-year standard deviation, So ,in milli­1\ 1

meter~ per hour, of rain rate expected at the 0.1 percent ·exceedance level for Southwest Asia.

o 50 100 200 300 400 500 600 MILESE3 E-3 E-3 t====IE3EE31EE311o 100 200 400 600 800 1000 KILOMETERS

o

I 1~1(iI I )

l\----I-~~I \ I I 'II L~ ~I(

~~ / ;;L.-I ?............-.---_w /-_ rJ'l'..,......_ 10 _____....

f I ~20 15 ~71//--!---+ T-r! I _

' .1

I a~-----~ I I I I100N~ ~ ~5° ~ - o~q5° 6,00 650 1,00

Figure 69. Contou~the estimated year-to-year standard deviation, sR ' inmillimeters per hour, of rain rate expected at the 0.01 percent .01exceedance level for Southwest Asia.

t..")lJl

--.---;-I--.---~l-- 12°-------11-.~.~----__,1-_.-

--+-, x.:'4ao I '.,. I I I 10°---

-~ ----+-f~.-_.-.---.. 1,.:1 I I i 14°--

••

2'j so 10e

•

.GUATEMALA

•

•

• , ! •

I ~

t1-"'14j . ~

jELI SA~VADOR

+-12'_-I--j-I I

i

Ii It-10 -'.c.-SC,:LE oj ~~~ESI '" S~ALE>~F KILO~ETERSI

Ls ----i-------+--.-.--.-------t----.-.-----.-.-...---..---,---I

92IIi

<...::>0)

Figure' 70. r·1ap of data locations in Central America.

25

SCALE OF KILOMETERS

14° _

---+-.__.__. I 12 "..._-_....

I._--1S00~·~--1

.~ l4 ,;." "--- >\ J

9:> '\.--ri~ --

)4: 8:' i__-1--------+-------- 8\ .. ~p.I C.~~. I ·-T-_·······_------1!----1(5--

I \: I I 'I ".... I' ! I500------ I I

3000 --r------t---·-+-160

--

i I

1 1

1- I

\

I ~~.,~'" I I :tIlIH' , 10°--.-

100(; :;,()

\.(")

'-I

Figure 71. Contour map of the average annual precipitation, M, in millimeters, for CentralAmerica.

___ ,I 10 0 ...._-

I I 14<>--

I leV I I I 12°--

'-+---l-_._.--_.~_. __._,,_.~._. __..- i I I I 16°----

)

50 100

MILES

9b

SCALE OF KILOMETERS

o 2S 50

I9'2I

--,.. ,_.. t-'i

I

II ] I-r16

0_.-"---,'-'-"

JJoo--+-""'-.14~~_"-' __--=+-"""'.....I"'-__

~

co

Figure 72. Contour map of the average annual number of days, 0 01' with precipitation greaterthan .01 in., for Central Amer~ca. ·

10°----~ .# I 1125,I-'

I flU I I I 12°--

L Ch ~--- I;) I I I 14°-

-i-~50--~-_. .._L__,..__. ...._._ ..__.~ --+-__ . I I 18°--

90'

'50 1()()

C! so 100

SCALE OF KILOMETERS

Ij 8 D

! I

1

9f"

II I+--'° 0 I I ----I--'-~&. 'c II. SCALE OFMfLES

l")l:.::/

Figure 73. Contour map of the average annual number of days, U, with thunderstorms forCentral America.

oo

~:::AI "" ~----, -I JJ I I I 14°_-

.1. 10' . I + I "c: 'f('-, I "I I ~-- -+-10°--r SCALE OF MILES

i0 2:) '.,()

1 SC:L:~°:0KiL,~,METERS

!

, , - .-r----- b . -----'-t------.-.-------------4-------------4----------------------. I .! , _...,

~

92

"'"Figure 74. Contour map of the thunderstorm ratio, U/D. Ol ' for Central America.

I78 (,I\ 18°,·---

I

~ . 8"- ""'\ I , !

l.i<~U~:..82 80' 7b J

I j ;

i I !

I I 80"82- +-_

34" j _.______ , _-'_._---+

I

. 7. I I I 14°--

QJII ~- I I guu I I I 16°-.--

iI~6 .~

j

SS"

o 25 50 100

SCALE OF M!LES

10" I I I \ \~"""\ I ,,~\: I I I~UU , 10°--

120~ I \ 1ft='-.. I I .LV I I I 12'--

!

SCALE OF KILOMETERS

j02('

j

r14~

1

2':, 5f) 10fJ

I 8,-J-· II 96,

92"!f

o

Figure 75. Contour map of the year-to-year standard deviation, sr1' in millimeters, of totalannual vrecipitation for Central America.

? 20

10;I

,84"

I

100 150

SCALE OF MILES

o 50 10e

SCALE OF KILOMETERS

......... J I I 14°--

o 25 50

I10 0-L I 1\ ~< I )''c I I \ 10

0

-

--12" i I I \. 1<f"A If.v I I I 12°--

oN

Figure 76. Contour map of the year-to-year standard deviation, sO' of the annual number ofdays with precipitation 9reater than .01 inch, for Central America.

!84

qO

20\ ... I-I " ~

SCALE OF KILOMETERS

(J 2:) 50 10e 15'

1 ---S!··-t-F· <60:=-----+-.--

~ '

Ij ~10 i 0),

" JI",J \

''4

...~.~:4:.c:;;:-.:;.:;;.:.:::-¥::_--~---A-r!--,,_._ ..._-_._.__.+ /)- ----+ i i i4c

--

Iaw

Figure 77. Contour map of the year-to-year standard deviation., sU' of the annual number ofdays with thunderstorms for Central America.

16°·~-·

~. "l ~ ~ J ,,/·~-~··_·-l J~- I \ , 14°_-

1GL

M~

lContour map of the rain rate, R,(U/O), in millimeters per hour, expected to beexceeded 1 percent of an average year and derived using the thunderstormratio, U/O. Ol ' for Central America.

2~)

igure 73.

~-8"! I i- I' '~IX-I< i " I, I ! II , : I! i j

Q0 90 " 8(1, BE '0

~L !""

2", so 100 FlO

SCALE OF KILOMETERS

10° I 1- I" ~ 1 '" 't ~- i--+-100-c" ~ 1SCALE OF MILES

-t-'14 0

,

III I • ~ ~ -(....I

-+--12'~ I l ~ -(....IlIA'". -l~' i -1 \ 12°-I .~~,

I

o+..::.

I I 16°------

I I i8

1

2-, +-800 --+-~8(I -i

O__

I -------. _._- I - 18

\I

i84°I!

~~ ~ L I ;- I ~ ~ 0~~ ::1" --- I 1-or I r---- r-I~-

100

I

~

o 25 50

120 I ---#o--~~ , ~' ~ 1 \12 0

-

Figure 79.

1')0 ISCALE OF KILOMETERS

() 25 50 I,m '50 I I_e 8" I - I I --- I SO~ 3~'::'!. "

I . I I n90" sac 86° . 0 I~Ii'" 84 1,,9-

, l l I 8«

Contour map of the rain rate, R.l(U/O), in millimeters per hour, expected to

be ~xceeded 0.1 percent of an average year and derived using the thunderstormratio, U/O. 01 for Central America.

t-- 10" I I I\:: ~'\: I "\: I i \ 10"-

SCALE OF MILES

c::) !

30~r 14~;:ta>ii ...-:

oCJ1

I 16°-.---

10° --

iiLi&iall'O

I' I I I 14°__

I feV I t I I 12°-

~

84°

I 82 80' /8 ,)

Contour map of the rain rate, R. 01 (U/O), in mil'limeters oer hour, expe'cted to

be exceeded 0.01 percent of an average year and derived using the thunderstormratio, UfO. Ol ' for Central America.

10

MILES

050 100 150

SCALE OF KILOMETERS

'j 2': 5a 10e

III

-12 0 I , __....--T-~I

Figure 80.

o(J'\

16°·····~_·

I84°

I86')

I

I

10.1.~i

I '\"..., r' I f! I I I 12°--

'~-'~ ~--_._. I 1.1 I I I 14"_-

100 150

U80 G

I

Contour map of the estimated year-to-year standard deviation, sR ' in millimetersper hour, of rain rate expected at the 1 percent exceedance 1 level forCentral America.

25 50 JOG

SC,ALE OF MILES

SCALE OF KILOMETERS

12" I

o 2~j')0

10° I I I \ \'t".... I "I I I _L U '10°--

I

-l--18"-;---+~~----;-

(~)gure 81 ..

a'J

16° -_...

I b'" I I I 12°--

~.,#!-._-~ I HE I I I 14° _

I

. ., I ~ ,.. , .. - I ... I-+- .- -.: .... _._. < I. I 10'--

I

I!

M

IContour map of the estimated year-to-year st~ndard deviation, sR' in millimetersper hour, of rain expected at the 0.1 percent exceedance level 1for Central America.

('> 2'::;

Figure 32.

o 25 <)(1 1()O

SCALE OF KILOMETERS

I II ,'-+--8~- I

i ;! ll 90 u

92'II

I !

I I--l-----12° i

I

I10° ~

SCALE OF MILES

o0')

_18"'---

i78°

I

BC) "t---II

---~-T- I 160

-

Ii

82!

34 <)

I

. " ~" • ="'1:=A ,,~ / I---- - I' I I~ I 14°----

12°-__ 1 I ""\ ~~ r ~.v I I I 12°--

10° I I I \c \~, I ", I I , 10°--·I SCALE OF MILES

I ;J S~~LE.~~F KILO:~TERSI () 2t) 51) lOG

I I I I, 8° I , i

I I _. _

I I ,- i I 12-5 I .~u ~I! I • I I

9?0 90. 0 88" ',., () .I..() , .I ; I ~b 84 C> I~ i, i I ! I ! . ! \1 ! 1 1 82:: 80 " 78 ~1 ; j ! I I I

Figure 83. Contour map of the estimated year-to-year standard deviation, s~ ,in mi11i-i"".01

meters per hour, of the rain rate expected at the 0.01 exceedance level forCentral America.

--I

o~

S, and obtain an alternative set of maps for the various rain rates (Figures 78 to

80) and their year-to-year standard deviations (Figures 81 to 83). As in previous

cases, the values of 0. 01 , sO' and Su were estimated from (19) through (21). Theseresults were based on the conclusion that most of Central America is represented

by Koppen (1918) zone A, with some of the interior portions represented by zone C.

3.6 The United States of America

The United States of America (USA), as discussed herein, consists of the con­terminous ("lower 43") United States, or CONUS, Alaska, and Hawaii. A good deal

more usable data are available for the USA. As a matter of fact, all of the 18parameters discussed in Section 3 are directly available, and do not need to be

estimated from formulations such as (19) through (21). An earlier report

(Dutton, 1977b) presented much of this material, yet all of the maps, with the

exception of Figure 88 for Mm, required revision to account for additional data now

available.

Figure 84 shows the 304 data locations used for contouring maps in the U.S.A.

There are 275 locations in CONUS, 25 locations in Alaska, and 4 locations in Hawaii.

Figures 85 through l05 show M, 0. 0" U, Mm~S, U/O. 01 ' sM' sO' sU~ R,(S), R.,fs),

R.O,(S), R,(U/O), R.,(U/O), R.O,{U/O), s~,(S), SR.,(S), SR.O,(S), SR1(U/O)~

sR (U/O), and sR (U/O), in that order. Because of the sufficiency of data in. 1 .01

the USA, it is possible to present contour maps of the rain-rate year-to-year

standard deviation (sR'S) as derived both from S; Figures '00 through '02, and from

U/O. Ol ' in Figures 103 through 105.

3.7- Southeast Asia

Southeast Asia, as can be seen from Figure 106, is taken here to include many

of the large islands in the Pacific Ocean (Sumatra, Borneo, New Guinea, etc.) nowpart of Indonesia. In this area of Southeast Asia, usable data are often lacking;as a consequence, many of the contour maps for Southeast Asia contain a IINO DATA"

region indicated thereon.Figure 106 shows the 243 data locations used for the purpose of contouring

maps of rain rate prediction parameters, and predicted rain rates and their

year-to-year variability in Southeast Asia. Figures 107 through 119 show M, 0. 01 ,

u, U/O. O,' sM' sO' su' R,(U/O), R.,(U/O), R.O,(U/O), SR,' SR.,' and SR.O,' in that

order. Once again there were insufficient data from which to prepare maps of Mm,

110

I -.-....- ..--.-----------.--.--.-,-. ''1_.'- -_.- --_..,.-

.~/'

~

&'J

(j

~ Q

\\.\

200 'O~~"J .\ !

~\ \ j

~ ~\ \jl\» .ClO ~Q. i__---l --L' ----.,.__,'----- ----.'1 tl .'

I

\

I /

1/~~I

---I

--'---I

Figure 84. Map of data locations in the United States of America.

---'---'N

, -

r- Ik......... /

I\

iI',

I!~

I i

I I

----------~----_ .._...,---_.__ •._------_. ----------------------------' ._, ..' --_.....'---~---_._~---,_._.--,._ ....-.<---"....."..---",------------------- ---

\;\;

I!

iI

\1~

I

I

~~II

i

o !

~IOO 200 300 \400 Miles i

I

-0""'l ~~ !

" ,- ,== \ j~ ~. ~! .I -"1200"\ \ IL__ _~ P .Q'" \ 1

, __ (f j i

,Ie

Figure 85. Contour map of the average annual precipitation, M, in millimeters, for the UnitedStates of America. '

-r_ I__'_~~'_ ._--~-_.-._. ---~'~-i

~ I··\~f1\ J

W~~·!/I~ \ I

·140 \ I"......, \ '\ i

\\1\ I" ~//l

/

I 100120~

/150

r:=--

t( I /

~\&I I

I

~ \, I

I /I \::)

/ l I f?J\ ~'7

~ v~

I t!Wl~\ I '\-~

(J

\\!.

I / .- ~;"""'.lI.''''~--· (~ ~ I ~\ .~ I;JV \. \

I;ui

,--'--'w

Figure 86. Contour map of the average annual number of days, 0 01' with precipitation greaterthan .01 in., for the United States of America. ·

--I

--I

+::-~

, - ..~-... •..._--_~ .._---_.._----

/

/

~

&'J

(j0

~CJ

\\ // (I '\ /'f r\!.

~'l

Figure 87. Contour map of the average annual number of days, U, with thunderstorms for the UnitedStates of America.

--...I

--...I

<J1

\300 400 Miles--===

Figure 88. Contour map of the greatest monthly precipitation, Mm, in 30 consecutive years, inmillimeters, for the United States of America.

.gO <)'1

.­----=-'j'"

200 300 400 Miles

.,

, \1\, \J

\ '\ :\ .~

P ~~/~----~ \ \

\\

\l~I

/~I!j

v

'\)

&

(I

~ 1;J

! ~ //~ 11\\,•. ,7~

I \~ \ ~C7

,-------------------------------------------------_.------ ._--_._----,----------,-------,-_. ---

--..l

--..l

0')

Figure 89. Contour map of the thunderstorm ratio, (3, for the United States of America.

~

JII

\\

\300 400 Miles-===

\\

\ ~/~~~'\ '

"t,\ \~\ \ :

~\ .

\ 1) 00

QO

\ fI,- __j

l)

I\)

&/ i /.~ /

I~ ~ ./.i~ 7~I \v~! C7

--l-~--TJI O.3~

(~ )

\..~

JO.1

--.I

--.I

"J

Figure 90. Contour map of the thunderstorm 'ratio, U/D.Ol, for the United States of America.

..

\300 400 Miles--====

v

\J

&

(J

~ 10

, --------- ~__~___ --'I, I

---I

0.:;.

Figure 91. Contour map of the year-to-year standarddeviation,sM, in millimeters, of totalannual ~precipitation for the United States of America.

--J

"r::

~

I

II C:a

\\l

&\J

(j

~ Q

tI

\,.1\ \V',~

!

Figure 92. Contour map of the year-to-year standard deviation, sO' of-the annual number ofdays with precipitation greater than .01 in., for the United States of America.

\

j ~ 1/ ~~&

~ liI~ 7~\J

16 \ \ ,=&

(/

~ (\

V

\ ~ (J

\~

I .. .....__..__._--=-:~ -==~~-=--=--=-_-===---=:-::----~_._.. -1

IIj

I

~ III / ~ '\), ~s-----~~__~~~ ;1n~\'\--J-'.i-C?--rI?7--=- ~ \ ~

Figure 93. Contour map of the year-to-year standard deviation, sU' of the annual number of dayswith thunderstorms for the United States of America.

.QO ()Q

(3,

---

&I\)

(j0

\~ Q

\l.

•..._---,

I'I

~,'

~

(~

3.0 2.0--~

/

I --------------------------------- .-.. ----.- .. -- ... ------- .. ------~--.-.- .._-: 1

N--'

"

.0° llQ

\ )

\

\'.j

\300 400 Miles

\ '

~~\I'~

&'J

~ l)

\~ Q

~

j i /,& /

I ~ I i\\. 7~~ I \V~\ =,0

-~--'" ~~-I \ I\

f',N

Figure 95. Contour map of the rain rate, R.l(S), in millimeters per hour, expectej to be

exceeded J.1 percent of an average year and derived from the thunderstorm ratio, S,for the United States of America.

NW

//

\\).

(j

~-I~--~~-~~

I\.- '.1\ . \\.-/-~t..:::> ,~

\:)

v

Q

\\

\\

~~~·il

../1

\ I\ '

Figure 96. Contour map of the rain rate, R.01(S), in millimeters per hour, expected to beexceeded 0.01 percent of an average year and derived from the thunderstorm ratio, S,for the United States of America.

--- 400 Miles

--_.-...-_.__.----- -_._._-_.__._----==:>--:---~ -..,

& '-\~--v ~ '-l

'\) n4·~ v

\\!.

.//--1

\--/~

------- :

"c.-, /. !

,!V I ~\' I

\ \ \\ '\ \I..... ~ \) . \V 0° QQ \

__ tt· 'j

i /,~ /

~ 111\\[~__ I \1J, =o~

--r---i-- J

------)I

II

~ (

1.5

~/

~~

31.

Figure 97. Contour map of the rain rate, Rl(U/D), in millimeters per hour, expected to beexceeded 1 percent of an average year and derived from the thunderstorm ratio,U/D. 01 ' for the United States of P'merica.

,

\

\

/~../.<

200 300

~\

~\ OQl;l.\ P ::1\ (j.\

l]

f'h---~~~.~_.

~ ,~

\J

(l

~ Q

,

II

/

~ (

10

/

! ~ 7~'~ I~~I &

I i~ 5'-------r--"--l--

? !.'\ ~-_. -

I '''--or - ~! I

-~-:--j' ~-

~ L ---r- ------l _, \: 5.'2.

NUl

Figure 98. Contour map of the rain rate, R.l(U/D), in millimeters per hour, expected to beexceeded 0.1 percent of an average year and derived from the thunderstbrm ratio,UfD. 01 ' for the United States of America.

I

~../--11

---------- \

,I,....--"-< I

./~

~~

o 100 200 300 400 Miles

&'J

(I\7

~ Q

I /

! ~ 0=/~ li~. 7~

. ~~ \ c7

'--

\

j

If

!--~-L__

HAWAII

~~OO

- ------ - --- ---------~~-----------------------~----- _._....._~_._,-------- .._,.._._._... _.'.- ,-/

~

NCJI

Figure 99. Contour map of the rain rate, R.Ol(U/D), in millimeters per hour, expected to beexceeded 0.01 percent of an average year and derived from the thunderstorm ratio,UfD.01' for the United States of America.

I!3c r

--l

\300 400 Miles~

l/

fL ~--\~-~-

~ -JtrJ

'J

(l

~ {J

\l

\\

~ (.)

//

/

/

i

1/k

I LI---------

t --- -=---=--===-=--=--:-.:==="=_==----._--"

N-.....J

Figure 100. Contour map of the estimated year-to-year standard deviation, sR (6), in milli- ~

meters per hour, of rain rate expected at the 1 percent exceedan~e level, derived ­from the thunderstorm ratio, 6, for the United States of America.

, ._._,,-~,-----,--,-------

f--JNco

//

31~7 ~3~5 I (\)~ 6.69

HA,WA, II 3.23 ~ Io ~100 V

r-"

\\).

&'\)

(I

~ CJ

l)

\,.1\ \V,/, Jl,-J

\

\

I !

____ ---1

i

10'

Fi gurel 01 . Contour map of the estimated year-to-year standard deviation Sn (6), in ~illi-K

meters per hour, of rain rate expected at the 0.1 percent .1exceedance level from the thunderstorm ratio, 6, for the United States of America.

\\

\

\

\:;0 <l<:l \:

(1- -- -----l

~//

\200 300 400 Miles

\.-j\ \~~~._---

,~

I\)

&

(I

~

I It'

! ~ /~ 11\\ 7~

I \V~! =o~5

I

II

~

~

I I --- .___ ..._~-=-~~=--:: ._______ ~--- 1

N~J

Fi gure 102. Contour map of the estimated year-to-year standard deviation, sR ~ (S)9 in milli-meters per hour. of rain rate expected at the G.Ol percent .ulexceedance level, derived from the thunderstorm ratio, S, for the United Statesof Amerjca.

~/'

.----'"

\200 300 400 Mileso 100

t?

\j

~

(;::J D

&

\!.

0.8 . \ \ ~

~ 0 1.. ~ ~~~//\\--fj ~\ "0.8°~ ~\

0.8"- \ \» :~o <10

Figure 103. Contour map of the estimated year-to-year standard deviation, sR (UfO), in milli-meters per hour, of rain rate expected at the.l percent exceedante level, derived'from the thunderstorm ratio, UfO.Ol' for the United States of America.

I -:_________________ ~-.--------~------~-.--~.--

wc

.-.,". ------..-...---.. -.---.---.---_.. -'--~-"" 1

!

v

-1-- -fL '.f\~~~ 'JtrJ

~

(j

(;:::> (:J

~

\

Figure 104.

r I //1':--- (,~(",( ~./ ~ ~\L 'l

'\

---I

W---I

\\\

.<:I00Q

\/

1:3

:-':::=~=-=:=~-=-=-===_:'._-----_._-=--:" '-.-- -----_.. -,.,~l

!

"J

(I

~ Q

~

\

WN

Figure 105. Contour map of the estimated year-to-ye~r standard deviation, SR A (UfO), inmillimeters oer hour, of rain rate exoected at the 0.01 oercent ~ulexceedance l~vel, derived from the th~nderstorm ratio, ujo 01' for the UnitedStates of America. ·

5°

5°

15°

II t! f

\\~100

~.~

1350

v! [).

-t'~'

'lK>'

.t:;" ~ . •

·-..·-·····--J..··--·....·-·-....··--....·--....--f .. ·--..·-----···-r--"---' 1Cf-'

1lib:'>11001 05(~:

o

~l DOc

,

I

r=.oJ! I '.. i I

5° -- :\: - ="\: ....;...:+. .,

15°

D10 C --.-t-----....IIk.

",I I / r r"{,. / { (;' J I

~ I~ ;.~ ,L ./r ((

J '''''' r' \ i'.. • ';/ {\ I \Ii" I. • ...... I of ........... 'f {\ 1

~_I I ;. ,-/ ... _--.. ....... r 'I : ~L.....r~ lv.'J I I

~ i I • -. i i '....! : ~T'lS?'- l,.; I I \ \r- I _~ I \ • !~\ ;; I I

f ; .........."""~..,; i. I" ~ ; I I I

200 i BORMA •-r/ ... ",;--.. ~..." ! \ \ 20°·~1--·:-;-~·?-~~-t-l-,.-.-~;_.. ~ - ..---i ----"---\-----~-------1-------r-----+--

,", \

"). I 1. \__L.....-'-...... ..... ( "', #'.... : i. ~.~.--=--- 1

\\·{Jr~·(~.f~~~J~~~!1~ I. 1-------- l,~~.·~\'~~.' \\ ,l) .... \ I _",.)-lJ.J. I : pt-lJjIJ)~lN1 ;L! '.~ • l . (' .. , l t ~ • v· ~. [\

·.~:Y~ 1 i·.4 17~,'JL .'~ 1.: -;I"" Wf~./,;Jl.. '•... ".• .. ..---- ·~~-k> ,.~

I 'J,;vr ~j't~ . f ~r••

•~ I ..M· i,?-ti ~ !:- ~)~

o ---r-- ~~~~t-=--~ :)0 JI 'v~[ / ~! !

I ~~ ,( •

0° I - -\i ·~'~ I , f~;~/~-'-~/I i:-~ ~ I Ii-0°.~ -tH ~I 0 !N _~~ A~ ~~~

t~ I~v~ · I

t;

ww

Figure 106. flap of data locations in Southeast Asia.

15°

20°

---- 5°600

135°

t==j t=====1 'o 100 200 400 600Scale of Kilom-eters

130°125°120°115°11001050100°

iIH ~ r/ t I ~~, I 1 \ 10°

95°

5° I I"~ I~ I ~I( ~I '" ~I 17 I i 5°\:.~ -...-.:::: -,~ ~

0° -+- -A~ ~-'iJ------l--W I ~r= ~ ~ I -)r"=. lWiiili ~ 0°

10° \ '\ \ \ ---- I ">[) JJ'l I I I _10°

J ~,-' I

~ ""'2000 1000 t ,I" I '- \~lOOPi! t , ~~

15°300d

I0

10°

. ,

Q- -

W-+::.';)

5°) It

\ I

()I, ., I \

Figure 107. Contour map of the average annual precipitation, M, .in millimeters, for SoutheastAsia.

0°

15°

'200

135°

-t7tP

E'"""f:-U

E===1 'o 100200· 400 600Scale' of Kilometers

1300125°120°1150110°105°100°

I ---e~r:C i i ~~, I I \ 10°

/

r ....1

95°

,.,,1

5° I I ~ I ) I I FI(~J]~ I I· I :.,. C\ I I 5°

10°' I I I I I ">-D J:J~ I I I 10°

15°

Itt

10C-

-.'Q

5°

w I~ \\ 1\ } I ()Ui

0°

Figure 108~ Contour map of the average annual number of Jays, U 01' with precipitationgreater than .01 in., for Southeast Asia. ·

5°

0°

10°

15°

20°

135°

t=1 t==--=-j I

Scale of Mileso ·100 200 ·400 600E23 I I I

125°120°115°110 0105°100°95°

Q

,..,,1

5° ----1 r =", 1-) ~ I I-~ Ilf ~ f r /I A_~ F" '; H- 5°

5° I,"~..I:\ ~ ~ ! ...,.1~ ~if,LJ I \

0°-+ - -,,~ ,~, ccr- 'I ( ~~ ~ I- ~ -..~, -1- r . ~_ ~

10° -----i \ \ \-- --r &-,,~ --~ f I I-10°

15° I ~/ I'I"V~ ~ "~ I I ~'" \I' t r-'\. .~~. ~-../10010!-i ;~ ~~ I X~ I t-

wC)

Figure 109. Contour map of the average annual number of days, U, with thunderstorms forSoutheast Asia.

10°

0°

15°

20°

I 5°

135°

-l7fP

I==f t====j ,

Scale of Mileso 1100 200 400 600E+3 I I I

130°125°120°115°1100105°100°95°

,.,1

50_1 I ~ I l ill ~ I '/ ~ ~p,,\ H-50

10°-\ II \ I I ~ - iJF I I r-10c

15°

I0

10°

-0'

Q

5°

---I

W'-J

0°

Figure 110. Contour map of the thunderstorm ratio, U/D.01

' for Southeast Asia.

15°

'20°

1350

.f7'rP

t==1 t===="f:_n J

o 100 200 400 600Scale of Kilom-eters

1300125°12001150110°105°100°

I --- ~·1 \ ~ ~,~ r: I I 44 7Jft#..U, I \ \ 10°

Scale of Mileso ,1100 200 400 600

" => -."'''' f' '1 If 4~ ~ f( I~ E3 I I I I 5°\, i { =-* ~ ..

95°

5° I (~ .• I J I Ill· '-fffR I 'I a f ~ c: I; 5°

10°' I I I I 1'='1~ J 7'1 I I I - 10°

15°

I0

10°

-.'Q

5°---oJ

W0:.

0°

Figure 111. Contour map of the year-to-year standard deviation, sM, in millimeters, of totalannual precipitation for Southeast Asia.

15°

20°

;J7

E=j ~ ---C--:Jo 100 200 400 600Scale of Kilometers

I .1IYJ ,~ I I 7~~ Ji._lli I \ \ 10°

I .- "-, V) :~J I ~ I I I ~I ~ I A.L'{\ I~ ~ I I 0°

Scale of Mileso 100 200 400 600E3 I I I I 50

~II~"~::"'::~~\""":-~-:::"TA~~J----J't-(-+I----~~t.~--~::::::>~~~~~-___?(~';!24_~~e~~~~~o~~c;;.~~~t~'~v~v!--

J

"

5° I I "I: I ) ! It . '-!f17r I -I a _ I ~ '"' I i 5°

10°' I 6 I I I ~ {,/I I I I 10°

15°

I0

10°

-.'.,

5°

--J

Wc.~:>

0°

95° 100° 1050 110° 115° 120° 125° 130° 135°

Figure 112. Contour map of the year-to-year standard deviation, sO' of the annual number ofdays with precipitation greater than .01 in., for Southeast Asia.

20°

13501300115011001050

o

100095°

,,,,,1

5° I I"\ 1 J I I ~JI" ~ nPc I I J • _I ~ I j

10°' I I I I '='-l~\:of ~~_ r I r

15°--- ,LI~ ~ (' "t I I '" '-.\I

V .,... I I I , _150

I0

10° I ;-J/( , vv?~,~ ~~ I I ~n/J)!A I \ , 10°

e.,

Q-~-

I _ __ _ .rI .....

I Scale of Mileso 100 200 400 600

5° ~~"'~'~'\ ~ I I ~30"'¥? k···~- ~ 20 E3 I I I I 5°E3 E--a. ,I ~ ~ ,._~ ·1 . ~ I

~

0

0° I - -'II "'~~Iq.Q I ~ I , , (1- {~I )~'I_- I I 0°

Figure 113. Contour map of the year-to-year standard deviation, sU' of the annual number ofdays with thunderstorms for Southeast Asia.

15°

20°

j7

E=' t====1 '

Q. I \ , .100

Scale of Mileso 100 200 400 600

,\: ==-'\ 1'\ " I ' I 4~:2 ft~ ~ ~ E3 I I I I 5°

I

50 I I '" <I I . J I I III ~ri!~ I ·1 a _ I =='=' c: I i 50

00 I - .-'\.1 ~';J J \ I ,/=- ~I JS::= IfSO ~ I _ I 0

0

100 ' I' 1 I I "'-r-'·. {If] I u I I 100

150

I0

10°

.',---'··f>---'

5,0

950 1000 1050 1100 1150 1200 1250 1300 1350

Figure 114. Contour map of the rain rate, Rl(U/D), in millimeters per hour, expected to beexceeded 1 percent of an average year and derived from the thunderstorm ratio,U/D. 01 ' for Southeast Asia.

15°

-17~

~ ,il ,£ j~ I 401~' L. \ \ '\ 20°

,.,,1

5° I ~ II I III \..r"fitrt I WI r =='-' \: I: 5°

10°' I J! I I I """-l'"\ { :;olj I I I 10°

'15°-rtt ~~' I t---\l i "~ ') I I ]\(, _. ..

v

0

100~ ;JfEJ \~~ I,

+1(;V~1R I \\10

0_ 40.- 4030 / I # 7J

-.'

--J 50~ "1'~ I /' l~~·:·g yr I Scale of Mileso 100 200 400 600+:a

I IF=3 I I I' I 5°N

\ l t

E3 "I

o 100 200 400 600

b\~ I rtr= / -~l&~iS=~S00 ~ - ..:. .~.~ I .. ,~,_./-,~, I! 0°

95° 100° 105° 110° 115° 120° 125° 130° 135°

Figure 115. Contour map of the rain rate, R.l(U/D), in millinleters per hour, expected to beexceeded 0.1 percent of an average year and derived from ihe thunderstorm ratio,U/D. 01 ' for Southeast Asia.

15°

E={--t=:===1 I

o 100 200 400 600Scale of .KiT6m-eters

f1~1 _)~ I~ I I 00

~ fr- /-11.,_"- )1\/ 7~ I 60~ I ~ + \ 20°

,..,J

--f -~ffi wi~~ I ~ uv ~9' I I t- 100, .-: .. I II vn", I..,,,, IT'·· .M · \

Scale of Mileso 100 200 400 -600

=- I~' I / I ~.f >:s<' IJ E3 I I I f 50\ ..- _ \ I ;7 (

50~ I _¥ 1-1 I I f j( .~ I 'I P ~ IT 50

0°

100

-\ \ I \ \ I '"'-~ hi t I ,100

950 1000 1050 1100 1150 1200 1250 1300 1350

Figure 116. Contour map of the rain rate, R.Ol(U/D), in millimeters per hour, expected to beexceeded 0.01 percent of an average year and derived from the thunderstorm ratio,U/D. Cl ' for Southeast Asia.

15°

ID

100

..'Q

~ 5°w

5°

0°

15°

20°

\\

f'

t==t t====-j ,

o 100 200 400 600Scale-of Kflom-eters

I Scale of Mileso 100 200 400 600E3 I , I

950 1000 1050 1110" 1150 1200 1250 1300 1350

Figure 117. Contour map of the estimated year-to-year standard deviation, So , in millimetersr\l

per hour, of rain rate expected at the 1 percent exceedance level forSoutheast Asia.

--+ .r:ft.-I A.~ I I P1 .~}j I ~ \ 100

5°_1 I ,,/, ~ I I Iii·~f '1- J A F~C\ t-t- 5°

10° \ \ I \ \ I S-t> hf I 1 I 10°

2.54

15°2.01.5

I1.0

010°

.'

~

5°---J

+::=-..p;:.

0°

15°

I 50

1350

t==1 t====:=C -::::Jo 100 200 400 600Scale 'of Kifom-eters

1300

Scale of Mileso ,1100 200 400 600F+3 I I I

125°12001150110°10501000

,.'

950

- I ~·1 \'t IC.·'-:_~I r-=I f I ~ ~ ,~t, I \ \ 10°

Q

n-r--t- ~- "'Vt.\,. ,1 / J.-R I I /h7.5 I l -l- \ 20°

. ,

I

5° I I '-~ , I I I III 'UffR I 'I r~ c: I i 5°

5° 1\~ ,\ ,

0° I .-'\] ~~f ~ \ I I r- ~I _)~ ICFa - ~=r---I 0°

10° I 1 I 1 I I ~"\ ( A I I '100

15°

+:::lo(....

Figure 118. Contour map of the estimated year-to-year standard deviation, sR ' in millimetersper hour, of rain rate expected at the 0.1 exceedance level for .1 Southeast Asia.

5°

15°

-t7r;P

t==j t:===1 J

o 100 200 400 600Scale of Kilometers

Scale of Mileso 1100 200 400 600E"+3 I I I

)/~ I I ,.;..20 I 1 + ! 20°

I ~·1 { I \ L<-j,r:= II I I ~, ~~- I \ \ 10°

I .-~I ~.::J' \ I I fJrr--- ~ I _~~ ICia I =T 0°

,/

"

5° I I "It I 'I III vnR I " r =-'-' c I; 5°

10°' I· 1'="-1"\ J A I I I 10°

I0

10°

."

Q

--..I

5°

~S"'>

0°

95°

Figure 119.100° 105° 110° 115° 120° 1250 130° 135°

Contour~ap of the estimated year-to-year standard deviation, sR ,in mi}li-meters per hour, of rain rate expected at the 0.01 exceedance .01 level forSouthe·a·st Asia.

S, and any of the modeled rain rate results dependent on the S paramE~ter. Also,

the values of 0. 01 , sO' and Su were estimated usin~ (19) through (21), and werebased on the assumption that the entire Southeast Asia area can be classified as aKoppen (1918) zone A.

4. SYNOPSISPrediction of annual rain rate distributions and their consequent attenuation

distributions on microwave terrestrial links have been extended and examined inquite some detail" in this report. Although there are seven geographical areas

covered rather exhaustively, there remains the rest of the world that has not beenexamined herein. For such areas, the likely best procedure at the present forobtaining rain rate and rain attenuation prediction results is from the worldwidezonal maps presented by the CCIR (1982). The CCIR (1982) results, however, arepresented on a good deal coarser geographical variability scale than has been pre­sented here, and are presented without the essential ingredient of year-to-year

variability.

5. REFERENCESBarsis, A. P., C. A. Samson, and H. T. Dougherty (1973), ~licrowave communication

links at 15 GHz,U. S. Army Communications Command Tech~ Report .ACC-ACO-2-73(NTIS Acces. No. 767-545).

Battesti, J., L. Boithais, and P. Misme (1971), Determination de llaffaiblissementdu ala pluie pour les frequencies superieures a 10 GHz, Ann. Telecom. (France),26, No. 11-12, pp. 439-444~

CCrR (1981), Statistics of rainfall rate and rain attenuation on a line-of-sightradio relay link operating at 11 GHz, CCIR Document 5/316-E,Brazil,4 June 1981.

CCIR (1982), Recommendations and Reports of the CCIR, 1982;Volume V: Propagationin Non-ionized Media, Report 338-4: Propagation data required for 1ine-of­sight radio-relay systems, ITU, Geneva, Switzerland, pp. 291-292~

Crane, R. K. (1980), Prediction of attenuation by rain, IEEE Trans. Commun.,COM-28, No.9, pp. 1717-1733.

Crane, R. k. {1982), A two-component rain model for the prediction of attenuationstatistics, Radio Sci. }Z, No.6, pp. 1371-1387.

Crow, E. L., F. A. Davis, and ~1. w. r'~axfield (1960), Statistics Manual (DoverPublications, Inc., New York, NY).

Dougherty, H. T., and E. J. Dutton (1984), The eva 1ua ti on of predi cti on model s formicrowave attenuation by rainfall, NTIA Report 84-145.

Dutton, E. J. (1977a), Earth-space attenuation prediction procedures at 4 to 16 GHz,Office of Telecommunications Report 77-123 (NTIS Acces. No. PB 269-228/AS).

147

Dutton, E. J. (1977b), Precipitation variability in the U. S. A. for microwaveterrestrial system design, Office of Telecom. Report 77-134 (NTIS Acces. No.AD A049041).

Dutton, E. J., H. T. Dougherty, and R. F. Martin, Jr. (1974), Prediction ofEuropean rainfall and link performance and coefficients at 8 to 30 GHz,USACC Tech. Report No. ACC-ACO-16-74 (NTIS Acces. No. A000804).

Dutton, E. J., H. K. Kobayashi, and H. T. Dougherty (1982), An improved model forearth-space microwave attenuation distribution prediction, Radio Sci .17, No.6,pp. 1360-1370. -

Goldhirsh, J. (1982), Yearly variations of rain rate statistics at Wallops Island,and their impact on predicted slant path attenuations, The Johns HopkinsUniversity/Applied Physics Laboratory Report SIR82U-031, November.

Jones, D. i\tl.A., and A. L. Sims (1971),Climatology of instantaneous precipitationrates, ReportAFCRl-72-0430, prepared by the Illinois State Water Survey/U.ofIllinois, Urbana, Illinois 61801, for the Air Force Cambridge Research Labs.,Bedford, MA 01730, December.

Koppen, w. (1913), Klassification der klimate nach temperatur, niederschlag undjahreslauf, Petermanns r\1itt. aus Justus Perthes· Geog. Anst. 64, pp. ]93-248.

Kanellopoulos, J. D. (1983), Extension of Lin empirical formula for the predictionof rain attenuation, Radio Sci. ~, No.2, pp. 237-240.

Lin, S. H. (1975.), A method for calculating rain attenuation distributions on micro­wave paths, Bell System Tech. J. 54, No.6, pp. 1051-1086.

Lin, S. H. (1977), Nationwide long-term rain rate statistics and empirical calcula­tion of ll-GHz microwave rain attenuation, Bell System Tech. J. 56, No.9,pp. 1581-1604. -

Medhurst, R~ G. {1965), Rainfall attenuation of centimeter waves: comparison oftheory and measurement, IEEE Trans. Ant. Prop. AP-13, No.4, pp. 550-564.

Misme, P., and J~ Fimbel (1975), Theoretical and· experimental determination ofattenuation due to rain on a radio-path, Ann. Telecom. (France) 30, Nos. 5-6,pp. 149-158. -.

Misme, P., and P. Waldteufel (1980), A model for attenuation by precipitation on amicrowave earth-space link, Radio Sci. ]i, No.3, pp. 655-665.

Morita, K., and I. Higuti (1976), Prediction methods for rain attenuation distribu­tions of micro and millimeter waves, Rev. Elect. Comm. Labs. (Japan) 24,Nos. 7-8, pp. 651-668. -

Olsen, R. C., D. V. Rogers, and D. B. Hodge (1978), The aRb relation fn the calcu­lation of rain attenuation, IEEE Trans. Ant. Prop. AP-26, No. 2,pp. 318-329.

Rice, P. L., and N. R. Holmberg (1973), Cumulative time statistics of surface'point-rainfall rates, IEEE Trans. Commun. COM-21 No. 10, p~. 1131-1136.

Ryde, J. W. (1946), The attenuation and radar echoes produced at centimetre wave­lengths by various meteorological phenomena, in Meteorological Factors in RadioWave Propagation (The Physical Society, London, U. K.), pp. 169-188.

148

APPENDIX: IDENTIFICATION OF SITES USED IN THE PREPARATIONOF CONTOUR MAPS IN SECTION 3

THE FEDERAL REPUBLIC OF GERMANY (FRG) AND VICINITY

LOCATION LATITUDE LONGITUDE1. Sylt, FRG 54°54 1 N 8°20 1 E2. List, FRG 55°01 IN 8°26 1 E3. Leck, FRG 54°47 1 N 8°56 1 E4. Husum, FRG 54°31 1 N 9°08 1 E5. Eggebeck, FRG 54°37 1 N 9°20 1 E6. Schleswig, FRG 54°27 1 N 9°30 1 E7. Jever, FRG 53°32 1 N 7°53 1 E8. Wittmundhaven, FRG 53°32 1_N 7°40 1E

9. Nordholz, FRG 53°46 1 N 8°39 1 E

1O. Hamburg, FRG 53°38 1 N looOOIE

11 . Emden, FRG 53°22 1 N 7°13 1 E12. Oldenburg, FRG 53°10 1 N 8°10 1 E13. Ahlhorn, FRG 52°53 1 N 8°13 1 E14. Bremen, FRG 53°02 1 N 8°47 1 E

15. Fassburg, FRG 52°55 1 N 10°11 IE

16. Hopsten, FRG 52°20 1 N 7°32 1 E

17. Gutersloh, RAF,FRG 51 056 1 N 8°19 1 E18. Diepholz, FRG 52°35 1 N S020 l E

19. Wunstorf, FRG 52°27 1 N 9°25 1 E20. Buckeburg, FRG 52°16 1 N 9°05 1 E

21 . Hannover, FRG 52°27 1 N 9°41 IE

22. Celle, FRG 52°35 1 N 10° 01 IE

23. Dusseldorf, FRG 51 0 16 1 N 6°45 1 E24. Bruggen, FRG 51 012 1 N 6°0S IE'25., Wildenrath, FRG 51 006 1 N 6°13 1 E26., Laarbruch, FRG 51 036 1 N 6°0S I E

27. Geilenkirchen, FRG 50057 1 N 6°02 1 E28. ' Norvenich, FRG 50049 1 N 6°39 1 E

29. Butzweilerhof, FRG 5005S IN 6°54 1 E

30. Koln-Bonn, FRG 50°51 IN 7°nS IE

149

The Federal Republic of Germany (FRG) and Vicinity (Continued)

LOCATION LATITUDE LONGITUDE

31 . Niedermendig, FRG 50022 1 N 7°18 1 E

32. Wiesbaden, FRG 50002 1 N 8°19 1 E33. Kleiner Feldberg, FRG 50013 1 N 8°27 1 E34. Rhe i n- ~1a in, FRG 50002 1 N 8°35 1 E35. Darmstadt, FRG 49°51 IN 8°41 IE

36. Sollingen, FRG 48°46 1 N 8°04 1 E

37. Karlsruhe, FRG 49°01 IN 8°23 1 E

38. Freiburg, FRG 48°00 1 N 7° 51 IE

39. Lahr, FRG 48°22 1 N 7°49 1 E

40. Bremgarten, FRG 47°54 1N 7°35 1 E

4l. Kasse1, FRG 51 019 1 N 9°27 1 E

42. Giessen, FRG 500 36 1 N 8°44 1 E

43. Wasserkuppe, FRG 50030 l N 9°57 1 E

44. Ohringen, FRG 49°12 1 N 9°31 IE

45. Nurburg, FRG 50°21 IN 6°57 1 E

46. Spangdahlem AB, FRG 49°58 1 N 6°42 1 E

47. Trier, FRG 49°43 1 N 6°36 1 E

48. Bitburg, FRG 49°56 1 N 6°33 1 E

49. Buchel, FRG 50010 l N 7°03 1 E

50. Ramstein, FRG 49°26 1 N 7°36 1 E

51. Hahn, FRG 49°56 1 N 7°15 1 E

52. Pferdsfeld City, FRG 49°51 IN 7°36 1 E

53. Sembach, FRG 49°30 1 N 7°52 1 E

54. Zweibrucken, FRG 49°12 1 N 7°24 1 E

55. Hoppstadten, FRG 49°36 1 N 7°11 IE

56. Giebelstadt, FRG 49°38 1 N 9°57 1 E

57. Wurzburg, FRG 49°48 1 N 9°54 1 E

58. Bamberg, FRG 49°53 1 N 10052 1 E

59. Hof, FRG 50019 1 N 11°55 1 E

60'. Weiden, FRG 49°41 IN 12°11 1 E

61. Stuttgart, FRG 48°41 IN 9°12 1 E

62. Weissenberg, FRG 49°02 1 N 10° 58 IE

63. Nurnberg, FRG 49°29 1 N 11004 1 E

150

The Federal Republic of Germany (FRG) and Vicinity (Continued)

LOCATION

64. Regensberg, FRG65. Grosser Falkenstein, FRG

66. Stotten, FRG

67. Ulm, FRG

68. Leipheim, FRG

69. Augsburg, FRG

70. Neuburg, FRG

71. Lechfeld, FRG

72. Landsberg, FRG73. Furstenfeldbruck, FRG

74. Ingolstadt-Manching, FRG

75. MUnchen-Neubiberg, FRG

76. MUnchen-Riem, FRG77. Erding, FRG

78. Passau, FRG

79. Memmingen, FRG

80. Kitzingen, FRG

81. Bayreuth, FRG82. Oberpfaffenhofen, FRG

83. Friedrichshafen, FRG

84. Kaufbeuren,FRG

85. Zugspitze, FRG

86~ Hohenpeissenberg, FRG

87. Garmisch, FRG

88. Berlin-Tegel, West Berlin

89. Berlin-Tempelhof, West Berlin

90. Gatow, West Berlin

91 . Essen, FRG

92. Geisenheim, FRG

93. Zurich, Switzerland

94. Santis, Switzerland

95. Innsbruck, Austria

96. Salzburg, Austria

97. Etain-Rouvres, France

151

LATITUDE

49°02 1 N

49°05 1 N48°40 1 N

48°24 1 N

48°26 1 N48°23 1 N48°42 1 N48°11 IN

48°04 1 N48°12 1 N48°43 1 N48°04 1 N

48°08 1 N

48°19 1 N

48°35 1 N

47°59 1 N49°44 1 N49°58 1 N

48°05 1 N47°39 1 N

47°51 IN

47°25 1 N47°48 1 N47°03 1 N52°33 1 N

52°28 1 N52°28 1 N

51°24 1 N49°59 i N

47°23 1 N47°15 1 N

47°16 1 N47°48 1 N

49°14 1 N

LONGITUDE12~O 04 I E

13°17 1 E

g052 1 E

g059 1 ElOo14 1 E

10°51 IE

11012 1 Elo052 1 E

10054 1 E

11016 1 E11031 l E

11038 1 E11042 1 E

11056 1 E

13°29 1 E

10013 1 E

10012 1 E

11034 1 E

11017 1 E

9°29 1 E10036 1 E

10,o59 1 E

1100liE

11006 1 E

13°l8 1 E

13°24 1 E

13 Q 08 1 E

6°58 1 E

7°'58 I E8Q 33 1 E

9°20 1 E11021 l E

13°00 1 E5°40 1 E

The Federal Republic of Germany (FRG) and Vicinity (Continued)

98.

99.

100.

101 .

102.

103.

104.

105.

106.

107 .

108.

109.

11 o.111 .

112.

113.

114.

115.

116.

117 .

118.

119.

120.

121 .

122.

123.

124.

125.

126.

127 .

128.

129.

130.

131 .

LOCATION

Metz-Frescaty, France

Tou1-Rosieres, France

Nancy-Essey, France

Nancy-Ochey, FrancePha1sbourg, FranceStrasbourg, France

Colmar-Meyerheim, France

Ba1e-Mu1house, France

Chambley, France

Gras Tenquin, France

Montmedy-Marville, France

Bree, Belgium

Spa, BelgiumDeelen, The NetherlandsVolkel, The Netherlands

Zuid Limburg, The Netherlands

DePeel, The Netherlands

Twenthe, The Netherlands

Clervaux, Luxembourg

Luxembourg City, Luxembourg

Luxembourg, Luxembourg

Echternach, Luxembourg

Berle, Luxembourg

Ettelbruck, Lux~mbourg

Mondorf-des-Bains, Luxembourg

Cheb, Czechoslovakia

Wernigerode, GDR

Meiningen, GDR

Kaltennordheim, GDR

Bracken, GDR

tf1agdeburg, GDR

Leipzig, GDRErfurt-B1indersleben, GDR

Praha-Ruzyne, Czechoslovakia

152

LATITUDE

49°04 1 N

48°47 1 N48°42 1 N

48°34 1 N48°46 1 N

48°32 1 N

47°55 1 N47°35 1 N49°01 IN

49°01 IN

49°27 1 N51 0 07 1 N50 0 28 1 N

52°03 1 N51 0 39 1 N

50 0 55 1 N51 0 3l ' N

52°16 1 N50 0 03 1 N49°37 1 N

49°37 1 N49°49 1 N49°57 1 N49°51 IN

49°30 1 N50 0 05 1 N

51 0 51 1 N

50 0 33 1 N

50 0 39 1 N

51 0 48 1 N52°06 1 N51 0 25 1 N

50 0 59 1 N50 0 06 1 N

LONGITUDE

6°08 1 E5°59 1 E

6°14 1 E

5°56 1 E

7°12 1 E

7°37 1 E

7°23 1 E

7°31 ' E

5°52 1 E6°43 1 E

5°25 1 E5°35 1 E

5°55 1 E

5°52 1 E5°42 1 E

5°46 1 E

5°51 1 E

6°53 1 E

6°01 IE

6°03 1 E

6°12 1 E

6°25 1 E

5°51 1 E

6°06 1 E

6°1,7 1 E

l2°24 1 E

10046 1 E10022 1 E

10009 1 E10 0 37 1 E11035 1 E12°14 1 E

10058 1 E

14°17 1 E

OKINAWALOCATION LATITUDE LONGITUDE

1. Naha AB, Okinawa 26° 11 1 N 1~~7°38IE

2. Kadena AS, Okinawa '26°20 IN 1~~7 °46 IE

3. Futema MCAF, Okinawa 26°16 1N 1~~7°45 IE

4. Hamby AAF, Okinawa 26°17 1 N 1~~7 °45 1 E

REPUBLIC OF KOREA (ROK) AND VICINITY

LOCATION LATITUDE LONGITUDE

1. Airfield (R-401); ROK 37°26 1 N 1~~7°581 E

2. Chunchon, ROK 37°53 1N 1~~7°43 IE

3. Kangnung, ROK 37°45 1N 1~~8°57 IE

4. Hoengsung, ROK 37°27 1N 1~~7°58 IE

5. Chipo-Ri, ROK 38°09 1 N lt~7°1gIE

6. Airfield (A-210), ROK 37°44 1 N 1~~7°02IE

7. Airfield (A-306), ROK 37°52 1 N 1~~7°43IE

8. Airfield (A-511), ROK 36°57 1N 127°02 1 E

9. Airfield (R-237), ROK 38°08 1 N 1~~7°18IE

10. Chunju West, ROK 36°58 1 N 1~~7°55IE

11 . Seoul, ROK 37°31 IN 1~~6 °55 IE

12. Airfield (A-102), ROK 37°30 1 N 126°42 1 E

13. Suwon AS, ROK 37°14 1N 1~~7°00 IE

14. Osan AB, ROK 37°05 1 N 127° 01 IE

15. Pyong Taek, ROK 36°57 1 N 127°02 1 E

16. Taejon, ROK 36°20 1 N 127°23 1E

17 . Kunsan AB, ROK 35°54 1N 126°37 1 E

18. Paengnyong do, ROK 37°59 1N 124°40 1 E

19. Kimpo International, ROK 37°33 1 N 126°47 1 E

20. Airfield (R-813), ROK 35°08 1N 128°41 IE

21 . Airfield (R-814), ROK 35°05 1 N 128°04 1 E

22. Airfield (R-815), ROK I 35°59 1 N 129°25 1 E

23. Pohang Dong, ROK 35°59 1N 1~~9°25IE

24. Taegu, ROK 35°53 1 N 1~~8°3gl E

25. Kimhae, ROK 35°10 1 N 128°56 1 E

26. Pusan, ROK 35°10 1 N 1~~go07IE

27. Kwangju AS, ROK 35°07 1N 1~~6°48IE

153

Republic of Korea (ROK) and Vicinity (Continued)

LOCATION LATITUDE LONGITUDE

28. Chinhae, ROK 35°08 1 N 128°42 1 E

29. Sachon, ROK 35°05 1 N 128°04 1 E

30. nosulpo, ROK 33°12 1 N 126°13 1 E

31 . Inchon, ROK 37°29 1 N 126°38 1 E

32. Mokpo, ROK 34°47 1 N 126°23 1 E

33. Wosan, North Korea 39°11 ' N 127°26 1 E

SOUTHWEST ASIA AND THE MIDDLE EAST

LOCATION LATITUDE

1. Riyan, Aden

2. Aden City, Aden

3. Mazar-I-Sharif, Afghanistan

4. Kunduz, Afghani stan5. Dehdadi, Afghanistan

6. Herot, Afghanistan

7. Farah, Afghanistan8. Kandahar East, Afghanistan

9. Kandahar International, Afghan.

10. Jalalabad, Afghanistan

11. Kabul International, Afghanistan

12. Bagram, Afghanistan

13. Mirzakai, Afghanistan

14. Ghazni, Afghanistan15. Bahrain-Muharraq16~ Paphos, Cyprus

17. Akrotiri, Cyprus

18. Morphou Bay, Cyprus

19. Nicosia, Cyprus

20. Cape Andreas, Cyprus

21. Gangagar, India

22. Bikaner-Nal, India

23. Jodhpur, India

24. Barmer, India

25. Udaipur, India

154

14°39 1 N

12°49 1 N

36°42 1 N36°41 IN

36°39Ir~

34°20 ' N32°24 1 N31 0 37 1 N

31 0 30 ' N

34°26 1 N

34°33 1 N

34°57 1 N33°45 1 N

33°07 1 N26°16 1 N

34°45 1 N

34°35 1 N

35°18 1 N

35°09 1 N

35°40 ' N

29°55 1 N

28°03 1 N

26°15 1 N25°45 1 N

24°35 1 N

LONGITUDE

49°19 1 E45°01 IE

67°14 1 E

68°54 1 E

67°00 ' E62°10 1 E62°06 1 E

65°46 1 E

65°51 1 E70 0 28 1 E

69°12 1 E

69°16 1 E69°25 IE"

69°07 1 E

50 0 37 1 E32°24 1 E32°59 1 E32°57 1 E

33°16 1 E

34°34 1 E

73°53 1 E

73°12 1 E

73°03 1 E

71 0 23 1 E

73°24 1 E

Southwest Asia and the Middle East (Continued)

LOCATION LATITUDE

61. Habbaniyah-Plate, Iraq

62. Habbaniyah, Iraq

63. As Salman, Iraq

64. Bandar Pahl evi, Iraq

65. Abadan, Iran

66. Khark Island, Iran

67. Bushehr, Iran

68. Jask, Iran

69. Tabas, Iran

70. Reza iyeh, Iran

71. Shahrud, Iran

72. Meshed, Iran

73. Teheran-Mehrabad, Iran

74. Teheran-Doshan, Iran

75. Teheran City, Iran

76. Shahroki AFB, Iran

77. Kermanshah, Iran

78. Hamadan, Iran

79. Vahdati AFB, Iran

80. Isfahan, Iran

81. Kerman, Iran

82. Shiraz (New), Iran

83. Zahedan, Iran

84. Eilat, Israel

85. Haifa, Israel

86. Ramat David, Israel

87. Tel Aviv, Israel

88. Kfir Sirkin, Israel

89. Lod, Israel

90. Egron, Israel

91. Jerusalem, Israel

92. Hatzor, Israel

93. Beersheba, Israel

94. Harkenaan, Israel

95. Gil git, Ka s hm i r

156

33°20 ' N

33°22 1 N30 0 28 1 N

37°28 1 N30°21 IN

29°15 1 N28°57 1 N25°45 1 N33°36 1 N37°32 1 N36°25 1 N36°17 1 N35°41 IN

35°42 1 N35°38 1 N35°11 ' N

34°19 1 N

34°38 1 N32°26 1 N32°37 1 N30 0 15 1 N29°32 1 N29°27 1 N29°33 1 N

32°48 1 N

32°39 1 N

32°06 1 N32°05 1 N31 0 59 1 N31 0 50 ' N31 0 47 1 N

31 0 45 1 N31 0 14 1 N33°59 1 N

35°55 1 N

LONGITUDE

43°35 1 E43°33 1 E44°43 1 E

49°29 1 E48°13 1 E50 0 20 ' E

50 0 49 1 E57°45 1 E

56°45 1 E45°05 1 E

55°01 IE

59°38 1 E

51 0 19 1 E

51 0 28 1 E

51 0 22 1 E

48°41 IE

47°07 1 E

48°31 IE

48°24 1 E51 0 41 ' E

56°57 1 E52°35 1 E60 0 54 1 E

34°57 1 E

35°02 1 E

35°10 ' E34°46 1 E

34°54 1 E

34°53 1 E34°49 1 E35°13 1 E34°43 1 E34°47 1 E35°31 IE

74°23 1 E

96.

97.

9B.

99.

100.

101 .

102.

103.

104.

105.

106.

107 .

108.

109.

110.

111 .

112.

113.

114.

115.

116.

117.

118.

119.

120.

121 .

122.

123.

124.

125.

126.

127 .

1£8.

129.

130.

Southwest Asia and the Middle East (Continued)LOCATION LATITUDE

Srinagar, Kashmir 33°58 1 NJammu, Jammu 32°41 J NJerusalem, Jordan 31°52 1 NKing Hussein, Jordan 32°21 IN

Mofraq, Jordan 32°20 1 NAmman, Jordan 31°58 1 NKuwait, Kuwait 29°14 1N

Nigra, Kuwait 29°21 IN

Beirut, Lebanon 33°48 1 NRiyaq, Lebanon 33°51 INKsarah, Lebanon 33°50 1 N

Al Qurayyah 33°49 1 NMuscat, Oman 23°45 1 NMasirah-Rashilf, Oman 20 0 40 l N

Salalah, Oman 17°01 IN

Drosh, Pakistan 35°34 1 N

Peshawar, Pakistan 33°59 1 NRisalpur, Pakistan 34°04 1 NKohat, Pakistan 33°34 1 NRawalpindi, Pakistan 33°35 1 NChaklala, Pakistan 33°36 1N

Khushab, Pakistan 32°18 1 NSargodha, Pakistan 32°02 1 NFort Sandaman, Pakistan 31°21 IN

Quetta/Samungli, Pakistan 30 0 15 1 NDalbandin, Pakistan 28°53 1 NPanjgur, Pakistan 26°58 1 NLahore, Pakistan 31°31 1 NMultan, Pakistan 30°11 INJacobabab, Pakistan 28°18 1 NKhanpur, Pakistan 28°39 1 N

Hyderabad, Pakistan 25°23 1 NJiwani, Pakistan 25°D4 1 N

Ormara, Pakistan 25°15 1 N

Karachi Civil, Pakistan 24°54 1 N

157

LONGITUDE74°46 1 E

74°50 1 E

35°13 1 E

36°15 1 E

36°14 1 E

35°59 1 E

47°58 1 E47°59 1 E35°29 1 E

35°59 1 E35°53 1 E

35°40 1 E58°35 1 E58°53 1 E

54°06 1 E

71°47 1 E

71°30 1 E71°58 1 E

71°26 1 E

73°03 1 E

73°·06 I E

72°21 IE

72°39 1 E69°27 1 E

66°56 1 E64°24 1 E64°04 1 E

74°24 1 E71°25 1 E

68°28 1 E

70°41 IE

68°25 1 E

61°48 1 E64°39 1 E67°09 1 E

Southwest Asia and the Middle East (Continued)

LOCATION LATITUDE

131. Mauripur~ Pakistan 24°54 1 N

132. Drigh Road, Pakistan 24°54 1 N

133. Doha, Qatar 25°16 1 N

134. Jidda, Saudi Arabia 21°30 1 N

135. Hail, Saudi Arabia 27°30 1 N

136. Dhahran, Saudi Arabia 26°16 1 N

137. Riyadh, Saudi Arabia 24°43 1 N

138. Wejh, Saudi Arabia 26°14 1 N139. MalAn, Jordan 30 0 10 lN

140. Medina, Saudi Arabia 24°31 IN

141. Taif, Saudi Arabia 21 0 29 1 N

142. Dumayr, Syria 33°36 1 N143. Damascus, Syria 33°28 1 N

144. Humaymim, Syria 33°28 1 N145. Sahles Sahra, Syria 33°34 1 N

146. Qamieliye, Syria 37°01 1 N147. Aleppo, Syria 36°11 IN

148. Rasin el Aboud, Syria 36°11 1 N

149. Deier Ez Zor, Syri~ 35°19 1 N

150. Dubai~ Trucial Oman 25°15 1 N

151. Sharja, Trucial Oman 25°20 1 N

152. Antalya, Turkey 36°53 1 N153. Adana Civil, Turkey 36°58 1 N

154. Incirlik, Turkey 37°00 1 N155. Malatya, Turkey 38°21 IN

156. Erhac, Turkey 38°26 1 N

157. Diyarbakir, Turkey 37°55 1 N

158. Batman, Turkey 37°55 1 N159. Kamaran I, Yemen 15°20 IN

160. Sana South, Yemen 15°31 IN

161. A1 Hudayah, Yemen 14°44 1 N162. Gassim, Saudi Arabia 26°17 1 N

163. Ratnagiri, India 16°59 1 N

164. Bandar Abbas, Iran 37°28 1 N

165. Chahbar, Iran 25°17 1 N

158

LONGITUDE

66°57 1 E

67°06 1 E51 °,33 IE

39°12 1 E

42°02 1 E50 0 10 ' E

46°43 1 E36°26 IE

35°47-E

39°42 1 E

40 0 32 1 E

36°45 1 E

36°13 1 E

36°13 1 E36°10 ' E41°11 1 E

37°13 1 E37°35 1 E40 0 09 1 E

55°20 1 E

55°23 1 E

30 0 44 1 E

35°16 1 E35°25 1 E38°15 1 E

38°05 1 E

40 0 13 1 E41°07 1 E

42°37 1 E44°11 IE

42°59 1 E

43°51 IE

73°18 1 E

49°29 1 E60 0 37 1 E

Southwest Asia and the Middle East (Continued)LOCATION LATITUDE

166. Seistan, Iran 31 000 ' N167 . Pasn i, Pa ki stan 25°16 1N

168. Khormaksar, Saudi Arabia 12°50 ' N169. Perim Island, Saudi Arabia 12°39 1N

170. Urfa, Turkey 37°07 1N

171. Van, Turkey 38°30 ' N172. Kamis r'~ushait, Saudi Arabia 18°18 1N

173. Len Koran, U.S.S.R. 38°46 1N174. Ashkabad, U.S.S.R. 37°58 1N175. Krasnovodsk, U.S.S.R. 40002 1N176. Famagusta, Cyprus 35°07 1N177. Prodromos, Cyprus 34°57 1N178. Kamishli, Syria 37°03 1N179. Palmyra, Syria 34°33 1N180. Lattakia, Syria 35°32 1N181. Chhor , Pakistan 25°31 1N182. Parachinar, Pakistan 33°52 1N

183. Dera Ismail Khan, Pakistan 31 049 1N184. Jhelum, Pakistan 32°56 1N185. Kalat, Pakistan 29°02 1N

CENTRAL AMERICALOCATION LATITUDE

1. Salina Cruz, Mexico 16°12 1N

2. Tapachula, Mexico 14°54 1N3. Coatzcolacos, Mexico 18°091N4. Chetumal, Mexico 18°28 1N5. Los Andes, El Salvador 13°52 1N6. San Salvador, El Salvador 13°40 ' N7. Acajulta, El Salvador 13°36Ir~

8. Labor Oualle, Guatemala 14°51 IN

9. Guatemala City, Guatemala 14°35 1N

10. La Fragua, Guatemala 14°58 1 N11. Huehuetengo, Guatemala 15°19 1N12. Caban, Guatemala 15°29 1N

159

LONGITUDE61 0 30 ' E63°2~91 E

43° 2~4 1E

38°46 1E

43°23 1E

42°4·8 I E48°5;2 1E

58°20 ' E52°5,9 IE

33°57 1E32°5;0'E

41 013 1E

38°18 1E35°4·8 IE69°47 1 E70 0 05 1 E70 0 55 1 E73°44 1E66°35 1E

LONGITUDE

95°12 1W92°15 1W94°2~4IW

88°19 1W89°39 1 W89°05 1t~

89°5;O'W

91 0 30 'W

90 0 32 1W89°32 1 W9102~81W

9002~O'W

Central America (Continued)LOCATION

13. El Provenir, Guatemala14. Santa Rosa, Honduras15. Tegucigalpa, Honduras

16. Amapala, Honduras17. Choluteca, Honduras18. La ~1esa, Honduras19. Catacamas, Honduras20. Tela, Honduras21 . Cei ba, Honduras22. Guanaja, Honduras23. Puerto Lempira, Honduras

24. Belize, Belize25. San Jose, Costa Rica26. Puerto Limon, Costa Rica27. Puentarenas, Costa Rica28. Stanley International, Belize29. £1 Cayo, Belize30. El Coco, Costa Rica31. La Sabana, Costa Rica

32. Limon, Costa Rica33. Ilopango, El Salvador

34. Albrook AFB, Panama35. LaAurora, Guatemala36. Retalhuleu, Guatemala37. loncotin, Honduras38. Las Mercedes, Nicaragua39. Cape Gracias, Nicaragua40. Puerto Cabezas, Nicaragua41. Bluefields, Nicaragua

42. Colon, Panama

43. David, Panama

44. Rio Hato, Panama45. Tocumen National, Panama46. Marcos a Gelaber, Panama

47. Howard AFB, Panama

160

LATITUDE16°31 ' N

14°47 1 N14°02 1 N

13°18 1 N

13°18 1 N

15°27 1 N

14°51 ' N15°46 I N

15°44 1 N16°28 1 N15°13 1 N17°32 1 N9°59 1 N9°58 1 N9°58 1 N

17°32 1 N17°10 ' N9°59 1 N

9°56 1 N

9°58 1 N13°41 ' N

8°58 1 N14°34 1 N

14°31 IN

14°03,'N

12°08 1 N

15°00 ' N14°03 1 N12°00 ' N9°22 1 N

8°23 1 N

8°22 1 N9°05 1 N

8°58 1 N8°54 1 N

LONGITUDE90029 1 W88°47 1 W87°15 1 W87°38 1 W87° 11 I W

87°56 1 W85°55 1 W87°27 1 W86°52 1 W85°54 1 W83°48 1 W88°18 1W84°13 1 W84°50 ' W84°49 1 W

88°18 1 W89°04 1 W84°12 1 W

84°06 1 W83°01 ' W89°07 1W

79°33 1 W90031 ' W

91 °41 I W

87°13 1 W86°]0'W

83°10 ' W83°23 1 W83°43 1 W79°54 1 W82°26 1 W80 0 07 1 W79°22 1 W79°30 ' W79°36 1 W

THE UNITED STATES OF AMERICA (USA)LOCATION LATITUDE LONGITUDE

1. Birmingham, AL 33°03 1 N2. Huntsville, AL 34°44 1 N3. Mobile, AL 30 0 04 1 N4. Montgomery, AL 32°22 1 N5. Anchorage, AK 61 0 10 ' N6. Anchorage, AK * 61 0 10 ' N7. Annette, AK 55°02 1 N8. Barrow, AK 71 0 16 1 N

9. Barter Island, AK 70 0 07 1 N10. Bethel, AK 60 0 49 ' N11. Bettles, AK 66°53 ' N12. Big Delta, AK 64°10 ' N13. Cold Bay, AK 55°10 ' N14. Fairbanks, AK 64°50 ' N15. Gulkana, AK 62°15 ' N

16. Homer, AK 59°40 ' N17. Juneau, AK 58°20 ' N18. King Salmon, AK 58°40 ' N19. Kodiak, AK 57°49 ' N20. Kutzebue, AK 66°51 IN

21. McGrath, AK 62°58 1 N22. Nome, AK 64°30 ' N23. St. Paul Island, AK 57°09 ' N24. Shemya, AK 52°45 ' N25. Summit, AK 63°19 ' N26. Talkeetna, AK 62°20 ' N27. Unalakleet, AK 63°52 ' N28. Valdez, AK 61 0 07 1 N29. Yakutat, AK 59°29 1 N30. Flagstaff, AZ 35°12 1 N

86°55 1 W

86°35"W

80 0 05 1 W

86°20 1l W

150 0 00 ll W

1500 00 'W131 0 36 1 W

156°50 'W

143°40 ' W161 0 49 1 W151 0 51 ' W

145°55 1 W

162°47 ' W

147°50 1 W

145°30 'W151 0 37 1 W

134°20 I W.

156°40 'W152°30 ' W

162°40·W

155°40 'W165°30 ' W1700 18 'W

174°05 1 W149°19 1 W150°09 I vJ

1600 50 ' W

146°17 1 W139°49 1 W111 °38 IIW

* There are occasions in the USA when two locations appear identical but are

actually slightly separated.

161

The United States of America (USA) (Continued)

LOCATION LATITUDE LONGITUDE

31 . Phoenix, AZ 33°30 ' N 112°03 1 W

32. Tucson, AZ 32°15 1 N 110057 1 W

33. Winslow, AZ 35°01 1 N 110043 1W

34. Yuma, AZ 32°40 ' N 114°39 1 W35. Fort Smith, AR 35°22 1 N 94°27 1 W

36. Little Rock, AR 34°42 1 N 92°17 1 W

37. Texarkana, AR 33°28 1 N 94°02 1 W

38. Bakersfield, CA 35°20 1 N 118°52 1 W39. Bishop, CA 37°20 1 N 118°24 1 W

40. Blue Canyon, CA 39°06 1 N 118°45 1 W

41 . Eureka, CA 40049 1 N 124°10 1 W

42. Fresno, CA 36°41 IN 119°47 1 W

43. Long Beach, CA 33°47 1 N 118°15 1 W

44. Los Angeles, CA 34°00 1 N 118°15 1 W45. Los Angeles, CA 34°00 1 N 118°15 IW·

46. Mt. Shasta, CA 41 019 1 N 122°20 1 W

47. Oakland, CA 37°50 1 N 122°15 1 W48. Red Bluff, CA 40° 11 IN 122°16 1 W

49. Sacramento, CA 38°32 IN 121 050 l W

50. Sandberg Ranch, CA 34°42 1 N 118°36 1 W

51 . San Diego, CA 32°45 1 N 117°10 1 W

52. San Francisco, CA 37°45 1 N 122°27 1 W

53. San Francisco, CA 37°45 1 N 122°27 1 W

54. Santa Catalina, CA 33°25 1 N 118°25 1 W

55. Santa Maria, CA 34°56 1 N 120025 1 W

56. Stockton, CA 37°59 1 N 121 0 20 l W

57. Alamosa, CO 37°28 1 N lO5°54 1 W

58. Colorado Springs, CO 38°50 1 N 104°50 1W

59. Denver, CO 39°45 1 N lO5°00 'W

60. Grand Junction, CO 39°04 1 N lO8°33 1 W

61. Pueblo, CO 38°17 1 N lO4°38 1 W

62. Bridgeport, CT 41 012 1 N 73°12 1 W

63. Hartford, CT 41 045 1 N 72°42 1 W

64. New Haven, CT 41 018 1 N 72°55 1 W

lG2

The United States of America (USA) (Continued)LOCATION LATITUDE LONGITUDE

65. Wi 1mi ngton, DE 39°46 1N 75°31 1W66. Washington, DC 38°55 1N 77°00 1W67. Washington, DC 38°55 1N 77()001 W

68. Appalachicola, FL 29°43 1N 85°01 IW

69. Daytona Beach, FL 29° 11 IN 81 0 01 l W

70. Ft. Myers, FL 26°39 1N 81051 l W71 . Jacksonville, FL 30 0 20 'N 81 0 40 l W72. Key West, FL 24°34 1N 81 0 48 1 W

73. Lakeland, FL 28°02 1N 81 059 1W74. Miami,FL 25°45 1 N 80015 1 W

75. Orlando, FL 28°33 1N 81 021 l W76. Pensacola, FL 30 0 26 1N 87°12 1W77. Tallahassee, FL 300 26 1N 84°19 1W78. Ta~npa, FL 27°58 1W 82°38 1W,

79. West Palm Beach, FL 26°42 1N 800 05 1W80. Athens, GA 33°57 1N 83°24 1W

81 . Atlanta, GA 33°45 1N 84°23 1W82. Augusta, GA 33°29 1N 82°00 1W83. Columbus, GA 32°28 1N 84°59 1 W84. ~lacon, GA 32°49 1N 83°37 1W

85. Rome, GA 34°01 IN 85°02 1W86. Savannah, GA 32°04 1 N 81 0 07 1W87. Hilo, HI 19°42 1N 155°04 1W88. Honolulu, .HI 21 0 19 1N 157°50 1W

89. Ka hu 1ui, HI 20 0 56 1N 156°29 1W

90. Lihue, HI 21 0 59 1N 159°23 1W91 . Boise, 10 43°38 1 N 116()12 J W

92. Idaho Falls, ID 43°30 1 N 112 0 01 I W

93. Idaho Falls, 101 43°30 1N 112°01 1W

94. Lewiston, 10 46°25 1N 117°00 1W

95. Pocatello, 10 42°53 1N 112°26 1W96. Cairo, IL 37°01 IN 89°09 1 W

97. Chicago-OIHare, IL 41 0 57 1N 87°53 1W

98. Chicago-Midway, IL 41 0 50 l N 87° 45 I ~~

99. Moline, IL 41 0 31 l N 90 0 26 1W

163

The United States of America (USA) (Continued)

LOCATION LATITUDE LONGITUDE

100. Peoria, IL 40043 1 N 89°38 1 W

101 . Rockford, IL 42°16 1 N 89°06'W

102. Springfield, IL 39°49 1 N 89°39 1 W

103. Evansville, IN 38°00 ' N 87°33'W

104. Fort Wayne, IN 41 005 1 N 85°08 1W

105. Indianapolis, IN 39°45 1 N 86°10 'W

106. South Bend, IN 41 0 40 ' N 86°15'W

107 . Burlington, IA 40050 ' N 91 007 1 W

108. Des ~1oines, IA 41 035 1 N 93°35'W

109. Dubuque, IA 42°31 IN 90°41 'W

110. Sioux City, IA 42°30'N 96°28 1W

111 . Waterloo, IA 42°30 ' N 92°20 'W

112. Concordia, KS 39°35 1 N 97°39 1 W

113. Dodge City, KS 37°45 1 N 100°02 I~~

114. Goodland, KS 39°20 ' N 101043 1W

115. Topeka, KS 39°02 1 N 95°41 'W

116. Wi chi ta " KS 37°43 1 N 97°20'W

117 . Covington, KY 39°04 1 N 84°30 'W

118. Lexington, KY 38°02 1 N 84°30 'W

119. Louisville, KY 38°13 1 N 85°48 1 W

120. Alexandria, LA 31 019 1 N 92°29 1 W

121 . Baton Rouge, LA 30030 ' N 91 010 'W

122. Lake Charles, LA 30 0 13 1 N 93°13 1W

123. New Orleans, LA 3000Q'N 90003 J W

124. Shreveport, LA 32°30 ' N 93°46 1W

125. Caribou, ME 46°52 1 N 68°01 'W

126. Por t 1and, r~E 43°41 IN 70018 1 W

127. Sa1t imore, t~D 39°18 1 N 76°38 1 W

128. Blue Hill, MA 42°13 1 N 71 007 J W

129. Boston, MA 42°20 ' N 71 005 1 W

130. Nantucket, t~A 41 0 17 1 N 70 0 05 1 W

131 . Pittsfield, MA 42°27 1 N 73°15 J W

132. Worcester, MA 42°17 1 N 71 0 48'W

133. Alpena, ~1 I 45°04 1 N 83°27'W

, 134. Detroit, MI 42°23 1 N 83°05 J W

1G4

The United States of America (USA) (Continued)

LOCATION LATITUDE135. Detroit, MI 42°23 1 N136. Detroit, MI 42°23 1 N

137. Flint, MI 43°03 1 N

138. Grand Rapids, MI 42°57 1 N

139. Houghton Lake, MI 47°06 1 N140. Lansing, MI 42°44 1 N

141. Marquette, MI 46°33 1 N

142. Muskegon, MI 43°13 1 N

143. Sault Ste. Marie, MI 46°29 1 N144. Duluth, MI 46°45 1 N

145. International Falls, MN 48°38 1 N

146. Minneapolis, MN 45°00 ' N147. Rochester, MN 44°01 IN

148. St. Cloud, MN 45°34 1 N149. Jackson, r~s J2°20 ' N·

150. Meridian, MS 32°21 'N

151 . Vic ksbu rg, ~1S 32° 21 IN

152. Columbia, MO 38°58 1 N153. Columbia, MO 38°58 1 N154. Kansas City, MO 39°02 1 N155. Kansas City, MO 39°02 1 N

156. St. Joseph, MO 39°45 1 N

157. St. Louis, MO 38°40 ' N

158. Springfield, ~·10 37°11 'N

159. Billings, MT 45°47 1 N160. Glasgow, MT 48°12 1 N

161. Great Falls, MT 47°30 ' N162. Havre, MT 48°34 1 N

163. Helena, MT 46°35 1 N164. Kalispell, MT 48°12 1 N165. Miles City, MT 46°24 1 N166. Missoula, MT 46°52 1N

167. Grand Island, NE 40 0 56 1 N

168. Lincoln, NE 40049 1 N

169. Lincoln, NE 40049 1 N

165

LONGITUDE83°05 1 W83°05 1 W83°40 'W86°40 'W88°34 1 W85°34 1 W87°23 1 W86°15 1 W84°22 1 W92°10 ' W93°26 1 W93°l5 1 W92°27 1 W94°10 'W90° 11 1 W

88°42 1 W90051 'W

92°20 'W92°20 'W94°33 1 W

94°33 1 W94°51 I W

900151~J

93°19 1 W108°30 'W106°37 1 W111016 1 W

l09°40 ' W112°00 1 W

114°19 1 W

105°48 1 W114°00 ' W

98°21 JW

96°41 'W96°41 J W

The United States of America (USA) (Continued)

LOCATION LATITUDE

170. Norfolk, NE 42°01 1 N171. North Platte, NE 41 009 1 N

172. Omaha, NE 41 015 1 N

173. Scottsbluff, NE 41 052 1 N

174. Valentine, NE 42°53 1 N175. Elko, NV 40050 l N176. Ely, NV 39°15 1 N

177. Las Vegas, NV 36°10 1 N

178. Reno, NV 39°32 1 N

179. Winnemucca, NV 40058 1 N

lEO. Concord, NH 43°13 1 N

181. Mt. Washington, NH 44°16 1 N

182. Atlantic City, NJ 39°23 1 N

183. Newark, NJ 40044 1 N184. Trenton, NJ 400l5 1 N

185. Albuquerque, NM 35°05 1 N

186. Clayton, NM 36°27 1 N187. Raton, NM 36°54 1 N

188. Roswell, NM 33°24 1 N189. Roswell, NM 33°24 1 N

190. Silver City, NM 32°41 1 N

191. Albany, NY 42°40 1 N

192. Binghampton, NY 42°06 1 N

193. Binghampton~ NY 42°06 1 N194. Buffalo, NY 42°52 1 N195. New York, NY 40 0 40 l N

196. New York, NY 40040 l N

197. New York, NY 40040 ' N

198. Rochester, NY 43°12 1 N199. Syracuse, NY 43°03 1 N

200. Asheville, NC 35°35 1 N

201. Cape Hatteras, NC 35°14 1 N

202. Charlotte, NC 35°03 1 N

203. Greensboro, NC 36°03 1 N

204. Raleigh, NC 35°46 1 N

166

LONGITUDE

97°25 1 W100045 1 W

96°00 1 W

103°40 1 W100031 l W115°46 1 Wl14°53 1 W115°10 1 W119°49 1 W117°45 1 W

71 0 34 1W71 °18 ·W

74°27 1 W74°11 1 W

74°43 1 Wl06°38 1 W103°12 1 Wl04°27 1 W104°33 1 W104°33 1 W

108°16 1 W73°49 1 W75°55 1 W75°55 1 W78°55 1 W73°50 1 W

73°50 1 W73°50 1 W

77°37 J W76°10 1 W82°35 1 W75°31 ·W

80 0 50 l W

79°50 1 W

78°39 1 W

The Un"ited States of America (USA) (Continued)LOCATION LATITUDE LONGITUDE

205. Wilmington, NC 34°14 1N 77°55 1W206. Bismarck, NO 46°50 1N 100048 1W

207. Fargo, NO 46°52 1N 96°49 1W

208. Williston, NO 48°09 1N 103°391~~

209. Akron, OH 41 004 1N 81 °31 I ~~

210. Cincinnati, OH 39°10 1N 84°301~~

211. Cleveland, OH 41 030 l N 81041 l W

212. Columbus, OH 39°59 1N 83°03 I ~J

213. Dayton, OH 39°45 1N 84°10 I vJ

214. Mansfield, OH 40046 1N 82°31 1 W215. Toledo, OH 41 040 l N 83°35 1 vJ

216. Youngstown, OH 41 005 1N 80040 l W

217. Oklahoma City, OK 35°28 1N 97°33 1 W

218. Tulsa, OK 36°07 1'N 95°58 1W

219. Astoria, OR 46°12 1N 123°50 1 W

220. Burns, OR 43°36 1 N 119°03 1W

221. Eugene, OR 44°03 1N 123°04 1 W

222. Meacham, OR 45°31 IN 118°26 1 W

223. Medford, OR 42°20 1 N 122°52 1W

224. PendJeton, OR 45°40 1N 118°46 1 W

225. Portland, OR 45°32 1 N 122°40 1 W

226. Salem, OR 44°57 1 N 123°01 1W

227. Sexton Summit, OR 42°36 1N 123°30 1W

228. Allentown, PA 40037 1 N 5°30 1 W229. Erie, PA 42°07 1 N 80 0 05 1W

230. Harrisburg, PA 40017 1N 76°54 1 W

231. Philadelphia, PA 40 0 00 l N 75°10 1 W

232. Pittsbur'gh Air'port, PA 40020 l N 79°55 1 W

233. Pittsburgh, PA 40026 1 N 80000 l W

234. Reading,PA 40020 l N 75°55 1 W

235. Scranton, PA 41 025 1 N 75°40 1 W

236. Williamsport, PA 41 016 1 N 77°03 1 W

237. Block Island, RI 41 °11 IN 71 0 34 1,W

238. Providence, RI 41 0 50 l N 71 025 1W

239. Charleston, SC 32°48 1 N 79°58 1 W

167

The United States of America (USA) (Continued)

LOCATION LATITUDE

240.

241.

242.243.

244.245.246.

247.

248.

249.

250.

251.

252.

253.

254.

255.

256.257.

258.

259.

260.

261.

262.

263.264.

265.266.

267.

268.

269.

270.

271.

272.

273.

274.

Columbia, SC

Greenville/Spartanburg, SC

Aberdeen, SOHuron, SORa pi d City, SOSioux Falls, SO'

Bristol, TN

Chattanooga, TN

Knoxville, TN

Memphis, TN

Nashville, TN

Oak Ridge, TN

Abilene, TX

Amarillo, TXAustin, TX

Brownsville, TX

Corpus Christi,TX

Dallas/Ft. Worth, TX

Da 11 as, TX

Del Rio, TX

El'Paso, TX

Galveston, TX

Houston Intercon., TX

Houston, TXHouston Hobby, TX

Lubbock, TX

r'~idland, TX

Port Arthur, TX

San Angelo, TX

San Antonio, TX

Victoria, TX

Waco, TX

Wichita Falls, TX

Milford, UT

Salt Lake City, UT

34°00 1 N

34°52 1 N45°28 1 N44°22 1 N

44°06 1 N43°34 1 N

36°35 1 N

35°02 1 N

36°Q0 1 N

35°10 1 N

36°10 1 N

36°02 1 N

32°27 1 N

35°14 1 N30018 1 N

25°54 1 N

27°47 1 N

32°47 1 N32°47 1 N

29°23 1 N31045 1 N

29°17 1 N

29°30 1 N

29°45 1 N29°55 1 N33°35 t N32°00 1 N27°50 1 N31 028 1 N

29°25 1 N

28°49 1 N

31 033 1 N

33°55 1N

38°22 1 N

40 045 1N

168

LONGITUDE81 0 0Q 1 W

82°25 1 W

98°30 1 W98° 12 I vJ

l03°14 1W96°42 1 W82°l2 1 W85°18 1 W83°57 1 W90 0 00 ' W86°5Q 1 W84°12 I ~~

99°45 1 W101 °50 I \i4

97°47 1 W97°30 1 W97°26 1 W97°051~J

96°48 1 W100056 1 W106°30 1 W99°48 1 W95°20 1 W95°25 1 W95°20 ' W

101053 1 W

l02°09 1 W97°05 1 W

lOo028 1 W

98°30 1 W97°01 1 W97°10 1 W98°30 1 W

113°00 ' W111055 1 W

The United States of America (USA) (Continued)LOCATION LATITUDE LONGITUDE

275. Wendover, UT 40045 1 N 114°O~~ 1 W

276. Burlington, VT 44°28 1 N 73°14 1 W277. Lynchburg, VA 37°24 1 N 79°09 1 W278. Norfolk VA 36°54 1 N 76°18 1 W279. Richmond, VA 37°34 1 N 77°27 1 W280. Roanoke, VA 37°15 1 N 79°5B ' W281. Olympia, WA 47°03 1 N 122°53 1 W282. Quillayute, WA 47°57 1 N 124°33' .~

283. Seattle, WA 47°35 1 N 122°20 ' W284. Seattle/Tacoma, WA 47°16 1 N 122°30'W

285. Spokane, WA 47°40 ' N 117°251 1 W286. Stampede Pa~s, WA 47°16 1 N l21022 1W287. Tatoosh Island, WA 48°23 1 N 124°44 1 W

288. Walla Walla, WA 46°05 1 N 118°18 1 W289. Yakima, WA 46°37 1 N 120030 ' W

290. San Juan, PR 18°29 1 N 66°08 1W291. Swan Island 17°24 1 N 83°56 1 W292. Beckeley, WV 37°46 1 N 81 012 1 W293. Charleston, WV 38°23 1 N 81 040 ' W

294. Elkins, WV 38°56 1 N 79°53 1L-J

295. Huntington, WV 38°24 1 N 82°26 1 W

296. Parkersburg, WV 39°17 1 N 81 033 1 W

297. Green Bay, WI 44°32 1 N 88°00 ' W

298. La Crosse, WI 43°48 1 N 91 004 1 W

299. ~1adis0 n, WI 43°04 1 N 89°22 1 W

300. Milwaukee, WI 43°03 1 N 87°56 1 W

301. Casper, WY 42°50 ' N 106°20 ' W

302. Cheyenne, WY 41 008 1 N 104°50 ' W

303. Lander, WY 4-2°49 1 N 108°44 1 W

304. Sheridan, WY 44°48 1 N 106°57 1W

169

SOUTHEAST ASIA

LOCATION LATITUDE LONGITUDE

1. Moulmein, Burma 16°26 1 N 97°39 1 E

2. Tavoy, Burma 14°06 1 N 98°13 1 E

3. Mergui, Burma 12°26 1 N 98°37 1 E

4. Victoria Point, Burma 9°58 1 N 98°35 1 E

5. Toungoo, Burma 18°55 1 N 96°"28 I E

6. Sandoway, Burma 18°27 1 N 94°18 1 E

7. Bassein, Burma 16°46 1 N 94°46 1 E

8. Mingaladon, Burma 16°54 1 N 96°08 1 E

9. Hmawbi, Burma 17°07 1 N 96°04 1 E

1o. Akyab, Burma 20 007 1 N 92°52 1 E

11 . Mandalay, Burma 21 056 1 N 96°05 1 E

12. Meiktila, Burma 20053 1 N 95°53 1 E

13. Minbu, Burma 20010 ' N 94°58 1 E

14. Pyinmana, Burma 19°43 1 N 96°13 1 E

15. Shanthe, Burma 20058 1 N 95°55 1 E

16. Lashio, Burma 22°58 1 N 97°45 1 E

17 . Heho, Burma 20044 1 N 96°47 1 E

18. Taunggyi, Burma 20047 1 N 97°03 1 E

19. Kengtung, Burma 21 018 1 N 99°37 1 E

20. Amherst, Burma 16°05 1 N 97°34 1 E

21. Diamond Island, Burma 15°51 ' N 94°19 1 E

22. Mergui, Burma 12°26 1 N 98°36 1 E

23. Rangoon, Burma 16°46 1 N 96° 11 1 E

24. Tavoy, Burma 14°07 1 N 94°18 1 E

25. Phrae, Thailand 18°10 ' N 100008 1 E

26. Prachnap Kirikhan, Thailand 11048 1 N 99°48 1 E

27. Ban Don, Thailand 9°08 1 N 99°18 1 E

28. Nakhon Si Tham., Thailand 8°25 1 N 99°58 1 E

29. Phuket, Thailand 7°58 1 N 98°24 1 E

30. Phuket/Hin Luk, Thailand 8°06 1 N 98°18 1 E

31. Trang, Thailand 7°30 ' N 99°40 ' E

32. Songkhla, Thailand 7° 11 1 N lOo037 1 E

33. Narathiwat, Thailand 6°26 1 N 101050 ' E

34. Pattani,- Thailand 6°46 1 N 101 009 1 E

35. Udorn, Thailand 17°23 1 N lO2°47 1 E

170

Southeast Asia (Continued)LOCATION LATITUDE LONGITUDE

36. Sakon Nakhon, Thailand 17°10 1 N 104°09 11 E37. Nakhon Phanom, Thailand 17°23 1 N 104°39 II E

38. Khon Kaen, Thailand 16°20 ' N 102° 51 II E

39. Mukdahan, Thailand 16°33 1 N 104°44 11 E

40. Chaiyaphum, Thailand 15°48 1 N 102001 liE

41 . Roi Et, Thailand 16°03 ' N 103°41 II E

42. Ubon, Tha i 1and 15°14 ' N 104°52 II E

43. Surin, Thaila.nd 14°53 1 N 103°29 11 E

44. Ban Nong Hoi, Thailand 17°17 1 N 104°06 II E

45. Nong Khai, Thailand 17°15 1 N 102°44 11 E46. Nam Phong, Thailand 16°39 IN 102°58 11 E

47. Mae Hong Son, Thailand 19° 16 'N 97°56 11 E

48. Muang Chiang Rai, Thailand 19°53 1 N 99°49 11 E49. Mae Sariang, Thailand 18°10 ' N 97°50"E

50. Chiang Mai, Thailand 18°46 1 N 98°58 11 E

51 . Lampang, Thailand 18°17 1 N 99°31 IE

52. Ban Mae Sot, Thailand 16°41 ' N 98°32 1 E

53. Uttaradit, Thailand 17°40 ' N 100014 1 E

54. Loei, Thailand 17°32 1 N 101030 R E

55. Phitsanu1ok, Thailand 16°47 1 N 100016 R E

56. Koke Kathiem, Thailand l4°53 1 N 100040 l E

57. Kanchanaburi, Thailand l4°0l 1 N 99°32 1 E

58. Bangkok, Thailand 13°44 1 N 100030 l E

59. Don Muang AFB, Thailand l3°54 1 N 100°36 II E

60. Aranyaprathet, Thaila~d l3°42 1 N 102°35 11 E

61 . Hua Hin, Thailand 12°34 1 N 99°48 1 E

62. Ban Sattahip, Thailand 12°39 1 N 100057 1 E

63. Chanthaburi, Thailand l2°37 1 N 102°07"E

64. Ban Ta Khli, Thailand l5°l6 1 N 10Qo17 1 E

65. U-Tapao, Thailand l2°4l ' N 101001'E

66. Sara Buri, Thailand l4°30 1 N 100°55 11 E

67. Nakorn Rajasima, Thailand l4°58 1 N 102°07 1 E

68. Udon Thani, Thailand l7°26 1 N 102°46 1 E

69. Nakhon Sawan, Thailand 15°48 IN 100010 l E

70. Chumphon, Thailand lo027 1 N 99°l5 1 E

171

71 .

72.

73.

74.

75.

76.

77.

78.

79.

80.

81.

82.

83.

84.

85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

99.

100.

101 .

102.

103.

104.

105.

Southeast Asia (Continued)

LOCATIONSongkhla, Thailand

Battambang, CambodiaSiem Reap, Cambodia

Krakor, CambodiaStung Treng, CambodiaKampot, CambodiaSvay Rieng, Cambodia

Luang-Prabang, laos

Xieng Khouang, Laos

Vientiane, LaosSavannakhet, LaosSeno, Laos

Pakse, Laos

Thakhek, LaosLao Cai, VietnamHanoi, VietnamPhu Lien, VietnamThai Nguyen, VietnamMoncay, Vietnam

Thanh Hoa" VietnamCao Bang, Vietnam

Chapa, Vietnam

Vinh, VietnamHatinh, VietnamDonghoi, VietnamRach-Gia, VietnamAn Xuyen, VietnamCon Son, VietnamBien Hoa, VietnamHo Chi Minh, Vietnam

Vung Tau, Vietnam

Vinh Long, VietnamCan Tho, VietnamBinh Thuy, VietnamSoc Trong, Vietnam

17-2

LATITUDE7°11 IN

13°06 1 N13°25 1 N12°31 1 N

13°31 1 N

10037 1 N11005 1 N

19°53 1 N19°26 1 N

17°58 1 N

16°33 1 N16°40 ' N15°07 1 N17°24 1 N

22°30 1 N21 0 03 1 N20 0 48 1 N21 0 36 1 N21 031 l N

19°48 1 N22°40 ' N22°21 IN

18°39 1 N18°41 'N

17°29 1 N10000'N

9°10 ' N8°42 1 N

10058 1 N10049 1 N

10022 1 N

10015 1 N

10002 1 N

10005 1 N

9°34 1 N

LONGITUDE100037 1 E

103°12 1 E103°49 1 E

104°11 1 E

105°58 1 E

104°13 1 E105°48 1 E

102°08 1 E

103°08 1 E102°34 1 E

104°45 1 E105°00 ' E

105°47 1 E

104°49 1 E

103°57 1 E105°52 1 E

106°38 1 E105°50 ' E

107°58 1 E

105°47 1 E

106°15 1 E103°49 1 E

105°41 IE

105°54 1 E106°36 1 E

105°05 1 E

105°10 ' E

106°35 1 E

108°49 1 E

106°39 1 E107°05 1 E

105°57 1 E105°45 1 E

105°43 1 E

105°57 1 E

Southeast Asia (Continued)

LOCATION

106. La i Khe, Vietnam

107. Long Xu~en, Vietnam108. Phan Thi et, Vi etnam

109. Cam Ranh, Vietnam

110. Pl ei ku Cu Hanh, Vietnam

111. Pleiku, Vietnam

112. An Khe, Vietnam

113. Ban Me Thout Eas, Vietnam

114. Dalat, Vietnam

115. Hensel AAF, Vietnam116. Kontum, Vietnam

117. Dong Ha, Vietnam

T18. Quang Tri, Vietnam

119. Hue Phu Sai, Vietnam120. Da Nang, Vietnam

121. Marble Mountain, Vietnam

122. Quang Ngai, Vietnam

123. Chu Lai, Vietnam

124. Qui Nhon, Vietnam

125. Tuy Hoa, Vietnam

126. Nha Trang, Vietnam

127. Phu Cat, Vietnam

128. Due Pho, Vietnam

129. Camp Evans, Vietnam

130. English, Vietnam

131. Butterworth, Malaysia132. Alor Star, Malaysia

133. Ipoh, Malaysia

134. Kuala Lumpur, Malaysia

135. Malaeea, Malaysia

136. Penang, Malaysia

137. Kota Bharu, Malaysia

138. Kuala Trengganu, Malaysia

139. Kuantan, r~a 1ayrs i a

140. Mersing, Malaysia

773

LATITUDE

11 012 1 N

10019 1 N

10 0 56 1 N

12°00 1 N

14°00 1 N13°58 1 N

13°58 1 N

12°39 1 N11°44 1 N13°51 1 N

14°21 1 N

16°49 1 N16°46 1 N16°23 1 N16°02 1 N

16°02 1 N

15°07 1 N15°25 1 N13°45 1 N

13°03 1 N

12°13 1 N13°57 1 N

14°49 1 N16°33 1 N14°28 1 N

5°27 1 N6° 11 1 N

4°34 1 N3°08 1 N2°16 1 N5°l7 1 N6°10 1 N

5°24 1 N

3°46 1 N

2°27 1 N

LONGITUDE

106°37 1 E

105°28 1 E10Bo06 1 E

109°14 1 ElOB °01 IE10Bo02 1 E10B040 l E1OBo07 IE

10B022 1 E

10Bo03 1 E10BoOl IE

10?006 1 E

10?010 1 E

10?042 1 E

10Bo12 1 E10Bo15 1 E

10B046 1 E

10B042 1 E

109°13 1 E109°20 1 E109° 11 IE

104°03 1 E10B058 1 E

10?023 1 E

109°02 1 E

100 0 23 1 E

100 0 24 1 E

10-,005 I E

10-1 °33 1 E

102°15 1 E10oo16 1 E

1O~~o 17 IE

103°06 1 E

103°12 1 E

103°50 1 E

141 .

142.

143.

144.

145.

146.

147.

148.

149.

150.

151 .

152.

153.

154.

155.

156.

157 .

158.

159.

160.

161 .

162.

163.

164.

165.

166.

167.

168.

169.

170.

171 .

172.

173.

174.

175.

Southeast Asia (Continued)

LOCATIONTemerloh, MalaysiaCameron Highlands, MalaysiaSingapore, SingaporeKuching, Malaysia

Padang, Indonesia

Medan, Indonesia

Pakanbaru, Indonesia

Singkep, Indonesia

Palembang, Indonesia

Pangkalpinang, IndonesiaTandjungpandan, IndonesiaTangerang, IndonesiaDjakarta, IndonesiaDjakarta, Indonesia

Bogor, IndonesiaKalidjati, IndonesiaSemarang, IndonesiaMadiun., IndonesiaSurabaja, IndonesiaSurabaja, IndonesiaBandung, Indonesia

Bandung, IndonesiaSurakarta, IndonesiaJogjakarta, Indonesia

Wedi-Birit, Indonesia

Tarakan, Indonesia

Pontianak, Indonesia

Pontianak, Indonesia

Balikpapan, Indonesia

Jefman, IndonesiaManokwari, Indonesia

Biak, IndonesiaBoruku, IndonesiaSentani, Indonesia

Tanahmerah, Indonesia

174

LATITUDE3°27 1 N

4°28 1 N

1020 l N

1032 1 N

0052 1 S

3°33 1 N0027 1 N0028 1 S

2°54 1 S2°09 1 S

2°45 1 S6°17 1 S6°09 1 S

6°16 1 S6°32 1 S

6°31 1 S

6°58 1 S

7°'36 I S

7°13 1 S

7°22 1S

6°58 1 S

6°45 1 S

7°31 1 S

7°47 1 S7°45 1 S3°19 1 N0008 1 S

OOOOIN

1°16 1 S

0°55 1 50053 1 S

1012 1 S

1°10 1 S

2°34 1 S

6°05 1 S

LONGITUDE102°26 1 E101023 1 E

103°50 1 E110020 l E

100° 21 'E

98°40 1 E

101°26 1 E

104°34 1 E104°42 1 E

106°08 1 E

107°45 1 E

106°34 1 E

106°50 1 E

106°53 1 E

106°45 1 E107°39 1 E

110 0 22 1 E

111°25 1 E

112°43 1 E112°47 1 E

107°34 1 E

107° 34 I E

110045 1 E

110025 1 E

110 0 36 1 E

117°33 1 E10g024 1 E

109°20 1 E

116°53 1 E

131°07 1 E

134°03 1 E

136°07 1 E

136°04 1 E

140 0 30 l E

1400 19 1 E

Southeast Asia (Continued)LOCATION LATITUDE LONGITUDE

176. r·1erau ke, Indonesia 8°31 1 5 1400 24 1 E177. Amaha i , Indonesia 3°19 1 5 128°55 1 E178. ~1enado , Indonesia 1032 1 N 124°55 1 E

,179. Makasser, Indonesia 5°03 1 S 119°33 1 E180. Bali, Indonesia. 8°44 1 5 ,115°10 I E

181 . Kupang, Indonesia 10° 10I5 123°39 1 E

182. Ambon, Indonesia 3°42 1 5 128°04 1 E

183. Tawau, Sabah 4°15 ' N 117°53 1 E184. Sandakar, Saba,h 5°54 1 N 118°03 1 E

185. Labuan, 5abah 5°17 1 N 115()14 I E

186. Kinabalu, Sabah 5°56 1 N 116°03 1 E

187. Seria, Brunei 4°38 ' N 114°22 1 E188. Brunei, Brunei 4°55 1 N 114°55 1 E

189. Kuehing, Sarawak 1029 1 N 1100 20 l E

190. Sibu, Sarawak 2°20 1 N 111050 l E

191 . Bintulu, Sarawa.k 3°12 1 N 113°02 1 E

192. ~li ri , Sarawak 4°23 1 N 113°59 1 E

193. Dili, Portuguese Timor 8°33 1S 125°32 1 E

194. Laoag, Philippines 18°11 1 N 120031 l E

195. Dagupan, Philippines 16°03 1 N 1200 20 l E

196. Basa, Philippines 14°59 1 N 120029 1 E

197. Clark AFB, Philippines 15°11 1 N 1200 33 1 E

198. Baguio, Philippines 16°25 1 N 1200 35 1 E

199. Loakan, Philippines 16°22 1 N 1200 37 1 E

200. San Fernando, Philippines 16°35 1 N 1200 18 1 E

201. Cubi Point, Philippines 14°47 1 N 1200 16 1 E

202. rvla nil a ,Phi 1i pp i nes 14°30 1 N 121 °01 IE

203. Sangley Point, Philippines l4°29 1 N 1200 54 1 E

204. Manila, Philippines 14°31 1 N 121 0 00 l E

205. Coron, Philippines 12°QO IN 1200 12 1 E

206. Calayan, Philippines, 19°16 1 N 121 0 28 1 E

207. Buseo, Philippines 20027 1 N 121 0 58 1 E

208. Aparri, Philippines 18°22 1 N 121 0 38 1 E

209. Tuguegarao, Philippines 17°37 1 N 121 0 44 1 E

210. Baler, Philippines l5°46 1 N l2l o 34 1 E

175

Southeast Asia (Continued)

LOCATION LATITUDE LONGITUDE211 . Casiguran, Philippines 16°17 1 N 122°07 1 E212. Daet, Philippines 14°07 1 N 122°57 1 E

213. Legaspi, Philippines 13°08 1 N 123°44 1 E

214. f~asba te Bay, Philippines 12°22 1 N 123°37 1 E

215. Borongan, Philippines 11037 1 N 125°26 1 E

216. Cebu, Philippines 10° 19 IN 123°54 1 E

217. Mactan, Philippines 10018 1 N 123°58 1 E

218. Surigao, Philippines 9°48 1 N 125°30 ' E

219. Cagayande Oro, Philippines 8°25 1 N 124°36 1 E

220. rv1a 1ayba1ay, Philippines 8°09 ' N 125°05 1 E

221. Francisco Bangoy, Philippines 7°07 1N 125°39 1 E

222. Davao, Philippines 7°07 1 N l25°38 1 E

223. Hinatuan, Philippines 8°22 1 N 126°20·E

224. Roxas, Philippines 11035 1 N 122°45 1 E

225. Iloilo, Philippines lOo42 1 N 122°32 1 E

226. Bacolod, Philippines 10°38 IN 122°55 1 E

227. Dumaguete, Philippines 9°18 1N 123° 18 IE

228. Dipolog, Philippines 8°36 1 N 123°21 ' E

229. Cotaba to, Philippines 7°14 1 N 124°15 1 E

230. Zamboanga, Philippines 6°55 1 N 122°03 1 E

231 . Puerto Princesa, Philippines 9°44 1 N 118°45 1, E

232. Cuyo, Philippines lo051 l N 121 °02 IE

233. Tolo Boy, Philippines 6°03 1 N 121 000 ' E

234. Sanga Samoa, Philippines 5°02 1 N 119°44 1 E

235. Echague, Philippines 16°42 1 N 121 042 1 E

236. Cap-St.-Jacques, Vietnam 10020 ' N 107°05 1 E

237. Pasuran, Indonesia 7°38 1S 112°55 1 E

238. Amboina, Indonesia 3°42 1S 128° 10IE

239. Koepang, Indonesia 10010'S 123°34 1 E

240. Pattle, Vietnam 16°33 1 N 111037 1 E

241 . Phnom Penh, Cambodia llo33 1 N 104°51 IE

242. Tacloban, Philippines 11015 1 N 125°00 ' E

243. Kota Kinabala, ~1alaysia 5°57 1 N 116°03 1 E

176

FORM NTIA-29(4-80)

U.S. DEPARTMENT OF COMMERCENAT'L. TELECOMMUNICATIONS AND INFORMATION ADMINISTRATION

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

NTIA Report 84-148

2. Gov't Accession No. 3. Recipient's Accession No.

4.. TITLE AND SUBTITLE

I~icrowave Terrestrial Link Rain Attenuation PredictionParameter Analysis

7. AUTHOR(S)

E. J. Dutton8. PERFORMING ORGANIZATION NAME AND ADDRESS

U.S. Dept of Commerce, NTIA/ITS.S3325 BroadwayBoulder, CO 80303

11. Sponsoring Organization Name and Address

USACEEIAFt. Huachuca, AZ

14. SUPPLEMENTARY NOTES

5. Publication Date

Apr; 1 '19846. Performing Organization Code

NTIA/ITS.S39. ProjectiTask/\Nork Unit No.

9104503

10. Contract/Grant No.

12. Type of Report and Period Covered

13.

15. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant hibliography or literaturesurvey, mention it here.)

Because rain attenuation continues to be a problem for the operation of microwavelinks worldwide, this report examines the behavior and the prediction of rain rateand rain attenuation distributions on a worldwide basis. Particular emphasis isplaced on seven areas of the world of special interest to the U. S. Army Communica­tions Electronics and Engineering-Installation Agency (USACEEIA).

16. Key Words (Alphabetical order, separated by semicolons)

attenuation distributions; contour maps; microwave links; model-data comparisons;rain attenuation

17. AVAILABILITY STATEMENT

tl UNLIMITED.

o FOR OFFiCIAL DISTRIBUTION.

18. Security Class. (This report)

UNCLASSIFIED19. Security Class. (This page)

UNCLASSIFIED

20. Number of pages

176

21. Price:

u U. S. GOVERNMENT PRINTING OFFICE: 1984-779-331/9326 REGION NO.8