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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FIGURE36
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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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FIGURE
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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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FIGURE113
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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
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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
3
lSfJ1210
Ob:served di:st.l'"'ibut.ion
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50% \\\\\_ 99.5~
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• 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
•
~_.,.J"l;~ )
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
I
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N
46
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~.
I
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I
",,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