a world atlas of atmospheric radio refractivity · contents page preface "' abstract...

$: A world atlas of atmospheric radio refractivity · Contents Page Preface "' Abstract '^ 1. Introduction 1 2.DiscussionofBasicData 2 3.WorldMapsofN(z) 4 3.1.Development 4 Figure1.Three-partexponentialfittomeanN-profile:$
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U. S. DEPARTMENT OF COMMERCEENVIRONMENTAL SCIENCE SERVICES ADMINISTRATION

A World Atlas of

Atmospheric Radio Refractivity

B. R. Bean, B. A. Cahoon, C. A. Samson, and G. D. Thayer

Institute for Telecommunication Sciences and Aeronomy

Institutes for Environmental Research

Boulder, Colo.

ESSA Monograph 1

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1966

U.S. DEPARTMENT OF COMMERCEJohn T. Connor, Secretary

ENVIRONMENTAL SCIENCE SERVICES ADMINISTRATIONRobert M. White, Administrator

Institutes for Environmental Research

George S. Benton, Director

This work was supported in part by the

U.S. Navy Weather Research Facility,

Contract Number 7560 : NABUSTDS 65 Ser. 300.

Library of Congress Catalog Card Number : Map 66-74

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. Price $2.25

Preface

This atlas has been prepared for the radio engineer who wants an estimate of the

behavior of the radio refractive index at any point on the earth. It has many limitations,

which the authors have tried to point out in the text, but should provide useful informa-

tion for engineering design and predictions of tropospheric radio circuits.

The work upon which this atlas is based has been in progress for several years in

the Radio Meteorology Section of the Central Radio Propagation Laboratory, National

Bureau of Standards, Boulder, Colo.* Many people have contributed to this research effort

through the years, and it is not feasible to acknowledge them all individually. Those most

directly involved with the preparation of material for this atlas include W. B. Sweezy and

W. A. Williams, who were responsible for most of the computer programming ; Mrs. B. J.

Weddle, who assisted in processing and cataloging of the data; T. D. Stevens, who did

most of the compiling, checking, and plotting of the maps, graphs, and tables; and

L. P. Riggs, J. D. Horn, and Mrs. G. E. Richmond (deceased), who contributed to the

atlas project in its early stages.

The National Weather Records Center of the U. S. Weather Bureau in Asheville,

N. C, supplied the meteorological data upon which this atlas is based, and also performed

the preliminary conversions of these data to refractivity parameters.

Finally, we thank the personnel of the U. S. Navy Weather Research Facility at

Norfolk, Va., who foresaw a need for such an atlas and liave arranged for support of the

project over a period of years.

Now the Institute for Telecommunication Sciences and Aeronoiny (ITSA), Environmental Science Services Administration.

HI

Contents

Page

Preface "'

Abstract '^

1

.

Introduction 1

2. Discussion of Basic Data 2

3. World Maps of N(z) 4

3.1. Development 4

Figure 1. Three-part exponential fit to mean N-profile : Koror . 5

Figure 2. Three-part exponential fit to mean A'^-profile : Dakar 6

3.2. Discussion of N(z) Map Contours 4

3.3. Reliability of Contours of N(z) Maps 6

3.4. Problem Areas of N(z) Maps 7

Figure 3. Five-year mean wet refractivity term: February 8

Figure 4. Five-year mean wet refractivity term : May 9

4. World Maps of A]V 10

4.1. Developmentj_lj_

10

4.2. Discussion of Contours and Reliability of AN Maps 10

5. World Maps of Extreme IV-Gradients 12

5.1. Development 12

5.2. Discussion of Gradient Map Contours (Subrefraction) 12

5.3. Discussion of Gradient Map Contours ( Superrefraction and Ducting) 14

5.4. Discussion of Cumulative Distributions of Ground-Based Gradients 15

Figure 5. Five-year mean vertical refractive gradient profile: Aden 16

Figure 6. Five-year mean vertical refractive gradient profile: Nicosia 17

5.5. Reliability and Limitations of Ground-Based Refractivity Gradient Data 17

6. World Maps of Mean Tropopause Altitudes 19

7. Appraisal of Results 20

7.1. Accuracy of N(z) Maps 20

Table 1. Standard errors of 5-year mean values of monthly mean A', for 40 stations 20

Figure 7. Correlation of A A'': monthly mean A'-profiles versus monthly mean exponential model 21

Table 2. Absolute errors in recovering mean A^ from map contours for 32 stations 21

Table 3. Approximate total standard errors, cj, for N (z) maps in appendix A 22

7.2 Accuracy of AiV Maps. 23

Figure 8. Correlation of A A': monthly mean N-profiles versus monthly mean weather

summary data 22

7.3. Accuracy of Gradient Maps 24

8. Conclusions 25

9. References 26

10. Appendix A. World Maps of N(z) Parameters 29

Table A-1. Cumulative distribution levels of surface refractivity 30

Figure A-1. Location of N(z) data stations 32

Figure A-2. Mean sea-level dry term, Do: Febrjiary 83

Figure A-3. Mean sea-level wet term, W^: February 33

Figure A-4. Dry-term tropospheric scale height in km, Hi: February 34

Figure A-.5. Dry-term stratospheric scale height in km, H~ : February 34

Figure A-6. Wet-term scale height in km, H^,: February 35

Figure A-7. Mean density tropopause altitude in km, Zt: February 35

Figure A-8. Mean sea-level dry term. Do : May 36

Figure A-9. Mean sea-level wet term, TT'o : May 36

Figure A-10. Dry-term tropospheric scale height in km. Hi : May 37

Figure A-11. Dry-term stratospheric scale height in km. Hi: May 37

Figure A-12. Wet-term scale height in km, H^: May 38

Figure A-13. Mean density tropopause altitude in km, zt: May 38

Figure A-14. Mean sea-level dry term, Do: August 39

Page

Figure A-15. Mean sea-level wet term, W„: August 39Figure A-16. Dry-term tropospheric scale height in km, Hi : August 40

Figure A-17. Dry-term stratospheric scale height in km, i/s : August 40

Figure A-18. Wet-term scale height in km, H„: August 41

Figure A-19. Mean density tropopause altitude in km, Zt: August 41

Figure A-20. Mean sea-level dry term, Do: November 42

Figure A-21. Mean sea-level wet term, PK„: November 42

Figure A-22. Dry-term tropospheric scale height in km, Hi : November 43

Figure A-23. Dry-term stratospheric scale height in km, Hi : November 43

Fig:ure A-24. Wet-term scale height in km, H^^: November 44

Figure A-25. Mean density tropopause altitude in km, zt: November 44

Figure A-26. Standard prediction error of the exponential fit to the meanwet-term profile : February 45

Figure A-27. Standard prediction error of the exponential fit to the meanwet-term profile : May 45

Figure A-28. Standard prediction error of the exponential fit to the meanwet-term profile : August 46

Figure A-29. Standard prediction error of the exponential fit to the meanwet-term profile : November 46

Figure A-30. Areas of doubtful applicability of three-part exponential model of N(z)for 2 < 6 km 47

11. Appendix B. World Maps of AN 48Table B-1. Mean surface refractivity 49

Figure B-1. Location of AA^ data stations 52

Figure B-2. Monthly mean AN : January 53

Figure B-3. Monthly mean AN : February 53

Figure B-4. Monthly mean AN: March 54

Figure B-5. Monthly mean AN : April 54

Figure B-6. Monthly mean AN : May 55Figure B-7. Monthly mean AN : June 55

Figure B-8. Monthly mean AN: July 56Figure B-9. Monthly mean A N : August 56

Figure B-10. Monthly mean AA^: September 57

Figure B-11. Monthly mean AA^: October 57Figure B-12. Monthly mean AN: November 58

Figure B-13. Monthly mean AN : December ._j. 58

Figure B-14. Annual mean of sea-level refractivity, A'^o 59

Figure B-15. Annual mean of refractivity gradient between surface and 1 km, AN 59

Figure B-16. Slope of regression line of AA'^ versus Ns, b 60

Figure B-17. Correlation coefficient of AA^ versus Ns 60

Figure B-18. Standard prediction error of the regression line of AA^ versus N, _^j_ 61

Figure B-19. Standard prediction error of the regression line of AN versus N, as a percent of AN 61

Figure B-20. Areas of doubtful applicability of using N, to predict AN 62

12. Appendix C. World Maps and Cumulative Distribution Charts of Gradients of

Ground-Based Atmospheric Layers 63

Fig^Jre C-1. Percent of time gradient ^ (N/km) : February 64

Figure C-2. Percent of time gradient ^ {N/km) : May 64

Figure C-3. Percent of time gradient ^ (N/km) : August 65

Figure C-4. Percent of time gradient ^ (N/km) : November 65

Figure C-5. Gradient (N/km) exceeded 10 percent of the time for 100-m layer: February 66

Figure C-6. Gradient {N/km) exceeded 2 percent of the time for 100-m layer: February 66

Figure C-7. Gradient {N/km) exceeded 10 percent of the time for 100-m layer: May 67

Figure C-8. Gradient {N/km) exceeded 2 percent of the time for 100-m layer: May 67

Figure C-9. Gradient {N/km) exceeded 10 percent of the time for 100-m layer: August 68

Figure C-10. Gradient {N/km) exceeded 2 percent of the time for 100-m layer: August 68

Figure C-ll. Gradient {N/km) exceeded 10 percent of the time for 100-m layer: November. ... 69

Figure C-12. Gradient {N/km) exceeded 2 percent of the time for 100-m layer: November 69

Figure C-13. Percent of time gradient t^ -100 {N/km) : February 70

Figure C-14. Percent of superrefractive layers thicker than 100 m: February 70

Figure C-15. Percent of time gradient ^ -100 {N/km) : May 71

Figure C-16. Percent of superrefractive layers thicker than 100 m: May 71

vi

Page

Figure C-17. Percent of time gradient ^ -lOO (iV/km) : August 72

Figure C-18. Percent of superrefractive layers thicker than 100 m : August 72

Figure C-19. Percent of time gradient ^ -100 (N^/km) : November 73

Figure C-20. Percent of superrefractive layers thicker than 100 m: November 73

Figure C-21. Percent of time gradient ^ -157 (A^/km) : February 74

Figure C-22. Percent of ducting layers thicker than 100 m: February 74

Figure C-23. Percent of time gradient ^ -157 (iV/km) : May 75

Figure C-24. Percent of ducting layers thicker than 100 m : May 75

Figure C-25. Percent of time gradient ::= -157 (A'^/km) : August 76

Figure C-26. Percent of ducting layers thicker than 100 m: August 76

Filgure C-27. Percent of time gradient ^ -157 (iV/km) : November 77

Figure C-28. Percent of ducting layers thicker than 100 m : November 77

Figure C-29. Percent of time trapping frequency < 3000 Mc/s : February 78

Figure C-30. Percent of time trapping frequency < 1000 Mc/s: February 78

Figure C-31. Percent of time trapping frequency < 300 Mc/s : February 79

Figure C-32. Percent of time trapping frequency < 3000 Mc/s : May 79

Figure C-33. Percent of time trapping frequency < 1000 Mc/s: May 80

Figure C-34. Percent of time trapping frequency < 300 Mc/s: May 80

Figure C-35. Percent of time trapping frequency < 3000 Mc/s: August 81

Figure C-36. Percent of time trapping frequency < 1000 Mc/s: August 81

Figure C-37. Percent of time trapping frequency < 300 Mc/s : August 82

Figure C-38. Percent of time trapping frequency < 3000 Mc/s : November 82

Figure C-39. Percent of time trapping frequency < 1000 Mc/s : November 83

Figure C-40. Percent of time trapping frequency < 300 Mc/s: November 83

Figufe C-41. Lapse rate of refractivity (iV/km) exceeded 25 percent of time for

100-m layer : February 84

Figure C-42. Lapse rate of refractivity (N/km) exceeded 10 percent of time for

100-m layer: February 84

Figure C-43. Lapse rate of refractivity (iV/km) exceeded 5 percent of time for


Figure C-44. Lapse rate of refractivity (AT/km) exceeded 2 percent of time for



100-m layer: May 86


100-m layer: May 86


100-m layer: May 87

Figure C-48. Lapse rate of refractivity (A/^/km) exceeded 2 percent of time for

100-m layer: May 87

Figure C-49. Lapse rate of refractivity (Af/km) exceeded 25 percent of time for

100-m layer : August 88






100-m layer: August 89

Figure C-53. Lapse rate of refractivity (A^/km) exceeded 25 percent of time for

100-m layer : November 90


100-m layer : November 90


100-m layer: November 91


100-m layer: November 91

Table C-1. Median and minimum trapping frequency (Mc/s) of ducting layers 92

Figure C-57. (a) Cumulative probability distributions of dN/dh for ground-based

100-m layer: Aden, Arabia (February, May) 93

Figure C-57. (b) Cumulative probability distributions of dN/dh for ground-based

100-m layer : Aden, Arabia (August, November) 94

vii

Page

Fi^re C-58. Cumulative probability distributions of dN/dh for ground-based100-m layer: Amundsen-Scott, Antarctica 95

Figure C-59. Cumulative probability distributions of dN/dh for ground-based100-m layer: Balboa (Albrook), Panama C. Z 96

Figure C-60. Cumulative probability distributions of dN/dh for ground-based100-m layer: Bangui, Central African Republic 97

Figure C-61. Cumulative probability distributions of dN/dh for ground-based100-m layer : Bordeaux, France 98

Figure C-62. (a) Cumulative probability distributions of dN/dh for ground-based

100-m layer; Dakar, Republic of Senegal (February, May) 99

Figure C-62. (b) Cumulative probability distributions of dN/dh for ground-based

100-m layer: Dakar, Republic of Senegal (August, November) 100

Figure C-63. Cumulative probability distributions of dN/dh for ground-based

100-m layer : Denver, Colo 101

Figure C-64. Cumulative probability distributions of dN/dh for grround-based

100-m layer : Ezeiza, Argentina 102


100-m layer: Fort Smith, Northwest Territories, Canada 103

Figure C-66. Cumulative probability distributions of dN/dh for ground-based100-m layer : Hilo, Hawaii 104

Figure C-67. Cumulative probability distributions of dN/dh for ground-based100-m layer: Long Beach, Calif 105


100-m layer: Lourenco Marques, Portuguese East Africa 106

Figure C-69. Cumulative probability distributions of dN/dh for ground-based100-m layer: Nandi, Fiji Islands

, 107


100-m layer: New York, N. Y 108

Figure C-71. Cumulative probability distributions of dN/dh for ground-based100-m layer : Nicosia, Cyprus 109


100-m layer: Ostersund, Sweden 110

Figure C-73. Cumulative probability distributions of dN/dh for ground-based100-m layer: Perth, Australia Ill

Figure C-74. Cumulative probability distributions of dN/dh for ground-based100-m layer: Saigon, Viet Nam 112


100-m layer : San Juan, P. R 113

Figure C-76. Cumulative probability distributions of dN/dh for ground-based100-m layer: Ship Station "C" 114

Figure C-77. Cumulative probability distributions of dN/dh for ground-based100-m layer: Tashkent, U.S.S.R 115

Figure C-78. Cumulative probability distributions of dN/dh for g^round-based

100-m layer: Vladivostok, U.S.S.R 116

13. Appendix D. World Charts of Tropopause Heights 117

Figure D-1. Tropopause heights (km), based on temperature lapse rate: February 117Figure D-2. Tropopause heights (km), based on temperature lapse rate: May 118Figure D-3. Tropopause heights (km), based on temperature lapse rate: August 118Figure D-4. Tropopause heights (km), based on temperature lapse rate: November 119

14. Appendix E. Sample Listing of the Computer Output for San Juan, P. R., andAmundsen-Scott, Antarctica 120

Table E-1. Mean A^-profiles: San Juan, P. R 121

Table E-2. Mean Af-proflles : Amundsen-Scott, Antarctica 123Table E-3. Cumulative distributions of ground-based gradients: Amundsen-Scott, Antarctica. .. 125Table E-4. Analysis of ground-based superrefractive and ducting layers:

Amundsen-Scott, Antarctica 127

VUl

Abstract

This atlas presents world maps and graphs of upper-air radio refractivity, N(z)(where z is the altitude), mean monthly AiV (the difference between the refractivity

at the surface and at 1 km above the surface) , extreme values of gradients of refrac-

tivity observed in the lowest layer of the atmosphere (including maps of minimumtrapped frequency ducting gradients) , and monthly mean tropopause heights. All

refractivity values were derived from radiosonde data. The 'N(z) maps are presented

in terms of a three-part exponential model, with separate exponentials for the watervapor and air density terms of N(z), with the latter separated into tropospheric andstratospheric terms. The AN data were derived by interpolation from fixed pressure-

level data.

IX

1. Introduction

There has been a need in radio engineeringfor a method whereby the radio refractivity,

A'^, at some height, z, or the gradient of A'^ withrespect to height, dN/dz, could be accurately

estimated for any world location during anyseason of the year. Previous studies have at-

tempted to solve this problem by determinationof the value of surface refractivity, N^, and the

use of an exponential decay with height [Beanet al., 1960a] S or by presenting seasonal meansand distributions of N at fixed pressure levels in

the atmosphere for various radiosonde stations

[U. S. Navy, 1955-59; Michaelis and Gossard,1958]. However, these results did not provideany means whereby N {z) could be obtained at

any arbitrary location, i.e., places for whichmeteorological measurements were not avail-

able. In addition, specific information on the

gradient of the refractive index has not beenavailable previously on a worldwide basis, espe-

cially for the very important layers of the at-

mosphere at or near the surface where the pres-

ence of superrefractive or ducting gradients canproduce anomalous propagation of microwaves.

This atlas presents maps, charts, and discus-

1 Literature references on page 26.

sions of the worldwide variations in the radiorefractive index. With the aid of this atlas,

estimates of the following parameters may bereadily determined for any part of the world

:

the refractivity at any height, N(z) ; the averagegradient of A^ over the first kilometer above thesurface, A.N ; and the gradient of A'' in the lowestlayer of the atmosphere (with emphasis on sub-refractive, superrefractive, and ducting layers

and the probability of trapping of radio wavesby ducting layers). The world distribution ofN (z) is presented in the form of a three-part

exponential model, with separate exponentialterms for the water-vapor term, the densityterm in the troposphere, and the density termin the stratosphere; the parameters used to

represent this Niz) model are the reduced-to-

sea-level values of surface water vapor and den-sity terms, the scale heights of the three ex-

ponential terms, and the transition heightbetween the tropospheric and stratosphericdensity exponentials. Seasonal maps of meantropopause heights, which were obtained in thecourse of the data reduction required for thethree-part exponential model, are also presented.

2. Discussion of Basic Data

The radio refractive index of the atmosphere,n, exceeds unity by at most 450 parts per mil-

lion ; it is therefore customary to utilize theradio refractivity, N, given by -

N = (n^l) X 10^ (1)

The radio refractivity of air for frequencies upto 30,000 Mc/s is given by Smith and Wein-traub [1953]

:

iV = 77.6^+ 3.73 X 10^^, (2)

where P is the total atmospheric pressure in

millibars (mb), T is the absolute temperaturein degrees Kelvin (K) , and e is the partial pres-sure of water vapor in millibars. [For the de-velopment of this equation from theory, c.f.

Bean, 1962]. The P/T term in (2) is freqiaently

referred to as the "dry term" (even thoughthere is a small water vapor component in thetotal pressure) and the e/T- term, as the "wetterm."The radiosonde is in general use throughout

the world to measure the pressure, temperature,and relative humidity of the upper air. Thesedata can be used to obtain the correspondingvertical profile of radio refractivity. However,there are a number of disadvantages in the useof radiosonde data for the purpose of obtainingiV-profiles ; perhaps the most important of theseis the relatively slow response (large lag con-stants) of the radiosonde temperature and hu-midity sensors [Bunker, 1953 ; Wagner, 1960,1961; Bean and Button, 1961]. Also of someimportance is the method of selecting levels forwhich data are reported. The procedure fol-

lowed by most meteorological services consistsof reporting temperature, humidity, and heightat certain fixed pressure levels, called "manda-tory levels" (e.g., 850 mb), plus a sufficient

number of additional "significant" levels toprovide a profile of temperature and relativehumidity such that linear segments betweenlevels will not depart from the original data atany point by more than 1°C or 10 percent rela-

tive humidity. Such tolerances, although ac-ceptable for most meteorological purposes, mayresult in errors of as much as 30 A'-units (under

- Throughout this atlas, the term atmosphere should be understoodto mean the nonionized atmosphere, i.e., excluding the ionosphere.

3 A list of these stations is included in appendix A.

extreme conditions) in a linear-segment A'^-pro-

file constructed from radiosonde data. Somepunched-card refractivity data are availablewhich were calculated from significant levels

chosen with an even wider tolerance, 2°C and30 percent relative humidity [Bean and Cahoon,1961a]. In spite of these deficiencies, this atlas

is based entirely upon radiosonde data, since noother worldwide, long-term upper-air data areavailable. (More detailed measurements, ob-tained primarily from wiresonde and aircraftrefractometer flights, are available only for avery few locations and for very limited periodsof time.)

The first step toward obtaining a broadsample of upper-air refractivity data was theselection (by geographic-climatic considerationsand period of record available) of 112 radio-sonde stations from the worldwide network.'Wherever possible, a total of 5 years of data wasobtained for each of the 4 representative "sea-sonal" months of February, May, August, andNovember.

Five-year means were selected for use in thepreparation of this atlas for two reasons : (a) alarge number of stations, including all of thosein the U.S.S.R., have available records datingback only to the International Geophysical Year(IGY), 1958; (b) 5 years seemed to representthe best compromise between the number ofstations and the length of record, since the total

amount of data which could be processed wasnaturally limited. A large number of stations

is desirable for mapping purposes (better cov-erage), while longer periods of record yield

more stable (accurate) estimates of long-termmeans (of climatic variables). For each radio-

sonde ascent, the reported values of pressure,temperature, and humidity at each mandatoryor significant level were converted by means of

(2) to radio refractivity values (by the Nation-al Weather Records Center, Asheville, N. C).These data, when received at ITSA, were usedto obtain four monthly mean N-profiles for theavailable period of record for each of the 112stations. The procedure followed was to obtain

for each profile the values of A' at a number of

standard height levels by assuming separate

exponentials for the dry and wet terms betweeneach reported level. The mean A'-profile for the

DISCUSSION OF BASIC DATA 3

standard height levels was then computed as thearithmetic mean of the individually interpolatedvalues of A'' at each standard height for all ofthe profiles in the sample. In this v\^ay, 5-yearmean values of refractivity were obtained fora large number of levels, ranging from the sur-

face to 30 km (or more) above the surface, fora worldwide sample of stations. Over 18,000 in-

dividual values of mean N were determined in

this way.In addition to these calculations, the approxi-

mate height of the tropopause was determinedfor each profile ; this was the height of the bot-tom of the lowest atmospheric layer which metthe following criteria:

(a) the layer thickness was ^ 2 km,(b) the temperature gradient ^ -2°C/km.

The 2-km thickness could be made up of two ormore consecutive layers from the radiosondedata. Mean monthly values of tropopauseheights were obtained for the period of recordfor each station by averaging the individualprofile tropopause heights ; maps of these tropo-pause heights are shown in appendix D.The monthly mean value of the average A^-

gradient between the surface and 1 km abovethe surface has been recognized as a radio-meteorological parameter of some importance

4 Data from these two publications (published by the NationalWeather Records Center, Asheville. N.C., under the sponsorship ofthe World Meteorological Organization [WMO] and the U.S. WeatherBureau) will hereafter be referred to as "weather summary data,"

[Saxton, 1951 ; Bean and Meaney, 1955 ; CCIR,1965]. Therefore, maps are included of themean value of this parameter for all 12 months,with a more comprehensive network of stationsthan was available from the complete radio-sonde data sample discussed above. For thispurpose a sample of 268 stations was chosenfrom those available in the Monthly ClimaticData for the World and the National Summaryof Climatological Data (U.S.A.).* These pub-lications list monthly mean values of pressure,temperature, and relative humidity or dew pointfor the surface and some of the mandatory pres-sure levels from radiosonde data. For stationsnear sea level, the 900-mb level is very close to1 km above the surface, but for most stationsoutside of the U.S.A. the 850-mb level was thelowest reported ; the altitude of this pressurelevel varies between roughly 1.3 and 1.5 kmabove sea level. However, it was felt that inter-polation from the 850-mb data, using separateexponentials for the wet and dry terms, wouldyield fairly accurate values of monthly mean Nat the required 1-km height.The radiosonde-derived data described in the

preceding paragraphs constitute the basic datafrom which this atlas has been prepared. In thefollowing sections the methods of reduction andpresentation of these data are discussed, as wellas the consistency and reliability of the resultsso obtained.

3. World Maps of N{z)

3.1. Development

In order to prepare worldwide maps of upperatmospheric N from the 5-year mean N-profiles

described previously, it was decided to reducethe quantity of necessary N (z) maps by ab-

stracting each mean profile in terms of a modelatmosphere which would use three negative ex-

ponential functions of altitude. The three func-

tions which are used to represent each mean pro-

file are a single exponential for the wet term, W,and two exponentials for the dry term, D. Twoexponential functions are necessary for the diyterm because of the change in the lapse rate of

the temperature from the normal 6.5°C/km in

the troposphere to the nearly isothermal strato-

sphere where the temperature may increase

with height. Least-squares fits were obtained for

log W versus height over the interval to 3 kmabove the surface. The ranges to be covered bythe two fits for the dry term were determinedfrom the mean tropopause heights and their

standard deviations which had been obtainedduring the analysis of the iV-profiles in eachsample. The tropospheric dry term, D^, was fit

over the interval to the tropopause heightminus one standard deviation, and the strato-

spheric dry term, D,, was fit from the tropo-

pause height plus one standard deviation to theupper limit of data for that profile. In both

cases, log D was fit to height using least squares.

The resulting model atmosphere is given by

Niz) =:Doexp(--|-)

+ Wo exp[—

-§^J,Z ^ Zt,

(3)

Niz) ^D„exp(--|--^^^)

+ Woexp(^~^y (4)

2 >zt;

Do and Wo are the mean sea-level values of thedry and wet terms (reduced from the surfacevalues using the free-atmosphere scale heights)

,

Hio is the wet-term scale height, H^ is the tropo-spheric dry-term scale height, H,. is the strato-

spheric dry-term scale height, and Zt is the

altitude above mean sea level of the point of

transition between the tropospheric and strato-

spheric dry-term exponentials. The altitude, Zt,

may thus be thought of as an effective densitytropopause.

Examples of the application of this model to

actual mean refractivity profiles are given in

figures 1 and 2: a very good fit (Koror) and oneof the worst fits encountered (Dakar). Thegood fit obtained in figure 1 is especially signifi-

cant since Koror represents a climatic type(equatorial station with a very high mean sur-

face refractivity, 387.6) for which exponentialmodels of N were previously thought to be un-satisfactory [Mismeet al., I960]. Dakar (fig. 2)is an example of the climatic type (character-ized by a persistent low-level temperature in-

version with dry subsiding air above) wherethis model (or any other simple model) of A^

versus z is inadequate to explain the N^-structure

at low latitudes. It was found that the behaviorof the wet term (measured on figs. 1 and 2 byS,i-, the rms error over the first 3 km) was a goodindicator of whether or not the data would pro-vide a good fit to the profile. However, it canbe noted in figure 2 that, even though the rmswet-term error below 3 km is 14.6 A^-units, theprofile at Dakar above an altitude of 6 km is

well represented by the three-part exponential.

Maps were prepared for each of the 4 "sea-sonal" months of the parameters necessary to

utilize the three-part exponential in estimatingupper-air refractivity. These are the reduced-

to-sea-level values. Do and Wo ; the three scale

heights. Ha, H^, and Hn',and the_transition alti-

tude, Zt. The surface values of N can be recov-

ered by substituting the elevation of the surfaceabove sea level at the desired location in (3),

which amounts to inverting the process used to

reduce the surface values of N to sea level. Theseries of maps given in appendix A can be usedto estimate the mean value of N at any desired

altitude for each of the seasonal months at anyworld location except those areas outlined in

figure A-30 (which summarizes the wet-termrms error values found in figures A-26 throughA-29).

3.2. Discussion of N{z) Map Contours

The world maps of Niz) parameters reveal

a number of interesting trends. Some of these

are:

( 1 ) The Di scale height, H,

:

(a) is smaller than average over the arctic

seas in winter because of dense stratified air

;

WORLD MAPS OF Niz)

(b) remains higher than average over land

areas during their warm seasons due to a steep

temperature lapse rate with height.

(2) The D, scale height, H.

:

shows a minimum in the equatorial region

because of the colder temperatures found abovethe tropical tropopause.

(3) The wet scale height, Hu,:

(a) is larger than average in the generalarea of the equatorial heat belt during all sea-

sons. This indicates a steep temperature gradi-ent with a very small lapse of absolute humiditywith height in the turbulently mixed deep layerof warm air. However, in some tropical areas

6 A WORLD ATLAS OF ATMOSPHERIC RADIO REFRACTIVITY

very dependent upon temperatures because of

the larger water content possible at high tem-peratures. There are two exceptions

:

(a) Large interior deserts, where moun-tains block the normal moisture flow, tend to

have low wet-term values relative to their tem-peratures.

(b) In August, when the monsoonal mois-

ture is trapped south of the Himalayas, India

shows unusually high wet-term values.

(6) The intersection height, Zt, is closely re-

lated to the height of the tropopause, but in

areas where an isothermal layer precedes the

stratospheric increase of temperature, the D,

WORLD MAPS OF N{z) 7

map was then carefully checked by another an-alyst to make certain all data points had beenproperly considered. The contours were modi-fied in some areas on the basis of other informa-tion or considerations not accounted for in themachine-analyzed radiosonde data. For in-

stance, supplementary surface data [Knoll,

1941; Serra, 1955; Bean and Gaboon, 1957;UNESCO, 1958; Bean et al., 1960b; Air Min-istry, 1961 ; Dodd, 1965] were considered in thecontouring of those parameters {Do and Wo)dependent upon surface observations. Also, if

spurious "high" centers of the wet term (suchas the isolated values found at Tananarive,Malagasy Republic) were produced at high ele-

vation stations by reduction-to-sea-level pro-cedures, these values were smoothed to someextent. It was also found that the wet scale

heights derived from mean N-profile data forstations at altitudes greater than 1 km tend to

give more unrealistic sea-level wet terms thanthe average wet-term scale height of 3.0 kmsuggested by Hann [List, 1958]. When this

"standard atmosphere" scale height was sub-stituted for Hw, the maximum error of A^(2)

values calculated from (3) or (4) for all sta-

tions above 1 km which are listed in table A-1was 6.2 percent of the true 5-year mean valueat Tananarive in August ; the second largesterror was 5.5 percent at Nairobi in February.

Another contouring check was made of all

modified contours ; a third analyst reviewed thesmoothing to be sure it was consistent with theoriginal plotted data as well as with the sup-plementary information.

To further check the contouring, calculatedN{z) values (using (3) and (4) with valuesread from figs. A-1 through A-25) were com-pared with actual observed values at 32 repre-sentative stations. The results of this check(reported in detail in table 2 of sec. 7) em-phasize that, although some error undoubtedlyresults in N{z) values below 1 km due to con-touring, it is not a problem for N{z) values at3 km or above.

3.4. Problem Areas of N{z) Maps

The use of wet and dry scale heights in a bi-

exponential radio refractive index model hasproved to be a good indicator of climatic differ-

ences [Bean, 1961; Misme, 1964]. The dryterm, or atmospheric density component of re-fractivity, decreases with height in a uniformmanner throughout the troposphere so that its

scale height is an accurate indicator of thedegree of density stratification, but the water-vapor component (the wet term) is not so well-behaved. Because the saturation vapor pres-sure, es, is itself an exponential function oftemperature (which generally decreases linearly

with height), one of the best wet-term modelsis probably an exponential curve [Reitan, 1963 ;

Button and Bean, 1965]. However, an exponen-tial model of the wet term must be used withdiscretion because humidity is extremely vari-

able, both vertically and horizontally (becauseof its high dependence upon the temperatureswithin the different air masses, as well as var-ious terrain and land-water effects)

.

To show actual physical changes in Hw, thewet scale height, it would be desirable to pre-sent contoured values based not only on a largenumber of stations, but also on data representa-tive of various times of day. Figures A-6, A-12,A-18, and A-24 present the seasonal values ofHw, but worldwide maps of the diurnal vari-ability of the wet scale heights are not yet avail-

able.

There are three specific areas of the worldwhere the assumption of an exponential distri-

bution of the wet term is largely invalid and canbe used only with reservations. Two of theareas have one thing in common— a low sea-level wet term. At continental stations in highlatitudes where strong temperature inversionspersist during winter months, the wet term at3 km may be as large as, or even larger than,that at the surface (because of the increase ofwater vapor "capacity" with temperature) , andthe result is a negative or a very large positivevalue of the wet scale height, neither of whichis physically realistic. At any tropical desertstation where the sea level wet term is < 30N-units, deceivingly high wet scale heights also

may result. Fortunately, because of the smallcontribution of the wet term in these cases, thetotal iV-error remains small. The wet-term pro-files at nine stations with low values of Wo wereexamined, and the largest error at any heightwas 3.7 percent of the true 5-year N(z) valueat Niamey (a desert station) in February (fig.

3). In the arctic areas (represented by Barrow,Alaska, in this same figure) the maximum errornever exceeded 1.5 percent of the total N (z)

value.

The third area presents a more serious prob-lem because it exists in a subtropical climate(15°-35° north and south of the equator) wherethe wet term contributes from 14 to 1/3 of thetotal N. The sharp decrease of humidity andincrease of temperature which is found in at-

mospheric layers between the surface and 3 kmin the subsidence regions of semipermanent sub-tropical highs destroys the exponential distri-

bution of the wet term. In fact, in regions suchas this, the exponential fit may be valid only at

two or three points. This can be noted in figure

4, where the mean wet term for May is graphed,and the Hw value from the least-squares fit from0-3 km of log W versus height is indicated, for


four dissimilar stations : Dakar (low-level sub-

sidence), Antofagasta (intermediate subsid-

ence-trade wind ducting) , Hilo (trade wind in-

version), and Balboa (steep exponential gra-

dient) . A check of figure A-30 reveals that the

first three of these stations are located in areaswhere, because the rms of the wet-term errorexceeds 5 A^-units for at least 1 month, the three-part exponential model is not recommended.

WORLD MAPS OF N{z)

4. World Maps of aN

4.1. Development

Twelve maps of monthly mean xN were pre-

pared from the 5-year mean values obtained byinterpolation of mandatory pressure level radio-

sonde data for the 268 stations listed in table

B-1 and located in figure B-1 in appendix B.

These maps, contoured in the same manner as

the N{z) maps (sec. 3.3), are figures B-2

through B-13.Previous work has shown that a good corre-

lation may exist between aZV and surface N on

a monthly mean basis [Bean and Thayer, 1959 ;

Bean and Gaboon, 1961b; CCIR, 1965]. In fact,

in many areas of the world this seasonal corre-

lation is very high, and in such areas a regres-

sion line might provide better estimates of

monthly mean A.V than the maps in appendix B(if the mean value of surface A' were available

for that particular month of that year for the

desired location). This regression line could

also be used with the Ns distribution data fromtable A-1 to provide estimates of the aA" distri-

bution. Correlations were therefore calculated

for the 12 monthly mean values of aA' and sur-

face A^ for each of the stations in the sample.

The equations resulting from these calculations

were put into the form of deviations from the

annual means

:

jN = b{Ns -Ws) +IN ±S.K., (5)

where Ns is the surface value of A^ the single

bar represents a monthly mean value, the dou-ble bar represents the annual mean, b is the

slope of the regression line, and S.E. is the

standard error of estimate. The equations wereput in this form because the intercept of the

equations in the ordinary form is equal to aA' -

bNs, which is too unwieldy for contouring onmaps. Maps, which appear in appendix B, wereprepared of the slope (&), the annual means

(aA' and A^o) , and the standard error of pre-

diction and correlation coefficient of the regres-sion lines.

^

4.2. Discussion of Contours and Reliability

ofAy^ Maps

The world aA'^ maps of this atlas do not showas much detail as may be found in other publi-

cations which consider only specific areas [Bean

5 No is an approximate sea-level value of Na, defined by the equa-tion No = Nsc"-^^, where z is the elevation above sea level in km.

et al., 1960b; du Castel, 1961; Rydgren, 1963;

CCIR, 1963]. It was necessary in this study to

omit some of the available radiosonde data in

areas with relatively dense weather networks(e.g., the U.S.A. and Europe) in order to obtain

a more nearly unifoi'm worldwide coverage.

Even with this coverage, the map scale size pre-

cluded the contouring detail which would benecessary if localized terrain effects were to beincluded ; for example, mountainous locations

(higher than 1 km) probably have lower values

of aA^ than those indicated in figures B-2through B-13. Some dissimilarity in the con-

tour patterns between the maps in appendix Band other aA' maps may also be found because

of the differences in the time period used in the

samples; such disagreements emphasize the

fact that 5 years of data are not adequate for

reliable means in many areas.

The map contours of worldwide AN indicate

that:

(1) Low values of aA" are characteristic of:

(a) large desert and steppe regions such as

the Sahara, the Australian interior, the south-

western U.S.A., and the Asian region southeast

of the Caspian Sea all year

;

(b) high plateau areas during all seasons

except winter.

(2) High values of aA" are found in:

(a) all areas where large masses of subsid-

ing air prevent the normal diffusion of watervapor, creating an unusually large A'-gradient

between the moist surface air and the very dryair at 1 km. Specific examples are

:

(1) continental west coasts at latitudes20°- 35° in the summer hemisphere and 10°-

25° in the winter. In fact, the true Aa' may behigher than indicated on the maps at locations

such as Dakar, Senegal, where a very thick

(~250 m) surface or near-surface ductinglayer occurs much of the time

;

(2) tropical ocean areas where a trade-

wind inversion leads to a persistent elevated

ducting layer below 1 km. [Note : In a few cases

where the entire thickness of an elevated layer

lies between 1 km and the height of the 850-mblevel, the interpolation method gives a mapvalue which may be 5 to 10 A"-units too high.]

(b) southeast Arabia and the Gulf of Per-

sia during July and August, when orographicsubsidence traps moisture from the southwestmonsoon in the gulf and lowlands between the

mountains.

10

(c) Siberia and the Canadian interior inwinter because of the intense surface tempera-ture inversion.

(d) the Mediterranean and Black Seasduring summer when convective mixing greatlyincreases the near-surface humidity.

(e) India in the spring, when increasedheating over land produces a low-pressure re-gion which leads to onshore winds and humid

WORLD MAPS OF A AT 11

weather conditions until the onset of the mon-soon.

In winter a combination of high and lowAN values appear near the tip of southwestAfrica as the subsidence from the South At-lantic High causes a large moisture gradient toappear off the coast, whereas a small humiditygradient is characteristic of the dry plateauregion inland.

5. World Maps of Extreme N-Gradients

5.1. Development

The gradient of A^ near the surface of the

earth is of particular importance in many appK-cations of telecommunications ; e.g., extremevalues of these initial gradients are responsible

for much of the unusual behavior of radio sys-

tems. Superrefractive gradients (defined here asvalues betvi'een -100.0 AVkm and -156.9 AVkm)are responsible for greatly extended service hori-

zons, and may cause interference between widelyseparated radio circuits operating on the samefrequency. Ground-based radio ducts (layers

having a negative gradient larger in absolutevalue than 156.9 A'/km) can cause prolongedspacewave fadeouts within the normal radio ho-rizon [Bean, 1954] and allow radar to track ob-

jects many hundreds of kilometers beyond thenormal radio horizon. On the other hand, subre-fractive gradients (zero or positive gradients)produce greatly reduced radio horizons, andmay result in diffraction fading on normallyline-of-sight microwave paths.

In the process of obtaining the mean A^-profile

for each station and month, cumulative distri-

butions were prepared of the gradients occur-ring between the surface and the 50-m and100-m levels. Each gradient was calculated asthe simple difference between the surface A^

and the value at 50 or 100 m above the surface,divided by the height interval. For 99 out of the112 stations in the mean A^ sample, cumulativedistributions were also prepared of the gradi-ents and thicknesses of all observed ground-based superrefractive or ducting layers, regard-less of the thickness of the layer (except thatno layer less than 20 m thick was included, be-cause the gradients obtained in such cases arenot considered to be reliable) . In addition,cumulative distributions were prepared of theminimum trapped frequency for each of the ob-served ducts in the sample. (This sample size

averaged 208 pieces of data for each month

;

for all months the smallest sample was 30 andthe largest, 620). The minimum trapped fre-quency refers to the approximate lower limit offrequencies that will be propagated in a duct ina waveguide-like mode, and is given by [Kerr,19511

fn1.2 X 10^ (c/s)

(0^/=[-dndz

(6)

-]

where /n,in is the minimum trapped frequency in

c/s, t is the total thickness of the duct in km,dn/dz is the average gradient over the duct(n/km) , and r is the radius of the earth in km.Equation (6) is derived under the assumptionof a constant gradient throughout the duct, butmoderate departures from this assumption donot seem to affect the results greatly. The fmmcorresponds to an absolute attenuation of theguided energy of about 3 dB/km (5 dB/mile)[Kerr, 1951].

The maps in appendix C were prepared fromthe cumulative distributions discussed above.The distributions of gradients for the to

100-m layer were used to obtain maps of thepositive (subrefractive) gradient exceeded for10 and 2 percent of the observations at any lo-

cation, and the percent of observations withor positive A-gradients. Maps were also pre-pared of the extreme values of negative gradi-ents observed ; these are referred to as "lapserates" of N (i.e., decrease with height, a termnormally used in referring to atmospheric tem-perature gradients ; it is used here to avoid theawkwardness of referring to a very strong nega-tive gradient as being "less than" a given nega-tive value). Included in appendix C are mapsof the lapse rate of A^ exceeded for 25, 10, 5,

and 2 percent of the observations for the 100-mlayer. Cumulative probability distributioncharts of the gradients at 22 representativeworld locations are also presented.

Other maps in appendix C were preparedfrom the distributions of superrefractive andducting layer gradients, thicknesses, and /mmvalues for ducts. These include the percent oftime that the lapse rate of A' in the ground-based layer is equal to or larger than 100 N/kmand equal to or larger than 157 AVkm (ductinggradient) , the percent of superrefractive layersthat were more than 100 m thick, and the per-cent of ducting layers that were more than 100m thick (the last two refer to the percent ofthick layers out of the number of observed lay-

ers of that type) . The distributions of /mmvalues were used to prepare maps of the per-cent of all observations which showed ground-based ducts having an /min value of less than3000 Mc/s, 1000 Mc/s, and 300 Mc/s.

5.2. Discussion of Gradient Map Contours(Subrefraction)

Ground-based subrefractive layers may be

12

WORLD MAPS OF EXTREME N-GRADIENTS 13

found in the same tropical and subtropical loca-

tions as superrefractive layers, because a smallchange in relative humidity at high tempera-tures produces a very noticeable change in ab-solute humidity, and the iV-change (either posi-

tive or negative) with height is highly depend-ent upon the variation of absolute humidity.For instance, subrefractive gradients occurquite often during the afternoon at stations

which experience superrefraction or ductingduring the night and early morning. Other sta-

tions may have nocturnal subrefraction duringwinter and superrefraction during the samehours in summer. However, subrefraction, un-like superrefraction, rarely occurs at surfacetemperatures below 10 °C (the only exceptionwould be locations greater than 1 km above sealevel)

.

The surface conditions conducive to subre-fractive gradients are of two rather oppositetypes

:

(a) temperature > 30°C; relative humidity< 40 percent

;

(b) temperature 10° to 30°C ; relative humid-ity > 60 percent.Type (a) is usually found during the day-

light hours of months v/hen intense solar heat-ing occurs at warm, dry continental locations

and forms a very nearly homogeneous surfacelayer (no decrease of density with height)which may be several hundred meters thick.

Since a moist parcel of air is less dense than adry parcel at the same temperature and pres-sure, the intense convection which occurs with-in such a layer of absolutely unstable air tendsto concentrate the available water vapor nearthe top of the layer, because a moist adiabaticupper boundary is formed where the super-adiabatic lapse rate changes abruptly to a sub-adiabatic or very stable lapse rate. The result is

an increase (sometimes as large as 50 percentof the surface value) with height of the wetterm through the ground-based layer. This in-

crease, coupled with no change in the dry term,leads to a subrefractive (or positive) gradient.

This layer may retain its subrefractive na-ture throughout the early evening hours at sta-

tions where conditions are favorable for thedevelopment of a temperature inversion. As theground cools rapidly, the air very near theground cools and becomes more dense, but thewater vapor which is trapped between the twostable layers causes the positive wet-term gradi-ent from surface to the top of the original layerto remain large enough to overbalance theslightly decreasing gradient of the dry term.This evening subrefraction is an outgrowth oftype (a) ; however, it may resemble type (b)at the surface because it can be found with atemperature as low as 20 °C and a relative hu-midity as high as 60 percent.

Type (b) occurs most often during night andearly morning hours, and is characteristic ofcoastal trade-wind and sea-breeze areas wheredifferential heating of land and sea results in

the advection of air which is warmer and morehumid than the normal surface layer. In this

type, both dry and wet terms may increase withheight, creating a surface layer of subrefrac-tion which is generally more intense in gradientthan type (a) but not so thick. This form of

subrefraction might also be found for shortperiods in any location where frontal passagesor other synoptic changes create the necessaryconditions.

Type (a) subrefraction is hard to evaluatefrom figures C-1 through C-4 because its per-centage occurrence at any specific location is so

dependent upon the time of day represented bythe radiosonde data at that location. For in-

stance, because the local radiosonde observa-tion times in the southwestern U.S.A. were0800 and 2000 for the data period used in this

atlas, only the subtype (a) of evening subre-fraction is recorded. Because conditions aremore suitable for inversions in February andMay, these months appear to have surface-

based subrefractive layers more often than Au-gust. However, a detailed check of midafter-noon observations near White Sands, N. Mex.,reveals that midday subrefractive conditions are

quite prevalent during much of August and Sep-tember. The same diurnal problem is found in

northern Africa and the desert region south andeast of the Caspian Sea, where many of the sta-

tions take observations between 0300 and 0600LST. Furthermore, even at those stations

which do have midday data, the "motorboating"problem (i.e., humidities too low to be mea-sured by the radiosonde — see sec. 5.5) duringthe warmest seasons at very dry locations prob-ably masks out a large percentage of subrefrac-tive occurrences ; e.g., the occurrence of subre-

fraction recorded in November and Februaryfor the interior of Australia (where afternoonobservations are included) is probably too low.

Figures C-1 through C-4 reveal that type (b)

subrefraction can be expected 10 to 20 percentof the time in the western Mediterranean Seaand the Red Sea area, and also in the Indone-sian-Southwest Pacific Ocean region. These lo-

cations seem to indicate a slight seasonal trend,

with a higher probability of occurrence duringwinter months. Another region with a 10 to 20percent level of subrefractive gradient occur-

rence is the Ivory Coast and Ghana lowlands of

Africa where onshore winds prevail all year.

Occurrences of type (b) subrefraction exceed5 percent at these locations and times of year

:

(1) Southeast coast of U.S.A. all months;


(2) Hawaiian Islands all months exceptMay;

(3) South Africa all months except Novem-ber;

(4) Southeast coast of South America in No-vember and February

;

(5) Southern California in November

;

(6) North Indian Ocean in May

;

(7) Isthmus of Panama in November.

5.3. Discussion of Gradient Map Contours(Superrefraction and Ducting)

Superrefractive and ducting gradients in

ground-based layers are most often associated

with temperature inversions (temperature in-

creasing with height within the layer) , not only

because a positive temperature height-gradient

causes a negative iV-gradient, but also becausethe low eddy diffusion qualities associated witha temperature inversion often lead to a steep

negative gradient of humidity through the in-

version. However, previous investigations[Bean, 1959] have shown that there are at least

two other typical situations encountered in the

formation of strong ground-based gradients:

The first of these is the arctic situation, where,with surface temperatures below about —20°C,a strong temperature inversion (typical of con-

tinental arctic air masses) produces a superre-fractive or ducting layer, while the vapor pres-

sure may actually increase with height. Moreoften, in this case, the wet term is negligible

throughout the layer. The second case is typical

of very humid tropical areas when the surfacetemperature is 30°C or greater. In these loca-

tions (which are usually coastal) a commonoccurrence is a slight decrease of temperaturewith height, accompanied by a very stronglapse of absolute, humidity. Such profiles mayshow only a slight decrease of relative humiditywith height, but, because the saturation vaporpressure is nearly an exponential function of

temperature, the resulting vapor pressure gra-dient may be very large, thus causing a steep

yV-gradient.

Figures C-41, C-45, C-49, and C-53 show thatpersistent ducting (D) or superrefractive (SR)initial gradients can be found more than 25percent of the time for at least two seasons in

seven general areas of the world

:

(1) Dakar -Fort Lamy transitional strip in

Africa (D : all seasons)

,

(2) northern Arabian Sea including coastal

areas of the Gulf of Aden and the Persian Gulf(D : all seasons),

(3) India, Bay of Bengal, southeast Asia,Indonesia, and north tip of Australia (SR: all

seasons),

(4) southwest coast of North America, in-

cluding portions of the North Pacific (SR : Feb-

ruary, May, November)

,

(5) Gulf of Mexico and Caribbean region(SR: May, August, November),

(6) northwest coast of Africa and westernMediterranean (SR: May, August),

(7) Antarctica (D: May, August).Area (1 ) : Tropical west coast locations in the

vicinity of 15°-22°N or S are affected annuallyby three or four latitudinal weather zones [Tre-wartha, 1961]. In winter the Dakar-Fort Lamyregion is under the influence of dry anticyclonic

Saharan air, but even at the time of low sun, theprevailing surface air movement is onshorefrom the southwest. The vertical depth of this

maritime current is more shallow than in sum-mer, but during the early morning hours, thesurface relative humidity is 80 to 90 percentcompared with 40 to 60 percent in the dry sub-siding air above. Even with radiational cooling,

the night temperatures throughout the marinelayer (from 50 to 600 m thick) still remain over20°C. This combination of temperature and hu-midity creates trapping conditions for frequen-cies below 300 Mc/s about 30 percent of thetime in February (fig. C-31).The weather zones advance rapidly north-

ward [Thompson, 1965], so that by July theDakar-Fort Lamy strip is in the wet tropical

regime associated with the fluctuating, unstableIntertropical Convergence Zone (ITC). Themarine current of the westerlies becomes muchdeeper, but the ducting layers are shallowerand can exist only intermittently between theturbulent, showery periods common to the re-

gion. Figures C-22, C-24, C-26, and C-28 indi-

cate that more than 30 percent of the ductinglayers are over 100 m thick for all seasons ex-

cept summer.Area (2): The coastal areas of Arabia ex-

perience high surface humidities all year frommonsoonal and sea-breeze effects, but duringMay and August these values are reinforced bytemperatures above 25 °C in a marine layer

which may extend up to a height of 800 to 900m before it meets the overrunning dry north-easterlies [Tunnell, 1964]. The percentage oc-

currence of ducts at Bahrain seems much high-er than at Aden because all observations at

Bahrain were taken at 0300 LST (when thesurface humidity is at its maximum of 75 to 90percent) , whereas the Aden observations, takentwice a day, include as many observations at

1500 LST (when the relative humidity value is

much less) as at 0300 LST. For instance, 50 ofthe 66 ducts recorded in August at Aden werefrom early morning observations. However, thefact that ducting gradients at Bahrain trap fre-

quencies below 300 Mc/s over 75 percent of thetime as compared to 5 percent at Aden (fig.

C-37) is due to another factor: the thickness of

the moist marine layer, when ducting is present

WORLD MAPS OF EXTREME iV-GRADIENTS 15

at Bahrain, is greater than 300 m over half thetime.Area (3) : A moist surface layer is also found

in the monsoonal areas. Its temperature is 25to 30°C and, during occurrences of ducting, the

surface relative humidity ranges from 85 to 100percent, but the trapping incidence is much less

than in either area (1) or (2). The surfacelayer is shallov^'er and its gradient is less intensebecause the humidity decrease between it andthe air mass directly above it is only 10 to 20percent. Because brief periods of stable weatheroccur even between surges of the summer mon-soon, the ducting incidence remains over 10 per-

cent for all of area (3)

.

Area (A) : Along the western coast of NorthAmerica, from Southern California to CentralMexico, the most important month for unusualradio propagation due to surface conditions is

February, when frequencies below 300 Mc/s aretrapped 10 percent of the time. During the pe-riod studied, 30 percent of the superrefractivegradients were at least 300 m thick in all 4

months. Closer examination of the ductingstructure in Mazatlan reveals that if near-sur-face layers (bases of 100-300 m) were included,

the percentage of occurrence would be increasedby 20 to 40 percent for all months except Au-gust. During February, May, and Novemberthe surface temperature of 20 to 30 °C remainsnearly constant through the ducting layer, butthe relative humidity decreases from a surfacevalue of 70 to 80 percent to values ranging from20 to 40 percent. The dry air in the upper layerresults from subsidence in the eastern marginof the Pacific high pressure cell, which shifts

northwestward in August, thus decreasing theducting incidence in Mazatlan but increasing it

in lower California and the Hawaiian Islands(figs. C-21, C-23, C-25, C-27).Area (5) : The center of most intense ducting

in the Caribbean Sea and Gulf of Mexico changeswith the seasons (figs. C-41 through C-56). Thesmallest percentage of superrefractive ground-based gradients is found in February, with thestronger gradients concentrated near the east

coast of Central America. By May the super-refractive area has shifted eastward into theCaribbean and northward into Florida. In Au-gust it includes parts of the eastern U.S. but is

still most intense in the Swan Island area, andin November the area encompasses all of theCaribbean. The ground-based superrefractivelayers are thicker than 100 m approximately70 percent of the year, but the ducting layers arenever intense enough to exceed the 1-percenttrapping level for 300 Mc/s.Area (6) : The cause of superrefraction in the

western Mediterranean and northwest Africais very similar to that in area (4) . During thesummer season, subsidence along the eastern

edge of the Atlantic high-pressure cell superim-poses a dry layer over the marine surface layer

;

during the winter season, the major subsidencearea shifts southward, the temperaturesthroughout the surface layer are 5 to 10 °C low-er, and the percentage of superrefraction andtrapping incidence decreases.Area (7) : During the long Antarctic night, in-

tense radiation from the snow-covered groundkeeps the surface temperature much lower thanthat in the air several hundred meters above.This temperature inversion of 10 to 25°C is thecause of all the ducting gradients in May andAugust, which trap frequencies <1000 Mc/s at

least 40 percent of the time (see appendix E).

5.4. Discussion of Cumulative Distributions

of Ground-Based Gradients

Data from 22 representative stations wereselected as a sample of the kinds of ground-based gradient distributions from the surfaceto 100 m which occur in various climates andlocations throughout the world.

Interesting similarities which exist amongthe gradient distributions imply that the re-

fractivity climate of any station may be related

more to the season or month of the year than to

any particular latitudinal location. For in-

stance, consider the interesting relationships

between Bangui (a tropical station), Bordeaux(temperate), and Amundsen-Scott (arctic).

The gradient distribution at Amundsen-Scottin February resembles that of Bordeaux in

February, but its August distribution slope re-

sembles that of Bangui in May. However, Ban-gui's distribution slope and range in Augustresembles Bordeaux in May. Amundsen-Scottforms another interesting climatic triad withSaigon and Long Beach. In August the distri-

bution slope and range of Amundsen-Scott is

very similar to that of Saigon (a tropical sta-

tion), but the negative gradient intensity is

about 100 A'^-units greater at all percentage lev-

els. However, Saigon in May, before the mon-soon, resembles Long Beach in February.

It was expected that a pronounced diurnaleff'ect would exist in the gradient structure nearthe surface, so two stations, Aden, Arabia, andNicosia, Cyprus, where data were available at

two thermally opposite times of day—2 and 3

a.m. and 2 and 3 p.m. (0000 and 1200 GMT*^)—were studied. Figures C-57 and C-71 in appen-dix C show the diurnal differences in the cumu-lative distribution of initial gradients fromto 100 m for these two stations for the 4 monthsstudied.

Superrefractive conditions normally accom-pany nocturnal inversions. At Nicosia this

''GMT {Greenwich Mean Time) is the same as UT (UniversalTime).


proves to be the case for all seasons, with a very-

definite maximum in August, when anticyclonic

upper air circulation intensifies the humiditydecrease aloft and radiational cooling lowers the

surface temperature 15 °C below that foundduring the day.

Aden, a coastal station with less change in its

diurnal temperature cycle than Nicosia (an in-

terior valley station on a fairly large island),

exhibits superrefraction day and night for all

seasons. During August and November initial

gradients have a wide range of values, with thelargest variation occurring at 0000 GMT, butin February and May the nocturnal stability

apparently is seldom destroyed by convectivemixing, and the 1200 GMT (1500 LST) initial

refractivity gradient may exceed the 0000 GMT(0300 LST) gradient. However, the early

morning inversion is usually more significant

from a radio-meteorological viewpoint because

X

WORLD MAPS OF EXTREME i^/-GRADIENTS 17

5.5. Reliability and Limitations of

Ground-Based Refractivity Gradient Data

Because ground-based gradients are so sen-

sitive to local effects, such as terrain and land-

water relationships, it was impossible to contour

figures C-1 through C-56 for individual small

areas. For instance, although Madrid (on the

high interior plateau of Spain) experiences

little ducting during the year, it is surrounded

by areas of high ducting incidence, and no at-

tempt was made to delineate this small regionof nonducting. Also, refractivity gradients cal-

culated from radiosonde observation levels sep-

arated by less than 20 m may be seriously affect-

ed by instrumental errors, so ground-based lay-

ers less than 20 m thick were not included in

the analysis. Consequently, very shallow duct-

ing (such as that found at certain times overoceans, under dense jungle canopies, and in

I


time would be distributed throughout the day as

one traversed the globe. For instance, the fol-

lowing stations (in tropical areas where the

occurrence of either subrefractive or superre-

fractive layers is especially dependent upon the

time of day) were used in this report

:

Station Local time GMT0300 0000

2000 0000

*Aden, Federation of SouthArabia

*Curacao, NetherlandsAntilles

Fort Lamy, Republic of Chad 0100 0000

*Hilo, Hawaii 1400 0000

Lae, Territory of New Guinea 1000 0000

Majuro Island, Marshall 1200 0000Islands

Singapore 0700 0000

Those stations marked with an asterisk also

take observations at 1200 GMT. However, whenevaluating the apparently low level of duct oc-

currence at some locations (e.g., Majuro) andhigh occurrence at others (e.g.. Fort Lamy),and when checking the subrefraction occurrenceat warm, dry continental locations, such as Ni-amey (where no midday observation is taken),the local time of the radiosonde ascent should beconsidered.

In addition to the spatial and temporal limita-

tions imposed by the use of available radiosondedata, there are instrument recording limitations

(see sec. 2) which must be considered whenevaluating A^-gradients. Although the alternat-

ing sequence system of observing the humidityand temperature can put a lower limit on thethickness and thus mask the true gradient ofatmospheric layers which can be detected byradiosonde, the response of the radiosonde tem-perature and humidity elements is a more se-

rious problem in the measurement of the in-

tensity and number of superrefractive gradientsat or near the surface. For example, in typical

ducting situations during May in a tropical

(Saigon) and in a temperate climate (Bor-deaux), correction of both humidity and tem-perature sensor time lags as suggested by Beanand Button [1961] would intensify gradients of—293 N/km (Saigon) and —212 N/km (Bor-deaux) to —377 N/km and —362 N/km, re-

spectively. This type of correction also wouldhave increased the percentage occurrence of

superrefractive and ducting gradients in themajority of cases. Such extensive recalcula-

tions were not possible in this study, but thepossibility that more intensive gradients mayoccur in larger percentages at some locations

(particularly in temperate, humid climates)

should be kept in mind when applying valuesobtained from any of the figures in appendix C.

Another limitation which applies primarily to

the detection of subrefractive layers (figs. C-1through C-12) in hot, dry regions is the highelectrical resistance of the lithium chloride hu-midity element at very low humidities whichcauses open-circuit signals ("motorboating").At stations such as Aoulef, Algeria, where thedaytime surface temperature often exceeds30°C, the relative humidity may be below themotorboating boundary at all levels from sur-

face upward, and all relative humidity values(except the surface) are estimated, usually in

values which are equal to, or less than, the sur-

face value. However, it is quite probable in

these highly convective conditions that the abso-lute humidity remains constant with height,

instead of rapidly decreasing (as the estimatedrelative humidity values would indicate) . If it

did remain constant, fairly persistent subre-fractive gradients would be found in such areasduring the hours of most intense solar heating.

6. World Maps of Mean Tropopause Altitudes

Maps have been prepared of the mean tropo-pause altitudes which were calculated in thecourse of obtaining the mean A'^-profiles for the112 station sample, as discussed previously. Themaps, for the 4 "seasonal" months, are shownin appendix D. The zone of maximum tropo-pause altitudes for each month seems to corre-spond quite well with the mean position of theIntertropical Convergence Zone.As stated earlier, the criterion for determin-

ing the tropopause altitude for each radiosondeascent was the altitude of the base of the first

layer or layers which had a total thickness ofat least 2 km and a temperature lapse rate ofless than 2°C/km. The mean tropopause alti-

tude for each station and for each month was

determined by a simple average of all of theindividual values for the profiles in the sample(usually of 5 years' length). The reliability orconsistency of these maps is diificult to assess,since the results of determining tropopause alti-

tudes depend to a great extent on the criteriaused for selection of the first stratospheric layer.

The criterion used here is the one in most com-mon usage [U.S. Weather Bureau, 1964], butother criteria may be applicable where the re-

sults are intended for use in specific atmosphericproblems. These maps supplement tropopausedata presented in other reports and atlases[For example, Willett, 1944 ; U.S. Navy, 1955-59 ; Smith, 1963 ; Smith et al., 1963 ; Kantor andCole, 1965].

19

7. Appraisal of Results

7.1. Accuracy of N{z) Maps

The general accuracy of the 5 - year meanvalues used in the N (z) study was checked bycomputing the standard deviation of the year-to-year monthly means and dividing by thesquare root of 5. This should be a good estimateof the rms (standard) error of the 5-year meanvalues as compared to the true long-term mean(assuming there are no trends in the data).Table 1 shovi's the estimated standard error ofthe 5-year mean Ns values for 40 stations, ar-

ranged by climatic classification. The percent-age errors should be similar for the N{z) pa-rameters (vi'ith the possible exception of scale

heights) at various altitudes. The combined(rms) standard error of 5-year mean Ns for the40 stations for February and August v^^as 2.37N-units, or about 0.7 percent of the mean jVs.

It is significant that even the standard 30-yearperiod recommended (e.g., by the WMO) forstandard climatological normals would have anominal standard error of about ±1.0 x¥-unit(2.37 divided by \/6), or about 0.3 percent ofmean Ns values.' The 30-year means would thus

Table 1. Slayidard errors of 5-year mean values of monthlymean Ns for 1^0 stations.

APPRAISAL OF RESULTS 21

which are characterized by a high (tropical-

type) tropopause showed larger errors at 16km than at 8 km, the reverse of the usual trend

in table 2. It is apparent from inspection oftable 2 that errors in recovering N (z) at alti-

tudes of 3 km or more are likely to be small.

10

POINTS AFFECTED BY LOW-LEVEL SUBSIDENCE

REGRESSION LINE

ANm = 14 64 + 6437 ANj i 6 40r - 795

J L30 30 40 50 60 70 M 90 100 110 120

iN( FROM EXPONENTIAL MODEL

FiGtJRE 7. Correlation of AN; monthly mean N-pro/iJes versus monthly

mean exponential model.

Table 2. Absolute errors in recovering mean N from mapcontours for 32 stations (in N-units).

Month


Table 3. Approximate total standard errors, o'T, for N(z)maps in appendix A.

AverageMinimumMaximum

3 km

In

APPRAISAL OP RESULTS 23

7.2 Accuracy of AN Maps

As a check on the method used to calculate the

aA^ values from which the maps in appendix Bwere derived, the aA^ values from the weathersummary data were obtained for all 90 of thestations which were also contained in the meaniV-profile sample ; the \N values for the monthsof February, May, August, and November werethen compared with the corresponding valuesfrom the actual mean A-profiles. However, theperiod of record involved in the mean A-profilestudy was not, in general, even partially coin-

cident with the 1960-64 period used for the aAstudy. Thus it was expected that the variance,

<^D-, of the differences between the weather sum-mary aN values (from which the maps given in

appendix B were obtained) and the aA valuesfrom the mean N-profiles would have two com-ponents,

<'d- = "r- + "e-, (8)

where <^r- is the variance of the real differencein the two 5-year mean values of aA^ (becausethey are obtained from different time periods),and <^£- is the variance of the differences whichare caused by the interpolation errors inherent

in the method used to obtain the \N from theweather summary data. Since the real differ-

ences (represented by "'r) would be expected to

have a near-zero mean for a worldwide datasample , a regression analysis of the two typesof aN values should reveal any bias which hadbeen produced by the interpolation method usedin the aA study. Figure 8 shows the results of

such a comparison, with aN from the meanA-profiles as the dependent variable, and aAfrom the weather summary data as the inde-pendent variable. There is no statistically sig-

nificant bias shown, since the regression line is

almost identical with the "perfect agreement"line (zero intercept and slope of unity).An evaluation of the relative sizes of "r and "^e

was made by calculating the rms difference be-

tween the two types of aN values for a restrict-

ed sample containing only those stations wherethe mandatory pressure level used to calculate

the A/V values from the weather summary datawas within it 100 m of 1 km above the surface;the rms difference thus calculated was 3.9 A'-

units. Since any interpolation errors would beexpected to be quite small for this restrictedsample, it was concluded that the 3.9 A-unitrms represented essentially the value of "^r asgiven in (8).The value of <^d as given in figure 8 is 5.2

TV-units ; thus by (8) the value of <yE is probablyon the order of 3.5 A-units. This should be agood approximation to that part of the overall

rms error in the aA maps which is assignable

to the interpolation method used on the weathersummary data.

The overall accuracy of the aA^ maps given infigures B-2 through B-13 depends on severalfactors : the accuracy of the interpolation meth-od, the variability of the 5-year mean period ascompared with a standard WMO 30-year meanperiod, and the heterogeneous nature of thelocal observation times included in the datasample. The weather summary data were most-ly derived from observations taken at 0000GMT, although many stations in different partsof the world supplied data taken at 1100 or 1200GMT, while others supplied data averaged attwo, or in a few cases four, times per day. Inthis study no attempt was made to correct fordiurnal variations imposed by the fixed observa-tion times of the various stations ; hence diurnalvariability must be added to the sources of pos-sible error in the maps. It is reasonable to

assume that the actual (unknown) standarderror of the' maps is not independent of the truevalue of monthly mean aA desired, but that it

is more likely a certain percentage of the truevalue. Since the overall correlation between thecontoured and true values is probably quitehigh, it is plausible to estimate the standarderror of the maps as a percentage of the con-toured values. On figure 8 it is found that anallowance of ± 10 percent from the perfect-agreement line (in the vertical) will excludeonly 23 percent of the 360 data points (40 abovethe limits, and 44 below the limits) ; for a nor-mal distribution, 32.5 percent of the pointsshould be excluded by the standard error limits.

Therefore, allowing for some added error fromdiurnal variability, it seems reasonable to esti-

mate the overall standard error of the maps ofaN as approximately 10 percent of the con-toured values.

This is equivalent to assuming an error model,

= '^,=,= + -^E^ + (9)

where the terms have the same meaning asthose in (7) and (8), with "^5- s <'r- (possibly

as low as V2 -^r^) in (8), and where V is the

variance assignable to diurnal variations in aA''.

The value of "t should be on the order of 2 to 4A'-units, which is an estimate based on inspec-

tion of the CCIR maps [CCIR, 1965].

There is doubtless some bias error in the aNmaps ; the discussion given for bias errors in

the N {z) maps is mostly applicable to the aAmaps. Here the bias due to the radiosonde is

relatively larger, because of the differencing

used to obtain aA^ values. This mean bias error

may be as high as 1 percent of the aA^ values,

but data adequate for checking on this possi-

bility are not available.


7.3. Accuracy of Gradient MapsIt is very difficult to assess the probable errors

in the maps of the different kinds of initial

gradients given in appendix C. The primaryreason for this is that no data are available ex-cept those used to prepare the maps. It is likely

that the most serious source of discrepancieswill arise because of the admixture of data taken

at widely differing local times. In line with theresults of the A^V error analysis, an overallerror of about 15 percent of the contoured val-ues seems reasonable, but may be higher orlower, depending on the area being considered.The maps in appendix C are probably best suit-

ed for the depiction of climatic tendencies ofsubrefraction and superrefraction.

8. Conclusions

It seems clear that the most significant con- important as obtaining larger samples. Theelusion which can be drawn from this study effects of such an analysis on the results given(pertaining to future requirements) is that in this atlas would probably be slight in the casecareful selection of data by local time of obser- of the Nj[z) maps, somewhat larger in the casevation, and the segregation of these data into of the AN maps, and might well have a profoundtypes, e.g., nighttime and midafternoon, prior effect on the ground-based gradient maps ofto analysis or mapping, is probably equally as appendix C.

25

9. References

Air Ministry, Meteorological Office (1961), Tables of

Temperature, Relative Humidity and Precipitation forthe World, vols. I-VI (Her Majesty's Stationery Office,

London).Baynton, H. W., H. L. Hamilton, Jr., P. E. Sherr, and

J. J. B. Worth (1965), Radio climatology of a tropical

rain forest, J. Geophys. Res. 70, No. 2, 504-508.Bean, B. R. (1954), Prolonged space-wave fadeouts in

1046 Mc observed in Cheyenne Mountain propagationprogram, Proc. IRE 42, No. 5, 848-853.

Bean, B. R. (1959), Climatology of ground-based radioducts, J. Res. NBS 63D (Radio Prop.), No. 1, 29-34.

Bean, B. R. (1961), Concerning the bi-exponential natureof tropospheric radio refractive index, Beitr. PhysikAtmosphiire 3-4, Nos. 1/2, 81-91.

Bean, B. R. (1962), The radio refractive index of air,

Proc. IRE 50, No. 3, 260-273.Bean, B. R., and B. A. Cahoon (1957), A note on the

climatic variation of absolute humidity. Bull. Am.Meteorol. Soc. 38, No. 7, 395-398.

Bean, B. R., and B. A. Cahoon (1961a), Limitations ofradiosonde punch-card records for radio-meteorologi-cal studies, J. Geophys. Res. 66, No. 1, 328-331.

Bean, B. R., and B. A. Cahoon (1961b), Correlation ofmonthly median transmission loss and refractive in-

dex profile characteristics, J. Res. NBS 65D (RadioProp.), No. 1, 67-74.

Bean, B. R., and E. J. Dutton (1961), Concerning radio-

sondes, lag constants, and refractive index profiles,

J. Geophys. Res. 66, No. 11, 3717-3722.Bean, B. R., and F. M. Meaney (1955), Some applications

of the monthly median refractivity gradient in tropo-spheric propagation, Proc. IRE 43, No. 10, 1419-1431.

Bean, B. R., and G. D. Thayer (1959), On models of theatmospheric refractive index, Proc. IRE 47, No. 5,

740-755.Bean, B. R., G. D. Thayer, and B. A. Cahoon (1960a),Methods of predicting the atmospheric bending of

radio rays, J. Res. NBS 64D (Radio Prop.), No. 5,

487-492.Bean, B. R., J. D. Horn, and A. M. Ozanich, Jr. (1960b),

Climatic charts and data of the radio refractive indexfor the United States and the world, NBS MonographNo. 22.

Behn, R. C, and R. A. Duflfee (1965), The structure ofthe atmosphere in and above tropical forests, Rept.No. BAT-171-8, Battelle Memorial Institute, Colum-bus, Ohio.

Bunker, A. F. (1953), On the determination of moisturegradients from radiosonde records. Bull. Am. Mete-orol. Soc. 34, 406-409.

CCIR (International Radio Consultative Committee)(1963), Influence of the atmosphere on wave propa-gation, Rept. 233, Documents of the 10th PlenaryAssembly, vol. 2 (Geneva).

CCIR (International Radio Consultative Committee)(1965), Propagation over the surface of the earth andthrough the non-ionized regions of the atmosphere,Rept. G.l.d(V), Conclusions of the interim meetingsof Study Group V (Geneva).

Dodd, A. V. (1965), Dew point distribution in the con-tiguous United States, Monthly Weather Rev. 93,No. 2, 11.3-122.

Dutton, E. J., and B. R. Bean (1965), The bi-exponentialnature of tropospheric gaseous absorption of radiowaves. Radio Sci. J. Res. NBS 69D, No. 6, 885-892.

du Castel, F. (1961), Propagation Tropospherique et

Faisceaux Hertziens Transhorizon, 140-141. (EditionsChiron, Paris.)

Hutchings, J. W. (1961), Water vapor transfer over theAustralian continent, J. Meteorol. 18, 615-634.

Jeske, H. (1964), Transhorizon-transmission and heightgain measurements above the sea with waves in therange of 1.8 cm to 187 cm under special considerationof meteorological influences, Proc. 1964 World Conf.on Radio Meteorology, Am. Meteorol. Soc, Boston,Mass. 458-463.

Kantor, A. J., and A. E. Cole (1965), Monthly atmos-pheric structure, surface to 80 km, J. Appl. Meteorol.4, No. 2, 228-237.

Kerr, D. E. (1951), Propagation of Short Radio Waves,MIT Radiation Lab. Series, vol. 13. (McGraw-HillBook Co., Inc., New York, N. Y.).

Knoll, D. W. (1941), Climatology Asiatic Station, Hy-drographic Office, U. S. Navy, Washington, D. C.

List, R. J. (1958), Smithsonian Meterological Tables,204. (Smithsonian Inst., Washington, D. C).

Michaelis, J., and E. Gossard (1958), Distribution of

refractive layers over the North Pacific and Arctic,

NEL Rept. No. 841, U. S. Navy Electronics Lab., SanDiego, Calif.

Misme, P., B. R. Bean, and G. D. Thayer (1960), Modelsof the atmospheric radio refractive index, Proc. IRE48, No. 8, 1498-1501.

Misme, P. (1964), A meteorological parameter for radio-climatological purposes. Radio Sci. J. Res. NBS 6SD,No. 7, 851-855.

Reitan, C. H. (1963), Surface dew point and watervapor aloft, J. Appl. Meteorol. 2, No. 6, 776-779.

Rydgren, B. (1963), Proposal for a Swedish radio stand-ard atmosphere. Rapport A518, Forsvarets, Forsk-ningsanstalt, Stockholm.

Saxton, J. A. (1951), Propagation of metre waves be-yond the normal horizon, Proc. Inst. Elec. Engrs.(London) 98, Pt. Ill, 360-369.

Serra, A. (1955), Atlas Climatologico do Brasil, vol. 1.

(Conselho Nacional de Geografia e Service de Meteor-ologia, Rio de Janeiro.)

Smith, E. K., and S. Weintraub (1953), The constants in

the equation for atmospheric refractive index at radiofrequencies, Proc. IRE 41, 1035-1037.

Smith, J. W. (1963), The vertical temperature distribu-tion and the layer of minimum temperature, J. Appl.Meteorol. 2, No. 5, 655-667.

Smith, 0. E., W. M. McMurray, and H. L. Crutcher(1963), Cross sections of temperature, pressure, anddensity near the 80th meridian west. National Aero-nautics and Space Administration, Washington, D. C.

Thompson, B. W. (1965), The Climate of Africa (OxfordUniversity Press, Nairobi).

Trewartha, G. T. (1961), The Earth's Problem Climates(Univ. of Wisconsin Press, Madison, Wise).

Tunnell, G. A. (1964), Periodic and random fluctuationsof the wind at Aden, Meteorol. Mag. 93, No. 1100,70-82.

UNESCO (1958), Arid Zone Research X, Climatology,Reviews of Research, 159 (Imprimerie Firmin-Didot,Paris).

U. S. Navy, Chief of Naval Operations (1955-1959),Marine Climatic Atlas of the World, vols. 1-5, NAV-AER 50-1C-528 through 50-1C-532, U. S. Govt. Print-ing Office, Washington, D. C.

26

REFERENCES 27

U. S. Weather Bureau (1964), Manual of Radiosonde Wagner, N. K. (1961), The effect of the time constant of

Observations, Circular P, 7th ed., U. S. Govt. P^rinting radiosonde sensors on the measurement of tempera-

Office, Washington, D. C. ture and humidity discontinuities in the atmosphere,

Wagner, N. K. (I960), An analysis of radiosonde effects Bull. Am. Meteorol. Soc. 42, No. 5, 317-321.

on the measured frequency of occurrence of ducting Willett, H. C. (1944), Descriptive Meteorology (Aca-

layers, J. Geophys. Res. 65, 2077-2085. demic Press, Inc., New York, N. Y.).

10. Appendix A. World Maps of N{z) Parameters

Data from the weather stations listed alphabetically in table A-1 were used to prepare

the maps in this appendix. Each station is preceded by a number to identify its location

on figure A-1 and followed by a listing of surface refractivity values at the 1, 5, 50, 95, and

99 percent cumulative distribution levels for the 4 months of February, May, August, and

November.The N{z) parameters (all referenced to sea level) which are necessary to calculate N

at any altitude, z, in kilometers, are Do, Wo, H„ H., i/i„, and Zt. These are given in figures

A-2 through A-25. The Zt chart for any particular month will determine which of the dry-

term curves will be used. If the desired altitude (above sea level) of N (z) is below the Zt

value at the specified location, use the tropospheric equation

N (z) = Do exp{~^ j

+ Wo exp{"^ (

(A-1)

If the desired altitude is above the Zt value, use

N iz) = Do exp [--§-- ^-^ } + Wo exp{- ^ } . (A-2)

All three scale heights are required for equation (A-2) , whereas only two, H^ and Hu,,

appear in the tropospheric equation. If the surface altitude of the location is greater than

1 km, it is suggested that the "standard atmosphere" value of 3 km be substituted for Hu,

(see sec. 3.3).

To illustrate the step-by-step procedure for determining refractivity from the N {z)

parameters, the following example (assuming heights of 2 km and 20 km above the surface

at a location 200 m above sea level, at latitude 15°N and longitude 0°, in August) is given

:

(a) Refractivity at 2 km above the surface

:

(1) At the assumed location, interpolate linearly between contours on figures A-19

to obtain Zt (13.8 km) to see whether the altitude above sea level, z (2.2 km), is above or

below the Zt value. It is below, so equation (A-1) should be used.

(2) The map values at 15 °N and 0° of the parameters needed to calculate (A-1)

are:

Do = 267.5 N-units (fig. A-14)

W^o= 105.0 iV-units (fig. A-15)

H, = 9.35 km (fig. A-16)

Hro = 2.19 km (fig. A-18)

(3) If these values are substituted in (A-1), N (z) is found to be 249.9 iV-units at

2 km above the surface. (Probable errors due to contouring and data restrictions would

suggest the use of only three significant figures, i.e., 250 iV-units.)

(b) Refractivity at 20 km above surface:

(1) Check to see whether the assumed altitude (2 = 20.2 km above sea level) is

above or below the Zt value. Since it is above, (A-2) should be used.

(2) All the parameters are needed for this calculation. In addition to the four

values listed in calculation (a) above, these are required:

Ho= 5.90 km (fig. A-17)

Zt =13.8 km (fig. A-19)

29


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180 150 90 60 30 60 90 120 150 180

ISO 150 120 90 60 30 60 90 150 180

Figure A-1. Location of N(z) data stations.

(3) If these values are substituted in (A-2), N (z) is found to be 20.7 iV-units at

20 km above the surface.

Figures A-26 through A-29 are seasonal maps of the standard prediction error of

the exponential fits to the mean wet-term profiles used in the N (z) parameter maps. Anrms error in the wet term of more than 5 A'-units was considered to be a reasonable

limiting criterion for locations where the N (z) model should be used with caution, if at

all. Figure A-30 delineates these areas ; the cross-hatched areas indicate that the error

was in excess of 5 A^-units for 2 or more of the seasonal months (February, May, August,

and November) and the single-hatching depicts areas where only 1 of the 4 monthsshowed such large errors. Further discussion of the uncertainty in these areas can be

found in section 3.4.

APPENDIX A 33

180 150 90 60 30 30 60 90 120 150 180

Figure A-2. Mean sea-level dry term, Do: February.

120 90 60 30 60 90 150 180

Figure A-3. Mean sea-level wel term. Wo: February.


180 150 120 90 60 30 30 60 90 120 15080

ISO 150 120 90 60 30 30 50 90 120 150

FlGUEE A-4. Dry-term tropospheric scale height in km. Hi: February.

180 15080

30 60 150 180

n80

ISO 150 120 90 60 30 30 90 120 150 ISO

Figure A-5. Dry-term xtralOi<pheric scale height in km, Hj: February.

APPENDIX A 35

Figure A-6. Wet-term scale height in km, H^-: February.

150 ISO

Figure A-7. Mean density tropopause altitude in km, Zt: February.


180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 ISO

Figure A-8. Mean sea-level dry term, D„: May.

ISO 150 30 30 60 90 120 150 ISO

-60

70ISO 150

J_ —^7030 60 90 120 150 18090 60 30

Figure A-9. Mean sea-level wet term, Wu: May.

APPENDIX A 37

180 150 90 50

180 150 120 90 60 30 30 60 90 120 150 ISO

Figure A-10. Dry-term tropospheric scale height in km. Hi: May.

ISO 150 90 120 150 180

Figure A-11. Dry-term stratospheric scale height in km, H2: May.


180 150 120 90 60 30 30 60 90 120 150 BO

180 150 120 90 60 30 30 60 90 120 150 180

Figure A-12. Wet-term scale height in km, H„: May.

180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure A-13. Mean density tropopause altitude in km, Zt: May.

APPENDIX A 39

180 150 90 60 30 60

180 150 120 90 60 30 60 90 150 180

Figure A-14. Mean sea-level dry term. Do: August.

ISO 150801

180 150 120 90 60 30 60 90 120 150

Figure A-15. Mean sea-level wet term, Wo: August.


180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure A-16. Dry-term tropospheric scale height in km, Hi: Augiwt.

Figure A-17. Dry-term stratospheric scale height in km. Ho: August.

APPENDIX A 41

180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure A-18. Wet-term scale height in km, H„: August.

180 15080

180 150 120 90 60 30 30 60 90 120 150 180

Figure A-19. Mean density tropopause altitude in km, zc August.


18080

180 150 120 90 60 30 30 90 120 150 180

Figure A-20. Mean sea-level dry term, DqI November.

Figure A-21. Mean sea-level wet term, Wo". November.

APPENDIX A 43

180 150 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 90 120 150 180

Figure A-22. Dry-term tropospheric scale height in km. Hi: November.

180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150

Figure A-23. Dry-term stratospheric scale height in km, H2: November.


60 90

Figure A-24. Wel-lerm scale height in km, H„-: Nooember.

Figure A-25. Mean density tropopause altitude in km, zc. November.

APPENDIX A 45

180 15080|

150 120

Figure A-2G. Standard prediction error of the exponential fit to the mean wet-term profile: February.

ISO 150 120 90 60 90 120 150

Figure A-27. Standard prediction error of the exponential fit to the mean wet-term profile: May.


Figure A-28. Standard prediction error of the exponential fit to the mean wet-term profile: Aug^tst.

180 150 120 90 30 60 90 120 150 BO

180 150 120 90 60 30 30 60 90 150 180

Figure A-29. Standard prediction error of the exponential fit to the mean wet-term profile: November.

APPENDIX A 47

150 120

180 150 60 90 150 ISO

Figure A-30. Areas of doubtful applicability of three-part exponential model o/ N(z) for z < 6 km.

11. Appendix B. World Maps of aN.

The weather stations from which data were obtained for this study are shown in

figure B-1. Their locations, elevations and the 5-year mean surface refractivity for each

month of the year are alphabetically listed in table B-1.

The monthly A^V values between the surface and 1 km above the surface are pre-

sented in figures B-2 through B-13. If the AiV at a specific location is desired for a cer-

tain month and year for which a monthly mean surface refractivity value, Ns, is avail-

able, the following relationships may be used

:

SiV = b {Ws- K) + In, (B-1)

where

Ns = A'o exp -oK^'

;

z — elevation above sea level in km.

World maps of A'o (the yearly sea-level value of refractivity) , b (the slope of the

regression line (B-1) ),and aA^ (the mean annual value of the refractivity difference be-

tween surface and 1 km) are presented in figures B-14 through B-16.

If the aA^ value were required at a station with an elevation of 300 m and a location

of 30 °N and 30 °E, here is the procedure which would be used. Available surface wea-

ther reports indicate that the mean Ns was 314 for a recent month for which a value of

aN is needed. Therefore, at the assumed location, these values are interpolated linearly

from the figures

:

Nl = 320 (fig. B-14)

A^ = 48 A' -units (fig. B-1 5)

b = 0.60 (fig. B-16)

.^= 320 exp-°-^'°-^' = 311

Using the value of 314 for Ns, AN is found to be 50 A'-units.

In some areas of the world (e.g., where the assumption of an exponential distribution

of the wet term is largely invalid ; see sec. 3.4) , the use of the regression method to predict

aA^ has definite limitations. To delineate these locations, figures B-17, B-18, B-19, and

B-20 are presented. The first two figures are world maps of the correlation coefficient and

the standard error of estimate of the regression line of aA' versus Ns for the 60 months of

station data, and figure B-19 gives the percentage of this standard error to the aN value.

Areas with correlation coefficients < 0.5 (fig. B-17), standard errors > 5 A^-units (fig.

B-18), and standard errors > 12 percent of aA'^ (fig. B-19) are shaded, but the use of

equation (B-1) for any location in these shaded areas may still be valid if:

(a) a low correlation coeflScient occurs with a small standard eiTor (typical of sta-

tions with a small seasonal range of variability in both A's and aA') , or

(b) a large error is found with a good correlation (typical of stations with distinct

wet-dry seasons)

.

However, if the coefficient is less than 0.7 (reducing the variance of aN to —' 50 per-

cent) and the standard error is greater than 10 percent of aA^ (as discussed in sec. 7), it

would be reasonable to assume that the yearly dependence of aA^ upon Ns is not sufficient to

justify the regression prediction method. Areas represented by these criteria are shaded

in figure B-20.

48

APPENDIX B 49

Table B-1. Mean surface refractivity.

station

Abidjan, Ivory CoastAdelaide, AustraliaAden, ArabiaAlbrook (Balboa), Panama C.ZAlbuquerque, N. Mex

Aldan, U.S.S.R.,

'.

Alert, Northwest TerritoriesAlexander Bay, South AfricaAlger /Maison, AlgeriaAlice Springs, Australia

Allahabad, IndiaAlma Ata, U.S.S.RAmundsen-Scott, AntarcticaAnadyr, U.S.S.RAnchorage, Alaska

Ankara, TurkeyAntofagasta, ChileAoulef , AlgeriaArgentia, NewfoundlandArkhangelsk, U.S.S.R

Ashkabad, U.S.S.RAswan, United Arab RepublicAthens, GaAthinai, GreeceAuckland, New Zealand

Bahia Blanca, ArgentinaBahrain IslandBaker Lake, Northwest Territories. .

Bangkok, ThailandBangui, Central African Republic. . . .

Barrow, AlaskaBeer Ya Aqov, IsraelB-Elan, U.S.S.RBeni Abbes /Colomb, AlgeriaBenina, Libya

Beograd, YugoslaviaBismarck, N. DakBjornoya IslandBlagoveshchensk, U.S.S.RBloemfontein, South Africa

Boise, IdahoBombay, IndiaBordeaux, FranceBrest, FranceBrisbane, Australia

Broken Hill, ZambiaBrownsville, TexBruxelles, BelgiumBukhta Tikhaya, U.S.S.RBukhta Tiksi, U.S.S.R

Byrd Station, AntarcticaCairo, United Arab RepublicCalcutta, IndiaCamaguey, CubaCanton Island

Cape Hatteras, N. CCaribou, MaineCharleville, AustraliaChatham IslandChiangmai, Thailand

Chita, U.S.S.RChristchurch, New ZealandClark Field, the PhilippinesCloncurry, AustraliaCocos Island

Columbia, MoCoppermine, Northwest Territories. .

Coral Harbour, Northwest TerritoriesCordoba, ArgentinaCuracao Island

Dakar, SenegalDar Es Salaam, TanzaniaDarwin, AustraliaDenver, ColoD.F. Malan (Capetown),South Africa

Dijarbakir, TurkeyDjakarta, IndonesiaDodge City, KansDouala, CameroonDurban, South Africa

Elevation(meters)

151149

1620

680622228

546

98851

2SOD6240

9021222901713

23019624610749

7229

16385

44923

498125

13950614

1371422

871114810341

12066

10068

1500686

1223

319129949

313

6718

170188

5

2399

5947916

5827

1625

49

6528

7911314

Latitude

05 15N34 56S12 SON08 58N35 03N

58 37N82 30N28 34S36 43N23 48S

26 27N43 14N90 OOS64 47N61 ION

39 67N23 2KS26 5SN47 18N64 35N

37 58N23 58N33 I57N37 5NN36 51S

38 44S26 16N64 18N13 44N04 23N

71 18N32 OON46 57N30 08N32 06N

44 48N46 46N74 31N50 16N29 07S

43 34NIS 54N44 51N48 27N27 28S

14 27S25 55N50 48NSO 19N71 35N

80 OOS30 OSN22 39N21 25N02 46S

35 16N46 52N26 2.5S

45 5SS18 47N

52 OSN43 32S15 OXN20 40S12 OSS

38 58N67 49N64 12N31 19S12 UN14 44N06 52S12 26S39 46N

33 S5S

37 55N06 lis37 46N04 OIN29 58S

Longitude

03 56W138 35E45 OlE79 33W106 37W

125 22E62 20W16 32E03 14E133 53E

81 44E76 S6E00 00

177 34E149 saw

32 53E70 26W01 05E54 OOW40 30E

58 20E32 47E83 19W23 43E174 46E

62 IIWSO 37E96 OOW100 30E18 34E

156 47W34 54E142 43E02 low20 16E

20 2SE100 4SW19 OlE

127 30E26 HE116 13W72 49E00 42W04 25W153 02E

28 2SE97 2SW04 21E52 48E

128 55E

120 OOW31 24E88 27E77 52W171 43W

75 33W68 OIW

146 17E176 33

W

98 59E

113 29E172 37E120 35E140 30E96 53E

92 22W115 15W83 22W64 13W68 S9W

17 30W39 16E130 52E104 53W

18 36E

40 12E106 50E99 58W09 43E30 57E

Jan.

383316365366254

297326342326283

327284221314307

284338294311312

307299308316339

320338329366348

323324312294323

310296310318283

284347320319351

319337314326332

253314337351374

319307325330338

300334345338373

305327324328372

342376380251

337

293*382285382365

Feb.

3893213643602S1

296327341323287

312283229317307

283341288310312

305287308314345

323339333377347

325322312289322

311296310311284

284352323316357

322344313320327

257312338353372

323305335339332

294335344339380

305329.324

331368

342376382249

341

292383286382367

Ma

389321371365248

289330340327288

303285243319305

283337283310311

305280312316341

328342326385359

325323311283319

308294310304288

279362322318351

315346315321324

259313346357377

324303329336336

287337345333372

306328322332*372

348382387250

337

293382"

287383365

Apr.

387321380368245

284321336329290

291287246321306

284333280313311

311280321317339

320348316393362

315327311275324

312289312299277

280371323321343

309359317316317

261313366363381

337305324330349

281334351311378

312318312321*376

351379372249

333

297383291382356

May

387322385375253

283312330337290

299293246310308

290330279320315

305278335325339

319361312393361

313332314274324

324296315304270

28638033032632S

293366324313312

267318381370377

349310316327368

279326362310379

327313310318380

358370359257

333

298382306382345

June

382323386375251

292313327346287

338294245312318

292327277323324

305276352325331

315365314391363

316339326276338

331306316325264

285386337332323

285377333312316

266329389377377

364325314323371

297324367305376

343318313305380

367362338259

330

289376316380333

July

377322379372267

305313326364289

385299246325324

290325274335331

303285360326327

316381318390361

318351339269350

335313320336265

283389343338319

282375338314319*

263341394378379

376332309322376

310323366307374

353318317303382

371359344264

329

289367*322379

Aug,

373319378381274

304315325365281

391295247321324

286327278339333

306288361323329

312386320391362

319355341273349

331308320339259

281388342337320

278377337315320

267347395379376

374330302324377

308323369299372

352322319298384

377367338269

327

282366318379336

Sept.

380318376382259

293310328354282

379286244313316

287326287331324

300291347326328

317382314393361

315347331284343

320299317318264

278384343336325

279370334313314

262338394379373

366323303322376

293324366296372

330316314300384

381361360256

328

276368308380343

Oct.

384313372379256

287313329344284

353285236308306

288328291320316

306294326327326

321370312390363

311337317291339

318293312306267

2833753.32

331326

282357328311311

259334379376373

347313304327369

288320363300370

316312309314382

379366373252

330

284376294379349

Nov.

387313366378251

291320334333285

325285226311307

286333294318314

305299316329329

320353317374362

318324312294331

317294311307279

285364324323337

305345321314322

254331346366373

332308303329358

291321357308369

306318313318379

360372374252

330

297380285381357

APPENDIX B 51


Table B-1. (Continued)

Station

APPENDIX B 53

60 30 60 90 150 ISO

Figure B-2. Monthly mean AN: January.

60 90 150 ISO

Figure B-3. Monthly mean AN: February.


180 150 120 90 60 30 30 60 90 150 180

Figure B-4. Monthly mean AN: March.

180801—

ISO 150 60 90 120 150

Figure B-5. Monthly mean SN: April.

APPENDIX B 55

Figure B-6. Monthly mean AN: May.

180 150 90 120 150 180

Figure B-7. Monthly mean AN: June.


180 150 120 90

180 150 90 60 30 30 60 90 120 150 180

Figure B-8. Monthly mean SN: July.

50 BO80

180 150 120 90 60 30 30 60 90 120 150 ISO

Figure B-9. Monthly mean AN: August.

APPENDIX B 57

180 150 120 90 60 30 60 90 150 180

Figure B-10. Monthly mean AN: September.

ISO 150 90 60

Figure B-11. Monthly mean AN: October.


180 150 90 60 30 30 60 90 120 150 ISO

180 150 120 90 60 30 90 120 150 180

Figure B-12. Monthly mean AN: November.

90 120 150 180

ISO 150 120 90 60 30 90 120 150 180

Figure B-13. Monthly mean AN: December.

APPENDIX B 59

180 150 120 90 60 30 60 90 120 150 ISO

Figure B-14. Annual mean of sea-level refracUviiy, No.

ISO 150 120 90 60 30 60 90 120 150 180

ISO 150 120 90 60 30 60 90 120 150 180

Figure B-15. Annual mean of refractivity gradient between surface and 1 km, AN.


180 150 120 90 60 30 30 60 90 120 150 180

Figure B-16. Slope of regression line of AN versus Ns, b.

18080

30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure B-17. Correlation coefficient of AN versus Ns.

APPENDIX B 61

Figure B-18. Standard prediction error of the regression line of AN versus N,.

Figure B-19. Standard prediction error of the regression line of AN versus Ns as a percent of AN.


Figure B-20. Areas of doubtful applicability of using Ns to predict AN.

12. Appendix C. World Maps and Cumulative Distribution Charts

of Gradients of Ground-Based Atmospheric Layers

Initial gradient data, obtained (see sec. 5) for 99 of the 112 stations listed in table

A-1, are presented in groups of seasonal world maps which illustrate various aspects of

the percentage distribution of gradients in ground-based layers. The specific map groups

are given below.

Figures C-1 through C-4: Percent of time gradient ^ (iV/km).

Figures C-5 through C-12 : Gradient exceeded 10 and 2 percent of the time for 100-m

layer.

Figures C-13 through C-20 : Percent of time gradient ^ -100 (N/km) and percent

of superrefractive layers > 100 m thick.

Figures C-21 through C-28: Percent of time gradient ^ -157 (iV/km) and percent

of ducting layers > 100 m thick.

Figures C-29 through C-40: Percentage of time trapping frequency is below 3000

Mc/s, below 1000 Mc/s, and below 300 Mc/s.

Figures C-41 through C-56: Lapse rate of refractivity (N/km) exceeded 25, 10, 5,

and 2 percent of the time for 100-m layer.

Cumulative probability distribution charts were prepared for 22 climatically diverse

locations for the months of February, May, August, and November (figs. C-57 through

C-78) . The alphabetical listing of these stations in table C-1 includes seasonal median andminimum trapping frequency values when these were available. Distribution data for twoseparate times of day at Aden and Nicosia are shown in figures C-57 and C-71. The nega-

tive gradient of 50 A^-units/km, which is generally considered to be a good normal value

for ground-based layers, has been indicated on each of the distributions by a dashed line to

provide a common reference for the vertical scale. The circled value on the distribution

line represents the mean ground-based gradient (of any layer thickness greater than20 m) for each month.

63


60 -60

70 ^ —170180180 150 120 90 60 30 30 60 90 120 150

Figure C-1. Percent of time gradient > (N/km): February.

180 150 120 90 60 30 90 120 150 180

Figure C-2. Percent of time gradient > (N/tm): May.

APPENDIX C 65

180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-3. Percent of time gradient > CH/km): August.

90 60

180 150 120 90 60 30 60 90 120 150 ISO

Figure C-4. Percent of time gradient > (N/fcm); November.


leo 150 120 90 150 eo

180 150 90 60 60 90 120 150

Figure C-5. Gradient {N 'km) exceeded 10 percent of the time for 100-m layer: February.

ISO 150

180 150 120 90 60 30 30 60 90 120 150

Figure C-6. Gradient (N/km) exceeded 2 percent of the time for 100-m layer: February.

APPENDIX C 67

180 150 120 90 60 30 30 60 90 120 150

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-7. Gradient (N /km) exceeded 10 percent of the time for 100-m layer: May.

180 150 120 90 60 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-8. Gradient (N/km) exceeded 2 percent of the time for 1 00-m layer: May.


180 150 120 90 30 60 90 120

180 150

Figure C-9. Gradient I'N.'km) exceeded 10 percent of the time for 100-m layer: August.

Figure C-10. Gradient (N/km) exceeded 2 percent of the time for 100-m layer: August.

APPENDIX C 69

ISO 150 120 90 60 30 60 90 120 150 ISO

ISO 150 120 90 60 30 30 60 90 120 150 ISO

Figure C-11. Gradient (N/fcm) exceeded 10 percent of the time for 100-m layer: November.

180 150 120 90 60 30 30 60 90 120 150

ISO 150 120 90 60 30 30 60 90 120 150 180

Figure C-12. Gradient (N/fcm) exceeded 2 percent of the time for 100-m layer: November.


Figure C-13. Percent of time gradient < —100 (N/fcmi; February.

Figure C-14. Percent of superrefractive layers thicker than 100 m: February.

APPENDIX C 71

180 150 120 90 60 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 ISO

Figure C-15. Percent of time gradient < —100 (N/km): May.

Figure C-16. Percent of superrefraciive layers thicker than 100 m: May.


30 60 90 120 150 180

180 150 120 90 60 30 60 90

Figure C-17. Percent of lime gradient < —100 (N/fcm); August.

Figure C-18. Percent of superrefractive layers thicker than 100 m: August.

APPENDIX C 73

Figure C-19. Percent of time gradient < —100 iN/km): November.

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-20. Percent of superrefractive layers thicker than 100 m: November.


180 150801

90 60

60

70180 150

^ —^70120 90 60 30 30 60 90 120 150 ISO

Figure C-21. Percent of time gradient < —157 (N/fcm); February.

Figure C-22. Percent of ducting layers thicker than 100 m: February.

APPENDIX C 75

180 150 120 90 60 30 30 60 90 120 150 eo

60- 60

701180 150

i^ —170180120 90 60 30 30 60 90 120 150

Figure C-23. Percent of time gradient < —157 (N/fcm): Maij.

ISO 15080

60- 60

7070'180 !50 120 90 60 30 30 60 90 120 150 180

Figure C-24. Percent of ducting layers thicker than 100 m: May.


180 150 90 60 30 60 90 120 150 180

180 150 120 90 60 30 60 90 120 150

Figure C-25. Percent of time gradient < —157 CN/km): August.

180 150 120 90 30 60 90 120 150 BO

180 150 120 90 90 120 150 ISO

Figure C-26. Percent of ducting layers thicker than 100 m: August.

APPENDIX C 77

180 150 120 90 60 30 60 90 150 180

Figure C-27. Percent of lime gradient < —157 (N/fcm); November.

180 150 120 90 60 30 30 60 90 120 150 ISO

60 60

7070180 150 120 90 60 30 30 60 90 120 150

Figure C-28. Percent of ducting layers thicker than. 100 m: November.


Figure C-29. Percent of time trap-ping frequency < 3000 Mc/s: February.

180 150

180 150 120 90 60 30 30 60 90 120 150 ISO

Figure C-30. Percent of time trapping frequency < 1000 Mc,'s: February.

APPENDIX C 79

60-

A.70'180 150 120 90 60 30

7030 60 90 120 150 180

Figure C-31. Percent of time trapping frequency < 300 Mc/s: February.

180 150 120 30 60 90 120 150 80

60-

A.701ISO 150 120 90 60 30

JSL. 7030 60 120 150

Figure C-32. Percent of time trapping frequency < 3000 Mc/s: May.


180 150 30 30 60 90 120 150 BO—180

60

70180 150 120 90 60 30 30 60 90 120 150

-170

Figure C-33. Percent of lime trapping frequency < 101)0 Mc/s: May.

ISO 150 120 90 60 30 30 60 90 120 150 180

70l

180 150 120 90 60 30 30^70

60 90 120 150 180

Figure C-34. Percent of time trapping frequency < 300 Mc/s: May.

APPENDIX C 81

180 150 30 60 150 180

\

^80

60

iL701ISO 150 120 90 60 30 30 60 90 120 150

—170180

Figure C-35. Percent of lime trapping frequency < 3000 Mc/s: August.

180 150 120 90 60 30

60

701ISO 150 120 90 60 30 30

—17018060 90 120 150

Figure C-36. Percent of time trapping frequency < 1000 Mc/s: August.


70180 150 120

-30

-15

^0

-15

-30

-60

60 30—170

30 60 90 120 150 180

Figure C-37. Percent of time trapping frequency < 300 Mc/s: August.

Figure C-38. Percent of time trapping frequency < 3000 Mc/s: November.

APPENDIX C 83


180 150 120 30 60 90 120 150 180

60- 60

70^701180 150 120 90 60 30 180



180 150 90 60 30 30 60 90 120 150 180

Figure C-41. Lapse rate of refractivity (N/km) exceeded 25 percent of time for 100-m layer: February.

ISO 150

Figure C-42. Lapse rate of refractivity [^,'km\ exceeded 10 percent of time for 100-m layer: February.

APPENDIX C 85

Figure C-43. Lapse rate of refractivity (N/fcm) exceeded 5 percent of time for 100-m layer: February.

Figure C-44. Lapse rate of refractivity (N/fcmi exceeded 2 percent of time for 100-m layer: February.


60

70l

180 150 120 90 60 30 60 90 120 150 180

Figure C-45. Lapse rale of refraelivity (N/fcra) exceeded 25 percent of lime for 100-m layer: May.

ISO 150 90 60

70 70150 120 90 60 30 180

Figure C-46. Lapse rate of refraelivity (N/fcm) exceeded 10 percent of time for 100-m layer: May.

APPENDIX C 87

75-

70-

180 150 120 90 60 30 60 90 120 150

Figure C-47. Lapse rate of refractivity (N/fcm) exceeded 5 percent of time for 100-m layer: May.

FiGXiRE C-48. Lapse rate of refractivity (N/km) exceeded 2 percent of time for 100-m layer: May.


180 150 120 90 30 60

180 150 120 90 60 30 60 90 120 150

Figure C-49. Lapse rate of refractiviiy (N/fcm) exceeded 25 percent of time for 100-m layer: August.

Figure C-50. Lapse rate of refractiviiy (N/fcm) exceeded 10 percent of time for 100-m layer: Augjist.

APPENDIX C 89

180 150 120 90 60 30 30 60 90 120 150

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-51. Lapse rate of refractitnty (N/im) exceeded 5 percent of time for 100-m layer: August.

Figure C-52. Lapse rate of refractiviiy (N/km) exceeded 2 percent of time for 100-m layer: August.


ISO 150 120 90 60 30 30 60 90 120 150 180

Figure C-53. Lapse rate of refractivity (U/km) exceeded 25 percent of time for 100-m layer: November.

ISO 150 120 90 60 30 60 90 120 150 180

Figure C-54. Lapse rate of refraclivity (N/km) exceeded 10 percent of time for 100-m layer: November.

APPENDIX C 91

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-55. Lapse rate of refractivity (N/fcm) exceeded 5 percent of time for 100-m layer: November.

180 150 120 90 60 30 60 90 120 150 180

180 150 120 90 60 30 30 60 90 120 150 180

Figure C-56. Lapse rate of refractivity (N/km) exceeded 2 percent of lime for 100-m layer: November.


Table C-1. Median and minimum trapping frequency (Mc/s) of ducting layers.

station

APPENDIX C 93

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APPENDIX C 95

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13. Appendix D. World Charts of Tropopause Heights

Five-year mean tropopause heights obtained in the process of computing N (z)

parameters for February, May, August, and November at the 112 stations listed in table

A-1 virere plotted and contoured. Maps of these heights, given in figures D-1 through D-4,

represent the average of all of the individual altitudes which marked the base of the first

layer which had a thickness of at least 2 km and a temperature lapse rate of less than

2°C/km (see sec. 6).

180 150 90 60

180 150 120 90 60 30 60 90 120 150

Figure D-1. Tropopause heights (km), based on temperature lapse rate: February.

117


180 150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30 30 60 120 150 ISO

Figure D-2. Tropopause heiglits ikm), based on temperature lapse rate: May.

180 150 120 90 60 30 30 60 90 120 150 180

Figure D-3. Tropopause heights (km), based on temperature lapse rate: August.

APPENDIX D 119

150 120 90 60 30 30 60 90 120 150 180

180 150 120 90 60 30

Figure D-4. Tropopause heights (km), based on temperature lapse rate: November.

14. Appendix E. Sample Listing of the Computer Output for

San Juan, P.R., and Amundsen-Scott, Antarctica

A sample listing of the complete computer output of the mean iV-profiles for February,

May, August, and November at a subtropical and an arctic station is given in the first

section of this appendix.

For instance, at station 11636 (San Juan, P. R.) in February (table E-1) , the heading

gives the number of pieces of data used to compute two types of tropopause height (based

on two types of temperature criteria) :

(a) the mean heights where the extreme minimum temperature occurred in 320 indi-

vidual profiles was 17.56 km ± a standard deviation of 0.65 km,

(b) the mean height of the bottom of the lowest atmospheric layer with a thickness

^ 2 km and a temperature gradient = —2°C/km in 307 temperature profiles was 16.44

km ± 0.96 km.

This February profile also gives refractivity information at 40 height levels ranging

from to 30 km. Following each height level is a listing of the values of total refractivity,

gradient, dry and wet terms, and their respective standard deviations at that height above

surface. For example, at 1 km, 383 radiosonde profiles were examined, and the refractivity

was found to be 306.7 with a standard deviation of 8.22 A'-units ; the gradient at that level

was — 47.66 N/km with a standard deviation of 17.38 N/km ; the dry term was 242.4 ±1.19 A^-units, and the wet term was 64.3 ±: 8.52 TV-units. The correlation coefficients for

the data fit, within various height ranges, of the wet term (W) and the tropospheric (D^)

and stratospheric {D2) dry terms to the line represented by a computed regression equation

are found at the bottom of each month's listing. In this example, for the dry term equation

(i^i), with a surface value of 271.9 and an exponential decay coefiicient of — 0.1088, the

correlation coefficient is 0.999 and the standard deviation is 3.01 N-units. (These figures

were based on 5 years of data from the surface to 15 km.)

At station 90001 (Amundsen-Scott, Antarctica) the wet-term value is so small at all

heights during the months studied that the regression equation from to 3 km becomes

meaningless. Because the South Polar region is not shown on the ground-based gradient

maps (figs. C-1 through C-56) , a complete computer listing for Amundsen-Scott is included

in this appendix. This also illustrates the form of the original station data which wereused to plot the various values needed for the gradient maps. All gradients are in A-units/

km and all frequencies are Mc/s. The "profiles skipped" represents the number of profiles

which had gradients > — 100 N/km.

120

APPENDIX E 121

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124 A WORLD ATLAS OF ATMOSPHERIC RADIO REPRACTIVITY

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APPENDIX E 125

Table E-3. Cumulative distribidion of ground-based gradients: Amundsen-Scott, Antarctica

(gradient followed by percentage level).


Table E-3. (Continued)

APPENDIX E 127



Table E-4. {Continued)

CUMULATIVE DISTRIBUTION OF SUPERREFRACTIVE LAYER THICKNESSES, STATION 90001

APPENDIX E 129


31 Profiles Skipped185 Profiles ReadNumber of Ducts 104Number of Superrefractive Layers 50

CUMULATIVE DISTRIBUTION OF DUCTING GRADIENTS, STATION 90001,


Table E-4. (Coutinued)

THICKNESS AND GRADIENT OF SUPERREFRACTIVE LAYERS OVER 300 METERS THICK