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Journal of Research of the National Bureau of Standards-D. Radio Propagation Vo!' 63D, No.2 , September-Odober 1959

Synoptic Study of the Vertical Distribution of the Radio Refractive Index I

B. R. Bean, L. P. Riggs, and J. D. Horn

(March 12, 1959 )

An ana lysis of the vert ical stru cture ?f an intense out break of co nt inental pola r a ir is p.resel~ted III term.s C?f the radIO refractIve Index of t he atmosphere . E mployed for t he first tllne IS a reduced mdex analogous to potent ial t emperature. The reduced valu e more clearly show:s .the refr act ive index stru cture t han t he classical methods used hereto fore. T.lu s newulHt IS a m easure of both atmospheric density a nd humidi ty and shows, on a single Cl OSS sectIOn, t he a n'mass stru cture and t he d ynamIC ml:\1ng of a ll' around th e fronta l interface.

I . Introduction

The problem of determining the verLical and hori­zon tal distribu Lion of th e index of refraction of the tropospherc for radiofrequencies has enga.ged th e attention of radi o meteorologists for th e past decade [1,2,3,4]2. Such information is vital to procedures and teclmiqu es for forecastin g th e occurrence of radio refractive-index profiles . The surface valu e and the ~radien t of th e refractive index arc impor tan t factors In the prediction of monthly median values of fi eld s~rength over communication links utilizing frequen­CleS from 50 to 50,000 Mc [5,6,7].

F or co:,,-venience, th e refractive index is give n in terms of Its scaled up valu e, N, commonly ca lled the refractivi ty: .

N =(n- 1) 106 •

N may be determined [8] from standard wraLh er observations by

where

N =( _1) 106= 77.G[ P + 48 IO e, RH] n 'J' T '

n = index of refraction of the atmosphere T= temperature in degrees K elvin, ' P = station pressure in millibars . ' es= satura tlOn vapor pressure, and

RH= relative humidity, in percen t.

2 . Background

A worldwide survey of N climatology [9] indica tes that the refractive index varies widely over the sur­face of the earth. If we take th e modern view that clima tology is a syn thesis of synop tic even ts th en ,~e may conclude that the frequency of occurrence of anmass types and fron tal passages play an importan t

1 T his work was su pported in part b y Task 31 of t he Navy Weather Research Facili ty, Naval Air Stat ion, Norfolk " a. .

, Figures in brackets indicate t he Ii'teratu re references a t t be cn r] of t b il paper.

role in determining the r efractive-index climate at any location .

l~eeen t stu~ies have shown that the N profile at a gIven I?CatlOll van es WI th synop tic pat tern [10] and that, If one redu ces N to sea level th e refractive index is a sensit ive indicator of largd-scale weather sys~ems ~ll ] when consider ed on a daily weather map baSIS. The presen t sLudy extends the work of refer­ence [I l l by .considering if the air mass proper ties assocIated vVlth a typIcal win te rtime ou tbreak: of polar air arc reflected in th e refractive-index s truc­ture. A sLorm . equence wi th strong contrasts of allm~ss prope ~-Ll es was chosrn for study under th e premIse th fl.L I [ the refractIve mdex failed to indicate the difJ'erences in airmass properties in thi case th en there Is lI Ltle hope of i Ls b eing effeetivr in situ fl.tions WI th less m.arked temperaLu re and humidi ty eon­trasLs.

B efo re proceeding one migh t inquire if th e par tic­ular case chosen for study was a reprcsenLative one or not. As a guide in this rcgard , idealized models (6gs. 1 and 2) of cold and warm fronts were con-

~ ~ oJ

0 :::> l-

S <{

COLD

-500 -400

WARM

-300 -zoo - 100

DISTANCE, km

LEGEND COLD FRONT ISOTHERM R H. ISOPLETH CU:XJO PATTERN --­PRECIP; PATTERN ~

AIR FLOW

100 200 300

FIGUR E 1. An idealized . cold front with associated tempemt1tre and humi lity pattems.

249

LEGEND WARM FRONT -­ISOTHERM R. H. ISOPLETH -------'~­CLOUD PATTERN-­PRECIP. PATTERN~ AIR FLOW

600 700 600 900

F I GUR E 2. An idealized warm front with associated tem perature and humidity pattems.

structed from generally accep ted concep ts of the polar fron t [12 ,13, 14]. Fro~ th.es~ mo~els, idealized N fi elds wer e constructed . fhlS IdealIzed N stru c­ture (figs. 3 and 4) is in agreem en t with tha t derived from a classic storm reported by Byers [1 3]. The most prominent feature of this idealized situa tion is th e laminar structure of th e N field reflec tmg a uniform decrease of N with height so pronounced that i t masks the airmass contrasts abou t the fron t which are th e main concern of this study. In the sections that follow we shall be concerned wi th the removal of th e normal N d ecrease with heigh t in order to more clearly see th e N changes associated wi th the storm under study.

3 . Height Dependence of N

It has long been recognized tha ~ th e l?re~sure te.I'm in N results in a steady decrease of N wIth mcre~smg heigh t . E arly attemp ts to compensate for this N decr ease used th e constan t gradien t of the effective ear th 's radius theory , 1/4a, where a is th e radius of the earth . As an illustration , the strong elevated layer

LEGEND COLD FRONT N ISOPLETH

] ~~----------------------ro,------------__ ~ W5 -...... o ;::> ISO

54 WARM ~ ~ __________ ~ ______ xo

COLD

-500 - 400 -300 -200 -100 300

DISTANCE, km

F I GURE 3. The N fi eld of an idealized cold front.

LEGEND WAR M FRONT N ISOPLET H

140

E 160 -'" ,5-

ISO W 0 ::J 200 ~ 4 I- WARM --' ~ 220

3

260 COLD

400 500 600 800 "'900

DISTAN CE. km

FIGURE 4. T he N field of an idealized wa1'1n /Tont.

< found during th e summer in Southern California ~vas studied in terms of a linearly correc ted expreSSlOl1, B , given by

B = N(h)+ 39,2h

where N(h) is t h e value of N at any h eight, h, in kilometers [1 5] . R ecen t studies of the average N structure of the atmosphere show tha t N tends to b e an exponen tial function of heigh t ra ther than th e linear function assumed by th e effec tive earth~s r adius theory, with the res u.1 t that the B umt approach overcorrects when h IS greater th an about 1 km. This is illustrated by figures 5 and 6 where the N data of figures 3 and 4 ar e r eplo tt ed in terms of B units. Note that this over correctlOn produces an N field that tends to incrcase with heigh t from 310 at th e surface to 360 at 5 Ian. If, however, on e presents th ese data in terms of an exponen tial function, A, of t he form

IO'~-----'-------------------------------'--,

W ___ ---360 - __

§5 - __ ............

~ -..250

<i 4L.-_ __ 340....--- ____

,L.-_-- 330 ---.~~

COLD L-__ - - 320

2 -

L---- 310

-SOD - 4 00

LEGEND COLD fRONT 8 ISOPLETH a=- N + kh k = 39.232 h= hi In km

360

350

I r320- _

300

FIGUUE 5. The ref ractive index structure in B units f0 1' an ideali zed cold fron t.

250

~

E -': w 0 ::l 5 -t: f--' «

330

380

370

360

350

340

WARM

LEGEND WARM FRONT B ISOPLETH S: N + kh k· 39.23"2 h = hi in km

320--_-1

F IGU R E 6. The rejmctive index Sb'uctU1'e in B units j or an idealized wann front.

A = N(h)+ 313[1- eA"}) { - 0.144h }],

as in figures 7 and 8, then i t is seen that the range of N values is now r edu ced to abou t 25 N units. Tho exponential decay coeffi cien t of 0.144 was determince! to correspond wi th th e average station value of N, 313 for the Uni ted States [16J. I t is signifieanL, however , that t ho usc of A uni ts produ ces a pa t tern similar to the airmass differences associated with th e fron tal zone. Note, in th e warm front case (fig. 8), that th o A values increase with heigh t until they reach a maximum associated wi th th e upglicling warm moist air overriding the fron tal surface. Tho r egion of maximum precipi tation 400 to 500 km ill advance of the front is shown as an area of high surface N. In th e eold-fron t case (fig. 7) th e classic push of warm a u' aloft by the encroaching cold air is

101.--r--r--'---'--'--~--r---r--''--'

.§ 6

W 0 -- ......... """ OJ 5 t: ':i « 4 325

-soo

LEGEND COLD FRONT A ISOPLETH A: N+ NoC I- exp(ch)] WHE RE No: 3j3

c=- .143859 h: ht In km

325

F IGURE 7. The refractive index 1Jatlern in A units f01' an ideali zed cold f ront.

251

eviden ced by the "dome" of high A values just b efore the fron t. S tratification in the cold air du e to subsidence-inversion effects , although impossible to detect in the N charts, is clearly seen by the use of the A charts.

A units were used in all subsequ en t analysis: in order to throw th e fron tal discontinuities and airmass differences in to sharp relief. To facilita te this tran s­formation , a Po tential R efractivity Chart (fig. 9)

7-

~ 6 -

w g 5 -1-

S "

100

LEGEND WARM FRONT A ISOPLETH A: N+NoCI-exP(ch)] WHERE No:: 313

C : -,143859 h : hlin km

325

315

sao

FIG UR E 8. The refract ive indox pal/ern i n A units f01' an idealized warm f ront.

FIGU RE 9. Potential rej1-activity chart with Tadiosonde data shown in A un'its.

A is obta incd by plot t ing N vcrsus a lt it ude and in terpolat ing (rom the lin es of consta nt potcntial l'cfructiviLy.

I __ J

was prepared for rapid conversion from N units to A units. This simplification eliminates the necess ty of using exponential tables for each individual al­culation of A and thus lends considerable ease to the preparation of charts of the new parameter.

Storm of February 18 to 21 , 1952

A large-scale outbreak of polar continental air which took place over the United States between the 18th and 21st of February 1952, was analyzed in terms of A units. Charts showing the structure of this outbreak of polar continental air have been prepared from the radiosonde measurements from stations located along a line normal to the front running from Glasgow, Mont. to Lake Charles, La. (fig. 10) . The height distributions of unit con­tours along this cross-section line were obtained at 12-hr intervals during the 4-day period. Examples are given (figs. 11 to 13) to represent the early, mature, and late stages of the outbreak. At the out­set of the period of observation, the A unit gradient was quite flat around the polar front. By 1500 Z on the 18th of February (fig. 11) the polar front was located midway between Glasgow and Dodge City. The contrast of the southward push of polar air and the northerly advection of tropical maritime air from the Gulf of .\i(exico into the developing warm sector of the polar-front wave is evidenced by the relatively large gradients in the neighborhood of Dodge City. The core of tropical maritime air has evidently not progressed far enough northward to displace the warm but dry air that had been over the great plains prior to the outbreak with the result that a region of low A values is found between the front and the tropical maritime air. Twen ty-four hours later (fig. 12) the core of tropical maritime air has become more extensive and now reaches to 3 km. A second cold front was reported on the daily weather map and the area of low A values is now confined between

SPACE CROSS SECTION IN A-UNITS 1500Z. FEBRUARY 18,1952 w ,,~'-~",-'~'-'-,,--7r'---,,-'''CT~

l5

O~~I -LI ~I-LI __ ~L-~ __ -L __ L-~~~~~LL~

o SOO \000

I DISTANCE ,km

GlASGOW OOOGE on

FIG URE 11. Early stage of the storm sequence.

SPACE CROSS SECTION IN A-UNITS 1500Z, FEBRUARY 19,1952

Q5

00 If-----~~--'--L----'---I - ' --L, o 500 1000 I 1500 2000 2300

I DISTANCE'l km I

GlASGOW OOOGE CITY LAKE CHARLES

FIGURE 12. Nlature stage of the stonn sequence.

--~ --- ----

FIGURE 10. Location chm·t of the stations furnishing radiosonde data for this study.

252

),

SPACE CROSS SECTION IN A-U NITS 15002 , FEBRUARY 20, 1952

~~~~~~~~~~'-~"-'-T""'7I7~r-rn if

w g I.S t-

S «

10

DISTANCE, km I

GlASGOW DODGE CITY LA CHARLES

FIG U RE 13. Late stage oj the stann sequence.

it and the main cold fronL. Finally, by the moming of February 20 (fig. 13), the fronL has passed to the south of Lake Charles and the polar air just behmd the front is characterized by relaLively low A values.

The use of space cro s sections does not always yield measurements at the most de irable P?ints along a frontal zone. Another method of arnvmg at the probable refractive-index structure ~bout t,he frontal interface is to present each succeSSIve radIO­sonde observation at a single location in terms of the distance between the front and the station. Thus, as the frontal system advances and p~sses over the statio n, one obtains a different perspectIve of the space cross section. 'rhis presentation is referred to as an epoch chart since the observations are normalized with r espect to the frolltal passage. S~ch a presen­tation is given on figures l4 and 15. FIgure 14 rep­resents a typical continental station located in the polar continental air tlu'o ughout the occurrence of

15

2n G E ~ 325

oX,

L

m~~~~~~~~~~~~~~~~~~ LEGE ND A ~p\'ETH

Q.5 COLO FRONT --

FIGURE 14. The A um:t pattern Jar Rapid City, S. Dak., ex­pressed as a Junction oj the distance /Tom the /Tont.

253

oLJ~-L~~~~~~~=C~~~~ ' K)OO ,500 0

DISTANCE FROM FRONT, Km

FIGUHE 15. The A 1mit pattern for Oklahoma City, Okla., expl'essed as a function of the distance /Tom the fl·ont.

Lhe storm. The essential feature here i the absence of deta il of A str ucture due to the presence of a uni­form airmass over this station. Compare this with the epoch char t for Oklahoma City (fig. 15) where the structure of the idealized model is clearly r eflected by the prefrontal A unit high ,. strong gr~dient across Lhe frontal zone, and the A untt low behmd the front. 'rhis rather fortuitous agreement is felt to be due to the sLrategic location of Olda~lom~ City with respect to the motion of the contrastmg aU'masses about the polar front. That is , thi~ epoch chart rep re ents a po int of confluence .of vIrtu.a~ly unmodified polar continental and tropIcal marItIme a ll'.

5. Conclusions

The major conclusion of the present study is. that an e)q)onential correcLion ~o the refract!ve-mdex heio'ht distribu tion allows aIrmass propertlOs to be mo~e clearly seen than is allowed by previoLls tech-niques. .,

By the use of this exponential ~olTect~on one may construct an idealized refractlve-mdex field abou t a fron tal transition zone that clearly shows the tem­perature and humidity contrasts of the different airmasses.

Further, when this technique is appli ed . to . the analysis of an actual storm , it does indeed hIghlight airmass differences.

6. References

[1] P . A. Sheppard, The structure a nd r efractive index ?f t he atmosphere, Rept. Conf. Meteorol. Factors RadIO Wave Propagation (1946) . .

[2] N. G. Gerso n, Va riations in the index of refractIOn of the atmosphere, Geo fisica Pura E Appli cata 13, 88 (1948) . . . . ' 0

[3] Andree P erlat, Meteorology and radlOeleetl'l clty, L nde E lec. 28, 44 (1948) .

[4] D. R. Hay, Airmass refractivity in central Canada, Can. J. Phys. 43, 12 (1958).

- -,

[5] K. A. Norton, P . L . Rice, and L. E. Vogler, The use .of angular distance in estimating transmission loss and fading range for propagat ion through a turbulent atmosphere over irregu lar terrain, Proc. IRE 43, 10 (1955).

[6] K. A. Norton, Point-to-point radio relaying via t he scatter mode of t ropospheric propagation , IRE Trans. CS- 4, 1 (1956).

[7] R . K Gray, The refractive in dex of the atmosphere as a factor in tropospheric propagation far beyond the hori­zon, IRE Nat!. Conv. Record Pt. 1,3 (1957) .

[8] E. K. Smith and S. Weintraub, The constants in the equation for atmospheric refractive index at radio frequencies, Proc. IRE 41, 1035 (1!)53).

[9] B. R. Bean and J . D . Horn , Radio refractive-index climate near the ground, J . Research N BS 63D, (1959) .

[10] '-Y. A. Arvola, R efractive index profi les and associated sy noptic patterns, Bull. Am. Meteorol. Soc. 38, 212 (1957).

[11] B. R. Bean and L. P. Riggs, On the synoptic variation of the radio refractive index, J. Research NBS 63D, (1959) .

[12] C. L. Godske, T. Bergeron , and R. C . Bundgaard , Dynamic meteorology a nd weather fo recasting, p . 526 (American Meteorological Society and Carnegie Insti­t ute of Washington , D .C., 1957) .

[13] H. B . Byers, General meteorology, p. 327 (McGraw-Hill Book Co ., Inc ., New York, N.Y. , 1944) .

[14] F. A. Berry, E. Bollay, and Norman F . Beers, Handbook of meteorology, p. 638 (McGraw-Hill Book Co ., Inc., New York, N.Y. , 1945).

[15] J . B. Smyth and L . G. Trolese, Propagation of radio waves in t he t roposphere, Proc. IRE 35, 1198 (1947) .

[16] B. R. Bean and G. D . Thayer , On models of t he atmos­pheric radio refractive index, Proc. IRE 47,740 (1959).

BOULDER, COLO. (Paper 63D2- 21.)

254