, technical report ecom-2592 - dtic · shows the warming trend during the day and the cooling trend...

., TECHNICAL REPORT ECOM-2592

00

0*: EFFECTIVE CLEAR SKY TEMPERATUJRES IN THlE 8- TO 14-MICRION BAND)

• e MAY 1,965

-7 11"'"'" "'" " "'" " "'""C,,IRA E

UNITED STATES ARMY ELECTRONICS COMMAND" FORT MONMOUTH, N.J.

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~0 TZCHICAL RPOIRT BCO)4-2592

- -~~ECTIVw CLEa sKI TZmUmERa 331fl TE 8- To 14-mciCoN Bw]

by

Albrt R. Tebo

Meteorological DivisionZW/.Meteorological Department

ma~r 1965

DA Task Nr. lVO-ll5Ol-B-53A-13

U. S. ARMY ELECTRONICS I1ABRATORIESU. S. ARMY ELETRONICS COMMWU

FORT MONVUTH, N. J.

Aplparent sky Umperturs were meu- on cand nights during a pefiod in July and August of 1964 atFlagstaff, Arizona. A portable radiometer, with a two-degree

o field -of view, sensing in the vavelength band 8 to 14 mic'rons,was used to read sky temperatures at 5-degree intervals ofzenith distances (angles). from the zenith to the borizon.These values were converted to radiances and suMMed over thewhole sky, to arrive at effective whole-sky temperatures.

The apparent sky-temperature at any zenith distance isnot dependent on azimuth, but does vary with the time of day.The elevation scan of temperatures at a given time is dupli-cated by that of an equally clear sky at a different time ifthe zenith temperatures are the sam. The effective whole-skytemperature is consistently the sam value as the apparent skytemperature at a zenith distance of 54 degrees. Asthematicalequations were developed empirically to express the dependenceof radiance or apparent sky temperature on zenith distance.

Graphs of the spectral radiance of the clear zenith sky,obtained from a report by Ohio State University ResearchFoundation. ere integrated over the band 8 to 14 microns toarrive at apparent zenith temperatures for locations at alti-tudes from sea level to 14,000 feet. These ranged from -21Cto -82"C.

9 -

cii

ABTRACT Li

IW D W'UsIO 1DISCUSSIOk 1

Instrweetation and Techniques of Measuremnt 1Analysis of ata, 2Develpmnt of a Mathematical Approximation 7Effective Whole-Sky Temperatures 13

SUWKtM 14

REFERENCES 15

TABLES

1. Effective Wh6le-Sky Teperatures and Apparent Zenith Temperaturesof Clear Skies in the 8- to lf-Micron Bnd., Flagstaff, Arizona 4

2. Clear Zenith Sky Temperatures, Integrated from 8- to 14-MicronSpectral Curves 5

FIGURES

1. 16to Apparent Sky Temperature vith Infrared Thermometer to23- 38

24. pa t Sky Temperature at Zenith with Infrared Thermometer 39

25. 40to Clear Zenith Sky Spectral Radiance to33. 48

34. 49and Spectral Radiance of Clear Sky and35. 50

36. Geometry for Determining Radiation from the Sky that 51Reaches an Element of the Earth's Surface

37. Effective Whole-Sky Temperature with Infrared Thermometer 52

ili

EFFECTIVE CLEAR SKY Tm nA IN THE 8- TO 14-MICRON BAND

INTRODUCTION

As part of a study of environmental processes in the atmosphere, tech-niques and equiment are being developed to measure the surface temperatureof the es.ths using infrarod radiometers. The accuracy of these measurementsis dependent on a knovile age of the emissivity of the soil examined, withinthe wavelength band of the instrument (8 to 14 microns). A technique ofmeasuring this emissivity has been devised that involves a measurement of theeffective sky temperature, using the same radiometer. It was a study of thismeasurement that led ts the work reported here.

Studies have been reported in the literature on infrared radiances of

the sky and on transmission of radiation through the atmosphere, but nonepresent the information needed here. Specifically, what was desired was aknowledge of the effective whole-sky infrared terxperature; in order to deter-mine the radiation in the 8 to 14 micron wavelength band that reaches theearth's surface.

Only clear skies were studied in order to simplify the handling of thedata. The plan was to take measurements at different elevation and azimuth

* angles, and at different times of day and night, in order to examine thesevariables:

(a) dependence of apparent infrared sky temperature on elevation

angle (or its complement, zenith distance),

(b) dependence on azimuth,

(c) dependence on time of day,

(d) consistency, that is, repeatability, from one day to another.

The ultimate aim was to arrive at a technique of measuring quickly theeffective whole-sky temperature in the infrared, so that subsequent measure-ments of infrared emissivity of soils could be accomplished rapidly. Thework on emissivity will be reported on separately.

DISCUSSION

Instrumentation and Techniques of Measurement

The instment used for measuring sky temperature was the portable radi-ation thermometer, PRT-4, made by Barnes Engineering Company. It was usedbecause it had been chosen for the technique of infrared emissivity measure-ments, and compatability of data was desired to simplify the handling ofcomputations. This instrument also happens to be convenient in that it hasa light-weight sensing head (three pounds): which can be easily mounted on atripod. It has a field of view of two degrees diameter, and it senses in the

1

wavelength band of j to 14 microns. The response time is listed as 150 milli-seconds, as afapted- for recorder use, and the accuracy as ±1F, or ±0.05microvatt/cm2 irradiauce.

The normal range of the instrumnt is 1OF to U1OeF, which is equivalentto an irradiance range of 3.4 to 8.4 microwatts/c22 . This range was modi-fied internally by the user to acccamodate the low temperatures expected fromthe sky. This modification was effective, even though the linearity was dis-torted. The modified instrument was calibrated by using it to read the sur-face temperatures of a well-stirred liquid b4th of a mixture of chloroformand carbon tetrachloride, cooled with dry ice. By observing the readings ofthis bath and of water at the same temperature above the ice point, it wasfound that the mixture had Just about the same emissivity as water. Fromthis fact, plus the fact that a normal reference point is the temperature ofmelting ice, a reliable calibration was made possible.

The portable radiation thermometer is calibrated by the manufacturerwith its meter marked iu degrees of temperature, on the assumption that alltargets are black bodies. Since the sky is very much a non-black body, theterm "apparent" sky temperature for the measurements is used in this report.

The nature of the variation of sky temperature with elevation angle, orwith its complement, zenith distance, was not known, so it was decided to takereadings at five-degree intervals from the zenith to the horizon. It was alsodecided to repeat these meaaurements at the four azimuth quadrants to get apicture of the variation of sky temperature with azimuth. For this purpose:a precision tripod, designed as a mount for a telephotometer, was used.Angles were marked off in degrees, and easily estimable to 0.2 degree.

Measurements were made at the airport in Flagstaff, Arizona, on 27 and28 July and 4 to 9 August 1964, during both day and night. Only clear skieswere measured, except that at night it was sometimes difficult to discernhigh haze and very light clouds. It is possible that several anomalous read-ings are attributable to these factors,. The tripod was located in a cleararea, so that the field of 'view in the NE, SR, SW, and NW directions was freefrom obstruction except at the horizon. The altitude of the airport isofficially 7012 feet.

Analysis_ of Data

The data obtained from these measurements are presented in Figs. 1through 23 as plots of apparent sky temperature versus zenith distance. Asoften as possible, a complete run of measurements was made at each of thefour azimuth directions. The duplication of temperature values at differentazimuths is indicated by circled dots on the graphs. On 9 August the sky wasclear in patches, so the measurements were made at various azimuth directionsfrom north to east instead of separate runs at each azimuth. Temperaturevalues on all runs were recorded and plotted to the neareet eC, since theaccuracy of the instrument was no better than that.

The general weather pattern at Flagstaff in July and August is a tendencyfor the sky to become completely clear by late evening, to remain clearthrough the night, W begin cloudiness in midmorning, and to become overcast

2

by noon. This routine prevented the taking of data on most afternoons andmany mornings. A continuous sampling throughout a whole 24-hour period wouldbe interesting, but would be difficult to obtsin.

The data showed many slight variations in sky temperature valuee at thedifferent aziimths, but no consistent pattern could be detected. So it isconcluded that clear sky temperature in the infrared wavelengths is notdependent on azimuth.

The time required for an elevation run at ono azimAth was 8 to 10minuten, thereby requiring about one-half hour for a complete run at all four

-J azimuths. The assumption that sky temperatures did not change appreciably1 during this time was validated in general by the data.

Curves were drawn through the smoothed averages of the data of all fourazimuth runs. Deviations from true averages were made in order to obtainuniform, smooth curves.

These plots show clearly a consistent shape of curve, and a repeata-jj bility of value. Different plots having the same zenith temperature have

almost identical curves, even if on different days. For example, the curves4 at 0256 and 0428 MST on 6 August, both having a zenith sky temperature of-j -55ec, are almost identical. The curves of 0640 on 28 July and 0845 on'1 5 August, both having a zenith sky temperature of -51eC, are almost identi-I cal, although separated In time by a week. Similarly, 0845 on 27 July andi 1106 on 7 August, more than a week apart, are almost identical, with a

zenith temperature of -45'C. This points out clearly that the thermal struc-ture of the sky repeats itself from time to time, at least insofar as itsinfrared emission is concerned.

Table 1 lists the dates and times of all the measurements, as well as

the zenith temperatures in each case. Other data in this table will be dis-cussed later. The lowest zenith temperature was -62Cc at 0600 m1T on5 August, and the highest was -34*C at 1127 on 9 August.

Figure 24 is a plot of these zenith temperatures by days and hours. Itshows the warming trend during the day and the cooling trend at night, andalso shows a general warming trend over the period 7 to 9 August.

Some data from reports by Ohio State T niversity Research Foundationl,2,3on work performed during 1955 to 1957 have provided the means of making coa-parisons of the clear zenith sky temperatures at other locations. The datawere obtained by a Farrand spectrometer in the form of spectral radiance andwere plotted as graphs over the wavelength band 2 to 20 microns. By integrat-ing over the band 8 to 14 microns with a planimeter, then dividing by thefraction of total black body radiance emitted within this band, and finallyconverting this equivalent black-body radiance to temperature, the equivalentapparent zenith sky temperature was obtained.

Table 2 is a compilation of these results, giving sky temperatures inNew Mexico, Colorado, and Florida, at altitudes from sea level to 14,000 feet.The coldest zenith temperature calculated was -82*C on Pike's Peak, Colorado,on 11 September 1956, at 0650. The warmest calculated was -21eC at Cocoa

3

!

II

Table 1. Effective Whole-Sky Texperatures and Alprent ZenithTemperatures of Clear Skies in the 8 to 14 micren band,Flagstaff, Arizona

Effective Zenith DistanceZenith Whole-Sky for Sky withTemperature Temperature Same Temperature

Date MU (MeT) TO T-ff as Teff

TI~T(T'O (degrees) 1Jul[

27 0845-0908 -45 -31 53128 o64o -51 -361 54

August4f 0630-0735 544 0915-0935 47

4 10140 18 -471 -3 5

5 0550-0615 4 -45 545 0845-0910 -51 -37 545 1037-1058 -47 -33 545 1210-1230 -44 -31 53J

6 0040-0111 -52 -37 546 0256-0323 -55 -39 546 o428- 45 -55 -40 546 0604-0613 -53J -381 54

6-7 2346-0005 -48 -331 547 1106-1133 -45 -31 547 14.08-1416 -4 ~-32 547 1.523.- -37 547 194 -954 -32 55

7-8 2348-o03. -47 -31 53

8 0237-02'-9 -47k -Pi 551 48 o4)35-o4A7 -40 -308 0918-0935 -41 -27 5348 1052-1112 -371 -24 5

9 1127 -34 -21-i 54j

14

Table 2. Clear Zenith Sky Temperatures, Integrated from 8 to 14Micron Spectral Curves

Reference Location Date Local Tim Altitude T(Feet) C

1 White mjs, N.M. 13 Aug 55 1730 4,300 -251 Sacramento Peak, N. K. 21 Auz 55 0040 9,000 -471 Climax, Colo. 30 Aug 55 1720 11,200 -691 Denver, Colo. 5 Sep 55 1205 5,300 -51

2 Pike's Peak, Colo. 10 Sep 56 1552 14,110 -772 11 Sep 56 o65o " -822 12 Sep 56 19,10 -592 14 sep 56 1040" -502 14 Sep 56 2153 "-55

2 15 Sep 56 0210 -572 " 15 Sep 56 0650 -622 Elk Park, Colo. 17 Sep 56 1305 11,750 -482 19 Sep 56 1430 -542 19 Sep 56 2058 -60

2 " 20 Sep 56 0705 -562 Fort Carson, Colo. 24 Sep 56 1338 5,960 -402 Peterson Field, Colo. 26 Sep 56 2210 6,130 44

3 Cocoa Beach, Florida 13 Jun 57 0923 0 -21to

2310

I Beach, Florida, 13 June 1957, between 0923 and 2310 (an average of three setsof readings). Times listed are local.

]These values agree well with the range of values obtained at Flagstaff.

A It is noted that the temperatures and radiances decrease with increasing alti-tude. This is expected, since the total mass of air available for radiatingis less at the higher altitudes, and at the lower altitudes the varner sur-face layer of the atmosphere predominates in determining the sky radiance.

Figures 25 through 33 are radiance plots of clea& zenith skies, in the8 to 14 micron band, copied from the Ohio State University reports. Theywere selected from the group listed in Table 2 to illustrate the form of thecurve and to emphasize the non-blackbodyness of the sky radiation. Two fea-tures are of note. One is the ozone band that causes a hump in the curves at9.6 microns, It is present in all the curves, to different degrees of inten-sity, &;though almost masked in the Cocoa Beach plot by the warm surfacelayer of the atmosphere. The other feature is the existence of sharp vingsin the curves at 8 and 14 microns. This is interesting because it means that,for a 3ky of low radiance, most of the energy lies in these wings. If adetecting instrument were used with sensitivity in the 9 to 13 micron bandinstead of 8 to 14 microns, the apparent sky temperatures would be

4 5

coriderablY l.ver than thse recorded bere. The texperatures cast~ted fromthe curves depe;A eritical y on the actual as$ barA of the nstru-_ nt.

wtber aspect of this otrrene nn-blackbodiness is the earor invited Inca~lulations vhen blackbod values are used. in ezissivi-y calalaio-s, a

Metorentr*to take int accnt, the frac-tion of the total radiance orxadiat ezittance that falls vitbin th e srectral bend seen by the Ins00nt.If tis fI-ractjO is taken from the !2anck cdstriution of a b-ackboey -,Ai-ator, it vl be quite differemt frM that taksm --r= a dist-i-bution

PL iedn i tbase c-urves of Yigt. 25 tlxou- 33, for the rawck djstrb-timn is convex upiard at these 'te atres, vhereas t:ese cu--ves are cccave.

This error is fter c oy the possible afce nty ftheacUal pass beni f the sx nt. It is customry for m6facturers tospecIfy the lizits of a pass 'od at the half-ipover po s. hfor atel2y,With te 3amres portable radiatom r eter, Vbich baa a pass bamnd of 8 to14 microns, t-e resplnse of the inst,r-=nt reduces ra~pdliy at the ving, ofthe band at the sam v v-eengts that th ene e sk ridlyULS". This mkes for. difficult ca "tions and uncertain results.

in the spectral studies of the clear sky =d by Male State UniversityResearch Foundation, ts re made over the spectal band 2 to 20micros, at various zenith distances from tbe zenith to the borizon. :t asfound that the response gradUally chaned from a concave curve umard, takenat the zenith, to a convex curve u1oard amwoxfating a blackbody at t.etemperature of the atostere near the grmnd, taken at the horizon. At 2ow-altitud. locations, this au Lxition to a blackbody cuve -was bet4e. thanat bhiger altitudes. This is to be expected, because at sea level thesPectrcmter looks tbroci a large air =ss on the horizon -which contains aveltively hi i density of solid aerosol larticles whose eissi:on is essen-

tially blackbo radiation. hese effects ae sbown in Figs. 34 ana 35.3

The spectral radiance cn the horizon at Cocoa Beach is very close tothat of a blackbody at the texp-.,tre of the atmosere near the grun, andthe envelope of the curves at Elk Fark, Colorado, a;gin apg-r tes that ofa blackbody. This feature was used by Ohio State University to make ananalysis of a mathematical approximation to the spectral curves at differentzenith distances, and will be discussed later. It is significant that notuntil the zenith distance approaches very near the horizon does the curveaProximte closely that of a blackbodY. Even at a zenith distance of 88.2degrees, hich is 1.8 degrees above the horizon, the dil2 in the spectralcurve is appreciable at sea level and is quite large at 11.000 feet altitude.The air mass at this angle is about 20 air mass units at sea level, and ismich less at 1,000 feet. It is evident that a very large air mass is neces-sary for the atmosphere to approximte a blackbody.

Of interest here, it is also significant that vithin the spectral band2 to 20 microns it is the central portion between 8 and 14 microns thatchanges so radically with viewing angle.

These above-described factors lead to the conclusions that the skytemperatures "seen" by the Barnes portable radiation thermometer are neverequivalent to the true blackbody temperatures except on the horizon at sea

6

1"P112andthed~itic f eablackbody values is dependent on both altitudeor,"sit an vieing=4 ence, al masred tezPeratures are c*3lIed

De~2!pntof a w~bematiea1 Aw oX3S1O

!ne al-. of the ssents at lagsta-ef vas to develop a metbd ofdbtaimin, by simple means, an efrective Tntegrated valu, Of' teratulre,revresent-iative ozf tt vbo--e sky in th-e a to Ai Micron vuatelength band. Me

4 aprva-ch taken ims to~ deirelop mab. U awluaz. * essixn fb. the radanc Ofthe skya, or for the radiant emlttancex as a f mction, of zenith distanice, andintegrate it f the senith to -.be ixorl"zon.

Fortt=&tlyM, th radac of tew, x In v~d vaepmt band see -to be

independent, of az$.=t_h,, 'within the err=o- of zezr0t !Mas Is borne outlby the plts of Figs. 1 tbroagh A'-. The data on these pl&ts indde3surenents a. -.mur diffferent azlxaithe, an AtII.bouhx ther-e 'eredifens in

rednfrm on azIxitb to arwtber. no cmnsistent pattern oif aatosboved up.. and. the TariatIons wre generaly s m xa t b onidrd.a'within exeri-antal er=c. ?Fhis eonclusi I= va baicafly the am as tbctreached -my (Oiio State University Beses.-ch 7ronndatiogi In thein azmrsavarious gaim" ne Jm*en c f radiane vith azlnetb s.r,31ie tderivation of a 3n

Our first attwt to find a ub .tdcal expression for thek deeneoff sky raiac on zenith distance 'was the rse of an equatioun fPOr aasetransmIssion develomed by E. Ni. Good9r" =nd adaped by Cbaio State UniVersity.Goody's lav describes tbe arerage tranwuissimof infrared radiation tbro1g1the atmorbre.

V

6L 2 a~ z T a 7,Tr J:]

beec s the b-vidth of the lorentzlan-sbaped absozrptIo liIes. a Is themean - sreegtt., isthe mean line sjiacingx, azd v is the mss of tbe

absorber- per unit cros s-sectional area caf the path.

A ~It is knoirn -that transission of sunligtt tbrou.& the atmospbere followsa dependence on the nass of air through vbich the radiation lasses.* It 'would

* be expected that the variation of radiant exittance, or the 'rarlationz ofradiance, 'would also follov such a dependence. The standard -values for airnass are very closely approximated by the simple expression -S - seec brw is the air- xss and cp is the zenith distance. This approxiation t goodto 0.4i percent for zenith distances up to 65 degrees and falls off to 3 per-cent at 80 degrees. 5

R. E. Bell of Ohio State6 sioplifiel Good-yts law by amsuming a strati-fied atmbphere,. for 'wich v is proportional to see cp, and assuming that theother quantities are constants. 55=k the abs orptivity, or exissi'rity, isgiven by

amicw-- 3 -- exp secL (A+B sec a )]

where A and B are 2=ped constants. Bell found., for the Ohio State data inthe infrared, egion, that 3 >')A and the equation reduced to

9 W - xp[-C(sec 40t]S=i- exp

where C is anotb=e" ]ned c =xta . ell considered tbat, the aky radiae atzenith distance c is

Vher-e No, Is the -blackbodY radiance et atoosiaeric texera e -' f&=Ithat 1ro vas satisfactor-4y aprr tdby tbe sky -.&14%=e atthe izn,Ube=4p = 9D degrees.

AL tast of fit of the M Oo State data in the wvree=lgth reg;Io 2 to 2Dmlcrn sbved goo~d apreeet 'hen tbe constant C 'was apr;Xi =ei 0.4. ?Forme set of ata, at 4.6 xisc=sz, C vas 0.-; for aoth.e- set at 9-3 x er.s,

C IAS O.O. he equati on f Its the data. ve-1 excet. at the brizon.

A zest vas ed of the fit of this e a tion to the data of thi reocrby Caeinthraiannces N and 19 to equivalent appznsyte erte,T aza 7 _, respectively, where _E Is the apevret s1W tex.ratare on theborIzon.

Nw- - = . - for a diff use sky.TSI

mTH L,-

Bere, aT is the Steizan-Boltzxann expression for blackbody radiantenittance.

The equation did not fit the data well using either value of C--O.4 or0.40. Deviations were in excess of 30 C over mci of the range of zerith dis-tances, and it appeared that cboosing a different val-e for the constant Cwould only shift the position of the deviations on the ozrve, and not elimi-nate tbhe. So this approach was abardoned.

The next approach was to look for an empirical relationship that wouldfit the data over part of the range of zenith distances and, if necessary,anoter to fit the rmnining pert. i was hoped that such expressions couldbe integrated to calculate the effective whole-sky temperatures, thus avoidingthe tedious work of suiing all the radiance values (or radiant emittancevalues) calculated at each zenith distance. However, it turned out that thework of calculating the constants of the empirical equations for each set ofdata, plus the work of calculating the resultant integral, was more tediousthan a sumation process. Hence the integral form was used only to verifythe accuracy of the suwation process. The development of these mathematicalrelations is given next.

8

i4 The bu tal _xysical quantity of a radiating body is radiant emit-

tance, exmpessed by the Stemhan-Boltz=enn relation

V-here is the rate of energy emitted p-er unit time fr= a unit surface areao1 the source into the vboe be=Upbere to vbich it is exposed, T Is absolutetemperatuxe, and a Is the Stepan-3o1t=an constant. Bence, a fourth-paver

;tea nsi be.w een sky teeratte and zenith distance Is somght.

Mie sziootbed et.a f -- tbe teratur cures of Figs. 1 tbroughi 2-3Sthat t fouh , ie-'y -o t ,.ate fitted caer a liner rv onltation-

thi-0 with the sec_n.t of the ze ih dista e , -was c = be=se of Its-~resent - an of the a!-- =ss.

-bere A is a= ar~bitr._axr const=.

-w adIat4,io seen by the porltable radiation tbezzmeter is only that--itbin the spcrlbn.8to 14 microms, but the instument registers thete=,eratare as tbhgb it were seeing a blackbody with spectral emittancerepresented by t a nt of energy. Bence we are justified in using, inthis aasaysis. this te =erature in its relation to the total radiantem-ittance.

One constant A can be evaluated by inserting the value of T at thezenith distance O, To - Then;

A = T0o x 10-9 - 1.

The total radiant emittance of a sky with an appaent temperature T is

W aT4 aTco+i09 (sec - i1. (2)

The coastant A is obviously different for each sky scan having a differentapparent zenith temperature.

Equation (2) fits the data of almost all elevation scans of temperaturewith an accuracy of ± "C through zenith distances 0* through 60. There area few exceptions, but they are small enough to be included in the errors ofmeasurement. For smooth data, this accuracy is correct. The relationdeviates rapidly from this accuracy at zenith distances greater than 60degrees, partly because the expression sec cp no longer holds accurately forthe value of air mass.

In an attempt to find a relation to express the radiant emittance atzenith diatances greater than 60 degrees, an exponential form was used. Athree-constant eqxmtion was found to be necessary to meet the requirements.

T a ebP + a, (3)

where T is absolute temperature, cp is zenith distance in radians, and a, b,and c are constants.

9

This equation fits the data of' two of the srooth-valued test runs inthi zenith distance range 60 to 9D degrees, with an accuracy of 4'C. Thete ousness of calculating t peratures -ith this equation discouraged ourusing it for more than two sets of. data. Bat it was decided that if theequatcz fit the data closely e Eo u, and If t:e in-tegratim of radiaenesvith this eqyation, agreed witthe SU=NtIzn teCnioue- closely enoug~h, thenthe sumation technimie vel1A' be ccsidered v IE"-Ian ! be rsed for alother data.

Me "-a e of enegr fr- the wbnle s!7 on a h-_izontal su-face oftZhe th is zs;gt. Ccuside an e32=ent of aea dAs of the s!-, taken =)-=61 to the dieci-m of the earth, -a~lting as a IEr!s radiator, i.e.,a diffuse so-uce, for -, hi the cosine la" holds. n ?ig. 36 the e.erfra tbis soce st-Ikes an elent of area dAe of the easth's sur:face thtis exposed to the vbole ha _ Ystexe of the sky. R is the distance betweenthe source and receiver elemean.. 0 is the zenith distance, the angebetween the dLrection of R and the normal to the receiver ele=net.

The radiance from d4., considering it as a blaclbod, is jig att cm 2

ster-', and the radiant intensity Js is IsA.s vatt ster - .LMe radiantpover striking dA. is

dAe

PA -Ns dAs x (-'Cos (P),

where the expression in parentheses is the solid angl, subtended by dAefrom dj.

For this Lambertian source, the relation between radiance and zadiantemittance is

Ns W= syIT

where Ws is the total radiation power emitted from a unit area of the sourceinto the whole hemisphere. The factor r enters here rather than 2 v becausethe radiance is defined in terms of radiation in a direction normal to theemitting surface. If the radiance multiplied by the cosine of the angle tothe normal is integrated over the whole hemisphere, the resultant quantity,the radiant emittance, is equal to I times the radiance. Then,

PAe .i Ws dAs dAe COs cp.

The infrared energy rate received by the portable radiation thermometerfrom the clear sky was found to be independent of azimuth. Since theinstrument records the radiation as though the source were a blackbody, theanalysis Is carried out in blackbody fashion with this assumption of azimuthiudependence.

The radiation power from a spherical band, described by the elementdAs,at the radius R, is

10

P~~~~ d ,__Pw .s d AL, cos

? Cos fo,.W dAe dA

.11 #R2 :3 JBn

'Ws ="4 ' , m q (2., xIr R

'W dA n o c(rze.

+t?- 41adiance -Aar. the band on d.A is

- W, sin 2 cp d9 = a Ts sin 2; d9VatC~2II

+ " raizc ro h oa eiphr ftesyi

Since the ain is to determ.ie the "eective" tetpers re of the vloesky as the instrwnt sees it, "effective" is i. It is the te raturethat the instrument would see if the energy were distributed uniformlythroughout the hemisphere.

If Ts is unifform, then the irradiance is

S sf TV2

fu - a .TS4I =Ws8, (5)

where the subscript u refers to a uniform sky. 'Thi states that the irradi-ance on a small surface element enclosed in a hemispherical blackbody radiat-ing uniformly is the same as the radiant emittance of the blackbody. Bnce,using this one-to-one relationship between irradiance on the receiver and

*effective radiant emittance of the sky, it can be said that the effectiveradiant emittance for any kind of sky is

eff W, r/ 2 T" sin 2 ,,(p a,, T4 (6)eHlf

The effective sky temperature is then

eff TS (1 eff W s)1/4. (7)

To obtain the total irradiance from the whole hemisphere, Eq. 6 isintegrated in two parts, one covering zenitb distances 0 to 60 degrees, the

31

Other covering zenith distances 6D to 90 degrees. Exantions (2) and (3) areused, inserted into egyuation (6).

r/3 4 +09c see P )]sin2;pdy.fvs1 [a 0 ' Oase -

+ f i/a (aeby + c) sn 2c? dc. (8)

Tis can be int-egrated, and reduces to

effW . a 1o+ x

a__ a bW2 bn/3 bjq 1 1()

b2 + 4 _ -e ( i +. (9)

Here, a is the Stefan-Boltzmmn constant, To is the apparent sky temperatureat O-3gree zenith distance, and a, b, and c are constants determined fromthe data of a set of ueasurennts.

nis eqatIon was used to calculate the effective ra nt emittance ofthe sky and the effective whole-sky temperature, Teff ef Ws)i/4, forthe data of 27 an. 2B july 1964.

A simation process was also Ade of the same data, using 18 equallyspaced segments of zenith distance (frox 0 to 90 degrees) to obtain the sameeffective radiant emittances and effective whole-sky temperatures. From thegeometry of Fig. 36, the solid angle of the spherical band as seen by theeeent of erxt~h's eurface dAe is

q = 2-r (cos a - cotcpu),

where ca and %P are the zenith distances of the edges of the band. If we let

T q 2 and Ap = cp - c&i, this converts to

OBand - A sin cA sin . If Acp4 8 degrees, we can approximate

sin A w N with an error of less than 0.1 percent. Since these data were2 2

taken in steps of 5-degree intervals of zenith distance, we can use theapproximation. Then,

Oand w 2n sin pA Ac

In a manner analogous to the develcient of the integral expression, it canbe stated that the irradiance on the elemental surface of the earth dAe fromthe spherical band is

HBand = NBand QBand cos CPA,

12

whiere NB - average radiance across the bud ! 1 : _ a 4 , COS q is

n A 1 TA

the factor due to Lsa~brt's law, and TA is the a&erage temperature acrossthe band.

H~~WA2n sinco TII

.2 a TA sin cK cos 4pA ac.

Sim:e T and cos are both nonlinear functions., the qustica arises asto the proper values to choose for the respective "ave-rape" values, TA andcos q. Ha ever, for s8Iplicity it is assumed that the band interval A issll enough so tht the midpoints of these variables my be used. Thenco0 ca and sin ,. refer to the same anigle. Then

Suming this over all values of zenith distances gives, in exact analogyto the integral expression of equation (6),

eff W. =H ay ~ 4 sin 2cpA A

This equation was used on the data of 27 and 28 July 19 to determine

T5 ft eff V )l14 . The results agreed with those of the integral equatione a_to beter than "C. With this verification, the suution equation (11) wasasumed valid, and it was used on the rest of the data.

Effective Whole-Sky Temperatures

*l The results of the calculations on effective whole-sky temperatures aregiven in Table 1. The last column gives the zenith distance at which theapparent sky temperature is the same value as the effective whole-sky tempera-tare. The values in this last column are surprisingly constant at 54 degreeszenith distance, which attests to the consistency of the form of the curveover all times of day and night, This fact enables the evolvement of a mchsimpler method of obtaining reliable measurements of effective whole-skytemperature. A single measurement of apparent sky temperature at a zenithdistance of 54 degrees is all that is needed, at least hypothetically. Thereliability of such a technique should be held with reservations, especiallywhen the measurements are extrapolated to all seasons of the year and otherlocations at different altitudes. But if high accuracy is not required, thegain in speed and simplicity makes this technique worth while.

By the same token, a linear relationship between effective whole-skytemperature and apparent sky temperature would be euxpected at the zenith.Such a relationship does exist in our data, as shown in the plot of Fig. 37,but it is not as definite a relationship as might be desired.

The calculations of effective whole-sky temperatures revealed the factthat the energy coming from the extremes of zenith distances--that is, at thezenith and at the horizon--contribute almost negligibly to the whole-skytemperature. At the zenith it is because of the cold temperature and

13

rarefied atmospere. At the borizon it is because of the cosine factor ofLanbrt's law.

A portable radiation tbezm.eter, made by Barnes 3nineering Company,was used to measure apparent sky tempertures during July and August 1964 atFlagtaff, Arizona, at an altitude of 7000 feet. The two-degree field ofview permitted point m e ts at selected zenith distances from thezenith to the borizon, which were then used in a sumtion equation to obtaineffective whole-sky temperatures.

The sensitivity of the instrument Is in the 8- to 14-micron band, so thetemperatures measured were not blackbody temperatures, nor even "true" skytemperatures. This was seen clearly in the spectral curves of sky radianceobtained by Ohio State University Research Foundation in measurenints madeover a period of time at different locations and at altitudes from sea levelto 14,,000 feet. These spectral curves show sharp "wings" in each case atabout 8 and 14 microns, featuring very rapid changes of response at thesepoints. Because of this the apparent sky temperature indicated by the Barnesinstrument is critically dependent on. the pass band of its filters. This isnot a criticism of the instrument, since it was designed to measure tempera-tures of war surfaces such as the earth and bodies of water, which approxi-mate blackbodies. But it does indicate precautions in using the instrumentfor this piurpose.

All the measurements indicate that the apparent sky temperature at anyzenith distance is not dependent on azimuth, but does vary with time of day.In general it follows the warming of the atmosphere by the sun. The plotsof apparent sky temperature as a function of zenith distance were quitesmooth and, consistent, and it was found that the s4 repeats itself thermallyto such an extent that a plot of temperatures is duplicated reliably by anyplxt at another time or another day if the zenith temperature is the same.

Apparent zenith temperatures of clear skies were obtained for altitudesfrom sea level to 14,000 feet by integration of the Ohio State Universitycurves. These temperatures ranged from -21*C to -82c0, and are generallyconsistent with the temperatures found at Flagstaff, which ranged from -34Cto -648c

The summation equation used to compute the effective whole-sky tempera-tures was found, by comparison with an integral equation, to fit the datafrom Flagstaff to within C. Being much simpler and faster to use, it wasused in preference to the integral equation.

It was found that the effective whole-sky temperature was consistentlythe same value as the apparent sky temperature at a zenith distance of54 degrees. This fact can simplify data-taking considerably.

The program of sky-temperature measurements was part of a program ofmeasuring the emissivity of soil surfaces, for which the sky temperature isneeded. The program of measuring the emissivity of soil surfaces will becovered in a separate report.

14

1. Bell, Z. E., Infrared Tecbniques and Measrent8, Obio State Univ.Res. Found., Interim Eng. Rpt No. 1, 20 Jan 56, Contr. AF 33(616)-3312.

2. Bell, E. E., Atlas of Sky and Terrain Infrared Measuremnts Program,Colorado Springs Region, 1956, OSURM , nt. lag. Rpt fo. 5, 20 Jun 57,Contr. A? 33(616)-3312.

3. Bell, Z. E., I. L. Eisner, J. B. Young, A. Abolins, and R. A. Oetjen,Infrared Tecbniques and Measurements, OSUR Final Eng. Rpt, Oct 1957,Co-tr. AF 33(616)-3312.

4. Goody, R. I., Quart. J. Roy. Met. Soc., 78, 165, 1952.

5. Smithsonian Meteorological Tables

6. Bell, X. E., Infrared Techniques and Measurements, OSUW int. sag. RptNo. 3, 27 Nov 56, Contr. AF 33(616)-3312.

15

20* 0

FLAGSTAFF, ARIZONA150- 27 JULY 1964

0845-0855 MST10, AND 0908 MST

5 o DUPLICATE VALUE

00-

500

w

w0

-200w

2 -250-

-30*

14 0(I,

(L MULTIPLE VALUES REPRESENT

DIFFERENT AZIMUTHS

-500-

0o 100 20* 300 400 500 600 700 800 900

ZENITH DISTANCE

FIG. I APPARENT SKY TEMPERATURE WITH INFRARED

THERMOMETER

200-

FLAGSTAFF ARIZONA

150 .8 JULY 1964

I;* 0640 MST

4

-50

,C ,

'I UI-w -2

W .00-I--

cc -2350-01Qw -300° -

-3 _50o

CL

50-

5 5 0 I I I I I0 Ioo 20 300 400 500 600 700 800 90*

ZENITH DISTANCE

FIG. 2 APPARENT SKY TEMPERATURE WITH INFRARED

THERMOMETER

17

15 -FLAGSTAFF, ARIZONA

10 0 4 AUGUST 1964

0630- 0735 MST5.-

0 DUPLICATE VALUE

50

w -10°-

-_150 -

wCL -20-

w = /250- ,/

o*-300

zw -350-

-400°

-450- 0 MULTIPLE VALUES REPRESENT0 DIFFERENT -AZIMUTHS

-500*0 0

-600 1 1 1 1 1 1 100 I00 200 300 400 500 600 700 800 900

ZENITH DISTANCE

FIG 3 APPARENT SKY TEMPERATURE WITH INFRAREDTHERMOMETER

18

200 FLAGSTAFF, ARIZONIAb

4 AUGUST 1964150 0915- 0935 MST

0 DUPLICATE VALUE

50-

0_ 0

-50

'i

o 150

-0

w -20

Y. -250

z -300w

-3* 0

0 0 .0 MULTIPLE VALUES REPRESENT-450 - 0DIFFERENT AZIMUTHS

00

06 100 200 3001 400- 500 600 700 800 900sZENITH DISTANCE

F G.4 APPARENT SKY TEMPERATURE WITH INFRARED

THERMOMETER

19

250

FLAGSTAFF, ARIZONA200 4 AUGUST 1964

1040-1108 MST

0 DUPLICATE VALUE10 -

5*_JhJ0 0-I

CC14W -lowC-

W -15*

-200 -

z -25 -

W 0

-35 - 0

-400 -

-45-MULTIPLE VALUES REPRESENT

-0 DIFFERENT AZIMUTHS

00 100 200 30' 400 50P 600 700 800 900

ZENITH DISTANCE

FIG.5 APPARENT SKY TEMPERATURE WITH INFRAREDTHERMOMETER

20

, 150 -

FLAGSTAFF, ARIZONAl0o - 5 AUGUST 1964

0550-0615 MST

0 DUPLICATE VALUE0

0

-5.

-15

AU

_ i- 5• -

tJ

- -250

! >- -306 -

n-350

I-4o. -

0S-45* -

j-500 - MULTIPLE VALUES REPRESENT_ CLOUDS DIFFERENT AZIMUTHS

-550 C

-600 - .0

K4 0

-650'

0' I0 20* 30° 40* 500 600 700 80* 900ZENITH DISTANCE


200 0FLAGSTAFF, ARIZONA

150- 5 AUGUST 19640845-0910 MST

0 DUPLICATE VALUE

5.-

0 0 -

w -50 -

w

-15-

wwa..w_ -200 -

--Co -25-

zow -300 -

a---350-

0

-400 - MULTIPLE VALUES REPRESENTDIFFERENT AZIMUTHS

-45* -

-50* 0

-550 *00 100 200 300 40" 500 600 700 800 900

ZENITH DISTANCE


22

25 FLAGSTAFF, ARIZONIA5 AUGUST 1964

20 1037-1058 MST

15" - 0 DUPUCATE VALUE

50

1w

w 1

w

1-2o" -

1- -20"

-25"zCL

-35< MULTIPLE VALUES REPRESENT

0DIFFERENT AZIMUTHS-400 -

S-4 5° 0

i I I 1 I I I I ,I

0* 100 200 30* 40* 500 600 70* 800 90*ZENITH DISTANCE


23

+2 5 [" FLAGSTAFF, ARiZONIA5 AUGUST 1964121 0-1230 MST

+15 01 e DUPLICATE VALUE

+5

Ii 0cr

I-

0 -e

>-

10

w

(n -25 -

zw0-3 c

-3.5 - MULTIPLE VALUES REPRESENTDIFFERENT AZIMUTHS

-40 0 - 0

-4 5*

0 10 20 300 40 50 600 700 800 900ZENITH DISTANCE

FIG 9 APPARENT SKY TEMPERATURE WITH INFRAREDTHERIWOMETER

24

200FLAGSTAFF, ARIZONA

150 6 AUGUST 19640040-0111 MST

So DUPLICATE VALUE

5.

-0*

wC,

* w

w

-30

zw

a. -35*

0.0

-45* 0

40

0* 200 30* 40* 500 600 700 800 900

ZENITH DISTANCE

JFIG 10 APPARENT SKY TEMPERATURE WITH INFRAREDTHERMOMETER

25

200 wFLAGSTAFF, ARIZONA

15o- 6 AUGUST 1964

0256-0323 MST

100 -0 DUPLICATE VALUE

5*

5-50

ci,

; -5o"

w

-20*C LOUDS--p

20

S-300 Lzp

9< -35o 04

0 ULTIPLE VALUES REPRESENT-450 - DIFFERENT AZIMUTHS

-500

-55 "

- 3 r* I I !00 100 200 300 400 500 600 700 80° 900

ZEN ITH DISTANCE

FIG 11 APPARENT SKY TEMPERATURE WITH INFRARED

THERMOMETER

26

I 0-FLAGSTAFF, ARIZONA

10 6 AUGUST 19640428-0450 MST

5 - 0 DUPLICATE VALUE

00-

._- 50-

w

-10 ° -

!- -150

C. -200-

w-250-

-30

zw 0, a -550

S-4-0-

-450- MULTIPLE VALUES REPRESENT

DIFFERENT AZIMUTHS

-500-

' _550

,, _60 • l. I 10 100 200 300 40* 50'* 600 700" 800 90*

~ZENITH DISTANCE


THERMOMETER

27

FLAGSTAFF, ARIZONAfi f k 6 AUGUST 1964

004-0613 MST

DUPLICATE VALUE

00-

D-J *

w -I10 -

4IwI

_r150 -

-_200 -

w

I- _25 •

cr -30-

-40 -

"-45o - 0 MULTIPLE VALUES REPRESENT* oDIFFERENT AZIMUTHS

-500 ,

-550 -

-600-! I00 100 200 300 400 500 600 700 800 900

ZENITH DISTANCE


28

250 -

FLAGSTAFF, ARIZONA200 - 6-7 AUGUST 1964

2346-0005 MSTJ 15o -

0 DUPLICATE VALUEIoo -

50 -

DFn 00 -IJ

0

1 -0 -

15

CH. -0 -

n -25 -

.

-.50 °

-40

zw

450

MULTIPLE VALUES REPRESENTS50 0DIFFERENT AZIMUTHS

-50

00 100 200 300 40* 500 600 70 80 900

ZENITH DISTANCE

FIG. 14 APPARENT SKY TEMPERATURE WITH INFRAREDTHERMOMETER

29

250

FLAGSTAFF,' ARIZONA200 - 7 AUGUST 1964

1106-1133 MST150 0 DUPLICATE VALUE

10o

50

Oo

w0

w.100

w -1..50a.

w

I- -2O °

' -20 -

-250

z

,w -30 -

-400 M0~ 0

-450 C)0

.. 45 C0 ) MULTIPLE VALUES REPRESENTS

DIFFERENT AZIMUTHS-500

-550 , I I I I I I I00 I00 200 300 400 500 600 700 800 900

ZENITH DISTANCE


30

250 FLAGSTAFF, ARIZONA20 7 AUGUST 1964

1408-1416 MS***150 - 1523 MST 000

0 DUPLICATE VALUEt0o

50

M)

00

w

wS-100

w -150aw

-Poo

U-250

W-300

-400

450( MULTIPLE VALUES. REPRESENTDIFFERENT AZIMUTHS

00 100 200 300 400 500 60& 700 800 90*

ZENITH DISTANCE


31.

25-FLAGSTAFF, ARIZONA

20 7 AUGUST 1964

1946-1954 MST

15* 0 DUPLICATE VALUE

100

Dl 50

S50

-4 -

w-150

20o

--25o

a.:-30*

-350 MULTIPLE VALUES REPRESENT

DIFFERENT AZIMUTHS

-400-

4 5 0 - _

_500

00 100 200 300 400 500 600 700 800 900

ZENITH DISTANCE


32

I5FLAGSTAFF, ARIZONA

20* 7-8 AUGUST 1964

2348-0011 MST

150

I? 0 DUPLICATE VALUE

Cl 50

Las

,iYir W 5

m

150

c-2004

-35* MULTIPLE VALUES REPRESE11TDIFFERENT AZIMUTHS

0* 10* 200 30p 400 50* 600 700 8010 900ZENITH DISTANCE

SFIG 18 APPARENT SKY TEMPERATURE WITH INFRAREDTHERMOMETER

33

FLAGSTAFF, ARIZONA15* 8 AUGUST 1964

0237-0259 MST

100-0 DUPLICATE VALUE

00 00w0 5

(L -150

-25P

zwm -30-

4 350

-400 -MULTIPLE VALUES REPRESENT0 DIFFERENT AZIMUTHS

0 100 200 300 4W0 500 600 700 800 900ZENITH DISTANCE


THERMOMETER34~

25- FLAGSTAFF, ARIZONIA

8 AUGUST 1964200 0435-0447 MST

50 0 DUPLICATE VALUE

500"

20

* -15!

w -20

S -30

-3 5" .MULTIPLE VALUES REPRESIENT

DIFFERENT AZIMUTHS-4e0 -

-4e -

-5 0

0• 10 20"0 3 0 ' 40'0 50'9 60'0 70'v 80 •' 90"'

, ZENITH DISTANCE


35

250FLAGSTAFF, ARIZONA

200 8 AUGUST 19640918-0935 MST

150 0 DUPLICATE VALUE

I0o

5*

00

-5.tI

w, -10° =

w -15 ° -

S-20 °

i0

-2 _250

zW -300 -

0-S-350 -

-400 - °

MULTIPLE VALUES REPRESENT-450 DIFFERENT DIRECTIONS OF VIEW

(AZIMUTHS)

-500

-550 ..

0 100 200 300 400 500 600 700 800 900ZENITH DISTANCE


THERMOMETER

36

250

FLAGSTAFF, ARIZONA

200 8 AUGUST 19641052--1112 MIT

15 -0 DUPLICATE VALUE

100

5.

-J

-50

S-100*

I-

w -10 -0-

w1-- -200

-_250 -I-zwJ -30-

-400MULTIPLE VALUES REPRESENT

-450- DIFFERENT AZIMUTHS

-500 -

55 I I00 100 200 300 400 500 600 700 800 900

ZENITH DISTANCE


THERMOMETER

37

250-

20 NEFLAGSTAFF, ARIZONA

150 9 AUGUST 1964

1127 MSTI0-

C.) 50-

w-150-

w

-20- NE

Ecn -250 E

- NWJ -300° -

NE DIRECTION OF VIEW

-400- VARIABLE, AS INDICATED

-450-FROM N TO E

-500 -

-550

00 100 200 3500 400 500 600 700 800 900ZENITH DISTANCE


THERMOMETER

38

A 0090 ~

00*0

* -0000

* 0003

* -00911

-- a * 0090

00*0 Zw

: 0000N-

-0091

- 00? 1:

0090 40~* ~wI-

0000L

Aoooz

0091 41

-0090 le

-00* F

a; 0000-j

-0002

4i o I

a.O I

I0 0 In 0 low)

sflIS130'H.LIN3Z LV fnl±VE3dVdIJ. A4S .LN38VddV

700 -

WHITE SANDS, NEW MEXICO

Iz 13 AUGUST 19550 ALTITUDE 4,300 FT.

2 600TIME 1730w/I--

500

E

cnS400-

0

j300-

w

z41

O200-

o100-w

0~0

8 9 10 11 12 13 14

WAVELENGTH - MICRONS

FIG. 25 CLEAR ZENITH SKY SPECTRAL RADIANCE

40

7004 7 SACRAMENTO PEAK, NEW MEXICO

z 21 AUGUST 19550- : ALTITUDE 9,000 FT.2 600-- ' 600 TIME 0040

wU' 500

400EU

3:

0

i 300

wz

200-

cj 1 00

wa.

p 0 1 1 1 , 1 1 ,, 1 1 t I 8 9 10 i 12 13 14

WAVELENGTH- MICRONS

FiG. 26 CLEAR ZENITH SKY SPECTRAL RADIANCE

41

TO00CLIMAX, -3LORAD0

z 30 AUGUST 19550 ALTITUDE 11,200 FT.

O600- TIME 1720

C)500-

F-F400

0

000

0 200

Ir

w

00

44

700-DENVER, COLORADO

z - 5 SEPTEMBER 19550

cr. ALTITUDE 5,300 FT.o 600- TI ME 1205

c,500

E

S400-

0

0

x. 300

z

O200-

0-, t OIO

89 1O 13 I14

WAVELENGTH -MICRONS

FIG 28 CLEAR ZENITH SKY SPECTRAL RADIANCE

I43

700PIKE'S PEAK, COLORADO

z II SEPTEMBER 1956

02 600 TIME 0650

w-cl 5.00

N

E0

. 400

0c.

¢ 300-

w0z

O 200-

J

o 100

Idfl

0 I A

8 9 10 II 12 13 14

WAVELENGTH - MICFRONS


144

I

700

ELK PARK, COLORADO

S -19 SEPTEMBER 19560 ALTITUDE 11750 FT

00 TIME 2058

u 500

'- 400

0

300wz

200.. 4

I-C..)ILl

8 9 10 Ii 12 13 14

,, WAVELENGTH-MICRONS


I15

700FORT C/ARSON . COLORADO/

T 24 SEPTEMBER 19560 ALTITUDE 5,960 FT.

2 600- TIME 1338

wU,500-

E

S400-

39

0

S300-

z

O200-

.

o 10

8 9 10 11 12 13 14

WAVELENGTH -MICRONS

FIG. 51 CLEAR ZEIHSYSPECTRAL RADIANCE

700-PETERSON FIELD, COLORADO

T 26 SEPTEMBER 1956z0 ALTITUDE ,130 FT

o 600 TIME 2210

wS500

0

3~ 00-

J4 4

000

C)

44

4Amo200

700COCOA BEACH, FLORIDA:

z 13 JUNE 19570l ALTITUDE 0 FT.

o 600 TIME 0923 TO 2310

7 THREE SETS OF READINGSIr

wc500

E

~-400-

0

i300-

w0 )z

S200-

wai.

8 9 10 11 12 13 14

WAVELE'NGTH - M ICRONS

FIG. 33 CLEAR ZENITH. SKY, SPECTRAL RADIANCE

4f3

ELK PARK, COLORADO. SEPT 1956., AT NIGHT

A ZENITH DISTANCES: 0OS 88.2,s 900

ELEVATION: 11,750 FT. AIR TEMP: Blc

7000

Tz0

_ 6000

4 400'0

4 C.)

w 3000z

2000

100

0 4 B 12 16 20

WAVELENGTH -MICRONS

FIG. 34 SPECTRAL RADIANCE OF CLEAR SKY

S90

88.2

800

Tz0

i 700

TwI- 75.50

600e4I

EU

z

<- 500

,-i

(z

€0

0 2000- COCOA BEACH, FLORIDA, 13 JUNE 1957

DURING DAY a EVENING, AT SEA LEVEL

ZENITH DISTANCES: 90 , 88.2 ° ,t 75.5 ° t 00

100000

0 4. 8 12 16 20

WAVELENGTtit- MICRONS

FIG 355 SPECTRAL RADIANCE OF CLEAR SKY

Lio

I

dA s

IR

dAE

FIG. 36 GEOMETRY FOR DETERMINING RADIATION FROM THE

SKY THAT REACHES AN ELEMENT OF THE EARTHS

SURFACE.

51

CFLAGSTAFF, ARIZONA

U27 JULY- 9 AUGUST 1964

w 0 DUPLICATE VALUEI

w

- 3 0 *r

wa.

20wI- _401

-500

N

_7I 0*I I

- - 50*-4 -0-0

z

w -6000r0.

-700II-500 -400 -3( -20

EFFECTIVE WHOLE - SKY

TEMPERATURE-CELSIUS

FIG. 37 EFFECTIVE WHOLE-SKY TEMPERATURE WITH

INFRARED THERMOMETER

52

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA- R&D(SOCnty claa.IiIc~timn of til, body of abstract and indexing mnnoation muat be enfterd when the overall report n clas sified

I ORIGINATIN ACTIVITY (Corpoatse author) 2a. REPORT SECURITY C LASSIFICATION

U. S. Army Electronics Cc:mnd UNICLASSIFIE)Fort Monmouth, New Jersey 2b GROUP

3. nEPORT TITLE

EFFECTIVE CLEAR SKY T um im Ta 8- TO 14-MICIwO BAD

4. DESCRIPTIVE NOTES (Typo of seport and inclusive date#)

Technical Report5 AUTHOR(S) (Last na irsst name. Initial)

Tebo, A. R.

6. REPORT DATE Ila. TOTAL NO. OF PAGES 7b, No, OF RE

May 196 5 52 6a ms. CONTRACT OR GRANT NO. 9a. ORIGINATORS REPORT HUMBER(S)

b, PROJECT NO. lVO-l4501-B-53A ECO-2592-tTask NO. -13 b. oTHER PORT NO(S) (Any oth.n tmb.er that ay be assine.d

d.

0. AVAILABILLTY/LIMITATION NOTICES

Qualified requesters my obtain copies of this report from MC.This report has been released to CFSTI.

It SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

U.S.Army Electronics Labs., ANSEL-RD-SMAU.S.A1W Electronics Ccsnd

__________________________Fort M)moth, N. J. 070313. ABSTRACT

Apparent sky temperatures were measured on clear days and nights during aperiod in July and August of 1964 at Flagstaff, Arizona. A portable radiometer,with a two-degree field of viev., sensing in the wavelength band 8 to i m.crons,van used to read sky temperatures at 5-degree interv&ls of zenith distances (anglesfroa the zenith to the horizon. These values were couverted to radiances andsumed over the whole sky, to arrive at effective whole-sky temperatures.

The apparent sky temperature at any zenith distance is not dependent on azi-auth, but does vary with the time of day. The elevation scan of temperatures at agiven tim is duplicated by that of an equally clear sky at a different time if thezenith temperatures are the sam. The effective whole-sky temperature is consist-ently the same value as the apparent sky temperature at a zenith distance of54 degrees Yhthematical equations were developed empirically to express thedependence of radiance or apparent sky temperature on zenith distance.

Graphs of the spectral radiance of the clear zenith sky, obtained frm areport by Ohio State University Research Foundation, were integrated over the band8 to i. microns to arrive at apparent zenith temperatures for locations at alti-tudes from sea level to i,000 feet. These ranged from -21C to -82"C.

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ESC-M1 3688-65 (2)S!!!!l Clsi Iton

, technical report ecom-2592 - dtic · shows the warming trend during the day and the cooling trend...

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