Comparison of Predicted and Observed Solar Radiation in an Urban Area

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  • a Theoretical and Planetary Studies Branch, Ames Research Center, NASA, Moffett Field, Calif. 94035
  • | b Meteorology Division, U. S. Environmental Protection Agency, Research Triangle Park, N. C. 27711
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Abstract

Measurements of the downward solar radiant flux in the St. Louis, Mo., area are compared with predictionsfrom an approximate solution to the radiative transfer equation. The atmospheric aerosols were assumedto have a power size distribution, dn/dr∼r-4, and the refractive indices suggested by Fischer (1973) foran urban area. On a relatively clean day, the predictions compared well with observations. On a hazy day,the comparison was poor with the a priori choice of aerosol properties. The particles on the hazy day apparently had more submicron particles than those found in the assumed size distribution, and the particleswere considerably less absorbing than those observed by Fischer. These changes could represent the effectsof relative humidity and different air mass characteristics.

Abstract

Measurements of the downward solar radiant flux in the St. Louis, Mo., area are compared with predictionsfrom an approximate solution to the radiative transfer equation. The atmospheric aerosols were assumedto have a power size distribution, dn/dr∼r-4, and the refractive indices suggested by Fischer (1973) foran urban area. On a relatively clean day, the predictions compared well with observations. On a hazy day,the comparison was poor with the a priori choice of aerosol properties. The particles on the hazy day apparently had more submicron particles than those found in the assumed size distribution, and the particleswere considerably less absorbing than those observed by Fischer. These changes could represent the effectsof relative humidity and different air mass characteristics.

0~~0~~~1977 ROBERT W. BERGSTROM AND JAMES T. PETERSON1107Comparison of Predicted and Observed Solar Radiation in an Urban AreaROBERT W. BERGSTROM~Theoretical and Planetary Studies Branch, Ames Research Center, NASA, MoJett Field, Calif. 94035 JAMES T. PETERSON283Meteorology Division, U. S. Environmental Protection Agency, Research Triangle Park, N. C. 27711 (Manuscript received 15 February 1977, in revised form 3 August 1977)ABSTRACTMeasurements of the downward solar radiant flux in the St. Louis, Mo., area are compared with predictionsfrom an approximate solution to the radiative transfer equation. The atmospheric aerosols were assumedto have a power size distribution, dn/dr~r-~, and the refractive indices suggested by Fischer (1973) foran urban area. On a relatively clean day, the predictions compared well with observations. On a hazy day,the comparison was poor with the a priori choice of aerosol properties. The particles on the hazy day ap-parently had more submicron particles than those found in the assumed size distribution, and the particleswere considerably less absorbing than those observed by Fischer. These changes could represent the effectsof relative humidity and different air mass characteristics.1. IntroductionKnowledge of the solar radiant energy flux at thesurface of the earth is essential for a number of applica-tions. Studies of the energetics of the atmosphererequire information about the solar radiant flux, as dostudies of the influences of man's activities on climateand investigations into the possibilities of convertingsolar energy to electrical power. However, it is difficultto make accurate predictions of the solar radiant energyflux in the atmosphere.There are two alternative ways to predict the solarradiant energy. The first is to take observed data anddevelop empirical formulas to compute the solar fluxincident on the surface as functions of the solar angle,amount of water vapor and an aerosol parameter. Suchmethods were originally designed for long-term orclimatological studies for which the daily variabilityof the aerosol could be averaged out (Houghton, 1954;Monteith, 1962 ; Idso, 1970). However, these formulashave been used to predict short-term (daily) values aswell (Davies et al., 1975; Atwater and Brown, 1974).These approaches account for the atmospheric aerosolempirically and the aerosol parameter cannot be easilyrelated to aerosol physical properties or number. There-fore, these methods cannot be used, for example, to1 National Research Council Associate. Present amiation :Systems Application, Inc., San Rafael, Calif. 94903.On assignment from NOAA.Now at Geophysical Monitoring for Climatic Change, NOAA,Boulder, Colo. 80302.study the effects of increases in the aerosol on theradiation balance or climate.The second approach is to solve the radiative transferequation. This technique, however, introduces otherdifficulties. For highly anisotropic scattering, the radia-tive transfer equation cannot be solved analyticallyand must be approximated. Considerable energy hasbeen spent over the last decade to produce methodsthat are fast and accurate [for recent reviews, seeIrvine (1975) and Hansen and Travis (1974)l. However,even at present, the relative accuracy and computa-tional expense of all the various methods is unclear.Many require considerable computational effort, whichprecludes them from certain applications, such as inatmospheric dynamics models.Perhaps the most serious problem, however, withpredicting the solar flux in a cloudless atmosphere isthat the atmospheric aerosols are highly variable. Mostoften the aerosol properties are not measured and inorder to predict the solar flux one is forced into un-realistic assumptions. These comparisons betweenpredicted and observed solar flux values can be usedto estimate the aerosol properties ; however, one mustbe careful since more than one set of properties mayfit the data.In this study, we use the comparison of predictedand measured solar fluxes to answer two questions:How well do predicted solar flux values, computed from"typical" aerosol properties chosen a priori, agree withmeasured values? What radiative properties of the1108 JOURNAL OF APPLIED METEOROLOGY VOLUME 16aerosol are indicated by the solar flux measurements?We restrict ourselves to very specific conditions. Weuse measured solar radiant fluxes from downtown St.Louis and from a rural site near Pacific, Mo. Weexamine the fluxes on two specific days, one weekapart. The first is a mild, clean day with low relativehumidity, and the second a warm, hazy day with highrelative humidity. The data are restricted to cloud-freeconditions. Section 2 briefly describes the measurements.As a prediction scheme for solar fluxes, we use anapproximate technique designed primarily for use instudies of the planetary boundary layer and empiricallyderived formulas as discussed in Section 3. For theaerosol properties, we employ, as an initial model, apower size distribution (de/d~-r--~), and we use therefractive indices suggested by Fischer (1973) in hisstudies of the Mainz area aerosol. Finally, the compari-son of the predicted and measured solar flux values ispresented in Section 4.2. MeasurementsThe solar radiant flux measurements were part of afield experiment designed to measure urban and ruralvalues of incident solar radiation and ambient aerosolconcentrations (Peterson and Flowers, 1976). Theexperiment was conducted in St. Louis, from mid-Julyto mid-August 1972 by the Meteorology Division of theU. S. Environmental Protection Agency, ResearchTriangle Park, N. C. Measurements were made con-tinuously for 28 days at two sites, one urban and onerural. The city location was on the rooftop of a 12-storybuilding about 2.5 km west of the Gateway Arch atthe western edge of the downtown district. The othersite was in undeveloped countryside about 55 km tothe west-south west of the city near Pacific, Mo.Among the measurements made at both sites were(i) incident global (direct plus diffuse) solar radiationfrom 0.3 to 3.0 pm (all-wave); (ii) incident globalsolar radiation from 0.3 to 0.38 pm (UV) ; (iii) normalincidence (direct beam) all-wave solar radiation withpyrheliometers ; (iv) normal incidence (direct beam)solar radiation at 0.38 and 0.5 pm with a sunphotometerto deduce the atmospheric aerosol optical thickness orturbidity; (v) atmospheric aerosol scattering coefficientwith a nephelometer ; and (vi) atmospheric temperatureand dew point. The maximum error in the flux measure-ments was 2%. The global fluxes were initially measuredas 15 min averages. Sunphotometer measurements weretaken about every half-hour, sky conditions permitting.Pyrheliometer and nephelometer data were reduced as3 and 15 min average values, respectively.3. Method of predictionThe prediction of solar radiation is made by utilizingthe Pa approximation of the spherical harmonics methodfor solving the radiative transfer equation. This method,discussed by Bergstrom and Viskanta (1973, 1974),agrees with more detailed methods for predicting thesolar flux and provides a considerable saving of compu-tational effort. For conditions similar to those studiedhere the error in the flux was a few percent (-3%).The equation of radiative transfer can be writtenP(drA/dT)= -1A+(60/4T)x (, /,. p(M`,$'; P,$)TX(P',$')dP'&', (1)where IA is the spectral intensity of radiation at wave-length X; p is the cosine of the zenith angle 0; + is theazimuthal angle; T is soz (k+u)dz the atmosphericoptical depth for which k and u are the absorption andscattering coefficients, respectively, between the surfaceand height z; 60 is u/(k+a); and p is the scatteringdistribution function or phase function between thedirection given by p, + and a reference direction p', +'.The spectral radiant flux is then defined to beand the total flux is simplyTo compute the solar energy at the surface, theintegrodifferential equation [Eq. (l)] must be solvedand then the angle and wavelength integrations [Eqs.(2) and (3)] performed. Input parameters are the solarenergy at the top of the atmosphere, the optical depthfor the total atmosphere (TJ, 60, p, the cosine of thesolar zenith angle (PO) and the surface reflectance.The specific computational details can be found inBergstrom and Viskanta (1974) ; however, there aretwo major assumptions that should be discussed here.First, the inhomogeneous atmosphere, which containsRayleigh scatterers, gaseous absorbers and aerosols, isreplaced by two homogeneous layers of equal opticalthickness at each wavelength interval. This means thatat every wavelength interval the total optical depthis computed, the atmosphere divided into two layers ofequal optical depth, and a mean value of the radiativeproperties evaluated for each layer. For an inhomoge-neous Rayleigh-aerosol atmosphere, the two-layerassumption was shown to give very good results (seeBergstrom and Viskanta, 1974, p. 37, Fig. 5) ; however,for gaseous absorption, the method is probably lessaccurate. Second, an effective mean gaseous absorptioncoefficient was computed for each layer so that the solardirectly transmitted flux through the layer agrees withexperimental transmission data for the wavelengthinterval.0~~0~~~1977 ROBERT W. BERGSTROM AND JAMES T. PETERSON 1109The directly transmitted solar flux at the atmosphericlevel corresponding to T is$,(~,po) = SX,~~~ expC- (T-- 7)/~01(4)and is a function of the solar spectrum at the top of theatmosphere, (taken from Thekaekara, 1974), thetotal optical depth as a function of wavelength, andthe cosine of the solar zenith angle. Aerosols affect thetransmitted beam by changing the wavelength-dependent optical thickness. The direct beam dependsonly on the aerosol extinction properties and not on theabsorption/scattering ratio.The wavelength integration of Eq. (3) was performedby using the 83 spectral intervals employed by Braslauand Dave (1973). The water vapor, carbon monoxideand ozone transmission data for each interval werealso taken from Braslau and Dave. The surface reflec-tion values were taken to be 0.15 for the urban surfaceand 0.17 for the rural surface, based on unpublishedmeasurements by one of us (JTP).The aerosol model initially used had a power sizedistribution (dn/dr-~~) and refractive indices sug-gested by Fischer (1973) for the Mainz, FederalRepublic of Germany, area aerosol. The refractiveindices as a function of wavelength are given in Table 1.No height dependence was assumed, neither for the sizedistribution nor for the refractive indices. The aerosolconcentrations were assumed to have an exponentialheight dependence with the total amount of aerosoldetermined from the St. Louis optical thicknessmeasurements. Recent aerosol measurements haveshown the tropospheric aerosol, particularly in urbanareas, to have a bimodal volume distribution (Whitbyet al., 1972; Willeke and Whitby, 1975). However, thelarger mode (whose importance for radiative propertiesis best shown on area distribution curves) includesparticles with diameters 210 pm. Thus, the largermode will primarily affect infrared computations(thermal spectrum), and should be negligible for thesolar spectrum since, at a particular wavelength, themajor contribution to the radiative properties is usuallyfrom particles whose radius approximately equals thewavelength.Fig. 1 shows the calculated aerosol optical thicknessand single scattering albedo as functions of A. Theaerosol thickness scale is arbitrary, but has beennormalized in this figure to 0.0948 at 0.55 pm (theRayleigh scattering optical thickness at that wave-length). The optical thickness displays an approximateA-' dependence, as expected from the form of the sizedistribution used. Since this aerosol model is for anurban area, the aerosol is quite absorbing (see Fig. lb)in comparison to most other choices of refractiveindices for the tropospheric aerosol (Toon and Pollack,1976). However, the aerosol model used here has some-what less absorption than that proposed by Shettleand Fenn (1975). The average cosine ((cos@)) of theTABLE 1. Index of refraction values used in initial aerosol model (Fischer, 1973).-Wavelength (A)(rm) Real part Imaginary part0.40.50.60.70.80.91 .o1.11.21.31.41.51.61.71.81.92.02.12.22.32.41.641.631.621.611.611.611.611.611.611.611.611.611.611.611.611.611.611.611.611.611.610.0300.0390.0450.0480.0530.0600.0660.0690.0720.0810.0780.0810.0810.0720.0780.0780.0830.0770.0660.0510.045phase function is about 0.66 and is relatively wave-length-independent for this wavelength region (0.2-3 .O pm) .The calculation Drocedure was as follows :1) The temperature and water vapor profiles (below3 km) were obtained from low-level radiosonde ascentsat the rural site taken by the University of Wyomingas part of the METROMEX project (Auer, 1975,personal communication).2) The upper air (above 3 km) data for temperature,pressure, gaseous concentrations (ozone, water vapor,carbon dioxide) were taken from McClatchey et al.(1972) mid-latitude summer values.3) The measured optical thickness at 0.5 pm wasused to normalize the wavelength-dependent aerosoloptical thickness ; i.e., the wavelength dependence ofthe optical thickness of the aerosol was that of Fig. 1,but the magnitude was adjusted so that the opticaldepth at 0.5 pm equalled the measured optical depth.4) The spectral flux in the 83 spectral intervals wasthen computed and the values summed to evaluate thetotal solar radiant energy received at the surface.Computations were generally made for solar zenithangles (e) from ~0~@=0.2-0.9 in increments of 0.1.An alternate prediction scheme, of the kind discussedin the Introduction based on empirical formulas, wasalso used to predict the solar radiant energy. Theequations are given by Davies et al., (1975) but wereoriginally derived by Houghton (1954). Monteith(1962) and Idso (1970) have also developed similarexpressions from Houghton's work. The equations aresimply presented here and the reader is referred to theJOURNAL OF APPLIED METEOROLOGYVOLUME 16I I I Illll I I I/X, WavelengthI I I I llll I I II2 3 45I12 3 4 567891X, WavelengthFIG. 1. Aerosol optical thickness (a) and single scatteringalbedo (b) as functions of wavelength. The optical thickness hasbeen normalized to 0.0948 at 0.55 pm for illustration.original references for the basic assumptions andreasoning.The direct flux at the surface is given asFt (Tm,PO) = FmPO$'wa$da$ws$'m#ds, (5)wheredirected diffuse flux at the surface isis the solar zenith angle. The downward-Fd~(Tm,~o)=Fw~o~wa~da(l-1C/ws~ra~ds)/2, (6)and the global flux is expressed asFB (Tm,PO) =Ft+FdL=FmP~#wa$da (J/ws$rs*ds+ 1)/2,(7)where the various @s account for attenuation due towater vapor absorption (wa), aerosol absorption (da),water vapor scattering (ws), Rayleigh scattering (rs)and aerosol scattering (ds). The J.'s are expressed asempirical functions of the amount of precipitable watervapor w (cm) in the atmosphere and the optical airmassm( = 1/p0). They are&,*= 1-0.0225wm0.972- 0.08262m+0.00933m2- 0.00095m3+0.000043 7m4fiWa= 1 - 0.077 (~m)"~$D=$'da#ds= km#da=$dswhere R, the aerosol transmission factor, was varied from0.88 to 0.98.4. Comparison of observed and predicted fluxesa. Clean day, 10 August 1972August 10, 1972, was a mild (maximum temperature25.6OC) dry, (relative humidity about 50%) summerday with only a few small afternoon cumulus cloudsand relatively little atmospheric haze. The visibilityat Lambert Field was about 18 km during the day.Surface winds were generally from the north-northwest.Fig. 2 shows the daily variation of the measured aerosoloptical thickness at 0.5 pm. The figure shows a sub-stantial aerosol increase from morning to late afternoon.For the rural site, Fig. 3 shows the directly trans-mitted solar flux measured at the surface. The valuespredicted from Eqs. (1)-(4) are also plotted and agreevery well with the measurements. Predictions from theformula given by Davies et al. (1975) are also shownfor R equal to 0.88 and 0.95. These predictions agreeonly in a particular solar angle range.The measured global solar flux is shown in Fig. 4for both the urban and rural sites. The predicted values,from the more rigorous method discussed in the firstpart of Section 3, for both sites are also plotted. Thepredictions overestimate the flux at low solar angles,whereas they give good agreement at higher angles.The average difference between observed and predictedvalues is about 4% for the rural site and about 3% forthe urban site.35I I I I I IXo ~urol site0 I I I I I I600 800 1000 1200 1400 1600 I800 2000 Time, hr1111lI I I I I I1I1111234567 8 9 9 8 7 654321p0, Cosine of solar zenith ongleFIG. 2. Daily variation of the measured aerosol opticalthickness at 0.5 pm on 10 August 1972.0~~0~~~1977 ROBERT W. BERGSTROM AND JAMES T. PETERSON 1111100' 0Pk" //I I I I I I III .2 .3 .4 5 .6 .7 .8 .9 I-/0 Observed rural siteX00X Predictions, Eq's 1-40 Empirical formula k=O 880 Empirical formula k=O 95The values computed from the formulas of Davieset al. [Eqs. (7)-(8)] are presented in Table 2. Use of0.88 for the aerosol parameter k gives good agreement.This was the value that also fit the data taken byDavies et al. for cloudless days. The formula could becomparison period, whereas the predicted differenceis about 3%. The all-wave solar flux differences forthe rural and urban sites were about 2% for the pre-dicted values, which is about what was observed (1%).useful to anyone who wishes to estimate the solar fluxfor cloudless days without specifying the aerosolproperties. It should be noted, however, that theformula evidently has compensating errors, since theprediction of the directly transmitted beam was insomewhat greater error.Urban and rural observed and predicted ultravioletfluxes are presented in Table 3. The comparison betweenthe values calculated for Eqs. (1)-(4) and the observa-tions is very good. This better agreement for the ultra-violet fluxes than that for the total solar flux is probablydue to the fact that Rayleigh scattering is more im-portant in the ultraviolet and is much more isotropicthan aerosol scattering. The rural site had about 5%more global UV radiation than the urban site during theTABLE 2. Global solar flux (W m-2) observed and predicted, fromempirical equations of Davies et 01. (1975), for 10 August 1972.Cosine ofsolar angle Observations Predictions-bo) Rural Urban k=0.95 k=0.880.10.20.30.40.50.60.70.80.950 50120 115215 2 10320 315435 43 5550 540670 665790 785915 91070 39175 125288 227402 334512 440634 558761 683874 793996 9131112JOURNAL OF APPLIED METEOROLOGYVOLUME 16po, Cosine solar zenith angleFIG. 4. Observed and predicted global solar flux values versus the cosine of the solar zenith angle (morning hours) on 10 August 1972.These clean-day comparisons showed that the apriori choice of aerosol properties produced computedresults that were in good agreement with the measureddirect solar beam (Fig. 2), the global solar flux (Fig. 3)and the ultraviolet global flux (Table 3). However, theoptical thickness of the aerosol was not large and, hence,this was not a critical test of the model. For example,changing the single scattering albedo from the valuesTABLE 3. Global ultraviolet (h0.38 pm) flux (W m") observed and predicted, from Eqs. (1)-(4), for 10 August 1972.Cosine ofangle GO) Rural Urban Rural Urbansolar zenith Observed UV Predicted W0.20.30.40.50.60.70.80.95.8 5.710.2 9.715.3 14.621.4 20.527.5 25.834.5 32.441.0 38.447.1 45.45.9 5.710.3 10.015.4 15.020.9 20.527.0 26.533.2 32.540.5 38.547.6 45.3shown in Fig. lb to 0.999 changed the UV flux by+7% and the global flux by +4S% at ~0=0.5. Also,changing the optical thickness of the aerosol wavelengthdependence to produced a -6% change in the UVflux, a +2S% change in the transmitted flux, and a+0.80/, change in the global flux at po=O.5. Thus, theresults are not extremely sensitive to the choice of theaerosol model.b. Hazy day, 17 August 1972August 17,1972, was a warm (maximum temperature3SoC), humid (relative humidity -70%) summer day.Surface winds were from the south, indicating an airmass that came from the Gulf of Mexico region. On 17August, the morning horizontal visibility was about7-8 km, and, during the afternoon, there were manycumulus clouds over both sites. Fig. 5 shows the ob-served aerosol optical thickness values at 0.5 pm. Fewvalues are shown for the afternoon since the presenceof clouds precluded measurements.For the rural site, Fig. 6 shows the observed andpredicted directly transmitted solar fluxes. The urban0~~0~~~1977 ROBERT W. BERGSTROM AND JAMES T. PETERSON 11131.2EdU-J0+p-VIW5 .6-u1+-0VE .400-2: 2-0I I I I I I I II--X0.xx xx oX00 xx ?isy oo0XX -0.Xe O0e*-- -- I I I I I I 1 I600 700 800 900 1000 1100 1200 1300 1400 1500e RuralX UrbanI1 I I I I I.4 .5 .6 .7 .8 .9 .9pLo, Cosine of solar zenith angleFIG. 5. Daily variation of the measured aerosol optical thickness at 0.5 Nrn on 17 August 1972.values are not shown since they are only slightlydifferent from the rural results. ,From the comparisonin Fig. 6, it can be seen that the predicted valuesconsiderably underestimate the observed fluxes. Thisdiscrepancy could be attributed to several factors ;however, a likely cause is an incorrect estimate of theaerosol size distribution. The spectral direct solar fluxat the surface [Eq. (4)] for T=O is a function of onlyE,,,, po and 7,. The major uncertainty is the atmo-spheric optical thickness r, to which water vapor andthe aerosols are the largest contributors. Since theaerosol optical thicknesses at 0.5 and 0.38 pm areknown from measurements, it is the optical thicknessesat longer wavelengths that are unknown. If the watervapor absorption calculation is accurate and the realpart of the aerosol refractive index (which is dominantfor extinction calculations) is not a strong function ofwavelength, the aerosol size distribution is the likelysource of discrepancy. Schere (1975) measured the sizedistribution for radii >OS pm in St. Louis on bothclean and hazy August days during atmospheric condi-tions similar to those modeled herein. On the clean day,his size distribution could be well described by an/&=p.a , and on the hazy day by dn/dr = r4.'j2.To test this possible effect, we changed the slope ofr to X-'.'j2 and recomputed the solar fluxes. The opticaldepth was still normalized to the measured values at0.5 pm. The recomputed points, also shown in Fig. 6,give considerably better agreement with the observa-tions. The difference between the transmitted fluxcomputed with the initial aerosol model and withA-1.62 is 25% at wo=0.5. This is considerably morethan the change produced by altering the wavelengthdependence of the optical thickness for the clean day(2.5%). It indicates the greater sensitivity of the solarflux to the aerosol properties on the hazy day whenthe optical thicknesses of the aerosols were much larger.Thus, while being far from conclusive, a reasonableexplanation of the discrepancy is that it is caused by adifferent size distribution on the hazy day than hadbeen assumed.Fig. 7 shows the observed and predicted global fluxvalues for 17 August. Again, the values predictedwith the initial aerosol model underestimate the radia-tion. In this case, changes in the wavelength dependenceof the aerosol optical thickness have a small effect.This results because most of the radiation attenuatedby the aerosol is scattered forward and eventuallyreaches the ground. For example, an optical thicknesschange from A-' to A-'.62 changes the global flux atpo=0.5 from 296.5 W m-2 to 315 W m-2, which is inthe right direction for better agreement, but still lowerthan the observed value. The results are more sensitiveto the value of the single scattering albedo GO. Thefluxes calculated with a single scattering albedo of0.999 (essentially no aerosol absorption) are also shownin Fig. 7. Since these predictions overestimate theobserved values, an intermediate albedo value wouldlikely predict fluxes in agreement with the observations.The lessened absorption hypothesis could indicate1114450400NE\VILc300-LL0)03VI03L L+x 200-LLO0 Y)Q0)-c cE 100:b-JOURNAL OF APPLIED METEOROLOGYI I 1 I I I 1 I I0Xe0Xe0Xe0Xe0 Observed0 Initial aerosol modelx a A-1.62VOLUME 160 .I 2 3 .4 .5 .6 .7 8 .9po, Cosine solar zenith angleFIG. 6. Observed and predicted directly transmitted solar fluxes received at the surface of the rural site versus the cosine of the solar zenith angle (morning hours) on 17 August 1972.the influence of relative humidity. On 17 August therelative humidity near ground level during the day wasabout 70%, but it had been much higher during theprevious night. It is likely that liquid water wasabsorbed by the particles during the night and then notevaporated completely during the morning hours(Covert et al., 1972; Hanel, 1970). If there were waterdroplets or water solution droplets, they should haverelatively less absorption per unit mass in the solarwavelengths than dry aerosols (Hanel, 1976).surements were made with an optical counter, so hecould not distinguish between water droplets, water-solution droplets and dry aerosols. However, his datadefinitely showed a more negative aerosol power distri-bution (relatively more small particles) for the humid,maritime-tropical air mass than the dryer, continental-polar air mass.The predictions from the empirical formula of Davieset al. (1975) for 17 August, presented in Table 4, over-TABLE 4. Global solar flux (W m") observed and predicted, fromempirical equations of Davies et al. (1975), for 17 August 1972.The presence of a proportionately greater number ofsmall particles than that indicated by an r-4 powerdistribution is difficult to attribute solely to relativehumidity, The effects of relative humidity on thecreation, growth and destruction of particles and water-solution droplets are not simply described. Observationshave shown more small water-soluble particles thanlarge particles in maritime aerosols (see Junge, 1972),but maritime aerosols typically have more largeparticles than an r4 power distribution (see Toon andPollack, 1976). Urban areas usually have more smallparticles than rural areas (see Willeke and Whitby,1975), but, in this case, since both the urban and ruralareas had similar turbidities, the aerosol at both sitesis probably not of urban origin. Schere's (1975) mea-Cosine ofsolar zenithangle CudObservationsRural UrbanPredictionsK = 0.95K = 0.880.10.20.30.40.50.60.70.80.940 40100 90175 175275 260375 360480 480600 600730 740785 70960 35159 115268 212378 315486 418606 534731 656841 763962 8820~~0~~~1977 ROBERT W. BERGSTROM AND JAMES T. PETERSON 1115estimate the global flux. For this case, calculations usinga value of k=0.82 (results not shown) fit the datafairly well. Thus, by relating the K values to routinelyobserved turbidity data, it would be possible to im-prove the accuracy of the global solar flux estimates.The observed and predicted [using Eqs. (1)-(4)]ultraviolet fluxes are shown in Table 5. In this casealso, the nonabsorbing aerosol assumption (Go= 0.999)gives better agreement than that for the absorbingaerosol. Also, the results with X-1.62 give somewhatbetter agreement with the observations than the initialaerosol model. However, the turbidity values at 0.38and 0.5 pm indicate that, in this spectral region, thewavelength dependence of the aerosol optical thicknesswas about A-1. Thus, the UV data tend to support theconsiderably lessened absorption hypothesis.The result of the hazy day comparison is that the apriori choice of aerosol properties gave results thatwere not in good agreement with the observed values.The predicted values could be made to agree with theobservations by assuming that there were proportion-ately more small particles and that the particles wereless absorbing than the model initially assumed. Whilethese assumptions are speculative, they are reasonable,900800N700VIc cgm- 600LLa, 00'E 500?c02 400-z-c? 30050U-2 20021000TABLE 5. Global ultraviolet (X0.38 rm) flux (W m-*) observedandpredicted, from Eqs. (1)-(4), for ruralsite on 17 August 1972.Cosinesolar zenith Observed Predicted Rural UVangle (po) Rural UV I I1 I11 IV0.5 15.5 11.74 9.37 18.65 17.560.6 22.5 15.25 12.07 24.21 22.750.7 28.4 19.43 15.42 30.38 28.520.8 35.1 25.74 21.02 37.67 35.60~~~~I, initial aerosol model.111, G0=o.999.IV, T=X-'.~', Go=O.999.11, TZ1-I 62.and could represent the influence of humidity anddifferent air mass origins.5. ConclusionsMeasurements of the solar radiant energy taken inthe St. Louis area in August 1972 have been comparedwith predictions from an approximate solution to theradiative transfer equation and from an empiricalequation. The comparisons show that :1) For the clear day, the predictions with the aI I I I I I I I II___ Observations. rural /- _-- Observations, urbano Predictions with initial aerosol modelx Predictions with ir, = 0.999/- X- 0-#I I I I I I 1I 2 .3 4 5 6 7 8 9 Ipo, Cosine solar zenith angleFIG. 7. Observed and predicted global solar fluxes versus the cosine of the solar zenith angle (morning hours) on 17 August 1972.VOLUME 161116 JOURNAL OF APPLIED METEOROLOGYpriori choice of aerosol properties were in good agree-ment with the observations.2) For the hazy day, the predictions with the initialaerosol model did not agree well with the observations.The predicted values could be made to agree with theobserved values by assuming that there were propor-tionately more small particles and that the particleswere less absorbing than the model initially assumed ;these changes could represent the influence of relativehumidity and different air mass characteristics.3) The simple formula given by Davies et al. (1975)could be made to give results that were in agreementwith the observations, if the aerosol transmission factoris appropriately chosen.4) In comparing predicted and observed solar radiantenergy values, it is important to determine separatelythe aerosol optical properties as a function of wave-length and the size distribution, since the variabilityof the aerosol makes it difficult to use typical or averagevalues.Acknowledgments. R. W. Bergstrom was supportedby a National Research Council Postdoctoral Associate-ship at the National Aeronautics and Space Admini-stration's Ames Research Center during the time of thisstudy. Support was also provided by the U. S. Environ-mental Protection Agency, Research Triangle Park,to NASA Ames under Interagency Agreement No.EPA-IAG-DS-F672. The authors wish to thank Drs.Pat Hamill and Brian Toon for many helpful discussions.REFERENCESAtwater, M. A,, and P. S. Brown, Jr., 1974: Numerical compu- tations of the latitudinal variation of solar radiation for anatmosphere of varying opacity. J. Appl. Meteor., 13,289-297.Bergstrom, R. W., and R. Viskanta, 1973: Prediction of the solarradiant flux and heating rates in a polluted atmosphere.Tellus, 75, 486-498._- , and -, 1974: Spherical harmonics approximation forradiative transfer in polluted atmospheres. Progress in Astro-nautics and Aeronautics, Val. 35, The MIT press, 23-40.Braslau, N., and J. V. Dave, 1973: Effect of aerosols on thetransfer of solar energy through realistic model atmospheres.Part 1: Nonabsorbing aerosols. J. Appl. Meteor., 21,601-615.Covert, D. S., R. J. Charlson and N. C. Ahlquist, 1972 : A studyof the relationship of chemical composition and humidityto light scattering by aerosols. J. Appl. Meteor., 11, 968-976.Davies, J. A,, W. Schertzer and M. Nunez, 1975: Estimatingglobal solar radiation. 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Res., 77, 5183-5200.McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz andJ. S. Garing, 1972: Optical properties of the atmosphere, 3rd. ed. AFCRL-72-0497.Monteith, J. L., 1962: Attenuation of solar radiation: a climato-logical study. Quart. J. Roy. Meteor. SOC., 88, 508-521.Peterson, J. T., and E. C. Flowers, 1976: Interactions between airpollution and solar radiation. Solar Energy (in press).Schere, K. L., 1975 : Characteristics of the ambient atmosphericaerosol structure over St. Louis, Ma. M.S. thesis, Dept.of Meteorology, Pennsylvania State University.Shettle, E. P., and R. W. Fenn, 1975 : Models of the atmosphericaerosols and their optical properties. Presented at 22ndTech. Meeting on Optical Propagation in the Atmosphere,27-31 October 1975, Lyngby, Denmark.Thekaekara, M. P., 1974: Extraterrestrial solar spectrum,3000-6100 A at 1-A intervals. Appl. Opt., 13, 518-522.Toon, 0. B., and J. B. Pollack, 1976: A global average model ofatmospheric aerosols for radiative transfer calculations. J.Appl. Meteor., 15, 225-246.Whitby, K. T., R. 3. Husar and B. Y. H. Liu, 1972 : The aerosolsize distribution of Los Angeles smog. J. Colloid Interface sei., 39, 177-204.Willeke, K., and K. T. Whitby, 1975: Atmospheric aerosols:Size distribution interpretation. J. Air Pollut. ControlASSOL., 25, 529-534.43, 119-132.33, 1120-1124.

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