A simple hourly clear-sky solar radiation model based on meteorological parameters

Sofur Em'rev, \ o] ~1, N o ~, pp 425-43 k It)8~ (~38~92X/83/05042s4)7503.00/0 Primed in Great Britain ~ Iq83 Pergamon Press Ltd

A SIMPLE HOURLY CLEAR-SKY SOLAR RADIATION MODEL BASED ON METEOROLOGICAL PARAMETERS

J. E. SHERRY and C. G. JUSTUS School of Geophysical Sciences, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

(Received 22 January 1982; accepted 18 June 1982)

Abstract--An hourly solar radiation model, based on observed meteorological data, was developed and tested. As a means of comparison, the Watt and Bird models and the Solmet regression models were also tested. Several conclusions were drawn about the parameterization of solar radiation-depleting parameters. It was determined that a reasonable estimate of lower layer aerosol extinction can be determined using humidity, visibility, and mixing height. The parameterization of water vapor absorption obtained by atmospheric rather than laboratory observations was found to give better model results.

INTRODUCTION

Solar energy received at the surface of the earth is an important and fundamental parameter in today's world. Solar data are used in diverse disciplines, including cli- matology, micro-meteorology, biology, agriculture, glaciology, urban planning, architecture, and mechanical and environmental engineering.

The primary objectives of the following discussion are: (1) to examine individual radiation-depleting atmospheric parameters and their application to a solar radiation model; (2) to develop an improved clear-sky radiation model based on observed meteorological data; (3) to compare the results of the newly-developed model with results from other existing models using data obtained in Atlanta, Georgia.

Atmospheric parameters which deplete solar radiation vary considerably in the magnitude of their effect. Ac- cording to Watt[l] the five clear-sky, solar-radiation- depleting atmospheric parameters and their relative effect on solar radiation are ozone (0.5-3.0 per cent), upper-layer aerosol (1.9-11 per cent), dry air (11-13 per cent), water vapor (3.5-14 per cent), and lower-layer aerosol (0.1-26 per cent). With the exception of ozone, which (except in certain wavelength regions) has a relatively small effect on solar radiation, the first five of these solar-radiation-depleting parameters were examined by Sherry[2] in order to determine an effective way to parameterize their effects in a clear-sky solar radiation model.

In the case of ozone, the parameterization of Lacis and Hansen[3] will be employed in the clear-sky solar radiation model without examination or discussion. The reason for this is that ozone has a relatively small effect on the depletion of solar radiation except within a range of UV wavelengths, and it is thought that there is not very much variability in this effect. The examination of the other four parameters (Sherry[2]) includes the results of previous studies, discussion of the physics of the individual parameters, and comparisons with measured data. In all cases, the physics of the optical properties of the atmosphere are stressed.

With the results obtained by Sherry [2], a simple broadband, clear-sky insolation model is developed, which

includes the effects of the first five solar-radiation depleting parameters. The basis of this model is the Suckling and Hay [4] clear-sky model. Some modifications are included to better represent the physical nature of the atmosphere.

CLEAR SKY INSOLATION MODEL

During cloudless periods, the direct-beam solar radiation received at the earth's surface is the extra-terrestrial radiation at the top of the atmosphere modified by atmospheric absorption and scattering. As defined by Suckling and Hay[4], the direct normal solar radiation for clear skies received at the surface can be expressed a s

I~.~= IoT.~T.oT~,T~,To,. (1)

where the T terms are transmission functions for water vapor absorption, aerosol or dust absorption, water vapor scattering, Rayleigh scattering and aerosol or dust scattering. Io (kJ/mZhr) is the extraterrestrial normal solar radiation which is expressed by Watt[l] as:

1 -< Nday-< 93

Io ~ 4914.0(1.0 - 0.0343 sin (1.0(Nday - 93))) (2)

94 --< Nday --< 277

Io = 4914.0(1.0-- 0.327 sin (0.978(Nday -- 277))) (3)

278 -< Nday ~ 365 (4)

Io -~ 4914.0 (1.0 + 0.0343 sin (0.989(Nday - 277))),

where Nday is the Julian day of the year, the solar constant is assumed to be 4914kJ/m2hr (1.365 kW/m 2) and degree measure is used in the sine functions.

But, as will be discussed later, the anomolous, large magnitude water vapor scattering can be dropped and a much smaller magnitude water vapor scattering can be included with the aerosol treatment. The aerosol terms can be separated to reflect upper and lower turbidity individually. The resulting expression for direct normal solar radiation, including a term for ozone absorption,

425

426 J.E. SHERRY and C. G. JUSTUS

can be expressed as solar radiation (Idh~) is then the sum of DS and DB

Idn c = I o T o z T w a T a a I T a a u Z r s T a s I T a s u , (5) Idh~ = DS + DB. (9)

where the T terms are transmission functions for ozone absorption, water vapor absorption, lower aerosol absorption, upper aerosol absorption, Rayleigh scattering, lower aerosol scattering, and upper aerosol scattering.

In clear-sky conditions, the diffuse (indirect) sky radiation is assumed to be made up of a portion of direct solar radiation, single scattered off atmospheric constituents (DS), plus a multiple-scattering component (DB), which is due to a single reflection of the direct beam and DS off the earth's surface followed by backscattering from atmospheric constituents.

The atmospheric-scattered, direct-beam portion of the diffuse radiation, DB, as received on the horizontal surface is modeled as

DS ~ Io cos (z) To~T,~T,,,T~,[(0.5 T~T~s,( I.O - T,,))

+ F~T~(1.0 - T, mT~,~,,)], (6)

where z is the solar zenith angle. Equation (6) assumes that one half the Rayleigh scattering is directed earthward and that the portion of the aerosol scattering directed earthward is represented by F~ which is expressed by Sherry [2] as

F~ = 1.0 - 10.0[(- 0.798 cos (z)) - 0.332]. (7)

The ground-reflected, atmospheric-backscattered diffuse term, DB, is modeled as

2 DB = Ag(ld,~ + DS) T~ab Ta~lb[(O.S T ~,~lb T~ob T,~lh

× ( l .O - L s ~ ) )

+ (0.16(1.0 - T, slb)) + (O.16T~bT~lbT~bT~a,bT2~lb

X (1.0 -- T~s,b)))], (8)

where Ag is the surface albedo; and Twob, T,~,,ib, T~,~b, Toa,b, To~b, and T~,b are the transmission functions for an air mass of 1.66 (Suckling and Hay[4] for water vapor absorption, lower aerosol absorption, lower aerosol scattering, upper aerosol absorption, upper aerosol scattering, and Rayleigh scattering respectively. The surface albedo is assumed to be 0.2 for all conditions except snow cover, for which the albedo is assumed to be 0.8 (Suckling and Hay[4]). At the average backscattering air mass of 1.66, as used by Suckling and Hay[4]), the coefficients 0.5 and 0.16 represent the concept that 50 per cent of the Rayleigh scattering would be backscattered to earth while only 16 per cent of the aerosol scattering would be directed earthward (i.e. backscattered).

Both the diffuse components as expressed here differ from the Suckling and Hay [4] version, in that the Suck- ling and Hay model has a 50 per cent earthward scatter for both aerosol and Rayleigh scattering, a turbidity always equal to a single assumed value, a water vapor scattering term, and the assumption that multiply-scattered radiation passes through each atmospheric layer only once. The horizontal component of clear-sky diffuse

Following is a summary of the methods to be used in calculating the transmissivities (T terms) to be used in the relations for the direct beam (lu,c) and diffuse (Iah~) radiation components, eqns (5) and (9). By using ap- proximations to the transmission curves of Houghton[5], the transmission function, T~, for Rayleigh scattering as a function of air mass can be expressed as

T,s = 0.972 - 0.08262m + 0.00933m 2 - 0.00095m 3

+ 0.0000437m 4, (10)

where m is the optical air mass with a pressure cor- rection, expressed by Kasten [6] as

m = (1.0/cos (z)+0.15(93.885- z) "25(p/Po), (11)

where z is the solar zenith angle in degrees, P is the surface pressure and Po is the standard atmospheric pressure. According to Kondratyev[7], for solar zenith angles less than 60 degrees, sufficient accuracy can be obtained using a simplified version of eqn (11), which can be expressed as

m = sec (z). (12)

As a result of geometric considerations (z-> 60 °) and effects of refractive index (z_>80°), a more involved expression than eqn (12) is required for large zenith angles. Bird and Hulstrom[8] found that eqn (11) was correct to within 1 per cent for z less than 89 °.

The transmission functions for water vapor absorption are expressed by Houghton [9] as

T~a = 1.0 - 0.09(Pwm) °39 (13)

o r

Tw, = 1.0 - 0.077(Pwm) °3°, (14)

where Pw is precipitable water in centimeters. The transmission function for ozone absorption, Toz,

was calculated by Lacis and Hansen[3] and expressed by Hay and Won[10] in two parts. For the Chappuis band (0.5-0.7 gin), the absorption for ozone can be expressed a s

vis 0.02118x (15) A oz (x) = 1.0 + 0.0042x + 0.00000323x 2'

where x is the product of the ozone depth in mm and the path length modifier Fz. Fz is expressed by Watt[l] as

Fz H2Fz:- HtFzl //2 - H~ ' (16)

where/-/1 and HE are the heights of the bottom and top of the ozone layer (i.e. 20 and 40 km) and Fzi can be

A simple hourly clear-sky

expressed as

F~ : [ ( (RJ~) cos (z)) z + 2.0(RJH~) + 1.0)] 0.5

- (RJH() cos (z) (17)

w h e r e Re is the radius of the earth, which is 6.4 x 10 ~ km. The second part of the ozone absorption is the Hartley and Huggins band (< 0.35 p~m) and is expressed by Hay and Won[10] as

A~,~(x) = 0 .1082x / (1 .0 + 13 .86x) °8°s + 0.006581

1.0 + (10.36x)3]. (18)

Lacis and Hansen[3] found that eqn (15) is precise to the fourth decimal and that eqn (18) has a maximum error of <- 0.5%. The total absorption by ozone is then the sum of A~ and A j : and is expressed as

Ato °ta' = A~ v + A~,~= '.

The transmissivity of ozone is then

T,,~ = 1.0 - A~o °~j.

The transmission functions for lower aerosol absorption and scattering (Sherry[l]) are:

Taa I = e ((l.O--taO)~lm)

Tasl = e ( ~°~lm)

where ~Oo is the single scattering albedo and ~-~ is the aerosol optical depth for the lower layer aerosol (Sherry[l]) and is expressed as:

7", = c ( m l v ) ,

where M is the mixing height (kin) as calclated by the NWS twice daily and interpolated throughout the day, v is the NWS-reported visibility (in kin), corrected to reflect the mid-marker visibility, and the coefficient c is 3.9 if the atmosphere is homogeneous in the lower aerosol layer. The single scattering albedo was determined using the AFGL models (Shettle and Fenn[ll]).

The transmission functions for upper aerosol absorption and scattering can be expressed as

Zaau = e ( (1 ~ou)TuFz(upperaerosot))

Tas u ~- e (-~ou~uFz(upperaerosol) ),

solar radiation model 427

where ~Oou is the single scattering albedo for the upper aerosol layer (Sherry[l], r~ is the average aerosol optical depth already defined for the upper aerosol layer which is approx. 0.025 as expressed by Sherry[l] and F:(upp . . . . . . . . ,> is determined in the same way for Fz( . . . . . >, via eqn (16) with H,=15.0km and /-/2 = 25.0 km. This is not to say that there are no aerosols in the 3-5 km region. The choice of 15 to 25km for the upper aerosol layer was made to coincide with Watt's constituent layers of the atmosphere in order to determine the path length.

Global horizontal solar radiation of clear skies (Ighc) is then simply the sum of the horizontal components of the direct beam, Iahc from eqn (5), and the diffuse radiation, Idhc from eqn (9),

lRh,. = Iah~ COS (Z) +Iah,. (26)

RESULTS AND DISCUSSION

(19) Two approaches were taken in the testing of the solar radiation models used in this study. The first was to test the sensitivity of the models to variations in certain input data, and the second was to test the accuracy of the

(20) modeled results with measured data. The first was accomplished by varying the types of input data available for use in the models. The second was accomplished by taking the ratio of the r.m.s, difference between the modeled and measured solar radiation and the average of

(2|) these two quantities. This ratio is defined as the (22) coefficient of variability but, for brevity, will be referred

to as the r.m.s, error (expressed in per cent). For the sake of convenience, the model developed in this paper will be referred to as the Georgia Tech (GT) model.

Water vapor (23) When eqns (13) and (14) were each used to determine

water vapor absorption in the Georgia Tech model, better results were obtained by using eqn (13) (see Table 1). The results in Table 1 were obtained by using modeled results from hours ending or beginning on the hour of the 3-hourly National Weather Service (NWS) observations, and conditions when the normal incidence pyrheliometer (NIP per cent sunshine indicator) recorded 100 per cent sunshine and the NWS 3-hourly report indicated no clouds. The results in Table 1, while not conclusively proving the validity of eqn (13), do indicate that the use of eqn (13) rather than eqn (14), in the Georgia Tech

(24) model does give slightly better results. This shows that a parameterization of Twa based on atmospheric

(25) measurements eqn (13) was more effective when used in

Table 1. Geor~a Tech Model, r.m.s./avg (per cent) April through December 1979 for Georgia Tech, Atlanta, Georgia

Horizontal Direct Horizontal Diffuse Normal Global

Twa (Equation 13) 37.5 ll.O 7.1

Twa (Equation 14) 43.8 11.7 9.1

428 J. E. SHERRY and C. G. JUSTUS

the Georgia Tech model rather than a parameterization based on laboratory measurements (eqn 14).

Aerosols The value of the constant (c) in eqn (23) was deter-

mined by first using the Georgia Tech model to calculate the direct normal solar radiation with an aerosol transmissivity of 1.0, for clear sky conditions (i,e. per cent sunshine as determined by the normal incidence pyrheliometer (NIP) equal to 100 per cent and no reported clouds). Then the ratio of the measured direct normal radiation (less the circumsolar radiation) and the calculated direct normal radiation yielded an inferred broadband lower layer aerosol transmissivity (Ta~) assuming that the Georgia Tech model accurately deals with all other solar radiation modifying parameters. The inferred aerosol optical depth was then found by solving for ~'~ in the relationship:

T., = e ~ ~,mJ (27)

where m = sec (z) is the air mass and z is the solar zenith angle. Table 2 shows the resulting values of c for ranges of relative humidities and different methods for determining water vapor absorption. When the inferred aerosol optical depth is plotted vs the ratio of the mixing height and visibility (Figs. 1 and 2), the values of c can be determined from the simple slope. Table 2 also lists the clear-sky, direct normal model results, which were calculated for elevation angles greater than 25 degrees, 100 per cent sunshine as recorded by the NIP and no reported clouds. Only modeled results for hours ending or beginning on the hour of the 3-hourly NWS report were considered. As can be seen in Table 2, the direct normal modeled results are slightly better using eqn (13) for determining Tw, as was already discussed.

The dependence of the optical properties of aerosol on moisture parameters is not a new concept. According to Peterson et al. [12], measured turbidity averages for relative humidities less than 40 per cent are plainly less than those for relative humidities greater than 40 per cent (Table 3). Peterson also found that there was no clear relationship between relative humidity and measured turbidity averages for relative humidities greater than 40 per cent. A similar step function of relative humidity dependent turbidity averages is indicated by the results of this study, as can be seen when the averages between

Table 2. Georgia Tech direct normal r.m.s./avg (per cent) April through December for Georgia, Atlanta, Georgia

Relative Direct Humidity (%) Twa c Normal

<48 Equation 13 3.16 { 11 .0

>48 Equation 13 4.49

<48 Equation 14 3.71 { I I .7

>48 Equation 14 4.98

RN<4B% 5S=II~0Z EL>?5

I

c~ LJ

C l u

cL c~

w

O-

EL Z

.6

L × × x . 2 ~ W × × x

.O ~ - - ~ J - - ~ . .D .2 .4 . - - - - - - a . 8

( 3 . 1 6 / V I 5 ( K M ) ) * M ] X H G T ( K M )

Fig. 1. Inferred vs calculated lower layer aerosol optical depth for relative humidity less than 48 per cent (Atlanta, Georgia,

Apr.-Dec. '79).

r.m.s, between x and y- - 0.0583 avg between x and y - - 0.1022 r.m.s./avg (per cent) --57.0 simple slope - - 1.0181

calculated and inferred aerosol depth obtained from Figs. 1 and 2 are included in Table 3. It should be noted that the relative humidity is this study was determined from measurements of dew point and ambient temperature at a height of 51 m above the surface. It is not known at what height the relative humidity was measured for the Peterson study. A possible explanation of why the average turbidity values are functions of relative humidity is that at low surface relative humidities the aerosols

C]

J

u

CD

t~

l%W>~flZ SS=IBg~ EL>?5

I q F

x x×

×××xx

~x

×× _ I

.0 .2

F T

x

x x

~ x

× x /

× ×

x

x x

.4 .6 .8 I

(4.49/V]S(KM))-M~ XHGT(KM)

Fig. 2. Inferred vs calculated lower layer aerosol optical depth for relative humidity greater than 48 per cent (Atlanta, Georgia

Tech, Apr.-Dec. '79).

r.m.s, between x and y-- 0.0964 avg between x and y -- 0.2229 r,m.s./avg (per cent) --43.2 Simple slope -- 1.0163

A simple hourly clear-sky solar radiation model 429

Table 3. Average optical depth as a function of relative humidity and time of the year (number of observations are in parenthesis)

Relative Humidity (%)

Study Time of Year 0 -40 41-70 71-85 >85

Peterson Spring 0.090 0 .128 0 .135 0 . I I I (848) (782) (176) (58)

Summer 0.146 0.262 0 .245 0.281 (123) (1063) (385) (145)

Autumn 0.053 0.099 0 .103 0.114 (516) (993) (336) (175)

Winter 0.048 0.056 0 .059 0.053 (821) (799) (200) (I05)

0-48 48-I00

Georgia Tech Apr-Dec 0.102 0.223 (74) (48)

throughout the mixing layer should be dry, and thus reduced in size. This would be consistent with the sug- gestion by Houghton[9] that the scattering attributed to water vapor molecules is probably due to particles of larger size than water vapor molecules. Houghton further suggests that these larger particles are nuclei of condensation which are known to be of approximately the required size and number to account for the observed scattering. The Georgia Tech model contains no explicit term for water vapor scattering, but rather includes the effect of water vapor on the scattering of solar radiation by using a larger coefficient in eqn (23) to allow for the condensation of water vapor in hygroscopic nuclei, for surface relative humidities greater than 48 per cent. The differences in the value of c for different relative humidities is thought to involve differing visibility effects caused by wet and dry hygroscopic aerosols. The fact that c is not equal to 3.9 indicates that the mixing layer is not homogeneous, which is what one would expect.

When several different direct-normal results were compared for clear-sky conditions, it was found that there was great difference in model perfol:mance. The Georgia Tech model and the Bird model by far gave the best results at 10.0 and 13.1 per cent r.m.s, error, respectively (Table 4). The Watt and Randall models gave poor results, with r.m.s, errors greater than 30 per cent (Table 4). Figures 3-5 are plots of measured vs modeled clear- sky direct normal radiation for the Georgia Tech, Bird and SOLMET regression (Randall) models, respectively.

For clear sky global radiation, the results of the Watt model are still poor, with r.m.s, error of 21.9 per cent, but the Georgia Tech model and the ARL model are excellent, with nearly equal r.m.s, errors of 7.0 per cent, respectively (Table 4). Figures 6 and 7 are plots of measured vs modeled clear-sky horizontal global radiation for the Georgia Tech and the SOLMET regression (ARL) models, respectively. It should be noted that most of the error in the Georgia Tech global model (Fig. 6) is

Table 4. Hourly model r.m.s./avg (per cent) for clear skies (Atlanta, Georgia Tech, Apt-Dec 1979).

Clearness Diffuse Direct Global MODEL Indicator Horizontal N o r m a l Horizontal

Watt NIP I 49.5 30.4 21,9

SOLMET NIP and Cloud 72.9 32.4 7.2 Regression 3 Report 2

Bird NIP and Cloud -- 13.1 --- Report

Georgia NIP and Cloud 37.1 IO.O 7.0 Tech Report

INormal Incidence Pyrheliometer

23-hourly NWS observations

3The SOLMET regression model uses the Randall regression model for d i rec t normal and the ARL regression model for horizontal global (Nashvi l le coe f f i c i en t s ) .

430 J .E. SHERRY and C. G. JUSTUS

N

v

c~ o z

p-

t~ LJ c~

co c~

1 9 7 9 ~PR-DEC 5 5 = 1 ~ I

4 0 0 0 - - ~ ~ --

3500

3000

2 5 0 0

2000

1500

I 0 0 0

500

0

5L= .BB5 Y= t l l 2 . E-~'56.3t~9

I I i t

Xxx x )c~ .,~t ~x x

x . I , × ~{ × 2

~ × × x x × ×

L L t_ Z A_ . . . ~ 500 i0OO 1500 2000 2500 3000 5500 4000

G T D I R E C T N O R M A L ( K J / M 2 )

Fig. 3. Measured vs modeled clear sky direct normal insolation using the Georgia Tech model• In this figure and in Figs. 4-9, SL is the slope of the least squares best fit line, Y is the y-intercept of the least squares best fit line, and E is the r.m.s, error between

the y-ordinate and the least squares best fit line.

r.m.s, between x and y-- 280.5 avg of x and y --2796.8 r.m.s./avg (per cent) - - 10.0

actually of a multiplicative nature. The regression slope (SL) is 0.945, compared to 1.01 for the SOLMET model (Fig. 7). If r.m.s, regression errors (E) are compared, the Georgia Tech model global has only 4.4 per cent compared to 6.7 per cent r.m.s, regression error for the SOLMET model. This effect could have been artificially corrected by an ad-hoc multiplier factor (e.g. 0.945) to the Georgia Tech model, but such a modification would not have illuminated the remaining physical effects which

1979 RPR-DEC S5=IgOI SL= .51t

4000 ~ ~ ~

5500 04

~ooo

d 2500

~E 07 C3 z 2000

~J uJ o: 1500

• I 000 u~ cE Ld

~- 500

0 0

Y= . 1 7 0 E 8 ~ E = ~ 6 5 . # 2 9

x x ~ xx

~ X x x x ~ x × x x

x × x × × x x × × {

× × x × × x

I

s0o i o'oc~- Is'oo 2000

I

2500 50100 35t00 4000

S O L M E T D I R E C T N O R M A L ( K J / M 2 )

Fig. 5. Measured vs modeled clear sky direct normal insolation using the SOLMET regression (Randall) model.

r.m.s, between x and y-- 823.4 avg between x and y --2541.6 r.m.s./avg (per cent) - - 32.4

should be accounted for to correct this, nor is it certain that this discrepancy should be similar for applying the model at other site locations.

The Watt diffuse model is a simplified way to deal with diffuse radiation• When the Watt model results are compared with the more complex Georgia Tech diffuse model, the Watt model is shown to be considerably less accurate. The coefficient of variability for the Watt clear- sky diffuse results is 49.5 per cent, compared with 37.1 per cent for the Georgia Tech model (Table 4). Figure 8 is a plot of the measured vs clear-sky horizontal diffuse radiation for the Georgia Tech model•

1 9 7 9 RPR-DEE SS=100Z SL .92/, Y= '428. E = 2 7 2 . 5 2 ~

4000 - - ~ I i 9 - ~ T - - - - " 9 - - i

'1

-~ 3000 × x

x :~ ×

cc x x x x X ~ x ~

2000 ~ '~ × # × × x x x

x ×

t • 1 0 0 0

500

O0 50O IO'O0 1500 2000 2500 5000 35O0 4000

B I R D D I R E C T N O R M R L ( K J / M 2 )

Fig. 4. Measured vs modeled clear sky direct normal insolation using the Bird model.


N ~E

v

GZ 123 0 J

uJ Cr_

uo cr LL~

1 9 7 9 ~PR-DEC S S = I O g 2

4500 - ~ ~

~000

3500

3 0 0 0

2500

2000

"'f / 10013 ×

500 ~ x

$ L = . 9 4 5 Y = 1 3 . 6 [= 8 3 . ~ 1 7

. q

0 .5o0 1000 1500 a00o 2500 3o0o 3500 4o00 4500

(ST G L O B A L M O D E L ( K J / M 2 )

Fig. 6. Measured vs modeled clear sky horizontal global insolation using the Georgia Tech model.


A simple hourly clear-sky solar radiation model

4500

4000

1 9 7 9 flPR-OEE S S = 1 8 ~ SL= 1 . e l ¥ = 2 3 . 1 E = 1 2 1 . 4 7 1

I f I I I ~ I I

5500 c~J

~. 5000

8500

% aO00

1500

% tn I000

50O

0 5;0 ,0'00 ~0 ~-0'00 ~5~0 30'00 ~5'00 4o;0 4~00 50LMET GLOBRL MODEL (KJ /M2)

Fig. 7. Measured vs modeled clear sky horizontal global insolation using the SOLMET regression (ARL) model.

d,×


Recently, Bird and Hulstrom[13] have also developed a model for diffuse radiation (in clear-sky only). This model has not yet been compared to the Georgia Tech model or to the measured data.

CONCLUSIONS

The individual solar-radiation-depleting atmospheric parameters were examined in this study, and from this

1 9 7 9 A P R ° D E E S S - I ~ Z S L = . 9 2 B Y = - $ 6 . 7 E ~ 9 1 . 6 6 2

1 8 0 0 i I i I i ~ I ; - -

431

x x x x x x

x

× x

×

×× ×

_ I ~ I I I _ _ / ~ Z _ _

2 0 0 4 0 0 6 0 0 8 0 0 I 0 0 0 1 4 0 0 t200 1600 1800

GT DIFFUSE MODEL (K J IM2)

Fig. 8. Measured vs modeled clear sky horizontal diffuse insolation using the Georgia Tech model.

r.m.s, between x and y--128.1 avg between x and y --345.2 r.m.s./avg (per cent) -- 37.1

1600

1400

1200

moo

L L L 800 C3

600 L O

tn 400 taJ

200

0

examination several conclusions can be drawn. In regards to water vapor, it was found that the apparent water vapor scattering was more properly treated in conjunction with the effect of aerosol scattering, since it is most probably caused by scattering by hygroscopic nuclei. Also, of the two most widely used water vapor absorption equations, the one developed from atmospheric measurements (eqn 13) proved to give better results in the Georgia Tech model. It was also determined that a reasonable estimate of aerosol extinction can be determined using relative humidity, visibility and mixing height data.

The comparison of model results indicates that for clear-sky, global-horizontal solar radiation, the Georgia Tech and SOLMET regression models gave the best results. However, the SOLMET regression, which uses calculated global horizontal Randall solar radiation to determine the direct and ultimately the diffuse solar radiation, was incapable of producing acceptable diffuse horizontal and direct normal solar radiation results.

REFERENCES

1. A. D. Watt, On the nature and distribution of solar radiation. HCPlT2552-OI, U.S. Department of Energy, Washington, D.C., U.S.G.P.O. (1978).

2. J. E. Sherry, A simple hourly solar insolation model based on meteorological parameters and its application to solar radiation resource assessment in the southeastern United States. Georgia Institute of Technology, Masters Thesis, Atlanta, Georgia (1981).

3. A. A. Lacis and J. E. Hansen, A parameterization for the absorption of solar radiation in the earth's atmosphere. J. Atmospheric Sci. 31, 118-133 (1974).

4. P. W. Suckling and J. E. Hay, Modeling direct, diffuse and total solar radiation for cloudless days. Atmosphere 14, 298- 308 (1976).

5. H. G. Houghton, On the annual heat balance of the northern hemisphere. J. Meteor. 11, 1-9 (1954).

6. F. Kasten, A new table and approximation formula for the relative optical air mass. Arch. Meteor. Geophys. Bioklin. 206-223 (1966).

7. K. Y. Kondratyev, Radiation in the Atmosphere. Academic Press, New York (1969).

8. R. E. Bird and R. L. Hulstrom, Direct insolation models. SERflTR-335-344, Solar Energy Research Institute, Golden, Colorado (1980).

9. H. G. Houghton, Physical meteorology prepared notes. Massachusetts Institute of Technology, Cambridge, Mas- sachusetts (1962).

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A simple hourly clear-sky solar radiation model based on meteorological parameters