Solar Energy Vol. 33, No. 6, pp. 493 499. 1984 0038-092X/84 $3,00 ÷ .00 Printed in the U.S.A. ~ 1985 Pergamon Press Ltd.

G R O U N D LEVEL SOLAR RADIATION PREDICTION MODEL INCLUDING CLOUD COVER EFFECTSt

RUSSELL BRINSFIELD~ Department of Agricultural Engineering, University of Maryland, Queenstown, MD 21658, U.S.A.

and

MELIH YARAMANOGLU§ and FREDRICK WHEATON¶ Department of Agricultural Engineering, University of Maryland, College Park, MD 20740, U.S.A.

(Received 2 August 1983; accepted 9 February 1984)

Abstract--The model Estimated Solar Radiation (ESR) was developed to predict solar radiation on a horizontal surface for any latitude as a function of total opaque cloud cover. ESR was verified by comparing predicted and observed daily totals of solar radiation on a horizontal surface for Salisbury, Maryland Oat. 38.5°N), and Ely, Nevada (lat. 39.2°N), using hourly values of observed total opaque cloud cover for each location obtained from the National Climatic Center, Asheville, North Carolina. Although the model slightly underpredicts on those days when total opaque cloud cover is high (9-10) and overpredicts on those days when total opaque cloud cover is low (0-1), it provides excellent correlation with observed data (R = 0.87 for Salisbury and 0.94 for Ely).

INTRODUCTION

Clouds and their accompanying weather patterns are the most significant atmospheric phenomena re- stricting the availability of solar radiation at the earth 's surface. If they shade the sun significantly, the direct normal solar radiation (Ia.) vanishes to zero, while diffuse solar radiation (la) does not change significantly with increasing cloud cover (CC) until CC 3-4 (expressed as tenths of the sky covered) [1 ]. Diffuse radiation continues to increase to a maximum at approximately CC - 8-9 then decreases as the clouds cover more of the sky[l] . Modeling both the spatial and temporal distribution of clouds is neces- sary to reliably predict radiation availability at a site.

LITERATURE REVIEW

Predicting solar radiation in places where no mea- surements have been made requires estimates of sun- shine hours or cloud cover. However, when consid- ering proposed regions for application of solar devices, it was found that very little information was available detailing hours of sunshine. Because of this limitation, several investigators[2-4] considered the possibility of correlating solar radiation with reported cloud cover, a variable for which data exists. As a result, several empirical equations were developed which related the two variables.

More recently, considerable effort has been di- rected to developing models to predict direct and

tScientific Article No. A-3734, Contribution No. 6710 of the Maryland Agricultural Experiment Station (Department of Agricultural Engineering).

:~Head, Wye Research and Education Center and Affiliate Assistant Professor.

§Assistant Professor. ¶Professor.

493

diffuse solar radiation for clear and cloudy days utiliz- ing the relationships mentioned above. For example, Barbaro et al.[5] developed a model to predict both direct and diffuse solar radiation by modifying a model developed by Cole[6] for direct solar radiation to include a cloudy sky condition. More general clear sky direct radiation models were developed by King and Buckius [7] and Hatfield et al. [8] utilizing the fun- damental relationships between the sun and earth. These models accounted for gaseous absorptions, as well aerosol scattering. A study by Iderial[9] extended the work of King and Buckius[7] by allowing calcu- lation of diffuse radiation, as well as direct radiation for cloudy skies. Several investigators [ 1 ~ 12] have de- veloped methods for estimating solar radiation sums based either on sunshine or cloudiness observations.

The applications of most of these models require detailed knowledge of local hourly sums of direct and diffuse radiation for clear skies as well as hourly cloud cover observations in various layers, data not avail- able for most locations. Thus, the above models need to be extended or new ones developed which will ade- quately predict solar radiation at sites lacking detailed meteorological data.

PROCEDURE

Model logic

The simplest method to model solar radiation on a horizontal surface for cloudy skies is to calculate the clear sky solar radiation (that which should occur in the absence of clouds) and multiply it by a factor that depends on the amount of cloud cover, CC. The model Estimated Solar Radiat ion (ESR) applies this concept by modifying a model developed by Brinsfield [13] to account for the influence of cloud cover.

494 R. BRINSFIELD el al.

The solar radiation quantities for cloudy skies are predicted in ESR using Imamura et al.[ll] modification of the method developed by Kusada [10]. Kusada's technique is based on analyses performed by Kimura and Stephenson[4]. Kimura and Stephenson analyzed 1967 Canadian meteorological data for ob- served solar radiation with respect to the cloud cover data, type of cloud, and the calculated solar radiation under clear sky conditions at the same solar time. Kusada's method estimates a parameter called the cloud cover factor (CCF)[4] which uses observed cloud cover data to modify the solar radiation for clear sky conditions with observed cloud cover data. The cloud cover data consists of observations of the amount of cloud cover on a scale of 0-10 and the type of clouds in four different layers. Imamura et al.[11] modified method uses a more readily available param- eter called the "mean sky cover" which is available in the National Climatic Atlas. ESR uses the Imamura et al . [ l l ] modification of the approach developed by Kusada[10]. However, further modifications were made based on research undertaken by the authors as discussed in the following sections.

Calculation procedure

Direct normal solar radiation--cloudy sky Hourly values of direct normal solar radiation

reaching the earth's surface for a clear sky condition as

defined by Imamura et al. [11] is

la, h = CN S P H R exp (-- TA U sec ( THETA )0). (1)

The hourly direct normal solar radiation on a horizon- tal surface for cloudy conditions is calculated in the model Estimated Solar Radiation (ESR) using the following relationship [4]

b.(h = bn~[K(I - CC/lO)] (2)

or substituting eqn (1) into eqn (2) yields

ld,ch = [CN S P H R exp ( - TAU sec (THETA)o)] [K(I - Cel lO)] . (3)

The daily direct normal solar radiation (Iu, cu) on a horizontal surface for cloudy conditions is determined by summing the hourly values determined by eqn (3) from sunrise to sunset.

The parameters K and CC are cloud cover modifiers developed by Kimura and Stephenson [4]. K is defined as follows

K = [sin(ALPHA ) ] / [ (C + sin (ALPHA)) + ( P -- 1)(1 - r ) ] (4)

250000

200000

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z ~50000 o H

j 100000 o

Q w u

0 W E 50000

+ + +

+ q+

..+,~('+~

+ +

+

+

+ M /

/ +

+

LEGEND

DATA POINTS REGRESSION LINE

----' IDEAL FIT LINE

0 , , , , I , , , I I , , , , l , , I , , , , ]

0 50000 iO0000 :150000 200000 250000

OBSERVED SOLAR RADIATION (KJ/SO.M)

Fig. 1. Correlation between predicted and observed daily totals of solar radiation for Salisbury, Maryland.

Ground level solar radiation prediction model

where C is the diffuse sky factor, A L P H A the altitude angle, P the "cloudless sky factor," and Y a second order polynomial such that

Y = 0.309 - 0.137 sin ( A L P H A ) + 0.394 sin 2 ( A L P H A ) . (5)

The product [K(1 -- CC/IO)] given in eqn (3) is the modifier that adjusts clear sky solar radiation for cloudy sky conditions. This quantity was originally determined by Kimura and Stephenson [4] from actual solar radiation observations as

CC = TCA - 0.5 C;. (6)

The method developed by Kimura and Stephen- son[4] requires detailed weather station observations which exist for only a limited number of sites in the United States. Imamura, et al . [ l l ] modified this method by assuming that under normal conditions the amount of cirrus type clouds make up approximately 25 per cent of the total cloud amount; therefore, eqn [6) becomes

CC = 0.875 TCA. (7)

Average monthly values for TCA can be obtained from the National Climatic Atlas or hourly values for

495

some sites can be obtained from the National Climatic Center, Asheville, North Carolina.

Test runs of ESR were made correlating predicted and observed daily totals of solar radiation on a hori- zontal surface for two separate sites using eqn (7) to estimate the effect of cloud cover. Additional runs were made using hourly values of total opaque cloud cover ( T O C C ) to estimate the effect of clouds for the same time period at both sites. For both sites consid- ered, T O C C provided a better estimator (i.e. a higher correlation between observed and predicted solar radiation) than TCA.

Diffuse solar radiat ion--c loudy sky Hourly values of diffuse solar radiation reaching the

earth's surface for a clear sky condition is defined by Imamura, et al. [11] as

lab - (C/CN) S P H R exp ( - T A U sec ( THETA)o) . (8)

Hourly diffuse solar radiation on a horizontal sur- face for cloudy sky conditions is calculated in ESR by the following relationship[4]

Idc h = Iuh[CCF - K(1 - CC/lO)] (9)

where

C C F = P + Q ( C C ) + R ( C C ) z. (10)

200000-

x ~50000 0

Z 0 H

I00000

<

0

0 W

o 50000 W

+

+ + ++

+ +

++;;

+ -F ++++ +~+ +

+ +L r .~-. +

+

+ +

+

+ + +

+

# + +

+

+

LEGEND

+ DATA POINTS - - REGRESSION L I N E

I D E A L F I T L I N E

I I i , I , , ~ J l , , , , I J

50000 ~00000 ~50000

OBSERVED SOLAR RADIATION (KJ/SQ.M)

2001000

Fig. 2. Correlation between predicted and observed daily totals of solar radiation for Ely, Nevada.

496 R. BRINSFIELD el al.

By substituting average annual values of P, Q and R into eqn (10), C C F as applied in ESR becomes

C C F = 1.028 + 0 . 0 1 9 5 ( C C ) - 0 . 0 0 9 5 ( C C ) 2. (11)

Limits for eqn (14) are for C C greater than or equal to 1 and less than or equal to 10. If C C = 0 for a given hour, (i.e. a clear sky condition) the total solar radia- tion for that hour is estimated by

Substituting eqn (8) into eqn (9) yields

l,l,h = [ ( C / C N ) S P H R exp ( - T A U sec ( T H E T A ) . ) ]

[CCF - K ( I - CC/IO)]. (I 2)

The daily diffuse solar radiation (la,.d) on a horizontal surface for cloudy sky conditions is determined by summing the hourly values determined by eqn (12) from sunrise to sunset.

Total solar radiation .for cloudy sk ies- -d irec t and d([]use

T h e hourly total solar radiation on a horizontal surface for cloudy skies is determined in ESR as

SGHRC = ld,,~ h + Id,. h (13)

Substituting eqns (3) and (12) into eqn (13) yields

S G H R C = SPHR e x p ( - TAU sec (THETA)o)

× {CN[K(1 - CC/lO)] + [(C/CN)(CCF - K ( I - CC/IO))]}.

(141

S G H R = S P H R e x p ( - TAU s e c (THETA)o)

[CN + (C/CN)]. (15)

ESR predicts the daily total solar radiation ( S G D C ) by summing the hourly values determined by eqns (14) and (15) from sunrise to sunset.

MODEL VERIFICATION

Since the daily total clear sky solar radiation on a horizontal surface (SGD) depends on the extent o f atmospheric interference, prediction by modeling is more tedious than modeling potential solar radiation. Furthermore, simulating the daily total of solar radi- ation on a horizontal surface for partly cloudy skies ( S G D C ) presents additional difficulties since the tem- poral and spartial distribution of clouds is difficult to predict. Evaluation and verification of the model ESR was accomplished by comparing daily totals of pre- dicted and observed values of SGD and SGDC for Salisbury, Maryland, and Ely, Nevada, The results are presented below.

o

C

3 O"

L LL

CO000

6 0 0 0

6 0 0 0

4 0 0 0

2 0 0 0 ~A ~ A

~A ~ A

f ~

f ~

F~ f~ f ~ f ~ f ~ ~ A

~A FA F~ F~ f~ f ~

2

LEGEND

I ] S a l i s b u r y

E l y

3 4 5 6 7 8 9 C l o u d Cover"

r ~

$d

: , d 7 ,d

- / t

.711

5d

~0

Fig. 3. Frequency distribution as a function of hourly observed total opaque cloud cover for Salisbury, Maryland and Ely, Nevada.

Ground level solar radiation prediction model 497

Hourly values of total opaque cloud cover for 4 yr and observed daily totals of solar radiation for the same time period for Salisbury, Maryland, and hourly values of total opaque cloud cover as well as observed daily totals of solar radiation for 3 yr for Ely, Nevada, were used in the analysis. A least squares analysis correlating pairs of daily totals of SGC predicted using ESR with observed daily totals for both locations are shown in Figs. 1 and 2. The correlation coefficients between predicted and observed daily totals is 0.87 for Salisbury, Maryland, and 0.94 for Ely, Nevada. Statis- tical comparisons indicate a difference between pre- dicted and observed daily totals of solar radiation of 1.28 kJ/m 2 for Salisbury, Maryland, and 0.74 kJ/m 2 for Ely, Nevada. On the average, ESR slightly under- predicts for cloudy sky conditions, while a slight over- prediction occurs for clear sky conditions (particularly for Salisbury, Maryland).

A detailed analysis shows that under-prediction at Salisbury, Maryland, occurred on those days when the total opaque cloud cover is high (9-10), while over- prediction occurred when the cloud cover is low (0-1). Since observations at this location are made on a somewhat subjective basis [14], some of the differences noted could be attributed to quantifying the cloud cover impact during both low and high overcast condi- tions.

Figure 3 compares frequency diagrams of hourly total opaque cloud cover value for 10yr for both Salisbury, Maryland, and Ely, Nevada. The results indicate that the observers at Salisbury, Maryland, had a tendency to record a value of 0 vs 1 for low overcast conditions and 10 vs 9 for high overcast conditions. This "human" biasing could account for most of the differences shown in Fig. 1.

Average monthly values of potential (radiation available outside the atmosphere), clear sky, observed, and predicted solar radiation for both locations are shown in Figs. 4 and 5. Although the predicted values for low daily totals are slightly less than observed values, the results indicate good agreement between the two for both locations.

CONCLUSIONS

The model ESR provides an excellent method for predicting solar radiation on a horizontal surface for those locations lacking detailed meteorological data sets. Given hourly values of total opaque cloud cover, ESR can predict daily, weekly, monthly, and seasonal trends of solar radiation using latitude and clearness numbers for the site. The model can serve as a valuable tool in assessing the feasibility of solar energy col- lection systems for sites lacking observed values.

5 0 0 0 0

4 0 0 0 0

Z

O

z 3 0 0 0 0 o H

j 20000 0

W J m

d H

> iO000 <

O B S E R V E D C A L C U L A T E D

0 ' ' ' ' I , , , , I , , , , I 0 5 ].0 ].5

TIME (MONTHS)

Fig. 4. Potential, clear sky, observed, and predicted monthly average solar radiation for Salisbury, Maryland.

498 R. BRINSFIELD et al.

50000-

4 0 0 0 0

z 3 0 0 0 0 O H P < H Q < E

E

j 20000 o

W J m

J H

> lO0OO

/

iii!i;iiio 0 ' ~ J ~ I , t ~ , I ~ ~ ~ , I

0 5 ~.0 :t5

TIME (MONTHS)

Fig. 5. Potential, clear sky, observed, and predicted month ly average solar radiation for Ely, Nevada.

Acknowledgements--The authors would like to express their ld,cJ gratitude to the Computer Science Center, University of Maryland, for providing the necessary computer funds for the project. We also appreciate the time Barbara South and ldnch Donna Harding spent preparing the manuscripts for publi- cation.

NOMENCLATURE

ld.h

K P Q R

SGD

C ratio of diffuse horizontal solar radiation to direct normal solar radiation, dimensionless

C~ sum of the cover of cirrus, cirrostratus, and cirrocumulus clouds, descrete numbers from 0 to 10, dimensionless SGDC

CC cloud cover observations, descrete numbers from 0 to 10, dimensionless S G H R C

CCF cloud cover factor, dimensionless CN "clearness number ," the ratio between actual SPD

(measured) clear sky normal incident direct S P H R global solar radiation at a given location and the TCA calculated value using average values of TAU with a given relative air mass, dimensionless

lah hourly total diffuse sky solar radiation on a horizontal surface for clear sky conditions, k J / TOCC m 2 hr

laca daily total diffuse sky solar radiation on a horizontal surface for cloudy sky conditions, k J / m 2 day Y

lath hourly total diffuse sky solar radiation on a ALPHA horizontal surface for cloudy sky conditions, ( T H E T A ) o kJ /m 2 hr TAU

daily direct normal solar radiation on a horizon- tal surface for cloudy sky conditions, k J / m 2 day hourly total direct normal solar radiation on a horizontal surface for cloudy sky conditions, k J / m 2 hr hourly total direct normal solar radiation on a horizontal surface for clear sky conditions, k J / m 2 hr coefficient, dimensionless cloudless sky factor, dimensionless coefficient, dimensionless coefficient, dimensionless daily total clear sky solar radiation on a hori- zontal surface, k J / m ~ day daily total solar radiation on a horizontal sur- face for cloudy sky conditions, k J / m 2 day hourly total solar radiation on a horizontal surface for cloudy sky conditions, k J / m 2 hr daily potential solar radiation, k J / m 2 hr hourly total potential solar radiation, k J / m 2 hr total cloud amount (i.e. the amount of celestial dome covered by clouds or obscuring phenom- ena), descrete numbers from 0 to 10, dimen- sionless total opaque cloud cover (i.e. clouds or obscura- tion through which the sky or higher cloud layers cannot be seen), descrete numbers from 0 to 10, dimensionless coefficient, dimensionless solar altitude angle, tad solar zenith angle, rad total optical depth, dimensionless

Ground level solar radiation prediction model 499

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2. F. E. Lumb, The influence of cloud on hourly amounts of total solar radiation at the sea surface. J. Roy. Meteor. Soc. 90, 383 (1964).

3. M. R. Sharma and R. S. Pol, Solar radiation in the tropics. Solar Energy 9, 183 (1965).

4. K. Kimura and D. G. Stephenson, Solar radiation on cloudy days. Res. Paper 418, Division of Building Research, National Research Council, Ottawa (1969).

5. S. Barbaro, S. Coppolino, C. Leone and E. Sinagra, An atmospheric model for computing direct and diffuse solar radiation. Solar Energy 22, 225-.228 (1979).

6. R. J. Cole, Direct solar radiation data as input into mathematical models describing the thermal perfor- mances of buildings. Building and the Environment, 2, 173 - 184. Pergamon Press, Oxford (1976).

7. R. King and R. O. Buckius, Direct solar transmittance for a clear day. Solar Energy 22, 297-301 (1979).

8. J. k. Hatfield, R. B. Giorgis, Jr. and R. G. Flocchini, A simple solar radiation model for computing direct and

diffuse spectral fluxes. Solar Energy 27, 323 329 (1981).

9. F. J. K. Ideriah, A model for calculating direct and diffuse solar radiation. Solar Energy 26, 447-452 (1981).

10. T. Kusada, NBSLD Computer Program for Heating and Cooling Loads in Buildings. National Bureau of Stan- dards, Thermal Engineering Systems Section, Building Environment Division, Institute for Applied Technology (1974).

11. M. S. lmamura, R. Hulstrom and C. Cookson, DelTni- tion Study for Photovoltaic Residential Prototype Sys- tem. U.S. Department of Commerce Report No. N77 13533 (1976).

12. A. J. Biga and R. Rosa, Estimating Solar Irradiation Sums from Sunshine and Cloudiness Observations. Solar Energy 25, 265-272 (1980).

13. R. B. Brinsfield, Predicting Solar and Wind Energy Trends Using Cloud Cover and Wind Velocity. Doctoral Dissertation, Department of Agricultural Engineering, University of Maryland ( 1981 ).

14. P. A. Herb, Personal communication. Federal Aviation Administration, Salisbury Airport, Salisbury, Maryland (1981).