EuroSun2008-13

# Formulas

The extraterrestrial solar radiation on the horizontal surface is the function of Latitude of the location. As the solar radiation passes through the earth’s atmosphere, it is further modified by the processes of scattering and absorption due to the presence of the cloud and atmospheric particles. Hence, the solar radiation incident on the horizontal surface is to some extent locality-dependent and less than the extraterrestrial irradiation.

Several climatic parameters have been used to develop empirical relations to predict the solar radiation incident on the horizontal surface. Among these existing correlations, the Angstrom-Prescott type regression equation related monthly average daily radiation to clear-day radiation at the location in question and average fraction of possible sunshine hours is considered to widely accept by the scholars :

h . S

= a+b (1)

H о ^

The Equation (1) has been proved to accurately predict the global solar radiation.

H : the monthly average daily global radiation on the horizontal surface(MJm-2 day-1)

H0: the monthly average daily extraterrestrial radiation on the horizontal surface (MJm-2day-1)

S : the monthly average daily number of hours bright sunshine

S0 : the monthly average daily maximum number of hours bright sunshine a, b : the regression constants to be determined

The extraterrestrial solar radiation  on a horizontal surface is determined by following equation.

24*3600 . 0 ■ п.

H0 = 10 f (cos л cos о sin a>s + a>s sin Asm0) (2)

n 180

Where I0 =1367 Wm 2 is the solar constant, Л is the latitude of the location, 0 is the declination angle.

n

and f = 1 + 0.033cos(360 ) (3)

365

Where n is the Julian number (for example Jan 1st is the number 1) (4)

And a>s is the sunset hours angle given as

cos = cos 1 (- tan Л tan 0) The maximum possible sunshine duration

S 2

s0 =

0 15 s

H>, So in the equation are obtained from the equation(2) and (6).The regression coefficient a H S

and. The values of the monthly average daily H 0 S0

global radiation and the average number of sunshine duration are obtained from daily measurements for a period of ten years.

The regression coefficient (a, b) can be computed by the following formulas: b

 (7) 1 H bA S

a = z - z

n і=1 H 0 n і=1 S0

Where n is the number of measured data points.

## EuroSun2008-13

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