Modeling Solar Radiation at the Earth’s Surface

Solar Horizontal Diffuse and Beam Irradiation on Clear Days

There exist a number of models to determine the solar horizontal diffuse irradia­tion on a clear day (Kondratyev 1969) but they are complex and have very stringent conditions. Similarly, there also exist models to determine solar horizontal beam ir­radiation on a clear day (Kondratyev 1969; Sivkov 1971 and Ohvril et al. 1999) but they are dependent on the Forbes effect (i. e., the atmospheric transparency is a function of the air density) and quite complex. Consequently, the clear day solar horizontal diffuse and beam irradiation is defined in terms of the clearness index KT.

3.1 Clear Day Horizontal Diffuse Irradiation

The clear day horizontal diffuse irradiation is defined as that incident on a horizontal surface on a clear day as defined by Iqbal, viz., when KT > 0.7. The clear day horizontal diffuse index Kd c is thus defined in terms of the extraterrestrial solar irradiation Ho as

£d, c = Hd/Ho for Kt > 0.7, (4.11)

where Hd is the horizontal diffuse irradiation measured on a clear day. If there is a particular month with either a very small number or zero days that meet the KT > 0.7 threshold, then it may be lowered by small deficits as was the case for Beer Sheva, cf., Table 4.4.

The solar horizontal diffuse irradiation database consisting of the years 1991 to 2006 (16 years) was utilized to perform an in-depth analysis for Beer Sheva. The monthly average daily extraterrestrial solar irradiation (Extraterrestrial) , the abso­lute monthly maximum measured daily horizontal diffuse irradiation (i. e., a single value for each month) (Max-absolute), the monthly average of the maximum daily horizontal diffuse irradiation measured each year (i. e., average of 16 values for each month) (Max-average), monthly average clear day horizontal diffuse irradiation us­ing the Iqbal filter (Iqbal), monthly average measured daily horizontal diffuse ir­radiation (Diffuse-average), the monthly average of the minimum daily horizontal diffuse irradiation measured each year (i. e., average of 16 values for each month) (Min-average) and the absolute monthly minimum measured daily horizontal dif­fuse irradiation (i. e., a single value for each month) (Min-absolute) during the years 1991 to 2006 is shown in Fig. 4.4.

It is observed from Fig. 4.4, that the magnitudes of the monthly average clear day horizontal diffuse irradiation values based upon the Iqbal filter are closest to the corresponding average of the minimum daily horizontal diffuse irradiation mea­sured each year. Also, it is observed that the magnitudes of the monthly average daily horizontal diffuse irradiation values approach that of the corresponding Iqbal filter values during the summer months. This, once again, testifies to the preva­lence of clear sky conditions during the summer months in Beer Sheva, cf., Ianetz et al. (2000).