This equation is used generally in the radiative transfer and solar engineering studies. Details of radiative transfer are given by Akinoglu in Chapter 5. Logically, if sunshine duration is high then received solar irradiation on the surface will be high. There are four related variables and two parameters in Eq. (6.10). The variables are extraterrestrial, terrestrial global solar irradiation, length of the day and sunshine duration properties, which are discussed to a certain extent above. Relationship between the ratio variables (H/H0 and S/S0) is achieved through parameters (a and b).
In Eq. (6.10) the ratio on the left hand side is H/H0 called as clearness index and it gives additional information about the astronomic position of the earth, conditions of the atmosphere and the characteristics of surroundings stations. It also depends on seasonal variations of the sun-earth distance. Similar seasonal sun characteristics, the time variation of this ratio has approximate periodicity. The ratio on the right hand side S/S0 gives information about atmospheric characteristics and conditions of the study area. It is referred to as cloudless index and it is as important as clearness index. This ratio is directly proportional to hydrometeors, especially water vapour content of atmosphere.
The first parameter a represents diffuse component of the global solar irradiation and generally approximates to zero at clear atmospheric conditions. When the sunshine duration ratio, S/S0, is zero at the overcast conditions, then the solar irradiation ratio is equal to this parameter. The second parameter b represents variation and relation of ratios in the Angstrom equation, which has four different conditions as shown in Fig. 6.2. In the case of no atmosphere, total extraterrestrial solar irradiation reaches the horizontal surface without any reduction and hence the relationship between the two ratios occurs along the 45° straight line. This is statistically possible but physically impossible situation on the earth.
The second regression line, corresponding to “observed^’ situation could represent some observable conditions in the earth. In this case a value represents “not high” total diffuse irradiation and hence there are cloudy and cloudiness separations
——- Without atm.
. . — Impossible 1.0
due to conditions in the area. The third curve, “observed2”, represents a very cloudy location with high amount of diffuse irradiation. This could be a good condition for electrical solar applications but not for thermal perspectives. In reality, the last curve cannot be represented physically by Angstrom equation because of inverse proportional linearity.