Modeling Solar Radiation at the Earth’s Surface

Frequency Distribution and Distribution Types for Clear Day Horizontal Beam Irradiation Index

The frequency distribution of the clear day horizontal beam irradiation index for the database consisting of all 12 months is shown in Fig. 4.9. Since the data are normalized, viz., Kb c = Hb/Ho, it is to be expected that the distribution type should be independent of month or season. This was in fact confirmed by comparing the

distribution types for the four seasons (the individual monthly databases were too narrow for distribution analysis). It is observed from Fig. 4.9 that the distribution of Kbc is a type V, i. e., a narrow peak with a negative tail, which is the most preferred type for solar energy conversion systems.

3.3 Frequency Distribution and Distribution Types for Clear Day Horizontal Diffuse Irradiation Index

The frequency distribution of the clear day horizontal diffuse irradiation index for the database consisting of all 12 months is shown in Fig. 4.10. It is apparent from Fig. 4.10 that the distribution of Kdc is a type III, i. e., a narrow peak with a posi­tive tail. In essence, it is a mirror image of that for Kbc, which is to be expected since their respective irradiation intensities constitute the clear day solar global irradiation.

4 Conclusions

The solar global irradiation intensity on a clear day provides both a platform for studying the influence of cloudiness and sets an upper, although unattainable, limit on the magnitude of the solar global irradiation. The Iqbal (1983) classification of days according to clearness index was applied to define a clear day and the Berlynd model for determining the solar global irradiation on a clear day was found to give the best agreement with the clear day solar global irradiation as defined by Iqbal’s criteria. Consequently, it is proposed that the Berlynd model be utilized to determine the solar global irradiation on a clear day and that the Berlynd coefficient ‘f’, cf. Eq. (4.8), be determined for the site being studied.

It is suggested that the daily clear day index Kc, defined as H/Hc, is a better in­dicator of the degree of cloudiness than the oft used KT, where the daily clear sky solar global irradiation is calculated utilizing the site-specific Berlynd model. The magnitude of KT is a measure of both atmospheric transparency and cloudiness. Consequently, the degree of cloudiness as determined on the basis of KT also in­cludes the other parameters contributing to the sky transparency. The daily clear sky index, Kc, is defined such that the effect of cloudiness is not a parameter. Viz., the daily clear day solar global irradiation, Hc, is determined under clear sky conditions and only those parameters contributing to sky transparency are involved.

The determination of the frequency distribution of the solar global/beam irradi­ation intensity or the corresponding indices, i. e., Kc and Kbc, are very important parameters in the design of solar irradiation conversion systems. They provide an­other criterion, in addition to the average magnitude of the solar irradiation, for determining the feasibility of conversion system with regard to both size and type (non-concentrating/concentrating). The availability of such information enhances the economic feasibility analysis of such solar energy conversion systems.

The relationship between the ratio of the daily diffuse on a horizontal surface to the daily extraterrestrial irradiation on a horizontal surface, Kd, and the ratio of the daily beam on a horizontal surface to the daily extraterrestrial on a horizontal surface, Kb, irrespective of day type, was found to be non-linear and of exponential form. When the database was limited to clear days only, linear regression equations give the best fit to the data, i. e., Kdc = aKb c + b. It can be concluded that the non­linearity observed in the first case is caused by inclusion of both cloudy and partially cloudy days within the database.