The first model for estimating monthly average daily global solar radiation (H) was proposed by Ångström, who derived a linear relationship between the ratio of average daily global radiation to the clear day radiation (Hc) at a given location and the ratio of average daily sunshine duration (S) to the maximum possible sunshine duration (S0). Prescott modified Ångström relationship by replacing clear sky radiation with extraterrestrial radiation (H0), which can be more readily determined. This replacement resulted in the formation of the Ångström-Prescott model, which has been the most widely used correlation for calculation of global solar radiation:

H/H0 = a + b (S/S0).

Later other sunshine models appeared which are based on quadratic, cubic, logarithmic or exponential relationship. The problem with these models is that they are location specific and require careful long-term measurements of sunshine duration and global radiation in order to obtain coefficients a and b by regression method. You can find review and statistical analysis of different global solar radiation sunshine models in the following article:

Article Review and statistical analysis of different global solar ra...