Statistical analysis of the Angstrom formula coefficients and application for Turkey

A simple substitution method is proposed for the dynamic estimation of Angstrom's coefficients which play a significant role in the relationship between the global radiation and the sunshine duration. After explaining the physical meaning of the coefficients, their mathematical estimation procedures are presented on the basis of successive global radiation and sunshine duration record substitutions into the model. This new procedure yields a series of parameter estimations, the arithmetic averages of which are closely related to the classical regression method estimates. The series of model parameters estimation provide an ability to assess these parameters statistically. Consequently, such a dynamic parameter estimation procedure evaluates and enables one to make interpretations with their normal and extreme values. The methodology is applied to 28 radiation measurement stations all over Turkey. Angstrom equation parameters' regional variations are obtained for the whole country. Additional necessary relative frequency distribution functions of these parameters appeared in the form of beta distribution.