Simple nonlinear solar irradiation estimation model

A simple nonlinear model with three parameters is proposed for global solar irradiation estimation from sunshine duration ratio measurements. Two of the parameters have almost the same interpretations for extreme weather conditions as in the classical Angström model but the third parameter appears as the power of the sunshine duration ratio. This model reduces to the classical Angström equation when power is equal to one. It contains the possible nonlinear effects in solar irradiation and sunshine duration relationship as a first-order mathematical approximation to the linear Angström equation. Power values different than one imply nonlinear models. The model parameter estimates are achieved through the nonlinear least-squares analysis. The application of the methodology is performed for eight irradiation measurement stations in Turkey.