Angström equation parameter estimation by unrestricted method

Abstract

Abstract Global solar irradiation is directly related to the sunshine duration record through a linear model which was first proposed by Angstrom in 1924. Generally, the parameter estimations of this model are achieved by using the regression technique based on the least squares method. This technique imposes procedural restrictions on the parameter estimations leading to under-estimations for clear sky condition and over-estimations in the case of overcast sky conditions. These restrictions include linearity, normality, means of conditional distribution, homoscedasticity, autocorrelation and lack of measurement error. In this paper, an alternative unrestricted method (UM) is proposed for preserving the means and variances of the global irradiation and the sunshine duration data. In the restrictive regression approach (Angstrom equation) the cross-correlation coefficient represents only linear relationships. By not considering this coefficient in the UM, some nonlinearities in the solar irradiation–sunshine duration relationship are taken into account. Especially when the scatter diagram of solar irradiation versus sunshine duration does not show any distinguishable pattern such as a straight line or a curve, then the use of UM is recommended for parameter estimations. The UM is contrasted with the Angstrom regression method for 27 solar irradiation stations in Turkey.