Angström equation parameter estimation by unrestricted method

Şen Z.

Solar Energy, vol.71, no.2, pp.95-107, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 2
  • Publication Date: 2001
  • Doi Number: 10.1016/s0038-092x(01)00008-1
  • Journal Name: Solar Energy
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.95-107
  • Istanbul Medipol University Affiliated: No


Global solar irradiation is directly related to the sunshine duration record through a linear model which was first proposed by Angström 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. (Angström 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. Espécially 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 Angström regression method for 27 solar irradiation stations in Turkey. © 2001 Elsevier Science Ltd. All rights reserved.