Spatial interpolation and estimation of solar irradiation by cumulative semivariograms

The main purpose of this paper is to find a regional procedure for estimating the solar irradiation value of any point from sites where measurements of solar global irradiation already exist. The spatial weights are deduced through the regionalized variables theory and the cumulative semivariogram (CSV) approach. The CSV helps to find the change of spatial variability with distance from a set of given solar irradiation data. It is then employed in the estimation of solar irradiation value at any desired point through a weighted average procedure. The number of adjacent sites considered in this weighting scheme is based on the least squares technique which is applied spatially by incrementing nearest site numbers successively from one up to the total site number. The validity of the methodology is first checked with the cross validation technique prior to its application to sites with no solar irradiation records. Hence, after the cross-validation each site will have different number of nearest adjacent sites for spatial interpolation. The application is achieved for monthly solar irradiation records over Turkey by considering 29 measurements stations. It has been shown that the procedure presented in this paper is better than the classical techniques such as the inverse distance or inverse distance square approaches.