Standard weighting function
It is said in the previous subsection that all the classical weighting functions appear as a non-increasing function with distance. It is, therefore, logical to execute the following steps in order to transform a given CSV into a SWF.
1. find the maximum distance, RM; and corresponding sample CSV value, VM. RM corresponds to the distance between the two farthest station locations in any study area,
2. divide all the distances (CSV values) by RM (by VM) and the result appears as a dimensionless form of the given CSV confined within 0 and 1 on both axis.
3. subtract the dimensionless CSV values from one and hence the result appears as a non-increasing function as shown in Fig. 27. This has similar pattern to all the classical weighting functions explained in the previous section. This function is referred to as the SWF.
Now a regional estimation procedure can be proposed for determining the regional solar irradiation variations through an interpolation technique by using SWF. In order to show the validity of the estimation methodology
a cross-validation procedure is applied with actual solar irradiation measurements at a given set of sites. There are two different spatial estimation procedures. The first one takes into consideration all the available measurement sites and the second alternative is restricted with a certain number of adjacent sites such that the spatial estimation error becomes the minimum. In the application of the latter methodology, each site has different number of adjacent sites for consideration in the spatial solar irradiation estimation. Its application has been presented by Sen and Sahin .