Support Domain Effects on Shape Parameter C in Mapping by Radial Basis Functions (RBFs)

In many water engineering studies, there is a need to fill lost rain data using mapping tools. In this research this has been done by 5 types of RBFs; the data used were extracted by 3 test functions in which the support domain varied from 0.1 by 0.1 meter net to 0.5 by 0.5 meter net with different numbers of stations in a unit area domain. The c parameter was optimized by cross validation method and the Normalized Mean Square Error (NMSE), Percent Average Estimation Error (PAEE) and Coefficient of determination (R2) were the statistical controlling tools for choosing suitable RBF function type. Compared to other works in literature, this work had a better performance in mapping. It is also shown that the c parameter that optimizes the RBF function is highly dependent on the support domain size; the finer the resolutions of support domain, the better the results achieved. The attribute was also found for an arbitrary station point, Z (0.25, 0.35) to show the model capability for an irregular domain. This work may be compared with meshless methods for further research.