Ordinary kriging and genetic programming for spatial estimation of rainfall in the Middle Yarra River catchment, Australia

Abstract

Rainfall maps with gridded data are frequently used as an important input for many hydrological models. In this study, two kriging-based interpolation methods (i.e., ordinary kriging (OK) and kriging with genetic programming (KGP)) and a deterministic interpolation method (inverse distance weighting (IDW)) are implemented to generate gridded rainfall maps from point rainfalls. The KGP is implemented as a new kriging method in which the genetic programming-based non-parametric variogram model is used with kriging. Rainfall records from existing 19 raingauges in the Middle Yarra River catchment, Australia are used for the analysis. The performance of each method is assessed through the cross-validation test. Results indicate that the kriging-based methods clearly outperform the IDW method. Among all the kriging-based methods, OK with the spherical variogram model yields the lowest prediction error and best estimates for all months. The KGP method gives an almost identical error to that given by the OK with the spherical variogram model for most of the months and a lower prediction error than that given by OK with the exponential or Gaussian variogram model. Thus, the KGP can be used in line with traditional kriging as a viable alternative technique for spatial estimation and mapping of rainfall.