Genetic Programming-Based Ordinary Kriging for Spatial Interpolation of Rainfall

Abstract

Rainfall data provide an essential input for most hydrologic analyses and designs for effective management of water resource systems. However, in practice, missing values often occur in rainfall data that can ultimately influence the results of hydrologic analysis and design. Conventionally, stochastic interpolation methods such as kriging are the most frequently used approach to estimate the missing rainfall values where the variogram model that represents spatial correlations among data points plays a vital role and significantly impacts the performance of the methods. In the past, the standard variogram models in ordinary kriging were replaced with the universal function approximator-based variogram models, such as artificial neural networks (ANN). In the current study, applicability of genetic programming (GP) to derive the variogram model and use of this GP-derived variogram model within ordinary kriging for spatial interpolation was investigated. Developed genetic programming-based ordinary kriging (GPOK) was then applied for estimating the missing rainfall data at a rain gauge station using the historical rainfall data from 19 rain gauge stations in the Middle Yarra River catchment of Victoria, Australia. The results indicated that the proposed GPOK method outperformed the traditional ordinary kriging as well as the ANN-based ordinary kriging method for spatial interpolation of rainfall. Moreover, the GP-derived variogram model is shown to have advantages over the standard and ANN-derived variogram models. Therefore, the GP-derived variogram model seems to be a potential alternative to variogram models applied in the past and the proposed GPOK method is recommended as a viable option for spatial interpolation.