Improved spatial interpolation of rainfall using Genetic Programming S. K. Adhikary a , A. G. Yilmaz a, b and N. Muttil a, b a College of Engineering and Science, Victoria University, PO Box 14428, Melbourne, VIC 8001, Australia b Institute for Sustainability and Innovation, Victoria University, PO Box 14428, Melbourne, VIC 8001, Australia Email: sajal.adhikary@live.vu.edu.au Abstract: Rainfall data provide an important input for various water resources management tasks. Hydrologists are often required to estimate areal average rainfall over the catchment and/or point rainfall values at unsampled locations from observed sample measurements at neighboring locations. Accurate spatial distribution of rainfall can be achieved through a dense network of rain gauges. However, the rain gauge network is usually sparse in most cases and thus sufficient point rainfall measurements are not available, which are often unable to characterize the spatial distribution of highly variable rainfall. Spatial interpolation method plays an important role in such cases to estimate rainfall at unrecorded locations (i.e., missing data) using the observed rainfall available at surrounding locations. Conventionally, variance-dependent stochastic spatial interpolation methods such as kriging are the most commonly used methods for estimating the point rainfall values at any desired locations based on the available recorded values at neighboring rain gauges. However, traditional kriging has a major weakness because it requires a priori definition of mathematical function for the variogram model that represents spatial correlations among data points and thus significantly impacts the performance of the methods. The robustness of kriging methods heavily depends on how the variogram model is constructed. Moreover, selection of appropriate variogram model, finding the optimal variogram parameters (i.e., nugget, range, sill) and the computational burden involved are some of the difficulties involved with the traditional kriging. More recently, data-driven models using evolutionary and biological principles including genetic algorithms, artificial neural networks have been used with kriging for spatial interpolation of rainfall. Genetic programming (GP) is another evolutionary data-driven modelling technique to approximate function. The key advantage of GP is that it does not assume any a priori functional form of the solution and GP inferred models offer some possible interpretations to the underlying process. The aim of this study is to investigate the suitability of GP for variogram modelling to derive the variogram model and use of the GP-derived variogram model in combination with traditional ordinary kriging for spatial interpolation of rainfall. This new variant of kriging is referred to as genetic programming-based ordinary kriging (GPOK) in which the GP-derived variogram model replaced the standard parametric variogram models (i.e., exponential, gaussian, spherical) in the traditional ordinary kriging. Developed genetic programming-based ordinary kriging (GPOK) method was then applied to estimate the unknown rainfall values at a rain gauge station through spatial interpolation using the historical rainfall data from 19 rain gauge stations in the Middle Yarra River catchment of Victoria, Australia. The results indicated that the GPOK method outperformed the traditional ordinary kriging method for spatial interpolation of rainfall and yielded better rainfall estimates. The results also showed that the function approximation capability of GP produces the best fitted GP-derived variogram model compared to the standard models. Moreover, variogram model fitting by GP was very quick since GP did not require identifying the variogram parameters in advance unlike the standard variogram models in the traditional kriging method. Thus, use of GP, as a universal function approximator, for variogram modelling eliminates the time consuming and tedious job of trial and error for determining the optimal variogram parameters as necessary with the standard variogram models. This results in the significant reduction in the computation complexity by the GPOK method. Therefore, the GP-derived variogram model seems to be a potential alternative to variogram models used in the past and the proposed GPOK method is recommended as a viable option for improved spatial interpolation. Keywords: Genetic programming, ordinary kriging, variogram model, rainfall data, spatial interpolation 21st International Congress on Modelling and Simulation, Gold Coast, Australia, 29 Nov to 4 Dec 2015 www.mssanz.org.au/modsim2015 2214