Neural Network Residual Kriging Application for Climatic Data

Direct Neural Network Residual Kriging (DNNRK) is a two step algorithm (Kanevsky et al. 1995). The first step includes estimating large scale structures by using artificial neural networks (ANN) with simple sum of squares error function. ANN, being universal approximators, model overall non-linear spatial pattern fairly well. ANN are model free estimators and depend only on their architecture and the data used for training. The second step is the analysis of residuals, when geostatistical methodology is applied to model local spatial correlation. Ordinary kriging of the stationary residuals provides accurate final estimates. Final estimates are produced as a sum of ANN estimates and ordinary kriging (OK) estimates of residuals. Another version of NNRK — Iterative NNRK (INNRK), is an iterated procedure when, the covariance function of the obtained residuals are used to improve error function, by taking into account correlated residuals and to specify residuals followed by ANN modelling, etc. INNRK allows reducing bias in the covariance function of the residuals. However, INNRK is not the subject of this paper. The present work deals with the application of DNNRK model. NNRK models have proved their successful application for different environmental data (Kanevsky et al. 1995; Kanevsky et al. 1997a, 1997b, 1997c)