Neural Network Residual Kriging Application For Climatic Data
V. Demyanov, M. Kanevski, S. Chernov, E. Savelieva, V. Timonin
Journal of Geographic Information and Decision Analysis, Vol. 2., No. 2, pp. 215-232, 1998
Direct Neural Network Residual Kriging (DNNRK) is a two step algorithm (Kanevsky M., 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, fairly well model overall non-linear spatial pattern. 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 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 covariance function of the residuals. However, INNRK is not the subject of this paper. The present work deals with application of DNNRK model. NNRK models have proved their successful application for different environmental data (Kanevsky, et. al. 1995; Kanevsky, Maignan et. al. 1997; Kanevski, Demyanov and Maignan 1997; Kanevsky, Arutyunyan, et.al. 1997).