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 (Kanevski et al. 1995;
Kanevski et al. 1997a, 1997b, 1997c).