INTERPOLATION AND ESTIMATION WITH SPATIALLY LOCATED DATA

Kriging is a regression method used with irregularly spaced data in 1-, 2- or 3-space for the estimation of values at unsampled locations or for the estimation of the spatial average over a length, area or volume. The estimator is linear in the data and the weights are obtained from a system of linear equations in which the coefficients are the values of variograms or covariance functions quantifying the correlation between data at two sample locations or between a sample location and the location to be estimated. The equations are obtained by minimizing the variance of the error of estimation, the variance being computed from a theoretical model for the correlation function rather than from empirical values as in most regression formulations. Estimation and modeling of this structure function is the most important and potentially the most difficult step in the process. While the method is not implemented in standard statistical packages, public domain software for use on an IBM personal computer or clone is available. The theory is briefly reviewed, practical aspects of the application of the method are discussed and available software and extensions are outlined. The US EPA Dallas Lead Study data is used to illustrate the problems and the method.