ON THE ESTIMATION OF SPATIAL PATTERN FOR ENVIRONMENTAL CONTAMINANTS R. O. Gilbert Battelle Memorial Institute, Pacific Northwest Laboratory Richland, Washington ABSTRACT The estimation of the spatial pattern or geographical distribution of environmental contaminants or other spatial variables is often of interest in environmental sampling programs. One approach to this problem is to estimate the variable of interest at regular intervals on a grid covering the study site using data collected at various locations over the area. In this paper, we examine the performance of an iterative procedure for estimating the grid values. A two-~phase least squares procedure is applied three times: first to the observed data, then to the residuals from the first fit, and finally to the residuals from the second fit. The three estimated grids are added together for the final grid estimates. Results are displayed as contour maps, three-dimensional surfaces, and plots of residuals. The iterative procedure is applied to untransformed as well as log-trans- formed data to investigate whether fitting in terms of logarithms followed by transforming back to the original scale (the “antilog" scale) is preferable to fitting untransformed data. This evaluation is made on a data set of 239°240py concentrations in surface soil samples collected by the Nevada Applied Ecology Group at the Area 13 (Project 57) "safetyshot" site on the Nevada Test Site. This data set is characterized by a very large concentration datum near ground zero with concentrations falling off rapidly with distance. For these data, the iterative procedure reduces the standard deviation and average absolute (mean and median) size of residuals and increases the percent of the total variation explained by fits in both untransformed and antilog scales. Smaller residuals are usually obtained by fitting log-transformed data and taking antilogs rather than fitting untransformed data. Also, the iterative procedure applied to the log-transformed data appears to result in more reasonable estimates of concentration surface 319