Description of Iterative Procedure The first iteration consists of estimating the plutonium concentration surface at grid nodes using the observed 39°240py data (y., i= 1,2,..., 170). (The subscript i will run from 1 to 170 throughout this paper.) This estimated surface is denoted as I; in Figure 2 and is presented in the Results section as contour and three-dimensional displays. Backward double linear interpolation between grid estimates yields the estimates of plutonium concentrations (¥,,) at sample locations. Residuals for en 1 at control (data) doints were obtained by computing R,_, = - 944 il In Iteration 2, the procedure of Iteration 1 is applied to the residuals R; to obtain a new grid matrix Ip (Figure 2). This is the estimated surface or fit to the residuals from Iteration 1. These residuals were estimated (%.,) at sample locations using backward double linear inter- polation from 5 nearest grid node estimates of the residual surface. The sum 9 is the new estimate of the plutonium concentration surface ott sanpiZ location i. The new residual is R,, = y. (F At each grid node, the estimates from Iteratidds 1 Sad 2 are a ded together (I; + I2; see Figure 2) to yield a new estimate of the plutonium concentration surface. Iteration 3 consists of applying the procedure of Iteration 2 to the residuals R., to obtain a new grid matrix, I3. I, + Ip + 13 is the final estimate of the concentration surface, and R,, = (¥., + 9s + 4, 3) is the final residual. Conceptually, this pracedurétcould be réseated?many times until all of the "structure" in the residuals has been removed by fitting. In this study, we have somewhat arbitrarily chosen to stop after three iterations. The question naturally arises, however, as to whether continued iteration will eventually reduce the residuals to zero so that the observed and fitted values agree exactly. This would seem to depend on the particular gridding algorithm used (GRID or kriging, e.g.), the data values themselves, and the spatial pattern and density of samples. A related question concerns whether continued iteration, while possibly resulting in progressively smaller residuals at sample collection points, might yield biased and distorted estimates of the concentration surface at other locations. As discussed below, there is some evidence of this happening for the Area 13 data after only three iterations. This is apparently related to the absence of data in certain areas near GZ. This suggests that survey design aspects of these kinds of studies need to be carefully considered. 326