Designing Field Sampling to Estimate Spatial Pattern Stratified random sampling, where soil samples are collected at random locations within strata (subregions based on 24lam activity), has been used to estimate 239Ppu inventory in soil at the safety-shot sites (Gilbert and Eberhardt, 1974; Gilbert et al., 1975, 1976). This design appears to have given more precise estimates of 239Pu inventory than would have resulted if stratification had not been used and soil had been collected at random over the entire study site. However, these data have not proved ideal for estimating the 239Dy concentration "surface" (depicted by contour lines) using computer algorithms since portions of the study area where concentration levels change rapidly were sometimes left unsampled. In these areas, the estimated contours are sometimes biased. For example, the soil Pu contours for GMX site in Area 5 obtained using the computer algorithm NEAR!2 on the computer package SURFACE II (Sampson, 1973) are erroneous west of GZ due to a lack of data immediately west of the GZ bunker (Gilbert et aZ., 1975, Figures 18, 24, and 25). Gilbert et al. (1976, Figure 3; also see Figure 8 in this report) showed that the magnitude of this problem was reduced if the contours were computed on logarithms of the data. Our experience suggests that we might consider the efficient estimation of the geographical distribution of Pu the primary objective of future sampling efforts at safety-shot or nuclear event sites on NTS. We can think of the concentrations in soil as a continuous three-dimensional surface, the height of which at a particular location gives the Pu concentration in soil at that point (examples are Figures 20, 21, 24, and 25 in Gilbert et aZ., 1975). It is possible to estimate this continuous surface in units of nCi/m? at grid points over the study site using SURFACE II. The inventory could then be estimated by simply summing the grid point concentration estimates and multiplying by a suitable constant to convert nCi/m* to nCi. The variance of an estimate of inventory obtained in this manner requires the variance of the estimated concentration at each grid node. It appears that it might be possible to obtain these estimates of variance if the grid node concentrations are estimated using a method called Universal Kriging (Davis, 1973; Delfiner and Delhomme, 1975). One version of this method should be available on SURFACE II (Sampson, 1975) by the fall of 1976. It is not yet apparent whether this approach would yield more or less precise estimates of inventory than stratified random sampling, or indeed, whether Universal Kriging is really suitable for estimating spatial pattern of Pu. An important aspect of the problem is to identify or develop field sampling designs that are optimum for estimating the spatial pattern or "location" of environmental contaminants such as plutonium. Sampling locations can be chosen many different ways (completely at random, random within strata, on a systematic (grid) pattern, combination of systematic and random, etc.). Gilbert et al. (1975, page 419) discuss some of the issues involved in choosing a particular design. Some aspects of the design problem for estimation of 12NFAR, as used here, finds the 8 nearest data points (regardless of their Orientation or distance) from the point at which the height of the surface is to be estimated. 260