Geostatistical Tools for Deriving Block-Averaged Values of Environmental Attributes

Abstract This paper reviews four different approaches for estimating the block-averaged value of an environmental attribute from point data: 1) the sample arithmetic average, 2) the declustered mean, 3) block kriging, and 4) stochastic simulation. The first approach is straightforward and well suited for estimation over large blocks that contain many randomly located observations. Declustering techniques can be used to correct for preferential sampling of specific subareas of such large blocks. The last two techniques, kriging and simulation, account for the pattern of spatial dependence of observations and allow one to compensate for the shortage of data inside small blocks by incorporating observations outside the block. The major advantage of stochastic simulation is that it provides a non-parametric measure of the uncertainty attached to the prediction of a single block or multiple spatially dependent blocks. Stochastic simulation can also be used to upscale properties like permeability that do not av...