A network design criterion for estimating selected attributes of the semivariogram

The semivariogram plays a central role in a geostatistical analysis of spatially correlated environmental data. A valid semivariogram model is selected, and the parameters of that model are estimated, before kriging (spatial prediction) of environmental variables is performed. These inference procedures are generally based upon examination of the empirical semivariogram, which consists of average squared differences of data taken at sites lagged the same distance apart in the same direction. In some situations, the investigator may wish to estimate some attributes of the semivariogram more precisely than others. The efficient estimation of such attributes is affected significantly by the spatial configuration of the network of sites where measurements are taken. In this paper, an approach to network design is proposed that emphasizes the utility of the network for estimating selected attributes of the semivariogram. Details are given as to how the approach can be applied to precisely estimate (a) the ratio of nugget effect to sill, (b) a set of compatibility‐determining attributes, and (c) a geometric anisotropy. Acid deposition data taken from a sampling network in the eastern United States are used to further illustrate the approach.