Kriging in estuaries: as the crow flies, or as the fish swims?

Abstract Geostatistical methods are becoming an essential tool for understanding the spatial distribution of biological and chemical species in estuaries. At the heart of these methods are the spatial prediction/mapping methods known as “kriging”; these can construct statistically optimal predictions for data at unobserved locations using a relatively small, spatially explicit sample. The prediction at any given location is a weighted average of the sample values, where the weights depend on the distances between the sample sites and the target location. For most geostatistical settings, distances are computed “as the crow flies”, i.e. Euclidean distance. For measurements made in estuarine streams, however, intuition suggests that distances between sites should be measured “as the fish swims”, i.e. the length of the shortest in-water path between two sites. Our study evaluated the relative accuracy of eight kriging methods for predicting contaminant and water quality variables measured in an urbanized estuary in South Carolina. The eight methods were defined by all combinations of three factors, each at two levels: (a) Distance metric (Euclidean vs. in-water); (b) semivariogram type (spherical vs. linear) and (c) model trend component (distance to the inlet mouth; without vs. with). For four of the eight variables studied, the in-water distances provided prediction accuracy improvement on the order of 10–30% of prediction error variance. In two of these cases, the improvement only occurred when in-water distances were used together with a model trend component. Choice of semivariogram did not have much effect on prediction accuracy. Although the overall improvement in prediction accuracy was unpredictable and modest, considering the additional difficulties associated with in-water distances, the results suggest that the integration of Geographic Information System (GIS)-based network analysis with kriging using in-water distances merits further research.