Geostatistical Interpolation and Simulation in the Presence of Barriers

Abstract

Statistical correlation between spatial variables depends on the distance between locations and the direction of travel from one to the other. Geostatistical interpolation most often uses the Euclidean distance between observations. But since most surfaces in nature are convoluted, with edges and breaks, anything that travels along them is thereby constrained. Smog, for instance, is blocked by hills and mountains. Animals migrate around lakes, mountains, and settlements. Contaminants in water follow the coastline. This paper proposes using cost weighted distance, a common raster function in GIS (Geographical Information Systems) that calculates the cost of travel from one cell of a grid to the next, making it the natural choice of the distance metric for spatial interpolation. Determining cost value at each location is discussed, as is calculation of distances between sampled locations and unsampled ones. Also covered is how to choose a valid covariance model with barriers defined by cost surface. We illustrate the approach using publicly available ozone data in California, where mountains are the natural barriers for smog propagation, and nutrients data in the Chesapeake Bay, where the coastline forms non-transparent barrier for chemical propagation.