A geostatistical model based on random walks to krige regions with irregular boundaries and holes

Classical kriging models use Euclidean distance when modeling spatial autocorrelation. However for regions with irregular boundaries and holes, such as estuaries and coastlines, a measure of within-domain distance may capture a system’s proximity dependencies more accurately. Standard kriging techniques are not guaranteed to yield a valid covariance structure when defined in terms of non-Euclidean distances. In this paper, we develop a new kriging model for irregularly shaped domains. Our model uses an approximation to a diffusion process to define a valid covariance structure that reflects the domain topology. A covariance matrix is defined through the use of random walks on a lattice, process convolutions, and the kriging equations. A simulation study demonstrates that for commonly encountered topologies, our diffusion kriging estimator is superior to a kriging estimator based on shortest within-domain distance. We also illustrate our method using water quality data from Puget Sound and Lake Peipsi to map chlorophyll concentration.