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

Ronald P. Barry, Julie McIntyre and Jordan Bernard

Ecological Modelling, 2024, vol. 491, issue C

Abstract: 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.

Keywords: Diffusion; Non-Euclidean distance; Process convolution; Spatial covariance; Spatial prediction (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:491:y:2024:i:c:s0304380024000541

DOI: 10.1016/j.ecolmodel.2024.110666

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