On the Use of Non-Euclidean Distance Measures in Geostatistics

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A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space (2013, methodology): “Although the validity of usual parametric variogram models is not guaranteed in non-Euclidean spaces (Curriero, 2006), both the spherical and the exponential models are valid in the spherical geometry (Huang et al., 2011) and thus can be used in this case.”
Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data (2014, unknown): “…been applied in (1) hydrology studies using kriging, where water distances are used for spatial prediction along a stream or river network (e.g. Curriero 2006, Money et al. 2009); (2) landscape studies using kriging, where landscape-based distance metrics are derived (e.g. Jensen et al.…”
Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances (2009, methodology): “The covariance matrix that results from applying the non-Euclidean distance metric (i.e., the final path in Fig. 4) will not result in a positive definite matrix even if a valid covariance function or variogram is used ( Curriero 2005 ).”
Complex Region Spatial Smoother (CReSS) (2014, background): “Rathbun (1998) and Curriero (2007) both proposed using a non-Euclidean metric with kriging methods.”