Spatial Interpolation in the Presence of Spatial Stratified Heterogeneity: Stratified Kriging or Ordinary Kriging?

ABSTRACT When spatial stratified heterogeneity exists, the second‐order stationarity assumption of geostatistical methods cannot be satisfied. To address this issue, a series of stratified kriging methods has been developed by partitioning the dataset into homogenous strata and then applying geostatistical methods within each stratum. Although stratified interpolation methods seem to be able to handle stratified heterogeneity, their effectiveness has not been thoroughly investigated. In this study, we used simulated data and four real‐world datasets of different geographical scenarios to compare the performance of ordinary kriging and three representative stratified kriging methods. Experiment results showed that whether with prior knowledge or using automatic clustering, stratified kriging methods usually perform worse than ordinary kriging, even in the presence of significant spatial stratified heterogeneity. The reason lies in two aspects: (i) estimation of an accurate variogram for the observations between strata is unrealistic, which reduces the interpolation accuracy of boundary positions; (ii) the variogram within each stratum amplifies the effect of local heterogeneity, which reduces the interpolation accuracy of some interior positions. Theoretical analysis demonstrated that the ability of ordinary kriging to handle spatial heterogeneity is underestimated. When the boundary is fuzzy, ordinary kriging is sufficient to address the spatial stratified heterogeneity issue in spatial interpolation.