Geostatistics and Spatial Interpolation in GIS: Classical Methods, Advanced Modelling Techniques, Uncertainty Assessment and Applications
Karunakar Virugu *
Department of Geography, Osmania University, Hyderabad, Telangana, India.
*Author to whom correspondence should be addressed.
Abstract
Spatial interpolation converts sparse point observations into continuous surfaces and underpins decisions in soil and agricultural management, hydrology and climatology, air-quality and health surveillance, mineral resource estimation and ecological monitoring. Geostatistics supplies the theoretical basis for much of this practice by modelling spatial dependence and attaching an error estimate to each prediction. Over the past two decades, the methodological landscape has diversified rapidly, from deterministic interpolators and kriging towards covariate-assisted hybrids, model-based and Bayesian geostatistics, scalable approximations for large datasets, and machine-learning and deep-learning predictors embedded in geographic information systems. These developments have generated conflicting claims about predictive accuracy, uncertainty quantification and the appropriate way to validate maps. This critical narrative review synthesises literature published between 2000 and 2026, supplemented by foundational earlier work, identified through structured searches of multidisciplinary and discipline-relevant scholarly sources and citation tracking, and appraised qualitatively for methodological transparency, validation design and comparative fairness. The evidence indicates that no interpolator is universally superior: relative performance depends on the strength and form of spatial dependence, the availability and relevance of covariates, sampling density and configuration, and the target of inference. Covariate-assisted geostatistics and spatially informed machine learning often outperform univariate methods where informative covariates exist, yet comparative studies are frequently compromised by unequal tuning, clustered samples and validation designs that do not represent the prediction domain. Uncertainty assessment remains the least mature component of practice. Kriging variances are conditional on an assumed model and ignore parameter uncertainty, many machine-learning workflows report no uncertainty at all, and probabilistic outputs are seldom validated for reliability and sharpness. Unresolved questions concern map-accuracy estimation from non-probability samples, uncertainty of spatial aggregates, extrapolation beyond the sampled feature space and the theoretical grounding of deep spatial models. Progress is likely to depend less on new algorithms than on probability-based validation, transparent reporting, explicit treatment of uncertainty and open, reproducible implementation within geographic information systems.
Keywords: Kriging, variogram, regression kriging, spatial machine learning, prediction uncertainty, spatial cross-validation, digital soil mapping, Gaussian process