The research, published in Discover Geoscience by Khirsagar Patel, Prasoon Soni, and Pushpraj Singh of Guru Ghasidas Central University in Bilaspur, drew on groundwater level records from 69 observation wells maintained by the Central Ground Water Board, spanning the years 2001 to 2025. Rather than treating the water table as a single static surface, the team divided the record into three hydrological seasons: the rainy monsoon months from June to September, the winter period from October to January, and the summer months from February to May. For each well and each season, they computed average depths to water in meters below ground level, then screened the dataset for completeness, duplicates, and spatial validity before any mapping began. All well locations were projected into a common coordinate system, and the interpolated surfaces were generated at a uniform 30-meter resolution, providing a consistent framework across every test.

The core of the study was a comparison between two fundamentally different families of interpolation. Deterministic methods, including inverse distance weighting and regularized spline, estimate values at unsampled locations using purely mathematical rules. Inverse distance weighting assumes that nearby wells exert more influence than distant ones, with the influence decaying according to a distance power parameter, while spline fits a smooth curved surface that passes exactly through every measured point and minimizes overall curvature. These methods are simple and fast, but they carry no statistical model of how groundwater actually varies across the landscape, and they offer no way to quantify how confident one should be in a prediction between wells.

Geostatistical methods take a different route. Ordinary kriging, the technique tested here, explicitly models the spatial autocorrelation of the data using a semivariogram, a function that describes how the variance between paired observations grows with their separation distance. From the experimental semivariogram, computed from the well data, the researchers fitted four theoretical models: Circular, Spherical, Exponential, and Gaussian. Each model captures a different character of spatial continuity. The Spherical model, a staple of hydrogeological work, shows spatial dependence rising with distance and then flattening at a defined range. The Exponential model rises quickly at short distances and approaches its sill asymptotically, suiting datasets with short-range variability. The Gaussian model produces very smooth surfaces, while the Circular model describes moderate continuity with an abrupt change in behavior at the range. Kriging then uses the fitted model to assign optimal weights to surrounding wells, and crucially, it also yields an estimate of prediction uncertainty at every location.

The semivariogram analysis itself revealed a great deal about how the Arpa Basin’s aquifer behaves. Across the rainy season, semivariance increased steadily with distance, indicating strong spatial dependence, with a low nugget effect suggesting minimal measurement error. Groundwater levels remained spatially correlated over distances of roughly 20 to 35 kilometers, meaning the water table varies in a structured, basin-scale way rather than randomly from well to well. In winter, the fitted models showed ranges of about 21.9 to 33.5 kilometers, with the Spherical and Exponential models extending furthest. Summer, when reduced recharge and heavy pumping stress the aquifer, showed weaker but still statistically significant spatial dependence, with model ranges between roughly 18.4 and 31.9 kilometers. These seasonal shifts matter because they demonstrate that the spatial structure of the water table is not fixed: it changes as recharge, abstraction, and hydrogeological conditions change through the year.

To judge which method and model performed best, the team used cross-validation, a demanding test in which each observation is removed in turn and predicted from the remaining wells, allowing predicted and observed values to be compared across the entire dataset. Five statistics were examined together: Mean Error, which measures bias; Root Mean Square Error, which measures overall prediction accuracy; Average Standard Error and Mean Standardized Error, which assess whether the model’s own uncertainty estimates are honest; and Root Mean Square Standardized Error, which should ideally sit close to one. The ideal model would show a mean error near zero, the lowest possible RMSE, an average standard error close to the RMSE, and a standardized error near one. No single candidate achieved all of these targets simultaneously, which is itself an instructive finding.

The Exponential semivariogram consistently delivered the lowest prediction errors. In the rainy season it produced an RMSE of 3.787 meters and a mean error of just 0.0282; in winter, an RMSE of 3.9939 meters; and in summer, a mean error of 0.0486 with an RMSE of 4.3308 meters. Yet when the researchers turned to the uncertainty measures, the picture shifted with the seasons. In the rainy season, the Spherical model’s root mean square standardized error of 0.9953 came closest to the ideal value of one, with good agreement between its average standard error and RMSE. In winter, it was the Circular model that best calibrated its uncertainty, with a standardized error of 0.9968 and closely matched error statistics. In summer, the Gaussian model took that role. In other words, the model that predicts most accurately is not always the model that most honestly reports how sure it is, and the balance between the two shifts from season to season.

The mapped surfaces told a consistent visual story that reinforced the statistics. Ordinary kriging with the Spherical semivariogram produced the most realistic and coherent groundwater surfaces in all three seasons, with smooth transitions and clearly defined zones of shallow and deep water tables. The deterministic methods fared less well: inverse distance weighting generated localized exaggerations and bull’s-eye patterns around observation wells, while spline produced surfaces that were overly smooth and prone to overshooting. The seasonal maps also exposed a pattern of concern for water managers, with the deepest water tables concentrated in the southern and central portions of the basin, particularly during summer, signaling significant groundwater stress in the dry months in those areas.

The broader lesson of the study is that there is no universally superior interpolation model, and that model selection should rest on the combined interpretation of prediction accuracy and uncertainty measures rather than on any single statistic. For the Arpa River Basin, the Spherical semivariogram within ordinary kriging emerged as the most balanced overall choice for seasonal groundwater mapping, while the Exponential model offers an alternative where raw prediction accuracy is the priority. The geostatistical approach outperformed the deterministic alternatives in reliability and spatial consistency across every season tested. The resulting seasonal groundwater level maps provide a scientific foundation for monitoring network design, watershed planning, and sustainable abstraction policies in the basin. The authors suggest that future gains could come from incorporating additional hydrological variables, densifying the monitoring network, and applying advanced geostatistical or machine learning techniques, steps that would be especially valuable as climate variability and growing demand place ever greater pressure on Central India’s hidden water reserves.

Subject of Research: Comparative evaluation of geostatistical and deterministic interpolation methods for seasonal groundwater level mapping in the Arpa River Basin, Central India

Article Title: Comparative assessment of geostatistical and deterministic interpolation methods for seasonal groundwater level mapping in the Arpa River Basin, Central India

Article References: Patel, K., Soni, P., & Singh, P. (2026). Comparative assessment of geostatistical and deterministic interpolation methods for seasonal groundwater level mapping in the Arpa River Basin, Central India. Discover Geoscience, 4(1), Article 377. https://doi.org/10.1007/s44288-026-00736-7

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00736-7

Keywords: groundwater, spatial interpolation, ordinary kriging, semivariogram, inverse distance weighting, spline, ArcGIS, Arpa River Basin, Central India, hydrogeology, seasonal variability, cross-validation