Estimating groundwater levels and their associated uncertainty through spatiotemporal kriging of groundwater-level data

Abstract Sustainable groundwater management requires, among other factors, reliable monitoring of groundwater levels (GWLs) and their spatiotemporal evolution in an aquifer with meaningfully quantified uncertainty. Geostatistical methods can estimate GWL surfaces directly from available groundwater monitoring data. This contrasts with groundwater flow modeling, which requires much more detailed data. This study estimates spatiotemporal GWL maps and quantifies associated uncertainties by spatiotemporal kriging, which combines spatial interpolation with temporal gap filling and noise filtering. The central hypothesis is that including hydrogeological information in kriging improves GWL predictions. To test this hypothesis, spatiotemporal trends and soft information inspired by hydrological understanding are included. These include digital elevation models, river exchange components, and the confinement status of aquifers. To test the necessity of full statistical involvement through Bayesian hyperparameter inference, universal kriging is operated in a fully Bayesian framework and then compared to simpler approaches like non-Bayesian and residual space–time kriging. The approach is demonstrated for the Wairau Plain aquifer, New Zealand, where the spatiotemporal GWL estimates can be compared with transient simulation results from a numerical groundwater flow model. The results indicate that space–time kriging is a valuable tool to estimate transient GWL maps, where auxiliary hydrogeological information is highly useful, that the fully Bayesian treatment of universal kriging is worth the effort, but that a posterior (Bayesian) uncertainty of geostatistical hyperparameters is close to irrelevant.