Spatiotemporal geostatistical modeling of groundwater levels under a Bayesian framework using means of physical background

Abstract

The joint spatiotemporal modeling of aquifer level fluctuations provides a significant tool in the prediction of groundwater levels at unvisited locations. Two types of variogram functions, appropriately modified to incorporate physical information, are presented and compared under Space-time Residual kriging methodology using the Bayesian Bootstrap idea to quantify uncertainty. The spatiotemporal trend is approximated using a component of physical meaning. A recently developed Spartan type non-separable variogram function employs tools of physical meaning to enhance the efficiency and reliability of spatiotemporal geostatistical modeling in groundwater applications. In addition, the product-sum space-time variogram is applied and involves in the separable variogram functions a scale factor of hydraulic conductivity directional ratio. The proposed variogram functions involve a non-Euclidean distance metric and are mathematically valid (i.e., constitutes permissible models). Herein, the efficiency of the proposed tools is tested using groundwater level data from an alluvial unconfined aquifer. Both functions provide improved results compared to those of the Space-time Ordinary kriging. Between the two, the non-separable one has the most efficient performance.