Bayesian data fusion for water table interpolation: Incorporating a hydrogeological conceptual model in kriging

Abstract

[1] The creation of a contour map of the water table in an unconfined aquifer based on head measurements is often the first step in any hydrogeological study. Geostatistical interpolation methods (e.g., kriging) may provide exact interpolated groundwater levels at the measurement locations but often fail to represent the hydrogeological flow system. A physically based, numerical groundwater model with spatially variable parameters and inputs is more adequate in representing a flow system. Because of the difficulty in parameterization and solving the inverse problem, however, a considerable difference between calculated and observed heads will often remain. In this study the water-table interpolation methodology presented by Fasbender et al. (2008), in which the results of a kriging interpolation are combined with information from a drainage network and a digital elevation model (DEM), using the Bayesian data fusion framework, is extended to incorporate information from a tuned analytic element groundwater model. The resulting interpolation is exact at the measurement locations whereas the shape of the head contours is in accordance with the conceptual information incorporated in the groundwater-flow model. The Bayesian data fusion methodology is applied to a regional, unconfined aquifer in central Belgium. A cross-validation procedure shows that the predictive capability of the interpolation at unmeasured locations benefits from the Bayesian data fusion of the three data sources (kriging, DEM, and groundwater model), compared to the individual data sources or any combination of two data sources.

Investigação geoestatística para um adequado mapeamento do nível do lençol freático: o caso de Bordéus (França)

“…Because of the inherent smoothing effects from these methods, a more realistic water table is obtained when the water-table data are evenly distributed over the domain. These methods generally fail to accurately replicate the water table close to boundaries (Kuhlman and Igúzquiza 2010;Fasbender et al 2008;Peeters et al 2010) and may also have difficulty in reproducing large local variations in the water table (e.g., large drawdown near pumping wells).…”

“…A water-table map is needed to solve Darcy's law. To obtain a water-table map requires solution of a differential equation for mass conservation that requires the proper definition of boundary conditions and the estimation of transmissivity for each grid cell (Brochu and Marcotte 2003;Fasbender et al 2008;Peeters et al 2010). Another approach is based on geostatistical modeling, which makes it possible to rebuild the map from data available at only a limited set of points.…”

Integração de modelos espaciais e temporais para predições de níveis freáticos extremos

“…Quando há disponibilidade de informações auxiliares, é possível melhorar a acurácia das predições espaciais, estimar padrões espaciais mais plausíveis e atribuir sentido físico aos mapas resultantes com uso de produtos, como os modelos digitais de terreno (MDT) e as imagens de satélite classificadas (Odeha et al, 1994;Hengl et al, 2004;Bogaert & Fasbender 2007;Manzione et al, 2010;Peeters et al, 2010). A partir dessas estimativas, é possível elaborar cenários na forma de mapas.…”

Bayesian Data Fusion (BDF) of Monitoring Data with a Statistical Groundwater Contamination Model to Map Groundwater Quality at the Regional Scale

“…The main advantage of a Bayesian approach is to put the problem of data fusion into a clear probabilistic framework. Since this original paper, the general method has been applied to various case studies of environmental sciences; remote sensing [16,17], hydrology [18,19] or air pollution [20]. Similarly to these applications, the present paper relies on some specific assumptions with the aim of spatial mapping of groundwater quality.…”