Bayesian Estimation of a Highly Parameterized Hydraulic Conductivity Field: A Study Case

Comprehensive characterization of the spatial variability of aquifer hydraulic parameters is fundamental to correctly design a structure that interacts with the groundwater system, e.g. a detention reservoir. A flood control structure has been planned to dampen the Baganza River floods, upstream the city of Parma (Northern Italy), storing a portion of the flood volume then released at a controlled rate. The location and the geometry of the planned reservoir are already set and the aquifer system beneath the structure is under investigation and monitoring. A large numbers of boreholes identified a sequence of gravel-sand and clayey layers that gives rise to two distinct aquifers (one unconfined and one confined). A numerical model has been developed by means of MODFLOW_2005 in order to simulate the unconfined aquifer under current conditions. The numerical model has been calibrated in steady-state conditions by means of 11 observations of water levels (collected during spring 2013). About 18000 hydraulic conductivity values have been defined and estimated by means of a Bayesian Geostatistical Approach. The inverse methodology estimates the hydraulic conductivity field using both field observations (head data) and prior information on the structure of the unknown parameters. The inverse procedure requires the calculation of the sensitivity of each observation to each of the estimated parameters that has been efficiently evaluated making use of an adjoint state formulation of the forward model MODFLOW_2005-Adjoint. The inverse code is the freeware bgaPEST, a highly parameterized inversion software package developed according to the PEST software concept. The Bayesian Geostatistical Approach is shown to be able to constrain the hydraulic conductivity field with a large number of parameters and just few observations. The results of the inversion are consistent with the alluvial nature of the investigated aquifer and the information content of the data. The calibrated model can then be used as a support tool for the design and the management of the new flood control structure.