Inverse Modeling Aided by the Classification and Regression Tree (CART) Algorithm

Abstract

Inverse modeling in hydrogeology is a powerful tool to improve the characterization of hydraulic conductivity and porosity. In the last few years, the use of data assimilation techniques, such as the ensemble Kalman filter, has proven very effective in this field. However, in some cases, the parameter updates by the filtering process may create artificial heterogeneity in certain zones in order to reduce the estimation error. This may happen when observations are scarce in time or space, but also when the parameters being updated are not the only responsible of the behavior of the aquifer (for instance, when high piezometric heads are due to an undetected recharge event, and the filter keeps reducing the conductivity to increase the gradients around high piezometric head observations). This study pretends to avoid those artifacts by the use of classification and regression trees. The decision and regression trees will be implemented using the CART algorithm with the aim of discriminating whether an updated parameter field is acceptable, and in case it is not acceptable how to proceed. When the algorithm marks as unacceptable a parameter field, it is swapped with another parameter field. The method is demonstrated for a contamination event in a synthetic aquifer based on real data. A numerical model has been created to reproduce flow and transport as observed in the real aquifer. The model has a rectangular-shaped area of 3000 m long by 500 m wide. For the inverse modeling process, two ensembles of fields are used, one for hydraulic conductivity and one for porosity; if needed, recharge can be modified smoothly using spline interpolation. The ensemble Kalman filter is used to update porosities and conductivities, and, if the decision algorithm requests it, the recharge is also modified.