Automatic Calibration of Groundwater Models With Bias Correction and Data Filtering: Working With Drawdown Data

The drawdown response to a hydraulic stress contains crucial information to characterize an aquifer. Modeling drawdowns is far easier than modeling heads because they are subject to homogeneous (zero) internal sink/sources, and boundary and initial conditions. The problem lies on the fact that drawdowns are not measured directly but derived from measurements of head fluctuations. Resulting drawdowns may suffer persistent inaccuracies in complex systems with uncertain long-acting external stresses, so that they are affected not only by errors in head measurements, but also in estimates of the natural head evolution. This hinders the use of drawdowns in groundwater models, and forces modelers to employ absolute heads and soft information. In this context, we present a method to filter systematic errors in drawdown data during the calibration of a groundwater model. To do this, we introduce a bias correction term in a composite inverse problem that combines a natural head model with a drawdown model. Since these two models share the same parameters, a two-stage iterative optimization algorithm is developed to jointly estimate the bias, natural trends, and parameters. The method is illustrated by a synthetic example in a heterogeneous aquifer. The example shows that the method converges to the best conditional estimate even when absolute head data is strongly biased. In the same example, we demonstrate that the use of biased absolute head data in the traditional inverse problem can also provide good fittings but, in this case, the bias leads to an incorrect estimation of the transmissivity field.The final version of the paper has greatly benefitted from comments by Keith Halford and two anonymous reviewers. The authors acknowledge the financial support provided by the Sociedad Química y Minera de Chile S.A. through project “Proyección de la evolución SOP, Salar de Atacama. Fase II: ensayos de campo y laboratorio” (SA 9500001785) and by the AGAUR (Agència de Gestió d'Ajuts Universitaris i de Recerca, Generalitat de Catalunya), through project AGAUR-2017-SGR1485. M. Trabucchi acknowledges the financial support from the AGAUR through the FI fellowship (2018FIB200079).Peer reviewe