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

Abstract

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 Worth of Stochastic Inversion for Identifying Connectivity by Means of a Long‐Lasting Large‐Scale Hydraulic Test: The Salar de Atacama Case Study

“…The method used to characterize the heterogeneous structure of the upper aquifer unit of the SdA nucleus and identify large‐scale preferential channels involves two main components: (a) a large‐scale, long‐term cross‐hole hydraulic test aimed at observing multiple aquifer responses over long (kilometers) distances, and (b) stochastic inversion of drawdown data obtained with the corrective‐filtering method proposed by Trabucchi et al. (2021a). The latter allows filtering systematic errors in head data (e.g., external trends of hydraulic heads caused by the normal exploitation of the aquifer) during calibration.…”

“…Applying the superposition principle, initial and boundary conditions are easily set to zero (Trabucchi et al., 2021a). The long‐term cross‐hole hydraulic test and production pumping rates are simulated by prescribing a time‐varying flow rate at each well.…”

“…The corrective‐filtering method of Trabucchi et al. (2021a) was used to obtain reliable estimates of drawdown data. In this case, the method requires to first estimate drawdowns with the natural flow model and then calibrate the parameters to fit drawdown estimates with the pilot point method.…”

“…Recently, Trabucchi et al. (2021a) have presented a corrective‐filtering method to filter systematic errors in drawdown data during the automatic calibration of a groundwater model.…”

Bias Correction of Hydrologic Projections Strongly Impacts Inferred Climate Vulnerabilities in Institutionally Complex Water Systems

“…A few other studies have used statistical biascorrection approaches to match the overall statistical moments of their simulated streamflow with observations, which implicitly takes into account groundwater dynamics (Hamlet and Lettenmaier 1999;Tiwari et al 2021). Finally, there are other methods, such as Bayesian filtering methods (Ait-El-Fquih et al 2016;Panzeri et al 2014;Rajabi et al 2018) or offline postprocessing procedures (Holtzman et al 2020;Trabucchi et al 2021), that implicitly improve the representation of groundwater dynamics and overall quality of streamflow simulations.…”