Joint Optimization of Measurement and Modeling Strategies With Application to Radial Flow in Stratified Aquifers

Abstract

When applying environmental models, the choice of model complexity and the design of field campaigns depend on each other and on the modeling/prediction goal. We propose jointly optimizing model complexity and data collection (design) by maximizing the expected performance for the modeling goal. We use ensembles of highly resolved virtual realities and of less complex modeling variants that differ in their degrees of upscaling and simplified parameterization. For each design under consideration, we simulate hypothetical measurement data (subject to noise) with all realizations of all models. To mimic model calibration with hypothetical data, we identify pairs of best fitting realizations between virtual reality and each model variant for each design. Then, we emulate model choice by selecting (across the model variants, for each design and for each virtual reality) the pair that shows the best predictive match in the modeling goal. Finally, we identify the model/design combination that offers, on average over all virtual realities, the best predictive match. As a test application, we consider a heterogeneous, stratified aquifer, in which the stratification enhances hydraulic anisotropy on the macroscale. We define two different modeling goals: (a) estimating the hydraulic conductivity tensor upscaled to the full aquifer thickness and (b) predicting the pumping rate needed to dewater a construction pit. Our results indicate that jointly optimizing observation networks and model selection can reduce the prediction uncertainty of parameters at lower experimental costs. We also show that the involved trade‐offs between model complexity and required design depend on the target quantity.

Revealing vertical aquifer heterogeneity and hydraulic anisotropy by pumping partially penetrating wells

“…To quantify the variability among the measurement points, the observation points that are arranged in different directions to the pumping well, but coincide by ±0.6 and ±0.5 m in their r-and z-coordinates, respectively, were clustered and the associated drawdown measurements s meas compared. These cluster ranges are realistic, since intended measurement locations of observation points may be misplaced in the installation of observation wells (Maier et al 2020). The mean value μ c p and standard deviation σ c p of all measurements n cp available in each cluster c p are computed by:…”

“…As mentioned before, a steady-shape pumping regime was considered in the simulations, in which drawdown differences between observation locations remain constant. Typically, this requires the specification of pairs of observation points by either setting one observation location as the superordinate reference point (Maier et al 2020) or by considering all feasible pairs of observation points (Bohling et al 2002). Each field measurement, however, is subject to measurement errors of different types, including measurement noise or the misplacement of observation wells (Maier et al 2020).…”

“…Typically, this requires the specification of pairs of observation points by either setting one observation location as the superordinate reference point (Maier et al 2020) or by considering all feasible pairs of observation points (Bohling et al 2002). Each field measurement, however, is subject to measurement errors of different types, including measurement noise or the misplacement of observation wells (Maier et al 2020). In trials not reported here, the effect of considering different observation points as the reference point had been tested, yielding different model-calibration results due to measurement error.…”

“…The present study builds upon a method introduced by Maier et al (2020) to estimate hydraulic anisotropy by inverting steady-shape aquifer tests using a partially penetrating pumping well. The approach follows the basic principles of hydraulic tomography.…”

“…While Maier et al (2020) described the application of steady-shape aquifer tests to jointly optimize modeling and measurement strategies with a synthetic scenario, the present study considers a field application, including the design of the experiments.…”