Towards a community-wide effort for benchmarking in subsurface hydrological inversion: benchmarking cases, high-fidelity reference solutions, procedure, and first comparison

Abstract

Inversion in subsurface hydrology refers to estimating spatial distributions of (typically hydraulic) properties often associated with quantified uncertainty. Many methods are available, each characterized by a set of assumptions, approximations, and numerical implementations. Only a few intercomparison studies have been performed (in the remote past) amongst different approaches (e.g., Zimmerman et al., 1998; Hendricks Franssen et al., 2009). These intercomparisons guarantee broad participation to push forward research efforts of the entire subsurface hydrological inversion community. However, from past studies until now, comparisons have been made among approximate methods without firm reference solutions. Note that the reference solutions are the best possible solutions with the best estimate and posterior standard deviation and so forth. Without reference solutions, one can only compare competing best estimates and their associated uncertainties in an intercomparison sense, and absolute statements on accuracy are unreachable. Our current initiative defines benchmarking scenarios for groundwater model inversion. These are targeted for community-wide use as test cases in intercomparison scenarios. Here, we develop five synthetic, open-source benchmarking scenarios for the inversion of hydraulic conductivity from pressure data. We also provide highly accurate reference solutions produced with massive high-performance computing efforts and with a high-fidelity Markov chain Monte Carlo (MCMC)-type solution algorithm. Our high-end reference solutions are publicly available along with the benchmarking scenarios, the reference algorithm, and the suggested benchmarking metrics. Thus, in comparison studies, one can test against high-fidelity reference solutions rather than discussing different approximations. To demonstrate how to use these benchmarking scenarios, reference solutions, and suggested metrics, we provide a blueprint comparison of a specific ensemble Kalman filter (EnKF) version. We invite the community to use our benchmarking scenarios and reference solutions now and into the far future in a community-wide effort towards clean and conclusive benchmarking. For now, we aim at an article collection in an appropriate journal, where such clean comparison studies can be submitted together with an editorial summary that provides an overview.