Bayesian Calibration and Sensitivity Analysis for a Karst Aquifer Model Using Active Subspaces

Abstract

In this article, we perform a parameter study for a recently developed karst hydrological model. The study consists of a high‐dimensional Bayesian inverse problem and a global sensitivity analysis. For the first time in karst hydrology, we use the active subspace method to find directions in the parameter space that dominate the Bayesian update from the prior to the posterior distribution in order to effectively reduce the dimension of the problem and for computational efficiency. Additionally, the calculated active subspace can be exploited to construct sensitivity metrics on each of the individual parameters and be used to construct a natural model surrogate. The model consists of 21 parameters to reproduce the hydrological behavior of spring discharge in a karst aquifer located in the Kerschbaum spring recharge area at Waidhofen a.d. Ybbs in Austria. The experimental spatial and time series data for the inference process were collected by the water works in Waidhofen. We show that this case study has implicit low dimensionality, and we run an adjusted Markov chain Monte Carlo algorithm in a low‐dimensional subspace to construct samples of the posterior distribution. The results are visualized and verified by plots of the posterior's push‐forward distribution displaying the uncertainty in predicting discharge values due to the experimental noise in the data. Finally, a discussion provides hydrological interpretation of these results for the Kerschbaum area.

Identifying More Realistic Model Structures by Electrical Conductivity Observations of the Karst Spring

“…Consequently, they may not deliver reliable predictions outside the hydrologic conditions that they were calibrated for (Kuczera & Mroczkowski, 1998). To establish more realistic model structures, one way is to exploit more information of spring discharge through extra evaluation objectives, such as flow duration curve or autocorrelation function (Hartmann, Weiler, et al., 2013; Moussu et al., 2011), or using extra tools to further explore the internal process (Bittner et al., 2020; Duran et al., 2020) and reduce the dimensions of the parameter space (Teixeira Parente et al., 2019). Another promising way is to incorporate auxiliary data into the model that can provide extra internal information, that is, flow path, residence time or runoff components, which are not involved in the discharge, to constrain the internal behavior of models to be more realistic and reduce the risk of selecting wrong model structures (Fenicia et al., 2008; Hartmann et al., 2017; Mudarra et al., 2019; Son & Sivapalan, 2007; Vache & McDonnell, 2006).…”

A physically-based distributed karst hydrological model (QMG model-V1.0) for flood simulations

“…However, modeling floods in karst regions is extremely difficult because of the complex hydrogeological structure. Karst water-bearing systems consist of multiple media under the influence of complex karst development dynamics (Worthington et al, 2000;Ková cs and Perrochet, 2008), such as karst caves, conduits, fissures, and pores, and are usually highly spatially heterogeneous (Chang and Liu, 2015;Mario et al, 2019). In addition, the intricate surface hydrogeological conditions and the hydrodynamic conditions inside the karst water-bearing medium result in significant temporal and spatial differences in the hydrological processes in karst areas (Geyer et al, 2008;Bittner et al, 2020).…”

Karst recharge-discharge semi distributed model to assess spatial variability of flows

“…The number of parameters and the possibility to determine their values is a common issue in environmental models (Ebel and Loague, 2006;Bittner et al, 2018b). This concern is made exacerbated for karst systems, because difficulties in characterizing karst heterogeneity widen the gap between available information and the number of model parameters required for distributed or semi-distributed modelling (Hartmann et al, 2014;Parente et al, 2019). Integration of measurable hydraulic parameters into semi-distributed models is also challenging.…”