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.

No abstract

Methane gas hydrates have increasingly become a topic of interest because of their potential as a future energy resource. There are significant economical and environmental risks associated with extraction from hydrate reservoirs, so a variety of multiphysics models have been developed to analyze prospective risks and benefits. These models generally have a large number of empirical parameters which are not known a priori. Traditional optimization-based parameter estimation frameworks may be ill-posed or computationally prohibitive. Bayesian inference methods have increasingly been found effective for estimating parameters in complex geophysical systems. These methods often are not viable in cases of computationally expensive models and high-dimensional parameter spaces. Recently, methods have been developed to effectively reduce the dimension of Bayesian inverse problems by identifying low-dimensional structures that are most informed by data. Active subspaces is one of the most generally applicable methods of performing this dimension reduction. In this paper, Bayesian inference of the parameters of a state-of-the-art mathematical model for methane hydrates based on experimental data from a triaxial compression test with gas hydrate-bearing sand is performed in an efficient way by utilizing active subspaces. Active subspaces are used to identify low-dimensional structure in the parameter space which is exploited by generating a cheap regression-based surrogate model and implementing a modified Markov chain Monte Carlo algorithm. Posterior densities having means that match the experimental data are approximated in a computationally efficient way.

With the advancement of artificial intelligence and machine learning methods, autonomous approaches are recognized to have great potential for performing more efficient scattering experiments. In our view, it is crucial for such approaches to provide thorough evidence about respective performance improvements in order to increase acceptance within a scientific community. Therefore, we propose a benchmarking procedure designed as a cost-benefit analysis that is applicable to any scattering method sequentially collecting data during an experiment. For a given approach, the performance assessment is based on how much benefit, given a certain cost budget, it is able to acquire in predefined test cases. Different approaches thus get a chance for comparison and can make their advantages explicit and visible. Key components of the procedure, i.e., cost measures, benefit measures, and test cases, are made precise for the setting of three-axes spectrometry (TAS) as an illustration. Finally, we discuss neglected aspects and possible extensions for the TAS setting and comment on the procedure’s applicability to other scattering methods. A Python implementation of the procedure to simplify its utilization by interested researchers from the field is also provided.