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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., Comment: 21 pages, 15 figures

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., 27 pages, 5 figures, 2 tables; 5 pages supplementary information

The use of the active subspace method was recently proposed to reduce the dimension of complex hydrological models, perform sensitivity analysis of model parameters and quantify the uncertainty affecting model parameters. Although this inversion method is highly promising in terms of computational performance, a clear hydrological interpretation of the meaning of the active subspace that it identifies is missing. In this work, we infer how the active subspace changes in dimension and feature depending on geometrical and hydrological properties of the karst aquifer model LuKARS. We find that both the hydrotope area coverage and model parameters describing the catchment characteristics (here: water storage and discharge properties of the hydrotopes) have major impacts on the active subspace. Our results show that the active subspace method can be used to investigate the relation between the model structure, the area of a hydrotope and the simulated spring discharge.