# Bayesian calibration and sensitivity analysis for a karst aquifer model using active subspaces

## TL;DR

This paper introduces a novel application of active subspaces for Bayesian calibration and sensitivity analysis of a complex karst aquifer model, improving computational efficiency and understanding of influential parameters.

## Contribution

It is the first to apply active subspace methods in karst hydrology for dimension reduction and sensitivity analysis, enhancing model calibration and interpretation.

## Key findings

- Active subspace method identifies dominant parameter directions.
- Low-dimensional Bayesian inference is feasible for high-dimensional models.
- Results provide hydrological insights and uncertainty quantification.

## 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.