  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.
