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.

Global sensitivity analysis is an important step in the process of developing and analyzing hydrological models. Measured data of different variables are used to identify the number of sensitive model parameters and to better constrain the model output. However, data scarcity is a common issue in hydrology. Since in hydrology we are dealing with multi‐scale time dependent problems, we want to overcome that issue by exploiting the potential of using the decomposed wavelet temporal scales of the discharge signal for the identification of sensitive model parameters. In the proposed methodology, we coupled the discrete wavelet transform with a technique for model parameter dimension reduction, that is, the active subspace method. We apply the proposed methodology to the LuKARS model, a lumped karst aquifer model for the Kerschbaum spring in Waidhofen/Ybbs (Austria). Our results demonstrate that the temporal scale dependency of hydrological processes affects the structure and dimension of the active subspaces. The results reveal that the dimensionality of an active subspace increases with the increasing number of hydrologic processes affecting a temporal scale. As a consequence, different parameters are sensitive on different temporal scales. Finally, we show that the total number of sensitive parameters identified at different temporal scales is larger than the number of sensitive parameters obtained using the complete spring discharge signal. Hence, instead of using multiple time series to determine the number of sensitive parameters, we can also obtain more information about parameter sensitivities from one single, decomposed time series.

Uncertainties in hydrologic model outputs can arise for many reasons such as structural, parametric and input uncertainty. Identification of the sources of uncertainties and the quantification of their impacts on model results are important to appropriately reproduce hydrodynamic processes in karst aquifers and to support decision-making. The present study investigates the time-dependent relevance of model input uncertainties, defined as the conceptual uncertainties affecting the representation and parameterization of processes relevant for groundwater recharge, i.e. interception, evapotranspiration and snow dynamic, on the lumped karst model LuKARS. A total of nine different models are applied, three to compute interception (DVWK, Gash and Liu), three to compute evapotranspiration (Thornthwaite, Hamon and Oudin) and three to compute snow processes (Martinec, Girons Lopez and Magnusson). All the input model combinations are tested for the case study of the Kerschbaum spring in Austria. The model parameters are kept constant for all combinations. While parametric uncertainties computed for the same model in previous studies do not show pronounced temporal variations, the results of the present work show that input uncertainties are seasonally varying. Moreover, the input uncertainties of evapotranspiration and snowmelt are higher than the interception uncertainties. The results show that the importance of a specific process for groundwater recharge can be estimated from the respective input uncertainties. These findings have practical implications as they can guide researchers to obtain relevant field data to improve the representation of different processes in lumped parameter models and to support model calibration.