Lumped hydrological models are tools commonly used in karst water resource management, however, their parameters cannot be obtained from field measurements and need to be estimated by model calibration. In general, the more hydrological processes are represented in a lumped parameter model, the higher the dimensionality of the parameter space. In particular, a large number of parameters is needed if we implement a karst hydrologic model that can reproduce the effect of land use changes.
We recently developed the LuKARS model (i.e. a hydrotope-based lumped karst aquifer model) with the particular aim to investigate the hydrological impacts of land use changes in the karstic system of the Kerschbaum springshed in Waidhofen a.d. Ybbs (Austria). The implemented model was calibrated for the years 2006 – 2008 and comprises 21 calibration parameters for 3 hydrotopes. While the model adequately reproduces the observed hydrological impacts of the land use changes, the model output uncertainties are high due to the 21-dimensional parameter space. For this reason, we applied the recently proposed active subspace method to the LuKARS model to investigate possibilities of reducing the high-dimensional initial parameter space and to quantify the related model uncertainties. The active subspace method searches for orthogonal directions in the parameter space that are relevant to update a defined prior to a well-constrained posterior parameter distribution. If relevant directions are identified, a lower dimensional subspace can be created which can be used to simplify the higher dimensional problem.
Applying the active subspace method to the LuKARS model of the Kerschbaum spring, we were able to investigate the model structure and model parameter uncertainties. In this regard, we show that the space covered by each hydrotope as well as its specific hydrological variability are decisive to reproduce the hydrological dynamics of the measured karst spring discharge. Moreover, relevant parameter directions were identified by the active subspace method, leading to a dimension reduction of the initial 21-dimensional parameter space to a 4-dimensional one. Using the model with a 4-dimensional parameter space, we still can reproduce the hydrological impacts of the land use changes in the Kerschbaum recharge area. Thus, we conclude that the LuKARS model is a robust modeling approach for assessing the effects of land use changes on karst water resources. Moreover, the active subspace method is a promising tool to reduce the uncertainties related to the structure and the parameters of lumped karst aquifer models.