Temporal Scale-Dependent Sensitivity Analysis for Hydrological Model Parameters Using the Discrete Wavelet Transform and Active Subspaces

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.