Karst spring discharge modeling based on deep learning using spatially distributed input data

Abstract

Despite many existing approaches, modeling karst water resources remains challenging as conventional approaches usually heavily rely on distinct system knowledge. Artificial neural networks (ANNs), however, require only little prior knowledge to automatically establish an input–output relationship. For ANN modeling in karst, the temporal and spatial data availability is often an important constraint, as usually no or few climate stations are located within or near karst spring catchments. Hence, spatial coverage is often not satisfactory and can result in substantial uncertainties about the true conditions in the catchment, leading to lower model performance. To overcome these problems, we apply convolutional neural networks (CNNs) to simulate karst spring discharge and to directly learn from spatially distributed climate input data (combined 2D–1D CNNs). We investigate three karst spring catchments in the Alpine and Mediterranean region with different meteorological–hydrological characteristics and hydrodynamic system properties. We compare the proposed approach both to existing modeling studies in these regions and to our own 1D CNN models that are conventionally trained with climate station input data. Our results show that all the models are excellently suited to modeling karst spring discharge (NSE: 0.73–0.87, KGE: 0.63–0.86) and can compete with the simulation results of existing approaches in the respective areas. The 2D models show a better fit than the 1D models in two of three cases and automatically learn to focus on the relevant areas of the input domain. By performing a spatial input sensitivity analysis, we can further show their usefulness in localizing the position of karst catchments.