Water balance estimation in high Alpine terrain by combining distributed modeling and a neural network approach (Berchtesgaden Alps, Germany)

Abstract. The water balance in high Alpine regions is often characterized by significant variation of meteorological variables in space and time, a complex hydrogeological situation and steep gradients. The system is even more complex when the rock composition is dominated by soluble limestone, because unknown underground flow conditions and flow directions lead to unknown storage quantities. Reliable distributed modeling cannot be implemented by traditional approaches due to unknown storage processes at local and catchment scale. We present an artificial neural network extension of a distributed hydrological model (WaSiM-ETH) that allows to account for subsurface water transfer in a karstic environment. The extension was developed for the Alpine catchment of the river "Berchtesgadener Ache" (Berchtesgaden Alps, Germany), which is characterized by extreme topography and calcareous rocks. The model assumes porous conditions and does not account for karstic environments, resulting in systematic mismatch of modeled and measured runoff in discharge curves at the outlet points of neighboring high alpine subbasins. Various precipitation interpolation methods did not allow to explain systematic mismatches, and unknown subsurface hydrological processes were concluded as the underlying reason. We introduce a new method that allows to describe the unknown subsurface boundary fluxes, and account for them in the hydrological model. This is achieved by an artificial neural network approach (ANN), where four input variables are taken to calculate the unknown subsurface storage conditions. This was first developed for the high Alpine subbasin Königsseer Ache to improve the monthly water balance. We explicitly derive the algebraic transfer function of an artificial neural net to calculate the missing boundary fluxes. The result of the ANN is then implemented in the groundwater module of the hydrological model as boundary flux, and considered during the consecutive model process. We tested several ANN setups in different time increments to investigate ANN performance and to examine resulting runoff dynamics of the hydrological model. The ANN with 5-day time increment showed best results in reproducing the observed water storage data (r2 = 0.6). The influx of the 20-day ANN showed best results in the hydrological model correction. The boundary influx in the subbasin improved the hydrological model, as performance increased from NSE = 0.48 to NSE = 0.57 for subbasin Königsseetal, from NSE = 0.22 to NSE = 0.49 for subbasin Berchtesgadener Ache, and from NSE = 0.56 to NSE = 0.66 for the whole catchment within the test period. This combined approach allows distributed quantification of water balance components including subsurface water transfer.