Supplementary files for: Long short-term memory networks enhance rainfall-runoff modelling at the national scale of Denmark

This study explores the application of long short-term memory (LSTM) networks to simulate runoff at the national scale of Denmark using data from 301 catchments. This is the first LSTM application on Danish data. The results were benchmarked against the Danish national water resources model (DK-model), a physically-based hydrological model. The median Kling-Gupta Efficiency (KGE), a common metric to assess performance of runoff predictions (optimum of 1), increased from 0.7 (DK-model) to 0.8 (LSTM) when trained against all catchments. Overall, the LSTM outperformed the DK-model in 80% of catchments. Despite the compelling KGE evaluation, the water balance closure was modelled less accurately by the LSTM. The applicability of LSTM networks for modelling ungauged catchments was assessed via a spatial split-sample experiment. The performance for a 20% hold-out showed poorer performance of the LSTM with respect to the DK-model. However, after pre-training, i.e. weight initialisation obtained from training against simulated data from the DK-model, the performance of the LSTM was effectively improved. This formed a convincing argument supporting the knowledge-guided machine learning paradigm to integrate physically-based models and machine learning to train robust models that generalise well.