Conceptual models in hydrology are widely used, allow for easy interpretation and require little data. Machine learning models in hydrology often outperform conceptual models but lack the ease of interpretability, require large amounts of data and and do not obey physical laws. Hybrid approaches aiming to combine the advantages of both approaches are becoming more popular. A Neural Ordinary Differential Equations approach is introduced to combine a differential equation-based conceptual model with a neural network. Additionally, conceptual models and LSTM models are used as benchmarks. The models are tested using the LamaH-CE dataset as well as the E-OBS dataset. In many cases the hybrid models outperform the conceptual model. However, to further improve the performance of hybrid models more research is needed to make the models more computationally efficient and optimized training strategies are required to explore the full potential of the approach.

Rainfall-runoff modelling is essential for short- and long-term decision-making in the water management sector. The accuracy of streamflow predictions of hydrologic models increases with the availability of and the access to streamflow observations. Therefore, one of the key challenges in the field of hydrology is to produce Predictions in Ungauged Basins (PUB), where observations are lacking. Recent research has shown the potential of deep learning neural networks as an alternative approach to conceptual and process-based hydrologic models for this purpose.  In this study, the existing Multi-Timescale LSTM (MTS-LSTM) architecture is used to investigate if such a deep learning network is able to learn universal hydrologic behaviour. Therefore, a MTS-LSTM is trained on a large variety of >500 US catchments and subsequently tested outside the US, in the European Meuse river basin. The model is not retrained or finetuned to simulate an ungauged situation and to asses whether the streamflow predictions can compete with those from the uncalibrated distributed model wflow_sbm.  Results indicate that the MTS-LSTM trained on US data cannot compete with wflow_sbm in the Meuse catchments. The simulated streamflow time series can be unrealistically shifted and scaled compared to the time series of observed streamflow due to sensitivity regarding static model input. This means, the values for catchment characteristics cannot be extremer in the testing data than in the training data. Therefore, it is recommended to select catchments for the model training such that the most extreme conditions are covered. In the case that the MTS-LSTM is trained for a specific region, results clearly compete with or outperform the distributed model. For the Meuse test catchments, the neural network achieves Nash-Sutcliffe Efficiency (NSE) values>0.46 where the application of wflow_sbm is problematic and yields negative NSE values. To exploit the potential of an LSTM, the model should be trained on all available data of the entire Meuse basin instead of on the subset of catchments used here. For some water management applications it is important to accurately predict high flow events. Training the MTS-LSTM with the Mean Quadrupled Error (M4SE) loss function showed that the peak flow representation can improve for catchments where the use of a NSE loss already leads to good predicting performance. Thus – for and ungauged catchments – an implementation of a combined loss function appears a valuable follow-up research.  For ungauged catchments, these results imply that the global neural network model as tested in this study should be supplemented with finetuning. Thereby, the global model could not yet be applied everywhere, however, in regions where only few years of streamflow records are available. Alternatively, a regional neural network model trained on nearby catchments could be applied for PUB, if streamflow observations are accessible in the surrounding area. Finally, it is of high importance to maintain and extend the network of streamflow gauging stations globally, and to ensure easy access to the data.