Abstract. Rainfall–runoff modelling is one of the key challenges in the field of hydrology. Various approaches exist, ranging from physically based over conceptual to fully data-driven models. In this paper, we propose a novel data-driven approach, using the Long Short-Term Memory (LSTM) network, a special type of recurrent neural network. The advantage of the LSTM is its ability to learn long-term dependencies between the provided input and output of the network, which are essential for modelling storage effects in e.g. catchments with snow influence. We use 241 catchments of the freely available CAMELS data set to test our approach and also compare the results to the well-known Sacramento Soil Moisture Accounting Model (SAC-SMA) coupled with the Snow-17 snow routine. We also show the potential of the LSTM as a regional hydrological model in which one model predicts the discharge for a variety of catchments. In our last experiment, we show the possibility to transfer process understanding, learned at regional scale, to individual catchments and thereby increasing model performance when compared to a LSTM trained only on the data of single catchments. Using this approach, we were able to achieve better model performance as the SAC-SMA + Snow-17, which underlines the potential of the LSTM for hydrological modelling applications.

Abstract. Regional rainfall–runoff modeling is an old but still mostly outstanding problem in the hydrological sciences. The problem currently is that traditional hydrological models degrade significantly in performance when calibrated for multiple basins together instead of for a single basin alone. In this paper, we propose a novel, data-driven approach using Long Short-Term Memory networks (LSTMs) and demonstrate that under a “big data” paradigm, this is not necessarily the case. By training a single LSTM model on 531 basins from the CAMELS dataset using meteorological time series data and static catchment attributes, we were able to significantly improve performance compared to a set of several different hydrological benchmark models. Our proposed approach not only significantly outperforms hydrological models that were calibrated regionally, but also achieves better performance than hydrological models that were calibrated for each basin individually. Furthermore, we propose an adaption to the standard LSTM architecture, which we call an Entity-Aware-LSTM (EA-LSTM), that allows for learning catchment similarities as a feature layer in a deep learning model. We show that these learned catchment similarities correspond well to what we would expect from prior hydrological understanding.

Long short-term memory (LSTM) networks offer unprecedented accuracy for prediction in ungauged basins. We trained and tested several LSTMs on 531 basins from the CAMELS data set using k-fold validation, so that predictions were made in basins that supplied no training data. The training and test data set included ∼30 years of daily rainfall-runoff data from catchments in the United States ranging in size from 4 to 2,000 km 2 with aridity index from 0.22 to 5.20, and including 12 of the 13 IGPB vegetated land cover classifications. This effectively "ungauged" model was benchmarked over a 15-year validation period against the Sacramento Soil Moisture Accounting (SAC-SMA) model and also against the NOAA National Water Model reanalysis. SAC-SMA was calibrated separately for each basin using 15 years of daily data. The out-of-sample LSTM had higher median Nash-Sutcliffe Efficiencies across the 531 basins (0.69) than either the calibrated SAC-SMA (0.64) or the National Water Model (0.58). This indicates that there is (typically) sufficient information in available catchment attributes data about similarities and differences between catchment-level rainfall-runoff behaviors to provide out-of-sample simulations that are generally more accurate than current models under ideal (i.e., calibrated) conditions. We found evidence that adding physical constraints to the LSTM models might improve simulations, which we suggest motivates future research related to physics-guided machine learning.

Abstract. Rainfall-runoff modelling is one of the key challenges in the field of hydrology. Various approaches exist, ranging from physically based over conceptual to fully data driven models. In this paper, we propose a novel data driven approach, using the Long-Short-Term-Memory (LSTM) network, a special type of recurrent neural networks. The advantage of the LSTM is its ability to learn long-term dependencies between the provided input and output of the network, which are essential for modelling storage effects in e.g. catchments with snow influence. We use 241 catchments of the freely available CAMELS data set to 5 test our approach and also compare the results to the well-known Sacramento Soil Moisture Accounting Model (SAC-SMA) coupled with the Snow-17 snow routine. We also show the potential of the LSTM as a regional hydrological model, in which one model predicts the discharge for a variety of catchments. In our last experiment, we show the possibility to transfer process understanding, learned at regional scale, to individual catchments and thereby increasing model performance when compared to a LSTM trained only on the data of single catchments. Using this approach, we were able to achieve better model performance 10 as the SAC-SMA + Snow-17, which underlines the potential of the LSTM for hydrological modelling applications.

This paper is derived from a keynote talk given at the Google's 2020 Flood Forecasting Meets Machine Learning Workshop. Recent experiments applying deep learning to rainfall-runoff simulation indicate that there is significantly more information in large-scale hydrological data sets than hydrologists have been able to translate into theory or models. While there is a growing interest in machine learning in the hydrological sciences community, in many ways, our community still holds deeply subjective and nonevidence-based preferences for models based on a certain type of "process understanding" that has historically not translated into accurate theory, models, or predictions. This commentary is a call to action for the hydrology community to focus on developing a quantitative understanding of where and when hydrological process understanding is valuable in a modeling discipline increasingly dominated by machine learning. We offer some potential perspectives and preliminary examples about how this might be accomplished.