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.

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.

We suggest that there is a potential danger to the hydrological sciences community in not recognizing how transformative machine learning will be for the future of hydrological modeling. Given the recent success of machine learning applied to modeling problems, it is unclear what the role of hydrological theory might be in the future. We suggest that a central challenge in hydrology right now should be to clearly delineate where and when hydrological theory adds value to prediction systems. Lessons learned from the history of hydrological modeling motivate several clear next steps toward integrating machine learning into hydrological modeling workflows.

Abstract. Deep learning is becoming an increasingly important way to produce accurate hydrological predictions across a wide range of spatial and temporal scales. Uncertainty estimations are critical for actionable hydrological prediction, and while standardized community benchmarks are becoming an increasingly important part of hydrological model development and research, similar tools for benchmarking uncertainty estimation are lacking. This contribution demonstrates that accurate uncertainty predictions can be obtained with deep learning. We establish an uncertainty estimation benchmarking procedure and present four deep learning baselines. Three baselines are based on mixture density networks, and one is based on Monte Carlo dropout. The results indicate that these approaches constitute strong baselines, especially the former ones. Additionally, we provide a post hoc model analysis to put forward some qualitative understanding of the resulting models. The analysis extends the notion of performance and shows that the model learns nuanced behaviors to account for different situations.

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