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1. On the need for physical constraints in deep learning rainfall–runoff projections under climate change: a sensitivity analysis to warming and shifts in potential evapotranspiration

   https://doi.org/10.5194/hess-28-479-2024  

   Wi, Sungwook; Steinschneider, Scott (January 2024, Hydrology and Earth System Sciences)

   Abstract. Deep learning (DL) rainfall–runoff models outperform conceptual, process-based models in a range of applications. However, it remains unclear whether DL models can produce physically plausible projections of streamflow under climate change. We investigate this question through a sensitivity analysis of modeled responses to increases in temperature and potential evapotranspiration (PET), with other meteorological variables left unchanged. Previous research has shown that temperature-based PET methods overestimate evaporative water loss under warming compared with energy budget-based PET methods. We therefore assume that reliable streamflow responses to warming should exhibit less evaporative water loss when forced with smaller, energy-budget-based PET compared with temperature-based PET. We conduct this assessment using three conceptual, process-based rainfall–runoff models and three DL models, trained and tested across 212 watersheds in the Great Lakes basin. The DL models include a Long Short-Term Memory network (LSTM), a mass-conserving LSTM (MC-LSTM), and a novel variant of the MC-LSTM that also respects the relationship between PET and evaporative water loss (MC-LSTM-PET). After validating models against historical streamflow and actual evapotranspiration, we force all models with scenarios of warming, historical precipitation, and both temperature-based (Hamon) and energy-budget-based (Priestley–Taylor) PET, and compare their responses in long-term mean daily flow, low flows, high flows, and seasonal streamflow timing. We also explore similar responses using a national LSTM fit to 531 watersheds across the United States to assess how the inclusion of a larger and more diverse set of basins influences signals of hydrological response under warming. The main results of this study are as follows: The three Great Lakes DL models substantially outperform all process-based models in streamflow estimation. The MC-LSTM-PET also matches the best process-based models and outperforms the MC-LSTM in estimating actual evapotranspiration. All process-based models show a downward shift in long-term mean daily flows under warming, but median shifts are considerably larger under temperature-based PET (−17 % to −25 %) than energy-budget-based PET (−6 % to −9 %). The MC-LSTM-PET model exhibits similar differences in water loss across the different PET forcings. Conversely, the LSTM exhibits unrealistically large water losses under warming using Priestley–Taylor PET (−20 %), while the MC-LSTM is relatively insensitive to the PET method. DL models exhibit smaller changes in high flows and seasonal timing of flows as compared with the process-based models, while DL estimates of low flows are within the range estimated by the process-based models. Like the Great Lakes LSTM, the national LSTM also shows unrealistically large water losses under warming (−25 %), but it is more stable when many inputs are changed under warming and better aligns with process-based model responses for seasonal timing of flows. Ultimately, the results of this sensitivity analysis suggest that physical considerations regarding model architecture and input variables may be necessary to promote the physical realism of deep-learning-based hydrological projections under climate change. 

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2. Assessing the Physical Realism of Deep Learning Hydrologic Model Projections Under Climate Change

   https://doi.org/10.1029/2022WR032123  

   Wi, Sungwook; Steinschneider, Scott (September 2022, Water Resources Research)

   Abstract This study examines whether deep learning models can produce reliable future projections of streamflow under warming. We train a regional long short‐term memory network (LSTM) to daily streamflow in 15 watersheds in California and develop three process models (HYMOD, SAC‐SMA, and VIC) as benchmarks. We force all models with scenarios of warming and assess their hydrologic response, including shifts in the hydrograph and total runoff ratio. All process models show a shift to more winter runoff, reduced summer runoff, and a decline in the runoff ratio due to increased evapotranspiration. The LSTM predicts similar hydrograph shifts but in some watersheds predicts an unrealistic increase in the runoff ratio. We then test two alternative versions of the LSTM in which process model outputs are used as either additional training targets (i.e., multi‐output LSTM) or input features. Results indicate that the multi‐output LSTM does not correct the unrealistic streamflow projections under warming. The hybrid LSTM using estimates of evapotranspiration from SAC‐SMA as an additional input feature produces more realistic streamflow projections, but this does not hold for VIC or HYMOD. This suggests that the hybrid method depends on the fidelity of the process model. Finally, we test climate change responses under an LSTM trained to over 500 watersheds across the United States and find more realistic streamflow projections under warming. Ultimately, this work suggests that hybrid modeling may support the use of LSTMs for hydrologic projections under climate change, but so may training LSTMs to a large, diverse set of watersheds. 

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3. A Deep State Space Model for Rainfall‐Runoff Simulations

   https://doi.org/10.1029/2025WR039888  

   Wang, Yihan; Zhang, Lujun; Yu, Annan; Erichson, N Benjamin; Yang, Tiantian (December 2025, Water Resources Research)

   Abstract The classical way of studying the rainfall‐runoff processes in the water cycle relies on conceptual or physically‐based hydrologic models. Deep learning (DL) has recently emerged as an alternative and blossomed in the hydrology community for rainfall‐runoff simulations. However, the decades‐old Long Short‐Term Memory (LSTM) network remains the benchmark for this task, outperforming newer architectures like Transformers. In this work, we propose a State Space Model (SSM), specifically the Frequency Tuned Diagonal State Space Sequence (S4D‐FT) model, for rainfall‐runoff simulations. The proposed S4D‐FT is benchmarked against the established LSTM and a physically‐based Sacramento Soil Moisture Accounting model under in‐sample and out‐of‐sample simulation setups across 531 watersheds in the contiguous United States (CONUS). Results show that S4D‐FT is able to outperform the LSTM model across diverse regions under both simulation setups, especially for regions that feature snowmelt‐driven or intermittent flow regimes. In contrast, S4D‐FT tends to underperform in flashier, high‐magnitude flow regimes, likely due to its global state‐space convolution computation that emphasizes slow, storage‐driven dynamics, which makes it less effective at picking up short bursts and noisy spikes in the data. In summary, our pioneering introduction of the S4D‐FT for rainfall‐runoff simulations challenges the dominance of LSTM in the hydrology community and expands the arsenal of DL tools available for hydrological modeling. 

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4. The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment

   https://doi.org/10.5194/hess-27-2357-2023  

   Feng, Dapeng; Beck, Hylke; Lawson, Kathryn; Shen, Chaopeng (January 2023, Hydrology and Earth System Sciences)

   Abstract. As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models based on daily hydrograph metrics (Nash–Sutcliffe model efficiency coefficient, etc.) and predicted decadal streamflow trends. For prediction in ungauged basins (PUB; randomly sampled ungauged basins representing spatial interpolation), δ models either approached or surpassed the performance of LSTM in daily hydrograph metrics, depending on the meteorological forcing data used. They presented a comparable trend performance to LSTM for annual mean flow and high flow but worse trends for low flow. For prediction in ungauged regions (PUR; regional holdout test representing spatial extrapolation in a highly data-sparse scenario), δ models surpassed LSTM in daily hydrograph metrics, and their advantages in mean and high flow trends became prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. The δ models' deep-network-based parameterization pipeline produced parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, the δ models are strong candidates for regional and global-scale hydrologic simulations and climate change impact assessment. 

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5. Using Deep Learning in Ensemble Streamflow Forecasting: Exploring the Predictive Value of Explicit Snowpack Information

   https://doi.org/10.1029/2024MS004582  

   Modi, Parthkumar; Jennings, Keith; Kasprzyk, Joseph; Small, Eric; Wobus, Cameron; Livneh, Ben (March 2025, Journal of Advances in Modeling Earth Systems)

   Abstract The Ensemble Streamflow Prediction (ESP) framework combines a probabilistic forecast structure with process‐based models for water supply predictions. However, process‐based models require computationally intensive parameter estimation, increasing uncertainties and limiting usability. Motivated by the strong performance of deep learning models, we seek to assess whether the Long Short‐Term Memory (LSTM) model can provide skillful forecasts and replace process‐based models within the ESP framework. Given challenges inimplicitlycapturing snowpack dynamics within LSTMs for streamflow prediction, we also evaluated the added skill ofexplicitlyincorporating snowpack information to improve hydrologic memory representation. LSTM‐ESPs were evaluated under four different scenarios: one excluding snow and three including snow with varied snowpack representations. The LSTM models were trained using information from 664 GAGES‐II basins during WY1983–2000. During a testing period, WY2001–2010, 80% of basins exhibited Nash‐Sutcliffe Efficiency (NSE) above 0.5 with a median NSE of around 0.70, indicating satisfactory utility in simulating seasonal water supply. LSTM‐ESP forecasts were then tested during WY2011–2020 over 76 western US basins with operational Natural Resources Conservation Services (NRCS) forecasts. A key finding is that in high snow regions, LSTM‐ESP forecasts using simplified ablation assumptions performed worse than those excluding snow, highlighting that snow data do not consistently improve LSTM‐ESP performance. However, LSTM‐ESP forecasts that explicitly incorporated past years' snow accumulation and ablation performed comparably to NRCS forecasts and better than forecasts excluding snow entirely. Overall, integrating deep learning within an ESP framework shows promise and highlights important considerations for including snowpack information in forecasting. 

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