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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. 

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. 

Abstract Stochastic Watershed Models (SWMs) are emerging tools in hydrologic modeling used to propagate uncertainty into model predictions by adding samples of model error to deterministic simulations. One of the most promising uses of SWMs is uncertainty propagation for hydrologic simulations under climate change. However, a core challenge is that the historical predictive uncertainty may not correctly characterize the error distribution under future climate. For example, the frequency of physical processes (e.g., snow accumulation and melt) may change under climate change, and so too may the frequency of errors associated with those processes. In this work, we explore for the first time non‐stationarity in hydrologic model errors under climate change in an idealized experimental design. We fit one hydrologic model to historical observations, and then fit a second model to the simulations of the first, treating the first model as the true hydrologic system. We then force both models with climate change impacted meteorology and investigate changes to the error distribution between the models. We develop a hybrid machine learning method that maps model state variables to predictive errors, allowing for non‐stationary error distributions based on changes in the frequency of model states. We find that this procedure provides an internally consistent methodology to overcome stationarity assumptions in error modeling and offers an important advance for implementing SWMs under climate change. We test this method on three hydrologically distinct watersheds in California (Feather River, Sacramento River, Calaveras River), finding that the hybrid model performs best in larger and less flashy basins.