On the need for physical constraints in deep learning rainfall-runoff projections under climate change

Abstract. Deep learning rainfall-runoff models have recently emerged as state-of-the-science tools for hydrologic prediction that outperform conventional, process-based models in a range of applications. However, it remains unclear whether deep learning models can produce physically plausible projections of streamflow under significant amounts of climate change. We investigate this question here, focusing specifically on modeled responses to increases in temperature and potential evapotranspiration (PET). Previous research has shown that temperature-based methods to estimate PET lead to overestimates of water loss in rainfall-runoff models under warming, as compared to energy budget-based PET methods. Consequently, we assess the reliability of streamflow projections under warming by comparing projections with both temperature-based and energy budget-based PET estimates, assuming that reliable streamflow projections should exhibit less water loss when forced with smaller (energy budget-based) projections of future PET. We conduct this assessment using three process-based rainfall-runoff models and three deep learning models, trained and tested across 212 watersheds in the Great Lakes basin. The deep learning models include a regional Long Short-Term Memory network (LSTM), a mass-conserving LSTM (MC-LSTM) that preserves the water balance, and a novel variant of the MC-LSTM that also respects the relationship between PET and water loss (MC-LSTM-PET). We first compare historical streamflow predictions from all models under spatial and temporal validation, and also assess model skill in estimating watershed-scale evapotranspiration. We then force all models with scenarios of warming, historical precipitation, and both temperature-based (Hamon) and energy budget-based (Priestley-Taylor) PET, and compare their projections for changes in average flow, as well as low flows, high flows, and streamflow timing. Finally, we also explore similar projections using a National LSTM fit to a broader set of 531 watersheds across the contiguous United States. The main results of this study are as follows:

1. The three Great Lakes deep learning models significantly outperform all process models in streamflow estimation under spatiotemporal validation, with only small differences between the DL models. The MC-LSTM-PET also matches the best process models and outperforms the MC-LSTM in estimating evapotranspiration under spatiotemporal validation.

2. All process models show a downward shift in average flows under warming, but this shift is significantly larger under temperature-based PET estimates than energy budget-based PET. The MC-LSTM-PET model exhibits similar differences in water loss across the different PET forcings, consistent with the process models. However, the LSTM exhibits unrealistically large water losses under warming as compared to the process models using Priestley-Taylor PET, while the MC-LSTM is relatively insensitive to PET method.

3. All deep learning models exhibit smaller changes in high flows and streamflow timing as compared to the process models, while deep learning projections of low flows are all very consistent and within the range projected by process models.

4. Like the Great Lakes LSTM, the National LSTM also shows unrealistically large water losses under warming. However, when compared to the Great Lakes deep learning models, projections from the National LSTM were more stable when many inputs were changed under warming and better aligned with process model projections for streamflow timing. This suggests that the addition of more, diverse watersheds in training does help improve climate change projections from deep learning models, but this strategy alone may not guarantee reliable projections under unprecedented climate change.

Ultimately, the results of this work suggest that physical considerations regarding model architecture and input variables are necessary to promote the physical realism of deep learning-based hydrologic projections under climate change.