Effects of mass balance, energy balance, and storage-discharge constraints on LSTM for streamflow prediction

We investigate the effects of physics-based constraints, added to the loss function of a Long Short-Term Memory (LSTM) network, on its performance in daily streamflow prediction. Three types of constraints (mass balance, energy balance, and storage-discharge relationship), along with their combinations, are tested across 34 river basins in Nebraska. We found that the addition of constraints improves the model performance in several basins, but there are also cases where the performance drops or does not differ significantly. Mass and energy balance constraints improve the performance in 38% and 32% of catchments, respectively, while storage-discharge constraints improve the performance in 12% of catchments. The combination of mass and energy balance constraints has a positive effect on 41% of catchments, while the combination of mass balance and storage-discharge constraints improves the performance in 26% of catchments. We recommend the use of constraints in cases where they boost the LSTM performance.