A Mass Conservation Relaxed (MCR) LSTM Model for Streamflow Simulation Across CONUS

Abstract The recent development of the physics‐aware Mass‐Conserving Long Short‐Term Memory network (MC‐LSTM) provides an alternative to other data‐driven Deep Learning (DL) models in hydrology. Mass‐Conserving Long Short‐Term Memory incorporates mass conservation directly into the LSTM architecture. Despite the theoretical advancements, studies have reported a surprisingly limited performance of the MC‐LSTM in streamflow simulation. We hypothesize that such a limitation is due to the unrealistic mass conservation scheme in MC‐LSTM, which overlooks unobserved incoming water fluxes beyond precipitation. As an attempt to verify this hypothesis, we propose a Mass Conservation Relaxed LSTM (MCR‐LSTM), which incorporates a bi‐directional mass relaxation (MR) component to account for potential incoming water fluxes beyond precipitation. We train and test the proposed MCR‐LSTM model across 531 watersheds in the contiguous United States (CONUS) against three baseline models: the Sacramento Soil Moisture Accounting, LSTM, and MC‐LSTM. Our results show that MCR‐LSTM outperforms MC‐LSTM despite its underperformance compared to LSTM. Specifically, MCR‐LSTM's advantage over MC‐LSTM is mainly seen in the Plains and Western U.S., where the newly incorporated MR component better simulates water loss and suggests the likely existence of additional incoming water fluxes beyond precipitation, respectively. The novelty and contribution of this study are twofold: firstly, it introduces an alternative physics‐aware DL tool (i.e., MCR‐LSTM) in hydrology with higher accuracy in specific regions compared to MC‐LSTM. Secondly, it provides a diagnosis of regions where strict, precipitation‐based mass conservation constraints may be unrealistic in streamflow simulation.