Streamflow forecasting in the Ebro river basin using Machine Learning (ML) and a physical mass constraint

In hydrology, the use of machine learning (ML) has gained traction due to its ability to provide alternative or complementary approaches to traditional process-based modelling. These models identify numerical patterns in time series data without needing to solve conservation equations. This flexibility enables hydrological calculations in areas where data sources are incomplete or non-existent.
Studies benchmarking ML models (SVM, RNN, CNN) against process-based models have shown that ML models deliver promising results with lower computational cost and less information about the physical processes they are modelling. Consequently, they can effectively utilize spatially discretized physical data on a large scale.
This study designs a Long Short-Term Memory (LSTM) neural network to learn sequential relationships between atmospheric, climatic and geographic features and daily streamflow data from 39 headwater gauging stations in the northern Ebro river basin. LSTM models include an internal state that can store information and learn long-term dependencies, enabling them to model sequential data effectively. However, the numerical patterns identified by LSTM models do not inherently respect universal physical laws, such as the conservation of mass.
To address the limitation, the Mass-Conserving LSTM (MC-LSTM) model has been employed and compared with the standard LSTM model. The MC-LSTM model introduces a modified cell structure that adheres to conservation laws by extending the learning bias to model the redistribution of mass.
This analysis highlights not only the high accuracy of LSTM models in predictive hydrologic modelling but also the critical importance of integrating physics-based features to enable ML models to effectively capture the hydrological dynamics of the basin.
Acknowledgments: This work is funded by the European Research Council (ERC) through the Horizon Europe 2021 Starting Grant program under REA grant agreement number 101039181-SED@HEAD.