Hybrid hydrological modeling with LSTM and physical simulators

Physical hydrological models provide interpretable and physically consistent data, yet their performance can degrade due to parameter uncertainty, forcing biases, or structural simplifications (e.g., simplified parameterizations of groundwater storage, snowmelt or evapotranspiration). In parallel, Long Short-Term Memory (LSTM) recurrent neural networks have demonstrated a high capacity for learning non-linear relationships and temporal dependencies in hydro-meteorological series. This work evaluates the potential of combining both approaches through a hybrid scheme, analyzing predictive performance gains and investigating the contexts where such improvements are limited.

The central hypothesis is that integrating physical model outputs as inputs to the LSTM, alongside meteorological forcings (maximum/minimum temperature and precipitation) and static catchment attributes, should enhance streamflow prediction by incorporating hydrological states and dynamical constraints that are difficult to infer from meteorology alone. Initial results show a clear improvement over pure physical models and superior performance of regional LSTMs compared to local versions (training with all headwater catchments vs with only one). Additionally, the inclusion of static parameters significantly increases the goodness of fit.

However, the added value of incorporating physical models into the hybrid approach is, on average, modest and primarily observed for low flows. To investigate this apparent lack of general improvement, two diagnostic tests were conducted. First, a conditional redundancy test was performed, removing meteorological influence by fitting a linear model (Ridge) to both observed streamflow and physical model output to evaluate residual dependency. Second, a knowledge distillation test was carried out, training an LSTM to reproduce physical model outputs using only meteorological forcings. Results indicate that the LSTM emulates the physical model almost perfectly, suggesting that much of the information provided by the simulator is not independent for the network but is instead derivable from the meteorological forcings.

Finally, regional dependency was analyzed by classifying catchments into five clusters based on climatic and physiographic characteristics. In humid/temperate clusters, high emulation and zero hybrid gain were observed. In dry/transitional clusters, the simulator may introduce bias or noise and, in a transitional cluster, with significant storage, catchments where hybrid modeling consistently improves were identified. Together, these results reveal a predictable "physical signature" that allows for anticipating in which basins the hybrid approach will provide consistent enhancements.

Acknowledgements: This research has been carried out within the framework of project PID2021-126401OB-I00, funded by MICIU/AEI/10.13039/501100011033 and by ERDF, EU.