Utilizing Physics-Based Predictions as Inputs to LSTM Models for Robust Data-Driven Discharge Simulations of Gauged Catchments Across Denmark

Hydrological modeling provides a quantitative foundation for effective water resource management. Simulating discharge from meteorological forecasts is essential for flood prediction and risk assessment.

Traditional hydrological models, such as the Hydrological Predictions for the Environment (HYPE) model, leverage explicit equations to represent well-known catchment characteristics and provide process-based discharge forecasts. However, these models often struggle to capture unknown or poorly understood spatio-temporal dependencies and nonlinear dynamics.

In contrast, machine learning approaches, such as Long Short-Term Memory (LSTM) networks, are able to learn complex patterns without requiring pre-defined relationships. However, these networks introduce variabilities into hydrological model simulations, which in turn complicates the development of well-supported arguments based on their findings.

A promising solution is a hybrid model in which the physical model's output serves as dynamic input to the LSTM. This approach preserves the strengths of physics-based models in representing well-understood hydrological processes while allowing the LSTM to capture implicit dependencies.

This study investigated the application of hybrid hydrological modeling for simulating discharge in Danish catchments by combining simulated discharge from the Danish HYPE model (DK-HYPE) with an LSTM model. The analysis encompassed 570 catchments, characterized by static attributes and dynamic variables. Dynamic variables were derived from a high-resolution CAMELS dataset (DK-CAMELS) with a spatial resolution of 1x1 km, from Danish weather stations covering the time period from 2001 to 2022.

Fifteen LSTM models were trained under various configurations: different sequence lengths (30, 90, and 365 days), inclusion of static attributes, and utilization of DK-HYPE outputs. Model training used two loss functions—Mean Squared Error (MSE) and the Nash-Sutcliffe model efficiency coefficient (NSE)—while performance was evaluated using the Kling-Gupta Efficiency (KGE), Flow Balance (FBAL), and Critical Success Index (CSI).

Incorporating static attributes enhanced model accuracy, while longer sequence lengths captured hydrological dependencies. Across all configurations, the LSTM models outperformed DK-HYPE. The best-performing hybrid model achieved a KGE of 0.7 and a CSI of 0.36, a significant improvement over DK-HYPE's baseline values of 0.01 for KGE and 0.18 for CSI. Similarly, the standalone LSTM model, which excluded DK-HYPE outputs during training, achieved a KGE of 0.71 and a CSI of 0.35.

While the hybrid model did not demonstrate a clear advantage over the pure LSTM model with longer sequence lengths, it outperformed the pure LSTM model with shorter sequence lengths. Specifically, comparing models using sequence length of 30 days, the hybrid model achieved a KGE of 0.65 and a CSI of 0.36, compared to the pure LSTM model's KGE of 0.59 and CSI of 0.31, which is most likely because it utilized information from DK-HYPE.

This project is a step towards combining physics-based models with data-driven models for the national flood warning system. Further work should focus on fine-tuning the hybrid models and integrate them into an ensemble towards building robust systems for flood forecasting.