Automating Water Balance Closure in Lake Hydrodynamic Models: a Machine Learning Approach

Physics-based lake hydrodynamic models require high-resolution forcing data to simulate thermal structures accurately. However, many lakes lack complete inflow/outflow measurements. In natural lakes, outlet hydrodynamics can correct outflows to artificially close the water balance, but this option is generally not available in managed reservoirs. This forces modelers to rely on backward water balance calculations based on changes in observed lake storage to determine a fixed time series for missing flows. This approach often fails during model calibration. Indeed, evaporation in these models is calculated using model parameters that may be adjusted during the calibration, leading to cumulative errors in the simulated storage or the need for frequent, time-consuming model warm restarts. In addition, unmeasured flows needed for balance closure are often attributable to various processes, which leads to ambiguity regarding where in the lake they happen, and about the water quality (e.g., temperature and nutrients) in these flows. Both affect vertical processes.

To address this, we develop a Machine Learning emulator that maps hydrodynamic model parameters directly to the unmeasured flow required for water balance closure. Using the General Lake Model (GLM), a state-of-the-art vertical 1D hydrodynamic model, and a water supply reservoir in England as a case study, we follow a four-stage methodology: (1)  Sensitivity Analysis for dimensionality reduction using the Method of Morris; (2) an optimization routine to define target unmeasured flows over a 10-year period; (3) emulator training using Random Forest Regression (RFR) and (4) validation on the reservoir storage.

The RFR emulator achieves very high predictive accuracy (R² = 0.99) while estimating the optimised unmeasured flows. In addition, it identifies water treatment losses – which recirculate to the reservoir – as the primary unmeasured flow. This finding corroborates operator evidence and accounts for a crucial uncertainty in the calibration. While long-term stability remains sensitive to secondary parameters and the training data size, the emulator using RFR significantly reduces cumulative storage errors compared to the traditional approach that uses fixed unmeasured flows, minimising the need for frequent model restarts and substantially decreasing total calibration time.