Estimation of Gate Discharge in Tidal River Reaches Based on Physical Formula and Random Forest Residual Learning

Accurate estimation of gate flow in tidal reach segments is a prerequisite for water balance calibration and water quality response assessment in gate group dispatch. Taking the three gates of Beilaojing, Dongjinggang, and Dazhangjing in the Qingsong control area as study objects, this paper proposes a hybrid estimation model combining a physics-based energy equation with random forest residual correction. The physical formula incorporates a submerged correction coefficient to handle flow regime transitions in tidal reaches, while the random forest model learns the residual correction term using 14-dimensional feature variables. The model parameters are calibrated with ACDP measured flow data from 2025 and validated with data from 2026. Compared with the direct use of the physical formula, the introduction of random forest residual correction improves R² from 0.789 to 0.908, reduces RMSE by 33.9%, and reduces MAE by 28.1%. Feature importance analysis reveals that upstream water head and gate opening ratio are key factors influencing the residuals. The results demonstrate that the combination of the physical formula and random forest residual correction can effectively enhance the accuracy of flow estimation.