Water-Balance Physics-Informed Neural Network for Daily Streamflow Prediction: A Single-Catchment Comparative Study Using CAMELS-GB v2

Abstract

Accurate daily streamflow prediction remains challenging because rainfall–runoff dynamics are nonlinear, temporally dependent, and subject to water-mass conservation. This study examines whether a simplified catchment water-balance constraint improves the internal consistency of a physics-informed neural network (WB-PINN) without compromising predictive accuracy. Using 18,993 daily observations (1970–2022) from Catchment 31010 in CAMELS-GB v2, the WB-PINN jointly estimates discharge, latent storage, and an evapotranspiration scaling factor. Its loss function combines prediction error with a water-balance residual weighted by λ. We evaluated performance on a chronological independent test period (2012–2022) against Ridge regression, support vector regression, XGBoost, a multilayer perceptron, and an LSTM. We tested five physics-loss weights and additional regularization controls to distinguish physical constraints from generic regularization effects. At λ = 0.001, mean validation water-balance loss decreased from 13.69 to 8.22, with nearly unchanged accuracy (NSE 0.8419 versus 0.8433 without the constraint). On the test set, LSTM performed best (NSE 0.8673; RMSE 0.3772 mm/day), while WB-PINN ranked second numerically (NSE 0.8209; RMSE 0.4381 mm/day). Paired bootstrap analysis found no statistically significant differences between WB-PINN and XGBoost or support vector regression, whereas LSTM achieved lower RMSE and higher NSE. Removing antecedent discharge reduced accuracy across all models. Because storage and actual evapotranspiration were unobserved, reduced residuals do not establish hydrological realism. Test-period diagnostics revealed a persistent mean water-balance residual of −0.7070 mm/day and predicted evapotranspiration substantially below the long-term water-balance estimate. Thus, weak water-balance regularization reduced the imposed residual with little loss of predictive accuracy but did not achieve close water-balance closure or outperform the strongest data-driven model.