A Data-Driven Approach to Close the Water Balance of a Cascaded Multiple Reservoir–Lake System

This study presents a data-driven methodology to develop and close the continuous water balance of a cascaded hydrological system consisting of two upstream regulating reservoirs and a downstream lake. The analysis is based on monthly hydrometeorological and hydrographic data for the period 1998–2024. A baseline water balance model using raw measured data was first implemented, followed by two bias correction approaches based on multiple linear regression coefficient estimation. The first approach applies uniform coefficients across all months, while the second accounts for seasonal variability by estimating coefficients only for the December–May period, when systematic errors are most pronounced. Model performance was evaluated using calibration (1998–2017) and validation (2018–2024) periods, with Nash–Sutcliffe efficiency (NSE) and residual diagnostics used as evaluation metrics. The baseline model showed substantial cumulative deviations due to systematic errors (NSE: −0.28 and −5.13 for the two reservoirs and −18.70 for the lake), confirming the need for bias correction. Both correction approaches significantly improved model performance, with NSE values up to 0.89 for reservoirs and 0.83–0.86 for the lake during calibration. In validation, the seasonally adjusted model performed more stably in simulating water levels for Lake Velence (NSE = 0.72) than the uniform coefficient model (NSE = 0.60), particularly under extreme hydrological conditions. Residual analysis further indicated improved independence and homoscedasticity when seasonal structure was considered. The results demonstrate that water balance closure in the system is affected by distributed errors across multiple components rather than a single dominant source. The proposed methodology provides a practical, scalable framework for reconstructing consistent water balance time series in data-limited, regulated systems and supports the development of water management scenarios.