G-grey-extrapolation combined modela grey-extrapolation combined model with self-review-correction mechanism for robust river water-level forecasting under small-sample hydrological conditions

Abstract

Floods and droughts threaten ecological security and sustainable development, so reliable river water-level forecasting is essential for early warning systems. However, existing models are often undermined by small-sample scenarios, data anomalies, and missing data. This study proposes the G-GECM (grey-extrapolation combined model), which is integrated with a self-review-correction mechanism. The G-GECM uses GM(1,1) to extract long-term water-level trends, ANOVA to identify extrapolation cycles, discrete Frechet distance to detect residual anomalies, and mean-based iterative correction rectify biases. When validated using 2017-2021 monthly maximum water-level data from three hydrological stations in Zhejiang Province (with 60 samples per station and 48 samples used for training), the G-GECM outperformed the ARIMA, LSTM, NBEATS, and original GECM models under small-sample conditions. Relative to the best-performing benchmark at each station, it reduced the RMSE by 5.0%-11.1% and the mean absolute error by 2.6%-9.9%, and it achieved the highest R² among all compared models at each station. Simulation experiments demonstrate the model’s robustness under random missing rates of 10%-30%, with G-GECM maintaining the lowest RMSE across the tested parameter configurations, and its high computational efficiency, with computation times of approximately 0.005-0.7 seconds per prediction. The G-GECM provides a reliable method for water-level forecasting in complex hydrological scenarios and supports practical applications in flood control and drought mitigation.