Multi-site joint correction method for real-time flood forecasting errors

Real-time correction is an essential technique for enhancing the accuracy of river flood forecasts. To overcome the challenges of terminal correction methods in describing spatial error propagation and the coefficient instability inherent in traditional autoregressive models, this study proposes a multi-site joint correction approach that integrates Adaptive Ridge Regression with the Muskingum Matrix Equation (RRAR-Mafa). The Muskingum matrix equation is refined to derive a generalized spatial error propagation formulation applicable to river networks with arbitrary topological configurations. By incorporating ridge regression, a unified correction framework is developed that simultaneously accounts for temporal and spatial dimensions. The framework is validated through case studies conducted in the middle reaches of the Huai River. Results demonstrate that the mean absolute relative error of peak discharge decreased from 21.56% before correction to 3.84% after correction, while the average Nash-Sutcliffe efficiency improved from 0.67 to 0.98. Greater improvements were observed in cases with lower initial forecast accuracy. The RRAR-Mafa method enables continuous multi-lead-time correction and outperforms both the Autoregressive (AR) and Ridge Regression (RRAR) models. It remained effective within 10 time steps for all eight analyzed flood events, with five events exhibiting particularly strong correction performance. This study provides a generalized and efficient solution for error correction in flood forecasting across complex river networks, offering substantial improvements in forecast accuracy and extended correction lead time.