Spatial multiple variables and single variable updating via hydrologic system differential response method in real-time flood forecasting

Error correction is crucial for reliable and accurate real-time flood forecasting. The simultaneous updating of multiple errors and selection of appropriate variables for updating remain challenging. This study respectively establishes spatial multiple variables and single variable updating using the Hydrologic System Differential Response (HSDR) method, which characterizes the relationship between model output errors and influencing variables. Three distinct HSDR-based approaches are proposed: a spatial multiple variables updating approach that simultaneously updates rainfall, evaporation and initial soil moisture (SDPEW) through the rainfallriverflow system, and two spatial single variable updating approaches that respectively update spatial rainfall (SDP) through the rainfall-riverflow system and spatial runoff (SDR) through the runoff-riverflow system. These approaches are implemented to correct the predictions of the Xinanjiang model in two basins in China. The results demonstrate that (1) the SDPEW, SDP and SDR updating can improve flood forecasting and maintain stable performance with increasing lead time; (2) the SDR generally performs better than the SDP and SDPEW; (3) the SDPEW generally outperforms the SDP when sufficient observed data are available. These findings indicate that the HSDR exhibits varying efficiencies in utilizing outlet discharge information for different spatial variables updating; the selection of appropriate variables for updating should consider the primary error sources and hydrological model structure. This study expands the HSDR method for spatial multiple variables updating and provides guidance for variable selection in real-time flood forecasting correction.