Spatial runoff updating based on the hydrologic system differential response for flood forecasting

Runoff controls water volume in the rainfall–runoff process and plays a dominant role in flood forecasting. This study proposes a spatial runoff updating approach based on the hydrologic system differential response (HSDR). The first-order partial derivative is employed to express the hydrologic response to runoff change. A stepwise approximation for the HSDR is suggested to reduce the effect of linearization of the nonlinear hydrologic system. The regularized least square algorithm is used to calculate the estimated errors of runoff. The HSDRs for spatial distributed runoff (SDR) updating and areal mean runoff (AMR) updating are examined to correct the predictions of the Xinanjiang model in two basins in China. The case results show that the HSDR for runoff updating can improve flood predictions; the HSDR with stepwise approximation outperforms that without it; the HSDR_SDR performs better than the HSDR_AMR; and with increasing lead time, the HSDR method exhibits more stable performance than the autoregressive (AR) technique on streamflow correction. The proposed HSDR_SDR method can decompose the information of residuals between observations and calculations to update spatial runoff through the response matrix for each sub-basin. With simple structure and stable performance, the HSDR_SDR is convenient and effective for real-time flood forecasting.