The accuracy of flood forecasts generated using spatially lumped hydrological models can be severely affected by errors in the estimates of areal mean rainfall. The quality of the latter depends both on the size and type of errors in point-based rainfall measurements, and on the density and spatial arrangement of rain gauges in the basin. Here we use error feedback correction, based on the dynamic system response curve (DSRC) method, to compute updated estimates of the rainfall inputs. The method is evaluated via synthetic and real-data cases, showing that the method works as theoretically expected. The ability of the method to improve the accuracy of real-time flood forecasts is then demonstrated using 20 basins of different sizes and having different rain gauge densities. We find that the degree of forecast improvement is more significant for larger basins and for basins with lower rain gauge density. The method is relatively simple to apply and can improve the accuracy and stability of real-time model predictions without increasing either model complexity and/or the number of model parameters.

The dynamic system response curve (DSRC) method has been shown to effectively use error feedback correction to obtain updated areal estimates of mean rainfall and thereby improve the accuracy of real‐time flood forecasts. In this study, we address two main shortcomings of the existing method. First, ridge estimation is used to deal with ill‐conditioning of the normal equation coefficient matrix when the method is applied to small basins, or when the length of updating rainfall series is short. Second, the effects of spatial heterogeneity of rainfall on rainfall error estimates are accounted for using a simple index. The improved performance of the method is demonstrated using both synthetic and real data studies. For smaller basins with relatively homogeneous spatial distributions of rainfall, the use of ridge regression provides more accurate and robust results. For larger‐scale basins with significant spatial heterogeneity of rainfall, spatial rainfall error updating provides significant improvements. Overall, combining the two strategies results in the best performance for all cases, with the effects of ridge estimation and spatially distributed updating complementing each other.

Error correction method is widely used to improve the performance of flood forecasting. The Dynamic System Response Curve method (DSRC) has been proposed as an error correction method to improve the performance of hydrological modeling. One of the critical problems is the unstable performance caused by the ill‐posed property of the model structure and the inability of estimating multiple variables. To address this problem, the original structure of DSRC was modified to enable the capability of estimating multiple variables. Using the variable forgetting factor recursive least squares algorithm (VFF‐RLS), we proposed an improved version of DSRC (VFF‐RLS‐MDSRC). The proposed method was tested in a synthetic case to examine the ability to correct state variables of a hydrological model. In addition, it was compared with the autoregressive technique in a real case study to evaluate the effects on the improvement of model performance. The results of the synthetic study indicate that the proposed method can significantly improve the performance of both the model output and the state variables. The results of the real case study indicate that the performance obtained by the proposed method tends to have a slower decline trend when increasing the lead time compared with autoregressive technique.

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Abstract:The dynamic system response curve (DSRC) is commonly applied as a real-time flood forecasting error correction method to improve the accuracy of real-time flood forecasting. It has been widely recognized that the least squares (OLS/LS) method, employed by DSRC, breaks down ill-posed problems, and therefore, the DSRC method may lead to deterioration in performance caused by meaningless solutions. To address this problem, a diagnostically theoretical analysis was conducted to investigate the relationship between the numerical solution of the Fredholm equation of the first kind and the DSRC method. The analysis clearly demonstrates the derivation of the problem and has implications for an improved approach. To overcome the unstable problem, a new method using regularization techniques (Tikhonov regularization and L-Curve criterion) is proposed. Moreover, in this study, to improve the performance of hydrological models, the new method is used as an error correction method to correct a variable from a hydrological model. The proposed method incorporates the information from a hydrological model structure. Based on the analysis of the hydrological model, the free water storage of the Xinanjiang rainfall-runoff (XAJ) model is corrected to improve the model's performance. A numerical example and a real case study are presented to compare the two methods. Results from the numerical example indicate that the mean Nash-Sutcliffe efficiency value (NSE) of the regularized DSRC method (RDSRC) decreased from 0.99 to 0.55, while the mean NSE of DSRC decreased from 0.98 to −1.84 when the noise level was increased. The overall performance measured by four different criteria clearly demonstrates the robustness of the RDSRC method. Similar results were obtained for the real case study. The mean NSE of 35 flood events obtained by RDSRC method was 0.92, which is significantly higher than the mean NSE of DSRC (0.7). The results demonstrate that the RDSRC method is much more robust than the DSRC method. The applicability and usefulness of the RDSRC approach for real-time flood forecasting is demonstrated via the numerical example and the real case study.