Development of a Regularized Dynamic System Response Curve for Real-Time Flood Forecasting Correction

Abstract

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.

Comparing the Hydrological Responses of Conceptual and Process-Based Models with Varying Rain Gauge Density and Distribution

“…As illustrated in Figure 2h, XAJ tends to underestimate total water volume in general. Sun et al [65] reported similar results and concluded that underestimates of free water storage lead to underestimates of total water volume. In addition, WetSpa systematically overestimates total runoff volume.…”

Improving Forecast Skill of Lowland Hydrological Models Using Ensemble Kalman Filter and Unscented Kalman Filter

“…It is worth noting that uncertainty may stem from several sources, such as model structure, model parameters, model states, and initial conditions (Clark & Vrugt, 2006; Kuczera et al, 2006; Sun, Bao, Jiang, Ji, et al, 2018). However, in this study, we only update the model state, indicating all the uncertainties are attributed to state uncertainty, which may result in model states being twisted but a satisfactory performance from the perspective of the model residual (Sun, Bao, Jiang, Si, et al, 2018). Therefore, future work is needed to take other uncertainties into account, such as extending the state estimation to the joint state parameter estimation, which considers the uncertainties of model state and model parameters simultaneously.…”

Improvement in Ridge Coefficient Optimization Criterion for Ridge Estimation-Based Dynamic System Response Curve Method in Flood Forecasting

“…With the help of the first-order Taylor linearization to approximate the hydrologic model, error correction is achieved by solving the corresponding equations using the least square method. The DSRC method was initially applied to correct single hydrological elements, including runoff [15], rainfall [16] and model state variables [17]. Then, it was used to correct several hydrological elements comprehensively [18].…”

“…Then, it was used to correct several hydrological elements comprehensively [18]. However, some studies [17][18][19][20] found that the correction results are not always stable, reflected in the excessive correction of hydrological element series and none-smooth simulated flow hydrographs. To solve the above problems, the DSRC-R method was developed by Si et al [19] from the point of the regularization known as ridge estimation, and this method has improved the stability of correction results to some degree.…”

“…Nevertheless, the selection criterion of the ridge coefficient still needs further study and improvement. Previous studies [17][18][19] often chose the ridge coefficient based on the L-curve criterion [21]. However, it has been found in practice that two aspects still need attention.…”