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Water 2018, 10(4), 450; https://doi.org/10.3390/w10040450

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

1
Department of Hydrology and Water Resources, University of Hohai, Nanjing 210000, China
2
Division of Hydrologic Sciences, Desert Research Institute, Las Vegas, NV 89154, USA
3
Bei Fang Investigation, Design & Research Co. Ltd., Tianjin 300000, China
*
Author to whom correspondence should be addressed.
Received: 2 March 2018 / Revised: 31 March 2018 / Accepted: 3 April 2018 / Published: 9 April 2018
(This article belongs to the Section Hydrology)
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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. View Full-Text
Keywords: flood forecasting; error correction; dynamic system response curve; ill-posed problem; Tikhonov regularization; regularized dynamic system response curve; Xinanjiang rainfall-runoff model flood forecasting; error correction; dynamic system response curve; ill-posed problem; Tikhonov regularization; regularized dynamic system response curve; Xinanjiang rainfall-runoff model
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Sun, Y.; Bao, W.; Jiang, P.; Si, W.; Zhou, J.; Zhang, Q. Development of a Regularized Dynamic System Response Curve for Real-Time Flood Forecasting Correction. Water 2018, 10, 450.

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