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

Kexin Liu,Yufeng Hu,Lili Liang,Yiqun Sun,Kuang Li,Weimin Bao,Dongjing Li

doi:10.3390/w13243483

Abstract

The ridge estimation-based dynamic system response curve (DSRC-R) method, which is an improvement of the dynamic system response curve (DSRC) method via the ridge estimation method, has illustrated its good robustness. However, the optimization criterion for the ridge coefficient in the DSRC-R method still needs further study. In view of this, a new optimization criterion called the balance and random degree criterion considering the sum of squares of flow errors (BSR) is proposed in this paper according to the properties of model-simulated residuals. In this criterion, two indexes, namely, the random degree of simulated residuals and the balance degree of simulated residuals, are introduced to describe the independence and the zero mean property of simulated residuals, respectively. Therefore, the BSR criterion is constructed by combining the sum of squares of flow errors with the two indexes. The BSR criterion, L-curve criterion and the minimum sum of squares of flow errors (MSSFE) criterion are tested on both synthetic cases and real-data cases. The results show that the BSR criterion is better than the L-curve criterion in minimizing the sum of squares of flow residuals and increasing the ridge coefficient optimization speed. Moreover, the BSR criterion has an advantage over the MSSFE criterion in making the estimated rainfall error more stable.

Highlights

Flood forecasting, an important non-structural measure, plays an important role in regional flood control, flood warning, risk decision making, etc. [1,2,3]
The autoregressive (AR) model estimates the flow error existing in a certain forecasting period by using the correlation of error series, and it was later developed into improved methods such as the recursive autoregressive model and the forgetting factor recursive autoregressive model [4,5,6]; Kalman filtering (KF) technology is widely used to update hydrological element time series in flood forecasting, and many improved types have been gradually formed, including the extended Kalman filter (EKF) [7]
In terms of the indicator Nash–Sutcliffe effiency coefficent (NSE), the BSR criterion and minimum sum of squares of flow errors (MSSFE) criterion have the same result, with a value of 0.999, which outnumbers that of the L-curve criterion, with 0.001

Summary

Introduction

Flood forecasting, an important non-structural measure, plays an important role in regional flood control, flood warning, risk decision making, etc. [1,2,3]. The autoregressive (AR) model estimates the flow error existing in a certain forecasting period by using the correlation of error series, and it was later developed into improved methods such as the recursive autoregressive model and the forgetting factor recursive autoregressive model [4,5,6]; Kalman filtering (KF) technology is widely used to update hydrological element time series in flood forecasting, and many improved types have been gradually formed, including the extended Kalman filter (EKF) [7]. Error correction technology still needs to be improved; for example, the autoregressive model assumes that the error series has a linear correlation, but its performance near the flood peak is often not satisfying [12]

Methods

Results

Discussion

Conclusion