Derivation of S-Curve from Oscillatory Hydrograph Using Digital Filter

An oscillatory S-curve causes unexpected fluctuations in a unit hydrograph (UH) of desired duration or an instantaneous UH (IUH) that may affect the constraints for hydrologic stability. On the other hand, the Savitzky–Golay smoothing and differentiation filter (SG filter) is a digital filter known to smooth data without distorting the signal tendency. The present study proposes a method based on the SG filter to cope with oscillatory S-curves. Compared to previous conventional methods, the application of the SG filter to an S-curve was shown to drastically reduce the oscillation problems on the UH and IUH. In this method, the SG filter parameters are selected to give the minimum influence on smoothing and differentiation. Based on runoff reproduction results and performance criteria, it appears that the SG filter performed both smoothing and differentiation without the remarkable variation of hydrograph properties such as peak or time-to peak. The IUH, UH, and S-curve were estimated using storm data from two watersheds. The reproduced runoffs showed high levels of model performance criteria. In addition, the analyses of two other watersheds revealed that small watershed areas may experience scale problems. The proposed method is believed to be valuable when error-prone data are involved in analyzing the linear rainfall–runoff relationship.

[1]  B. Hunt.  The meaning of oscillations in unit hydrograph S-curves , 1985 .

[2]  Xin He,et al.  Instantaneous Unit Hydrograph Evaluation for Rainfall-Runoff Modeling of Small Watersheds in North and South Central Texas , 2006 .

[3]  S. Ghosh.  Flood control and drainage engineering , 1997 .

[4]  Time Step Issue in Unit Hydrograph for Improving Runoff Prediction in Small Catchments , 2012 .

[5]  Rajib Kumar Bhattacharjya,et al.  Optimal design of unit hydrographs using probability distribution and genetic algorithms , 2004 .

[6]  T. Bree.  The stability of parameter estimation in the general linear model , 1978 .

[7]  Dawei Han,et al.  Derivation of unit hydrograph using a transfer function approach , 2006 .

[8]  D. P. Vijayalakshmi,et al.  Estimation of Nash's IUH parameters using stochastic search algorithms , 2008 .

[9]  S. Mishra,et al.  Analytical Approach for Derivation of Oscillation-Free Altered Duration Unit Hydrographs , 2016 .

[10]  S. Jain,et al.  An Analytical S-Curve Approach for SUH Derivation , 2020 .

[11]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[12]  季織 吉村,et al.  Microsoft Excelを用いたケモメトリクス計算(5) , 2012 .

[13]  B. Zhao,et al.  Estimation of Unit Hydrograph by Ridge Least-Squares Method , 1995 .

[14]  Alexander Lattermann.  System-Theoretical Modelling in Surface Water Hydrology , 1991 .

[15]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[16]  L. Mays,et al.  Optimization of Unit Hydrograph Determination , 1980 .

[17]  Mohammad Ali Ghorbani,et al.  Probability distribution functions for unit hydrographs with optimization using genetic algorithm , 2017, Applied Water Science.

[18]  Determination of Optimal Loss Rate Parameters and Unit Hydrograph , 2001 .

[19]  J. E. Nash,et al.  The form of the instantaneous unit hydrograph , 1957 .