Derivation of S-Curve from Oscillatory Hydrograph Using Digital Filter

Kee-Won Seong,Jang Hyun Sung

doi:10.3390/w13111456

Abstract

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.

Highlights

The S-curve is the integral of an instantaneous unit hydrograph (IUH) produced from a unit impulse rainfall so that the IUH is the first derivative of the S-curve
A T-h S-curve is derived by adding a series parent T-h UHs that are lagged by period
The oscillation of a UH is fundamentally generated by the combined effect of the intensity of the rainfall and the condition number of a covariance matrix in deconvolution formulation [10]

Summary

Introduction

Despite its very long history, the S-curve concept is still an integral part of linear system-based hydrology. The S-curve stands for a direct runoff caused by the effective rainfall (ER) applied over an infinite time, and its intensity is one-unit depth per unit of time (e.g., 1 cm h−1 ). The S-curve is mainly used to alter a unit hydrograph (UH). Of specified duration into a UH of desired duration. The S-curve is the integral of an instantaneous unit hydrograph (IUH) produced from a unit impulse rainfall so that the IUH is the first derivative of the S-curve. The slope of the S-curve at a particular time is proportional to the IUH ordinate at that time

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