A Polynomial Method Approximating S-Curve with Limited Availability of Reliable Rainfall Data

Kee-Won Seong,Jang Hyun Sung

doi:10.3390/w13233447

Abstract

A methodology named the step response separation (SRS) method for deriving S-curves solely from the data for basin runoff and the associated instantaneous unit hydrograph (IUH) is presented. The SRS method extends the root selection (RS) method to generate a clearly separated S-curve from runoff incorporated in mathematical procedure utilizing the step response function. Significant improvements in performance are observed in separating the S-curve with rainfall. A procedure to evaluate the hydrologic stability provides ways to minimize the oscillation of the S-curve associated with the determination of infiltration and baseflow. The applicability of the SRS method to runoff reproduction is examined by comparison with observed basin runoff based on the RS method. The SRS method applied to storm events for the Nenagh basin resulted in acceptable S-curves and showed its general applicability to optimization for rainfall-runoff modeling.

Highlights

This paper is the sequel of a previously suggested methodology for smoothing the oscillatory S-curve [1], in which a model was presented for determining the oscillationreduced S-curve and associated instantaneous unit hydrograph (IUH) model using the Savitzky-Golay smoothing and differentiation filter.The concept of the S-curve has been widely applied in rainfall–runoff analysis since its introduction in the unit hydrograph (UH) method [2,3]
This paper develops the procedure for estimating an S-curve solely from basin runoff data by improving the defects of the existing method and examines the hydrologic stability of the resulting rainfall-runoff system
The proposed methodology using cumulative function of the runoff (CFR) and the Argand diagram is applied to the estimation of the S-curve Sz−1

Summary

Introduction

This paper is the sequel of a previously suggested methodology for smoothing the oscillatory S-curve [1], in which a model was presented for determining the oscillationreduced S-curve and associated instantaneous unit hydrograph (IUH) model using the Savitzky-Golay smoothing and differentiation filter.The concept of the S-curve has been widely applied in rainfall–runoff analysis since its introduction in the unit hydrograph (UH) method [2,3]. Estimating accurately the effective rainfall for S-curve generation is difficult mainly because of problems related to the estimation of a real rainfall and to the determination of the reduction in total rainfall due to infiltration, which is affected by the uncertain soil moisture condition of basins and groundwater behavior [4,5]. These difficulties result in a hydrologically unstable system. This problem can be circumvented by developing a method deriving an S-curve without using rainfall data

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