Comparison of cubic, quadratic, and quintic splines for soil erosion modeling

Sarita Gajbhiye Meshram,P L Powar,Chandrashekhar Meshram

doi:10.1007/s13201-018-0807-6

Abstract

Approximate curve is constructed using quadratic, quintic, and cubic splines and examination between these splines. The point of this construction is to predict sediment yield index (SYI) corresponding to curve number. This strategy is outlined with a contextual analysis of Manot watershed of Narmada Basin, India. The relation among calculated SYI and observed SYI esteems is associated with a coefficient of determination (R2) of 0.36 and 0.48 for the corresponding quadratic and quintic splines, while the cubic spline showed R2 of 0.87 (Meshram et al. Arab J Geosci 10:155–168, 2017b; Appl Water Sci 7:1773–1779, 2017c). Numerical results seemed to indicate that the cubic spline method is more accurate than the quadratic/quintic spline method.

Highlights

Rainfall–runoff–sediment yield modeling, being highly complex, dynamic, and nonlinear, exhibits temporal and spatial variability and comprises several physical processes (Meshram et al 2017a, b, c)
Varying complexity from lumped empirical to physically based space and time-distributed, several models are available in the literature to model runoff and subsequent soil erosion/sediment yield, while physically based models have demonstrated exceptionally helpful as an exploration device, yet they are of restricted use in field, in creating nations like India as they require expansive measure of information
In order to develop the model, we have taken the data of sediment yield index (SYI) and curve number (CN) from the previous studies of Meshram et al (2017a, b, c)

Summary

Introduction

Rainfall–runoff–sediment yield modeling, being highly complex, dynamic, and nonlinear, exhibits temporal and spatial variability and comprises several physical processes (Meshram et al 2017a, b, c). Keywords Sediment · Curve number · Quadratic spline · Quintic spline In spite of the fact that the sediment yield from large basin can be found from such observations, it is not conceivable to find out the reason for soil loss of small watershed inside a basin.

Results

Conclusion