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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 (R 2) of 0.36 and 0.48 for the corresponding quadratic and quintic splines, while the cubic spline showed R 2 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.