Van Genuchten–Gupta model
The van Genuchten–Gupta model is an inverted S-curve applicable to crop yield and soil salinity relations. Equation. The mathematical expression is: where Y = yield, Ym = maximum yield of the model, C = salt concentration of the soil, C = C value at 50% yield, P = an exponent to be found by optimization and maximizing the model's goodness of fit to the data. In the figure: Ym = 3.1, C = 12.4, P = 3.75 Alternative one. As an alternative, the "logistic S-function" can be used. The mathematical expression is : where: with Y =Yield, Yn = minimum Y, Ym = maximum Y, X = salt concentration of the soil, while A, B and C are constants to be determined by optimization and maximizing the model's goodness of fit to the data. If the minimum Yn=0 then the expression can be simplified to: In the figure: Ym = 3.43, Yn = 0.47, A = 0.112, B = -3.16, C = 1.42. Alternative two. The third degree or "cubic regression" also offers a useful alternative. The equation reads: with Y =Yield, X = salt concentration of the soil, while  A, B, C and D are constants to be determined by the regression. In the figure: A = 0.0017, B = 0.0604, C=0.3874, D = 2.3788. These values were calculated with Microsoft Excel The curvature is more pronounced than in the other models.