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, C50 = 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, C50 = 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.