Van Genuchten–Gupta model

The Van Genuchten–Gupta model is an inverted S-curve applicable to crop yield and soil salinity relations.[1] It is named after Martinus Theodore van Genuchten and Satyandra K. Gupta's work from the 1990s.

Van Genuchten-Gupta model for crop response to soil salinity.

Equation

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The mathematical expression is:

 

where Y is the yield, Ym is the maximum yield of the model, C is salt concentration of the soil, C50 is the C value at 50% yield, and P is 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

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Logistic S-curve model for the relation between crop yield and soil salinity

As an alternative, the logistic S-function can be used.

The mathematical expression is:

 

where:

 

with Y being the yield, Yn the minimum Y, Ym the maximum Y, X the 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

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Cubic regression to find the relation between crop yield and soil salinity

The third degree or cubic regression also offers a useful alternative.

The equation reads:

 

with Y the yield, X the 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.

See also

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References

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  1. ^ M. Th. van Genuchten and S.K. Gupta, 1993. USDA-ARS, U.S. Salinity Laboratory 4500 Glenwood Drive, Riverside, California, USA, 92501. A reassessment of the Crop Tolerance Response Function. Journal of the Indian Society of Soil Science, Vol. 41, No. 4, pp 730–737.