The Van Genuchten–Gupta model is an inverted S-curve applicable to

crop yield In agriculture, the yield is a measurement of the amount of a crop grown, or product such as wool, meat or milk produced, per unit area of land. The seed ratio is another way of calculating yields. Innovations, such as the use of fertilizer, the c ...

and

soil salinity Soil salinity is the salt content in the soil; the process of increasing the salt content is known as salinization. Salts occur naturally within soils and water. Salination can be caused by natural processes such as mineral weathering or by the ...

relations.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. It is named after

Martinus Theodore van Genuchten Martinus may refer to: * Martin (magister militum per Armeniam), 6th-century Byzantine/East Roman general * Martinus (son of Heraclius), 7th-century Byzantine/East Roman co-emperor * Martinus of Arles, doctor of theology, priest, and author on dem ...

and Satyandra K. Gupta's work from the 1990s. Van Genugten-Gupta model

Equation

The mathematical expression is: :

Y = \frac

where ''Y'' is the yield, ''Y''_m is the maximum yield of the model, ''C'' is salt concentration of the soil, ''C''₅₀ is the ''C'' value at 50% yield, and ''P'' is an exponent to be found by

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

and maximizing the model's

goodness of fit The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measure ...

to the data. In the figure: ''Y''_m = 3.1, ''C''₅₀ = 12.4, ''P'' = 3.75

Alternative one

As an alternative, the '' logistic S-function'' can be used. The mathematical expression is: :

Y^ = \frac

where: :

Y^ = \frac

with ''Y'' being the yield, ''Y''_n the minimum ''Y'', ''Y''_m the maximum ''Y'', ''X'' the salt concentration of the soil, while ''A'', ''B'' and ''C'' are constants to be determined by

and maximizing the model's

to the data. If the minimum ''Y''_n=0 then the expression can be simplified to: :

Y = \frac

In the figure: ''Y''_m = 3.43, ''Y''_n = 0.47, ''A'' = 0.112, ''B'' = -3.16, ''C'' = 1.42.

Alternative two

The third degree or ''

cubic regression Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system w ...

'' also offers a useful alternative. The equation reads: :

Y=AX^3+BX^2+CX+D

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 Microsoft Excel is a spreadsheet developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (comp ...

The curvature is more pronounced than in the other models.

References

Soil science Mathematical modeling Crops {{soil-sci-stub

Equation

Alternative one

Alternative two

See also

References