The Maas–Hoffman model is a mathematical tool to characterize the relation between crop production 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 ...

. It describes the crop response by a broken line of which the first part is horizontal and the second is sloping downward.Maas EV, Hoffman GJ, 1977. ''Crop salt tolerance-current assessment''. Journal of the Irrigation and Drainage Division, American Society of Civil Engineers 103: 115-134. The ''breakpoint'' (Pb) or ''threshold'' is also called ''tolerance'' because up to that point the yield is unaffected by the salinity, so the salt is tolerated, while at greater salinity values the crops are affected negatively and the yield goes down.

Mathematics

Mathematically the two lines are represented by the equations: :

\left\{\begin{array}{l}
        Y=C, & X P_{\rm b}
        \end{array}\right.

where ''Y'' is the crop production or yield, ''C'' is the maximum yield, ''X'' is the soil salinity, ''A'' is the slope (regression coefficient) of the descending line, and ''B'' is the regression constant of that line. In the example of the figure: ''C'' = 1.2, ''A'' = —0.10, ''P''_b = 7.0 The value of ''P''_b is to be found by regression analysis and optimization so that the goodness of fit of the data to the model is maximum. The Maas–Hoffman model is used in crop tolerance to seawater. Maas-Hoffman model inverted

Inverted model

For growth factors, like the depth of the watertable, that affect crop production negatively at low values while there is no effect at high values, the inverted Maas–Hoffman model can be used.

References

{{reflist Mathematical modeling Crops Soil science

Mathematics

Inverted model

See also

References