Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 408

of water use, the impact on yield may be differed due to differential response of plant
to irrigation timing and stress history (Ali et al., 2007 ) . Hence, a singular production
function may not appropriate for all circumstances.

10.4.5 Development of Crop Production Function

Generally two approaches for estimation of crop-water production function are
available in the literature. One approach synthesizes production functions from the-
oretical and empirical models of individual components of the crop-water process.
The second approach estimates production functions by statistical inference from
observations of the effect of different water applications and salinity levels on crop
yield.
The first set of approach is quite useful but due to their implicit assumptions and
complication, their applications are restricted; whereas, the second set of approach
estimates production by direct relationship. By using the second set of approach,
many production functions have been estimated both for saline and non-saline water.
Such empirically derived water production functions are usually valid only for a
single crop at a single location under conditions of optimal deficit sequence. These
functions are usually highly empirical and difficult to generalize. Economic solu-
tions derived from such empirical functions are only useful for specific situations.
These functions are based on the assumption that, considering all the other factors
of production at their optimum level, it is the water scarcity that limits the final
yield.
The effect of water stress on crop yield during individual growth stages has been
investigated using an additive model (Minhas et al., 1974; Howell and Hiler, 1975)
and a multiplicative model (Jensen, 1968; Hanks, 1974). An additive production
function implies that the total absence of water at any stage would only result in
some discrete reduction in yield, whereas the multiplicative model implies that the
plant would die if water input falls to zero at any growth stage. Singh and Aggarwal
(1986) reported that three-degree polynomial crop yield model without the consid-
eration of the time of water stress gave the best results. However, the quadratic crop
yield model was found to be more suitable for practical use.

10.4.6 Some Existing Yield Functions/Models

Model of de Wit

According to the theory of de Wit (1958), crop yield ( Y ) is a linear function of its
transpiration ( T ):

Y = mT / E 0 (10.29)