Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 409

In which E 0 represents the evaporation of a free water surface and “ m ” a crop coef-
ficient. This relationship was the basis for several models to predict yield from
evapotranspiration.

Stewart and Hagan Model

The model proposed by Stewart and Hagan (1973) is

Y = Y m − Y m K y ETD/ET m (10.30)

where

Y crop yield

Y m =

=

maximum crop yield under the same condition of soil texture, fertil-
ity, etc.
K y =

crop coefficient

ETD cumulative evapotranspiration deficit during the growth period, calcu-

lated as

=

ETD = ET m − ET a (10.31)

where ET m = actual evapotranspiration.

The model is simple and practical and can be used when the sensitivity to
moisture stress is the same during the whole growing period.

maximum evapotranspiration; ET a =

Stewart et al. Model

For the case that the sensitivity differs significantly among growth periods, Stewart
et al. (1977) proposed a model that takes into account the effect of moisture stress
during successive phenological stages. They used a different coefficient for each
stage, according to

1

k y ( n ) 1

m

y
y m =

ET
ET m

− − (10.32)

n

n = 1

where n is generic growth stage, and m is the number of growth stage considered,
and k y is the crop or yield response factor.
Stewart's formula is based on the theory that, considering all other factors of
production at their optimum level, it is the water scarcity factor (estimated as the
ratio of actual to maximum evapotranspiration, ET/ET m ) that limit the final yield.
This is an attempt to generalize the production function.

Determination of Response Factor of Stewart Model

To determine yield response factor k y , the following procedure may be followed
(Doorenbos and Kassem, 1979):