Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 411

where λ i usually refers to as sensitivity index, express the response of the crop to

water deficiency during the i th period within the growth cycle; w i is the relative
water content of the root zone.
If the evapotranspiration is suppressed only during a certain stage, say the l th
(i.e., I

= l ), then w i = 1 for all except the l th stage. Therefore Eq. ( 10.36 ) yields

y
y 0 =

W λ l
l

(10.37)

or,

log( y / y 0 ) = λ l log w l (10.38)

Thus by taking the logarithms of the data i.e., y / y 0 and w l , the sensitivity index for
the l th period λ l , can be determined. Similarly, the sensitivity index can be obtained

for all the m stages.

10.4.7 Limitations/Drawbacks of Crop Production Function

Although yield-seasonal ET relations have been widely used for management pur-
poses in water-deficient areas as a guideline for irrigation, they do not account for
the effect of timing of water application. Water stress during certain growth stages
may have more effect on grain yield than similar stress at other stages. In addition,
effect of alternate stress and previous stress history have an impact on subsequent
stress (or stress hardening), and hence on yield.

10.5 Regression-Based Empirical Models for Predicting Crop
Yield from Weather Variables

10.5.1 Need of Weather-Based Prediction Model

Extensive experiments and research have provided the basic information regarding
the culture and methods of treatment needed for the successful production of crops
under field conditions. Such information includes the selection of appropriate loca-
tions, optimum fertilization, irrigation requirement and effective methods of plant
protection. Even so, crop yields fluctuate considerably from year to year, a fact
attributable to the variation in environmental conditions.