Established crop water production functions are based on
linear relationships proposed by Doorenbos and Kassam
(1979), assuming that irrigation is applied with the goal of
fully meeting plant water requirements, without considering
the crop yield response to DI strategies. Another relevant
question is related to the effect of DI in yield models when
the deficit is applied at different phenological stages. In this
sense, data normalization becomes necessary for all the
terms of yield response ratio and relative irrigation, as was
studied in the present work, separating the seasonal crop
yield variation. Along this line, Hexem and Heady (1978)
proposed several non-linear crop production functions (i.e.,
quadratic, Cobb–Douglas and Mitscherlich–Spillman), in
which irrigation water applied was related to the crop yield
ratio, with better results than linear relationships. Similar
models were applied by Martin et al. (1984), achieving
highly significant functions