Probability Analysis of Crop Water Stress Index: An Application of Double Bounded Density Function (DB-CDF)

Soil moisture is an uncertain variable due to rainfall randomness. Furthermore, its density function is hybrid in nature, with spikes at maximum and minimum soil moisture (saturation and field capacity). Both of these properties are also considered for crop water stress index. The crop water stress index can be used to show the sensitivity of a crop to deficit irrigation. In this paper, a new methodology is proposed to probability analysis of water stress index using Double Bounded Density Function (DB-CDF) and moment analysis of crop water stress index. For this purpose, two equations were developed for the first and second moments of water stress index. To find out the value of the proposed moment equations, they are used as constraints in a stochastic model of crop water allocation as developed previously by Ganji and Shekarrizfard (Water Resour Manage 25:547–561, 2010). After verification of the model, the DB-CDF of soil moisture stress index was estimated using the value of proposed moments in the growing periods. The results show that in case of deficit irrigation, the probability of crop water stress occurrence is high and as a consequence, any unpredictable water shortage leads to yield reduction. The application of the proposed methodology is novel and has not been reported in the literature to date.

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