Abstract
Integrated and holistic approach of water resources management is important for sustainability. Since the optimum use of water resources needs taking into account different environmental issues. Accordingly, the use of supportive models in decision making as an effective tool is significantly important. To addressing uncertainty in crop water allocation, several methodologies have been proposed. The most of these models consider rainfall as a stochastic variable affecting soil moisture. Applying a new methodology/model while considering the stochastic variable in nonnormal state and uncertainties for both irrigation depth and soil moisture looks more realistic. In this research, a mathematical model was developed based on Constraint-State equation optimization model and Beta function. The first and the second moments of soil moisture are used as constraints in optimization process. This model uses the soil moisture budget equation for a specific plant (winter wheat) on a weekly basis, considering the root depth, soil moisture, irrigation depth, rainfalls, evapotranspiration, leaching depth, soil physical properties and a stochastic variable. The model was written in MATLAB and was run for winter wheat in Badjgah, south of Iran. The results were compared with the results obtained from a simulation model. Based on the results, the optimum net irrigation depth of winter wheat including the rainfall was 306.2 mm. The insignificant difference of simulation and optimization results showed that, the optimization model works properly and is acceptable for optimization of irrigation depth, as its reliability index is 96.86 %.
Highlights
In the recent decades the problem of water scarcity and inappropriate distribution of water resources have made many scholars to put a great effort into extending some new integrated and sustainable approaches of watershed and water resources management (Loucks et al 1988)
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
This paper proposes a new optimization model for crop water allocation based on Constraint-State model in arid and semi-arid regions by the assumption of nonnormal stochastic variable
Summary
In the recent decades the problem of water scarcity and inappropriate distribution of water resources have made many scholars to put a great effort into extending some new integrated and sustainable approaches of watershed and water resources management (Loucks et al 1988). Optimal policies of crop water allocation can be divided into two states of static and dynamic (Loucks et al 1981). Static and dynamic models can be outlined in states of stochastic and deterministic and continuous and discrete (Hung et al 2002; Karamouz et al 2003). Discrete dynamic models have two problems of time and memory requirement in computations (curse of dimensionality). Among the discrete dynamic models DP (Dynamic Programming) and SDP (Stochastic Dynamic Programming) are more popular. These models have been used by some researchers for crop water allocation (Dudley and Burt 1973; Rhenals and Bras 1981)
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