Probabilistic description of crop development and irrigation water requirements with stochastic rainfall

Supplemental irrigation represents one of the main strategies to mitigate the effects of climatic variability on agroecosystems, stabilizing yields and profits. Because of the significant investments and water requirements associated with irrigation, strategic choices are needed to preserve productivity and profitability while ensuring a sustainable water management, a nontrivial task given rainfall unpredictability. Decision-making under uncertainty requires the knowledge of the probability density function (pdf) of the outcome variable (yield and economic return) for the different management alternatives to be considered (here, irrigation strategies). A stochastic framework is proposed, linking probabilistically the occurrence of rainfall events and irrigation applications to crop development during the growing season. Based on these linkages, the pdf of yields and the corresponding irrigation requirements are obtained analytically as a function of climate, soil, and crop parameters, for different irrigation strategies and both unlimited and limited water availability. Approximate expressions are also presented to facilitate their application. Our results employ relatively few parameters and are thus broadly applicable to different crops and sites, under current- and future-climate scenarios, offering a quantitative tool to quantify the impact of irrigation strategies and water allocation on yields. As a tool for decision-making under uncertainty (e.g., via expected utility theory), our framework will be useful for the assessment of the feasibility of different irrigation strategies and water allocations, toward a sustainable management of water resources for human and environmental needs.