A tiered stochastic framework for assessing crop yield loss risks due to water scarcity under different uncertainty levels

Abstract

Agricultural production in arid and semi-arid regions is threatened by increased droughts (climate change) and groundwater depletion. Farmers increasingly must weigh the short-term economic gains from irrigation against the long-term aquifer longevity needs. Risk-based deficit irrigation is proposed to tackle this trade-off. A tiered risk assessment approach is developed to evaluate crop yield loss risks as a function of crop water supply (CWS) from irrigation and precipitation. Risk is defined as the probability of obtaining a crop yield below a pre-specified threshold. Logistic regression is used to quantify risks as a function of CWS, if the producer can specify a fixed minimum yield threshold. Distribution regression is used to develop the cumulative distribution function of the crop yield assuming heterogeneous model parameter and is useful when the producer can estimate CWS but cannot specify a minimum yield threshold. Finally, the CWS is also modeled as a stochastic variable and the crop yield risk conditioned on CWS risk is computed using the Kolmogorov axiom. The methodology is illustrated using a cotton production case-study in the Southern High Plains of Texas. Logistic regression indicated that crop yield risk was a nonlinear function of CWS. CWS corresponding to ∼80 % of the total crop water demand was enough to reach negligible crop yield risks. Heterogeneous cotton yield distribution was modeled using Box-Cox-Cole-Green function with location and scale parameters being nonlinear and linear functions of CWS respectively and a stationary shape parameter. Irrigation at lower CWS reduced the risks substantially but the risk reductions were marginal at higher CWS. The conditional distribution of crop yield risk indicated that CWS corresponding to ∼80 %–85 % of crop water demand was enough to bring down risks. The tiered risk assessment provides a rational risk-based approach to evaluate the impacts of crop water supply reductions and promote deficit irrigation practices.