New Steady-State Models for Water-Limited Cropping Systems Using Saline Irrigation Waters: Analytical Solutions and Applications.

Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters.  In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity.  Two new explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function.  The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops.  Model predictions are shown to be mostly consistent with existing models and available experimental data.  Yet the new solutions possess clear advantages over available alternatives, including: (i) the new solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the new analytical solutions are explicit and can be evaluated without iterative techniques; and (iii) the utilized modeling framework is compatible with leading transient-state numerical models.