Transpiration: Moving From Semi-Empirical Approaches to First Principles.

The Penman Equation was a major advance in accounting for evaporation from an open-water surface based on the energy balance.  However, plants are not open-water surfaces due to the additional restriction on diffusion of water vapor through stomata pores.  One attempt to solve this problem was the Penman-Monteith modification but application of this equation is impractical due to the need to define an integrated value of stomata resistance for the entire crop canopy.  In practice, the application of the Penman Equation requires empirical "adjustments" in estimating transpiration.  An alternate approach is to estimate transpiration based directly on crop growth.  There exists a first-principles relationship between the diffusion of both carbon dioxide and water vapor since they both must move through the stomata pores.  Based on this obligatory link between CO2 assimilation rate (A) and transpiration rate (T), Tanner and Sinclair derived an expression at the crop scale for this relationship:  A/T = k/VPD, where k is defined by several physical and physiological variables and VPD is atmospheric vapor pressure deficit.  The value of k is fully defined and is essentially constant across advanced genotypes within a species.  Rearranging the equation, T = A k/VPD.  Therefore, transpiration can be directly calculated from crop growth, which can be estimated from A and provide the crucial link in understanding crop water use.