Modeling Water Use and Water Use Efficiency of Plant Canopies in a High CO2 World.

Water use efficiency (w, g biomass accrued / kg water evaporated from the leaves) is controlled by factors that control CO₂ uptake and water evaporation from leaves. It is typically accepted that, since evaporation depends on vapor pressure deficit (D, kPa), w is inversely proportional to D. For this to hold true, among other assumptions, the ratio of CO₂ concentration in the leaves to that in the bulk atmosphere is assumed relatively constant. Thus, w will increase proportionally to CO₂. Transpiration, however, will decrease due to stomatal closure under increasing CO₂ and thus growth will increase in a non-linear fashion with increasing CO₂. Since transpiration depends on the leaf energy balance which in turns depends on the surface conductance to vapor, and this variable in turns depends on photosynthesis, understanding the coupling of these processes seems daunting. We show that a direct application of the stomatal optimization theory proposed by Cowan in the 1970s allows developing a simplified equation that predict w in current conditions, and as earlier empirical work by us indicates, that w is proportional to the inverse of the square root of D, a significant departure to the prevailing view.  In addition, we show that it is possible to scale this approach along with a dependence of the stomatal conductance on CO₂ to model both transpiration and growth under increasing atmospheric CO₂ concentration.