Leaf-scale experiments reveal an important omission in the Penman–Monteith equation

Abstract. The Penman–Monteith (PM) equation is commonly considered the most advanced physically based approach to computing transpiration rates from plants considering stomatal conductance and atmospheric drivers. It has been widely evaluated at the canopy scale, where aerodynamic and canopy resistance to water vapour are difficult to estimate directly, leading to various empirical corrections when scaling from leaf to canopy. Here, we evaluated the PM equation directly at the leaf scale, using a detailed leaf energy balance model and direct measurements in a controlled, insulated wind tunnel using artificial leaves with fixed and predefined stomatal conductance. Experimental results were consistent with a detailed leaf energy balance model; however, the results revealed systematic deviations from PM-predicted fluxes, which pointed to fundamental problems with the PM equation. Detailed analysis of the derivation by Monteith(1965) and subsequent amendments revealed two errors: one in neglecting two-sided exchange of sensible heat by a planar leaf, and the other related to the representation of hypostomatous leaves, which are very common in temperate climates. The omission of two-sided sensible heat flux led to bias in simulated latent heat flux by the PM equation, which was as high as 50 % of the observed flux in some experiments. Furthermore, we found that the neglect of feedbacks between leaf temperature and radiative energy exchange can lead to additional bias in both latent and sensible heat fluxes. A corrected set of analytical solutions for leaf temperature as well as latent and sensible heat flux is presented, and comparison with the original PM equation indicates a major improvement in reproducing experimental results at the leaf scale. The errors in the original PM equation and its failure to reproduce experimental results at the leaf scale (for which it was originally derived) propagate into inaccurate sensitivities of transpiration and sensible heat fluxes to changes in atmospheric conditions, such as those associated with climate change (even with reasonable present-day performance after calibration). The new formulation presented here rectifies some of the shortcomings of the PM equation and could provide a more robust starting point for canopy representation and climate change studies.