Abstract
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.
Highlights
A vast number of current global land surface models, hydrological models and inverse approaches to deduce evaporation from remote sensing data employ the analytical solution for the latent heat flux from plant leaves derived by Monteith (1965), based on an earlier formulation for a wet surface by Penman (1948), see e.g. Overgaard et al (2006) and Dolman et al (2014)
This is because under conditions where the leaf temperature is lower than ambient, sensible heat flux is a source of energy for transpiration, whereas under conditions where the leaf is warmer than the air, sensible heat flux competes for energy with transpiration
Our experimental results clearly illustrate that the inconsistencies we found in the PM and MU equations are not just semantic, but lead to very significant biases in simulated transpiration rates for known stomatal resistance, which would alternatively lead to biases in deduced resistance for known transpiration rates
Summary
A vast number of current global land surface models, hydrological models and inverse approaches to deduce evaporation from remote sensing data employ the analytical solution for the latent heat flux from plant leaves derived by Monteith (1965), based on an earlier formulation for a wet surface by Penman (1948), see e.g. Overgaard et al (2006) and Dolman et al (2014). Overgaard et al (2006) and Dolman et al (2014) This so-called Penman–Monteith equation ( referred to as the PM equation), which introduced stomatal resistance into Penman’s formalism, found widespread use in the prediction of latent heat flux based on estimates of leaf and canopy resistance to water vapour. : Omission in the Penman–Monteith equation leaf-canopy scaling and use of data at daily or monthly scales has led to various empirical corrections to the PM equation (Allen, 1986), which may have obscured more fundamental issues with the derivations by Monteith (1965). On the other hand, Langensiepen et al (2009) proposed a detailed leafscale parametrisation of the PM equation and averaging over the canopy and time that yielded reasonable agreement with sap-flow-derived canopy transpiration estimates, without empirical corrections to the PM equation
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