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

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.

[1]  A. Verhoef,et al.  A SVAT scheme describing energy and CO2 fluxes for multi-component vegetation: calibration and test for a Sahelian savannah. , 2000 .

[2]  Dan Rosbjerg,et al.  Land-surface modelling in hydrological perspective – a review , 2006 .

[3]  Eva Boegh,et al.  Canopy-scale biophysical controls of transpiration and evaporation in the Amazon Basin , 2016 .

[4]  M. Raupach.  Vegetation-atmosphere interaction and surface conductance at leaf, canopy and regional scales , 1995 .

[5]  J. Ardö,et al.  A Surface Temperature Initiated Closure (STIC) for surface energy balance fluxes , 2014 .

[6]  A. Dolman,et al.  Fifty years since Monteith's 1965 seminal paper: the emergence of global ecohydrology , 2014 .

[7]  Stanislaus J. Schymanski,et al.  Stomatal Control and Leaf Thermal and Hydraulic Capacitances under Rapid Environmental Fluctuations , 2013, PloS one.

[8]  I. S. Bowen.  The Ratio of Heat Losses by Conduction and by Evaporation from any Water Surface , 1926 .

[9]  J. Lhomme,et al.  Evaporation from Heterogeneous and Sparse Canopies: On the Formulations Related to Multi-Source Representations , 2012, Boundary-layer Meteorology.

[10]  D. Hartmann.  Global Physical Climatology , 1994 .

[11]  J. Monteith.  Evaporation and surface temperature , 2007 .

[12]  D. Or,et al.  Wind effects on leaf transpiration challenge the concept of "potential evaporation" , 2015 .

[13]  D. Or,et al.  Wind increases leaf water use efficiency. , 2016, Plant, cell & environment.

[14]  Raupach,et al.  Single layer models of evaporation from plant canopies are incorrect but useful, whereas multilayer models are correct but useless: discuss , 1988 .

[15]  Quantifying the uncertainties of transpiration calculations with the Penman-Monteith equation under different climate and optimum water supply conditions , 2009 .

[16]  U. KyawThaPaw,et al.  Applications of solutions to non-linear energy budget equations , 1988 .

[17]  D. Or,et al.  Effects of stomata clustering on leaf gas exchange. , 2015, The New phytologist.

[18]  Richard G. Allen,et al.  A Penman for All Seasons , 1986 .

[19]  J. Monteith.  Evaporation and environment. , 1965, Symposia of the Society for Experimental Biology.

[20]  P. Milly.  A refinement of the combination equations for evaporation , 1991 .

[21]  K. G. McNaughton,et al.  Stomatal Control of Transpiration: Scaling Up from Leaf to Region , 1986 .

[22]  H. L. Penman.  The physical bases of irrigation control , 1952 .

[23]  D. Or,et al.  Technical note: An experimental set-up to measure latent and sensible heat fluxes from (artificial) plant leaves , 2017 .

[24]  J. Parlange,et al.  Boundary layer resistance and temperature distribution on still and flapping leaves: I. Theory and laboratory experiments. , 1971, Plant physiology.

[25]  R. Leuning,et al.  Leaf energy balances: developments and applications , 1989 .

[26]  C. B. Tanner,et al.  Evaporation from unsaturated surfaces: A generalized combination method , 1968 .

[27]  Joshua B. Fisher,et al.  Latent Heat Flux and Canopy Conductance Based on Penman–Monteith, Priestley–Taylor Equation, and Bouchet’s Complementary Hypothesis , 2013 .

[28]  H. L. Penman.  Natural evaporation from open water, bare soil and grass , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[29]  Michael H. Unsworth,et al.  Principles of Environmental Physics: Plants, Animals, and the Atmosphere , 2013 .

[30]  G. Bange,et al.  ON THE QUANTITATIVE EXPLANATION OF STOMATAL TRANSPIRATION , 1953 .

[31]  Peter Widmoser,et al.  A discussion on and alternative to the Penman-Monteith equation. , 2009 .

[32]  A. J. Mcarthur.  An accurate solution to the Penman equation , 1990 .