Wind effects on leaf transpiration challenge the concept of “ potential evaporation ”

Abstract. Transpiration is commonly conceptualised as a fraction of some potential rate, driven by so-called "atmospheric evaporative demand". Therefore, atmospheric evaporative demand or "potential evaporation" is generally used alongside with precipitation and soil moisture to characterise the environmental conditions that affect plant water use. Consequently, an increase in potential evaporation (e.g. due to climate change) is believed to cause increased transpiration and/or vegetation water stress. In the present study, we investigated the question whether potential evaporation constitutes a meaningful reference for transpiration and compared sensitivity of potential evaporation and leaf transpiration to atmospheric forcing. A physically-based leaf energy balance model was used, considering the dependence of feedbacks between leaf temperature and exchange rates of radiative, sensible and latent heat on stomatal resistance. Based on modelling results and supporting experimental evidence, we conclude that stomatal resistance cannot be parameterised as a factor relating transpiration to potential evaporation, as the ratio between transpiration and potential evaporation not only varies with stomatal resistance, but also with wind speed, air temperature, irradiance and relative humidity. Furthermore, the effect of wind speed in particular implies increase in potential evaporation, which is commonly interpreted as increased "water stress", but at the same time can reduce leaf transpiration, implying a decrease in water demand at leaf scale.


Introduction
Potential evaporation is a measure for atmospheric water demand, i.e. how much water can be evaporated from a wet surface under given atmospheric conditions.The concept of potential evaporation is used commonly in catchment and water balance studies to estimate actual evapotranspiration (McMahon et al., 2013), an important hydrologic pathway of water out of a catchment beside drainage and runoff.Therefore, sensitivity of potential evaporation to changes in atmospheric conditions is generally assumed to scale into sensitivity of actual evapotranspiration and hence catchment water balance (Barella-Ortiz et al., 2013).Similar to actual evapotranspiration in hydrology, the latent heat flux is commonly estimated in global circulation models (GCM) by multiplying potential evaporation by a reduction factor representing water supply limitation to the surface (Milly, 1992).However, recent studies have suggested that 60 to 90 % of latent heat flux on land and half of all solar energy absorbed by terrestrial land surfaces can be attributed to transpiration (Jasechko et al., 2013;Schlesinger and Jasechko, 2014).In contrast to evaporation from wet surfaces, transpiration is commonly controlled by plant stomata, which, by gradually opening and closing, impose a varying resistance on the surface-to-air vapour transfer.Despite this fundamental distinction, it is a surprisingly widely adopted assumption that transpiration scales with "atmospheric evaporative demand" or potential evaporation.Recently, Barella-Ortiz et al. (2013) analysed the sensitivity of different formulations of potential evaporation to climate change, and found large differences in climate sensitivities, depending on the processes included in the formulations.They concluded that those formulations that represent the most complete consideration of physical processes contributing to evaporation are most robust and reliable for the characterisation of the impact of climate change on surface processes.
Physically based definitions of potential evaporation consider all or a subset of the following atmospheric variables or various transformations their-of: -sky radiation -air temperature -vapour concentration -wind speed.
All variables except for vapour concentration generally enhance potential evaporation if considered in the formulation, while increasing vapour concentration reduces potential evaporation.Interestingly, it has been pointed out by several researchers a long time ago, that actual transpiration can actually decrease with increasing wind speed under certain conditions (e.g.Raschke, 1958;Mellor et al., 1964;Monteith, 1965;Dixon and Grace, 1984).
Therefore, in the present study, we challenge the assumption that common definitions of potential evaporation provide a meaningful measure for the sensitivity of transpiration to wind speed and potentially other components of atmospheric forcing.The objective of the present study is to analyse how transpiration from a leaf scales with evaporation from a wet surface with similar properties under the same variations of atmospheric conditions.

Methods
In order to consider all relevant atmophseric forcing variables explicitly, and to avoid ambiguities between a "reference crop" and an actual plant, we adopt a detailed physically based leaf transpiration and energy balance model published previously (Schymanski et al., 2013) and compare simulated evaporation from wet leaves with simulations of transpiration from leaves with relatively low stomatal conductance (0.001 m s −1 ), representing water-stressed plants.Wet leaf evaporation is simulated as transpiration from a leaf with infinite stomatal conductance.All simulations are done for 5 cm wide leaves with stomata on one side of the leaf only.In the present study we focus in particular on the sensitivity to wind speed and in a first step evaluate the model using previously published experimental data on the effect of wind speed on transpiration (Dixon and Grace, 1984).

Summary of leaf transpiration model
The model was described in detail by Schymanski et al. (2013) and will only be summarised here.Relevant closure equations are also provided in the appendix, while the variables and their units respective standard values are described in Table A1.
The leaf energy balance is determined by the dominant energy fluxes between the leaf and its surroundings, including radiative, sensible, and latent energy exchange (linked to mass exchange).In this study we focus on steady-state conditions, in which the energy balance can be written as: where R s denotes absorbed shortwave radiation, R ll is the net longwave radiation, i.e. the emitted minus the absorbed, H l is the sensible heat flux away from the leaf and E l is the latent heat flux away from the leaf.In the above, extensive variables are defined per unit leaf area.As in Schymanski et al. (2013), this study considers spatially homogeneous planar leaves, i.e. full illumination and a negligible temperature gradient between the two sides of the leaf.Following Schymanski et al. (2013) and Monteith and Unsworth (2007), the net longwave emission is represented by the difference between blackbody radiation at leaf (T l ) and that at air temperature (T a ): where σ is the Stefan-Boltzmann constant and the factor 2 represents the two sides of a broad leaf.
The sensible heat flux or the total convective heat transport away from the leaf is represented as: where h c is the average one-sided convective heat transfer coefficient, which depends on leaf size and roughly scales with the square root of wind speed (see Schymanski et al. (2013) for details).
The latent heat flux (E l ) is directly related to the transpiration rate (E l,mol ) by: where M w is the molar mass of water and λ E the latent heat of vaporisation.E l,mol (mol m −2 s −1 ) was computed in molar units as a function of the concentration of water vapour inside the leaf (C wl , mol m −3 ) and in the free air (C wa , mol m −3 ) (Incropera et al., 2006, Eq. 6.8): where g tv (m s −1 ) is the total leaf conductance for water vapour, depending on the leaf boundary layer and stomatal conductance (g bv and g sv respectively): Due to their reliance on leaf boundary layer properties, the one-sided heat transfer coefficient (h c ) and the mass transfer coefficient for water vapour (g bv ) across the leaf boundary layer are directly related and both scale roughly with the square root of wind speed (see Appendix A for details).Note For given atmospheric forcing including shortwave irradiance (R s ), water vapour concentration (C wa ), temperature (T a ) and wind speed (v w ), the system of equations (see also Appendix A, B and C) is solved numerically for steady state leaf temperature (T l ), returning steady-state values of leaf temperature, net longwave radiation, latent heat flux and sensible heat flux for given leaf size and stomatal conductance.

Model evaluation
Dixon and Grace (1984) placed different plants in a wind tunnel and recorded transpiration rates and leaf temperatures at various wind speeds.To deduce variations in stomatal conductance from the measurements, they also estimated leaf boundary layer resistances for each species using brass leaf replicas.These are plotted in Fig. 2 and we fitted the characteristic leaf length scale in order to reproduce these measurments as close as possible.The resulting characteristic length scales resemble typical leaf widths of these species very closely, with 2.5 mm for pine (Pinus sylvestris), 2 cm for mountain-ash (Sorbus aucuparia), 3 cm for oak (Quercus robur) and 4 cm for beech (Fagus sylvatica), while observed and simulated boundary layer resistances match very closely (Fig. 2).Dixon and Grace (1984).Lines represent inverse of boundary layer conductance (Eqs.A1, A4 and A7), converted to the same units as in Dixon and Grace (1984).Characteristic length scales of leaves (L l ) are chosen to achieve closest match with dots extracted from Fig. 1 in Dixon and Grace (1984).The experimental conditions were reported as 70-75 % relative humidity and 100-200 W m −2 absorbed net radiation.Taking a relative humidity of 70 %, assuming that the wind tunnel experiments were conducted under the same air temperature as the growth conditions of the plants (20 • C), and taking into account the ranges of stomatal conductances estimated by Dixon and Grace (1984), we simulated the responses of latent heat flux and leaf temperatures of the different species to variations in wind speed by choosing constant values for absorbed shortwave radiation (R s ) and stomatal conductance (g sv ) to best represent the data points in the original study (Fig. 3 in Dixon and Grace, 1984).The results are given in Fig. 3 and the values chosen for R s and g sv are reported in the figure caption.Our simulations predicted a decrease in both latent heat flux and leaf temperature for all experiments, which is consistent with the experimental results, except for P. sylvestris, where an initial increase in transpiration was observed, followed by a decrease at higher wind speeds.Simulated leaf temperatures were generally higher than observed and the discrepancy increased with increasing wind speed.Dixon and Grace (1984).Symbols represent data points extracted from Fig. 3 in Dixon and Grace (1984), converted to units used in the present paper.Absorbed shortwave radiation (R s ) and stomatal conductance (g sv ) were adapted within the ranges quoted in the paper to best reproduce the data.

Simulations of relative evaporation
In order to evaluate the effect of stomatal conductance on the transpiration rate under various conditions, we plotted relative transpiration rates, i.e. transpiration rate at low stomatal conductance (g sv = 0.001 m s −1 , close to those reported by Dixon and Grace, 1984) divided by transpiration at infinite stomatal conductance as functions of wind speed, shortwave irradiance, relative humidity and air temperature (Fig. 4).Our results illustrate a high sensitivity of relative transpiration to wind speed, with a 3-fold decrease for an increase in wind speed from 0.5 to 5.0 m s −1 and weaker, positive sensitivities to shortwave irradiance, relative humidity and air temperature.

Discussion
Model simulations and predictions of a decrease in transpiration rates with increasing wind speed were consistent with the experimental results presented by Dixon and Grace (1984).The fact that simulated leaf temperatures were generally higher than the observed and that the discrepancy increased with increasing wind speed is not surprising, considering that temperatures recorded using thermocouples in contact with the leaf surface are influenced by the air passing over the thermocouple (Mott and Peak, 2011), and assuming that this influence increases with increasing wind speed.Note that the simulations in Fig. 3 are performed using constant stomatal conductance, whereas stomatal conductances have likely varied to some extent during the experiments by Dixon and Grace (1984).Considering these uncertainties, the correspondence between observations and model simulations gives us some confidence that the model simulations do rep- resent the dominant physical processes determining the leaf energy balance.
The analogy with the representation of actual evapotranspiration as a fraction of potential evaporation, in which the reduction coefficient represents soil moisture limitations, is equivalent to assuming that the ratio between potential and actual evapotranspiration is constant as long as surface properties do not change.Figure 4 clearly illustrates that this analogy is inappropriate for plant leaves, particularly with respect to variations in wind speed.At low stomatal conductance, the sensitivity of transpiration to wind speed can even have a different direction than that of potential evapotranspiration, as illustrated in the experimental results, where transpiration decreased with increasing wind speeds.This is of particular relevance for plants in water-limited environments, as higher wind speeds may mean that they can achieve the same amount of carbon assimilation with less water use, indicating more favourable conditions for growth, despite in-creased potential evaporation.Considering transpiration as a result of a trade-off between water loss and CO 2 uptake, it is also evident that increased solar radiation does not always translate to increased water stress despite its positive effect on potential evaporation.Since solar radiation supplies the energy for photosynthesis and CO 2 assimilation, greater radiation levels enable greater rates of photosynthesis, and hence an environment with a given potential evaporation under high radiation is much more favourable to a plant than an environment with the same potential evaporation under low solar radiation (e.g.wet tropics vs. cold desert).Consideration of the leaf energy balance in the assessment of possible impacts of climate change on vegetation water use and productivity can lead to very different results than if the effect of atmospheric forcing is summarised in the magnitude of "atmospheric water demand" or "potential evaporation".In a related study (Schymanski and Or, 2015), we found that the documented global decrease in wind speeds over land areas (McVicar et al., 2012) may have led to a similarly strong effect on water use efficiency as the rise of atmospheric CO 2 concentrations (Battipaglia et al., 2013;De Kauwe et al., 2013;Barton et al., 2012), but in the opposite direction, implying increase in leaf-scale water use by a similar amount as the decrease expected due to rising CO 2 concentrations (Drake et al., 1997;Gedney et al., 2006;Betts et al., 2007;Gopalakrishnan et al., 2011).In contrast, the effect of decreasing wind speeds on potential evaporation would suggest a general decrease in evaporation and accordingly, increase in streamflow in energy-limited catchments (McVicar et al., 2012).

Conclusions
The use of potential evaporation to estimate actual evapotranspiration or to describe the suitability of a given climate for plant growth confounds different effects of atmospheric drivers on transpiration from plant leaves versus evaporation from wet surfaces and may lead to wrong conclusions about the consequences of climate change on plant growth and water relations.This is most pronounced for effects of wind speed, which increases potential evaporation, but may reduce actual transpiration.Therefore, we recommend to avoid using the concept of potential evaporation in relation to plants and transpiration from leaves, and rather address the effects of different atmospheric drivers on plant water use separately.Wind velocity m s −1 nents using the ideal gas law: where n a is the amount of matter (mol), M a is the molar mass (kg mol −1 ), P a the pressure, T a the temperature and R mol the molar universal gas constant.This equation was used for each component, i.e. water vapour, N 2 and O 2 , where the partial pressures of N 2 and O 2 are calculated from atmospheric pressure minus vapour pressure, yielding: where M N 2 and M O 2 are the molar masses of nitrogen and oxygen respectively, while P N 2 and P O 2 are their partial pressures, calculated as:

Figure 1 .
Figure1.Dependence of the leaf-air water vapour concentration difference (C wl − C wa ) on leaf temperature (T l ).In this example (70 % relative humidity, 300 K air temperature (T a )), the water vapour concentration difference doubles for an increase in leaf temperature by 5 K relative to air temperature, or drops to 0 for a decrease in leaf temperature by 6 K.

Figure 4 .
Figure 4. Simulated relative transpiration (latent heat flux at low stomatal conductance (0.001 m s −1 ) divided by that at infinite stomatal conductance as functions of (a) wind speed, (b) shortwave irradiance, (c) relative humidity and (d) air temperature.(b)-(c) display two curves, one for low wind speed (v w = 0.5 m s −1 , solid line) and one for high wind speed (v w = 5.0 m s −1 , dashed line).Standard simulation conditions: 5 cm wide leaf, 600 W m −2 shortwave irradiance, 300 K air temperature and 50 % relative humidity.

Table A1 .
Symbols, standard values and units used in this paper.All area-related variables are expressed per unit leaf area.