canopy-atmosphere water vapour exchange: can we scale from...

Estimation ofArealEvapotranspfration(Proceedmgs of a workshop held at Vancouver,B.C., Canada, August 1987). IAHSPubl. no. 177,1989. 21

Canopy-atmosphere water vapour exchange: Can we scale from a leaf to a canopy?

Dennis Baldoechl Atmospheric Turbulence and Diffusion Division/NOAA/ARL P.O. Box 2456 Oak Ridge, TN 37831 U.S.A.

Abstract A goal of canopy micrometeorology is to understand mass and energy exchanges at the leaf and canopy levels and to scale these exchanges from one level to another. This paper discusses the processes governing evaporation that are amenable to scaling and the environmental and physiological conditions under which such scaling may be applicable. Factors affecting the scaling of evaporation from a leaf to a canopy include: the degree of canopy development, the relationship between the aerodynamic and surface resistance, the degree of coupling between the leaf, plant and canopy and their environment, and whether or not certain processes are operational or significant at one scale, but are not on another scale.

L'échange de vapeur d'eau entre le couvert végétal et l'atmosphère: peut-on graduer de la feuille au couvert végétal?

Résumé II peut s'avérer difficile de graduer les processus qui, de la feuille au couvert végétal, gouvernent l'évaporation. Cela vient du fait que la graduation dépend: de l'importance du développement du couvert végétal, du rapport entre les résistances aérodynamique et de la surface, et de savoir si oui ou non, certains processus peuvent être opérants ou significatifs à une échelle donnée et ne pas l'être à une autre. On a présenté les processus qui se prêtent à la graduation et les conditions physiologiques et de l'environnement en présence desquelles on peut procéder à une telle graduation.

INTRODUCTION

The structure of a plant canopy is a function of the spatial and species distribution of individual plants and the different positions and shapes of leaves, stems, branches, flowers and seed pods on those plants (see Ross, 1981). The presence and structure of a plant canopy affects its local microclimate by intercepting radiation, attenuating wind and by acting as a source or sink for mass and energy exchange. Conversely, the environment about a plant canopy affects its physiological processes, growth and development, which in turn influences the exchanges of carbon dioxide, water vapour and biogenic gases and aerosols.

22 Dennis Baldocchi

A goal of micrometeorology is to understand the exchanges of mass and energy at the canopy-atmosphere interface. A reductionist approach is often used by scientists to study such exchanges in a plant canopy. This entails studying subcomponents of this system in great detail and then integrating the obtained relations to explain processes operating on the larger scale. The problem with applying the reductionist approach in plant canopies is that canopy elements may not respond to their environment equally throughout the canopy; individual leaves may respond differently to a given stimulus due to differences in age, species, and acclimation to the local microenvironment. Furthermore, leaf-level processes may not be representative of the entire canopy because some processes may be significant or operable at one scale, but not at other scales. How one scales a system from the subcomponents of the reductionist level to the wholistic level, is therefore a complicated and challenging problem.

The objective of this paper is to discuss the scaling of processes associated with evaporation from a leaf to a canopy scale and the environmental and physiological conditions under which such scaling may be applicable.

THEORETICAL FRAMEWORK

The net radiation balance provides a framework for the examination of the processes associated with scaling evaporation. The available net radiation (Rn) at a canopy or leaf surface is comprised of the balance between incoming and outgoing short and long wave radiation. On a leaf surface, Rn is partitioned primarily into latent and sensible heat exchange and photosynthesis (Campbell, 1977). Net radiation, at a canopy surface, is partitioned into latent and sensible heat exchange of the plants and soil, soil heat flux, canopy heat storage and photosynthesis (Thorn, 1975). The advection of sensible and latent heat can also influence the Rn partitioning if the canopy is not horizontally homogeneous, the terrain is irregular or if ambient conditions are not steady-state.

Water vapour exchange from a leaf or plant canopy can be defined on the basis of a simple resistance-analogue relationship: the flux of an entity is the ratio of its potential and the sum of the resistances to its transfer. The evaporation of a leaf (E|) can be written as:

E| = (Pvs - Pva) / (rai + rS|) (1)

where pVa and pvs are the densities of water vapour in the air outside the leaf boundary layer and at the leaf surface, respectively, rai is the diffusive resistance to water vapour transport through the leaf boundary layer and rS| is the stomatal resistance for water vapour.

A resistance network often used to scale evaporation from a leaf to a canopy is shown in Fig. 1. This network includes ra| and rsi and introduces the aerodynamic resistance between the interstitial canopy layers (ram). The mesophyll resistance (rmeSo) introduced in Fig. 1 is negligible for water vapour exchange, but can be important for CO2 and SO2 transfer. Using a multi-layer approach, the divergence of the evaporative flux (E) must balance the source-sink term:

dE(z)/dz = -ai(z) (pvs(z)-pva(z)/(rai(z) + rsi(z)) (2)

where ai(z) is the leaf area density. The canopy evaporative flux can be solved by integrating (2), in conjunction with a closure scheme (e.g., Paw U et al., 1985; Meyers & Paw U, 1987). When applying (2), leaf angle classes, sunlit and shaded leaf fractions and the axial distribution of the stomata should be considered (see Paw U et al., 1985).

Canopy-atmosphere water vapour exchange 23

ATDL-M86/518

R n ( n - I )

FIG. 1. Resistance model for a plant stand.

The evaporation of a canopy (Ec) can also be computed by assuming that the canopy acts as "big-leaf", e.g., the Penman-Monteith equation (Monteith, 1973):

p _ S A + p cD D/fac

^ " s + Y(1 +rs c /rac) ( 3 )

where A is the available energy, p is air density, cp is the specific heat of air, D is the vapour pressure deficit of the air above the canopy, y is the psychrometric constant and s is the slope of the saturation vapour pressure-temperature curve. The canopy aerodynamic resistance (rac) is composed of the sum of rmc, the aerodynamic resistance for momentum transfer, and rb, the quasi-laminar boundary layer or "excess" resistance (Verma & Barfield, 1979), and rsc is the canopy stomatal resistance.

SCALING EVAPORATIVE SUBPROCESSES

The scaling of leaf evaporation to a canopy level depends on how well the subcomponents associated with leaf evaporation are scaled. Below, we examine the scaling of the aerodynamic and stomatal subcomponents.

Aerodynamic considerations

The ability to transfer water vapour from a leaf surface to the free-stream atmosphere is often characterised by the resistance to molecular diffusion through the leaf boundary layer and the aerodynamic resistances through the canopy and the atmosphere.

24 Dennis Baldocchi

The boundary layer resistance to the molecular diffusion of water vapour can be evaluated as:

rai=l/DvSh (4)

where l is a characteristic length scale, Dv is the molecular diffusivity of water vapour and Sh is the Sherwood Number (Campbell, 1977; Grace, 1981). Computations of Sh are generally based on engineering relationships developed over flat plates and depend on whether the wind flow is turbulent or laminar.

This treatment of the leaf boundary layer resistance is limited because air flow inside a canopy is a mixed regime of turbulent and laminar flow, due to leaf flutter, leaf pubescence and transition distances over leaves (Grace & Wilson, 1976), and because of natural variations in leaf size and orientation. In practice, Grace and Wilson (1976) recommend multiplying Sh by two to account for the above-mentioned complicating factors.

The eddies that transfer momentum in a plant canopy also transfer mass (Unsworth, 1981). Thus, in order to examine the scaling of the aerodynamic factors, as related to evaporation, it can be instructive to examine the scaling of momentum transfer from a leaf to a canopy scale. However, one should use this analogy with caution, since the resistances for momentum and mass exchange need not be identical. This is because the source and sink locations for mass and momentum transfer are different in the plant canopies and because momentum transfer is affected additionally by form drag, which has no analogous process to heat and mass transfer (Grace, 1981).

Momentum transfer to a flat leaf, parallel to the wind, is dominated by viscous drag forces. This transfer is defined as:

T| = pu(z)/rm! = pC|U(z)2 (5)

where u is free-stream wind speed at height z, rmi is the aerodynamic resistance to momentum transfer and C| is the leaf drag coefficient for momentum transfer due to viscous drag. After Campbell (1977), rmi and Ci can be defined as:

rmt = 388 (d/u)0.5 (6a)

C| = 1 / (388 u (d/u)0.5) (6b)

Theoretically, C| decreases with increasing u and increases with decreasing leaf width (d). Thus, a decrease in leaf width leads to greater momentum transfer and a smaller aerodynamic resistance.

Momentum transfer to a canopy, on the other hand, is dominated by a combination of form and viscous drag forces. This transfer is defined as

tc = p 1 Cm(z) a ,(z) u(z)2 dz = p u(zr)/rmc = p Cd ufe)2 = p u*2 (7) o

where zr is a reference height, Cm is the effective within-canopy drag coefficient, and u* is the friction velocity. The bulk canopy aerodynamic drag coefficient (Cd) is defined, under near-neutral conditions, as:

Cd = (u/u*)2 (8)

and can be determined under such condition via measurements of wind speed profiles above the canopy (see Bradley, 1972).


Whether or not simple relationships developed for individual leaves hold when extended to a canopy can be examined by considering the effect of leaf width on momentum transfer. Baldocchi et al. (1985a) report that u* was greater over a fully-developed soybean canopy with normal-width leaves than over one with narrow leaves (Fig. 2). On the other hand, slightly greater u* values were observed over the canopy with narrow leaves when the two soybean canopies were not fully-developed.

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FIG. 2. A comparison of friction velocities (u*) measured over a soybean canopy with narrow leaves (CLN) and with normal leaves (CN). The data are from Baldocchi et al. (1985a).

Greater u* values were observed over the fully-developed canopy with normal-width leaves because that canopy had greater leaf area. Since momentum transfer to a plant canopy is influenced primarily by bluff-body effects and mutual sheltering of leaves, any effect on momentum transfer due to the influence of leaf shape on "skin-friction" is overwhelmed. On the other hand, the theoretical influence of leaf width on momentum transfer seems to be manifested when the canopies are not fully-developed. This is probably because lower leaf area indices of the partially-developed canopies result in a reduction of bluff-body effects and mutual sheltering of the leaves.

How well do simple relationships for momentum transfer scale from a leaf to a canopy level? This question can be examined by comparing estimates of u* measured above the canopy with micrometeorological techniques against integrated values (u*\):

u*j = J u(z)2 ai(z) C| dz lo (9)

where h is canopy height.

Integrated friction velocities (9) underestimate u* values, derived with micrometeorological techniques, over soybean canopies by 10 to 30% (Fig. 3a) and over an almond orchard by 60 to 80% (Fig. 3b). This underestimation occurs because: variable leaf orientations lead to a gradation of skin-friction and bluff-body effects; leaves

26 Dennis Baldocchi

in a canopy shelter each other from full exposure to the wind (Thorn, 1971, 1975); canopies sway in the wind, which affects their roughness and the penetration of wind into the canopy (Finnigan, 1985; Bache, 1986); and for the case of the almond orchard, woody biomass extracts an appreciable amount of momentum.

u# , INTEGRATED (m s"' )

FIG. 3. A comparison between friction velocities (u*) measured over two soybean canopies and an almond orchard using micrometeorological techniques and those computed by integrating a leaf-based relationship (Eq. 8). CLN is a soybean isoline with narrow leaves and CN is a soybean isoline with normal-width leaves. These data were derived from measurements discussed in Baldocchi et al. (1985a) in soybean and Baldocchi & Hutchison (1987a; 1987b) in almonds.

The poor agreement between friction velocities estimated with (9) and those measured with micrometeorological methods is expected a priori because the drag coefficient of an isolated leaf is not equal to the effective drag coefficient of leaves, stems and trunks in a canopy layer (Landsberg & Thorn, 1971). Incorporating shelter factors into (9) will improve the scaling of momentum from a leaf to a canopy scale. Shelter factors (P) are computed as the ratio Vxc, where f is the canopy momentum transfer occurring only via viscous forces (f = p u?0 (Thorn, 1971). In practice, the shelter factors are a function of leaf inclination, plant species and the amount and distribution of leaves and woody biomass.

Shelter factors are examined for: a) two soybean canopies with a planophile leaf angle distribution, but with differing leaf width and leaf area; and b) an almond orchard, with an appreciable amount of woody biomass (Fig. 4). Values of P increase with increasing u* and range between about 1.4 and 2.0 in soybeans (Fig. 4a) and between 8 and 13 in an almond orchard (Fig. 4b). The soybean shelter factors agree with the results of Thorn (1971) for a planophile bean canopy. The almond shelter factors are in broad agreement with values observed in a bean canopy with erect foliage.

The leaf area index of the almond orchard was about one-third of the soybean canopies and its foliage was less clumped than that in the soybeans. Yet, the shelter factors for the orchard are on the order of six to seven times larger than those in soybeans. The presence of substantial amounts of woody biomass, which exerts large bluff-body drag on the wind flow, accounts for these large shelter factors. Thus,


information regarding the leaf inclination angles and leaf sheltering, distribution of woody biomass and the drag coefficients of the leaves and woody biomass is essential in scaling momentum transfer from the component level to a wholistic level.

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FIG. 4. The influence of friction velocity (u*) on the sheltering factor (P) in soybeans and almonds. CLN is a soybean isoline with narrow leaves and CN is a soybean isoline with normal-width leaves. These data were derived from measurements discussed in Baldocchi et al. (1985a) in soybeans and Baldocchi & Hutchison (1987a, 1987b) in almonds.

Sheltering in conifers differ from what is observed in broadleaf species. Mutual sheltering in conifers occurs on two scales (Grant, 1984). First, there is sheltering by needles within a shoot, which is important at low wind speeds (less than about 1.5 m s-1). Second, there is mutual sheltering by the shoots themselves in their canopy array, which is important at higher wind speeds.

The models used above, to scale momentum transfer from a leaf to a canopy, are based on "K-theory" (Monteith, 1973; Thorn, 1975). This approach has been criticised because K-theory models assume that turbulence is transported along mean gradients and that the length scales of the turbulence are often small in comparison to the length scales associated with the changes in wind speed or concentration gradients (see Corrsin, 1974; Legg & Monteith, 1975). Many of these assumptions are often violated in practice because within-canopy turbulence is an intermittent process, driven by

a: 2.2

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28 Dennis Baldocchi

predominantly large eddies, and because counter-gradient flow can occur inside a canopy (e.g., Denmead, 1984; Denmead &. Bradley, 1985; Baldocchi & Hutchison, 1987a). Simulation of within-canopy turbulence structure is, thus, improved with higher-order closure and Lagrangian models.

Higher-order closure models, for example, are based on the conservation equations of mean wind velocity, turbulent kinetic energy and momentum stress. They can accourt for counter-gradient flow by considering the divergence of the vertical transport of tangential momentum stress (e.g., Wilson & Shaw, 1977; Meyers & Paw U, 1986). Consequently, they estimate the vertical profiles of momentum transfer reasonably well (Fig. 5).

ÛTOL-M86/547 2

x

u j

0 0 0.2 0.4 0.6 0.8 1.0

TANGENTIAL STRESS (-U' W ' / u» )

FIG. 5. Vertical profile of tangential momentum stress measured in a corn canopy and computed with a third order closure model. (After Meyers & Paw U, 1986).

Several limitations, however, are associated with higher order closure models. Some models rely on K-theory relationships to parameterise third-order moments (Wilson & Shaw, 1977). Other limitations include using mixing lengths to estimate the dissipation rate of turbulent kinetic energy and optimizing drag coefficients to reproduce the mean wind flow structure (see Wilson & Shaw, 1977; Meyers & Paw U, 1986). The parameterisation of the dissipation of turbulent kinetic energy with mixing lengths may be faulty because plant elements can breakdown the length scales of turbulent energy and accelerate the rate of the energy cascade in the inertial subrange (Shaw & Seginer, 1985; Baldocchi & Hutchison, 1987b).

Lagrangian models are based on the simulation of the dispersion of an ensemble of marked fluid particles (Finnigan & Raupach, 1987; Raupach, 1987). The utility of Lagrangian models, however, is limited by the need to specify length and time scales and the wind field. Furthermore, no Lagrangian models have yet been developed to estimate canopy evaporation.

K-theory models are least valid when they are used to estimate within-canopy water vapour, heat and CO2 exchange (see Legg & Monteith, 1975). These entities have strong source-sink regions in the canopy, which affect the curvature of their respective profiles. On the other hand, Bache (1986) and Meyers (1987) argue that K-theory models can be used for some applications. Bache (1986) shows that K-theory models work well for momentum transfer in the upper portion of typical plant canopies because


turbulent length scales are smaller than the length scales associated with vertical variations in the wind speed gradient. Errors introduced by not considering counter-gradient transport of momentum are generally small, since this phenomenon occurs deep inside the canopy, where little momentum transfer occurs. Meyers (1987) concludes that fluxes of some pollutant gases, e.g., SO2 and O3, can be computed accurately with multiple resistance models because concentration gradients of some pollutants are generally weak inside a plant canopy and because the transfer is generally directed downward, as with momentum transfer.

Stomatal regulation

The amount of water vapour evaporating from a leaf is strongly controlled by the stomata. The degree of stomatal control is usually quantified in terms of the stomatal conductance, or its inverse the resistance. The stomatal conductance of a leaf is a non-linear function of light, leaf temperature, carbon dioxide concentration, humidity, leaf water potential, leaf age and position, acclimation, and species (e.g., Jarvis, 1976; Korner et al., 1979; Jarvis et al., 1985; Chazdon & Pearcy, 1986). Stomatal conductance of a leaf is often scaled up to a canopy by coupling leaf-level process models with a canopy radiative transfer model and microclimate model (e.g., Norman, 1982; Jarvis et al., 1985; Baldocchi et al., 1987; Baldocchi & Hutchison, 1986).

The functional relationship between canopy stomatal conductance (gc) and photosynthetically active radiation (PAR) can be computed by weighting leaf conductances according to the amount of sunlit and shaded leaf area and the flux densities of PAR incident on those leaves:

F gc(PAR) = J (gs(ls(f))ALs(f) + gs(lsh(f))AUh(f)) df (10)

0

where gs is the stomatal conductance for the leaf, F is the cumulative leaf area index of the canopy, ls and lSh are the flux densities of PAR on the sunlit and shaded leaves, respectively, and ALg and ALgh are the differences in sunlit and shaded leaf area, respectively, at a particular leaf area f. The canopy stomatal conductance can be computed by introducing multiplicative factors in to (10) that are functions of temperature, leaf water potential and humidity (Jarvis, 1976). These functions range between zero and one and can vary with height in the canopy due to vertical variations in leaf temperature, humidity, water potential, age and adaptation.

How well leaf stomatal conductance scales up to a canopy value depends, in part, on the accuracy of estimating the microclimatic variables that drive the submodels. As an example, we can compare the estimates of stomatal conductance derived from measured profiles of photosynthetically active radiation (PAR) against conductance values derived from theoretical PAR profiles.

Theoretical estimates of PAR in a plant canopy are often based on the assumption that a canopy can be abstracted as a turbid medium, with its foliage being randomly distributed in space and having a spherical leaf inclination angle distribution (Norman, 1979; Ross, 1981). Using these assumptions, a simple canopy radiative transfer model can be formulated based on the Poisson distribution (see Lemeur & Blad, 1974; Norman, 1979).

Fig. 6 shows that stomatal conductances in a deciduous forest are underestimated when computed with a canopy radiative transfer model based on the

30 Dennis Baldocchi

Poisson distribution. The foliage distribution of a deciduous forest, however, is not random, but is clumped. A canopy radiative transfer model, based on the negative binomial distribution, accounts for clumping of the foliage (Baldocchi & Hutchison, 1986). However, this distribution leads to an overestimate in canopy sîomatal conductance.

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FIG. 6. Mean daily vertical profile of canopy sîomatal conductance in a deciduous forest computed from photosynthetically active radiation (PAR) profiles measured and computed with the spherical and negative binomial canopy radiative transfer models. (After Baldocchi & Hutchison, 1986).

These errors, in the estimates of gc(PAR), are associated with errors in modelling canopy radiative transfer processes. In the case of a deciduous forest, the optical properties of the clumped leaves may differ from those of individual leaves since light can be trapped in the clumps (Norman & Jarvis, 1975). Secondly, clumped foliage permits greater beam penetration to a given layer than if the foliage is randomly distributed. Thus, the Poisson radiative transfer model underestimates the penetration of beam radiation into a clumped canopy (Lemeur & Blad, 1974; Baldocchi & Hutchison, 1986). Consequently, sunlit and shaded leaf area and the flux density of radiation on those leaves are also underestimated. Thirdly, tall vegetation casts a substantial amount of penumbral shade (Norman & Jarvis, 1975; Baldocchi et al., 1986). Penumbral shade presents a large potential source of error in the scaling of stomatal conductance from a leaf to a canopy. This is because shaded leaves are often not light saturated and are, thus, very responsive to small changes in PAR caused by the penumbra. Fourthly, a canopy cannot always be abstracted as a turbid medium. Plants may be arrayed in rows or in discontinuous clumps. The ellipsoid, three-dimensional model of Norman and Welles (1983) and the procedural approach of Myneni & Impens (1985) account for the effect of spatial variability on radiative transfer in non-continuous plant canopies.

In spite of the theoretical problems associated with modelling radiative transfer in plant canopies, errors in the estimates of canopy stomatal conductance, discussed above, are relatively small; they are on the order of ± 10%. Thus, for many applications, the scaling of stomatal conductance for a leaf to a canopy, using simple canopy radiative transfer models, may be acceptable.


Further improvements in the estimate of integrated canopy stomatal resistance can be brought about by incorporating estimates of the vertical variation in leaf temperature and humidity by considering the leaf energy balance (see Paw U et al., 1985; Meyers & Paw U, 1987). Studies of stomatal dynamics in fluctuating light environments show that induction effects may also need to be considered. Chazdon & Pearcy (1986) report that leaves exposed to saturating light, following a long period at low light levels, need about 1000 to 2000 seconds to reach steady-state conditions.

Bulk canopy stomatal resistance is generally estimated using either a top-down approach, via the Penman-Monteith equation (3), or a bottom-up approach, using either the ratio between the mean measured stomatal resistance and leaf area index, or an integrated value based on the calculated stomatal resistance of individual leaves (Jarvis et ai, 1985; Baldocchi et ai, 1987). Recently, Finnigan & Raupach (1987) show that canopy stomatal resistance computed from the top-down approach does not equal that computed via the bottom-up approach; under certain conditions these two estimates of canopy stomatal resistance can differ by a factor of two. They show theoretically that the Penman-Monteith canopy stomatal resistance is not only composed of the parallel, area-weighted sum of resistances of individual leaves, but that rsc is also a function of the vertical variation in available net radiation and the aerodynamic resistances. Additionally, the Penman-Monteith canopy resistance is influenced by soil evaporation (see Denmead, 1984; Shuttleworth & Wallace, 1985).

Experimental and inferential evidence from a soybean canopy supports the conclusions of Finnigan & Raupach (1987). Fig. 7 shows that integrated estimates of canopy stomatal resistance are consistently 30 to 50% smaller than the Penman-Monteith estimates for periods when the water status of the canopy ranged from well-watered to water-stressed conditions. On the other hand, the integrated canopy stomatal resistances are about 5 to 30% greater than estimates derived from porometer measurements. These differences, however, are primarily due to a biased field-sampling and weighting of the sunlit leaves.

20 50 (OO 200 CANOPY STOMATAL RESISTANCE (s m_l)

FIG. 7. Comparison between canopy stomatal resistance for water vapour computed with the model of Baldocchi et al. (1987) and two estimates of canopy stomatal resistance derived from measurements. The measured estimates are: the ratio between the mean stomatal resistance of sunlit leaves in the upper canopy and leaf area index (open circles); and the Penman-Monteith equation (Monteith, 1973) (closed circles). (After Baldocchi et al., 1987).

32 Dennis Baldocchi

Fortunately, errors attributed to the different estimates in canopy stomatal resistance will not yield great errors in canopy evaporation computed with the Penman-Monteith equation, due to its non-linear dependence on canopy stomatal resistance (Finnigan & Raupach, 1987). On the other hand, transpiration measurements should be used with caution to compute a bulk canopy stomatal resistance because the associated non-linearities can result in great errors in canopy resistance estimates.

SCALING EVAPORATION

There are several processes associated with evaporation that operate differently or are insignificant on a leaf or a canopy scale. Below we discuss five cases as they relate to leaf and canopy evaporation. They are: the inter-relationship between evaporation, humidity and stomatal conductance; the effect of leaf width on evaporation; advection; canopy heat storage; and soil evaporation.

Evaporation-humidity-stomatal conductance interaction

If the stomatal conductances of leaves were always constant, leaf transpiration would increase linearly with increasing leaf-air vapour pressure deficits. Physiological evidence, however, shows complex feedback and feedforward responses between leaf transpiration, leaf-air vapour pressure deficits and stomatal conductance (Schulze et al., 1972; Schulze, 1986; Farquhar, 1978; Jarvis, 1980; Mansfield, 1985). For example, a change in the leaf-air vapour pressure deficit can simultaneously affect the leaf in three direct ways: by changing stomatal and cuticular transpiration; via a direct effect on leaf conductance; and via effects of humidity on photosynthesis (Schulze, 1986). These primary responses can also initiate secondary responses. Increasing transpiration will affect the water potential of the mesophyll cells, which has a feedback on stomatal conductance through hydraulic or metabolic responses. Consequently, as the stomata close transpiration will decrease and the water deficit will be corrected (Mansfield, 1985; Schulze, 1986). This reduction in transpiration, however, can lead to an increase in leaf temperature, an exponential increase is the saturated humidity of the leaf, a greater leaf-air humidity and a greater evaporative demand.

Field measurements on individual conifer shoots shows that transpiration increases with increasing vapour pressure deficits at small deficits and reaches an asymptote at large deficits and that stomatal conductance decreases with increasing vapour pressure deficits (Sanford & Jarvis, 1986). On a canopy scale, the interactions between canopy evaporation, vapour pressure deficits and canopy resistance can be mediated in a different manner. For example, evaporation of a soybean canopy seems to decrease with increasing vapour pressure deficits (Fig. 8). This response, however, is due primarily to a drought-induced reduction in soil water, which leads to stomatal closure and reduces canopy evaporation (Fig. 9). It is this reduction in canopy evaporation that, consequently, increases the ambient vapour pressure deficit above the crop. The physiological status of this canopy, thus, affects the humidity of the surrounding air through its evaporation. On the other hand, we cannot claim whether or not a direct vapour pressure effect simultaneously exerts a secondary influence on the relationship between evaporation and stomatal resistance as the soil dries.

A decrease in canopy evaporation with increasing D is not a universal response. Evaporation of a well-watered deciduous forest can increase with increasing D over a


ATDL-MB7/673

FIG. 8. The relationship between the ratio of latent heat flux to net radiation (LE/Rn) and vapour pressure deficit (D) over a soybean canopy. Data are from Baldocchi et al. (1985b).

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FIG. 9. The relationship between LE/Rn and canopy stomatal resistance (rc), computed as the ratio between the mean sunlit stomatal resistances in the upper canopy and leaf area index. (After Baldocchi et al., 1985b).

wide range of conditions (Fig. 10). Here increasing D increases the potential for evaporation. Above a Douglas fir forest, Tan et al. (1978) found evaporation to increase with D at low deficits and decrease at high deficits.

Differences in the response of the evaporation rates of leaves and forest and crop canopies to D can be explained in terms of the coupling between canopies and leaves and their environment. McNaughton & Jarvis (1983) and Jarvis & McNaughton (1986) noted that there was a conflict in the evaporation literature in regards to scaling evaporation from a leaf to a canopy. They observed, in the physiological literature, that evaporation was claimed to be controlled by stomatal conductance and D. In the meteorological literature, emphasis was placed on the influence of available net radiation

34 Dennis Baldocchi

for controlling evaporation. They concluded that the response of leaf or canopy evaporation to a variation in a controlling factor is affected by how well the leaf or canopy is coupled to its environment. They re-expressed the Penman-Monteith evaporation equation (3) in terms of an Omega factor, which is a function of the stomatal and aerodynamic resistances and acts as an index of coupling.

Ec= OEeq + (1 - 0 ) E j (11)

where Eeq and Ej are equilibrium and imposed evaporation, respectively. The vapour pressure deficit at the effective canopy surface (Do) is

Do = O Dea + (1 - O) Dn (12)

where Deq is the equilibrium saturation vapour deficit and Dm the saturation vapour deficit in the mixed layer. Rough, tall canopies, like coniferous and deciduous forests, have low Omega values (approaching zero). These canopies are well coupled to their environment, causing Ec to respond sensitively to Dm and rsc and to respond less sensitively to net radiation, as has been observed by Tan et al. (1978) for a Douglas fir stand and is shown in Fig. 10. On the other hand, short smooth crops, like soybeans and alfalfa, have high Omega values (approaching one) and are relatively decoupled from the vapour pressure deficit of their environment. Evaporation of smooth crops responds strongly to changes in net radiation and does not respond strongly to changes in Dm and rso. For example, Van Bavel (1967) shows that it takes a ten-fold increase in canopy resistance to reduce evaporation of alfalfa by half, while Fig. 9 shows a similar relationship for soybeans.

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FIG. 10. The relationship between the ratio of latent heat flux to net radiation (LE/Rn) and vapour pressure deficit (D) over a deciduous forest. (After Verma et al., 1986).

Leaf width effects

From an aerodynamic perspective, a reduction in leaf width reduces the boundary-layer resistance to water vapour transfer, which can lead to an increase in evaporation (Eqs. 1 and 4), assuming no complex leaf transpiration/temperature interactions (Parkhurst &


Loucks, 1972). Such an increase in evaporation over a canopy with narrow leaves is not found. Baldocchi et al. (1985a) report that latent heat exchange is reduced over a soybean canopy with narrow leaves (Fig. 11). This occurs because net radiation penetrates deeper into the canopy with narrow leaves, which increases soil heat exchange and alters the partitioning of Rn into latent heat exchange. The differences in latent heat exchange between soybean canopies with different leaf widths vary with canopy development. Differences in latent heat exchange are large (20 to 40%) before canopy closure and are small (about 10%) after canopy closure.

ATDL-M67/683

-600

_ - 4 0 0

'E 3

- 2 0 0

0 0 -200 -400 -600

LE (W m"2) CN

FIG. 11. A comparison between latent heat exchange (LE) of a soybean canopy with narrow leaves (CLN) and one with normal leaves (CN). (After Baldocchi et al., 1985a).

Advection

Advection is defined as the transport of an atmospheric property by the motion of the atmosphere. Conceptually, the evaporation of a vegetated surface is enhanced by the horizontal advection of dry air (u dD/dx < 0) and depressed by the advection of moist air (u 3D/3x > 0). Evaporation, however, can remain unchanged with the advection of heat and humidity if the potential saturation deficit remains unchanged (see McNaughton & Jarvis, 1983).

In relation to the evaporative processes, advection can be significant on several scales. Regional advection occurs on the scale of tens and hundreds of kilometers. It arises from the adjustment of the planetary boundary layer due to regional variations in land use and surface conductance (see Jarvis & McNaughton, 1986). Local advection occurs on the scale of tens and hundreds of meters. It generally arises from the adjustment of the surface boundary layer caused by adjacent fields differing in roughness, water status and evaporation potential. Irregular terrain and shadows, caused by scattered clouds, can also cause advection and affect evaporation of a crop or forest. On a smaller scale, inter-row advection can be significant in crops with incomplete cover. For example, sensible heat generated between rows can be advected laterally to enhance the evaporation of a row crop (Hanks et al., 1971).

n = 3 0

t = 5.55

. - *

36 Dennis Baldocchi

On the length scale of a leaf, advective effects can occur since considerable temperature gradients have been observed across a leaf (see Clark & Wigley, 1975). These effects, however, are generally assumed to be small and are generally neglected in canopy models since volume averaging is involved in the computation of fluxes and profiles.

Canopy Heat Storage

Enough woody biomass is present in forests and orchards to significantly alter the partitioning of net radiation into latent and sensible heat via the storage of heat in the woody biomass. The storage term of a mixed forest (McCaughey, 1985) and a tropical forest (Moore & Fisch, 1986) can be on the order of 5 to 10% of net radiation. Computations of biomass heat storage must be incorporated into mufti-layer canopy heat and mass exchange models of tree canopies. To properly evaluate the biomass storage of heat, the vertical distribution of the radial heat transfer in trunks and stems must be computed (see Moore & Fisch, 1986). This computation relies on measurements of biomass temperature and on information about the average vertical biomass distribution, and thermal conductivity and specific heat of the biomass.

So/7 Evaporation

Soil evaporation depends on soil wetness, the amount of net radiation available at the surface and the amount of soil litter. Evaporation from a forest floor can account for up to 40% of total evaporation after a rainfall event (Denmead, 1984). This value, however, is inversely proportional to the number of days after the rainfall event. Whether or not the soil surface is covered with detritus also affects soil evaporation. Denmead (1984) states that evaporation from a forest floor covered with litter typically ranges between 10 and 30% of total vapour toss, which is about one-half of what is expected from a bare exposed soil.

EVAPORATION MODELS

An indication of our current ability to scale leaf evaporation to a canopy level can be determined by comparisons between integrated, multi-layer evaporation models and measurements of canopy evaporation. The ability to scale evaporation may differ for a forest and an agricultural crop canopy. Thus, we present a case for each canopy type.

Fig. 12a compares latent heat fluxes measured over Sitka spruce {Picea sitchensis) against fluxes computed with the multi-layer model of Jarvis ef a/. (1985). Some differences between measured and modelled values of latent heat exchange are observed. However, Jarvis et al. (1985) conclude that the model estimates are quite good considering the errors associated with the measurements, which were based on the Bowen ratio technique.

The structure of a forest both simplifies and complicates the task of scaling evaporation. Because a forest canopy is aerodynamically rough, the aerodynamic resistances are much smaller than the surface resistances (Tan & Black, 1976; Verma et al., 1986). Thus, limitations in our ability to model canopy turbulence do not lead to great errors in the integrated estimate of canopy evaporation. For example, Tan ef al. (1978) show that reasonable estimates of evaporation from a Douglas-fir forest can be computed based on simple measurements of vapour pressure deficit, stomatal resistance and leaf


area index. On the other hand, canopy heat storage strongly influences the partitioning of net radiation into latent heat exchange. The past treatment of canopy heat storage in multi-layer models has often been crude, at best, or ignored. Recent work by Moore & Fisch (1986) improves upon the estimate of canopy storage. However, this treatment needs to be incorporated into multi-layer canopy evaporation models.

Fig. 12b. compares latent heat fluxes measured over soybeans, with the Bowen ratio technique, against values computed with a third order closure model (Paw U et ai, 1985). Here the agreement is quite good. The improvements in turbulence modelling, brought about by higher order closure models, seems to improve our ability to model evaporation of crops.

6 8 10 (2 14 16 18 0 100 200 3 0 0 4 0 0 5 0 0

T IME, GMT THIRD ORDER CLOSURE MODEL, LE (Wm" 2 }

FIG. 12. Comparisons measured and modelled fluxes of latent heat, (a) Sitka spruce forest. (After Jarvis et al., 1985). The solid line represents calculated values and the dashed line represents measured values. The shaded area represents the range of calculated values as the radiation regime ranges from 100% direct radiation to 100% diffuse radiation, (b) Soybean canopy. (Adapted from Paw U et al., 1985).

Since the aerodynamic resistances of agricultural crops are of a similar magnitude as the stomatal resistances, sophisticated turbulence models should be used in modelling crop evaporation. Higher order closure models are more accessible and are relatively easy to implement on desk-top computers (Meyers & Paw U, 1986). However, as discussed above, these models are not the final solution to the scaling problem since improvement in the parameterisation of certain terms is still needed and additional modelling parameters are needed in the more complex models.

CONCLUSIONS

The ability to scale evaporative exchange from a leaf to a canopy depends on many factors. These include the degree of canopy development, the degree of coupling between the plant or canopy and its environment, the relative differences between the aerodynamic and the surface resistances and whether or not certain process are operating at one scale, but not on the other.

38 Dennis Baldocchi

For the case of momentum transfer, it is difficult to scale leaf-level relationships to a fully-developed canopy because of bluff-body effects and the influence of mutual sheltering of leaves. Higher order closure models improve upon treatments based on K-theory models. However, improvement in the parameterisation of certain terms is needed. Simple scaling arguments for momentum transfer are reasonable when the canopy is small. This is because the leaves are not greatly sheltered and they are relatively parallel to the wind flow. Furthermore, errors attributed to the scaling of the aerodynamic resistance do not lead to great errors in the scaling of evaporation when the aerodynamic resistances are much smaller than the canopy resistances.

The phenomena of penumbral shade, soil evaporation, advection and canopy heat storage are examples of processes that operate at one scale but are inoperative or operate differently at other scales. Stomata are very sensitive to penumbral shade since often the irradiance in this shade is at levels where the stomata are not light-saturated and are very responsive to light. Canopy radiative transfer models should accommodate this phenomenon for use in tall vegetation. Consideration of advection is important since it can enhance or depress the evaporation of water vapour. Canopy heat storage, soil heat flux and evaporation need to be considered since they affect the amount of net radiation available for latent heat exchange by the canopy.

Comparisons between computations of canopy evaporation made with multi-layer models agree fairly well with measurements. This agreement may be fortuitous due to cancelling errors, because there are many complex component processes they do not simulate well or ignore.

In conclusion, we must concur with Jarvis & McNaughton (1986): "one cannot naively extrapolate directly from one scale to the next".

Whenever we attempt to scale biophysical processes, such as evaporation, we must be cognisant of the factors influencing scaling and make measurements and computational extrapolations appropriately.

ACKNOWLEDGEMENTS

This work was partially supported by the U.S. Department of Energy and the National Oceanic and Atmospheric Administration as a contribution to the National Acid Precipitation Assessment Program (Task Group on Deposition Monitoring). The author is grateful for comments by Drs. B.A. Hutchison, T.P. Meyers, P. G. Jarvis and T.A. Black.

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