a canopy stomatal resistance model for gaseous deposition to

~rnospkric l?~~~iromunr Vol. 21. No. I. pp. 91-101. 1987 Printed in Gnxr B&in.

ooo4-69al/s?s1.00+0.00 Pergmon Jourmlr Ltd.

A CANOPY STOMATAL RESISTANCE MODEL FOR GASEOUS DEPOSITION TO VEGETATED SURFACES

DENNIS D. BALDOCCHI, BRUCE B. HICKS and PAMELA CAMARA*

Atmospheric Turbulence and Diffusion Division, Air Resources Laboratory/NOAA, P.O. Box 2456. Oak Ridge, TN 37831. U.S.A.

(First received 24 December 1985 and in_fi~ljon 27 June 1986)

Abstract-A gaseous deposition model, based on a realistic canopy stomata1 resistance submodel, is described, anal@ and tested. This model is designed as one of a hierarchy of simulations, leading up to a “big-leaf” model of the processes contributing to the exchange of trace gases between the atmosphere and vegetated surfaas. Computations show that differences in plant species and environmental and physiological conditions can affect the canopy stomatal resistance by a factor of four. Canopy stomata1 r&stances to water vapor transfer computed with the present model arc compared against values measured with a poromcter and computed with the Penman-Montcith equation. Computed stomata1 resistances from a soybean canopy in both well-watered and water-stressed conditions yield good agreement with test data. The stomata1 resistance submodcl responds well to changing environmental and physiological conditions. Model predictions of deposition velociticsareevaluated for the case of ozone, transferred to maize. Calculated deposition velocities of 0, overestimate measured values on the average by about 30%. probably largely as a consequence of uncertainties in leaf area index, soil and cuticle resistances, and other modeling parameters, but also partially due to imperfect measurement of O3 deposition velocities.

Key word index: Dry deposition, stomata1 conductance, environmental physiology, micrometeorology.

I. INTRODUCTION

The consequence of deposition of gaseous pollutants to vegetated surfaces is perceived by many to be one of the major environmental problems of our time. Gaseous deposition is popularly identified as a major factor damaging forests in eastern North America and Europe, and as a possible contributor to the elimi- nation of aquatic life in some Adirondack and Scandanavian Lakes. Assessments of area-wide deposition budgets are presently hindered by the inability to compute (or model) trace gas exchange with specific kinds of vegetation; the ability to decide on the comparative adequacy of potential emission control strategies is correspondingly limited. An important task confronting the atmosphere-surface exchange community is therefore to develop better methods to quantify flux densities of gaseous pollutants to land- scapes, both for inclusion in larger scale numerical models and for use in interpreting air chemistry observations made in areas of special interest.

The flux density of a gaseous pollutant that is known to be depositing at the surface can be expressed as the product of the mean concentration of the pollutant (C) and an appropriate deposition velocity (IQ). For many chemical species of interest, mean concentrations atn he measured using available technology. The deposition velocity, on the other hand, is difficult to

l Formerly Lowell University, presently State University of New York, Albany.

determine, since it depends on the chemical species and is a function on many meteorological, biological and surface variables (see Sehmel, 1980; Hosker and Lindberg, 1982; Hosker, 1986).

Most efforts to model and parameterize Up employ a “big-leaf “, multiple-resistance analog model (Wesely and Hicks, 1977; O’Dell et al, 1977; Unsworth, 1980; Sehmel, 1980; Hosker and Lindberg, 1982; Hicks, 1984). Such big-leaf models are one-dimensional and are most applicable over relatively tlat, horizontally homogeneous terrain. The most important individual resistances to pollutant transfer are usually identified as an aerodynamic resistance (R,,) associated with atmospheric turbulence, a quasi-laminar boundary layer resistance (RJ which is influenced by the diffusivity of the material being transferred, and a net canopy resistance (&) which is dominated by surface factors (mainly biological, see Fig l).t To a large extent, it is the uncertainty surrounding specification of the canopy resistance which has limited abilities to infer dry deposition rates from air concentration data. Although this uncertainty is often large, big-leaf models are being applied to infer rates of pollutant uptake in a trial dry deposition monitoring network presently operational in North America (Hicks er al.. 1985). The inclusion of simple ecophysiological con-

t For clarity, upper case symbols will be used to signify rcaistanas asaociatcd with the whok anopy, as in a big-kaf model. Lower aae symbols are used for the corresponding quantities expressed as an individual-kaf basis.

91

1 c STONE B OTHER -- MATEd?IALS

PLANT TISSUE

WATER SURFACES

Fig. 1. Pathway of resistances to the deposition of gaseous pollutants. The dotted line illustrates a probable route for

SO2 transfer.

cepts into such models is needed to make them adaptable to different vegetated surfaces and regions.

The canopy resistance is a function of environ- meatai and physiological conditions, surface wetness and chemistry, leaf area index, and diffusivity of the pollutant (Jarvis, 1971, I976; Turner et al., 1973; Sehmel, 1980; Unsworth, 1980; Hosker and Linderg, 1982). In comparison, the aerodynamic and quasi- laminar components are relatively simple products of factors not strongly influenced by the physiology of the surface. For a gas such as SO*, R, is known to be influenced by stomatal (R,) and (somewhat less cer- tainly) mesophyll (R_) resistances, which are in series with each other, and are in paraIM with resistances exerted by the leaf cuticle fk), the soil CR,&, surface wetness (R,,& and any other surface material CR,& (Unsworth, 1986 Hosker and Lindberg, 1982; Hicks, 1984; Hosker, 1986). High ambient pollutant concentrations can ah0 influence the canopy resistance to pollutant uptake by increasing or decreasing stomatal resirtdnce (Black, 1982).

To our knowledge the only gaseous deposition model which estimates canopy stomata1 resistance on the basis of sunlit and shaded leaf area is that of Murphy ef al. (1977), for loblolly pine. The generality of their model, however, is limited by its dependence on empirically derived, species-specific, attenuation coefficients for beam and diffuse radiation. The model also does not consider the effects of other environmental and physiolo~~l variables on stomata1 resistance.

Here, we develop a canopy stomata1 resistance submodel which couples a canopy radiative transfer model (see Norman, 1979, 1982) with a leaf stomata1 resistance model (see Jarvis, 19763, and incorporate the submodel into a “big-leaf”, resistance-analog, gaseous deposition model. The objectives of this paper are: (1) to present and discuss this gaseous deposition model and canopy stomata1 resistance submodel; (2) to examine the effects of environmental, physiological and structural variables and plant species on the canopy stomata1 resistance of several ~l~utant gases; and (31 to compare computed deposition velocities, based on this model. against measured vatues.

It is usual to take the canopy-level aerodynamic, quasi-laminar boundary layer and canopy resistances to be in series. Thus, v,, is computed as:

Many measurements of canopy resistance to gaseous deposition are available in the literature (e.g. Bennett and Hill, 1973; Fowler, 1978; Fowler and Unsworth, 1979; Wcsely et al., 1978, 1982; Leuning et al., 19X& 1979b; Lenschow et al., 1982; Hicks et al., 1982; Fowkr and Cape, 1983; Greenhut, i983). A much greater level of attentjon has been focused on the resistance components at the individual-l~f level; the

v, = 1 /(R,, + R4 + R,). (1)

The aer~y~mic resistance is the resistance to mass or energy transfer exerted by the turbulent internal bcmnd:trv l;tvcr bctwecn ;I hckht L’ :tnd thy’ surf:tcc.

ATMOSPHERIC SOURCE

AERODYNAMIC. R,

DIFFUSIVE BOUNBARY, Rb

STOMATA PLANT TISSUE

92 DENNIS D. BALDOCCHI er d.

way in which these detailed resistances can be com- bined to represent the behavior of an entire vegetated canopy are still not well understood. All studies have shown, however, that stomata1 resistance is the most dynamic and most influential resistance to 03, SO2 and NO, transfer, when the canopy is dry.

Most gaseous deposition models (e.g. Turner et al., 1974; Waggoner, 1975; Belot et al., 1976; Fowler and Unsworth, 1979; Unsworth, 1980) treat the role of foliar-element stomata1 resistance (rr) without considering the detailed role of radiation and other controlling factors, most of which vary with height within a canopy. In concept, it appears preferable to compute canopy stomata1 resistance (R,) on the basis of the irradiance on both sunlit and shaded leaves and weighting these resistances according to the fraction of sunlit and shaded leaf area (Murphy et al., 1977; Norman, 1982). This approach is preferred because the stomata1 resistance responds non-linearly to light (Turner and Begg, 1974; Jarvis, 1976). Since the light environment within a vegetated canopy is quite complex, the canopy stomata1 resistance to gaseous deposition should be computed by coupling a leaf resistance model with a canopy radiation transfer model.

2. THEORY

, _

characterized by a displacement height (d) and a roughness length (zO). This resistance is a function of wind speed, surface properties and atmospheric stability. It can be expressed as:

R, = (k a*)-’ [In ((~-d)l~~)-hl

or under near neutral conditions as:

04

R, = u/u: (W

where u is windspeed, ut is friction velocity, k is von Karman’s constant (k = OAO), and Jl,, is the integral form of the diabatic stability correction for heat and mass transfer.

D, and Di are the molecular diffusivities for water vapor and the pollutant gas, respectively, and are incorporated into Equation (6) to extend the standard formulation to the case of a general trace gas that is transferred via stomata. Values of the functions g(T), g(JI) and g(D) range from 0 to 1. Equation (6) can be expanded to incorporate additional elfects (such as the physiological effects of other pollutants) by introduc- ing further multiplicative factors.

The response of stomata1 resistance to PAR is estimated using a rectangular hyperbola relationship (Turner and Begg, 1974):

The quasi-laminar boundary layer resistance is an “excess” resistance which is introduced because the resistance to mass and energy transfer is different from that for momentum (see Thorn, 1975; Hicks, 1984; Hosker, 1986). In the immediate vicinity of a surface, mass and energy transfer are controlled by the molecular properties of the fluid, whereas the rate of momentum transfer is inlluenced by bluff-body effects of the surface elements-a process which has no precise analog in cases of heat and mass transfer. The “excess” resistance is a function of wind speed and surface properties and can be conveniently written as:

r,(PAR) = r,(min)+ b,,r,(min)/PAR (7a)

g,(PAR) = l/r,(PAR) (W

where r,(min) is the minimum stomata1 resistance under optimal conditions and b, is a constant equal to the PAR flux density at twice the minimum stomata1 resistance. Korner et al. (1979) and Pospilova and Solarova (1980) provide a comprehensive survey of minimum stomata1 resistances of many native and cultivated plants.

Rb = Cl l(k u,)l IIn (~o/zc)l (3)

where z, is the roughness length for the pollutant or entity under investigation.

The canopy stomata1 conductance (G,) is computed as a function of PAR according to the fractions of sunlit and shaded leaf area and the PAR flux densities on those leaves:

Since the roughness length, zc, is dillicult to evaluate, the quasi-laminar resistance is often expressed in terms of the inverse Stanton number (B) (Owen and Thompson, 1963; Chamberlain, 1966):

k u* Rb = k Be1 = In (zO/zr). (4)

Empirical evidence indicates that kB_’ can be estimated in terms of the surface roughness, Reynolds number and the Schmidt number (see Garratt and Hicks, 1973; Brutsaert, 1975).

‘Z(PAR) = s )Jf,,,(J)dPAL(1)1

+%-,,deU)O’&,,a,,eU)l df (8)

wherejis leaf area, dj;,, and dfrbde are the differences in sunlit (/,,,) and shaded (Itide) leaf areas, respectively, betweenjandj+ dfand PA&,, and PAhhade are the flux densities of PAR on sunlit and shaded leaves, respectively.

The canopy resistance (R,) is computed as:

where R, is the canopy stomata1 resistance, R, is the canopy mesophyll resistance, and the remaining sub- scripts are self-explanatory.

Stomata1 resistance of a leaf is primarily a function of photosynthetically active radiation (PAR), air temperature (T), leaf water potential (IL) and vapor pressure deficit (D). To a lesser extent it is dependent on CO1 concentration and the concentrations of many lrace gases in the atmosphere.

In order to compute I,,, , j;ude, PAR,,,, and PAhb,, a canopy radiative transfer model must be introduced. Sunlit leaf area is a function of solar elevation, the leaf orientation distribution and cumu- lative leaf area. The functional relationship for sunlit leaf area is derived on the assumption that the foliage in a canopy is randomly distributed in space and that the distribution of leaf inclination angles is spherical. This assumption is reasonable for many agricultural and forest canopies (Lemeur, 1973; Jarvis and Leverenz, 1983). Based on this assumption the cumu- lative sunlit leaf area between the top of the canopy and a level inside the canopy (I) is computed as:

Jarvis (1976) prcscnts ;I model for 111~ clnnputittion of the stomata1 resistance (rr) to water vapor transfer of a leaf that is biologically and physically realistic. It is a multiplicative model which is expressed in terms of stomata1 conductance (g,), the inverse of r,. Stomata1 conductance for a leaf is computed as the product of the functional relationships for PAR, T, D and $:

L (/) = [I - exp (- 0.5/b UN1 2 sin VI (9)

where /f is the solar elevation angle. The shndcd leaI area is expressed as:

LJUL (/) = /-/,,” * (10)

The flux density of PAR incident on a sunlit leaf is a function of direct and diffuse radiation penetrating through the canopy and scattered mdiation generated . . by the transmission and reflection of intercepted 91 =s(PAR)g(T)g(D)s(IL)D,lDi. (6)

A canopy stomata1 resistance model for gaseous deposition to vegetated surfaces 93

94 DENNIS D. BALDOCCHI et al.

radiation. PAR,,,, is also dependent on the mean angle between leaves and the sun. PAR flux densities within the canopy are computed with the radiation transfer model reported by Norman (1979, 1982). The flux density of FAR on the sunlit leaves is:

PA&, (I) = PA%, cos @)/sin (8) + PA&,, (f) (II)

where PA%, is the flux density of direct PAR above the canopy and a is the angle between a leaf and the sun. For a canopy with a spherical leaf inclination distribution a can be assumed constant at 60 degrees.

PAR,,,,& is computed semi-empirically using Norman (1982):

PA&,(/) = PA&, exp (- O.Sj O.‘)

+0.07 PAR,,(l.l -O.l/)

xexp[-sin(j?)]. (12)

Equations (9)-(12) are generally evaluated for differences in f (dj) of less than 0.25 to minimize the influence of leaf overlap.

Stomata1 conductance increases with increasing temperature until a threshold temperature, after which it decreases. This dependence on temperature is the result of energy balance feedbacks between humidity and transpiration of the leaf (see Schulz and Hall, 1982) and the influence of temperature on enzymes associated with stomata1 operation (Jarvis and Morison, 198 1). The response of stomata] conductance to temperature (T) is computed using the relationship presented by Jarvis (1976):

g(V= lI(T-T&~)l(TO-T~in)l C(T--TT)/

(T,,, - To)lb~ (13)

where Tmin and T_ are the minimum and maximum temperatures at which stomata1 closure occurs, To is the optimum temperature and b, is defined as b,

= V,, - To)/(T- - Knin). Stomata1 conductance is linearly related to vapor

pressure deficit (D):

g(D) = 1 -b,D

where b, is a constant.

(14)

Water stress can be quantified in terms of leaf water potential ($), a thermodynamic quantity. Stomata1 conductance is relatively independent of $ until it drops below a threshold value (tie), after which the stomata close rapidly. The function g($) is computed using a discontinuous linear model (Fisher et al., 198 1) since parameters for this model are readily available in the literature (e.g. Pospisilova and Solarova, 1980). This function is expressed as:

SW = 1, if*>*0 UW

and as:

8($) = a$ + b,, if$<ti0 WV

where a and b, are constants.

We assume that temperature, vapor pressure deficit and leaf water potential are constant with height in the canopy. The canopy stomata] resistance is thus computed by combining Equations (8), (13), (14) and (15):

After a pollutant gas diffuses through a stomata] pore it comes into contact with the moist environment of the leaf mesophyll. The resistance to uptake of soluble gases by the rnesophyll cells is influenced by the surface area of the mesophyll and the solubility of the gas (Hill, 1971; O’Dell et al., 1977; Hosker and Lindberg, 1982). The magnitude of this resistance is usually small on a leaf basis, IO to 50 s m - ’ (Hosker and Lindberg, 1982). On a canopy basis, this resistance is usually evaluated as ratio between the leaf value and the canopy leaf area index.

The cuticular resistance is associated with gaseous uptake at the surface of the leaf. This resistance will depend on the chemical characteristics of the trace gas under consideration, but will also be influenced by the amount of leaf surface area, leaf pubescence and waxes and exudates on the leaf surface. The cuticular resistance of a dry leaf is typically quite large for many pollutant gases, exceeding 1000 s XII- I. However, leaf surface uptake is a significant pathway for HNO, and lipid-soluble HCs. The degree of leaf wetness also afTects the cuticle resistance. For example, leaf wetness caused by condensation (i.e. dewfall and distillation) enhances SO2 uptake (Fowler and Unsworth, 1979) and inhibits OJ and NO, uptake (Wesely et al., 1982).

The soil resistance to pollutant uptake of a par- ticular species is influenced by soil moisture, soil type and texture and soil litter (Turner er al., 1973). There are no models available in the literature for estimating the cuticle and soil resistances to pollutant uptake. Consequently, we must rely on published values reported in the literature.

3. RESULTS

Canopy stomata1 resistance

In terms of the canopy resistances, gas transport through the stomata generally provides the path of least resistance for the uptake of SOs, 0, and NO*, assuming the canopy is dry and transpiring. In this section we will discuss the influence of varying environmental and physiological variables on canopy stomata] resistance in order to illustrate the magnitude of the role that the stomata have on the uptake of gaseous pollutants.

Figure 2 shows the relationship between calculated canopy stomata] resistance [R,, as specified by Equation (16)] and PAR for SOz, OJ and NOZ uptake. Curves for soybean, maize (corn), oak and spruce are presented since these plant species represent some of the different classes of vegetation growing in the eastern U.S. The data used to generate these curves are

A canopy stomata1 rcsistancc model for gaseous deposition to vegctatcd surfaces

1 0 SOYBEAN 201 I I I I I I I I I I

0 100 200 300 400 a ml 200 300 400 PAR 1Wd2) PAR (WI@)

Fig. 2. Response of canopy stomata1 resistance to PAR for corn (maize), soybeans, spruce and oak: (a) S02: itO NCh and 0~.

based on clear-day (10% diffuse radiation), non- stressful (JI > tie), summertime conditions (T = 25°C) for fully developed canopies (LAI = 5). The modeling parameters used in the computations of R, are listed in Table 1.

Canopy stomata1 resistances for each species decrease curvilinearly with increasing PAR (Figs 2a and 2b). A factor of 2-4 decrease in Rx is observed as PAR increases from low light levels (50 W m - ’ ) to high light levels (400 W mm*). A pronounced difierence in R, among plant species is also evident. Based on the parameters used in these computations, a factor of 8 difference between the extremes (soybeans and maize) at high PAR levels is observed even though the respective minimum stomata1 resistances dialer by only a factor of 4. This is due in part to differences in the g,-PAR curvature coefficient, b,. Actual differences in R, among these species may vary from that presented in Fig. 2 since the minimal stomata1 resistance can vary

by an order of magnitude for herbaceous plants (Korner et al., 1979).

Greater canopy stomata1 resistances are found for SO2 than for NO2 and O3 (Fig. 2) This is a consequence of the differences in molecular diffusivities. Pollutants with greater molecular weights have lower molecular diffusivites, and correspondingly greater canopy stomata1 resistances.

Cloudiness affects the relationship between R, and PAR since it influences the dist~bution of light inside a canopy. Under low FAR levels, R, for Olt transfer to a soybean crop is reduced by 50 % as the percentage of diffuse radiation increases from 10 to 80% (Fig. 3). Under high PAR levels R, is reduced by only 25 % as the percentage of diffuse radiation increases from 10 to 80 “/, This reduction is less at higher PAR levels since a greater proportion of shaded and sunlit leaves are exposed to PAR levels exceeding light saturation iPAR 9 b,J.

Table 1. A list of the parameters used to compute canopy stomata1 resistance

Variable Units Spruce Ref. Oak Ref. Corn Ref. Soybean Ref.

min r, sm-’ 232 1 145 5.6 242 10 65 b(PAR) Wm-* 25 2 22 6 66 10 IO 132

*fin ’ -5 I 7 35 I ii 7

5 8 S 17* LX 17’ T b;$d)

: 9 24-32 s,7 22Y5 ! kPa-’ -0.0026 I,:4 0

t: 16, 5 0 0 13

*Cl MPa -2.1 2. I I -2.0 S,l -0.8 $9 -1.1 3.9

(1) Jawis, 1976; (2) Jarvis n rrL, 1976; (3) Eafdocchi et af., 1985; (4) Boycr, 1970; (5) Hinckicy eta& 1978; f6) Baldorxhi and Hutchison (unpublished); (7)Aubuchon et al.. 1978; (8) Rodriqwz and Davis 1982; (9) Pospisiiova and Sok~ova, 198Q (t 0) Turner and Bcg& t973;(I1~Jarvit,l989~12)Ha~~and~rlson.t978;(l3~Rawsoneraf.,1977;(I4)Gm~ ct ol, 197% (1s) Boy~r, 1976; (16) Jeffcrs and Shibles, t%R (17) Harley et al., 1985: *assumed based on p~to~nthet~ data.

96 DENNIS D. BALDCKCHI et d.

201 I I I I

0 loo 200 300 400 500 PAR ( WC~‘~)

Fig. 3. lnfluenceof PAR on thecanopystomatal resistana of ozone transfer to soybeans at different levels of diffuse

radiation.

Canopy stomata1 resistance is strongly linked to the amount of vegetation covering the surface, expressed in terms of leaf area in&x (LA1 f. At a given PAR level, R, for ozone deposition to a soybean canopy decreases pro~~onal~y with inning LA1 (Fig. 4). For example, at high FAR levels R, decreases by a factor of 5 as LA1 increases from 1 to 5.

Often R, is estimated from poromctcr mcasure- mcnts as QLAI. where is is the average of stomata1 resistances of individual leaves within the canopy. Superimposed on Fig. 4 is a plot of (R, = l)/LAI, a surrogate for </LAI. It is evident that this ratio underestimates values of R, computed with the canopy radiative transfer model. For example, when the canopy LAI is 5 (R, = l]JLAJ can lead to a 25% und~esti~tion in canopy stomata1 resistance. The relative difference is smaller at lower leaf area indices. Differences between the two estimates of R, reflect the importance of considering stomata1 resistance in terms of the sunlit and shaded leaves.

The model suggests that canopy stomata1 resistance for soluble trace gas transfer to a soybean canopy decreases as Tincreases up to about 35°C at all levels of PAR (Fig. 5). At higher temperatures R, decreases since these temperatures cause high transpiration rates, which may trigger plant water stress (Schulxe and Watt 1982), and denature enzymes, which conlrol stomata1 operation (Jarvis and Morison, 198f). Thcoreticaliy, R, should be smallest at the optimal temperature (To = ZY’C), not at 35°C. The functional form presented

400 SOVBEANS O3

T:25*C

0 loo 200 300 400 500 PAR IWm-*I

Fig. 4. Influence of PAR on the soybean canopy stomata1 resistance to ozone transfer for different leaf area indices. The dotted line illustrates canopy stomata1 resistance computed as the ratio between stomata1 resistance per unit

leaf area and canopy leaf area index.

7 E

”

$ 90 IO0

z 80

k 70

60

50

40

30

201 0 !oo 200 300 400 500

PAR (Wm-*I

Fig. 5. Muence of FAR on the soybean canopy stomata1 resistance for ozone transfer under di~erent temperature

regimes.

A canopy stomata1 resistance model for gaseous deposition to vegetated surfaces 97

by Jarvis (1976) for b, appears to be in error; a better form is b, = (F,, - T,)/(To - 7&)*

The model indicates that plant water stress, quantified by kaf water potential, dots not affect ozone deposition to soybeans when $ values exceed the threshold level for stomata1 closure (Fig. 6). However, R, increases rapidly when Jr drops below the threshold kvel. For example, a factor of 4 increase in R, results as ]Jtl drops 0.3 MPa below the threshold level of - 1.1 MPa.

A rest of the canopy stomafal resistance model

As yet, there are no comprehensive data sets on trace gas exchange with enough supporting biological infor- mation to test predictions of the canopy stomata1 resistance model developed here. Generation of such data is a major goal of experimental programs presently under way, with initial focus on SO2 and Ot In this context, it shouid be noted that O3 data are considered relevant even though O3 is poorly soluble in pure water. Field ex~ments have invariably shown that O3 dry deposition rates are stomatally controlled during daytime and over surfaces that are biologically active (see Hicks, 1984). However, some confidence in model performance can be generated by testing it against observations of water vapor exchange. For this purpose, independent estimates of canopy stomata1 resistance have been derived from: (a) measurements of c/LAI, made with a steady-state porometer; and (b) computations based on the Penman-Monteith model for latent heat exchange

500f

‘E 2

$ ‘g-

3. ao- n’ 70 -

60 -

50 -

40 -

30 -

.

\ l

i_~

\

+-%__ .

Yi(w PAR (Wi f

Fig. 6. Influence of PAR on the soybean canopy stomata1 resistann for ozone transfer under different levels of leaf

water potential.

(LE) (Monteith, 1973), which is expressed as:

LE=C(sA+pC,D/(R.+Rb))l/

[s+rJW&+Rc)] (17)

where s is the slope of the relationship between saturation vapor pressure and temperature, y is the ~~hromet~c constant, p is air density, C, is the specific heat of air at constant pressure and A is the available heat energy (A = R, -G, where R, is net radiation and G is transfer into the ground). The data used for this test were obtained in a field study of the energy budget of a soybean canopy, as reported by Etaldocchi et al. (1985). These data represent a wide range of canopy conditions, ranging from well-watered to water-stressed (J/ ranged between -0.6 and - 1.9 MPa).

Figure 7 presents the comparison between the three estimates of canopy stomata1 resistance to water vapor transfer. The computed values of R,, using the model described in this paper [Equation (16)], are well correlated with the values from the two other methods, for the wide range of environmental and physiological conditions used in the test; the correlation coefhcients between calculated values of R, and those from porometer measurements and the Penman-Monteith equation are 0.95 and 0.89, respectively. Furthermore, the magnitude of computed values of R, are in relatively good agreement with values estimated as f;ILAI and with the Penman-Monteith equation.

There is a tendency for the computed values of R,

-; 200 - o R,- i;/LAl E

Z l R, - ?rom Penman-Mont&h Eq.

z

I I lilltt 20 SO 100 200 CANOPY STOMATAL RESISTANCE fr IV-‘)

Fig. 7. Comparison betwwm canopy stomata1 resistance for water vapor (R,), computed with Equation (16) (.v axish against two estimples of canopy stomatat resistance derived from measurements (x axis). The measured estimates are: (a) R, = rT/&AI, where rS is the mean stomata1 resistance measured with a steady-state diffusion porometer, and (bj & derived from the Penman-Mont&h equation (17). The measured and computed canopy stomata1 r&&ma values were derived from Phil and ~~1~1 measurements made over a soybean anopy near Mead, NE and

are reported in Wdocchi rz ot. (19RS).

98 DENNIS D. BALWXCHI CI ul.

[using Equation (IQ] to overestimate Qt.41 by about 5sm-‘, or 5-30%. This overestimate, however, appearsacceptable since it is consistent with the results presented in Fig. 4 and because the measured values of canopy stomata1 resistance were derived from only sunlit leaves in the upper canopy. On the other hand, values of R, predicted by the present model con- sistently underestimate values derived with the Penman-Montejth modei. The difference between these two models is on the order of 30-50%. This dinirence is expected, considering the theoretical arguments of Thorn (1975) and Finnigan and Raupach (1987), who show that the canopy stomata1 resistance in the Penman-Monteith equation does not equal the parallel, area-weighted sum of the stomata1 resistance of individual leaves in the canopy. Instead, the Penman-Monteith canopy resistance [R,( PM)] is a function of the stomataland aerodynamic resistance of the leaves in the canopy and net radiation incident on those leaves (Finnigan and Raupach, 1987) or it can be expressed, after Thorn (1975), as:

R,(PM)=R,+(l-sB,/y)R, (18)

where B,is the Bowen ratio, the ratioof sensible heat to latent heat flux. In view of Equation (is), R,, derived from the Penman-Monteith equation, can overestimate canopy stomata1 resistance computed as the parallel, area-weighted sum of the individual leaves in the canopy. The data used in the present comparison permit the second term on the right hand side of Equation (18) to be evaluated. Under well-watered conditions, E, was typically less than 0.1 and Rb was of the order of 20-30 s m _ I. Hence, the second term on the right hand side of Equation (18) was about 20 s m- ‘, thus accounting for part of the factor of two difference observed between R, and R,( PM) under well-watered conditions. The errors involved in de- termining the model parameters and in measuring the input variables used to compute R, (PM) also account for differences between R, and R,( PM). Callander and Woodhead (1981) report that typical errors associated with canopy ~onduct~Inccs, computed with the Penman-Monteith equation, are of the order of + 25-35 2,.

A comparison of ~ulc#lared and measured reposition velocities

Deposition velocities computed using Equation (1) have been tested against measured vaiucs of O.$ deposition vclocitics measured values over ;I mature maize canopy (We&y et a/., 1978).

Deposition v&cities for ozone transfer to maize werecomput~ assuming that the leafarea index of the canopy was 4. The parallel resistances due to the soil and cuticle were assumed to be constant at 400 s m- ‘, as given by Wescly el al. (1978). The mesophyll resistance was assumed to be zero (Leuning er al., 1979a, 1979b). Canopy stomata1 resistance was computed using the parameters I&ted for maize in Table 1.

Calculated and measured deposition velocities are well correlated for conditions with od values ranging between 0.3 and 0.7 cm s- I (Table 2); the correlation coefficient is 0.76. This high correlation suggests that much of the variation in measured p., value can be accounted for by variations in R,, Rb and R,. However, calculated v,, values overestimate measured values by an average of about 0.11 ems- ‘, or about 27x-a relatjveiy small difference considering measurement and modeling errors.

One possible explanation for the differences between measured and predicted 03 deposition velocities is the assumption used for the canopy leaf area index. An overestimation of LA1 can account for some of the underestimate in the calculated ud ValUeS; no measurement of LAI was made in the experiment from which these data were derived. Other sources of error are doubtlessly associated with both the measurement of Y, and with the specification of inputs and parameters used in the model computations. For example, Wesely and Hart (1985) show that measured values are subject to experimental error and large run-to-run variability due to sensor noise.

Table 2. ~~sitjon velocities of ozone measured over a well-watered, mature corn canopy (Wesely et al., 1978) and computed

with the deposition velocity model

Time meaUsdured K!

calculated

Day (h) (ems- ‘) (ems-‘)

Ii29 945 1015 IO45 111s 1145 1315 f 345 1415 1515 154s 1615 l&IS 1715 1745

0.563 0.55 0.528 0.54 0.479 0.53 0.466 0.54 0.427 0.55 0.278 0.59 0.398 0.59 0.501 0.53 0.452 0.53 0.351 0.49 0.276 0.45

0.282 0.45 0.224 0.35 0.236 0.34

7/30 915 0.527 0.57

94s 0.402 0.44 1015 0.28 0.43 1045 0.699 0.63 1115 0.6 11 0.68 1145 0.514 0.67 1215 0.56 fl.6 i 1245 0.397 0.6 1315 0.479 0.6 1345 0.345 0.51 1415 0.243 0.49 1515 0.259 0.44

mean 0.415 0.527

s.d. 0.128 0.085

I, paired = -9.66 t, 0.05 = - 1.67

A canopy stoma&l resistance model for gaseous deposition to vegetated surfa~ 99

4. DlSClJSSlON

The hierarhy asscciated with canopy-atmosphere mass and energy transfer models involves three distinct levels of detail. These correspond to single-layer “big- leaf n rcsistana+analog mod& multilayer resistance- analog or K-theory models (e.g. Waggoner, 1975; Norman, 1979; Unsworth, 1980) and higher order closure models (e.g. Finnigan and Raupach, 1987). The model presented here is designed to provide a link between a simple “big-leaf” model and a multi-layer resistance model, and is intended to permit detailed data on plant physiology to be utilized in practical applications concerning the determination of pollutant dry deposition.

The practical utility of a more complicated model is often limited by the need for complex parameters, which are often unknown or difficult to obtain. These parameters include vertical variations in leaf area index, canopy drag coefhcients, the wind profile attenuation coefficient, and coegkients used to close higher order moment quations (see Wagoner, 1975; Finn@ and Raupach, 1987). Complex models are also limited somewhat by the incomplete theoretical understanding of within-canopy turbulent exchange processes. For example, K-theory models are based on the assumption that withincanopy turbulent transfer is dominated by eddies which have length scales similar to the kngth scales associated with the canopy and its elements. Recently, this has been shown not to be the case; within-canopy turbulent transfer is dominated by eddies much larger than the length scale of the canopy (see Finnigan and Raupach, 1987).

The present ~mpu~tjon of canopy stomatal resistana is based on the assumption that the leaf inch- nation distribution is spherical and the foliage distribution is uniform in space. In reality, these assump- tions arc not always appropriate. Leaf orientation can be planophile, plagiophile. spherical or ercctophile, among other distributions. Alterations in leaf orientation inffuence the probability of beam penetration and the irradiancc incident on the leaf (see Lemeur, 1973; Norman, 1979). Spatial distribution of leavescan also vary. For example, individual leaves can be clumped or the plant stand can be clumped or in rows. Rcccntly, Raldocchi and Hutchi~n (1987) examined the influence on clumped foliage on the penetration of PAR in a deciduous forest and its impact on the estimation of canopy stomata1 conductance. It was found that clumping of the foliage increases PAR penetralion and leads to greater values of G,.

The model computations also assume that parameters and variables used to compute R, are constant with height inside the canopy. Values of such parameters as r, (min) and leaf scattering cocmcients vary with leaf age and position in the canopy (see Jarvis er

al., 1976; Jarvis and Lcverenx, 1983), as do canopy air and leaf temperatures and vapor pressure deficits. Compu~tions of canopy stomata1 resistance can doubtlessly be improved by including computations of

the net radiation balance of leaves to estimate leaf temperature and the vapor pressure deficit between the leaf and air (e.g. Waggoner, 1975; Norman, 1979). and by accounting for the vertical variation of some of the more sensitive parameters.

5. CONCLUSIONS

A multilayer canopy stomata1 resistance model has been developed, with the intent to provide more realistic descriptions of biological processes than arc presently included in “big-leaf” models of trace gas dry deposition processes. The model is based on the leaf stomata1 resistance model of Jarvis (1976) and in- corporates the canopy radiative transfer model of Norman (1979, 1982).

Computations ofcanopy stomata1 resistance show a strong dependence on PAR, leaf area index, tcmpera- ture and leaf water potential. Diguse radiation and the distribution of plant and chemical species also affect R, . Variations in these environmental and physiological variables can affect R, by a factor to 24, and could cause corresponding “errors” if such factors are omit- ted from models of trace gas deposition velocity.

The canopy stomata1 resistance model was tested for water vapor against values derived from data obtained over soybeans. Predictions of canopy stomata1 rcsist- antes differed from field observations by an average that could be explainable in terms either of errors in m~urement (or in the interpretation of field obscr- vations) or of erroneous model gumptions. In general, predictions are well correlated with test values, for water vapor exchange.

The model has been used to predict deposition velocities for OJ. Comparisons with field data ob- mined over maize show that measured and computed deposition velocities are well correlated and agree, on the average, within 27 %.

Major limitations of the present model lie with its omission of within-canopy turbulent exchange processes, its inherent inability to address questions concerning the flux of bi-directional pollutants such as NHS, CH, and NO, and its lack of detail concerning transfer with soil, m~ophyll and cuticle. ~v~~opment of a complete multi-layer model is under way at this time.

Acknowkdgcmmts-This work was conducted under agree- ments between the National Dceanic and Atmospheric Administration and the U.S. Department of Energy, as a contribution to the National Acid tiipitation Assessment Program, and under the auspice of the Task Group on Deposition Monitorink The senior author is a biometcoro- logist at Oak Ridge Associated Universities which conducts rcscaxch for the U.S. Department of Enera under contract DE-A~~7~R#33. We arc grateful to Ernst and rdvicz provided by Dr Gcorgc Taylor, Dr RuI Jarvis and Dr Marvin W&y.

loo DENNIS D. BALDOCCHI et o/.

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