ooo4-69al/s?s1.00+0.00
~rnospkric l?~~~iromunrVol. 21. No. I. pp. 91-101. 1987
Pergmon Jourmlr Ltd.
Printed in Gnxr B&in.
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 December1985 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 hierarchyof 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 differencesin plant species and environmentaland physiological
conditions can affect the canopy stomatal resistanceby a factor of four. Canopy stomata1r&stances to water
vapor transfercomputed with the present model arc compared against values measuredwith a poromcter and
computed with the Penman-Montcith equation. Computed stomata1resistances from a soybean canopy in
both well-watered and water-stressedconditions yield good agreement with test data. The stomata1resistance
submodcl responds well to changing environmental and physiological conditions. Model predictions of
deposition velociticsareevaluated for the case of ozone, transferredto maize. Calculated deposition velocities
of 0, overestimate measured values on the average by about 30%. probably largely as a consequence of
uncertaintiesin 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.
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 Upemploy 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-
I. INTRODUCTION
determine,
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 elimination 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 landscapes, 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
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.
Formerly Lowell University, presently State University
of New York, Albany.
91
92
DENNIS D. BALDOCCHI er d.
ATMOSPHERIC
SOURCE
AERODYNAMIC.
DIFFUSIVE
R,
BOUNBARY,
Rb
STOMATA
PLANT
TISSUE
PLANT
WATER
1
c--
TISSUE
SURFACES
STONE B OTHER
MATEd?IALS
way in which these detailed resistances can be combined 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.
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
SO2 transfer.
Murphy ef al. (1977), for loblolly pine. The generality
of their model, however, is limited by its dependence
on empirically derived, species-specific, attenuation
cepts into such models is needed to make them coefficients for beam and diffuse radiation. The model
adaptable to different vegetated surfaces and regions. also does not consider the effects of other environThe canopy resistance is a function of environ- mental and physiolo~~l
variables on stomata1
meatai and physiological conditions, surface wetness resistance.
and chemistry, leaf area index, and diffusivity of the
Here, we develop a canopy stomata1 resistance
pollutant (Jarvis, 1971, I976; Turner et al., 1973; submodel which couples a canopy radiative transfer
Sehmel, 1980;Unsworth, 1980;Hosker and Linderg,
model (see Norman, 1979, 1982) with a leaf stomata1
1982). In comparison, the aerodynamic and quasi- resistance model (see Jarvis, 19763,and incorporate the
laminar components are relatively simple products of submodel into a “big-leaf”, resistance-analog, gaseous
factors not strongly influenced by the physiology of the deposition model. The objectives of this paper are: (1)
surface. For a gas such as SO*, R, is known to be to present and discuss this gaseous deposition model
influenced by stomatal (R,) and (somewhat less cer- and canopy stomata1 resistance submodel; (2) to
tainly) mesophyll (R_) resistances,which are in series examine the effects of environmental, physiological
with each other, and are in paraIM with resistances and structural variables and plant species on the
exerted by the leaf cuticle fk),
the soil CR,&, canopy stomata1 resistance of several ~l~utant gases;
surface wetness (R,,& and any other surface material and (31 to compare computed deposition velocities,
CR,& (Unsworth, 1986 Hosker and Lindberg, 1982; based on this model. against measured vatues.
Fig. 1. Pathway of resistances to the deposition of gaseous
pollutants. The dotted line illustrates a probable route for
Hicks, 1984; Hosker, 1986).High ambient pollutant
concentrations can ah0 influencethe canopy resistance
to pollutant uptake by increasingor decreasing stomatal resirtdnce (Black, 1982).
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
2. THEORY
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:
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.
93
A canopy stomata1 resistance model for gaseous deposition to vegetated surfaces
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
04
or under near neutral conditions as:
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.
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:
Rb = Cl l(k
u,)l IIn(~o/zc)l
(3)
where z, is the roughness length for the pollutant or
entity under investigation.
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).
The canopy resistance (R,) is computed as:
where R, is the canopy stomata1 resistance, R, is the
canopy mesophyll resistance, and the remaining subscripts 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.
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 $:
91 =s(PAR)g(T)g(D)s(IL)D,lDi.
(6)
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 introducing further multiplicative factors.
The response of stomata1 resistance to PAR is
estimated using a rectangular hyperbola relationship
(Turner and Begg, 1974):
r,(PAR) = r,(min)+ b,,r,(min)/PAR
g,(PAR)
= l/r,(PAR)
(7a)
(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.
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:
‘Z(PAR) =
)Jf,,,(J)dPAL(1)1
s
+%-,,deU)O’&,,a,,eU)ldf
(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.
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 cumulative 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 cumulative sunlit leaf area between the top of the canopy
and a level inside the canopy (I) is computed as:
L
(/) = [I - exp
(- 0.5/b UN12 sinVI (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
94
DENNISD. 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, 1981).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
(T,,,
C(T--TT)/
- To)lb~
(13)
where Tminand T_ are the minimum and maximum
temperatures at which stomata1closure occurs, To is
the optimum temperature and b, is defined as b,
= V,,
- To)/(T-
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 particular 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.
- Knin).
Stomata1 conductance is linearly related to vapor
pressure deficit (D):
g(D) = 1 -b,D
(14)
where b, is a constant.
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($) is computed
using a discontinuous linear model (Fisher et al., 198 1)
since parameters for this model are readily available in
the literature (e.g. Pospisilova and Solarova, 1980).
This function is expressed as:
SW
We assume that temperature, vapor pressure deficit
and leaf water potential are constant with height in the
canopy. The canopy stomata] resistance is thus computed by combining Equations (8), (13), (14) and (15):
= 1,
if*>*0
UW
8($) = a$ + b,,
if$<ti0
WV
and as:
where a and b, are constants.
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
201
1 0 SOYBEAN
I
I
I
0
100
200
300
PAR 1Wd2)
I
400
I I
a
I
ml
I
I
200
300
PAR (WI@)
Fig. 2. Response of canopy stomata1 resistance to PAR
I
400
for corn
(maize),
soybeans, spruce and oak: (a) S02: itO NCh and 0~.
based on clear-day (10% diffuse radiation), nonstressful (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
145
22
242
66
5
10
10
8
65
IO
S
22Y5
0
!
t:
0
-0.8
$9
-1.1
min r,
sm-’
232
1
b(PAR)
Wm-*
25
*fin
’
-5
2
I
T
:
I
ii
b;$d)
kPa-’
MPa
35
9
-0.0026
I,:4
24-32
0
5.6
6
7
7
s,7
5
-2.1
2. I I
-2.0
S,l
LX
*Cl
Ref.
132
17*
17’
16,
13
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
DENNISD.
BALDCKCHIet d.
400
SOVBEANS
O3
T:25*C
201
0
I
I
loo
200
PAR
I
I
300
( WC~‘~)
400
500
Fig. 3. lnfluenceof PAR on thecanopystomatal resistana
of ozone transfer to soybeans at different levels of diffuse
radiation.
Canopy stomata1resistance 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 mcasuremcnts 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 valuesof 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 stomata1resistancein terms
of the sunlit and shaded leaves.
The model suggeststhat canopy stomata1resistance
for soluble trace gas transfer to a soybean canopy
decreasesas Tincreases up to about 35°Cat all levelsof
PAR (Fig.5).At higher temperatures R, decreasessince
these temperatures cause high transpiration rates,
whichmay trigger plant water stress (Schulxeand Watt
1982),and denature enzymes, which conlrol stomata1
operation (Jarvis and Morison, 198f). Thcoreticaliy,
R, should be smallestat the optimal temperature (To
= ZY’C),not at 35°C. The functional form presented
0
loo
200
PAR
300
400
500
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 resistanceper unit
leaf area and canopy leaf area index.
7
E
”
$
IO0
90
z
80
k
70
60
50
40
30
201
0
!oo
200
PAR
300
400
500
(Wm-*I
Fig. 5. Muence of FAR on the soybeancanopystomata1
resistance for ozone transferunder di~erent temperature
regimes.
A
97
canopy stomata1resistance model for gaseousdeposition to vegetated surfaces
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 information 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
(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,
-;
E
Z
200
-
o R,- i;/LAl
l R, - ?rom Penman-Mont&h
Eq.
z
‘E
2
$ ‘g3. ao-
.
n’ 70 60
-
\
I
I
lilltt
20
SO
CANOPY STOMATAL
l
50 -
100
RESISTANCE
200
fr IV-‘)
\
40 -
+-%__
.
30 -
i_~
Yi(w
Fig. 6. Influence of PAR
PAR (Wi
f
on the soybean canopy stomata1
resistann for ozone transfer under different levels of leaf
water potential.
Fig. 7. Comparison betwwm canopy stomata1 resistance
for water vapor (R,), computed with Equation (16) (.v
axish against two estimplesof canopy stomatat resistance
derived from measurements (x axis). The measured estimates are: (a) R, = rT/&AI,
where rS is the mean
stomata1resistancemeasured with a steady-statediffusion
porometer,
and
(bj
&
derived
from
the
Penman-Mont&h
equation (17). The measured and
computed canopy stomata1r&&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 consistently 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 determining 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,.
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 (Weselyet al., 1978)and computed
with the deposition velocity model
K!
Time
Day
(h)
Ii29
945
1015
IO45
111s
1145
1315
f 345
1415
1515
154s
1615
l&IS
1715
1745
0.563
0.528
0.479
0.466
0.427
0.278
0.398
0.501
0.452
0.351
0.276
0.282
0.224
0.236
0.55
0.54
0.53
0.54
0.55
0.59
0.59
0.53
0.53
0.49
0.45
0.45
0.35
0.34
915
94s
1015
1045
1115
1145
1215
1245
1315
1345
1415
1515
0.527
0.402
0.28
0.699
0.6 11
0.514
0.56
0.397
0.479
0.345
0.243
0.259
0.57
0.44
0.43
0.63
0.68
0.67
fl.6 i
0.6
0.6
0.51
0.49
0.44
mean
s.d.
0.415
0.128
0.527
0.085
7/30
A comparison
velocities
of ~ulc#lared and measured reposition
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.
meaUsdured calculated
(ems- ‘)
(ems-‘)
paired = -9.66
t, 0.05 = - 1.67
I,
A canopy stoma&l resistance model for gaseous deposition to vegetated surfa~
4. DlSClJSSlON
The hierarhy
asscciated with canopy-atmosphere
mass and energy transfer models involvesthree distinct
levels of detail. These correspond to single-layer“bigleaf n rcsistana+analog mod& multilayer resistanceanalog 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 scalessimilar
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 inchnation distribution is spherical and the foliage distribution is uniform in space. In reality, these assumptions 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 includingcomputations of
99
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 stomata1resistance 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 incorporates the canopy radiative transfer model of
Norman (1979, 1982).
Computations ofcanopy stomata1resistance show a
strong dependence on PAR, leaf area index, tcmperature and leaf water potential. Diguse radiation and the
distribution of plant and chemical species also affect
R, . Variations in these environmental and physiological variablescan affect R, by a factor to 24, and could
cause corresponding “errors” if such factors are omitted from models of trace gas deposition velocity.
The canopy stomata1resistancemodel was tested for
water vapor against values derived from data obtained
over soybeans. Predictions of canopy stomata1 rcsistantes 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 obscrvations) or of erroneous model gumptions. In general, predictions are wellcorrelated with test values,for
water vapor exchange.
The model has been used to predict deposition
velocities for OJ. Comparisons with field data obmined 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 agreements 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 MonitorinkThe senior author is a biometcorologist 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. BALDOCCHIet o/.
REFERENCES
Aubuchon R. R., Thompson D. R. and Hincklcy T. M. (1978)
Environmental influences on photosynthesis within the
crown of a white oak. Oecologia 35, 295-306.
Baldocchi D. D., Verma S. B. and Rosenberg N. J. (1985)
Water use efficiency in a soybean field-influence of planr
water stress. Agric. For. MPteorol.
34. 54-65.
Baldocchi D. D. and Hutchison B. A. I 1987) On cstimatinr
canopy photosynthesis and stomata1 conductance in a
deciduous forest with clumped foliage. Tree Physiology
(in
press).
Belot Y., Baille A. and Delmas J. L. (1976) Modclc numcriquc
de dispersion des polluants atmosphcriques en presence de
couvert vcgetaux application aux couvcrt. Atmospheric
Enoironmenl 10, 89-98.
Bennett J. H. and Hill A. C. (1973) Absorption of gaseous air
pollutants by a standardized plant canopy. J. Air Pollur.
Control
Assoc.
Z&203-206.
Black V. J. (1982) ENects of sulphur dioxide on physiological
processes in plants. In Eficrs 01 Gaseuus Air Pollution in
Agriculfure and Horticulmre (edited by Unsworth M. H.
and Ormrod D. P.), pp. 67-92. Butterworth Science,
London.
Boycr J. S. (1970) DilTcring sensitivity of photosynthesis IO
low leaf water polentials in corn and soybean. PIonr
Physiol. 46, 236-239.
Boyer J. S. (1976) Water deficitsand photosynthesis. In Waler
Deficits and Plum Growrh. I V (edited by Kozlowski T.), pp.
153-190. Academic Press. New York.
Brutsaert W. H. (1975)Thc roughness length for water vapor,
sensible heat and other scalars. J. ulmos. Sci. 32.2028-203 I.
Callander B. A. and Woodhead T. (1981) Canopy conductance of estate tea in Kenya. Agric. Mereorol.
23, 151-167.
Chamberlain A. C. (1966) Transport of gases to and from
grass and grasslike surfaces. Proc. Royo/ Sot. London ser. A
290, 236265.
Finnigan J. J. and Raupach M. R. (1987) Modern theory of
transfer in plant canopies in relation to stomata1 characteristics. In Sromaral Function
(edited by Zeip;cr E..
Farquhar G. and Cowan I.). Stanford University Press,
Stanford, CA.
Fisher M. J., Charles-Edwards D. A. and Ludlow M. M.
(1981) An analysis of the cfiicts of repeated short-term soil
water deficits on stomata1 conductance to carbon dioxide
and leaf photosynthesis by the legume, Macropfilium
olropurpureum,
cv. Siratro. AUS!. J. P/ON
Physiol. 8,
347-357.
Fowler D. (1978) Dry deposition of SO2 on agricultural
crops. Atmospheric
&&onmenf
12, 369-373.
Fowler D. and Caoe J. N. 11982) Air pollutants in agriculture
and horticulture. In Eflecls oj Gaseous Air Pollution
in
Agriculrure
and Horriculrure
(edited by Unsworth M. H.
and Ormrod D. P.), pp. 3-26. Butterworth
Science,
London.
Fowlcr D. and Unswonh M. H. (1979) Turbulent transfer of
sulphur dioxide to a wheat crop. Quart. J. Roy. met. Sot.
105, 767-783.
Garratt J. R. and Hicks B. B. (1973) Momentum, heat and
water vapor transfer to and from natural and artificial
surfaces. Quart. J. Roy. mef. Sot. 99, 680-687.
Grace !., Malcolm D. C. and Bradbury I. K. (1975) Tbc c&cl
of wmd and humidity on leaf diffusive resistance in sitka
spruce seedlings. J. appl. Ecol. 12, 931-940.
Gr&nhut G. (1483) Resistance of a pine forest to ozone
uptake. Bound. Layer Mefeorol. 27, 387-391.
Hailcy P. C., Wcber j. A. and Gates D. M. (1985) Interactive
cfTects of light, leaf temperature, CO* and O2 on photosynthesis in soybean. Plonla. 165, 249-263.
Haifield J. L. anb Carlson R. E. (1978) Photosynthetically
active radiation, CO2 uptake and stomata1 dimusivc resistance profiles within soybean canopies. Agron.
J. 70,
592-596.
Hicks B. B. (1984) Dry deposition processes. In The Acidic
Deposition
Phenomenom
and ifs Ej/ecfs: E.P.A.
Crirical
Assessmenr Reoiew Pupers. Vol. I, Almos. Sci. Chapter 7.
Hicks B. B., Baldocchi D. D., Hoskcr R. P. Jr, Hutchison B.A.,
Matt D. R., McMillcn R. T. and Satterfield L. C. (1985) On
the use of monitored air concentrations to infer dry
deposition (1985). NOAA Technical Memorandum ERL
ARL-141, 65 pp.
Hicks B. B., Wescly M. L., Coulter R. L., Hart R. L., Durham
J. L., Speer R. E. and Stedman D. H. (1982) An expcrimcntal study of sulfur deposition to grassland. In Precipirarion
Scavenging, Dry Deposition and Resuspension,
Vol. 2.
(edited by Pruppacher H. R., Semonin R. G. and Slinn W.
G. N), pp. 933-942. Elscvicr, New York.
Hill A. C. (1971) Vegetation: a sink for atmospheric pollutants. J. Air Pollut Control Assoc. 21, 341-346.
Hinckley T. M., Aslin R. G., Aubchon R. R., Metcalf C. L. and
Roberts J. E. (1978) Leaf conductance and photosynthesis
in four species of the oak-hickory type. Fores/ Sci. 24,
7384.
Hoskcr R. P. Jr (1986) Practical application of air pollutant
deposition models-current
status, data requirements and
research needs. Proc. Internal.
Con/ on Air Polluronrs
and
their Effects on the Terrestrial
Ecosysrem
(edited by Leggc
A. H. and Krupa S. V.), pp. 546-567. Wiley, New York.
Hoskcr R. P. Jr and Lindberg S. E. (1982) Review:
atmospheric deposition and plant assimilation of gases
and particles. Almosphcric
Environmenr
16, 889-910.
Jarvis P. G. (1971) The estimation of resistances to carbon
dioxide. In P/on! Phorosyn,nllu,tic
Production:
Munu~l
oj
Merhods
(edited by Sestak Z., Catsky J. and Jarvis P. C.).
pp. 566-631. Dr Junk, The Hague.
Jarvis P. G. (1976) The interpretation of the variations in leaf
water potential and stomata1 conductance found in canopies in the field. Phil. Trons. R. Sot. London ser. B. 273,
593610.
Jarvis P. G. (1980) Stomata1 conductance, gaseous exchange
and transpiration.
In Plunrs
and
their
Atmospheric
Enoironment
(edited bv Grace J.. Ford E. D. and Jarvis P.
G. pp. 175-204. Blackwells, Oxford.
Jarvis P. G.. James J. B. and Landsberg J. J. (1976) Coniferous
forest. In Vegetation
and the Atmosphere
(edited by
Monteith J. L.), Vol. II. pp. 171-240. Academic Press,London.
Jarvis P. G. and Levcrenz J. W. (1983) Productivity of
temperate,
deciduous
and
evergreen
forests.
In
Encyclopedia
o/ Plum
Phy.SicJ/Og)‘,
vol.
I2D (edited by
Lanec 0. L.. Nobel P. S.. Osmond C. B. and Zienler H.)...aDD.
1
231-0279. Springer, Berlin.
Jarvis P. G. and Morison J. 1. L. (1981) The control of
transpiration and photosynthesis by stomata. In S~omatol
Phvsiolaav
(edited bv Jarvis P. G. and Mansfield T. A.), rm.
24&279.%mbridge
Univ. Press, Cambridge.
.’
Jeffcrs D. L. and Shibles R. M. (1969) Someeffects ofleafarea,
solar radiation, air temperature and variety on net photosynthesis in field-grown soybeans. Crop Science 9,762-764.
Korner C.. Schecl J. A. and Bauer H. (1979) Maximum leaf
diffusive conductance in vascular plants. Phorosynrherica
13, 45-82.
Lemeur R. (1973) A method for simulating the direct solar
radiation regime in sunflower, Jerusalem artichoke. corn
and soybean canopies using actual stand structure data.
Agric. Meteorol. 12, 229-247.
Lcnschow D. H., Pearson R. Jr and Stankov B. 8. (1982)
Measurements of ozone vertical flux to ocean and forest. J.
Geophys. Res. 87.8833-8837.
Leuning R., Unsworth M. H., Neumann H. H. and King K.
M. (1979a) Ozone fluxes to tobacco and soil under field
conditions. Atmospheric
Environmcnr
13, 115-I 163.
Leuning R., Neumann H. H. and Thurtcll G. W. (1979b)
Ozone uptake by corn: a general approach. Agric.
M~JflVJr~J/.
20,
1 15. 136.
Montcith J. L. (1973) Principles
01 Environmental
Physics.
Edward Arnold, London.
A canopy stomata1 rcsistancc model for gaseous deposition to vegetated surfaces
C, E. Jr, Sinclair T. R. and Knoen K. R. (1977) An
assessment of the use of forests as sinks for the removal of
atmospheric sulfur dioxide. J. Environ. Quority Q,388-3%.
Norman J. M. (1979) Modeling the complete crop canopy. In
Mod$cotion ojrhe Aerial Enoironment ofPlants (edited by
Barfield B. 1. and Gerber 1. F.), pp. 249-277. Am. Sot. Agric.
Engr. St. Joseph, Ml.
Norman J. M. (1982) Simulation of microclimates. In
Biometeorology in Integrated Pest Monugement (edited by
Hatfield 1. L. and Thompson I. J.), pp. 65-99. Academic
Press, New York.
O’Dell R. A., Tahcri M. and Kabel R. L. (1977) A model for
uptake of pollutants by vegetation. J. Air Pollut. Control
Assoc. 27, 1104-l 109.
Owen P. R. and Thompson W. R. (1963) Heat transfer across
rough surfaces. .I. Fluid Mech. 15.321-334.
Pospisilova 1. and Sotarova 1. (1980) Environmental and
biological control of diffusive condone
of adaxial and
abaxial leaf epidermis. Photosyntherica 14,9@-127.
Rawson H. M., Beg8 1. E. and Woodward R. G. (1977) The
effect ofatmospheric
humidity of photosynthesis, transpiration and water use efficiency of leaves of several plant
speqies. Planta 134, 5-10.
Rodriguez 1. L. and Davies W. J. (1982) The effects of
temperature and ABA on stomata of Zea muys L. J. Expt.
Botany 33,973-987.
Schulz E.-D. and Hall A. E. (1982)Stomata1 responses, water
loss and CO1 assimilation rates of plants in contrasting
environments. In Encyclopedia of Plant Physiology, Vol.
128 (edited by Lange 0. L, Nobel P. S., Osm&d d.B. and
Ziegler H.), pp. 181-230. Springer, Berlin.
Sehmcl G. A. (1980) Particle and gas dry deposition: a review.
Atmospheric Endronmenr 14.983-1012.
Thorn A. S. (1975) Momentum, mass and heat exchange of
Murphy
101
plant communities, In Yegeration and the Atmosphere, Vol.
1 (edited by Monteith 1. L.), pp. 57-109. Academic Press,
New York.
Turner N. C. and Begs 1. E. (1973) Stomata1 behavior and
water status of maize, sorghum and tobacco under field
conditions, 1:at high soil water potential. Planr Physiol. 51,
31-36.
Turner N. C., Rich S. and Waggoner P. E. (1973) Removal of
ozone
by soil. J. Environ. Quafiry 2, 259-264.
Turner N. C., Waggoner P. E. and Rich S. (1974) Removal of
ozone from the atmosphere by soil and vegetation. Nnture
250.486-489.
Unsworth M. H. (1980) The exchange of carbon dioxide and
air pollutants between vegetation and the atmosphere. In
Plants and their Armaspheric Enuironmenr (edited by Grace
J., Ford E. D. and Jarvis P. G.), pp. 111-138. Blackwells,
London.
Wagoner P. E. (1975) Mi~ometeorola~~l
models. In
pe>ernrion and the Atmosphere (edited bj Monteith 1. L.),
Vol. 1. DD. 205-228. Academic Press. London.
Wesely M. L., Eastman 1. A., Stedman d. H. and Yalvac E. D.
(1982) An eddy-correlation measurement of NOI flux to
vegetation and comparison to 0, Run. Atmospheric
Environment 16,8 1S-820.
We&y M. L., Eastman 1. A, Cook D. R. and Hicks 8. B.
(1978) Daytime variations of ozone eddy fluxes to maize.
Bound. Layer Mereorol. 15, 361-373.
Wesely M. L. and Hart R. L. (1985) Short term eddycorrelation estimates of mass exchanae. In The
Forest-Armosphere
Inreracrion (edited by HGtchison B. A.
and Hicks B. B.), pp. 591-612. D. Reidel, Boston.
Wesely M. L. and Hicks B. B. (1977) Some factors that affect
the deposition rates of sulfur dioxide and similar gases on
vegetation. J. Air Polka. Control Assoc. 27, 1110-l116.
..1