Agricultural and Forest Meteorology 127 (2004) 159–173
www.elsevier.com/locate/agrformet
Reactive hydrocarbon flux footprints during canopy senescence
C. Stronga, J.D. Fuentesa, D. Baldocchib,*
a
Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22904, USA
Department of Environmental Science Policy and Management, Ecosystem Science Division,
University of California at Berkeley, 151, Hilgard Hall, Berkeley, CA 94720-3110, USA
b
Received 10 August 2003; received in revised form 19 December 2003; accepted 15 July 2004
Abstract
A coupled Lagrangian random walk and atmospheric turbulence model was employed to investigate the magnitude of
isoprene source distribution within a mixed deciduous forest canopy undergoing defoliation. Modeled source distributions were
studied to understand how the flux footprint evolved as the total amount and vertical distribution of foliage changed during the
leaf senescing and abscission period. The modeled ensemble air parcel residence times inside the forest canopy were also studied
to quantify the fraction of isoprene destroyed inside forest canopies due to rapid chemical reactions. Defoliation in the canopy
affected the footprint by vertically redistributing the flux sources, and by reducing the leaf drag area encountered by flows within
the canopy. For air parcel releases in the upper canopy, the increased in-canopy turbulence associated with defoliation shifted the
footprint peak probability closer to the measurement point. However, when integrated through the depth of the canopy, the net
effect of defoliation was to increase the upwind source areas farther from the flux measurement point. Defoliation also impacted
air parcel residence times within the canopy. Under fully foliated conditions, air parcels remained within the canopy for periods
ranging from 2 to 50 min, depending on levels of atmospheric turbulence and air parcel release height. Under 25–75% defoliated
conditions, air parcels remained in the forest canopy for periods lasting less than 10 min. The estimated air parcel residence
times inside the fully leafed canopy resulted in significant isoprene chemical processing. Based on Lagrangian footprint
simulations with active chemistry, the integrated rates of isoprene destruction from reactions with ozone, hydroxyl, and nitrate
radicals ranged from 12% for air parcels released in the upper canopy to 40% for air parcels released from the lower canopy. We
conclude that active scalar flux estimates, often based only on the footprint transfer function and source strength distribution, can
be substantially improved by incorporating an active chemistry term.
# 2004 Elsevier B.V. All rights reserved.
Keywords: Lagrangian model; Flux footprint; Atmospheric turbulence; Friction velocity; Reactive scalars; Isoprene; Biogenic hydrocarbons
1. Introduction
* Corresponding author. Tel.: +1 434 982 2654;
fax: +1 434 982 2137.
E-mail address: [email protected] (J.D. Fuentes).
Extensive research has been accomplished to define
and quantify the spatial and temporal distribution of
biogenic volatile organic compounds (BVOCs), and to
assess the role and contribution of these gases to the
0168-1923/$ – see front matter # 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.agrformet.2004.07.011
160
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
overall oxidant formation potential within the lower
troposphere (Lamb et al., 1993; Guenther et al., 1994,
2000; Geron et al., 1997). To make such assessments
employing photochemical models, BVOC inventories
are determined using climate information together
with local land-use data that indicate vegetation types
and hydrocarbon-active biomass. Emission rates for
different vegetation types are measured by placing
foliage in enclosures and determining the hydrocarbon
concentration difference between the airstreams
entering and leaving enclosure systems (Lerdau et
al., 1997). BVOC emissions can be modeled based on
plant-specific basal emission rates modulated by
foliage temperature and intercepted photosynthetically active irradiance. To verify landscape-level
emissions (Lamb et al., 1993; Geron et al., 1997),
BVOC flux measurements are made above forest
ecosystems (Fuentes et al., 1996; Goldstein et al.,
1998; Guenther et al., 1996).
When placing instruments above forest canopies to
determine hydrocarbon flux densities, it is crucial to
identify the spatial distribution of sources contributing
to the fluxes (Baldocchi et al., 1999; Lamb et al., 1996).
Definition of the flux magnitude requires knowledge of
the hydrocarbon source strength and distribution
throughout the landscape. The strength and distribution
of sources are especially important for BVOCs as not all
plant species produce hydrocarbons (Baldocchi et al.,
1999; Kesselmeier and Staudt, 1999), and hydrocarbon
source strength varies substantially with canopy depth
(Harley et al., 1996). Flux footprint analyses (Schuepp
et al., 1990; Leclerc and Thurtell, 1990; Schmid, 2002;
Lee, 2003) provide a valuable framework for making
proper interpretation of BVOC fluxes for forest
ecosystems whose hydrocarbon sources vary with
canopy depth and are spatially heterogeneous. To date,
substantial research has been accomplished to define
flux footprints in atmospheric surface layers above
vegetated landscapes, employing several approaches
including analytical closure solutions to differential
diffusion equations (Gash, 1986; Horst, 1999; Leclerc
and Thurtell, 1990; Schuepp et al., 1990). Using
Lagrangian random flight simulations, footprint analyses have more recently been applied to tall canopies
which exhibit strong gradients of turbulent mixing
(Baldocchi, 1997).
This study addresses three related research
objectives. First, we investigate how foliage senes-
cence and abscission impact the source distribution of
isoprene (C5H8) for a mixed deciduous forest canopy.
These influences are studied by examining the
evolution of the two-dimensional (horizontal distance
and height) flux footprint as the total amount and
vertical distribution of foliage change during the
senescing period. Second, to quantify the isoprene
amounts destroyed inside forest canopies due to rapid
chemical reactions, we determine the ensemble
residence times of isoprene molecules within a mixed
deciduous forest. Third, using measured and estimated
concentrations of isoprene-reacting chemical species
we determine the fraction of isoprene destroyed by
fast chemistry as a function of distance from the
measurement point for periods corresponding to the
flux determination. To achieve the research objectives,
we incorporate active chemistry into an existing
Lagrangian stochastic (LS) model (Baldocchi, 1997),
and configure it to simulate isoprene flux footprints
from several heights within the canopy. We use the
one-dimensional atmospheric turbulence model developed by Massman (1996) and Massman and Weil
(1999) to define the temporal and spatial variations of
atmospheric turbulence within the LS model domain.
The atmospheric turbulence model prescribes vertical
profiles of the Lagrangian time scale, turbulence
statistics, wind speed and momentum transfer as a
function of leaf distribution. The modeling studies
apply to the Borden forest whose description is
provided below.
2. Site characteristics and field measurements
The data used in the modeling work described
below were obtained during the 1995 growing season
at a mixed deciduous forest in southern Ontario,
Canada (Borden forest, 448190 N, 808560 W). Within
the flux footprint area of the 45 m scaffolding tower,
the 20 m high forest is comprised of: red maple (Acer
rubrum L.), trembling aspen (Populus tremuloides
Michx.), big-tooth aspen (P. grandidentata Michx.),
white ash (Fraximus americana L.), black cherry
(Prunus serotina Ehrh.), birch (Betula lenta L.), beech
(Fagus drandifolia Ehrh.), and scattered stands of red
pine (Pinus resinosa Ait.). During 1995, the total
forest plant area index (PAI, wood, stem and foliage
area) was 5.1 when the canopy became fully foliated
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
161
measured using the gradient diffusion approach.
Within and above canopy profiles of ozone mixing
ratios, temperature and humidity were measured as
well (for additional details, see Fuentes and Wang,
1999; Makar et al., 1999).
3. Methods
Fig. 1. Seasonal plant area index (PAI) measured at the Borden
forest during 1995. Averaged values were deduced from a sample of
10 data points, and bars around the mean denote the standard
deviation. The open symbols (*) represent the PAI data included
in the model simulations (e.g., DOY 256, 285 and 298).
on day of year (DOY) 256. On DOY 298, the forest
PAI value was approximately 1.0 (Fig. 1). The
seasonal PAI and leaf area index (LAI) data were
obtained using a canopy analyzer (model LI-2000,
LiCor, Inc., Lincoln, NB). At the end of the growing
season, total forest leaf area was established by
collecting leaf litter fall in baskets with upper diameter
0.5 m, lower diameter 0.4 and depth 0.3 m. The leaf
litter fall measurements permitted the establishment of
forest foliage clumpingness and thus verification of
the information derived with the plant canopy
analyzer. Using the leaf litter fall and the LI-2000
measurements, the degree of foliage overlapping (i.e.,
clumping index, V) was determined. The ensemble
average V value for the forest was 0.85 0.1
(Staebler et al., 1997). The LAI profiles considered in
this study were reconstructed based on the LI-2000
measurements and the vertical foliage distribution
reported in Neumann and den Hortog (1989). The
reconstructed LAI profiles are realistic as the Borden
forest architecture has changed little since the detailed
foliage survey conducted by Neumann and den Hortog
(1989). At the Borden forest, the primary isopreneemitting species (aspen) were concentrated in the
upper canopy (>10 m above ground), producing the
foliage maximum at z/hc = 0.75 (z is height above
ground and hc is the canopy height). Momentum,
sensible, and latent heat flux densities at 33 m above
the ground were continuously obtained during the
growing season employing eddy covariance methods.
Throughout the growing season, isoprene flux was
In this section, we outline the principal features of
the modified footprint model and the associated
chemical reactions incorporated in the model simulations. Sample chemical reactions are included for the
simple hydrocarbon molecule of isoprene.
3.1. Footprint model description
The source flux footprint or ‘‘effective fetch’’
concept has traditionally applied to momentum
(Pasquil, 1972) or passive scalars such as water vapor
(Gash, 1986). With the traditional footprint framework, one can calculate the probability that air parcels,
detected at the measurement reference height (zm),
emanated from a given source location. For passive
scalars, the footprint is defined as the transfer function
between the downwind flux measurement point (xm,
zm) and the upwind spatial distribution of underlying
sources or sinks (Pasquil and Smith, 1982). The
footprint transfer function for the upwind source
region, f(xm x, z, zm), can be multiplied by the source
distribution, Q(x, z), and integrated over the measurement domain to calculate the passive scalar flux, F(xm,
zm) (Pasquil and Smith, 1982; Schmid, 2002):
Z xm Z zm
Fðxm ; zm Þ ¼
Qðx; zÞf ðxm
1
0
x; z; zm Þ dz dx
(1)
Relationship (1) is shown in the two-dimensional form
for consistency with the modeling methods. In this
study, footprint probability density functions (pdfs)
were determined by releasing 5000 marked parcels at
0.25 m intervals from the ground level to the canopy
crown, giving a total of 405,000 parcels for a 20-m
canopy. We adopt this approach for generality, noting
that isoprene molecules for the Borden forest are
released from the layer defined from 10 to 20 m above
the ground. Parcels released from a given source level
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C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
were allowed to travel until they reached the measurement height. In this study, the sensor height was 27 m
above the ground when active chemistry was considered, corresponding to the lower of two intakes used at
Borden by Fuentes et al. (1996) to estimate isoprene
flux by the gradient diffusion method. When passive
air parcel travel times were tracked, the average height
(33 m) between the two intakes was used. Each parcel
arriving at the sensor height was logarithmically
binned according to the horizontal distance it traveled
while moving vertically between the source level and
the flux measurement level. The number of parcels in
each bin was normalized to the total number of parcels
released from the source level and the size of the bin,
yielding the desired units of probability per meter. The
released parcels moved through the atmosphere due to
advection and turbulent diffusion in two dimensions
(horizontal x and vertical z). Parcel vertical displacement (dz) is the product of the vertical velocity (w) and
the travel time increment (dt) as defined in Eq. (2):
dz ¼ w dt
(2)
Parcels arriving at the forest floor were reflected
perfectly (i.e., z = z and w ¼ w), an assumption
valid for Gaussian turbulence modeling (Wilson and
Sawford, 1996; Baldocchi, 1997). Changes in the
particle vertical velocity (dw) were determined with
the Langevin equation (3):
dw ¼ aw ðz; t; wÞ dt þ bw ðz; t; wÞ dj
(3)
The corresponding relationships for the change in
particle horizontal position (dx) and horizontal velocity (du) were determined following relationships (4a)
and (4b):
dx ¼ ðU þ u0 Þ dt
(4a)
du ¼ au ðz; t; u0 Þ dt þ bu ðz; t; u0 Þ dj
(4b)
u0
where u is the mean horizontal flow and
is the
deviation from the mean flow. In (3) and (4b), the
coefficients aw , au, bw and bu are nonlinear functions
of the particle’s momentum and the statistics of the
flow. When multiplied by dt, the aw and au coefficients
act as the parcel motion’s ‘‘memory’’ to ensure that the
change in velocity deviates appropriately from the
particle’s most recent motion. The bw and bu coefficients are multiplied by a Gaussian random forcing
term (dj) to include the random component of the
parcel motion. The coefficients must be valid solutions
to the budget equation for the Eulerian pdf of the
appropriate flow component (i.e., the Fokker–Planck
equation). In this study, Gaussian turbulence is considered and the u0 and w0 quantities are required to
determine the aw and au coefficients. The aw and au
coefficients are defined in Baldocchi (1997) (see his
Eqs. (10a)–(10d) and (11)), based on the derivation by
Flesch and Wilson (1992). The coefficients for the
random forcing terms in (3) and (4b) are given in (5):
sffiffiffiffiffiffiffiffiffi
2s 2w
bu ¼ bw ¼
(5)
TL
where s w is the standard deviation of the vertical wind
speed. The Lagrangian time scale (TL) is defined as
2ðw0 Þ2 =e, where w0 is the deviation of the vertical wind
speed from the average w and e is the average rate of
turbulent kinetic energy dissipation (Luhar and Britter,
1994). The value for e is given by u2 ðu =kzÞ, where u*
is the friction velocity and k is the von Karman’s
constant (=0.4).
The footprint model described above requires
detailed description of atmospheric turbulence within
and above the forest canopy. To obtain the necessary
atmospheric turbulence information inside a forest
canopy with evolving, vertically inhomogeneous leaf
distributions, the model described by Massman (1996)
and Massman and Weil (1999) was used to define the
vertical profiles of the Lagrangian time scale,
turbulence statistics, wind speed and momentum
transfer. These evolving profiles are an important
addition to the LS model described in Baldocchi
(1997) because of the bimodal leaf distribution found
at the Borden forest (Fig. 2). As formulated in
Massman and Weil (1999), the vertical profile of
kinematic momentum flux (u0 w0 ðzÞ) is defined in (6):
u0 w0
z
¼ e2nð1&ðzÞ=&ðhc ÞÞ
u2
(6)
The overbar on u0 w0 (z) represents the temporal average of kinematic momentum flux. The function z(z) is
the cumulative plant drag area per unit plant form area
and is given in (7):
Z z
Cd ðzÞaðzÞ
zðzÞ ¼
dz
(7)
Pm ðzÞ
0
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
163
kinetic energy variance (s 2u þ s 2v þ s 2w ) for which
Massman and Weil (1999) provide Eq. (10a) with
parameters defined in (10b)–(10d):
s e ðzÞ
¼ ½v3 eLzðhc Þð1zðzÞ=zðhc ÞÞ
u
þ B1 fe3nð1zðzÞ=zðhc ÞÞ
eLzðhÞð1zðzÞ=zðhc Þ g1=3
B1 ¼
L2 ¼
Fig. 2. Vertical plant area density profiles (in units of m1) representing the three scenarios included in the model simulation during
fully leafed (DOY 256, *), 50% defoliated (DOY 285, *) and 75%
defoliated (DOY 298, &) canopy.
9ðu =uðhc ÞÞ
2av1 ½9=4 L2 u4 =uðhc Þ4 1=3 g 23 v21
7
þ
3a2 v1 v3
3a2 v1 v2
n¼
zðhc Þ
2
2u =uðhc Þ2
(8)
The vertical profiles of normalized, within-canopy
turbulent standard deviations were calculated using
(9) (Massman and Weil, 1999):
s i ðzÞ g i y1 s e ðzÞ
¼
u
u
(9)
The subscript i is summation notation for the east-west
(u when i = 1), north-south (v when i = 2), and vertical
(w when i = 3) components of wind, and the g
parameters values g1 = 2.40, g2 = 1.90, and g2 =
1.25 were based on an ensemble of forest observations
(Raupach, 1991). In Eq. (9), se represents the turbulent
(10b)
(10c)
v1 ¼ ðg 21 þ g 22 þ g 23 Þ1=2 ;
v2 ¼
where Cd(z) is the drag coefficient, a(z) is the foliage
area density, and Pm(z) is the foliage shelter factor for
momentum. For this study, the Cd(z) and Pm(z)
assumed the values of 0.2 and 1.0, respectively. The
foliage area density function a(z) includes both the
leaf area and the wood area, and only the wood area
remained after full foliage senescence. A simplifying
assumption is that the drag coefficient is valid for the
plant area (i.e., the Cd(z) is equal for wood and leaf
area). In (6), n is a wind extinction coefficient defined
as shown in (8):
(10a)
v3 g 23
;
6 2v1
(10d)
v3 ¼ ðg 21 þ g 22 þ g 23 Þ3=2
Within the canopy, the wind speed was assumed to
decrease exponentially with depth as shown in (11)
(Massman, 1996):
ūðzÞ ¼ ūðhc Þ enð1zðzÞ=zðhc ÞÞ
(11)
Above the canopy, under static neutral conditions the
wind was modeled to increase with height according to
the logarithmic wind profile
u
zd
ūðzÞ ¼
ln
(12)
z0
kz
where d is the forest zero plane displacement height
and z0 is the roughness length for momentum transfer.
Massman (1996) expressed d and z0 as functions of the
leaf distribution as shown in (13) and (14):
Z 1
2nð1zðzÞ=zðhc ÞÞ
d ¼ hc 1 e
dj
(13)
0
z0 ¼ hc
1 d kuðhc Þ=u þ0
e
hc
(14)
In Eq. (13), z(z) = z/hc, and the +0 in (14) indicates that
no roughness sublayer influences are included. In the
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C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
simulations included in this study, static neutral stability conditions were assumed.
The model described above (Eqs. (2)–(14)) was
applied to the Borden forest utilizing estimated
quantities (e.g., coefficient of drag) and measured
values (e.g., wind speed, momentum flux, etc.) during
the periods when the deciduous forest underwent
defoliation. The period considered in the model
includes DOY 256–298 when the PAI changed from
5.1 to 1.0 (see Fig. 1). To develop the required vertical
PAI profiles after the onset of leaf fall (Fig. 2), the leaf
area profile was reduced according to the total
measured decrease in plant area between model runs,
and the reduction was distributed in proportion to the
modeled wind speed and plant area at each level in the
canopy. The results for three different PAI cases are
reported, including DOY 256 when the canopy was
still fully foliated, DOY 285 when the forest had
approximately 50% of its full PAI, and DOY 298 when
the forest canopy retained about 25% of its full PAI.
For these days, mean u* values estimated from
measurements made above the canopy during the 2 h
about local noontime were used to initialize the model
and obtain the required atmospheric turbulence
information inside the forest canopy. Before leaves
started to fall, strong normalized wind speed, u(z)/
u(hc) (>1.5, Fig. 3) prevailed in the upper region (z >
15 m) of the forest canopy which acted as an effective
momentum sink. Between the ground surface and
15 m, the normalized wind speed remained largely
invariant with altitude, with values <0.1 (Fig. 3). After
the onset of leaf fall, momentum transfer reached
deeper levels in the canopy as revealed by the larger
u(z)/u(hc) values close to the ground (Fig. 3). These
turbulence regimes impacted the profiles of sw(z)
normalized to u* (Fig. 4) as well as the Lagrangian
time scale (Fig. 5). The sw(z)/u* profiles at 1 m above
the ground ranged from 0.2 when the canopy was fully
foliated to 0.6 when the canopy was almost defoliated.
Fig. 3. Vertical wind profiles, u(z), normalized to the wind speed at
the canopy height, u(hc), representing the three scenarios considered
in the atmospheric turbulence model during fully leafed (DOY 256,
*), 50% defoliated (DOY 285, *) and 75% defoliated (DOY 298,
&) canopy.
3.2. Chemical reactions
This section describes how chemical reactions were
incorporated into the LS footprint simulation to
achieve the third research goal. Once in the atmosphere, isoprene (C5H8) rapidly reacts with ozone
(O3), hydroxyl radicals (HO), and nitrate radicals
(NO3) (Atkinson, 1997; Fuentes et al., 2000).
Fig. 4. Vertical profiles for the standard deviation of the vertical
wind speed, sw(z), normalized to the friction velocity, u* (obtained at
33 m above the ground) representing the three scenarios considered
in the atmospheric turbulence model during fully leafed (DOY 256,
*), 50% defoliated (DOY 285, *) and 75% defoliated (DOY 298,
&) canopy.
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
165
scale at the canopy top or 3 s) then [O3], [HO], and
[NO3] can be assumed relatively constant and Eq. (15)
can be solved as a system of first-order simultaneous
reactions. The result is shown in Eq. (16):
½C5 H8 t ¼ ½C5 H8 0 expðk1 ½O3 tÞ expðk2 ½HOtÞ
expðk3 ½NO3 tÞ
Fig. 5. Vertical profiles for the Lagrangian time scale, TL(z),
normalized to the ratio of the canopy height and friction velocity,
hc/u*, representing the three scenarios considered in the atmospheric
turbulence model during fully leafed (DOY 256, *), 50% defoliated
(DOY 285, *) and 75% defoliated (DOY 298, &) canopy.
Ordinarily, the daytime reaction of isoprene with NO3
can be ignored as NO3 radicals can be rapidly
photolyzed. Inside forest canopies, however, the levels
of actinic irradiance are substantially attenuated and
thus photolytic processes are less effective in destroying NO3 radicals. As a result, the NO3 radicals formed
from the reaction of nitrogen dioxide (NO2) with O3
can exist in amounts sufficient to measurably reduce
isoprene concentration (W. Stockwell, 2003; personal
communication). In this study, the three reactions
outlined above (C5H8 + O3 ! products, C5H8 + HO !
products, and C5H8 + NO3 ! products) are used as the
principal destruction mechanism for isoprene at any
level inside and immediately above the forest canopy.
The overall rate of isoprene chemical destruction is
described by Eq. (15):
@½C5 H8 ¼ k1 ½C5 H8 ½O3 k2 ½C5 H8 ½HO
@t
k3 ½C5 H8 ½NO3 (15)
The quantities in brackets, [C], denote the concentrations of the compounds and ki represents the reaction
rate constant for the ith reaction (Table 1). If we
assume a short time step (10% of the Lagrangian time
(16)
where t is the time required for air parcels to travel
from the isoprene emission level to the measurement
point. Within the LS simulation, air parcels released at
a given level within the canopy were assigned an
initial isoprene concentration, x = 1.0 (arbitrary units).
Arbitrary units were employed for convenience of
calculation, and were acceptable because the chemical
reaction rates (Table 1) did not depend on isoprene
levels. During each simulation time step, the isoprene
in each air parcel reacted and became depleted according to Eq. (16), given the air temperature and mean
concentrations of O3, HO and NO3 within the atmospheric layer traversed by air parcel during that time
step. The necessary O3 concentrations were derived
from in situ measurements whereas the HO and NO3
concentrations were estimated using a photochemical
model (see additional details in Section 4.2).
Relationship (1) can be redefined to capture the
flux-reducing effect of active chemistry between the
source release point and the measurement level. Under
conditions of active chemistry, the number of active
isoprene molecules was reduced according to the
cumulative effects of the reactant concentrations along
the isoprene molecule’s travel path and the molecule’s
exposure time to reactants. In this investigation, we
introduce a function, c(xm x, zm), to quantify the
fraction of unreacted isoprene molecules from
emission sites located at xm x to the measurement
point. When each air parcel arrived at the measurement point, its isoprene concentration, x, became less
than or equal to one arbitrary unit. For a given source
location, the unreacted fraction of isoprene molecules
Table 1
Rate constants for reactions involving isoprene (Atkinson, 1997)
Reaction
Rate constants
C5H8 + OH
C5H8 + NO3
C5H8 + O3
k1 = 2.54 1011 exp(410/T)
k2 = 1.0 1012
k3 = 7.86 1015 exp(1913/T)
T = absolute temperature.
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C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
arriving at the measurement point, c(xm x, zm), is
calculated using relationship (17):
PN
p¼1 xp
(17)
cðxm x; zm Þ ¼
N
where N is the number of simulated air parcels arriving
at the measurement point from the emission source
level and xp is the isoprene concentration in each fluid
parcel. The active scalar flux may be estimated by
incorporating c(xm x, zm) into the integrand of Eq.
(1) as shown in (18):
Z xm Z z m
Fðx; zm Þ ¼
cðxm x; zm ÞQðx; zÞf
1
0
ðxm x; z; zm Þ dz dx
(18)
It is useful to couple the traditionally passive footprint
function with the unreacted fraction function (Eq.
(18)) in relating the measured ecosystem flux of active
scalars to the source strength.
4. Results
In this section, we show how defoliation influences
the transport and footprint function of isoprene.
4.1. Effects of defoliation
The estimated atmospheric turbulence characteristics (Figs. 3–5) were incorporated in the canopy
footprint model to evaluate the influences of changing
foliage total amount and vertical distribution. As noted
above (Section 3.1), the atmospheric turbulence
characteristics inside the forest canopy were modeled
based on measurements made above the Borden
forest. The footprint calculations included in Fig. 6
apply to the 27 m level for the leaf area distribution
and the various ranges of friction velocities represented in Figs. 2–5. Flux footprint pdfs are shown in
Fig. 6 as a function of upwind distance from the
measurement point (x) and release height within the
canopy (z), and the integration of each with respect to
x and z yields unity. Before canopy defoliation (with u*
= 0.60 m s1), the footprint results indicated that the
most probable source location for air parcels
contributing to flux was 40 m away from the
measurement point, along a vertical line from the
forest floor to 15 m above the ground (Fig. 6a). After
DOY 256, one effect of forest defoliation was to
enhance the vertical inhomogeneity of the isoprene
source footprint. For example, for the case of DOY
285 (with u* = 0.66 m s1) the peak footprint
probability for the lower and mid-canopy depths
was still approximately 40 m from the measurement
point, but the peak footprint probability in the forest
crown shifted to within 25 m of the measurement point
(Fig. 6b). The footprint vertical inhomogeneity was
maximized on DOY 298 (with u* = 0.89 m s1), when
the peak probability in the lower canopy shifted to
55 m away from the measurement point and the peak
probability in the upper canopy moved to within 15 m
of the measurement point (Fig. 6c). The increased
tilting of the peak probability region (area within the
log10 pdf contour 2.5 m1) between DOY 256 and
298 (Fig. 6a–c) reflected two changes that accompanied canopy defoliation at the Borden forest. First,
increased TL and higher values of sw/u* in the forest
crown yielded relatively high air parcel vertical
velocities, thereby increasing the probability that
crown sources near the measurement point could
contribute to the measured flux. Second, greater
horizontal wind penetration into the lower canopy
caused air parcels to travel farther horizontally before
ejecting from the canopy, thus increasing the
probability that low-level sources far from the
measurement point could contribute to the measured
flux.
To further understand the effects of defoliation, the
footprint results shown in Fig. 6 were integrated with
respect to z (Fig. 7a). Although the forest crown
footprint shifted closer to the measurement point
during defoliation (Fig. 6a–c), the integrated effect for
the entire forest depth was to increase the influence of
farther upwind sources, shifting the vertically integrated footprint peak away from the measurement
level. For the fully leafed canopy, the footprint pdf
reached maximum values within 30–40 m upwind
from the measurement point. Under 75% defoliation
(DOY 298), the peak footprint probability was situated
approximately 40% farther from the measurement
point. When considering the cumulative footprint
functions (Fig. 7b), the distance capturing 90% of the
source region is approximately 46% farther from the
measurement point on DOY 298 compared to DOY
256.
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
4.2. Effects of parcel travel time and rapid chemistry
A second goal of this study was to determine the
amount of time air parcels reside within the forest
canopy, thereby providing information about the
potential rate of isoprene destruction due to chemical
reactions. To perform general numerical simulations
(not for just isoprene), fluid parcels were released from
four source levels: z/hc = 0.25, 0.50, 0.75, and 0.90.
For the Borden forest, these four release levels
represent the maple foliage maximum (z/hc = 0.25),
the midpoint between the maple and aspen foliage
maxima (z/hc = 0.50), the middle aspen foliage
167
maximum (z/hc = 0.75), and the upper crown (z/hc =
0.90). Each air parcel’s residence time was determined
by tracking the total time the parcel stayed in the
canopy before reaching the 33 m height (this altitude
represents half way between the two intakes used to
determine the canopy isoprene fluxes reported in
Fuentes et al. (1996)). Two scenarios were considered:
fully foliated and partially foliated conditions (Fig. 8).
For fully foliated conditions (DOY 256), median
within-canopy parcel residence time for each of the
four source levels ranged from 20 s to approximately
40 min. For the sources located from z/hc = 0.25 to z/hc
= 0.75, the median residence time decreased roughly
Fig. 6. Contour plot of the flux footprint probability density function (pdf) representing the conditions during (a) fully leafed canopy (DOY 256),
(b) 50% defoliated canopy (DOY 285) and (c) 75% defoliated canopy (DOY 298).
168
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
Fig. 6. (Continued ).
logarithmically with release height (Fig. 8). For
partially defoliated conditions (DOY 298), the median
residence time exhibited less variability with release
altitude, and the maximum residence time was
reduced to approximately 10 min. We conclude that
these within-canopy air parcel residence times, for
fully and partially foliated conditions, are sufficient to
allow substantial chemical destruction of isoprene in
Fig. 7. (a) Flux footprint probability density functions (pdfs) for the
27 m sensor level during fully leafed (DOY 256, *), 50% defoliated
(DOY 285, *) and 75% defoliated (DOY 298, &) conditions. (b)
Cumulative flux footprint probability density functions during fully
leafed (DOY 256) and 75% defoliated (DOY 298) conditions.
Fig. 8. Air parcel residence times in the Borden canopy for four
release heights (z/hc = 0.25, 0.50 0.75 and 0.90) under fully foliated
conditions (DOY 256) and late fall conditions (DOY 298). The
associated plant density profiles are shown in Fig. 2. For the box
plots, the bold horizontal line is the mean, the thin horizontal line is
the median, the shaded box shows the inner-quartile range, the error
bars denote the 10th and 90th percentiles, and outlier data are shown
as circles.
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
environments with well-mixed reactant chemical
species in amounts similar to those observed at the
Borden forest (see details in discussion of Figs. 11–
13).
To account for the parcel exposure time to reactants
above as well as within the forest canopy, it is useful to
study the total travel time between air parcel release
and arrival at the measurement point. The results for
the air parcel total travel times are shown in Fig. 9a–c,
along with the associated footprint functions to
indicate the relative probability of the various travel
times. For the releases from z/hc = 0.25, the footprint
peaked approximately 50 m from the measurement
point, and 90% of the integrated footprint was
captured within 200 m upwind from the measurement
point (Fig. 9a). The air parcel travel times ranged from
0.8 to 114 min, and were distributed approximately
log-normally for any given distance from the
measurement point. For air parcels released from z/
hc = 0.75 (Fig. 9b), median travel times increased
approximately linearly away from the measurement
level (similar to the results for release from z/hc =
0.25), but the total range of travel times was somewhat
shorter (0.15–85 min). In addition, the median travel
time from each distance was generally shorter than in
the z/hc = 0.25 case, and the travel time distributions
exhibited an enhanced positive skewness. The travel
time distributions for air parcels released from z/hc =
0.90 (Fig. 9c) exhibited even greater positive
skewness, and had median travel times of less than
a minute for an upwind distance of 63 m from the
measurement point (compare to a distance of 50 m for
z/hc = 0.75 and the absence of such short median travel
times for z/hc = 0.25). At any particular upwind
distance from the measurement point, the travel times
for air parcels released from z/hc = 0.90 became
comparable to, or even longer than, travel times for
releases from the z/hc = 0.25 level. These longer travel
times were associated with air parcels that re-entered
the canopy air space from above the forest, and the
lower wind speeds inside the canopy.
The third objective of this study was to estimate
isoprene destruction rates due to chemical processing
inside the forest canopy. The O3 concentration profiles
included in the model simulation were taken from
measurements made at the Borden forest on 1
September 1995 (Fig. 10). Ozone levels above and
within the forest canopy are included in Fig. 10 to
169
illustrate the temporal, prevailing O3 concentrations
considered in the model simulations. Between 11:00
and 17:00 h (local time), ozone was relatively well
mixed in and above the canopy, with a maximum mean
concentration observed at 16:30 h local time. To
evaluate the greatest magnitude of the chemistry effect
being studied, the O3 levels selected for the simulation
correspond to the 16:00–17:00 h period. The O3
profile extracted from 16:30 h varied from 7 1011 molecules per cm3 at the forest floor to about 8 1011 molecules per cm3 above the forest canopy (data
not shown). The HO profiles, estimated using a
photochemical model (Makar et al., 1999) run for
16:30 h conditions at Borden, ranged from 7 106 radicals per cm3 near the forest floor to
approximately 2 107 radicals per cm3 above the
forest canopy (data not shown). Daytime NO3
concentrations were assumed to be 1 108 radicals
per cm3 within the canopy, and 0.0 radicals per cm3
above the canopy. To quantify the relative importance
of the three reactions involved in isoprene destruction,
Figs. 11–13 show the fraction of isoprene molecules
remaining after reacting with different concentrations
of O3, HO and NO3. Based on local O3 measurements
(Fig. 10) made at the Borden forest, the three baseline
O3 concentrations included in the modeling study
(each 0.8 1012 molecules per cm3) produced only
a 10% depletion of isoprene (Fig. 11), even with the
longest recorded air parcel travel times (>100 min,
Fig. 9). The isoprene destruction rate through reaction
with HO was higher than the one associated with O3
reactions (Fig. 12). Inside the canopy, the HO
concentrations showed gradients with values of 10
106 hydroxyl radicals per cm3 at the top of the
canopy and 50 106 hydroxyl radicals per cm3 close
to the forest floor (see also Makar et al., 1999). Due
to these HO concentrations alone, approximately
30% of the isoprene was destroyed within 10 min.
This time represented the median travel time for
air parcels originating from the z/hc= 0.25 level
and 100 m away from the measurement level. The
NO3 radical concentrations used in this study can
cause 30% isoprene depletion after 30 min of travel
time.
The integrated isoprene rate of destruction was
obtained by running the LS footprint simulation with
active chemistry at each step for a fully leafed canopy.
The results reported here (Fig. 14) are for release
170
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
Fig. 9. (a) Flux footprint probability density function (pdf) and cumulative flux footprint pdf for the 33 m level above the Borden canopy, release
at z/hc = 0.25, and fully foliated conditions (DOY 256). Box plot symbols are as described in Fig. 8. (b) The same as (a), except for release at z/hc
= 0.75. (c) The same as (a), except for release at z/hc = 0.90.
heights of z/hc = 0.25, z/hc = 0.75 and z/hc = 0.90, and
correspond to the chemical concentration profiles
during 16:30–17:00 h (Fig. 10). The simulated
footprints integrated to 90% approximately 200 m
upwind from the 33 m measurement height (Fig. 14a,
integrated footprints not shown). Within this 200 m
range, median travel times were generally less than
20 min and air parcels arrived at the measurement
level with approximately 70% of their original
isoprene molecules (Fig. 14b). When examining the
unreacted fraction of isoprene as a function of distance
from the measurement level for the various release
heights, the greatest differences occurred 100 m from
the measurement point (0.89 unreacted for z/hc = 0.90,
0.86 unreacted for z/hc = 0.75, and 0.74 for z/hc =
0.25). Air parcels emanating from 800 m upwind from
the measurement point experienced 60% depletion of
the original isoprene molecules before they reached
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
171
Fig. 10. Time series of ozone concentrations measured above and
below the Borden forest canopy during 1 September 1995.
the measurement level (shown as arriving with 0.40
unreacted fraction, Fig. 14b). This 60% isoprene
depletion constituted a substantial isoprene sink for air
parcels originating from within an 800-m upwind
distance. When considering the footprint and
unreacted fraction functions together, most of the
isoprene molecules contributing to the total flux
observed above the canopy emanated from within 20–
200 m of the measurement level. The size of these
effective source areas, combined with the computed
air parcel travel times for fully foliated conditions,
produced an overall rate of isoprene destruction
ranging from 12 to 40% for the conditions observed
during 16:30–17:00 h (Fig. 10) at the Borden forest.
Fig. 11. Fraction of isoprene remaining as a function of time after
reacting with various concentrations of ozone.
Fig. 12. Fraction of isoprene remaining as a function of time after
reacting with hydroxyl radicals. The hydroxyl levels were obtained
from a photochemical model (Makar et al., 1999) and from global
annual averages based on the emissions, atmospheric concentrations
and chemistry of methyl chloroform (Prinn et al., 1995; Hein et al.,
1997).
These results may explain and confirm the discrepancies reported between measured and modeled
ecosystem-level isoprene fluxes (Fuentes et al., 1996;
Geron et al., 1997; Lamb et al., 1996; Makar et al.,
1999).
Fig. 13. Fraction of isoprene remaining as a function of time after
reacting with nitrate radicals. The nitrate levels were based on
Atkinson’s (1991) recommendation for nocturnal lifetime calculations (for inside the forest canopy).
172
C. Strong et al. / Agricultural and Forest Meteorology 127 (2004) 159–173
Fig. 14. (a) Borden forest flux footprints for the 33 m sensor level
and air parcels releases from z/hc = 0.25, 0.75 and 0.90. (b) Fraction
of isoprene remaining in air parcels based on execution of Eq. (6) in
each time step from parcel release to arrival at the measurement
point.
5. Summary and conclusions
A coupled modeling system was employed to
investigate the influences of active chemistry and
foliage senescence/abscission on the effective source
distribution of isoprene for a mixed deciduous forest.
We conclude that forest defoliation modified atmospheric turbulence characteristics in such a manner as to
increase the size of the area contributing to the isoprene
flux densities (i.e., the upwind distance at which the
footprint integrates to 0.90 moved farther from the
measurement point). As leaves abscised, maximum
footprint probabilities for source releases within the
crown shifted toward the measurement point, but the net
effect was a footprint peaking farther from the
measurement point due to increased turbulence reaching the deeper levels of the forest canopy. For example,
when the forest retained 50% of its total foliage, the size
of the footprint (0.90 integration distance) was
approximately 46% larger than the case for the fully
leafed canopy. This constitutes an important result that
will aid in deriving proper interpretation of biogenic
hydrocarbon fluxes from larger source areas whose
basal emissions are heterogeneous.
It is also concluded that defoliation impacted air
parcel residence times within the canopy. Under fully
foliated conditions, air parcels released from the z/hc =
0.25 level sometimes remained within the canopy for
periods reaching up to 1 h, depending on levels of
atmospheric turbulence and the upwind horizontal
distance of particle release (with releases closest to the
forest floor showing the longest residence times).
After defoliation, mean residence times were more
uniform as a function of release height. Under the
influence of 25–75% defoliated conditions, air parcels
remained in the forest canopy for periods lasting less
than 10 min. The estimated air parcel residence times
inside the fully leafed canopy resulted in substantial
isoprene chemical processing. Based on the Lagrangian stochastic footprint simulations with active
chemistry, the integrated portion of isoprene destroyed
by reactions with ozone, hydroxyl, and nitrate
radicals, ranged from 12 to 40% for parcels within
forest crown and floor, respectively. These results
provide an explanation for reported discrepancies
between measured and modeled isoprene fluxes at the
landscape level. We conclude that active scalar flux
estimates, often based only on the footprint transfer
function and source strength distribution, can be
substantially improved by incorporating an active
chemistry term.
Acknowledgements
This material is based on work supported under a
National Science Foundation (NSF) graduate research
fellowship provided to C. Strong. J.D. Fuentes
acknowledges NSF support through award OPP0137420. Two anonymous reviewers provided excellent comments to improve the original manuscript. Prof.
Timo Vesala, University of Helsinki, is acknowledged
for inviting and providing partial funding for the
authors’ participation in the Third INTAS Workshop on
Flux and Concentration Footprints at the Hyytiälä
Forestry Field Station, University of Helsinki, Finland.
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