Tree Physiology 21, 815–830
© 2001 Heron Publishing—Victoria, Canada
Importance of needle age and shoot structure on canopy net
photosynthesis of balsam fir (Abies balsamea): a spatially inexplicit
modeling analysis
PIERRE Y. BERNIER,1 FRÉDÉRIC RAULIER,1 PAULINE STENBERG2 and CHHUN-HUOR
UNG1
1
Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre, 1055 du P.E.P.S., P.O. Box 3800, Sainte-Foy, Québec, G1V 4C7,
Canada
2
Department of Forest Ecology, P.O. Box 24, FI-00014 University of Helsinki, Finland
Received August 18, 2000
Summary We have developed a spatially inexplicit model
of canopy photosynthesis for balsam fir (Abies balsamea (L.)
Mill.) that accounts for key processes of light–shoot interaction including irradiance interception by the shoot, spatial aggregation of shoots into branches and crowns, the differential
propagation of diffuse and direct light within the canopy, and
an ideal representation of penumbra. Also accounted for in the
model are the effects of the average radiative climate and shoot
age on needle retention, light interception, and photosynthetic
capacity. We used reduced versions of this model to quantify
the effects of simplifying canopy representation on modeled
canopy net photosynthesis. Simplifications explored were the
omission of direct beam transformation into penumbral light
and the use of different constant shoot properties throughout
the canopy. The model was parameterized for a relatively
dense balsam fir stand (leaf area index of 5.8) north of Québec
City, Canada, and run using hourly meteorological data obtained at the site. The overall performance of the complete
model was satisfactory, with maximum values of canopy net
photosynthesis of 23 µmol (m 2 ground) –1 s –1 (83 mmol m –2
h–1), and a near-saturation of the canopy at a photosynthetically
active radiation photon flux density of about 750 µmol m –2 s –1
(2.7 mol m –2 h –1). The omission of penumbral effects through
the use of unattenuated direct (beam) radiation at all layers of
the canopy, as used for broad-leaved species, reduced canopy
net photosynthesis by 3.7%. Analysis of the results show that
the small impact of penumbra on canopy net photosynthesis
stems from the high proportion of diffuse radiation (73%) estimated from our meteorological data set; single-hour results under clear sky conditions approach theoretical bias values of
about 30%. Use of mean shoot photosynthetic, light capture
and light transmission properties throughout the canopy biased
canopy net photosynthesis by less than 3%. However, simulations carried out based on properties of 1-year-old shoots
throughout the canopy overestimated canopy net photosynthesis by 9%. Use of the shoot as our smallest functional
unit was a potential source of bias because the differential ab-
sorption of direct and diffuse radiation within the shoot could
not be factored into the model. Other sources of potential bias
are discussed.
Keywords: diffuse radiation, direct beam radiation, leaf mass
per unit area, penumbra, STAR.
Introduction
Process-based modeling of forest productivity requires an unbiased modeling of canopy net photosynthesis. Recent advances in our understanding of the distribution of internal and
external resources within the canopy have permitted the development of canopy photosynthesis models for broad-leaved
hardwoods and conifers (Ellsworth and Reich 1993, Aber et
al. 1995, Leuning et al. 1995). The key to these models is the
representation of the interaction between light and the photosynthetic properties of foliage.
Spatial interactions between light and photosynthetic properties within a canopy can be represented at different resolutions, and choosing the proper resolution usually depends on
the intended use. For application to a variety of sites, it is advantageous to develop a model with a functional description of
canopy properties, in which the canopy properties are captured by the distribution function of selected leaf or shoot
properties, not by the spatial distributions of their elements.
Nitrogen (Leuning et al. 1995, De Pury and Farquhar 1997)
and leaf mass per unit leaf area (Aber et al. 1995) have been
used to achieve spatially inexplicit descriptions of canopies.
Such functional representations can accurately describe the
spatial distribution of the photosynthetic properties within the
canopy. In broad-leaved species, this can be combined with a
sun-shade, single-layer light environment to further simplify
canopy representation (Leuning et al. 1995).
The development of a spatially inexplicit model for conifers
faces difficulties linked to three specific characteristics of conifer foliage. First, the aggregation of conifer needles into
shoots exerts substantial control over the light–leaf interaction
816
BERNIER, RAULIER, STENBERG AND UNG
through the angular distribution of the needles and the selfshading within the shoots (Oker-Blom and Smolander 1988,
Leverenz 1995). In turn, the spatial arrangement of this aggregation is often influenced by the light regime in which it developed (Carter and Smith 1985). Second, the small size of the
needles, with respect to the solar disk, permits transmission of
direct radiation deep within the canopy, but in an attenuated
form known as penumbra (Stenberg 1995). The prevalence of
penumbra enhances the efficiency of light capture by needles
(Stenberg 1998). Third, the retention and aging of needles has
the double effect of decoupling the needle and shoot properties
from their ambient light environment, and of impairing the
photosynthetic response of needles. Our measurements show
needle retention of up to 12 years in balsam fir. A complete
canopy model of evergreen conifers should account for all of
these needle characteristics.
Mean shoot properties and total leaf area can be derived
with relative ease at the plot level. Determining the distribution of properties such as age and shoot structure within the
plot or stand requires additional intensive sampling that can be
carried out only on a restricted number of sites. In order to facilitate application of the model to diverse sites, we must then
strive to develop models that accurately represent the shoot–
light interactions within coniferous canopies, but at the same
time to simplify the canopy representation and thus the input
requirements of the model. The objectives of this work were,
therefore, to develop a spatially inexplicit model of balsam fir
canopy photosynthesis, and to determine the bias incurred
when age effects on physiological and morphological variables were omitted, and when shoot geometry was considered
uniform throughout the canopy.
Material and methods
Study site
Field measurements were performed at a research site located
within Université Laval’s Forêt Montmorency. Forêt Montmorency is located in the Laurentian highlands about 100 km
north of Québec City, (71°06′ 00′′W, 47°19′00′′Ν), and lies
within the balsam fir–white birch domain, ecological region 8f
of Thibault and Hotte (1985) with between 890 and 1000 degree-days above 5 °C annually. The site lies on a west-facing
slope, at an altitude of 800 m, and is underlain by a welldrained, coarse glacial deposit with a moderate stone content.
Slope varies between 15 and 25%. The stand is nearly pure and
even-aged balsam fir, forming a dense, closed canopy with a
sparse ground cover of mosses and small vascular plants. The
stand originated from a clearcut in the 1930s. Mean tree height
is 17 m. Composition by percent contribution to basal area is
91% balsam fir (Abies balsamea (L.) Mill.) and 9% white
birch (Betula papyrifera Marsh.). Total basal area of the stand
is 19.8 m2 ha –1.
In the spring of 1997, a 17-m canopy access tower was
erected at the Forêt Montmorency site to permit the measurement of leaf gas exchange in canopies of three adjacent balsam
fir trees. A meteorological tower was also built and instru-
mented with various sensors to monitor above- and belowcanopy environmental variables. Incident shortwave radiation
was measured above the canopy with Li-Cor silicon pyranometers (Model LI-200S, Li-Cor, Lincoln, NE). Other environmental sensors were mounted on or around the towers. All
sensors were scanned every 5 min. The hourly mean of their
readings was recorded with a data logger.
Leaf gas exchange
Light response curves were obtained on four 1-year-old shoots
on July 6, 1998. Shoots were considered the elemental units
for gas exchange measurements. The light response measurements were carried out on attached shoots with an open-mode,
portable, gas-exchange measurement system (LCA4, Analytical Development Corporation, Hoddesdon, U.K.) using a cylindrical cuvette designed for use with conifers. Shoots were
placed in the cuvette with their upper side facing the light
source. Cuvette and needle temperatures were monitored with
built-in sensors and energy balance corrections. The light
source consisted of a white halogen bulb and reflector
mounted on the cuvette. Air gaps and thermal filters prevented
heating within the cuvette. Irradiance was controlled with a
built-in voltage regulator, coupled with a diffuser and small
neutral-density filters. Irradiance in the cuvette was measured
before each measurement with a small detachable quantum
meter. All irradiance measurements reported in this text are
for photosynthetically active radiation (PAR) wavelengths.
Five measurements were performed for each shoot at or near
irradiances of physiological interest according to the recommendations of Hanson et al. (1987). Total darkness was obtained by wrapping aluminum foil around the cuvette.
The effect of light climate on photosynthetic properties was
measured on nine 1-year-old shoots evenly distributed on
three trees in reach of the access tower and selected to span the
whole range of radiative environments, on May 8 and 27,
1998. On each occasion, maximum photosynthesis was measured on the attached shoots in artificial light at PAR irradiances greater than 1200 µmol m –2 s –1.
The effect of age on shoot morphology and photosynthetic
properties was measured on four branches on two occasions:
two branches of the upper canopy on June 12, 1998, and two
branches of the middle and lower canopy on June 11, 1999. On
each occasion, maximum photosynthesis was measured on the
shoots of all age cohorts along the main axis of the branch,
with the youngest shoot being that of the preceding year. Measurements were performed on detached shoots in artificial
light in excess of 1300 µmol m –2 s –1. Terminal shoots were cut
and immediately placed in the cuvette. The cut end of the
shoot was covered with vacuum grease. Measurement of maximum photosynthesis was carried out within 2 to 3 min. We
worked our way sequentially down the main axis of the
branches until needles became sparse in the older age cohorts
(foliage up to 9 years old).
One possible confounding factor with leaf age is branch respiration because older cohorts are supported by branch segments of larger diameters. We therefore measured respiration
TREE PHYSIOLOGY VOLUME 21, 2001
NEEDLE AGE, SHOOT STRUCTURE AND CANOPY NET PHOTOSYNTHESIS IN BALSAM FIR
of leafless branch segments of different diameters. The segments were cut and placed in the cuvette after covering the cut
ends with vacuum grease. Respiration rates of a total of
25 segments with diameters ranging from 3 to 15 mm were
measured. The data were used to produce a simple model of
respiration as a function of branch surface area, which was
then used to correct the measured photosynthetic rates of the
different age cohorts.
All gas exchange measurements are expressed on a needle
hemisurface area basis. Measurement methods for obtaining
total leaf area are detailed below.
Light measurements
We determined the mean irradiance for shoots on which gas
exchange measurements were made using the technique of
Parent and Messier (1996). Under completely overcast conditions, simultaneous horizontal measurements of PAR were
made above the canopy and at the exact location of the shoots.
Light response curves were made with detached shoots. Labels were placed in the tree to indicate the original location of
the detached shoots. Shoots used in the age cohort measurements were made only on the 1999 branches before photosynthesis measurements on the different age cohorts were
destructively sampled. Measurements were made with Li-Cor
quantum sensors (Model LI-190SB) scanned and recorded every second with a data logger. The ratios of shoot-level to
above-canopy PAR measurements were computed from 10-s
means.
Sampling the canopy
Destructive sampling was performed to determine four canopy characteristics: total canopy leaf area, distribution of leaf
area per class defined by needle mass per unit hemisurface
area (NMA, g m–2 needle), distribution of leaf area per classes
of shoot age, and distribution of leaf area per classes defined
by mean STAR (silhouette to total area ratio). The measurements were made within the stand, in two 400-m2 satellite
plots located about 100 m from the central plot containing the
canopy access tower and the meteorological instruments.
Within each satellite plot, we measured tree diameter at breast
height and assigned trees to one of three social classes: dominant, codominant and intermediate or suppressed. One or two
trees from each social class were selected and felled for destructive determination of needle mass and area. The crown
was separated into two portions, above and below greatest
crown width. The upper portion was further subdivided vertically into three equal parts. All the branch diameters at their
insertion point were measured in each crown part. A branch of
the median whorl was then selected at random by a process
based on the cross-sectional area of the branch at its insertion
point, which is considered proportional to needle area (Shinozaki et al. 1964), and by extension to total shoot area.
Randomized branch sampling (RBS, Gregoire et al. 1995)
was applied once within each branch for shoot sampling. With
RBS, each branch is considered as a network of segments and
nodes. Starting at the base of the branch, each node of the seg-
817
ment to follow was selected at random after weighting the different segments at that node according to their basal area.
Foliated segments on the path were divided into yearly growth
units (shoots) and collected for further analysis.
To estimate the distribution of total shoot area per class of
needle mass per unit hemisurface area (NMA), age or mean
STAR, we first estimated the frequency at the stand level that
each collected shoot would represent. The frequency, ν, represented by a single sampled shoot was calculated as:
ν sbptc =
c
S sbptc
Aptc G c
Qsbptc Acptc G cc S plot
,
(1)
where subscripts s, b, p, t and c represent a shoot (s) on a
branch (b) selected in crown portion (p) of a tree (t) in social
class (c). Superscript c indicates a collected sample. Variable S
is shoot hemisurface area (m2, includes needle and twig areas),
Q is the expansion factor of shoot s on the branch (Gregoire et
al. 1995), A is the sum of branch basal areas (cm2), G is basal
area at the plot level (m2 ha–1) and Splot is the plot shoot area.
Distribution of properties within the canopy were computed
from these frequencies, as in Raulier et al. (1999). Table 1 lists
the main symbols used in the text.
In each satellite plot, measurements of irradiance below the
canopy at a range of incident angles were obtained with a plant
canopy analyzer (PCA, LAI-2000, Li-Cor) under an overcast
sky and before the destructive sampling. Measurements were
carried out at three points near the plot center. For each point,
the measurements were repeated three times with the PCA.
Another PCA was programmed to measure open-sky irradiance continuously in a nearby clearing.
Shoot analysis
After the measurements or samplings were completed, the
shoots were detached and brought to the laboratory for further
analysis. Shoot silhouette areas were measured with a 600 dpi
video camera (Elmo CCD Model SE360, Plainview, NY)
mounted above a light table. Projected areas of the shoots were
measured at five different combinations of elevation (φ) and
rotation (γ) of the shoot main axis (sensu Stenberg 1996) (φ,γ
in degrees are: 0,0; 0,45; 0,90; 45,0; 45,45). Area measurements of the scanned images were carried out with image analysis software (NIH Image v1.61, National Institutes of Health,
Bethesda, MD).
Total needle area per shoot was obtained in a two-step process. First, total projected needle area was measured by scanning all detached needles with a Hewlett Packard 600 dpi
scanner (Scanjet IIcx/T). Image analysis was performed with
the WinNeedle software (Régent Instruments, Québec, Canada). Within shoots, we selected five needles at random, and
obtained thin cross sections at their midpoint. The cross sections were scanned at 1850 dpi (ScanMaker 1850S, Microtek,
Redondo Beach, CA) and measurements of their perimeter
and width obtained with the NIH image analysis software and
averaged for each shoot. Total needle area of each shoot was
computed by multiplying the projected area by the mean cal-
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818
BERNIER, RAULIER, STENBERG AND UNG
Table 1. List of the main symbols used. Secondary symbols are explained in the text.
Symbol
Description
Ac
Amax
An
as
Ib, Ib0, Id, Id0
Canopy net photosynthesis (µmol (m2 ground)–1 s –1)
Photosynthetic capacity (µmol (m2 needle)–1 s –1)
Shoot net photosynthesis (µmol (m2 needle)–1 s –1), expressed on a hemisurface area basis
Shoot age
Mean direct (b) or diffuse (d ) PAR irradiance on a horizontal surface (µmol (m2 ground)–1 s –1), Ib0 and Id0 are measured at
the top of the canopy
PAR irradiance intercepted per unit of shoot hemisurface area at the compensation point (µmol (m2 shoot)–1 s –1)
Extinction coefficients for direct (b) and diffuse (d) irradiances
Mean direct (b) or diffuse (d) irradiance intercepted per unit of shoot hemisurface area (µmol (m2 shoot)–1s–1) either for
a given shoot layer (s.b, s.d) or for its sunlit fraction (s.b0)
Needle mass per unit area (g m –2), expressed on a shoot hemisurface area basis
Needle hemisurface area per unit of shoot hemisurface area
Needle dark respiration (µmol (m2 needle)–1 s–1)
Shoot STAR, shoot mean STAR and canopy mean STAR
Shoot area index (m2 shoot (m2 ground)–1), expressed on a hemisurface area basis
Azimuth
Rotation angle of the plane separating the upper and lower parts of a shoot
Zenithal angle
Elevation angle of shoot main axis
Shoot clumping index
Ic
k b, k d
I s.b0, I s.b, I s.d
m*
n*
Rd
s*, s *, s c*
S*
α
γ
θ
φ
Ω
culated perimeter:width ratio of the five cross sections. Measured needles were weighed after drying at 65 °C for 48 h.
Cross section measurements were performed on all shoots
used for gas exchange measurements. Based on these measurements, a mean value of 2.45 was used to convert projected
to total leaf area in the 258 shoots sampled for canopy description. Values of NMA were computed as the ratio of needle dry
mass per unit of needle hemisurface (half total surface) area.
Values of STAR were determined for each shoot used in the
gas exchange measurement, as well as for each of the 258
shoots obtained from RBS sampling in the two satellite plots.
First, each of the five values per shoot of STAR (φ,γ) was computed as the corresponding silhouette area divided by the total
shoot area. Total needle and twig areas were combined to estimate total shoot area. Inclusion of the twig surface is important in order to obtain sensible values of STAR (sensu Lang
1991) for older shoots in which needle density is low. The five
observed STAR values were then fitted to a function modified
from Equation 4 of Stenberg (1996):
s* (φ,γ) = a + b cos φ − c γ cos φ ,
s* =
2
π
π 2π 2
∫ ∫ s ( φ,γ) cos φ dφ dγ
*
0
0
(3)
c π
π
= a +  b − .
4
4
The mean canopy STAR was estimated for each satellite
plot by summing the mean STAR of the sampled shoots
weighted by their frequency at the plot level (Equation 1).
Mean canopy STAR’s of both plots were then averaged to produce a mean canopy STAR for the stand.
Model development
The model developed below uses the shoot as the smallest
functional unit, and considers all factors except light as nonlimiting for photosynthesis. In that context, a multilayer model
needs to detail three properties of the canopy: the transmission
of irradiance through the canopy, the irradiance interception
by the foliage and the sensitivity of photosynthesis to irradiance. Scattering of photosynthetically active radiation is not
considered (Baldocchi 1993).
(2)
Choice of covariables characterizing the shoot population
where s* is STAR, and a, b and c are fitted parameters. Parameter a is the minimum STAR, the sum of parameters a and b
corresponds to the maximum STAR and parameter c characterizes the effect on STAR of the lateral asymmetry of the
shoot. Mean STAR, or s *, of each shoot was then obtained by
substituting the values of the three corresponding parameters
in the following equation obtained by integrating Equation 2
over φ, γ (Stenberg 1996):
Spatially inexplicit multilayer models can stratify the canopy
into layers specified by a given shading leaf area index (LAI)
between the open-sky and the considered layer (e.g., Reich et
al. 1990, Leuning et al. 1995). In turn, this shading LAI serves
to estimate the average light climate observed within the layer,
which itself is well correlated to the photosynthetic properties
of foliage. This is especially true with deciduous broad-leaved
species (Reich et al. 1995, Raulier et al. 1999) but also holds
for fir. Needles of fir are known to adapt morphologically and
TREE PHYSIOLOGY VOLUME 21, 2001
NEEDLE AGE, SHOOT STRUCTURE AND CANOPY NET PHOTOSYNTHESIS IN BALSAM FIR
physiologically to their radiative environment (Clark 1961,
Morgan et al. 1983, Brooks et al. 1996, Sprugel et al. 1996). In
conifers, average light climate within the canopy is known to
be correlated to shoot properties like needle density and STAR
(Piene 1983, Carter and Smith 1985, Boyce 1993, Sprugel et
al. 1996, Stenberg et al. 1998), as well as NMA (Morris 1951).
In a preliminary analysis, we therefore focused on two of these
variables, STAR and NMA, as possible covariables to represent the light climate distribution within the canopy. A preliminary analysis of the data revealed that NMA of needles less
than 4 years old was better related to both mean, diffuse light
environment and shoot, maximum photosynthetic rates than
mean STAR (see Results section). The NMA was therefore
chosen as the main covariable to describe the shoot population.
Shoot age also needs to be considered. The light environment at the time of shoot formation affects needle morphology
and shoot STAR. On the other hand, the light environment of
the needle changes during its life span, and needle photosynthetic properties are simultaneously affected by age and
current light environment (Brooks et al. 1996). In addition, the
NMA of needles may increase with age (Morris 1951, Gilmore et al. 1995). Age must therefore be taken into account in
the relationship between the NMA and both the mean light climate (and shading LAI) and leaf photosynthetic properties.
For each satellite plot, we therefore computed the distribution frequency of the shoot population by classes of NMA and
age by cumulating the shoot frequencies (Equation 1) in each
class. The NMA and age classes were chosen to have 20 g m –2
and 1-year amplitudes, respectively. A mean of plot frequency
values was calculated for each class to scale at the stand level.
The average radiative environment of each NMA and age
class was estimated from a linear model adjusted to our field
data that considered both simple effects and the interaction of
NMA and age:
Td = τ1 + τ 2 m * + τ 3 a s + τ 4 m *a s ,
(4)
where Td is the observed canopy transmission of diffuse
irradiance, m* is NMA (g m –2 ), as is shoot age and τ1 to τ4 are
parameters estimated by ordinary least squares (OLS) (Table 2).
Light transmission through the canopy
Irradiance needs to be separated into its diffuse and direct
(beam) components because they differ in canopy penetration
dynamics (Norman 1993). Because of the small size of the
needles relative to canopy depth, penumbra also needs to be
considered for modeling PAR distribution, as it reduces the
fraction of foliage in full shade and evens out direct sunlight
deep into the canopy (Stenberg 1995). Explicit solutions for
the correct representation of penumbral effects quickly become intractable, and approximations have been elaborated
that separate between- and within-shoot shading (Stenberg
1995, 1998). Within-shoot shading is not explicitly modeled
here because the effect of needle angle and sunlit/shaded frac-
819
tions within the shoot are implicitly integrated in our measurements of shoot photosynthesis. Shoot-level measurements are
made with the assumption that the radiation field inside the
cuvette is similar to that under natural conditions.
Greater simplification often results in larger errors or biases. In order to bound our errors, we used two mathematical
representations that should underestimate or overestimate
canopy photosynthesis. In the first model, penumbra is ignored and a shoot is assumed to be either in full (above-canopy) sunlight or in full shade (ML-1). Canopy photosynthesis
will be underestimated with ML-1 because the effect of penumbra on irradiance variance is ignored (Stenberg 1995). In
the second model, diffuse and direct irradiances are represented by their mean values (ML-2). Canopy photosynthesis
will be overestimated in ML-2 because of the absence of stochastic variation in irradiance within each shoot class
(Stenberg 1995). Thus, it represents an upper estimate of
penumbral effects (Norman 1980).
The penetration of diffuse and direct irradiance is treated
separately. Considering the clumping of needles in shoots, and
neglecting the interception of irradiance by the non-foliated
parts of the canopy, the profile of mean direct irradiance in a
canopy can be approximated with the Beer–Lambert model
(Nilson 1971, Chen et al. 1997):
I b = I b 0 exp( − kb S * ),
(5)
where Ib is the mean direct irradiance on a horizontal surface
(µmol (m2 ground)–1 s –1) observed under a shading shoot area
index (SAI) of S*, Ib0 being the direct irradiance above the canopy. As shoots, but not needles, are treated as the elemental
functional units, the shoot area index, expressed on a hemisurface area basis, is considered instead of LAI. The shoot area
is computed as the sum of total needle and twig surface areas.
Assuming a spherical distribution of shoot angles with respect
to the incoming radiation, the extinction coefficient for direct
irradiance (kb) is expressed as (Stenberg et al. 1994):
kb =
2Ω s c*
,
cos θ b
(6)
where Ω is a shoot clumping index for scales larger than the
shoot, s c* is mean shoot STAR averaged over the canopy and θb
is solar zenith angle. A factor of two appears in Equation 6 as
mean canopy STAR is expressed per unit of total shoot area,
whereas SAI is expressed per unit of shoot hemisurface area.
The shoot clumping index was obtained from the PCA measurements and the destructive SAI estimates were obtained in
the satellite plots. Logarithms of transmittance values for each
of the five PCA rings were averaged (Lang and Xiang 1986).
Equations 5 and 6 were used to estimate Ω for each ring of the
PCA. Examination of the results showed a strong dependence
of Ω on the zenithal view angle. This dependence was explicitly taken into account with the following empirical function:
Ω ij = cos(ω1 (θ j − ω 2 )) + ρε i(j −1 ),
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(7)
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BERNIER, RAULIER, STENBERG AND UNG
Table 2. Model specification. Number of observations (n), mean square error (MSE), adjusted coefficient of determination (r 2 adj), parameter estimates, standard error (SE) and correlation matrix.
Equation n
MSE
r 2 adj
Parameters
4
0.0144
0.531
τ1
τ2
τ3
τ4
76
7
24
10
11
22
378
23
74
24
76
0.0145
0.678
3.99E-7
1.000
0.0014
0.458
0.913
0.705
0.0040
0.619
Estimated value
SE
Correlation matrix
–0.539
6.20E-3
0.111
8.43E-4
0.156
9.2E-4
0.038
2.2E-4
1
–0.99
–0.85
0.86
1
0.83
–0.86
ω1
ω2
ρ
1.410
0.585
0.975
0.125
0.052
0.161
1
0.10
–0.07
1
0.06
κ1
κ2
0.451
–0.0407
4.4E-4
2.3E-4
1
–0.89
1
σ1
σ2
σ3
σ4
σ5
σ6
–0.0756
42.37
4.75E-3
–0.205
1.378
0.411
0.022
3.00
1.66E-3
0.024
0.150
0.061
1
–0.93
–0.57
0.11
–0.06
–0.05
1
0.29
–0.18
0.13
0.04
1
0.02
0.02
–0.13
1
0.97
0.72
β1
β2
β3
β4
0.0295
–1.96E-3
–0.180
–7.21
1.12E-3
3.0E-4
0.097
1.92
1
–0.78
0.11
–0.14
1
–0.07
0.09
1
–0.61
1
η11
η21
η22
5.56E-4
–10.86
–37.44
4.7E-5
1.56
8.22
1
–0.81
–0.79
where Ωij is the shoot clumping index taken for ring ( j) of spot
(i); θj is the zenithal angle of the ring midpoint (7°, 23°, 38°,
53° and 68°); ω1, ω 2 and ρ are parameters to estimate with
nonlinear OLS (Table 2); and εi(j-1) is the residual of the preceding observation. The inclusion of a first-order autocorrelation process in the model with parameter ρ causes the
loss of one degree of freedom per PCA measurement. Ring
measurements were thus ordered in ascending order of zenithal angle, causing the loss of the fifth ring. Equation 7 was
fitted with the PROC NLIN module of the SAS software package (SAS Institute, Cary, NC).
Assuming an isotropic distribution of diffuse radiation in
the sky, the irradiance per unit solid angle is Id/π (Thornley
and Johnson 1990, their Equation 8.4d), Id being the diffuse
irradiance incident on a horizontal surface (µmol (m2
ground)–1 s –1) below a given SAI. The profile of mean diffuse
irradiance is then obtained with (Oker-Blom and Kellomäki
1982, their Equation 20):
Id =
2π π 2
∫ ∫
0
0
I d0
exp( − kh S * ) cos θ h sin θ h dθ h dα h
π
π 2
=
(8)
∫ 2 I d0 exp(− kh S ) cos θh sin θh dθh ,
*
0
where Id0 is the mean diffuse radiation on a horizontal surface
above the canopy, θh is zenithal angle, αh is the azimuth of the
1
1
1
–0.99
1
1
1
–0.85
1
view direction in the hemisphere and kh is the irradiance extinction coefficient in the view direction and defined by Equation 6. The term cosθh is included because Id refers to irradiance on the horizontal, and sinθh corresponds to the relative
area of the hemisphere in the zenith angle band around θh.
For both multilayer models, the transmission of diffuse
irradiance measured for each class of NMA and shoot age
(Equation 4) is needed to estimate the shading SAI lying between the considered class and the open sky. The shading SAI
value can then be used to estimate the transmission of direct
and diffuse irradiances reaching the class in question. For this
purpose, a mean extinction coefficient for diffuse irradiance
(kd) was derived from Equation 8:
ln( Td )
S*
π 2

1 
= − * ln  ∫ 2 exp ( − kh S * ) sin θ h cos θ h dθ h.
S  0

kd = −
(9)
The right-hand term of Equation 9 was solved numerically
by dividing the sky hemisphere into 10 zenithal angle classes.
Because the value of kd depends on the SAI considered, it was
estimated for values of shading SAI between 2 and 12 in steps
of 2. Results were used to adjust the following function from
which the kd was iteratively estimated with the shading SAI
from the diffuse transmission estimated for each class of NMA
and shoot age:
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NEEDLE AGE, SHOOT STRUCTURE AND CANOPY NET PHOTOSYNTHESIS IN BALSAM FIR
kd = κ 1 + κ 2 ln( S * ),
 sin θ b sin(α b − α s ) 
γ = sin −1 
.
cos φ


(10)
where κ1 and κ2 are parameters estimated with OLS (Table 2).
The shading SAI of any considered class of NMA and shoot
age was estimated iteratively from Equation 8, together with kd
(Equation 10).
−
dIb
≈
d S*
∑ ∑ νb νθ , α I s. b0 ,
θ
−
(11)
α
where:
ν b = Ω exp( − kb S * ),
ν θ , α = sin θ s ∆θ s
∆α s
,
2π
(12)
(13)
dI b
≈
dS *
∑ ∑ νθ , α I s. b ,
θ
(17)
α
where:
I s. b =
2 s*
ε p I b0 ,
cos θ b
(18)
and
ε b = Ω exp( − kb S * ),
(19)
where I s. b is the mean direct irradiance intercepted per unit of
shoot hemisurface area (µmol (m2 shoot)–1 s –1) for ML-2. The
factor εp corresponds to the effect of penumbra on direct irradiance. The frequency νθ,α is estimated with Equation 13.
For both ML-1 and ML-2 representations, the diffuse irradiance intercepted by a given SAI layer is equal to (see Appendix 1):
−
dI d
≈
dS *
∑ ∑ νθ , α I s. d ,
θ
(20)
α
where:
I s. d =
and
(16)
For ML-2, the same equations apply except that direct irradiance is treated differently:
Irradiance interception by the shoots
When scattering is ignored, the irradiance is either transmitted
through the canopy or intercepted by it. The intercepted irradiance (–dI ) divided by the intercepting area (dS*) of a canopy
layer gives the mean irradiance on the shoot area for that layer.
The shoot population within a given layer needs to be further
subdivided into angular subclasses as irradiance interception
by a shoot depends on the elevation and rotation angle of the
shoot (Equation 3). Finally, the interception of diffuse and direct irradiances is to be treated separately.
For the first multilayer model (ML-1), the direct irradiance
intercepted by a given SAI layer is equal to (demonstrated in
Appendix 1):
821
I
∑ ∑ 2 s* Ω exp( − kh S * ) πd0 sin θh ∆θh ∆α h .
(21)
θh αh
I s. b0 =
2 s*
I b0 ,
cos θ b
(14)
if the shoots within a considered layer are subdivided into zenithal and azimuthal classes. Because shoots are assumed to
be spherically oriented, the frequency of a considered angular
class is equal to the product of the probability density functions of the zenith angle ( f(θ s ) = sin θ s dθ s , 0 ≤ θ s ≤ π / 2) and
of the azimuthal angle (α), which is uniformly distributed over
(0,2π)(f(αs) = dαs /(2π)). The frequency νb corresponds to the
shoot proportion that is sunlit within the considered layer and
I s. b0 is the mean direct irradiance intercepted per unit of sunlit
shoot hemisurface area (µmol (m2 shoot)–1 s –1) within a given
angular subclass. Note that s* is defined by Equation 2 that depends on the shoot elevation and rotation angles (φ,γ). Given
the sun zenith and azimuth angles (φb,γb), the correspondence
between both reference systems is (Stenberg 1996, her Equations 1 and 2):
φ = sin −1 ( sin θ s sin θ b cos(α s − α b ) + cos θ s cos θ b ), (15)
The hemisphere was divided into 60 classes (5 for the zenith
and 12 for the azimuth). The other terms remain as defined
above.
Individual and mean STAR values need to be calculated to
estimate the interception of irradiance (Equations 14, 18 and
21). For each class of NMA and shoot age, STAR and mean
STAR are defined once values are given to the parameters a, b
and c of Equation 2. Consequently, using the parameter estimates for the shoots for which we had measured the average
light environment, we related the estimated parameters with a
linear combination of NMA and shoot age (because average
light climate is already explained by NMA and age). In a last
step, the parameters a, b and c were replaced with their respective parameterized equations, and the full model was estimated once more with nonlinear OLS (West et al. 1984). For
this purpose, we have taken advantage of the definition existing between horizontal STAR (STAR of a shoot with elevation and rotation angles equal to zero) and a and b of Equation
2 (s*(0,0) = a + b) (Stenberg 1996). Furthermore, a relatively
strong relationship appeared during the parameterization between parameters b and c of Equation 2:
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822
BERNIER, RAULIER, STENBERG AND UNG
s* ( φ, γ ) = a + b cos φ − cγ cos φ,
(22)
σ
 *
s ( 0, 0) = σ1 + 2* + σ 3 a s

m

*
where  b = σ 4 + σ 5 s ( 0, 0)
 a = s* ( 0, 0) − b

 c = σ6 b
and where σ1 to σ6 are parameters estimated with nonlinear
OLS (Table 2).
Light response curves
n* = 1 −
The photosynthetic response to light was represented by the
non-rectangular hyperbola of Hanson et al. (1987), modified
to account for the arrangement of the needle surface in a shoot.
We followed the fitting procedure described in Raulier et al.
(1999) to relate the parameters of Hanson’s model to NMA
and needle age. We first fitted Hanson’s model with PROC
NLIN using our light response measurements. In a second
step, using the results from the fitted functions, we related the
estimated parameters of Hanson’s model to values of NMA
and age. In a third step, the parameters were replaced with
their respective parameterized equations, and the full model
estimated once more with nonlinear OLS (West et al. 1984):
I

1− s 
Rd  I c 
 
An = Amax 1 − 1 −
,


 
Amax 


shoot photosynthesis needs to be converted into units of shoot
hemisurface area. The needle area per unit of shoot area (n*)
can be expected to vary primarily with shoot age and average
radiative environment. We used all shoots for which we measured the average radiative environment and a preliminary examination of n* showed a concave function of shoot age. To
express the relationship, we chose a variant of the reciprocal
function (Ratkowsky 1990) and replaced its parameters with
simple functions of NMA, because the average radiative environment of the shoot is already modeled in Equation 4 as a
function of NMA and shoot age:
(23)
 Amax = (β1 + β 2 a s )m *

where  Rd = β 3 Amax
I = β R
4 d
 c
in which An is shoot net photosynthesis (µmol (m2 half needle)–1 s–1), I s is the mean intercepted irradiance per unit of shoot
hemisurface area (µmol (m2 half shoot)–1 s –1) in the photosynthetically active wavebands (PAR = 400–700 nm), and Amax,
Rd and Ic are intermediate parameters that depend on the parameters β1 to β4 estimated with nonlinear OLS (Table 2). Parameter Amax corresponds to the photosynthetic capacity (µmol
(m2 half needle)–1 s –1), i.e., to An at I s above saturation. Parameter Rd corresponds to the respiration rate at I s = 0 (µmol (m2
half needle)–1 s –1). Parameter Ic is the irradiance at the compensation point (µmol (m2 half shoot)–1 s –1). For the calibration of Equation 23, values of I s were obtained by multiplying
the irradiance value measured with the quantum meter by
twice the horizontal STAR value (s*(0,0), Equation 14). In the
last step, all our photosynthetic measurements were combined
to estimate the parameters. Also, the contribution of a quadratic effect of shoot age in explaining photosynthetic capacity was tested with a likelihood ratio (Bates and Watts 1988).
Shoot photosynthesis is expressed per unit of needle hemisurface area to allow comparisons with standard measurements. However, for our canopy photosynthesis calculations,
η1
,
1 + η2 a s
(24)
 η1 = η11 m *

where 
η21
 η2 = η + m *
22

and where as is shoot age and η11, η21 and η22 are parameters
estimated with nonlinear OLS (Table 2).
Prediction of canopy net photosynthesis
All the elements are gathered to allow a formal definition of
the canopy photosynthesis models. Shoot population is thus
distributed into observed classes of NMA and shoot age,
themselves subdivided into classes of shoot zenith and azimuth. In turn, the elements necessary to characterize the average radiative environment, the irradiance interception and the
photosynthetic sensitivity to irradiance are derived from NMA
and shoot age with empirical functions based on field data.
These elements are: shoot average radiative environment,
shading SAI, proportion of needle area included in shoot area,
shoot STAR and needle photosynthetic capacity. To bound
our canopy photosynthesis predictions, we used two simple
but biased models of light transmission within the canopy that
either ignore penumbra (ML-1) or incorporate an ideal representation of penumbra in a fully diffusive canopy (ML-2). For
comparative purposes, we consider ML-2 as our closest match
to true canopy photosynthesis.
With model ML-1, canopy net photosynthesis is estimated
as:
n 

 ν A ( I + I s. d )   
*
Ac = S * ∑  ν i ni ∑ ∑  ν θ , α  b n s. b0
  , (25)
1
+
−
A
I
(
ν
)
(
)

  
i =1 
θ
α

b
n
s.
d
s
s


where Ac is canopy net photosynthesis (mol (m2 ground)–1 s –1),
An( I s ) is shoot net photosynthesis (Equation 23) for a mean intercepted irradiance (Equations 14 and 21), νi is the distribution frequency of shoot hemisurface area within a class i of
NMA and age (Equation 1), νθ,α is the distribution frequency
of shoot area within an angular class (Equation 13) and νb corresponds to the fraction of sunlit shoot area in a given NMA
and age class (Equation 12). Term n* is estimated with Equation 24. Sixty shoot angular classes were considered (five for
TREE PHYSIOLOGY VOLUME 21, 2001
NEEDLE AGE, SHOOT STRUCTURE AND CANOPY NET PHOTOSYNTHESIS IN BALSAM FIR
the zenith and 12 for the azimuth). With model ML-2, canopy
net photosynthesis is calculated with:


*
Ac = S * ∑  νi ni ∑ ∑ ν θ , α An( I s. b + I s. d ) ,
i =1 
θs αs

n
[
]
(26)
This time, direct irradiance interception ( I s. b ) is estimated
with Equation 18. Otherwise, all other terms are similar to
those of Equation 25.
Simulations with multilayer models
The consideration of shoot age in a multilayer, conifer photosynthesis model demands a much greater quantity of field data
than in a model of deciduous trees. We have found in the literature at least three approaches for dealing with the photosynthetic properties of non-deciduous foliage. The first is to
measure photosynthesis in all age classes and to model the effect of age on photosynthetic capacity (Wang and Jarvis 1990,
Zhang et al. 1994). The second is to consider only the youngest age classes (McMurtrie et al. 1992, Bonan 1993). The last
is to estimate the photosynthetic capacity of the shoot of mean
age or even to consider the invariance of average shoot properties through the canopy (Aber et al. 1995, Frolking et al.
1996). The impact of these different approaches in dealing
with shoot age were investigated by modifying the ML-2
model.
In both ML-1 and ML-2, all shoot properties are defined as
empirical functions of NMA and age. Model ML-2 was thus
altered to consider either a fixed shoot age of 1 year but letting
NMA vary (ML-2a), a fixed mean shoot age with a variable
NMA (ML-2b) or a fixed mean shoot age and NMA (ML-2c).
All three options therefore constrained both STAR and
photosynthetic properties, from varying with light availability
and shoot age (ML-2). Rather, they were made to conform
throughout the canopy to the properties of either 1-year-old
shoots (ML-2a) or mean-aged shoots (ML-2c). All five models (ML-1, ML2 and their variants a, b and c) were used to estimate hourly canopy photosynthesis from May 15 to October 1,
1997. All environmental variables, except irradiance, were
considered to be optimal. The incident shortwave radiation
measured above the canopy drove the simulations. The relative importance of diffuse and direct radiation was estimated
with the relationship between hourly and daily amounts of diffuse radiation of Liu and Jordan (1960). This fairly accurate
algorithm (Collares-Pereira and Rabl 1979, Gates 1980) requires the hour angle of sunset and solar time considered, derived from the Astronomical Almanac (Michalsky 1988), and
the daily amount of diffuse radiation, estimated from the measured daily total shortwave radiation and a daily clearness index (Raulier et al. 2000). Similarly, the solar elevation
required by Equation 6 was obtained from the Astronomical
Almanac.
823
Results and discussion
Characterization of shoot population
Mean LAI of the two sites selected for destructive sampling
within the stand was 5.76 and mean SAI was 6.55. Shoot area
distribution among age cohorts conformed to a regular exponential decay-type model (Kleinschmidt et al. 1980) (Figure 1). The strong departure from this distribution in our data
for the 1998 foliage was caused by an above average flowering
year. Shoots supporting the clusters of male flowers were
short, and their needles smaller than those of the previous
year’s shoots. Morris (1951) reports a reduction of up to 45%
in needle production during years of heavy flowering in balsam fir stands in northern New Brunswick. Needle shedding in
our samples was also quite gradual. Using Equation 24, and
field-derived parameter estimates shown in Table 2, the contribution of needle surface to total shoot surface area went
from 91% at Age 0 to 70% at Age 10, with an area-weighted
mean of 87%. Absolute decrease in needle surface with age
was even less, because the increase in twig size by itself tends
to cause a decrease in needle surface to total shoot surface. The
area-weighted mean shoot age was 3 years.
Results of the stand-level sampling of mean STAR and of
NMA are shown in Figures 2a and 2b. The canopy mean
STAR was 0.145 (SD = 0.033). Canopy mean NMA was 179 g
m–2 (SD = 30). The frequency distributions of both variables
are slightly skewed toward the left and cannot be assimilated
to normal distributions (for mean STAR: χ 2obs = 65.8, χ 20. 05 ; 6 =
12.6 and for NMA: χ 2obs = 14.9, χ 20. 05 ; 4 = 9.5).
Shoot geometry and needle morphology of fir are both influenced by the light environment during development (Clark
1961, Carter and Smith 1985). Measurements on shoots between 1 and 3 years old revealed a relatively good relationship
between either NMA, mean STAR or horizontal STAR and
mean radiative environment of the shoots (irradiance transmission under conditions of diffuse radiation) (Figures 3a–c).
However, no relationship appeared between either mean or
horizontal STAR and photosynthetic capacity (expressed on
the basis of needle hemisurface area) (Figures 3d–e). We
chose NMA as our scaling variable for balsam fir because it is
Figure 1. Observed frequency distributions of SAI by age class in the
Forêt Montmorency site.
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824
BERNIER, RAULIER, STENBERG AND UNG
et al. 1995). The increase in NMA with age also coincided
with a decrease in light environment, a non-causal relationship
that countered the positive relationship between NMA and either radiative environment (Figure 3a) or photosynthetic capacity (Figure 3d) observed in young cohorts.
The measured value of Ω (Table 2, Equation 7) depends on
the zenithal view angle (Figure 6) in a manner similar to that
described by Chen and Black (1991) for Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), by Cescatti (1997) for Norway spruce (Picea abies Karst.), and by Chen (1996) for
boreal conifers for zenithal angles up to 60°. The clumping of
the shoots in branches, which are typically horizontal for balsam fir (Gilmore and Seymour 1997), strongly increased the
gap fraction at large zenith angles and the clumping of the
branches within crowns had the same effect for low zenith angles. At a zenith angle of approximately 34° (phasing parameter ω 2, Table 2, Equation 7), Ω tended toward unity (which is
implicitly assumed in Equation 7) and, for some plots,
exceeded one. A likelihood ratio test showed that the amplitude of Equation 7 is not different from unity (Fobs = 0.28,
F[0.05;1;20] = 4.35). One note of caution, however, is that our indirect computational method makes the values of Ω strongly
dependent on the assumption related to crown and shoot geometry, and particularly the assumption of spherical shoot angular distribution.
Figure 2. Frequency distributions of mean STAR (a) and NMA (b) in
the canopy of the Forêt Montmorency site.
Canopy photosynthesis
more closely related than STAR to both light environment and
photosynthetic capacity, although its relationship with photosynthetic capacity was weak (Figure 3d). The photosynthetic
capacity of shoots less than 4 years old varied from 2.8 to
6.1 µmol m–2 s–1, and this variability was unrelated to the mean
radiative environment of the shoots (Figure 4). These results
contrast with those obtained on sugar maple (Raulier et al.
1999), in which the photosynthetic capacity varies nearly
fourfold (from 3.5 to 12 µmol m –2 s –1), and is strongly related
to leaf mass per unit area and average radiative environment.
However, our current observation on the narrow range of
shoot photosynthetic capacity in balsam fir agrees well with
those of Carter and Smith (1985) and Leverenz (1995). Shoot
photosynthetic capacity also dropped with increasing shoot
age (Figure 5a). This linear decrease in photosynthetic capacity was slow, going from a mean of 4.3 µmol m–2 s–1 in
1-year-old foliage to 2.6 µmol m–2 s–1 in 7-year-old shoots
(Figure 5a). Similar observations have been made on Abies
amabilis (Dougl.) Forbes (Teskey et al. 1984) and Picea
mariana (Mill.) BSP (Hom and Oechel 1983). Shoot age was
weakly correlated with NMA (Figure 5b) but the much larger
shoot sample of the satellite plots (258 versus 41) was needed
to obtain a significant relationship. When all other factors
were confounded, mean NMA shifts from 173 to 206 g m –2
between 0 and 7 years. This increase in NMA with age was
probably caused by secondary growth (Ewers 1982, Gilmore
Results of hourly and daily simulations over the course of the
growing season are shown in Figure 7, as modeled by ML-1
(Equation 23), a model without penumbra, and ML-2 (Equation 24), a model that simulates the effect of an ideal penumbra
on the propagation of direct light between shoots. For model
ML-2 (the reference model), the absolute maximum value of
23 µmol (m2 ground)–1 s –1 (83 mmol m –2 h –1) for net photosynthesis (27.5 µmol m –2 s –1 for gross photosynthesis) is as
expected for a coniferous canopy (Jarvis et al. 1976, Fan et al.
1995, Ruimy et al. 1995, Goulden et al. 1997, Jarvis et al.
1997). Light saturation of the canopy (irradiance required to
reach 95% of the canopy photosynthetic capacity) occurs at
PAR values of about 750 µmol m –2 s –1 (2.7 mol m –2 h –1). This
result agrees with measurements on boreal conifers (Jarvis et
al. 1997, Goulden et al. 1997), and contrasts with modeled values of up to 1500 µmol m –2 s –1 for sugar maple (Raulier et al.
1999). Although the canopy appears light-saturated in Figure 7, not all the shoots of the canopy are at their photosynthetic capacity because of shading. If all shoots were at
their photosynthetic capacity, canopy net photosynthesis
would reach 27 µmol m –2 s –1 (97 mmol m –2 h –1).
The model without penumbra produced estimates of canopy
photosynthesis that were within 3.7% of those predicted by
simulating an ideal penumbra. This result is in apparent contradiction to results predicted by the theoretical analysis of
Stenberg (1998), in which the omission of penumbra at high
LAI decreases canopy net photosynthesis by up to 30%. What
is apparent from this comparison is that the impact of penumbra on canopy net photosynthesis is greatly reduced when the
TREE PHYSIOLOGY VOLUME 21, 2001
NEEDLE AGE, SHOOT STRUCTURE AND CANOPY NET PHOTOSYNTHESIS IN BALSAM FIR
825
Figure 3. Relationships between either NMA, mean STAR or horizontal STAR and transmission of diffuse irradiance in the canopy (a–c)
or photosynthetic capacity (d–f) for
shoots between 1 and 3 years old.
Horizontal STAR corresponds to
STAR with elevation and rotation
angles of the shoot equal to zero.
Only the shoots for which we measured the five variables are considered in this figure. Linear regressions are indicative only of the
strength of the relationships and
were not used in the canopy photosynthesis models.
proportion of diffuse radiation increases, because diffuse radiation produces a more uniform radiation field within the canopy. For her simulation, Stenberg (1998) used a clear sky condition with a proportion of diffuse radiation of 13% at the
Figure 4. Relationship between canopy transmission of diffuse
irradiance and photosynthetic capacity for shoots between 1 and
3 years old.
sun’s zenith. In contrast, for the present simulations, we used
meteorological data from the Forêt Montmorency, a high precipitation area (1500 mm per year), with a predicted mean diffuse radiation component of 73% of incoming photosynthetically active radiation. Figure 8 shows the relative difference
between ML-1 (without penumbra) and ML-2 (with penumbra). The results are expressed as a function of the ratio of diffuse to total radiation obtained using the Forêt Montmorency
data. Under clear skies, when this proportion dips below 0.2,
the omission of penumbra reduces canopy net photosynthesis
by 20–25%, a value comparable with that of Stenberg (1998).
This result is encouraging given the differences in detail between the studies. Stenberg (1998) built her theoretical analysis from the needle level, and included within-shoot processes
of needle shading and differences in needle areas receiving direct and diffuse irradiance.
The proportion of diffuse radiation at the Forêt Montmorency is high at 73%. The Jean Brébeuf weather station, near
Montreal (annual precipitation of about 1000 mm), shows
long-term monthly ratios of diffuse to total radiation of 44%
for the months of May to August (Anonymous 1982a, 1982b).
Data from the Old Aspen site of BOREAS (Sellers et al. 1997)
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826
BERNIER, RAULIER, STENBERG AND UNG
Figure 7. Predicted canopy net photosynthesis at the scale of hours (a)
and days (b) (䊊: multilayer model ML-1, +: multilayer model ML-2).
Figure 5. Observed relationships between age and photosynthetic capacity (a), NMA (b) and the proportion of needle hemisurface area in
the shoot hemisurface area (c). Linear regressions are indicative only
of the strength of the relationships and were not used in the canopy
photosynthesis models.
Figure 6. Variation of the shoot clumping index (Equation 7) with the
zenithal view angle.
north of Prince Albert, Saskatchewan, in 1995 shows a diffuse
component of 43% of total incident shortwave radiation. It is
to be expected that simulations performed for drier areas with
less diffuse radiation will reveal greater bias when omitting
penumbra, close to the 15% estimated by Norman and Jarvis
(1975).
Shoot age and NMA are used to define the mean STAR, the
proportion of needle to total shoot area and the photosynthetic
properties (Amax, Rd and Ic) of shoots through empirical rela-
Figure 8. Relationship between the hourly proportion of diffuse
irradiance and the relative difference between multilayer models
ML-1 and ML-2.
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NEEDLE AGE, SHOOT STRUCTURE AND CANOPY NET PHOTOSYNTHESIS IN BALSAM FIR
tionships based on field measurements (Equations 22–24). By
assuming constant values for age (ML-2a and ML-2b) or for
both age and NMA (ML-2c) in these equations, the variability
of three shoot properties within the canopy is either reduced or
eliminated, without altering other NMA or age-dependent
properties such as the mean radiative environment. The mean
age and NMA are weighted averages, the weights being the
proportion of total canopy shoot area in any particular class of
NMA and shoot age. For our stand, mean age is 3.16 years and
mean NMA is 179 g m –2.
The results show that using only 1-year-old shoots (ML-2a)
causes an overestimation of canopy net photosynthesis of
8.9% as modeled with ML-2. Use of mean shoot age (ML2-b)
produced a 2.6% underestimation in canopy net photosynthesis. The underestimation caused by the use of mean age
and NMA (ML2-c) is 2.5%.
The results of this analysis therefore support the use of
mean shoot properties for modeling canopy net photosynthesis. The low bias caused by switching to mean properties
results from two compounding factors. The first is that aging
needles retain a large photosynthetic capacity, as seen from
Figure 5a, which shows that 7-year-old shoots retained 60% of
the photosynthetic capacity of 1-year-old shoots. The second
is that the older and less productive shoot cohorts are represented by an ever-decreasing leaf area with respect to the total
leaf area of the canopy (Figure 1). In addition, the use of a constant average NMA is supported by the relatively weak relationship that was found between NMA and shoot photosynthetic capacity (Figure 3d).
On the other hand, use of the more conveniently accessed
1-year-old shoots to characterize STAR and photosynthetic
properties causes a strong bias in the predictions, as newer
shoots will have consistently higher rates of net photosynthesis than the canopy mean. A more detailed analysis of
the results reveals that most of the bias resulted from the
higher photosynthetic activity of newer foliage, whereas differences caused by more uniform STAR properties (parameters a, b and c of Equation 2) are minimal. The use of mean
STAR properties for complete canopies has already been suggested by Norman and Jarvis (1974) for Picea sitchensis
(Bong.) Carr.
Sources of bias
Aside from their compatibility with published measurements
of CO2 uptake rates, a striking feature of the hourly estimates
was the strong regularity of the curve. The modeled canopy
appears responsive only to the amount of light, and is not
strongly sensitive to the hourly variability in the direct/diffuse
mix and in the angle of direct beam incidence. This is contrary
to expectations. For example, measurements on black spruce
(Picea mariana) in Manitoba indicated greater absorption efficiency of diffuse light in conifers (Goulden et al. 1997, their
Figure 8). Closer analysis of the model reveals several necessary assumptions and simplifications that could alter the
model’s response.
One key simplification of this work is the use of shoots as
827
functional units. This choice was conditioned by the desire to
obtain in situ measurements of net photosynthesis and of light
response curves, and by acceptance of this unit of organization
as the basic foliage element of conifers (Gower and Norman
1991). As a consequence, within-shoot processes, outside
those broadly captured by the shoot-level measurements, are
not explicitly represented in the model, with unknown consequence to the simulation results. One such process is the
change with canopy development in the proportion of needle
area subjected to direct and diffuse radiation. In ML-2 and its
variants, both components of intercepted radiation are applied
to the needle hemisurface within the shoot. This is compatible
with the expression of the light response curves obtained in the
field. However, these curves were obtained under predominantly direct light conditions, and thus cannot accurately represent the additional shoot response to diffuse light. Because
we assume that both light fractions are applied uniformly to
the needle hemisurface, we likely overestimate the actual net
photosynthesis in a mixed light regime.
A second assumption linked to the use of shoots as functional units is that, under varying illumination angle, shoot
photosynthesis is determined only by how much light the
shoot intercepts (Equations 14 and 18), following a relationship obtained in the field with the shoots placed perpendicular
to the light beam. In reality, however, the needles have preferential angular distributions that may affect the shape of the
photosynthetic response curve when the angle of incidence of
radiation changes. For Scots pine (Pinus sylvestris L.), Smolander et al. (1987) concluded that the effect of differences in
needle angular distribution with respect to solar angle had a
minor impact on shoot photosynthesis. In balsam fir, needles
have preferential angular distributions, with a strongly horizontal arrangement of needles for shade shoots, and a strongly
vertical one for sun shoots (see Figure 1 of Carter and Smith
1985). It is difficult to assess the bias introduced by this assumption, because it will vary with the importance of the diffuse component in the incoming solar radiation. More diffuse
radiation will tend to reduce the importance of needle angular
distribution.
Another implicit assumption in our models is reflected in
the absence of stochastic variability in the radiative environment. By including an ideal penumbra, ML-2 produces a representation of light distribution within the canopy that is likely
closer to reality than the simple use of unattenuated direct and
diffuse radiation. However, by treating penumbra-attenuated
direct light as a constant within each NMA layer, the model
fails to represent the gap-and-shade distribution still present in
a particular layer. Because of the nonlinearity of the light response curve, using only the average irradiance without accounting for its distribution should result in an overestimation
of canopy photosynthesis (Stenberg 1995). Again, however,
the large proportion of diffuse radiation should homogenize
the within-canopy radiative environment and thus reduce the
bias induced by the assumed homogeneity in the radiative environment.
One last assumption is the spherical distribution of shoots
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
828
BERNIER, RAULIER, STENBERG AND UNG
within the crowns. This assumption has driven the integration
of net photosynthesis over the various representations of
STAR(φ,γ) in Equations 3 and 13, as well as the computation
of Ω. But this assumption is only partially valid because shoot
angular distribution within a canopy with respect to the solar
beam is constrained within limits smaller than 0, π/2. Use of
an elliptical shoot angle distribution is realistic (Cescatti
1997), and the values of the two axes should be a function of
shading SAI or NMA to account for the variability observed in
the field. If we assume that the natural orientation of shoots
within the canopy optimizes light capture and net photosynthesis at the needle level, then it is likely that the spherical
assumption causes a decrease in modeled direct radiation penetration in the canopy and a resulting underestimation of canopy net photosynthesis.
Conclusion
The objective of the present study was to determine the bias
incurred in the estimation of canopy net photosynthesis when
age effects on physiological and morphological variables are
omitted, and when shoot geometry is considered uniform
throughout the canopy. Results for balsam fir showed that the
use of mean shoot properties induces a bias of less than 3%.
The weakness of the bias can be explained by the weak relationships between shoot photosynthetic properties and shoot
age or mean radiative environment. Sampling methods, however, should be designed to allow the estimation of the mean
canopy shoot properties. For example, the use of an age of
1 year for all shoots overestimates canopy net photosynthesis
by 9%. The results highlight the importance of diffuse radiation within the canopy both because of the great efficacy with
which it is absorbed by the shoots, and because its presence
tends to reduce differences linked to the geometry of shoot (or
needle)–light interactions.
Acknowledgments
We thank Sébastien Dagnault, Adrien Forgues, Gérard Laroche,
Roger Mongrain, Nicolas Tremblay and René Turcotte for their dedicated work in obtaining field data, Richard Fournier for the use of his
PCA data in the computation of the Ω factor, and Robert Boutin for
his upkeep of the meteorological records on our various experimental
sites. We are also grateful to Pamela Cheers for her editorial comments. This work is part of the ECOLEAP project, an effort dedicated
to the modeling of forest productivity in Canada over large areas but
with a spatial resolution pertinent to forest management applications
(Bernier et al. 1999).
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s*
s c* S * = ∫ s * dS *
thus:
2 Ω cos θ
d( s c* S * )
= 2 s * Ω cos θ b .
dS*
(A4)
Note that s * is evaluated under a shading SAI of S* and is
thus a property of the layer dS* for which Equation A2 is calculated. When Equation A4 is introduced into Equation A2 and
the definition of mean STAR is expanded (Equation 3), Equation A2 becomes:
−
dI b
=
dS *
2π π 2
2 s*
dα
∫ ∫ cos θb Ω exp( − kb S )I b0 sin θs dθs 2 πs .
0
*
(A5)
0
Equation A5 can be evaluated numerically by either Equation 11 or 17, depending on the multilayer model (ML-1 or
ML-2).
Appendix: Irradiance interception
The following shows that for both ML-1 and ML-2, incoming
photosynthetically active radiant energy is conserved within
the system, (i.e., it is either absorbed or transmitted through
the canopy). Scattering of PAR has not been considered.
Direct (beam) irradiance
When scattering is ignored, the direct irradiance intercepted
by the canopy can be expressed as:
I b0 − I b = (1 − Tb ) I b0 ,
Diffuse irradiance
By following the same procedure developed for direct
irradiance, the first derivative of diffuse irradiance (Equation 6) with respect to SAI is equal to:
−
d Id
=
dS*
2π π 2
∫ ∫ 2 s Ω exp( − kh S )
*
0
0
*
Id 0
sin θ h dθ h dα h .
π
(A6)
(A1)
where Tb is the canopy transmisssion of direct irradiance (see
Equation 5). The first derivative of Equation A1 with respect
to SAI gives the amount of irradiance intercepted by a shoot
layer dS*:
By expanding the definition of mean STAR (Equation 3) in
Equation A6 and by rearranging the terms, we have:
−
d Id
=
dS*
2π π 2
 d( k S ) 
dI
− b* = I b0 exp( − kb S * )  b

dS
 dS 

d( s c* S * ) 
.
= I b0 exp( − kb S * )  2Ω cos θ b
d S * 

 Id 0 2 π π /2 *

s Ω exp( − kh S * ) sin θ h dθ h dα h 
∫
∫
 π 0 0

∫ ∫ 2
*
Then (by definition):
(A3)
0
0
(A2)
0
× sin θ s dθ s
(A7)
dα s
.
2π
As for Equation A5, Equation A7 can be numerically solved
with Equation 20.
TREE PHYSIOLOGY VOLUME 21, 2001