Directory UMM :Data Elmu:jurnal:T:Tree Physiology:Vol16.1996:
Tree Physiology 16, 99--108
© 1996 Heron Publishing----Victoria, Canada
Simulations of the effects of shoot structure and orientation on vertical
gradients in intercepted light by conifer canopies
PAULINE STENBERG
Department of Forest Ecology, P.O. Box 24, FIN-00014 University of Helsinki, Finland
Received March 2, 1995
Summary Coniferous tree canopies typically carry more leaf
area than is necessary to intercept most of the incoming light.
I postulated that an excessively large leaf area will reduce net
productivity at tree level, unless the net photosynthetic production of the most shaded shoots in the canopy remains positive.
The hypothesis tested was that a coniferous tree canopy maintains a large productive leaf area by increasing the efficiency
of light capture as the available light decreases.
The light interception efficiency of a shoot was quantified
by the ratio of shoot silhouette area to total needle surface area
(STAR). The STAR depends on shoot geometry and varies
with shoot orientation relative to the direction of light. Shade
shoots have a larger STAR and, in particular, higher values of
STARmax than sun shoots. In addition, shade shoots tend to be
horizontally inclined, which may increase the advantage of a
large STARmax in the lower canopy, where radiation is incident
from angles closer to the zenith. Adaptation to shade (changes
in STAR and shoot orientation) was described on the basis of
empirical data for several coniferous species, and the vertical
gradient of seasonal light interception by shoots was simulated
assuming different adaptive strategies. Simulations were performed at two latitudes, to account for differences in the
amount and directional distribution of light during the growing
season.
Results support the hypothesis that increases in STAR, shoot
zenith angle and shoot asymmetry (flatness) with shading
increase the efficiency of light interception by deeply shaded
shoots. However, because competition for light among shoots
increases progressively as soon as shade acclimation occurs,
there cannot exist a deep layer of shade shoots, such that the
net productivity of each shoot remains positive (i.e., irradiance
is above the compensation point). Therefore, if maximization
of productive leaf area is the goal, the optimal strategy is to
maintain an inefficient deep canopy and to increase light interception efficiency only when shading becomes severe.
Keywords: leaf area, productivity, shade acclimation, STAR.
there is a cost associated with the formation of a new shoot,
and because each additional layer of leaves increases the
amount of energy lost by maintenance respiration, a high leaf
area potentially reduces net productivity (Sprugel 1989). I
hypothesized that a tree can maintain a large productive leaf
area by increasing the efficiency of light capture as the available light decreases (e.g., with depth in the canopy). Because
shoot geometry has an important impact on the efficiency with
which shoots intercept light (Oker-Blom et al. 1991, Smolander et al. 1994), the capacity of shoots to alter their structure in
response to the light environment has been proposed as an
adaptive strategy (Leverenz and Hinckley 1990).
Light interception efficiency of a shoot can be quantified by
the ratio of shoot silhouette area to total needle surface area
(STAR) (e.g., Oker-Blom and Smolander 1988). The STAR
depends on shoot structure and varies with the shoot orientation relative to the view direction (sun). Generally, STAR is
maximal when the shoot axis is perpendicular to the direction
of projection (view direction). Shade-acclimated shoots have a
larger STARmax than sun shoots (Carter and Smith 1985,
Tucker et al. 1987, Leverenz and Hinckley 1990, SorrensenCothern et al. 1993, Stenberg et al. 1995). In addition, the shoot
angle changes so that shoots are more horizontally inclined the
lower they are in the canopy (Stenberg et al. 1993). These
factors tend to increase a shoot’s light interception efficiency
when the distribution of incident radiation is shifted toward
smaller zenith angles as a result of shading.
Based on empirical data on the range and variation in STAR
of different coniferous species, I analyzed whether changes in
shoot structure and shoot zenith angle in response to increased
shading imply a more even distribution of light between
shoots, thus allowing a larger productive leaf area to be maintained. I simulated the vertical gradient of light interception by
shoots assuming different adaptive strategies (changes in
STAR and shoot zenith angle in response to shading), and
compared it to the case where no shade adaptation was assumed.
Introduction
Material and methods
I studied the adaptation of shoot geometry to modifications in
the light environment in conifer species. Coniferous tree canopies often carry large leaf areas (high leaf area index). Because
Model and data on shoot geometry and STAR
The silhouette leaf area to leaf area ratio (STAR) of a shoot is
100
STENBERG
defined as the ratio of the shoot’s silhouette leaf area (SAs) on
the plane perpendicular to the direction of projection (view
direction) to its total needle area (TAn). The STAR depends on
the internal shoot structure (mutual shading of needles) and
varies with shoot orientation relative to the view direction
(sun). Two types of shoots were considered (Figure 1): (a)
rotationally symmetrical sun shoots representative of many
Pinus species, and (b) flat (rotationally asymmetrical) shoots
typical of the shade shoots of Picea and Abies species.
The silhouette area (SAs) of the symmetrical shoot was
assumed to vary with the angle (φ) of the shoot axis to the plane
of projection. The SAs of the flat shoot also varies with the
shoot’s rotation angle (γ) relative to the view direction (Figure 1). To define the rotation angle, let r denote a vector normal
to the shoot axis and pointing toward the shoot’s upper side
(i.e., r is normal to a hypothetical plane through the shoot axis,
which divides the shoot into an upper side and a lower side).
The rotation angle (γ) (0 ≤ γ ≤ π/2) is here defined as the angle
between r and the plane determined by (going through) the
shoot axis and the view direction.
Let (α,β) and (θ,ϑ) denote the zenith angle and azimuth of
the shoot axis and view direction, respectively. The angle of the
shoot axis to the plane of projection (φ) (0 ≤ φ ≤ π/2) is obtained
as:
φ = sin −1 (|sinαsinθcos(β − ϑ) + cos αcosθ|).
(1)
Calculation of the rotation angle (γ) is straightforward, given
the directions of the shoot axis, the vector r, and the view
direction. If r is assumed to lie in the vertical plane through the
shoot axis (implying that, for a vertical view direction, γ = 0),
the rotation angle is given by:
−1 |sinθsin(β
γ = sin
− ϑ)|
.
cosφ
shoot orientation
is independent of view direction. Analo_____
gously, STAR is obtained as the mean STAR taken over all
directions (θ,ϑ) of the (hemi)sphere. If the view direction is
random in space (or if shoots are spherically oriented), the
probability density function of the angle (φ) is f(φ) = cosφ (0 ≤
φ ≤ π/2), and the
rotation angle (γ) is uniformly distributed over
_____
(0, π/2). The STAR is thus obtained as:
_____ 2
STAR =
π
π/2 π/2
∫0 ∫ 0
STAR(φ,γ)cosφdφdγ.
(3)
To separate the dependency of STAR on the angles φ and γ
from other factors related to the internal shoot structure, STAR
is modeled as:
_____
STAR(φ ,γ) = STAR(a + bcosφ − cγcosφ ),
(4)
where the empirically derived factor (a + bcosφ − cγcosφ) is
called the shape factor, and a, b and c are the shape coefficients.
Substituting Equation 4 into Equation 3, it follows that the
parameters a, b and c (≥ 0) must satisfy the condition:
a+
bπ cπ2
−
= 1.
16
4
(5)
Φροµ Εθυατιον 4 ιτ φολλοωσ τηατ (ωηερε ξ ισ ανψ
ϖαλυε):
_____
STARmax = STAR(0,0) = (a + b)STAR,
_____
STARmin = STAR(π/2,x) = aSTAR,
(6)
(7)
and
(2)
In the following simulations, the rotation angle was calculated by Equation 2 whenever the shoot orientation was not
assumed to be spherical (in which case γ is uniformly distributed). The angles φ and γ change
with shoot and view direction;
_____
however, the mean STAR (STAR) with respect to a spherical
Figure 1. Illustration of a sun shoot and a shade shoot. The STAR of
the sun shoot varies with the inclination (φ) of the shoot axis to the
plane of projection. For the shade shoot, STAR also varies with the
rotation angle (γ).
_____
STAR(0,γ) = (a + b − cγ)STAR .
(8)
Because the spherically averaged ratio of silhouette area to
total surface area for a single needle is 0.25, irrespective of its
shape
_____ as long as it is convex (Lang 1991), this is the value of
STAR for a shoot with no within-shoot shading (disregarding
the contribution
of the twig in the shoot silhouette area). The
_____
departure of STAR from the value of 0.25 is caused
_____ by the
overlap of needles on the shoot, e.g., a value of STAR = 0.15
implies that the shoot silhouette area is reduced by, on average,
40% because of mutual shading of needles on the shoot. A
large value of the ratio (a + b)/a = STARmax /STARmin (Equations 6 and 7) indicates a strong dependency of inclination
angle (e.g., a long and narrow shoot). The parameter c (Equation 8) is a measure of the asymmetry of the shoot around its
axis. For the typical sun shoot, c = 0.
Measured values of STAR for several coniferous species are
shown in Table 1. In two cases (Leverenz and Hinckley 1990,
Stenberg et al. 1995), projected instead of total needle surface
area was used as the denominator in computing the silhouette
area ratios (Rmax , SPAR). These values were divided by π to
obtain
_____ the STAR values given in Table 1. Note that values of
STAR larger than 0.25 represent shoots with a large proportion
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
Table 1. Measured values of STAR of different conifer species.
_____
Species
STAR
Pinus sylvestris
Pinus sylvestris
Pinus sylvestris
Pinus contorta
Picea abies
Mean ± SD
Range
0.142 ± 0.023
0.135 ± 0.033
0.163 ± 0.049
0.116
0.161 ± 0.020*
0.216 ± 0.020*
(0.09--0.21)
(0.09--0.26)
(0.08--0.31)
(0.07--0.20)
(0.11--0.27)
(0.16--0.36)
Picea engelmannii
Abies lasiocarpa
Pinus contorta
Sequoia sempervirens
Abies grandis
Pseudotsuga menziesii
Abies amabilis
Tsuga heterophylla
Picea abies
Picea orientalis
Picea sitchensis
Abies procera
Abies lasiocarpa
Pinus sylvestris
Pinus contorta
1
101
STARmax
STARmin
Source
0.16
0.17
0.17
0.11
0.08
0.08
0.21
0.29
0.12 (sun shoot)
0.18 (shade shoot)
0.15 (sun shoot)
0.31 (shade shoot)
0.13 (sun shoot)
0.14 (shade shoot)
0.31*
0.32*
0.28*
0.28*
0.27*
0.27*
0.26*
0.24*
0.23*
0.21*
0.17*
0.16*
0.09
0.11
Oker-Blom and Smolander 1988
Smolander et al. 1994
Smolander et al. 1994
Oker-Blom et al. 1991
Stenberg et al. 1995
Stenberg et al. 1995
Carter and Smith 1985
Leverenz and Hinckley 1990
* = Values of SPAR or Rmax divided by π.
of twig area (included in the nominator but not in the denominator of STAR).
The most extensive data on the range, and the vertical and
directional variation of STAR are available for Scots pine
(Pinus sylvestris L.) and Norway spruce (Picea abies (L.)
Karst.) (Table 1). The material for Norway spruce (Stenberg et
al. 1995) included shoots from different locations (whorls)
_____ in
control and fertilized trees. In the control trees, STAR increased from about 0.14 in Whorl 4 to about 0.18 in Whorl 13,
and in the fertilized trees it increased from 0.18 to 0.26. In the
upper crown, shoots were fairly symmetrical around the shoot
axis (c ≈ 0). The increase in STARmax with depth
in the crown
_____
was proportionally larger than the increase in STAR , indicating an increase in shoot asymmetry
(parameter c). Also
_____
STARmin increased more than STAR because of a decrease in
shoot length.
Measured and modeled values of the shape factor for a sun
shoot (upper crown) and a shade
shoot (lower crown), esti_____
mated on the basis of measured STAR , STARmax and STARmin
(Equations 4--7), are shown in Figure 2. Estimated parameter
values were a = 0.45, b = 0.70 and c = 0 for the sun shoot, and
a = 0.58, b = 0.87 and c = 0.43 for the shade_____
shoot. For the sun
shoot, STARmax was only 15% higher than STAR , whereas for
the shade shoot it was_____
45% higher.
In the simulations, STAR was allowed to vary between 0.1
and
0.25. The effect of shading was modeled by an increase in
_____
STAR and increases in the parameters a, b and c.
Above-canopy light regime
The momentary irradiance of direct (Is), diffuse (Id) and total
(I) radiation received on a horizontal plane on the ground can
be expressed as:
Is = S0τm cosθ s,
(9)
Id = S0τd cosθ s,
(10)
I = S0(τm + τ d)cosθs ,
(11)
and
where S0 represents the solar irradiance on a plane normal to
the sun at the top of the atmosphere, θs is the solar zenith angle,
τ is the transmittance of the atmosphere to direct sunlight in the
zenith direction, m is the air mass, and τd is the transmittance
to diffuse skylight (Gates 1980). The air mass is approximated
by m = 1/cosθs, and the solar zenith angle can be calculated
from Julian date, latitude and time of the day.
In the simulations, only photosynthetically active radiation
(PAR) was considered, and the amount of PAR available at the
top of the atmosphere was given the value S0 = 600 W m −2
(Weiss and Norman 1985). Simulations were performed at two
latitudes, 43.45° N and 63.45° N, and the time period (T)
considered (the growing season) was taken as April 1 to October 31 and May 1 to September 30 at each latitude, respec-
102
STENBERG
Figure 2. Measured and modeled values
of the shape factor for a sun shoot and a
shade shoot. The shape coefficients (a, b
and c) were estimated based on measured
_____
STAR, STARmax and STARmin in Norway spruce.
tively. At the chosen latitudes, the minimum solar zenith angle
(at the time of the summer solstice) is 20 and 40°, respectively.
The momentary irradiance (Equation 11) integrated over
time, Q(T), represents the radiant energy received per unit of
horizontal area during this time period. During the time of
integration, clear sky conditions were represented by instantaneous transmittance coefficients of τ = 0.7 and τd = 0.271 −
0.294τm (Liu and Jordan 1960, Gates 1980), and overcast days
were represented by diffuse radiation only (τ = 0). The durations of clear and overcast sky conditions were determined
based on the average total, direct and diffuse transmittances
during the time period. At the more northern latitude, a cloudiness index (average total transmittance) of 0.5 during the time
period (T) was assumed, i.e., Q(T) was fixed to be equal to
50% of the extraterrestial insolation, Q0(T), received on a
horizontal surface outside the atmosphere. The average direct
and diffuse transmittances were chosen as 0.3 and 0.2, giving
the proportions Qs(T) = 0.6Q(T) and Qd(T) = 0.4Q(T) of direct
and diffuse radiation, respectively, for the growing season
(Oker-Blom 1986). At the more southern latitude, a somewhat
larger fraction of direct radiation was assumed, and the average
direct and diffuse transmittances were chosen as 0.35 and 0.20,
respectively, giving an average total transmittance (cloudiness
index) of 0.55.
The extraterrestial insolation received on a horizontal surface outside the atmosphere, Q0(T), was calculated by integrating the extraterrestial irradiance (S0cosθs) over time (T). First,
the (potential) direct and diffuse radiation received during the
time period, assuming all days to be clear, Qs(T,clear) and
Qd(T,clear), were calculated. The proportion (p) of clear days
was then solved by Equation 12:
pQs (T,clear ) = Q s(T ).
The angular intensity distribution of incoming total (= direct
+ diffuse) radiation during the time period T [q(θ,T) = qs(θ,T)
+ qd(θ,T)], defined so that:
π /2
Q(T) = ∫
q(θ,T ) dθ
0
=∫
π/2
[qs(θ,T ) + qd (θ,T )] dθ ,
was estimated by assuming a uniform distribution of the diffuse component, in which case qd(θ,T) = 2Qd(T)cosθsinθ.
Figure 3 shows the estimated angular distributions of incoming (above-canopy) direct and diffuse PAR. Notice that only
diffuse radiation is received from zenith angles smaller than 20
and 40° at the southern and northern latitutdes, respectively.
Within-canopy light regime
The penetration of light through the canopy was described by
a negative exponential function of L/cosθ, where L is the
downward cumulative total needle surface area per unit of
ground area. Two models were applied. In Model 1, only the
grouping of needles on shoots was considered (i.e., shoots
were assumed to be the most important clumping elements in
the stand). The extinction coefficient (Gs) is then equal to the
mean ratio (STAR) of projected (light intercepting) area to
total needle area of the shoots located along the path of the
solar beam (Stenberg et al. 1993, Stenberg et al. 1994):
(12)
G s(L,θ,ϑ) =
The diffuse radiation received during overcast days,
Qd(T,overcast), was obtained from Equation 13:
=
pQd(T,clear) + (1 − p)Qd(T,overcast) = Qd(T).
(14)
0
1 L π/2 2π
STAR(θ,γ)fL(α,β)dαdβdL
L ∫0 ∫0 ∫0
1 L
g (θ,ϑ)dL,
L ∫0 L
(15)
(13)
At both latitudes, the calculated proportions of clear (p) and
overcast days (1 − p) were about 63 and 37%, respectively.
where fL(α,β) denotes the probability density function of the
direction (α,β) of shoots located at the depth L in the canopy,
and
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
103
Figure 3. Angular distribution of incoming
(above-canopy) direct (cross-hatched
bars) and diffuse (solid bars) PAR received on a horizontal plane during the
growing season.
gL(θ,ϑ) = ∫
π/2 2π
0
∫0
STAR(θ,γ)fL(α,β)dαdβ
(16)
represents the mean STAR in the direction (θ,ϑ).
The angles φ and γ in Equations 15 and 16 depend on the
shoot direction (α,β) and solar (view) direction (θ,ϑ) according to Equations 1 and 2. In all simulations, the azimuth (β) of
the shoot axis was assumed to be uniformly distributed over
(0,2π), implying that Gs(L,θ,ϑ) = Gs(L,θ) and gL(θ,ϑ) = gL(θ)
are independent of the azimuth (ϑ).
The penetrated radiation, Q(L,T), i.e., the amount of radiation received on a horizontal plane at depth L in the canopy,
during the time period T is then given by:
Q(L,T ) = ∫
π/2
−Gs(L,θ)L
q(θ,T ) exp
0
cosθ
dθ.
(17)
The difference between incoming and penetrated (lost) radiation, Qabs = Q(T) − Q(L,T), represents the radiation absorbed
by the canopy above L.
The seasonal rate of light interception, QL, was defined as
the derivative of Qabs with respect to L and represents the
amount of intercepted radiation per unit of leaf area in the
shoot layer at depth L during the growing season (T). Because,
by definition, dGs(L,θ)L/dL = gL(θ) (Equation 15), the derivative of Qabs is (from Equation 17):
Q L(L,T ) = ∫
π/2
0
gL(θ)
q(θ,T ) −G s(L,θ)L
exp
dθ .
cosθ
cos θ
(18)
The seasonal rate of light interception (QL) as a function of
shading leaf area (L) was first simulated_____
assuming that shoots
in all layers had, on average, the same STAR , and were randomly distributed and spherically oriented (the standard simulation). For a spherical shoot orientation (fL(α,β) =
(1/2π)sinα), G_____
s and gL are independent of the view direction
and equal to STAR . In the standard simulation, Q(L,T) and
QL(L,T)_____
are obtained from Equations 17 and 18 by putting gL
= Gs = STAR for all values of θ and L.
Results from the standard simulation were compared to
simulations
_____ considering two responses to shading: an increase
in STAR , and changes in shoot zenith angle and directional
variation (shape coefficients) of STAR. In addition, by Model
2 the effect of additional grouping (other than the clumping of
needles on the shoot) was taken into account by multiplying
the extinction coefficient (Gs) by a crown clumping factor,
CCF, which was assumed to increase with solar zenith angle
(Oker-Blom et al. 1991). In Model 2, Equations 15--18 remain
formally similar, but values of Gs and gL decrease by the factor
CCF (< 1).
Results
At a fixed L, the penetrated radiation Q(L,T) (Equation 17) was
smaller
_____the larger the extinction coefficient (Gs, which is equal
to STAR in the standard run). Consequently,
the fraction of
_____
absorbed PAR by the canopy increased with STAR . Combinations of L and the extinction coefficient, for which the canopy
intercepts 95% of the incoming radiation _____
(Qabs = 0.95Q(T)),
are shown in Figure 4. At a fixed L and STAR , the relative
absorption was higher at the more northern latitude because a
larger fraction of light came from angles closer to the horizon
(Figure 3), where light extinction is more effective (Equation
17).
The seasonal interception
rates (QL) as a function of L for
_____
_____
STAR = 0.1 and STAR = 0.25 (standard run) are shown in
Figure 5. At a fixed L, total light absorption_____
(the area under the
curve) was always higher the larger the STAR . However, at
large values of L the difference became minor, i.e., relative
absorption was close to one irrespective
_____ of the extinction
coefficient (see Figure 4). A small STAR implied that QL was
smaller in the upper canopy, but decreased less rapidly with L.
Consequently, after some value of L (L ≈ 4 in Figure 5) the
seasonal
_____ interception rate (QL) became higher the smaller the
STAR . Assuming that there exists a critical value of QL below
104
STENBERG
which net photosynthesis becomes negative, the leaf area operating above that critical value _____
(the productive leaf area) is
larger for the smaller value of STAR . The tentative critical
level depicted in Figure 5 _____
corresponds to 5% of the reference
value of QL at L = 0 and STAR = 0.25, which represents the
interception rate of a spherical surface at the top of the canopy.
_____
Effect of increased STAR
Figure 4. Combinations of leaf area index (L, total leaf area basis) and
extinction coefficient, for which the canopy absorbs 95% of the incoming PAR; h = latitude 43.45° N, and n = latitude 63.45° N.
In Figure _____
6, shoots were assumed to be spherically oriented,
but mean STAR increased from 0.1 to 0.25 with the degree of
shading. The degree of shading (DS) was defined as the ratio
of radiation absorbed by the canopy (Qabs ) to the total radiation
incident on a_____
horizontal surface above the canopy (Q(T)). The
increase in STAR was modeled in two
ways: (a) as a linear
_____
function of the degree of shading, i.e., STAR = 0.1 + 0.15(DS),
and (b) as a quadratic
_____ function of the degree of shading
_____ exceeding 50%, i.e., STAR = 0.1 for DS ≤ 0.5 and STAR = 0.1 +
2
0.15((DS − 0.5)/0.5)_____
when DS > 0.5.
The increase in STAR first resulted in an increase in the
interception rate (QL), but later, because of more effective
Figure 5. The seasonal light interception rate (QL, MJ
m −2) as a
_____
function
of
L
for
STAR
= 0.1 (h)
_____
and STAR = 0.25 (d).
Figure 6. The seasonal light interception rate
(QL) as a function of
_____
L when STAR increases from 0.1
to 0.25: (a) as a linear function of
the degree of shading (e), and (b)
as a quadratic function of the degree of shading exceeding 50%
(s). The curve obtained
_____ in the
standard run with STAR = 0.1
(h) is shown for comparison.
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
105
absorption and the consequent decrease in _____
available light, QL
became
_____ smaller despite the larger value of STAR . The sooner
STAR started to increase, the smaller was the value of L at
which the positive effect of this increase on QL disappeared.
Effect of shoot zenith angle and shape coefficients
Figure 7 shows mean values of the shape factor (relative
interceptance) for the modeled sun shoot and shade shoot (see
Figure 2), as a function of the solar zenith angle. The curves
represent shoots with different zenith angles (α = 0, 30, 60 and
90°), and values are averaged over the azimuth (β) (assumed
to be uniformly distributed). Note that the shape factor varies
with
_____solar (view) and shoot angles, but is normalized by
STAR (see Equation 4). The spherical mean of the shape factor
is always equal to 1.
Variation in the relative interceptance was small for solar
zenith angles between 40 and 60° (Figure 7), suggesting that
the effect of shoot zenith angle on light absorption would be
minor at latitude 63.45° N, where the main part of radiation
comes from these angles (see Figure 3). At latitude 43.45° N
much of the radiation comes from solar zenith angles smaller
than 40°, at which variation in relative interceptance with shoot
zenith angle is larger (Figure 7). However, differences in the
seasonal interception rate (QL) were small even for the extreme
cases of a canopy composed of horizontally inclined shade
shoots, or vertically inclined sun shoots (Figure 8). (Note that
because the aim was
to study the effect of shoot angle and
_____
shape coefficients, STAR of sun and shade shoots was assumed
to be the same.)
The relative seasonal interception by a shoot (Table 2) was
obtained by averaging the shape factor with respect to the
angular distribution of light incident on the shoot during the
growing season (T). It represents the light interception by a
shoot in its real (simulated) radiation environment relative to
the spherical mean (e.g., light interception of the same shoot in
an isotropic radiation field). In the open, the relative seasonal
interception was similar for the shade shoot and the sun shoot,
and was not sensitive to the shoot_____
zenith angle (Table 2). This
implies that, for a fixed value of STAR , neither the shape nor
the angle of an unshaded shoot significantly affected its rate of
Figure 8. Seasonal rates of light interception in a canopy of (a)
vertically inclined sun shoots (r), and (b) horizontally inclined shade
shoots (e).
light interception. With increasing shade (depth in the canopy),
the directional distribution of incident light was shifted toward
smaller zenith angles (Figure 9) and, therefore, a horizontally
inclined shoot with a large STARmax becomes relatively more
efficient deeper down in the canopy. At the 95% level of
shading, the relative absorption by a horizontal shade shoot
was 20% (latitude 43.45° N) and 14% (latitude 63.45° N)
higher than the reference (spherical mean), and 43% (latitude
43.45° N) and 25% (latitude 63.45° N) higher than that of a
vertically inclined sun shoot (Table 2).
Combined effects of shoot plasticity and grouping in crowns
The effect of grouping into crowns was considered by multiplying the extinction coefficient by the crown clumping factor,
CCF, which was given the value of 0.5 at θ = 0° and increased
linearly with solar zenith angle, being equal to 1 at θ = 90°.
The
combined effects of grouping into crowns and changes
_____
in STAR , shoot zenith angle, and shape coefficients a and b are
Figure 7. The relative light interceptance
(mean values of the shape factor) of the
modeled sun and shade shoots (Figure 2),
for different shoot and solar zenith angles.
The value of 1.0 corresponds to the spherical mean.
106
STENBERG
Table 2. Relative seasonal interception of PAR by a sun shoot and a shade shoot as a functionof shoot zenith angle.
Relative seasonal interception
Upper canopy (0% shade)
Lower canopy (95% shade)
Latitude 43.45° N
Shoot angle (α)
Sun shoot
Shade shoot
0°
0.97
0.98
30°
0.97
0.98
60°
1.00
1.03
90°
1.02
1.06
0°
0.84
0.88
30°
0.89
1.95
60°
1.02
1.12
90o
1.08
1.20
Latitude 63.45° N
Shoot angle (α)
Sun shoot
Shade shoot
0°
1.02
1.01
30°
1.01
1.00
60°
1.00
0.99
90°
1.00
1.00
0°
0.91
0.93
30°
0.94
0.97
60°
1.01
1.07
90°
1.06
1.14
Figure 9. Angular distribution of PAR at
the 95% shade level (the depth in the canopy where 95% of incoming seasonal
PAR has been absorbed by layers above).
Cross-hatched bars refer to direct radiation, and solid bars to diffuse radiation.
_____
shown in Figure 10. Increases in STAR (from 0.1 to 0.25),
shoot zenith angle (from 30 to 90°), and shape coefficients a
(from 0.45 to 0.58) and b (from 0.7 to_____
0.87) (note that increased
a and b implies a larger STARmax /STAR (Equation 6)) were
modeled as a quadratic function of the degree of shading (DS)
exceeding 50%. Because grouping results in a smaller extinction coefficient (less shading at a given L), the value of L where
QL started to increase was higher than in the case where
grouping into crowns was not considered (Figure 6). In addition, the total depth of the layers where a higher QL can be
maintained was larger.
Discussion
Because total light absorption as a function of the leaf area
index (L) becomes saturated at moderate values of L (Figure 4), excessive leaf area does not appreciably increase the
amount of energy captured by a tree canopy. The rate of
photosynthesis is known to be a concave function of irradiance, and this implies that total photosynthesis at a fixed
amount of absorbed light is maximized when the leaf surface
area is illuminated as evenly as possible. In terms of photosynthesis, the potential advantage of carrying a large leaf area is
associated with a canopy structure (leaf display) that makes the
distribution of light on the leaf surface area more even. In
particular, because there cannot exist a structure that would
produce a constant interception rate (QL) throughout the canopy, a ‘‘suboptimal’’ strategy would be to maximize the (time
integrated) leaf area operating below saturation, but above the
light compensation point.
Light absorption by a shoot can be seen as the product of
available light and the efficiency with
which it is captured by
_____
the shoot. Consequently, a small STAR in the upper
canopy,
_____
where light is abundant, and a gradual increase in STAR with
increased shading makes the vertical gradient in light absorption more even (Figures _____
5 and 6). However, as soon as the light
interception efficiency (STAR ) of the shoots starts to increase,
the available (penetrated) light decreases more rapidly and, as
a result, there comes a point where this strategy can no longer
increase the interception rate (QL). Therefore, the leaf area
operating above some specified threshold (e.g.,
the light com_____
pensation point) is larger if the increase in STAR does not
occur before the degree of shading becomes critical (Figure 6).
Because grouping results in a smaller extinction coefficient
(less shading at a given L), the value of L where QL starts to
increase was higher in the case where grouping into crowns
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
107
Figure 10. Combined effects of
grouping into crowns, and increases in STAR, shape coefficients and shoot angle (e). The
curve_____
obtained in the standard run
with STAR = 0.1 (h) is shown
for comparison.
was considered (Figure 10). Also, the total depth of the layers
where a higher QL could be maintained was larger.
In the simulations, an increase in the shoot zenith angle and
shoot asymmetry (flatness) enhanced the light interception rate
of more severely shaded shoots in the lower canopy (Table 2),
where light comes from angles closer to the zenith (Figures 7
and 9). The effect of these factors (increased shoot zenith angle
and flatness) on light absorption (QL) was not large (Figure 8);
however, another aspect of the typical shade shoot structure
might be important.
In the lower canopy, the spatial distribution of radiation is
fairly even. This is more generally true for diffuse radiation,
but deeper down in the canopy it applies also to direct solar
radiation, because of strong penumbral effects (Stenberg
1995). I conclude, therefore, that the available light is fairly
evenly distributed (varying temporally but not spatially)
among shoots in the lower canopy. However, the distribution
of light among needles on the same shoot may not be even.
This is because the needles are situated close together and so a
single needle can obscure a large part of sky for another needle,
throughout the day or the whole season (Leverenz and Hinckley 1990). The only way for a shoot to prevent this from
happening would be to have parallel and horizontally inclined
needles. Thus the flat shoot structure in combination with a
horizontal shoot inclination is an effective way to minimize
differences in light interception by needles on the same shoot.
Consequently, such a shoot would be able to survive longer in
shade and be more productive than a shoot in the same light
conditions, but with an uneven distribution of light on its
needle surface.
All of the adaptive strategies analyzed in this study----an
increase in the STAR, shoot zenith angle, and shoot asymmetry----were shown to be reasonable responses to shading under
the assumptions used in the analyses. That is, they all tended
to increase the efficiency of light interception by a shoot. I
conclude that the ideal shade shoot is flat, horizontally
in_____
clined, and subject to little_____
within-shoot shading (large STAR ).
In theory, a large STAR (STAR ) is not necessarily associated
with shoot flatness (i.e., a cylindrical, brush-like shoot may
have a large STAR); however, this combination may provide
an extra advantage because it minimizes differences in light
interception by needles on the same shoot. The same argument
was used by Leverenz and Hinckley (1990) to explain their
finding that high leaf area index and high productivity were
found in species with shade-acclimated shoots of large
STARmax .
The capacity to produce shoots that are efficient in deep
shade is a prerequisite for maintaining a high leaf area index.
However, the competition for light among shoots increases
progressively as soon as shade-acclimation starts to occur. As
a result, there cannot exist a very deep layer of shade shoots,
such that the net productivity of each shoot remains positive
(i.e., irradiance is above the compensation point). Because
grouping into crowns implies a slower rate of light extinction,
shade-acclimation started later (at higher values of L) and the
number of layers where a higher rate of light interception could
be maintained was larger in the grouped stands (Figures 6 and
10). I conclude that, if maximization of the productive leaf area
is the goal, the optimal strategy would be to maintain an
inefficient canopy and only increase the light interception
efficiency when the shading becomes severe.
References
Carter, G.A. and W.K. Smith. 1985. Influence of shoot structure on
light interception and photosynthesis in conifers. Plant Physiol.
79:1038--1043.
Gates, D.M. 1980. Biophysical ecology. Springer-Verlag, New York,
611 p.
Lang, A.R.G. 1991. Application of some of Cauchy’s theorems to
estimation of surface areas of leaves, needles and branches of
plants, and light transmittance. Agric. For. Meteorol. 55:191--212.
Leverenz, J.W. and T.M. Hinckley. 1990. Shoot structure, leaf area
index and productivity of evergreen conifer stands. Tree Physiol.
6:135--149.
Liu, B.Y. and R.C. Jordan. 1960. The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Sol.
Energy 4:1--19.
108
STENBERG
Oker-Blom, P. 1986. Photosynthetic radiation regime and canopy
structure in modeled forest stands. Acta For. Fenn. 197:1--44.
Oker-Blom, P. and H. Smolander. 1988. The ratio of shoot silhouette
area to total needle area in Scots pine. For. Sci. 34:894--906.
Oker-Blom, P., M.R. Kaufmann and M.G. Ryan. 1991. Performance
of a canopy light interception model for conifer shoots, trees and
stands. Tree Physiol. 9:227--243.
Smolander, H., P. Stenberg and S. Linder. 1994. Dependence of light
interception efficiency of Scots pine shoots on structural parameters. Tree Physiol. 14:971--980.
Sorrensen-Cothern, K.A., E.D. Ford and D.G. Sprugel. 1993. A model
of competition incorporating plasticity through modular foliage and
crown development. Ecol. Monogr. 63:277--304.
Sprugel, D.G. 1989. The relationship of evergreenness, crown architecture, and leaf size. Am. Nat. 133:465--479.
Stenberg, P., H. Smolander and S. Kellomäki. 1993. Description of
crown structure for light interception models: angular and spatial
distribution of shoots in young Scots pine. Stud. For. Suec. 191:43-50.
Stenberg, P., S. Linder, H. Smolander and J. Flower-Ellis. 1994.
Performance of the LAI-2000 plant canopy analyzer in estimating
leaf area index of some Scots pine stands. Tree Physiol. 14:981-995.
Stenberg, P., S. Linder and H. Smolander. 1995. Variation in the ratio
of shoot silhouette area to needle area in fertilized and nonfertilized
Norway spruce trees. Tree Physiol. 15:705--712.
Tucker, G.F., T.M. Hinckley, J.W. Leverenz and S. Jiang. 1987. Adjustments of foliar morphology in the acclimation of understory Pacific
silver fir following clearcutting. For. Ecol. Manage. 21:249--268.
Weiss, A. and J.M. Norman. 1985. Partitioning solar radiation into
direct and diffuse, visible and near-infrared components. Agric. For.
Meteorol. 34:205--213.
© 1996 Heron Publishing----Victoria, Canada
Simulations of the effects of shoot structure and orientation on vertical
gradients in intercepted light by conifer canopies
PAULINE STENBERG
Department of Forest Ecology, P.O. Box 24, FIN-00014 University of Helsinki, Finland
Received March 2, 1995
Summary Coniferous tree canopies typically carry more leaf
area than is necessary to intercept most of the incoming light.
I postulated that an excessively large leaf area will reduce net
productivity at tree level, unless the net photosynthetic production of the most shaded shoots in the canopy remains positive.
The hypothesis tested was that a coniferous tree canopy maintains a large productive leaf area by increasing the efficiency
of light capture as the available light decreases.
The light interception efficiency of a shoot was quantified
by the ratio of shoot silhouette area to total needle surface area
(STAR). The STAR depends on shoot geometry and varies
with shoot orientation relative to the direction of light. Shade
shoots have a larger STAR and, in particular, higher values of
STARmax than sun shoots. In addition, shade shoots tend to be
horizontally inclined, which may increase the advantage of a
large STARmax in the lower canopy, where radiation is incident
from angles closer to the zenith. Adaptation to shade (changes
in STAR and shoot orientation) was described on the basis of
empirical data for several coniferous species, and the vertical
gradient of seasonal light interception by shoots was simulated
assuming different adaptive strategies. Simulations were performed at two latitudes, to account for differences in the
amount and directional distribution of light during the growing
season.
Results support the hypothesis that increases in STAR, shoot
zenith angle and shoot asymmetry (flatness) with shading
increase the efficiency of light interception by deeply shaded
shoots. However, because competition for light among shoots
increases progressively as soon as shade acclimation occurs,
there cannot exist a deep layer of shade shoots, such that the
net productivity of each shoot remains positive (i.e., irradiance
is above the compensation point). Therefore, if maximization
of productive leaf area is the goal, the optimal strategy is to
maintain an inefficient deep canopy and to increase light interception efficiency only when shading becomes severe.
Keywords: leaf area, productivity, shade acclimation, STAR.
there is a cost associated with the formation of a new shoot,
and because each additional layer of leaves increases the
amount of energy lost by maintenance respiration, a high leaf
area potentially reduces net productivity (Sprugel 1989). I
hypothesized that a tree can maintain a large productive leaf
area by increasing the efficiency of light capture as the available light decreases (e.g., with depth in the canopy). Because
shoot geometry has an important impact on the efficiency with
which shoots intercept light (Oker-Blom et al. 1991, Smolander et al. 1994), the capacity of shoots to alter their structure in
response to the light environment has been proposed as an
adaptive strategy (Leverenz and Hinckley 1990).
Light interception efficiency of a shoot can be quantified by
the ratio of shoot silhouette area to total needle surface area
(STAR) (e.g., Oker-Blom and Smolander 1988). The STAR
depends on shoot structure and varies with the shoot orientation relative to the view direction (sun). Generally, STAR is
maximal when the shoot axis is perpendicular to the direction
of projection (view direction). Shade-acclimated shoots have a
larger STARmax than sun shoots (Carter and Smith 1985,
Tucker et al. 1987, Leverenz and Hinckley 1990, SorrensenCothern et al. 1993, Stenberg et al. 1995). In addition, the shoot
angle changes so that shoots are more horizontally inclined the
lower they are in the canopy (Stenberg et al. 1993). These
factors tend to increase a shoot’s light interception efficiency
when the distribution of incident radiation is shifted toward
smaller zenith angles as a result of shading.
Based on empirical data on the range and variation in STAR
of different coniferous species, I analyzed whether changes in
shoot structure and shoot zenith angle in response to increased
shading imply a more even distribution of light between
shoots, thus allowing a larger productive leaf area to be maintained. I simulated the vertical gradient of light interception by
shoots assuming different adaptive strategies (changes in
STAR and shoot zenith angle in response to shading), and
compared it to the case where no shade adaptation was assumed.
Introduction
Material and methods
I studied the adaptation of shoot geometry to modifications in
the light environment in conifer species. Coniferous tree canopies often carry large leaf areas (high leaf area index). Because
Model and data on shoot geometry and STAR
The silhouette leaf area to leaf area ratio (STAR) of a shoot is
100
STENBERG
defined as the ratio of the shoot’s silhouette leaf area (SAs) on
the plane perpendicular to the direction of projection (view
direction) to its total needle area (TAn). The STAR depends on
the internal shoot structure (mutual shading of needles) and
varies with shoot orientation relative to the view direction
(sun). Two types of shoots were considered (Figure 1): (a)
rotationally symmetrical sun shoots representative of many
Pinus species, and (b) flat (rotationally asymmetrical) shoots
typical of the shade shoots of Picea and Abies species.
The silhouette area (SAs) of the symmetrical shoot was
assumed to vary with the angle (φ) of the shoot axis to the plane
of projection. The SAs of the flat shoot also varies with the
shoot’s rotation angle (γ) relative to the view direction (Figure 1). To define the rotation angle, let r denote a vector normal
to the shoot axis and pointing toward the shoot’s upper side
(i.e., r is normal to a hypothetical plane through the shoot axis,
which divides the shoot into an upper side and a lower side).
The rotation angle (γ) (0 ≤ γ ≤ π/2) is here defined as the angle
between r and the plane determined by (going through) the
shoot axis and the view direction.
Let (α,β) and (θ,ϑ) denote the zenith angle and azimuth of
the shoot axis and view direction, respectively. The angle of the
shoot axis to the plane of projection (φ) (0 ≤ φ ≤ π/2) is obtained
as:
φ = sin −1 (|sinαsinθcos(β − ϑ) + cos αcosθ|).
(1)
Calculation of the rotation angle (γ) is straightforward, given
the directions of the shoot axis, the vector r, and the view
direction. If r is assumed to lie in the vertical plane through the
shoot axis (implying that, for a vertical view direction, γ = 0),
the rotation angle is given by:
−1 |sinθsin(β
γ = sin
− ϑ)|
.
cosφ
shoot orientation
is independent of view direction. Analo_____
gously, STAR is obtained as the mean STAR taken over all
directions (θ,ϑ) of the (hemi)sphere. If the view direction is
random in space (or if shoots are spherically oriented), the
probability density function of the angle (φ) is f(φ) = cosφ (0 ≤
φ ≤ π/2), and the
rotation angle (γ) is uniformly distributed over
_____
(0, π/2). The STAR is thus obtained as:
_____ 2
STAR =
π
π/2 π/2
∫0 ∫ 0
STAR(φ,γ)cosφdφdγ.
(3)
To separate the dependency of STAR on the angles φ and γ
from other factors related to the internal shoot structure, STAR
is modeled as:
_____
STAR(φ ,γ) = STAR(a + bcosφ − cγcosφ ),
(4)
where the empirically derived factor (a + bcosφ − cγcosφ) is
called the shape factor, and a, b and c are the shape coefficients.
Substituting Equation 4 into Equation 3, it follows that the
parameters a, b and c (≥ 0) must satisfy the condition:
a+
bπ cπ2
−
= 1.
16
4
(5)
Φροµ Εθυατιον 4 ιτ φολλοωσ τηατ (ωηερε ξ ισ ανψ
ϖαλυε):
_____
STARmax = STAR(0,0) = (a + b)STAR,
_____
STARmin = STAR(π/2,x) = aSTAR,
(6)
(7)
and
(2)
In the following simulations, the rotation angle was calculated by Equation 2 whenever the shoot orientation was not
assumed to be spherical (in which case γ is uniformly distributed). The angles φ and γ change
with shoot and view direction;
_____
however, the mean STAR (STAR) with respect to a spherical
Figure 1. Illustration of a sun shoot and a shade shoot. The STAR of
the sun shoot varies with the inclination (φ) of the shoot axis to the
plane of projection. For the shade shoot, STAR also varies with the
rotation angle (γ).
_____
STAR(0,γ) = (a + b − cγ)STAR .
(8)
Because the spherically averaged ratio of silhouette area to
total surface area for a single needle is 0.25, irrespective of its
shape
_____ as long as it is convex (Lang 1991), this is the value of
STAR for a shoot with no within-shoot shading (disregarding
the contribution
of the twig in the shoot silhouette area). The
_____
departure of STAR from the value of 0.25 is caused
_____ by the
overlap of needles on the shoot, e.g., a value of STAR = 0.15
implies that the shoot silhouette area is reduced by, on average,
40% because of mutual shading of needles on the shoot. A
large value of the ratio (a + b)/a = STARmax /STARmin (Equations 6 and 7) indicates a strong dependency of inclination
angle (e.g., a long and narrow shoot). The parameter c (Equation 8) is a measure of the asymmetry of the shoot around its
axis. For the typical sun shoot, c = 0.
Measured values of STAR for several coniferous species are
shown in Table 1. In two cases (Leverenz and Hinckley 1990,
Stenberg et al. 1995), projected instead of total needle surface
area was used as the denominator in computing the silhouette
area ratios (Rmax , SPAR). These values were divided by π to
obtain
_____ the STAR values given in Table 1. Note that values of
STAR larger than 0.25 represent shoots with a large proportion
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
Table 1. Measured values of STAR of different conifer species.
_____
Species
STAR
Pinus sylvestris
Pinus sylvestris
Pinus sylvestris
Pinus contorta
Picea abies
Mean ± SD
Range
0.142 ± 0.023
0.135 ± 0.033
0.163 ± 0.049
0.116
0.161 ± 0.020*
0.216 ± 0.020*
(0.09--0.21)
(0.09--0.26)
(0.08--0.31)
(0.07--0.20)
(0.11--0.27)
(0.16--0.36)
Picea engelmannii
Abies lasiocarpa
Pinus contorta
Sequoia sempervirens
Abies grandis
Pseudotsuga menziesii
Abies amabilis
Tsuga heterophylla
Picea abies
Picea orientalis
Picea sitchensis
Abies procera
Abies lasiocarpa
Pinus sylvestris
Pinus contorta
1
101
STARmax
STARmin
Source
0.16
0.17
0.17
0.11
0.08
0.08
0.21
0.29
0.12 (sun shoot)
0.18 (shade shoot)
0.15 (sun shoot)
0.31 (shade shoot)
0.13 (sun shoot)
0.14 (shade shoot)
0.31*
0.32*
0.28*
0.28*
0.27*
0.27*
0.26*
0.24*
0.23*
0.21*
0.17*
0.16*
0.09
0.11
Oker-Blom and Smolander 1988
Smolander et al. 1994
Smolander et al. 1994
Oker-Blom et al. 1991
Stenberg et al. 1995
Stenberg et al. 1995
Carter and Smith 1985
Leverenz and Hinckley 1990
* = Values of SPAR or Rmax divided by π.
of twig area (included in the nominator but not in the denominator of STAR).
The most extensive data on the range, and the vertical and
directional variation of STAR are available for Scots pine
(Pinus sylvestris L.) and Norway spruce (Picea abies (L.)
Karst.) (Table 1). The material for Norway spruce (Stenberg et
al. 1995) included shoots from different locations (whorls)
_____ in
control and fertilized trees. In the control trees, STAR increased from about 0.14 in Whorl 4 to about 0.18 in Whorl 13,
and in the fertilized trees it increased from 0.18 to 0.26. In the
upper crown, shoots were fairly symmetrical around the shoot
axis (c ≈ 0). The increase in STARmax with depth
in the crown
_____
was proportionally larger than the increase in STAR , indicating an increase in shoot asymmetry
(parameter c). Also
_____
STARmin increased more than STAR because of a decrease in
shoot length.
Measured and modeled values of the shape factor for a sun
shoot (upper crown) and a shade
shoot (lower crown), esti_____
mated on the basis of measured STAR , STARmax and STARmin
(Equations 4--7), are shown in Figure 2. Estimated parameter
values were a = 0.45, b = 0.70 and c = 0 for the sun shoot, and
a = 0.58, b = 0.87 and c = 0.43 for the shade_____
shoot. For the sun
shoot, STARmax was only 15% higher than STAR , whereas for
the shade shoot it was_____
45% higher.
In the simulations, STAR was allowed to vary between 0.1
and
0.25. The effect of shading was modeled by an increase in
_____
STAR and increases in the parameters a, b and c.
Above-canopy light regime
The momentary irradiance of direct (Is), diffuse (Id) and total
(I) radiation received on a horizontal plane on the ground can
be expressed as:
Is = S0τm cosθ s,
(9)
Id = S0τd cosθ s,
(10)
I = S0(τm + τ d)cosθs ,
(11)
and
where S0 represents the solar irradiance on a plane normal to
the sun at the top of the atmosphere, θs is the solar zenith angle,
τ is the transmittance of the atmosphere to direct sunlight in the
zenith direction, m is the air mass, and τd is the transmittance
to diffuse skylight (Gates 1980). The air mass is approximated
by m = 1/cosθs, and the solar zenith angle can be calculated
from Julian date, latitude and time of the day.
In the simulations, only photosynthetically active radiation
(PAR) was considered, and the amount of PAR available at the
top of the atmosphere was given the value S0 = 600 W m −2
(Weiss and Norman 1985). Simulations were performed at two
latitudes, 43.45° N and 63.45° N, and the time period (T)
considered (the growing season) was taken as April 1 to October 31 and May 1 to September 30 at each latitude, respec-
102
STENBERG
Figure 2. Measured and modeled values
of the shape factor for a sun shoot and a
shade shoot. The shape coefficients (a, b
and c) were estimated based on measured
_____
STAR, STARmax and STARmin in Norway spruce.
tively. At the chosen latitudes, the minimum solar zenith angle
(at the time of the summer solstice) is 20 and 40°, respectively.
The momentary irradiance (Equation 11) integrated over
time, Q(T), represents the radiant energy received per unit of
horizontal area during this time period. During the time of
integration, clear sky conditions were represented by instantaneous transmittance coefficients of τ = 0.7 and τd = 0.271 −
0.294τm (Liu and Jordan 1960, Gates 1980), and overcast days
were represented by diffuse radiation only (τ = 0). The durations of clear and overcast sky conditions were determined
based on the average total, direct and diffuse transmittances
during the time period. At the more northern latitude, a cloudiness index (average total transmittance) of 0.5 during the time
period (T) was assumed, i.e., Q(T) was fixed to be equal to
50% of the extraterrestial insolation, Q0(T), received on a
horizontal surface outside the atmosphere. The average direct
and diffuse transmittances were chosen as 0.3 and 0.2, giving
the proportions Qs(T) = 0.6Q(T) and Qd(T) = 0.4Q(T) of direct
and diffuse radiation, respectively, for the growing season
(Oker-Blom 1986). At the more southern latitude, a somewhat
larger fraction of direct radiation was assumed, and the average
direct and diffuse transmittances were chosen as 0.35 and 0.20,
respectively, giving an average total transmittance (cloudiness
index) of 0.55.
The extraterrestial insolation received on a horizontal surface outside the atmosphere, Q0(T), was calculated by integrating the extraterrestial irradiance (S0cosθs) over time (T). First,
the (potential) direct and diffuse radiation received during the
time period, assuming all days to be clear, Qs(T,clear) and
Qd(T,clear), were calculated. The proportion (p) of clear days
was then solved by Equation 12:
pQs (T,clear ) = Q s(T ).
The angular intensity distribution of incoming total (= direct
+ diffuse) radiation during the time period T [q(θ,T) = qs(θ,T)
+ qd(θ,T)], defined so that:
π /2
Q(T) = ∫
q(θ,T ) dθ
0
=∫
π/2
[qs(θ,T ) + qd (θ,T )] dθ ,
was estimated by assuming a uniform distribution of the diffuse component, in which case qd(θ,T) = 2Qd(T)cosθsinθ.
Figure 3 shows the estimated angular distributions of incoming (above-canopy) direct and diffuse PAR. Notice that only
diffuse radiation is received from zenith angles smaller than 20
and 40° at the southern and northern latitutdes, respectively.
Within-canopy light regime
The penetration of light through the canopy was described by
a negative exponential function of L/cosθ, where L is the
downward cumulative total needle surface area per unit of
ground area. Two models were applied. In Model 1, only the
grouping of needles on shoots was considered (i.e., shoots
were assumed to be the most important clumping elements in
the stand). The extinction coefficient (Gs) is then equal to the
mean ratio (STAR) of projected (light intercepting) area to
total needle area of the shoots located along the path of the
solar beam (Stenberg et al. 1993, Stenberg et al. 1994):
(12)
G s(L,θ,ϑ) =
The diffuse radiation received during overcast days,
Qd(T,overcast), was obtained from Equation 13:
=
pQd(T,clear) + (1 − p)Qd(T,overcast) = Qd(T).
(14)
0
1 L π/2 2π
STAR(θ,γ)fL(α,β)dαdβdL
L ∫0 ∫0 ∫0
1 L
g (θ,ϑ)dL,
L ∫0 L
(15)
(13)
At both latitudes, the calculated proportions of clear (p) and
overcast days (1 − p) were about 63 and 37%, respectively.
where fL(α,β) denotes the probability density function of the
direction (α,β) of shoots located at the depth L in the canopy,
and
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
103
Figure 3. Angular distribution of incoming
(above-canopy) direct (cross-hatched
bars) and diffuse (solid bars) PAR received on a horizontal plane during the
growing season.
gL(θ,ϑ) = ∫
π/2 2π
0
∫0
STAR(θ,γ)fL(α,β)dαdβ
(16)
represents the mean STAR in the direction (θ,ϑ).
The angles φ and γ in Equations 15 and 16 depend on the
shoot direction (α,β) and solar (view) direction (θ,ϑ) according to Equations 1 and 2. In all simulations, the azimuth (β) of
the shoot axis was assumed to be uniformly distributed over
(0,2π), implying that Gs(L,θ,ϑ) = Gs(L,θ) and gL(θ,ϑ) = gL(θ)
are independent of the azimuth (ϑ).
The penetrated radiation, Q(L,T), i.e., the amount of radiation received on a horizontal plane at depth L in the canopy,
during the time period T is then given by:
Q(L,T ) = ∫
π/2
−Gs(L,θ)L
q(θ,T ) exp
0
cosθ
dθ.
(17)
The difference between incoming and penetrated (lost) radiation, Qabs = Q(T) − Q(L,T), represents the radiation absorbed
by the canopy above L.
The seasonal rate of light interception, QL, was defined as
the derivative of Qabs with respect to L and represents the
amount of intercepted radiation per unit of leaf area in the
shoot layer at depth L during the growing season (T). Because,
by definition, dGs(L,θ)L/dL = gL(θ) (Equation 15), the derivative of Qabs is (from Equation 17):
Q L(L,T ) = ∫
π/2
0
gL(θ)
q(θ,T ) −G s(L,θ)L
exp
dθ .
cosθ
cos θ
(18)
The seasonal rate of light interception (QL) as a function of
shading leaf area (L) was first simulated_____
assuming that shoots
in all layers had, on average, the same STAR , and were randomly distributed and spherically oriented (the standard simulation). For a spherical shoot orientation (fL(α,β) =
(1/2π)sinα), G_____
s and gL are independent of the view direction
and equal to STAR . In the standard simulation, Q(L,T) and
QL(L,T)_____
are obtained from Equations 17 and 18 by putting gL
= Gs = STAR for all values of θ and L.
Results from the standard simulation were compared to
simulations
_____ considering two responses to shading: an increase
in STAR , and changes in shoot zenith angle and directional
variation (shape coefficients) of STAR. In addition, by Model
2 the effect of additional grouping (other than the clumping of
needles on the shoot) was taken into account by multiplying
the extinction coefficient (Gs) by a crown clumping factor,
CCF, which was assumed to increase with solar zenith angle
(Oker-Blom et al. 1991). In Model 2, Equations 15--18 remain
formally similar, but values of Gs and gL decrease by the factor
CCF (< 1).
Results
At a fixed L, the penetrated radiation Q(L,T) (Equation 17) was
smaller
_____the larger the extinction coefficient (Gs, which is equal
to STAR in the standard run). Consequently,
the fraction of
_____
absorbed PAR by the canopy increased with STAR . Combinations of L and the extinction coefficient, for which the canopy
intercepts 95% of the incoming radiation _____
(Qabs = 0.95Q(T)),
are shown in Figure 4. At a fixed L and STAR , the relative
absorption was higher at the more northern latitude because a
larger fraction of light came from angles closer to the horizon
(Figure 3), where light extinction is more effective (Equation
17).
The seasonal interception
rates (QL) as a function of L for
_____
_____
STAR = 0.1 and STAR = 0.25 (standard run) are shown in
Figure 5. At a fixed L, total light absorption_____
(the area under the
curve) was always higher the larger the STAR . However, at
large values of L the difference became minor, i.e., relative
absorption was close to one irrespective
_____ of the extinction
coefficient (see Figure 4). A small STAR implied that QL was
smaller in the upper canopy, but decreased less rapidly with L.
Consequently, after some value of L (L ≈ 4 in Figure 5) the
seasonal
_____ interception rate (QL) became higher the smaller the
STAR . Assuming that there exists a critical value of QL below
104
STENBERG
which net photosynthesis becomes negative, the leaf area operating above that critical value _____
(the productive leaf area) is
larger for the smaller value of STAR . The tentative critical
level depicted in Figure 5 _____
corresponds to 5% of the reference
value of QL at L = 0 and STAR = 0.25, which represents the
interception rate of a spherical surface at the top of the canopy.
_____
Effect of increased STAR
Figure 4. Combinations of leaf area index (L, total leaf area basis) and
extinction coefficient, for which the canopy absorbs 95% of the incoming PAR; h = latitude 43.45° N, and n = latitude 63.45° N.
In Figure _____
6, shoots were assumed to be spherically oriented,
but mean STAR increased from 0.1 to 0.25 with the degree of
shading. The degree of shading (DS) was defined as the ratio
of radiation absorbed by the canopy (Qabs ) to the total radiation
incident on a_____
horizontal surface above the canopy (Q(T)). The
increase in STAR was modeled in two
ways: (a) as a linear
_____
function of the degree of shading, i.e., STAR = 0.1 + 0.15(DS),
and (b) as a quadratic
_____ function of the degree of shading
_____ exceeding 50%, i.e., STAR = 0.1 for DS ≤ 0.5 and STAR = 0.1 +
2
0.15((DS − 0.5)/0.5)_____
when DS > 0.5.
The increase in STAR first resulted in an increase in the
interception rate (QL), but later, because of more effective
Figure 5. The seasonal light interception rate (QL, MJ
m −2) as a
_____
function
of
L
for
STAR
= 0.1 (h)
_____
and STAR = 0.25 (d).
Figure 6. The seasonal light interception rate
(QL) as a function of
_____
L when STAR increases from 0.1
to 0.25: (a) as a linear function of
the degree of shading (e), and (b)
as a quadratic function of the degree of shading exceeding 50%
(s). The curve obtained
_____ in the
standard run with STAR = 0.1
(h) is shown for comparison.
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
105
absorption and the consequent decrease in _____
available light, QL
became
_____ smaller despite the larger value of STAR . The sooner
STAR started to increase, the smaller was the value of L at
which the positive effect of this increase on QL disappeared.
Effect of shoot zenith angle and shape coefficients
Figure 7 shows mean values of the shape factor (relative
interceptance) for the modeled sun shoot and shade shoot (see
Figure 2), as a function of the solar zenith angle. The curves
represent shoots with different zenith angles (α = 0, 30, 60 and
90°), and values are averaged over the azimuth (β) (assumed
to be uniformly distributed). Note that the shape factor varies
with
_____solar (view) and shoot angles, but is normalized by
STAR (see Equation 4). The spherical mean of the shape factor
is always equal to 1.
Variation in the relative interceptance was small for solar
zenith angles between 40 and 60° (Figure 7), suggesting that
the effect of shoot zenith angle on light absorption would be
minor at latitude 63.45° N, where the main part of radiation
comes from these angles (see Figure 3). At latitude 43.45° N
much of the radiation comes from solar zenith angles smaller
than 40°, at which variation in relative interceptance with shoot
zenith angle is larger (Figure 7). However, differences in the
seasonal interception rate (QL) were small even for the extreme
cases of a canopy composed of horizontally inclined shade
shoots, or vertically inclined sun shoots (Figure 8). (Note that
because the aim was
to study the effect of shoot angle and
_____
shape coefficients, STAR of sun and shade shoots was assumed
to be the same.)
The relative seasonal interception by a shoot (Table 2) was
obtained by averaging the shape factor with respect to the
angular distribution of light incident on the shoot during the
growing season (T). It represents the light interception by a
shoot in its real (simulated) radiation environment relative to
the spherical mean (e.g., light interception of the same shoot in
an isotropic radiation field). In the open, the relative seasonal
interception was similar for the shade shoot and the sun shoot,
and was not sensitive to the shoot_____
zenith angle (Table 2). This
implies that, for a fixed value of STAR , neither the shape nor
the angle of an unshaded shoot significantly affected its rate of
Figure 8. Seasonal rates of light interception in a canopy of (a)
vertically inclined sun shoots (r), and (b) horizontally inclined shade
shoots (e).
light interception. With increasing shade (depth in the canopy),
the directional distribution of incident light was shifted toward
smaller zenith angles (Figure 9) and, therefore, a horizontally
inclined shoot with a large STARmax becomes relatively more
efficient deeper down in the canopy. At the 95% level of
shading, the relative absorption by a horizontal shade shoot
was 20% (latitude 43.45° N) and 14% (latitude 63.45° N)
higher than the reference (spherical mean), and 43% (latitude
43.45° N) and 25% (latitude 63.45° N) higher than that of a
vertically inclined sun shoot (Table 2).
Combined effects of shoot plasticity and grouping in crowns
The effect of grouping into crowns was considered by multiplying the extinction coefficient by the crown clumping factor,
CCF, which was given the value of 0.5 at θ = 0° and increased
linearly with solar zenith angle, being equal to 1 at θ = 90°.
The
combined effects of grouping into crowns and changes
_____
in STAR , shoot zenith angle, and shape coefficients a and b are
Figure 7. The relative light interceptance
(mean values of the shape factor) of the
modeled sun and shade shoots (Figure 2),
for different shoot and solar zenith angles.
The value of 1.0 corresponds to the spherical mean.
106
STENBERG
Table 2. Relative seasonal interception of PAR by a sun shoot and a shade shoot as a functionof shoot zenith angle.
Relative seasonal interception
Upper canopy (0% shade)
Lower canopy (95% shade)
Latitude 43.45° N
Shoot angle (α)
Sun shoot
Shade shoot
0°
0.97
0.98
30°
0.97
0.98
60°
1.00
1.03
90°
1.02
1.06
0°
0.84
0.88
30°
0.89
1.95
60°
1.02
1.12
90o
1.08
1.20
Latitude 63.45° N
Shoot angle (α)
Sun shoot
Shade shoot
0°
1.02
1.01
30°
1.01
1.00
60°
1.00
0.99
90°
1.00
1.00
0°
0.91
0.93
30°
0.94
0.97
60°
1.01
1.07
90°
1.06
1.14
Figure 9. Angular distribution of PAR at
the 95% shade level (the depth in the canopy where 95% of incoming seasonal
PAR has been absorbed by layers above).
Cross-hatched bars refer to direct radiation, and solid bars to diffuse radiation.
_____
shown in Figure 10. Increases in STAR (from 0.1 to 0.25),
shoot zenith angle (from 30 to 90°), and shape coefficients a
(from 0.45 to 0.58) and b (from 0.7 to_____
0.87) (note that increased
a and b implies a larger STARmax /STAR (Equation 6)) were
modeled as a quadratic function of the degree of shading (DS)
exceeding 50%. Because grouping results in a smaller extinction coefficient (less shading at a given L), the value of L where
QL started to increase was higher than in the case where
grouping into crowns was not considered (Figure 6). In addition, the total depth of the layers where a higher QL can be
maintained was larger.
Discussion
Because total light absorption as a function of the leaf area
index (L) becomes saturated at moderate values of L (Figure 4), excessive leaf area does not appreciably increase the
amount of energy captured by a tree canopy. The rate of
photosynthesis is known to be a concave function of irradiance, and this implies that total photosynthesis at a fixed
amount of absorbed light is maximized when the leaf surface
area is illuminated as evenly as possible. In terms of photosynthesis, the potential advantage of carrying a large leaf area is
associated with a canopy structure (leaf display) that makes the
distribution of light on the leaf surface area more even. In
particular, because there cannot exist a structure that would
produce a constant interception rate (QL) throughout the canopy, a ‘‘suboptimal’’ strategy would be to maximize the (time
integrated) leaf area operating below saturation, but above the
light compensation point.
Light absorption by a shoot can be seen as the product of
available light and the efficiency with
which it is captured by
_____
the shoot. Consequently, a small STAR in the upper
canopy,
_____
where light is abundant, and a gradual increase in STAR with
increased shading makes the vertical gradient in light absorption more even (Figures _____
5 and 6). However, as soon as the light
interception efficiency (STAR ) of the shoots starts to increase,
the available (penetrated) light decreases more rapidly and, as
a result, there comes a point where this strategy can no longer
increase the interception rate (QL). Therefore, the leaf area
operating above some specified threshold (e.g.,
the light com_____
pensation point) is larger if the increase in STAR does not
occur before the degree of shading becomes critical (Figure 6).
Because grouping results in a smaller extinction coefficient
(less shading at a given L), the value of L where QL starts to
increase was higher in the case where grouping into crowns
SHOOT STRUCTURE AND LIGHT INTERCEPTANCE BY CONIFERS
107
Figure 10. Combined effects of
grouping into crowns, and increases in STAR, shape coefficients and shoot angle (e). The
curve_____
obtained in the standard run
with STAR = 0.1 (h) is shown
for comparison.
was considered (Figure 10). Also, the total depth of the layers
where a higher QL could be maintained was larger.
In the simulations, an increase in the shoot zenith angle and
shoot asymmetry (flatness) enhanced the light interception rate
of more severely shaded shoots in the lower canopy (Table 2),
where light comes from angles closer to the zenith (Figures 7
and 9). The effect of these factors (increased shoot zenith angle
and flatness) on light absorption (QL) was not large (Figure 8);
however, another aspect of the typical shade shoot structure
might be important.
In the lower canopy, the spatial distribution of radiation is
fairly even. This is more generally true for diffuse radiation,
but deeper down in the canopy it applies also to direct solar
radiation, because of strong penumbral effects (Stenberg
1995). I conclude, therefore, that the available light is fairly
evenly distributed (varying temporally but not spatially)
among shoots in the lower canopy. However, the distribution
of light among needles on the same shoot may not be even.
This is because the needles are situated close together and so a
single needle can obscure a large part of sky for another needle,
throughout the day or the whole season (Leverenz and Hinckley 1990). The only way for a shoot to prevent this from
happening would be to have parallel and horizontally inclined
needles. Thus the flat shoot structure in combination with a
horizontal shoot inclination is an effective way to minimize
differences in light interception by needles on the same shoot.
Consequently, such a shoot would be able to survive longer in
shade and be more productive than a shoot in the same light
conditions, but with an uneven distribution of light on its
needle surface.
All of the adaptive strategies analyzed in this study----an
increase in the STAR, shoot zenith angle, and shoot asymmetry----were shown to be reasonable responses to shading under
the assumptions used in the analyses. That is, they all tended
to increase the efficiency of light interception by a shoot. I
conclude that the ideal shade shoot is flat, horizontally
in_____
clined, and subject to little_____
within-shoot shading (large STAR ).
In theory, a large STAR (STAR ) is not necessarily associated
with shoot flatness (i.e., a cylindrical, brush-like shoot may
have a large STAR); however, this combination may provide
an extra advantage because it minimizes differences in light
interception by needles on the same shoot. The same argument
was used by Leverenz and Hinckley (1990) to explain their
finding that high leaf area index and high productivity were
found in species with shade-acclimated shoots of large
STARmax .
The capacity to produce shoots that are efficient in deep
shade is a prerequisite for maintaining a high leaf area index.
However, the competition for light among shoots increases
progressively as soon as shade-acclimation starts to occur. As
a result, there cannot exist a very deep layer of shade shoots,
such that the net productivity of each shoot remains positive
(i.e., irradiance is above the compensation point). Because
grouping into crowns implies a slower rate of light extinction,
shade-acclimation started later (at higher values of L) and the
number of layers where a higher rate of light interception could
be maintained was larger in the grouped stands (Figures 6 and
10). I conclude that, if maximization of the productive leaf area
is the goal, the optimal strategy would be to maintain an
inefficient canopy and only increase the light interception
efficiency when the shading becomes severe.
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