Tree Physiology 28, 559–577
© 2008 Heron Publishing—Victoria, Canada
Actual and potential transpiration and carbon assimilation in an
irrigated poplar plantation
HYUN-SEOK KIM,1,2 RAM OREN1 and THOMAS M. HINCKLEY3
1
Nicholas School of Environmental & Earth Sciences, Duke University, Durham, NC 27708-0328, USA
2
Corresponding author ([email protected])
3
College of Forest Resources, University of Washington, Seattle, WA 98195-2100, USA
Received May 15, 2007; accepted October 4, 2007; published online February 1, 2008
Summary We examined the tradeoffs between stand-level
water use and carbon uptake that result when biomass production of trees in plantations is maximized by removing nutrient
and water limitations. A Populus trichocarpa Torr. × P. deltoides Bartr. & Marsh. plantation was irrigated and received
frequent additions of nutrients to optimize biomass production.
Sap flux density was measured continuously over four of the
six growing-season months, supplemented with periodic measurements of leaf gas exchange and water potential. Measurements of tree diameter and height were used to estimate leaf
area and biomass production based on allometric relationships.
Sap flux was converted to canopy conductance and analyzed
with an empirical model to isolate the effects of water limitation. Actual and soil-water-unlimited potential CO2 uptakes
were estimated with a canopy conductance constrained carbon
assimilation (4C-A) scheme, which couples actual or potential
canopy conductance with vertical gradients of light distribution, leaf-level conductance, maximum Rubisco capacity and
maximum electron transport. Net primary production (NPP)
was about 43% of gross primary production (GPP); when estimated for individual trees, this ratio was independent of tree
size. Based on the NPP/GPP ratio, we found that current irrigation reduced growth by about 18% compared with growth with
no water limitation. To achieve maximum growth, however,
would require 70% more water for transpiration, and would reduce water-use efficiency by 27%, from 1.57 to 1.15 g stem
wood C kg –1 water. Given the economic and social values of
water, plantation managers appear to have optimized water use.
Keywords: gas-exchange, gross primary production, leaf area
index, leaf water potential, light-use efficiency, net primary
production, soil water, water-use efficiency.
Introduction
Plantation managers traditionally increase yield by controlling
genotype, tree density and nutrient availability. A few intensively managed plantations are irrigated to further increase
production (Romero et al. 2004, Coyle and Coleman 2005).
Although irrigation can be tailored to alleviate soil water limitation completely, it is inefficient to do so because yields do
not increase proportionally with water use (Harvey and van
den Driessche 1999, Romero et al. 2004, Choi et al. 2005).
Given the increased scarcity of water resources (Vörösmarty
et al. 2000), an approach to assess the tradeoffs between
stand-level water use and carbon uptake (Jackson et al. 2005)
that can be employed accurately and broadly is highly desirable. We developed a data-intensive approach to assess the carbon–water tradeoff, and compared the outcome to less realistic
but simpler approaches that can be applied more broadly. Our
approach was designed to accurately distribute assimilation
down the canopy, thus facilitating spatially explicit physiological studies.
Although CO2 uptake and transpiration (E ) by forests are
not easily measured, models are available to estimate these
variables (Collatz et al. 1991, Leuning 1995, Williams et al.
1996, Landsberg and Waring 1997, Thornton et al. 2002).
Canopy-level gas exchange models rely on estimates of
stomatal conductance (gs ). Jarvis (1976) empirically described
stomatal response to the external environment as:
gs = gs,max f1 (D ) f2 (QP ) f3 ( Ψ ) ...
(1)
where gs,max is maximum stomatal conductance, which is
largely determined by the hydraulic characteristic of a plant
under optimal conditions, D is vapor pressure deficit, QP is
photosynthetic photon flux and Ψ is soil or leaf water potential
(see Table 1 for a summary of abbreviations). Carbon assimilation is related to conductance through Fick’s law:
Anet = gc (C a − C i ) = gcC a (1 − C i / C a )
(2)
where Anet is net carbon assimilation, gc is canopy conductance
to CO2, which includes the boundary layer conductance (gbl ) in
addition to gs, Ca is atmospheric CO2 concentration and Ci is
the CO2 concentration in the intercellular space of the leaf.
Measures of Ca are readily available. The ratio Ci /Ca is often
assumed constant (Norman 1982) or can be estimated from
knowledge of QP, D (or relative humidity), water-use efficiency (WUE) and gc (Cowan and Farquhar 1977, Collatz et
al. 1991, Katul et al. 2000). To scale leaf-level Ci /Ca to the canopy, the vertical distribution of leaf area is needed to estimate
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KIM, OREN AND HINCKLEY
Table 1. Model parameters and their definitions.
Parameter
Definition
Unit
Anet
Anet,c
Anet,sun(z)
Anet,shade(z)
Ca
Ci
d
d(z)
D
DBH
E
Ea
gbl
gbl(z)
gc
gs
gs(z)
gs,max
gs,sun(z)
gs,shade(z)
gs,ref
Gc
Gs
Gs(z)
Gs,ref
GPP
Jmax
KL
LA
LAI
LAI(z)
LMA
m
Qi
QP
Qavg
R
Rday
fred
SA
Ta
U
U
v
Vcmax
WUE
WRub
WJ
z
Net carbon assimilation
Canopy net carbon assimilation
Net carbon assimilation of sunlit leaves in the zth layer
Net carbon assimilation of shaded leaves in the zth layer
Leaf surface CO2 concentration
Intercellular CO2 concentration
Leaf characteristic length
Leaf characteristic length in the zth layer
Vapor pressure deficit
Diameter at breast height (1.4 m)
Transpiration
Transpiration per unit leaf area
Boundary layer conductance
Boundary layer conductance in zth layer
Leaf canopy conductance
Leaf stomatal conductance
Leaf stomatal conductance in the zth layer
Maximum stomatal conductance
Stomatal conductance of sunlit leaves in the zth layer
Stomatal conductance of shaded leaves in the zth layer
Stomatal conductance at D = 1 kpa
Sap flux scaled canopy conductance
Sap flux scaled canopy mean stomatal conductance
Sap flux scaled stomatal conductance in the zth layer
Sap flux scaled stomatal conductance at D = 1 kPa
Gross primary production
Light saturated rate of electron transport
Leaf specific hydraulic conductance
Tree leaf area
Leaf area index
Leaf area index in the zth layer
Leaf mass per area
Sensitivity of gs to D
Incoming solar radiation
Photosynthetic photon flux
Canopy mean photosynthetic photon flux
Universal gas constant (= 0.462)
Leaf day respiration rate
Reduction factor
Sapwood area per unit ground area
Air temperature
Wind speed above canopy
Mean wind speed in zth layer
Sap flux density
Maximum Rubisco capacity per unit leaf area
Water-use efficiency
Rubisco-limited carbon assimilation rate
Electron transport limited carbon assimilation rate
Height from the ground
Slope of the –dgs /dlnd over gs,ref
Water potential
Leaf water potential
Midday leaf water potential
Predawn leaf water potential
Soil water potential
Density of water (= 998)
Sunlit proportion
Sunlit proportion in the zth layer
µmol C m –2 leaf s –1
µmol C mgr–2 s –1 or µmol C tree –1 s –1
µmol C mleaf–2 s –1
µmol C mleaf–2 s –1
ppm
ppm
m
m
kPa
cm
mm
mmol m –2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
mmol mleaf–2 s –1
g C mgr–2
µmol mleaf–2 s –1
mmol m –2 s –1 MPa –1
m2 tree –1
–
–
g m –2
–
W m –2
µmol mgr–2 s –1
µmol mleaf–2 s –1
m3 kPa K –1 kg –1
µmol C mleaf–2f s –1
–
m2 mgr–2
°C
m s –1
m s –1
mmol m–2 s –1
µmol CO2 mleaf–2 s –1
g C kg –1 H2O
µmol CO2 mleaf–2 s –1
µmol CO2 mleaf–2 s –1
m
–
MPa
MPa
MPa
MPa
MPa
kg m –3
–
–
L
md
pd
S
w
τb
τb(z)
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TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
QP on leaf surfaces, which in turn is used to estimate gs and the
biochemical properties controlling photosynthesis. Such a
scheme is incorporated in the canopy conductance constrained
carbon assimilation (4C-A) model (Schäfer et al. 2003) where
the leaf-level estimates of gs are matched with mean canopy
stomatal conductance (Gs ) obtained from measurements of
sap flux, leaf area and evaporative demand. (Hereafter, G denotes conductance based on sap-flux-scaled measurements
and g denotes conductance derived from gas-exchange measurements.)
We investigated the regulation of stomatal conductance and
carbon assimilation of 3-year-old Populus trichocarpa Torr. ×
P. deltoides Bartr. & Marsh trees in an intensively managed
hybrid poplar plantation situated on the east side of the Washington Cascades. Poplars are known to transpire up to 8 mm
day –1 when growing in non-arid environments (Allen et al.
1999), and even higher rates have been recorded in trees along
streams in arid areas (9.3 mm day –1; Pataki et al. 2005). Thus,
hybrid poplar plantations in arid environments require much
irrigation. Our study objectives were to: (1) analyze the effects
of various environmental factors on actual conductance and
modeled potential conductance under conditions of non-limiting soil water, thus allowing estimates of transpiration in the
absence of water stress; and (2) calculate carbon assimilation
with both actual and potential conductance, and assess the effects of soil water limitation on both the reduction in biomass
production and stand-level WUE.
Materials and methods
Plantation and treatments
Most poplar plantations in the Pacific Northwest are either on
flood plain sites (west side of the Cascade Mountains) or on irrigated land (east side). This study was conducted at the Boise
Cascade Corporation’s Wallula Cottonwood Fiber Farm
(46°10′ N, 118°28′ W) located 50 m a.s.l. on a sandy soil near
Wallula, in eastern Washington, during four growing-season
months (mid-June to mid-October). Mean annual temperature
is 12.3 °C and mean annual precipitation is 160 mm. The plantation was established in the late 1980s on formerly irrigated
agricultural land. The study block was harvested in 1996 and
replanted in July 1997 with P. trichocarpa × P. deltoides hybrid cuttings at 0.9 × 3.5 m spacing. Drip irrigation was initiated at leaf expansion and terminated in mid- to late-October
of each year. Dissolved nutrients were frequently supplied in
the irrigation stream, and herbicides were applied during the
first two growing seasons. Trees were in their third growing
season when this study began, with mean height greater than 8
m. During the study, mean maximum and minimum temperatures were 28.3 and 14.7 °C, respectively, and total precipitation was 19.3 mm.
Measurements
Diameter at breast height (DBH; measured at a height of
1.4 m) of 50 to 51 trees (4 rows, 12–13 trees per row), at least
15 m from the block’s edge, was measured at the start and end
561
of the study, and at around the middle of the period when the
heat dissipation probes (see below) were moved from the first
to the second set of five trees. This relocation of probes defines
the two study periods (before and after relocation) for which
some analyses were performed separately. Leaf area of individual trees was estimated five times during the study at intervals of 4–6 weeks. Each time, a relationship between branch
diameter and its projected leaf area was developed from a subsample of branches from the crowns of four to five trees covering a wide range of canopy positions and diameter classes. A
total of 45 sample branches representing nine to ten canopy
layers about 1-m deep were harvested, keeping track of the
branch diameter and its insertion height. Samples were taken
from trees in which sap flux was not monitored, except at the
end of the study after sensor removal. The area of each leaf
was measured with an LI-3200 leaf area meter (Li-Cor, Lincoln, NE), summed for each branch, and related to branch diameter.
Concurrently with branch sampling, diameters and heights
of all branches were measured on four of the trees that were
monitored for sap flux and which were accessible from two
towers. The study trees represented the 22nd to 94th, and 24th
to 84th percentile of the DBH range in the two periods. Based
on relationships derived for branches, the leaf area of each
branch was estimated and summed to tree-level leaf area (LA),
which was then related to the percentile of DBH represented
by the four sample trees at each of the five sampling times.
Leaf area index (LAI) was estimated from the leaf area of
the 50th percentile tree multiplied by tree density (3175 trees
ha –1). We converted LA and LAI to biomass based on leaf
mass per area (LMA; 65 g m –2 on average, ranging from 81 g
m –2 at the top to 48 g m –2 at the bottom of the canopy) obtained
from 32 oven-dried (78 °C for 48 hours) circular disks (2 cm in
diameter) collected from leaves in the outer envelope of
crowns and in the inner core from top and bottom branches
about halfway through the study. Leaf nitrogen concentration
(g g –1) was determined six times during the growing season,
corresponding to most of the eight gas exchange measurement
campaigns. On each date, 16 leaves were sampled: four samples of four leaves taken from each of the outer envelope and
inner core of crowns from canopy top and bottom branches.
The leaves were dried for 48 hours, ground to a fine powder
and 0.05 g samples sent to the Phytotron at Duke University
for mass spectrum analysis.
The bottom of the canopy extended to the ground throughout the study, and the top of the canopy grew from about 8 to
11 m in height. The profiles of leaf characteristic dimension
(d ) and leaf area index (LAI(z)) were estimated in each 1-m
canopy layer. We estimated d assuming a circular leaf shape,
calculating diameter from the mean area of a leaf in the layer
and multiplying by 0.81 (Campbell and Norman 1998). Values
of LAI(z) and its seasonal variation were obtained from the
four sample trees for which branch diameter and insertion
height were measured. Based on observations, the leaf area of
branches with basal diameter < 25 mm was assigned to the
layer in which the branch was attached, whereas the leaf area
of branches with basal diameter ≥ 25 mm was split between
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KIM, OREN AND HINCKLEY
the layer of insertion and that above. Because LAI(z) was unrelated to tree size, it was expressed relative to total tree leaf
area, normalized by height, and the product averaged for the
four sample trees and employed for all trees in the plot. The
sum of LAI(z) of individual trees yielded the canopy-level
LAI(z).
Sap flux density (v) was measured with Granier-type sensors. Because of the fast growth of the trees, the sensors were
repositioned after 6 weeks and moved to different trees to increase the sample size. The trees sampled during the first period ranged from the 10th to 94th percentile of DBH, and during the second period from 24th to 84th percentile of DBH.
Four sensors were installed in each tree, except for the smallest
tree, in which two sensors were installed. Sensors were installed in the outer 20 mm on the north and south sides, and toward east and west in the next 20 mm of the hydro-active xylem (Granier 1987, Phillips et al. 1996, Oren et al. 1998,
Oliveras and Llorens 2001).
Meteorological variables were obtained with a weather station positioned at the top of a 12-m tower, at the approximate
crown height of the dominant trees. Incoming solar radiation
was measured with a Li-Cor pyranometer (LI-200S). Air temperature and humidity were obtained from a shielded combination of a capacitance relative humidity sensor and a thermistor probe (HMP35C, Campbell Scientific, Logan, UT). Wind
speed was measured with a cup anemometer (Model 03001-5,
R.M. Young, Traverse City, MI). Meteorological variables and
sap flux were measured every 10 s, and 30-min means were recorded (CR10 data logger, Campbell Scientific). Repositioning of sensors and power outages resulted in a loss of data for
11 days during the 126-day study.
We measured leaf-level stomatal conductance (gs ) with a
steady-state porometer (LI-1600, Li-Cor) and leaf water potential (ΨL ) with a Scholander-Hammel pressure chamber
(PMS Instruments, Corvallis, OR) on the four trees accessible
from the towers. Eight 2–3-day measurement campaigns, beginning at 0800 h (later on two windy days) and lasting until
nightfall, allowed diurnal gs representation based on five to
eight sets of measurements per day. Each measurement set
comprised 24 leaves, four leaves from a sunny microenvironment and four leaves from a shady microenvironment from the
top, middle and bottom crown thirds. To eliminate variation
associated with leaf development, we measured only mature
leaves (leaf plastochron index > 3). On seven of these campaigns, leaf water potential was measured on eight leaves per
tree, four from the top and four from the bottom of the crown,
split between crown envelope and core foliage. Measurements
were taken at predawn and solar noon.
Data processing
Biomass production
Biomass production of stems and
branches was estimated from species-specific allometric equations based on diameter and height at the beginning and end of
each growth period (Scarascia-Mugnozza et al. 1997, Zabek
and Prescott 2006), and then calculating the weighted mean
based on the density of trees in our study relative to those in
published studies. Foliage biomass production during the first
growth period only was calculated by multiplying the increase
in leaf area by mean LMA. Root biomass production was assumed to be 14% of total aboveground biomass production, as
estimated for another similar-aged hybrid poplar stand with
drip-irrigation (Gielen et al. 2005).
Modeling of actual Anet by the canopy (Anet,c) and gross primary productivity (GPP) was based on the 4C-A scheme
(Schäfer et al. 2003). 4C-A is a multi-layer canopy photosynthesis model where sap-flux-scaled total conductance constrains estimates of stomatal conductance and the aerodynamics of boundary layer conductance, and the constrained conductance is coupled to a Farquhar-type photosynthesis model
(Farquhar et al. 1980, Farquhar and von Caemmerer 1982).
For details, see Appendix B.
To calculate the solar energy available for photosynthesis,
incoming solar radiation (Qi ) was partitioned into incoming
QP according to Alados et al. (1996). The interception and
transmission of QP were calculated based on Beer and Lambert’s law with two levels of clumping: (1) tree and shoot, and
(2) tree only (Nilson 1999, Niinemets et al. 2004). For details,
refer to Appendix C.
Total canopy conductance (Gc) was calculated from the sum
of the boundary layer conductance and stomatal conductance
to water vapor. The boundary layer conductance to water vapor (gbl(z)) was calculated as described by Campbell and Norman (1998) based on the wind speed at each layer U(z)—modeled with measured U above the canopy and LAI(z) (see Appendix D for U(z) calculations)—and the d profiles in the canopy. Boundary layer conductance for the entire canopy was
scaled from gbl(z) based on LAI(z):
gbl =
1 12
∑ gbl ( z) LAI( z)
LAI z =1
Canopy stomatal conductance Gs was estimated from sapflux-scaled Gc after adjusting for gbl:
Gs =
G c gbl
( gbl − G c )
(3)
and Gc was calculated based on a simplified equation (Köstner
et al. 1992):
Gc =
( Ta + 273)R ρw Ea
D
(4)
where R is the universal gas constant adjusted for water vapor,
Ta is air temperature (°C) and ρw is the density of water at Ta
(see Table 1 for parameter values). Only conditions of D ≥
0.6 kPa (~70% of the time) were used to ensure that errors in
estimates of Gc remained below 10% (Ewers and Oren 2000).
Stomatal conductance to water vapor was estimated based
on the distribution of QP within the canopy and response functions of gs to Q P, and was constrained by sap-flux-scaled Gs
(Equation 3). At each layer, gs of sunlit (gs,sun(z)) and shaded
(gs,shade(z)) leaves was estimated from the response functions of
TREE PHYSIOLOGY VOLUME 28, 2008
TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
gs to QP, from porometric measurements. Values were converted to a mean gc by scaling based on the sunlit fraction of
leaf area (τb ) and LAI(z) (Appendix C), summing for the entire
canopy, and dividing by LAI. This value was then constrained
with sap-flux-scaled Gs by linearly adjusting gs(z), such that:
Gs =
f red 12
∑ LAI( z)( gs, sun ( z) τb ( z) +
LAI z =1
gs, shade ( z)(1 − τ b ( z) ) )
where fred is the linear reduction factor, which makes the
leaf-area weighted gs equal to Gs. This operation was used to
account for conditions not captured by the curves describing
the light response of stomatal conductance. Under optimal
conditions, fred was about 1.
The above calculations produced two profiles, one for gbl
and one for gs, the sum of which over the entire canopy was
forced to match the sap-flux-scaled Gc by adjusting the total gs.
Before gbl and gs were used in the calculations of photosynthesis (Appendix B), they were converted to their equivalents for
CO2 by dividing gbl to water vapor by 1.42 and dividing gs to
water vapor by 1.6 (Jones 1992).
Modeled canopy stomatal conductance Canopy stomatal conductance, Gs, was modeled for gap-filling during hours in
which D was low (i.e., less than 0.6 kPa) or days with missing
data due to power outages or switching of sample trees. We
used a modified Jarvis-type model (Equation 1) to simulate
missing data.
In Equation 1, f2(QP ) was best described as a piece-wise linear function with a saturated region, effectively similar to a
saturation function (Jarvis 1976). For f1(D), the stomatal sensitivity to D (i.e., the relative change in both Gs and gs with a
change in D), is proportional to the conductance at low D
(Sandford and Jarvis 1986, Oren et al. 1999a). Thus, the response of Gs to D can be predicted by:
G s = b − m ln D
tial Gs and Gs,ref. Ideally for our approach, the model would estimate Gs,ref based on QP and some measure of soil water availability, such as that reflected in predawn leaf water potential
(Ψpd), and then adjust Gs,ref to Gs based on D and sensitivity of
Gs to D. Thus, the following equation would emerge:
G s = G s, ref (Qavg ,Ψpd ) − m ln D
(5)
(6)
where b is a reference Gs at D = 1 kPa (hereafter, Gs,ref) and –m
is the sensitivity of Gs to D (–dGs /dlnD). For various species
under moderate environmental conditions, m averages about
0.6b (e.g., Oren et al. 1999a, Ewers et al. 2000, 2001). However, the ratio of m to Gs,ref (γ ) is higher where mean D is lower
and the range of D is narrower, and it increases with decreasing
ratio of gbl to Gs,ref (Oren et al. 1999a). The expected value of
can be calculated by (1) assuming a constant leaf-specific hydraulic conductivity and water potential gradient driving flow,
(2) solving for Gc = c (1/D), where c is a constant (mmol m –2
s –1 ) for a wide range of D, (3) based on assumed values of
gbl /Gs,ref, extracting the corresponding values of Gs from Gc,
and (4) regressing Gs over different ranges of natural log transformed D.
The functions described thus far do not account for soil water limitation on Gs, and therefore can be used to estimate Gs
and Gs,ref only when the soil is wet, or when predicting poten-
563
(7)
m = m ( D range , gbl /G s, ref , G s, ref )
where Drange is the daily range of D to which the stand had been
exposed. However, we lacked continuous measurements of a
surrogate for soil water availability, namely an f3(Ψ)-type
function. We solved this problem by assessing whether Gs,ref
estimated with a model that ignores water limitation (i.e., the
above model without f3(Ψ)) overestimated sap-flux-based
Gs,ref, and whether the overestimation could be explained by
Ψpd over the subset of days when Ψpd was measured. If so, we
rescaled Gs,ref estimated by the model for a specific data gap by
its mean ratio to Gs,ref calculated from sap flux in the period immediately before and after the gap.
Transpiration per unit leaf area Transpiration per unit leaf
area (Ea), used to calculate Gc, was estimated based on leaf area
(LA), sapwood area (SA, i.e., all cross-sectional area inside
bark) and mean v. To account for potential nighttime conductance (Oren et al. 2001, Daley and Phillips 2006), the baseline
for each sap flux sensor output was set between nights in which
D was about 0 kPa, rather than between consecutive nights. Because v changed radially but not azimuthally, mean v was calculated by weighting the outer v by the SA represented in that
xylem band and the inner v by the remaining SA (Ewers et al.
2001, Oren and Pataki 2001). Transpiration per unit leaf area
was estimated from mean v as:
Ea = v
SA
LA
(8)
Actual photosynthetic rates Actual photosynthetic rates were
calculated as explained in Appendix B based on QP and gc estimated for each layer. Net photosynthesis (Anet ) integrated over
an individual tree and over the entire canopy (Anet,c) was calculated as:
Anet, c =
12
∑ LAI( z)( Anet, sun ( z) τb ( z) +
z =1
(9)
Anet, shade ( z)(1 − τ b ( z) ) )
where τb(z) is the proportion of sunlit area, Anet,sun(z) and
Anet,shade(z) are the net assimilation rates of sunlit and shaded
leaves in the zth layer, respectively. Gross primary production
was calculated and integrated over the canopy by a similar approach, but accounting for daytime respiration (Appendix B).
Estimation of potential Anet,c and GPP To estimate potential
Anet,c and GPP in the absence of soil water limitation to gs, we
modeled Gs based on Equation 7 without Ψpd, by performing a
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KIM, OREN AND HINCKLEY
boundary-line analysis on sap-flux-scaled Gs (Schäfer et al.
2000; see Data Analysis below) fitting only Gs,ref, f1(D) and
f2(QP). Doing so ignores any limitation imposed by Ψ, thus
generating potential Gs.
Whole-plant, liquid-phase hydraulic conductance Wholeplant liquid-phase hydraulic conductance (KL ) was calculated
after Granier and Loustau (1994) to check the equality of gas
and liquid phases:
KL =
Ea
ΨS − ΨL
(10)
where ΨS, the soil water potential, is substituted by Ψpd of the
lower canopy, and ΨL, the leaf water potential, is taken as the
leaf-area-weighted mean Ψmd. Daily gs,ref and KL of individual
trees were calculated for days in which both ΨL and gs were
measured. We calculated KL by dividing morning maximum Ea
by the difference between Ψpd and Ψmd. Daily gs,ref was calculated by selecting gs values, the gs(z) scaled by LA, beginning
at the time of daily maximum gs to the time of daily maximum
D, then by fitting through Equation 6.
21.7 °C and 1.5 kPa over the 126-day study during which
19.3 mm of rain fell in 10 events. Maximum half-hourly D was
5.5 kPa. The quadratic mean diameter increased more during
the first period of the study (1.11 cm, from 7.66 to 8.77 cm)
than during the second period (1.0 cm, from 8.77 to 9.77 cm),
whereas the change in basal area increment was less pronounced (14.3 versus 14.5 cm2 for the average tree during the
first and second period, respectively). Leaf water potential varied slightly over the study period, was always greater in the
lower canopy during midday, but mostly similar to the upper
canopy at predawn.
Sap flux density was unrelated to tree size (P = 0.85) and unaffected by azimuth (P = 0.71), but decreased appreciably
from the outer 20 mm of xylem to the next 20 mm layer (P =
0.006; Figure 2). Scaling v to E resulted in a similar seasonal
pattern to that observed in D (Figure 1D), with E reaching a
maximum of about 6.2 mm day –1 in mid July, and averaging
Data analysis
Parameters for the functions describing stomatal response to
variations in QP and D were generated with boundary-line
analyses of gs and Gs versus D by a method described by
Schäfer et al. (2000). Briefly, conductance was partitioned into
six D intervals, the mean and standard deviation (SD) of gs
were calculated, and outliers were removed based on Dixon’s
test (Sokal and Rohlf 1995). The data, represented by more
than five observations, were selected for the subset falling at
least 1 SD above the mean, which were averaged and used to
generate the response to D. Leaf-level data from the same canopy position were treated as a single dataset because of the
small number of measurements from individual trees. At the
tree level, two sets of data were generated for boundary-line
analysis: (1) data were partitioned to five canopy mean QP
(Qavg; estimated from QP in the light model; Appendix C)
classes, four classes were 65 µmol m –2 s –1 wide from 0 to 260
µmol m –2 s –1, and one for Qavg > 260 µmol m –2 s –1, and (2) data
were partitioned into two sets, one above and one below gbl =
700 mmol m –2 s –1.
Estimates of Gs were gap-filled based on the above functions and meteorological data (air temperature, relative humidity and wind speed available from a weather station located within 0.6 km). This gap-filled dataset was used to estimate E and carbon assimilation over the entire study period.
Results
Daily values of meteorological conditions, diameter increment and water potential measurements are shown in Figure 1.
Except for an occasional cloudy day, the pattern of Qi followed
the maximum sun angle, with mean daytime Ta and D lagging
maximum radiation by about 6 weeks. Maximum mean daytime daily Ta and D were 31.3 °C and 3.26 kPa, averaging
Figure 1. Daily daytime means of weather data at the poplar (Populus
trichocarpa × P. deltoides) plantation near Wallula, WA: (A) total incoming radiation (Q i ); (B) air temperature (Ta ); (C) vapor pressure
deficit (D); (D) stand transpiration (E, 䊉) and precipitation (P, bars);
(E) leaf area index (LAI, 䊉) and diameter at breast height (DBH, 䊊);
and (F) mean predawn (closed symbols) and midday (open symbols)
leaf water potential ( L ) at the top (䉱, 䉭) and bottom (䊉, 䊊) of the
canopy. In F, error bars are 1 standard error (n = 4). In B–D, the symbols are measurements and the line is gap-filled data. Vertical lines indicate the start of each study period.
TREE PHYSIOLOGY VOLUME 28, 2008
TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
3.4 mm day –1 for the study period.
Leaf area of branches was linearly correlated with branch
diameter on each sampling date (r 2 > 0.72; maximum P <
0.001), and the relationship did not change with height (minimum P = 0.18). Whole-tree LA was linearly correlated with
the percentile of DBH at each sampling time (r 2 > 0.88; maximum P = 0.04). The LA was distributed vertically based on the
vertical distribution of branch diameter (Figure 3A); normalizing the distribution by each tree height and maximum LA(z)
revealed no height-related pattern. Based on the time-specific
equations and stand-level diameter measurements, LAI was
5.9 at the beginning of the study in May, rose rapidly to a maximum of 9.5 in July, and declined slowly to 6.0 by the end of the
study in September (Figure 1E).
565
estimated from the ratio gbl /gs,max (Oren et al. 1999a), calculated from the porometry-generated constant wind speed (generating a steady high gbl of about 2800 mmol m –2 s –1), and the
maximum measured gs(z) (about 500 mmol m –2 s –1). Based on
the resulting gbl /gs,max of about 5.6 and the range in D used in
the measurements, the expected γ was estimated at 0.53, similar to the observed sensitivity (P = 0.58).
A diurnal pattern of QP at the top of the canopy on the same
Conductance
The 4C-A scheme for estimating Anet and GPP relies on leaflevel gas exchange measurements to generate gs(z) versus QP
responses in several canopy layers, scale gs(z) to gs, and
constrain gs with sap-flux-scaled Gs to account for the effects
of other factors such as D and soil water. We constructed QP response curves with data from campaigns with many (about
1650) gs(z) measurements and assessed how well gs(z) scaled
to gs agreed with Gs.
Leaf-level gs measurements for sun and shade leaves from
different canopy positions showed a commonly observed pattern of increasing conductance with increasing irradiance, and
decreasing conductance with increasing D (Figure 4A). By
boundary-line analysis, the result of which for one category
(canopy-top sun leaves) is shown by the line through the large
symbols in Figure 4A, gs,ref and sensitivity to D (i.e., m) were
estimated with Equation 6 for each of the six categories of
crown positions (Figure 4B). Mean leaf-level γ (the slope of
the relationship between –dgs /dlnD and gs,ref) for the six categories was about 0.45 ± 0.06 (P = 0.003). The expected γ was
Figure 2. Mean sap flux density (v) of the outer (䊉, 0–20 mm, n = 10)
and inner (䊊, 20–40 mm, n = 8) xylem of poplar (Populus trichocarpa × P. deltoides) trees on a partially cloudy day (June 22, 1999).
Error bars represent one standard error.
Figure 3. (A) Vertical profiles of (right) leaf length (d, 䊊) and leaf area
index (LAI, 䊉), and (left) individual tree leaf area (LA) of five poplar
(Populus trichocarpa × P. deltoides) trees of different diameters at
breast height (DBH) monitored for sap flux in the first study period.
(B) Diurnal pattern of photosynthetic photon flux (QP ) at the top of
the canopy on the same cloudy day as in Figure 2 (June 22, 1999). (C)
Modeled mean QP incident on the horizontal surface in each canopy
layer.
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KIM, OREN AND HINCKLEY
Figure 4. Leaf-level stomatal conductance (gs ) responses based on
porometer measurements in poplar (Populus trichocarpa × P. deltoides). (A) The gs response to vapor pressure deficit (D) in leaves
from the outer crown envelope compared with the inner core, for three
canopy layers. A boundary-line analysis is shown (line) for envelope
leaves at the top of the canopy (large 䉭). (B) The slope of the response
of gs to ln(D) (m in Equation 7) versus the intercept of the response
(gs,ref = gs at D = 1 kPa) for crown envelope (sun) and inner core
(shade) leaves at the three canopy layers. Dashed lines are 95% confidence intervals of the regression line. (C) The gs–light response of
leaves from the three canopy layers (Q P = photosynthetic photon
flux).
cloudy day as depicted in Figure 2, is shown in Figure 3B. Figure 3C shows the corresponding estimate of mean modeled QP
based on the light model with tree clumping (LM2; see Appendix C for details of the light models) on the horizontal surface in each layer. These estimates were made with four light
models differing in their specification of canopy structure, and
converted to light at the leaf surface to estimate gs(z). The
porometry data for each leaf category were related to QP to
generate the gs–QP responses. After testing if the lines differed, the crown envelope and core foliage in each canopy
layer were combined into three relationships (Figure 4C); a
procedure supported by the observation that LMA differed between canopy layers but not within a layer (P = 0.60 and 0.11
for top and bottom of the canopy, respectively).
Tree-level Gs decreased with D once D was above 0.6 kPa.
Boundary-line analysis was performed for each tree after partitioning the data to five consecutive ranges of Qavg, two of
which are shown for one tree in Figure 5A. From this analysis,
Gs,ref and m were obtained for each period. For both periods, m
was similarly related to Gs,ref with a slope (γ, i.e., the sensitivity
of Gs to D at a given Gs,ref) of 0.64 (Figure 5B), which did not
differ significantly (P = 0.75) from the general slope obtained
in many studies (about 0.6; Oren et al. 1999a). This analysis
did not account for the effects on γ of (1) the range in D values
occurring when Gs was analyzed, and (2) gbl /Gs,ref (see Surface
in Figure 6). We evaluated more precisely the change in the
sensitivity of Gs to D with changes in Gs,ref by accounting for
the effects of both factors. We first partitioned data for individual trees into above and below gbl = 700 mmol m –2 s –1. Values
of Gs,ref and m were estimated from boundary-line analysis by
gbl and plotted against the observed range in D and the mean
gbl /Gs,ref ratio (Figure 6). The inset in Figure 6 shows that actual and predicted γ were similar (Oren et al. 1999a).
As a final check on the consistency between gs and both
sap-flux-scaled Gs and KL, daily values were calculated for
each measurement day. For each measurement, gs(z) was
scaled to the canopy by estimating the sunlit and shaded leaf
areas in each of the three canopy layers based on the light
model (Appendix C; see example for average light in Figure 2), and summing and dividing by LA. This generated a diurnal pattern of gs for each tree. Selecting the portion of the diurnal patterns between the time of maximum conductance and
the time of maximum D, the relationships of gs and Gs with D
were analyzed (Equation 6) to obtain gs,ref and Gs,ref for the
same day for each tree. Excluding a cold morning, a windy day
(which prevented measurements at the top of the canopy) and a
pesticide application, allowed 15 comparisons, all of which
showed close agreement between the two estimates (Figure 7A; P = 0.87 based on a paired t-test). Similarly, gs,ref was
closely correlated to KL (P = 0.003; Figure 7B). Thus, both in
terms of expected Gs–D behavior and in relation to gs and KL,
Gs provided a good representation of the canopy, and can
therefore be scaled based on light and LA or LAI profile to
Gs(z).
Next we established the relationship between Gs,ref and Qavg
for each tree (Figure 5C). The mean of the two parameters in
the fit Gs,ref = bQavg + a (a = 34.5, SE = 4.79; b = 0.40, SE =
TREE PHYSIOLOGY VOLUME 28, 2008
TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
567
Figure 5. (A) An example of canopy conductance scaled from sap flux measured in a single poplar (Populus trichocarpa × P. deltoides) tree (Gs )
versus vapor pressure deficit (D). Boundary-line analysis is shown for two (䊉, 䉱) of the five light categories, the unselected points from the analysis are shown as 䊊; the vertical line at D = 1 kPa intersects the boundary lines at the reference Gs (Gs,ref ). (B) The slope of the response of Gs to lnD
(m in Equation 6) versus Gs,ref from data from 10 poplar trees and (C) the light response of stand-level Gs,ref, partitioned to five irradiances in the
first (䊉) and second (䊊) study periods (Q avg = canopy mean photosynthetic photon flux).
0.03) described the average response (r 2 = 0.81, P < 0.001). In
general, Gs,ref increased with Qavg similarly in both periods (P =
0.18), saturating for Qavg above 195 µmol m –2 s –1.
To fill gaps in the data during the study period, and to estimate Gs for D below 0.6 kPa, we predicted Gs of P. trichocarpa
× P. deltoides from Qavg, D and its daily range, gbl /Gs,ref, and the
functional relationships established above, such that:
G s = G s, ref (Qavg )(1 − γ ( D range , gbl /G s, ref ) ln D )
(11)
thus ignoring the effect of soil water limitations, which were
indicated by days with low Ψpd (Figure 1F). This model overestimated Gs over much of its range (Figure 8A), and we considered that these values represented potential canopy conductance and used them to calculate potential Anet,c and GPP. Daily
Gs,ref values from modeled Gs were expressed as a ratio of the
observed Gs,ref for individual trees. The ratio was linearly correlated with Ψpd during days when it was measured, showing
overestimation at low soil water content and underestimation
at high soil water content. We therefore calculated a soil-water-dependent correction factor (actual Gs,ref /modeled Gs,ref for
D > 0.6 kPa) for each day, and employed it to adjust the modeled Gs,ref used to estimate Gs when D was less than 0.6 kPa.
The same ratio was used to gap-fill 11 days of missing data by
averaging the correction factor before and after each gap.
Actual and potential carbon assimilation and biomass
production
Figure 6. Actual γ, the ratio of the slope of gs response to the natural
logarithm of the vapor pressure deficit (m) over the intercept of the response (Gs,ref ) obtained from analysis of data from 10 poplar (Populus
trichocarpa × P. deltoides) trees. The mesh surface shows the expected γ based on different ranges in vapor pressure deficit (D) and the
ratio of boundary layer conductance to reference stomatal conductance (gbl /Gs,ref). Inset shows the relationship between actual and expected γ, for which the 95% confidence interval encloses unity.
Most of the biomass produced during the study was in the stem
(Table 2). We missed the early part of the growing season in
which, based on the foliage produced before and during the
study, about 90 g C m –2 was invested in foliage. We have no estimates of production in other components during the growing
season before or after the study period.
Estimates of photosynthesis were sensitive to the specification of canopy properties in the models employed to calculate
light at the leaf surface at different layers in the canopy. The
most realistic canopy specification employed (LM1) included
both tree-level and shoot-level clumping, the latter varying
with height. A less detailed model employed only tree-level
clumping (LM2), and the least detailed was a simple BeerLambert without clumping (LM3). A comparison of the output from the models with data collected by a light sensor of
porometry demonstrated that light attenuation in LM3 was excessive, but that LM1 and LM2 attenuated light similarly and
without bias (Figures 9 and A3). Below we present the results
of photosynthesis estimated based on 4C-A with LM2, the
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568
KIM, OREN AND HINCKLEY
Figure 7. (A) Comparison between reference conductance (conductance at a vapor
pressure deficit of 1 kPa) obtained from
porometry at the leaf level (gs,ref ) and from
sap flux at the tree level (Gs,ref ) for days in
which leaf-level gas exchange was measured in poplar (Populus trichocarpa ×
P. deltoides). (B) Comparison between
gs,ref and leaf-specific hydraulic conductance (KL ) obtained from sapflux and leaf
water potential within the same measurement campaign.
simplest of the unbiased models.
Individual tree Anet,c per unit time was related to LA, and the
relationship did not change between the early and late parts of
the growing season (r 2 = 0.90; P = 0.07 for differences between periods). Net primary productivity (NPP) during the
study increased as a function of Anet,c to 0.41 (SE 0.08; r 2 =
0.67; P < 0.01), similar to the mean NPP/Anet,c of the 10 trees
(0.50, SE 0.03), with the difference attributable to a significant
intercept of the relationship (P < 0.001). At the stand level,
NPP/GPP was 0.43, and like NPP/Anet,c, it increased from the
first to the second period (Table 2). To assimilate 2371 g C
mgr–2 (LM2 in Table 2) over the study period, the stand used
438 mm of water. After removing soil water limitations to
stomatal conductance and associated effects on photosynthesis, potential GPP was estimated to increase to 2900 g C mgr–2
for the study period, associated with an increase in water use to
742 mm of water.
Discussion
Expected annual biomass production from a short-rotation
poplar plantation is 12–15 Mg ha –1 year –1 (Ben Brahim et al.
2000), but can approach 45 Mg ha –1 year –1 (Dawson 1976).
During the study, tree height increased by about 4.5 m, a
growth rate similar to those observed in other studies (e.g.,
Dawson 1976, Ben Brahim et al. 2000). The high rate of biomass production is attributed to high photosynthetic capacity
and carboxylation efficiency (Nelson 1984) and high LA. In
our study plantation, both LA and LAI were high, with LAI
reaching a maximum of 9.5, similar to published values for hybrid poplar (Hinckley et al. 1994, Scarascia-Mugnozza et al.
1997). As expected based on the coupling between photosynthesis and transpiration, poplar stands use large quantities of
water (Allen et al. 1999, Zhang et al. 1999), especially in arid
environments. Thus, even with irrigation, soil water limitation
may constrain water use and photosynthesis.
Stomatal conductance
Because the mechanism of stomatal function remains unclear
(Buckley and Mott 2002, Comstock 2002), empirical models
are commonly used to describe stomatal behavior (e.g., Jarvis
1976, Ball 1987, Tardieu and Davies 1993, Leuning 1995, Gao
et al. 2002). Empirical models are usually parameterized by
varying individual environmental variables and describing
their effects on stomatal conductance (Rayment et al. 2000).
Our model is a modified version of the Jarvis (1976) type
model with six variables (Equation 7).
The model overestimated Gs when soil water was assumed
to be non-limiting, because the other variables—Gs,ref, f(Qavg ),
f (D) and f (gbl /Gs,ref)—were generated by boundary-line analyses and thus represented the highest values (except outliers)
within the specified ranges of environmental conditions (e.g.,
Figures 4A and 5A). Stomatal conductance has often been
shown to increase linearly with irradiance up to a maximum,
Figure 8. (A) Comparison between modeled canopy stomatal conductance assuming no soil water limitation (Gs), and
measured Gs that reflects these limitations
in poplar (Populus trichocarpa × P. deltoides) trees. (B) Relationship between the
ratio of modeled and measured reference
Gs (Gs,ref ; i.e., Gs at D = 1 kPa) and predawn leaf water potential (Ψ pd ) measured
in the lower canopy and used to represent
soil water limitation in the first (䊉) and
second (䊊) study periods.
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TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
as we show at both the leaf and canopy levels in Figures 4C
and 5C. At the canopy level, Gs,ref reached a maximum at Qavg ≅
290 µmol m –2 s –1, about 75% of the maximum value of canopy
mean irradiance (~380 µmol m –2 s –1), corresponding to incoming QP ≅ 1320–1440 µmol m –2 s –1. At both the leaf and
canopy levels, the response of stomatal conductance to D was
similar to that expected based on theory for isohydric plants
(Oren et al. 1999a, Sperry et al. 2002), such as Populus, that
maintain ΨL above the threshold at which xylem cavitation occurs (Figures 4, 5A, 5B and 6). We found that stomatal responses to D at different irradiances can be described as a general increase in both gs,ref and m with irradiance, consistent
with previous studies (Tinoco-Ojanguren and Pearcy 1993,
Meinzer et al. 1997, Yong et al. 1997, Allen and Pearcy 2000).
However, the absolute increase in the sensitivity of stomatal
conductance to D caused no change in the relationship between these parameters (Figures 4B and 5B), a behavior ob-
Table 2. Net primary production (NPP), biomass production from
each tree part and estimates of canopy net assimilation (Anet,c ), gross
primary production (GPP) and ratio of NPP to GPP from different
models. The unit is g C mgr–2 .
Period 1
Period 2
Total
56
334
72
57
519
–
355
74
60
489
56
689
146
117
1008
4C-A approach
Light model 1
Anet,c
GPP
NPP/GPP
1190
1315
0.39
929
1042
0.47
2119
2357
0.43
Light model 2
Anet,c
GPP
NPP/GPP
1200
1325
0.39
933
1046
0.47
2133
2371
0.43
Light model 3
Anet,c
GPP
NPP/GPP
679
832
0.62
597
716
0.68
1279
1548
0.65
Light model 4
Anet,c
GPP
NPP/GPP
839
989
0.52
798
912
0.54
1637
1901
0.53
BIOME-BGC
Anet,c
GPP
NPP/GPP
851
981
0.53
753
860
0.57
1604
1841
0.55
BIOME-BGC/4C-A1
Anet,c
GPP
NPP/GPP
992
1122
0.46
837
944
0.52
1829
2066
0.49
Net primary production
Leaf
Stem
Branch
Root
Total
1
Stomatal conductance was based on sap flux measurements
569
served in many species (Oren et al. 2001, Addington et al.
2004, Ewers et al. 2005).
In this study, Ψmd (about –2.0 MPa) was lower than some
published values for P. trichocarpa, its hybrid, and P. deltoides
(e.g., Pezeshki and Hinckley 1988, Sperry et al. 1991, Tyree
and Ewers 1991, Cochard et al. 1996), all of which are considered prone to cavitation (Tyree and Ewers 1991, Tyree et al.
1992, Cochard et al. 1996). However, in other studies on hybrid poplars, including P. trichocarpa × deltoides (Gebre et al.
1998, Tschaplinski et al. 1998), a range of Ψmd (about –1.6 to
–2.2 MPa) and Ψpd (about –0.65 to –0.75MPa) values have
been determined similar to the ranges we obtained. Stomatal
conductance of P. tricocarpa remains nearly stable to ΨL of
–2.0 MPa, whereas that of P. deltoides decreases sharply below –0.5 MPa (Scarascia-Mugnozza et al. 1986, Schulte et al.
1987). Hybrids of these species show variable responses, some
behaving like P. trichocarpa (Scarascia-Mugnozza et al.
1986), others more like P. deltoides (Schulte et al. 1987). In
other studies, however, both species and their hybrids showed
similar sensitivities to soil water content (Braatne et al. 1992,
Allen et al. 1999) and reductions in photosynthetic rates as ΨL
decreases (Scarascia-Mugnozza et al. 1986). By utilizing
LA(z)-weighted Ψpd and Ψmd, we demonstrated that changes
in KL were largely in response to changes in Ψpd , which controlled gs,ref (Figures 7B and 8B) and reflected canopy-level
Gs,ref (Figure 7A).
The height difference between the top and bottom of the
canopy generated at most a hydrostatic gradient of 0.1 MPa,
yet Ψpd was occasionally about 0.5 MPa lower at the top of the
canopy than at the bottom (Figure 1F). Nighttime stomatal
closure is incomplete in many species (Oren et al. 1999b,
Dawson et al. 2007) (because of nighttime stomatal conductance, the baseline for converting temperature difference to
sap flux was set between nights when D ≅ 0 kPa). Higher gs in
upper-canopy leaves may have caused the vertical gradient in
Ψpd observed when the nighttime desert air was dry, rendering
Figure 9. Comparison of relative light on the leaf surface from different light models and porometric measurements. Mean ratio between
the light on the leaf surface and the light above the canopy from eight
porometric measurement campaigns (䊉), least-squares fit line and
model predictions.
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KIM, OREN AND HINCKLEY
Ψpd measured at the bottom of the canopy a more appropriate
surrogate for soil water potential. The residuals between Gs
modeled assuming no soil water limitation and Gs scaled from
measurements were strongly and linearly related to Ψpd of the
lower canopy (Figure 8B), indicating that modeled Gs is a
good approximation of potential conductance.
Actual and potential carbon assimilation
Although the trees varied in diameter, they shared a common
vertical space because of the small height differences (~1 m)
among individuals. Thus, although Anet(z) declined from the
top of the canopy downward (based on any of the vertically explicit light models), estimated tree-level Anet,c was linearly related to LA. The difference between Anet,c and GPP is foliar
respiration during the day (Table 2), the estimate of which
contains additional uncertainty and for stand carbon balance
merely represents a quantity that is added and then subtracted.
We prefer to use Anet,c for comparisons to tree-level NPP, but
we revert to GPP for comparison with the more commonly
available literature values. Comparison of the vertical light
gradients obtained with LM2 (tree-level clumping) with those
obtained with LM1 (tree-shoot-level clumping) showed little
effect due to the minimal clumping in this species (Figures 9
and A3). Thus, LM1 with a more complete account of canopy
properties produced only about 0.6% difference in GPP (Table 2), and will not be discussed further.
Based on 4C-A with LM2, the daily rates of canopy-level
Anet,c, GPP and E were higher in the first period than in the second (Figure 10A) because of higher LAI and photosynthetic
parameter values, (Table 2 and Figure A1). Over the entire
study, Anet,C was estimated at 2133 g C mgr–2, and GPP at 2371 g
C mgr–2 (Table 2). These estimates leave enough carbohydrates
for maintenance respiration after accounting for NPP and its
25% construction respiration cost (1008 + 252 = 1260 g C
mgr–2, after Wullschleger et al. 1997).
When the Beer-Lambert radiative transfer scheme (which
accounts for sun angle, vertically variable leaf angle distribution, and thus Ke, and vertically variable clumping at the shoot
level and crown level) is simplified by ignoring clumping (e.g.,
as in Campbell and Norman 1998), GPP was estimated at
1548 g C mgr–2 (LM3)—too little for a reasonable rate of maintenance respiration (about 40% of GPP; after Waring et al.
1998, and accounting for construction respiration). Further
simplification by using a constant Ke = 0.5 (i.e., assuming a
spherical leaf angle distribution, and that the sun is at zenith all
day), but keeping irradiance changing over the day, increased
GPP to 1901 g C mgr–2 (LM4), leaving almost enough carbohydrates for maintenance respiration. As a final simplification,
we reduced the canopy to a single layer and used daily means
of light and temperature, in effect employing BIOME-BGC
(Thornton et al. 2002); again, a low estimate of GPP (1841 g C
mgr–2 ) was obtained (Table 2). We also employed canopy conductance from the sap flux measurements in BIOME-BGC instead of the model’s own estimates, thereby focusing on differences caused by the vertical specification of the canopy. This
single leaf model produced an estimate of GPP (2066 g C
mgr–2) only 10% lower than the 4C-A/LM2 estimate (Table 2).
This indicates that the simplification of the radiation transfer
scheme used in BIOME-BGC (essentially LM4 with daily average light) can produce reasonable estimates of GPP, but difficulties with its conductance estimates may result in unacceptable underestimates. In addition, single-leaf models are
incapable of reproducing the vertical distribution of GPP.
The most simplified multi-layer approach (4C-A/LM4),
which increases light penetration into the canopy at the expense of realistic solar tracking, underestimated light on the
surface of foliage at the bottom of the canopy: in our stand this
would result in the bottom four layers of the canopy having
zero to negative net photosynthesis on a 24-hour basis. The
simulation suggested that the bottom 44% of LAI (averaged
over the study) contributed no carbohydrates to the stand (Figure 10B). Thus, even this unrealistic approach that forces light
down the canopy underestimated both GPP and its vertical distribution in the canopy. In contrast, based on estimates from
4C-A/LM2, only foliage in the bottom two layers (averaging
16% of LAI) contributed no photosynthates to the stand (Fig-
Figure 10. (A) Daily actual (black) and potential (gray) stand transpiration (E ), canopy net assimilation (Anet,c ), gross primary production
(GPP) and net primary productivity (NPP) in a poplar (Populus
trichocarpa × P. deltoides) plantation in the two study periods. (B)
The vertical distribution of Anet,c based on three Beer–Lambert radiative transfer formulations: with correct sun angle, vertically varying
leaf angle distribution and tree-level clumping (LM2, 䊉); with correct
sun angle and vertically varying leaf angle distribution, but no clumping (LM3, 䊊); and assuming no clumping and constant Ke (i.e., sun always at zenith and leaf-angle spherically distributed) (LM4, 䉲).
Horizontal dashed line represents the lowest level of branch mortality.
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TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
ure 10B). This agrees with the observed 45% reduction in living branches in the bottom two layers of the canopy over the
study period, with no loss of branches recorded above; at the
end of the study, the bottom canopy layer had one third of the
live branches, and the next layer had one half of the live
branches found in the layer above. Therefore, although reasonable estimates of Anet,c and GPP can be made with greatly simplified models, a realistic vertical distribution of carbohydrate
production can be obtained only if tree-scale clumping (and
shoot-scale clumping in some species; e.g., Schäfer et al.
2003) is incorporated into a radiative transfer model with realistic solar tracking.
Our 4C-A/LM2 approach produced a GPP value that is appreciably higher than NPP. For the stand and over the entire
study period, the NPP/GPP ratio was 0.43, similar to the mean
of a large number of species (Waring et al. 1998). Based on a
big leaf approach (as in BIOME-BGC) and solar tracking (as
in LM3), recent estimates of NPP/GPP for poplar species and
their hybrids range from 0.58 to 0.72 (Gielen et al. 2005), similar to our 4C-A/LM3 estimate of 0.64 (Table 2) but substantially higher than the 0.49 estimated by the sap-flux-constrained BIOME-BGC.
The model estimates allow calculations of water- and lightuse efficiencies. Water-use efficiency in forests is expressed in
several ways. For hybrid poplars, published values of photosynthetic WUE range from 3.6 to 4.2 g C kg –1 H2O based on
leaf gas-exchange measurements (Bassman and Zwier 1991),
and production-based WUE of 2.1 g dry matter C kg –1 H2O
from studies on potted plants of the same hybrid (Souch and
Stephens 1998). These values are similar to those we obtained
with the 4C-A/LM2 model to estimate Anet,c (4.9 g C kg –1 H2O,
or 5.3 g for GPP) and growth measurements to estimate NPP
(2.3 g C kg –1 H2O). Photosynthetic light-use efficiency was estimated at 0.42 g C mol –1 of PAR, or 2.02 g C MJ –1, higher
than estimates with other models in forests with slightly lower
LAIs (Whitehead and Walcroft 2005). However, it was similar
to values for other poplar species and deciduous oak and maple
forests (Waring et al. 1995). For example, light-use efficiency
was 1.74 g dry matter MJ –1, similar to other stands of the same
genus growing on nutrient-rich soils (Calfapietra et al. 2003,
Green et al. 2003).
We used 4C-A/LM2 to estimate GPP if irrigation were sufficient to remove all water limitations. The estimated potential
GPP was 21% higher than actual GPP, which, based on an
NPP/GPP of 0.43, would have increased NPP by about 217 g
C m –2 ground area and associated stand E by 70% (Table 2).
Assuming further that this extra carbon would not be used for
foliage production because LAI is already high, and that about
70% would be invested in stem wood production (ScarasciaMugnozza et al. 1997, Zabek and Prescott 2006), 162 g C m –2
would be added to the stem in the absence of soil water limitation to photosynthesis, decreasing stem-wood yield-based
WUE by 27% (from 1.57 to 1.15 g C kg –1 H2O). Thus, the
large increase in irrigation necessary to remove all water limitation is difficult to justify in economic terms. The use of this
technique to examine the tradeoffs between production and
water limitations offers opportunities to explore the impacts of
increasing or decreasing water use on carbon gain.
571
Acknowledgments
This research was supported by the Biological and Environmental Research Program (BER), U.S. Department of Energy, through the
Western Regional Center of the National Institute for Global Environmental Change (NIGEC) under Cooperative Agreement no. DEFC03-90ER61010 and by the Office of Science (BER), U.S. Department of Energy, Grant no. DE-FG02-95ER62083. We thank personnel at the Wallula Fiber Farm (Boise Cascade Corp.) and especially
Drs. Chuck Wierman and Peggy Payne. We thank Dr. Sari Palmroth
for critical review of this paper. Morgan Dutton provided outstanding
field assistance.
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Appendix A
Table A1. List of additional symbols.
Parameter
Definition
Unit
a(z,θ)
cd
em
h
J
Jmax,25
Ke(z)
Ke,avg(z)
K CO 2
Km
KO 2
k
LAIcum(z)
n
Na
Oa
p(φ)
Qb
Qb(z)
Qd
Qd(z)
QL,b(z)
QL,d(z)
QL,s(z)
QL,tot
Qo,b
Qo,d
Qs
Qs(z)
Q2
R
S(z,θ)
u*R
u′w ′
Vcmax,25
x(z)
Mean gap fraction of the zth layer in a single tree crown at the view angle θ
Drag coefficient (0.2; Katul and Chung 1999)
Maximum quantum efficiency (0.08)
Canopy height
Electron transport rate
Light saturated electron transport rate at 25 °C
Extinction coefficient in the zth layer
Mean extinction coefficient to the zth layer weighted with leaf area in each layer
Michaelis constant for CO2 fixation
Turbulent diffusion coefficient
Michaelis constant for oxygen inhibition
von Karman constant (0.41)
Cumulative leaf area index to the zth layer
Stand density
Nitrogen concentration per unit leaf area
Ambient oxygen concentration (210000 µmol mol –1)
Probability of leaf angle in φ degree
Direct radiation
Direct radiation at the bottom of the zth layer
Diffuse radiation
Diffuse radiation at the bottom of the zth layer
Direct radiation on leaf surface in the zth layer
Diffuse radiation on leaf surface in the zth layer
Scattered radiation on leaf surface in the zth layer
Total radiation on leaf surface
Direct radiation at the top of the canopy
Diffuse radiation at the top of the canopy
Scattered radiation
Scattered radiation at the bottom of the zth layer
Maximum fraction of quanta used in electron transport
Universal gas constant (8.314)
Projected area of tree crown in zth layer at view angle θ
Friction velocity at z = h
Momentum flux
Maximum Rubisco capacity at 25 °C
Ratio of mean pojected areas of canopy leaves on horizontal and vertical surfaces
in the zth layer
Leaf absorptivity (0.83)
CO2 compensation point
Convexity term for electron transport rate
Maximum dark-adapted quantum yield of photosystem II
Clumping factor in the zth layer
Mean clumping factor to the zth layer weighted with leaf area in each layer
Zenith angle of the sun
Mean direct radiation transmission coefficient to the zth layer weighted with
leaf area in each layer
Total radiation transmission coefficient in the zth layer
Diffuse radiation transmission coefficient in the zth layer
–
–
mol mol –1
m
µmol mleaf–2 s –1
µmol mleaf–2 s –1
–
–
µmol mol –1
m2 s –1
mmol mol –1
–
–
trees m –2
g m –2
µmol mol –1
–
µmol mgr–2 s –1
µmol mgr–2 s –1
µmol mgr–2 s –1
µmol mgr–2 s –1
µmol mleaf–2 s –1
µmol mleaf–2 s –1
µmol mleaf–2 s –1
µmol mleaf–2 s –1
µmol mgr–2 s –1
µmol mgr–2 s –1
µmol mgr–2 s –1
µmol mgr–2 s –1
–
J mol –1 K –1
m2
m s –1
–
µmol mleaf–2 s –1
α
Γ*
ΘPSII
ΦPSII,max
∏(z)
∏avg(z)
θ
τb,avg(z)
τb,tot(z)
τd(z)
TREE PHYSIOLOGY VOLUME 28, 2008
–
–
µmol mol –1
–
–
–
–
radians
–
–
–
TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
575
We calculated Vcmax, Jmax, Q2 and ΘPSII as (Bernacchi et al.
2001, 2003):
Appendix B
Net assimilation and gross primary production
The 4C-A model (Schäfer et al. 2003) calculates canopy photosynthesis from canopy conductance constrained by sapflux-measurement conductance with the Farquhar-type photosynthesis model (Farquhar et al. 1980, Farquhar and von
Caemmerer 1982). At each canopy layer, gs(z) values of sun
and shade leaves were estimated from the stomatal light response curves generated from porometric measurements (Figure 4C). The gs(z) values were converted to GS by multiplying
by the respective sun and shade leaf areas of each layer and
summing over the canopy. This GS was constrained by sapflux-measured conductance by linearly adjusting the mean of
canopy gs (Equation 5).
We calculated Anet for sun and shade leaf areas in each layer
by solving Ci from two potential capacities and taking the minimum (Farquhar and von Caemmerer 1982):
Anet = min(WRub , WJ ) − R day = gc (C a − C i )
(B1)
where WRub and WJ are Rubisco-limited and electron-transport
limited rates of ribulose-1,5-bisphosphate regeneration, Rday is
daytime respiration rate assumed to be 0.015Vcmax (Casella and
Ceulemans 2002), gc is converted from water to CO2 because
of the different diffusivities, and Ca is ambient CO2 concentration, ranging from 364 to 371 µmol mol –1 over the study period (Keeling and Whorf 2005). The two linear algebraic
equations for Ci were solved at half hourly time-steps, and the
minimum Anet was selected.
In Equation B1, WRub and WJ were calculated as:
WRub = Vcmax
WJ = J
C i − Γ*
⎛
O ⎞
C i + K CO2 ⎜1 + a ⎟
KO2 ⎠
⎝
C i − Γ*
4.5 C i + 10.5 Γ*
Vcmax = Vcmax,25 e
65. 33 ⎞
⎛
⎜ 26. 35 −
⎟
Ta + 273 ⎠
⎝
(B8)
43. 54 ⎞
⎛
⎟
⎜ 17. 57 −
Ta + 273 ⎠
Jmax = Jmax,25 e⎝
(B9)
Q2 = 0.5 QL( z) αΦPSII,max
Θ PSII = 0.76 + 0.018 Ta − 0.00037 Ta
(B10)
2
(B11)
where ΦPSII,max was calculated as (Bernacchi et al. 2003):
ΦPSII = 0.352 + 0.022 Ta − 0.00034 Ta
2
(B12)
Finally, Vcmax,25 and Jmax,25 were calculated from the measured
nitrogen concentration based on a relationship derived by
Casella and Ceulemans (2002) for the same species at a similar
age (Vcmax = 28.9Na and Jmax = 67.3(Na – 18.3); see Figure A1).
Our nitrogen concentration ([N]) data were obtained for upper- and lower-canopy leaves; there was no difference in [N]
between sun (crown envelope) and shade (inner core) leaves
(P = 0.11), so data for both canopy layers were pooled. We assumed that the [N] in upper-canopy leaves remained unchanged until 60% of the light (estimated as the percent of cumulative light above the canopy during the study period) was
(B2)
(B3)
where Γ*, K CO2, K O2 and J are calculated according to Bernacchi et al. (2001, 2003):
J=
Q2 + Jmax − (Q2 + Jmax ) 2 − 4Θ PSII Q2 Jmax
2Θ PSII
(B4)
37830 ( Ta − 25 )
Γ* = 42.75 e 298 R (Ta − 273 )
(B5)
79430 ( Ta − 25 )
K CO2 = 404.9 e 298 R (Ta − 273 )
(B6)
36380 ( Ta − 25 )
K O2 = 278.4 e 298 R (Ta − 273 )
(B7)
Figure A1. Seasonal variation in maximum rates of (A) carboxylation
(Vcmax,25 ) and (B) electron transport (Jmax,25 ) at the top (䊊) and bottom (䊉) of a poplar (Populus trichocarpa × P. deltoides) canopy in
1999 (DOY = day of year).
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576
KIM, OREN AND HINCKLEY
attenuated, reflecting the saturating portion of the photosynthetic light response curve. Over the lower-canopy zone in
which light was assumed to affect foliar [N] (typically about
half of total height), [N] was interpolated between the values
measured in the upper- and lower-canopy. The interpolation
was linear with the reduction in irradiance estimated with each
of the light models (LM1–4). Upper- and lower canopy [N]
values were linearly interpolated over time between consecutive measurements. For BIOME-BGC, [N] values from the
upper- and lower canopy were used for sun and shade leaves,
respectively.
Gross primary production (GPP) was calculated by adding
Rday to Anet.
Appendix C
Canopy radiative transfer
(C1)
The proportion of sunlit area was calculated as by Nilson
(1999):
z
⎞
⎛
τ b ( z, θ) = exp ⎜ – n ∑ S (i, θ)(1 − a (i, θ) ) ⎟
⎠
⎝ i =1
x( z) + tan 2 θ
K e ( z, θ) =
− 0. 733
x( z) + 1.774( x( z) + 1182
. )
(C2)
(C4)
Values of x(z) were similar to those of an oak canopy (Kull et
al. 1999, Wirth et al. 2001), changing from 1.5 to 2.75 from the
top to the bottom of the canopy (Figure A2B).
We calculated Qd and Qs at the bottom of each layer as:
Qd ( z) = τ d( z) Qo, d
(C5)
Qs ( z) = ( τ b,tot( z, θ) − τ b( z, θ) )Qb ( z)
(C6)
where d(z) and
Above-canopy QP was partitioned into Qo,b and Qo,d components using measured and expected clear day radiation
(Spitters et al. 1986). We assumed Qs to be zero above the canopy. Then, the interceptions of Qb, Qd and Qs were estimated
separately in each 1-m canopy layer. In every layer, Qb on the
sunlit horizontal surface is the same as at the top of the canopy:
Qb ( z) = Qo, b
was 0.95, indicating little clumping in the top shoots of this
species (Figure A2A).
We calculated Ke(z,θ) in Equation C3 as:
b,tot(z,
) were calculated as:
2π
τ d ( z) = 2 ∫ τ b,tot( z, θ) sin θ cos θ dθ
(C7)
0
τ b,tot ( z, θ) = e
− α n S( z , θ ) ( 1 − a ( z , θ ) )
(C8)
and b,avg(z, ) was calculated with LAIcum(z), Ke,avg(z,θ) and
Πavg(z) as:
τ b,avg ( z, θ) = e
− n S( z , θ ) (1 − a avg ( z , θ ) )
⎛ K e, avg( z, θ ) LAI cum( z) Π avg( z) ⎞
a avg( z, θ) = exp ⎜
⎟
nS ( z, θ)
⎠
⎝
(C9)
(C10)
(C3)
Values of Ke,avg(z,θ) and Πavg(z) were mean values weighted
with leaf area in each layer from the top of the canopy to the zth
layer.
where n is stand density, S(z,θ) is projected area of a conical
crown with a radius of 75% of the distance between trees,
a(z,θ) is mean gap fraction in a single tree crown at the view
angle θ (Nilson 1999) and Π(z) is the mean ratio of shoot silhouette area to the projection area of all leaves in their natural
orientation, but spread out so they do not shade each other
(Stenberg 1998). In light models LM2–4, shoots were assumed to have leaves with no clumping, i.e. Π(z) = 1. However, for light model LM1, we assumed an additional shootlevel clumping that varied vertically. Shoot-level clumping
was estimated according to the following approach: (1) based
on observations, we assumed that shoots were not clumped at
the bottom of the canopy; (2) we assumed that the mean of total clumping (shoot + tree) was similar to that measured in a
stand of the same species (Niinemets et al. 2004); (3) the vertical pattern in clumping was similar to the vertical pattern of
leaf mass per area in a stand with high LAI (Liberloo et al.
2007); and (4) solving for the unique shoot-level clumping at
the top of the canopy. Shoot-level clumping at the canopy top
Figure A2. Canopy specification. Vertical distributions (with height z)
of (A) shoot-level clumping factor used in LM1 (Π) and (B) leaf angle
distribution (x).
a ( z, θ) = e
−
K e ( z , θ ) LAI ( z ) Π ( z )
n S( z , θ )
TREE PHYSIOLOGY VOLUME 28, 2008
TRANSPIRATION AND CARBON ASSIMILATION IN POPLAR
We calculated QL,b(z) by multiplying the light on the leaf
surface by the probability of leaf angle distribution (p(φ)):
π
1 2
QL,b( z) =
Qb( z − 1) cos φ p( φ) dφ
cos θ φ∫= 0
(C11)
For QL,d(z) and QL,s(z), we used the mean radiation at the top
and bottom of each canopy layer.
QL,d( z) =
QL,s( z) =
1
2
1
2
(QL,d( z − 1) + QL,d( z) )
(C13)
1 12
∑ LAI( z) Qbp( z) QL,b( z) + QL,d( z) + QL,s( z)
LAI z =1
(
(
(
)
)(
∂u′w ′
= − cd LAI( z) U( z) 2
∂z
u′w ′ = − Km
The average light incident on the sunlit leaf was calculated
by summing direct, diffuse and scattered radiation, and that on
the shaded leaf by summing diffuse and scattered radiation
only. We calculated Qavg as:
Qavg =
where gbl,(z), U (z) and d(z) are boundary layer conductance,
mean wind speed and leaf characteristic length of the zth layer,
respectively.
We calculated U (z) by numerically solving differential
equations with 10 iterations of the Thomas algorithm with 0.5
relaxation at each iteration (Kreyszig 1988):
(C12)
(QL,s( z − 1) + QL,s( z) )
577
∂U( z)
∂z
(D2)
(D3)
where Km is assumed to change only with h and is calculated
as:
Km = khu* R
(D4)
(C14)
))
+ 1 − Qbp( z) QL,d( z) + QL,s( z)
We tested the performance of the light models with three
canopy specifications, the most complicated tree-shoot clumping (LM1), the less complicated tree clumping (LM2), and the
simple Beer-Lambert (LM3). We calculated QL,tot (total light
at the surface of leaves) for each time in which a gas exchange
measurement (with associated PPF) was made. Because the
porometric measurements were made on a leaf in its natural inclination, we expected a large scatter in the comparison between model output and measurements, and only tested for
bias. Models LM1 and LM2 showed no bias at any of the three
measurement heights (Figure A3), and as expected given the
small value of shoot clumping employed in LM1, there was little difference in performance between models. In contrast,
LM3 underestimated at the top canopy layer, and the error became so pronounced with depth that the model estimates essentially described the lower bound of the data in both the middle and lower canopy.
Appendix D
Boundary layer conductance
For gbl calculations, U(z) was modeled with a first-order closure model for a planar-homogeneous, stationary and high
Reynolds number flow based on the half-hourly mean U above
the canopy (Landsberg and James 1971). The boundary layer
conductance of each canopy layer was calculated as:
gbl ( z) = 0147
.
U ( z)
d ( z)
(D1)
Figure A3. Light comparison among three light models and porometric measurements from the (A) upper, (B) middle and (C) lower
poplar (Populus trichocarpa × P. deltoides) canopy. Open circles represent the mean light on the leaf surface from porometric measurements (n ≥ 4). Data were fit with a least-squares fit line (solid line),
and lines fit through the data from the three light models are shown.
Abbreviations: QL,tot, total radiation incident on leaf surface; and QP ,
photosynthetic photon flux.
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