The relationship between reference canopy 
conductance and simplified hydraulic 
architecture
Authors: Kimberly Novick, Ram Oren, Paul C. Stoy, 
Jehn-Yih Juang, Mario Siqueira, and Gabriel Katul
"NOTICE: this is the author’s version of a work that was accepted for publication in Advances in 
Water Resources. Changes resulting from the publishing process, such as peer review, editing, 
corrections, structural formatting, and other quality control mechanisms may not be reflected in 
this document. Changes may have been made to this work since it was submitted for 
publication. A definitive version was subsequently published in Advances in Water Resources, 
VOL# 32, ISSUE# 6, (June 2009), DOI# 10.1016/j.advwatres.2009.02.004.
Novick, Kimberly, Ram Oren, Paul C. Stoy, Jehn-Yih Juang, Mario Siqueira, and Gabriel Katul. 
“The Relationship Between Reference Canopy Conductance and Simplified Hydraulic 
Architecture.” Advances in Water Resources 32, no. 6 (June 2009): 809–819. doi:10.1016/
j.advwatres.2009.02.004.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
The relationship between reference canopy conductance and simplified
hydraulic architecture
Kimberly Novick a,*, Ram Oren a, Paul Stoy b, Jehn-Yih Juang c, Mario Siqueira a,d, Gabriel Katul a
aNicholas School of the Environment, Duke University, Box 90328, Durham, NC 27708, USA
bDepartment of Atmospheric and Environmental Science, School of GeoSciences, University of Edinburgh, Edinburgh EH9 3JN, UK
cDepartment of Geography, National Taiwan University, Taipei, Taiwan
dDepartamento de Engenharia Mecanica, Universidade de Brasília, Brazilare do
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Terrestrial ecosystems
water movement from
ductance regulates pla
tance is coordinated w
been formulated at a
published conductance
mates were used to ex
parsimonious hydrauli
able agreement with m
time scales, the functi
hydraulic architecture
tem. Prognostic applic
In this study, we did no
variables that are read
a mediating influence
forests, canopy height alone e
ðr2 ¼ 0:68Þ and this relation
models.minated by vascular plants that form a mosaic of hydraulic conduits to
il to the atmosphere. Together with canopy leaf area, canopy stomatal con-
r use and thereby photosynthesis and growth. Although stomatal conduc-
t hydraulic conductance, governing relationships across species has not yet
l level that can be employed in large-scale models. Here, combinations of
rements obtained with several methodologies across boreal to tropical cli-
lationships between canopy conductance rates and hydraulic constraints. A
l requiring sapwood-to-leaf area ratio and canopy height generated accept-
ments across a range of biomes ðr2 ¼ 0:75Þ. The results suggest that, at long
nvergence among ecosystems in the relationship between water-use and
s inter-specific variation in physiology and anatomy of the transport sys-
of this model requires independent knowledge of sapwood-to-leaf area.
strong relationship between sapwood-to-leaf area and physical or climatic
rminable at coarse scales, though the results suggest that climate may have
relationship between sapwood-to-leaf area and height. Within temperate
xplained a large amount of the variance in reference canopy conductance
ship may be more immediately applicable in the terrestrial ecosystem1. Introduction
Canopy stomatal conductance to water vapor ðGsÞ is a primary
determinant of ecosystem transpiration rates. Over the past few
decades, much attention has been focused on describing the re-
sponse of Gs to the variables that act on fast time scales (e.g.
hourly). In comparison, little attention has been paid to processes
that may impact canopy conductance on longer time scales (e.g.
yearly). Generic relationships that are valid across species have
been developed for the fast responses of Gs to photosynthetically
active radiation (PAR, [1]), vapor pressure deficit (D, [2]), and soil
moisture content (h, [1]) and have been implemented in large-scale
models. These models typically rely on a reference canopy conduc-
tance rate ðGsref Þ, defined at a specific environmental state that can
vary across applications and adjusted for the fast-acting meteoro-logical variables. These adjustments can be based on multiplicative
functions that take a range of mathematical forms (hereafter re-
ferred to as f1ðVPDÞ; f 2ðPARÞ, and f3ðhÞ). One such formulation is
the widely used ‘‘Jarvis-type” model which can be expressed as [3]:
Gs ¼ Gsref  f1ðVPDÞ  f2ðPARÞ  f3ðhÞ: ð1Þ
Gsref significantly varies across stands of different age, structure and
vegetation type, and changes predictably with measurable features
of canopy structure, at least within a species [4–6]. However, the
current suite of the terrestrial ecosystem models do not account
for mechanisms that impact Gsref over longer time scales. Some dy-
namic global vegetation models (DGVMs) and stand-level models
assume that the canopy stomatal conductance parameters are ‘sta-
tic’ for a range of canopy architectural scenarios, while others
change the parameters empirically with stand age, or require spe-
cies-specific allometric relationships that are difficult to implement
over large and biologically diverse land areas [7,8]. Traditionally,
these assumptions were necessary given the lack of spatial datasets
of elementary hydraulic parameters known to impact Gs. Recent
advances in LIght Detection and Ranging (LIDAR) imaging technol-
ogy now facilitate detailed mapping of key properties of canopy
architecture for large land areas [9,10], and elevation datasets from
the Shuttle Radar Topography Mission (SRTM) appear capable of
producing maps of canopy height ðhÞ over most of the global land
surface [11].
Mechanistic relationships between the parameters controlling
Gs and remotely sensed features of canopy architecture (such as
h), if present, could improve biosphere–atmosphere mass and en-
ergy exchange estimates at large spatial scales. To our knowl-
edge, no attempt has been made to determine whether such
generic relationships exist between measurable features of
hydraulic architecture and canopy conductance among diverse
species at the level of simplicity that permits incorporation into
coarse-scale models. On the other hand, relationships between
canopy conductance and features of canopy architecture have
been well documented within species. A predictable decrease
in both leaf-level and mean canopy stomatal conductance with
canopy height has been reported for a range of species, including
Fagus sylvatica [4], Picea abies [12], Pinus palustris [13], Pinus pin-
aster [5], Pinus ponderosa [14], Pinus taeda [15], and Quercus garr-
yana [16]. In many cases, this decrease is attributed to an
increased hydraulic resistance associated with an increased path
length. However, several of these studies also suggest that sap-
wood-to-leaf area ratio ðAS=ALÞ is another important determinant
of Gs [4,17,18,5], and in some cases alterations in AS=AL can
nearly compensate for height or physiologically based reductions
in Gs [19]. It is therefore likely that the most parsimonious gen-
eric model of canopy conductance accounting for readily measur-
able features of hydraulic architecture must consider, at
minimum, AS=AL and h. This investigation was made to assess
the performance of such a model over a wide range of climatic
regimes and species.
2. Theoretical considerations and hypotheses
2.1. Relating transpiration and conductance to hydraulic architecture
The cohesion–tension theory for water transport in trees [20]
has been used to explain the contribution of hydraulic characteris-
tics to variations in Gs. Within species, theoretical relationships be-
tween canopy stomatal conductance and canopy architecture are
often derived by equating the soil-to-leaf water flux to the leaf-le-
vel transpiration rate ðTr ;mmol m2 s1Þ under steady-state flow
conditions [21,22], yielding:
Tr ¼ KðWsoil Wleaf  qwghÞ; ð2Þ
where K ðmmol m2 s1 MPa1Þ is the leaf-level hydraulic conduc-
tivity from the soil to the leaf, g is the gravitational acceleration
ðm s2Þ;qw is the density of water ðkg cm3Þ, and Wsoil Wleaf
(MPa) is the soil-to-leaf pressure difference. Noting that K is propor-
tional to the sapwood area and inversely proportional to soil-to-leaf
path length [2,4] yields:
Tr ¼ ks ASALh ðWsoil Wleaf  qwghÞ; ð3Þ
where the path length from Wsoil to Wleaf is approximated by h, and
ks is the tissue-specific hydraulic conductivity per unit sapwood
area ðmmol m1 s1 MPa1Þ.
Ecosystem- and coarse-scale carbon cycling models often as-
sume that, at long time scales, leaf boundary layer conductance
has negligible influence on total canopy conductance. With this
assumption, the stomatal response to changes in hydraulic archi-
tecture can be predicted by substituting Gs and the vapor pressure
deficit (D, MPa) for the transpiration rate in Eq. (3) [3,23,24,13],
yielding:GsD ¼ ks ASALh ðWsoil Wleaf  qwghÞ: ð4Þ2.2. Separating fast and slow responses
As noted earlier, Gs responds rapidly to the changes in PAR;D,
and h via the multiplicative functions f1ðVPDÞ; f2ðPARÞ, and f3ðhÞ.
Therefore, to isolate the effects of AS=AL; ks;Wleaf , and h on Gs
from the effects of rapidly changing variables, a conductance
rate at a reference environmental state (Gsref ) is used. In this
analysis, the reference environmental state is characterized by
non-limiting light and soil moisture (i.e. f2ðPARÞ ¼ f3ðhÞ ¼ 1),
and a reference VPD of 1 kPa. Estimates of Gsref may be adjusted
to reflect varying environmental conditions to produce a contin-
uous estimate of Gsref as per Eq. (1) with multiplicative func-
tions, if they are known. In the case of inter-specific
application of the Jarvis model, at least one variant of the three
functions f1ðVPDÞ; f 2ðPARÞ, and f3ðhÞ had already been formulated
(see Oren et al. [2] for f ðVPDÞ, and Granier et al. [1] for f ðPARÞ
and f ðhÞ).
When only non-limiting soil moisture states are considered (as
specified by the reference environmental state), jWsoilj is typically
an order of magnitude less than jWleaf j. Therefore, we neglect
jWsoilj in Eq. (4) relative to jWleaf j, noting that this may introduce
a bias on the order of 10–20% in plants with relatively low jWleaf j
(Fig. 1). With this assumption, Gsref can be expressed as a function
of AS=AL; ks;Wleaf , and h using:
Gsref ¼ ks ASALh ðWleaf  qwghÞ: ð5Þ
This formulation assumes that canopy height is a proxy for the
mean path length from the soil through the rooting zone to
the leaf. Conditions in which h does not represent this path
length for water flow are likely to occur in two types of ecosys-
tems: (a) canopies with deep rooting relative to the total path
length (i.e., mature short stature forests), and (b) canopies where
complicated vertical branch architecture patterns make h a poor
proxy for the mean path length. In the former scenario, a rooting
length of 1 m results in a 5% error in ks ASALh for a 10 m canopy
(Fig. 1). Similarly, a rooting length of 2 and 3 m results in errors
of ca. 15% and 20%, respectively. In the case of taller canopies,
the error introduced by equating h with the path length de-
creases with increasing h.
To assess the relative contribution of each of these four vari-
ables to inter-specific variation in the reference conductance rates,
the observed natural variation in these parameters is considered
first. In general, Wleaf is typically around 2 MPa [5,25,26],
although values as high as Wleaf ¼ 1:0 MPa (Picea mariana, [27])
and Wleaf ¼ 1:1 MPa (Eucalyptus saligna, [19]), and as low as
Wleaf ¼ 3:28 MPa (tropical species, [28]) and even much lower
have been reported. The hydraulic conductivity, ks, varies
across species by about an order of magnitude,
from < 30 mmol m1 s1 MPa1 for gymnosperms to > 130
mmol m1 s1 MPa1 for some evergreen angiosperms [29].
Variations in AS=AL across species are comparable to variations
in ks, ranging from values as low as 0:7 cm2 m2 for tropical E. sal-
igna [19] and 0:5 cm2 m2 for boreal species [27] to ratios as high
as 13 cm2 m2 for P. palustris [13] and 14 cm2 m2 for Taxodium
distichum [30]. Even greater variations are found over the land-
scape in h, which can range from less than a meter to over 100 m.
Therefore, if independence is assumed among all the driving
variables in Eq. (5), we expect that both the products
ksðWleaf  qwghÞ and AS=AL=h vary by approximately an order of
magnitude across species, and each group of variables could ex-
plain roughly 50% of the interspecies variation in Gsref if all other
10 20 30 40
−0.25
−0.2
−0.15
−0.1
−0.05
0
h (m)
Er
ro
r i
n 
k s
⋅
A
s/A
L/
h(Ψ
le
af
 
−
 
ρ w
gh
)
(a)
RL = 3 m
RL = 2 m
RL = 1 m
1 1.5 2 2.5 3
Ψleaf (MPa)
(b)
Ψ
soil
 = −0.1 MPa
Ψ
soil
 = −0.2 MPa
Ψ
soil
 = −0.3 MPa
Fig. 1. The error introduced by some of the assumptions leading to Eq. (5). Fig. 1(a) shows the error in ks ASAL hðWleaf  qwghÞ incurred by neglecting root length (RL) in the total
path length for a range of assumed root depths. Fig. 1(b) shows the relative error associated with neglecting jWsoilj, which is typically an order of magnitude less than jWleaf j for
a range of soil water potentials. The dotted lines indicate 10% and 20% errors.assumptions in the model are valid. In actuality, some coordination
among these variables is likely. For example, within species, AS=AL
and h are often tightly correlated [4,31,27] and are linked by a sim-
ple linear relationship:
AS
AL
¼ ahþ b: ð6Þ
However, a can be either positive or negative [31], and can vary
from as low as 0:41 cm2 m3 (P. mariana, [27]) to as high as
0:21 cm2 m3 (Pinus sylvestris, [32]). Hence, across species, AS=AL
and h are expected to be less correlated than among stands of the
same species. Furthermore, compensating relationships between
Wleaf and ks should be considered. Trees growing in dry environ-
ments conducive to producing low (i.e., more negative) Wleaf pro-
duce tissues with lower xylem vulnerability to cavitation
accompanied by lower ks [33,24]. Conversely, plants producing tis-
sues with high ks must maintain higher Wleaf to prevent xylem cav-
itation [34]. Thus, a change in Wleaf that could have a positive effect
on Gsref would probably be accompanied by an opposing change in
ks and vice versa. We note, however, than a recent review article
failed to find a strongly significant relationship between Wleaf and
ks across species [35].
In this article, we focus on the relationship between Gsref and
AS=AL=h as canopy height is an easily measurable feature of canopy
architecture, and sapwood-to-leaf area is far simpler to measure at
the stand-scale than Gsref . Furthermore, AS=AL may be determined a
priori for some species based on established allometric relation-
ships or LIDAR remote sensing. We hypothesize that, hydraulically,
AS=AL and h should exert a strong control over Gsref , explaining
approximately 50% of the variation in reference conductance via:
Gsref / ASALh : ð7Þ
Within this framework, results from two literature surveys are used
to examine whether general relationships between Gsref , h, and
AS=AL emerge which are sufficiently strong to eclipse inter-specific
variation in Wleaf and ks.3. Methods
Two independent literature surveys were conducted. The first
survey was designed to explore inter-specific variation between
Gsref ;h, and AS=AL. The second survey was used to determine the ex-
tent of inter-specific variability in a (and hence, AS=AL), and to eval-
uate whether such variations can be related to climate controls,
phylogenetic similarity, or other ecosystem features.
3.1. Survey 1 – Relationships between Gsref ; h, and AS=AL
Published estimates of h and Gsref were obtained and analyzed
for 42 closed-canopy forest ecosystems representing a wide range
of species from boreal to tropical climates (Survey 1, Table 1). Esti-
mates of AS=AL were available for 29 of these sites. These studies
relied on canopy transpiration obtained by either sap-flux or eddy
covariance methodologies, averaged over a range of time scales
from half-hourly to daily. Typically, canopy conductance was de-
rived in these studies from the estimates of transpiration and D
using [36]:
Gs ¼ KuðTÞ  TrD  AL ; ð8Þ
where KuðTÞ is a temperature-dependent constant derived from the
latent heat of vaporization, the specific heat capacity of dry air,
mean air density, and the psychrometric constant, and AL is, as be-
fore, the leaf area. In the case of the six eddy-covariance estimates,
measures were taken at each site to ensure that conductance was
derived from measured water vapor fluxes that did not include a
significant contribution from soil evaporation. In the case of the
Populus tremuloides and Pinus radiata canopies, soil evaporation
was measured independent of whole-canopy evaporation using
lysimeters. In the P. mariana stand, soil and sub-canopy evapotrans-
piration were measured with a below-canopy eddy-covariance sys-
tem. In the 6.8 m P. taeda stand, Gs estimated from whole-canopy
evapotranspiration fluxes and from sap-flux data responded
Table 1
Summary of studies used to assess the relationship between reference canopy conductance ðGsref ;mmol m2 s1Þ, canopy height (h, m), and sapwood-to-leaf are ratio
ðAS=AL; cm2 m2Þ. TM is mean annual temperature ðCÞ, and LAI is leaf area index ðm2 m2Þ. ‘E’ denotes eddy-covariance measurements, and ‘S’ denotes sap-flux measurements. In
the case of mixed stands, family type is assigned based on the phylogeny of the dominant species in the stand. AS=AL is the ratio of sapwood area at breast height to projected leaf
area unless otherwise noted.
Dominant species Location Family TM h Gsref LAI AS=AL Method Reference
Boreal Forests
Picea abies 64.12 N, 19.27 E Pinaceae 2 9.7 49 6.0 4.9 S [58]
Picea abies 60.08 N, 17.48 E Pinaceae 5.5 23 180 4.5 S [61]
Populus temuloides 53.63 N, 106.20 W Salicaceae 0.4 22 134 3.3 11.3 E [59]
Picea mariana 55.88 N, 90.30 W Pinaceae 0.8 9 55 7.5 2.5a S [27]
Picea mariana 55.88 N, 90.30 W Pinaceae 0.8 10 42 6.1 2.1a S [27]
Picea mariana 55.88 N, 98.48 W Pinaceae 3.2 12 35 4.6 2.2b E [60]
Pinus sylvestris 60.72 N, 89.13 E Pinaceae 5.5 17.4 82 5.0 7.1 S [62]
Pinus sylvestris 60.08 N, 17.48 E Pinaceae 5.5 26.8 33 4.5 10.1 S [62]
Temperate Forests
Abies bornmulleriana 48.73 N, 6.23 E Pinaceae 9.6 11 75 8.9 S [1]
Crataegus monogyna 51.6 N, 1.7 W Rosaceae 9.5 4 241 4.8 8.8c S [44]
Cryptomeria japonica D. 33.13 N, 130.72 E Cupressaceae 15 22 29 5.4 6.7 S [63]
Cryptomeria japonica D. 33.13 N, 130.72 E Cupressaceae 15 32 39 5.7 8.1 S [63]
Fagus sylvatica 48.2 N, 7.25 E Fagaceae 9.8 22.5 75 5.7 S [1]
Fagus sylvatica 48.67 N, 7.08 E Fagaceae 9.2 14 87 5.7 S [1]
Fagus sylvatica 49.87 N, 10.45 W Fagaceae 6 23 83 6.2 3.9 S [4]
Mixed deciduous 33.93 N, 79.13 W Juglandaceae 15.5 23 67 5.5 5.4 S [64]
Mixed deciduous 46.24 N, 89.35 W Aceraceae 3.9 22 32 7.5 2.6 S [65]
Mixed deciduous 33.93 N, 79.13 W Juglandaceae 15.5 25 93 6.1 5.4 E [37]
Mixed deciduous 51.79 N, 1.3 W Aceraceae 9.7 21 109 3.6 S [66]
Mixed deciduous 51.45 N, 1.27 W Fagaceae 10.9 22 82 3.9 S [66]
Quercus alba 35.87 N, 80.00 W Fagaceae 15.5 25 40 3.1 1.1 S [67]
Picea abies 48.73 N, 6.23 E Pinaceae 9.6 11 66 9.5 S [1]
Picea abies 48.2 N, 7.25 E Pinaceae 6 13 93 6.1 S [1]
Picea abies 50.15 N, 11.87 E Pinaceae 5.8 16.1 66 5.3 3.8 S [49]
Picea abies 50.15 N, 11.87 E Pinaceae 5.8 14.7 84 6.4 3.6 S [49]
Picea abies 50.15 N, 11.87 E Pinaceae 5.8 17.8 62 7.1 3.7 S [49]
Picea abies 50.15 N, 11.87 E Pinaceae 5.8 24.1 44 7.9 2.6 S [49]
Picea abies 50.15 N, 11.87 E Pinaceae 5.8 25.7 56 7.6 2.4 S [49]
Picea abies 50.15 N, 11.87 E Pinaceae 5.8 25.2 31 6.5 2.1 S [49]
Pinus pinaster 44.70 N, 0.77 W Pinaceae 9.8 12 104 4.4 8.4 S [68]
Pinus pinaster 44.08 N, 0.08 W Pinaceae 12.5 18 87 12.5 5.7 S [68,69]
Pinus taeda 34.80 N, 72.20 W Pinaceae 15.5 6.8 154 3.5 6.8 E [15,70]
Pinus taeda 33.93 N, 79.13 W Pinaceae 15.5 16 113 4.5 8.2 E [37]
Pinus radiata 42.87 S, 172.75 E Pinaceae 10.8 8 75 6.5 E [71]
Populus trichocarpa 46.17 N, 118.47 W Salicaceae 12.3 8 148 9.5 3.3 S [72]
Quercus petraea 48.7 N, 6.4 E Fagaceae 9.6 15 95 6.0 S [1]
Tropical Forests
Eperua falcata 5.2 N, 52.7 W Fabaceae 25.8 10 43 10.8 S [1]
Eucalyptus saligna 19.84 N, 155.12 W Myrtaceae 21 7 40 4.9 0.7 S [19]
Eucalyptus saligna 19.84 N, 155.12 W Myrtaceae 21 26 37 5.1 1.8 S [19]
Goupia glabra 5.2 N, 52.7 W Goupiaceae 25.8 15 74 4.3 S [1]
Mixed tropical 5.2 N, 52.7 W Fabaceae 25.9 33 57 8.6 1.5 S [1]
Simarouba amara 5.2 N, 52.7 W Simaroubaceae 25:8 4.7 108 3.5 S [1]
a These values are the ratio of sapwood area to total leaf area.
b Derived from tree-averaged sapwood area.
c Derived from sapwood area measurements taken at a height of 15 cm.similarly to D, suggesting that the eddy-covariance evapotranspira-
tion fluxes in this canopy were driven primarily by transpiration.
And finally, transpiration in the 16 m P. taeda stand and the mixed
deciduous forest was partitioned from the measured evapotranspi-
ration fluxes using a simple radiation transfer model as described in
Stoy et al. [37].
For sites with high leaf area, it is well known that not all the fo-
liage contributes to transpiration. Because total conductance rates
are normalized by the measured LAI to obtain Gs rather than the LAI
contributing to stand transpiration, an adjustment is necessary for
sites with high LAI. The LAI (and hence the reference conductance
rates) was corrected for sites with exceptionally high (i.e.
LAIP 8) by multiplying by a factor f ¼ LAI=8. This correction is
similar to that suggested by Granier et al. [1] though we choose
to implement the correction only for sites with LAIP 8 (as op-
posed to LAIP 6) because this is roughly the value of LAI at which
the fraction of absorbed radiation in the canopy reaches 95% during
midday hours when it is modeled from Beer’s Law [38].The reported values of Gsref obtained from the literature were
estimated using a range of analytical procedures, including bound-
ary line analyses, optimization routines, and data binning. In all
cases, the extracted value represents the authors’ estimate of the
conductance rate at the reference D of 1 kPa under the conditions
of non-limiting light and soil moisture content. In this analysis,
Gsref is expressed in mmol m2 s1. Reference conductance mea-
surements presented in units of mm s1 in the original source were
converted using the molar density of water vapor in air at 25 C
after Oren et al. [2].
Our analysis is restricted to closed canopies because trees in
open canopies are more likely to have a conical or complicated
branch architecture, which weakens the link between h and mean
path length. We also excluded data from manipulation experi-
ments because sapwood permeability and AS=AL may respond to
abrupt changes in nutrient or light regimes, achieved through fer-
tilization [27,39], stand density reduction [40], CO2 enrichment
[41,42], and foliage removal [43,2], and the adjustment to new
conditions may take several years. In nearly all these studies, Gsref
is normalized by maximum projected leaf area in the growing sea-
son, and AS=AL represents the ratio of sapwood-to-leaf area at
breast height to projected leaf area during the growing season.
However, we did not exclude studies that reported estimates of
these parameters derived from total as opposed to projected leaf
area [27], or studies for which sapwood area estimates are taken
from a different height [44], to maximize the sample size in Table
1. No other exclusionary criteria were employed in this survey.
The variables of interest were treated as canopy averages in
these surveys. In the cases where data were reported for individual
trees or species, canopy averages were calculated by weighting
individual- or species-specific values according to their LAI.
3.2. Survey 2: Allometric equations for AS=AL
In a second literature survey, the slope and intercept of the
change in AS=AL with h were compiled from studies on 21 closed-
canopy forest ecosystems (Survey 2, Table 2), representing differ-
ent species growing in a broad range of climates. We used the esti-
mates of canopy-averaged values of AS=AL and h along
chronosequence stages, as well as whole-tree estimates of AS=AL
for trees of different heights in the same stand. The same exclu-
sionary criteria employed for Survey 1 were employed for Survey
2. Survey 2 is similar to a survey conducted by McDowell et al.
[31] yet less than a quarter of the studies cited in Table 2 are com-
mon to both surveys. However, in this study, we expanded consid-
erably the sample size and the number of sites which have a
negative relationship between AS=AL and h (i.e. negative a).
3.2.1. Statistical tests and optimization
Statistical performance indicators such as the correlation coeffi-
cient ðr2Þ and t-statistics for slope significance (i.e. P) were per-
formed in Matlab version 6.0. Because correlation coefficients are
often compared between datasets of different sample sizes in this
study, adjusted R2 is used. Unless otherwise stated, slope signifi-
cance was interpreted using two-tailed t-tests with a null hypoth-Table 2
Summary of studies in closed-canopy forests used to assess the relationship between sapw
temperature and precipitation, respectively. Min h (m) and min AS=AL ðcm2 m2Þ are the val
the slope and intercept of the linear relationship between AS=AL and h (see Eq. (7)). The num
data types are: (1) C: whole-canopy measurements, and (2) T: individual tree measureme
otherwise noted.
Species Family Location TM PM
Abies balsamea Pinaceae 46–49 N, 65–73 W  4 1000
Abies balsamea Pinaceae 44.9 N, 68.6 W 6.6 1060
Abies lasiocarpa Pinaceae 46–47 N, 114 W 2 720
Eucalyptus delegatensis Myrtaceae 35.7 S, 148.5 E 9.5 1400
Eucalyptus saligna Myrtaceae 19.8 N, 155.1 W 21 4000
Fagus sylvatica Fagaceae 55.0 N, 10.5 W 7.5 750
Larix occidentalis Pinaceae 46–47 N, 114 W 7.2 430
Picea abies Pinaceae 50.2 N, 11.9 E 5.8 1100
Picea abies Pinaceae 64.1 N, 19.3 E 2 600
Picea mariana Pinaceae 55.9 N, 90.3 W 0.8 440
Picea sitchensis Pinaceae 53.0 N, 7.3 W 9.3 850
Pinus albicaulis Pinaceae 46–47 N, 114 W 2 720
Pinus monticola Pinaceae 48.4 N, 116.8 W 6.6 810
Pinus ponderosa Pinaceae 48.4 N, 116.8 W 6.6 810
Pinus ponderosa Pinaceae 46–47 N, 114 W 7.2 430
Pinus sylvestris Pinaceae 53.4 N, 0.65 E 10 550
Pinus sylvestris Pinaceae 57.3 N, 4.8 W 6.5 1215
Pseudotsuga menziesii Pinaceae 45.8 N, 122.0 W 8.7 2500
Pseudotsuga menziesii Pinaceae 48.4 N, 116.8 W 6.6 810
Pseudotsuga menziesii Pinaceae 46–47 N, 114 W 7.2 434
Quercus garryana Fagaceae 44.6 N, 123.3 W 11 1100
a Ratio of sapwood area to total leaf area.
b Sapwood-to-leaf area averaged over the entire stem.esis of zero slope. When necessary, nonlinear optimization was
performed in Matlab using the Gauss–Newton algorithm [45].
4. Results
4.1. Changes in Gsref with AS=AL and h
Using Eq. (3) along with simplifications leading to Eq. (6), Gsref
was shown to be analytically related to the product of AS=AL and
h1, a finding that appears to be accurate across the 29 sites for
which all three variables were available (Survey 1, Table 1,
Fig. 2). A simple linear regression of these variables gives:
Gsref ¼ 98:2 ASALhþ 37:3; ð9Þ
with r2 ¼ 0:75 and P < 0:0001. Separating the relative importance
of AS=AL and h
1, we find that approximately 27% of the variability
in Gsref is driven by AS=ALðP < 0:01Þ and 46% is driven by
h1ðP < 0:0001Þ. The relationship is also quite strong when refer-
ence canopy rates uncorrected for high LAI are considered (inset
to Fig. 2, r2 ¼ 0:73; P < 0:0001).
The sites in the above analysis included 19 temperate, seven
boreal and three tropical forest ecosystems. The small sample size
of boreal and tropical forest sites prevents this relationship from
being analyzed within each of these climatically distinct subsets.
However, in temperate sites, the slope of the relationship
Gsref ¼ 95:8 ASALhþ 43:2; r2 ¼ 0:92
 
is not statistically distinguish-
able from the slope derived with data from all three climate zones
(P = 0.81).
Among the 29 sites, seven are dominated by P. abies, three are
dominated by P. mariana, and two each are dominated by Crypto-
meria Japonica, P. pinaster, P. taeda, E. saligna, and P. sylvestris. To as-
sess the influence of replicates of single species, a replication
analysis procedure proposed by McDowell et al. [31] was adopted.
Specifically, the analysis was repeated for 672 unique combina-
tions of sites such that no more than one site dominated by each
species was included. Each combination resulted in a positive slopeood-to-leaf area ratio ðAS=ALÞ and mean canopy height ðhÞ. TM and PM are mean annual
ues associated with the shortest tree in each dataset. a ðcm2 m3Þ and b ðcm2 m3Þ are
ber of individual measurements used to derive the relationships is denoted by n. The
nts. AS=AL is the ratio of sapwood area at breast height to projected leaf area unless
Min h Min AS=AL a b n Data type Reference
2 2.61 0.14 3.61 56 C [73]
7.6 0.76 0.13 0.39 3 T [74]
3.8 0.31 0.06 0.24 9 T [75]
3 2.62 0.04 3.25 23 T [76]
7 0.68 0.06 0.27 2 C [19]
11 2.83 0.16 1.5 9 T [4]
11 2.44 0.05 4.2 11 T [75]
14.7 3.55 0.13 5.8 6 C [49]
8.73 3.27 0.72 11.47 6 T [58]
2.8 0.8a 0.41 6.1 19 T [27]
4.4 1.82 0.03 3.6 6 C [77]
3.5 2.28 0.28 7.63 14 T [78]
5 2.98 0.08 2.89 21 T [78,79]
4 5.71 0.16 9.33 22 T [78,79]
13.2 5.97 0.01 5.74 11 T [75]
8 9.31b 0.17 7.6 5 C [32]
4 5.77 0.22 7.86 19 T [80]
15 1.93 0.01 1.7 3 C [13]
6 2.94 0.01 3.02 23 T [9,10]
11 1.95 0.17 2.04 17 T [50]
10 4.34 0.11 5.4 2 C [16]
0 0.5 1 1.5 2 2.5
0
50
100
150
200
250
AS/AL/h (cm
2
m
−3)
G
sr
ef
 
(m
mo
l m
−
2
s−
1 )
Boreal Forests
Temperate Deciduous Forests
Temperate Evergreen Forests
Tropical Forests
0 0.5 1 1.5 2 2.5 3
0
50
100
150
200
250
300
Fig. 2. The relationship between reference conductance ðGsref Þ and the product of the ratio of sapwood-to-leaf area ðAS=ALÞ and the inverse of canopy height ðh1Þ. The solid
line is determined from least squares regression using all data, and the dotted line is the least squares regression for temperate forests only. Open symbols denote canopies
dominated by species that are known to have a decreasing relationship between AS=AL and h. The inset shows the same relationship for the estimates of Gsref uncorrected for
high LAI as described in Section 3.(ranging 92:5—98:4 mmol m1 s1) that was statistically different
from zero (P < 0:0001 for all combinations). Furthermore, none
of the slopes differed significantly from the slope derived from
the entire dataset (P > 0:6 for all combinations).
Aweak relationship betweenGsref and h
1 emergedwhen analyz-
ing all 42 datasets presented in Table 1 ðr2 ¼ 0:24; P < 0:001Þ. Gsref
andh1weremoresignificantlycorrelatedwhentemperatesiteswere
analyzed separately. Across temperate sites, reference conductance
increased strongly with h1ðr2 ¼ 0:68; P < 0:0001, Fig. 3a). Again
adopting theanalysis replicationprocedure (giving192uniquecom-0 0.05 0.1
1/h
(b)
0 0.05 0.11 0.15 0.2 0.25
0
50
100
150
200
250
G s
re
f
 
(m
mo
l m
−
2  
s−
1 )
(a)
Fig. 3. Reference canopy conductance ðGsref Þ vs. the inverse of canopy height ðh1Þ for
Regression lines are not shown for tropical and boreal sites as no significant relationshibinations), we found that the relationship betweenGsref and h
1 was
significantforallcombinationsofsitesinwhichonlyonestandofeach
species was represented (P < 0:001 for all combinations). This rela-
tionship,however, is drivenstronglyby thedata fromthe4 mhedge-
rowstand(Table1).Excludingthissite fromtheanalysis, the increase
inGsref withh
1 was significantly different fromzero (at the 95% con-
fidence level) for all combinations that included the 6.8 m P. taeda
stand.
Among tropical species, h1 explained 19% of the variance in
Gsref , although the slope is not statistically significant (Fig. 3b,0.15 0.2
 (m−1)
0 0.03 0.06 0.09 0.12 0.15
(c)
(a) temperate, (b) tropical, and (c) boreal species. Symbols are the same as Fig. 2.
ps between Gsref and h
1 emerged for these small samples.
3 4 5 6 7 8 9 10 11 12 13
0
50
100
150
200
250
LAI (m2 m−2)
G
sr
ef
 
(m
mo
l m
−
2
s−
1 )
Fig. 4. Reference canopy conductance ðGsref Þ as a function of leaf area index ðLAIÞ for
all sites in Table 1. Symbols are the same as those shown in Fig. 2.
0 5 10 15 20 25 30 35 40 45 50
0
50
100
150
200
250
h (m)
G
sr
ef
 
(m
mo
l m
−
2  
s−
1 )
Fig. 5. Reference canopy conductance ðGsref Þ vs. canopy height ðhÞ for all sites from
Table 1. The dotted line represents the quantity Gsref  ðahþ bÞ 1h referenced to the
conductance data by minimizing the standard error ðr2 ¼ 0:24; P < 0:001Þ, where a
and b are the average slope and intercept, respectively of the relationships
presented in Table 2. The shaded area represents the range of expectation bounded
by Gsref  ðða raÞhþ bÞ 1h, where ra is the standard deviation of the slopes ðaÞ
presented in Table 2. Symbols are the same as those shown in Fig. 2.P = 0.17). The tropical subset includes two E. saligna stands, but
repeating the analysis using one or the other of these sites resulted
in a derived slope that was statistically indistinguishable from the
slope calculated from all tropical sites.
Gsref decreased weakly and insignificantly with h
1 among the
boreal sites (Fig. 3c, r2 ¼ 0:18; p ¼ 0:17) though the decrease is sig-
nificant for some combinations of boreal sites that included only
one representation of each species. This negative relationship is
driven by reference conductance rates of P. mariana (i.e. – the three
boreal sites with the highest value of AS=AL=h). P. mariana has a
strongly decreasing a [27], and would be expected to have rela-
tively low reference conductance rates.
Roughly 50% of the studies considered in Survey 1 are from the
Pinacaea family. Therefore, for the significant relationships that
emerged from this analysis (i.e. Figs. 2 and 3a), we conducted
two additional tests to assess the impact of phylogenetic similari-
ties among the ecosystems: (1) we performed an additional repli-
cation analysis procedure whereby the relationships were assessed
for unique combinations of sites such that no more than one spe-
cies from each family was represented, and (2) the relationships
were derived independently for angiosperms and gymnosperms.
For the relationship between Gsref and AS=AL=h shown in Fig. 2, all
512 unique combinations resulted in a statistically significant
slope ðP < 0:001Þ with a high degree of correlation
ðr2 ¼ 0:79—0:91Þ. The correlation for the relationship derived with
angiosperms alone Gsref ¼ 45:0 ASALhþ 71:1
 
improved significantly
when compared to the relationship derived with gymnosperms
alone ðr2 ¼ 0:92 and 0.78, respectively), though we note that this
higher correlation is driven strongly by the reference canopy rate
in the 4-m hedgerow (an angiosperm site). For the relationship be-
tween Gsref and 1=h among temperate forests (Fig. 3a), all 1008 un-
ique combinations resulted in statistically significant slopes
ðP < 0:01Þ. The amount of variance in Gsref explained by 1=h is high-
er for angiosperms alone ðr2 ¼ 0:92Þ, though again, this relation-
ship is driven strongly by the hedgerow.
Finally, because reference conductance rates have previously
been shown to vary with leaf area within species, we also assessed
the generality of this relationship. Total reference conductance (i.e.
reference conductance per unit ground area) should increase with
LAI; however, due to the saturation of canopy light absorption at
high LAI, reference conductance per unit leaf area should decrease
with LAI. A significant but very weak linear negative relationship
between Gsref and LAI was observed based on the 42 sites of Survey
1 (r2 = 0.08, P < 0:05, Fig. 4), with correlation improving slightly for
the relationship between Gsref and logðLAIÞ ðr2 ¼ 0:10Þ.
4.2. Relationship between AS=AL and h
The linear relationship between AS=AL and h compiled from the
literature varied considerably among the 21 sites considered in
Survey 2 (Table 2). A majority of the studies reported a positive lin-
ear relationship, though due to the presence of some strongly neg-
ative slopes, the overall mean values were a ¼ 0:03 and b ¼ 4:3,
with standard deviations of ra ¼ 0:18 and rb ¼ 2:65, respectively.
To determine whether this variation is sufficient to explain the var-
iation observed in the general relationship between Gsref and h
(Fig. 3), the quantity Gsref  ðahþ bÞ 1h was referenced to the con-
ductance data by minimizing the standard error between this
quantity and the measurements (Fig. 5). This model clearly ac-
counts for very little of the variability; however, more than 70%
of the data points fall within the range of expectation bounded
by Gsref  ðða raÞhþ bÞ 1h (shaded area in Fig. 5), suggesting that
much of the observed variability in Gsref may be explained by the
large variations of a among species.
The mean values a and b did not change significantly when the
analysis was repeated to eliminate multiple data sets of one spe-cies. Furthermore, the mean values of a and b for relationships de-
rived using whole-canopy values of AS=AL and h among
chronosequences ðachr ¼ 0:015; bchr ¼ 4:0Þ were statistically
indistinguishable from the mean values of a and b for relationships
derived using measurements of AS=AL and h on individual trees
within a single stand ðastand ¼ 0:030; bstand ¼ 4:3Þ using a t-test
for differences between the means assuming unknown but equal
variances.
The slope factor a was not related to mean annual precipitation
(which can be considered a proxy for soil water availability) across
sites, consistent with the previous inter-specific observations [31]
and with the previous finding that a was indistinguishable be-
tween xeric and mesic P. palustris stands [13]. However, a increases
significantly with the natural log of mean annual temperature (TM ,
Fig. 6, r2 ¼ 0:39; P < 0:01), consistent with the previous
observations of a significant relationship between TM and a among
−0.5 0 0.5 1 1.5 2 2.5 3 3.5
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
ln(Ta) (° C)
α 
(cm
2  
m
−
3 )
Fig. 6. The change in AS=AL with hðaÞ as a function of the natural log of mean annual
temperature ðr2 ¼ 0:39; P < 0:01Þ for the studies presented in Table 2. Circles
represent relationships derived from whole-tree measurements, and squares
represent relationships derived from whole-canopy measurements.
Table 3
The relative change in conductance ðGsÞ, height ðhÞ, and sapwood-to-leaf area ratio
ðAS=ALÞ for the four ecosystems in Table 1 for which all three variables were available
at various heights.
DGSref
GSref
Dh
h
DAS=AL
AS=AL
DAS=AL
AS=AL
 Dhh
Eucalpytus saligna 0.1 2.6 1.7 0.9
Fagus sylvatica 1.6 2.5 1.0 1.4
Picea abies 0.6 0.7 0.4 1.1
Picea mariana 0.2 0.1 0.2 0.3mature P. sylvestris stands [18], though much of the variation in a is
not explained by temperature.
5. Discussion
5.1. The hydraulic controls on stomatal conductance across species
In 1997, Ryan and Yoder [46] proposed that the nearly universal
declines in tree growth with forest age may be related to decreas-
ing stomatal conductance as trees grow taller and hydraulic resis-
tance to water flow increases with the transport path length. Since
then, numerous analysis and experiments have been conducted to
test this so-called ‘‘hydraulic limitation hypothesis”. Some experi-
ments support the hypothesis [14,4,15,12,47,5,13], while others
suggest that AS=AL is more important than h in controlling stomatal
conductance [17,18,39,27], and some point to the importance of
age or size-related changes in physiology [48,19]. Our results con-
firmed the importance of homeostatic changes in both h and AS=AL
to the whole-plant water balance. We found only a weak general
relationship between reference conductance and height alone
among 42 forested ecosystems representing a large number of spe-
cies from a wide range of climates, although a strong relationship
exists within the better represented temperate climate subset
(Fig. 3a). Adding AS=AL to h explains 75% of the variation in Gsref
among 29 sites representing a wide range of biomes (Fig. 2). This
degree of explanatory power exceeded that predicted by the theo-
retical arguments of Section 2, which projected equal influence of
ksðWleaf  qwghÞ and AS=AL=h on Gsref . That AS=AL=h eclipses
ksðWleaf  qwghÞ in terms of impact on reference conductance rates
across species suggests compensatory interactions between ks and
Wleaf limiting the range of ksðWleaf  qwghÞ that may exist across
species, or that these interactions are mediated by height or AS=AL.
Many of the species considered in Survey 1 are phylogenetically
similar, and over half are from the family Pinacaea. The significant
relationships that emerged from these surveys remain relatively
unchanged when only one representative of each species or family
is considered in the analysis, and the dataset is more largely lim-
ited by a paucity of data from short forests as the correlations for
the relationships in Figs. 2 and 3a are driven strongly by the two
shortest canopies (i.e. the 4 m hedgerow stand and the 6.8 m P. tae-
da stand). Short stands, in addition to being underrepresented inthis dataset, are also more subject to biases associated with equat-
ing path length to h. As demonstrated in Fig. 1, neglecting rooting
length in short canopies results in an overestimation of the product
AS=AL=h on the order of 10–20%. Conversely, canopy architecture
patterns may be significantly different in shorter stands (i.e. more
branching) such that h may either over or under-estimate path
length. While the results shown in Figs. 2 and 3a are robust and re-
main highly significant when the assumed height of these two
shortest stands is altered by 2 m, an overestimation of canopy
height in these stands may suggest a relationship between Gsref
and AS=AL=h or 1=h that is linear when a saturating function is actu-
ally a better model.
We also note that the estimates of Gsref extracted from the liter-
ature for Survey 1 are subjective estimates determined using a
range of regression and modelling procedures that vary from study
to study. However, the high correlation between these estimates
and AS=AL=h suggests that the error associated with difference in
methodology between the studies is relatively small.
5.2. Mechanisms and limits to hydraulic compensation within species
To assess the predictive ability of this model within a species,
the four sites for which changes in Gsref and AS=AL were reported
for trees or stands of different heights were further explored. These
were Eucalpytus saligna [19], F. sylvatica [4], P. abies [49], and P.
mariana [27]. Following the sensitivity analysis presented in the
Appendix, the quantity 1=ð1 qwghðWleaf Þ1Þ can be assumed to
equal unity for a wide range of ecosystems, noting that
qw  103 kg m3; g  10 m s2, and Wleaf  106 kg m2 s. This
approximation can be used to explicitly assess the relative contri-
bution of @h=h and @AS=ALAS=AL to @Gsref=Gsref within a species (Table 3).
For the four datasets, the relative change in AS=AL is insufficient
to compensate for the observed reductions in conductance with
increasing height. For E. saligna and F. sylvatica, the ratio of the rel-
ative change in AS=AL to the relative change in h is 0.64 and 0.41,
respectively. For P. mariana and P. abies, the observed decreases
in AS=AL with height compounds the relative decreases in Gsref ob-
served in taller stands.
Spruce and fir species often exhibit negative relationships be-
tween AS=AL and h [12,31,27], which confers no known hydraulic
advantage. It was proposed that this negative relationship may re-
flect a longer period of juvenile wood development, which has low-
er conductivity than latewood [50], or increased leaf life span,
which would increase nutrient recycling in poor quality sites
[31]. The latter hypothesis is supported in part by the observation
that a is related across species to the site quality [31], which re-
flects, among other factors, the effect of site nutrient availability
on growth.
The relative rates of change shown in Table 3 can also be used to
assess the assumptions of the proposed model for Gsref . For F. sylv-
atica and P. mariana, the ratio of the relative change in Gsref to the
quantity DAS=ALAS=AL  Dh=h is close to 1 (0.93 and 1.13, respectively),
which suggests that the assumptions in this model are correct.
However, the predicted change in conductance for P. abies
(1.11) and E. saligna (0.93) is inconsistent with the observed rel-
ative decrease (0.6 and 0.1, respectively), which indicates that,
in some species, compensatory mechanisms other than AS=AL and h
may represent important controls on reference stomatal conduc-
tance. Other compensatory changes may include height-related in-
creases in sapwood permeability [51], decreases in leaf water
potential [52,53,19], increased reliance on stored water [47], in-
creased allocation to fine roots [32], and changes in crown archi-
tecture such as increased branching and decreased stem
diameter [54]. Data on these homeostatic mechanisms are scarce
and do not support an analysis of a general relationship.
5.3. Variation in the rate of change of AS=AL with height
The primary result from Survey 1 is Eq. (9), which shows that
when AS=AL and h are measured or independently estimated, Gsref
can be well reproduced, though h alone appears to be a good pre-
dictor for temperate species. However, as we have stated before,
AS=AL and h are typically not independent within species, and
may not be independent among species. Hence, Survey 2 was con-
ducted to assess whether variations in h may provide prognostic
information about variations in AS=AL.
The change in sapwood-to-leaf area ratio with height varies
considerately among the species of Survey 2, with the rate of
change ranging from 0:72 cm2 m3 in P. abies to 0:21 cm2 m3
in P. sylvestris [32]. A mechanistic model for this variation would
greatly enhance the generality of the derived relationship between
Gsref ;h and AS=AL, (Fig. 2, Eq. (9)). While a significant relationship
emerged from Survey 2 between a and mean annual temperature,
we do not believe that this relationship is strong enough for gen-
eral application at this time. In this section, some additional likely
controls on height related changes in AS=AL are discussed.
McDowell et al. [31] observed that in species exhibiting a posi-
tive relationship between AS=AL and h;a was approximately an or-
der of magnitude higher in vessel bearing species when compared
to tracheid bearing species. In species having such positive rela-
tionships among those assembled for our analysis, we found that
the mean rate of change was only marginally higher in vessel bear-
ing species ðavessel ¼ 0:018 cm2 m3Þ than tracheid bearing species
ðatracheid ¼ 0:045 cm2 m3Þ. Positive and negative values of a were
reported for both tracheid and vessel bearing species, and the aver-
age rate of change for each functional type was statistically indis-
tinguishable from the average rate of change for all species
according to a t-test for differences between the means assuming
unknown but equal variances (null hypothesis of equivalent
means). This rate of change also varies across sites occupied by
the same species. For example, the values of a ¼ 0:01 and
a ¼ 0:17 m2 m3 were reported for Pseudotsuga menziesii stands,
and considerable variation in a among P. sylvestris and P. ponderosa
has also been observed (see [31]). Thus, a simple categorization
into plant functional type, or even analysis limited to a species,
does not introduce much ‘prognostic’ utility for specifying the rate
of change of AS=AL with height.
The lack of similarity in the sensitivity of AS=AL to hwithin plant
functional types or within a species suggests that climatic controls
may influence inter-site differences in a. Additionally, the fact that
we failed to find a strong relationship between Gsref and h among
all sites in the dataset, but observed significant relationships with-
in the temperate zone suggests that AS=AL reflects the prevailing
climate conditions. Examination of Eq. (4) shows that acclimation
for the purpose of sustaining Gsref in dry climates could be achieved
through a proportional increase in AS=AL with D. While long-aver-
age D was not available for most of the sites considered in this
study, the observed relationship between a and TM could imply a
relationship between a and D, as long-term average vapor pressure
deficit and temperature are correlated across ecosystems that arenot persistently water limited. In other studies, this theoretical
prediction has been confirmed for P. sylvestris [18] and other spe-
cies of the genus Pinus [55], though no relationship between D
and AS=AL was observed among other conifer species (i.e., Abies
and Picea spp., P. menziesii [55]).
Lastly, the light environment may influence the rate in which
sapwood-to-leaf area ratio changes with height even within closed
canopies [56]. No significant differences in a were observed be-
tween canopy-level values obtained along chronosequences of
closed-canopy stands and tree-level values obtained from mea-
surements in single stands. Because the average light environment
is similar among closed-canopy stands in a chronosequence but
the light environment of individual crowns varies considerably
depending on position in the canopy, the similarity of average a
in these two situations implies that the rate of change of AS=AL with
h is not strongly related to light availability. Indeed, the values of a
for open stands (i.e. LAI < 3:0 m2 m2) of Pinus ponderosa
(a ¼ 0:17 cm2 m3, [14]), P. sylvestris (a ¼ 0:16 cm2 m3, [5]), and
P. palustris (a ¼ 0:21 cm2 m3, [13]) are well within the range of
variation observed for closed stands. In summary, future research
on the sensitivity of AS=AL to h should focus on the potential im-
pacts of climate conditions and perhaps also soil nutrient regimes,
which were not explicitly considered here.
5.4. Broader implications for ecosystem-to-regional scale carbon and
water cycle modeling
The response of canopy conductance to rapid changes in envi-
ronmental drivers is often described with Jarvis-type multiplica-
tive functions applied to a species-specific reference state (here
Gsref ). Because the Jarvis model and its variants are widely used,
much effort has been invested in deriving generic representations
of the model’s reduction functions. For example, Oren et al. [2]
showed that across a wide range of boreal to tropical species the
sensitivity of Gs to D can be well described by the function
f2ðDÞ ¼ 1 0:6lnðDÞ. Generic relationships for the light and soil
water response functions have also been developed using datasets
for a broad range of species [1]. Therefore, a representation for Gsref
that explains inter-site variability can be used in coordination with
these generic reduction functions to specify canopy conductance
rates a priori for a wide range of ecosystems at a high temporal
resolution.
Our results suggest that differences among species in leaf phys-
iology and the anatomy of the transport tissue, and differences in
soil properties among sites, may exert a smaller effect on Gsref rel-
ative to the direct effects of canopy architecture, and that height
and sapwood-to-leaf area ratio explain most (75%) of the variation
in Gsref among closed-canopy ecosystems. To our knowledge, only
one other attempt was made to derive a generic formulation for
reference conductance, in which total canopy conductance at a ref-
erence state (i.e. GTref ) was related to LAI [1]. In that study, which
considered a wide range of forested ecosystems (n = 18), GTref in-
creased linearly with LAI, saturating at about the midpoint of the
LAI range. Here, the observed relationship between Gsref and LAI
ðr2 ¼ 0:10Þ is much weaker than the observed relationship of Gsref
to AS=AL=h ðr2 ¼ 0:75Þ proposed here.
For this parsimonious formulation to have prognostic utility at
coarse spatial scales, AS=AL must be specified. At the ecosystem
scale, this hydraulic characteristic is relatively simple to estimate
when compared to the effort required to collect eddy-covariance
or sap flux data and the suite of meteorological measurements typ-
ically required to estimate Gsref at single stand. At the landscape
scale, sapwood area may be estimated for monospecific stands
with well-established allometric relationships with height or basal
area measurements [57], both of which can be derived with rea-
sonable accuracy from LIDAR measurements [11,9,10]. However,
we do not at this time know of a generic, prognostic model for
AS=AL that would facilitate the application of Eq. (9) over coarse
spatial scales (i.e. regional), though our results suggest limatic
mediation of the relationship between AS=AL and h that could moti-
vate future research. Finally, we did find a strong relationship be-
tween Gsref and h within temperate forests that could be more
immediately useful in coarse-scale modelling efforts.
Acknowledgements
Support was provided by the U.S. Department of Energy (DOE)
through the Office of Biological and Environmental Research
(BER) Terrestrial Carbon Processes (TCP) program (Grants #
10509-0152, DE-FG02-00ER53015, and DE-FG02-95ER62083), the
United States-Israel Binational Agricultural Research and Develop-
ment Fund (IS3861-06), by the National Science Foundation (NSF-
EAR 06-28342 and 06-35787) and through their Graduate Research
Fellowship Program, and by the James B. Duke Fellowship program
at Duke University.
Appendix A
To assess the sensitivity of Gsref to AS=AL;Wleaf ; ks, and h, consider
a Taylor series expansion of Gsref :
@Gsref ¼ @Gsref
@AS=AL
dAS=AL þ @Gsref
@Wleaf
dWleaf þ @Gsref
@ks
dks þ @Gsref
@h
dh: ðA:1Þ
Upon computing all the partial derivatives in Eq. (A.1) using Eq. (5)
and expressing the outcome as relative changes, the above equation
simplifies to
dGsref
Gsref
¼ dAS=AL
AS=AL
þ dks
ks
þ 1
1 qwghðWleaf Þ1
dWleaf
Wleaf
 dh
h
 
: ðA:2Þ
Eq. (A.2) analytically demonstrates that the relative change in Gsref
scales linearly with the relative changes in AS=AL and ks, but not
with Wleaf and h. Using typical literature values as ‘reference states’
(Wleaf ¼ 2 MPa; ks ¼ 3 m2;h ¼ 20 m and AS=AL ¼ 4 cm2 m2Þ, Eq.
(A.2) is evaluated for a range of values bounded by the extremes ci-
ted in the text. The results suggest that Gsref varies by a factor of
 10 with h, by a factor of  3:5 with AS=AL, and by a factor of
 0:5 with Wleaf and ks. Stated differently, the sensitivity analysis
in Eq. (A.2) demonstrates that when considering the reported vari-
ations in the literature in each of these parameters across species,
dks=ks  dAS=ALAS=AL and dWleaf =Wleaf  dh=h, although this argument need
not hold for all species.
Nevertheless, among many species a reasonable approximation
is:
Gsref  dAS=ALAS=AL 
1
1 qwghðW1leaf Þ
dh
h
: ðA:3Þ
As expected, Eq. (A.3) analytically predicts that Gsref diminishes rap-
idly with increasing height for small h if no adjustments in AS=AL
occur.
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