Tree Physiology 17, 571--576
© 1997 Heron Publishing----Victoria, Canada
Estimation of leaf area with an integrating sphere
LYDIA SERRANO,1 J. A. GAMON1,2 and J. BERRY3
1
Department of Biology and Microbiology, California State University, Los Angeles, 5151 State University Drive, Los Angeles, CA 90032, USA
2
Author to whom correspondence should be addressed
3
Carnegie Institution of Washington, Department of Plant Biology, 290 Panama Street, Stanford, CA 94305, USA
Received June 25, 1996
Summary Relative absorptance of intact branches measured
with an integrating sphere was compared to leaf area estimated
by conventional methods (volume displacement and scanning
area meter) for three conifer species: Picea mariana (Mill.)
BSP, Pinus banksiana (Lamb.) and Pseudotsuga menziesii
(Mirb.) Franco. A consistent relationship between relative absorptance and surface area emerged for the three species. The
ability to predict leaf area from absorptance was further explored by measuring branches of Pseudotsuga menziesii grown
in varying light and nutrient regimes. When a single equation
was used to predict leaf area under all growth conditions, errors
were as large as 40% primarily because of variation in leaf
absorptivity, with the largest errors associated with extremely
nutrient-deficient foliage. When separate empirical equations
were developed for each growth treatment, predicted leaf surface area agreed to within 5% of the area determined by the
volume displacement method. Leaf surface area estimated
from theoretical principles was also in good agreement with
total surface area estimated independently by conventional
methods. With proper accounting for needle absorptivity,
which varied with growth conditions, leaf area estimates obtained by the integrating sphere method were of similar accuracy to those obtained by conventional methods, with the added
advantage that the method allowed intact foliage to be sampled
nondestructively in the field. Because the integrating sphere
method preserves branch structure during measurement, it
could provide a useful measure of needle area for photosynthetic or developmental studies requiring repeated sampling of
the same branch.
Keywords: absorptance, leaf area determination, light absorption, Picea mariana, Pinus banksiana, Pseudotsuga menziesii.
Introduction
Leaf area is a key parameter for gas exchange measurements
and is often determined by methods that are both destructive
and time-consuming. Leaf area measurement of needle-leaved
species is notoriously difficult and may be confounded by
differences between surface area and projected area. Most
‘‘leaf area meters’’ involve estimates of projected surface area,
which may be a poor representation of actual surface area,
particularly in sclerophyllous, needle-shaped leaves (e.g., most
conifers and many chaparral shrubs). For such cases, the volume displacement method (Johnson 1984) is often employed
to provide a more direct estimation of total surface area.
However, use of either a scanning leaf area meter or, depending
on how it is employed, the volume displacement method,
typically involves destruction of the sample, which precludes
repeated measurements of growing tissue.
Because light absorption scales with leaf area (Oquist et al.
1978), optically based absorption techniques present a possible alternative to conventional methods of leaf area determination. Integrating spheres provide a readily standardized
method of determining light absorption (Idle and Proctor
1983). When a leaf or branch tip is enclosed in an integrating
sphere, the decrease in internal light flux relates directly to the
radiation absorbed by the enclosed sample, which in turn can
be related to the surface area of the sample (Oquist et al. 1978).
However, absorption depends not only on sample size or area
but also on other factors, including leaf structure and pigmentation (Gates et al. 1965, Gausman 1985), and degree of mutual
shading. We have used integrating spheres to explore the relationship between relative absorptance and leaf area for three
needle-leaved species grown under a variety of conditions. The
objective of the study was to develop a fast, reliable, and
nondestructive method for leaf area determination.
Materials and methods
Two integrating spheres measuring 10.2 and 12.7 cm in diameter, respectively, were constructed from copper spheres, available commercially as floats for water tanks. Each sphere was
cut in half, a copper gasket was soldered to the rim of each
hemisphere, and the gasket surfaces were padded with white
foam (Li-Cor spare part 6000-10, Li-Cor, Inc., Lincoln, NE),
providing a light-tight surface for complete enclosure of a
branch tip (Figure 1). The inside of each sphere was first sealed
with a high temperature paint (Colorworks, Krylon, Solon,
OH) followed by several layers of barium sulfate suspension
(white reflectance coating #6080, Eastman Kodak Co., Rochester, NY). Illumination was provided with a 1.2 A halogen
lamp (L1030, Gilway Technical Lamp, Woburn, MA) located
in a port at the top of the sphere. Quantum flux density was
sampled with a Li-Cor quantum sensor (Model LI-189) placed
572
SERRANO, GAMON AND BERRY
Figure 1. Schematic of the sphere illustrating the light source (L) at the
top and a detector (D) at the bottom. A cone (C) directly underneath
the lamp scatters the light.
in a port at the bottom of each sphere. To distribute the light
homogeneously and to avoid direct illumination of the quantum sensor by the lamp, a small cone was mounted directly
underneath the light bulb. The cone and the corresponding
support were also painted with white reflectance coating.
During measurements, voltage was set to 3.3 V to provide a
quantum flux of approximately 150 µmol m −2 s −1 within the
empty sphere. Absorptance was calculated as:
Absorptance = (Isphere − Ileaf )/Isphere,
(1)
where Isphere is the irradiance at the bottom of the empty sphere,
and Ileaf is the irradiance with the branch in the sphere. An
absorptance determination for a single branch normally required about 30--60 s to complete. To assess sphere radial
symmetry, repeated measurements were taken by changing the
position of the branch inside the sphere or by rotating the upper
hemisphere. Standard errors associated with changes in either
twig or lid position were, on average, smaller than 0.6% of the
average relative absorptance value.
Measured absorptance can be affected by the interaction
between sphere size and sample area (Idle and Proctor 1983),
and possibly by geometric and optical variations between
spheres. Preliminary measurements performed on the same set
of twigs using both spheres showed that the measured absorptance values were slightly higher for the smaller, 10.2-cm-diameter sphere (data not shown). For these reasons, we apply
the term ‘‘apparent’’ or ‘‘relative’’ absorptance to our results.
Unless otherwise noted, the results reported are those measured with the larger, 12.7-cm-diameter sphere.
We tested the absorptance--area relationship for three needle-leaved species: Picea mariana (Mill.) BSP (black spruce),
Pinus banksiana (Lamb.) (jack pine), and Pseudotsuga menziesii (Mirb.) Franco (Douglas-fir). The Picea and Pinus
branches were collected near Candle Lake, Saskatchewan,
Canada in the summer of 1994, as part of the BOREAS study
(Sellers et al. 1995). Pseudotsuga menziesii branches were
sampled in 1995 and 1996 in Los Angeles, CA, from potted,
nursery-grown seedlings (California Department of Forestry,
Ben Lomand Nursery, Santa Cruz, CA). For at least a year
before measurement, the Pseudotsuga menziesii seedlings
were exposed to one of two growth irradiance regimes (full sun
and shade) and the sun-exposed seedlings were grown in one
of two nutrient regimes (high and low), determined by the
addition of a slow-release fertilizer (Osmocote 17,7,12, Grace
Sierra Co., Milpitas, CA) to the potting mix. The low-nutrient
treatment had no supplemental fertilizer, resulting in visibly
chlorotic needles (chlorophyll contents, as determined by
HPLC, ranged from 114 to 372 µmol m −2, expressed on a
projected area basis). Shade treatments were provided by a
grove of Pinus canariensis Sweet ex K. Spreng. trees, which
provided a monthly average integrated daily PPFD that ranged
from 2.73 to 14.1 mol m −2, whereas sun treatments ranged
from 9.49 to 38.9 mol m −2. The irradiance treatments had
marked effects on branch tip morphology; the needles of sun
branches were more erect than the relatively horizontal needles
of shade leaves. Measurements were also conducted on two
needle-age classes (current-year and 1-year-old foliage) that
differed slightly in cross-sectional shape (mature needles had
a larger area to volume ratio than current-year needles; data not
shown).
Projected leaf area was determined with a flatbed scanner
(Scanmaker IIXF, Microtek Laboratories Inc., Torrance, CA)
attached to a Macintosh Centris 650. Images were digitized
using Adobe Photoshop (Adobe Systems Inc., Mountain View,
CA) and analyzed for area using IPLab Spectrum (Signal
Analytics Corp., Vienna, VI). Surface area (SA) was also
estimated from volume displacement (Johnson 1984) using the
following formula:
SA = F√

VnL ,
(2)
where L is the average length in cm from a subsample of 10 to
12 needles, n is the number of needles, V is the branch tip
volume in cm3, and F is an empirical shape factor usually
considered constant for a given species. (For this study, we
used F values of 4.00 for Picea mariana, 4.10 for Pinus
banksiana, and 4.17 for Pseudotsuga menziesii, as reported in
Sellers et al. 1994.) In some cases, results were expressed as
‘‘hemi-surface area’’ (half of the surface area) to allow closer
comparison with projected area measurements.
As a further test of sphere behavior, we compared empirically derived absorptance measurements (using the methods
described above) with leaf area estimates determined with the
two spheres using theoretical principles. According to Idle and
Proctor (1983), the radiant flux (Q) entering a sphere can be
related to absorbing area (A), absorptivity (α), and flux density
within the sphere (Φ1) as follows:
Q = Φ 1(Asα s).
(3)
Adding a branch segment of area AB and absorptivity αB
reduces the flux density to Φ2, allowing Equation 3 to be
modified as follows:
Q = Φ 2(Asα s + ABα B).
TREE PHYSIOLOGY VOLUME 17, 1997
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ESTIMATION OF LEAF AREA WITH AN INTEGRATING SPHERE
573
Branch tip area can be estimated by combining Equations 3
and 4 and solving for AB:
AB = (Asα s /αB) ((Φ 1/Φ 2) − 1).
(5)
Absorptivity of each sphere was estimated according to Idle
and Proctor (1983) and Equations 3--5 by inserting pieces of
black paper with known area and absorptivity. Paper absorptivity was determined with a separate integrating sphere (LI1800, Li-Cor, Lincoln NE). Absorptivity of the small and large
sphere was determined to be 0.049 and 0.060, respectively.
Internal surface area was estimated to be 372.3 and 547.6 cm2
for the small and large sphere, respectively. Branch tip absorptivity (absorptance) was determined according to Equation 6
by measuring bidirectional reflectance with a fiber optic probe
attached to a leaf reflectometer (Gamon et al. 1993) and assuming negligible transmittance for these thick needles and
twigs.
Absorptance = 1 − (reflectance + transmittance).
(6)
Branch tip absorptivity estimated in this way was approximately 0.875, which is midway between the measured values
of 0.85 (stems, assuming no transmittance) and 0.90 (needles,
assuming no transmittance).
Hemi-surface and projected area data were log-transformed
before statistical analysis (Statview 4.5, Abacus Concepts,
Berkeley, CA). Analysis of covariance was used to study the
effect of species and treatments on the absorptance--area relationship and simple linear regressions were used to establish
the relationship between ln(area) and absorptance.
Results and discussion
The relationship between branch relative absorptance and leaf
area was nonlinear, and could be roughly described by a single
relationship for all three species (Figure 2). This nonlinearity
is an inherent function of canopy light absorption; the fraction
of photosynthetically active radiation absorbed in canopies is
an exponential function of leaf area (Monteith 1973).
When leaf area was determined by the volume displacement
method, the absorptance--area relationship of Pseudotsuga
menziesii was noticeably affected by the treatments (Figure 3A). Even though the general relationship for all Pseudotsuga menziesii treatments combined was highly significant
and the standard error of the estimate was small, analysis of
covariance yielded significant differences between treatments
(results not shown). Consequently, further analysis of the absorptance--hemi-surface area relationship was performed with
a separate linear regression for each treatment (Table 1). Unlike the results from the volume displacement method, the
comparison of leaf area, estimated by the projected area
method, with relative absorptance yielded very little scatter
(Figure 3B). Because no significant treatment differences were
found (data not shown) for this comparison, only one linear
regression was calculated (Table 1).
Figure 2. Relationship between relative absorptance and hemi-surface
area estimated by the volume displacement method for twigs of
Pinus banksiana, Picea mariana, and Pseudotsuga menziesii. Values
for Pseudotsuga menziesii are the mean and standard error of three
values determined with a 12.7-cm-diameter integrating sphere,
whereas data for Pinus banksiana and Picea mariana are single values
obtained with a 10.2-cm-diameter sphere.
Because the sphere provided diffuse illumination during
area estimation, we expected absorptance to scale more closely
with surface area than with projected area. It is likely that the
better agreement with projected area than with surface area
was due to errors inherent in applying a single species ‘‘shape
factor’’ (F = 4.17) when using the volume displacement
method. In reality, needle shape varied slightly with growth
stage and treatment, as illustrated by a comparison of areas
determined by the other methods (Figure 4). Although not a
direct measure of F, variation in the ratio of areas determined
by these two methods indicated variation in needle surface to
volume ratio. Among treatments, the biggest variation in needle shape was associated with needle age (Figure 4). This
finding is consistent with the pattern reported in Figure 3A,
indicating the highest absorptance--area values were for the
mature, older foliage. These observations suggest that greatest
accuracy with the volume displacement method could be obtained by empirically determining separate shape factors (F
values) for each growth stage and condition encountered.
However, calculation of multiple shape factors would significantly lengthen the time it takes to obtain an area estimate,
reducing the simplicity of this method. Because the sphere
method samples the effective light absorption of intact
branches, it presumably minimizes potential errors associated
with varying needle anatomy and branch morphology.
To test the predictive ability of the sphere method, we
applied the empirical equations shown in Table 1 to estimate
leaf areas of an independent set of branches, and then compared these estimated areas with leaf areas determined by the
volume displacement method (Figure 5). When a general equation for all treatments together was used, leaf areas of high-nutrient plants grown in either sun or shade were close to the
expected values, but leaf areas of severely chlorotic branches
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574
SERRANO, GAMON AND BERRY
Figure 3. Panel A: Relationship
between relative absorptance
and hemi-surface area estimated by the volume displacement method for Pseudotsuga
menziesii, where different symbols indicate different growth
treatments. Treatments include
high and low nutrient treatments in full sun, 1-year-old foliage (old) and current-year
(young) foliage, and shade
branches. Panel B: Relationship
between relative absorptance
and projected area for Pseudotsuga menziesii.
Table 1. Regression parameters for the linear relationship between ln(hemi-surface area) (HA) or ln(projected area) (PA) and absorptance of Picea
mariana, Pinus banksiana or Pseudotsuga menziesii. For Pseudotsuga menziesii, the effects of several treatments on the relationship were
considered: high nutrient (HN), low nutrient (LN), current-year twigs (Y), 1-year-old twigs (O) and shade plants (SH). The SEE indicates standard
error of the estimates.
Species
Area measurement
method
Picea mariana
Pinus banksiana
Pseudotsuga menziesii
Pseudotsuga menziesii
Pseudotsuga menziesii
Pseudotsuga menziesii
Pseudotsuga menziesii
Pseudotsuga menziesii
HA
HA
HA
HA
HA
HA
HA
PA
Treatment
HN-Y
LN-Y
HN-O
LN-O
SH
x-Intercept
Slope
r2
P
n
SEE
−0.054
−0.556
−0.450
−0.363
−0.283
−0.327
−0.206
−0.337
0.116
0.308
0.272
0.239
0.230
0.019
0.215
0.253
0.87
0.96
0.99
0.99
0.98
0.99
0.99
0.98
0.006
0.001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
6
6
7
7
7
7
11
27
0.016
0.026
0.010
0.008
0.022
0.007
0.023
0.018
Figure 4. Relationship between area determined by the volume displacement method (hemi-surface area) and area determined by a leaf
area meter (projected area) for Pseudotsuga menziesii. Treatments
include high and low nutrient treatments in full sun, 1-year-old
foliage (old) and current-year foliage (young) in full sun, and shade
branches. The ratio of projected to hemi-surface area varied slightly
with age and growth treatment, with the highest ratios obtained in
mature (1-year-old) foliage, indicating variability in needle surface/volume ratio (F).
(chlorophyll content of 33 µmol m −2) were underestimated by
as much as 40% (Figure 5A). Use of specific regressions for
each treatment (sun, shade, and low nutrient; Table 1) reduced
this error to approximately 5% (Figure 5B). Similar error
estimates for projected area were even smaller (< 1%, data not
shown). Clearly, to obtain accurate area estimates with the
integrating sphere method, careful consideration must be given
to growth conditions and to leaf pigmentation when developing empirical absorptance--area calibrations, because these
factors can influence leaf absorptivity and thus apparent leaf
area.
Needle areas estimated with the sphere from theoretical
principles (Equation 5) were in good agreement with both
twice the projected area measured by the scanner and total
surface area estimated by volume displacement (Figure 6).
Compared to the volume displacement method, the scanner
yielded values that were in slightly closer agreement to the
sphere-determined needle areas (Table 2). Compared to the
smaller sphere, the larger sphere yielded values that were in
slightly better agreement with areas determined by either the
scanner or volume displacement method (Table 2). Because
each method carries inherent errors, it is not possible to determine which of these methods provides the most accurate
TREE PHYSIOLOGY VOLUME 17, 1997
ESTIMATION OF LEAF AREA WITH AN INTEGRATING SPHERE
Figure 5. Panel A: Relationship between actual and predicted hemisurface area for Pseudotsuga menziesii derived from a single equation
for all treatments (Table 1). Panel B: Relationship between actual and
predicted area derived from separate equations for each treatment.
measurements, and the choice of method is probably best
determined by the particular experimental goal and tools at
hand. The good agreement between sphere measurements
based on theoretical principles and needle areas estimated by
conventional empirical methods further confirms the ability of
the integrating sphere to determine needle area accurately,
even in the absence of the calibrations presented in Table 1.
However, according to Equation 5, the accuracy of this theoretical approach depends on accurate estimates of sphere area,
sphere absorptivity, and needle absorptivity. In particular, needle absorptivity can be difficult to measure, especially in the
field. For this reason, empirical calibration of sphere-determined needle areas with conventional methods would typically be needed.
The most meaningful expression of conifer leaf area is open
to debate and a subject of continued research. Several recent
studies have considered the ratio of shoot silhouette area to
total needle surface area (‘‘STAR’’), which may be an important factor in the photosynthetic responses of conifer shoots
(Smith et al. 1991, Oker-Blom et al. 1992, Hemmerlein and
Smith 1994). Clearly, the interpretation of gas exchange results, which are typically expressed on an area basis, and the
comparison of results from different studies and species can be
confounded by the lack of a single, standard method for sampling leaf area. The issue of ‘‘effective leaf area’’ versus measured area is further complicated by the complex light fields
575
Figure 6. Comparison between needle areas for Pseudotsuga menziesii
estimated with two spheres (10.2 and 12.7 cm diameter) according to
first principles (Equation 5), and total needle area estimated with
either the scanner (panel A) or the volume displacement method (panel
B). The dashed line shows the 1:1 line. Regression equations for each
relationship are given in Table 2.
Table 2. Regression parameters for the relationships in Figure 6.
Regressions were forced through the origin. The SEE indicates standard error of the estimates.
Figure
panel
Sphere
diameter
(cm)
Slope
r2
P
SEE
A
A
B
B
12.7
10.2
12.7
10.2
0.995
1.010
1.061
1.091
0.997
0.987
0.997
0.987
< 0.0001
< 0.0001
< 0.0001
< 0.0001
8.003
16.379
7.860
14.954
present in forest canopies, which can vary from largely direct
to largely diffuse. Although the integrating sphere method
presented here does not resolve these issues, it does present a
simple, rapid, and field portable tool for assessing leaf area on
intact shoots. Because it is nondestructive, the integrating
sphere method could be especially useful in developmental or
photosynthetic studies requiring repeated sampling of the
same branch.
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576
SERRANO, GAMON AND BERRY
Acknowledgments
This work was supported by grants from NSF (# DEB-9220258 to
J.G.) and NASA(# NAGW-3707 to J.G., and # NAG52239 to J.B.).
Technical support was provided by R. Stuber, R. Johnson, D. Horvarth
and B. Welsh. Additional thanks go to J. Collatz for the provision of
one of the copper spheres and to A. Fredeen, B. Yoder, and D. Sprugel
for comments on the manuscript.
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