Tree Physiology 25, 723–732
© 2005 Heron Publishing—Victoria, Canada
Allometry and evaluation of in situ optical LAI determination in Scots
pine: a case study in Belgium
I. JONCKHEERE,1,2 B. MUYS1and P. COPPIN1
1
Katholieke Universiteit Leuven, Department of Land Management, Laboratory for Forest, Nature and Landscape Research, Vital Decosterstraat
102, 3000 Leuven, Belgium
2
Corresponding author ([email protected])
Received June 10, 2004; accepted October 15, 2004; published online April 1, 2005
Summary We evaluated several optical methods for in situ
estimation of leaf area index (LAI) in a Belgian Scots pine
(Pinus sylvestris L.) stand. The results obtained were compared with LAI determined from allometric relationships established in the same stand. We found high correlations
between branch cross-sectional area, diameter at breast height
(DBH) and basal area as dependent variables, and leaf mass,
needle area and crown projection as independent variables. We
then compared LAI estimated by allometry with LAI determined by three optical methods (LAI-2000, TRAC and digital
hemispherical photography) both before and after corrections
for blue light scattering, clumping and non-leafy material. Estimates of stand LAI of Scots pine ranged from 1.52 for hemispherical photography to 3.57 for the allometric estimate based
on DBH. There was no significant difference (α = 0.01) between the allometric LAI estimates and the optical LAI values
corrected for blue light scattering, clumping and interception
by non-leafy material. However, we observed high sensitivity
of the optical LAI estimates to the various conversion factors,
particularly to the clumping factor, indicating the need for caution when correcting LAI measured by optical methods.
Keywords: destructive sampling, indirect LAI, optical devices,
Pinus sylvestris.
Introduction
In situ leaf area index determination
Leaf area index (LAI), defined as one half the total intercepting leaf area per unit ground surface area (Chen and Black
1992), is a useful measure of canopy structure because it is related to many biological and physiological processes, including canopy interception, respiration, transpiration and net photosynthesis (Pierce and Running 1988), water, carbon and energy exchange (Gower and Norman 1991), and net primary
productivity (Gholz and Cropper 1991). Furthermore, LAI
is an important explanatory parameter for the variability in
aboveground net primary productivity, and is consequently of
major importance for scaling-up physiological mechanisms
from the leaf level to the forest canopy level (Running and
Coughlan 1988).
Direct methods of LAI measurement (e.g., Hutchison et al.
1986) are theoretically more accurate than semi-direct, e.g., by
allometry (Norman and Campbell 1989) and indirect, i.e., optical, methods (for a review of methods, see Jonckheere et al.
2004); however, direct methods are time-consuming, making
large-scale implementation difficult. Indirect methods are
quicker and amenable to automation, thereby allowing a larger
spatial sample to be obtained.
Allometric LAI determination
Allometry is a semi-direct method that relates forest inventory parameters (e.g., stem diameter, tree height, basal area)
to aboveground biomass components (e.g., leaves, branches,
stems). Allometric equations are widely used to generalize and
scale measured values of leaf area at the individual branch or
tree level to the stand level, primarily by using stem diameter
at breast height (DBH). Because of their accuracy, allometric
equations are the standard against which other LAI measurement methods are validated (Gower et al. 1999). However,
allometric equations are site-specific and vary with stand age
and density, and climatic conditions (Mencuccini and Grace
1995, Le Dantec et al. 2000). Hence the validity of allometric
relationships developed from measurements in one forest
stand when applied to another stand, even of the same species,
is uncertain (Duursma et al. 2003).
Optical LAI determination
Optical methods are commonly used to estimate LAI indirectly and involve ground-based measurement of total, direct
or diffuse light transmittance through the canopy to the forest
floor. These methods apply the Beer-Lambert law, taking into
account that the total amount of radiation intercepted by a canopy layer depends on incident irradiance, canopy structure and
optical properties. Leaf area index of plant canopies can be estimated by real time analysis of “gap fraction” (e.g., determined with the LAI-2000 (Li-Cor, Lincoln, NE)) or “gap size
distribution” (e.g., determined with the TRAC (Third Wave
Engineering, Ottawa, ON, Canada), or by hemispherical photography). In gap fraction analysis, LAI is calculated from
above- and below-canopy light measurements in accordance
with relationships between gap fraction and canopy geometry
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JONCKHEERE, MUYS AND COPPIN
Table 1. Symbols used for the variables related to leaf area index (LAI).
Symbol
Definition
Reference
LAI
LAI e
LAI c
LAI B
LAI F
Half the total leaf surface area per unit ground area
Effective LAI estimated by optical methods
LAI estimated by correcting LAI e for needle clumping in conifers; Equation 1
LAI estimated by correcting LAI e for clumping at branch and tree level in conifers; Equation 5
LAI estimated by correcting LAI e for needle clumping, tree branch distribution and
non-leafy material; Equation 6
LAI estimated with allometric relationships in conifers
Chen and Black 1992
Chen et al. 1991
Chen 1996
Chen and Cihlar 1995
Chen et al. 1997
LAIA
derived from light extinction models that link LAI, canopy architecture and the penetration of light through the canopy. Gap
fraction, as a function of zenith angle, is the essence of such
mathematical formulas and models (Norman and Campbell
1989, Chason et al. 1991, Welles and Norman 1991). Although
it has been claimed that optical instruments provide a reliable
means of estimating LAI in coniferous (Stenberg et al. 1994,
Chen et al. 1997, Kucharik et al. 1999) and deciduous stands
(Chason et al. 1991, Cutini et al. 1998, Planchais and
Pontailler 1999), most of these instruments determine effective LAI (LAIe, for other symbols, see Table 1) based on the assumption of random spatial distribution of leaves (Dufrêne
and Bréda 1995). However, foliage clustered at the shoot level
invalidates this assumption, resulting in an underestimation of
LAI (e.g., Cutini et al. 1998).
We used several optical methods for estimating LAI in a
Scots pine stand and compared the results, with and without
correction for foliage clumping at different levels, with LAI
estimated from allometric equations developed for the stand
based on destructive sampling.
Marklund 1988
thinning in 1994, 320 trees ha –1 remained. Canopy coverage
(upward around the zenith) was about 55–60%. No significant
understory was present.
Destructive sampling: direct leaf area estimation
Between October 1 and 11, 2002, measurements were made in
a 50 × 50-m plot near the stand center where edge effects were
minimal (Figure 1). Eighty Scots pine trees between 60 and 65
years old were sampled. Each tree was sequentially numbered
as it was measured. Over-bark diameter at breast height
(DBHb) of each tree was measured with a tree calliper, and
tree height and crown height were measured with a clinometer.
Crown radius in the four cardinal directions was determined
with the aid of a mirror mounted on a gimbal with a sight ensuring a vertical reflection. The diameter measurements of
trees in the study plot were used to determine actual diameter
distribution, which was in turn divided by stem-diameter class
into six quantiles each representing approximately the same
Materials and methods
Experimental site description
This study was performed in a Scots pine stand in the Pijnven
state forest at Hechtel-Eksel in southern Limburg, Belgium
(51°10.2′ N, 5°19.2′ E), at a mean elevation of 56 m. The
Pijnven State Forest is an 850-ha managed forest comprising
mainly Corsican pine (Pinus nigra L.) and Scots pine (Pinus
sylvestris L.). It includes a wide range of forest conditions with
stands differing in age and management history. The climate
of the region is moist sub-humid, rainy and mesothermal.
Mean annual temperatures at the site are 2.5 °C in January and
14.3 °C in July, and mean annual precipitation is around
850 mm. The soil is classified as Carbic Podsol (PZc) (median
94% sand, 4% lime, 2% clay) with a thick litter layer (C varies
between 16–63 Mg ha – 1).
The experimental Scots pine stand of 2.49 ha (stand 49 in
Canton II, Kerselaren) was planted in 1936–1937, and consists
of even-aged trees that were ± 65 years old at the time of our
study. The original, homogeneous stocking density was high
and the stand has been frequently thinned, most recently in
1994. Stocking density was 7353 trees ha –1 in 1964, 4167 trees
ha –1 in 1970 and 959 trees ha –1 in 1988. As a result of windfall
only 591 trees ha –1 remained in the stand in 1992. After the last
Figure 1. (A) Location of the plot where leaves were sampled destructively for the direct estimation leaf area and (B) the nondestructive
sampling scheme for optical LAI measurements in the Scots pine
stand in Pijnven Forest, Hechtel-Eksel, Belgium.
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ALLOMETRY AND EVALUATION OF OPTICAL LAI DETERMINATION
725
Table 2. Detailed forest inventory for the six quantiles of trees in the experimental Scots pine stand in Pijnven Forest, Hechtel-Eksel, Belgium. The
overall stand mean and total values for all classes of the stand are also given. Values are based on observations in the 0.25-ha study plot and are expressed on a per hectare basis. Abbreviation: DBH = diameter at breast height (1.3-m high).
Class
DBH range
(cm)
1
2
3
4
5
6
17–23
23–24
24–26
26–28
28–30
30–39
Stand mean
Total
Frequency
(ha –1)
52
52
56
56
48
52
Mean DBH
(cm)
Mean basal
area (m2 )
Mean height
(m)
Height of crown
base (m)
19.5
23.0
24.5
26.5
28.5
37.5
26.29
0.03
0.04
0.05
0.06
0.07
0.11
0.06
17.41
16.2
17.5
17.9
18.5
18.9
20.1
18.2
11.0
11.7
11.4
11.3
12.4
12.2
11.7
316
number of trees. Detailed forest inventory data for the six
DBH classes are presented in Table 2. Stocking density was
316 trees ha –1 and the stand had a basal area of 17.41 m2 ha –1.
Mean diameter of all trees at breast height (DBH) was 26.29 ±
4.14 (mean ± SE) and mean canopy height was 18 m ± 2 m
(mean ± SE).
Six Scots pine trees, one for each diameter class, with the
mean class diameter, were selected as a representative
subsample of the stand for destructive measurements.
Dendrometric data of the sample trees are summarized in Table 3.
Because leaf area and mass vary within the tree crown
(Kershaw and Maguire 1995), we divided the live crown of
each sample tree into three strata of equal depth (Temesgen
2003, Bartelink 1996). For every first-order branch on the tree,
height above ground and diameter at 4 cm from the junction
with the stem were measured (Battaglia et al. 1998). Sample
branches were selected at random, the number from each stratum being proportional to the total number of branches in that
stratum. Three to five first-order branches were excised per
tree and the relationship between branch basal diameter and
needle surface area determined (Küßner and Mosandl 2000).
High branches were accessed with a cherry picker.
Freshly cut branches were placed in plastic bags and stored
at 4 °C. Branch needle area was determined by random subsampling from all age cohorts. Branches were subsequently
Table 3. Dendrometric data for the six Scots pine sample trees that
were destructively sampled at the study plot in Pijnven Forest,
Hechtel-Eksel, Belgium. Abbreviation: DBHb = over-bark diameter
at breast height (DBHb).
Tree No.
DBHb
(cm)
Basal
area (m2 )
Total
height (m)
Height of
crown base
(m)
1
2
3
4
5
6
21.7
23.8
25.0
26.4
28.0
31.8
0.037
0.044
0.050
0.055
0.062
0.080
18.1
20.4
18.7
19.4
18.3
16.6
13.0
13.4
11.6
12.8
12.1
14.6
dried for 72 h at 40 °C and then to constant mass at 80 °C
(Èermák and Michalek 1991). Small branches with needles
were dried in paper bags for 1 to 5 days, after which twigs were
separated and removed. The dried needles were weighed to the
nearest 0.1 mg. Projected leaf area (the vertical projection of
needles; PLA) of each sample was measured with a semi-automatic optical planimeter (LI-3100, Li-Cor).
Branch- and tree-level leaf area (LA) were related by a
three-step regression procedure. First, regression equations
were developed for needle dry mass, or area, versus the diameter of primary branches. Second, with the branch diameter versus needle dry mass regression equations, we estimated
whole-crown needle dry mass and needle area. Third, regression equations were developed for estimated crown needle
mass and area versus DBH.
For up-scaling of leaf area to the branch and tree levels, we
evaluated the following least square equations: the Gaussian,
Log-normal, Linear, Polynomial, Power and Rayleigh (Müller
1983, Table 4). All statistical analyses were performed with
SAS software (SAS version 8.2, SAS Institute, Cary, NC).
Optical measurement of leaf area index
We estimated LAI indirectly at the stand level with two purpose-built optical instruments, the LAI-2000 (Li-Cor) and the
TRAC (Tracing Radiation and Architecture of Canopies,
Third Wave Engineering, Ottawa, ON, Canada) and by digital
hemispherical canopy photography (DHP). All measurements
were made within 7 days of branch harvest. To provide adequate LAI-2000 measurements and hemispherical photographs for the stand, a grid of 30 sample points (five rows at
30, 50, 70, 90 and 110 m; six points per row at 30, 53, 76, 99,
122 and 145 m) was established (Figure 1). The TRAC measurements were made along five parallel transects, perpendicular to the sun’s position. Stakes were located every 10 m
along each transect. The TRAC measurements were acquired
during the afternoon of October 7, 2002, with the view zenith
angle at about 57.5°.
Measurements with the LAI-2000 With the LAI-2000 we simultaneously measured diffuse solar radiation below and
above the canopy. The instrument has a fisheye light sensor divided into five concentric rings, with mid-point zenith angles at
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726
JONCKHEERE, MUYS AND COPPIN
Table 4. Regression models used to establish allometric equations in
the experimental Scots pine stand in Pijnven Forest, Hechtel-Eksel,
Belgium.
Regression
Equation
Logarithmic
Gaussian
Log-normal
Rayleigh
Power
Polynomial
Linear
ln y
y=
y=
y=
y=
y=
y=
= a + b ln x
2
ae − b ( x − c )
2
a /(b − x)e ( − (ln( b − x ) − c ) / 4 )
a (1 − e ( − x / b ) ) c
ax b
ax 2 + bx + c
ax + b
(10)
(11)
(12)
(13)
(14)
(15)
(16)
7, 23, 38, 53 and 68°. A built-in optical filter blocked incoming
radiation with wavelengths above 490 nm, to ensure maximum
contrast between leaf and sky. A reference measurement was
taken in an open area directly before and after the point measurements to estimate above-canopy irradiance. A 90° view
lens cap blocked the investigator from the field of view. Leaf
area index was automatically calculated by the built-in C2000
software (Li-Cor 1992), based on inversion of the Poisson light
extinction model for comparing transmittances. The extinction
model is based on four assumptions: (1) foliage is an optical
black body that absorbs all the light it receives; (2) light-blocking plant elements are randomly distributed in the canopy; (3)
plant elements have the same projection as simple geometrical
convex shapes; and (4) plant elements are small compared to
the area covered by each ring. Additional information on the
operational theory of the instrument has been given by Welles
and Norman (1991) and Jonckheere et al. (2004).
Measurements with TRAC The TRAC instrument measures
the gap fraction at the solar zenith angle. Specifically, TRAC
measures the photosynthetic photon flux (PPF) through a canopy (Chen and Cihlar 1995). The instrument is carried by a person walking at a rate of about 0.3 m s –1, and accounts for both
canopy gap fraction and canopy gap size distribution. The measured gap fraction is used to estimate effective LAI (LAI e), and
the gap size distribution is used to estimate the element-clumping index (Ω e ).
The value of Ω e , which quantifies the effects of nonrandom
spatial distribution of foliage, was obtained by comparing the
measured gap size distribution with a theoretical gap size distribution associated with a canopy having randomly distributed foliage elements (Chen and Cihlar 1995). The value of Ω e
depends on the leaf inclination angle (G-function), which in
turn varies with the view angle. However, for a view angle of
57.5°, G ≅ 0.5 and can be considered independent of leaf inclination. Therefore, by keeping the solar radiation angle constant at 57.5°, Ω e and LAI e values for the stand can be obtained
with TRAC alone (Leblanc et al. 2002).
Measuring LAI by hemispherical photography To estimate
LAI by digital hemispherical photography, images of the canopy are acquired from below through a hemispherical (fisheye)
lens with a 180° field of view. Leaf area index is computed from
the hemispherical photographs from gap fraction estimates in
different zenithal and azimuthal ranges. We used a Kodak DCS
660 digital camera (Eastman Kodak, New York, NY) with an
8-mm fisheye lens (8 mm, f/4, Sigma, Tokyo, Japan). The camera and lens were placed in a self-leveling mount oriented by
corner pins on a tripod. The top of the lens was 1.3 m above
ground and the camera was oriented such that the magnetic
north was always located at the top of the photographs. Photographs were taken during overcast conditions to minimize
glare from direct sunlight.
For every grid point, six photographs were taken with an aperture of f/8 at five shutter speeds (1/60, 1/125, 1/250, 1/500
and 1/1000 s) and at the highest possible resolution, i.e., 3040
× 2008 pixels. The photograph resulting in the best contrast
between sky and canopy was selected visually from these
bracketed exposures. A total of 30 photographs provided input
for analysis by the Gap Light Analyzer (GLA) software which
computes gap fraction data and LAI (Frazer et al. 1999, Frazer
et al. 2001). First, a threshold value was interactively selected
for each photograph to distinguish between visible sky and foliage, thereby converting the RGB color images to black and
white. The border can be difficult to estimate because of the
penumbral effect; therefore, all photographs were analyzed by
the same experienced operator to reduce variation (Beaudet
and Messier 2002). To compare LAI estimates from the hemispherical photography technique with the LAI-2000 results,
gap fractions from the photographs were similarly separated in
five zenith rings from 0–75°. The five zenith rings were divided into sky sectors by 10° azimuth angles (36 azimuth sectors). In a second step, LAI e was calculated for each
photograph from the gap fraction data obtained by inversion of
the Poisson model using 4 and 5 rings, representing 0–60° and
0–75°, respectively (Stenberg et al. 1994). The software takes
terrain corrections, based on local aspect inputs and lens corrections, into account. As input to the GLA program, data for
the terrain corrections were gathered in the field and data for
the lens correction were supplied by Sigma. We then converted
LAI e to corrected LAI by correcting for clumping and nonleafy material.
Foliage clumping Estimates of LAI acquired by optical techniques are based on light interception by both foliage and
stems, and assume a random foliage distribution (Chen and
Cihlar 1995). The resulting index is therefore considered to be
the effective leaf area index (LAI e) (Chen et al. 1991). Consequently, when converting LAI e to LAI it is necessary to correct
both for light obstruction from non-leafy canopy material and
for the effects of foliage clumping. Foliage clumping occurs
mostly at the shoot level in conifers (Stenberg et al. 1994). Foliage clumping also occurs at the branch and crown levels for
most forest types (Chen and Black 1992), as a result of branching patterns and irregular tree distribution (Chen et al. 1997).
We applied several corrections to investigate the influence of
clumping at the shoot, branch and tree levels on the conversion
of LAI e measured optically to corrected LAI.
Shoot-level clumping We corrected for clumping at the shoot
level based on the method of Gower and Norman (1991), which
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ALLOMETRY AND EVALUATION OF OPTICAL LAI DETERMINATION
determines shoot clumping as the ratio of the projected area of
the needles within the shoot to the vertically projected shoot
area. This technique was further developed by Fassnacht et al.
(1994) and corrected by Chen (1996) to include a greater number of shoot projections for the calculation of needle-to-shootarea ratio, γe. The shoot area is interpreted as the imaginary surface area of a sphere enveloping the leaf-clump and is calculated as a weighted mean ratio of the projected shoot silhouette
area (Ap) for different projection angles. Chen (1996) found
good agreement between results of shoot analysis for three projection (camera incidence) angles and shoot analysis for 21 and
39 projection angles, respectively, and thus recommended the
use of the method by which each shoot from a calibration sample is imaged and analyzed from three camera incidence angles
to estimate the correction parameter (Chen 1996):
LAI c = LAI e γ e
(1)
sampling strategy) as the transmittance of direct or diffused radiation at the zenith angle of 57.5°. We derived Fmr from the
measured gap size distribution by a gap removal approach. All
transects were analyzed with the TRACWin software provided
with the instrument. The calculated value for Ω e was 0.836.
We calculated LAIB as (Chen and Cihlar 1995):
LAI B = LAI e / Ω e
As = 2
(2)
° ,0 ° )cos (45° )
° , 0 ° ) cos (75° )
+ A (90
A (0p °, 0 ° ) cos (15° ) + A (45
p
p
cos(15° ) + cos(45° ) + cos(75° )
(3)
where LAI c is LAI corrected for shoot-level clumping, LAI e is
effective LAI as estimated by the optical devices, γ e is the ratio
of needle-to-shoot area, An is half the total needle area for all
the needles of a shoot, As is half the total shoot imaginary surface area, and A p (θ, φ) is the projected area for given angles of
θ and φ, where θ and φ are the azimuth and zenith projection
angles in relation to the main axis of the shoot, respectively.
Ten intact shoot samples were taken from each model tree
and different model branches to obtain the within-shoot clumping factor. Half the total needle area in the shoot (A n ) was
measured as the projected area of needles multiplied by a correction factor dependent on the hemi-cylindrical shape of the
needles. Projected area for the needles of the shoots was determined with a Li-Cor planimeter, and the correction factor of
1 + π/2 (Bond-Lamberty et al. 2003) was applied. The imaginary shoot area was obtained from the projected shoot area
(Ap) at three viewing angles (0, 45 and 90°) with a Kodak DCS
660 digital camera. The corresponding images were digitally
analyzed according to the methodology developed by Chen
(1996) to assess the shoot silhouette area. Mean γe (= 2.001)
was calculated as the arithmetic mean of the shoot samples.
Stand-level clumping To correct for clumping within a stand
at all scales greater than the shoot, including within-crown
clumping, Ω e was obtained from TRAC (Leblanc 2002) as:

( F − Fm r ) ln Fm
Ω e = 1 + m

1 − Fm  ln Fmr

(4)
where Fm is the measured total canopy gap fraction and Fmr is
the gap fraction of an imaginary canopy with the same LAI as
the clumped canopy, but where the foliage elements are considered spatially random. We measured Fm with TRAC along
transects in the stand on October 7, 2002, (see Figure 1 for
(5)
where LAI B is LAI corrected for branch- and tree-level clumping and LAI e is the effective LAI as estimated by the optical
devices.
Plant area index To correct for clumping at the within-shoot
and above-shoot levels and account for the contribution of
non-photosynthetic components of the canopy in the optical
measurements, we calculated the LAI associated specifically
with foliage (LAI F ) as did Chen et al. (1997):
with:
γ e = An / As
727
LAI F =
(1 − α )LAI e γ e
Ωe
(6)
where LAI F is LAI corrected for within-shoot and above-shoot
level clumping and α is the woody-to-total area ratio. The
value of α was derived from destructive sampling (Chen et al.
1997): α = W/LAI total , where W is the woody area index and
LAI total is the total LAI from woody and green foliar material
combined.
Our calculation of α was based on in situ measurements of
foliage and woody area per tree, derived from destructive measurements of the branches and measured total tree height,
bole length, crown dimensions and crown length, and plotted
against DBH. We applied these relationships to determine the
mean α of the whole stand and obtained a value of 0.18, which
is consistent with the analysis of the digital hemispherical images, where the amount of woody material was estimated by
means of image classification, assuming the stems and
branches seen on the photographs were simple cone shapes
(Barclay et al. 2000).
Results
Allometric relationships
Allometric relationships at the branch and tree levels Regression equations at the branch and tree levels were derived from
measurements of the six experimental trees (Table 5). The relationships in Table 5 are the best fits of the fitted regressions and
were in all cases significant at P < 0.001. They were applied in
this study to calculate canopy cover and PLA at the stand level
(Table 5). Allometric relationships between tree height and
bole length and between tree height and tree diameter were established by means of the Rayleigh equation (Table 6).
At the branch level, a good relationship was found between
branch cross-sectional area and needle leaf area (as well as
needle dry mass) (r 2 ≥ 0.80) (Figure 2). In agreement with
other studies (e.g., Mencuccini and Grace 1995), significant
regression relationships were found at the tree level between
basal area and DBH as independent variables, and needle area,
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JONCKHEERE, MUYS AND COPPIN
Table 5. Allometric relationships for Scots pine branches, trees and stand at Hechtel-Eksel, Belgium, based on the destructive sampling of six sample trees. Abbreviations: DM = dry mass; and DBH = diameter at breast height.
Variables
Regression equation
r2
Branch
x = Branch cross-sectional area (cm2 )
y = Needle area (m2 branch –1 )
y = Needle DM (kg branch –1 )
y = 15.543x 0.9906
y = 29.908x 0.6604
0.86
0.83
Tree
x = DBH (cm)
y = Needle area (m2 tree –1 )
y = Crown projected area (m2 tree –1 )
y = Needle DM (kg tree –1 )
y = 0.2988x 2 – 7.5336x + 74.075
y = 0.0066x 2 + 0.2115x
y = –0.001x 2 + 0.0527x – 0.4586
0.94
0.88
0.95
Stand
x = Basal area (m2 )
y = Needle area (m2 ha –1 )
y = Crown projected area (m2 ha –1 )
y = Needle DM (kg ha –1 )
y = Number of needles (thousand ha –1 )
y = 5791.9x 2 + 1344.7x – 7.1147
y = – 492.83x 2 + 173.86x
y = 23.036x 2 + 204.42x
y = 1.789x (x in cm2 )
0.94
0.84
0.91
0.95
needle dry mass and crown projected area as dependent variables (Figure 3).
Stand-level canopy coverage estimate Regression equations
between DBH and basal area and between DBH and crown
projected area of the trees (Table 5) were used to estimate the
ground projection area of the average tree from all DBH
classes, and these values were then used to scale up the crown
projection of the individual trees to the entire stand to obtain an
estimate of canopy coverage at the stand level. Canopy cover
calculated based on the DBH versus basal area and DBH versus
crown projected area regressions yielded values of 0.37 and
0.44, respectively. Because these allometric estimates of canopy cover (including within-crown gaps) are lower than the visual estimate of canopy cover (55–60%), we calculated canopy
cover from hemispherical photographs as described by
Soudani et al. (2002). The photographs gave a mean canopy
cover of 61% for the stand, which is in good agreement with the
visual estimate of coverage. Consequently, we concluded our
crown radius was underestimated by our allometric regression
equations. The subsampling of the six trees may have been insufficient to account for the high variability in crown projection
area in the stand. These regression equations were therefore not
used to calculate stand-level LAI.
by measuring detached needles directly with an optical planimeter, were calculated as functions of DBH and basal area. Total projected needle area (PLA) for the stand was then
calculated by applying the relationship between DBH and projected needle area:
y = 0.2988 x 2 − 7. 5336 x + 74.075
(7)
or by applying the equation linking basal area and projected
needle area:
.
y = 5791.9 x 2 + 1344.7 x – 71147
(8)
From Equations 7 and 8 we obtained stand-level PLA values
of 2.77 and 2.74, respectively.
To make a reliable comparison of the projected needle area
with estimates of LAI from optical methods, hemi-surface leaf
area (HSLA), defined as one half the total surface area (Chen
Stand-level LAI estimates Based on the regression equations
in Table 5, empirical values of projected needle area, obtained
Table 6. Regression equations (Equation 13; Rayleigh equation) for
the relationship between tree height (both for total height and bole
length) and stem diameter at breast height (DBH) for Scots pine trees.
Variables
Regression equation
x = DBH, y = bole length
x = DBH, y = total height
y = 12.27(1 – e –x / 5.05 )7.66
y = 29.96(1 – e –x / 39.34 )0.69
Figure 2. Relationship between needle area and branch diameter for
Scots pine in Pijnven Forest, Hechtel-Eksel, Belgium. The solid line
represents the needle area per branch (cm 2 ) based on a simple regression with branch diameter as the independent variable ( y =
15.543x 0.9906; r 2 = 0.86; n = 23).
TREE PHYSIOLOGY VOLUME 25, 2005
ALLOMETRY AND EVALUATION OF OPTICAL LAI DETERMINATION
Figure 3. Relationship between total needle area per tree and diameter
at breast height (DBH) for Scots pine in Pijnven Forest, HechtelEksel, Belgium. The solid line represents the up-scaled needle area
per tree (m 2 ) based on a simple regression with DBH as the independent variable ( y = 0.2988x 2 – 7.5336x + 74.075; r 2 = 0.94; n = 6).
et al. 1997), was calculated from PLA based on assumptions
about the cross-sectional needle geometry (Brand 1987,
Bond-Lamberty et al. 2003). The cross section of a Scots pine
needle was assumed to be hemicylindrical with the ratio of the
major to minor axis being equal to one. The assumptions about
the geometry of Scots pine needles were verified based on
analysis of needles from a random sample of all age cohorts
from the sample trees. Given the total measured needle projected area and the cross-sectional shape of randomly oriented
Scots pine needles, the surface area can be calculated and divided by 2 to yield HSLA (Chen et al. 1997):
 1 + π /2 
HSLA = 
 PLA

2 
(9)
The HSLA equalled 3.57 and 3.53 for the LAI estimates
based on DBH and basal area, respectively.
Optical gap fraction and LAI measurements
Gap fraction estimation Figure 4 shows the variation in mean
gap fraction as a function of zenith angles, estimated with the
LAI-2000 or from hemispherical photographs. The LAI-2000
data showed an increase in gap fraction from the zenith to the
Figure 4. Mean gap fraction values obtained for the Scots pine stand at
various zenith angles with an LAI-2000 plant canopy analyzer ( 䊐 )
and with hemispherical photographs (with 36 azimuth sectors) (䊉).
Symbols represent the mean and error bars represent the standard deviations of the respective measurements.
729
viewing angles in the third ring, with a peak around the 40°
viewing angle, after which the gap fraction decreased toward
the horizon. Nilson and Kuusk (2004) recently reported that the
gap fraction in the uppermost rings is frequently underestimated because the sampling points are situated under tree
crowns. The low gap fraction at near-zenith angles and the increase between ring 1 and ring 3 is likely caused by the instability of the instrument in the first two rings as well as by a
positioning effect of the LAI-2000 causing a slightly different
view of the canopy. The decrease in gap fraction with distance
from the sampling point was attributed to increasingly dense
foliage (and stems) toward the horizon. The LAI-2000 data
also showed a regular decrease in data dispersion with increasing zenith angle. This agrees with expectations, because gap
fraction values are highly variable especially in the uppermost
ring(s) because of inadequate spatial sampling (Nilson and
Kuusk 2004). These trends were less clear in the hemispherical
photographs, perhaps reflecting the higher intra-variability
among photographs, because the sky sectors used for gap fraction calculations were small. Nevertheless, discrepancies between the data sets from the LAI-2000 and hemispherical
photographs were low, never exceeding 5%.
Leaf area index estimation Mean stand-level LAI (LAI stand )
values from both tree allometry and the various indirect optical
methods are shown in Table 7. To investigate the influence of
clumping at the shoot, branch and tree levels and the influence
of non-leafy material on LAI measurements, three methods
were used to correct the LAI e estimates based on measurements with the optical devices. As expected, the LAI estimates
based on indirect optical measurements were lower than the direct LAI estimates. Agreement between LAI values estimated
by direct and indirect methods increased substantially when
only the four central sky sectors were considered, indicating
that the fifth sky sector, which is centered on a zenith angle of
around 68° and includes that portion of the stands that is far
from the measuring point (Li-Cor 1992), increases the likelihood that measurements will be influenced by light at low zenith angles.
Figure 5 shows the pairwise comparison of the mean LAI
values for all tested methods after correction for clumping and
non-leafy material. Solid bars in Figure 5 represent the mean
LAI based on the whole field-of-view of the optical instruments, whereas open bars represent the mean LAI based on
four rings ( 0–60°). Error bars indicate the 99% confidence intervals (CI), which were generated by a pair-wise Bonferroni
test with α = 0.01.
An increase in estimated LAI was observed when data from
the outer ring were omitted from both the LAI-2000 measurements and hemispherical photographs. The indirect estimates
agreed fairly well with the allometric estimates after correction, highlighting the importance of correcting LAI before
making comparisons.
Discussion
We found that LAIe derived from optical measurements underestimated LAI calculated from direct measurements (Table 7),
as reported in many previous studies (e.g., Fassnacht et al.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
730
JONCKHEERE, MUYS AND COPPIN
Table 7. Comparison of the different methods for determining the leaf area index (LAI) of Scots pine, based on measurements from a stand in
Pijnven Forest. Means followed by an asterisk are significantly different from the allometric estimates in the pairwise Bonferroni test at an α =
0.001 level. Abbreviation: DBH = diameter at breast height.
Method
Mean LAI
SD
TRAC (LAI e T)
3.53
3.57
3.17
0.02
0.02
1.38
All rings
LAI-2000 (LAI e LAI-2000 )
Hemispherical photography (LAI e hem )
Integrated approach: LAI-2000 with TRAC (LAI e T-LAI-2000)
LAI-2000 corrected for clumping at the shoot level (LAI C LAI-2000 )
LAI-2000 corrected for clumping at the branch and tree levels (LAI B LAI-2000 )
LAI-2000 corrected for clumping and non-leafy materials (LAI F LAI-2000 )
Hemispherical photography corrected for clumping at the shoot level (LAI C hem )
Hemispherical photography corrected for clumping at the branch and tree levels (LAI B hem )
Hemispherical photography corrected for clumping and non-leafy materials (LAI F hem )
1.61
1.46
3.42
3.22
1.94 *
3.18
2.84
1.52 *
2.75
0.25
0.45
0.56
0.77
0.28
0.46
0.83
0.58
0.82
Ring 5 masked
LAI-2000 (LAI e LAI-2000 )
Hemispherical photography (LAI e hem )
Integrated approach: LAI-2000 with TRAC (LAI e T-LAI-2000)
LAI-2000 corrected for clumping at the shoot level (LAI C LAI-2000 )
LAI-2000 corrected for clumping at the branch and tree levels (LAI B LAI-2000)
LAI-2000 corrected for blue light scattering, clumping and non-leafy materials (LAI F LAI-2000 )
Hemispherical photography corrected for clumping at the shoot level (LAI C hem )
Hemispherical photography corrected for clumping at the branch and tree levels (LAI B hem )
Hemispherical photography corrected for clumping and non-leafy materials (LAI F hem )
1.79
1.61
3.54
3.46
2.15
3.53
3.22
1.75 *
3.16
0.33
0.51
0.75
0.92
0.37
0.61
0.95
0.69
0.95
Allometry
Based on basal area (LAI A (BA))
Based on DBH (LAI A (DBH))
1994). The LAI-2000 underestimated the directly estimated
LAI by 52%, and the underestimation for hemispherical photographs averaged 55%. Thus, the order of magnitude of the
underestimations corresponded to the 50% observed by Chen
and Cihlar (1995) and is within the range of 30–70% for coniferous forests reported by others (Smolander and Stenberg
1996, Nackaerts et al. 1999). However, the allometric LAI estimates did not differ significantly (α = 0.01) from the corrected optical LAI estimates, except for the LAI-2000 and
DHP measurements that were corrected for clumping only at
the branch and tree level (Table 7). Based on the assumptions
used in the gap fraction models, this finding indicates that
clumping at the shoot level is the main reason that LAI was underestimated by the optical methods. There was no significant
difference between the allometric LAI estimates and the final
optical LAI (LAI F ) values corrected for blue light scattering,
clumping and non-leafy material, indicating that, following
corrections, the indirect optical measurements are reliable.
In agreement with the general observation that removal of
the outer ring of the LAI-2000 results in higher LAI values, because scattering is greatest at larger zenith angles (Chen 1996),
our LAIe measurements, based on the first four rings of the
LAI-2000, were systematically 11% larger than the LAIe values calculated with all five rings. Similarly, Chen et al. (1997)
reported that the LAI-2000 underestimates the effective LAI
by about 15% because of multiple scattering.
The TRAC gave a relatively high LAI values because the in-
strument calculates LAI on the basis of a nonrandom distribution of leaves (i.e., with a clumping index of 0.836). The
clumping index value indicated that foliage at the site was not
perfectly randomly distributed, which explains why the optical
LAI estimates, when corrected for clumping, approximated
Figure 5. Mean stand estimates of leaf area index (LAI) by the indirect
optical methods after correction for clumping and non-leafy material
compared with direct estimates of LAI based on allometric relationships. Bars represent mean LAI; and bars are indicative of the 99%
confidence intervals (CI). The CIs were generated by a pairwise
Bonferroni test with α = 0.01. Filled bars are based on the whole field
of view and open bars are based on four rings (i.e., 0–60°). Abbreviations: DHP = digital hemispherical photography; and All(BA) and
All(DBH) = allometric estimates based on basal area and DBH, respectively.
TREE PHYSIOLOGY VOLUME 25, 2005
ALLOMETRY AND EVALUATION OF OPTICAL LAI DETERMINATION
the LAI values estimated from direct measurements. The
higher mean LAI obtained by an integrated approach, which
combined the LAIe measurement of the LAI-2000 with the
clumping index provided by TRAC, compared with the LAIe
of the LAI-2000 alone, highlights the usefulness of combining
the two instruments to correct for clumping.
Correction of the optical estimates involved a trade-off between correction for clumping (underestimation of LAI) and
correction for the non-leafy parts of the crown (overestimation). Because these factors have opposing effects on
estimated LAI depending on the proportion of woody area, either the real foliage distribution of the stand is as clumped as
estimated by the TRAC instrument or the calculated woodyto-total area α = 0.18 is a reasonable estimate for this stand. A
consensus concerning the influence of woody material and
tree boles on LAI estimates is still lacking.
Chen et al. (1997), Cutini et al. (1998) and Barclay et al.
(2000) found that woody material influenced optical estimates
of LAI significantly at their test sites, whereas Fournier et al.
(1996) suggested that branches and boles exaggerated LAI by
less than 5% in three relatively dense stands of conifers. However, because of the large amount of work necessary to assess
the effects of wood and other non-foliage components of the
canopy on LAI, most studies have ignored this variable. In
view of the difficulty in evaluating the effects of W on LAI estimates and its high variability, the importance of correcting
for this factor must be carefully assessed. A solution to the
time-consuming determination of the correction factor α
could be an automated classification method based on imagery
from a digital camera allowing imaging in several wavebands.
Finally, the difference in LAI e values between hemispherical photography and LAI-2000 (15%) can be explained by differences in light measurements and gap fraction calculation.
Hemispherical photography deals with diffuse and direct light,
whereas the LAI-2000 accounts only for diffuse light. The
LAI-2000 provides a mean gap fraction, integrated over the
azimuth for every zenith ring, whereas the hemispherical photography accounts for the real gap fraction over the rings because gap fraction data are derived from 36 azimuth sectors
(10° azimuth angles). The assumption of uniformly oriented
needles in each azimuth sector is more likely to be valid in the
latter case.
Acknowledgments
We acknowledge the useful comments and criticisms provided by
Kris Nackaerts, Ben Bond-Lamberty and Pauline Stenberg. We thank
Dave Nys for helpful assistance in the measurements, as well as
Bruno De Vos (Institute for Forestry and Game Management) for data
delivery. Assistance in finding suitable stands and permission to do
destructive measurements were supplied by Johan Agten, forest ranger at State Forest Pijnven. We thank VITO for supplying the TRAC
instrument. Funding support for this research was provided by FWO
Vlaanderen (Project No. G.0085.01) and OSTC, Belgium.
731
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