Allometry and evaluation of in situ optical LAI ... - Tree Physiology

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. MUYS 1 and P. COPPIN 1 

1 

Katholieke Universiteit Leuven, Department of Land Management, Laboratory for Forest, Nature and Landscape Research, VitalDecosterstraat 

102, 3000 Leuven, Belgium 

2 

Corresponding author (inge.jonckheere@agr.kuleuven.ac.be) 

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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724 JONCKHEERE, MUYS AND COPPIN 

Table 1. Symbols used for the variables related to leaf area index (LAI). 

Symbol Definition Reference 

LAI Half the total leaf surface area per unit ground area Chen and Black 1992 

LAIe Effective LAI estimated by optical methods Chen et al. 1991 

LAIc LAI estimated by correcting LAIe for needle clumping in conifers; Equation 1 Chen 1996 

LAIB LAI estimated by correcting LAIe for clumping at branch and tree level in conifers; Equation 5 Chen and Cihlar 1995 

LAIF LAI estimated by correcting LAIe for needle clumping, tree branch distribution and Chen et al. 1997 

non-leafy material; Equation 6 

LAIA LAI estimated with allometric relationships in conifers Marklund 1988 

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. 

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 

TREE PHYSIOLOGY VOLUME 25, 2005 

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 

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. 



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 Frequency Mean DBH Mean basal Mean height Height of crown 

(cm) (ha –1 ) (cm) area (m 2 ) (m) base (m) 

1 17–23 52 19.5 0.03 16.2 11.0 

2 23–24 52 23.0 0.04 17.5 11.7 

3 24–26 56 24.5 0.05 17.9 11.4 

4 26–28 56 26.5 0.06 18.5 11.3 

5 28–30 48 28.5 0.07 18.9 12.4 

6 30–39 52 37.5 0.11 20.1 12.2 

Stand mean 26.29 0.06 18.2 11.7 

Total 316 17.41 

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 m 2 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 Basal Total Height of 

(cm) area (m 2 ) height (m) crown base 

(m) 

1 21.7 0.037 18.1 13.0 

2 23.8 0.044 20.4 13.4 

3 25.0 0.050 18.7 11.6 

4 26.4 0.055 19.4 12.8 

5 28.0 0.062 18.3 12.1 

6 31.8 0.080 16.6 14.6 

TREE PHYSIOLOGY ONLINE at http://heronpublishing.com 

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 




Table 4. Regression models used to establish allometric equations in 

the experimental Scots pine stand in Pijnven Forest, Hechtel-Eksel, 

Belgium. 

Regression Equation 

Logarithmic lny = a + bln x 

(10) 

Gaussian 

−b( x−c) y = ae 2 

(11) 

Log-normal 

2 

( −(ln( b−x) −c) 

/ 4) 

y = a/( b − x) e 

(12) 

Rayleigh 

x b c 

y = a −e − ( / ) 

( 1 ) 

(13) 

Power y ax b 

= (14) 

Polynomial 

2 

y = ax + bx+ c 

(15) 

Linear y = ax+ b 

(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 (Ωe). 

The value of Ωe, 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 Ωe 

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°, Ωe 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 



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): 

with: 

LAIc = LAIeγ 

e 

(1) 

γ e = An/ As 

(2) 

A 

s 

(0 ° , 0 ° )cos (15 ° ) (45 ° ,0 ° )cos (45 ° ) (90 ° , 0 ° )cos(75 ° ) 

A p + A p + A p 

= 2 

cos(15 ° ) + cos(45 ° ) + cos(75 ° ) 

where LAI c is LAI corrected for shoot-level clumping, LAI e is 

effective LAI as estimated by the optical devices, γe 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 Ap (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 (An) 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, Ωe was obtained from TRAC (Leblanc 2002) as: 

Ω e 

⎛ ( Fm − Fmr) 

⎞ lnF 

= ⎜1 

+ ⎟ 

⎝ 1− 

F ⎠ lnF 

m 


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 

m 

mr 

(3) 

(4) 

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 Ωe was 0.836. 

We calculated LAIB as (Chen and Cihlar 1995): 

LAI = LAI / Ω 

(5) 

B e e 

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 (LAIF) as did Chen et al. (1997): 

LAI 

F 

( 1 − α) LAI γ 

= 

Ω 

e 

e e 

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/LAItotal, where W is the woody area index and 

LAItotal 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, 

(6) 




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 r 2 

Branch 

x = Branch cross-sectional area (cm 2 ) 

y = Needle area (m 2 branch –1 ) y = 15.543x 0.9906 

y = Needle DM (kg branch –1 ) y = 29.908x 0.6604 

Tree 

x = DBH (cm) 

y = Needle area (m 2 tree –1 ) y = 0.2988x 2 – 7.5336x + 74.075 0.94 

y = Crown projected area (m 2 tree –1 ) y = 0.0066x 2 + 0.2115x 0.88 

y = Needle DM (kg tree –1 ) y = –0.001x 2 + 0.0527x – 0.4586 0.95 

Stand 

x = Basal area (m 2 ) 

y = Needle area (m 2 ha –1 ) y = 5791.9x 2 + 1344.7x – 7.1147 0.94 

y = Crown projected area (m 2 ha –1 ) y = – 492.83x 2 + 173.86x 0.84 

y = Needle DM (kg ha –1 ) y = 23.036x 2 + 204.42x 0.91 

y = Number of needles (thousand ha –1 ) y = 1.789x (x in cm 2 ) 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. 

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 y = 12.27(1 – e –x /5.05 ) 7.66 

x = DBH, y = total height y = 29.96(1 – e –x / 39.34 ) 0.69 


0.86 

0.83 

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: 

2 

y = 02988 . x − 75336 . x + 74. 075 

(7) 

or by applying the equation linking basal area and projected 

needle area: 

2 

y = 5791.9x + 1344.7x – 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 

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). 



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 ⎠ 


Figure 3. Relationship between total needle area per tree and diameter 

at breast height (DBH) for Scots pine in Pijnven Forest, Hechtel- 

Eksel, 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). 

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 ( � ) 

and with hemispherical photographs (with 36 azimuth sectors) (�). 

Symbols represent the mean and error bars represent the standard deviations 

of the respective measurements. 

(9) 


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. 




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 

Allometry Based on basal area (LAIA(BA)) 3.53 0.02 

Based on DBH (LAIA(DBH)) 3.57 0.02 

TRAC (LAIe T) 3.17 1.38 

All rings 

LAI-2000 (LAIe LAI-2000) 1.61 0.25 

Hemispherical photography (LAIehem) 1.46 0.45 

Integrated approach: LAI-2000 with TRAC (LAIe T-LAI-2000) 3.42 0.56 

LAI-2000 corrected for clumping at the shoot level (LAIC LAI-2000) 3.22 0.77 

LAI-2000 corrected for clumping at the branch and tree levels (LAIB LAI-2000) 1.94 * 0.28 

LAI-2000 corrected for clumping and non-leafy materials (LAIF LAI-2000) 3.18 0.46 

Hemispherical photography corrected for clumping at the shoot level (LAIC hem) 2.84 0.83 

Hemispherical photography corrected for clumping at the branch and tree levels (LAIB hem) 1.52 * 0.58 

Hemispherical photography corrected for clumping and non-leafy materials (LAIF hem) 2.75 0.82 

Ring 5 masked 

LAI-2000 (LAIe LAI-2000) 1.79 0.33 

Hemispherical photography (LAIehem) 1.61 0.51 

Integrated approach: LAI-2000 with TRAC (LAIe T-LAI-2000) 3.54 0.75 

LAI-2000 corrected for clumping at the shoot level (LAIC LAI-2000) 3.46 0.92 

LAI-2000 corrected for clumping at the branch and tree levels (LAIB LAI-2000) 2.15 0.37 

LAI-2000 corrected for blue light scattering, clumping and non-leafy materials (LAIF LAI-2000) 3.53 0.61 

Hemispherical photography corrected for clumping at the shoot level (LAIC hem) 3.22 0.95 

Hemispherical photography corrected for clumping at the branch and tree levels (LAIB hem) 1.75 * 0.69 

Hemispherical photography corrected for clumping and non-leafy materials (LAIF hem) 3.16 0.95 

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. 



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 LAIe 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. 

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