IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 5, MAY 2010

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Estimation and Error Analysis of Woody Canopy
Leaf Area Density Profiles Using 3-D Airborne
and Ground-Based Scanning Lidar
Remote-Sensing Techniques
Fumiki Hosoi, Yohei Nakai, and Kenji Omasa

Abstract—Vertical profiles of the leaf area density (LAD) of aJapanese zelkova canopy were estimated by combining airborneand portable ground-based light detection and ranging (lidar)
data and using a voxel-based canopy profiling method. The profiles
obtained by the two types of lidars complemented each other,eliminating blind regions and yielding more accurate LAD profiles than could be obtained by using each type of lidar alone.
In the combined results, the mean absolute errors (MAEs) of
LAD ranged from 0.20 to 0.42 m2 m−3 , and the mean absolute
percentage errors (MAPEs) of the leaf area index (LAI) ranged
from 22.3% to 27.2%, for ground areas from 4 to 32 m2 , respectively. A laser beam coverage index Ω incorporating the lidar’s
beam settings and a beam attenuation factor was proposed. This
index showed general applicability to explain the LAD estimation
error for LAD measurements using different types of lidars andwith different beam settings. Parts of the LAD profiles that were
underestimated even when data from both lidars were combined
were interpolated by using a Gaussian function. The interpolation
yielded improved results for ground areas of 16 and 32 m2 ; therespective MAEs of LAD were 0.17 and 0.11 m2 m−3 , and therespective MAPEs of LAI were 8.0% and 9.4%. The proposed
method improves lidar-derived LAD estimation and is adapted tobroadleaved canopies. The index Ω was tested against an actual
canopy scenario and could be used to determine appropriate lidar
measurement settings when data from different sources of lidar
data are combined to estimate LAD profiles.
Index Terms—Airborne scanning light detection and ranging(lidar), composite remote sensing, laser beam coverage index, leaf
area density (LAD), leaf area index (LAI), portable ground-based
scanning lidar, three-dimensional (3-D), voxel-based canopy
profiling (VCP).

I. I NTRODUCTION

T

HE plant canopy plays important functional roles in thecycling of materials and energy through photosynthesis
and transpiration, the maintenance of plant microclimates, andthe provision of habitats for various species [1]–[3]. Determining the vertical structure of the canopy is very important,because the 3-D composition of the canopy helps to sustain
those functional roles [4]–[7]. The vertical canopy structure
Manuscript received December 14, 2008; revised July 25, 2009 andNovember 2, 2009. First published February 17, 2010; current version published April 21, 2010.
The authors are with the Graduate School of Agricultural and Life Sciences,
University of Tokyo, Tokyo 113-8657, Japan (e-mail: aomasa@mail.ecc.
u-tokyo.ac.jp).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TGRS.2009.2038372

is often represented by the vertical distribution of the leaf
area density (LAD) in each horizontal layer, defined as the
distribution of the one-sided leaf area per unit of the horizontal
layer volume [8]. Vertical integration of the LAD profile data
yields the leaf area index (LAI).
Although various ways of measuring LAD and LAI havebeen used in previous works, the measurement of these parameters is still difficult. A direct method is stratified clippingof biomass samples [9]. Although this straightforward method
gives accurate results, it has limited applicability in the field
because it is destructive and very laborious. Another direct
method involves 3-D digitizing by ultrasonic or electromagnetic
devices, whereby geometric information is recorded in a 3-D
spatial coordinate system by a pointer to the position of eachplant component [10]–[12]. This technique can nondestructively provide detailed information about the 3-D structure ofplants, but it is also labor intensive because numerous components must manually be measured, point by point. An indirect
method, the gap-fraction method, is widely applied in fieldsurveys by using commercially available tools such as cameras
with fish-eye lenses and optical sensors (e.g., the LI-COR LAI2000 Plant Canopy Analyzer) [13], [14]. This method, which
is based on light transmittance through the canopy, allows automatic nondestructive estimation of LAI and LAD. However,
the method also has a weak point because the accuracy of themeasurement is affected by the spatial distribution of leaves andby sunlight conditions [15], [16].
Light detection and ranging (lidar), which is an active
remote-sensing technique that uses a laser scanner, has also
been applied to canopy measurements. The vertical profile ofthe structure of a forest canopy can be estimated by an airborne
large-footprint lidar from the waveforms of the returned pulses[5], [17]. However, the image resolution is not fine enoughto describe the canopy structure at the individual tree scale.
Canopy structure has been measured more accurately by using
an airborne small-footprint lidar, which has fine spatial resolution [18]–[29]. This type of lidar has been used for estimating
the LAI values of several species of coniferous trees [30], [31]and crops [32]. However, these studies focused on LAI estimation rather than on the estimation of the vertical LAD
profile, because they captured insufficient information about thevertical canopy structure to estimate the latter. Attempts havebeen made to measure vertical canopy profiles in eucalyptus

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 5, MAY 2010[33] and Douglas-fir [34] forests by using an airborne smallfootprint lidar. However, the profiles showed little response
from the lower canopy levels, known to be present in the actual
foliage profile, apparently because the laser beams from thelidar could not reach the lower canopy due to obstruction by theupper canopy. As a result, the lower canopy level is regarded
as a blind region to airborne lidar measurement. Thus, themeasurement of the vertical LAD profile by airborne smallfootprint lidar is still problematic.
Portable ground-based lidars have been used for accurate
measurements of whole plants and vegetation canopies [7],[26], [35]–[42]. A ground-based lidar is expected to compensate for the weaknesses of an airborne lidar in LAD estimation, because its fine spatial and range resolutions andsmall beam size permit measurement of the inner canopiesof trees, allowing an accurate estimation of LAD profiles.
Portable ground-based scanning lidars have been applied tothe measurement of both LAI [33], [43] and LAD profiles[44]–[47] by the gap-fraction method. However, the estimatesobtained were insufficiently accurate because it was difficult toevenly illuminate the full canopy. The results were also affectedby the nonuniformity of the actual foliage distribution and thepresence of nonphotosynthetic tissue.
Three-dimensional imaging by portable ground-based scanning lidars has been demonstrated to provide accurate estimatesof LAD based on the voxel-based canopy profiling (VCP)
method [7], [37]–[39]. In this method, the canopy is fully andevenly scanned by using optimally inclined laser beams emitted
from several points surrounding the canopy. Information about
the laser traces is included in a 3-D array of voxels. A voxel
can refer to 1) the presence of lidar data or 2) one or morelaser beams passing without touching the canopy [37]. Basedon the voxels, LAD profiles and the LAI of individual trees canaccurately be estimated by counting the frequency of contact
between the laser beams and foliage within the canopy in eachhorizontal layer. This method has been tested on a broadleaved
woody canopy tree [38], in a study in which several lidar
positions were established both on the ground and 10 m above
the ground. The measurements on the ground yielded good
estimates when a sufficient number of laser beams penetrated
the full canopy, but the ground-level measurements showed an
overall tendency to underestimate the upper canopy, because
the laser beams were obstructed by the middle and lower partsof the target canopy itself and the other trees surrounding thetarget, keeping the beams from adequately reaching the upper
canopy. Thus, the upper part of a woody canopy often becomesa blind region in ground-level lidar measurement, a situation
opposite to that in airborne lidar measurement. Consequently,
better LAD results were obtained in this study [38] by combining the measurements obtained at the ground level withthose obtained at 10 m above the ground. The results suggested
that above-ground measurement can complement ground-levelmeasurement to eliminate blind regions. However, it is difficultin the field to set portable ground-based lidar systems at highabove-ground positions. Meanwhile, another study [26] showedthat ground-level lidar measurements could effectively be combined with above-ground lidar measurements obtained by anairborne scanning lidar. By combining the data from both typesof lidar, a 3-D model of standing trees without any blind region
could be produced, and some variables such as the canopy
volume, the trunk volume, and the canopy cross-sectional area
could be estimated. In this study [26], only an outer surfaceof the canopy was reproduced as a 3-D model. Such a modelcannot be used for LAD estimation because information on theinternal canopy is required for LAD estimation.
The results in [26] and [38] indicate that the combinationof airborne and portable ground-based scanning lidars could
potentially allow an accurate estimation of LAD by eliminating
the blind regions of each lidar. Combining both lidar systems
requires the appropriate determination of the measurement
configuration (e.g., laser beam settings and lidar position)according to the canopy structure to obtain more accurate
LAD estimates. A criterion is thus needed but should require
being commonly applicable to both types of lidar system withdifferent characteristics. However, such criterion has not yet
been proposed.
In the present study, we estimated the LAD in a woody
canopy by data from both airborne and portable ground-based
lidars and using the VCP method. We then evaluated the accuracy of the LAD estimation by comparing the results of eachseparate lidar with those of the combined lidars. The results ofthe evaluation were used to establish a criterion for determining
the appropriate lidar measurement settings applicable to different types of lidars, and an index that relates lidar setting values
to the accuracy of LAD estimates was proposed. In addition,
to further improve the accuracy of the composite results, weapplied Gaussian fitting to the composite profiles.
II. M ATERIALS AND M ETHODS
A. Study Site and Direct Measurement of LAD
The study was carried out in a mixed plantation with nearlyflat topography in Ibaraki Prefecture, 40 km northeast of central
Metropolitan Tokyo, Japan (35◦ 59 N, 140◦ 02 E). The dominant tree species were Japanese cedar (Cryptomeria japonica[L.f.] D. Don), Japanese red pine (Pinus densiflora Siebold &Zuccarini), ginkgo (Ginkgo biloba Linnaeus), and Japanesezelkova (Zelkova serrata [Thunberg] Makino). The understory
included grasses, forbs, and young evergreen trees such as
Camellia japonica Linnaeus, Ilex integra Thunberg, and Ternstroemia gymnanthera Sprague. A Japanese zelkova canopy
was chosen for measurement, and a 4 m × 8 m measurement
plot was established beneath the canopy. The measurement plot
was divided into eight 2 m × 2 m quadrats, and then, the region
above the plot was divided into 128 cells (each 2 m × 2 m ×
0.5 m high) between the heights of 5 and 13 m. The actual
LAD in each cell was directly measured by stratified clipping in
September 2005, the month following the lidar measurementsof the leafy canopy. Details about the measurement plot and the
direct measurement can be found in [38].
B. Measurements Using Portable Ground-Based and Airborne
Scanning Lidars
Measurements using portable ground-based scanning lidars were conducted in August 2005 (leafy condition) andAuthorized licensed use limited to: UNIVERSITY OF TOKYO. Downloaded on May 18,2010 at 04:05:33 UTC from IEEE Xplore. Restrictions apply.

HOSOI et al.: ESTIMATION AND ERROR ANALYSIS OF WOODY CANOPY LEAF AREA DENSITY PROFILES

February 2006 (leafless condition), as reported in [38]. The
measurement plot and the area around the plot were alsoscanned in August 2005 from above by a lidar mounted on ahelicopter (ALTM 3100 DC, Optech Company, and Aero Asahi
Company, Japan). The airborne lidar calculated the distance toa target by the time-of-flight method and had four receiving
modes—the first-, second-, third-, and last-pulse modes—in
which the first, second, third, and last returned laser pulses, respectively, were detected. Laser pulses returned from the upper
canopy were received as the first-pulse mode, so only the firstpulse-mode data were used in this study. The laser wavelength
was 1064 nm, and its repetition frequency was 50 000 Hz.
The scanning frequency and angle were set to 25 Hz and20.0◦ , respectively. The flight speed and height were 50 km/h
and 400 m, respectively. The range accuracy and horizontal
accuracy were within 15 and 13 cm, respectively. The latter was
calculated from the angular accuracy of the scanning system.
The beam divergence was 1.0 mrad, and the footprint diameteron the ground was estimated to be about 0.40 m. The footprintinterval, i.e., the distance between centers of adjacent laser
beams on the ground, was 0.29 m in the direction of the scanand 0.26 m in the direction of flight. The 3-D geographic
position was determined with helicopter-borne inertial measurement unit and high-resolution Global Positioning System
receivers, both in the helicopter and on the ground.
C. Computation of LAD From Portable Ground-Based andAirborne Scanning Lidar Data
1) Data Registration and Removal of Nonphotosynthetic
Tissues: The 3-D point cloud data obtained by airborne andportable ground-based lidars were registered into a common
coordinate system using the iterative closest point algorithm[48]. The scans done with the portable ground-based lidar
in August 2005 oriented at a central zenith angle of 57.8◦
permitted effective correction for leaf inclination without angle
measurements [37], [38] and were used for the registration.
Nonphotosynthetic tissues such as trunks and branches andunderstory were excluded with a method similar to the one
found in [38]. Then, the voxel-based computation of LAD
described below was conducted separately for the portable andairborne lidar data.
2) Voxel-Based Computation of LAD: LAD computationfrom portable ground-based lidars has been previously reported
in [38], with a voxel size of 5 × 5 × 5 mm. A similar computation process was applied to airborne lidar data with a voxel
size of 100 × 100 × 100 mm. The voxel size was chosen to
be at least finer than the lidar spatial resolution to adequately
convert the airborne lidar data to the voxel representation. In
the computation for airborne lidar data, the influence of theleaf inclination angle and laser beam direction was correctedby using the correction factor of cos(θlmn )[G(θlmn )]−1 , whereθlmn is the mean zenith angle for all laser beam incidences
within a cell, and G(θlmn ) is the mean projection of a unit leaf
area on a plane perpendicular to the direction of the laser beamat θlmn [8], [13], [14], [16]. To determine the correction factor,
θlmn was set to 180◦ (i.e., vertical), and the distribution of leaf
inclination angles obtained in [38] was used.

22173) Evaluation of the Accuracy of the Lidar-Derived LAD:
From the LAD values of each lidar computed for each of thecells, vertical LAD profiles were estimated for each type of lidar
for ground areas of 4, 8, 16, and 32 m2 , corresponding to one,
two, four, and eight quadrats, respectively. For ground areas of
8 m2 or more, the LAD profiles were obtained by horizontally
averaging the LAD profiles of as many adjacent quadrats ascorresponded to the ground area. For instance, an LAD profile
for the ground area of 16 m2 was obtained by averaging the
LAD profiles of four horizontally adjacent quadrats. Thus, by
combining adjacent quadrats, four different LAD profiles were
estimated for a ground area of 8 m2 . Similarly, four different
LAD profiles were also estimated for a ground area of 16 m2 .
In the case of the ground area of 32 m2 —that is, the whole
region of the measurement plot—just one LAD profile wasestimated. The accuracy of the LAD profiles estimated foreach ground area was evaluated by comparing the estimatedand actual profiles and calculating the mean absolute error(MAE). Vertical integration of each LAD profile yielded the
LAI, and the mean absolute percentage error (MAPE) of the
LAI was also estimated by comparing the actual values withthe estimated values for each ground area.
To obtain more accurate LAD profiles, the profiles derived
from the two types of lidars were combined, with the LAD
values from the portable ground-based lidar data being replacedwith those from the airborne lidar data for heights over 10 m.
The accuracy of the composite profiles of the two lidars wasevaluated for ground areas of 4 to 32 m2 by comparing the MAE
values. The LAI values for all ground areas were derived byvertically integrating the composite profiles, and their MAPE
values were compared.
D. Derivation of the Laser Beam Coverage Index
The evaluation of LAD estimation accuracy showed that asufficient ground area for applying the composite method was
16 m2 or more. Then, an index that was related to the LAD
estimation error was derived for the ground areas of 16 and
32 m2 . On the assumption that the LAD estimation error
is affected by the laser beam coverage within the canopy,
three factors that relate to the coverage were selected: thehorizontally projected area of the laser beam (Abeam ), thenumber of incident laser beams from above (airborne lidar) or
below (portable ground-based lidar) the canopy per unit areaof a horizontal plane (N ), and a laser beam attenuation factor(K · LAIcum ). In the laser beam attenuation factor, K is aparameter for the influence of the leaf inclination angle and thelaser beam direction on laser beam attenuation and is equivalent
to the inverse of the correction factor cos(θlmn ) [G(θlmn )]−1 ,described in Section II-C2. LAIcum is the lidar-derived cumulative LAI at a certain height. K and LAIcum reflect the structural
attributes of the canopy, while Abeam and N relate to the laser
beam settings. The laser beam coverage index Ω was made in
relation to these three factors as follows:Ω = Abeam × N exp(−K · LAIcum ).

(1)

The index Ω is defined as the total horizontally projected areaof the incident laser beams per unit area of a horizontal plane

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 5, MAY 2010

within the canopy at a certain height. This is also translated
as the proportion of the area of a horizontal plane within the
canopy covered by laser beams at a certain height. Abeam andN were determined from the laser beam settings of each lidar.
K · LAIcum was calculated for each height by using the voxel
attributes as follows (see [37]):mtop

K · LAIcum =k=mhnI (k)nI (k) + np (k)for airborne lidar data
K · LAIcum =mh
k=mbottom(2)

nI (k)nI (k) + np (k)for portable ground-based lidar data(3)

where nI (k) is the numbers of voxels at which laser beams
were intercepted, and nP (k) is the ones through which laser
beams passed. mh , mtop , and mbottom are the voxel coordinates on the vertical axis equivalent to height h and theheights of the canopy top (= 12.5 m) and bottom (= 5 m).
Ω was calculated for each height in regions corresponding to
the LAD profiles estimated for ground areas of 16 and 32 m2 .
Then, the relationships between Ω and the absolute errors of thecorresponding LAD estimates were investigated for each typeof lidar.
E. Interpolation
For ground areas of 16 and 32 m2 , the composite profilesof the two lidars underestimated the LAD at heights of around
10 m, a height corresponding to the peak of the actual LAD profile. The underestimated parts of the profiles were interpolated
by using the following Gaussian function:f (h) = a + b exp(h − hp )2
2c2

(4)

where h is the height, hp is the height of the Gaussian function
peak, and a to c are parameters that determine the form of
the fitting function. The Gaussian function was chosen for theinterpolation, since the Gaussian function has been used as afunction that fits vertical LAD profiles of broadleaved canopies
in a previous study [49]. To determine the function, several
points had to be picked up from the composite profile. The LAD
profiles derived from each lidar used to obtain the composite
profile had a peak above (in the case of the airborne lidar) or
below (in the case of the portable ground-based lidar) 10 m. By
using these two peaks from the profiles of the two lidars, fourto eight points were picked up from the composite profile andused in the interpolation as follows:
1) four points, i.e., the two peaks (one from the airborne lidar
profile and one from the portable ground-based lidar LAD
profile), a point 50 cm higher than the airborne lidar profile
peak, and one 50 cm lower than the portable ground-based
lidar profile peak (corresponding to points B , C , B, and C
in Fig. 2);

Fig. 1. Three-dimensional image of the Japanese zelkova canopy at the study
site. This image was obtained by the registration of the images measured fromabove with the airborne lidar and from the six ground positions with the portableground-based lidar. White dots represent the data obtained from the airborne
lidar and gray and black dots represent the data from the ground-based lidar (inthe online version of this paper, leaves are green, and other parts are brown for
the ground-based lidar data, and the data obtained from the airborne lidar arecolored red). Shading effect was added to this image by changing the brightnessof each point. The number of data from the airborne lidar was quite less thanthe one from the portable ground-based lidar. The area enclosed by the broken
white line corresponds to the measurement plot. Arrows show the directions oflidar scanning from side A on the ground and from above the canopy.

2) six points, i.e., the four points in (1), one 100 cm higher than
the airborne lidar profile peak, and one 100 cm lower thanthe portable ground-based lidar profile peak (corresponding
to points B to D and B to D in Fig. 2);3) eight points, i.e., the six points in (2), one 150 cm higher
than the airborne lidar profile peak, and one 150 cm lower
than the portable ground-based lidar profile peak (corresponding to points B to E and B to E in Fig. 2).
In each point set (sets 1–3), parameters hp and a to cwere determined by the least-squares method to interpolate theunderestimated parts of the composite profiles. The relative accuracy of the interpolation with each point set was evaluated bycomparing the MAE values. The LAI values of the interpolated
profiles were also estimated by vertical integration, and their
MAPEs were evaluated.
III. R ESULTS
Fig. 1 shows the 3-D lidar image of the zelkova canopy after
the registration of the images measured from the upper air byusing the airborne lidar and from the six ground positions byusing the portable ground-based lidar. For the ground-based
lidar data, each tissue is clearly distinguishable because of thefine resolution of the image. The number of data obtained fromthe airborne lidar was quite less than the one of the portableground-based lidar due to the difference in laser beam density
between the two lidars.
Fig. 2 shows the LAD profiles for the entire measurement
plot (32 m2 ), obtained from actual measurements and fromthe two lidars. The portable ground-based lidar data and theactual ones were cited from [38]. LAD estimates from theairborne and portable ground-based lidar data agreed well withthe actual values for the upper and lower canopies, respectively,

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HOSOI et al.: ESTIMATION AND ERROR ANALYSIS OF WOODY CANOPY LEAF AREA DENSITY PROFILES

Fig. 2. Comparison of LAD profiles for the measurement plot estimated fromairborne and portable ground-based lidar measurements and the actual LAD
profile. The portable ground-based lidar data and the actual ones were citedfrom [38]. Points A to K and A to E indicate the points corresponding to thecomposite profile.

Fig. 3. Relationships between the ground area used for the LAD measurement
and the MAEs of LAD for profiles obtained by the airborne lidar and theportable ground-based lidar and the composite profile.

but underestimated the values at around 10-m height. As aresult, the peaks of the airborne and portable ground-based
lidar profiles were above and below, respectively, the peak of
the profile of actual measurements. The MAEs of the airborne
lidar and portable ground-based lidar profiles were 0.35 and0.26 m2 m−3 , respectively, and the MAE of the composite
profile based on the data of both lidars was 0.20 m2 m−3(A to K and A to E in Fig. 2 indicate the points corresponding
to the composite profile).
Fig. 3 shows the relationships between the measurement
ground area and the MAEs of LAD obtained with different
types of lidar and from the composite data without interpolation, as shown in Fig. 2. Comparison of data between the two
lidars showed that the MAEs of the airborne lidar were larger
than those of the portable ground-based lidar for all groundareas, and the LAD estimates in the composite profile had thelowest MAEs for all ground areas. The MAEs associated with
the LAD profile of each lidar and with the composite profile
were almost constant for ground areas of 16 m2 or more but
increased in relation to ground area for ground areas of lessthan 16 m2 . In addition, the rate of increase in the MAE for

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Fig. 4. Relationship between the laser beam coverage index Ω (= Abeam ×
N exp(−K LAIcum ), given in (1), and the absolute errors of LAD in all
airborne and portable ground-based lidar measurements for ground areas of 16
and 32 m2 .

ground areas of less than 16 m2 was higher with the airborne
lidar than with the portable ground-based lidar. The MAPEs of
LAI for ground areas of 4, 8, 16, and 32 m2 were, respectively,
50.8%, 51.9%, 56.7%, and 59.8% for airborne lidar; 36.7%,
36.6%, 36.8%, and 37.2% for portable ground-based lidar; and22.3%, 25.5%, 25.7%, and 27.2% for the composite profiles.
The relationships between the laser beam coverage index Ω[see (1)] and the absolute error of the LAD estimates of eachlidar for ground areas of 16 and 32 m2 are shown in Fig. 4.
In spite of the different laser beam settings of the two lidars,
the points from both lidars in the scatter plot were found in thesame general region on the plot, indicating that the relationshipbetween the index Ω and the LAD estimation error was similar
between the two lidars. The absolute errors of both lidars began
to drastically increase when Ω decreased to around 1.0. Largeerrors were associated with values of Ω less than or equal toapproximately 1.0, whereas smaller errors were associated withvalues of Ω increased above 2.0.
Fig. 5(a) shows examples of the composite LAD profile forthe ground area of 16 m2 and the profile interpolated witha Gaussian function. For this interpolation, four points were
picked up from the composite profile, with the result that theunderestimated part of the composite LAD profile was improved by the interpolation, decreasing the MAE from 0.16 to
0.13 m2 m−3 . The MAE of all four profiles for the ground areaof 16 m2 decreased from 0.21 to 0.17 m2 m−3 , and the MAPE
of LAI decreased from 25.7% to 8.0%. A similar improvement
can also be observed in the profiles for the whole measurement
plot (a ground area of 32 m2 in Fig. 5(b); the actual LAD
profile was cited from [38]). In this interpolation as well, four
points were picked up from the composite profile. The MAE
was decreased from 0.20 to 0.11 m2 m−3 , and the absolute
error of LAI was also decreased, from 27.2% to 9.4%, by theinterpolation.
The relationship between the number of points picked up
for the Gaussian interpolation and the MAE of LAD after interpolation was evaluated for ground areas of 16 and
32 m2 . The MAEs in four, six, and eight picked-up points were,respectively, 0.16, 0.16, and 0.17 m2 m−3 in a ground area of

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 5, MAY 2010

Fig. 6. Comparison of MAEs of LAD estimates for ground areas of 16 and
32 m2 among airborne lidar measurements, portable ground-based lidar measurements, and the composite of the lidar measurements and after interpolationof the composite by a Gaussian function.

Fig. 5. Comparison of the composite LAD profile obtained by combining datameasurement from the airborne and portable ground-based lidars, the profile
obtained by interpolation of the composite profile by a Gaussian function, andthe actual profile. (a) Examples for a ground area of 16 m2 and (b) 32 m2 . The
actual LAD profile at 32 m2 was cited from [38].

16 m2 and 0.11, 0.11, and 0.13 m2 m−3 in a ground area of
32 m2 . For both ground areas, the MAEs were similar wheneither four or six points were picked up, and the MAE slightly
increased when eight points were picked up.
Fig. 6 shows the MAEs of LAD estimates for ground areasof 16 and 32 m2 for four different cases. The MAE decreased
for both ground areas in the order airborne lidar > portableground-based lidar > the composite of both lidars without interpolation > the composite with interpolation using four pickedup points. This result clearly shows that the LAD estimation
accuracy was improved by using the composite of the two
lidars and then interpolating the composite profile by using a
Gaussian function.
IV. D ISCUSSION
In the case of the studied canopy, the whole canopy could
not be covered by either lidar by itself (Fig. 2), because thecanopy at around 10-m height obstructed laser beams fromthe airborne lidar from reaching the lower canopy, and thosefrom the portable ground-based lidar from reaching the upper canopy. The accuracy of the LAD profiles was improved(as shown in Fig. 3) by combining the profiles of the two
lidars, so that they complemented each other, eliminating blind
regions. However, ground areas of less than 16 m2 were notsuitable candidates for this technique (Fig. 3), because the errorof each profile increased as the ground area decreased, with theresult that the error of the composite profile also became higher
for ground areas of less than 16 m2 . A possible reason for thiserror increase is that each lidar’s measurement error in relation
to the range accuracy became non-negligible as the groundarea decreased below 16 m2 . This error increase was larger
for the airborne lidar than for the portable ground-based lidar,
because the range accuracy of the former is 15 cm, whereasthat of the latter is 8 mm. Other possible reasons for this error
increase with decreasing ground area are the heterogeneity of
the canopy and the differences in the positions of the cellboundaries between the direct and lidar measurements [37].
The heterogeneity of the canopy gradually affected the error
below 16 m2 . Moreover, for the stratified clipping, the cellboundaries were measured with a tape measure. As a result,slight differences in the positions of the boundaries could exist
between the lidar measurements and the direct measurements,
which would cause the error to become larger as the groundarea became smaller. This source of error would affect measurements by both lidars. Although not caused by the lidar
measurement itself, this error increases the difficulty of accurate
validation of lidar-derived results. To reduce these sources oferror, LAD estimation by this technique (combining the data of
two types of lidar) should be used for ground areas of sufficient
extent, which, in this study, corresponded to 16 m2 or more.
Because of these considerations, subsequent analyses should bedone for ground areas of 16 m2 or more.
It is obvious that a more accurate LAD estimation obtained ineach lidar offers a more accurate estimation after the combination of both lidars. The LAD estimation accuracy of each lidar
increases when its measurement settings such as the laser beamsettings and the lidar positions are appropriately determinedaccording to the canopy structure. The index Ω was proposed
to be such a criterion for determining appropriate measurement
settings. The Ω index is an indicator of the proportion of
the area of a horizontal plane within the canopy covered bylaser beams. This index depends on the laser beam settings(Abeam , N ) and the canopy structural attributes (K, LAIcum ).

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HOSOI et al.: ESTIMATION AND ERROR ANALYSIS OF WOODY CANOPY LEAF AREA DENSITY PROFILES

Thus, the appropriate settings can be determined according to
the canopy structural attributes. When the value of Ω exceeds
1.0, the laser beams can illuminate the entire horizontal plane,
but when it is less than 1.0, then some parts of the horizontal
plane cannot be illuminated by the laser beams. In the former
case, the LAD error decreases because the number of laser
beams incident into the canopy is sufficient, but in the latter
case, the error increases due to the lack of information about
the canopy caused by an insufficient number of laser beams
incident into the canopy. This explains the results shown in
Fig. 4, in which the LAD error began to drastically increaseat values of Ω near 1.0. Thus, for better LAD estimation, thevalue of Ω should exceed 1.0. In practice, the value of Ω should
be more than 2.0 to be certain of obtaining accurate results.
Therefore, in practical lidar measurements, the measurement
settings such as the laser beam settings and the lidar positions
should be chosen such that Ω becomes as large as possible
exceeding 2.0. In addition, it is notable that a similar tendency
was observed in the relationship between Ω and the LAD error
for both airborne and ground-based lidars in spite of theirdifferent setting values for Abeam and N , as shown in Fig. 4.
This means that Ω can be used to assess the LAD error oflidar measurements made by using different settings and alsosuggests that Ω—that is, the proportion of the area covered bylaser beams in a horizontal plane—is an essential and practicalfactor that relates to estimation accuracy in lidar-based LAD
measurements. This result indicates that Ω can be used to obtainbetter combinations of LAD estimates derived from different
types of lidars. By comparing the values of Ω between the
different types of lidars at each height, it can be determinedwhich lidar’s LAD estimate is more accurate and, thus, which
LAD value should be selected.
A Gaussian function could interpolate well the underestimated part of the LAD profiles obtained by combining theresults from the two types of lidar. With regard to the numberof points picked up for the interpolation, the two points corresponding to the peaks of the two lidar profiles were insufficientfor fitting the Gaussian function; thus, four or more points,
including the two peaks, were picked up. However, the MAEs
were larger when eight points were picked up, compared to thecase with four or six points. In the case of eight points, thesubstructure of the lower layer apparently affects the form of
the fitting function, resulting in an increased error. Thus, thepoints should be selected such that the substructure is not included, as with four and six picked-up points. The interpolation
by a Gaussian function is effective when the LAD profile ismonomodal, as in the present study and a previous study [49].
Monomodal profiles are typical of sites dominated by a single
species [34], [49], [50]. However, at sites where several species
grow, the canopy can have an LAD profile with a multimodal
structure [34], [41]. For multimodal structures, interpolation
can be performed by applying the fitting function to each peakseparately, as suggested by a previous study [34]. The applicability of this method needs to be explored by additional works.
In future works, the applicability of the index Ω should
be assessed through a wider range of scenarios. For instance,
the horizontal extent of the canopy must be considered in theestimation of the LAD for a large area, and we could consider

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adding measurement positions for the ground-based lidar to
reduce the occlusion effect. By determining the positions suchthat the index Ω becomes as large as possible, better estimationof LAD would be obtained. The above interpolation method
would also perform well when the sufficient value of Ω cannot
be obtained. In terms of laser beam penetration into the internal
canopy, the size of Abeam in an airborne lidar should be moreconsidered. In particular, an airborne lidar with a much smaller
Abeam may increase the laser beam penetration through the
canopy. The lidar settings (e.g., flight speed and laser scanningfrequency) could properly be adjusted according to the index
Ω by doing a series of tests for different Abeam values. It
would also be significant for the applicability of the index tobe tested with a lidar system based on a different measurement
principle, such as a waveform-recording ground-based lidar[47]. Moreover, it would be interesting to examine whether
the index is applicable to increase the accuracy of the otherstructural attributes of the canopy measured by lidar systems.
V. C ONCLUSION
Vertical LAD profiles of a woody canopy have been estimated by combining airborne and portable ground-based lidar
data and using the VCP method. The two data sets complemented each other, eliminating the blind regions of thetwo lidars and improving the accuracy of the LAD profiles.
MAEs have been calculated to evaluate the method for different
ground areas, and it has been shown that a ground area ofsufficient extent—16 m2 or more in the present study—yielded
better results. The laser beam coverage index Ω, which incorporates the lidar laser beam settings and a laser beam attenuation
factor, has been proposed. This index can predict the LAD
estimation error of LAD measurements obtained by different
types of lidar and with different laser beam setting values. In
practical lidar-based LAD measurements, this index could be
used as a criterion for determining appropriate lidar measurement settings or for obtaining a better combination of LAD
profiles from different types of lidar. The underestimated partof the composite LAD profile resulting from the combinationof data from the two lidars has been improved by applying
Gaussian interpolation. The methods demonstrated here would
be suitable for other broadleaved canopies. Coniferous canopies
have different structures such as the permanent presence of
foliage material for evergreen species, and the applicabilityof the proposed method should be examined in more detailfor this type of canopy. Moreover, the effectiveness of theindex Ω could be tested in additional scenarios to enhance its
general applicability.
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Fumiki Hosoi received the M.E. and Ph.D. degrees
from the University of Tokyo, Tokyo, Japan, in 1995
and 2008, respectively.
In 1995, he joined the Opto-Technology Laboratory, Furukawa Electric Company, Ltd., Ichihara,
Chiba, Japan. He is currently with the Graduate
School of Agricultural and Life Sciences, Universityof Tokyo.

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Yohei Nakai received the B.E. degree in 2008 fromthe University of Tokyo, Tokyo, Japan, where heis currently working toward the M.E. degree in the
Department of Agricultural and Life Sciences.

Kenji Omasa received the M.E. degree from Ehime
University, Ehime, Japan, in 1975 and the Ph.D.
degree in engineering from the University of Tokyo,
Tokyo, Japan.
He is currently a Professor with the Department ofAgricultural and Life Sciences, University of Tokyo.
His research interests include imaging of cell levelto plants, remote sensing, modeling of ecosystems,
analysis of global change effects on ecosystems, andinformation engineering for biological and environmental systems.

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