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International Journal of Applied Earth Observation and Geoinformation 13 (2011) 792800

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InternationalJournal ofApplied Earth Observation andGeoinformation

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3D modeling oflight interception in heterogeneous forest canopies usingground-based LiDARdata

Dimitry Van der Zande a,b,,Jan Stuckens b, Willem W. Verstraeten c,d, Simone Mereu e,Bart Muys f, Pol Coppin b

a Royal Belgian Institute of Natural Science,MUMM,Gulledelle, 100, BE-1200, Brussels, Belgiumb KatholiekeUniversiteit Leuven, Biosystems Department,M3-BIORES,Willem de Croylaan 34, BE-3001, Heverlee, Belgiumc Royal NetherlandsMeteorological Institute, Climate Observations, PO Box201, NL-3730 AE, De Bilt, TheNetherlandsd EindhovenUniversity of Technology, Applied Physics, PO Box513, 5600 MB, Eindhoven, The Netherlandse University of Sassari, Department of Economicsand Woody Plant Ecosystems, ViaE. De Nicola, 9, 07100 Sassari, ItalyfKatholiekeUniversiteit Leuven, Department of Earthand Environmental Sciences, Celestijnenlaan200E, BE-3001, Heverlee, Belgium

a r t i c l e i n f o

Article history:

Received 17 January 2011Accepted 10 May 2011

Keywords:

Forest canopyTerrestrial LiDARVoxel-based Light Interception Model

a b s t r a c t

A methodology is presented that describes the direct interaction ofa forest canopy with incoming radi-ation using terrestrial LiDAR based vegetation structure in a radiative transfer model. The proposedVoxel-based Light Interception Model (VLIM) is designed to estimate the Percentage ofAbove CanopyLight (PACL) at any given point ofthe forest scene. First a voxel-based representation oftrees is derivedfrom terrestrial LiDARdata as structural input to model and analyze the light interception ofcanopies atnear leaflevel scale. Nine virtual forest stands ofthree species (beech, poplar, plantain) were generatedby means ofstochastic L-systems as tree descriptors. Using ray tracer technology hemispherical LiDARmeasurements were simulated inside these virtual forests. The leafarea density (LAD) estimates derivedfrom the LiDARdatasets resulted in a mean absolute error of32.57% without correction and 16.31% whenleaf/beam interactions were taken into account. Next, comparison of PACL estimates, computed withVLIM with fully rendered light distributions throughout the canopy based on the L-systems, yielded a

mean absolute error of5.78%. This work shows the potential ofthe VLIM to model both instantaneouslight interception by a canopy as well as average light distributions for entire seasons.

2011 Elsevier B.V. All rights reserved.

1. Introduction

Light interception is a driving variable for many key ecosystemprocesses like photosynthesis and transpiration. It was proven tobe the factor that varies most dramatically throughout the canopydepending on its structure (Brunner, 1998) and is fundamental inunderstanding forest stand dynamics, forest growth, forest regen-eration, understory biodiversity, etc.

Given the importance of light for these biophysical processes,many techniques for light measurement and modeling have beendeveloped (Engelbrecht and Herz, 2001; Fermenta et al., 2001) dif-fering on their detail in canopy structure representation. Canopystructure description ranges from a zero-dimensional (0D) object(e.g. Big Leaf models: Wullschleger et al., 2000; Kosugi et al., 2005)

Corresponding author at: Royal Belgian Institute of Natural Science, MUMM,Gulledelle, 100, BE-1200, Brussels, Belgium.

E-mail addresses: [email protected], [email protected](D. Vander Zande).

to a full 3D reproduction of the canopy (Whitehead et al., 1990;Brunner, 1998; Groot, 2004; Piboule et al., 2005). If the level ofdetail at which the structure is described is low, the object/lightinteraction is simplified using statistical approaches.

BeerLamberts law is a widely used radiation model whichdescribes the exponential attenuation of monochromatic radia-tion in a canopy and approximates vegetation as a turbid medium(Monsi and Saeki, 1953; Ross, 1981). It allows the use of envi-ronmental and physiological profiles and achieves a considerableprecision as long as the assumption of horizontal homogeneity ofthe canopy is satisfied.

Theavailabilityof a detailed architecturaldescription of thecon-sidered canopy enables the use of ray tracing technology to tracksimulated solar rays as they originate at a given point in the upperhemisphere and then travel through a geometric representation ofthe forest canopy (Brunner, 1998; Sinoquet et al., 2001; Chen et al.,1994). Detailed modeling of the interaction (i.e. reflection, absorp-tion and transmission) between radiation and individual elements(i.e. leaves, branches, stems, etc.) of the canopy is possible. In the-ory,given a highly detailed 3D description of thestructure,material

0303-2434/$ seefrontmatter 2011 Elsevier B.V. All rightsreserved.

doi:10.1016/j.jag.2011.05.005
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D. Vander Zande et al./ International Journal of Applied Earth Observation andGeoinformation 13 (2011) 792800 79

specificopticalpropertiesandifthescatteringoflightisconsidered,the fidelity of the reproduced light environment is very high. Raytracing technology, however, is limited by technical difficulties ofacquiring a realistic 3D description of the object of interest. A 3Dvegetation structure is not only tedious and time consuming, butalso impossible to obtainin a non destructivemanner forfull growntrees or entire forest stands.

Ground-based LiDAR systems on the other hand are capable

of yielding the necessary structure information for geometricallyexplicit models with a level of detail that depends mainly ontwo factors: the resolution of the LiDAR dataset and the den-sity of vegetative elements (i.e. leaves, branches, stem, etc.) inthe scenery of interest (Van der Zande et al., 2008, 2011). Therequirements of geometrically explicit light models are best metwhen the actual 3D distribution of above-ground density of phyto-elements (leaf, stem, twig, etc.) is available. This 3D structure isoften represented by the leaf area density (LAD) per volume unit,where LAD is defined as the total one-sided leaf area per unitvolume (Weiss et al., 2004).

Traditional radiative transfer models (e.g. turbid mediummodel and multi-layer model) are limited by a basic structuredescription of forest canopies and as such they deliver averagelight interception or irradiance values for the entire canopies.In contrast, a light interception model combining LiDAR dataand ray-tracing technology has the potential of studying theactual relationship between canopy architecture and light regimes.Since light conditions for each individual element (i.e. voxel)in the 3D space can be considered, dynamic leaf-level modelsdescribing biophysical processes like photosynthesis and tran-spiration can be used. For example, the contribution of a singlevegetative element to the whole biophysical process in a tran-spiration process modeling study (Van der Zande et al., 2009)and in light regimes in homogeneous Populus stands (Van derZande et al., 2011). While these studies are promising, elabo-rate testing of the methodology combining low resolution LiDARscanning with ray tracing technology is required to determine itsactual potential for light interception determination at the standlevel.

The main objective of this research is to perform an accuracyassessmentof the proposed Voxel-based Light Interception Model(VLIM) which describes the light absorption by forest canopiesat the voxel level by combining ground-based LiDAR data withphysical radiation modeling. Since detailed reference data of theactual 3D structure of forest stands and light distribution insidetreecrownsarescarce(Ctetal.,2009), a virtual environment waschosen in this study. Current technologies cannot retrieve detailedreference data of light interception at leaf-level in a full grownforest canopy yet. Working with virtual photo-realistic deciduousforest stands, ray tracing technology for LiDAR simulation, andphysically based light/vegetation interactions as reference data,makes it feasible to study the functionality of the VLIM as a func-

tion of tree structure and light dispersion inside the canopies indetail.

2. Materials andmethods

Anoverviewof the differentsteps of the methodologyis giveninthe following paragraphs and schematically represented in Fig. 1.

Fig. 1. Schematicrepresentation of theaccuracy assessment of theproposedVoxelbased Light Interception Model (VLIM).

2.1. 3D canopy simulation

The required level of structure detail and the ability to simulate light environments under controlled conditions was obtainedfrom virtual forest stands generated using stochastic L-systemas tree descriptors. L-systems are sets of rules and symbols thamodel growth processes and are named after Lindenmayer (1968From a remote sensing modeling point of view, realistic descriptions of the forest stand should comply with three main criteri

and based on: (i) architectural growth processes capable of simulating various tree species over various conditions (tree age, plandensity, etc.); (ii) on experimental data; and (iii) the capacity oproviding realistic 3D trees (Castel et al., 2001). The forest standwere simulated using the dynamic plant modeler and plant nursery natFX which interfaces withan architectural plant model calleAMAPmod (Bionatics, CIRAD, Montpellier, France). The AMAPmod software allowed a photo-realistic visualization of the foresscenery, including botanically correct forest tree models and ibased on a standardized method of describing and codingthe structural relationship between different tree components (e.g. leavesbranches,stem)created by means of analysis of the rules in individualtree species using a large amount of field measurements of eachspecies (Godin, 2000). Nine homogeneous forest plots with fully

grown broadleaf trees of three important species (Fig. 2) of Flanders, Belgium (Fagus sylvatica L., Platanusacerifolia (Ait.) WilldPopulus nigra L. var. italica Muenchh.) were simulated. Each ploconsisted of 16 individual and structurally different trees of thsame species placed in a regular pattern with 8m tree spacingresulting in a total plot size of 30m30 m (Fig. 3). Each tree wamodeled separately and thus unique in terms of foliage distribution, branch patterns, height, and stem shape. The regular pattern

Table 1

Structural characteristics of simulated trees and forest stands.

Species Mean height (m) Mean crown diameter (m) Mean leaf zenithangle () Stems (ha) Mean canopy closure (%)

Fagus sylvatica 13.87 10.15 42.47 156 93.26Platanusacerifolia 18.81 12.27 51.53 156 91.14

Populus nigra 19.97 5.26 72.40 156 65.21



794 D. Vander Zande et al./ International Journal of Applied Earth Observation andGeoinformation 13 (2011) 792800

Fig. 2. Full grown broadleaftreesof three species simulated in a virtual environment:(a) Fagussylvatica, (b) Platanusacerifolia, and (c) Populus nigra. Structural differencesare visible in thevertical Leaf Area Density (LAD) distributionprofiles (d) and theleaf zenith distributions (e).

was rotated 15 in azimuth to avoid strong lineareffects in thesim-ulation of theLiDAR measurementsdescribed below. Each tree was

characterized by a specific structure based on its age (i.e. 20 yearsold) as shown in Table 1. The leaf density of the tree crowns wasadjusted by randomly removing leaves enabling the generation offorest stands with different LAI settings.

This resulted in three forest scenes per species with LAI-valuesof 2, 4, and 6. Although no competition between the trees in thecanopy could be simulated, the architectural differences betweenthe species (Fig. 2ac) resulted in a structurally diverse group offorest plots enabling an analysis of the accuracy of the VLIM to

Fig. 3. Schematic overview of the virtual built-up of the virtual forest stands. 16trees were positioned in a regular pattern that was rotated 15 in azimuth to avoidstrong linear effects in the simulation of the LiDAR measurements. Five individ-ual hemispherical laser measurements were performed in the center of the stand

positioned in the diamond shape set-up.

describe the light environment inside a forest canopy. The foreststand structures varied significantly as illustrated by comparing

the actual vertical leaf surface distributions and leaf angle distri-bution. They were directly derived from the virtual forest stands(Fig. 2d and e). Only stems and first order branches are included inthe modeled trees due to the resolution settings of the used LiDARsystem.

2.2. Laser measurement simulations

For both LiDAR data simulation and the subsequent light inter-ception modeling, a Physically Based Ray-Tracer (PBRT) was used(Phar and Humphreys, 2004). Using this ray-tracer, viewing rayscanbe shot into a scene to seewhether they interact with any of theobjects in the considered 3D volume, whichstronglyresembles theLiDAR principles. The low resolution Laser Measurement System

200 (LMS200,SickAG, Germany)specifications wereusedas a stan-dardtemplateto characterize simulatedlaser beams and geometricmeasurement pattern (GMP). The LMS200 is a non-contact opticalactive sensor which scans its direct surroundings in a 2D pattern.A 3D hemispherical measurement pattern is enabled by mountingit on a rotating table (for details see Van der Zande et al., 2006).Each beam was described by its polar coordinates (, ), wherethe zenith angle () ranged from 0 to /2 and the azimuth angle() f r o m 0 t o 2. The zenith and azimuth resolutions were fixed at0.25and 0.1respectively andbeam divergence wasset at 4.36mrad.Laser beam divergence was taken into account by generating mul-tiple random rays within a small solid angle. LiDAR datasets weregenerated by setting the light source (point light source) and cam-era (hemispherical camera) exactly in the same location. Since the

LiDAR device is a first return laser scanner, simulation was lim-




Table 2

mean absolute percentage error (MAPE) of leaf area density (LAD) estimations for the different forest stands, with and without correction for leaf/beam interactions (i.ecos(beam)[G(beam)1]).

Forest stand LAI Mean n o. leaves/voxel MAPE L AD (%) ( normal) MAPE L AD ( %) ( corrected) Shadowing (%) ( normal) Shadowing ( %) ( corrected)

Fagus 2.00 1.13 12.40 7.28 9.57 0.91Fagus 4.00 1.26 28.16 11.19 26.63 9.13Fagus 6.00 1.38 39.09 18.19 40.35 18.82Plantanus 2.00 1.08 23.36 9.60 17.49 1.70Plantanus 4.00 1.16 34.19 10.76 30.64 2.04

Plantanus 6.00 1.24 42.84 11.48 43.36 4.62Populus 2.00 1.23 23.23 17.44 7.08 0.11Populus 4.00 1.35 39.54 25.27 30.97 14.48Populus 6.00 1.52 50.35 34.60 45.18 25.16

ited to single scattering. For each generated ray, the distance to thefirst object intersection was recorded. For minimizing shadowing(the occlusion of canopy elements by others from the viewpointof the LiDAR instrument), five individual hemispherical laser mea-surements were performed in each forest stand positioned in thediamond shape set-up. A single hemispherical laser measurementwas positioned in the center of the forest plot and one in each ofthe four cardinal points(north, east, south, west) with a displace-mentof 0.5m fromthat center (Van der Zande et al., 2008) (Fig. 3),

all at a height of 1.5m. The diamond set-up yields a better lasercoverage of the forest stands in comparison with a single high res-olution hemispherical laser measurement because of the multiplemeasurement points.

2.3. Laser data pre-processing

After registration, the five hemispherical laser scans resulted ina total of 6,480,000 separate distance measurements in each for-est stand used to create a detailed structural representation of themeasured canopy. The 3D space considered with a ground surfaceof30m30m and a height of 25m was systematically subdividedinto small cubic voxels of 0.1m0.1m0.1m. This resulted inarrays of 300300250 voxels. The voxel size was set at 0.1m to

obtainsufficientdetail(sizeapproximatedtheactualleaf)andavoidthe use of a statistical description of the leaf distribution (Table 2).All laser beams emitted from the different measurement positionswere traced through the voxel array. Following the methodologyofHosoi and Omasa (2006), the voxels were characterized by thetypeof beam/voxel interaction.Voxels withat leastone interceptedlaser beam were given the attribute F (filled). Voxels intersectedby laser beams without interception have the attribute E (empty).Only the laser beams exiting a voxel in the opposite side as fromwhich they entered were considered for further processing. Thisensured a minimal travelingpath of 0.1m through the voxel whichis required for an accurate characterization. Attribute X (no data)was granted to voxels that were not touched by any laser beam. Ingeneral, the probability of a voxel to be reached by a laser beam

is negatively correlated with (i) the distance of that voxel to thelaser position, and (ii) the canopy density causing shadowing (Vander Zande et al., 2006). This results in a lower beam density, andthus in a higher proportion of voxels with attribute X, in the upperpart of the canopy when the laser scanner is placed below the treecanopy measuring upwards (Lovell et al., 2003; Van der Zande etal., 2008). To obtain an accurate and complete structure descrip-tion of the canopy from LiDAR datasets, these X voxels needed tobe given an attribute F or E. 1000 small voxels were grouped intolarge voxels of 1m 1 m1m and for each of these large voxelsthe contact frequency (CF) was calculated as follows:

CF =

h+h

k=h

nf(k)

nF(k) + nE(k) (1)

WithnF(k) the numberof small voxelswithattribute F andnE(k)thnumber of voxels with attribute E. h is the vertical thickness oflarge voxel, h andh+hdenotethe height of thebottom and topothevoxelrespectively.Compensation for leaf/beaminteraction wadescribed by the correction factor cos(beam)[G(beam)

1] enablinto calculate the effective contact frequency:

CFeff =

h+

k=h

cos(beam)

G(beam)

nF(k)

nF(k) + nE(k) (2

where beamrepresents the mean zenith angle for all laser beampenetrating the voxel.G(beam) is the mean projection of a unit leaarea on a plane perpendicular to the direction of the laser beamat beam(Welles and Norman, 1991; Jonckheere et al., 2004; Weiset al., 2004). The term cos(beam)[G(beam)

1] describes the probability of a laser beam that enters a filled voxel to actually hit thleaf or leaves inside that voxel as a function of laser beam andleaf inclination angles. It corrects for the situation that voxels werincorrectly given the attribute E while they were actually filledUsing this correction factor, randomly chosen empty voxels (witattributeF) were considered filled to compensate forthe leaf/beam

interactions. The effective CF for each large voxel was then extrapolated to the voxels which could not be reached by any beam (withattribute X). This procedure was followed for the voxel data of ninforest stands.

The accuracy of the corrected LiDAR data was tested by comparing the retrieved vertical LAD distributions from the voxel datwith the actual LAD values. Only voxels containing leaves werconsidered. Since the LiDAR datasets were obtained in a virtuaenvironment, direct comparison of the voxel array with the actuavirtual forest scenes allowed for a direct segmentation of the filledvoxels into leaf (Fleaf) and stem voxels (Fstem). In case a filled voxecontained leaf and stem material, the predominantly element waused to identify the voxel. In case of an equal presence of leaand stem material, a leaf voxel was assigned. LAD values wer

reproducedusing thecontact frequencyand thefollowingequatio(Hosoi and Omasa, 2006):

LADvoxel =

cos(beam)

G(beam)

1

H

h+h

k=h

nFleaf(k)

nFleaf(k) + nFstem(k) + nE(k) (3

Vertical LAD profiles derived from the LiDAR datasets usingEq. (3) were compared with reference profiles calculated from thvirtual forest stands for direct evaluation of the voxel-based representations.TheaccuracyoftheLADestimationsandthusthequalityof the LiDAR data, is quantified with the mean absolute percenerrors (MAPE) between the estimated and reference LAD profile

for the nine forest stands.




Fig. 4. Theleaves of thevirtual referencetrees(a) were represented as a collection of trianglesshaping theleaves (b). A voxel-based representationof theforest standswasgeneratedfromthe simulatedLiDAR measurements(c) andeach of thefilled leaf voxels(small redvoxel) was abstracted by a disc forray tracing purposes (c andd). Both thereferencetrees andthe voxel/disc representationwere used to determinethe light distributionby renderingthe foreststands with a path tracing algorithm using a modifiedversion of thePBRT path tracer (d and e).The LiDAR-based light distributions were then compared to thereference light distributionfor validation purposes.

2.4. Reference data for light interception

Reference data for the accuracy assessments of the VLIM wasprovided with generated forest stands in the Physically Based Ray-Tracer (PBRT), an accepted algorithm in the scientific communityaccording to the RAMI Online Model Checker (ROMC) (Widlowski

etal.,2008) asindicatedby Stuckenset al. (2009). Thetermlightwillbe used for photosynthetically active radiation (PAR). Leaves andstems were represented by triangle meshes as obtained from theAMAPmod simulated canopies. All leaves were assigned a constantreflectance and transmittance of 6.50% in the PAR (400700nm).Trunks and branches were assigned a constant reflectance of 18.0%and 0% transmittance. These data were derived by averaging mea-sured reflectance spectra of healthy leaves and trunk over the400700nm range and are supported by findings ofHosgood et al.(1994). The forest scene illumination was composed of a combina-tion of direct and diffuse light that was modeled to closely agreewith the average circadian illumination from April until Septem-ber, correspondingto a mid-latitude northernhemisphere growingseason. For each month, the average hourly direct and diffuse irra-

diance (PAR) and solar positions for Brussels, Belgium (lat. 50.85,

lon. 4.37) were obtained from Meteosat data recorded from 1996until 2000 (www.satel-light.com, Hammer et al., 1998). Averagedirect solar illumination was simulated in the ray-tracer at theaverage monthly solar positions from 5.30am until 9.30pm athourly intervals, from April until September. Diffuse irradiancewas simulated by producing a homogeneous skymap (i.e. illumi-

nation from each spherical direction is constant) for the sameperiod.

Light interception was calculated by placing virtual cameras onboth surfaces of 20 000 randomly chosen leaves within the fullcanopy. Eachcamera recorded theaverage seasonal irradianceontothe leaf surface. Irradiance was composed of direct irradiance, dif-fuse skylight irradiance and first order scattering irradiance fromneighboring leaves. For each virtual camera, irradiance was com-puted by integrating the radiance (with cosine correction relativeto the leaf normal) of 256 rays originating from a random posi-tion at the leaf surface pointing into a random spherical direction.The modeled irradiance was expressed in terms of Percentage ofAbove Canopy Light (PACL) which shows the irradiance reachinga certain camera relative to the initial irradiance reaching the top

of canopy (see above). To exclude edge effects, light interception
http://www.satel-light.com/http://www.satel-light.com/




Fig. 5. The vertical LAD profiles derived from the LiDAR scans (normal and corrected) of the beech stands with LAI 2 (a), LAI 4 (b) and LAI6 (c) compared with the referencLAD profiles.

computations were limited to the four central trees in the 16 treedatasets.

2.5. Voxel-based Light Interception Model (VLIM)

The VLIM is a light interception model designed to estimatethe PACL at any given point in the forest scene using a ter-restrial LiDAR derived voxel-based representation of the trees.Light interception for the VLIM and reference dataset was cal-culated analogous. The main difference is the applied geometricrepresentation of leaves and stems. LiDAR derived voxels repre-senting leaf material were abstracted by discs with a fixed area of0.01m2, a random azimuth angle and a fixed zenith angle corre-sponding to the average zenith angle of the tree being simulated

(42.5, 51.5, 72.4 for Fagus, Platanus and Populus respectively)(Fig. 4).

All leaves were assigned identical optical characteristics as usedforthe reference data set. Voxels representingtrunks andbrancheswere abstracted by a volume grid and placed in a 3D grid. Eachtrunk/branchvoxel wasassignedan infiniteoptical thickness. Otherempty voxels were assigned zero optical thickness. Illuminationconditions and camera description were identical to the referencesimulations. Since geometrically explicit leaves were used for boththe reference and VLIM dataset, PACL was determined using theactual light/leaf interactions.

Shading by neighboring crowns is a major constraint on theavailable light of trees in the forest stand and should be sim-ulated as realistically as possible. The considered voxel volume

(30m30 m25m) wasdividedintotwosubvolumes:(i)thecen-tral zone and (ii) the buffer zone surrounding the central zone. Thevolume of the central zone measured 15m15 m25m and thewidth of the buffer around this central area was 7.5 m in all direc-tions. Per light interception calculation, a total of 20,000 randomlychosen leaves in the central zone of the forest stand were sampledto obtain a detailed overview of the light interception within thecanopy.

3. Results and discussion

3.1. 3D LiDAR representation

The quality of the 3D representation was studied by assess-

ing the accuracy of the LiDAR derived LAD modeling. Fig. 5 shows

the vertical LAD profiles for the three beech stands with varyingLAI allowing a direct comparison of the modeled LAD distribution with the reference data. Also a profile corrected for leaf/beaminteractions, using the correction factor described in Eq. (2), ipresented. A general underestimation in LAD, which increasewith increasing total LAI and with height, is present. An overviewof the mean absolute percent errors (MAPE) between the estimated LAD profiles and the reference values for the nine foresstands are presented in Table 2. Additional information on thaverage number of leaves per voxel of 0.1m in size and the percentage of voxels that were not sampled by a single laser beam(i.e. shadowed voxels) is also provided. The LiDAR derived LADmodeling technique resulted in a mean MAPE value of 32.57%and 16.31% for the uncorrected and corrected LAD estimations

respectively.Errors in LAD measurement were caused by the angular mea

surement pattern and shadowing which resulted in variable lasebeam densities throughout the measured volume. With decreasing laser beam density with height, the LAD modeling accuracdecreased as supported by findings ofHosoi and Omasa (2007who studies factors contributing to the accuracy of LAD estimations using a high resolution LiDAR system. They also stated thathe presence of non-photosynthetic tissues and G(beam) stronglyaffected the accuracy of LADestimates. While the angular measurement pattern is device dependent, shadowing can be minimizedusing the diamond sampling design (i.e. multiple viewing angles(Van der Zande et al., 2008). The shadowing was corrected for bgiving an attribute E or F to the X-voxels dependent on the CF o

the voxels in their direct vicinity. Values were on average reducedfrom 27.92% to 8.55% with this procedure. As shadowing is linkedto canopy density, also MAPE values increased with increasinLAI.

Differences in LAD modeling efficiency between the different species are caused by varying laser beam distributioninside the forest canopies (Van der Zande et al., 2008). Foexample, the modeling process yields a higher reduction othe MAPE values for LAD for the Platanus stand while similar levels of shadowing are present compared to the Populustand. This was due to localized high densities of the leaves ithe Populus stands which are more impenetrable for the lasebeams.

While the reference LAD profiles were calculated considering

all the leaves it is possible that the presence of grouped leave




Fig. 6. Distribution of leaves as a function of received PACL for the Fagus (a), Platanus (b) and Populus (c) stands with LAI 2, 4, and 6 resulting in an overview of the lightavailability throughout thecanopy. Thefully rendered light distributions arealso illustrated as a referenceand areindicated with ref.(df) Show thepercentage differencebetween the modeled and reference light availability dataset.

by relative positioning and clumping would result in lower con-tact frequencyvalues andthus lower LAD estimates. Still, clusteredleaves can be accurately represented by a single voxel since lighttransmittance of a single leaf (6.50% transmittance) only differsminimally from two or more stacked leaves (0.42%) within thePAR-range.

3.2. Voxel-based Light Interception Model

Nine modeled light interception datasets (i.e. 3 tree species3leaf densities) consisting of 20,000 sampled points located on ran-domly chosen leaves in the central zone of the forest stand wereavailable for comparison. Fig. 6 shows the leaf distribution as a

Fig. 7. Vertical light extinction in terms of PACL for the Fagus (a), Platanus (b) and Populus (c) stands. (df) show the percentage difference between the modeled and

reference light extinction profiles.


http:///reader/full/3d-upscaling-of-transpiration-from-leaf-to-tree-using-ground-base


Fig. 8. 3D visualizationof light interception calculated with theVLIM forthe Fagus (a), Platanus (b) and Populus stand (c) with LAI 4.

function of received PACL illustrating the canopy light availabilitytogether with the fully rendered light distributions from the refer-ence data. Fig. 6 indicates minimal errors comparing modeled andreference light interceptions, although a general overestimation isobserved with occasional underestimations of light interception inthe lowest light classes. This overestimation of light interception isdirectly caused by the error in LAD estimation allowing too muchlight penetration. Even after correction, shadowing is still respon-sible for an underestimation in LAD modeling causing the VLIM to

underestimate light attenuation.A vertical light extinction profile through the canopywas calcu-

lated for each of the nine light distributions (Fig. 7) for retrievingthe accuracy of the VLIM as a function of the vertical location inthe canopy. Also the reference profiles were provided for directcomparison.

As a general measure of accuracy,the MAPE of PACL estimationsperheight binwere calculated for the differentsituations (Table 3).

Comparing the modeled light extinction profiles with the ref-erence data resulted in an average MAPE of 5.78%. According toBeerLamberts law, the mean average percentage of light reach-ing the forest floorfor canopies withLAI-values of 2, 4 and 6 shouldbe 25.43%, 8.29% and 2.14% respectively.

Using VLIM, the mean PACL reaching the floor was 31.73%,

26.36% and 19.57% for the scenarios with the same LAI-valueswith a significant difference between the three species (Fig. 7).The main difference between the two approaches is caused by thecanopieswhich are not homogeneous.Irregular gapswith a hetero-geneous distribution allow additional light to reach lower parts ofthe canopy. The differences in light penetration for the canopieswas also reported by de Castro and Fetcher (1999) stating thatcanopy light transmittance showed a positive linear relationshipwith percent of clustering of which the slope increased with LAI.

Fig. 7 shows a decrease of accuracy of the modeled light inter-ception with increasing LAI. This occurred for two reasons. Firstly,an increase in leaf density resulted in a less accurate geometricdescription of the forest stand as indicated by the increasing MAPEvalues of LAD estimations (Table 2). Secondly, because of higher

Table 3

Meanabsolutepercentageerror (MAPE) of Percentageof AboveCanopy Light(PACL)estimationsper height bin for thedifferent modeled light distributions.

Forest stand LAI MAPE (%)

Fagus 2.00 2.83Fagus 4.00 5.59Fagus 6.00 7.89Plantanus 2.00 1.78Plantanus 4.00 2.95Plantanus 6.00 5.43Populus 2.00 5.81Populus 4.00 7.40Populus 6.00 12.38

Average 5.78

leaf densities, more complex leaf/light interactions are modeledimplying a potential error increase. Populus stands with LAI 4 and6 (Fig.6a) suffered from a significant shadoweffect dueto localizehigh leaf densities not corrected with modeling. Low shadowing values in the Platanus stands resulted in more correct result(Fig. 6b). The profiles show a typical exponential extinction of lighdownwards through the canopy.

The incident radiation per sampled leaf during an averaggrowth season for the spatially regular Fagus, Platanus and Pop

ulus stands with LAI 4 is shown in Fig. 8. The leaves were classifieinto five classes according to their average incoming radiationcomparedtotheinitialincidentradiationabovethecanopyforvisu-alization purposes: 020%, 2040%, 4060%, 6080%, 80100% andan extra class was added forthe voxels containing stem and brancmaterial.

Fig. 8 illustrates the distribution of the different light classeand how they are shaped according to the main structure of thtree crowns. The threeforest canopies have thesameamountof leamaterial butshow distinct differences in canopystructure and thulightpenetration. The Fagus canopywas typified by a closedcanopywherethe individual tree crowns were still observable as they werdelineated by large gaps in the higher parts of the canopy betweenneighboring tree tops. Through these gaps, light penetrated deepe

into the canopyin comparison to the Platanus canopy. The Platanucanopy showed morehorizontalhomogeneityas theindividual trecrowns were bigger causing a more uniform closure of the canopanda higher light attenuation.The Populus stand consisted of individual trees without any real crown closure. This resulted in higlight penetration between the crowns which allowed the light treach the tree crowns from multiple angles.

As can be seen in Fig. 8, the level of detail of light interceptionmodeling of the VLIM allows studies on the interaction betweenlight and canopy at near leaf level scale. While these findings arpromising, it is noted that the results were obtained under perfecvirtual measurement conditions. In reality, additional errors in thdifferentmodelingstepswill be unavoidable. In addition to the discussed shadowing, the accuracy of the LiDAR data will also suffe

from errors during the registration process, leaf angle measurements and leaf/stem segmentation algorithms. Other effects whichcandecreasethe accuracy of theproposed model arewindand edgeffects. The edge effect is caused by the imperfect scanning of thedge of vegetative elements such as branches, stems and leavesThis results in incorrectly measured points or ghost points whiccan effect following processing steps. While such ghost points arnot present in the virtual dataset, they could significantly affectreal LiDAR data, especially when measuring complex objects liktrees. This would require removal of these ghost points before thLiDAR data can be used. Nevertheless, the accuracy of the modeledlight interception for the nine forest stands illustrated the VLIMfunctionality in light interception modeling for forest stands withvarying structural composition in terms of leaf density, leaf distri

bution and leaf angle distribution. Also, the flexibility of the VLIM




allows theuse of differentvoxel sizes adapted to the measured for-est canopy characteristics such as size, clumping and amount ofleaves. Still, additional research is needed to better understand theimpactof the choice ofvoxel sizeon the accuracyof the canopyandlight modeling. Since high-resolution scanners will deliver evenmore detail, they will therefore provide the option to decreasethe size of the small voxels. This allows adjustments to the VLIMfor trees with small size or the width/length ratio of the leaves

(coniferous trees). Considering the filling up of the shadowed vox-els more fundamental methods need to be developed. A possibleapproach might be the one described by Ct et al. (2009) whichis based on radiative transfer modeling to estimate the light pen-etration to these areas with shadowed voxels and determine themaximum quantity of leaves a tree can grow withinthat area giventhe available light.

4. Conclusions

The proposed VLIM creates the possibility to studyphotonvegetation interactions at a high level of detail with-out expensive equipment or labor-intensive direct measurements.Simulated low resolution ground-based LiDAR data were used

to obtain a detailed structural representation of the forest scenefor light interception modeling purposes. Virtual forest scenesand LiDAR data were used to access the accuracy of the recentlydeveloped technique. Using the VLIM it was possible to obtaingood estimates of light interceptionfor different forest stands withonly small errors. As general illumination depends of geographicallocation and climate conditions, the VLIM was designed so thatdifferent initial light conditions could be used. This flexibilityenabled instantaneous light interception estimates as well as aver-age light distributions for entire seasons. Future work will focuson method optimizing, especially in increasing the accuracy of thevoxel-based representation of the forest canopies derived fromLiDAR measurements. As shadowingwill be an ever present factor,methods to correct for its influence will be further investigated.

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