Retrieval of forest structural parameters usinga ground-based lidar instrument (Echidna®)

Alan H. Strahler, David L.B. Jupp, Curtis E. Woodcock, Crystal B. Schaaf,Tian Yao, Feng Zhao, Xiaoyuan Yang, Jenny Lovell, Darius Culvenor,

Glenn Newnham, Wenge Ni-Miester, and William Boykin-Morris

Abstract. A prototype upward-scanning, under-canopy, near-infrared light detection and ranging (lidar) system, the Echidna®

validation instrument (EVI), built by CSIRO Australia, retrieves forest stand structural parameters, including mean diameterat breast height (DBH), stand height, distance to tree, stem count density (stems/area), leaf-area index (LAI), and standfoliage profile (LAI with height) with very good accuracy in early trials. We validated retrievals with ground-truth datacollected from two sites near Tumbarumba, New South Wales, Australia. In a ponderosa pine plantation, LAI values of 1.84and 2.18 retrieved by two different methods using a single EVI scan bracketed a value of 1.98 estimated by allometricequations. In a natural, but managed, Eucalypus stand, eight scans provided mean LAI values of 2.28–2.47, depending onthe method, which compare favorably with a value of 2.4 from hemispherical photography. The retrieved foliage profileclearly showed two canopy layers. A “find-trunks” algorithm processed the EVI scans at both sites to identify stems,determine their diameters, and measure their distances from the scan center. Distances were retrieved very accurately (r2 =0.99). The accuracy of EVI diameter retrieval decreased somewhat with distance as a function of angular resolution of theinstrument but remained unbiased. We estimated stand basal area, mean diameter, and stem count density using theRelaskop method of variable radius plot sampling and found agreement with manual Relaskop values within about 2% aftercorrecting for the obscuring of far trunks by near trunks (occlusion). These early trials prove the potential of under-canopy,upward-scanning lidar to retrieve forest structural parameters quickly and accurately.

Résumé. Un lidar proche infrarouge prototype à balayage vers le haut et opérant sous le couvert, l’instrument EVI(Echidna® validation instrument), construit par CSIRO Australia, a permis d’extraire les paramètres structurels despeuplements forestiers incluant le diamètre moyen à hauteur d’homme (DBH), la hauteur du peuplement, la distance parrapport à l’arbre, la densité des tiges (tiges/surface), l’indice de surface foliaire (LAI) et le profil du feuillage du peuplement(LAI plus hauteur) avec une très bonne précision lors des premiers essais. Nous avons validé les extractions avec desdonnées de réalité de terrain acquises sur deux sites situés près de Tumbarumba, New South Wales, en Australie. Dans uneplantation de pins ponderosa, les valeurs de LAI de 1,84 et de 2,18 extraites à l’aide de deux différentes méthodes utilisantun seul balayage de EVI ont enregistré une valeur de 1,98 estimée selon les équations allométriques. Dans un peuplementd’eucalyptus à l’état naturel mais sous gestion, huit balayages ont donné une valeur de LAI de 2,28 à 2,47, dépendant de laméthode, ce qui se compare favorablement avec la valeur de 2,4 dérivée de la photographie hémisphérique. Le profil dufeuillage extrait montrait clairement deux couches de couvert. Un algorithme pour trouver les troncs (« find trunks ») atraité les balayages d’EVI pour les deux sites dans le but d’identifier les tiges, de déterminer leurs diamètres et de mesurerleurs distances à partir du centre du balayage. Les distances ont été extraites de façon très précise (r2 = 0,99). La précisionde l’extraction des diamètres d’EVI a diminué quelque peu avec la distance en fonction de la résolution angulaire del’instrument, mais elle est demeurée non biaisée. Nous avons estimé la surface terrière du peuplement, le diamètre moyen etla densité des tiges à l’aide de la méthode Relaskop d’échantillonnage à rayon variable et nous avons trouvé uneconcordance avec les valeurs manuelles de Relaskop à l’intérieur de 2 % après correction pour le phénomène des troncsarrières qui sont cachés par les troncs plus en avant (occlusion). Ces premiers essais démontrent le potentiel du lidar opérantsous le couvert et à balayage vers le haut pour l’extraction rapide et précise des paramètres structurels de la forêt.[Traduit par la Rédaction]

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Received 21 February 2008. Accepted 23 June 2008. Published on the Canadian Journal of Remote Sensing Web site athttp://pubs.nrc-cnrc.gc.ca/cjrs on 28 November 2008.

A.H. Strahler,1 C.E. Woodcock, C.B. Schaaf, T. Yao, F. Zhao, X. Yang, and W. Boykin-Morris. Department of Geography andEnvironment, Boston University, 675 Commonwealth Avenue, Boston, MA 02215, USA.

D.L.B. Jupp and J. Lovell. CSIRO Marine and Atmospheric Research, P.O. Box 3023, Canberra, ACT 2601, Australia.

D. Culvenor and G. Newnham. CSIRO Forest Biosciences, Private Bag 10, Clayton South, Victoria 3169, Australia.

W. Ni-Meister. Department of Geography, Hunter College of the City University of New York, 695 Park Avenue, New York, NY10065, USA.

IntroductionRapid and accurate measurement of vegetation structure,

particularly that of forests, is an important goal forbiogeoscience applications, including carbon balance modelingand the surface radiation balance modules of regional andglobal climate models (Hyde et al., 2006). Light detection andranging (lidar) is particularly well suited to this task, since itallows accurate measurement of light scattering by vegetationlayers, and a number of recent papers have documented theapplication of downward-looking airborne lidar for thispurpose (Lim et al., 2003, provides a recent review). Some ofthese papers have focused on small-footprint (usually less than1 m diameter) lidars that are used primarily for topographicmapping (e.g., Lim and Treitz, 2004; Hudak et al., 2006). Theseinstruments typically return the distance to the first and lastscattering events, which provides canopy height and itsvariance. By contrast, wide-footprint aircraft research lidarshave been designed particularly for vegetation studies. Theyhave a footprint typically ranging from 15 to 30 m, dependingon altitude, and digitize the full-waveform return; examples arescanning lidar imager of canopies by echo recovery (SLICER;Means et al., 1999) and laser vegetation imaging scanner(LVIS; Blair et al., 1999). Both instruments yield signals thatcorrelate well with canopy structural parameters. A review inthe context of the present work and its ground-basedinstrumentation can be found in Jupp et al. (2005b).

Many previous studies have used ground-based lidar forforest structural assessments. However, they have to dateconcentrated on the use of simple lidar rangefinders (Wellesand Cohen, 1996; Radtke and Bolstad, 2001) or discrete-returnlidar systems (Parker et al., 2004; Van der Zande et al., 2006).The latter have shown the ability to measure bole diameter andstem count density with good accuracy (Hopkinson et al., 2004;Watt and Donoghue, 2005; Henning and Radtke, 2006).Regarding leaf area index (LAI), Lovell et al. (2003), in a pilotstudy for our present effort, retrieved LAI and foliage profileusing a discrete-return lidar system in an Australian eucalyptforest that matched LAI from hemispherical photographswithin 8%. Most recently, Clawges et al. (2007) demonstratedmeasurement of leaf area using discrete-return lidar by imagingseveral young larch trees before and after leaf fall. Workingwith the lidar instrument described and used in this paper, Juppet al. (2008) described the theory for and demonstrated retrievalof LAI and the foliage profile from a waveform-digitizingground-based lidar.

This study serves to further validate retrieval of foreststructural parameters using a ground-based, waveform-digitizing lidar, the Echidna® validation instrument (EVI), builtby CSIRO Australia, with ground-truth data collected from aconifer plantation and a natural forest stand located in NewSouth Wales, Australia.

Echidna validation instrument and studyarea

The Echidna validation instrument (EVI) is based on aconcept for an under-canopy, multiple-view-angle, scanninglidar, with variable beam size and waveform digitizing termedEchidna. The Echidna has been patented in Australia, theUnited States, New Zealand, China, and Japan, with patents inother countries pending.2 The EVI, which is the first realizationof the Echidna concept, utilizes a horizontally positioned laserthat emits pulses of near-infrared light at a wavelength of1064 nm. The pulse is sharply peaked so that most of the energyis emitted in the middle of the pulse. The time length of thepulse, measured as the time at which the pulse is at or abovehalf of its maximum intensity, is 14.9 ns, which corresponds toabout 2.4 m in distance. Pulses are emitted at a rate of 2 kHz.The pulses are directed toward a rotating mirror that is inclinedat a 45° angle to the beam. As the mirror rotates, the beam isdirected in a vertical circle, producing a scanning motion thatstarts below the horizontal plane of the instrument, rises to thezenith, then descends to below the horizontal plane on the otherside of the instrument. Coupled with the motion of the mirror isthe motion of the entire instrument around its vertical axis,rotating the scanning circle through 180° of azimuth. In thisway, the entire upper hemisphere and a significant portion ofthe lower hemisphere of the instrument are scanned (Figure 1).

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Figure 1. Schematic of the Echidna validation instrument (EVI)components.

2 US patent 7,187,452; Australian patent 2002227768; New Zealand patent 527547; Japanese patent 4108478.

Although the laser beam is a parallel ray only 29 mm inwidth, it passes through an optical assembly that causes thebeam to diverge into a fixed solid angle. This expansion of thebeam with distance allows the laser pulses to census the entirehemisphere. The size of the solid angle can be varied from 2 to15 mrad. The rotation speeds of the mirror and the instrumenton its mount are also varied so that the hemisphere can becovered slowly by many fine pulses or rapidly by fewer coarserpulses.

As the light pulse passes through the forest, it may hit anobject and be reflected. The light is scattered back toward theinstrument and focused on a detector that measures theintensity of the light it receives as rapidly as 2 gigasamples persecond. Since the pulse is traveling at a known speed, the timebetween emission of the pulse and its receipt at the detectorindicates the distance to the object. At its most rapid samplingrate, the sampling distance is about 7.5 cm, but the range to thepeak of a pulse can be determined more accurately byinterpolation after digitizing. The output of the detector isdigitized electronically and stored by computer to provide afull-waveform return that records the scattering of the pulsefrom within a metre or less of the instrument to about 100 maway. More information on the EVI and its early trials can befound in Jupp et al. (2005b).

Data from the EVI and coordinated ground measurementswere acquired within the Bago-Maragle Forest (35°36 2 42′ ′′. S,148°06 29 25′ ′′. E), New South Wales, Australia, in November2006 at two different sites. The pine site was located in a twice-thinned, 30-year-old plantation of Pinus ponderosa managedby the New South Wales Forestry Department. Site LAI wasnot observed independently but was estimated as 1.98 usingallometric equations for ponderosa pine (Jupp et al., 2008).Here, EVI scans were acquired at a single instrument location.In manual measurements, the diameter at breast height (DBH)of each stem within a 50-m radius of the instrument wasrecorded, along with the distance and compass bearing to thestem.

The tower site was located in a large area of native forest thathas been used for wood production for many years. Eucalyptusdelagatensis and Eucalyptus dalrymplean dominate the open,wet sclerophyll forest, with canopy heights around 40 m. Thecanopy contains two more or less distinct layers, with a sparseupper story of large crowns and a denser understory of shrubsand small trees. Using hemispherical photographs, Leuning etal. (2005) determined the LAI to be about 1.4 for the upperstory and about 1.0 for the lower shrub layer. At the tower site,eight instrument scans were positioned in eight cardinalcompass directions arranged in a square with sides of 200 m,northeast, southeast, southwest, and northwest at the fourcorners of the square, and the Tumbarumba flux tower(Leuning et al., 2005) at the center of the square. Manual stemmeasurements at the eight scan points used the Relaskopmethod (Bitterlich, 1947; 1956), in which a variable-radius plotsample is selected with probability proportional to the DBH ofeach stem. The DBH, distance to tree, and compass azimuthwere recorded for each tree sampled. An alternate systematic

sample of four trees, chosen as the first tree encountered inazimuth sectors of 90° width, were measured for height andcrown shape.

MethodologyThe main approaches we have used to analyze the data from

the EVI have been described in Jupp and Lovell (2005a) andJupp et al. (2005b; 2008). Briefly, there are two modes ofanalysis, namely direct “object” measurement and statistical or“stand” measurement. If the beam size is small, the returns willbe a few separated “hits” at measurable distances withreflectances that depend on the object shape, orientation, andbasic (diffuse) reflectance at the wavelength of the laser. Large“hard” targets usually return a single “hit,” and diffuse targets,such as leaves and small stems, can return many (see Figure 2).

Direct measurement can be used to sample individual treesfor trunk size and growth form, and these can then be combinedto estimate stand statistics. It is relatively straightforward tounderstand this form of measurement. In contrast, the statisticalapproach involves two steps. One is to process the signal toapparent reflectance, and the other to interpret it.

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Figure 2. Typical waveforms digitized by the EVI. (a) Waveformreturned from a trunk. The shape of the waveform echoes thesteep, but Gaussian shape of the lidar pulse. (b) Waveform returnfrom scattering by canopy leaves. The waveform shows asuperposition of several small Gaussians, indicating multiple “hits”from clumps or clusters of leaves.

Calculation of apparent reflectance (ρapp) is basically acalibration step and is defined as

ρτ

appR B

a

=−Φ Φ

ΦTCR

22 (1)

where ΦR is the (filtered) received power from the target, ΦT isthe energy output at the laser oscillator exit aperture, τa is theatmospheric transmission through a distance R at wavelength λ,R is the distance from the laser transmitter (and receiver) to thereflecting object, C is the system calibration factor, and ΦB isthe background radiation field that contributes to the measuredsignal.

The statistical model for the calibrated data is

ρ ρ ρappA

v FC vgapd

d( )

( )

( )( ) ( )r

r

C r

E r e

t EP r

P

rr= − = = −

2

20

(2)

where r is the range, C is the instrument optics calibrationfactor, E is the measured power, E0 is the signal energy atsource, tA is the atmospheric transmission, e is the backgroundsignal power, ρv is the effective volume reflectance, PFC(r) isthe probability of first contact at range r, and Pgap(r) is theprobability of gap between the source and point at range r.

If the returns are combined statistically or the beam size isincreased, the waveform becomes more closely related with thestatistics of the canopy. A primary statistic is the probability ofa gap to a given range as defined previously. Another is thesecond-order probability of a gap to a range in one directionand to a different range in another.

We have used a number of these approaches in this paper. Forexample, LAI and foliage profile measurements are based onstatistics of gap probability with range in a particular directionas measured by the return lidar waveform from that direction.The statistical approach also provides the ability to estimatecanopy parameters through a canopy reflectance model (e.g.,the GORT model; Ni-Meister et al., 2008). On the other hand,stem DBH, count density, and related descriptors are derivedfrom a “find-trunks” algorithm that recognizes individual treestems in a horizontal data slice at or near the height of theinstrument (Jupp et al., 2005b).

LAI and foliage profile

Overall LAI and the vertical foliage profile (called“structure” by some people) play prominent roles in climateand ecosystem models (e.g., Bonan, 1996; Sellers et al., 1997).To retrieve LAI, optical methods that rely on the measurementof light transmission through the canopy are in wide use, assummarized most recently by Bréda (2003). However, thefoliage profile is currently only measured with great difficultyand high variance in the field. The analysis of these data is oftenbased on the following simple relationship:

P(θ) = exp[–G(θ)L/cos θ] (3)

where P(θ) is the gap probability through the complete canopyfrom the ground at zenith angle θ, L is the leaf area index, andG(θ) is the fraction of the leaf area projected on a plane normalto the zenith angle θ (Ross G function; Ross, 1981). Invertingthis relationship for L,

LP

G= − ln ( ) cos

( )

θ θθ

(4)

Thus, the leaf area index L may be retrieved from the gapprobability if the G function is known and the model isappropriate. If the G function is not known, Warren-Wilson(1963) showed that the G-function pivots around a “hingeangle” θ ≈ tan–1(π/2), or 57.5°, at which the value of G/cos θ isabout 0.9 for all leaf angle distributions. Following Jupp et al.(2008), we refer to 57.5° as θHA, and thus

L P≈ −11. ln( gap, HA) (5)

where Pgap,HA is the gap probability at θHA. In the more generalcase, we can consider leaf area index as a function of height z inthe canopy, which varies from 0 at the base to H at the top, andcompute

L z P( ) . ln(≈ −11 gap, HA(z)) (6)

The foliage profile f(z) is then obtained as

f zL z

z( )

( )= ∂∂

(7)

In this paper, we follow the procedure outlined in Jupp et al.(2008) for deriving Pgap(θ, z) from Echidna lidar returnsaveraged within “zenith rings” or solid angles containing allzenith angles within a zenith increment (e.g., 5°) and over allazimuths. To retrieve zenith ring values, digitized lidar returnsare converted to apparent reflectance and scaled as described inJupp et al. As described previously, using a zenith ringcontaining θHA allows an estimate for L and foliage profile to bederived. However, as shown later in the paper, although thisapproach provides a useful and simple estimate, it tends to benoisy and only sample a part of the stand.

The situation can theoretically be improved using multiplezenith rings. First, following ideas in Lang (1987; 1991) andCampbell (1986), Jupp and Lovell (2005a) and Jupp et al. (2008)use a simple linear model for the Ross G function and for theproportion of the LAI at a particular zenith angle in terms ofhorizontal (Lh) and vertical (Lv) components of the LAI:

Lh + LvX(θ) ≈ –ln Pgap(θ, H) (8)

where X(θ) = (2 tan θ)/π, and L = Lh + Lv. Following this model,their procedure fits a simple linear regression to values of X(θ)and –ln Pgap(θ, H) for zenith rings, usually from 5° to 60°,yielding the slope and intercept Lv and Lh, respectively. The

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retrieved value of L is then based on up to 11 zenith rings (theexact number depending on the range of angles where the laserbeam emerges from the top of the canopy) rather than one.

Second, to overcome the variation in the single-angleestimate of the foliage profile, Jupp et al. (2008) suggested asolid angle weighted profile that reflects the unbiased average.The average normalized foliage profile is defined as follows:

L z P z

P H

( ) log ( , )

log ( , )LAIgap

gap

=θ

θ

f zz

P z

P H( )

log ( , )

log ( , )= ∂

∂LAI

gap

gap

θ

θ(9)

where the notation θ is to be taken as an indication that thenormalized data have been averaged over zenith angle ratherthan a mean angle. Both estimates are used with the field data inthe analysis of the site data.

As a technical point, we note here that the leaf area indexretrieved by optical methods, including hemisphericalphotography, sunfleck ceptometers, the commonly used LAI-2000 (LI-COR, Inc.), and the EVI, usually includes not onlyleaves but also fine branches and small stems, and so issometimes referred to as a “plant area index” or “surface areaindex” (Bréda, 2003). Moreover, the processing described hererepresents a “standard” approach and does not address theeffects of clumping (Chen et al. 1991; 2003) on the estimate.These effects, together with the morphological issuesassociated with the recognition of small gaps, which modifyLAI in the opposite direction from clumping, are under activeresearch. The Echidna is already providing a rich and valuabledata source for the investigations.

Trunk identification

A lidar return from a tree trunk, when the beam is assumed tobe fully within the angular span of the trunk from the EVIstation, can be looked at as a reflection from a “wall,” possiblyat a sloping angle to the beam, and at a specific range. The

projection shown in Figure 3, where a horizontal cross sectionof the laser returns is estimated, has the potential to provideinformation such as tree size and basal area as a function ofheight, which can provide volume estimates or mean taper(form factors) at plot or stand level.

Because the EVI pulse is quite broad in time, the signalappears to be distributed in range, even for a target that is asolid wall. This is shown in Figure 3 by the “smear” of thetargets. However, since the pulse has a very clear and sharppeak, it is possible to recognize a pulse from noise and identifythe peak position. By convention we have taken the time at thepeak of the pulse as it leaves the EVI as zero EVI time andrange. By locating the peak of a return from a hard object, thetime difference between the outgoing peak and the(interpolated) return peak provides an estimate of the (true)range to the hit. A shot that is positioned at one edge of the treebut still fully within the trunk is a useful edge point to locate. Itcan be modeled as one in which the central azimuth is IFOV/2back from the extreme edge azimuth. The objective is toidentify the shots that are all “within” the trunk and to assumethat those at either end of the sequence of “tree” returns arecritically within the trunk, in that the outer edge of the beam isjust grazing the trunk tangent. To get an estimate of the angularspan of the tree (assuming the end shots are right out to theedges), the beam IFOV is added to the angular span betweenthe end shots.

The geometry and notation being used are shown inFigure 4. The range to the central point is denoted R, and it isassumed that the tree has a diameter D. The EVI scan is marked“EVI,” and the outer tangents to the tree define the (true) fullangular span of the tree from the EVI station. For a given shot,the angle between the normal to the tree and the shot is denotedψ, and the angle between the shot and the path to the centralpoint on the trunk is denoted ξ. The complete angle between thetangent shots to the trunk is denoted φspan. At the “central” pointof the lidar return, the apparent reflectance will be maximal.For a model tree of the kind shown in Figure 4 which is closeenough to be resolved by a number of shots, we can compute,for each shot, the ratio of apparent reflectance to that at themaximum (nearest front and central) point of the tree:

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Figure 3. EVI lidar returns, processed as a color composite of three horizontal planes below, at,and above instrument height for the Tumbarumba pine stand. The horizontal axis is azimuth, andthe vertical axis is distance from the instrument. Vertical linear features are individual trunks,which appear elongated by the length of the lidar pulse. Features acquire color when returns aredifferent at different heights, for example, due to leaning or bending of the trunk.

ρρ

ψψ

app

max

= < >< >

cos

cos max

< ≈cos maxψ > 1 (10)

where < cos ψ > denotes the mean cosine within the pixel. Forshots away from the center, the average cosine could be takenas the cosine at the azimuth of the pixel center. Taking thecosine at the center of the range as an estimate of the average,and assuming that the scan is horizontal and that the “tree” is avertical cylinder with constant diameter D, we can derive anumber of useful quantities. Assuming that the full angularspan (span between the nominal bearings of the end shots plusthe IFOV) is φspan as defined by the two tangent points acrossthe tree, it follows that if the range to the center of the treesurface nearest the EVI is R and the tree diameter is D, then therelationship between the three is

tD

R D= =

+sin( / )

/

/φspan 2

2

2

D Rt

t=

−2

1(11)

Thus bearing, distance, and DBH for individual trees can beestimated from EVI data using these relationships and drawnon a stem map as “EVI trees.” The value of estimating angularspans is that Relaskop-type methods can theoretically be usedto estimate basal area. As described later in the paper, however,

the success of the method depends on handling occlusion oftrees by other trees and foliage as well as achieving accuracy inthe estimation of angular spans at the distances involved.

These equations assume a horizontal scan of a vertical trunk.However, it is possible to modify them for the case of a gentleto moderate slope. Note that EVI can “see” the horizon and soobserve the slope angle and orientation at each scan location.Two approaches are possible. First, diameters can be retrievedin a horizontal plane, with DBH values adjusted for the truedistance between the horizontal plane and the tree base using anaverage taper factor. Second, DBH can be determined in a planeparallel to the slope, since EVI has a full circle of observationsin that plane for gentle to moderate slopes. These approacheshave not yet been implemented.

To investigate the lidar retrievals of canopy parameters, fieldmeasurements were also collected manually. Since the EVI is ata fixed location, not all of the trees will be “visible” (in thesense that the laser beam does not illuminate them), since theymay be obscured by plant material closer to the EVI, and somemay only be partly visible. For the field records, there weretherefore three classes of tree established according to visualestimates from the plot center: (i) fully visible tree in which thefull span of the trunk in a height range can be seen by theobserver; (ii) partly occluded trees in which parts are obscuredbut the centerline of the trunk is visible (this may occur fromone or both sides); and (iii) occluded trees, which are assumedto be obscured if the centerline is not visible to the observer.These estimates of visibility were at times difficult to make andthus contain some errors.

Stem count density and mean DBH retrieval

Using Echidna as a RelaskopThe Echidna was used in a manner similar to that of a

Relaskop during the data processing. The basic Relaskopmethod (Bitterlich, 1947; 1956; Holgate, 1967; Bell andDillworth, 1988) uses a wedge or instrument that enables theoperator to select trees (the “in” trees) for which the angularspan across the tree as seen from a central point of a field site isgreater than a given value. The Relaskop can measure the standbasal area (G) by tallying the number of “in” trees visible fromthe center of the site. Trees around an observation point canalso be confirmed to be “in” or “out” based on the DBH of eachtree and its distance to the sample point. Taking these additionalmeasurements for the “in” trees provides estimates of diameterdistribution and tree density in addition to stand basal area. Ifthere are m “in” trees at a site, the estimated stand basal area ata site is

G m= = ×λBA BAF (12)

where λ is the tree density (number of trees per square metre orper hectare); BA is the mean tree cross-sectional area (squaremetres) at breast height for the stand (or mean individual treebasal area); and BAF is the basal area factor, which includesfactors relating to the size of the angular wedge used to define

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Figure 4. Geometry of EVI trunk returns.

the “in” trees and also factors to bring the stand basal area intothe units that are convenient to the user. In practice, theRelaskop angle is selected so that BAF is a convenient number(such as 2 m2/ha). Using this method, small trees in the neardistance can be seen, and only large trees at farther distancescan be counted “in.” The “in” trees therefore form a biasedsample with probability of selection proportional to the cross-sectional area of the tree.

The basal area of an individual tree is the cross-sectional areaat breast height. That is, BAindividual = π(DBH/2)2. Therelationship between the probability of selection discussedpreviously and the size of the stem is simply prob ∝BAindividual.Using these ideas, an estimate for the density of trees at a site isprovided that is not affected by the bias involved in selectingthe “in” trees. The estimate is

λ ==∑ BAF

BAindividual, jj

m

1

(13)

Because of the bias in selection of the trees, if a quantity isrelated to tree DBH, then the “in” trees are not an unbiasedsample of that quantity, and so the mean and variance of thequantity need to be corrected for the bias. For example, if q(D)is a quantity that depends on D for a tree (e.g., diameter, cross-sectional area, height, crown size, volume), then it can beshown that the following estimate is not biased:

q W q Dii

m

i==∑

1

( )

σ2 ( ) [ ( ) ]q W q D qii

m

i= −=∑

1

2 (14)

Wii

i

m

j

=

=∑

BAF / BA

BAF / BA1

Because the Echidna data have been processed to provideangular span, it is possible to make similar estimates based onthe Relaskop theory and carry out equivalent measurements inthe field using a traditional Relaskop instrument and processingfor comparison and validation.

Occlusion correctionIn the use of the Relaskop data in the way described

previously, it is assumed that every “in” tree can be seen fromthe central point. This is usually achieved in practice by theoperator changing position to see behind occluding near trees tosee a more distant “in” tree. However, the Echidna as used inthis experiment cannot move in this way, and so the bias due toobscuring of trees by other trees and foliage needs to becorrected.

It can be shown from geometrical probability arguments thatwith horizontal attenuation of the form Pgap = exp(–λDEz)

N D RR

D RD R D R( , ; )

( )[ exp( )( )]λ πλ

λλ λE

EE E= − − +2

1 12

2(15)

where N(λ, DE; R) is the number of trees “apparently” withinradius R, given a true tree count density of λ and an effectivetree diameter of DE. We can use DE = D + δDE, δDE ≥ 0, whereD is the mean diameter of the tree trunks, and the added termtakes into account low branches, understory etc. DE depends onthe stem density and distribution in the sample plot. Theproduct λDE is the overall attenuation in units of m–1 that couldbe estimated from the Pgap in the 85–90° zenith ring. As adefault, we may use

D D CE V≈ +( ) /1 2 1 2

where C V2 is the squared coefficient of variation for tree

diameters. By manipulating Equation (15), we may obtain

N D R N R F t( , ; ) ( ; ) ( )λ λE = 0

F tt

t t( ) [ exp( )( )]= − − +21 1

2(16)

t D R= λ E

N R R02( ; )λ λπ=

in which the number of trees N(λ, DE; R) within distance Rexpected with occlusion is the product of the true expectednumber N0(λ; R) and a factor F(t) that depends on λDE.Applying this to the Relaskop equations and assuming thecoefficient of variation of tree sizes is not too large, it isstraightforward to show that

M D M F t( , ; ) ( )λ α = 0

tD D

=λ E

BAF2(17)

where M(λ, D; α) is the expected number of “in” trees observedwith occlusion for Relaskop wedge angle α, and M0(λ, D; α) isthe true expected number. The function F(t) is as defined inEquation (16), but with the argument t as shown in Equation(17). Note that BAF must be expressed here in square metres ofbasal area per square metre, not square metres per hectare.

ResultsPine site

LAI and foliage profileFigure 5A shows the regression of –ln(Pgap) against X(θ) =

(2 tan θ)/π, following Equation (8), for the 11 zenith ringsbetween 5° and 60°. According to the regression, Lh = 0.59 ±

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0.12 and Lv = 1.25 ± 0.23, giving a value of Lreg = 1.84 ± 0.26.This value is somewhat smaller than LHA = 2.18 retrieved at thehinge angle alone, which is consistent with the position of thiszenith ring above the regression line in Figure 5A. Althoughthere are no independent field measurements of leaf area indexat this site, Jupp et al. (2008) reported a value of L = 1.98 usingAmerican allometric equations for ponderosa pine (Law et al.,2001) as applied to measured diameters of trees in a 50-mradius from the instrument.

Figure 5B shows the foliage profiles derived from the hingeangle only and from an averaged gap function for 11 zenithrings. The averaged profile is clearly smoother than the profileobtained at the hinge angle. The derived profile fits ourexpectation for a tall, even-aged plantation with a reducedunderstory rather well.

Trunk identification and stand parametersFigure 6 shows an image of the Tumbarumba pine site

obtained from the EVI scan. Displayed is the mean lidar return,averaged over range in an equal-angle azimuth (x axis) andzenith (y axis) grid. Figure 7 shows a stem map for the site. Theblue circles indicate the locations and DBHs of the stems asthey are retrieved from EVI data using the find-trunksalgorithm applied to an apparent reflectance horizontal slicesimilar to that shown in Figure 3. Of the 102 trees manuallyrecorded within a 50-m radius of the instrument, the find-trunksalgorithm found about 40% using the EVI data (Table 1). Ofthese, about half were judged visible, one quarter were judgedpartially occluded, and one tenth were judged occluded.

We evaluated the performance of the find-trunks algorithmby comparing measured distances and DBHs with retrievedvalues for trunks in both sets of data. Here we excluded trees ofdiameters ≤ 2 EVI beam widths, which were regarded as toosmall and (or) too far from the instrument for accurate retrieval,leaving 22 trees at distances ≤ 30 m for analysis. Distance totree is retrieved with very high accuracy (r2 = 0.99), which isnot surprising given the range resolution of EVI. Diameters ofnear trees were retrieved with better accuracy than those of fartrees, as might be expected.

Given the noise in DBH retrieval, we processed both datasetsin a Relaskop mode, identifying “in” trees that would have beenobserved with a basal area factor of 2 m2/ha. Table 2summarizes the results. Both of the Relaskop retrievalsmatched the field measurements of basal area, mean DBH, andstem count density very well. As might be expected fromocclusion, the Relaskop method applied to the EVI data foundone fewer tree and slightly underestimated basal area and stem

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Figure 6. Equal-angle projection of the mean lidar return, scaled by squared range, for theTumbarumba pine site. The horizontal axis is azimuth, the vertical axis is zenith angle, andnadir is at the top.

Figure 5. Leaf area index (LAI) retrieved from the Tumbarumbapine site. (A) Regression model for LAI. (B) Foliage profiles forregression and hinge angle retrievals. Profiles are scaled to thetotal LAI retrieved using the regression method.

count density. We did not correct the EVI data for occlusion,since the formulas given in Equation (15) are inappropriate fora plantation with a systematic distribution of stems. The meanDBH was very close to the true mean. In this even-aged stand,all the “in” trees were relatively close to the instrument, and allhad about the same diameter.

Tower site

LAI and foliage profileThe LAI and foliage profile for each of the eight

measurement locations around the tower were calculated in themanner described for the pine site. Table 3 shows LAIretrievals for each site and their averages for both hinge angleand regression methods. Both the simple average of the eightscans and the LAI values derived from averaged Pgap values areshown. In general, regression and hinge angle values are quitesimilar for the eight scan sites. Figure 8 shows the foliageprofile for each scan using the regression method based on 11zenith rings and the regression-method profile for all eightlocations using averaged Pgap values. The canopy clearly hastwo layers that are separated by a region of reduced leaf area atabout 20 m, with the leaf area of the upper layer somewhatgreater than that of the lower layer. The profiles also show someindividual variation. For example, the east site (EE) has a highLAI in the lower layer and a somewhat reduced LAI in theupper layer. The west (WW) and northwest (NW) sites havelower overall leaf area, with a less prominent lower layer. At thewest site, the upper layer is much thinner than that at other sites.The average LAI of the eight profiles is 2.26. Dividing theaverage profile in two at 20 m, the LAIs in the upper and lowerlayers are 1.42 and 0.84, respectively. These compare quite

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Figure 7. Stem map of the Tumbarumba pine site. Blue circlesindicate DBH and location of trunks retrieved using the find-trunksalgorithm; green, magenta, and red circles locate stems manuallymeasured within a 50-m radius and observed as visible, partiallyoccluded, or occluded, respectively. Diameters are shown on anexaggerated scale. Black circles indicate dead trees.

Occlusioncategory

No. of treesmeasured

No. ofmatching treesfound by EVI

Percentidentified

Visible 61 34 55.7Partially occluded 21 5 23.8Occluded 20 2 10.0Total 102 41 40.2

Table 1. Tree counts for the Tumbarumba pine site, comparingtrees located and measured and matching trees retrieved by thefind-trunks algorithm.

Parameter

Fieldmeasurement(all trees)

Relaskopmeasuredtrees

RelaskopEVI trees

No. of trees 102 13 12Basal area (m2/ha) 28.4 26.0 24.0Mean DBH (m) 0.53 0.54 0.52Standard error of

sample, σ (m)0.12 0.08 0.08

Standard error ofmean, σM (m)

0.012 0.023 0.024

Stem count density,λ (no. of trees/m2)

0.0128 0.0140 0.0110

Table 2. Stand parameters retrieved at the Tumbarumba pine site.

Figure 8. Vertical foliage profiles for eight scans at theTumbarumba tower site. Profiles are scaled to the leaf area indexretrieved using the regression method. The average profile isderived from averaged Pgap data.

favorably with the Leuning et al. (2005) LAI estimate fromhemispherical photographs of 1.4 and 1.0.

Trunk identificationRather than inventory all trees within a fixed radius of the

instrument location, we used a Relaskop at the tower site toselect a basal-area weighted sample of “in” trees at each EVIlocation, using a basal area factor of 2 m2/ha. For this factor, thewedge angle is 1.62°, or 28.3 mrad (milliradians). Since theEVI scans at a rate of 4 mrad with a 5 mrad beam divergence,“in” trees will be more than 6 EVI pixels wide, allowing forbetter accuracy in determining tree diameter.

Table 4 shows how the find-trunks algorithm performed atindividual sites and for all sites pooled together. It identified86% of all “in” trees judged visible, 38% judged partiallyoccluded, and 20% judged occluded. All told, the find-trunksalgorithm found 102 of 163 “in” trees for an identification rateof 62%. Best performance was at the north (NN) and northeast(NE) sites, where a reduced shrub layer allowed bettervisibility. The heavy shrub layer at the southeast (SE) site, asshown in the foliage profiles of Figure 8, caused difficulty forthe find-trunks algorithm. Figure 9 shows EVI mean-returnimages for the northwest (NW) site, where the algorithmperformed well, and the southeast (SE) site, where it performedpoorly.

Figure 10 shows reduced major axis regressions of measuredand retrieved distance and DBH for all matching trees at allscans. Distance is retrieved exceptionally well (r2 = 0.99), butDBH is less accurate. As expected, r2 is higher for trees close tothe instrument, with values of 0.660 for trees at 0–10 m, 0.429for trees at 0–20 m, and 0.335 for trees at 0–30 m. However, theestimates are unbiased in this sample, since confidenceintervals on slopes include unity.

Stand parametersTable 5 summarizes the timber stand parameters retrieved

using three methods: “Relaskop” indicates manualmeasurements of “in” trees; “EVI” indicates measurementsderived from EVI “in” trees using the same Relaskop criteria;and “adjusted EVI” indicates measurements that have beencorrected for occlusion according to the Methodology section.

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Visibilitya Field EVI Match (%)

EEV 14 12 85.71P 4 0 0.00O 3 1 33.33All 21 13 61.90

NEV 9 9 100.00P 4 1 25.00O 1 0 0.00All 14 10 71.43

NNV 12 11 91.67P 3 3 100.00O 2 0 0.00All 17 14 82.35

NWV 12 12 100.00P 4 3 75.00O 2 1 50.00All 18 16 88.89

SEV 11 6 54.55P 7 3 42.86O 3 1 33.33All 21 10 47.62

SSV 14 12 85.71P 7 2 28.57O 3 0 0.00All 24 14 58.33

SWV 7 5 71.43P 15 7 46.67O 1 1 100.00All 23 13 56.52

WWV 12 11 91.67P 9 1 11.11O 4 0 0.00All 25 12 48.00

AllV 91 78 85.71P 53 20 37.74O 19 4 21.05All 163 102 62.58

aO, occluded; P, partially occluded; V, visible.

Table 4. Tumbarumba tower site stem map statisticsfor individual sites and for all sites pooled together(EVI versus field “in” trees).

EVI scan Lv Lh Lreg LHA

NN 2.14 0.17 2.31 2.42SE 1.45 0.67 2.12 2.07EE 1.96 0.56 2.52 2.50NE 2.35 0.14 2.49 2.61NW 1.22 0.65 1.87 1.82SS 1.42 1.09 2.51 2.45SW 2.15 0.40 2.55 2.43WW 1.24 0.62 1.86 2.12Average of scans 1.74 0.54 2.28 2.30Profile average 1.57 0.69 2.26 2.47

Table 3. Retrievals of leaf area index at tower scan sites usinghinge angle and regression methods.

For the Relaskop and EVI entries, basal area is simply theproduct of the number of “in” trees and the basal area factor of2 m2/ha. Mean DBH is an average of values for the “in” treesweighted by their basal areas, which provides an unbiasedmean (Methodology section). The standard error of the mean isalso based on weighted values. Stem density is a sum of stemdensity values for individual “in” trees, each weighted by itsbasal area.

At five of the eight sites, the find-trunks algorithm foundfewer trees than were manually identified with the Relaskop,which would be expected given the occlusion present in theEVI scans. At the remaining three sites, the find-trunksalgorithm found more trees. Considering all sites, 163 “in”trees were found with the Relaskop, and the find-trunksalgorithm identified 143 “in” trees. Accordingly, EVI tallies amean basal area that is about 11% lower and estimates a stemdensity that is 9% lower. A t test of these pairs of means showsthat neither pair is significantly different, with significancelevels of 0.256 and 0.803 for mean basal area and stem density,respectively. However, this is a test with quite low power, basedon the number of samples (8) and their variance, and we canexpect that the effects of occlusion will be detected with moreprecision when a larger sample is used. With the effects ofocclusion corrected, the EVI retrievals of basal area and stemdensity closely approach the Relaskop retrievals. Both fallwithin 2%, and significance levels are 0.865 and 0.974.

Basal-area weighted mean diameter using “in” trees producesa mean diameter that is about 11% larger than the Relaskop meandiameter. Near trees are most heavily weighted in the mean and,

as shown in the regression of 0–10 m distance (Figure 10), thereare more trees with diameters overestimated than underestimatedin this range. Still, the difference is not significant, with aprobability of 0.248, despite the large number of samples, due tothe large underlying variance in DBH.

DiscussionOverall, our study shows the great potential value of the

Echidna under-canopy, upward-scanning lidar (as realized bythe EVI instrument described in Jupp et al., 2005b) to measureforest stand structural parameters with ease and high accuracy.However, as a technology still in development, moreimprovements will be needed to achieve this goal with a laserscanner.

Leaf area index (LAI) measurements are of great value inmodeling applications but are difficult to make objectively andrepeatedly (Bréda, 2003). Destructive sampling, although mostaccurate, is extremely costly and time-consuming. Allometricequations, which may be used to estimate LAI from DBH,DBH and height, or sapwood area, are site dependent and maynot generalize well to trees with a wide range of growth formand damage frequently seen in forest management applications.Nondestructive optical methods are in wide use but requireexacting conditions for forest applications, including a uniformsky for hemispherical photographs, clear skies for under-canopy sunfleck probes, and a need for both above- and below-canopy measurements for angular optical sensors such as theLAI-2000.

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Figure 9. Equal-angle projections of the mean lidar return, scaled by squared range, fornorthwest (NW) (upper image) and south (SE) (lower image) scans at the Tumbarumba towersite. The horizontal axis is azimuth, the vertical axis is zenith angle, and nadir is at the top.

The Echidna concept, as implemented in the Echidnavalidation instrument (EVI), provides an optical approach withmany advantages. Because illumination is provided by thelaser, LAI retrieval does not depend on sky conditions.Moreover, the instrument digitizes the full-waveform return,and thus associates scattering events with their three-dimensional position in the canopy. This allows themeasurement of gap probability as a function of range anddirection over a complete hemisphere, which in turn allowsderivation of both LAI and the foliage profile. In addition, theability to discriminate between return pulses striking trunksfrom return pulses that strike more diffuse targets provides away of reducing the effect of trunks and branches on theestimate of LAI.

In this paper we have explored LAI retrieval using the EVI ina conifer plantation and a natural, although managed, eucalyptforest using the approach of Jupp et al. (2008). Although ourresults for these sites do not have a full and complete validation,

retrievals using several different approaches are consistent andagree with what is known about the sites. Based on the abilityto census the entire hemispherical field and beyond, as well asobserve scattering as a function of range, the Echidna approachshould provide more accurate results than alternate methods,and we are presently conducting a more intensive validation ofEVI LAI retrievals in New England forests.

Optical LAI retrievals are also known to be sensitive toclumping, which causes underestimates of leaf area (Chen andCihlar, 1995a; 1995b). Although we have not resolved thecompensating interactions between clumping and dilation ofsmall gaps in Echidna, the ability to measure scattering as afunction of range and angle clearly opens the door to finding thedistribution of within- and between-crown gaps directly from theoptical measurements. Not only is gap distribution useful forretrieving more accurate LAI, but it is also a key parameter invegetation canopy reflectance models. We can anticipate that the

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Figure 10. Comparisons of distance and diameter (DBH) retrievals using the find-trunks algorithm at theTumbarumba tower site.

Echidna will become an important source of directmeasurements of gap and clumping parameters in the future.

We have also demonstrated the use of the EVI to locate treesand measure their trunk diameters automatically, thus providingretrievals of such stand parameters as basal area and stem countdensity. The present version of the find-trunks algorithm couldbe improved, for example, by enhancing its vertical tracing ofstems. Looking at the mean return images of Figures 5 and 9, itis obvious that most trees are imaged well enough at some heightto allow accurate diameter retrievals, and a more complex but“smarter” algorithm should be possible.

Although we have not explored the problem of topographicslope in this paper, we should note that a gentle to moderateslope should not provide a significant limitation of the method.In an earlier section titled Trunk identification we outlined twoapproaches to retrieving proper DBH values on sloping terrain.For LAI and the foliage profile, all that is needed is to transformheight to height above terrain. Although somewhat tedious, allthe equations presented in this paper can be transformed into aspace with a z axis that does not intersect the x–y planeorthogonally. This allows the trees to be represented verticallyabove a sloping ground plane. Derivation of the appropriate

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Source Basal area (m2/ha) Mean DBH ± σM (m)Stem density,(no. of trees/m2) “In” treesa

EERelaskop 42 0.14±0.027 0.150 21EVI 46 0.17±0.032 0.100 23Adjusted EVI 50.3 0.110 25.2

SERelaskop 42 0.15±0.027 0.110 21EVI 30 0.21±0.048 0.053 15Adjusted EVI 32.2 0.057 16.1

SSRelaskop 48 0.27±0.054 0.061 24EVI 40 0.25±0.053 0.058 20Adjusted EVI 44.9 0.065 22.4

SWRelaskop 46 0.15±0.026 0.100 23EVI 22 0.41±0.110 0.012 11Adjusted EVI 23.4 0.013 11.7

WWRelaskop 50 0.23±0.039 0.061 25EVI 46 0.28±0.053 0.050 23Adjusted EVI 52 0.057 26

NWRelaskop 36 0.48±0.110 0.016 18EVI 30 0.49±0.120 0.014 15Adjusted EVI 33.4 0.016 16.7

NNRelaskop 34 0.13±0.028 0.130 17EVI 36 0.10±0.021 0.210 18Adjusted EVI 38.4 0.224 19.2

NERelaskop 28 0.19±0.042 0.046 14EVI 36 0.16±0.034 0.088 18Adjusted EVI 38.6 0.094 19.3

AllRelaskop 42.0±2.86 0.22±0.017 0.085±0.017 163EVI 37.4±3.14 0.25±0.019 0.078±0.024 143Adjusted EVI 41.3±3.27 0.084±0.028 156.7

aNumber of stems included using Relaskop method.

Table 5. Tumbarumba tower site stand parameters retrieved using three different methods.

formulas and testing on sloping terrain will be the subject offuture work.

The use of the Echidna as a virtual Relaskop to construct abasal-area weighted sample of trees provides a good responseto the difficulty of identifying far-field trees and finding theirdiameters. Since the Relaskop method is angle-based, itmatches well with the angular data acquired by the Echidna.Accuracy of diameter retrieval could be enhanced by using asmaller angular measurement interval, for example, 3 mradinstead of the present 4 mrad.

The problem of occlusion of distant trunks by near trunks isamenable to both theoretical and practical solutions. From thepractical perspective, it makes sense to locate the instrument ata point where it is not too close to nearby trees that wouldunduly block the field of view. Since this position will be morelikely to be under a gap in the canopy, it will bias LAI retrievalsin the uppermost zenith ring, and accordingly we do not use the0–5° zenith ring for LAI retrieval. However, it should not affectretrievals of stand parameters, since they are derived from amuch larger area. It may also make sense to clear near shrubsand low branches so that they do not obscure large sectors ofthe field of view. With a field of view cleared of near and largeimpediments, the correction for occlusion is likely to workbetter. We also note that the random occlusion model is notappropriate for a plantation where trees are spaced moreregularly. However, it is not difficult to derive an occlusionfunction for a systematic grid, provided the instrument islocated at a carefully chosen position relative to the standgeometry, and this limitation should not be as much of aproblem in the future.

The ability of Echidna to image near-field trees from groundto top also presents an opportunity to sample stem andbranching characteristics, such as taper and sweep, which areoften used in forest mensuration. We can envision augmentinga Relaskop-type sample with a selection of “measure trees” forwhich additional form and canopy data are acquired eitherautomatically or by later guided processing of the data. Thispossibility is currently being explored by coauthorsD. Culvenor and G. Newnham of CSIRO Forest Biosciences.

We also envision the use of Echidna data for directmeasurement of leaf and wood aboveground biomass withoutallometric equations that are based on species, diameter, andcount density. This would involve three-dimensionalprocessing of the point cloud of scattering measurements by anadvanced algorithm, but it is clear from looking at Echidnaimages that the information is there to make this possible.Another potential improvement would be to scan withshortwave infrared light, as well as near-infrared, by operatingthe laser at 1540 nm. This would produce a distinctive signalunique to leaves, which absorb strongly in the shortwaveinfrared due to their water content while reflecting strongly inthe near-infrared at 1064 nm.

In the near term, our future work will continue to focus onimproving automated retrievals of forest structure using anEchidna instrument, with more testing in a North Americanenvironment. Ultimately, we plan to link under-canopy

scanning lidar with above-canopy imaging aircraft andspacecraft lidar using a common scattering model driven bygeometric optics with radiative transfer (Ni-Meister et al.,2008). This will open the door to large-area inventories offorest structure for carbon and ecosystem modeling on regionalscales.

ConclusionThe Echidna concept for an under-canopy, upward-scanning,

full-waveform-digitizing lidar, as realized in the Echidnavalidation instrument (EVI), provides a new way to remotelymeasure forest canopy structure quickly and accurately. Astested in early trials in a ponderosa pine plantation and a naturalstand of eucalypts in New South Wales, Australia, this newtechnology can easily locate and map trees and readily retrievevalues of mean diameter, stand height, stem count density, andleaf area index (LAI) that closely match values obtained byconventional methods. Moreover, the measurement of gapprobability with height provides a foliage profile that fits ourexpectations well for the sites scanned. We are only justbeginning to tap the potential of the lidar data for applicationsin forest inventory, biomass monitoring, and carbon balancemodeling. Based on this early work, this new technology has abright future.

AcknowledgementsSupport for this research was provided by the National

Aeronautics and Space Administration (NASA) under grantNNG0166-192G. We also gratefully acknowledge the supportof CSIRO Marine and Atmospheric Research and CSIROForest Biosciences.

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