Retrieval of forest structural parameters using a ground-based lidar ...

Can. J. Remote Sensing, Vol. 34, Suppl. 2, pp. S426–S440, 2008

Retrieval of forest structural parameters using a 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 diameter at breast height (DBH), stand height, distance to tree, stem count density (stems/area), leaf-area index (LAI), and stand foliage profile (LAI with height) with very good accuracy in early trials. We validated retrievals with ground-truth data collected from two sites near Tumbarumba, New South Wales, Australia. In a ponderosa pine plantation, LAI values of 1.84 and 2.18 retrieved by two different methods using a single EVI scan bracketed a value of 1.98 estimated by allometric equations. In a natural, but managed, Eucalypus stand, eight scans provided mean LAI values of 2.28–2.47, depending on the method, which compare favorably with a value of 2.4 from hemispherical photography. The retrieved foliage profile clearly 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 the instrument but remained unbiased. We estimated stand basal area, mean diameter, and stem count density using the Relaskop method of variable radius plot sampling and found agreement with manual Relaskop values within about 2% after correcting 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 des peuplements forestiers incluant le diamètre moyen à hauteur d’homme (DBH), la hauteur du peuplement, la distance par rapport 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 des données de réalité de terrain acquises sur deux sites situés près de Tumbarumba, New South Wales, en Australie. Dans une plantation de pins ponderosa, les valeurs de LAI de 1,84 et de 2,18 extraites à l’aide de deux différentes méthodes utilisant un seul balayage de EVI ont enregistré une valeur de 1,98 estimée selon les équations allométriques. Dans un peuplement d’eucalyptus à l’état naturel mais sous gestion, huit balayages ont donné une valeur de LAI de 2,28 à 2,47, dépendant de la méthode, ce qui se compare favorablement avec la valeur de 2,4 dérivée de la photographie hémisphérique. Le profil du feuillage extrait montrait clairement deux couches de couvert. Un algorithme pour trouver les troncs (« find trunks ») a traité les balayages d’EVI pour les deux sites dans le but d’identifier les tiges, de déterminer leurs diamètres et de mesurer leurs distances à partir du centre du balayage. Les distances ont été extraites de façon très précise (r2 = 0,99). La précision de l’extraction des diamètres d’EVI a diminué quelque peu avec la distance en fonction de la résolution angulaire de l’instrument, mais elle est demeurée non biaisée. Nous avons estimé la surface terrière du peuplement, le diamètre moyen et la densité des tiges à l’aide de la méthode Relaskop d’échantillonnage à rayon variable et nous avons trouvé une concordance avec les valeurs manuelles de Relaskop à l’intérieur de 2 % après correction pour le phénomène des troncs arrières qui sont cachés par les troncs plus en avant (occlusion). Ces premiers essais démontrent le potentiel du lidar opérant sous le couvert et à balayage vers le haut pour l’extraction rapide et précise des paramètres structurels de la forêt. [Traduit par la Rédaction] 440

Received 21 February 2008. Accepted 23 June 2008. Published on the Canadian Journal of Remote Sensing Web site at http://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 and Environment, 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, NY 10065, USA. S426

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Canadian Journal of Remote Sensing / Journal canadien de télédétection

Introduction Rapid and accurate measurement of vegetation structure, particularly that of forests, is an important goal for biogeoscience applications, including carbon balance modeling and the surface radiation balance modules of regional and global climate models (Hyde et al., 2006). Light detection and ranging (lidar) is particularly well suited to this task, since it allows accurate measurement of light scattering by vegetation layers, and a number of recent papers have documented the application of downward-looking airborne lidar for this purpose (Lim et al., 2003, provides a recent review). Some of these papers have focused on small-footprint (usually less than 1 m diameter) lidars that are used primarily for topographic mapping (e.g., Lim and Treitz, 2004; Hudak et al., 2006). These instruments typically return the distance to the first and last scattering events, which provides canopy height and its variance. By contrast, wide-footprint aircraft research lidars have been designed particularly for vegetation studies. They have a footprint typically ranging from 15 to 30 m, depending on altitude, and digitize the full-waveform return; examples are scanning 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 that correlate well with canopy structural parameters. A review in the context of the present work and its ground-based instrumentation can be found in Jupp et al. (2005b). Many previous studies have used ground-based lidar for forest structural assessments. However, they have to date concentrated on the use of simple lidar rangefinders (Welles and Cohen, 1996; Radtke and Bolstad, 2001) or discrete-return lidar systems (Parker et al., 2004; Van der Zande et al., 2006). The latter have shown the ability to measure bole diameter and stem 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 pilot study for our present effort, retrieved LAI and foliage profile using a discrete-return lidar system in an Australian eucalypt forest that matched LAI from hemispherical photographs within 8%. Most recently, Clawges et al. (2007) demonstrated measurement of leaf area using discrete-return lidar by imaging several young larch trees before and after leaf fall. Working with the lidar instrument described and used in this paper, Jupp et al. (2008) described the theory for and demonstrated retrieval of LAI and the foliage profile from a waveform-digitizing ground-based lidar. This study serves to further validate retrieval of forest structural parameters using a ground-based, waveformdigitizing lidar, the Echidna® validation instrument (EVI), built by CSIRO Australia, with ground-truth data collected from a conifer plantation and a natural forest stand located in New South Wales, Australia. 2

Echidna validation instrument and study area The Echidna validation instrument (EVI) is based on a concept for an under-canopy, multiple-view-angle, scanning lidar, with variable beam size and waveform digitizing termed Echidna. The Echidna has been patented in Australia, the United States, New Zealand, China, and Japan, with patents in other countries pending.2 The EVI, which is the first realization of the Echidna concept, utilizes a horizontally positioned laser that emits pulses of near-infrared light at a wavelength of 1064 nm. The pulse is sharply peaked so that most of the energy is emitted in the middle of the pulse. The time length of the pulse, measured as the time at which the pulse is at or above half of its maximum intensity, is 14.9 ns, which corresponds to about 2.4 m in distance. Pulses are emitted at a rate of 2 kHz. The pulses are directed toward a rotating mirror that is inclined at a 45° angle to the beam. As the mirror rotates, the beam is directed in a vertical circle, producing a scanning motion that starts below the horizontal plane of the instrument, rises to the zenith, then descends to below the horizontal plane on the other side of the instrument. Coupled with the motion of the mirror is the motion of the entire instrument around its vertical axis, rotating the scanning circle through 180° of azimuth. In this way, the entire upper hemisphere and a significant portion of the lower hemisphere of the instrument are scanned (Figure 1).

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

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

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Although the laser beam is a parallel ray only 29 mm in width, it passes through an optical assembly that causes the beam to diverge into a fixed solid angle. This expansion of the beam with distance allows the laser pulses to census the entire hemisphere. The size of the solid angle can be varied from 2 to 15 mrad. The rotation speeds of the mirror and the instrument on its mount are also varied so that the hemisphere can be covered slowly by many fine pulses or rapidly by fewer coarser pulses. As the light pulse passes through the forest, it may hit an object and be reflected. The light is scattered back toward the instrument and focused on a detector that measures the intensity of the light it receives as rapidly as 2 gigasamples per second. Since the pulse is traveling at a known speed, the time between emission of the pulse and its receipt at the detector indicates the distance to the object. At its most rapid sampling rate, the sampling distance is about 7.5 cm, but the range to the peak of a pulse can be determined more accurately by interpolation after digitizing. The output of the detector is digitized electronically and stored by computer to provide a full-waveform return that records the scattering of the pulse from within a metre or less of the instrument to about 100 m away. More information on the EVI and its early trials can be found in Jupp et al. (2005b). Data from the EVI and coordinated ground measurements were acquired within the Bago-Maragle Forest (35°36′2.42′′S, 148°06′29.25′′E), New South Wales, Australia, in November 2006 at two different sites. The pine site was located in a twicethinned, 30-year-old plantation of Pinus ponderosa managed by the New South Wales Forestry Department. Site LAI was not observed independently but was estimated as 1.98 using allometric 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 was recorded, along with the distance and compass bearing to the stem. The tower site was located in a large area of native forest that has been used for wood production for many years. Eucalyptus delagatensis and Eucalyptus dalrymplean dominate the open, wet sclerophyll forest, with canopy heights around 40 m. The canopy contains two more or less distinct layers, with a sparse upper story of large crowns and a denser understory of shrubs and small trees. Using hemispherical photographs, Leuning et al. (2005) determined the LAI to be about 1.4 for the upper story and about 1.0 for the lower shrub layer. At the tower site, eight instrument scans were positioned in eight cardinal compass directions arranged in a square with sides of 200 m, northeast, southeast, southwest, and northwest at the four corners of the square, and the Tumbarumba flux tower (Leuning et al., 2005) at the center of the square. Manual stem measurements at the eight scan points used the Relaskop method (Bitterlich, 1947; 1956), in which a variable-radius plot sample is selected with probability proportional to the DBH of each stem. The DBH, distance to tree, and compass azimuth were recorded for each tree sampled. An alternate systematic S428

sample of four trees, chosen as the first tree encountered in azimuth sectors of 90° width, were measured for height and crown shape.

Methodology The main approaches we have used to analyze the data from the EVI have been described in Jupp and Lovell (2005a) and Jupp et al. (2005b; 2008). Briefly, there are two modes of analysis, namely direct “object” measurement and statistical or “stand” measurement. If the beam size is small, the returns will be a few separated “hits” at measurable distances with reflectances that depend on the object shape, orientation, and basic (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 trees for trunk size and growth form, and these can then be combined to estimate stand statistics. It is relatively straightforward to understand this form of measurement. In contrast, the statistical approach involves two steps. One is to process the signal to apparent reflectance, and the other to interpret it.

Figure 2. Typical waveforms digitized by the EVI. (a) Waveform returned from a trunk. The shape of the waveform echoes the steep, but Gaussian shape of the lidar pulse. (b) Waveform return from scattering by canopy leaves. The waveform shows a superposition of several small Gaussians, indicating multiple “hits” from clumps or clusters of leaves. © 2008 CASI


Calculation of apparent reflectance (ρapp) is basically a calibration step and is defined as ρ app =

ΦR − ΦB Φ TCτ 2a

R2

(1)

where ΦR is the (filtered) received power from the target, ΦT is the energy output at the laser oscillator exit aperture, τa is the atmospheric transmission through a distance R at wavelength λ, R is the distance from the laser transmitter (and receiver) to the reflecting object, C is the system calibration factor, and ΦB is the background radiation field that contributes to the measured signal. The statistical model for the calibrated data is ρ app ( r) =

dPgap r 2 E( r) − e = ρ v PFC ( r) = − ρ v ( r) 2 C ( r) t A E 0 dr

ln P( θ) cos θ G ( θ)

(4)

Thus, the leaf area index L may be retrieved from the gap probability if the G function is known and the model is appropriate. If the G function is not known, Warren-Wilson (1963) showed that the G-function pivots around a “hinge angle” θ ≈ tan–1(π/2), or 57.5°, at which the value of G/cos θ is about 0.9 for all leaf angle distributions. Following Jupp et al. (2008), we refer to 57.5° as θHA, and thus L ≈ −11 . ln(Pgap, HA)

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

© 2008 CASI

L =−

(2)

where r is the range, C is the instrument optics calibration factor, E is the measured power, E0 is the signal energy at source, tA is the atmospheric transmission, e is the background signal power, ρv is the effective volume reflectance, PFC(r) is the probability of first contact at range r, and Pgap(r) is the probability of gap between the source and point at range r. If the returns are combined statistically or the beam size is increased, the waveform becomes more closely related with the statistics of the canopy. A primary statistic is the probability of a gap to a given range as defined previously. Another is the second-order probability of a gap to a range in one direction and to a different range in another. We have used a number of these approaches in this paper. For example, LAI and foliage profile measurements are based on statistics of gap probability with range in a particular direction as measured by the return lidar waveform from that direction. The statistical approach also provides the ability to estimate canopy 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 derived from a “find-trunks” algorithm that recognizes individual tree stems in a horizontal data slice at or near the height of the instrument (Jupp et al., 2005b).

P(θ) = exp[–G(θ)L/cos θ]

where P(θ) is the gap probability through the complete canopy from the ground at zenith angle θ, L is the leaf area index, and G(θ) is the fraction of the leaf area projected on a plane normal to the zenith angle θ (Ross G function; Ross, 1981). Inverting this relationship for L,

(3)

(5)

where Pgap,HA is the gap probability at θHA. In the more general case, we can consider leaf area index as a function of height z in the canopy, which varies from 0 at the base to H at the top, and compute L( z) ≈ −11 . ln(Pgap, HA(z))

(6)

The foliage profile f(z) is then obtained as f ( z) =

∂L( z) ∂z

(7)

In this paper, we follow the procedure outlined in Jupp et al. (2008) for deriving Pgap(θ, z) from Echidna lidar returns averaged within “zenith rings” or solid angles containing all zenith angles within a zenith increment (e.g., 5°) and over all azimuths. To retrieve zenith ring values, digitized lidar returns are converted to apparent reflectance and scaled as described in Jupp et al. As described previously, using a zenith ring containing θHA allows an estimate for L and foliage profile to be derived. However, as shown later in the paper, although this approach provides a useful and simple estimate, it tends to be noisy and only sample a part of the stand. The situation can theoretically be improved using multiple zenith rings. First, following ideas in Lang (1987; 1991) and Campbell (1986), Jupp and Lovell (2005a) and Jupp et al. (2008) use a simple linear model for the Ross G function and for the proportion of the LAI at a particular zenith angle in terms of horizontal (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 S429

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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, and the 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 are different at different heights, for example, due to leaning or bending of the trunk.

retrieved value of L is then based on up to 11 zenith rings (the exact number depending on the range of angles where the laser beam emerges from the top of the canopy) rather than one. Second, to overcome the variation in the single-angle estimate of the foliage profile, Jupp et al. (2008) suggested a solid angle weighted profile that reflects the unbiased average. The average normalized foliage profile is defined as follows: L( z) log Pgap ( θ, z) = LAI log Pgap ( θ, H ) f ( z) = LAI

∂ log Pgap ( θ, z) ∂z log Pgap ( θ, H )

(9)

where the notation θ is to be taken as an indication that the normalized data have been averaged over zenith angle rather than a mean angle. Both estimates are used with the field data in the analysis of the site data. As a technical point, we note here that the leaf area index retrieved by optical methods, including hemispherical photography, sunfleck ceptometers, the commonly used LAI2000 (LI-COR, Inc.), and the EVI, usually includes not only leaves but also fine branches and small stems, and so is sometimes referred to as a “plant area index” or “surface area index” (Bréda, 2003). Moreover, the processing described here represents a “standard” approach and does not address the effects of clumping (Chen et al. 1991; 2003) on the estimate. These effects, together with the morphological issues associated with the recognition of small gaps, which modify LAI in the opposite direction from clumping, are under active research. The Echidna is already providing a rich and valuable data source for the investigations. Trunk identification A lidar return from a tree trunk, when the beam is assumed to be fully within the angular span of the trunk from the EVI station, can be looked at as a reflection from a “wall,” possibly at a sloping angle to the beam, and at a specific range. The S430

projection shown in Figure 3, where a horizontal cross section of the laser returns is estimated, has the potential to provide information such as tree size and basal area as a function of height, 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 signal appears to be distributed in range, even for a target that is a solid wall. This is shown in Figure 3 by the “smear” of the targets. However, since the pulse has a very clear and sharp peak, it is possible to recognize a pulse from noise and identify the peak position. By convention we have taken the time at the peak of the pulse as it leaves the EVI as zero EVI time and range. By locating the peak of a return from a hard object, the time 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 tree but still fully within the trunk is a useful edge point to locate. It can be modeled as one in which the central azimuth is IFOV/2 back from the extreme edge azimuth. The objective is to identify the shots that are all “within” the trunk and to assume that those at either end of the sequence of “tree” returns are critically within the trunk, in that the outer edge of the beam is just grazing the trunk tangent. To get an estimate of the angular span of the tree (assuming the end shots are right out to the edges), the beam IFOV is added to the angular span between the end shots. The geometry and notation being used are shown in Figure 4. The range to the central point is denoted R, and it is assumed that the tree has a diameter D. The EVI scan is marked “EVI,” and the outer tangents to the tree define the (true) full angular span of the tree from the EVI station. For a given shot, the angle between the normal to the tree and the shot is denoted ψ, and the angle between the shot and the path to the central point on the trunk is denoted ξ. The complete angle between the tangent shots to the trunk is denoted φspan. At the “central” point of the lidar return, the apparent reflectance will be maximal. For a model tree of the kind shown in Figure 4 which is close enough to be resolved by a number of shots, we can compute, for each shot, the ratio of apparent reflectance to that at the maximum (nearest front and central) point of the tree: © 2008 CASI


the success of the method depends on handling occlusion of trees by other trees and foliage as well as achieving accuracy in the 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 gentle to moderate slope. Note that EVI can “see” the horizon and so observe the slope angle and orientation at each scan location. Two approaches are possible. First, diameters can be retrieved in a horizontal plane, with DBH values adjusted for the true distance between the horizontal plane and the tree base using an average taper factor. Second, DBH can be determined in a plane parallel to the slope, since EVI has a full circle of observations in that plane for gentle to moderate slopes. These approaches have not yet been implemented. To investigate the lidar retrievals of canopy parameters, field measurements were also collected manually. Since the EVI is at a fixed location, not all of the trees will be “visible” (in the sense that the laser beam does not illuminate them), since they may be obscured by plant material closer to the EVI, and some may only be partly visible. For the field records, there were therefore three classes of tree established according to visual estimates from the plot center: (i) fully visible tree in which the full span of the trunk in a height range can be seen by the observer; (ii) partly occluded trees in which parts are obscured but the centerline of the trunk is visible (this may occur from one or both sides); and (iii) occluded trees, which are assumed to be obscured if the centerline is not visible to the observer. These estimates of visibility were at times difficult to make and thus contain some errors.

Figure 4. Geometry of EVI trunk returns.

ρ app ρ max

=

< cos ψ > < cos ψ > max

< cos ψ > max ≈ 1

(10)

where < cos ψ > denotes the mean cosine within the pixel. For shots away from the center, the average cosine could be taken as the cosine at the azimuth of the pixel center. Taking the cosine at the center of the range as an estimate of the average, and assuming that the scan is horizontal and that the “tree” is a vertical cylinder with constant diameter D, we can derive a number of useful quantities. Assuming that the full angular span (span between the nominal bearings of the end shots plus the IFOV) is φspan as defined by the two tangent points across the tree, it follows that if the range to the center of the tree surface nearest the EVI is R and the tree diameter is D, then the relationship between the three is t = sin( φspan / 2) = D = 2R

t 1 −t

D/ 2 R+ D/ 2 (11)

Thus bearing, distance, and DBH for individual trees can be estimated from EVI data using these relationships and drawn on a stem map as “EVI trees.” The value of estimating angular spans is that Relaskop-type methods can theoretically be used to estimate basal area. As described later in the paper, however, © 2008 CASI

Stem count density and mean DBH retrieval Using Echidna as a Relaskop The Echidna was used in a manner similar to that of a Relaskop during the data processing. The basic Relaskop method (Bitterlich, 1947; 1956; Holgate, 1967; Bell and Dillworth, 1988) uses a wedge or instrument that enables the operator to select trees (the “in” trees) for which the angular span across the tree as seen from a central point of a field site is greater than a given value. The Relaskop can measure the stand basal area (G) by tallying the number of “in” trees visible from the center of the site. Trees around an observation point can also be confirmed to be “in” or “out” based on the DBH of each tree and its distance to the sample point. Taking these additional measurements for the “in” trees provides estimates of diameter distribution and tree density in addition to stand basal area. If there are m “in” trees at a site, the estimated stand basal area at a site is G = λBA = m × BAF

(12)

where λ is the tree density (number of trees per square metre or per hectare); BA is the mean tree cross-sectional area (square metres) at breast height for the stand (or mean individual tree basal area); and BAF is the basal area factor, which includes factors relating to the size of the angular wedge used to define S431

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the “in” trees and also factors to bring the stand basal area into the units that are convenient to the user. In practice, the Relaskop angle is selected so that BAF is a convenient number (such as 2 m2/ha). Using this method, small trees in the near distance can be seen, and only large trees at farther distances can be counted “in.” The “in” trees therefore form a biased sample with probability of selection proportional to the crosssectional area of the tree. The basal area of an individual tree is the cross-sectional area at breast height. That is, BAindividual = π(DBH/2)2. The relationship between the probability of selection discussed previously and the size of the stem is simply prob ∝ BAindividual. Using these ideas, an estimate for the density of trees at a site is provided that is not affected by the bias involved in selecting the “in” trees. The estimate is m

BAF

λ=∑

j =1 BA individual, j

(13)

Because of the bias in selection of the trees, if a quantity is related to tree DBH, then the “in” trees are not an unbiased sample of that quantity, and so the mean and variance of the quantity 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, crosssectional area, height, crown size, volume), then it can be shown that the following estimate is not biased: q = ∑ Wi q ( D i ) i =1

m

σ 2 ( q ) = ∑ Wi [ q ( D i ) − q ] 2

(14)

i =1

( λDE R) 2

[1 − exp( −λDE R)(1 + λDE R)]

(15)

where N(λ, DE; R) is the number of trees “apparently” within radius R, given a true tree count density of λ and an effective tree diameter of DE. We can use DE = D + δDE, δDE ≥ 0, where D is the mean diameter of the tree trunks, and the added term takes into account low branches, understory etc. DE depends on the stem density and distribution in the sample plot. The product λDE is the overall attenuation in units of m–1 that could be estimated from the Pgap in the 85–90° zenith ring. As a default, we may use DE ≈ D (1 + C V2 ) 1/ 2 where C V2 is the squared coefficient of variation for tree diameters. By manipulating Equation (15), we may obtain N ( λ, DE ; R) = N 0 ( λ; R) F(t) F(t) =

2 t2

[1 − exp( −t)(1 + t)]

(16)

t = λ DE R

BAF / BA i m

∑ BAF / BA j

in which the number of trees N(λ, DE; R) within distance R expected with occlusion is the product of the true expected number N0(λ; R) and a factor F(t) that depends on λDE. Applying this to the Relaskop equations and assuming the coefficient of variation of tree sizes is not too large, it is straightforward to show that M ( λ, D; α) = M 0 F(t)

i =1

Because the Echidna data have been processed to provide angular span, it is possible to make similar estimates based on the Relaskop theory and carry out equivalent measurements in the field using a traditional Relaskop instrument and processing for comparison and validation. Occlusion correction In the use of the Relaskop data in the way described previously, it is assumed that every “in” tree can be seen from the central point. This is usually achieved in practice by the operator changing position to see behind occluding near trees to see a more distant “in” tree. However, the Echidna as used in this experiment cannot move in this way, and so the bias due to obscuring of trees by other trees and foliage needs to be corrected. It can be shown from geometrical probability arguments that with horizontal attenuation of the form Pgap = exp(–λDEz) S432

2πλR 2

N 0 ( λ; R) = λπR 2

m

Wi =

N ( λ, DE ; R) =

t=

λ DE D

(17)

2 BAF

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

Results Pine site LAI and foliage profile Figure 5A shows the regression of –ln(Pgap) against X(θ) = (2 tan θ)/π, following Equation (8), for the 11 zenith rings between 5° and 60°. According to the regression, Lh = 0.59 ± © 2008 CASI


Figure 5B shows the foliage profiles derived from the hinge angle only and from an averaged gap function for 11 zenith rings. The averaged profile is clearly smoother than the profile obtained at the hinge angle. The derived profile fits our expectation for a tall, even-aged plantation with a reduced understory rather well.

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

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 the hinge angle alone, which is consistent with the position of this zenith ring above the regression line in Figure 5A. Although there are no independent field measurements of leaf area index at this site, Jupp et al. (2008) reported a value of L = 1.98 using American allometric equations for ponderosa pine (Law et al., 2001) as applied to measured diameters of trees in a 50-m radius from the instrument.

Trunk identification and stand parameters Figure 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) and zenith (y axis) grid. Figure 7 shows a stem map for the site. The blue circles indicate the locations and DBHs of the stems as they are retrieved from EVI data using the find-trunks algorithm applied to an apparent reflectance horizontal slice similar to that shown in Figure 3. Of the 102 trees manually recorded within a 50-m radius of the instrument, the find-trunks algorithm found about 40% using the EVI data (Table 1). Of these, about half were judged visible, one quarter were judged partially occluded, and one tenth were judged occluded. We evaluated the performance of the find-trunks algorithm by comparing measured distances and DBHs with retrieved values for trunks in both sets of data. Here we excluded trees of diameters ≤ 2 EVI beam widths, which were regarded as too small and (or) too far from the instrument for accurate retrieval, leaving 22 trees at distances ≤ 30 m for analysis. Distance to tree is retrieved with very high accuracy (r2 = 0.99), which is not surprising given the range resolution of EVI. Diameters of near trees were retrieved with better accuracy than those of far trees, as might be expected. Given the noise in DBH retrieval, we processed both datasets in a Relaskop mode, identifying “in” trees that would have been observed with a basal area factor of 2 m2/ha. Table 2 summarizes the results. Both of the Relaskop retrievals matched the field measurements of basal area, mean DBH, and stem count density very well. As might be expected from occlusion, the Relaskop method applied to the EVI data found one fewer tree and slightly underestimated basal area and stem

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

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

Table 1. Tree counts for the Tumbarumba pine site, comparing trees located and measured and matching trees retrieved by the find-trunks algorithm. Occlusion category

No. of trees measured

No. of matching trees found by EVI

Visible Partially occluded Occluded Total

61 21 20 102

34 5 2 41

Percent identified 55.7 23.8 10.0 40.2

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

Parameter No. of trees Basal area (m2/ha) Mean DBH (m) Standard error of sample, σ (m) Standard error of mean, σM (m) Stem count density, λ (no. of trees/m2)

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Field measurement (all trees)

Relaskop measured trees

Relaskop EVI trees

102 28.4 0.53 0.12

13 26.0 0.54 0.08

12 24.0 0.52 0.08

0.012

0.023

0.024

0.0128

0.0140

0.0110

Figure 8. Vertical foliage profiles for eight scans at the Tumbarumba tower site. Profiles are scaled to the leaf area index retrieved using the regression method. The average profile is derived from averaged Pgap data.

count density. We did not correct the EVI data for occlusion, since the formulas given in Equation (15) are inappropriate for a plantation with a systematic distribution of stems. The mean DBH was very close to the true mean. In this even-aged stand, all the “in” trees were relatively close to the instrument, and all had about the same diameter. Tower site LAI and foliage profile The LAI and foliage profile for each of the eight measurement locations around the tower were calculated in the manner described for the pine site. Table 3 shows LAI retrievals for each site and their averages for both hinge angle and regression methods. Both the simple average of the eight scans and the LAI values derived from averaged Pgap values are shown. In general, regression and hinge angle values are quite similar for the eight scan sites. Figure 8 shows the foliage profile for each scan using the regression method based on 11 zenith rings and the regression-method profile for all eight locations using averaged Pgap values. The canopy clearly has two layers that are separated by a region of reduced leaf area at about 20 m, with the leaf area of the upper layer somewhat greater than that of the lower layer. The profiles also show some individual variation. For example, the east site (EE) has a high LAI in the lower layer and a somewhat reduced LAI in the upper layer. The west (WW) and northwest (NW) sites have lower overall leaf area, with a less prominent lower layer. At the west site, the upper layer is much thinner than that at other sites. The average LAI of the eight profiles is 2.26. Dividing the average profile in two at 20 m, the LAIs in the upper and lower layers are 1.42 and 0.84, respectively. These compare quite © 2008 CASI

Canadian Journal of Remote Sensing / Journal canadien de télédétection Table 3. Retrievals of leaf area index at tower scan sites using hinge angle and regression methods. EVI scan

Lv

Lh

Lreg

LHA

NN SE EE NE NW SS SW WW Average of scans Profile average

2.14 1.45 1.96 2.35 1.22 1.42 2.15 1.24 1.74 1.57

0.17 0.67 0.56 0.14 0.65 1.09 0.40 0.62 0.54 0.69

2.31 2.12 2.52 2.49 1.87 2.51 2.55 1.86 2.28 2.26

2.42 2.07 2.50 2.61 1.82 2.45 2.43 2.12 2.30 2.47

favorably with the Leuning et al. (2005) LAI estimate from hemispherical photographs of 1.4 and 1.0. Trunk identification Rather than inventory all trees within a fixed radius of the instrument location, we used a Relaskop at the tower site to select a basal-area weighted sample of “in” trees at each EVI location, using a basal area factor of 2 m2/ha. For this factor, the wedge angle is 1.62°, or 28.3 mrad (milliradians). Since the EVI scans at a rate of 4 mrad with a 5 mrad beam divergence, “in” trees will be more than 6 EVI pixels wide, allowing for better accuracy in determining tree diameter. Table 4 shows how the find-trunks algorithm performed at individual sites and for all sites pooled together. It identified 86% of all “in” trees judged visible, 38% judged partially occluded, and 20% judged occluded. All told, the find-trunks algorithm found 102 of 163 “in” trees for an identification rate of 62%. Best performance was at the north (NN) and northeast (NE) sites, where a reduced shrub layer allowed better visibility. The heavy shrub layer at the southeast (SE) site, as shown in the foliage profiles of Figure 8, caused difficulty for the find-trunks algorithm. Figure 9 shows EVI mean-return images for the northwest (NW) site, where the algorithm performed well, and the southeast (SE) site, where it performed poorly. Figure 10 shows reduced major axis regressions of measured and retrieved distance and DBH for all matching trees at all scans. Distance is retrieved exceptionally well (r2 = 0.99), but DBH is less accurate. As expected, r2 is higher for trees close to the instrument, with values of 0.660 for trees at 0–10 m, 0.429 for trees at 0–20 m, and 0.335 for trees at 0–30 m. However, the estimates are unbiased in this sample, since confidence intervals on slopes include unity. Stand parameters Table 5 summarizes the timber stand parameters retrieved using three methods: “Relaskop” indicates manual measurements of “in” trees; “EVI” indicates measurements derived from EVI “in” trees using the same Relaskop criteria; and “adjusted EVI” indicates measurements that have been corrected for occlusion according to the Methodology section. © 2008 CASI

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

Field

EVI

EE V P O All

14 4 3 21

12 0 1 13

85.71 0.00 33.33 61.90

NE V P O All

9 4 1 14

9 1 0 10

100.00 25.00 0.00 71.43

NN V P O All

12 3 2 17

11 3 0 14

91.67 100.00 0.00 82.35

NW V P O All

12 4 2 18

12 3 1 16

100.00 75.00 50.00 88.89

SE V P O All

11 7 3 21

6 3 1 10

54.55 42.86 33.33 47.62

SS V P O All

14 7 3 24

12 2 0 14

85.71 28.57 0.00 58.33

SW V P O All

7 15 1 23

5 7 1 13

71.43 46.67 100.00 56.52

WW V P O All

12 9 4 25

11 1 0 12

91.67 11.11 0.00 48.00

91 53 19 163

78 20 4 102

85.71 37.74 21.05 62.58

All V P O All a

Match (%)

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

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

For the Relaskop and EVI entries, basal area is simply the product of the number of “in” trees and the basal area factor of 2 m2/ha. Mean DBH is an average of values for the “in” trees weighted by their basal areas, which provides an unbiased mean (Methodology section). The standard error of the mean is also based on weighted values. Stem density is a sum of stem density values for individual “in” trees, each weighted by its basal area. At five of the eight sites, the find-trunks algorithm found fewer trees than were manually identified with the Relaskop, which would be expected given the occlusion present in the EVI scans. At the remaining three sites, the find-trunks algorithm found more trees. Considering all sites, 163 “in” trees were found with the Relaskop, and the find-trunks algorithm identified 143 “in” trees. Accordingly, EVI tallies a mean basal area that is about 11% lower and estimates a stem density that is 9% lower. A t test of these pairs of means shows that neither pair is significantly different, with significance levels of 0.256 and 0.803 for mean basal area and stem density, respectively. However, this is a test with quite low power, based on the number of samples (8) and their variance, and we can expect that the effects of occlusion will be detected with more precision when a larger sample is used. With the effects of occlusion corrected, the EVI retrievals of basal area and stem density closely approach the Relaskop retrievals. Both fall within 2%, and significance levels are 0.865 and 0.974. Basal-area weighted mean diameter using “in” trees produces a mean diameter that is about 11% larger than the Relaskop mean diameter. Near trees are most heavily weighted in the mean and, S436

as shown in the regression of 0–10 m distance (Figure 10), there are more trees with diameters overestimated than underestimated in this range. Still, the difference is not significant, with a probability of 0.248, despite the large number of samples, due to the large underlying variance in DBH.

Discussion Overall, our study shows the great potential value of the Echidna under-canopy, upward-scanning lidar (as realized by the EVI instrument described in Jupp et al., 2005b) to measure forest stand structural parameters with ease and high accuracy. However, as a technology still in development, more improvements will be needed to achieve this goal with a laser scanner. Leaf area index (LAI) measurements are of great value in modeling applications but are difficult to make objectively and repeatedly (Bréda, 2003). Destructive sampling, although most accurate, is extremely costly and time-consuming. Allometric equations, which may be used to estimate LAI from DBH, DBH and height, or sapwood area, are site dependent and may not generalize well to trees with a wide range of growth form and damage frequently seen in forest management applications. Nondestructive optical methods are in wide use but require exacting conditions for forest applications, including a uniform sky for hemispherical photographs, clear skies for undercanopy sunfleck probes, and a need for both above- and belowcanopy measurements for angular optical sensors such as the LAI-2000. © 2008 CASI


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

The Echidna concept, as implemented in the Echidna validation instrument (EVI), provides an optical approach with many advantages. Because illumination is provided by the laser, LAI retrieval does not depend on sky conditions. Moreover, the instrument digitizes the full-waveform return, and thus associates scattering events with their threedimensional position in the canopy. This allows the measurement of gap probability as a function of range and direction over a complete hemisphere, which in turn allows derivation of both LAI and the foliage profile. In addition, the ability to discriminate between return pulses striking trunks from return pulses that strike more diffuse targets provides a way of reducing the effect of trunks and branches on the estimate of LAI. In this paper we have explored LAI retrieval using the EVI in a conifer plantation and a natural, although managed, eucalypt forest using the approach of Jupp et al. (2008). Although our results for these sites do not have a full and complete validation, © 2008 CASI

retrievals using several different approaches are consistent and agree with what is known about the sites. Based on the ability to census the entire hemispherical field and beyond, as well as observe scattering as a function of range, the Echidna approach should provide more accurate results than alternate methods, and we are presently conducting a more intensive validation of EVI LAI retrievals in New England forests. Optical LAI retrievals are also known to be sensitive to clumping, which causes underestimates of leaf area (Chen and Cihlar, 1995a; 1995b). Although we have not resolved the compensating interactions between clumping and dilation of small gaps in Echidna, the ability to measure scattering as a function of range and angle clearly opens the door to finding the distribution of within- and between-crown gaps directly from the optical measurements. Not only is gap distribution useful for retrieving more accurate LAI, but it is also a key parameter in vegetation canopy reflectance models. We can anticipate that the S437

Vol. 34, Suppl. 2, 2008 Table 5. Tumbarumba tower site stand parameters retrieved using three different methods. Stem density, (no. of trees/m2)

“In” treesa

0.14±0.027 0.17±0.032

0.150 0.100 0.110

21 23 25.2

42 30 32.2

0.15±0.027 0.21±0.048

0.110 0.053 0.057

21 15 16.1

SS Relaskop EVI Adjusted EVI

48 40 44.9

0.27±0.054 0.25±0.053

0.061 0.058 0.065

24 20 22.4

SW Relaskop EVI Adjusted EVI

46 22 23.4

0.15±0.026 0.41±0.110

0.100 0.012 0.013

23 11 11.7

WW Relaskop EVI Adjusted EVI

50 46 52

0.23±0.039 0.28±0.053

0.061 0.050 0.057

25 23 26

NW Relaskop EVI Adjusted EVI

36 30 33.4

0.48±0.110 0.49±0.120

0.016 0.014 0.016

18 15 16.7

NN Relaskop EVI Adjusted EVI

34 36 38.4

0.13±0.028 0.10±0.021

0.130 0.210 0.224

17 18 19.2

NE Relaskop EVI Adjusted EVI

28 36 38.6

0.19±0.042 0.16±0.034

0.046 0.088 0.094

14 18 19.3

All Relaskop EVI Adjusted EVI

42.0±2.86 37.4±3.14 41.3±3.27

0.22±0.017 0.25±0.019

0.085±0.017 0.078±0.024 0.084±0.028

163 143 156.7

Source

Basal area (m2/ha)

Mean DBH ± σM (m)

EE Relaskop EVI Adjusted EVI

42 46 50.3

SE Relaskop EVI Adjusted EVI

a

Number of stems included using Relaskop method.

Echidna will become an important source of direct measurements of gap and clumping parameters in the future. We have also demonstrated the use of the EVI to locate trees and measure their trunk diameters automatically, thus providing retrievals of such stand parameters as basal area and stem count density. The present version of the find-trunks algorithm could be improved, for example, by enhancing its vertical tracing of stems. Looking at the mean return images of Figures 5 and 9, it is obvious that most trees are imaged well enough at some height to allow accurate diameter retrievals, and a more complex but “smarter” algorithm should be possible.

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

© 2008 CASI


formulas and testing on sloping terrain will be the subject of future work. The use of the Echidna as a virtual Relaskop to construct a basal-area weighted sample of trees provides a good response to the difficulty of identifying far-field trees and finding their diameters. Since the Relaskop method is angle-based, it matches well with the angular data acquired by the Echidna. Accuracy of diameter retrieval could be enhanced by using a smaller angular measurement interval, for example, 3 mrad instead of the present 4 mrad. The problem of occlusion of distant trunks by near trunks is amenable to both theoretical and practical solutions. From the practical perspective, it makes sense to locate the instrument at a point where it is not too close to nearby trees that would unduly block the field of view. Since this position will be more likely to be under a gap in the canopy, it will bias LAI retrievals in the uppermost zenith ring, and accordingly we do not use the 0–5° zenith ring for LAI retrieval. However, it should not affect retrievals of stand parameters, since they are derived from a much larger area. It may also make sense to clear near shrubs and low branches so that they do not obscure large sectors of the field of view. With a field of view cleared of near and large impediments, the correction for occlusion is likely to work better. We also note that the random occlusion model is not appropriate for a plantation where trees are spaced more regularly. However, it is not difficult to derive an occlusion function for a systematic grid, provided the instrument is located at a carefully chosen position relative to the stand geometry, and this limitation should not be as much of a problem in the future. The ability of Echidna to image near-field trees from ground to top also presents an opportunity to sample stem and branching characteristics, such as taper and sweep, which are often used in forest mensuration. We can envision augmenting a Relaskop-type sample with a selection of “measure trees” for which additional form and canopy data are acquired either automatically or by later guided processing of the data. This possibility is currently being explored by coauthors D. Culvenor and G. Newnham of CSIRO Forest Biosciences. We also envision the use of Echidna data for direct measurement of leaf and wood aboveground biomass without allometric equations that are based on species, diameter, and count density. This would involve three-dimensional processing of the point cloud of scattering measurements by an advanced algorithm, but it is clear from looking at Echidna images that the information is there to make this possible. Another potential improvement would be to scan with shortwave infrared light, as well as near-infrared, by operating the laser at 1540 nm. This would produce a distinctive signal unique to leaves, which absorb strongly in the shortwave infrared due to their water content while reflecting strongly in the near-infrared at 1064 nm. In the near term, our future work will continue to focus on improving automated retrievals of forest structure using an Echidna instrument, with more testing in a North American environment. Ultimately, we plan to link under-canopy © 2008 CASI

scanning lidar with above-canopy imaging aircraft and spacecraft lidar using a common scattering model driven by geometric optics with radiative transfer (Ni-Meister et al., 2008). This will open the door to large-area inventories of forest structure for carbon and ecosystem modeling on regional scales.

Conclusion The Echidna concept for an under-canopy, upward-scanning, full-waveform-digitizing lidar, as realized in the Echidna validation instrument (EVI), provides a new way to remotely measure forest canopy structure quickly and accurately. As tested in early trials in a ponderosa pine plantation and a natural stand of eucalypts in New South Wales, Australia, this new technology can easily locate and map trees and readily retrieve values of mean diameter, stand height, stem count density, and leaf area index (LAI) that closely match values obtained by conventional methods. Moreover, the measurement of gap probability with height provides a foliage profile that fits our expectations well for the sites scanned. We are only just beginning to tap the potential of the lidar data for applications in forest inventory, biomass monitoring, and carbon balance modeling. Based on this early work, this new technology has a bright future.

Acknowledgements Support for this research was provided by the National Aeronautics and Space Administration (NASA) under grant NNG0166-192G. We also gratefully acknowledge the support of CSIRO Marine and Atmospheric Research and CSIRO Forest Biosciences.

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