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Computational-Geometry-Based Retrieval of Effective Leaf Area Index Using Terrestrial Laser Scanning Guang Zheng and L. Monika Moskal
Index Terms—Canopy structure, extinction coefficient, gap fraction, leaf area index (LAI), light detection and ranging (LiDAR), terrestrial laser scanning (TLS), voxelization.
long-lasting evolutionary process of trees [6] and determine the spatial distribution of photosynthetic active radiation [(PAR); 380–710 nm]. As a critical component of the canopy structure, the spatial distribution (including both azimuthal and angular distributions) of foliage elements and the direction of incident radiation will primarily affect the radiation regime below and within the canopy [7]. Leaf area index (LAI) is one of the most important biophysical canopy structure parameters, which has been successfully obtained using remotely sensed data at different scales [8]–[11]. Point quadrat analysis [12] is one of the most acceptable and fundamental indirect methods for measuring foliage area index; it has been well developed and discussed during the past decades and successfully applied in the theoretical research on LAI [7]. Based on the point quadrat method, a theoretical model aimed to quantitatively describe the canopy spatial structure had been developed by treating the canopy as different horizontal layers [7]. Moreover, it was further developed by Chen and Black [13] as follows:
I. I NTRODUCTION
P (θ) = exp [−G(θ)ΩL/ cos θ]
Abstract—Quantifying the 3-D forest canopy structure and leaf area index of an individual tree or a forest stand is challenging. The canopy structural information implicitly contained within point cloud data (PCD) generated from terrestrial laser scanning (TLS) makes it possible to characterize directly the spatial distribution of foliage elements. In this paper, a new voxel-based method titled “point cloud slicing” is presented to retrieve the biophysical characteristics of the forest canopy including extinction coefficient, gap fraction, overlapping effect, and effective leaf area (ELA) from PCD. These extractions were performed not only from the whole canopy but also from layers of the canopy to depict the distribution patterns of foliage elements within the canopy. The results showed that the TLS-based ELA estimation method could explain 88.7% (rmse = 0.007, p < 0.001, and n = 30) variation of the destructive-sample-based leaf area measurement results. It was found that the sampling resolution was a key parameter in defining the dimension of a single voxel. Furthermore, the TLS-based method can also serve as a calibration tool for airborne laser scanning application with ground sampling.
C
ANOPY structure plays an important role in soil–canopy– atmosphere interactions and with respect to energy and mass exchanges by controlling biogeochemical cycles [1]–[3]. At the forest stand level, the variation of foliage elements’ vertical spatial density will significantly affect the output of ecological models [4], [5]. Therefore, more comprehensive understanding of the canopy structure is required to reveal the Manuscript received September 4, 2011; revised January 19, 2012; accepted February 2, 2012. Date of publication June 28, 2012; date of current version September 21, 2012. This work was supported in part by the University of Washington National Science Foundation Industry/University Cooperative Research Center (NSFI/UCRC) (Award #0855690), by the State Key Fundamental Science Funds of China under Grant 2010CB950701, by the High Technology Research and Development Program of China (863 program: #2012AA12A306), by the Open Research Fund Program of the State Key Laboratory of Hydroscience and Engineering in Tsinghua University under Grant sklhse-2012-B-04, and by the University of Washington Precision Forestry Cooperative. A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. G. Zheng is with the International Institute for Earth System Science, Nanjing University, Nanjing 210093, China (e-mail:
[email protected]). L. M. Moskal is with the Remote Sensing and Geospatial Analysis Laboratory, Precision Forestry Cooperative, School of Environmental and Forest Sciences, University of Washington, Seattle, WA 98195-2100 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2012.2187907
(1)
where P (θ) is the gap fraction defined as the probability of a beam transmitted through the canopy with an incident angle θ, G(θ) is the extinction coefficient defined as the mean projection of a unit foliage area on the plane normal to the direction of the beam, and Ω is a clumping index. ΩL is defined as the effective LAI (Le ). Furthermore, Chen and Black [13] developed a theoretical model to predict LAI considering the clumping effect among foliage elements using the Poisson model. In addition, two gap size theories [14] had also been developed to convert the effective LAI to true LAI by characterizing the clumping and overlapping effects resulted from the nonrandom distribution of foliage elements within the canopy. The ability of producing 3-D point cloud data (PCD) makes light detection and ranging (LiDAR) a popular tool, particularly in forestry applications. Airborne laser scanning (ALS) and terrestrial laser scanning (TLS) are the two most common methods for acquiring LiDAR data. ALS has been used to characterize canopy structure and biophysical parameters from landscape and stand level [15]–[21]. The 3-D canopy structure model was reconstructed by Thomas et al. [22] to explore the profile of laser interception through the canopy. It has also been used to estimate the net primary productivity by coupling a photosynthesis model with the 3-D canopy structural profile obtained from Scanning LiDAR Imager of Canopies by Echo
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ZHENG AND MOSKAL: COMPUTATIONAL-GEOMETRY-BASED RETRIEVAL OF EFFECTIVE LAI
Recovery (SLICER) data set. LAI and canopy cover fraction estimation was reported by Houldcroft et al. [23] with discrete small-footprint ALS. Aside from the discrete LiDAR system, full-waveform LiDAR was also used by Morsdorf et al. [24] to invert the forest biophysical parameter; they combined the radiative transfer model with the full-waveform large-footprint LiDAR data source to successfully invert the forest biophysical parameters such as fractional cover, maximum tree height, and vertical crown extension. Voxels have already been applied to ALS and TLS, for example: as a method to visualize multiple-return LiDAR [25], for forest inventory [8], to estimate crown base height [26], for feature classification [27], for canopy geometry characteristics [23], and for estimating leaf area density [28], [29]. TLS has also shown great potential to estimate LAI and woody-to-total area ratios [30] with careful consideration of instrument specification and sampling design. A voxel-based 3-D gap fraction method was proposed by Clawges et al. [31] to estimate the plant area density with TLS. Due to the occlusion effect, their method underestimated the upper layers’ plant area density and overestimated the plant area density compared with solar radiation reversion method. In addition, Danson et al. [32] proposed a geometrical-projection-based directional gap fraction estimation method using TLS data. Their results showed that the TLS-based gap fraction results were slightly higher than those of the digital-hemispherical-photography-based method, which oppose the findings by Lovell et al. [33]. The differences may be a result of impact variability in densities, crown cover, and tree height in the experimental forest stand. In terms of experimental design, factors affecting the accuracy of estimating leaf area density with TLS had also been investigated by Takeda et al. [34]. It was found that the presence of nonphotosynthesis organisms, the distribution of leaf inclination angles, the number of incident laser beams, and the extinction coefficient were very important factors directly affecting the final results. A waveform near-infrared (NIR) TLS system called “Echidna” was used to explore the forest structural parameters [35] and LAI profile [36] through upward scanning under the canopy. However, there are few studies concerning the essential parameter extinction coefficient from voxel level for direct incoming solar beams; in addition, most of the research studies treat the canopy as a whole rather than estimating the LAI in different planes at different heights. This research aims to introduce a novel method to estimate the LAI from voxel level at different spatial locations for the whole domain of PCD. As an analogy to the point quadrat analysis, each laser pulse could be regarded as a very thin long needle which could penetrate through the canopy until being blocked by some objects. Each point from PCD represents one time contact between a laser beam and foliage elements. The only difference between laser scanning and point quadrat method is that all the contacts of needles with foliage could be recorded in the point quadrat method but laser scanning can only record the first contact with spatial coordination and distance information. Based on the analogy, a novel method titled “point cloud slicing” (PCS) based on voxel data structure was proposed to estimate LAI for the PCD of an individual tree or a forest stand.
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TABLE I C HARACTERISTICS OF THE T ERRESTRIAL L ASER S CANNER L EICA S CAN S TATION 2
We assumed that the PCD collected from multiple locations could comprehensively represent the tree canopy and foliage element; it is probably not always true, particularly for some very dense forest stands. However, three-direction scanning has been shown to be a good approximation [29] minimizing occlusion by other trees. The specific goals of this research were as follows: 1) to develop a method for extracting structural and biophysical parameters directly from PCD generated by TLS; 2) to explore the diversity of structural and biophysical information which can be obtained from TLS; 3) to characterize the vertical and horizontal distribution variation patterns of foliage elements; 4) to develop an approach for estimating effective LAI from PCD. II. M ATERIALS AND M ETHODS A. Terrestrial Laser Scanner In this experiment, we collected two data sets using the terrestrial laser scanner Leica ScanStation 2 [37] in an outdoor environment. Leica ScanStation 2 uses a neodymium-doped yttrium aluminum garnet laser with a wavelength of 1064 nm. The origin of the laser was located at the top of the tribranch with a distance of 0.3072 m. More details about the laser scanner can be found in Table I. B. TLS Data Collection We first collected a scan of a well-isolated individual Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) tree with a height of 25 m, scanned from one single-side-lateral location with a sampling spacing of 2 cm [Fig. 1(a)]. The Douglasfir tree was located in Washington Park Arboretum, near the University of Washington, Seattle. This preliminary data set was used to develop and illustrate the algorithm. Then, an experiment was set up with a triangular plot with three tree species in the Center for Urban Horticulture, School of Environmental and Forest Sciences, University of Washington, Seattle. The three forest species seedlings were Douglas-fir (P. menziesii (Mirb.) Franco), big-leaf maple (Acer macrophyllum Pursh), and western red cedar (Thuja plicata Donn ex D. Don). Each side of the triangle was populated by one species. We scanned this triangular plot from three locations (scans A, B, and C in Fig. 1) in order to obtain the comprehensive PCD with 8-mm sampling spacing at 50 m. At the same time, eight targets were used as reference points to align the three scans. The mean
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Fig. 1. Experimental setup and the corresponding PCD colored by height. (a) PCD for an individual Douglas-fir tree with 25-m height. (b) Close-up of the big-leaf maple tree top PCD. (c) Close-up of the western cedar tree top PCD. (d) Close-up of the Douglas-fir tree top PCD. (e) PCD for an individual big-leaf maple tree with 2-m height. (f) PCD of the triangular plot with different species comparing each arm of the triangle: A is the central scanning location and 360◦ horizontal scanning, B and C are the side-lateral scanning locations, and the gray gradient area represents the two-side-lateral scanning area. (Please note that (a) and (e) are not scaled equally.)
absolute error (MAE) is an indicator of the accuracy of the registration process. The three location scans were combined with a MAE value of 0.034 m. Then, the registered PCD was mosaicked to remove all points within and out of the plot, as shown in Fig. 1(f). We manually removed the ground points and isolated the individual seedling trees in order to postprocess the PCD for LAI estimation. In order to better illustrate the representation of the PCD for the three species, three up-close tree top images were produced as shown in Fig. 1(b)–(d). The complete individual big-leaf maple tree’s PCD was also provided as shown in Fig. 1(e). C. Algorithm Development All of the methodologies developed below are based on the following assumptions. 1) The PCD generated from multilocation scanning for a given target object using TLS fully represents the surface of the target object. 2) The sampling resolution predefined by the user remains constant. It determines the level of detail of the canopy structure using PCD. The total amount of radiation energy received by the forest canopy consists of three components. First, the incoming direct solar radiation (280–4000 nm) accounts for nearly half of PAR; the rest is in NIR. The second component is the incoming diffuse sky long-wave radiation. The third part is the incoming diffuse scatter radiation [38], [39]. In this work, we only work with the direct solar radiation component. In order to explore the spatial arrangement of a tree’s foliage elements by analyzing PCD, a framework was first defined as follows. 1) Voxelization: A bounding box was first constructed to represent the PCD’s domain. It was defined by the eight corners’ Cartesian coordinates determined by the minimum and maximum values of the X, Y , and Z coordinates, respectively. Then, a voxel-based data structure with full flexibility to control the dimension of each voxel was used to divide the domain into a finite number of small parts; this process was called “voxelization” [Fig. 2(b)]. By defining the width (w), length (l), and height (h) for each voxel, the PCD’s
domain will be divided into m × n × p voxels, where m = (Xmax − Xmin )/w, n = (Ymax − Ymin )/l, and p = (Zmax − Zmin )/h; they were the numbers along the X-, Y -, and Z-axes of the PCD’s domain, respectively. {w, l, h} ∈ R+ ; if w = l = h, the single voxel will be a cube. The 3-D central point of this PCD, computed as [(Xmax − Xmin )/2, (Ymax − Ymin )/2, (Zmax − Zmin )/2], was used to construct the new Cartesian coordinate system for PCD as the origin point; the Z-axis will be the direction of stem growth, which is perpendicular to the horizontal surface plane. The X- and Y -axes lied in the plane perpendicular to the Z-axis; the Z-axis was defined as the column direction, and the X- and Y -axes were defined as row directions. 2) PCS Scheme: After the voxelization process of the domain of a given PCD, each row or column layer was regarded as a plane which extracted a part of the data set; this was defined as a slice plane [Fig. 2(a)]. The PCS could be implemented vertically and/or horizontally, which corresponded to each column or row layer. For example, all voxels could be indexed as (i, j, k) (i = 1, 2, . . . , m; j = 1, 2, . . . , n; k = 1, 2, . . . , p); if k = 1 and i and j take any values within the given range, it represents all voxels in the first layer or the first row plane. In order to approximate the relative positional relation between incoming direct solar radiation beams and forest canopy, another slicing way was developed by either rotating the PCD or slicing planes. In this work, the first procedure was adopted, which means that the given PCD will be first rotated to a needed position with a relative position that we want to simulate; then, the voxelization procedure will be applied to the rotated PCD. Thus, all horizontal slice planes were parallel with the X−Y plane, and all vertical slice planes would be parallel with the Z-axis. According to this procedure, we always treated the direct solar radiation beams as coming from the zenith direction or parallel with the Z-axis direction. Different directions for incoming direct solar radiation beams could be simulated by rotating the PCD. More specifically, the 3-D central point of the PCD was first translated to the origin point of the Cartesian coordinate system; then, the PCD was rotated around the X-, Y -, or
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Fig. 2. Schematic diagrams illustrating the concept of PCS algorithm and voxelization. (a) Seven horizontal slicing planes for a Douglas-fir tree PCD with bounding box and (b) (5 × 5 × 5)-voxel-based voxelization result for a horizontally sliced PCD obtained from the PCD in (a) with height ranging from 17 to 18 m.
Z-axis respectively to the required relative position between the PCD and slice planes. For example, rotating the PCD around the Y -axis with 30◦ amounts to that the PCD will be sliced by a slicing plane or the coming direction of the direct solar radiation beams, with 30◦ inclination angle. Based on the procedures discussed earlier, PCD could be sliced by a plane at any position (horizontally 0◦ to 360◦ ; vertically 0◦ to 90◦ ). This was named directional slicing. Any part of PCD could be extracted as a thin slab through directional slicing to explore the 3-D canopy structure information. 3) Line Quadrat Analysis: In this work, the spatial distribution of foliage elements at slice plane level was analyzed by line quadrat analysis. For each row or column slice plane with a fixed relative position with PCD, it was composed of an arrangement of line quadrats, whose directions were either normal or parallel to the direction of incoming direct solar beams r(θ, β). Since we focused on dispersion condition of foliage elements along the direction r, only the line quadrats parallel to direction r were considered. If the 3-D parameters of each single voxel were assigned to the same as 1.5 times of the sample spacing of TLS, we can guarantee that there was, at most, only one point in each single voxel. Thus, the number of nonempty voxels (N ) for each line quadrat represents the times of contacts between the line quadrat and foliage elements, and N was a statistically random event. Otherwise, we should project all points in each line quadrat to a plane parallel to the direction of the line quadrat, counting the number of different Z coordinate values as the number of contacts with foliage elements. We define Pn as the probability that a line quadrat has n-times contact with a foliage element during penetration through the PCD. P0 is defined as the probability of the line quadrat encountering gaps along its path; the overlapping index was zero. By averaging N for all line quadrats over plant volume, the mean (m) and variance (σ 2 ) of the number of
contacts between the line quadrat and foliage element over the whole volume of the PCD could be calculated. This number of contacts recorded by the line quadrat was not the actual foliage point density (FPD) but the projected FPD (pFPD) projected onto the plane that was perpendicular to the line quadrat direction. According to Nilson [7], the dispersion condition of a foliage element in real space will be reflected by the relative variance, computed as variance (σ 2 )/mean (m) for each line quadrat. The dispersion condition of foliage elements for an individual tree or a stand could be divided into three situations including regular, random, and clumped according to the relative variance (σ 2 /m = 1, > 1, or < 1). Voxel-based PCS could provide us with the vertical variation of the point density and the extinction coefficient of the whole canopy at sliced planes with different heights. By using the line quadrat analysis, various biophysical parameters could be extracted such as point density, extinction coefficient, pFPD, and the dispersion condition of the canopy. As an example, we extracted a vertical line quadrat for the individual Douglasfir tree PCD as shown in Fig. 3(a); the corresponding partial PCD was horizontally laid down [Fig. 3(b)] in order to do the comparison between the histograms of the point density [Fig. 3(c)]. 4) Calculating Mean Projection Coefficient: We only worked with incoming direct solar radiation with a direction r(θ, β), which means that we calculated the projection coefficient at the kth-layer slice plane Gk (r) for a fixed direction r(θ, β). In addition, the mean projection coefficient at the kth-layer slice plane Gk (θ) for the incident radiation with an inclination angle θ could be calculated by integrating the azimuth angle β over the range [0, 2π] as 2π Gk (θ) =
Gk (r)dβ. 0
(2)
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Fig. 3. Line quadrat analysis for an individual Douglas-fir tree PCD. (a) Original PCD of an individual Douglas-fir tree; the transparent red solid volume is a line quadrat, and the blue lines are voxels for the voxelization process. (b) Profile of a line quadrat extracted from the original PCD (the Z-axis lies horizontally in order to provide a comparison between the histogram and original PCD). (c) Point density histogram of the line quadrat.
5) Projection Coefficient for a Given Direction: We first considered directional slicing at a fixed direction r(θ, β); after the voxelization process of PCD, bounding volume that was the entire 3-D domain of PCD, horizontal and vertical slice planes and line quadrats were all determined. For example, if all slice planes were parallel at a direction r(θ, β), all the line quadrats will have the same parallel directions, and the longitudinal axis direction of each line quadrat represents its direction. A plane that was perpendicular to this primary axis could be constructed in each voxel, and then, all of the points could be projected into that plane. In the voxelization framework defined previously, the projection plane was one of the two sides of each voxel that was normal to the direction of the line quadrat. The number of points within each nonempty voxel was n. 1) If n = 1, a unit square, defined as a 2-D square with the sampling distance or the sampling space set by the user, will be assigned with this point as a center to represent the foliage area. When the sampled resolution was known as s, the area of this single foliage could be computed as s × s. Thus, the projection coefficient will be assigned as the ratio of a square area calculated by the length of the sampling space (i.e., s × s) over the square area with the side of a single voxel determined by its length (l) and width (w). 2) If n = 2, a line will be constructed to represent the foliage area, and its projected foliage area was the projected length of this line multiplied by a unit square area. The projection coefficient could be obtained by computing the ratio of after to before projected line length. 3) If n ≥ 3, a test about whether all points were coplanar or on the same line will be performed first; if they were on the same line, it will degenerate to lower dimensional circumstance (n = 2). If on the same plane, a triangle will be constructed to represent the foliage area, and the projected foliage area will be calculated based on the three projected points’ coordinates. The three projected points’ coordinates were denoted as (x1 , y1 ), (x2 , y2 ),
Fig. 4. Schematic diagrams illustrating the extinction coefficient calculation in an individual voxel. The solar beams come from the overhead direction. (a) Single-maple-leaf PCD. (b) Three-dimensional convex hull construction for a single-maple-leaf PCD with surface representation. (c) Wire-frame representation for the 3-D convex hull of a single-maple-leaf PCD. (d) Twodimensional convex hull construction result for a single-maple-leaf PCD at the X−Y projection plane.
and (x3 , y3 ); then, the area of this projected triangle (Ap ) representing the projected foliage area amounts to compute the determinant value of the following matrix: x1 1 Ap = × x2 2 x3
y1 y2 y3
1 1 . 1
(3)
4) If all of the original points within the voxel were neither coplanar nor on the same line, a 3-D convex hull will be constructed, and one-half of the total surface area of this 3-D convex hull will be used to represent the foliage area (A) in reality. Then, all the original points were projected on the plane right to the line quadrat direction; the area of the 2-D convex hull constructed from the projected points will represent the projected foliage area (Ap ). For example, we computed the extinction coefficient for a single-maple-leaf PCD using the procedures described earlier. We first visualized the PCD with three-axis ranging [Fig. 4(a)], since all of the points were not coplanar and n was above three; then, we constructed the bounding box and computed the 3-D convex hull for the PCD with two representations including surface [Fig. 4(b)] and wireframe [Fig. 4(c)]. In addition, we constructed the 2-D convex hull for the projection PCD of the single maple leaf on the plane normal to incoming solar beams’ direction or the X−Y plane in this case [Fig. 4(d)]. The ratio of the area of the 2-D convex hull to one-half of the surface area of the 3-D convex hull was used to represent the extinction coefficient for this single maple leaf in the single voxel. Based on the procedures discussed earlier, the projection coefficient Ap /A was computed for all of the nonempty voxels.
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Fig. 5. Computational results for a single horizontal slice plane spanning 17–18 m in height range for an individual Douglas-fir tree PCD with a voxel size of 0.5 m × 0.5 m × 1 m. (a) Visualization results for the horizontal slice plane with bounding box. (b) Three-dimensional visualization of the extinction coefficient for each voxel. (c) Point density for the horizontal slice plane. (d) Two-dimensional grid visualization of the extinction coefficient for a horizontally sliced plane.
By summing up the projection coefficients for a single slice plane normal to the direction of incident radiation, we get N 1 Gk (r) = Apξ /Aξ N
to the Z-axis around the 3-D center point into 18 equal parts with 10◦ interval and computed the mean projection for the kthlayer slice plane as follows:
(4)
2π
ξ=1
Gk (θ) = where N is the total number of nonempty voxels in the kthlayer slice plane and k is the number of layers sliced by the PCS method. In the case of the individual Douglas-fir tree, by using the voxelization and PCS algorithms, we obtained the spatial distributions of point density and extinction coefficient in each voxel for different sliced planes at different heights. For example, we applied the PCS algorithm based on the voxel with a size of 0.5 m × 0.5 m × 1 m and acquired one horizontally sliced plane with a height ranging from 14 to 16 m, as shown in Fig. 5(a). The 3-D extinction coefficient spatial distribution map for this slice plane was produced as shown in Fig. 5(b). In addition, two 2-D spatial distribution maps for the point density and extinction coefficient of this slice plane were also generated as shown in Fig. 5(c) and (d). It can be found from Fig. 5 that TLS could provide more information about the 3-D information of the vertical variation of foliage density and its horizontal distribution in certain height. 6) Mean Projection Coefficient for the kth-Layer Slice Plane: By rotating 180◦ each slice plane around the Z-axis at the 3-D center location of a given PCD, we cover the whole canopy 3-D space. Thus, we divided the unit circle plane normal
Gk (r) dβ = 0
N 18
Apγξ /Aγξ .
(5)
γ=1 ξ=1
7) Gap Fraction Estimation: In (1), P (θ) is the gap fraction of a beam transmitted through the canopy with an incident angle and all possible azimuth angles β ∈ [0, 2π]; in the case of only parallel direct solar beams with a fixed direction, they will be a number of parallel solar beams. The gap fraction P (r) in the fixed direction r = (θ, β) would be computed instead of the gap fraction for all possible points of compass, which was the probability of a beam transmitted through the canopy with incident angle θ and azimuth angle β. By employing the directional slicing way, we could obtain the gap fraction of the kth-layer slice plane at direction r = (θ, β), denoted by Pk (r). In terms of the computation of Pk (r), we will consider the following different conditions. 1) If all the voxels in a given slice plane were empty, it meant that all direct solar beams could totally penetrate this layer; then, Pk (r) will be 100%. 2) If both empty and nonempty voxels exist in a given slice plane, we will calculate Pk (r) by two different components. One was named as pure-gap fraction [Pk (r)],
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defined as the ratio of the number of empty voxels over the total number of voxels for a single slice plane Pk (r) =
Nempty Ns
(6)
where Nempty is the number of empty voxels in the kthlayer slice plane and Ns is the total number of voxels in the kth-layer slice plane computed as m × n. It characterized how many percentages of the direct solar radiation beam could penetrate this layer without any interception. The second component of Pk (r) is the probability that light could penetrate those nonempty voxels resulting from incomplete filling by foliage elements within a voxel. Within those nonempty voxels, all of the points were projected into a plane normal to the direction of incoming direct solar radiation within the projection plane; the points were nonrandomly distributed. Thus, the sample resolution of a given PCD (s) was used as the edge size of a square to pixelate this projection plane, which was used to divide the projection plane. Then, by calculating the fraction of empty pixels over the total pixel number, we got the second component of gap fraction for a slice plane Pk (r) named nonpure-gap fraction, denoted as Pk (r). The nonpure-gap fraction for the ξth nonempty voxel Pk (r) is calculated as neξ Pkξ (r) = (7) nvξ where neξ is the number of empty pixels in the projection plane of a single voxel normal to the direction of incoming direct solar radiation. nvξ is the total number of pixels within the nonempty voxels of this projection plane determined by the following equation: nvξ =
l w × d d
(8)
where d is the sample distance constant for a given PCD. w and l are the width and length of each voxel defined by the voxelization process. By summing up all nonpure-gap fractions of nonempty voxels, the nonpure-gap fraction for the kth-layer slice plane Pk (r) is computed as Pk (r) =
Nn
Pkξ (r).
(9)
ξ=1
Since the sample resolution d was used to pixelate the projection plane, it meant that the total number of pixels in each nonempty voxel projection plane normal to incoming direct solar radiation with direction r(θ, β) is the same as and equal to nvξ . By combining (7) and (8), (10) is rewritten as N n
Pk (r)
=
Nn ξ=1
neξ ξ=1 = N n nvξ
N n
neξ = nvξ
neξ
ξ=1
Ns − Nempty
(10)
ξ=1
where the denominator in (10) represents the total number of nonempty voxels within the kth-layer slice plane and the
numerator denotes the total number of nonempty pixels within the projection plane of the kth-layer slice plane which was perpendicular to the incoming direct solar radiation direction. Pk (r) was required for knowing the fraction of direct solar radiation with direction r(θ, β) penetrating through the nonempty voxels at the kth-layer slice plane. Therefore, the gap fraction for the kth-layer slice plane at direction r(θ, β) was obtained by computing N n
Pk (r) = Pk (r) +
Pk (r)(Ns − Nempty ) = Ns
neξ + Nempty
ξ=1
Ns
. (11)
If the azimuth angle β was integrated over the range [0, 2π], the gap fraction for a beam transmitted through the canopy with an inclination angle θ at the kth-layer slice plane was obtained. By employing directional slicing, the specific number of slice planes was obtained. We divide the unit circle plane normal to the Z-axis around the 3-D center point into 18 equal parts with 10◦ interval; the gap fraction for the kth-layer slice plane of beams transmitted through the canopy with an inclination angle θ is obtained as follows: 2π Pk (θ) =
Pk (r)dβ = 0
18
Pkγ (r).
(12)
γ=1
By combining (1), (6), and (12), we predict the effective LAI (Le ) for the kth-layer slice plane by rewriting (1) as follows: Pk (θ) = exp [−Gk (θ)Le / cos θ] .
(13)
Once Le for a single layer was obtained, we got the total effective LAI for the whole canopy by summing up the Le values from all p-layer slice planes. In each vertical line quadrat that composed of many voxels, the voxels were either empty or nonempty voxels. In terms of the estimation of the gap fraction, the empty voxel would be considered as a gap, and light will penetrate through it completely. The overlapping index was defined in this study as a factor to identify layers of canopy by counting the nonempty voxels along a line quadrat [Fig. 6(a)]. As for the nonempty voxel, since the nonrandom distribution of foliage elements in space, not all of the space in the nonempty voxel had been occupied by foliage elements; pure-gap fraction [Fig. 6(b)] and nonpure-gap fraction were computed. The most important thing that we considered during this process was to set the appropriate dimensional information for computing the nonpure-gap fraction, which relates with the sample resolution predefined by the user before scanning. 8) Predicting Gap Fraction of the Whole Canopy: Once the probability of a direct solar beam penetrating a single line quadrat was known, we easily obtained the total gap fraction below the canopy by summing up the gap fractions of all line quadrats, or the total number of line quadrats was m × n. In order to calculate the gap fraction for a single line quadrat, the probability of each voxel within this line quadrat was computed first. The gap fraction P0 (ξ, k) for the ξth line quadrat of the
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Fig. 6. Overlapping index and pure-gap fraction results for the individual Douglas-fir tree PCD (voxel size: 0.5 m × 0.5 m × 1 m). (a) Overlapping index for the PCD with 25 horizontal slice planes; the color gradient represents the number of nonempty voxels along the vertical line quadrat with 25 voxels. (b) Pure-gap fraction result from line quadrat analysis.
voxel at the kth-layer slice plane was obtained based on the following equation: P0ξ =
p
P0 (ξ, k).
TABLE II S UMMARY OF D ESTRUCTIVE -S AMPLING LAI M EASUREMENT FOR THE T HREE T REE S PECIES IN THE T RIANGULAR E XPERIMENTAL P LOT
(14)
k=1
Thus, the total gap fraction under the canopy for incoming direct solar beams with direction r = (θ, β) equals P0 =
m×n
P0ξ .
(15)
ξ=1
D. Algorithm Test and Validation In order to test our algorithm, we first collect the PCD of an individual live Douglas-fir tree using side-lateral scanning. The point density, extinction coefficient, and pure- and nonpure-gap fractions were computed based on the methods described earlier for all horizontally sliced planes. In addition, to fully validate our algorithm, we collected the PCD for three live seedling tree species shown in the triangular plot in Fig. 1. In addition, the destructive-sampling measurement of leaf area for all seedling trees was taken through optical scanning in an indoor laboratory environment in order to validate the results from the TLS. Every single leaf of big-leaf maple trees was scanned, followed by image analysis using the WinFOLIA software (Regent Instruments Inc. Quebec City, QC, Canada) [40], which is a leaf area meter and a leaf morphology analyzer, to determine the one-side leaf area. In the case of Douglas-fir, we obtained two LAI measurements, one for shoot and one for needles. First, all stripped needles and branches were scanned, and then, only needles were scanned. As for the western red cedar trees, we scanned each single leaf using the same method as the big-leaf maple trees. Statistical analysis between the TLS-based and manually measured effective leaf areas (ELAs) was taken for all the results from the three species. Moreover, the Breusch–Pagan test was performed to evaluate the performance of the linear regression model and test for heteroskedasticity issues. E. Sensitivity Analysis of Voxel Size on Gap Fraction Voxelization and PCS were the technical foundation of this work; the dimension of each voxel directly affects the comput-
ing efficiency and the level of details of the extracted canopy structure information. In order to explore the effects of the dimension of each voxel on the gap fraction, the horizontal PCS algorithm was used to extract 18 different horizontal planes with 1.5-m height interval. In each slice plane, the pure-gap fractions were computed with the 20 dimensional settings; the width and length of each single voxel were defined from 0.02 to 0.4 m with 0.02-m interval. Then, the gap fraction for each slice plane with different voxel sizes was computed in order to explore the effects of changing of voxel size on gap fraction estimation. III. R ESULTS By scanning and measuring every stripped single leaf, the shoot, or both shoot and needles, the leaf area for each single seedling tree is obtained and summarized in Table II. Based on the PCS algorithm, the point density spatial distributions along the horizontal and vertical directions were obtained, respectively. They were used as the basis to compute the key parameters such as extinction coefficient and gap fraction for directly retrieving the ELA from PCD. By computing the gap fraction and extinction coefficient of each individual tree in the triangular plot, ELA was obtained based on (1) for the three species. Then, the TLS-based ELA results were compared with those from destructive-sample-based LAI
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Fig. 7. Scatterplot comparing the TLS and destructive-sampling measured leaf areas for the three species. The black dashed line is a 1:1 line, the black solid line is the linear regression model for the TLS and destructive-sampling measured leaf areas, R2 = 0.887, and n = 30.
measurement for the three tree species; the results are shown in Fig. 7(a). It was shown that the current TLS-based ELA estimation method tends to overestimate ELA. The results showed that the TLS-based ELA results for canopies with lower density well captured the variation of manually measured leaf areas. However, for those canopies with high density, the TLSbased methods tend to underestimate ELA for all three species. The linear regression model was built for the TLS-based and destructive-sample leaf areas as Y = 0.968X − 0.165 (R2 = 0.887, rmse = 0.007, p < 0.001, and n = 30) [Fig. 7(b)]. The pure-gap fraction graph is arranged according to height in alphabetical order in Fig. 8. For example, Fig. 8(a) and (r) show the first and last horizontally sliced planes, respectively. In general, the pure-gap fraction decreased as the size of the voxel increases; the pure-gap fractions for all 18 sliced planes ranged from 0 to 0.93 with the voxel size from 0.02 to 0.4 m. By observing the pattern of the curve variation, there were two broad types for all pure-gap fraction distributions. One was the pure-gap fraction decreasing continuously as the voxel size increases [Fig. 8(e)–(r)]; the other one was the pure-gap fraction decreasing to a certain point and then stay unchanged with the voxel size increasing [Fig. 8(a)–(d)]. The first four sliced planes were the PCD only from the trunk surface; starting from Fig. 8(e), more canopy points were added to the sliced planes, and thus, a new pattern of the pure-gap fraction appeared. One interesting phenomenon observed was the pattern shown in Fig. 8(p); there was little variation of the pure-gap fraction regardless of the voxel size increase. By visually checking the PCD for this sliced plane, it was found that the points were clustered in a small area of this horizontally sliced plane; it was probably from a single shoot or a small branch of the Douglas-fir tree’s PCD. By comparing the effects of voxel dimensions on the puregap fraction, it was found that changing the dimensions of a voxel greatly affects the gap fraction estimation results for both the single layer and the whole canopy. By using a smaller voxel size, one can obtain a more precise pure-gap fraction; accordingly, the nonpure-gap fraction will account for a small portion of the total gap fraction. By contrast, a bigger size of voxels will significantly underestimate the pure-gap fraction; therefore, the nonpure-gap fraction was needed to capture the total gap fraction for each slice plane or the whole canopy. Once the size of the voxel was defined as the sampling space, only
Fig. 8. Variation for the pure-gap fraction while changing the voxel size for 18 horizontally sliced planes with 1.5-m height interval for the individual Douglas-fir tree PCD. The X-axis is the width and length of each single voxel, the Y -axis is the pure-gap fraction, and all graphs are arranged in alphabetical order for the slice planes (i.e., (a) shows the first horizontal slice plane).
the pure-gap fraction could be used to represent the total gap fraction for the sliced plane. IV. D ISCUSSIONS This work was based on the assumption that the PCD could fully represent the foliage element surface with even FPD. However, the occlusion effect among foliage elements will limit the ability to gather a comprehensive PCD, particularly in very dense canopies. Multilocation scanning can approximate a comprehensive point sample from the foliage surface. However, there are still no robust and widely acceptable ways to quantify the occlusion effect, at least for forestry application. This is a question deserving further research. As with most remote sensing applications, the resolution at which the voxels were produced was a key parameter to obtaining structural information and affecting the accuracy of effective LAI estimation. The voxel resolution directly determines the level of detail of the canopy structure that we captured with PCD. The effect of 3-D spatial resolution or voxel size in this case for PCD application is similar to that of 2-D spatial resolution or pixel size, in terms of optical remotely sensed imageries. For example, per-pixelbased approaches, such as maximum-likelihood classification, and feature-analysis-based approaches, such as object-based image analysis (OBIA) classification, are two different methods to classify raster remote sensing images. Maximum-likelihood
ZHENG AND MOSKAL: COMPUTATIONAL-GEOMETRY-BASED RETRIEVAL OF EFFECTIVE LAI
classification is mostly applied to coarse-pixel data such as Landsat imagery, and OBIA is often utilized in hyperspatial (submeter pixel resolution) image analysis. Therefore, 3-D spatial resolution or voxel size could result in different new methods to deal with PCD for an array of applications. For example, the voxel-morphology feature-analysis-based method could be a direction for future research. In this work, the extinction coefficient, illuminated surface area, and effective interception area of foliage elements were approximated by computing the convex hull for 3-D and 2-D points. Due to complicated and dense canopy and branch structure, it might introduce errors due to the gaps between the needles and shoot; furthermore, the clumping could happen at different canopy levels. For those canopies with clumping effect under the shoot level, one should use some other elegant algorithms to improve the accuracy of extinction coefficient approximation such as the alpha shape algorithm [41]. Due to the different angular distributions of foliage elements in space, the projected foliage points sampled from the surface of foliage elements will vary from FPD. Thus, the pFPD could reflect the effective points contributing to the interception of light coming from a given direction. To some extent, the pFPD could indicate the distribution of gap fraction that was an important parameter for determining the radiation regime not only under the canopy but also for a single slice plane at different heights. It will be helpful to determine the variation pattern of the light intensity in both the horizontal and vertical directions. Based on the calculation of the FPD and the pFPD, we found that the pFPD was usually smaller than PFD due to the inclination angle of the foliage elements that usually do not uniformly distribute horizontally. By converting the point density to foliage area based on the procedures discussed in Section II-C6, we could obtain the foliage element surface area and the projected foliage area; furthermore, the projection coefficient was computed based on the ratio of Ap /A for each voxel. More importantly, a very important difference between the effective interception leaf area and the illuminated leaf area was illustrated. The effective interception leaf area should be considered from the physical characteristic in terms of the light direct transmission. The illuminated leaf area will tell us all the leaf area contributing to the photosynthesis reaction. Usually, the effective interception leaf area would be smaller than the illuminated leaf area due to the angle between the leaf and the incoming direct solar beams. Knowing the difference between effective interception leaf area and illuminated leaf area could improve our understanding of the differences between effective LAI and true LAI and the reason why we need to estimate the true LAI. In addition, it reveals the importance of true LAI as a key input parameter into a process-based model for simulating ecological processes such as photosynthesis, tree growth, evapotranspiration, and net primary productivity. When a multilocation scanning sampling strategy is applied, it is possible to generate a comprehensively sampled PCD for the surface of the target object. Then, a virtual long needle (hereafter referred to as the line quadrat) would be used to explore the canopy structure based on the point quadrat analysis theory. A number of different factors as follows will affect the completeness of sampling for the surface of the target object:
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1) the relative height and distance between the scanner and the target object or a tree in this case and 2) the orientation distribution of foliage elements will greatly determine the representation of PCD for a given tree. This is a more complicated issue for TLS, which is beyond the scope of this paper but should be addressed by future research. This research compliments the results found by Hosoi and Omasa [28] that the voxel-based method could capture the horizontal and vertical variation of leaf area density. They also provided an optimal angle to collect the PCD for an individual tree with 57.5◦ inclination angle. However, this optimal angle could be varied due to the different forest tree species and the leaf characteristic size, which has been explored and verified by Chen and Black [13]. Therefore, this research presented an approach to estimate the gap fraction and extinction coefficient at voxel level, which requires the comprehensive PCD for fully representing the individual tree or the forest stand. In terms of the number and location of TLS, one recommended that the experimental setup will be the three locations demonstrated by Hilker et al. [29] in a circle with 120◦ interval for an individual tree and one central location combined with four-square-cornerlocation scanning for a forest stand. One voxel-based method for gap fraction estimation was proposed in this research; it computed the gap fraction for different incoming solar beams by rotating the PCD and keeping the direction of the solar beam from overhead and unchanged. It consisted of two components including pure- and nonpure-gap fractions, which could improve the computation efficiency. In addition, it not only computed the total gap fraction for the whole canopy but also could provide the information of gap fraction for each sliced plane at different heights within the canopy, which could benefit research related to precipitation interception, radiation-regime distribution within the canopy, and canopy wind-resistant ability. It is a 3-D-based method for gap fraction estimation. Some other research studies have explored the method for gap fraction by projecting the 3-D PCD into a 2-D space. For example, Danson et al. [32] presented an approach to estimate the directional gap fraction by converting the 3-D PCD into 2-D raster images through geometrical projection techniques. Compared with a 2-D-based method, the approach proposed in this work could improve the accuracy of gap fraction for different height planes of the canopy and provided more information about the light penetration condition within the canopy. V. C ONCLUSION In this paper, we have presented a voxel-based PCS algorithm to quantitatively identify the canopy structure and predict the effective LAI directly from PCD generated from TLS. We show that this method can capture the essential characteristics of the canopy structure such as foliage element orientation distribution, gap fraction, effective LAI, and extinction coefficient. The method presented in this work not only can generate the effective LAI for the whole canopy but also extracts the spatial distribution of foliage elements at different heights of the canopy, which is necessary for understanding precipitation interception [42], radiation regime [43], and habitat environment for animals [44]. The TLS-based LAI method
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provides a good tool to calibrate the results from the related ALS platform. In addition, the abundant information implicitly contained within the 3-D PCD obtained using TLS could provide more detailed information about canopy structure and LAI. This will provide useful continuous observations and calibration data for long-term ecological studies such as the National Ecological Observatory Network in experimental forest and the Long Term Ecological Research Network. With the advance of the TLS technology, the speed of TLS data collection will increase, which will also enhance the portability and flexibility of TLS. A PPENDIX Some terms used in this paper are defined as follows. 1) Line quadrat—According to the definition of the PCS scheme, each slicing plane was composed of a number of user-defined-constant-size voxels. For example, with horizontal slicing way, each slicing plane had m × n voxels. If only one single ith column or jth row of a single slice plane was extracted, it could be regarded as a long “line quadrat” for PCD. 2) FPD—It is defined as the number of points per unit voxel, measured in Npt /cm3 , and computed as Npt (i, j, k)/Vvoxel , where Npt (i, j, k) is the number of points in each voxel and Vvoxel is the volume of a single voxel. Since the foliage elements do not randomly distribute in real space, FPD varies as the position of the voxel over the domain of a given PCD. It is a function of voxel location (i, j, k), where i, j, and k are the indexes to locate each voxel respectively; by summing up the FPDs over all voxels in the individual tree or forest stand volume, we could get the average FPD as F P Daverage =
1 m×n×p
i=m;j=n;k=p
Npt (i, j, k)/Vvoxel .
i=1;j=1;k=1
(A1) If only summing up the foliage points over the voxels whose height ranges from top layer (k = 0) to current layer (k = z), the quantity that we obtained was defined as downward cumulative FPD. If it was divided by the projection area of bounding volume, we could get the downward cumulative FPD index; it is measured in Npt /cm2 . If the thickness from layer k to layer z is equal to the height of a voxel’s height, it could be regarded as the FPD for a slice plane. 3) Foliage area (A)—It is one-half of the total surface area of foliage elements from an individual tree or a forest stand, measured in square centimeters. The foliage area index is defined as foliage area per unit ground surface area. 4) pFPD—It is defined as the ratio of the number of foliage points over their occupied projected area onto a plane perpendicular to the longitudinal axis of line, which is measured in Npt /cm2 . The projection area viewed from the direction of a single line quadrat will be one of the two sides perpendicular to the incoming light direction.
5) Projected foliage area (Ap )—It is defined as the projected area of foliage elements onto the plane perpendicular to the line quadrat direction, measured in square centimeters. 6) Overlapping index—It is defined as the ratio of the number of nonempty voxels over the total number of voxels per line quadrat, which could indicate the overlapping effect in a certain direction. If all voxels of a line quadrat were empty, the overlapping index was zero, which means that the solar radiation penetrating the tree canopy at the same path will go down to the ground without any interception. This serves as an indicator for identifying the location of gap within canopies and the denseness of foliage elements along the direction of the line quadrat. ACKNOWLEDGMENT The authors would like to thank X. Wang and the anonymous reviewers for the valuable discussion and help concerning the numerical analysis. The authors would also like to thank Dr. J. Richardson and Dr. A. Kato for coordinating the destructivesampling effort. This research was conducted at the University of Washington Remote Sensing and Geospatial Analysis Laboratory and the Nanjing University International Institute for Earth System Science. The trees used in the destructive sampling were provided by Dr. G. Ettl at the Center for Sustainable Forestry at Pack Forest, School of Environmental and Forest Sciences, University of Washington. R EFERENCES [1] E. Dufrene, H. Davi, C. Francois, G. le Maire, V. Le Dantec, and A. Granier, “Modelling carbon and water cycles in a beech forest Part I: Model description and uncertainty analysis on modelled NEE,” Ecol. Model., vol. 185, no. 2–4, pp. 407–436, Jul. 2005. [2] N. T. Nikolov and D. G. Fox, “A coupled carbon–water–energy– vegetation model to assess responses of temperate forest ecosystems to changes in climate and atmospheric CO2 . 1. Model concept,” Environ. Pollution, vol. 83, no. 1/2, pp. 251–262, 1994. [3] J. Liu, J. M. Chen, J. Cihlar, and W. M. Park, “A process-based boreal ecosystem productivity simulator using remote sensing inputs,” Remote Sens. Environ., vol. 62, no. 2, pp. 158–175, Nov. 1997. [4] G. P. Asner, C. A. Wessman, and S. Archer, “Scale dependence of absorption of photosynthetically active radiation in terrestrial ecosystems,” Ecol. Appl., vol. 8, no. 4, pp. 1003–1021, Nov. 1998. [5] J. M. Chen, X. Y. Chen, W. M. Ju, and X. Geng, “Distributed hydrological model for mapping evapotranspiration using remote sensing inputs,” J. Hydrol., vol. 305, no. 1–4, pp. 15–39, Apr. 2005. [6] J. M. Norman and G. S. Campbell, “Canopy structure,” in Plant Physiological Ecology. Field Methods and Instrumentation., J. E. R. W. Pearcy, H. A. Mooney, and P. W. Rundel, Eds. New York: Chapman & Hall, 1989, pp. 301–325. [7] T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteorol., vol. 8, pp. 25–38, 1971. [8] L. M. Moskal and G. Zheng, “Retrieving forest inventory variables with terrestrial laser scanning (TLS) in urban heterogeneous forest,” Remote Sens., vol. 4, no. 1, pp. 1–20, 2011. [9] J. M. Chen and J. Cihlar, “Retrieving leaf area index of boreal conifer forests using Landsat TM images,” Remote Sens. Environ., vol. 55, no. 2, pp. 153–162, Feb. 1996. [10] J. M. Chen, C. H. Menges, and S. G. Leblanc, “Global mapping of foliage clumping index using multi-angular satellite data,” Remote Sens. Environ., vol. 97, no. 4, pp. 447–457, Sep. 2005. [11] G. Zheng and L. M. Moskal, “Retrieving leaf area index (LAI) using remote sensing: Theories, methods and sensors,” Sensors, vol. 9, no. 4, pp. 2719–2745, Apr. 2009.
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[33] J. L. Lovell, D. L. B. Jupp, D. S. Culvenor, and N. C. Coops, “Using airborne and ground-based ranging lidar to measure canopy structure in Australian forests,” Can. J. Remote Sens., vol. 29, no. 5, pp. 607–622, Oct. 2003. [34] T. Takeda, H. Oguma, T. Sano, Y. Yone, and Y. Fujinuma, “Estimating the plant area density of a Japanese larch (Larix kaempferi Sarg.) plantation using a ground-based laser scanner,” Agric. Forest Meteorol., vol. 148, no. 3, pp. 428–438, Mar. 2008. [35] F. Hosoi and K. Omasa, “Factors contributing to accuracy in the estimation of the woody canopy leaf area density profile using 3D portable lidar imaging,” J. Exp. Botany, vol. 58, no. 12, pp. 3463–3473, Oct. 2007. [36] A. H. Strahler, D. L. B. Jupp, C. E. Woodcock, C. B. Schaaf, T. Yao, F. Zhao, X. Yang, J. Lovell, D. Culvenor, G. Newnham, W. Ni-Miester, and W. Boykin-Morris, “Retrieval of forest structural parameters using a ground-based lidar instrument (Echidna (R)),” Can. J. Remote Sens., vol. 34, no. S2, pp. S426–S440, Nov. 2008. [37] I. Leica Geosystems HDS, HDS Scanning & Cyclone Traning Manual, St. Gallen, Switzerland, 2008. [38] E. E. Miller and J. M. Norman, “Sunfleck theory for plant canopies: 1. Lengths of sunlit segments along a transect,” Agronomy J., vol. 63, no. 5, pp. 735–738, 1971. [39] J. Ross, The Radiation Regime and Architecture of Plant Stands. Boston, MA: Kluwer, 1981. [40] D. W. Hilbert and C. Messier, “Physical simulation of trees to study the effects of forest light environment, branch type and branch spacing on light interception and transmission,” Funct. Ecol., vol. 10, no. 6, pp. 777– 783, Dec. 1996. [41] CGAL, Computational Geometry Algorithms Library. [Online]. Available: http://www.cgal.org [42] J. Dietz, D. Holscher, C. Leuschner, and Hendrayanto, “Rainfall partitioning in relation to forest structure in differently managed montane forest stands in Central Sulawesi, Indonesia,” Forest Ecol. Manage., vol. 237, no. 1–3, pp. 170–178, Dec. 2006. [43] N. J. Balster and J. D. Marshall, “Eight-year responses of light interception, effective leaf area index, and stemwood production in fertilized stands of interior Douglas-fir (Pseudotsuga menziesii var. glauca),” Can. J. Forest Res., vol. 30, no. 5, pp. 733–743, May 2000. [44] P. V. Bolstad, B. J. Bentz, and J. A. Logan, “Modelling micro-habitat temperature for Dendroctonus ponderosae (Coleoptera: Scolytidae),” Ecol. Model., vol. 94, no. 2/3, pp. 287–297, Jan. 1997.
Guang Zheng received the B.Eng. degree in urban planning from Nanjing Forestry University, Nanjing, China, in 2004, the M.Sc. degree in cartography and geographic information systems from Nanjing University, Nanjing, in 2007, and the Ph.D. degree in forest resources and management from the University of Washington (UW), Seattle, in 2011. He worked as a Research Assistant with the Remote Sensing and Geospatial Analysis Laboratory, Precision Forestry Cooperative, School of Environmental and Forest Sciences, College of the Environment, UW. He is currently a Research Scientist with the International Institute for Earth System Science, Nanjing University. His research interests are the application of light detection and ranging in retrieving forest canopy structural parameters and the application of remote sensing and geographic information systems in the field of forest ecosystem.
L. Monika Moskal is an Assistant Professor of remote sensing with the School of Environmental and Forest Sciences, College of the Environment, University of Washington (UW), Seattle, where she directs the Remote Sensing and Geospatial Analysis Laboratory founded by her in 2003. She is one of the core faculties in the UW Precision Forestry Cooperative. Her goal is to understand multiscale and multidimensional dynamics of landscape change through the application of remote sensing. Her research has been applied to the following themes: ecosystem services and function, bioenergy/biomass, forest inventories, forest health, change analysis, biodiversity, habitat mapping, spatiotemporal wetland assessment, geostatistical analysis of prairie vegetation communities, urban growth, and forest fragmentation.
