Retrieval of Effective Leaf Area Index in ... - Semantic Scholar

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 51, NO. 2, FEBRUARY 2013

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Retrieval of Effective Leaf Area Index in Heterogeneous Forests With Terrestrial Laser Scanning Guang Zheng, L. Monika Moskal, and Soo-Hyung Kim

Abstract—Terrestrial laser scanner (TLS)-based leaf area index (LAI) retrieval is an appealing concept, due to the ability to capture structural information of canopies as 3-D point cloud data (PCD). TLS-based LAI estimation methods promise a nondestructive tool for spatially explicit calibration of LAI estimated by aerial or satellite remote sensing techniques. These methods also overcome the sky condition restrictions of on-ground optical instruments such as hemispherical photography frequently used for LAI estimation. This paper presents a new method for estimating the effective LAI (LAIe) directly from PCD generated by TLS in heterogeneous forests. We converted the 3-D PCD into 2-D raster images, similar to hemispherical photographs, using two geometrical projection techniques in order to estimate gap fraction and LAIe using a linear least squares method. Our results indicated that the TLS-based algorithm was able to capture the variability in LAIe of forest stands with a range of densities. The TLS-based LAIe estimation method explained 89.1% (rmse = 0.01; p < 0.001) of the variation in results from digital hemispherical photographs taken of the same stands and used for validation. The Breusch–Pagan test score confirmed that the stereographic-projection-based TLS LAIe model was more robust compared to the Lambert azimuthal equal-area projection TLS LAIe model. Finally, we explore and show significant relationships between airborne-laser-scanner (ALS)-based and TLS-based LAIe estimates, showing promise for further exploration of utilizing TLS as a calibration tool for ALS. Index Terms—Hemispherical photography, heterogeneous forest, leaf area index (LAI), Light Detection And Ranging (LiDAR), terrestrial laser scanner (TLS).

Manuscript received August 16, 2011; revised January 31, 2012 and April 9, 2012; accepted June 3, 2012. Date of publication July 26, 2012; date of current version January 17, 2013. This work was supported in part by the National Science Foundation (NSF)-funded University of Washington (UW) Center for Advanced Forest Systems under NSF Award 0855690, by the UW Precision Forestry Cooperative, by the State Key Fundamental Science Funds of China under Grant 2010CB950701, by the Open Fund of the State Key Laboratory of Remote Sensing Science under Grant OFSLRSS201211, and by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The work of S.-H. Kim and L. M. Moskal was supported by the UW Royalty Research Fund under Grant 65-1853. 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]). S.-H. Kim is with the Center for Urban Horticulture, School of Environmental and Forest Sciences, University of Washington, Seattle, WA 98195-4115 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.2012.2205003

I. I NTRODUCTION

W

ATER and carbon cycles are two of the most important processes governing the biogeochemistry of global climate change and its impacts on the biosphere [1]–[4]. Leaf area index (LAI) is one of the most important ecosystem variables driving process-based models coupling water and carbon cycles [1], [5]. LAI influences canopy microclimate, determines ecosystem radiation use efficiency, and controls the fluxes of carbon, water, and energy between the atmosphere and vegetation, and consequently governs net primary productivity [6]–[11]. Remote sensing has advanced our ability to estimate LAI at different spatial and temporal grains and extents [12]; an array of methods from ground to aerial and satellite remote-sensing-based techniques had been reviewed by Jonckheere et al. [13] and Zheng and Moskal [14]. Light Detection And Ranging (LiDAR) is a promising active remote sensing technique and has been applied in many scientific fields to extract biophysical key parameters [15]–[18]. Airborne laser scanner (ALS) and terrestrial laser scanner (TLS) are the two most common platforms of LiDAR. Recent studies have demonstrated the usage of ALS to estimate LAI in a range of forested ecosystems [19]–[23]. Most ALS studies utilized the analogy between direct solar beam and the laser pulse penetrating the canopy, and thus applied the Monsi–Saeki theory of light attenuation following Beer’s law inside a canopy [24], [25]. For example, Morsdorf et al. [26] presented a method based on the ratio of the number of ground return points to canopy return points to estimate LAI similar to Beer’s law. Another common type of statistical model employing ALS is to estimate LAI based on the canopy physical metrics derived from LiDAR, such as height [27], crown depth [28], crown diameter [29], or crown volume [30]. However, no techniques exist to utilize TLS as a tool for developing ALSbased LAI estimates from a 3-D perspective. There are two commonly used methods for estimating LAI or leaf area density from the point cloud data (PCD) generated using TLS; one is a 3-D approach [31]–[35], and the other is the 2-D [36] approach. Usually, the 3-D approach is more computationally intensive because of the need for direct manipulation of large PCD. Compared with the 3-D-based method, the 2-D-based method is easily applicable to practical work since it is based on commonly accepted theories such as the Monsi and Saeki model [25] that was adopted in digital hemispherical photograph (DHP) techniques.

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In 2-D-based methods, the 3-D PCD are first converted to 2-D raster images to estimate the gap fraction that is used to retrieve LAI accordingly. For example, Danson et al. [36] presented a TLS-based method through projection techniques to measure canopy directional gap fraction distribution in forest stands and to determine the expected number of laser pulses in all directions in comparison with hemispherical photographs. They found good agreements between the two methods despite a narrow range of scan angles between 80◦ and 180◦ which only partially covered the hemispherical view of the canopy through cylindrical projection to convert the 3-D PCD to 2-D raster images. There are four types of most commonly used projections for converting object from hemisphere to a plane: polar, orthogonal, Lambert azimuthal equal-area, and stereographic equalangle [37]. The orthogonal projection is the simplest of the projection methods, displaying points on the hemisphere onto a plane normal to the projection line. The polar projection is limited because it cannot represent solid angles viewed from the hemispherical lens on the plane image as same area, and the similar area projected from the edge of the hemispherical lens is usually 50% larger than the area projected from the optical axis of the lens [37]; because hemispherical lenses are the most commonly available lens used, this limits the utility of this projection technique. In comparison, the Lambert azimuthal equalarea projection preserves the area and keeps the point density the same in both the projected region and hemisphere regions, while the stereographic equal-angle projection preserves the angle information [37]. It is really important and necessary to investigate the variation of projected area of similar region in hemisphere with different projection techniques. Thus, we chose these two more advanced projections in this work. Most of the optical-based instruments used for LAI estimation require specific light condition. For example, digital hemispherical photography should be collected in cloudy, dusk, or dawn light conditions, limiting the time when the data can be acquired. In this paper, we aimed to provide the first comparison, highlighting the strengths and limitations between these two projections when applied to effective leaf area estimation. The objectives of this work are as follows. 1) One of the goals of this research was to develop a scannerindependent approach to estimate effective LAI (LAIe) from PCD without light restriction. Different point densities and scanning directions of TLS and ALS result in different LAIe results for the same plot. 2) The second goal was to explore the relationships between LAIes generated from ALS and TLS and validate an ALS-based model with our TLS data. II. M ATERIALS AND M ETHODS A. Study Area The study was conducted in the Washington Park Arboretum (WPA) and used a 2004 aerial LiDAR-based LAIe map produced by Richardson et al. [19] for the same location to stratify 30 plots into three LAIe classes of low, medium, and high (10 plots per class). The WPA is located on the shores of Lake

TABLE I C HARACTERISTICS OF L EICA S CAN S TATION 2 TLS I NSTRUMENT

Washington, which is east of downtown Seattle, WA, and south of the University of Washington campus. WPA contains over 4600 species and cultivated varieties, including one of the most diverse collections of woody plants in the U.S. Among WPA’s 20 000 trees, shrubs, and vines, more than 10 000 are catalogued in collections. The range of tree species at the 30 circular plots with a radius of 30 m included such diverse species as Acer macrophyllum (big leaf maple), Pseudotsuga menziesii (Douglas-fir), Thuja plicata (Western red cedar), Araucaria araucana (monkey-puzzle tree), Magnolia grandiflora (southern magnolia), Robinia Neomexicana (New Mexican locust), number of trees per plot ranged from 5 to 17, and the diameter at breast height (DBH) range was from 18 to 56 cm. The LAI ranges from 0.37 to 6.96 across the 30 plots in this study area; although higher LAI values are found in other forest types, this range is common for urban canopies [38]. B. TLS and Hemispherical Camera Data Thirty plots were surveyed between September 8, 2008, and September 15, 2008, in the WPA. At each plot, the PCD were collected with Leica ScanStation 2 (Leica Geosystem AG, St. Gallen, Switzerland), and hemispherical photographs were captured with fish-eye-lens (Nikon FC-E9, 8 mm, f /2.8) mounted digital camera (Nikon CoolPix 4500, Nikon Inc., Melville, NY), which recorded all objects in a full 180◦ hemisphere. The Leica ScanStation 2 can collect 90% reflectivity at 300 m away from the scanner for general objects; the visible green light wavelength of the laser beam ensures that sufficient energy will illuminate and then be reflected by the green leaves. We set up the scanner for all 30 plots in the center of the plot; this assured that the distance between the scanner and all of the foliage elements in the 30-m plot was 15 m or less. More characteristics of the TLS used in this research, the Leica ScanStation 2, are found in Table I. In each plot, the TLS was leveled on the X- and Y -axes with the built-in dual-axis compensator function. A second digital adjustment was also performed to ensure that the leveling errors were within 0.002 m [39]. Then, the plots were scanned using a hemispherical method (horizontal: 0◦ to 360◦ ; vertical: −45◦ to 90◦ ) with 0.02-m sampling spacing with 4-mm spot size at 30 m; the minimum angle resolution of the scanner used in this work is 3 × 10−6 rad. In addition, we took 2-D hemispherical photographs for all plots at dawn or dusk with an image resolution of 2048 by 1360 pixels using three exposure lengths. The first image was taken with automatic exposure

ZHENG et al.: RETRIEVAL OF LAIe IN HETEROGENEOUS FORESTS WITH TERRESTRIAL LASER SCANNING

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Fig. 1. Stages of LAIe estimation from PCD with TLS and its comparison with DHP, where (a) shows the original PCD for the 30th forest plot, (b) shows the spherical projection, (c) shows the stereographic projection, (d) shows the annulus ring analysis, (e) shows the processed binary image of the hemispherical photograph, and (f) shows the true color hemispherical photograph; images are colored by height with red as low height and blue as high height (the solid lines in (a), (b), and (c) are the bounding boxes for 3-D PCD and 2-D image; the grid lines in (d) are the annulus rings and radial lines which divide the hemispherical area into small sections).

value setting, the second with the shutter speed that is one stop lower than the automatic shutter speed, and the third with two stops lower than the automatic shutter speed [40]. The images were acquired at the same height as the TLS PCD of 1 m to allow for comparisons between data captured by DHP and TLS. C. ALS Data For this research, we acquired ALS waveform data provided by Terrapoint USA, who flew a RIEGL LMS-Q560 laser scanner, with waveform signal digitization, over the WPA on August 8, 2007. This instrument was set to digitize waveforms at a sample interval of about 1 ns or 15 cm in linear distance. The scan angle ranged from −30◦ to 30◦ , and the pulse frequency was set at 133 000 Hz, resulting in a pulse density of about 10 pulses/m2 near nadir at ground level. The data were converted by the vendor to a discrete point format, yielding PCD with a density of at least 20 points/m2 and four returns per laser pulse, including labeled first and last returns. More detailed information regarding this data acquisition has been described by Vaughn et al. [41]. D. TLS PCD Processing In this paper, only the geometrical information of PCD (i.e., X, Y , and Z) was considered, and the spectral information (i.e., intensity) was ignored due to the inability to calibrate the intensity values. We first clipped the PCD of each plot to a circle with a 30-m radius and then removed all points with a height lower than the scanner (i.e., the Z coordinate was less than zero) [Fig. 1(a)]. We then converted the canopy-only PCD from Cartesian coordinate system to spherical coordinate system with a radius of one [Fig. 1(b)]. In order to compute the LAIe using the Gap Light Analyzer (GLA) software [42], the PCD of each plot were converted from 3-D to 2-D discrete

points using stereographic projection [Fig. 1(c)] and then saved as raster images. Once the TLS-based 2-D raster hemispherical photograph-like image was successfully produced, we imported them into the GLA to estimate the LAIe through steps that included registering images, setting the appropriate threshold, and computing the canopy structure parameters [Fig. 1(d)]. We generated the binary raster image where 0 or black represents the foliage elements and 1 or white represents the sky [Fig. 1(e)], in order to estimate the gap fraction and LAIe for each of the annulus rings representing the zenith angle ranges. 1) Linear Least Squares Inversion Algorithm: The DHP technique is one of the most common ways of estimating the LAIe for a forest stand. The key step in this method was setting up the appropriate exposure value in order to differentiate the foliage elements (0) and the sky (1) from the pixels in the raster hemispherical photographs generated using a mounted digital camera with a fish-eye lens. The theoretical foundation behind the DHP was the linear least squares inversion algorithm which was successfully developed and tested during the past few decades [43], [44]. We chose a method which describes the theoretical foundation and provides a good fit ellipsoidal model for approximating the leaf orientation distribution. Our method is summarized as follows: − ln P (θ) = G(θ, α) × Le / cos(θ)

(1)

where P (θ) is the gap fraction, θ is the zenith angle of incoming solar beams, α is the inclination angle of foliage element, and Le is the LAIe. After defining the following expressions: T (θ) = − ln P (θ) G(θ, α) K(θ, α) = cos θ

(2) (3)

where G(θ, α) is the mean projection of unit element area on a plane normal to the direction of incident light and is defined

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by [45] G(θ, α) =


cos α cos θ, cos α cos θ 1 +

2(tan x−x) π

θ ≤ π/2 − α

θ > π/2 − α (4)

,

where x = cos−1 (cot α cot θ), (1) can be rewritten as T (θ) = K(θ, α) × Le .

(5)

Once the value of α and the gap fraction P (θ) were obtained, Le was calculated based on (5) for a specific area with the same zenith angle. The leaf inclination angle distribution function was described using the ellipsoidal distribution [46] by ξ(α) =

2χ3 sin α Λ(cos2 α + χ2 sin2 α)

2

(6)

where α is the leaf inclination angle, χ = b/a, 0 ≤ α ≤ π/2, and ⎧ 1 ⎨ χ + (sin−1 ε)/ε, χ < 1; ε = (1 − χ2 ) 2 (1+ε) Λ= 1 ⎩ χ + ln (1−ε) , χ > 1; ε = (1 − χ−2 ) 2 . 2εχ a and b are the semishort and semilong axes, respectively. In this paper, the leaf inclination angle distribution was assumed to have a spherical distribution. Therefore, ellipsoidal distribution defined by (6) becomes spherical distribution, and Λ = 2. However, if Le is distributed at several inclination angles, as is generally the case, for example, having Le1 , Le2 , . . . , Len at α1 , α2 , . . . , αn, respectively, (5) can be rewritten as T (θ) = K(θ, α1 ) × Le1 + K(θ, α2 ) × Le2 + · · · + K(θ, αn ) × Len

(7)

where Le = Le1 + Le2 + · · · + Len . In this paper, the 3-D PCD of each plot were converted to “hemispherical photograph” like the 2-D raster images through two projection techniques and pixelization processes. Then, the TLS-based hemispherical photographs were analyzed using the GLA software using the linear least squares inversion algorithm. Each image was divided into nine annulus rings with 10◦ interval. By computing the T (θ) and K(θ, α) for each annulus ring [Fig. 1(d)] with a range of zenith angles, respectively, the extinction coefficient for each annulus ring was estimated using the ellipsoidal model. We obtained the Le for each annulus by only considering the annulus rings with zenith angles lower than 70◦ ; this helped to remove the geometrical distortions. 2) Stereographic Projection of PCD: The stereographic projection accurately preserves angle information; however, it is neither isometric nor area preserving. We projected the canopy-only PCD to 2-D raster images for all 30 plots. As shown in Fig. 2(a), we first converted the canopy-only PCD into spherical coordinate system with a radius of one, which projects the PCD onto the surface of a hemisphere. Point O was the origin point used to take projection for all points in the upper hemisphere surface. The projection plane intersected the sphere through a tangent point and was normal to the unique line between O and the center point. The aim of the stereographic projection was to project all points from the surface of the

Fig. 2. Schematic diagram illustrating the two projection techniques, where (a) shows the geometrical relationship of stereographic projection, XOY Z is the Cartesian coordinate system, P is any point on the unit sphere, and P is the projected point on the projection plane of point P and (b) shows the geometrical relationship of Lambert azimuthal equal-area projection, O is the intersected point of the projection plane with the unit sphere, P is any point on the unit sphere, and P is the projected point on the projection plane of point P .

upper hemisphere (3-D space) into the projection plane that is a 2-D space. For example, the projection of point P (x, y, z) on the surface of the upper hemisphere on the projection plane would be P (X, Y ). When both points were represented using the Cartesian coordinate system, these were computed and converted using the following formula:

x X = 1+z (8) y Y = 1+z 2X 2Y −1 + X 2 + Y 2 , , (x, y, z)= . 1 + X2 + Y 2 1 + X2 + Y 2 1 + X2 + Y 2 (9) 3) Lambert Azimuthal Equal-Area Projection of PCD: The Lambert azimuthal equal-area projection is commonly used from sphere to plane mapping technique. One of its characteristics is that it can accurately represent area in all regions of the sphere. However, the angles will not be accurately represented. We repeated the first two steps as shown in Fig. 1(a) and (b) to produce the canopy-only PCD for the 30 plots and converted it to the spherical coordinate system with a radius of one to generate the unit sphere. As shown in Fig.1(b), point O was the origin point used to take a projection for all points in the lower hemisphere surface. The projection plane intersected the sphere through the center and normal to the unique line between O and the center point. The aim of the Lambert azimuthal equal-area projection was to project all points from the surface of the lower hemisphere (3-D space) into the projection plane that is a 2-D space. For example, the projection of point P (x, y, z) on the surface of the sphere on the projection plane would be P (X, Y ); if both the points were represented using the Cartesian coordinate system, these were computed and converted using the formula

⎧ 2 ⎨X = x

1−z (10) 2 ⎩Y = y 1−z (x, y, z) =

X

X2 + Y 2 ,Y 1− 4

X2 + Y 2 −1 + 2

1−

X2 + Y 2 , 4

.

(11)


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Fig. 3. Comparison of the hemispherical photography raster images produced based on two projection techniques. (a) Stereographic projection. (b) Lambert azimuthal equal-angle projection. (c) Corresponding gap fraction distribution along the zenith angle direction.

E. Calculation of LAIe 1) DHP-Based Method: After examining the hemispherical photographs with the three exposure settings, we found that the photographs with the two stops lower than the automaticexposure-value best differentiated foliage elements from the background sky. By processing the digital hemispherical photographs using the GLA software [42], DHP-based LAIe values for 30 plots were computed. First, the digital hemispherical photographs were registered using the annulus rings with 10◦ interval to define the range of the photographs which were processed. Due to the geometrical distortion of fish-eye lens, only the annulus rings with zenith angles ranging from 0◦ to 70◦ were used for estimating LAIe. Second, by visually examining the logarithm of the gap fraction for each annulus ring, the appropriate threshold was determined in order to convert the hemispherical photographs into binary images which could well differentiate the sky and foliage elements. The TLS PCD were processed using the methods described in Section II-D. 2) ALS-Based Method: We cropped the 2007 ALS discreet point data for 26 of the 30 study plots using a 30-m radius and applied the model of Solberg et al. [47] previously identified by Richardson et al. [19] as the most appropriate existing model for these heterogeneous stands. A spherical leaf distribution was assumed in our calculations. Not all plots were used in the analysis, three were not in the 2007 ALS coverage, and the fourth was identified as an outlier with unexpectedly low DHPLAIe values based on the residual analysis and the DHP image; this conclusion was corroborated by comparing the plot to the model of Richardson et al. [19] derived from a 2004 discreet ALS coverage where the same pattern of much higher ALSbased LAIe values for the plot was observed. The LAI values found in the WPA, although representative for heterogeneous urban forests [38], limit our ability to test the technique on extreme (either high or low) LAI values; therefore, future research should consider other forest types such as disturbance sites for low LAI values and clonal plantation to explore high LAI values. III. R ESULTS A. Geometrical Projection Comparisons By using the two projection techniques, we obtained two 2-D raster hemispherical photograph-like images [Fig. 3(a) and (b)] for each of our 30 sites. The Lambert azimuthal equal-area pro-

Fig. 4. LAIe values obtained from DHP-based method for 30 plots.

jection preserves the area information while the stereographic projection preserves the angle information, resulting in slightly different gap fraction estimations for the final raster projection results. As shown in Fig. 3, the percentages of sky (black color) from the Lambert equal-area projection account for more than the sky portion from stereographic projection for this specific forest stand. B. LAIe Comparisons Based on the methods described, we estimated the LAIe values for all 30 plots, ranging from 0.185 to 6.96. We categorized the 30 plots according to the forest types, including broad leaf trees, coniferous trees, and mixed forest (Fig. 4). The broad leaf plots 1 through 6 had a high LAIe value, ranging from 4.3 to 6.9. However, it was one of the coniferous plots, i.e., plot 15, that held the highest LAIe value of all 30 plots at 6.96. In all three forest types, a range of high, medium, and low densities was recorded, which reflects the variation of LAIe estimation using our methods. The Lambert method tended to have the highest LAIe estimates of the three methods in the broad leaf forest and coniferous forest for plots with higher ranges of LAIe, i.e., over 3.4 LAIe. However, the same method tended to have the lowest LAIe, compared to the other two methods in the mixed forest. The stereographic method showed estimates closest to the DHP; this tends to hold true for all forest types and all ranges of LAIe.

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Fig. 5. Linear regression analysis using the TLS-based LAIe, where (a) shows the stereographic projection and DHP-based LAIe and (b) shows the Lambert equal-area projection and DHP-based LAIe. The solid line is the linear regression model, the thinner black line is the 1 : 1 line, and the gray dashed lines are the confidence interval (95%) for linear regression line. TABLE II L INEAR LAIe M ODELS U SING T WO P ROJECTION T ECHNIQUES

In the plots with a medium range of LAIe values (plots 7, 16, 19, and 25), the Lambert azimuthal equal-area projection method worked better than the stereographic projection method. In particular, in plot 24, the DHP method held the highest value of LAIe as 6.482; however, the Lambert and stereographic projection methods held values of 6.16 and 5.75 of LAIe, respectively. In general, it is difficult to determine which method is the best. Both methods capture the variation in LAIe for plots of different densities, and both tended to underestimate the LAIe. By plotting the LAIe values from the two tested projection methods with 1 : 1 line, as shown in Fig. 5, our results indicated that the stereographic projection explained 89.1% (rmse = 0.010; p < 0.001) variation of LAIe, while the Lambert azimuthal equal-area projection method explained 84.5% (rmse = 0.014; p < 0.001) (Table II). We observed from the trend lines that stereographic-projection-based LAIe estimation tended to underestimate the LAIe; however, it captured the general trend of the variation of LAIe obtained from the DHPbased method well. The linear regression line was almost parallel with the 1 : 1 line, which suggested that the TLSbased LAIe estimation method captured the variation of DHPbased LAIe values for three types of forest stand with a range of densities. The Lambert-equal-area-projection-based LAIe tended to overestimate the lower LAIe values. In addition, by observing the residuals between the predicted and actual values, in order to test the heteroskedasticity of our linear regression models, we took the Breusch-Pagan (B-P) test [48] (Table III) and found that there were issues with the Lambert-azimuthalequal-area-based linear regression models with our data. It

TABLE III B-P T EST S CORES FOR H ETEROSKEDASTICITY

indicated that the linear regression model might not be the best model for Lambert-azimuthal-equal-area-projection-based method. Moreover, in order to examine the performances of the linear models, we performed a residuals analysis for both linear regression models. It was shown that the standardized residuals from stereographic projection were evenly distributed around the zero line, and the error was larger with the overestimated predicted values compared with the underestimated predicted values. However, in the case of Lambert projection method, the standardized residuals were evenly distributed in both overestimated and underestimated predicted values. Our results show that there was a significant correlation of 0.844 (p < 0.001) between the TLS-based (stereographic projection) and ALS-based LAIe estimates (Fig. 6). Thus, we used the TLS-based LAIe estimate to validate 2007 ALS-based LAIe estimates. Using a linear regression model, we found an R squared of 0.713, with a standard error of estimate of 1.03. The scatterplot with the model for this analysis is shown in Fig. 6. IV. D ISCUSSION The TLS-based method worked well for LAIe estimation based on two geometrical projection methods. Both the Lambert azimuthal equal-area and stereographic projection methods adequately explained the variation of LAIe for three types of forest stand. Overall, the stereographic projection method correlated better to the DHP-based LAIe values used for validation. This research only focused on the LAIe estimation, as pointed out by Hosoi and Omasa [33]; the nonphotosynthetic tissues and leaf angular distribution contribute


Fig. 6. Linear regression analysis used to validate the 2007 ALS-based LAIe using TLS-based LAIe. The solid line is the linear regression model, the thinner black line is the 1 : 1 line, and the gray dashed lines are the confidence interval (95%) for linear regression line.

4.2%–32.7% and 7.2%–94.2% for estimation errors of LAI, respectively. Since an abundant amount of 3-D information is contained in PCD generated with TLS, it might be possible to directly retrieve the leaf inclination distribution and percentage of nonphotosynthetic materials (for example, woody-to-totalarea ratio), which could greatly improve true LAI estimation. Initial work in this direction, applying LiDAR intensity, has been demonstrated by Lim and Suter [49]; however, further analysis relying on scanner intensity in canopy environments is needed, and methods for calibration of scanner intensity are still required. This research is in agreement with the results obtained from Danson et al. [36] focused on gap fraction estimation from TLS-based PCD through projection techniques. Their results also showed that TLS-based methods tend to underestimate gap fraction; we further corroborate this finding by showing that TLS-based methods tend to overestimate LAIe. We affirmed that TLS-based method for gap fraction estimation has a high processing efficiency combined with the existing software package such as GLA, which has also been realized by Huang and Pretzsch [34]. The method developed in this research is repeatable and showed consistency with the DHP-based LAIe methods, which has been verified by Jupp et al. [50]. There are still some bottlenecks in practical applications of TLS that may be improved as the technology is enhanced over time. • First, the TLS cost is higher compared with the existing instruments used for tree structural information estimation such as DHP techniques, Tracing Radiation and Architecture of Canopy (TRAC), or range finder. • Second, TLS is not portable to use in the field. • Third, the scanning speed at very high resolutions is slow, increasing the time required in the field to collect the data. • Fourth, there is no standard protocol for TLS field setup and sampling protocol for forest inventory parameters and LAI estimation. The linear regression analysis applying B-P test revealed that the Lambert azimuthal equal-area projection method had the heteroskedasticity issue. By analyzing the residuals, it was

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found that the residuals of Lambert projection increase as the LAIe values increase significantly. It is suggested that the cubic or polynomial regression models should be used to predict the LAIe values using the Lambert-projection-based method. By projecting the PCD generated by TLS into 2-D hemispherical photograph-like raster images, one could obtain LAIe results, which hold good agreement with the DHP method. In the meantime, the 3-D structural information of the scanned canopy is lost. One alternative approach is to estimate the LAIe or even true LAI from PCD without converting to 2-D images. This could enhance our ability to capture both 2-D information and 3-D information. For example, one could estimate the leaf orientation through computing the normal vectors for PCD to characterize the spatial and angular distributions and then further estimate the projection coefficient and gap fraction from a 3-D perspective. This is a direction deserving further research. The methods demonstrated in this work were used to estimate LAIe instead of true LAI, which removes the clumping and overlapping effects inherent in true LAI estimates [51], [52]. However, woody materials also highly contribute to light interception that can greatly affect the accuracy of true LAI estimation. Since the wavelength of laser beam used in this research was green visible light, the alternative method might be to apply the near-infrared-laser-beam-based TLS system, which might separate the photosynthetic and nonphotosynthetic materials based on their different spectral characteristics. Therefore, methods for estimating percentage of nonphotosynthetic tissues and leaf angular distribution directly from PCD are needed and are suggested here as a direction for future research using TLS technology. One possible approach to tackle this problem is to separate the points representing nonphotosynthetic materials from the entire PCD using the principle component analysis based on the 3-D distribution pattern. The methods developed here allowed us to use our TLS-based LAIe to validate an ALS-based LAIe model previously shown to be the best existing model for our types of heterogeneous forests [19]. The model shows good agreement with the TLS data, confirming the results of Richardson et al. Similarly, as with other ALS-based models, the ALS-based approach underestimates the LAIe [19]–[21]. Since our results show that the TLS-based estimates fit well with the DHP-based estimates, one could consider using TLSbased estimates as a covariate in geostatistical modeling of biophysical variables such as LAI. However, this would be a complicated issue in heterogeneous forest, where sampling design with the TLS is also an issue; both topics should be explored in future research, particularly the sampling design, which could help us understand the impacts of within-stand and within-canopy occlusions on LAI estimation. In addition, destructive sampling for an array of tree species should be considered in future work in order to test this method. In this research, we demonstrated a new method to estimate LAIe from PCD generated using TLS in a heterogeneous forest through two geometrical projection techniques. Compared with the traditional optical-instrument-based LAI estimation methods such as DHP LAI-2000 or TRAC [53], the TLS-based LAIe estimation methods have some advantages.

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• First, the TLS-based LAIe estimation method was not affected by the light environment in the forest stands. For example, cloudy skies are ideal light conditions for DHP to differentiate foliage elements from the background of hemispherical photographs [40]. In comparison, a direct sunlight beam is necessary for TRAC to retrieve the clumping effects through measuring the radiation frequency from gap size distributions [52]. By contrast, the TLS-based LAIe estimation method can work in both cloudy and sunny light conditions. • Second, the PCD obtained using TLS are not only used to estimate the LAIe from a 3-D perspective but can also permanently record the 3-D structural information of forest canopy. In addition, the true color images collected with the built-in cameras for some TLS equipment can reflect the forest health condition of leaves. • Third, the abundant information implicitly contained within the PCD generated using TLS could provide more information about the canopy structure besides LAI. This includes canopy volume, fractional cover to estimate carbon, or water fluxes. In addition, the permanently recorded forest canopy structural information when collected at multiple dates can allow for monitoring of phenology, leaf senescence, tree death, and disease progression. The additional information will enhance our ability to monitor forest tree structure from a 3-D perspective dynamically, which could provide useful data for the long-term ecological studies such as the National Ecological Observation Network in experimental forest, Long Term Ecological Research (LTER), and Evergreen Ecological Observation Network. Similarly, TLS could serve as a calibration tool or an automated ground-truthing tool for large-scale ALSbased modeling. This research only focused on the geometrical information implicitly contained within PCD; at the same time, the PCD also recorded the returned energy information, per pulse intensity. Therefore, full-waveform LiDAR system could be an alternative method since it records the full returned energy instead of only one single return above a certain threshold. Based on the intensity information, one might obtain more accurate gap fraction information using a discrete or fullwaveform TLS system. Some ALS-based methods used for gap fraction estimation had been developed by Hopkinson and Chasmer [54]. However, TLS intensity-based methods for gap fraction or LAIe estimation are still an unsolved question. This is a direction deserving further research. V. C ONCLUSION Our results have shown that the TLS could be used to estimate LAIe for heterogeneous forests at forest plot level without the restriction of the light environment. It also can permanently record the 3-D structural information through collecting PCD and taking the true color images for the forest stand. With the advancement of LiDAR instrument technology, TLS may become faster and more portable for fieldwork. For example, vehicle-based laser or mobile laser scanning is already being explored by some [55]. In addition, by collecting PCD for a

given forest stand, one can estimate other biophysical parameters such as diameter at breast height [17], [56], [57]. Although, ideally, we would have liked to explore the LAIe relationships with destructively sampled LAI, this type of approach was not feasible in urban forests such as our arboretum site. Furthermore, species-based allometric-equation-driven LAI is also problematic since the allometric equations were developed for closed canopy forest with different lighting conditions compared to the heterogeneous canopies in our urban forest. We were able to demonstrate relationships between ALS and TLS LAIe estimates, suggesting that TLS could serve as a calibration tool for large-extent ALS and potentially satellite LiDAR-based LAIe estimation. Similar exploration of these complimentary tools was undertaken by Lovell et al. [16]; our research focuses specifically on LAIe and not general forest structure but demonstrates the same patterns in strong relationships between TLS and ALS. Thus, TLS is showing to be the ideal tool for noncontact nondestructive sampling of heterogeneous canopies, with promising potential for calibration of ALS-based spatially explicit LAIe models. With further development of these tools, and methods for extracting biophysical and ecological parameters from TLS data sets, long-term forest ecosystem monitoring will benefit from repeatable techniques assuring data for sustainable forest management practices. ACKNOWLEDGMENT The authors conducted this research at the University of Washington Remote Sensing and Geospatial Analysis Laboratory and the International Institute for Earth System Science, Nanjing University. The authors would like to thank N. Hackman, J. Richardson, and P. Johnsey for their help in the field data collection. R EFERENCES [1] 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. [2] 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. [3] N. Nikolov and K. F. Zeller, “Modeling coupled interactions of carbon, water, and ozone exchange between terrestrial ecosystems and the atmosphere. I: Model description,” Environ. Pollut., vol. 124, no. 2, pp. 231– 246, Jul. 2003. [4] P. J. Sellers, Y. Mintz, Y. C. Sud, and A. Dalcher, “A simple biosphere model (SiB) for use within general-circulation models,” J. Atmos. Sci., vol. 43, no. 6, pp. 505–531, Mar. 1986. [5] 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. Pollut., vol. 83, no. 1/2, pp. 251–262, 1994. [6] H. A. Cleugh, R. Leuning, Q. Z. Mu, and S. W. Running, “Regional evaporation estimates from flux tower and MODIS satellite data,” Remote Sens. Environ., vol. 106, no. 3, pp. 285–304, Feb. 2007. [7] R. E. E. Jongschaap, “Run-time calibration of simulation models by integrating remote sensing estimates of leaf area index and canopy nitrogen,” Eur. J. Agronomy, vol. 24, no. 4, pp. 316–324, May 2006. [8] G. B. Bonan, “Importance of leaf area index and forest type when estimating photosynthesis in boreal forests,” Remote Sens. Environ., vol. 43, no. 3, pp. 303–314, Mar. 1993. [9] 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.


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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, Seattle, in 2011. 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 system in the field of forest ecosystem.

L. Monika Moskal is currently 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.

Soo-Hyung Kim is currently an Assistant Professor of plant ecophysiology with the Center for Urban Horticulture, School of Environmental and Forest Sciences, College of the Environment, University of Washington, Seattle. His research investigates how plants function and interact with the environment. He applies experimental approaches to study the coordination and integration of low-level physiological processes (e.g., photosynthesis, water use, and nitrogen relations) into whole-plant and ecosystem behaviors. In addition, his research program develops and applies process-based plant models for evaluating plant–environment interactions, optimizing resource use and productivity, and developing adaptive solutions to climate change in agricultural and other managed ecosystems. He is particularly interested in investigating the linkages between crop production, climate change, and human health.