Remote Sensing of Environment

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1 Remote Sensing of Environment 115 (211) Contents lists available at ScienceDirect Remote Sensing of Environment journal homepage: Satellite lidar vs. small footprint airborne lidar: Comparing the accuracy of aboveground biomass estimates and forest structure metrics at footprint level Sorin C. Popescu a,, Kaiguang Zhao a, Amy Neuenschwander b, Chinsu Lin c a Spatial Sciences Laboratory, Department of Ecosystem Science and Management, Texas A&M University, 15 Research Parkway, Suite B 223, TAMU 212, College Station, TX 77845, United States b Center for Space Research, University of Texas, United States c Department of Forestry, National Chiayi University, Taiwan article info abstract Article history: Received 3 January 29 Received in revised form 23 November 21 Accepted 19 January 211 Available online 23 May 211 Keywords: ICESat GLAS Airborne lidar Biomass Height The use of lidar remote sensing for mapping the spatial distribution of canopy characteristics has the potential to allow an accurate and efficient estimation of tree dimensions and canopy structural properties from local to regional and continental scales. The overall goal of this paper was to compare biomass estimates and height metrics obtained by processing GLAS waveform data and spatially coincident discrete-return airborne lidar data over forest conditions in east Texas. Since biomass estimates are derived from waveform height metrics, we also compared ground elevation measurements and canopy parameters. More specific objectives were to compare the following parameters derived from GLAS and airborne lidar: (1) ground elevations; (2) maximum canopy height; (3) average canopy height; (4) percentiles of canopy height; and (5) above ground biomass. We used the elliptical shape of GLAS footprints to extract canopy height metrics and biomass estimates derived from airborne lidar. Results indicated a very strong correlation for terrain elevations between GLAS and airborne lidar, with an r value of.98 and a root mean square error of.78 m. GLAS height variables were able to explain 8% of the variance associated with the reference biomass derived from airborne lidar, with an RMSE of 37.7 Mg/ha. Most of the models comparing GLAS and airborne lidar height metrics had R-square values above Elsevier Inc. All rights reserved. 1. Introduction Lidar remote sensing from three platforms ground, airborne, and spaceborne has the potential to acquire direct three-dimensional measurements of the forest canopy that are useful for estimating a variety of forest inventory parameters, including tree height, volume, and biomass, and also for deriving useful information for characterizing wildlife habitat or forest fuels. While airborne lidar methods have been intensely researched for deriving measurements such as tree height and crown dimensions at stand level (Hall et al., 25; Næsset & Bjerknes, 21), plot level (Holmgren et al., 23a; Hyyppä et al., 21; Lim & Treitz, 24; Popescu et al., 24), or individual tree level (Chen et al., 26; Coops et al., 24; Holmgren & Persson, 24; Persson et al., 22; Popescu & Zhao, 28; Roberts et al., 25; Yu et al., 24), the use of airborne lidar data is usually limited to local or regional scale (Zhao & Popescu, 29), rarely at the extent of state-level in the continental United States (Nelson et al., 23, 28). In Scandinavian countries, lidar has been used operationally, in ongoing efforts towards national forest Corresponding author. address: s-popescu@tamu.edu (S.C. Popescu). inventories with lidar (Næsset, 27). Despite advances in airborne systems that afford pulse repetition rates of more than 1 khz and handling of multiple pulses in the air, the cost of airborne lidar is still high at large extents. Small footprint airborne lidar, sometimes referred to as airborne laser scanning (ALS), provides the best measurement accuracy of terrain elevation and vegetation heights, even on sloped terrain or for dense forests. However, large footprint, full waveform satellite lidar data, such as data provided by the Geoscience Laser Altimeter System (GLAS) aboard the Ice Cloud and land Elevation Satellite (ICESat), proved to have the potential for assessing vegetation parameters at unprecedented scales, from regional to continental and global extents. An overview of the ICESat mission is provided in Schutz et al. (25). ICESat laser measurements were designed with the primary objective of monitoring ice sheets mass balance. Measurements are currently distributed in 15 science data products which have interdisciplinary applications, including the characterization of land topography and vegetation canopy heights. The system operates by sending laser pulses with a frequency of 4 Hz and a pulse duration of about 5 ns. The returning echo is sampled every nanosecond and the digitized pulses are referred to as laser waveforms. The ICESat platform orbits at an altitude of approximately 6 km and from that height above ground, the laser footprints have approximately a 64 m circular /$ see front matter 211 Elsevier Inc. All rights reserved. doi:1.116/j.rse

2 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) diameter. In fact, the footprints are elliptical, with their size and ellipticity varying during the course of the mission, and are spaced at about 172 m intervals (Schutz et al., 25). GLAS surface elevations are reported with respect to the TOPEX reference ellipsoid. Among all GLAS standard products, the Level-1 altimetry products, GLA1, contain waveforms digitized in 544 bins with a bin size of 1 ns or equivalently 15 cm; however, beginning with the data acquisition phase L3A (October, 24), the bin size has been changed to 4 ns (6 cm), to reduce the risk of waveform truncation. The Level-2 global land surface products, GLA14, provide an alternate fitting which locates up to six Gaussian components (mode, amplitude, and sigma) to characterize the shape of the total waveform. The ICESat spacecraft allows for off-nadir pointing of the laser, by up to ±5, to target areas of interest or to compensate for orbit drift (Schutz et al., 25). For this study, we did not evaluate the effects of off-nadir laser pointing. A series of studies using GLAS data have successfully demonstrated the capabilities of GLAS data for estimating forest canopy heights (Harding & Carabajal, 25; Lefsky et al., 27; Rosette et al., 28) and forest biomass (Boudreau et al., 28; Lefsky et al., 25; Nelson et al., 29). Boudreau et al. (28) and Nelson et al. (29) used a similar methodology in a multiphase sampling approach to relate GLAS waveforms and profiling lidar measurements to field estimates of total aboveground dry biomass in Québec, Canada. An airborne profiling lidar system was flown (PALS, Nelson et al., 28) over existing ground plots and along ICESat orbital transects and two sets of equations were developed to enable biomass estimates for satellite waveforms: ground-pals and PALS GLAS. In their study of 25, Lefsky et al. used only maximum canopy height derived from GLAS and SRTM (Shuttle Radar Topography Mission) measurements as independent variables to estimate aboveground biomass. Their reference biomass values were derived from ground measurements on plots along the GLAS footprints, of rectangular shape, by using allometric equations based on diameter at breast height (dbh). In this study, biomass is defined in dry weight terms. Aboveground tree biomass refers to the weight of the tree portion that is found above the ground surface, when oven-dried until a constant weight is reached. Comparisons of airborne lidar measurements and GLAS waveform parameters are described in several other studies, such as Rosette et al. (29), Sun et al. (28a), or Boudreau et al. (28). Sun et al. (28a) evaluated the surface elevation and heights of waveform energy quartiles from GLAS with those derived from LVIS data (Laser Vegetation Imaging Sensor LVIS; Blair et al., 1999). Our study contributes to the existing research efforts of estimating biomass and height parameters with satellite lasers by using a wall-to-wall biomass map derived from individual tree measurements with airborne lidar and by using GLAS footprints of elliptical shape, as opposed to using the approximation of a circular shape employed in the previously mentioned studies. In addition, we used a Gaussian weighting of airborne lidar points when comparing airborne and GLAS data, to accommodate the Gaussian distribution of laser energy within the elliptical footprint. The footprint ellipse is determined by major ellipse axis, eccentricity, and azimuth orientation. Pang et al. (28) and Neuenschwander et al. (28) also used the exact shape of the GLAS footprint ellipse to compare height metrics derived from satellite waveforms and airborne lidar. By locating the study area on mainly flat terrain, we compared the accuracy of GLAS biomass and height measurements with only minimal effects of varied topography within the footprint. The use of the exact footprint ellipse shape for extracting corresponding airborne-lidar parameters further reduced the influence of unwanted errors in our comparison and, therefore, allows us to quantify the accuracy of satellite laser systems for estimating vegetation structure and biomass. For investigating canopy height metrics and biomass, we used airborne and satellite lidar collected during leaf-off season, February and March, respectively, to avoid any impact due to seasonal differences that might be a source of inconsistency in the regression between airborne and spaceborne lidar data, as indicated by Boudreau et al. (28). Future NASA Decadal Survey satellite missions, such as ICESat II, DESDynI, or LIST (NRC, 27), will need calibration and ground proofing of their methodologies for deriving vegetation structural parameters and airborne lidar can provide appropriate means of assessing the accuracy of spaceborne lidar canopy estimates. The overall goal of this study was to compare biomass estimates obtained by using GLAS waveform data and spatially coincident discrete-return airborne lidar data of forests in east Texas, which are characteristic of most of the southeastern United States. Since biomass estimates are derived from waveform height metrics, we also compared ground elevation measurements and canopy parameters. As such, more specific objectives were to compare the following parameters derived from GLAS and airborne lidar: (1) ground elevations; (2) maximum canopy height; (3) average canopy height; (4) percentiles of canopy height; and (5) above ground biomass. 2. Methods 2.1. Study area The study area is located in the southern United States (3 42 N, W), in the eastern half of Texas (Fig. 1) and covers approximately 48 ha. The study area includes Loblolly pine (Pinus taeda L.) plantations in various developmental stages, old growth Loblolly pine stands in the Sam Houston National Forest, and upland and bottomland hardwoods comprising Water Oak (Quercus nigra L.), Southern Red Oak (Quercus falcata Michx.), White Oak (Quercus alba L.), Sweetgum (Liquidambar styraciflua L.), and Winged Elm (Ulmus alata Michx.). Much of the southern U.S. is covered by forest types similar to the ones included in our study area, with similar forest types, productivity, and patterns of land use change. A mean elevation 1 2 Kilometers Legend L3I (Oct. 7) L3H (Mar. 7) L3G (Oct. 6) L3F (May 6) L3D (Oct. 5) L3C (May 5) L3B (Feb. 5) L3A (Oct. 4) L2C (May 4) L2B (Feb. 4) L2A (Oct. 3) Fig. 1. GLAS footprints over our study area in Texas, USA (QuickBird image) as of March, 28: For comparison of terrain elevation, only the GLAS shots acquired under no or low cloud conditions were chosen, which include L2A, L2B, L2C, L2B, L3D, L3F and L3G, and for comparison of vegetation structure against airbornelidar data, onlyl2b (Feb. 4) was used due to the closeness of acquisition dates for the two data sets.

3 2788 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) of 85 m, with a minimum of 62 m and a maximum of 15 m, and gentle slopes characterize the topography of the study area Field measurements Field measurements were acquired to provide accuracy information for measurements obtained from airborne lidar, such as tree height, crown width, and height to crown base. These lidar-measured parameters were used to derive a wall-to-wall aboveground biomass, as explained in Section Field data were acquired during May June 24 in 62 randomly selected circular plots, including 26.1-ha plots and 36.1-ha plots. The smaller plots were located in very dense and uniform young pine stands. A total of 14 trees were tallied with respect to height, crown width, height to crown base, diameter at breast height (dbh), species, and crown class (Kraft, 1884). The protocol for field mapping of individual trees and the comparison to airborne lidar-measured trees are described in great detail in Popescu and Zhao (28). Due to difficulties in matching with high accuracy lidar-identified and field-measured trees, we paired 117 lidar-field trees, out of 14. An objective matching of all trees is difficult, due to errors with GPS location of plot centers, automated lidar tree mapping, and location differences between tree tops identified on lidar data and stem bases mapped on the ground. Descriptive statistics for 117 lidar-ground matched trees, including 94 pines and 23 deciduous trees, are summarized in Table 1, to provide information on average forest condition and structure in the study area Lidar data Airborne lidar Discrete return lidar data were acquired in early March 24 from an average altitude of 1 m above ground level (AGL). The lidar system (Leica-Geosystems ALS4) recorded two returns per laser pulse, first and last, and used a laser with a wavelength of 164 nm. The reported horizontal and vertical accuracies with the Leica- Geosystems ALS4 system for the mission specifications of this project are 2 3 cm and 15 cm, respectively. Based on the beam divergence of.3 mrad and flight altitude, the average footprint size was 3 cm. For our dataset, the lidar system provided a 1 swath from nadir, for a total scan angle of 2. With a cross-hatch grid of flight lines, the average laser point density was 2.6 laser points per m 2. The point density corresponds to an average distance between laser points of about.62 m, for the entire point cloud. The average swath width was 35 m, with 19 and 28 flight lines in a north south direction and east west direction, respectively. A digital surface model (DSM) of the canopy top was created by interpolating lidar point elevations to a regular grid with a spatial resolution of.5 m using the Delaunay triangulation method. The lidar points used for creating the DSM included only the highest points in.5 by.5 m cells, to allow for an accurate characterization of the top canopy surface, as explained in Popescu et al., 24. The data provider produced a digital terrain model (DTM) with a resolution of 2.5 m. A canopy height model Table 1 Descriptive statistics of the field-measured trees that have been correctly matched with LiDAR-derived trees. Adapted from Popescu & Zhao (28). dbh (cm) Height (m) Crown diameter (m) Minimum Maximum Range Standard deviation Average Height to crown base (m) (CHM), which represents a three-dimensional surface that characterizes vegetation height across the landscape, was created at a resolution of.5 m by subtracting the resampled DTM from the DSM GLAS data ICESat was equipped with three lasers, L1 through L3, which were used to collect data at different times during the mission. All three of the ICESat lasers stopped collecting data, L1 on March 29, 23, L2 on October 11, 29, and L3 on October 19, 28. The GLAS data available over our study area were acquired with either L2 or L3 from February 24 to October 27, including the GLAS subcycles from L2A to L3I. Our analysis considered only the level-1 product GLA1 (GLAS waveform) and level-2 product GLA14 (land surface altimetry) of Release 28, and these two products were requested from nsidc.org/data/icesat/ via the GLAS data subsetter. The GLAS data were prescreened by examining quality flags, such as i_frir_qaflg and i_cld1_mswf, to select only waveforms that were acquired under no or little cloud conditions, which include the sub cycles of L2A, L2B, L2C, L2B, L3D, L3F and L3G. All these selected waveforms were used for extracting terrain elevation to be compared against airborne lidar-derived elevation, with a total of 184 waveforms. For the analysis relevant to forest canopies, only the L2B GLAS products on Day 51 (February) of 24 were used in order to reduce the temporal discrepancy between GLAS and airborne lidar data, which were acquired in early March 24. These L2B data contain 33 waveforms, all including trees within their footprints Multispectral imagery Our data set included a QuickBird (Digital Globe, Inc.) scene acquired in the spring of 24 during leaf-off (Fig. 1). The image has a spatial resolution of 2.4 m with four spectral bands, i.e., blue (45 52 nm), green (52 6 nm), red (63 69 nm), and NIR (76 9 nm). Radiometric calibration and ortho-rectification were applied to the image by Digital Globe, Inc. An examination of 1 conspicuous feature points revealed that the image and lidar canopy height model (CHM) geographically registers well with an error of less than 2.4 m. The QuickBird image was used in this study to extract thematic information for distinguishing forest types. For this purpose, we applied the maximum likelihood classifier to the image for mainly differentiating pines, hardwood, mixed forests, and grassland. The classification produced an overall accuracy of 86.5% through an onscreen evaluation of a random subset of 2 testing pixels. The QuickBird image was used in the process of deriving the reference biomass map with information extracted from airborne lidar (Section 2.5.1). In addition, visual interpretation of GLAS footprints overlaid on the QuickBird image was used to find footprints covering mixed stand conditions Data processing Biomass derivation with airborne lidar Individual tree parameters, including tree height, crown width and tree locations, were derived from the CHM using an individual-tree isolation software package called TreeVaw (Popescu & Wynne, 24). This software implemented a local maximum filtering with a variable circular window to locate individual trees. The window size is determined locally and adaptively according to the CHM height at the window center, assuming that a taller tree has a wider crown. Crown width is estimated by fitting polynomial functions on two perpendicular vertical profiles through each identified tree crown. Furthermore, the crown base height for each lidar-derived tree isolated by TreeVaw was calculated with the lidar voxel-based approach of Popescu and Zhao (28). To summarize the investigations of Popescu and Zhao (28), the best regression models for assessing individual trees with airborne lidar were able to explain 95%

4 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) of the variance associate with total tree height, 8% of the variance associated with crown base height, and 6% for crown width. Next, the aforementioned lidar-derived tree dimension variables, including tree height, crown width, and crown base height, were related to the field-measured dbh in two separate multiple linear regression models for the 94 pines and 27 deciduous trees, respectively. The two linear models provided R 2 values of.87 and.89 for pines and deciduous trees respectively, as detailed in Zhao et al. (29). Popescu (27) describes a similar method applied only to the pine trees. The two linear models were then applied in conjunction with the thematic information of the classified QuickBird image to predict dbh for the rest of the lidar-derived trees. Subsequently, these dbh estimates were inputted to the dbh-based general biomass equations for pine and mixed hardwood as compiled in Jenkins et al. (23) to compute above-ground component biomass. The classified QuickBird image was used to select between generalized biomass equations for pines and hardwoods when creating the biomass map. A study based on the same lidar dataset, Popescu and Zhao (28), includes a report on the accuracy of estimating individual tree heights. The estimated component biomass of each lidar-derived tree was then used to generate a spatiallyexplicit biomass map at a resolution of.5 m. The generation process proceeded tree by tree. The stem biomass was assigned to the pixel at the tree location and the foliage biomass was distributed uniformly over the pixels covered by the crown, as shown in Fig. 2. The resultant biomass map derived at individual tree level was used as the dependent variable in our investigations of deriving biomass using GLAS variables. Popescu (27) provides results on how well the individual tree biomass correlates to biomass values obtained by ground measurements of dbh used with generalized biomass equations provided by Jenkins et al. (23). Linear regressions models using lidar-derived biomass as the independent variable explained 87% of the variance associated with field-derived aboveground biomass for individual trees, with an RMSE of 169 kg (47% of dependent mean, i.e., field-measured aboveground biomass). Aboveground biomass at scales above tree levels can be derived by integrating tree-level results up to the desired scale. A similar method for obtaining a biomass map used as reference was employed by Zhao et al., GLAS data processing Ground-finding is crucial to the appropriate use of GLAS waveform metrics for vegetation analysis. We employed two independent approaches, one automatic and the other manual, to identify ground peaks for each GLA1 waveform. First, due to the observed presence of detector noise, a standalone peak finding algorithm based on the Gaussian mixture model was implemented to increase the probability that the last Gaussian reflection corresponds to the ground return (as per Neuenschwander et al., 28); second, using the GLAS's IDL reader library, a visualization program was developed to allow interactively and manually identification of ground peaks. The last 392 records (392 ns) of each GLAS waveform (GLA1) were geolocated using the latitude and longitude provided in the GLA14 product by matching the time-tags reported in both products. Since the last 392 records of GLAS waveforms are sampled at a 1 ns rate, the GLAS energy can be equated to height above the TOPEX Fig. 2. (a) The detailed biomass map at a.5.5 m resolution that was derived from airborne LiDAR data; (b) a zoom-in over the highlighted rectangular subset of (a). The map uses a gray scheme such that brighter pixels indicate higher biomass. Adapted from Zhao et al. (29).

5 279 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) ellipsoid in ~15 cm increments based on the speed of light and laser vectors. In addition to the Gaussian components, the signal start and signal end times are provided in the GLA14 product. The signal start time represents the maximum height within the canopy as it is when the detector signal exceeds background noise. The ground elevation is determined as the elevation at the maximum location on the last peak that was determined to be ground. The relative heights were derived by computing a cumulative distribution function of the waveform energy from the ground peak to the signal start, as in Sun et al. (28a, 28b). RH1 represents energy at the top of the canopy, RH5 is energy at 5% above the ground, and RH would correspond to the ground location. Moreover, waveform height metrics were also computed for the canopy energy, since some of the airborne lidar variables characterize only the canopy, such as the average canopy height from the CHM. These are comprised of the integrated energy for the canopy portion of the waveform, which is from signal start to location (N-1), where N is the number of peaks. The ground energy is the integrated energy distribution for the last detected peak. An energy penetration index (EPI) was also calculated as the ratio between ground energy and total waveform energy Co-registration and comparison of airborne and GLAS data GLAS waveforms were co-registered to the airborne lidar point data and its derivatives such as CHM and biomass maps. First, the coordinates of GLAS waveforms were converted from the TOPEX/ Poseidon ellipsoid to the WGS-84 ellipsoid, which is the georeference system of the airborne lidar data. In the conversion, we only accounted for the vertical shift between the two ellipsoids because the horizontal shift is practically negligible as compared to the nominal horizontal accuracies of airborne lidar and GLAS data; for example, the horizontal difference of the two ellipsoids at a longitude of 45 is less than 2. cm in magnitude, far less than 2 3 cm of the horizontal accuracy of the airborne lidar data. The vertical shift between the two ellipsoids can be well approximated by the following empirical formula: h i z TOP z WGS = ða TOP a WGS Þ cos 2 φ + ðb TOP b WGS Þ sin 2 φ where a and b are equatorial and polar radii for the corresponding ellipsoid, and φ is the longitude. The difference z TOP z WGS is approximately.71 m over our study area. ð1þ Fig. 3. Simulation of pseudo-waveforms from airborne lidar data: (a) the raw airborne lidar points within a GLAS FOV of about 228 m in diameter (see the text for the reason for choosing 228 m); (b) the Gaussian energy distribution of a GLAS laser pulse which can be used as a weighting function in simulating pseudo-waveforms; the inner oblique ellipse in white indicates the nominal footprint size as recorded in GLA6 and GLA14 products; and (c) a sample airborne lidar-simulated pseudo-waveform that was generated by across- and along-beam Gaussian weighting functions, as compared to the observed GLAS waveform.

6 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) The energy distribution of an incoming GLAS shot is approximately Gaussian both along and across the laser beam, i.e., the vertical and horizontal directions, (Fig. 3). Specifically, the relative magnitude of horizontal energy distribution over a footprint on ground is approximated by: ( " x 2 w h ðx; yþ = exp 2 + y #) 2 a b x = ðx x o Þ sinϕ + ðy y o Þ cosϕ y = ðx x o Þ cosϕ + ðy y o Þ sinϕ where (x o,y o ) refers to the footprint centroid, a and b are the semimajor and semi-minor axes of the footprint ellipse at which the intensity drops to e ( 2) of the maximum, and ϕ is the orientation of the major axis that is defined clockwise with respect to the north direction. Footprint sizes as determined by a and b could vary during the course of operation periods or sometimes even from one shot to the next, and the actual values of 2 a are provided in GLA14 products (i_tpmajoraxis_avg). The along-beam energy distribution of an emitted pulse is mainly specified by the pulse duration and thus can be defined by ð w v ðþ= t exp 2 t t 2 Þ σ 2 t where t is a reference time corresponding to the peak of an emitted pulse, and σ t is the duration from t to the time at which the intensity along the beam drops to e ( 2) of the maximum. The pulse duration parameter σ t varies slightly from one shot to another or during the course of operation, and its value can be estimated by fitting a ð2þ ð3þ Gaussian curve to transmitted pulses (GLA1); for example, σ t is about 5.727±.18 ns for the L2A GLAS shots used in this study. Pseudo-waveforms can be simulated from airborne lidar data by convoluting the airborne lidar points distribution with both Gaussian weighting functions w h (x,y) and w v (t); hence, metrics similar to those of GLAS can be extracted from these simulated pseudo-waveforms. In our simulation, an effective field of view (FOV) of 228 m in diameter was used, assuming a constant gain for the receiver telescope. This choice (3 6%) is based on Harding and Carabajal (25) who reported that the nominal diameter of the GLAS telescope FOV is ~38 m on the ground and that the detector sensitivity remains relatively uniform across the central 6% of the FOV and declines quickly beyond. Given the airborne lidar laser echoes (x i,y i,z i ) within a GLAS FOV, the pseudo-waveform is symbolically represented as 2 z WVðÞ= z I i w h ðx i ; y i Þ w v i U c rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U = i : ðx i x o + Δr x Þ 2 + y i y o + Δr y 228 and jz i zj Δh 2 where Δh specifies a height interval used to discretize pseudowaveforms, which in our simulation it was set to the GLAS bin size of.15 m; Δr x and Δr y jointly denote the horizontal offset of the footprint centroid relative to that of FOV, which is caused mainly by the boresight misalignment of the GLAS system, but this offset is practically difficult to measure and thus, we ignored the misalignment effect by simply assuming Δr x = and Δr y =; U denotes the set of those airborne lidar points that can be seen by the telescope; and I i represents the attributes of the ith airborne lidar echo, be it a first or last return. Following our prior work (Popescu & Zhao, 28; Zhao & Popescu, 29), we considered two attributes for I i, i.e., count and intensity. For count, the value for I i is equal to 1 for all i's, and the resulting pseudo-waveforms tend to only characterize the presence or absence of reflecting vegetation components. In contrast, pseudowaveforms simulated by using echo intensity for I i can potentially account for the variation in magnitude of reflected energy from different layers of canopies and the ground. It is noted that the ð4þ Table 2 Parameters compared in the regression analysis (height units are in meters). R-squared RMSE MODEL Terrain elevation ALS_terrain=.9944 GLAS_ground MaxH Maxh =.8277VH th percentile HP25=.1987EPI th percentile HP5=.431RH th percentile HP75=.49122RH th percentile HP9=.89RH9 1.8 AHAL AHAL = *RH *EPI AHCHM AHCHM = *RH *EPI Biomass biomass=7.5429*vh Fig. 4. A shift-searching procedure to assess the potential geo-registration error for a GLAS shot: the pixel position relative to the center (the cross) indicates the relative shift, and the value of an image pixel represents the correlation between the GLAS waveform and the airborne lidar pseudo-waveform simulated using the shift corresponding to that pixel. The cross sign indicates the location of (,), i.e., no shifting. The black dot indicates the shifting that yields the highest correlation between the GLAS and airborne lidar-simulated waveforms, which is the estimated geo-location error. Where variable abbreviations are: Airborne lidar: ALS_Terrain terrain elevation MaxH maximum vegetation height HP25 HP9 height percentiles (25th 9th) calculated from all laser returns AHAL average height of all laser returns AHCHM average canopy height from the CHM (canopy height model) GLAS: GLAS_ground terrain elevation manually derived from GLAS VH vegetation height RH 9, 75, 5, 25 relative height percentiles EPI energy penetration index

7 2792 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) magnitude of pseudo-waveforms generated by Eq. (4) is relative in unit. The pseudo-waveforms generated in our study for representing the vertical profiles of airborne lidar points frequency or echo intensity do not attempt to completely simulate true GLAS lidar waveforms. As mentioned in Blair and Hofton (1999), the true waveform represents the spatial distribution of the laser beam intensity across and along the beam path, given the usual definition of the laser beam width as full width at half maximum. Nevertheless, the pseudo-waveforms generated from laser points over the large area of a footprint are indicative of the vertical distribution of reflecting surfaces in the forest canopy and, therefore, they are expected to resemble closely the true observed GLAS waveforms. To compare airborne lidar- and GLAS-derived elevation at the footprint level, the airborne lidar DTM pixels intercepted by a GLAS footprint were averaged to produce an overall elevation by applying the across-beam weighting function of Eq. (2): Z ALS = j h z j w h x j ; y j h ð5þ x j ; y j j w h where the summation is over all pixels encircled by the GLAS FOV, and z j is the airborne lidar-derived elevation of the pixel at (x j, y j ). In addition, aboveground biomass at the footprint level was aggregated from the airborne lidar-derived fine-resolution biomass map, but no Gaussian weighting was applied due to a lack of clear physical meaning. GLAS geo-location as reported in GLA14 is subject to random errors. To assess the potential magnitude of such errors in GLAS pointing, we (a) ICEat elevation - manual (meter) ICESat (manual) vs. ALS Y=X ρ=.995 Bias= -.22 m RMSE=.78 m ALS Elevation (meter) (b) ICEat elevation - algorithm (meter) ρ= Bias=.42 m RMSE= 4.17 m 75 ICESat (algorithm) vs. ALS 7 Y=X An outlier ALS Elevation (meter) (c) Fig. 5. Comparison of terrain elevation at the footprint level between GLAS and airborne lidar data; (a) GLAS ground elevations were manually determined through visual inspection of individual GLAS waveforms (RMSE =.78); (b) GLAS ground elevations were derived using the ground-finding algorithm based on a Gaussian mixture model (RMSE=4.17 m); (c) example of waveform for which the ground-finding algorithm failed to correctly identify the true ground peak.

8 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) shifted each footprint center in both x and y directions within a window of [ 5, 5] m using a.5-m step, relative to its nominal location obtained from the GLA14 product; then, we identified as the potential geo-location error the relative shift that provides the best match between the GLAS waveform and the simulated pseudo-waveform (Fig. 4). We assumed the geo-coordinates of airborne lidar to be correct, since errors in airborne lidar geo-referencing are negligible compared to those of GLAS. Similar procedures were also used in Harding and Carabajal (25) and Zhao and Popescu (29), to pinpoint the registration errors between two independent data sources. (a) Mean X shift = -.73 m Mean Y shift = m Mean Radial shift = 25.4 m (b) -5 Fig. 6. a) Potential geo-location errors for the 33 L2B GLAS shots (Feb., 24) estimated by the shift-searching method of Fig. 4; b) an example corresponding to the filled circle of a) to demonstrate how the correlation between the GLAS and simulated waveforms is improved after accounting for the geo-location error of ( 11 m, 25 m).

9 2794 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) Regression analysis Statistics parameters from airborne lidar data and GLAS products for each registered GLAS footprint were extracted after co-registering the two datasets. These airborne lidar parameters include average canopy height, maximum canopy height, average height of all returns, height percentiles, and terrain elevation. All these airborne lidarderived parameters represent averages per GLAS elliptical footprint, except percentile heights. Linear regression models with a significance level of.5 were used to develop equations relating airborne lidar parameters as dependent variables and GLAS parameters as independent variables. As explained in Section 2.5.2, we extracted similar GLAS variables from both the entire waveform and from the canopy portion of it, and investigated the correlation with airborne lidar parameters for both sets of variables independently. 3. Results and discussion Linear regression results for estimating airborne lidar-derived parameters with GLAS data are shown in Table 2. However, Table 2 shows only results obtained when extracting variables from the entire waveform, since results were almost identical when using variables obtained from the canopy portion of the waveform. When comparing ground elevation from GLAS and airborne lidar for 184 waveforms, the manually derived GLAS elevations correlate well to those of airborne lidar (r=.995) with a bias of.22 m and a root mean square error (RMSE) of.78 m (Fig. 5b). This slight negative bias is most likely attributed to the off-nadir pointing or the atmospheric multiplescattering delay that has not been fully compensated by the correction algorithm. In contrast, for the automatic ground-finding procedure, elevations for 24 waveforms clearly do not follow the linear relationship between terrain elevations (Fig. 5b). These likely erroneous elevations are due to the failure of the GLAS groundfinding algorithm to correctly identify the ground elevation in some instances. For example, Fig. 5c depicts an outlier situation, although not in a statistical sense, for which the higher waveform peak above the true ground was misidentified as the ground. Furthermore, running a Kruskal Wallis test on the differences between the manually derived GLAS and airborne lidar terrain elevations, we noticed that GLAS estimation of ground elevation has shown considerable consistency across different laser operations (p=.21), similarly to the conclusion reached in Sun et al. (28b). In some other instances, it is possible that tree cover and moderate-relief ground are coalesced into a single broad return, as indicated by Harding and Carabajal (25). Out of the 24 waveforms with elevations located away from the linear trend, 1 were from 27, day 298, and nine were from 25, day 144, both leaf-on days when the recorded data contained noise, possibly due to atmospheric effects or cloud cover. Over sloped terrain, for a footprint that ranges from 52 to 9 m diameter, GLAS returns from both the canopy and ground surfaces can be mixed at the same elevation (Lefsky et al., 27), but with appropriate algorithms and topography information, the separation of waveforms into ground and canopy components is conceptually possible. For forests on level topography, discrete peaks in the waveform separate the height distribution of reflecting canopy surfaces from that of the underlying topography within the large GLAS footprint (Harding & Carabajal, 25), which explains the strength of the relationship between GLAS and airborne lidar terrain elevations in our study. Results for comparing GLAS waveforms and airborne lidar pseudowaveforms are counterintuitive. First, we had expected that the use of Gaussian energy weighting would improve similarities between GLAS waveforms and the simulated pseudo-waveforms, but the opposite is observed; for example, the correlation between GLAS waveforms and the count-based pseudo-waveforms using the Gaussian weighting is statistically lower than that without weighting, i.e., with the mean correlation coefficient of.8447 versus.885 (p-value=.11 from a one-tailed paired-t test). Second, the strength of correlation between GLAS waveforms and the pseudo-waveforms simulated from airborne lidar intensities is similar to that simulated from airborne lidar counts, regardless of whether the Gaussian weighting is used or not (e.g., p-value=.134 for paired comparison of correlation coefficients involving the intensity-based pseudo-waveforms with the Gaussian energy weighting). It appears difficult to determine what factors have led to the above counterintuitive results, but this does stress a need to better understand the linkage between airborne lidar canopy profiles and GLAS waveforms, preferably via rigorous, physically-based modeling approaches. Potential geo-location errors of GLAS, identified as the shift yielding the best match between the GLAS waveforms and simulated airborne lidar pseudo-waveforms, were estimated to be 25.5±11.6 m based on the 33 L2B waveforms (Fig. 6a). Accounting for these geolocation errors increases the correlation between the GLAS and airborne lidar waveforms to a significant degree (p-value less than.1 for a paired-t test) (Fig. 6b). However, it needs to be reminded that these identified shifts, though indicative of the possible misregistration errors, may not represent the true errors because of many confounding factors, such as the GLAS boresight misalignment. Fig. 7a shows the linear regression results for maximum height obtained for all 33 leaf-off waveforms. The significant variable that remained in the model was vegetation height obtained from GLAS. a) Maximum height (99.9 percentile) of ALS (m) b) Pines Hardwood/mixed Best fit (ALS vs. ICESat) An outlier y=.8277*x R 2 = ICESat vegetation height (m) Fig. 7. a) Regression line for maximum height; b) outlier footprint overlay on the airborne lidar-derived CHM.

10 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) The height value identified as an outlier in Fig. 7a, not in a statistical sense, depicts a situation when forest vegetation is only located towards the edges of the footprint, as indicated in Fig. 7b, with a low canopy height indicated by the waveform data. A situation like this may occur when the energy return from the edges of a footprint is too weak to be identified as a peak in the waveform, since the incident laser energy within a footprint shows a Gaussian horizontal distribution, with the peak located at the footprint center. Another possible explanation resides in the laser pointing inaccuracy, especially for L2B data collected in March 24, which did not include the latest geo-location calibration corrections. According to Carabajal and Harding (25), the laser pointing error can have a horizontal geo-location error of 2.4±7.3 m. Fig. 7a does not reveal any pattern of the regression fit for pine or deciduous footprints. For lower percentiles of the airborne laser height distribution within waveform footprints, the correlation between satellite and airborne variables was weak, e.g., for the 25th and 5th percentiles, with R-square values of.12 and.68, respectively. All other regression models for canopy height metrics had strong correlations, with R-square values above.9. The lower correlation observed for the smaller percentiles does not have a large impact on assessing biomass. Other studies, such as Næsset (27), which used lower percentiles among other explanatory variables to estimate forest characteristics, found that only higher percentiles, such as 6th a) 5 th percentile 5 percentile of ALS (m) c) 9 th percentile 9 percentile of ALS (m) ALS vs. ICESat Linear (ALS vs. ICESat) y =.431x R 2 = ICESat RH9_entire(m) ALS vs. ICESat Linear (ALS vs. ICESat) y =.89x R 2 = ICESat vegetation height (m) b) 75 th percentile 75 percentile of ALS (m) d) AHAL Average height of all returns of ALS (m) ALS vs. ICESat Linear (ALS vs. ICESat) y =.9122x R 2 = ICESat RH9_entire(m) ALS vs. ICESat Prediction Linear (ALS vs. ICESat Prediction) y = 1.2x -.11 R 2 = ICESat predicted AHAL (m) e) AHCHM f) Biomass Average height of CHM of ALS (m) ALS vs. ICESat Prediction Linear (ALS vs. ICESat Prediction) y = x + 3E-6 R 2 = ICESat predicted AHCHM (m) Biomass (Mg/ha) Biomass vs. VH Linear (Biomass vs. VH) y = x R 2 = ICESat vegetation height (m) Fig. 8. Regression results for canopy height metrics and biomass.

11 2796 S.C. Popescu et al. / Remote Sensing of Environment 115 (211) and 9th, remained significant in stepwise regression models for estimating ground-measured height characteristics. In our study, the highest R-square value was obtained for the 75th percentile (.95), followed closely by the average height of all laser returns (.94), which had a lower RMSE of 1.1 m. A weaker correlation between satellite and airborne variables for lower percentiles could potentially be explained by factors such as the influence of the airborne lidar scanning angle and the temporal pulse width for GLAS. Holmgren et al. (23b) found that the upper airborne lidar height percentiles were not affected much by the scanning angle for a laser with a footprint of.26 m. Their study indicated that a critical value of the scanning angle is a function of the ratio between crown length and diameter, being 1 for pine forests and 5 for spruce forests. Overall, Holmgren et al. (23b) found that a scan angle up to 1 has little effect on height measurements. With a maximum scanning angle of 1 for our airborne lidar data, our study did not consider the effects of scanning angle on the correlations between GLAS waveforms and airborne lidar. Results from stepwise regression analysis for the canopy height metrics, shown in Fig. 8, provide an interesting finding. From a pool of six candidate variables (i.e., RH 9, 75, 5, and 25, VH, EPI), the final models include a small set of GLAS canopy metrics that remained significant in all regression models, mainly the RH9, i.e., the 9th percentile of the waveform energy, and the energy penetration index (EPI). Except the models for the 25th percentile of the airborne laser hits distribution, which only included EPI as the independent variable, and for the maximum height, which was only based on GLAS vegetation height (VH), all other models included RH9. Several previous studies on waveform lidar, although using LVIS data, e.g., Drake et al. (22) and Anderson et al. (26), reported that the HOME (Height Of Median Energy) metric, which is equivalent to RH5 in this study, is useful in estimating forest structural attributes at the footprint level, but none of our final models included RH5 as a significant variable. Instead, VH or RH9 are significant variables consistently selected in all the fitted models except the one for the 25th airborne lidar percentile height, but the two variables did not enter any model simultaneously due to the high correlation between them (Table 3). Interestingly, to predict the average airborne lidar canopy heights, neither RH9 nor VH, which is equivalent to RH1, provided enough information as single variables in the models, because the higher percentiles represent the upper level of the canopy. Therefore, the addition of EPI the energy penetration index which can be considered as a proxy for canopy cover, improves the estimation of mean canopy heights (Neuenschwander et al., 28). Other studies found a good correlation between GLAS canopy height metrics and field estimates of the forest canopy. In their study of 27 which focused on algorithms for removing the terrain slope effects, Lefsky et al. were able to explain 83% of the variance in forest canopy height, with an RMSE of 5 m, in forest conditions from seven geographically distinct areas with either field-measured or airborne lidar-derived heights. Lefsky et al. (25) developed regression models that were able to explain between 59% and 68% of variance in field-measured forest canopy height (RMSE between 4.85 and m). Table 3 Correlation matrix of waveform metrics derived from GLAS. RH9-25 was calculated from the entire waveform energy. VH(RH1) RH9 RH7 RH5(HOME) RH25 EPI VH(RH1) 1 RH RH RH5(HOME) RH EPI For biomass, the only significant GLAS variable we found was the vegetation height (VH), which was able to explain 81% of the variance associated with aboveground biomass, with an RMSE of 37.7 Mg/ha. Boudreau et al. (28) obtained an R-square value of.59 for the profiling laser PALS GLAS relationship, although PALS data was acquired during the leaf-on season, while GLAS data was obtained during leaf-off. In a study of 25, Lefsky et al. found that GLASderived heights for forests in Brazil were correlated with fieldestimates of aboveground biomass, with R-square values of 73% and RMSE of 58.3 Mg/ha. Part of the unexplained variance in our model could be attributed to the presence of hardwood trees with leaf-off condition mixed with pines within the extent of some of the GLAS footprints located towards the southern part of the GLAS path. Although we used the airborne lidar-derived biomass as reference for assessing GLAS biomass estimates, we also acknowledge that there is unexplained variance in the airborne lidar biomass map when compared to ground measurements, as explained in Popescu (27). Whenever an allometric method is used to estimate biomass, errors are potentially introduced no matter what the scale is, from individual tree, GLAS footprint, to larger extents. Potential sources of errors can include statistical error associated with estimating coefficients and form of selected equations, measurement and data processing errors, and errors associated with developing national scale equations by compiling species- and site-specific equations that may be biased in favor of species for which published equations exist, e.g., Jenkins et al. (23). With our approach, part of the unexplained variance in the reference biomass map is associated with errors of estimating biomass with field measurements of dbh and errors associated with estimating dbh from lidar measurements of individual trees. Nevertheless, by using as reference a biomass map spatially coincident with the waveform footprints instead of estimating biomass on plots of a reduced size, we reduced the uncertainties of collocating GLAS biomass to the reference data and captured the relationship at the entire footprint level. 4. Conclusions With this study we investigated the retrieval of aboveground biomass estimates and canopy height metrics using GLAS data. A unique feature of our study is the parameter comparison at GLAS footprint level by extracting biomass values and height metrics within the exact shape of the footprint from spatially coincident airborne lidar data. This approach has clear advantages over field estimates of biomass and height. While other studies have used airborne lidar height metrics within the elliptical footprints for GLAS airborne lidar comparisons, to our knowledge, previous studies used only field estimated biomass with various plot configurations or a profiling laser, such as PALS (Boudreau et al., 28). By placing the study on terrain with negligible terrain slope effects, we eliminated errors associated with varied topography and present a measure of the ability of GLAS data to retrieve canopy structure metrics and biomass under favorable terrain conditions, possibly to serve as reference for methods aiming at separating terrain and canopy response with satellite waveforms. Other aspects of interest for future investigations could include the effects of lidar off-nadir looking on forest biomass assessment or data fusion and extrapolation techniques for extending lidar sample measurements to continuous areal coverage with high spatial resolution. Under favorable topographic conditions, GLAS data proved to be accurate in retrieving terrain elevation. Similarly, height metrics are highly correlated with equivalent parameters derived with airborne lidar data and can be used to estimate aboveground biomass at footprint level. However, as Lu (26) pointed out in a review article on remote sensing-based biomass estimation, biomass assessment remains a challenging task, especially for areas with complex forest structure and environmental conditions.