ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

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ISPRS Journal of Photogrammetry and Remote Sensing

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Assessment of terrain elevation derived from satellite laser altimetry overmountainous forest areas using airborne lidar dataQi Chen ∗Department of Geography, University of Hawai`i at Manoa, 422 Saunders Hall, 2424 Maile Way, Honolulu, HI, 96822, USA

a r t i c l e i n f o

Article history:Received 11 December 2008Received in revised form21 September 2009Accepted 21 September 2009Available online 2 October 2009

Keywords:GLASGaussian decompositionElevationLidar

a b s t r a c t

Gaussian decomposition has been used to extract terrain elevation from waveforms of the satellite lidarGLAS (Geoscience Laser Altimeter System), on board ICESat (Ice, Cloud, and land Elevation Satellite). Thecommon assumption is that one of the extracted Gaussian peaks, especially the lowest one, correspondsto the ground. However, Gaussian decomposition is usually complicated due to the broadened signalsfrom both terrain and objects above over sloped areas. It is a critical and pressing research issue toquantify and understand the correspondence between Gaussian peaks and ground elevation. This studyuses ∼2000 km2 airborne lidar data to assess the lowest two GLAS Gaussian peaks for terrain elevationestimation over mountainous forest areas in North Carolina. Airborne lidar data were used to extract notonly ground elevation, but also terrain and canopy features such as slope and canopy height. Based on theanalysis of a total of ∼500 GLAS shots, it was found that (1) the lowest peak tends to underestimateground elevation; terrain steepness (slope) and canopy height have the highest correlation with theunderestimation, (2) the second to the lowest peak is, on average, closer to the ground elevation overmountainous forest areas, and (3) the stronger peak among the lowest two is closest to the ground forboth open terrain and mountainous forest areas. It is expected that this assessment will shed light onfuture algorithm improvements and/or better use of the GLAS products for terrain elevation estimation.

© 2009 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published byElsevier B.V. All rights reserved.

1. Introduction

Terrain elevation is a key input in numerous environmentalapplications and its quality plays a critical role in understandingvarious earth surface processes (Kenward et al., 2000; Clarke andBurnett, 2003; Neeson et al., 2008). Laser altimetry, also calledlidar (light detection and ranging), is a frontier remote sensingtechnology for mapping earth surface elevation with high verticalresolving ability (Sun et al., 2003; Lefsky et al., 2005; Hofton et al.,2006; Chen, 2007; Simard et al., 2008). As the only operatingsatellite laser altimeter, GLAS (Geoscience Laser Altimeter System)on board ICESat (Ice, Cloud, and land Elevation Satellite), provideshigh-precision elevation data with nearly global spatial coverage.For flat, non-vegetated surfaces the vertical accuracy of GLAS hasbeen measured at better than 10 cm and with a vertical precisionof 2–3 cm (Fricker et al., 2005; Martin et al., 2005; Magruder et al.,2007; Neuenschwander et al., 2008). GLAS data have been used formany scientific studies such as measuring sea ice elevation (Kurtzet al., 2008), mapping canopy height (Lefsky et al., 2005; Simard

∗ Tel.: +1 808 956 3524; fax: +1 808 956 3512.E-mail address: qichen@hawaii.edu.

0924-2716/$ – see front matter© 2009 International Society for Photogrammetry anddoi:10.1016/j.isprsjprs.2009.09.004

et al., 2008), and validating SRTM elevation (Bhang et al., 2007; Sunet al., 2008).As an active remote sensor, GLAS transmits laser pulses at a

frequency of 40 Hz and illuminates the earth’s surface with∼60mfootprints and ∼170 m spot spacing (Zwally et al., 2002). Thereturned signals are waveforms typically characterized with oneor multiple peaks. Over flat areas, the lowest distinct peak usuallycorresponds to the ground elevation if there is enough laser energyreflected from the ground. However, over mountainous areas withhigh relief, the peaks from ground and surface objects can bebroadened and mixed, which makes the extraction of groundelevation very difficult (Zwally et al., 2002; Harding and Carabajal,2005; Lefsky et al., 2005). The current practice is to decomposewaveforms intomultiple Gaussian distributions, assuming that thelowest peak corresponds to the ground surface while the higherpeaks correspond to the overlaying vegetation and/or culturefeatures (Hofton et al., 2000; Brenner et al., 2003; Wagner et al.,2006; Duong et al., 2008). However, the elevation of the lowestGaussian peak has not been widely tested for ground elevationestimation over mountainous areas. Given the significance ofextracting ground elevation from GLAS data, it has become anurgent research issue to investigate the correspondence betweenwaveform Gaussian peaks and ground elevation (Brenner et al.,2003).

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112 Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

Assessing the terrain elevation over large areas is challengingbecause it is very time-consuming and costly to acquire highquality elevation data using field equipments such as GPS andtotal stations. This is especially true for mountainous forestareas where the accessibility is limited and the GPS errors areusually large. Conventional remote sensing technologies suchas photogrammetry or radar cannot generate an accurate DEMover forest areas either (Hodgson et al., 2003). Carabajal andHarding (2005, 2006) compared SRTM with the GLAS waveformhighest, centroid, and lowest elevation and they found thatSRTM DEM is relatively unbiased with respect to the waveformcentroids. However, neither waveform centroid nor SRTM DEMtruly represents the ground elevation over vegetated areas(e.g. Weydahl et al., 2007).Airborne lidar seems the most ideal technology to obtain

accurate DEM over large forested areas because of its highprecision and its ability to obtain ground returns over vegetatedareas. Nevertheless, only a paucity of studies have used airbornelidar data to evaluate the ground elevation derived from GLASdata over forested areas. Sun et al. (2008) compared the groundelevations from ∼200 GLAS shots and a medium-size (10 m)footprint lidar (LVIS: Laser Vegetation Imaging Sensor) in a mixedforest dominated by pines (Pinus virginia) and oaks (Quercusspp.) within the USDA’s Beltsville Agricultural Research Center inMaryland, USA. They found that the ground elevation from GLASis about 5.8 m higher than that from LVIS. Neuenschwander et al.(2008) found that GLAS-estimated ground elevations were biasedby +1 m compared to small-footprint (10–20 cm) airborne lidarin a savanna woodland ranch (∼17 km2) near San Marcos, Texasbased on the analysis of 37 GLAS shots. The topography of theirstudy site, the Freeman Ranch, is relatively flat with low hills.Overall, the areas and the number of GLAS shots evaluated in thesetwo studies are relatively small. This is not only because it is costlyto acquire airborne lidar data over large area, but also becauseautomatically generating DEM from the sheer volume of airbornelidar data presents a big challenge. (Chen, 2007). Recently, Duonget al. (2007, 2009) compared terrain and feature heights derivedfrom 3172 GLAS shots with a countrywide airborne lidar dataset(the Actual Height model of the Netherlands: AHN). They foundthat the average differences between GLAS- and AHN-derivedterrain heights are below 25 cm over bare ground and urban areas;over forests, the differences are even smaller but with a slightlylarger standard deviation of about 60 cm (Duong et al., 2009).Focusing on themountainous forest areas, this study is to assess

the ground elevation extracted from GLAS for ∼1000 shots overthe Appalachians in North Carolina using large-area airborne lidardata. This study area was chosen not only because the statewideairborne lidar data for North Carolina were available through theNorth Carolina Floodplain Mapping Program (NCFMP) but alsobecause the terrain is steep with dense canopy cover. The mainobjectives of this study are to (1) evaluate the differences betweenthe elevation of the lowest two GLAS peaks resulted by Gaussiandecomposition and the ground elevation derived from airbornelidar data, (2) examine how terrain and canopy properties affectthese differences, and (3) investigate how GLAS data can be betterused for estimating ground elevation.

2. Study area and data

2.1. Study area

Two regions in North Carolina were chosen for this study(Fig. 1). Each region consists of a mosaic of individual 3048 by3048 m tiles of airborne lidar data that coincided with GLAS shots.The first region (denoted as region 1 hereinafter) is within IredellCounty and has an area of about 794 km2. The elevation varies from

Fig. 1. The location of study areas (region 1 and 2). A subset of the shaded DEM isto show details of the topography.

183 m to 401 m and the mean slope is 5.8◦ (Fig. 2(a)). The majorland covers are pasture, deciduous forest, shrubs, and developedareas. The second region (denoted as region 2 hereinafter) islocated in themountainous forest area of the Appalachians, mainlytraversing 4 counties from north to south: Watauga, Avery, Burke,andMcDowell (Fig. 1) and covering about 1164 km2. The elevationvaries between 300 m and 1806 m with a mean elevation of681 m. Compared to region 1, the slopes in region 2 are muchsteeper with a mean of 15.7◦ and maximum of 82.6◦ (Fig. 2(b)).Region 2 is dominated by deciduous forests with a minority ofevergreen trees. In the southern part of the region, mainly inBurke andMcDowell counties, the landscape is amosaic of pasture,grassland/herbaceous, developed areas, deciduous, and evergreenforests. In this study, region 1 is used to search GLAS shots overopen terrain and to examine howGLAS peak elevations correspondwith ground elevation without the effects of vegetation; region 2is used to assess the effects of both terrain and vegetation on GLASpeak elevation bias.

2.2. GLAS data

There are three lasers on GLAS. Laser 1 started to collect data inFebruary, 2003, but it failed shortly after its launch. Lasers 2 and 3

Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122 113

a b

Fig. 2. DEM and slope for region 1 (a) and region 2 (b).

have collected data with a number of 33 day sub-cycle campaignsto increase their longevity. The receiver on GLAS records thereflected waveforms in 544 bins over ice sheets and land (Brenneret al., 2003), which yields an 81.6 m height range for Laser 1A and2A campaigns with 1 ns (equivalent to 15 cm range) sampling rateat each bin. For subsequent operations, the height range has beenincreased to 150 m with 1 ns sampling at the lower 392 bins and4 ns sampling at the higher 152 bins to avoid truncating returnsfrom tall objects and steep slopes (Harding and Carabajal, 2005).The GLAS data used in this study are from campaign L3C

(May–Jun 2005), L3D (Oct–Nov 2005), L3F (May–Jun 2006), L3G(Oct–Nov 2006), L3H (Mar–Apr 2007), L3I (Oct–Nov 2007), andL3J (Feb–Mar 2008), where L3 stands for Laser 3 and each letterstands for different acquisition periods of that laser. The heightranges of these waveforms are all 150 m (or 1000 ns). The GLASLaser 3 aboard the ICESat satellite failed on October 19, 2008while collecting data for the L3K campaign. The NSIDC (NationalSnow and Ice Data Center) distributed 15 Level-1 and Level-2 dataproducts. The GLAS products used in this analysis include GLA01(L1A Global Alimetry) and GLA14 (L2 Land Surface Altimetry). Theformer stores the transmitted and received waveforms from thealtimeter while the latter contains land surface elevations, thelaser footprint geolocation and reflectance, as well as geodetic,instrument, and atmospheric corrections for rangemeasurements.These two datasets can be linked by the record index.This study uses data from Release 428. At the moment of

writing, Release 429 data is available for Laser 3I and 3J cam-paigns with improvements of atmospheric processing, correctionsto waveform and elevation processing, and incorporating a newtidemodel. However, this new release datawill not be available forall laser periods until summer 2009 (Donna Scott, NSIDC, personalcommunication), so the data from Release 428 is used for consis-tency.A total of 980 shots are analyzed in this study, including 498

shots from region 1 and 482 from region 2. The GLAS shots inregion 1 traverse a distance of about 55 km from north to southwhile those in region 2 traverse with a north–south distance ofabout 78 km. GLAS footprint size may vary significantly duringthe span of each campaign, over the course of one orbit, and evenshot by shot (Neuenschwander et al., 2008). Table 1 summarizesthe footprint parameters (major axis, minor axis, and azimuth)for different laser periods over these two regions. It seems thatthe variability of footprints within the regions is relatively small,indicated by the small standard deviation of each parameter for

different laser periods (except the azimuth angle for L3G shots inregion 1).

2.3. Airborne lidar data

Airborne lidar data were collected in early 2003 by EarthDataInternational using a Azimuth Aeroscan system with a maximumof 5 returns per pulse. The field of view was 25◦ from the nadirand the flight height was about 3600 m above mean terrain,leading to a swathe width of approximately 3400 m. The grounddistance between flightlines was approximately 2400 m. Nominalpost spacing for the finalized bare earth product was 3 m.All data collection flights were initialized and finalized during

periods of GPS Position Dilution of Precision smaller than 4 (USGS,2008). An average of 10–20 rapid static GPS survey collectedground control points were established per base airport project todetect and correct horizontal and vertical bias. The lidar providerwas required to perform daily calibration checks to ensure thatthe horizontal accuracy was equal to or better than 1.73 m atthe 95% confidence level. North Carolina Geodetic Survey (NCGS)field survey checkpoints were obtained to evaluate the accuracyof lidar DEM products through a statistical analysis between thedifference in elevations of the field survey checkpoints and lidar-interpolated bare earth elevations at the same locations. At least20 checkpoints for 5 different land cover types (open terrain,weeds/crop, scrub, built-up, and forest) were tested. The qualitycontrol results over five land cover types are summarized in Table 2for all counties except McDowell, which has no report availablefrom NCFMP (2004). NCFMP requires the vertical accuracy at the95% confidence level less than 0.36m for open terrain and less than0.49 m for all land cover types consolidated. This requirement issatisfied for these counties with the maximum vertical accuracy of0.27 m and 0.39 m for open terrain and consolidated land cover,respectively. Over vegetated areas, forest has the largest RMSE,followed by scrub and weeds/crops. The largest RMSE is 0.34 m forforest in Watauga County. The mean difference varies from−0.12to 0.08m over forest. Horizontal X and Y values of lidar returns arerepresented in North Carolina State Plane with a NAD83 datum.Vertical Z values are referenced in NAVD88.

3. Methods

3.1. GLAS data processing

Over land, aGLASwaveformmight showmultiple distinct peakscorresponding to the groundand overlaying vegetation and/or

114 Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

Table 1GLAS footprint characteristics for region 1 and 2.µ and σ represents mean and standard deviation, respectively. The subscripts maj, min, and az represent major axis, minoraxis, and azimuth, respectively.

Region 1 Region 2µmaj (m) σmaj (m) µmin (m) σmin (m) µaz (◦) σaz (◦) N µmaj (m) σmaj (m) µmin (m) σmin (m) µaz (◦) σaz (◦) N

L3C 56.6 0.1 41.8 0.1 56.0 0.4 140 52.5 0.2 44.0 0.1 240.6 1.2 42L3D 52.6 0.0 43.2 0.0 144.3 0.5 112 51.2 0.2 42.5 0.2 343.7 0.8 184L3F 49.5 0.1 47.8 0.2 259.5 5.9 31 52.8 0.3 45.0 0.2 102.0 2.0 136L3G 52.9 0.3 47.2 0.3 92.8 40.6 70 53.7 0.3 48.7 1.2 165.0 1.8 55L3H 59.7 0.2 45.5 0.1 340.6 0.6 62 54.1 0.3 48.7 0.1 181.5 0.8 27L3I 59.9 0.1 43.3 0.1 165.2 0.4 42 56.8 0.3 45.7 0.1 351.1 4.4 31L3J 59.9 0.2 47.6 0.1 158.1 0.3 41 61.6 0.4 49.8 0.2 343.3 0.4 7

Table 2Assessment of the vertical accuracy of ground elevation derived from airborne lidar data using field survey measurements.

Land covercategory

Watauga Avery Burke Iredell

RMSE(m)

Mean(m)

Verticalaccuracy(m)

RMSE(m)

Mean(m)

Verticalaccuracy(m)

RMSE(m)

Mean(m)

Verticalaccuracy(m)

RMSE(m)

Mean(m)

Verticalaccuracy(m)

Open Terrain 0.12 (21) 0.02 0.27 0.13 (20) 0.12 0.20 0.14 (21) −0.08 0.24 0.11 (26) −0.08 0.19Weeds/Crops 0.16 (19) 0.11 0.29 0.17 (20) 0.16 0.29 0.09 (21) −0.02 0.16 0.09 (31) −0.05 0.17Scrub 0.20 (20) 0.13 0.32 0.23 (20) 0.18 0.33 0.18 (19) 0.08 0.37 0.15 (23) −0.01 0.33Forest 0.34 (40) 0.08 0.82 0.26 (40) 0.15 0.44 0.18 (40) −0.09 0.32 0.17 (54) −0.12 0.30Built Up 0.10 (20) −0.02 0.18 0.09 (21) 0.06 0.16 0.21 (19) −0.16 0.36 0.23 (18) −0.22 0.37Consolidated 0.23 (120) 0.07 0.39 0.20 (121) 0.14 0.39 0.16 (120) −0.06 0.34 0.15 (152) −0.09 0.31

Vertical accuracy is at 95% confidence level. The number within the parenthesis after RMSE is the number of checkpoints.

culture features. Since the transmitted pulse is expected to beGaussian, thewaveform can bemodeled as a sumof Gaussians plusa bias (Brenner et al., 2003):

w(t) = ε +Np∑m=1

Wm (1)

Wm = Ame−(t−tm)2

2σ2m (2)

where w(t) is the amplitude of the waveform at time t ,Wm is thecontribution from themth Gaussian,Np is the number of Gaussiansfound in the waveform, Am is the amplitude of mth Gaussian, tmis the Gaussian position, σm is the 1/e half-width (standard devi-ation) of the mth Gaussian, and ε is the bias (noise level) of thewaveform.The above equations are solved using nonlinear least squares

iteratively subject to a couple of constrains by fitting with thereceived waveforms (Brenner et al., 2003). The parameters of thefitted peaks (up to 6) are provided in the GLA14 products. Theranges of these peaks have been corrected for atmospheric delaysand tides. Each peak’s elevation zm (m = 1, . . . ,Np) was derivedby combining the GLA14 elevations and range offsets of waveformcentroids and the range offsets of all peaks relative to the farthestgates. Based on the Gaussian peak elevation(s), three metrics (zlp,zsp, and zmp)were extracted: zlp is simply the elevation of the lowestpeak, whichmeans zlp = min(zm); zsp is the elevation of the secondto the lowest peak, if it exists; zmp is the elevation of the peak withhigher amplitude between the lowest two peaks. Let Al and As bethe amplitude of the lowest peak and the second to the lowestpeak. Then,

zmp ={zlp, if Al >= As or zsp does not existzsp, if Al < As.

(3)

The Gaussain decomposition algorithm is inaccurate when awaveform is deformed due to atmosphere forward scattering. Asimulation study showed that the atmosphere forward scatteringcaused a bias of 6.9 cm in the fitted Gaussian of a ground surface(Brenner et al., 2003). Moreover, where the return energy exceedsthe linear response range of the receiver, the GLAS waveforms

become saturated and thus flat-topped (Harding and Carabajal,2005). Therefore, only the cloud-free (the flag FRir_qaFlag = 15in the GLA14 products) and saturation-free (the saturation indexsatNdx = 0 in the GLA14 products) shots were analyzed in thisstudy. Another cloud filter was applied to make sure that theelevation of a waveform must be less than 100 m above theSRTM (Shuttle Radar TopographyMission) elevation (Carabajal andHarding, 2005). Shots were also excluded when their waveformcentroid elevations were out of the elevation ranges of thecoincident airborne lidar points. These four filters combinedremoved∼82% of the total 5327 original shots. The flag FRir_qaFlagalone removed 69% of the shots. Some studies (e.g. Nguyen andHerring, 2005) have used another ‘‘pseudo cloud filter’’, i_gval_rcv(in the GLA14 products) less than a threshold, to select cloud-free shots. However, it was found that the number of shotsremoved is sensitive to the threshold. More research is required tofind the most reliable filter to remove cloud contaminated shots.Nevertheless, given the very small percentage of shots left, it islikely that the current criteria are strict enough to remove mostquestionable shots. The complete waveforms were extracted fromGLA01 and linked with the waveform parameters in GLA14 usingthe record index.

3.2. Airborne lidar data processing

To generate DEM from airborne lidar data, ground returnsneed to be extracted from the lidar point cloud, a process calledfiltering. The ground returns tiles, each of 3048 by 3048 m, wereobtained through NCFMP. These ground returns were interpolatedinto DEMs of about 1.5 m (equivalent to 5 ft) cell size using theTiffs (Toolbox for Lidar Data Filtering and Forest Studies) software(Chen, 2007). To generate vegetation information from lidar, theraw lidar point cloud files obtained from the USGS CLICK (Centerfor LIDAR Information Coordination and Knowledge) were firstorganized into tiles of the same extents as DEMs, and then theraw lidar tiles were processed to generate DSMs (Digital SurfaceModels) of the same cell size as DEMs using Tiffs (Chen et al.,2007; Chen, 2009). OHMs (Object HeightModels), representing thecanopy height over vegetated areas, were derived by subtractingDEMs from DSMs. Slope grids were generated from DEMs using

Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122 115

Fig. 3. Boxplots of ∆lp (the lowest GLAS peak elevation minus ground elevation),∆sp (the second to the lowest GLAS peak elevation minus ground elevation), and∆mp (the stronger GLAS peak elevation minus ground elevation) for open terrainshots in region 1.

gradients of the four immediate neighbors along x and y directionswithin a 3 by 3 neighborhood window of each cell (Bolstad, 2008).

3.3. Comparison of elevation from GLAS and airborne lidar data

To compare the elevation from GLAS and airborne lidar data,the first step is to convert them into the same horizontal andvertical datums. The geodetic latitude, longitude, and elevationof GLAS data are referred to as the TOPEX/Poseidon ellipsoid,which was converted into the WGS 84 datum. The airborne lidardata have orthometric elevations in the NAVD 88 datum, whichwere converted to ellipsoid heights in the NAD 83 datum usingthe GEOID 99 model of National Geodetic Survey (NGS). TheWGS 84 datum is earth-centered while the NAD 83 datum isnot even though they use almost the same ellipsoid. Thereforeit is important to convert them to the same datum, which isaccomplished using the NGS HTDP (Horizontal Time DependentPositioning) software. The final coordinates of both airborne lidardata and GLAS shots are referred to as the WGS 84 ellipsoidhorizontally and vertically.The energy of GLAS pulses follows a Gaussian distribution in

their footprints. The received waveform is a convolution betweenthe Gaussian distribution and the elevations of the illuminatedsurface within footprints. To generate from airborne lidar dataelevation metrics comparable to GLAS data, the airborne lidarelevations within each GLAS footprint are averaged using thefollowing weight function:

wi = e(−2√(x′i/a)

2+(y′i/b)2)

x′i = (xi − x0) sinα + (yi − y0) cosαy′i = (yi − y0) sinα − (xi − x0) cosα

(4)

where wi is the weight for any airborne lidar grid cell i within afootprint; a and b are the semi-major and semi-minor axes of thefootprint; α is the azimuth angle of themajor-axis of the footprint;(xi, yi) and (x0, y0) are the coordinates for the cell and the footprintcenter, respectively; x′i and y

′

i are coordinates of the cell alongmajor and minor axes, respectively, with the footprint center asthe origin of the coordinate system. The weights in Eq. (4) arenormalized so that the sum is 1 before averaging.Based on Eq. (4), the mean ground elevation (zgw) within a

footprint is calculated as follows:

zgw =n∑i=1

(zg,i ∗ wi) (5)

where zg,i is the ground elevation of any individual cell iwithin thefootprint, and n is the total number of cells within the footprint.To

assess the threeGLAS elevationmetrics (zlp, zsp, and zmp) for groundelevation estimation, the differences between them and weightedground elevation (zgw) (denoted as∆lp,∆sp, and∆mp, respectively)are calculated. T -test (Moore and McCabe, 1998) will be used totest whether the difference is statistically different from zero.Using similar equations as (5), slope and canopy height of in-

dividual cells within any footprint were also averaged to gener-ate the weighted mean slope (sw) and canopy height (hw) from theslope grids and OHMs. Other metrics extracted from airborne li-dar data include (1) the percentage of non-terrain returns, whichis a proxy of canopy cover (CC) over vegetated areas, (2) slope andcanopy height variance, denoted as sv and hv , respectively, and (3)the maximum canopy height (h). sv was calculated from the slopegrids as follows:

sv = var(si) (6)

where si is the slope of any cell within a footprint.hv and hwere calculated from the OHMs:

hv = var(hi) (7)h = max(hi) (8)

where hi is the height of any cell within a footprint in an OHM.Once these terrain and canopy metrics had been extracted, simpleregression models and stepwise regression models (Nether et al.,1996) were used to analyze the relationships between them andthe biases of the three elevation metrics (zlp, zsp and zmp).

4. Results and discussion

4.1. Comparison of elevation over open terrain

In order to explore the terrain effects on GLAS elevationestimation, a total of 41 GLAS shots over open terrain (withoutvegetation and culture features on it) were extracted from region1. If the percentage of non-terrain returns is zero, the GLAS shotis considered as an open terrain shot. Fig. 3 shows the elevationbiases (∆lp and ∆sp) of the lowest two Gaussian peak elevationmetrics (zlp and zsp) for open terrain shots over region 1. The bias ofthe lowest GLAS peak,∆lp, is−0.97m, which is different from zeroat the 5% significance level (Table 3). The standard deviation of∆lpis 1.78 m. At the individual shot level, ∆lp varies from −5.98 m to0.49 m. The above analysis indicates that there is a tendency thatthe lowest GLAS peak underestimates the ground elevation overopen terrain.To further investigate the causes of the underestimation, the

GLAS shots were divided into two classes, A and B, by visuallychecking the waveforms and the locations of peaks detected byGaussian decomposition. A shot is classified as class-A if there isonly one distinct peak in the waveform and the lowest detectedGaussian peak coincides with it (see Fig. 5(a) for an example);otherwise, it is a class-B shot (see Fig. 5(b) and (c)). The within-footprint weighted mean slopes (sw) for class-A shots are lowwitha mean and standard deviation of 3.7 ± 1.4◦ and a maximumof 6.8◦. Therefore, the peaks of class-A shots should indicate thecentral tendency of ground elevations and have minimum errorsfrom Gaussian decomposition, making them ideal to assess thesystematic elevation differences between GLAS data and airbornelidar data.A total of 21 out of 41 open terrain shots were identified as

class-A shots. At the individual shot level,∆lp varies from−0.24 to0.45m, with amuch smaller range than those from all open terrainshots. The mean difference between zlp and zgw is 0.15 ± 0.20 m,different from zero at the 0.05 significance level. This differencemight indicate there is some systematic bias between GLAS dataand airborne lidar data. The sources of the bias are unknown, butthey could be related to the airborne lidar accuracy and/or GLAS

116 Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

a b

c

Fig. 4. Boxplots of (a)∆lp (the lowest GLAS peak elevation minus ground elevation), (b)∆sp (the second to the lowest GLAS peak elevation minus ground elevation), and (c)∆mp (the stronger GLAS peak elevation minus ground elevation) for shots in region 2. The x-axis is different laser periods or all campaigns combined.

Table 3∆lp (the difference between the lowest GLAS peak elevation zlp and the ground elevation zgw),∆sp (the difference between the second to the lowest GLAS peak elevation zspand the ground elevation zgw), and∆mp (the difference between the stronger GLAS peak elevation zmp and the ground elevation zgw) for open terrain shots over region 1.

Metric All open terrain shots Class-A open terrain shots Class-B open terrain shotsn Mean

(m)Std(m)

Max(m)

Min(m)

n Mean(m)

Std(m)

Max(m)

Min(m)

n Mean(m)

Std(m)

Max(m)

Min(m)

∆lp 41 −0.97* 1.78 0.49 −5.98 21 0.15* 0.20 0.45 −0.24 20 −2.16* 1.94 0.49 −5.98∆sp 38 3.43* 5.26 21.98 −2.87 18 6.11* 6.42 21.98 0.93 20 1.02* 2.01 5.32 −2.87∆mp 41 0.00 0.77 0.79 −3.36 21 0.15* 0.20 0.45 −0.24 20 −0.16 1.07 0.79 −3.36* Indicates the difference is different from zero at 0.05 significance level using t-test.

laser pointing error (Urban et al., 2008). An analysis was also doneto explore the effects of the interpolation algorithmused in Tiffs onthe calculation of zgw . It was found that the difference of zgw fromTiffs DEMs and NCFMP DEMs is as small as 0.004 ± 0.03 m for allshots. This indicates that the Tiffs interpolation algorithm mightnot be reason for the bias. Overall, the systematic bias betweenGLAS data and airborne lidar data is small, given that GLAS datahave a RMSE of∼0.14m (Zwally et al., 2002) and the airborne lidardata has a RMSE of 0.11–0.14 m when compared with GPS surveymeasurements (see Table 2).The class-B open terrain shots were examined to analyze the

causes for the differences between the lowest GLAS peaks andground elevation. On average, the lowest GLAS peaks zlp underes-timate ground elevation by −2.16 ± 1.94 m for all class-B shots.At the individual shot level, ∆lp varies from −5.98 to 0.49 m. Theweighted mean slope for class-B shots is 5.4 ± 2.6◦ with a max-imum of 12◦. This indicates that the class-B shots are located interrain steeper than that of the class-A shots. To investigate the ef-fects of terrain characteristics on ground elevation estimation, theweightedmean slope (sw) and slope variance (sv) within footprintsare related to ∆lp for class-B shots (Fig. 6). The correlation coeffi-

cients between ∆lp and sw and sv are −0.37 and −0.02, respec-tively. Although the p-value is greater than 0.05, there is still a clearpattern that the lowest peaks depart more from the ground eleva-tion as slope increases. The smaller correlation coefficient and largep-value for slope variance indicates that terrain roughness (quanti-fied by sv) does not relate to∆lp as strongly as steepness (quantifiedby sw).Individual class-B shots were further examined to analyze the

causes for the negative bias of the lowest Gaussian peak. Foropen terrain shots, the peak with the maximum amplitude shouldapproximate the mean ground elevation. However, as terrainbecomes steeper and if the slope within the footprint is variable,it was found that the lowest Gaussian peak does not necessarilycorrespond to themaximumpeak so itmay not represent themeanground elevation. For example, in thewaveform shown in Fig. 5(b),it is the second to the lowest peak that is closer to themean groundelevation zgw . Evenwhen the terrainwithin a footprint is smoothlychanging (such as Fig. 5(c)), it is still possible that the lowest peakunderestimates the mean ground elevation. This happens whenthe terrain elevation shows multiple modes vertically, especiallywhen there are discrete surfaces (such as a cliff) within footprints.

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Fig. 5. GLAS waveforms and the coincident airborne lidar points for individual selected shots. (a) is a class-A shot and (b)–(d) are class-B shots from region 1. (e) and (f)are shots from region 2. Airborne lidar points are plotted in a X (the upper horizontal axis) and Z view, but the Z coordinates have been converted from original values towaveforms bins to match the GLAS waveforms and the X coordinates have been subtracted by their minimum for better visualization.

Fig. 5(d) shows a waveform with −5.98 m negative bias of thelowest Gaussian peak. The coincident airborne lidar point cloudshows that there are no surface features corresponding to thelower small peak within the footprint. However, the analysis of itssurrounding area indicates that at 70 m away from the footprintcenter there is a pond, which corresponds to the lowest peak.This pond is outside the footprint because the major axis of thefootprint is only 53 m. This indicates that (1) reflection from

features can generate a peak when these features are flatter (anextreme situation is water surface in this case) compared to thoseover other portions of the footprint, and (2) these features mightproduce distinct signals even when they are outside the ‘‘fitted’’footprint.The bias (∆sp) of the second to the lowest peak zsp was also

analyzed (Table 3). Taking all open terrain shots together, zspoverestimate the ground elevation zgw by 3.43 m, which is larger

118 Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

a b

Fig. 6. Effects of terrain characteristics (weighted mean slope (a) and slope variance (b)) on∆lp (the lowest GLAS peak elevation minus ground elevation) for class-B openterrain shots.

than −0.97 m of the lowest peaks. This means that, overall, zsp isnot a better metric than zlp for ground elevation estimation overopen terrain. If two classes of shots are treated separately, it wasfound that, for class-A shots, zsp overestimates ground elevationby 6.11 m, which is not surprising because zlp coincides withzgw for them. What is interesting is that, for class-B shots, zsponly overestimates zgw by 1.02 m on average, compared to thedifference of −2.16 m for zlp. This means that, if an open terrainshot’s lowest peak does not coincide with the ground elevation, zspis a good metric for ground elevation estimation.

4.2. Comparison of elevation over mountainous forest areas

Compared to region 1, the overlaying terrain for shots in region2 is much steeper (the mean slope sw is 20◦ and the maximumslope is 49◦). All shots are located over vegetated areas. On average,the canopy height (h) and canopy cover (CC) within footprints are23.9 ± 11.9 m and 0.61 ± 0.24, respectively. As in region 1, thelowest peaks zlp underestimate ground elevation but with a muchlarger mean of−7.68 m and a standard deviation of 7.11 m acrossall laser periods (Table 4 and Fig. 4(a)). For the second to the lowestpeak elevation zsp, it is interesting to note that on average it onlyoverestimates the ground elevation by 0.70± 7.17 m (Table 4 andFig. 4(b)).To investigate the effects of terrain and canopy on GLAS

elevation estimation, simple linear regression models were usedto relate terrain and canopy metrics with∆lp and∆sp, respectively(Figs. 7 and 8). The terrain metrics used are weighted mean slopesw and slope variance sv . The canopy metrics used are weightedmean height hw , maximum height h, canopy height variance hv ,and canopy cover CC. For ∆lp, the slope has the largest coefficientof determination (R2) of 0.26, followed by two canopy heightmetrics hw and h (Fig. 7). The slope variance sv has a much weakercorrelation (R2 = 0.02) with ∆lp, showing that terrain roughnessis not as important as steepness in affecting the negative bias ofthe lowest peak. The relationship between canopy cover and ∆lpis also weak (R2 = 0.04), but it seems that the variability of ∆lpincreases with canopy cover. This shows that denser canopy doesmake the Gaussian decomposition algorithm more unstable forground elevation estimation. TheR2 for canopyheight variance (hv)is 0.01, indicating the canopy height variability does not affect∆lpmuch. Overall, the terrain and canopy metrics have very small R2with∆sp (Fig. 8), whichmeans if zsp can be used to estimate groundelevation over high relief with dense vegetation cover, it would beless affected by the terrain and canopy properties. It is worthwhileto note that, different from ∆lp, ∆sp has almost no relationship(R2 = 0) with the terrain slope sw .

To evaluate the relative importance of terrain and vegetationproperties on GLAS peak elevation estimation, the above 6 metricswere standardized and then used to develop stepwise regressionsmodels for predicting∆lp and∆sp. The final models are as follows:

∆lp = −7.68− 3.59s′w − 1.78h′

w + 0.96h′ (9)

∆sp = 0.7− 2.28h′w + 1.23h′ (10)

where s′w , h′w , and h

′ are the standardized weighted mean slope,mean canopy height, and maximum canopy height, respectively.The coefficients in Eq. (9) show that∆lp is mostly affected by slope,followed bymean canopy height; themaximum canopy height hasthe least impacts. Different from the lowest peak, the model for∆sp does not include the terrain slope (see Eq. (10)). These resultsare consistent with the former simple regression analysis whilehighlighting the significant factors that affect∆lp and∆sp.At the individual shot level, ∆lp has a large variability, varying

from−40.83 m for L3D to 22.62 m for L3C (Table 4). To investigatethe causes for such large negative and positive biases, five shotswith the largest negative and positive biases, respectively, wereanalyzed. It was found that the large negative biases are all moreor less related to the terrain variability within or near the ‘‘fitted’’footprint. Fig. 5(e) shows a waveform over a very steep (slope =49◦) area. Similar to the open terrain shot in Fig. 5(d), outside the‘‘fitted’’ footprint there is a valley, the bottom of which has smallerslope than the terrain within the footprint. This valley bottomproduces a peak in the waveform not only because of its relativelyflat surface but also possibly because of its higher reflectivity. Sincethe valley is outside the footprint (itsmajor axis is 52m), this againhighlights the importance of revisiting the algorithm for fittingfootprints for the GLAS team. Contrary to the negative biases, thelarge positive biases are mainly related to the weak signals fromthe terrain over dense canopy. Fig. 5(f) shows such an examplearea where forests are dense and the terrain signal is too weak toproduce a distinct peak.Since the lowest peak does not match the mean elevation well,

its relationship with the minimum elevation was also assessed. Itwas found that zlp is slightly higher than the minimum elevationwith a difference of 0.90±6.02m, which is much smaller than thedifference of−7.68± 7.11 m between zlp and the mean elevationzgw . This provides additional evidence to show that zlp cannotrepresent the mean ground elevation well; it is likely linked tosurface that has smaller slope than the majority of the terrainor features that can produce peaks at the elevation lower thanthe mean elevation (e.g., trees growing at the lower side of thefootprint while there are less trees elsewhere).

Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122 119

Fig. 7. Effects of terrain and vegetation on∆lp (the lowest GLAS peak elevation minus ground elevation) for shots over region 2.

Table 4The statistics for∆lp (the lowest GLAS peak elevation minus ground elevation) and∆sp (the second to the lowest GLAS peak elevation minus ground elevation) for all shotsover region 2.

Laser period ∆lp (m) ∆sp (m) ∆mp (m)N Mean Std Max Min Mean Std Max Min Mean Std Max Min

L3C 42 −4.08* 10.78 22.62 −31.16 5.33* 9.29 27.85 −16.38 5.33* 9.29 27.85 −16.38L3D 184 −7.77* 6.23 12.18 −40.83 −1.42* 4.59 18.01 −14.00 −1.82* 4.02 12.18 −14.00L3F 136 −7.94* 7.26 15.89 −33.68 4.53* 8.15 28.17 −13.86 4.07* 8.59 28.17 −18.00L3G 55 −11.45* 5.59 −3.81 −35.94 −4.11* 4.06 5.22 −21.11 −4.11* 4.06 5.22 −21.11L3H 27 −7.37* 7.61 12.21 −22.70 −0.66 6.07 20.13 −8.95 −1.44 4.37 12.21 −8.95L3I 31 −6.03* 3.09 −0.13 −13.51 0.13 5.24 15.80 −6.68 0.13 5.24 15.80 −6.68L3J 7 −0.63 3.51 2.08 −8.02 −0.38 10.54 6.91 −22.50 0.46 3.32 5.83 −4.79All 482 −7.68* 7.11 22.62 −40.83 0.70* 7.17 28.17 −22.50 0.38 7.02 28.17 −21.11* Indicates the difference is different from zero at 0.05 significance level using t-test.

120 Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

Fig. 8. Effects of terrain and vegetation on∆sp (the second to the lowest GLAS peak elevation minus ground elevation) for shots over region 2.

4.3. Evaluation the stronger peak for ground elevation estimation

For open terrain shots, it was found that the Gaussian peakwitha stronger intensity between zlp and zsp corresponds to or is closerto the ground elevation zgw (see Fig. 5). This is reasonable becausethe stronger peaks are typically related to themajority, if not all, ofterrain surface. Given such facts, another metric zmp, which is theelevation of the stronger peak, is evaluated for ground elevationestimation. The difference∆mp between zmp and ground elevationzgw was calculated for both regions. For open terrain shots overregion 1, the mean∆mp is 0 m (see Table 3). The t-test shows that∆mp is still not significantly different from zero. Compared to ∆lpor ∆sp, it seems that ∆mp can estimate the ground elevation ofopen terrain shots much better, indicated by its small mean andstandard deviation (see Table 4 and Fig. 3). For shots over region 2,

∆mp varies from−4.11± 4.06 m for L3G to 5.33± 9.29 m for L3F(Table 4). The distribution of∆mp is more similar to the one of∆sp(Fig. 3(b) and (c)), which means that the second to the lowest peakhas stronger intensity than the lowest peak over the forest areas. Itis encouraging to see thatwhen all laser periods are combined,∆mpis reduced to 0.38 m, which is not significantly different from zeroat the 0.05 level. The standard deviation of∆mp is 7.02 m, which isalso smaller than the ones for∆lp and∆sp (Table 4).To explore the effects of terrain and vegetation on ∆mp, the 6

metrics introduced in 4.2 are used to predict ∆mp using stepwiseregression models. It was found that the final model does notinclude any metric. This implies that zmp is not greatly affectedby terrain slope and canopy when used for estimating groundelevation. Simple regression models were also developed to relateground elevation zgw with three elevation metrics derived from

Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122 121

Fig. 9. The relationship between zgw (the ground elevation derived from airborne lidar data) and zlp (the lowest GLAS peak elevation), zsp (the second to the lowest GLASpeak elevation), and zmp (the stronger GLAS peak elevation).

GLAS data: zlp, zsp, and zmp (Fig. 9). The results confirm that zmp isa better metric because the intercept of the model using zmp is thesmallest and its slope is closer to 1 than the other two.Several recent studies have used GLAS for vegetation height

mapping, assuming one of the Gaussian peaks to be the ground(e.g. Rosette et al., 2008; Duong et al., 2008). Rosette et al. (2008)used zmp to calculate canopy height from GLAS data and foundthat it has better correlation with field measurements of canopyheight than using the lowest peak for 19 shots over a woodland inGloucestershire, UK. Duong et al. (2008) detected the vegetationheight change between winter (leaf-off) and summer (leaf-on)seasons in 2003 for a GLAS track traversing Netherlands, Belgium,and France. Their method of calculating vegetation height is asfollows: if the energy intensity ratio at zlp and zsp is less than 15%,zsp instead of zlp is used to represent ground elevation. They foundthat their approach is better than using the lowest peak to detectvegetation change between two nearly spatially coincident epochsof GLAS data. The GLAS peak elevation extracted using Duonget al. (2008)’s approach was tested for all shots over region 2. Itwas found that the mean difference is −0.82 ± 8.06 m, whichis not better than zmp. Obviously, although this might be the firststudy to assess the GLAS peaks for ground elevation estimationwith a focus on mountainous forest areas, more research needto be done for other forest types to achieve a more objectiveassessment of different metrics. This is especially true for tropical

and boreal forests because the dense canopy with high biomassover those forests might make the Gaussian decomposition evenmore difficult.

5. Conclusion

This study assessed the lowest two GLAS peaks extracted byGaussian decomposition for ground elevation estimation, for thefirst time, focusing on the mountainous forest areas and usingspatially extensive (∼2000 km2) airborne lidar data. Based on theanalysis of a total of∼500 shots, it was found that:• The lowest peak tends to underestimate the weighted groundelevation (zgw) within footprints by −0.97 m for 41 shots overopen terrain and by−7.68 m for 482 shots over forest areas;• The terrain steepness (slope) followed by canopy height havethe highest correlation with the underestimation of the lowestpeak;• The second to the lowest peak overestimates the groundelevation by 3.43 m for the open terrain shots and by 0.70 mfor the forest shots. On average, the second to the lowest peakis closer to the ground elevation than the lowest peak overmountainous forest areas;• The elevation of the stronger peak of the lowest two extractedfrom current Gaussian decomposition algorithm is the bestmetric for ground elevation for both open terrain (∆mp = 0 ±0.77 m) and mountainous forest areas (∆mp = 0.38± 7.02 m).

122 Q. Chen / ISPRS Journal of Photogrammetry and Remote Sensing 65 (2010) 111–122

It is expected that this assessment will result in better use ofcurrent GLAS products for terrain elevation estimation. Moreover,since estimating canopy height from GLAS data involves theextraction of the canopy top and ground elevation, the results inthis study can help us understand the error budgets in vegetationheight estimation from GLAS data. This assessment will also shedlight on the design of next generation satellite lidar systems such asDESDynI (Deformation, Ecosystem Structure and Dynamics of Ice)and ICESat II to satisfy measurement requirements for forest areas.One of the uncertainties in the analysis of this study could be theflags used to select cloud-free shots. More work is expected fromthe GLAS team and other scientists to determine the most reliablecriteria to reduce the omission and commission errors in findingcloud-free shots.

Acknowledgements

Many thanks are extended toNCFMP (North Carolina FloodplainMapping Program) and USGS CLICK (Center for LIDAR InformationCoordination and Knowledge) for providing airborne lidar data andNSIDC (National Snowand IceData Center) for providingGLAS dataproducts. I am also very thankful to the two anonymous reviewersand Dr. George Vosselman for their constructive comments onimproving the manuscript.

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