Forest Ecology and Management 257 (2009) 1136–1147

A comparison of lidar, radar, and field measurements of canopy height in pine andhardwood forests of southeastern North America

Joseph O. Sexton a,*, Tyler Bax a, Paul Siqueira b, Jennifer J. Swenson a, Scott Hensley c

a Nicholas School of the Environment, Duke University, Durham, NC 27708-0328, USAb Microwave Remote Sensing Laboratory, Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003-9284, USAc National Aeronautics and Space Administration Jet Propulsion Laboratory, Pasadena, CA 91109-8099, USA

A R T I C L E I N F O

Article history:

Received 16 June 2008

Received in revised form 10 November 2008

Accepted 19 November 2008

Keywords:

Forest structure

Canopy height

Radar interferometry

InSAR

Lidar

GeoSAR

SRTM

A B S T R A C T

Forest canopy height is essential information for many forest management activities and is a critical

parameter in models of ecosystem processes. Several methods are available to measure canopy height

from single-tree to regional and global scales, but the methods vary widely in their sensitivities, leading

to different height estimates even for identical stands. We compare four technologies for estimating

canopy height in pine and hardwood forests of the Piedmont region of North Carolina, USA: (1) digital

elevation data from the global Shuttle Radar Topography Mission (SRTM) C-band radar interferometry,

(2) X- and P-band radar interferometry from the recently developed airborne Geographic Synthetic

Aperture Radar (GeoSAR) sensor, (3) small footprint lidar measurements (in pine only), and (4) field

measurements acquired by in situ forest mensuration. Differences between measurements were smaller

in pine than in hardwood forests, with biases ranging from 5.13 to 12.17 m in pine (1.60–13.77 m for

lidar) compared to 6.60–15.28 m in hardwoods and RMSE from 8.40 to 14.21 m in pine (4.73–14.92 m for

lidar) compared to 9.54–16.84 in hardwood. GeoSAR measurements of canopy height were among the

most comparable measurements overall and showed potential for successful calibration, with R2 = 0.87

in pine canopies and R2 = 0.38 in hardwood canopies from simple linear regression. An improved

calibration based on differential canopy penetration is presented and applied to SRTM measurements,

resulting in canopy height estimates in pine forests with RMSE and standard error <4.00 m. Each of the

remotely sensed methods studied produces reasonable and consistent depictions of canopy height that

can be compared with data of similar provenance, but due to differences in underlying sensitivities

between the methods, comparisons between measurements from various sources require cross-

calibration and will be most useful at broad scales.

� 2008 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

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1. Introduction

Forest canopy structure is a key determinant of forest ecosystemprocesses, and its measurement is essential for ecosystem monitor-ing, modeling, and management. As the primary attribute of verticalstructure, canopy height affects plant community dynamics andcomposition (e.g., Welden et al., 1991; Kruger et al., 1997), boundarylayer meteorology and microclimate (e.g., Raupach, 2004), andwildlife habitat value (e.g., James, 1971). Horizontal variations incanopy height (e.g., ‘‘edges’’ and ‘‘gaps’’) also affect plant and animalcommunities and their dynamics (e.g., Andren and Angelstam, 1988;Matlack, 1994; Didham and Lawton, 1999). Through allometric

* Corresponding author at: LSRC Box 90328, Duke University, Durham, NC 27708-

0328, USA. Tel.: +1 919 613 8069; fax: +1 919 684 8741.

E-mail addresses: joseph.sexton@duke.edu (J.O. Sexton), tyler.bax@duke.edu

(T. Bax).

0378-1127/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.foreco.2008.11.022

relationships, canopy height can be used to estimate stand age andfoliage-height profile (e.g., Aber, 1979), stand volume (e.g., Cadeeet al., 1997), site productivity (e.g., Monserud, 1984; Doolittle, 1979),and biomass (Dubayah and Drake, 2000).

Estimation of carbon content in forest ecosystems is ofincreasing importance for compliance with international environ-mental treaties aiming to offset greenhouse gas emissions (Balzteret al., 2007). However, considerable uncertainty surroundsregional stocks of carbon (Schimel et al., 2001), limiting thepotential to effectively monitor and manage global carbon andhydrological cycles. These quantitative uncertainties could begreatly reduced by accurate measurement of forest canopy heightacross broad spatial scales (Balzter et al., 2007).

Canopy height is a fundamental variable in allometric equationsthat estimate forest biomass and productivity (Patenaude et al.,2005; Andersen et al., 2006). Many studies have shown the powerof using vegetation height from traditional and remotely sensedmeasurements in ecosystem models to estimate aboveground

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–1147 1137

biomass and carbon stocks, from plot to landscape scales (Lefskyet al., 2002a,b; Drake et al., 2002; Hurtt et al., 2004; Balzter et al.,2007). More recently, vegetation height measurements are beingcombined with ancillary data to develop regional estimates ofaboveground biomass in order to generate a cohesive biomass andcarbon database on a national scale (e.g., Kellndorfer et al., 2006).

Comparable measurements of canopy height require a con-sistent definition of the canopy itself, as well as what is measuredas its height. Semantic distinctions become important whenmethods with different sensitivities are employed to measure astructure as complex as a forest canopy. A forest canopy is acomplex volume, composed of the stems, branches, leaves, andother solid plant parts, as well as the gaps between them. Fromthis, canopy height refers to the vertical distance from the groundsurface to the highest tree part (i.e., non-gap) at that horizontallocation. Because of the three-dimensional roughness of treecrowns and the gaps between trees (which often extend to theground), measurements of height are affected by the horizontalresolution at which data are collected.

Accurate estimates of forest canopy height are thereforedependent on measurements that capture both the horizontalcover and vertical structure of aboveground vegetation (Kelln-dorfer et al., 2004). Traditional forest inventory methods ofmeasuring tree height with poles or trigonometric transformationsof distance and angle measurements are technically simple andinexpensive over small areas, but are difficult to apply in closedstands and impossible to implement over large areas (Andersenet al., 2006). Alternatively, airborne and satellite remotely senseddata provide an economical and efficient means of obtaining heightmeasurements over much larger areas (Naesset, 1997; Dubayahand Drake, 2000; Andersen et al., 2006).

Passive optical remote sensing systems are suited to measurehorizontal vegetation cover, and recent advances in active remotesensors have made it possible to acquire reliable measures ofvertical forest structure as well (Waring et al., 1995; Treuhaft et al.,1996; Lefsky et al., 2002a; Treuhaft and Siqueira, 2000). Activeremote sensors used for forest canopy height estimation includelight detection and ranging (lidar) and interferometric synthetic-aperture radar (InSAR) (Balzter et al., 2007; Brown and Sarabandi,2003). Currently, airborne lidar sensors can estimate height withsub-meter vertical accuracy and spatial resolution (e.g., Brandt-berg et al., 2003), but are economically and computationallyconstrained at broad regional scales (Kellndorfer et al., 2004). Incontrast, due to their capacity to systematically scan large areasand record data through cloud cover, airborne and spaceborneInSAR missions have produced an abundance of landscape- andglobal-scale data that have proven useful in determining canopyheight in a number of studies (Balzter et al., 2007; Brown andSarabandi, 2003; Kellndorfer et al., 2004; Townsend, 2002; Walkeret al., 2007).

Lidar remote sensing uses high-frequency pulses, or ‘‘posts’’ oflaser light to measure the distance from the sensor to targetobjects. Lidar sensors are most frequently carried aboard aircraft;and some satellite-based systems have recently been developedfor cryosphere applications as well, e.g., ICESat (http://icesat.gsfc.-nasa.gov). Calculation of height from lidar requires precisepositioning of the sensor by a Differential Global Position System(DGPS) and an Inertial Measurement Unit (IMU) carried aboard theaircraft, and is based on the time elapsed from the round-trip travelof each laser pulse between the sensor and the target. Each of theselidar returns is recorded as a point in three-dimensional space;height above the ground is calculated as the vertical differencebetween laser returns from the target and those from the ground,or ‘‘bare earth’’ surface.

Lidar sensors vary according to the electromagnetic wavelengthof the laser (e.g., 500 nm for bathymetric vs. 900–1064 nm for

terrestrial applications), by power, by duration and frequency ofthe pulse, and by the laser beam’s cross-sectional diameter,determined by its divergence angle and flight altitude (Lefsky et al.,2002a,b). Lidar sensors can be further divided into two types:discrete- (including multiple-) return vs. continuous waveform.Discrete-return lidar provides one or several height measurement,returns per post, and is the more common of the two. Thesesystems can be tailored to specific applications by varying aircraftspeed, altitude, pulse rate, and other parameters. Alternatively,continuous-waveform lidar provides measurements of lightinterception continuously along the vertical axis of each postand can be used to describe the vertical distribution of biomass orfoliage within vegetation canopies. Forest characterization usingsmall-footprint, continuous-waveform lidar is an active researchfield, and discrete return, small footprint lidar has been success-fully used for some time to measure tree height within stands(Maclean and Krabill, 1986). While evolving the potential to recordinformation from each post similar to continuous-waveform lidar(Carter et al., 2007), discrete-return lidar methods continue to berefined for many forest types as well as well as for detailedcharacterizations such as mapping of individual crowns (e.g.Roberts et al., 2005).

Interferometric SAR uses two radar receivers carried aboard air-or spacecraft and separated by a known distance, termed the‘‘baseline’’. The two receivers may be two physical units or a singledevice passed over the target twice. These receivers record thephase of a radar signal reflected from the ground or other targets inthe ‘‘range’’, or ‘‘cross-track’’ direction, perpendicular to the flight-line of the receivers (i.e., the ‘‘azimuth’’ direction). This phasecycles over the travel time of the radar pulse and can be used tomeasure the round-trip distance between the radar transmitter,target, and receivers. Through knowledge of the observinggeometry, the difference between phases of the signal receivedat the two ends of the baseline can be translated into a topographicheight via geometric transformation (Rosen et al., 2000). In thepresence of vegetation, the topography measured from interfero-metric SAR may be anywhere from the ground surface to the top ofthe canopy, depending on the signal scattering and extinctioncharacteristics of the vegetation. These characteristics vary withradar frequency (and inversely, wavelength)—longer microwaves(30–100 cm and larger, commonly referred to as P-band or UHF)tend to penetrate deeper into the canopy to the ground surface,whereas shorter-wavelength signals, including C-band (�6 cm), X-band (�3 cm), and smaller, tend to reflect nearer the top of thecanopy.

Methods for estimating canopy height from SAR vary. Somecompare interferometric height with an independent measure-ment of the ground surface (Kellndorfer et al., 2006; Simard et al.,2006). Others, including polarimetric interferomtetric syntheticaperture radar (PolInSAR), use both interferometric height andcorrelation, along with multiple baselines and/or polarizations forestimating vegetation height directly (Cloude and Papathanassiou,1998; Treuhaft and Siqueira, 2000). A third approach, applied inthis study, uses the difference in sensitivity between multiplewavelengths, measuring interferometric heights at two frequen-cies and calculating height as the difference in elevation betweenthe two measurements (Wheeler and Hensley, 2000).

Each of these methods – lidar, radar interferometry in thevarious wavelengths, and field measurement – responds uniquelyto the physical structure of the forest canopy. Empirical studies arenecessary to understand the methods’ sensitivities and compar-ability for various forest types, and to inform selection among themethods for specific purposes. Between February 2000 andOctober 2001, four datasets were acquired over the Duke Forest(North Carolina, USA): (1) digital elevation data from the ShuttleRadar Topography Mission (SRTM) C-band radar, (2) X- and P-band

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–11471138

radar interferometric heights from an experimental flight of theairborne Geographic Synthetic Aperture Radar (GeoSAR), (3)airborne small-footprint lidar measurements acquired in leaf-off(winter) conditions, and (4) stand-inventory field measurements.Although initially for various purposes (only the GeoSAR and fieldmeasurements were originally intended for measuring canopyheight), their nearly simultaneous collection presents a rareopportunity for comparing four of the dominant methods formeasuring canopy height.

With this dataset, we conducted three analyses: (1) evaluationof the scaling behavior of lidar-derived canopy heights in pineforests, (2) comparison of canopy height measurements producedby the methods in pine and hardwood forests, and (3) calibration ofthe globally available SRTM elevation data to extract canopy heightfor southeastern forests. These analyses illustrate the relationshipsbetween canopy height measurements from the four methods inforests characteristic of southeastern North America, providemethods to extract canopy height measurements from availabledatasets, and facilitate adoption of remotely sensed methods formapping canopy height at regional scales.

2. Methods

2.1. Study area

The Duke Forest (368N, 798W) covers 7050 ha of the SouthernAppalachian Piedmont Section of the Southeastern Mixed ForestProvince (Bailey, 1995) in central North Carolina, USA (Fig. 1).Forest communities, characteristic of the region, are seral mixes ofplanted and natural pine (predominantly loblolly pine, Pinus taeda)and many species of deciduous hardwoods, including oaks(Quercus spp.), hickories (Carya spp.), elms (Ulmus spp.), red maple(Acer rubrum), sweetgum (Liquidambar styraciflua), and tulippoplar (Liriodendron tulipifera). Mature forest canopies aretypically closed and two-storied with pines and hardwoods

Fig. 1. Study area arrangement and ecoregional context. Stands and inventory plots were s

and represent forests of the Southern Appalachian Piedmont Section (inset, stippled area)

is exaggerated 5�.

reaching heights >30 m in the overstory, and shorter hardwoodsin the under- and mid-story, but this varies in response to siteproductivity, timber management, and natural disturbances.Ground elevation ranges from 90 to 210 m, and local relief isgentle to moderate.

Management of the Forest is partitioned into stands ofhomogeneous forest composition and structure, ranging from0.9 to 14.7 ha. Data were analyzed at two levels: (1) 112 standscovered by all four data sets (SRTM, lidar, GeoSAR, and field),including four treeless herbaceous stands digitized from ortho-imagery to represent the shortest (near-zero) canopy heights inboth the pine and hardwood types, and (2) 139 forest inventoryplots, including five located in recently cleared stands (withremaining stumps, slash, and debris) to represent zero-height pineand hardwood types.

2.2. Data

2.2.1. Field measurement

A timber inventory of the Duke Forest was conducted in thesummer and fall of 2000. Mensuration plot centers were spaced�400 m apart on a regular sampling grid, and inclusion of treeswithin plots was determined based on a prism tally. At each plot,trees were selected with a 10 basal-area-factor (BAF) prism pivoted1.3 m above the ground at the plot center. Border cases were decidedby measuring and comparing the distance between the tree and plotcenter to the tree’s diameter at breast height (DBH); if the distancefrom the plot center to the tree (in feet) was less than the DBH (ininches)� 2.75, then the tree’s height was measured and recorded.Height was measured with a HagaTM altimeter (http://www.haga-metallwaren.de/en_altimeter.htm) by an observer positioned66 feet (�20.1 m) from the base of each tallied tree.

An index of pine dominance was used to quantify thecontribution of evergreen (i.e., predominantly pine species andoccasionally eastern redcedar, Juniperus virginiana) canopies to

elected from the Durham, Korstian, Blackwood, and Eno Divisions of the Duke Forest

of the Southeastern Mixed Forest Province (inset, white) (Bailey, 1995). Topography

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–1147 1139

each plot’s height measurements. The index was calculated as:

pineDom ¼P

heightpinePheightall

� 100; (1)

where the numerator is the sum of heights for all pines in the tallyand the denominator is the sum of heights for all trees in the tally.The index was used to categorize plots into discrete ‘‘pine’’(pineDom � 90) and ‘‘hardwood’’ (pineDom � 5) types, whichwere then verified against aerial photos and the 2001 NationalLandcover Database Landcover Layer (Homer et al., 2004). Fieldmeasurements were focused on forest stands, and so did notinclude height measurements in short vegetation. To representshort vegetation in both pine and hardwood types, zero canopyheight was assigned to five plots placed in areas of recently clearedforest, identified in 1998 aerial photos.

2.2.2. Lidar

In response to extensive damage from Hurricane Floyd (1999),the North Carolina Floodplain Mapping Program (NCFMP; http://www.ncfloodmaps.com) was established to update maps used toidentify areas vulnerable to flooding. Two private engineeringfirms were contracted to collect elevation data for the purpose ofupdating statewide flood insurance maps. One of the firms, 3Di(http://www.3ditech.com/), acquired elevation measurementswith small-footprint lidar over the Cape Fear River basin inFebruary and March 2001. Because the primary intent of theprogram was to map the bare-earth surface, the measurementswere acquired in winter, when deciduous hardwood canopies werein dormant, ‘‘leaf-off’’ condition. Measurements were acquiredfrom Datis 1, Datis 2, Optech 1225 and Optech 1210 lidar sensorsflying aboard aircraft at 7100–8300 m above sea level. Pulse rateswere 45,000–50,000 pulses per second for Datis sensors and 50,000pulses per second for Optech sensors. Average post-spacing was 4–6 m, beam diameter was 0.5–1.0 m, and swath widths were�1000 m. Vertical accuracy of lidar measurements was <25 cmRMSE.

Sensors used by NCFMP acquired up to four returns per post.Heights of first and last returns were recorded, but were notdifferentiated by order (Hope Morgan, NCFMP, personal commu-nication). To estimate canopy height from the undifferentiatedreturns, we subtracted the value of a bare-earth DEM from theelevation recorded at each return and selected the maximumheight difference within pixels at a range of resolutions—from 3 to30 m (i.e., between the resolutions of GeoSAR and SRTMmeasurements, or 0.5� to 5� the average lidar posting). Thebare-earth DEM used for this and the SRTM canopy measurementswas derived from the NCFMP lidar measurements by convertinglidar returns representing local minima to a Triangulated IrregularNetwork (TIN) specifying known break lines, and then interpolat-ing the TIN to raster at 6.096 m (i.e., 20 foot) resolution.

2.2.3. SRTM

In February 2000, the first space-borne, fixed-baseline inter-ferometric synthetic-aperture radar (InSAR) was carried aboardthe Space Shuttle Endeavor to compile a digital topographicdatabase of Earth’s surface between 608N and 578S (Rabus et al.,2003). Acquisition occurred during winter in the northern hemi-sphere, when deciduous forest canopies were leafless. The ShuttleRadar Topography Mission (SRTM) used the SIR-C and X-SAR radarantennas to collect information in C-band (5.6 cm, 5.3 GHz) and X-band (3.1 cm, 9.6 GHz) wavelengths. The C-band data wereprocessed at the NASA Jet Propulsion Laboratory (JPL) and releasedto the public at a resolution of 1-arc second (�30 m) within theUnited States and 3 arc seconds (�90 m) elsewhere (Hensley et al.,2000). Absolute vertical accuracy for the C-band DEM was

specified as <16 m globally, with relative accuracies of <6 m inany 225 km � 225 km area (Rabus et al., 2003). Because of theshort wavelength of the SRTM C-band sensor, the height responseover vegetated terrain is influenced by integrated scattering fromleaves, branches, and stems, measuring a phase center height thatis higher than the underlying bare-Earth surface in vegetated areas.

Vegetation canopy height can be derived from the SRTM DEMby subtracting from it another DEM that represents the groundelevation (Brown and Sarabandi, 2003; Kellndorfer et al., 2004;Dubayah et al., 2007). The method assumes negligible canopypenetration by the SRTM C-band radar—an assumption that israrely met in vegetation canopies, and so calibration of theelevation differences to reference canopy heights is necessary(Kellndorfer et al. (2004). Whereas Kellndorfer et al. (2004) usedthe National Elevation Dataset (NED) as the bare-earth DEM, wesubtracted the more precise bare-earth DEM derived from lidarfrom the SRTM DEM to improve comparability with our fully lidar-derived canopy height measurements.

2.2.4. GeoSAR

The GeoSAR instrument was initially constructed at NASA’s JetPropulsion Laboratory (JPL), and is currently operated by Fugro,EarthData Inc. (http://www.fugroearthdata.com), a global geos-ciences mapping and remote sensing company. GeoSAR fliesaboard a Gulfstream II aircraft at a nominal altitude of 10 km andconsists of two dual side-looking interferometric systems – one atP-band (86 cm wavelength) and one at X-band (3 cm wavelength)– to cover a >10 km swath on either side. GeoSAR records severalmeasurements (backscatter power, interferometric height, andinterferometric correlation) for each of the two bands at 3 mresolution, with 1 m and 1–4 m vertical accuracy for X- and P-bandDEMs, respectively.

In its early development stages, GeoSAR collected science dataover a number of regions in the United States, including the DukeForest and surrounding area on October 11, 2001. For this area, wecalculated canopy height as the difference between X- and P-bandinterferometric heights. Due to low signal-to-noise ratios in the Pband in sparsely vegetated fields, missing height measurements inthese areas were filled with lidar measurements for calibratingSRTM data (Section 2.3.3).

2.3. Analysis

2.3.1. Lidar scaling

We selected four pine stands to assess the effect of horizontalresolution on lidar-based canopy height measurement. The casestudies represented stands with: (1) dense, homogeneous canopycover; (2) small gaps; (3) narrow, linear gaps between plantedrows; and (4) large, irregularly shaped gaps. Each stand boundarywas internally buffered by 30 m to avoid errors due to spatial mis-registration between datasets. Lidar heights were rasterized atresolutions equal to 0.5-, 1-, 2-, 3-, 4-, and 5-times the averageposting (�6 m) and extracted from within the buffers. Pixel sizestherefore equaled the 3-m resolution of GeoSAR, the 6-m originallidar posting, and ranged up to the 30-m resolution of SRTM inincrements of 6 m. Relative frequency histograms across the rangeof resolution were overlaid on one another to track changes in thedistribution of measured height. Measures of central tendency(mean, median, and mode) were also calculated for each stand ateach resolution and plotted over resolution.

2.3.2. Measurement comparison

Relative frequency distributions from all measurements werecompared graphically for six representative hardwood stands andfive representative pine stands. Results are shown using one standof each type. Inventory plots were then divided into pine and

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–11471140

hardwood types (n = 30 and 50, respectively) based on the field-measured pine dominance index. Means of field-measured treeheights and lidar, GeoSAR, and SRTM rasters were extracted fromwithin 30-m-radius buffers centered on each plot. Measurementswere compared via their plot means following Willmott (1982),interpreting the term ‘‘error’’ simply as ‘‘difference’’ to avoidmisrepresenting any of the measurements as truth a priori. Themean bias:

B ¼ N�1XN

i¼1

xi � yi (2)

quantifies the average vertical offset of one measurement (x) overanother (y) across N plots. The standard deviation of bias:

sB ¼ ðN � 1Þ�1XN

i¼1

ðxi � yi � BÞ2" #0:5

(3)

quantifies the variability around the bias. The root-mean-squarederror:

RMSE ¼ N�1XN

i¼1

ðxi � yiÞ2

" #0:5

(4)

and mean absolute error

MAE ¼ N�1XN

i¼1

xi � yij j (5)

quantify the magnitude of difference between measurements;whereas MAE better represents the average magnitude ofdifferences between measurements, RMSE is more sensitive tolarge differences and is included for comparison to previousstudies. Willmott (1982) also provides metrics describing ‘‘sys-tematic’’ and ‘‘unsystematic’’ differences between two measure-ments, x and y. The systematic error:

MSEs ¼ N�1XN

i¼1

ðxi � xiÞ2

(6)

is the mean squared difference between the measurements xi andtheir estimated values based on another measurement (y) that hasbeen calibrated to x via a linear model x ¼ f ðyjxÞ. MSEs quantifiesthe error remaining between two measurements after linearcalibration. The unsystematic error:

MSEu ¼ N�1XN

i¼1

ðxi � yiÞ2

(7)

is the mean ‘‘residual’’ error between the original measurements yi

and those that have been calibrated to x. MSEu quantifies thevariation in y removed by linear calibration to x. The twocomponents MSEs and MSEu sum to MSE, with MSEs � 0 andMSEu approaching MSE for a well-specified, well-fit model(Willmott (1982). We report their square roots (RMSEs andRMSEu), which are in units of the response (m).

2.3.3. SRTM calibration

Stand canopy-height averages from each method were dividedinto pine and hardwood classes based on the 2001 National LandCover Database (NLCD 2001), taking the landcover value of thenearest pixel to the plot center. To represent zero-height stands ofeach type, the four herbaceous stands were included in bothhardwood and pine classes. After removing one outlier from thepine subset, the final sample included 37 pine and 84 hardwoodplots.

We calibrated the SRTM height measurements by least-squaresregression, fitting functions of form:

H ¼ aþ bHSRTM (8)

and

H ¼ aþ bHSRTM þ cðHSRTMÞ1=3; (9)

where H is canopy height, a and b are the intercept and slope of alinear relationship between the SRTM C band (minus bare-earthDEM) measurements and H, and c fits the cube-root-transforma-tion of SRTM-based canopy height to model the effect of canopypenetration by the C band over increasing height. Negative or zeroSRTM heights were recoded to an arbitrarily small, positive value(0.0001) to accommodate the cube-root transformation, andseparate regressions were fit for pine and hardwood types, withlidar used as reference in pine and field data in hardwood plots.

3. Results

3.1. Lidar scaling

Lidar-based rasters of canopy height in pine stands weresensitive to the area over which returns were aggregated (Fig. 2). Ata pixel-resolution equal to half the average lidar posting (3 m), thewithin-stand distributions of canopy height were heavily influ-enced by ground returns. This effect was greatest in sparselycanopied stands and weakest in densely canopied stands. Theeffect diminished quickly as resolution was coarsened beyond theaverage posting and was negligible in every stand at 3� theaverage posting (18 m). Whereas the ground effect was visible inthe means, medians, and modes of the within-stand distributions,the mean was impacted most, with medians and modes stabilizingat relatively finer scales.

The scale at which the measures stabilized was impacted byhorizontal variations in canopy cover, with a stand exhibiting largegaps (DU-39-18) showing a greater ground effect at fine scalesthan the more homogeneous stands (Fig. 3). A nearly closed-canopy stand with narrow (<5 m) linear gaps between plantedrows (DU-39-18) was affected by ground returns more similarly tohomogeneous, closed-canopy stands than to the stand with large,irregularly shaped gaps. Occasional tall trees – visible as secondarymodes in the height distribution (Fig. 3.) – also affected stand-levelestimates, by increasing the estimates at coarse resolution. At bothfine and coarse resolutions, the mode was least affected byheterogeneity, followed by the median, and then the mean.

In all stands, a range of resolutions existed in which the mean,median, and mode were similar. For homogeneous stands, thisrange was from 2� to 4� the lidar posting (i.e., 12–24 mresolution). In heterogeneous stands, the range was narrower,with canopy gaps increasing the minimum and emergent crownsdecreasing the maximum of the range. Across all stands in thisstudy, the mean, median, and mode were most similar at 3� theoriginal posting (18 m).

3.2. Measurement comparisons

Each of the four methods produced internally consistent,interpretable estimates of canopy height when examined graphi-cally, but to a lesser degree for SRTM in hardwoods (Figs. 3 and 4).However, direct (i.e., uncalibrated) comparison among methodswas variable (Fig. 5). Both stand- and plot-level height distribu-tions were more comparable overall in pine than in hardwoodstands, with greater visual similarity between distributions (Fig. 4),approximately 1–2 m smaller RMSE and MAE (Table 1), andapproximately 1.5–3 m smaller, more constant biases (Table 2) in

Fig. 2. Scaling characteristics of stand-level canopy height measurements (mean, median, and mode) across a range of pixel resolutions in pine stands of different structural

characteristics: narrow, linear canopy gaps between planted rows (DU-33-10); large, irregularly shaped gaps (DU-39-18); small gaps (KO-04-04); and dense, homogeneous

cover (KO-06-05).

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–1147 1141

pines than in hardwoods. Linear calibration between measure-ments was also more effective in reducing differences betweenmeasurements in pines than in hardwoods (Table 3).

In both pine and hardwood forests, field and lidar methodsprovided the tallest canopy height measurements, with lidar

Fig. 3. Effects of varying aggregation of lidar returns on within-stand distributions of can

cover (DU-39-18) and tall, homogeneous canopy cover (KO-04-04).

measurements slightly taller than those collected in the field. Inorder of decreasing height, these were followed by GeoSAR andthen SRTM (Table 2). Because of this sorting, GeoSAR exhibited thegreatest direct (i.e., uncalibrated) comparability to other measure-ments, followed by lidar, field, and SRTM (Table 1). Lidar

opy heights measured in pine stands representing: medium-height, patchy canopy

Fig. 4. Comparison of within-stand distributions of canopy height measurements in a representative pine stand (DU-33-10) and a representative hardwood stand (EN-19-09).

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–11471142

measurements were most directly comparable to field data, butthis could only be evaluated in pine forests. Due do its negative biasand imprecise relationships to other methods, SRTM measure-ments were the most weakly comparable overall.

In terms of improvements measured by R2, linear calibrationswere most effective when based upon lidar (Table 3), with all othermeasurements serving similarly to one another in this regard.However, remaining ‘‘systematic’’ errors (RMSEs) were smallestwhen calibrations were based upon GeoSAR, followed by field data,

Fig. 5. Comparison of field-measured and remotely sens

lidar, and then SRTM. Likely due to shared sensitivity to within-canopy variation, linear calibration to GeoSAR provided thegreatest overall reduction of RMSE in SRTM-based canopy heightmeasurements.

3.2.1. SRTM calibration

SRTM exhibited a delayed response to canopy height in pineplots (Fig. 6), with reference (lidar) height rising more steeply thanSRTM measurements in short stands where the ground surface

ed canopy heights among pine and hardwood plots.

Table 1Pairwise RMSE and MAE (in parentheses) between averages of canopy height

measurements (m) in 30-m radius plots. Values for pine plots are in the upper-right

half of the matrix and values for hardwood plots are in the lower left.

Field 4.73 (4.11) 8.40 (7.24) 14.21 (12.17)

– Lidar 8.45 (7.53) 14.92 (13.77)

9.54 (8.25) – GeoSAR 7.88 (7.04)

16.84 (15.33) – 9.85 (8.74) SRTM

Table 3Linear regression summaries for plot-level pine (n = 30) and hardwood (n = 50)

canopy height measurements. MSEu is mean ‘‘unsystematic’’, or ‘‘residual’’ error

between original and calibrated measurements, and MSEs is the ‘‘systematic’’ error

remaining between calibrated and reference measurements (see text for full

explanation).

Regression Slope Intercept R2 RMSEu RMSEs

Pine

Lidar � Field 0.856 (P < 0.00) 4.409 (P < 0.01) 0.83 4.18 2.22

GeoSAR � Field 0.451 (P < 0.00) 5.577 (P < 0.00) 0.70 3.13 7.79

SRTM � Field 0.471 (P < 0.00) �1.845 (P < 0.32) 0.54 4.67 13.42

GeoSAR � Lidar 0.534 (P < 0.01) 3.106 (P < 0.00) 0.87 2.05 8.20

SRTM � Lidar 0.570 (P < 0.16) �4.692 (P < 0.01) 0.70 3.78 14.43

SRTM � GeoSAR 1.024 (P < 0.00) �7.384 (P < 0.11) 0.73 3.53 7.04

Hardwood

GeoSAR � Field 0.416 (P < 0.00) 5.916 (P < 0.00) 0.38 4.63 8.34

SRTM � Field 0.322 (P < 0.00) �0.744 (P < 0.62) 0.35 3.87 16.39

SRTM � GeoSAR 0.516 (P < 0.00) �1.498 (P < 0.30) 0.40 3.69 9.14

Table 2Mean bias (B) between paired averages of canopy height measurements within 30-

m radius plots. Values for pine plots are in the upper-right half of the matrix and

values for hardwood plots are in the lower left. Biases between pairs of

measurements (e.g., field vs. GeoSAR) are reported as the difference of the first

element of the pair along the diagonal over the second—e.g., the B (field, GeoSAR) is

reported as height (field) � height (GeoSAR). Standard deviations of bias are in

parentheses.

Field �1.60 (17.79) 5.13 (57.17) 12.17 (135.61)

– Lidar 6.73 (74.96) 13.77 (153.40)

6.60 (94.28) – GeoSAR 7.04 (78.45)

15.28 (218.30) – 8.68 (124.02) SRTM

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–1147 1143

dominated scattering of the C band. In taller pine canopies(>10 m), where the signal’s penetration to the ground wasreduced, SRTM increased in approximate 1:1 proportion to canopyheight. The linear model accommodated for this pattern with asteep slope (1.48) and a high intercept (8.93). The cube-root modelfollowed the data more consistently over its range, with aninsignificant intercept (Table 4) and a slope nearly parallel to the1:1 line in tall (�20 m) pine canopies (Fig. 6).

The pattern was much less clear in hardwood canopies, withlittle difference in fit between the linear and quadratic models.Whereas the addition of a cube-root term decreased standarderror, RMSE, and MAE by�1 m in pine forests, improvements in fit

Fig. 6. Calibration of SRTM-derived canopy height based on lidar and GeoSAR measurem

reference values measured with lidar in pine plots and by field methods (Haga altimet

Table 4Regression summaries for plot-level calibration of SRTM- on lidar- and field-based can

Model a b

Pine (n = 37)

H = a + bHSRTM 8.93 (P < 0.00) 1.48 (P <

H = a + bHSRTM + c(HSRTM)1/3 a 0.435 (P <

Hardwood (n = 84)

H = a + bHSRTM 17.14 (P < 0.00) 0.79 (P <

H = a + bHSRTM + c(HSRTM)1/3 10.92 (P < 0.00) a

a Removed due to statistical insignificance (P > 0.10).b Reported for full model.

from the cube-root term were slight in hardwoods (Tables 4 and 5).Also in opposition to pine canopies, the cube-root term tended toover-correct the SRTM data in tall hardwood stands, forcing anexcessively shallow slope in the tallest stands.

The greatest difference between linear and cube-root calibra-tions occurred in the extremes of both pine and hardwood canopyheight. Whereas the linear transformations over-predicted canopyheight in the shortest (�0 m) stands, the logarithmic correctionsproduced more even and accurate height estimates across thelower range of canopy heights, although the bias was notcompletely removed in hardwoods (Fig. 7). At the high end ofthe range of canopy heights, the equations diverged as well, withlinear functions producing higher estimates than cube-rootcalibrations. The effect was extreme in hardwood stands.

ents in pine (n = 48) and hardwood (n = 84) plots. Calibrated curves are overlaid on

er) in hardwoods plots.

opy height in NLCD 2001 pine and hardwood types.

c R2 S.E. (m)

0.00) – 0.75 5.05

0.03) 9.92 (P < 0.00) 0.85b 3.99

0.00) – 0.19 6.73

6.67 (P < 0.00) 0.25b 6.48

Table 5Validation of SRTM calibration for canopy height in pine and hardwood plots. Plots

were stratified based on NLCD 2001 landcover types.

Model B (sd) MAE RMSE RMSEs RMSEu

Pine (n = 37)

H = a + bHSRTM 0.00 (0.00) 4.20 4.94 0.00 4.94

H = a + bHSRTM + c(HSRTM)1/3 0.15 (2.10) 3.11 3.90 0.47 2.10

Hardwood (n = 83)

H = a + bHSRTM 0.00 (0.00) 5.13 6.65 0.00 6.65

H = a + bHSRTM + c(HSRTM)1/3 0.00 (0.00) 4.94 6.41 0.00 6.41

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–11471144

4. Discussion

4.1. Measurement of canopy height by lidar

Our results corroborate studies confirming discrete-returnlidar’s reliability for measuring canopy height in coniferous forests(Naesset, 1997; Dubayah and Drake, 2000; Means et al., 2000;Lefsky et al., 2002a,b; Roberts et al., 2005). Stand-level distribu-tions of lidar height maxima provided intuitive representations ofthe vertical structure of pure loblolly pine stands of different sizes,including negligible mid-story cover and loss of apical dominancewith increasing height (Fig. 2). Canopy heights measured by lidaralso had greater accuracy and fewer systematic errors with respectto field measurement in pine forests than methods based on radarinterferometry. Further, judged by their increased precisionrelative to field data (Table 3), lidar measurements are preferableover field data for calibrating interferometric measurements ofcanopy height, including those of SRTM and GeoSAR.

Canopy height measured by lidar is sensitive to the scale atwhich the data are collected and aggregated into raster pixels,revealing an interaction between canopy heterogeneity and dataresolution. By increasing the number of returns from which per-pixel maxima are calculated, coarsening raster resolution removesthe effect of gaps on canopy height measurement. This effect varieswith the size and shape of canopy gaps, and so the scaling behaviorof lidar measurements also has the potential to provide ancillarymeasurements of fine-scale (i.e., sub-pixel) canopy heterogeneity.Ongoing studies are needed to show the interaction betweenspatial heterogeneity of the canopy and lidar posting so that dataacquisition and processing parameters can be tuned to variousforest types (Dubayah and Drake, 2000).

The winter acquisition of our lidar data restricted its utility inhardwood stands. In preliminary analyses, the sub-canopy andground signals were dominant in leafless stands and were not fully

Fig. 7. Comparison of raw and calibrated SRTM measurements to reference height measu

measurements, and those in hardwood plots are from field measurements. Calibrated m

removed even at 30-m resolution. High-density (�12 returns m�2),small-footprint lidar acquired in winter has been used to analyzevertical structure of deciduous trees at fine scales (Brandtberget al., 2003), suggesting that regional characterizations are alsopossible at far coarser resolution than those studied here. However,as resolution was coarsened, hardwood pixels became increasinglycontaminated by pine cover, which overshadowed the weak signalfrom the bare hardwood canopy. Because commercial lidar sensorstypically operate at near-infrared wavelengths, the need for datafiltering could possibly be met by using the reflection intensity ofeach return to discriminate returns from leaves vs. those frombranches etc. (Lillesand et al., 2008).

Our lidar dataset was originally developed for the purpose ofmapping bare-earth elevation, but our results also encouragefurther study and use of this statewide dataset for mappingstructural characteristics of evergreen vegetation in NorthCarolina. Following national guidelines (FEMA, 2003), similar lidarmapping programs are being implemented in other states as well.The increasing coverage of these datasets shows great promise formapping and studying evergreen canopy structure, biomass,growth, and habitat value at regional scales.

4.2. Measurement of canopy height by Interferometric Synthetic

Aperture Radar (InSAR)

Scattering of microwave energy is dependent on the size andarrangement of target objects, with strong signals returned to thesensor from objects with length approximately equal to thewavelength of radiation (Lillesand et al., 2008). Objects muchlarger than the wavelength do not transmit, but instead tend toreflect the signal away from the sensor. Within a forest canopy,short-wavelength (e.g., X-band) signals are dominated by leavesand twigs, intermediate wavelengths (e.g., C-band) by medium-sized branches, and long wavelengths (e.g., P-band) by large-diameter trunks and the ground surface. Due to the verticaldistribution of canopy elements, a radar signal’s penetration into aforest canopy is likewise proportional to its wavelength, resultingin scattering heights of X, C, and P bands sorting vertically from topto bottom in the canopy (Jensen, 2000).

This leads to a sorting of elevation values measured byinterferometry based on the different wavelengths, with heightsmeasured by the X band representing nearly the top of the canopy,those from the P band representing the bare earth, and from the C-band intermediate between these two. By pairing a long-wavelength with a short-wavelength band, canopy height isestimated by subtracting bare-earth (BE) from top-of-canopy

rements in pine and hardwood plots. Reference heights in pine plots are from lidar

easurements are from a cubic fit in pine plots and a linear fit in hardwood plots.

Fig. 8. Schematic representation of the idealized response of X-, C-, and P-band

radar interferometric heights to ‘‘true’’ canopy height; and the resulting canopy-

sensitive ranges of GeoSAR and SRTM measurements. Axes are not drawn to scale.

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–1147 1145

(TOC) height measurements. In canopies shorter than thepenetration depth (denoted by ‘‘*’’ in Fig. 8) of both the BE andTOC bands, canopy height is unreliably measured as approximatelyzero because the two signals are both dominated by the groundsurface. In canopies with height between the penetration depths ofthe TOC and BE bands, subtracted canopy height is proportional totrue canopy height minus the TOC penetration depth. In canopiestaller than the penetration depth of both bands, height isunreliably measured as the difference between canopy-sensitiveportions of each curve.

Therefore, the response of measured to true canopy height for agiven pair of bands follows a three-stage curve, with the mostreliable measurements obtained between the penetration depthsof the shorter (TOC) and longer (BE) bands. Although sampling wassparse below 15 m, the transition from the first to the second stageof the curve is apparent in the SRTM measurements (Fig. 5) andfrom the second to the third stages in the GeoSAR measurements(Figs. 5 and 6). Canopy heights derived from SRTM used a relativelylong-wavelength (C band) for TOC measurements and used BEelevations from lidar measurements capable of deep canopypenetration. The bias in the SRTM-derived canopy heights istherefore likely due to excessive penetration by the TOC band inshort canopies, resulting in a delayed, but nearly constant negativebias in canopies taller than 10 m. Alternatively, GeoSAR, whichuses a very short-wavelength TOC band, is likely more affected byincomplete penetration by its P-band BE measurements. This leadsto a saturation effect with increasing canopy height, observed as adecreasing slope resulting from the measured BE surface liftingabove the true ground elevation in canopies greater thanapproximately 20 m.

Scattering of microwave radiation in forest canopies isinfluenced by canopy water content, structure, and viewinggeometry (Jensen, 2000; Lillesand et al., 2008), so variation in anyof these factors leads to imprecision in canopy height measure-ments. The effect of forest structure is apparent in differencesbetween GeoSAR’s precision in hardwood and pine forests. Withstrong apical dominance of the dominant species and low speciesdiversity, southeastern pine forests are structurally simpler thanhardwood forests, which are richer in species composition andcontain species capable of greater structural complexity than thepines. GeoSAR measured height more precisely in pine canopiesthan in hardwoods, suggesting that structural diversity plays a

large role in measurement precision. SRTM’s precision was alsolikely affected, but this effect was overshadowed by the data’sdormant-season acquisition. Whether to avoid noise fromstructural or other variations, frequent calibration will likelyimprove precision when using InSAR to measure canopy height,especially over large, heterogeneous areas.

4.3. Calibration of SRTM for canopy height measurement

Uncalibrated differences between the SRTM DEM and bare-earth elevation measurements are known to underestimatecanopy height of various forest types due to C-band radar’spenetration of the vegetation canopy (Kellndorfer et al., 2004). Wealso observed this bias in southeastern pine and hardwood forests,noting a substantially larger, more variable bias in dormanthardwood canopies. The increased bias in hardwood canopiesshows that the effect of canopy penetration is exacerbated by theleafless condition of deciduous forests at the time of dataacquisition.

Although uncalibrated SRTM-derived canopy heights under-estimated true canopy height, a consistent physical relationshipbetween SRTM measurements and canopy height allowedcalibration of SRTM to more accurate measurements in pinestands. In pine forests, this relationship between canopy height (H)and the difference between the SRTM and a bare-earth DEM(HSRTM) can be represented as:

H ¼ 0:435� HSRTM þ 9:92� ðHSRTMÞ1=3: (10)

Unfortunately, although errors in both pine hardwood forestswere reduced substantially by calibration (from 14.92 to 3.90 m inpine and from 16.84 to �6.5 m in hardwood), such simplecalibration does not appear nearly as effective in dormantdeciduous as in fully canopied forests. Disagreement betweencalibrated SRTM- and lidar-derived canopy height in this study isgreater than that between SRTM and field measurement inmanaged pine plantations on flat topography after outlier removal(Kellndorfer et al., 2004), but is more comparable to errors in mixedconiferous forest in the Sierra Nevada Mountains in NorthernCalifornia (Dubayah et al., 2007). The picture emerging from theseregional studies is that both forest structural complexity andunderlying bare-earth topography effect the accuracy of SRTM-based canopy height measurements (Bourgine and Baghdadi,2005; Bhang et al., 2007), but that calibration is possible in manysituations.

In southeastern pine or structurally similar forests for which areliable bare-earth DEM is available, linear or cube-root calibra-tion of SRTM measurements substantially reduces vertical errorsof SRTM-based canopy height estimates. Previous studies haverecognized the potential for correcting SRTM underestimates ofcanopy height through simple linear regression against referenceheight measurements (Kellndorfer et al., 2004; Dubayah et al.,2007). Our addition of a cube-root term based on the effect ofcanopy penetration is important to prevent over-predicting theheight of the shortest stands. However, in regions with a mixtureof extremely tall and very short stands, or where bare-earth DEMsmight be influenced by the forest canopy, calibrations will need toincorporate canopy penetration artifacts from both the SRTM (astop-of-canopy) and bare-earth DEMs. Canopy-height under-estimation by SRTM data is a function of vegetation structureand will likely vary if vegetation varies considerably within anarea of interest (Bhang et al., 2007; Dubayah et al., 2007). It wouldbe beneficial for future efforts to focus on fitting context-dependent corrections to more accurately map vegetation heightacross large heterogeneous landscapes with SRTM or other C-band data.

J.O. Sexton et al. / Forest Ecology and Management 257 (2009) 1136–11471146

4.4. Selection among methods

Consideration of sensitivity, scale, and comparability shouldinform selection of methods for estimating canopy height. Due to itsexpediency and low cost, in situ field measurement remains the bestchoice for measuring individual or small numbers of tree heights.However, field measurement requires extrapolation from smallsamples and is not capable of mapping canopy height over any butthe smallest stands. Remote sensing provides an economicallyefficient means to map larger regions, with the various methodssorting along an axis of scale. Due to its fine resolution andcustomizable post-spacing, lidar is best suited at scales from severalto several million hectares and is useful for calibrating broader-scaleInSAR measurements. With larger swaths and systematic proces-sing, airborne InSAR sensors such as GeoSAR achieve economy ofscale for larger regions—from hundreds of thousands to millions ofhectares. Especially in tall pine forests, GeoSAR’s precision shouldalso support increased accuracy through calibration to lidarmeasurements. At the coarsest scales, an increasing number ofspaceborne InSAR sensors – including the European ERS-2 andEnvisat, the Japanese PALSAR, the German TerraSAR-X, the ItalianCOSMO SkyMed constellation, and Canadian RADARSAT series –promises the capacity to monitor forest resources at the global scalein the near future (Lillesand et al., 2008). The SRTM dataset iscurrently the only potential source of tree canopy height for theentire Earth. Although the SRTM DEM was collected only in 2001 andrequires calibration with a separate bare-earth DEM to extractcanopy height, it has the potential to provide a baseline measure-ment against which future measurements can be compared tomeasure forest growth. For this, calibrations stratified by ecoregio-nal forest types should be conducted wherever circa-2001 canopyheight datasets are available.

5. Conclusions

Forest canopies are complex volumes, and several methods –each with characteristic sensitivities, biases, and limitations ofscale – are available to measure their height. Due to simplerstructure and phenology, pine forests allow greater precision ofheight measurements than do hardwood forests in the south-eastern United States. In southeastern pine forests, lidar measure-ments acquired in the dormant season have the highest precisionof all methods studied, followed by those from field measurementsand interferometric synthetic aperture radar (InSAR). Rastercanopy-height surfaces produced from lidar returns are sensitiveto the resolution at which they are aggregated. InSAR-derivedcanopy height measurements are subject to biases from factorsincluding variable canopy penetration, but show potential forcalibration based on lidar. X- and P-band interferometric radarmeasurements from airborne sensors (e.g., GeoSAR) provide moreprecise, accurate measurements than C-band data from space-borne sensors (i.e., SIR-C/SRTM), but even the SRTM DEM can becalibrated to estimate canopy height across broad regions. Each ofthe remotely sensed methods studied produces reasonable andconsistent depictions of canopy height that can be compared withdata of similar provenance, but due to differences in underlyingsensitivities between the methods, comparisons between mea-surements from various sources require cross-calibration and willbe most useful at broad scales.

Acknowledgements

Lidar data were provided by the North Carolina FloodplainMapping Program. Forest inventory measurements were providedby the Office of the Duke Forest, Duke University. John Kerkeringperformed and reported analyses of a pilot study, and John P. Fay

assisted lidar data processing. Analyses were performed in theDuke University Landscape Ecology Laboratory, with technicalassistance from Dean Urban, Ben Best and Ibrahim Alameddine.This research was supported by a NASA Earth System ScienceFellowship, ‘‘Suburban forest dynamics: fusing remote sensing andecological models’’ (J.O. Sexton, 2005–2008). Two anonymousreviewers provided suggestions that improved the manusctriptgreatly.

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