Estimating plot-level tree heights with lidar: local ......Estimating plot-level tree heights with lidar: local ﬁltering with a canopy-height based variable window size Sorin C

Estimating plot-level tree heights with lidar: localfiltering with a canopy-height based variable

window size

Sorin C. Popescu a,�, Randolph H. Wynne a, Ross F. Nelson b

a Department of Forestry, Virginia Tech, Blacksburg, VA 24061, USAb Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, MD, USA

Abstract

In recent years, the use of airborne lidar technology to measure forest biophysical

characteristics has been rapidly increasing. This paper discusses processing algorithms for

deriving the terrain model and estimating tree heights by using a multiple return, high�/

density, small-footprint lidar data set. The lidar data were acquired over deciduous,

coniferous, and mixed stands of varying age classes and settings typical of the southeastern

US. The specific objectives were: (1) to develop and test algorithms to estimate plot level tree

height using lidar data, and (2) to investigate how ground measurements can help in the

processing phase of lidar data for tree height assessment. The study area is located in the

Piedmont physiographic province of Virginia, USA and includes a portion of the

Appomattox-Buckingham State Forest (37825?N, 78841?W). Two lidar processing algorithms

are discussed*/the first based on single tree crown identification using a variable window size

for local filtering, and the second based on the height of all laser pulses within the area covered

by the ground truth data. Height estimates resulted from processing lidar data with both

algorithms were compared to field measurements obtained with a plot design following the

USDA Forest Service Forest Inventory and Analysis (FIA) field data layout. Linear

regression was used to develop equations relating lidar-estimated parameters with field

inventories for each of the FIA plots. As expected, the maximum height on each plot was

predicted with the highest accuracy (R2 values of 85 and 90%, for the first and the second

algorithm, respectively). The variable window size algorithm performed better for predicting

heights of dominant and co-dominant trees (R2 values 84�/85%), with a diameter at breast

height (dbh) larger than 12.7 cm (5 in), when compared with the algorithm based on all laser

� Corresponding author. Address: Department of Forestry, 319 Cheatham Hall, Virginia Tech,

Blacksburg, VA 24061, USA

E-mail address: [email protected] (S.C. Popescu).

Computers and Electronics in Agriculture 37 (2002) 71�/95

www.elsevier.com/locate/compag

0168-1699/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 1 6 9 9 ( 0 2 ) 0 0 1 2 1 - 7

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heights (R2 values 57�/73%). The use of field-based height thresholds when processing lidar

data did not bring significant gains in explaining the total variation associated with tree height.

The technique of local filtering with a variable window size considers fundamental forest

biometrics relationships and overall proved to give better results than the technique of all laser

shots.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Lidar; Forest inventory and analysis; Tree height; Interpolation; Digital elevation model;

Variable window size

1. Introduction

Airborne laser sensors allow scientists to analyze forests in a 3-D format over large

areas. In contrast to monoscopic optical remote sensing methods, which yield

information on horizontal forest pattern, modern lidar systems provide georefer-

enced information of the vertical structure of forest canopies. Laser pulses from a

sensor carried aboard an aircraft are directed toward the ground to collect ranging

data to the top of the canopy, and in some instances, to subcanopy layers of

vegetation and to the ground. Airborne lidars have been used to describe

topographic relief (e.g., Krabill et al., 1984; Schreier et al., 1985; Bufton et al.,

1991; Ritchie, 1995), and forest vegetation characteristics, such as percent canopy

cover, biomass (e.g., Nelson et al., 1984, 1988a,b), and gross-merchantable timber

volume (Maclean and Krabill, 1986). Previous studies that focused on estimating

forest stand characteristics with scanning lasers used lidar data with either relatively

large laser footprints, 5�/25 m, (Harding et al., 1994; Lefsky et al., 1997, 1999;

Weishampel et al., 1997; Blair et al., 1999; Means et al., 1999) or small-footprints,

but with only one laser return (Næsset, 1997a,b; Magnussen and Boudewyn, 1998;

Magnussen et al. 1999). A small-footprint lidar with the potential to record the entire

time-varying distribution of returned pulse energy or waveform was used by Nilsson

(1996) for measuring tree heights and stand volume.

In recent years, the use of airborne lidar technology to measure forest biophysical

characteristics has been rapidly increasing. In addition to providing a characteriza-

tion of ground topography, lidar data give new information about the canopy

surface and vegetation parameters, such as height, stem density, and crown

dimensions, which is critical for environmental modeling activities. Airborne lidar

data combine both surface elevations and accurate planimetric coordinates, and

processing algorithms can identify single trees or groups of trees in order to extract

various measurements on their 3-D representation.

Laser scanner systems currently available are in a fairly mature state of art, while

the processing of airborne scanning lidar data still is in an early phase of

development (Axelsson, 1999). Airborne laser scanning represents an emerging

technology that is making the transition from the proof-of-concept to reliable uses

(Flood and Gutelius 1997). It is a general feature of new technologies that technical

potential opens the ground for new applications. Airborne laser scanning is presently

S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71�/9572

in that process, spreading into other fields beyond the generation of terrain models

(Ackermann, 1999).

Existing processing algorithms for lidar data are implemented through proprietary

software and generally try to filter vegetation to obtain the terrain elevation model.

The basic processing task that needs to be accomplished before attempting to

estimate forest parameters is the characterization of the terrain elevation and

creation of a digital elevation model (DEM), as a subset of the digital surface model(DSM) obtained from raw laser points. It is the unique ability of laser scanning to

measure ground elevation directly, most often through penetrating the tree canopy;

that is one of the major advantages that lidar offers over traditional photogram-

metry when operated in forested areas. However, few papers published on the

subject of separating lidar data into vegetation and terrain points provide all the

algorithmic details. In most of the forestry studies of lidar, the terrain elevation is

computed by the lidar data providers (e.g., Næsset, 1997a,b; Means et al., 2000).

Most of the algorithms for removing the vegetation laser hits are based on iterativealgorithms that combine filtering and thresholding methods (Kraus and Pfeifer,

1998; Axelsson, 1999; Jaafar et al., 1999; Petzold et al., 1999). The irregularly

dispersed laser points assumed to correspond to the ground are used with

appropriate interpolation methods to derive the high�/accuracy DEM. Lam (1983)

offers a comprehensive review of spatial interpolation methods. For point

interpolation, the numerous methods can be classified into exact and approximate.

Exact methods include distance-weighting, Kriging, spline interpolation, triangula-

tion, and finite-difference methods. Approximate methods include power-seriestrend models, Fourier models, distance-weighted least squares, and least-squares

fitting with splines. Despite intense efforts in the creation of high�/resolution DEMs

from lidar data, driven by either commercial or scientific purposes, the characteriza-

tion of terrain topography under forest conditions is still a challenge.

Some lidar sensors (e.g., Optech ALTM 1020, Optech Inc.) can be toggled to

record either the first or the last return, thus two flights are necessary over the same

area to get the bare ground terrain model and the top of the canopy surface. Image

subtraction with first- and last-return interpolated data can be used to derive treeheights (Young et al., 2000), though not all of the last-return hits penetrate to the

ground. Surveys in the U.S. Pacific Northwest carried out using the Optech ALTM

1020 scanning system indicated a minimum 20�/30% penetration of coniferous

canopies (Flood and Gutelius, 1997). In the same region, with conifer-dominated

stands and dense overstory, Means (2000) experienced a very low penetration to the

ground, only 1�/5%, for a small-footprint lidar. Kraus and Pfeifer (1998) estimated a

penetration rate of less than 25% for their lidar study in the Vienna Woods

(Wienerwald) in Austria, using an Optech ALTM 1020 lidar system.Measurement of stand height by current photogrammetric or field survey

techniques is time consuming and expensive. Tree heights have been derived from

scanning lidar data sets and have been compared with ground-based canopy height

measurements (Næsset, 1997a,b; Magnussen and Boudewyn, 1998; Magnussen et al.,

1999; Young et al., 2000). Recent studies show that, in moderate to dense forests,

small-footprint lidars tend to underestimate stand height (Nilsson, 1996; Næsset,

S.C. Popescu et al. / Computers and Electronics in Agriculture 37 (2002) 71�/95 73

1997a). More frequent laser sampling of the crown shoulders than the tree apex

biases canopy heights toward low values.

Potential future uses of the lidar technology that have been foreseen in the

literature (e.g., Means, 2000) include the assessment of forest biomass, measurement

of forest structural attributes critical to understanding forest ecosystem condition,

and automated processing and integration with co-registered multi- and hyperspec-

tral digital imagery. Data from large-footprint lidar may become publicly availablewith the launch of the vegetation canopy lidar in the year 2004, as a result of the

collaboration between NASA and the University of Maryland (Dubayah et al.,

1997). Small-footprint lidars are available commercially and more research on their

potential for forestry applications is needed. Applications of small-footprint lidar

have not progressed too far, mainly because of the current cost of lidar data.

However, with an anticipated decline of lidar data cost in the near future combined

with promising current research efforts, the use of lidar in forestry is expected to

extend over many aspects of forest measurements. Situated in this context, theoverall objective of this study is to develop robust processing and analysis techniques

to facilitate the use of airborne laser data for forest tree height assessment. The

specific objectives are: (1) to develop and test algorithms to estimate plot level tree

height using lidar data, and (2) to investigate how ground measurements can help in

the processing phase of lidar data for tree height assessment.

2. Materials and methods

2.1. Study site

The study area is located in the southeastern US, in the Piedmont physiographic

province of Virginia (Fig. 1). It includes a portion of the Appomattox-Buckingham

State Forest that is characterized by deciduous, coniferous, and mixed stands of

varying age classes (37825?N, 78841?W). Fig. 2 provides a map of forest stand types

covered by the lidar data. A mean elevation of 185 m, with a minimum of 133 m anda maximum of 225 m, and gentle slopes characterize the topography of the study

area.

2.2. Ground reference data

The ground-truth data collection took place in the leaf-off season in December

1999, while the lidar was flown at the beginning of September, with leaf-on canopy

conditions. Three forest vegetation types were covered by the field sampling*/pine-hardwoods, upland hardwoods and pine plantations. The leaf-off canopy condition

for hardwoods allowed a more accurate measurement of tree heights from the

ground. The stand age varied, being approximately 15 years for the pine plantations,

35�/55 years for the pine-hardwood mixed stands, and up to 100�/115 years for the

upland-hardwood stands. The tree species found in the pine-hardwoods stands were

white oak (Quercus alba L.), chestnut oak (Quercus prinus L.), northern red oak


(Quercus rubra L.), southern red oak (Quercus falcata Michx.), yellow poplar

(Liriodendron tulipifera L.), red maple (Acer rubrum L.), and three species of

pines*/Virginia pine (Pinus virginiana Mill.), loblolly pine (Pinus taeda L.), and

shortleaf pine (Pinus echinata Mill.). In addition to the hardwood species mentioned

above, the following species were inventoried in the upland-hardwood stands: pignut

hickory (Carya glabra (Mill.) Sweet), scarlet oak (Quercus coccinea Muenchn.),

black oak (Quercus velutina Lam.), blackgum (Nyssa sylvatica Marsh.), and

American beech (Fagus grandifolia Ehrh.). Of the two subplots located in pine

plantations, one was in a pure loblolly pine plantation, and one in a mixed pine

species plantation.The plot design followed the USDA Forest Service Forest Inventory and Analysis

(FIA) field data layout. An FIA plot consists of a cluster of four subplots

approximately 0.017 ha (0.04 acres) each, with a radius of 7.32 m (24.0 ft) (National

Forest Inventory and Monitoring CORE Field Guide, 1998). One plot is distributed

over an area of approximately 0.4 ha (1 acre), thus it represents a sample of the

conditions within this area. The center plot is subplot 1. Subplots 2, 3, and 4 are

Fig. 1. Map of eastern US indicating the location of the study area.


located 36.58 m (120.0 ft) at azimuths 0, 120, and 2408 from the center of subplot 1

(Fig. 3). Subplots are used to collect data on trees with a diameter at dbh of 12.7 cm

(5.0 in), or greater. To allow a more detailed inventory of trees within the subplots,

Fig. 2. Forest stand types covered by lidar data.

Fig. 3. Layout of a single FIA plot with four subplots.


we collected tree height and tree position data on trees with a dbh of at least 6.35 cm

(2.5 in). Except for the microplot, FIA standards only require measurement of trees

with a dbh larger than 12.7 cm. A microplot with a radius of 2.07 m (6.8 ft) was

located at the center of each subplot, to account for seedlings and saplings with a

dbh above 2.54 cm (1 in), but less than 6.35 cm (2.5 in). A total of 6 plots were

measured in the study area, each with 4 subplots. Plot centers (subplot 1 centers)

were located on a 200�/200 m2 grid (656�/656 ft2), with two rows oriented East�/

West, and three columns oriented North�/South (Fig. 2). The centers of subplots 1,

for all plots, were laid out in the field using a navigational GPS unit. In addition, all

FIA subplot locations were determined using 60 s static measurements with a 12-

channel GPS receiver, HP-GPS-L4 with a PC5-L data collector (Corvallis Micro-

technology, Inc.). The reported mapping accuracy for the HP-GPS-L4 unit, obtained

under open sky for 60 s of static measurements is 30 cm (Corvallis Microtechnology

and Inc., 2001). Under forest canopy, GPS systems tend to yield from 1.5�/3 times

less accurate solutions (Craig Greenwald, 2001, Corvallis Microtechnology, Inc.,Technical Support, personal communication). Therefore, we estimate sub-meter

accuracy for locating the plot centers. For this study, the subplots were pooled

together with no reference to the full plot to which they belong, and the results were

compared on a subplot basis. From the total of 24 subplots, 11 were located in

upland hardwood stands, 11 in pine-hardwood stands, and 2 in pine plantations.

On each subplot, the heights of all trees were measured. Trees higher than 7.62 m

(25 ft) were measured using a Vertex hypsometer, while smaller trees were measured

using a height pole. Several heights less than 7.62 m were measured with bothmethods and the height difference never exceeded 15 cm (0.5 ft). Diameter at dbh

was measured on all trees within the subplots using a diameter tape. Crown width

was measured on all trees with a dbh larger than 12.7 cm (5.0 in). Crown width was

determined as the average of four perpendicular crown radii measured with a tape

from the tree bole towards the subplot center, away from it, to the right and to the

left. The location (x ,y ) of each tree relative to the subplot center was determined by

bearing and distance using a distance tape and a compass, with an expected standard

error of up to 30 cm (1 ft), depending on the distance to the subplot center. Takinginto account the positional accuracy of the differential GPS unit for determining the

location of the subplot centers, the maximum error of a tree’s position is expected to

be approximately 1.5 m. This error only refers to the position of the base of the tree,

without considering the deviation of the tree top relative to the base.

2.3. Lidar data set

The lidar data were acquired over an area of 1012 ha, on September 2, 1999. The

canopy condition at that time was leaf-on. The lidar system (AeroScan, EarthData,Inc.) utilizes advanced technology in airborne positioning and orientation, enabling

the collection of high�/accuracy digital surface data. The aerial platform is a Piper

Navajo Chieftain aircraft capable of carrying aerial cameras, airborne GPS, inertial

measuring units, and the lidar sensor. The carrier airspeed was between 110�/145

knots. The scanning system uses an oscillating mirror with a scanning rate of 10 Hz


and a scanning angle that can be adjusted from 1 to 758. For the Appomattox-

Buckingham data set the scanning angle was 108, giving a total field of view of 208.The laser wavelength was 1064 mm and the pulse rate 15 kHz. The area was flown at

an average altitude of 1980 m above ground level. With a laser beam divergence of

0.33 mrad, the average footprint on the ground was 0.65 m. The laser instrument

field of view and the average flying height resulted in an average ground swath width

of 699 m. The entire research area was covered by 21 parallel flight lines, oriented

North�/South. The mission was designed with up to 70% overlap between adjacent

swaths to increase the point density on the ground and to correct for the scanning

pattern evident in Fig. 4(a) and (b). The sensor had a pulse time width of 12 ns.

The AeroScan system is not capable of recording the intensity of the backscattered

laser echo, but it is able of recording up to five returns for each laser pulse,

depending on the ground cover. We used only the first and last returns. The last

return could coincide with the first return where there was only one return per laser

pulse, or it could be the second, the third or the fourth, depending on how many

returns there were per pulse and which one of the subsequent returns was the last

one. The laser point density on the ground, for one swath, was of 0.47 points/m2 for

the first return, 0.20 points/m2 for the second return, 0.02 points/m2 for the third

return, and 0.0001 points/m2 for the fourth return. None of the pulses were able to

produce a fifth return for the given ground conditions. The point density for the first

or last return translates into an average point distance of 1.5 m. The resulting 3-D

coordinates of laser hits were compiled in an ASCII mass point file of x , y , z on the

UTM projection for each of the laser returns. By pooling all the laser points from

adjacent swaths into the same point file, the average interpoint distance decreased to

0.7 m. The provider performed an evaluation of the lidar data, including a

comparison of the data from flight line to flight line. This comparison showed

Fig. 4. Lidar scanning pattern on the ground; (a) at the center of the swath, (b) at the edge of the swath.


high�/accuracy of overlapping lidar lines and no anomalies in the data. All ranges

were post-processed by EarthData and corrected for atmospheric refraction and

transmission delays.

The reported accuracies for the AeroScan lidar system flying at less than 2400 m

above ground, over open homogeneous flat terrain, are as follows: an elevation or

vertical accuracy of 9/15 cm and an horizontal accuracy of 9/25 cm (EarthData Inc.,

2001).

2.4. Ground digital elevation model

As previously stated, one must characterize the ground elevation before estimating

the vegetation height. A high laser point density allows an adequate filtering ofvegetation hits for the derivation of terrain elevation, since only a relatively low

number of laser pulses are able to entirely penetrate the canopy. The separation of

laser points into terrain and vegetation hits still remains a difficult task even for lidar

data provided by systems that are able to record multiple returns. A 2-D black-and-

white representation of lidar data (Fig. 5) depicts higher points with lighter pixels

and lower points with darker pixels. The images in Fig. 5 were created by

interpolating the cloud of first-return (a) and last-return (b) lidar points to a regular

grid using linear kriging. The interpolated grid cell size was 0.5 m. Both images showthe same area with a deciduous stand in the upper-left part of the scene and a young

pine plantation in the lower right corner. Though it is evident that Fig. 5(b) shows

points of lower heights, with darker pixels, parts of the deciduous tree crowns are

still apparent. Assumed ground returns are also noticeable in the young coniferous

stand, as they appear as small areas of darker pixels. It is clear that the last return

does not necessarily penetrate dense canopy layers to record the ground elevation

Fig. 5. (a) First- and (b) last-return, lidar image of a deciduous-coniferous wooded area.


and most of the returns are still vegetation points. In areas with low penetration

rates, filtering vegetation points proved to be a difficult task.

The step-by-step approach used to construct the terrain model from the raw lidar

data points, using only the last return elevation values, is shown in Fig. 6. The first

step of our algorithm for constructing the terrain elevation model overlays a grid

with a cell size of 5 m (Fig. 7) over the laser points and identifies the minimum laser

point elevation in each cell. The terrain slopes are gentle and a smaller grid cell size is

not justified, while a larger size would not adequately characterize the micro-relief.

Up to this point, the raw laser heights, without interpolation, are used. By

interpolating, some information in the original laser points is lost, thus it is

recommended to use original laser point values for as long as possible in the

processing phase (Axelsson, 1999). Some of the large hardwood crowns, like the one

depicted in the rectangle outlined in Fig. 5(a) and (b), cover an area larger than one 5

m grid cell, thus, the minimum elevation laser hit in such situations would not

correspond to a ground hit. Fig. 8 shows the result of the second step of the

algorithm. The image in Fig. 8 was interpolated using linear kriging from the lidar

points selected at the first step. The high laser points hitting vegetation above the

ground, though the lowest points in some grid cells, are clearly pictured in Fig. 8 as

small tops, with light colored pixels. Also evident in Fig. 8, the darker ‘sinks’

correspond most probably to true ground hits. The third step of the algorithm

identifies the laser points (corresponding to the dark pixels in Fig. 8) by running a

local minimum filter with a window size of 3�/3 pixels (i.e., 1.5 m) through the

interpolated lidar grid. The final DEM (Fig. 9) is interpolated using linear kriging

from the irregularly dispersed points identified in step 3. The average point distance

for the presumed ground points left in step 2 is 9.8 m. The grid cell size for the

interpolated DEM is 0.5 m.

The linear kriging technique was chosen for interpolating from dispersed lidar

points to a regular grid. Two other techniques were tried for the final DEM:

distance-weighting and triangulation with linear interpolation. The inverse distance

or distance-weighting gridding method is a weighted average interpolator. The

weight given to a particular data point when calculating a grid node is proportional

to the inverse of the distance of the observation from the grid node. Kriging is a

geostatistical gridding method that uses a variogram to analyze the spatial variation

Fig. 6. Flow chart of terrain finding algorithm.


present within an area. Triangulation with linear interpolation is an exact

interpolator that works by creating triangles by drawing lines between data points.

Residuals were calculated as the difference between original laser heights for the first

lidar return and interpolated elevation values at the same points in the gridded

Fig. 7. Grid overlay on the laser points.

Fig. 8. Interpolated image from the lowest lidar elevations in 5 m grid cells.


surface, for each of the interpolation methods. Residuals were analyzed and theirdistribution represented graphically using box-and-whiskers plots.

The derivation of the DEM was only an intermediate step towards estimating the

tree heights. No ground truth data with points of known elevation were collected to

estimate the accuracy of the DEM itself. The accuracy of the DEM is reflected

indirectly in the accuracy of estimating tree heights. The laser penetration rate was

estimated by analyzing the residuals of the original last return laser points and the

interpolated DEM. The penetration rate was considered the percent of original laser

points that have residuals less than 15 cm (9/15 cm being the reported lidar verticalaccuracy for the AeroScan system, EarthData, Inc.).

2.5. Tree heights

As mentioned before, the frequency of ground returns can be low and the

characterization of terrain elevation might degrade the accuracy of the derived

canopy heights. The tree canopy height model (CHM) was computed as the

difference between tree canopy hits and the corresponding DEM values. The same

method was also used by Næsset (1997a), though details on the algorithm used to

compute the DEM are not provided. The tree canopy surface is the DSM obtained

by interpolating the first lidar returns to a regular grid. A portion of the CHMcovering 36.5 ha is presented in Fig. 10, along with the ortho-image of the entire area

covered by lidar data. The ortho-image is derived from 1:13 000 color-infrared

photography acquired by NASA in the fall of 1999. Fig. 11 shows a vertical profile

through the CHM and a ground photo taken from the same location as the profile.

The ground photo was taken in the leaf-off season, but a hardwood stand is visible

Fig. 9. 3-D view of the terrain DEM (vertical exaggeration of 3).


Fig. 10. (a) Ortho-image and (b) CHM.


to the left of a fire line and a pine plantation to the right. The fire line is also clearly

visible as a linear feature oriented west-east on the ortho- and CHM-images in Fig.

10(a) and (b).

Two approaches were used to estimate the tree height on the same circular areas

covered by the field FIA subplots. The first approach is based on the height of all

laser pulses within the area covered by a subplot. The FIA subplot circumferences

were used to extract all pixel values from the CHM. Pixel values represent

Fig. 11. Ground photo showing the location of the vertical profile through the CHM. The arrow to the

left of the CHM image indicates the direction of sight for the photo. The vertical profile corresponds to a

portion of the left edge of the CHM image. The vertical bar on the profile corresponds to the location of

the arrow. (Illustrations in colour online in Science Direct).


interpolated laser heights for the canopy surface. A priori information from the field

data collection regarding the minimum tree height was used to threshold the laser

height values in order to eliminate the effect of shrubs and understory vegetation.

The minimum tree height measured on the ground in the 24 subplots, including the

microplots measurements, was 2.44 m, thus all observations with height values less

than that were excluded from computations. In an operational setting, a quick

ground inspection and possibly a reduced forest inventory could give indications onforest condition for use in lidar processing.

Statistics were extracted for each subplot, and they include mean height of all

height values within the circular plot, standard deviation, and percentiles of the

heights distribution for 1, 5, 10, 25 (first quartile), 50 (median), 75 (third quartile),

90, 99%, maximum and mode. The standard deviation of laser heights within a

subplot was computed, since it is an additional characteristic of the vertical stand

structure. Three sets of statistics were extracted from both the field data and lidar

data and used with linear regression (Table 1). The first threshold, 2.44 m, was usedto eliminate the effect of bushes, stumps, and low-lying vegetation. Næsset (1997b)

used a threshold of 2 m to eliminate the effect of stones, shrubs, etc. Similarly, trees

with a dbh larger than 6.35 cm were higher than 3.96 m on the ground. The rationale

behind using this threshold is that in operational use, a forest inventory with a

reduced sample size could provide information regarding the minimum height of

trees in this category. It is very improbable that the lidar processing would be done

without a preliminary investigation of the ground and vegetation condition. Except

for the microplots, the FIA field measurements include only trees with a dbh largerthan 12.7 cm. As such, lidar height values below a certain threshold, in this case 7.62

m, should be ignored, since they are probably returns from smaller trees. Linear

regression with stepwise selection was used to investigate the estimation of tree

heights. The dependent variables were the mean height values for all the trees in each

subplot, all trees with dbh larger than 6.35 cm, all trees with dbh larger than 12.7 cm,

and the maximum tree height for each subplot.

The second method to estimate tree heights is based on single tree identification. A

common technique used to identify tree locations on high�/resolution optical imagesuses a local maximum (LM) filter with a static-sized, user specified, moving window,

commonly 3�/3, 5�/5, and 7�/7 pixels, depending also on the pixel size (Niemann

et al., 1999; Pinz, 1999). The LM technique used with optical images is based on the

fact that the reflectance of a tree crown is typically greatest at its apex. The LM

technique used with lidar data operates on the assumption that the highest laser

elevation value among laser hits of the same tree crown is the apex. Successful

identification of the tree location using the LM technique depends on the careful

selection of the filter window size. If the filter size is too small or too large, errors ofcommission or, respectively, omission occur. The static nature of this technique is

inconsistent with the complex canopy structure of hardwood and mixed pine-

hardwood stands. Thus, the second method for estimating tree height uses a variable

window size LM technique that operates under the assumption that there are

multiple tree crown shapes and sizes and that the moving LM filter should be

adjusted to an appropriate size that corresponds to the spatial structure found on the


Table 1

Variables used in linear regression

Set of vari-

ables

Dependent variables (measured

on the ground)

Independent variables

Method based on all laser heights/

subplot: percentiles, maximum, and

mode for

Variable window size method: mean height, minimum and maximum

height, standard deviation of height, median, 1st and 3rd quartiles,

and number of trees for

1 Mean height of all trees and

maximum height

Heights distribution of pixel values

higher than 2.44 m

Lidar identified trees higher than 2.44 m

2 Mean height of all trees with a

dbhE/6.35 cm and maximum

height


higher than 3.96 m


3 Mean height of all trees with a

dbhE/12.7 cm and maximum

height


higher than 7.62 m


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lidar image and on the ground. Daley et al. (1998) used texture analysis of high�/

resolution optical images (MEIS-II) with a variable window size to estimate crown

position in stands of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco). The LM

filter works best for trees with a single, well defined, apex, such as the conifer species.

The derivation of the appropriate window size to search for tree tops is based on a

relationship between the height of the trees and their crown size. Basically, the higher

the trees, the larger the crown size. Thus, tree height and crown size data from the

field inventory, a total of 189 trees, were used to derive a relationship between tree

height and crown size. Crown size was considered the dependent variable and linear

and nonlinear regression models were tested. The best prediction for crown size

based on tree height, with an R -square value of 0.51, was obtained when using linear

regression with a quadratic model as shown below in Eq. (1):

Crown width (m)�2:21�0:01022H2 (1)

where H is the tree height (m ).

For loblolly pine plantations in the same area, with ages from 1 to 10 years,

Sharma (Mahadev Sharma, 2001, unpublished data) obtained higher R -square

values for predicting crown width from height (0.7 with height alone and 0.76

using height and height-squared, with both variables significant). However, at early

ages in plantations, when tree competition is not very strong, it is expected to find a

better correlation between crown width and height. In our study, using only

height as the predictor variable, the relationship is not as strong as between dbh and

height, but it offers a base to continuously vary the LM filter size when moved across

the grid of laser height values. By using the equation above, the window size varied

between 3�/3 and 25�/25 pixels, which would correspond to crown widths between

1.5 and 12.5 m. The algorithm reads the height value at each pixel and calculates the

window size to search for the LM. If the current pixel corresponds to the LM, it is

flagged as

a tree top (Fig. 12). Each pixel has a window size associated with it, but Fig. 13

shows only the windows that identified tree tops. Once the location of each

identified tree crown has been established, the canopy 3-D surface of laser heights

(CHM) is sampled only at the positions of the tree apex to find out the height of

each tree. The total number of local maxima within one plot is an indicator of

the number of stems. Three sets of height estimates were extracted from the CHM

for each subplot, with the same thresholds used for the first method of estimating

heights*/2.44, 3.96, and 7.62 m (Table 1). Each set of lidar estimates included

mean height, minimum and maximum heights, standard deviation of tree heights,

median, first and third quartiles, and number of trees. Each set of height

estimates was compared to the corresponding set of field measurements using linear

regression with stepwise selection (0.15 significance level). Height estimates from

both the first and the second methods were compared to the same field data

values.


3. Results

Residuals from the three interpolation techniques, inverse distance, kriging, and

triangulation, are represented graphically using box-and-whiskers plots in Fig. 14.

The kriging method shows a smaller range, interquartile range, and standard error of

the mean and was chosen for interpolation.

Fig. 15 shows the frequency of residuals for the first and last returns from the

calculated DEM. These residuals are basically canopy heights for the first and last

Fig. 12. Ortho-image (a) and tree tops identified in the pine-hardwood mixed stand (b) and the pine

plantation next to it (c). Rectangle on the ortho-image shows approximate location of zoom window (b).

Window (c) is located to the right of (b). Plantation row pattern oriented SW-NE is visible in (a) and (c).

(Illustrations in colour online in Science Direct).


returns. They give an indication of the vertical distribution of canopy heights for the

entire area. The penetration rate for the last return laser hits, when consideringresiduals less than 15 cm, was estimated to be 3.9%.

Linear regression was used to develop equations relating lidar-estimated

parameters with field inventories for each of the FIA subplots. The results for

both methods are shown in Table 2. The presence of multicollinearity effects was

investigated using eigenvalues and eigenvectors of the correlation matrix. The

condition number of the correlation matrix (Myers, 1990, p. 369�/370), that is, the

ratio of the largest to the smallest eigenvalue, and ratios of eigenvalues were implied

for diagnosing the impact of a dependency. No multicollinearity effects were found.

4. Discussion and conclusions

The results of the current study show that the technique of estimating mean tree

height by identifying the location of individual trees performed better than the first

Fig. 13. A portion of the lidar derived CHM and the variable windows that identified tree tops. The dark

portions of the CHM corresponds to pine plantations, with smaller and denser trees, while the lighter area

covers hardwoods crowns, with larger windows.


technique that makes use of all laser height values within the subplots. However,

only a small percent of the variation in mean tree height was explained by lidar

variables (35% for the variable window size method and only 21% for the all laser

heights method). These results could be attributed to the influence of intermediate

and overtopped trees measured on the ground to the calculation of mean height.

Such trees have crowns partially or entirely below the general level of the canopy and

intercept very few of the laser hits and have very little influence on the lidar variables.

The results show a rather intuitive behavior by obtaining better R2 values (all above

80%) for estimating the height of dominant trees, in this case of trees with a dbh

larger than 12.7 cm. The upper layer of dominant trees intercept most of the laser

shots, and thus, estimates better correlate with their mean height. Dominant and co-

dominant trees, with large dbh and tall height, account for a major portion of the

timber volume and above-ground biomass.One crucial aspect that could strongly affect the results is the accurate co-location

of lidar data and field subplots. Also, the top of the trees could be horizontally

displaced from the base of the stem due to leaning caused by competition and/or

defective stem structure. Assuming an accurate location of the subplot center on the

lidar image, outwards-leaning marginal trees would be tallied in the field but their

top would not be included in the subplot area on the lidar image. Part of the

unexplained variance could also be attributed to the terrain DEM. As expected, the

Fig. 14. Boxplots of residuals (m) for three interpolation techniques.


best prediction was obtained for the maximum height. The variable window size

method gave consistent results for all situations (R2 of 85%). Maximum height was

best predicted with the second method, by taking into account all laser height values

per plot. When using the height threshold of 3.96 m, the maximum height was

predicted with an R2 value of 90%. For the first method of estimating tree height, the

variables that appeared significant in most of the regression models were mean

height and maximum height estimated from the lidar data. For the method that

considered all laser heights per plot, upper quartile values of the tree heights

distribution proved to be significant. The 90th percentile was most significant for

estimating mean height for all trees and for trees with a dbh larger than 6.35 cm.

Similarly, for trees with a dbh larger than 12.7 m, the most significant for estimating

mean height was the 95th percentile. Predictably, when estimating maximum height,

the uppermost 99th percentile was among the significant variables in the regression

models.

With the exception of estimating maximum height for trees higher than 3.96 m (R2

of 90% when using the method of all laser heights per plot), processing lidar data

Fig. 15. Residuals of first return (a) and last return (b) laser points from the calculated DEM.


Table 2

Regression results

Method Predicted variable Regression model with significant var-

iablesa (P B/0.05)

R2

(%)

(a) Independent variable*/estimates for all

laser heights in each subplot

1 (all laser heights) Mean height 7.13�/0.26 Q90 20

Maximum height 0.77�/1.00 Q75�/1.82 Q99 79

Mean height for

dbh�/6.35 cm

6.48�/0.33 Q90 35

Mean height for

dbh�/12.7 cm

2.93�/4.37 STDEV�/1.13 Q5�/1.84 Q99 73

2 (individual trees) Mean height 5.45�/0.32 LMAX 35

Maximum height �/0.13�/0.25 LMEAN�/1.21 LMAX 85

Mean height for

dbh�/6.35 cm

4.67�/0.40 LMAX 55

Mean height for

dbh�/12.7 cm

2.86�/0.57 LMEAN�/0.22 LMIN�/�/

0.31 LMAX

85

(b) Independent variable*/estimates for laser

heights�/3.96 m in each subplot


Maximum height 1.63�/2.35 LMEAN�/1.49 Q25�/1.37

Q75�/1.14 Q90�/1.81 Q99

90

Mean height for

dbh�/6.35 cm

6.43�/0.34 Q90 36

Mean height for

dbh�/12.7 cm

4.78�/2.17 LMEAN �/1.12 Q25 �/1.27

Q99

73


Maximum height �/0.13�/0.25 LMEAN�/1.21 LMAX 85

Mean height for

dbh�/6.35 cm

4.67�/0.40 LMAX 55

Mean height for

dbh�/12.7 cm

2.86�/0.57 LMEAN�/0.22 LMIN�/

0.31 LMAX

85

(c) Independent variable*/estimates for laser

heights�/7.62 m in each subplot


Maximum height 4.77�/0.40 Q25�/1.1 Q99 55

Mean height for

dbh�/6.35 cm

7.11�/0.30 Q95 33

Mean height for

dbh�/12.7 cm

6.08�/4.78 Q50�/0.91 Q99 57


Maximum height 0.06�/0.28 LMEAN�/1.22 LMAX 85

Mean height for

dbh�/6.35 cm

4.67�/0.40 LMAX 55

Mean height for

dbh�/12.7 cm

1.65�/0.45 LMEAN�/0.35 LMAX 84

a Variables notation is as follows: LMAX, lidar estimated maximum height/subplot; LNR, lidar

estimated number of trees/subplot; LMIN, lidar estimated minimum height/subplot; LMEAN, lidar

estimated mean subplot height; Q5�/Q99, quartiles of heights distribution.


with a priori field information did not prove to be useful. The gain in explaining the

total variation of maximum tree height was 11% in that case. Low R2 values (below

57%) were obtained for all predicted variables with the method of all laser height

values per plot, when using laser heights above 7.62 m. Thus, we conclude that the

use of height thresholds when processing lidar data was not particularly useful for

this study.

The LM technique with a variable window size considers fundamental forestbiometrics relationships. It seems more appropriate than the static LM filter or the

grid approach that arbitrarily selects only the highest values in a grid with a user

defined size (e.g. Næsset, 1997a). The terrain DEM lacks a field based estimation of

its accuracy, but judging by the results obtained for tree heights, it is assumed to

model the terrain topography fairly accurately. However, the study was based on a

rather limited sample of FIA subplots, with no stratification based on tree species or

age, and the lidar data were not fully exploited by neglecting secondary returns from

within the tree canopy. Thus, the analysis, though very encouraging, indicates apotential for improvements in stand height determination by using scanning laser

data. Further research on extracting other parameters, such as crown width, or

canopy closure, could help in improving estimates of volume and biomass.

Acknowledgements

We gratefully acknowledge the help provided with the field data collection by Dr

John Scrivani at the Virginia Department of Forestry, by Jan van Aardt, and

Rebecca Musy at Virginia Tech, Neil Clark at the USDA Forest Service, JaredWayman at Questerra, Inc., Karsten Nitsch at the University of Berlin, FIA crew

members at the Virginia Department of Forestry and Wayne Bowman, David

Houttekier, Donald Jamerson, and Ralph Totty at the Appomattox-Buckingham

Forest Office. This research has been supported by NASA Earth System Science

Fellowship Program (NGT5-30198), NASA Laboratory for Terrestrial Physics,

NCASI, McIntire-Stennis research program (VA-136589), Virginia Tech Depart-

ment of Forestry, and USDA Fund for a Rural America (97-36200-5231).

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