estimating tree heights and number of stems in young forest stands using airborne laser scanner data

Estimating tree heights and number of stems in young forest stands

using airborne laser scanner data

Erik Næsseta,*, Kjell-Olav Bjerknesb

aAgricultural University of Norway, Department of Forest Sciences, P.O. Box 5044, N-1432 As, NorwaybCity Council Administration of Enebakk, Norway

Received 20 November 2000; accepted 8 April 2001

Abstract

The mean heights of dominant trees and the stem numbers of 39 plots of 200 m2 each were derived from various canopy height metrics

and canopy density measured by means of a small-footprint airborne laser scanner over young forest stands with tree heights < 6 m. On the

average, the laser transmitted 12,019 pulses ha � 1. Ground-truth values were regressed against laser-derived canopy height metrics and

density. The regressions explained 83% and 42% of the variability in ground-truth mean height and stem number, respectively. Cross-

validation of the regressions revealed standard deviations of the differences between predicted and ground-truth values of mean height and

stem number of 0.57 m (15%) and 1209 ha� 1 (28.8%), respectively. A proposed practical two-stage procedure for prediction of mean height

of dominant trees in forest stands was tested. One hundred and seventy-four sample plots were distributed systematically throughout a 1000-

ha forest area. Twenty-nine of the plots were sited in young stands with tree heights < 11.5 m. In the first stage, mean height of dominant

trees of the 29 plots were regressed against laser-derived canopy height metrics and density. In the second stage, the selected regression was

used to predict mean height of 12 selected test stands. The prediction revealed a bias of 0.23 m (3.5%) (P > .05) and a standard deviation of

the differences between predicted and ground-truth mean height of 0.56 m (8.4%). D 2001 Elsevier Science Inc. All rights reserved.

1. Introduction

In order to reduce the expenses of forest management

planning in Norway, remote sensing techniques have

become an integral part of the forest inventories. For more

than about 50% of the area inventoried annually, the forest

and tree characteristics required in the planning process are

derived by aerial photo interpretation (Næsset, Skramo, &

Tomter, 1992). In Norway, forest management planning of

individual forest holdings is usually carried out according to

an area-based approach (Anon., 1995), which implies that

the individual forest stands are the basic units of the

inventories and the plans.

However, in young stands with tree heights less than, say,

8–10 m, practical experiences have shown that determina-

tion of important stand characteristics by photo interpreta-

tion and photogrammetric methods is difficult and often

inaccurate (Næsset, 2001b). Such characteristics have there-

fore either been recorded by expensive field inventories or

omitted from the surveys. Two of the most important

characteristics for forest management planning in young

stands are the mean height of the dominant trees and number

of stems per hectare. They are both key inventory attributes

in growth projections, whereas the number of stems also

indicates the need for active treatments in the near future,

such as reduction of stem number by tending if the density

is too high or additional planting if the number of trees is

too small.

During the last 10–15 years, several experiments have

been carried out in order to determine various tree height

metrics and stem number by different airborne laser

profiling and scanning systems (e.g., Lefsky, Cohen,

et al., 1999; Magnussen & Boudewyn, 1998; Means

et al., 1999, 2000; Næsset, 1997a; Nelson, Krabill, &

Tonelli, 1988). So far, estimation of forest stand character-

istics from airborne laser scanner data has focused mostly

on old forest stands or forests where the mean tree height

exceeds about 15 m. At least in such forests, small-scale

trials have revealed that both small-footprint (Magnussen

& Boudewyn, 1998; Magnussen, Eggermont, & LaRiccia,

1999; Means et al., 2000; Næsset, 1997a) and large-foot-

print lasers (Lefsky, Cohen, et al., 1999; Means et al.,

0034-4257/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved.

PII: S0034 -4257 (01 )00228 -0

* Corresponding author. Tel.: +47-64948906; fax: +47-64948890.

E-mail address: [email protected] (E. Næsset).

www.elsevier.com/locate/rse

Remote Sensing of Environment 78 (2001) 328–340

1999) may produce quite accurate estimates of tree or

canopy height and stem number.

In forest management planning in Norway, the typical

size of a stand is 1.5 ha. For such small units, it is important

that the stand boundaries are accurately located to avoid

serious errors in stand attributes that are estimated on a per-

unit area basis, such as timber volume and stem number

(Næsset, 1999b). Large-footprint laser scanners with foot-

print diameters of 10–25 m may therefore be inappropriate

for detailed area-based forest inventories. Large-footprint

systems are at present not available commercially (Means

et al., 1999), whereas small-footprint systems with footprint

diameters of, say, 10–30 cm are becoming widely available

and operated by a large number of firms (Baltsavias, 1999).

The typical horizontal accuracy on the ground of each laser

pulse of 20–30 cm for small-footprint systems (Baltsavias,

1999) seems to meet the accuracy requirements of detailed

stand inventories.

The lasers are pulsed systems that transmit a laser

pulse and determine the distance to the surface (the tree

canopy or the ground) according to the time taken for the

pulse to travel back to the sensor. A pulse may pass

vertically through a forest canopy, and there may be

several secondary returns as the light from a single pulse

is reflected from within canopy layers of vegetation.

Small-footprint systems usually record either the first or

the last return, or both the first and last returns. The

scanning device provides a large distribution of samples

from across the flight line and would thus be appropriate

for large-scale inventories. Commercial systems currently

available may also produce quite dense samples of meas-

urements with an average spacing on the ground of, for

example, 1.5 m. In this study, we used a small-footprint

scanning laser with the ability to record both the first and

last returns.

In dense forests, only a small portion of the pulses will

penetrate the foliage and hit the ground. The average height

derived from the laser pulses will therefore be larger in

dense stands than in stands with more scattered trees. Thus,

at least in forest stands with trees of a certain height, the

density will affect the relationship between the heights

derived from the laser data and the true tree heights (e.g.,

Næsset, 1997a). Furthermore, the crown shape affects laser

measurements of height (Nelson, 1997). Since different tree

species often develop different crown shapes, it is likely that

the relationship between the heights derived from the laser

data and the true tree heights will differ between species as

well. Finally, height metrics derived from laser data have

been shown to be correlated with stem number (Lefsky,

Cohen, et al., 1999). The objective of the current study was

to assess the accuracy of (1) mean height of the dominant

trees and (2) number of stems per hectare derived from

airborne laser scanner data of a commercially operated

small-footprint system in young forest stands. The effects

on the accuracy of different tree species and densities were

also assessed.

Recently, various sampling procedures in which stands

of an entire forest could be mapped from laser data using

small field samples have been proposed (Means et al.,

2000; Næsset, 1997b), and it is advocated that there is a

large potential for savings as compared to conventional

methods (Means et al., 2000). In practical forest manage-

ment inventories in Norway, all stands of most forest

properties in a municipality are surveyed, and a sample

plot inventory that covers the entire municipality is often

carried out. Such plot inventories typically comprise an

area of 50–500 km2 and often consist of more than 1000

sample plots. In practical applications of laser scanner data,

small georeferenced sample plots could be used to build

empirical relationships between various metrics derived

from the laser data and tree heights measured in field.

These relationships could finally be used to provide corre-

sponding estimates of tree height from the laser data for

every stand in the forest area in question. In the current

study, the performance of such a two-stage application in

young stands was evaluated.

2. Materials and methods

2.1. Study area and stand delineation

A forest area in the municipality of Valer (59�300N10�550E, 70–120 m a.s.l.), southeast Norway, of about

1000 ha was selected for the trial. The main tree species

in the area were Norway spruce (Picea abies (L.) Karst.) and

Scots pine (Pinus sylvestris L.).

As part of a large-scale practical forest inventory going

on in the district, aerial photographs were acquired on the

13th of May 1996. The stand boundaries of all forest stands

in the study area were delineated by means of stereoscopic

photo interpretation and the boundary coordinates were

stored in digital format. The stands were classified accord-

ing to criteria such as age class, site quality, and tree species.

The photo interpretation was accomplished using a Wild B8

stereoplotter equipped with linear encoders. The stereo

models were referenced to the terrain by means of elevation

points and terrain details of the analog official Economic

Map Series. The root mean square error (RMSE) of the

planimetric coordinates (x and y) of the Economic Map

Series is 2 m. The RMSE of the planimetric coordinates

after absolute orientation was expected to be 1.5–2.0 m.

Thus, the total planimetric RMSE of the coordinates was

approximately 2.5–3.0 m.

2.2. Field data collection

Three different ground-truth datasets were acquired in

this study. The first one consisted of selected plots used to

study the accuracy of dominant tree height and number of

stems of small plots derived from airborne laser scanner

data. These plots were denoted as ‘‘experimental plots.’’

E. Næsset, K.-O. Bjerknes / Remote Sensing of Environment 78 (2001) 328–340 329

The last two datasets were used to test the performance of

the practical two-stage procedure in which dominant tree

heights of entire stands were estimated by means of relation-

ships between laser data and field data derived from a

sample of field plots. The first of these datasets comprised

sample plots distributed systematically throughout the entire

1000-ha study area used to build the relationships. These

plots were denoted as ‘‘sample plots.’’ The last dataset

consisted of selected stands of young forest employed to

test the performance of the proposed procedure. These

stands were denoted as ‘‘test stands.’’

2.2.1. Experimental plots

A total of 39 circular plots with an area of 200 m2 each

were selected subjectively in young forest to represent

different combinations of tree heights, densities, and tree

species mixtures. They were inventoried during June and

July 1999. Each plot was divided into four quadrants of

50 m2 each according to the four cardinal directions in order

to ensure equal representation of all parts of the plot. The

number of stems with height taller than 1.5 m was counted

for each quadrant and tree species, i.e., Norway spruce,

Scots pine, and broad-leaved species. Trees with height

smaller than 1.5 m were excluded from the trial. The

number of stems per plot was calculated as the sum of the

individual tree species and quadrant counts, and it ranged

from 1650 to 7100 ha� 1 (Table 1).

The heights of approximately five trees were measured in

each quadrant. Height poles were used for most of the trees,

but trees that exceeded a height of about 4 m were measured

with a Vertex hypsometer. The trees were selected with

equal probability, and they were sampled as every n-th tree

according to the number of stems per quadrant (N), where

n =N/5, i.e., tree number 1, 1 + n, 1 + 2n, 1 + 3n, 1 + 4n. In

forest management planning in Norway, the mean height of

the 2000 tallest trees per hectare is often used as a measure

of dominant tree height in young stands (Eid, 1993). Based

on the measured tree heights and the counted number of

stems in each quadrant, the dominant height of each plot

was computed to conform to this definition. A total of 841

tree heights were measured on the 39 plots. The mean

dominant height of the 39 plots ranged from 1.76 to

6.01 m with an average of 3.80 m (Table 1).

Differential GPS was used to determine the position of

the centre of each experimental plot. Two different receivers

were used in the forest during the field work, i.e., a

Magellan ProMark X-CM 10-channel receiver and a Javad

Legacy 20-channel receiver. The first is a single-frequency

receiver observing C/A code and L1 carrier phase of GPS.

The latter is a dual-frequency receiver observing dual-

frequency pseudorange and carrier phase of both GPS and

GLONASS. Three different receivers were used as base

station for differential correction, i.e., a Magellan ProMark

X-CM receiver, a Javad Legacy receiver, and an Ashtech

Super C/A 12-channel single-frequency receiver. The dis-

tance between the plots and the base stations ranged from

2.8 to 18.7 km. The observation period at each plot was at

least 15 min and a 2-s logging rate was used. The antenna

height was approximately 4 m, which implies that the

antenna was placed above the tree canopy for most of the

plots. Coordinates were computed by postprocessing in an

adjustment with coordinates and carrier phase ambiguities

as unknown parameters using both pseudorange and carrier

phase observations (float solution). The MSTAR (Anon.,

1997) and Pinnacle version 1.00 (Anon., 1999) postprocess-

ing software packages were used. Even for the plots with the

highest trees, it is likely that the accuracy of the planimetric

coordinates (x and y) was better than 0.2–0.3 m (Jonsson,

1999; Næsset, 2001a).

2.2.2. Sample plots

A total of 174 sample plots were distributed systemati-

cally throughout the entire 1000-ha study area according to

a regular grid. Twenty-nine of these plots were classified as

young forest according to the preliminary photo interpreta-

tion, and they were used in this study.

Ground-truth data of the 29 sample plots were collected

during summer and autumn 1998. Each of the 29 plots

consisted of a cluster of four subplots to ensure equal

representation of all parts of the plot. A square with size

7.21� 7.21 m was defined with the centre of the square

being the major plot centre. The corners of the square were

used as centres of four circular subplots of 40 m2 each. Each

subplot was divided into four quadrants of 10 m2 each, and

the two tallest trees in the first quadrant of each subplot

Table 1

Summary of experimental plot reference data, sample plot reference data,

and test stand reference data

Characteristic Range Mean

Experimental plots (n = 39)

Mean dominant height (m) 1.76–6.01 3.80

Number of stems (ha� 1) 1650–7100 4197

Tree species distribution

Spruce (%) 0–89 26

Pine (%) 0–97 57

Broad-leaved species (%) 1–48 17

Sample plots (n = 29)


Age (year) 8–30 16


Spruce (%) 0–100 50

Pine (%) 0–100 41


Test stands (n = 12)

Area (ha) 0.7–5.0 1.7


Age (year) 11–22 15


Spruce (%) 7–97 54

Pine (%) 3–90 42


E. Næsset, K.-O. Bjerknes / Remote Sensing of Environment 78 (2001) 328–340330

were identified. The height of the first of these trees selected

clockwise in each subplot was measured. If the first quad-

rant did not contain any trees, the second quadrant was

sampled. Height poles and a Vertex hypsometer were used

for the height measurements. The arithmetic mean of the

measured heights of the four subplots was computed, which

is in accordance with the definition of dominant height, i.e.,

the mean height of the 2000 tallest trees per hectare. To

synchronize these mean dominant height values to the date,

the laser scanner data were acquired, the individual plot

heights were prorated by up to 1 year. The prorating was

done via age- and site quality-specific height growth rates

(Braastad, 1975, 1980). The prorated mean heights were

used as ground-truth. The mean dominant height ranged

from 2.57 to 11.45 m (Table 1).

The tree species of the two tallest trees in each quadrant

of the four subplots was recorded. The age of these trees

was assessed subjectively. The mean age of the 29 plots was

16 years (Table 1), and more than 90% of the trees were

spruce and pine.

Differential GPS was used to determine the position of

the centre of each major plot. An Ashtech Super C/A 12-

channel single-frequency receiver observing C/A code and

L1 carrier phase was used. Observations were carried out for

about 15 min with a 2-s logging rate. Postprocessing using

another Ashtech Super C/A receiver as base station was

carried out with the PNAV program (Anon., 1994) of the

Prism Precise GPS Survey Software. Coordinates were

computed in an adjustment with coordinates and carrier

phase ambiguities as unknown parameters using both pseu-

dorange and carrier phase observations. The height of the

antenna used for the rover receiver was approximately 4 m.

Considering the small tree heights and the small amount of

stem volume in young stands, it is likely that the average

accuracy of the computed planimetric coordinates (x and y)

was better than 0.5 m (Næsset, 1999c).

2.2.3. Test stands

The study comprised a total of 12 test stands. They were

selected subjectively among the stands delineated by photo

interpretation to represent different tree heights in young

stands. The stands were selected independently of the 29

sample plots.

The ground-truth data of the 12 test stands were col-

lected during summer and autumn 1998. Circular sample

plots with an area of 40 m2 each were distributed system-

atically within each stand according to a regular grid with a

spacing of 20–45 m depending on the stand area. The total

number of plots per stand ranged from 16 to 26 with an

average of 20. The sample plots were divided into four

quadrants of 10 m2 each. The two tallest trees in the first

quadrant were identified, and the height of the first of these

trees selected clockwise was measured. If the first quadrant

did not contain any trees, the second quadrant was

sampled. Height poles were used for most of the trees,

but trees that exceeded a height of about 4 m were

measured with a Vertex hypsometer. The mean dominant

height of each stand was calculated as the arithmetic mean

of the individual plot heights, which is in accordance with

the definition of dominant height, i.e., the mean height of

the 2000 tallest trees per hectare. To synchronize these

mean dominant height values to the date, the laser scanner

data were acquired, the individual stand heights were

prorated by up to 1 year. The prorating procedure described

above was used. The prorated mean heights were used as

ground-truth. The mean dominant height ranged from 4.36

to 9.05 m (Table 1). The standard error of the mean height

ranged from 0.27 to 0.74 m with an average for all stands

of 0.46 m.

The tree species of the two tallest trees in each quadrant

of the plots was recorded. The age of these trees was

assessed subjectively, and the mean stand age was calcu-

lated. The mean age of the 12 test stands was 15 years

(Table 1), and more than 90% of the trees were spruce

and pine.

2.3. Laser scanner data

A Piper PA31-310 aircraft carried the ALTM 1210 laser

scanning system produced by Optech, Canada. The laser

transmits at 1064 nm (near-infrared). The major components

of the ALTM 1210 are the infrared laser, the scanner

transmitting the laser pulse and receiving the first and last

echoes of each pulse, the time interval meter measuring the

elapsed time between transmittance and receipt, the global

positioning system airborne and ground receivers, and the

inertial reference system reporting the aircraft’s roll, pitch,

and heading.

The laser scanner data were acquired on the 8th and 9th

of June 1999. The plane was flown approximately 690 m

above the ground (Table 2) at an average speed of 71 m/s. A

total of 43 flight lines were flown in a cross pattern. First, 19

parallel flight lines with approximately 50% overlap

between adjacent flight lines were flown in one direction.

Finally, 24 parallel flight lines were flown perpendicular to

the first 19 flight lines. Thus, every location in the study

area was covered by laser measurements from four stripes.

The pulse repetition frequency was 10 kHz and the scan

frequency was 21 Hz. Maximum scan angle (off nadir) was

17�, which according to the flying height corresponded to anaverage swath width of about 420 m. However, pulses

transmitted at scan angles that exceeded 14� were excludedfrom the final dataset. The beam divergence of 0.30 mrad

produced a roughly circular spot size on the ground (‘‘foot-

print’’) with a diameter of about 21 cm. The average

distance between footprints on the sample plots and in the

test stands was approximately 0.9 m. First and last returns

were recorded.

After postprocessing, it was found that a few long last

return ranges that exceeded the distance to the ground by up

to 50 m were present in the data. According to the manu-

facturer, these erroneous ranges were caused by a faulty last


return sensor. A second flight was therefore carried out on

the 6th of June 2000 to collect last return data only. Flying

height corresponded to that of the first flight, but 14 parallel

flight lines were flown in only one direction.

A complete postprocessing of the first and last pulse

data was undertaken by the operating firm, Fotonor, Nor-

way, by means of the proprietary postprocessing software

supported by Optech. All ranges measured by the laser at

an off nadir angle, i.e., distances to the ground as well as

to the tree canopy, were automatically converted to

vertical distances.

The ranging device was calibrated by Optech. The

operating firm always calibrates the system after installa-

tion in the aircraft. In addition, 30 circular plots were

located on plane road segments distributed throughout the

study area. Their positions were determined by differential

GPS +GLONASS based on accurate dual-frequency carrier

phase observations. Based on this calibration, the com-

puted ranges of the first pulse data acquired in 1999 and

the last pulse data collected in 2000 were reduced by 0.13

and 0.11 m, respectively.

The last return data collected in 2000 were used to model

the ground surface. In forest areas, a large portion of the last

returns of the laser pulses usually represent hits above the

ground, such as tree canopy and bushes. The last return data

were therefore filtered during postprocessing by the operat-

ing firm. In the filtering local maxima assumed to represent

vegetation hits were discarded. A triangulated irregular

network (TIN) was generated from the planimetric coordi-

nates (x and y) and corresponding height values of the

individual terrain ground points retained in the last pulse

dataset. This TIN model of the ground was denoted as the

‘‘digital terrain model’’ (DTM). The ellipsoidic height

accuracy of the DTM was expected to be around 25 cm,

at least in relatively plane parts of the area. Studies of terrain

surfaces in wooded areas based on more scattered laser

datasets than the current and similar filtering procedures

indicate an accuracy of 25–30 cm (Kraus & Pfeifer, 1998;

Opseth, 1996).

The first return data collected in 1999 were used to

derive tree canopy heights. All first return observations

(points) were spatially registered to the DTM according

to their coordinates. Terrain surface height values were

computed for each point by linear interpolation from the

DTM. The relative height of each point was computed as

the difference between the height of the first return and

the terrain surface height. In wooded areas, this relative

height can be considered as the canopy height. In open

areas and in gaps between the trees, this height will be

close to zero and thus represent ground hits. Small

height values may also indicate hits of stones, shrubs,

etc., or actually be ground hits that due to the inaccur-

acies of the DTM and the ellipsoidic first pulse heights

are computed as values greater than zero. According to

previous experiences (Kraus & Pfeifer, 1998; Opseth,

1996) and the manufacturer’s specifications (Baltsavias,

1999), an accuracy of 35–50 cm of the difference

between first pulse heights and DTM heights was

expected. Therefore, observations with a relative height

value < 0.5 m were excluded from the dataset. The

remaining first pulse observations were considered to

be canopy hits. Thus, two datasets were developed from

the laser scanner data: (1) geographically registered data

on canopy height and (2) geographically registered data

on all reflected pulses.

2.4. Georeferencing field and laser data

The laser datasets were spatially registered to the three

ground-truth datasets by means of a geographical informa-

tion system (GIS). The first ground-truth dataset, i.e., the 39

experimental plots were developed in GIS by means of

buffers created around each of the plot centres determined

by GPS. A radius of 7.98 m was used, which corresponded

to circular plots with size 200 m2.

The second ground-truth dataset, i.e., the 29 clustered

sample plots distributed systematically throughout the entire

study area, were constructed by means of buffers around

each major plot centre determined by GPS. A radius of

8.67 m was used, which produced circular plots with size

236 m2. The periphery of these circles were tangent to the

periphery of the four 40 m2 subplots located around each

major plot centre. The spatial position of the third ground-

truth dataset, i.e., the 12 inventoried test stands, were taken

directly from the coordinates derived by the stereoscopic

photo interpretation.

The numbers of transmitted pulses and canopy hits were

calculated for each observation of the three ground-truth

Table 2

Summary of laser scanner and flight data

Mean

flying

height

Mean

footprint

diameterNo. of transmitted pulsesa (ha� 1) No. of canopy hitsa (ha� 1)

Mean rate of

Dataset (m) (cm) Range Mean Range Mean penetrationa (%)

Experimental plots 690 21 10,000–15,856 12,019 1450–10,200 4844 60

Sample plots 689 21 7712–13,729 11,686 3093–12,924 8834 24

Test stands 693 21 11,234–12,274 11,868 6680–11,083 8787 26

a Refers to first pulse data.


datasets. The number of canopy hits varied significantly

between plots and between stands. The average number of

canopy hits ranged between 4844 and 8834 ha� 1 (Table 2).

The mean rate of penetration, i.e., the percentage of pulses

that hit ground, was 24–60%.

2.5. Estimating dominant height and stem number from

laser data

The experimental plots were used to assess the accuracy

of mean height of dominant trees and of number of stems

per hectare derived from the laser scanner data.

Næsset (1997a) found that the maximum height value

of laser canopy hits for a certain fixed area could be used

to estimate the mean tree height. Later, Magnussen and

Boudewyn (1998) advocated that, for a given crown

shape and a certain plot size, there exist a certain quantile

of the distribution of the canopy heights of a plot that

matches the tree height of interest, e.g., the mean height.

Since crown shape, tree species, and density that affect

the relationship between the distribution of canopy

heights and tree heights will tend to vary between differ-

ent plots, it is probably useful to model mean height of

dominant tree by means of several such quantiles. As a

matter of fact, other variables of the distribution of

canopy heights, such as the mean and median values,

standard deviation divided by the mean (coefficient of

variation), and various quantiles, have been found to be

correlated with mean tree height, dominant height, and

other biophysical properties by others (Lefsky, Harding,

Cohen, Parker, & Shugart, 1999; Magnussen et al., 1999;

Means et al., 1999, 2000; Næsset, 1997a; Nelson, 1997;

Nelson et al., 1988; Nelson, Oderwald, & Gregoire,

1997). Furthermore, since the tree density will affect the

relationship between heights derived from the laser data

and the true tree heights (e.g., Næsset, 1997a), variables

related to canopy density, such as the number of canopy

hits divided by the total number of transmitted pulses,

will be useful in modelling of dominant tree height from

laser scanner data.

Thus, multiple regression analysis was used to develop

models for mean height of dominant trees related to pre-

dictor variables derived from the laser data. Eight predictor

variables were tested: the quantiles corresponding to the: (1)

25, (2) 50 (median), (3) 75, and (4) 90 percentiles of the

height distribution of laser pulses classified as canopy hits,

(5) the maximum value, (6) the mean value, (7) the

coefficient of variation, and (8) the canopy density calcu-

lated as the number of canopy hits divided by the total

number of transmitted pulses.

In the multiple regression analysis, multiplicative models

were estimated as linear regressions in the logarithmic

variables because multiplicative models and/or logarithmic

transformations were found to be suitable for estimation of

mean height and timber volume, which is related to tree

density, by others (Means et al., 2000; Næsset, 1997b). The

multiplicative model was formulated as (Eq. (1)):

h ¼ b0hb125h

b250h

b375h

b490h

b5maxh

b6meanh

b7cvD

b81 ð1Þ

whereas the linear form used in the estimation was

lnh ¼ lnb0 þ b1lnh25 þ b2lnh50 þ b3lnh75 þ b4lnh90

þ b5lnhmax þ b6lnhmean þ b7lnhcv þ b8lnD1 ð2Þwhere h = ground-truth mean height of dominant trees (m);

h25, h50, h75, h90 = the quantiles corresponding to the 25, 50

(median), 75, and 90 percentiles of the laser canopy heights,

respectively (m); hmax =maximum laser canopy height (m);

hmean =mean of the laser canopy heights (m); hcv = coeffi-

cient of variation of the laser canopy heights (%); Dl = laser

canopy density.

Stepwise selection was performed to select variables to

be included in the final model. The 5% significance level

was chosen for variables to stay in the model. The standard

least-squares method was used (Anon., 1989). Since the

objective was to assess the accuracy of the selected regres-

sion in predictions, the selected regression was converted

back to original scale. By conversion of the log-linear

equations to original scale a bias will be introduced (e.g.,

Goldberger, 1968). The selected regression was therefore

converted back to original scale by adding half of the

residual variance to the intercept before conversion (Gold-

berger, 1968).

No independent data were available to assess the accu-

racy of mean dominant tree height determined from the

laser data applying the selected regression model. Cross-

validation was therefore used to assess the accuracy. One of

the 39 experimental plots was removed from the dataset at a

time, and the selected model was fitted to the data from the

38 remaining plots. The mean height of the dominant trees

was then predicted for the removed observation. This

procedure was repeated until predicted values were obtained

for all plots.

Simple linear regression was applied to assess how tree

species and tree density affected the accuracy of mean

height of dominant trees derived from the laser data. The

difference between laser mean height predicted by means of

the developed regression equation and ground-truth mean

height was regressed against the proportion of broad-leaved

tree species and the number of stems according to the

following model:

DIFF ¼ b0 þ b1BLþ b2N ð3Þwhere DIFF = difference between predicted and ground-

truth mean height of dominant trees (m); BL= proportion of

broad-leaved species; N = number of stems (ha � 1).

Multiple regression analysis was used to develop models

for number of stems related to predictor variables derived

from the laser data. Previous studies based on ground data

(e.g., Eid, 2001) and data derived by interpretation of aerial

photographs (e.g., Næsset, 1996) have shown that tree

height and measures of density such as basal area and

crown or canopy density are interrelated with stem number.


The eight predictor variables used for modelling of mean

height (see above) were therefore tested, and a similar

multiplicative model was applied. The multiplicative model

was estimated as linear regressions in the logarithmic

variables on the following form:

lnN ¼ lnb0 þ b1lnh25 þ b2lnh50 þ b3lnh75 þ b4lnh90

þ b5lnhmax þ b6lnhmean þ b7lnhcv þ b8lnD1 ð4Þ

Stepwise selection was performed to select variables to

be included in the final model, and cross-validation was

used to assess the accuracy.

Finally, simple linear regression was applied to assess

how tree species and tree height affected the accuracy of

stem number derived from the laser data. This was done by

regressing the difference between laser-derived stem num-

ber and ground-truth stem number against the proportion of

broad-leaved tree species and the mean height of dominant

trees according to the following model:

DIFF ¼ b0 þ b1BLþ b2h ð5Þ

where DIFF = difference between predicted and ground-

truth number of stems (ha � 1); BL= proportion of broad-

leaved species; h =mean height of dominant trees (m).

2.6. Estimating dominant height of entire forest stands

We assessed the accuracy of a practical two-stage pro-

cedure in which dominant tree heights of entire forest stands

were estimated from laser data by means of relationships

between laser data and field data derived from a sample of

systematically distributed field plots. The procedure was

based on the assumption that, for a certain cell size, i.e., a

fixed area, there exist a certain relationship between the tree

height of interest and predictor variables derived from the

height distribution of laser pulses classified as canopy hits

(cf. Magnussen & Boudewyn, 1998; Næsset, 1997a).

A regular grid with cell size corresponding to the plot

size of the sample plots was generated by means of the

GIS. Thus, the individual cell size of the grid was

15.36� 15.36 m (236 m2), and the grid covered the entire

1000-ha study area.

To relate the test stand boundaries and two laser datasets

(first pulse data and all transmitted pulses) to the grid, the

grid was laid over the stand boundary map from the

practical forest inventory and spatially registered to the

laser data.

For each of the 29 sample plots with size 236 m2, the

height distribution of laser pulses classified as canopy hits

were derived. In the first stage, the ground-truth mean

height of the dominant trees on the sample plots (hp) were

related to the eight predictor variables derived from the

distribution of laser canopy heights, including the canopy

density (see above), by a multiplicative regression model.

The multiplicative model was estimated as a linear regres-

sion in the logarithmic variables (Eq. (6)):

lnhp ¼ lnb0 þ b1lnh25 þ b2lnh50 þ b3lnh75 þ b4lnh90

þ b5lnhmax þ b6lnhmean þ b7lnhcv þ b8lnD1 ð6ÞStepwise selection was performed to select variables to

be included in the final model, which after conversion

back to original scale turned out to be of the following

form (see below):

hp ¼ b0hb150h

b2meanD

b31 ð7Þ

In the second stage, the heights of the individual grid cells

of the test stands corresponding to the mean height of

dominant trees were denoted as hc, and they were predicted

from the variables derived from the individual cell distribu-

tions of laser canopy heights (h50c, hmean c, Dlc) and regres-

sion Eq. (7)

hc ¼ b0hb150ch

b2mean cD

b31c ð8Þ

For each test stand, the mean height of dominant trees

was estimated as the arithmetic mean of the individual

predicted cell height values. Grid cells of size < 150 m2

were excluded since the relationship between the ground-

truth heights and the predictor variables derived from the

height distributions were assumed to be valid only for cells

of size 236 m2. The differences between the stand heights

Table 3

Regression coefficients and their standard errors, coefficient of determi-

nation (R2), square root of mean square error (RMSE), coefficient of

variation (CV), and condition number (k) for selected regressions of mean

height of dominant trees (Eq. (2)) and stem number (Eq. (4)) based on the

experimental plots (n= 39)a

Eq. (2) Eq. (4)

Variable Estimate S.E. Estimate S.E.

ln b0 1.406*** 0.211 8.800*** 0.109

ln h90 0.269* 0.111

ln Dl 0.406*** 0.091 0.505*** 0.097

R2 0.830 0.421

RMSE 0.131 0.279

CV (%) 10.16 3.36

k 3.73 1.00

a Level of significance: * < .05; *** < .001. h90 = quantile corresponding

to the 90 percentile of the laser canopy heights (m),Dl = laser canopy density.

Table 4

Differences (D) between predicted and ground-truth values of mean height

of dominant trees and stem number, respectively, and standard deviation for

the differences in cross-validation of the selected regressions in Table 3

based on the experimental plots (n= 39)a

D

Variable Observed mean Range Mean S.D.

h (m) 3.80 � 1.47 to 1.61 0.01 NS 0.57

N (ha� 1) 4197 � 2587 to 2581 30 NS 1209

a Level of significance: NS = not significant (>.05). h=mean height of

dominant trees (m), N= number of stems (ha� 1).

ˆ ˆ ˆ ˆˆ

ˆ ˆ ˆ ˆ ˆ


estimated according to the applied two-stage procedure and

the ground-truth heights were evaluated.

3. Results

3.1. Dominant height and stem number

First, the mean height of dominant trees of the exper-

imental plots was regressed against the predictor variables

derived from the height distribution of laser pulses classi-

fied as canopy hits. According to the stepwise selection

procedure, the final model comprised the quantile corre-

sponding to the 90 percentile (h90) and the laser canopy

density (Dl). The coefficient of determination (R2) was

.830 (Table 3).

Principal component analysis based on the correlation

matrix was used to assess the presence of collinearity in the

regression analysis. The square root of the largest eigen-

value divided by the smallest eigenvalue (condition number)

was used as a means for suggesting collinearity. The

condition number (k) of 3.73 in Eq. (2) (Table 3) indicated

no serious collinearity problems. A condition number larger

than 30 has been proposed to indicate collinearity (Weis-

berg, 1985).

Cross-validation of the selected model revealed that the

mean difference between predicted and observed mean

dominant height of 0.01 m was far from significant in the

statistical sense (Table 4 and Fig. 1). The standard deviation

for the differences between predicted and observed heights

was 0.57 m. According to the error analysis (Eq. (3)), neither

the proportion of broad-leaved species nor the density, as

expressed by stem number, seemed to have any impact on

the differences between predicted and observed heights

(Table 5). The proportion of broad-leaved species and stem

number explained only 8% (R2=.08) of the variability of the

deviation between predicted and observed heights.

The regression analysis of the number of stems on the

experimental plots revealed that laser canopy density (Dl)

was the only predictor variable that could be related to stem

number. None of the other laser-derived variables were

included in the final model (Eq. (4)) at the 5% level of

significance (Table 3). The coefficient of determination in

the selected model was .421.

According to the cross-validation, the mean difference

between predicted and observed stem number was not

statistically significant (Table 4), but the minimum and

Fig. 1. Scatterplots of observed mean height of dominant trees (left) and observed stem number (right) as functions of mean height and stem number predicted

using cross-validation with regression models estimated from the experimental plots (n= 39 experimental plots).

Table 5

Regression coefficients, P values, and coefficient of determination (R2) for

the differences between predicted and observed mean height of dominant

trees (Eq. (3)) and predicted and observed stem number (Eq. (5)),

respectively, regressed against factors that may affect accuracy of prediction

on the experimental plots (n= 39)a

Eq. (3) Eq. (5)

Variable Estimate P Estimate P

b0 � 0.356 NS .246 � 889.0 NS .242

N 0.00003 NS .566

h 157.3 NS .346

BL 0.0126 NS .093 18.05 NS .284

R2 0.080 0.049

a Level of significance: NS = not significant (>.05). N = number of

stems (ha� 1), h=mean height of dominant trees (m), BL= proportion of

broad-leaved species.

Table 6

Differences (D) between laser-derived and ground-truth values of mean

height of dominant trees, and standard deviation for the differences in the

test stands (n= 12)a

D

Comparison Mean h (m) Range (m) Mean (m) S.D. (m)

h–h 6.64 � 0.67 to 1.10 0.23 NS .56

a Level of significance: NS = not significant (>.05). h= ground-truth

mean height of dominant trees (m), h =mean height of dominant trees

predicted from laser data by the proposed two-stage procedure based on a

sample of field plots (m).


maximum differences deviated as much as � 62%

(� 2587 ha� 1) and 61% (2581 ha� 1), respectively, from

the observed ground-truth values (Table 4 and Fig. 1). The

standard deviation of the differences was 28.8%

(1209 ha� 1) of observed mean. The error analysis revealed

that neither the tree height nor the proportion of broad-

leaved species could explain the differences between the

predicted and observed stem number (Table 5).

3.2. Estimated stand heights

The mean height of dominant trees of the 29 clustered

sample plots were regressed against the predictor variables

derived from the laser data. The selected regression equa-

tion was

hp ¼ 6:566h1:60050 h�1:430mean D0:616

1 ð9ÞThe coefficient of determination was .620. The regres-

sion in Eq. (9) was used to predict the height of the

individual grid cells of each of the 12 test stand. The mean

height of each stand estimated from the individual grid cell

predictions was compared to the ground-truth. The mean

difference between laser-derived and ground-truth stand

heights was 0.23 m (Table 6), which was far from

significant. The standard deviation for the differences was

0.56 m. The largest deviation for a single stand was 1.10

m, which corresponds to 16.6% of the observed mean

(Table 6 and Fig. 2).

4. Discussion and conclusions

The results of the current study revealed that the proposed

two-stage procedure for estimation of mean tree heights of

entire stands using a sample of field plots seemed to be very

robust with respect to bias. Although the sample plots used to

estimate the regression equation that related tree heights to

predictor variables derived from the laser data were distrib-

uted independently of the test stands throughout a 1000-ha

area, the mean difference between laser-derived and ground-

truth tree heights of the 12 test stands was as small as 0.23 m

(Table 6). In accordance with Magnussen and Boudewyn

(1998), it is probably essential for a successful removal of

bias that the size of the field sample plots corresponds to the

grid cell size used to predict the tree heights of each stand.

Furthermore, this result may imply that for a certain forest

type, for example, young forest as in the present trial, the

height distributions of laser canopy hits of a unit size of area

at different sites are quite equal. In practical forest invento-

ries, it would therefore be efficient to stratify the area

according to the form of the height distributions. Although

height distributions of individual plots or grid cells have not

been investigated in our study, recent research indicate that,

for example, different age classes will generate distributions

with significantly different forms (e.g., Lefsky, Cohen, et al.,

1999). Commonly used stratification criteria such as age

class and site quality, which is correlated with density, are

therefore probably useful for an efficient stratification of

practical inventories.

The present trial was conducted in an area with small

variations in altitude (70–120 m a.s.l.). The flying height

above the terrain was therefore quite stabile (Table 2), and

thus the ranges of the laser returns were quite constant. In

practical forest inventories in Norway where the altitude

may vary from 100 to 1000 m a.s.l. within relatively short

distances, it may be difficult to keep the flying height above

the terrain constant when an airplane is used as platform.

With variations in laser return ranges, the footprint diameter

will vary accordingly. Increased footprint size tends to

elevate the canopy height inferred from laser data (cf.

Aldred & Bonnor, 1985; Nilsson, 1996). It is therefore

likely that practical applications of the proposed procedure

will benefit from stratification of the forest area according to

flying height above the terrain.

The precision of dominant height determined by means

of the proposed two-stage procedure of 0.56 m for entire

stands (Table 6) coincided seemingly with the precision

revealed by cross-validation of the experimental plots

(0.57 m, Table 4). However, the significant average standard

error of mean ground-truth height of the 12 test stands of

0.46 m may indicate that the true error of the tested practical

procedure is somewhat smaller than 0.5 m and at least

smaller than the error observed on the experimental plots.

This seems reasonable since the laser-derived stand heights

were estimated as a mean value from a sample of several

grid cells (cf. Magnussen & Boudewyn, 1998). Further-

more, the trees in the test stands were about 75% taller than

the trees on the experimental plots (Table 1). It is likely that

the random error increases as the tree heights approach zero

since the height distribution of laser pulses classified as

canopy hits will be more seriously affected by ground hits

erroneously classified as vegetation hits and vice versa than

Fig. 2. Scatterplots of observed stand mean height of dominant trees as a

function of stand mean height of dominant trees predicted using regression

model estimated from the sample plots (n= 12 test stands).

ˆ


in cases with tall vegetation and tree crowns high above the

ground surface.

The estimated regression equations for dominant height

of the experimental plots and the sample plots explained

83% (Table 3) and 62% (Eq. (9)), respectively, of the

variability in observed heights. These proportions are some-

what smaller than the R2 values of .93–.98 reported for

small-footprint data (Means et al., 2000; Næsset, 1997a) and

the R2 value of .95 found for large-footprint data (Means et

al., 1999). However, the three latter studies comprised

samples of plots and stands with size more than 10 times

greater (>2500 m2) the size of the present sample plots.

Furthermore, the referred trials were mainly dealing with

mature forest with tree heights >15 m, where the laser height

distributions are likely to be less affected by erroneous

classification of hits close to the ground surface. Still, the

precision of dominant height determined for entire stands by

means of the proposed two-stage procedure of approxi-

mately 0.5 m seems to be somewhat higher than what could

be expected in older forest. For forest stands with mean tree

heights in the range between 8 and 24 m, standard devia-

tions for the differences between laser-derived and ground-

truth mean heights of 1.2–1.3 m have been reported

(Næsset, 1997a).

Whether the proposed practical procedure could be a

competitive alternative to existing inventory methods

depends on the total inventory costs and the expected

precision of the estimated tree heights. As far as precision

is concerned, current practice is based on subjective esti-

mation of mean height by field inventories, since photo-

grammetric measurements of tree heights roughly ranging

from 1 to 8 m is difficult. Subjective field estimation of

height is expensive and not very accurate. Standard devia-

tions between subjectively estimated and ground-truth mean

heights of 1.1–1.2 m have been reported (Eid, 1993), which

represents a significantly lower precision than indicated in

our study.

It was somewhat surprising that the coefficient of deter-

mination for the experimental plot regression equation

(R2=.830) was significantly higher than the corresponding

coefficient for the clustered sample plots (R2=.620), taking

into consideration that the plot sizes were almost equal (200

and 236 m2) and that the trees were much taller on the

sample plots. However, the experimental plots were subject

to a much more intensive field sampling effort than the

sample plots. Approximately 25% of all recorded trees were

selected for height measurement on the experimental plots.

The stem number was not recorded on the sample plots, but

assuming an average stem number equal to that of the

experimental plots of 4197 ha� 1 (Table 1), the sampling

rate was only 4%. Thus, the estimated ground-truth mean

height of dominant trees on the sample plots were subject to

a significantly higher sampling error, which will affect the

estimated regression. Assuming that the sampling errors

were uncorrelated with constant variance only the regression

residuals will be affected, which may explain the low

proportion of variability accounted for. However, further

inspection of the 841 individual tree heights measured on

the 39 experimental plots indicate that height measurements

of a fixed number of trees on sample plots in young forest

seriously violate the assumptions of uncorrelated sampling

errors and constant variance of the errors. Thus, the random

errors associated with the field measurements may have

affected the variance estimates of the coefficients in the

regression used to predict stand heights. It is therefore likely

that a more intensive field sampling of the clustered sample

plots could have improved the performance of the practical

procedure used to estimate mean heights of entire stands. A

more intensive sampling effort should be considered in

future applications of the procedure.

Number of stems per hectare was determined from the

laser data over the experimental plots only. The low R2

value (.421) of the estimated regression (Table 3) indicated

that it is much more difficult to derive tree numbers than tree

heights from laser data in very young forest. For large stems

(>100 cm) in mature forest, it has been shown that laser data

may explain most of the variability (R2=.85) in observed

stem number (Lefsky, Cohen, et al., 1999). It is reasonable

that it becomes more difficult to determine stem number as

the tree height decreases. Stem number is highly correlated

with laser canopy density (Dl). As a matter of fact, Dl was

the only predictor variable selected in the final regression

equation for stem number (Table 3). Since the canopy

density in young forest with small tree heights will be very

prone to classification errors of hits close to the ground

surface, dependent variables that are related to density only

will be more difficult to estimate precisely than variables

that are related to height metrics of the laser as well, such as

dominant tree height. Furthermore, for a given number of

trees, the canopy density as estimated from the laser data

may change dramatically as the tree heights approach zero,

which is illustrated by the different penetration rates of the

laser data over the three ground-truth data sets applied in our

study. The mean penetration rates of the sample plots and

the test stands, where the mean tree heights were 7.14 and

6.64 m (Table 1), respectively, were 24% and 26% (Table 2).

Over the experimental plots with a mean height of 3.80 m

(Table 1), the mean rate of penetration was 60%. Thus, the

canopy density dropped from approximately 75%–40% as

the tree height decreased by about 3 m.

Nevertheless, the cross-validation (Table 4) revealed

that unbiased estimates of stem number may be derived

from laser data, which may indicate that stem number of

young forest stands may be calculated by means of the

proposed two-stage procedure. Theprecision of 28.8%

(S.D. = 1209 ha � 1) indicated by the cross-validation

(Table 4) is probably lower than what might be expected

for entire stands, since stand estimates must be based on a

sample of several grid cells (cf. Magnussen & Boudewyn,

1998). If a precision of 28% or higher could be expected in

practical applications, stem number derived from laser data

would be an efficient alternative to current field invento-


ries, which are expensive and with a documented precision

of not higher than 22–34% (Eid, 1993).

The ability to predict tree height did not seem to be

affected by the observed stem number and the proportion

of broad-leaved species (Table 5). Neither did errors in

predicted stem number seem to be affected by the true tree

heights and the proportion of broad-leaved species. These

findings may indicate that tree species is not an efficient

criterion for stratification of practical inventories based on

laser data, at least in very young stands. However, it is

likely that more pronounced distinctions between canopy

height distributions derived from laser data for different

tree species will appear as the trees become older and

develop different crown shapes (cf. Nelson, 1997; Nelson

et al., 1988).

The fact that the true number of trees did not affect the

errors in predicted mean height was not surprising since

canopy density was included as predictor variable in the

selected regression (Eq. (2), Table 3). Canopy density and

stem number are intercorrelated variables (Eq. (4), Table 3).

As long as canopy density is made available as candidate

variable in the regression analysis of the proposed two-stage

procedure, further stratification of young forest stands seems

superfluous. Taking the large variability of canopy density

when the tree heights approach zero into account, it was

somewhat surprising that the true tree height did not seem to

affect the errors of predicted stem number. However, the

mean dominant height of the experimental plots ranged

from 1.76 to 6.01 m (Table 1). It is likely that height metrics

derived from laser data will become significant variables in

the prediction of stem number if stands with tree heights

ranging from, say, 1–10 m are pooled into a single stratum.

The applied practical procedure for estimation of mean

tree height of entire stands assumed that the same trees were

observed by the laser and by field measurements. Applica-

tions that utilize corresponding observations of the same

objects on the ground and from the air are sensitive to

positional errors (x and y) for either of the observations. In

many boreal forest types, large variation in important

characteristics such as tree heights and timber volume are

experienced over very short distances. Eid and Fitje (1993)

reported from a study in southeast Norway that mean tree

height of sample plots varied by 11–22% between sample

plots within stands with an average size of 2.1 ha, whereas

Bolduc, Lowell, and Edwards (1999) stated in a Canadian

study that small movements (5–10 m) in any direction had

the potential to place a sample plot in a forest type of

completely different density due to spatial heterogeneity. In

our study, the accuracy of the planimetric coordinates

(x and y) of 25–30 cm on the ground for the laser data

and accuracies of < 0.5 m for the field plot coordinates

computed from GPS and GLONASS observations seem to

ensure a proper correspondence between the two data

sources. It should be noted, however, that the positioning

of the sample plots by GPS probably is the most critical

factor (Bolduc et al., 1999), and that the most relevant

procedures for positioning with GPS and GLONASS under

forest canopies are required (cf. Næsset, 1999c, 2001a;

Næsset et al., 2000).

The indication of a relative robust relationship between

tree heights and laser-derived height distributions for a unit

size of area may extend the applicability of laser data from

small-footprint systems. It has been advocated that small-

diameter beams frequently oversample crown shoulders and

miss the tops of the trees (cf. Dubayah & Drake, 2000), and

that modelling of waveforms which is typified as an

advantage of large-footprint systems, is difficult with

small-footprint systems since they do not record the entire

sequence of reflected energy for individual footprints (Blair

& Hofton, 1999). Using a unit size of area as sampling unit,

it is possible to derive height distributions that have many

properties common to those of waveforms of large foot-

prints. This study has shown that mean height of dominant

trees in young stands can be determined from laser data for

given sampling units assuming that proper calibration is

provided. The proposed two-stage procedure offers such a

calibration. It is likely that maximum tree height for a given

sampling unit can be derived as well. Furthermore, height

distributions derived from small-footprint lasers for a given

sampling unit seem to be proportional to the vertical

distribution of leaf area (Magnussen & Boudewyn, 1998).

Thus, it is likely that the vertical structures of leaf area,

biomass, and vegetation material in general that have been

modelled by means of large-footprint waveforms (Blair &

Hofton, 1999; Lefsky, Cohen, et al., 1999; Weishampel,

Blair, Knox, Dubayah, & Clark, 2000) can be modelled

from small-footprint data as well, although distributions

derived from small-footprint systems will tend to reflect

the outer canopy surface and not the entire canopy (Lefsky,

Harding, et al., 1999). However, further research is required

for empiric verification of this hypothesis.

On the other hand, small-footprint systems have some

attractive properties as compared to large-footprint systems.

In forest areas with abrupt changes in topography and

complex spatial configuration of forest stands, small posi-

tional errors of stand boundaries may seriously affect the

accuracy of characteristics estimated on a per-unit area

basis, e.g., stem number and timber volume per hectare

(Næsset, 1999a, 1999b). It is therefore essential that the

spatial allocation of remotely sensed data can be adjusted

according to a given spatial configuration. With the fine

spatial resolution of small-footprint systems, it is feasible to

define the sampling units in accordance with given bounda-

ries and derive proper laser canopy height distributions

thereafter. The spatial location of a large-footprint wave-

form, however, is fixed.

The present trial has indicated that at least mean tree

heights can be derived from laser data in very young forest

stands with tree heights < 10 m. Furthermore, the proposed

practical stand inventory procedure has proved to yield

unbiased estimates. However, the methodology may be even

more relevant in older and mature forest since the utility in


monetary terms of reduced inventory costs and improved

precision of attributes characterising the timber resources is

higher in stands that are expected to generate revenues in a

near future than in younger stands where logging is not

expected to take place for some decades. Further large-scale

research should therefore be conducted to test the appli-

cability of the methodology in old and mature forest.

Acknowledgments

This research has been funded by the Borregaard

Research Fund and the Research Council of Norway, and

is a contribution to research project no. 133303/110. We

wish to thank Mr. Jo Heringstad and Mr. Petter Økseter at

the Agricultural University of Norway who carried out some

of the fieldwork. Thanks also to Fotonor, Norway for

collection and processing of the airborne laser scanner data,

and to Fotokart, Norway for accomplishing the photo-

grammetric work.

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