estimating forest growth using canopy metrics derived from airborne laser scanner data

sin

ase

Ter

egian

vised

airborne laser scanner data with a sampling density of 0.91.2 m

(swath width) of up to many hundred meters in one

overflight are now being used operationally in commercial

precise information about the timber resources and biomass

stocks, airborne lasers might also be considered as useful

tools in monitoring systems. At a large scale it has been

can provide useful

Remote Sensing of Environment 96stand-based forest inventories (Nsset, 2004c; Nsset et al.,1. Introduction

Airborne laser systems offer an opportunity to determine

biophysical properties of forest stands such as mean tree

height, basal area, and timber volume from detailed three-

dimensional information about tree canopies retrieved from

the laser data (e.g., Maclean & Krabill, 1986; Magnussen &

Boudewyn, 1998; Means et al., 2000; Nsset, 1997a,

1997b; Nelson et al., 1984). Scanning systems with the

ability to collect laser data along a corridor with a width

2004). Application of profiling lasers which collect a narrow

line of data beneath the platform, has already been

demonstrated as a sampling-based tool for forest and

biomass inventory in large areas, such as regions and states

(Nelson et al., 2003, 2004; Weller et al., 2003). It is

therefore evident that airborne lasers have a role to play in

resource assessment.

In an operational context in forestry, scanning and

profiling lasers have mainly been used for inventory and

assessment purposes. However, with the ability to providecollected over 133 georeferenced field sample plots and 56 forest stands located in young and mature forest. The plot size was 300400 m2

and the average stand size was 1.7 ha. Spruce and pine were the dominant tree species. Canopy height distributions were created from both

first and last pulse data. The laser data were acquired in 1999 and 2001. Height percentiles, mean and maximum height values, coefficients of

variation of the heights, and canopy density at different height intervals above the ground were computed from the laser-derived canopy

height distributions. Corresponding metrics derived from the 1999 and 2001 laser datasets were compared. Forty-five of 54 metrics derived

from the first pulse data changed their values significantly due to forest growth. The upper height percentiles increased their values more than

the field-based height growth estimates. The 50 and 90 height percentiles increased by 0.41.3 m whereas the field-estimated mean height

increased by 0.20.9 m. Metrics derived from the last pulse data were less influenced by growth.

Mean tree height (hL), basal area (G), and volume (V) were regressed against the laser-derived variables to predict corresponding values

of hL, G, and V based on the 1999 and 2001 laser data, respectively. Forest growth was estimated as the difference between the 2001 and

1999 estimates. Laser data were able to predict a significant growth in all the three biophysical variables over the 2-year period. However, the

accuracy of the predictions was poor. In most cases the predictions were biased and the precision was low. Finally, several key issues of

particular relevance to laser-based monitoring of forest growth are discussed.

D 2005 Elsevier Inc. All rights reserved.

Keywords: Forest growth; Forest monitoring; Laser scanning; Canopy height; Canopy densityCanopy height distributions were created from small-footprintAbstract

2Estimating forest growth u

from airborne l

Erik Nsset*,

Department of Ecology and Natural Resource Management, Norw

Received 10 December 2004; received in re0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.rse.2005.04.001

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

E-mail address: [email protected] (E. Nsset).g canopy metrics derived

r scanner data

je Gobakken

University of Life Sciences, P.O. Box 5003, N-1432 As, Norway

form 1 April 2005; accepted 2 April 2005

(2005) 453 465

www.elsevier.com/locate/rsedemonstrated that profiling lasersinformation about the change in biomass over time (Sweda

et al., 2003). At a very local scale, it has even been shown

temporal resolution at which reliable change estimates can

be provided. Yu et al. (2004) demonstrated that height

singgrowth of individual trees could be estimated over a 2-year

period in a pine forest using laser data with a pulse density

of 10 m2. However, they only reported the accuracy oflaser-derived height growth estimates as compared to a

ground reference for three selected sample plots. Their

findings indicated an under-estimation of height growth of

1493%, but stated this under-estimation in part was caused

by systematic differences between the two digital terrain

models used to derive the canopy heights from the laser

data. The work by Yu et al. (2004) was based on

identification of each treea feasible method due to the

high density of the laser data. In monitoring of large forest

areas, it is not economically feasible to collect data with

current scanning systems of more than, say, one laser pulse

per square meter (Nsset, 2004c). In operational large-area

monitoring programs, the estimation is most likely to be

based on a statistical approach, i.e., statistical metrics like

percentiles and mean values derived from a collection of

laser pulses for a group of trees represented by a sample plot

(Nsset, 2002a, 2004b) or a sample line (Nelson et al.,

2003) are used to estimate regression equations that relate

the laser data to field observations of the properties of

interest, for example timber volume. These equations are

then used to make predictions over the entire area of

interest. Such a statistical approach has proven to provide

precise estimates of timber volume and other biophysical

variables of interest in individual forest stands, for entire

forest properties, in municipalities, and entire states

(Holmgren, 2004; Nsset, 2002a, 2004b, 2004c; Nelson

et al., 2003, 2004).

In the present work, we analysed multi-temporal laser

data acquired for a boreal forest site in 1999 and 2001. The

laser sampling density was approximately 0.91.2 m2.The objectives of this research were (1) to assess how and to

what extent the laser-derived metrics used to estimate

biophysical forest properties were affected by forest growth

and to examine how forest type influenced on these effects,

and (2) to assess the accuracy of laser-based growth

predictions over a 2-year period of three major biophysical

properties, i.e., mean tree height, basal area, and volume.

2. Materials and methods

2.1. Study area

This study was based on data from a forest inventory inthat high-resolution laser data from scanning systems can be

used to detect growth and harvest of single trees and groups

of trees (plots) (St-Onge & Vepakomma, 2004; Yu et al.,

2004).

In monitoring it is important to find an appropriate

E. Nsset, T. Gobakken / Remote Sen454southeast Norway conducted in the municipality of Valer

(59-30VN, 10-55VE, 70120 m a.s.l.). The size of theinventory was approximately 1000 ha. The main tree

species were Norway spruce [Picea abies (L.) Karst.] and

Scots pine (Pinus sylvestris L.). Further details about the

study area can be found in Nsset (2002a).

Interpretation of aerial stereo photography was used to

delineate and classify forest stands according to the criteria

age class, site index, and tree species. The photo interpre-

tation was used as prior information in designing the

inventory. Two different ground reference datasets were

acquired; (1) one consisting of sample plots distributed

systematically throughout the entire study area, and (2) a

dataset consisting of forest stands. Both datasets were used

to analyze the effect of forest growth on the laser-derived

metrics. Both datasets were also used to assess the accuracy

of laser-based growth predictions of mean tree height, basal

area, and volume, see further details below.

2.2. Sample plots

All field data were collected during summer of 1998, see

Nsset (2002b). Since the laser data were acquired in 1999

and 2001 (see below), the area was revisited in field in

December 2001 to verify that the plots had not been subject

to any harvests or serious natural disturbances. However, it

is likely that some natural mortality had occurred during the

34-year period, although plots where it was observed that

significant mortality had taken place were discarded from

the data.

In total, 133 circular sample plots were distributed

systematically throughout the 1000-ha study area. The plots

were divided into three strata according to age class and site

quality, i.e., (1) young forest (stratum I), (2) mature forest

with poor site quality (stratum II), and (3) mature forest

with good site quality (stratum III). The plot size was 300

m2 in stratum I and 400 m2 in strata II and III. On each plot,

all trees with diameter at breast height (dbh) >4 and >10 cm

were callipered on young and mature plots, respectively,

which conforms to ordinary inventory practice in Norway.

Basal area (G) was computed as the basal area per hectare

of the callipered trees. The heights of sample trees selected

with probability proportional to stem basal area at breast

height using a relascope were measured by a Vertex

hypsometer. Mean height of each plot was computed as

Loreys mean height (hL), i.e., mean height weighted by

basal area. Total plot volume (V) was computed as the sum

of the individual tree volumes for trees with dbh>4 cm and

dbh>10 cm, respectively, using volume equations for

individual trees (Braastad, 1966; Brantseg, 1967; Vestjordet,

1967). hL, G, and V were prorated by 0.23.8 years using

growth models (Blingsmo, 1984; Braastad, 1975, 1980) to

correspond to the dates on which the 1999 and 2001 laser

data were acquired. These prorated values were used as

ground reference (Table 1).

The plot center coordinates (x and y) were determined

of Environment 96 (2005) 453465by differential Global Positioning System (GPS) and

Global Navigation Satellite System (GLONASS) using

respectively. Sample trees were selected with probability

proportional to stem basal area. The number of sample

trees per stand ranged from 24 to 87 with an average of

44. Loreys mean height (hL) was computed as the

arithmetic mean of the sample tree heights. Stand basal

area (G) was computed as basal area per hectare for the

callipered trees. Stand volume (V) was computed accord-

ing to standard volume equations for individual trees (see

above) and diameterheight relationships derived from the

sample trees (see Nsset, 2002a for further details). hL, G,

and V were prorated according to the procedure outlined

above to correspond to the dates of the laser data

acquisition. The prorated values were used as ground

reference. A summary of the ground-truth stand data is

displayed in Table 2.

2.4. Laser scanner data

Laser scanner data for this study were acquired on 8 and

9 June 1999 (Nsset, 2002a; Nsset & Bjerknes, 2001) and

on 16 and 17 July 2001 (Nsset, 2004a) under leaf-on

canopy conditions. On both occasions, a fixed-wing Piper

PA31-310 aircraft carried the Optech ALTM 1210 laser

scanning system. The same instrument was used in 1999

and 2001. The major components of the ALTM 1210 are the

nsing of Environment 96 (2005) 453465 455Table 1

Summary of sample plot reference dataa

Characteristic 1999 Growth Mean

Range Mean 2001

Young forest-stratum I (n=53)

hL (m) 6.521.2 13.6 0.9 14.5

G (m2 ha1) 9.741.4 24.5 2.9 27.4V (m3 ha1) 36.3460.1 178.6 28.6 207.2Tree species distribution

Spruce (%) 0100 53

Pine (%) 097 34

Deciduous species (%) 069 13

Mature forest, poor site quality-stratum II (n=34)

hL (m) 11.421.5 16.1 0.2 16.4


Spruce (%) 089 29

Pine (%) 0100 66


Mature forest, good site quality-stratum III (n=46)

hL (m) 11.425.9 20.0 0.5 20.5


Spruce (%) 0100 68

Pine (%) 0100 23

E. Nsset, T. Gobakken / Remote Setwo Javad Legacy 20-channel dual-frequency receivers

observing pseudorange and carrier phase as rover and

base-station receivers. The estimated accuracy of the plot

coordinates ranged from 4 and

>10 cm were callipered on young and mature plots,

near-infrared laser (1064 nm), the scanner transmitting theDeciduous species (%) 049 9a hL=Loreys mean height, G =basal area, V =volume.Table 2

Summary of stand reference dataa

Characteristic 1999 Growth Mean

Range Mean 2001

Young forest-stratum I (n=22)

hL (m) 10.119.7 13.7 0.7 14.4


Spruce (%) 9100 48

Pine (%) 086 39


Mature forest, poor site quality-stratum II (n=17)

hL (m) 13.617.9 16.0 0.2 16.2


Spruce (%) 476 31

Pine (%) 1892 62


Mature forest, good site quality-stratum III (n=17)

hL (m) 15.922.7 19.2 0.4 19.6


Spruce (%) 4490 70

Pine (%) 043 20Deciduous species (%) 122 10

a hL=Loreys mean height, G =basal area, V =volume.

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 GPS airborne and

ground receivers, and the inertial reference system reporting

the aircrafts roll, pitch, and heading.

The average flight altitude was approximately 700 and

850 m a.g.l. in 1999 and 2001, respectively (Table 3). The

pulse repetition frequency was 10 kHz. First and last returns

were recorded.

In 1999, 43 flightlines were flown in a cross pattern.

Nineteen parallel flightlines with approximately 50%

overlap were flown in one direction and 24 parallel

flightlines were flown perpendicular the first 19 lines.

E. Nsset, T. Gobakken / Remote Sensing456Thus, every location in the study area was covered with

laser data from four strips. Maximum scan angle was 17-,but pulses transmitted at scan angles that exceeded 14-were excluded from the final datasets. Average footprint

diameter at the ground was 21 cm and the average pulse

density was 1.18 m2.Thirty-three parallel flightlines were flown in 2001.

Maximum scan angle was 16-, and pulses transmitted atscan angles >15- were discarded. Average footprintdiameter was 26 cm. Average pulse density was 0.87 m2.

The initial processing of the laser data was accom-

plished by the contractor (Blom Norkart Mapping, Nor-

way). Planimetric coordinates (x and y) and ellipsoidic

height values were computed for all first and last returns.

Unlike the 1999 data, a matching between swaths was

performed on the 2001 data in order to remove orientation

errors. We decided to co-register the height values of both

first and last return data from 1999 as well as 2001 to the

same terrain model to eliminate effects of systematic shifts

in the heights (the z coordinates). The last return data

acquired in 2001 were therefore used to model the ground

surface.

In a filtering operation on the last return data from 2001

undertaken by the contractor using a proprietary routine

(Anon., 2004), local maxima assumed to represent vegeta-

tion hits were discarded. A triangulated irregular network

(TIN) was generated from the planimetric coordinates and

corresponding height values of the individual terrain ground

Table 3

Summary of laser scanner data and flight parameters for the 1999 and 2001

laser data acquisitions

Parameter 1999 2001

System ALTM 1210 ALTM 1210

Repetition frequency 10 kHz 10 kHz

Scan frequency 21 Hz 30 Hz

Date 89 June 1617 July

Mean flying altitude 700 m a.g.l. 850 m a.g.l.

No. of flightlines 43 33

Max. scan angle 17- 16-

Max. processing angle 14- 15-

Mean footprint diameter 21 cm 26 cmMean pulse density 1.18 m2 0.87 m2points retained in the last pulse dataset. The ellipsoidic

height accuracy of the TIN model was expected to be

around 25 cm (Kraus & Pfeifer, 1998; Reutebuch et al.,

2003).

Four different datasets were derived from the laser data

for further analysis, i.e., first and last returns from 1999 and

2001. All first and last return observations (points) were

spatially registered to the TIN according to their coordi-

nates. Terrain surface height values were computed for each

point by linear interpolation from the TIN. The relative

height of each point was computed as the difference

between the height of the first or last return and the terrain

surface height. These datasets were spatially registered to

the sample plots and stands measured in field.

To calibrate the height values of the first and last pulse

data from 1999 and the first pulse data from 2001 according

to the TIN model derived from the 2001 last pulse data, we

identified a public road that goes through the entire study

area and divides it into two parcels of almost equal size. Six

paved road segments along the flattest part of the road were

selected. Within each segment, a square with an approxi-

mate size of 33 m was laid out in the middle of the road.Within the square we identified all the last pulses from 2001

that were node points in the TIN, i.e., they were classified as

ground points according to the TIN model. Within a search

radius of 0.5 m from each of these node points, we

identified the points that were first and last returns from

the 1999 laser data and first returns from the 2001 data. The

height values of the node points were compared with the

height values within the 0.5 m search radius. For the first

return data from 2001, no systematic shift was found. For

the first and last return data from 1999, the computed mean

differences were 13.7 and 3.9 cm, respectively, i.e., the1999 laser data were shifted downwards as compared to the

TIN surface. The standard deviations for the differences

were 5.8 and 5.7 cm, respectively. All laser pulses of the

1999 datasets were corrected according to the estimated

differences.

2.5. Computations

For each sample plot and stand inventoried in field,

height distributions were created for those laser pulses that

were considered to belong to the tree canopy, i.e., pulses

with a height value of >2 m (Nilsson, 1996). Some sample

height distributions are presented in Fig. 1. Separate

distributions were created for the first and last pulse data,

respectively, and percentiles for the canopy height for 10%

(h10), 50% (h50), and 90% (h90) were computed. In addition,

also the maximum (hmax) and mean values (hmean) and the

coefficient of variation (hcv) of the canopy height distribu-

tions were computed. Furthermore, several measures of

canopy density were derived. The range between the lowest

laser canopy height (>2 m) and the maximum canopy height

of Environment 96 (2005) 453465was divided into 10 fractions of equal length. Canopy

densities were then computed as the proportions of laser hits

nsingFirst pulse

E. Nsset, T. Gobakken / Remote Seabove fraction #0 (>2 m), 1,. . ., 9 to total number of pulses.The densities for fraction #1 (d1), #5 (d5), and #9 (d9) were

selected for further studies.

-202468

10121416182022242628

0 30 40 50 70

19992001

Stand # = 42

-202468

10121416182022242628

0 20 40 60

Stand # = 52

-202468

10121416182022242628

0 20 60 70

Stand # = 29

Lase

r hei

ght (

m)

2010 60

Relative frequency (%)

Lase

r hei

ght (

m)

10 30 40 50


Lase

r hei

ght (

m)

10 30 50 70


Fig. 1. Height distributions (relative frequencies in 1 m height intervals) of first an

from stratum I (stand #42: age=53 years, site quality=high, 100% spruce, hLquality=poor, 92% pine, hL=16.1 m, G =13.4 m

2 ha1), and stratum III (stanG =30.1 m2 ha1).Last pulse

of Environment 96 (2005) 453465 457To assess how forest growth affected the laser-derived

metrics, differences between corresponding metrics derived

from the 2001 and 1999 laser data were computed for each

-202468

10121416182022242628

0 20 40 60

Stand # = 42

-202468

10121416182022242628

0 20 40

Stand # = 52

-202468

10121416182022242628

0 30 40 50 70

Stand # = 29 La

ser h

eigh

t (m)

10 30 50 70


Lase

r hei

ght (m

)

Relative frequency (%)10 20 60

Lase

r hei

ght (

m)

10 30 50 60 70


d last pulse laser data from 1999 and 2001 for three sample stands selected

=19.7 m, G =37.2 m2 ha1), stratum II (stand #52: age=135 years, sited #29: age=132 years, site quality=medium, 64% spruce, hL=20.3 m,

singsample plot and forest stand. The standard deviations of the

differences were also computed to assess the stability of the

respective metrics. Separate comparisons between laser

scanner data from 1999 and 2001 were carried out for first

and last pulses, respectively.

The mean differences between data acquired in 1999 and

2001 of the investigated height and density-related metrics

were compared for different strata by means of t-tests to

assess how forest type influenced on the effects of forest

growth on the laser-derived metrics. Correspondingly, the

variances of the differences between laser scanner data from

1999 and 2001 were compared for different strata by means

of F tests. In the comparisons of the nine laser-derived

metrics between the 1999 and 2001 laser datasets within

strata and in the comparison between strata, nine t-tests or F

tests were accomplished simultaneously. In order to control

the total Type I error, Bonferroni tests were applied (Miller,

1981). Thus, the level of significance for each of the nine

tests was a / 9.To assess the accuracy of laser-based growth predictions

of mean tree height, basal area, and volume over the 2-year

period from 1999 to 2001, we followed the two-step

procedure proposed by Nsset and Bjerknes (2001) and

Nsset (2002a) to (1) relate the three biophysical properties

of interest to the laser data of the sample plots, and (2) to use

these relationships to predict corresponding values of the 56

test stands based on the 1999 and 2001 laser data,

respectively. As an additional step, (3) the growth was

estimated as the difference between the predicted values in

2001 and 1999.

Thus, in step 1, multiple regression analysis was used to

create stratum-specific relationships between the three

biophysical properties and the laser-derived metrics for

the 133 field training plots (sample plots). We only used the

1999 laser data, and not the 2001 datasets, to develop these

models to avoid effects on the growth predictions of using

different models. The estimation of regression models was

based on the height and density-related metrics derived

from the first and last pulse height distributions as

candidate explanatory variables. However, the maximum

values of the height distributions were not included as

candidates since a higher variability seems to be associated

with these variables than the other height-related metrics

(Nsset, 2004a). In the regression analysis, multiplicative

models were estimated as linear regressions in the

logarithmic variables. The linear form used in the

estimation was

lnY lnb0 b1lnh10f b2lnh50f b3lnh90f b4lnh101 b5lnh501 b6lnh901 b7lnhmeanf b8lnhmeanl b9lnhcvf b10lnhcvl b11lnd1f b12lnd5f b13lnd9f b14lnd11 b15lnd51 b16lnd91 1

where Y=field values of hL (m), G (m2 ha1), or V (m3

1

E. Nsset, T. Gobakken / Remote Sen458ha ); h10f, h50f, h90f=percentiles of the first pulse laser

canopy heights for 10%, 50%, and 90% (m); h10l, h50l,h90l=percentiles of the last pulse laser canopy heights for

10%, 50%, and 90% (m); hmeanf, hmeanl=mean of the first

and last pulse laser canopy heights (m); hcvf, hcvl=coeffi-

cient of variation of the first and last pulse laser canopy

heights (%); d1f, d5f, d9f=canopy densities corresponding

to the proportions of first pulse laser hits above fraction 1,

5, 9 to total number of first pulses; d1l, d5l, d9l=canopy

densities corresponding to the proportions of last pulse

laser hits above fraction #1, 5, 9 to total number of last

pulses. Stepwise selection was performed to select vari-

ables to be included in these models. No predictor variable

was left in the models with a partial F statistic with a

significance level greater than 0.05. The standard least-

squares method was used (Anon., 1989).

By conversion of the loglog equations to original

scale for prediction purposes a bias will be introduced in

the intercept (e.g., Goldberger, 1968). It is therefore

essential that proper corrections are undertaken to avoid

serious bias of predictions. Under given circumstances,

proper corrections may be rather complicated to accom-

plish. However, when the differences between the training

data and the data used in the predictions are small,

MSE0.5, and nk30, i.e. the number of observationsminus the number of predictor variables, an approximate

and simple correction that will introduce an error of less

than 1%, is to add half the variance to the regression

intercept before conversion (Flewelling & Pienaar, 1981).

In the present context, even a bias of 1% may have a

serious impact on the interpretation of the predictions.

Based on the training plots used in the regression analysis,

we therefore computed the corrected intercepts as the ratio

between the respective mean values of the response

variables and the mean estimated values without the

intercept.

In step 2, the estimated regression models with

adjusted intercepts were used to predict the three

biophysical properties of interest in each of the 56 large

test stands. Separate predictions were made for the laser

data acquired in 1999 and 2001, respectively. This was

done by dividing each stand into regular grid cells with a

cell size of 350 m2. Laser canopy height distributions

were created for each cell from the assigned first and last

pulse laser data, and the biophysical properties were

predicted at cell level using the estimated stratum-specific

equations and the derived laser metrics. Predicted values

at stand level were computed as mean values of the

individual cell estimates.

In step 3, the growth from 1999 to 2001 was estimated as

the difference between the predicted values of hL, G, and V

in 2001 and 1999.

Finally, to assess how the size of the target area affected

the accuracy of the growth predictions, we also made

predictions of the three biophysical properties for the 133

sample plots based on the 1999 and 2001 laser datasets, and

of Environment 96 (2005) 453465estimated the growth as the difference between the predicted

values in 2001 and 1999.

3. Results

3.1. Height percentiles

Laser-derived canopy height and density metrics were

first computed for the 133 sample plots and 56 test stands.

For the percentiles (h10, h50, h90) of the first pulse height

distributions, all the mean differences between data acquired

in 1999 and 2001 were found to be statistically significant.

The differences for the first pulse ranged from 0.38 to 1.32

m for the sample plots (Table 4) and from 0.29 to 1.12 m for

the test stands (Table 5). The testing based on the stand

material revealed that the differences between the 1999 laser

data and the 2001 laser data were of similar magnitude for

strata I and III (Table 6). However, the increase in percentile

values was significantly greater in strata I and III than in

stratum II, indicating a higher height growth rate in the

young and highly productive forest than in the old forest on

poor sites. The standard deviations for the differences of the

percentiles between laser data acquired in 1999 and 2001

ranged from 0.34 to 0.98 m for the sample plots (Table 4)

and from 0.20 to 0.39 m for the test stands (Table 5). None

of the variances for the differences were found to be

significantly different in the statistical sense ( p >0.05) when

comparisons between forest types were made (Table 6).

When we compared the percentiles of the last pulse

height distributions acquired in 1999 and 2001, it was

revealed that the highest percentile (h90) was the only one

Table 4

Differences (D) between laser scanner data from 1999 and 2001 for laser-

derived metrics of small sample plots and standard deviation (S.D.) for the

differences for first and last pulse data, respectivelya

Metricsb D, first pulse D, last pulse

Mean S.D. Mean S.D.

Young forest-stratum I (n=53 sample plots)

h10 (m) 1.01*** 0.74 0.09 NS 1.25

h50 (m) 1.30*** 0.47 1.10*** 0.75

h90 (m) 1.32*** 0.46 1.30*** 0.49

hmax (m) 1.09*** 0.88 0.99*** 0.87

hmean (m) 1.24*** 0.43 0.90*** 0.64

hcv (%) 2.09*** 1.99 1.71* 3.87d1 (%) 0.06*** 0.04 0.03*** 0.05d5 (%) 0.11*** 0.05 0.01 NS 0.06

d9 (%) 0.01*** 0.02 0.01** 0.02

Mature forest, poor site quality-stratum II (n=34 sample plots)

h10 (m) 0.42* 0.71 0.42 NS 1.29h50 (m) 0.48*** 0.38 0.40 NS 1.06h90 (m) 0.38*** 0.34 0.42*** 0.49

hmax (m) 0.26 NS 0.74 0.08 NS 0.77

hmean (m) 0.42*** 0.31 0.14 NS 0.46hcv (%) 1.41* 2.45 3.45*** 3.86d1 (%) 0.05*** 0.05 0.04** 0.06d5 (%) 0.05*** 0.03 0.03*** 0.04

d9 (%) 0.00 NS 0.00 0.00 NS 0.00

Mature forest, poor site quality-stratum II (n=17 test stands)

h10 (m) 0.29** 0.27 0.28*** 0.21h50 (m) 0.44*** 0.25 0.16 NS 0.46h90 (m) 0.44*** 0.20 0.33*** 0.21

hmax (m) 0.28 NS 0.59 0.30* 0.38

hmean (m) 0.40*** 0.22 0.14 NS 0.27hcv (%) 0.81 NS 1.07 3.56*** 2.21d1 (%) 0.05*** 0.03 0.03* 0.04d5 (%) 0.03*** 0.02 0.01 NS 0.02d9 (%) 0.00 NS 0.00 0.00 NS 0.00

Mature forest, good site quality-stratum III (n=17 test stands)

h10 (m) 0.65*** 0.34 0.38 NS 0.53h50 (m) 0.90*** 0.36 0.35 NS 0.54

h90 (m) 0.83*** 0.36 0.66*** 0.37

hmax (m) 0.46 NS 0.78 0.58 NS 0.76

hmean (m) 0.81*** 0.32 0.23 NS 0.41

hcv (%) 1.53*** 0.74 2.32*** 1.51d1 (%) 0.05*** 0.01 0.03*** 0.02d5 (%) 0.07*** 0.03 0.00 NS 0.03

d9 (%) 0.00 NS 0.00 0.00 NS 0.00

a Level of significance (Bonferroni test, a / 9): NS=not significant(>0.05). *

singTable 6

Comparisons between strata of mean differences (D) and standard

deviations for the differences (S.D.) between laser derived metrics from

laser scanner data from 1999 and 2001 for the forest standsa,b,c

Metrics DI

DII

DI

DIII

DII

DIII

S.D.I

S.D.IId

S.D.I

S.D.IIId

S.D.II

S.D.IIId

First pulse data

h10 ** NS * NS NS NS

h50 *** NS ** NS NS NS

h90 *** NS ** NS NS NS

hmax NS NS NS NS NS NS

hmean *** NS *** NS NS NS

hcv ** NS NS NS NS NS

d1 NS * NS NS NS ***

d5 * NS ** ** * NS

d9 NS NS NS NS NS NS

Last pulse data

h10 NS NS NS NS NS NS

h50 *** NS NS NS NS NS

h90 *** NS * * NS NS

hmax NS NS NS *** NS NS

hmean *** NS * NS NS NS

hcv NS NS NS NS NS NS


d5 ** NS NS NS NS NS

E. Nsset, T. Gobakken / Remote Sen460all strata. For the lowest percentile (h10), only one of the six

comparisons that were made between 1999 and 2001 was

statistically significant. The comparison revealed, however,

that the differences for h10 tended to be negative, indicating

a decline in percentile values from 1999 to 2001. For h50and h90, the differences across data acquired in 1999 and

2001 differed significantly between young forest (stratum I)

and low-productive mature forest (stratum II) (Table 6).

The standard deviations for the differences were in the

range between 0.49 and 1.29 m for the plots and between

0.21 and 0.54 m for the stands. When comparisons between

forest types were made (Table 6), none of the variances for

the differences were found to deviate significantly

( p >0.05), except for the comparison of h90 between young

forest (stratum I) and mature forest dominated by pine

(stratum II).

3.2. Height maximum, mean, and variability

For the sample plots, the maximum values of the first as

well as the last pulse canopy height distributions (hmax)

differed significantly between the data acquired in 1999 and

2001 for all the comparisons that were made except for the

low-productive pine forest (stratum II) (Table 4). For the


a Roman subscript refers to stratum.b Level of significance (Bonferroni test, a / 9): NS=not significant

(>0.05). *

1999 and 2001 laser datasets, respectively. The growth was

computed as the difference between the predicted values for

2001 and 1999. For all the three investigated biophysical

properties a major finding was that the laser-based predic-

tions indicated either a non-significant change or a

significant and positive growth over the 2-year period

(Table 8). In four of the nine tested combinations of variable

and stratum the growth was not significant in the statistical

sense. However, the laser-predicted growth was positive for

all variables in the stratum with the highest growth rate

(stratum I).

The laser-based height growth predictions differed

significantly from the field-estimated height growth in all

three strata. The height growth was over-predicted in the

low-productive forest (stratum II) and under-predicted in the

young and productive forest (strata I and III).

Basal area growth was significantly over-predicted in the

spruce-dominated forest (strata I and III) and under-

predicted in the pine forest as compared to the field-based

estimates. For volume, the growth was significantly under-

predicted in the mature forest (strata II and III) and over-

predicted in the young forest (stratum I). In the cases where

nsing of Environment 96 (2005) 453465 461Table 7

Selected models for biophysical properties (response variables) from

stepwise multiple regression analysis of the sample plots using metrics

derived from the laser data acquired in 1999 as explanatory variables

Response variablea Expl. variablesb R2 RMSE

Young forest-stratum I (n=53 plots)

lnhL lnh10f, lnhmeanl 0.91 0.08

lnG lnh10f,lnh50f, lnd1f 0.91 0.11

lnV lnhmeanl, lnd1f 0.95 0.13

Mature forest, poor site quality-stratum II (n=34 plots)

lnhL lnh90l 0.71 0.09

lnG lnh90f, lnhcvl, lnd5l 0.78 0.14

lnV lnh50f, lnd1l 0.85 0.15

Mature forest, good site quality-stratum III (n=46 plots)

lnhL lnh10f, lnh90l, lnd5l 0.85 0.07

lnG lnhmeanf, lnd1f, lnd5l 0.86 0.12

lnV lnhmeanl, lnd1l 0.91 0.13

a hL=Loreys mean height (m), G =basal area (m2 ha1), V =volume (m3

ha1).b h10f, h50f, and h90f=percentiles of the first pulse laser canopy heights

for 10%, 50%, and 90% (m); h90l=percentile of the last pulse laser canopy

heights for 90% (m); hcvl=coefficient of variation of the last pulse laser

canopy heights (%); hmeanf and hmeanl=arithmetic mean of first or last pulse

laser canopy heights, respectively (m); d1f=canopy density corresponding

to the proportion of first pulse laser hits above fraction #1 to total number of

first pulses (see text); and d1l and d5l=canopy densities corresponding to

the proportions of last pulse laser hits above fraction #1 and 5, respectively,

to total number of last pulses.

E. Nsset, T. Gobakken / Remote Sethe last pulse data, the differences ranged from 0.04% to0.03% (Tables 4 and 5). Only the canopy density of the

lowest vertical layer (d1) differed significantly between data

acquired in 1999 and 2001 across all comparisons. The

change in density from 1999 to 2001 in the intermediate

canopy layer (d5) differed significantly between the low-

productive, mature pine forest (stratum II) and the other

forest types.

3.4. Growth predictions

To assess the accuracy of laser-based growth predictions,

stepwise regression analysis based on the 133 field training

plots was carried out to create stratum-specific relationships

between the three biophysical properties of interest (hL, G,

and V) and metrics derived from the 1999 laser data. The

selected loglog regression models explained 7195% of

the variability (Table 7). The models contained from one to

three explanatory variables. The models selected to be the

best ones for example for volume, were based on one

laser-derived variable related to canopy height and one

variable related to canopy density. Multicollinearity issues

were addressed by calculating and monitoring the size of the

condition number. None of the selected models had a

condition number greater than 6.3, indicating that there was

no serious collinearity inherent in the selected models

(Weisberg, 1985).

The selected stratum-specific regression models were

used to predict hL, G, and V for the test stands based on thea significant growth was predicted by the laser data, the

mean prediction error for basal area and volume ranged

from approximately 50% to 110%. In the cases where the

predicted growth was not significant, the relative prediction

error was greater.

The growth was also estimated from laser-based predic-

tions for the sample plots according to a similar procedure

as we followed for the test stands. In general, there was a

good correspondence between the findings for the test

stands and the results revealed for the sample plots

Table 8

Growth (19992001) of the forest stands estimated from field measure-

ments, growth predicted from laser data (19992001) using the regression

equations in Table 7, and mean difference and standard deviation for the

differences (S.D.) between laser-predicted and field-estimated growtha

Response

variablebMean field-

estimated

growth

Mean laser-

predicted

growth

Difference

Mean S.D.

Young forest-stratum I (n=22 stands)

hL (m) 0.70 0.33** 0.37*** 0.34G (m2 ha1) 2.20 3.70*** 1.50*** 0.66V (m3 ha1) 19.8 29.2*** 9.4*** 6.0

Mature forest, poor site quality-stratum II (n=17 stands)

hL (m) 0.21 0.42*** 0.21*** 0.18

G (m2 ha1) 0.81 0.37 NS 1.18*** 1.15V (m3 ha1) 7.7 1.2 NS 6.5* 10.2

Mature forest, good site quality-stratum III (n=17 stands)

hL (m) 0.44 0.19 NS 0.25* 0.47G (m2 ha1) 1.65 3.53*** 1.88*** 0.67V (m3 ha1) 19.2 1.0 NS 20.2*** 9.9a Level of significance: NS=not significant (>.05). *

sing4. Discussion and conclusions

The major findings of this study indicate that:(Table 9). However, the standard deviations for the

differences between the predicted and field-based growth

estimates were in general larger for the sample plots.

Table 9

Growth (19992001) of the sample plots estimated from field measure-

ments, growth predicted from laser data (19992001) using the regression

equations in Table 7, and mean difference and standard deviation for the

differences (S.D.) between laser-predicted and field-estimated growtha

Response

variablebMean field-

estimated

growth

Mean laser-

predicted

growth

Difference

Mean S.D.

Young forest-stratum I (n=53 plots)

hL (m) 0.95 0.80*** 0.15 NS 0.94G (m2 ha1) 2.92 4.23*** 1.31*** 1.49V (m3 ha1) 28.6 38.4*** 9.8*** 17.7

Mature forest, poor site quality-stratum II (n=34 plots)

hL (m) 0.23 0.50*** 0.27*** 0.47

G (m2 ha1) 0.84 1.28** 2.12*** 2.37V (m3 ha1) 8.3 1.5 NS 9.8* 24.7

Mature forest, good site quality-stratum III (n=46 plots)

hL (m) 0.48 0.25 NS 0.23 NS 1.28G (m2 ha1) 1.66 3.46*** 1.80*** 1.55V (m3 ha1) 21.0 1.4 NS 19.6*** 25.8a Level of significance: NS=not significant (>.05). *

nsingThe estimated change in height distribution variability

(hcv) from 1999 to 2001 gives a strong proof of the different

properties of the first and last pulse data indicated above.

For both plots and test stands, and across all forest types, the

variability of the height distributions decreased significantly

for the first pulse data and increased for the last pulse data

(Tables 4 and 5). As canopy gaps become more closed by

growth, the first pulse reflections tend to become concen-

trated (reduced variability) in the upper parts of the canopy

because of the high sensitivity of being reflected by a small

amount of biological matter obstructing the laser beams. On

the other hand, a moderate increase in biomass over a 2-year

period has little impact on beam penetration deep into the

canopy from where the last significant returns are reflected.

However, as the change in maximum height (hmax) and the

upper percentiles (h90) indicate, a small portion of even the

last returns will be reflected from the upper canopy. The last

return height distribution will therefore tend to be more

stretched (increased variability) as the growth elevates the

height of the canopy.

The second objective of this study was to assess the

accuracy of laser-based growth predictions over a short

growth period of three important biophysical properties,

namely, mean tree height, basal area, and volume. It has

been demonstrated that laser data can predict a significant

forest growth over a short period, although with substantial

deviations from what is considered to be the true

growth. However, errors are also associated with the

field-based true growth estimates since they are based

on general growth models and not measurements of the

actual growth. Ground-truth growth projections do not take

annual variations into account, such as those caused by

differences in temperature and rainfall. Errors in the

ground-truth itself can therefore in part be inherent in the

observed differences between laser-predicted and field-

estimated growth. As a matter of fact, airborne lasers may

provide a method for observing the actual growth without

having to rely on the average conditions over, for example,

a 5-year period as do the growth models.

To make precise growth predictions from laser data

over short time intervals, say 5 years or less, it is utmost

important that (1) the data acquisitions routines, (2) the

data themselves, (3) the data processing, and, (4) finally,

the growth estimation are as robust as possible, so that

the predicted growth can be attributed to the growth as

such and not to any imperfections in the procedures. The

problem of calibrating multi-temporal data from, for

example, optical remote sensing for any kind of change

detection is well-known. In airborne laser-scanning, data

acquisition parameters that seem to be critical are flying

altitude, footprint size, time of the yearespecially when

broad-leaved species are measured, laser sampling density,

and last but not least, the sensor used. Flying altitude and

footprint size as such seem to have little influence on the

E. Nsset, T. Gobakken / Remote Secharacteristics of first pulse data, at least within certain

limits (Nsset, 2004a). Last pulse data, however, aremuch more sensitive to changes in flying altitude/footprint

size, and flying altitude and/or the use of first versus last

pulse data are therefore factors that require careful

consideration in laser-based growth studies. According

to the experience gained by comparing flying altitudes of

540 and 850 m a.g.l. (Nsset, 2004a), the effects of

differences in flying altitudes in the present study (700

versus 850 m a.g.l., Table 3), are probably neglectable.

Laser sampling density, i.e., the number of laser

measurements per unit area, may affect the laser-derived

variables used to predict tree growth. The maximum height is

probably one of the most affected variables, because the

probability of hitting the tree apex of a specific tree in the

context of single-tree based approaches or the top of a

dominant tree for a certain area (e.g., sample plot or forest

stand) in statistically based methods, is a direct function of

the number of measurements per unit area. The laser

sampling density should therefore be kept stable across

acquisitions. This is particularly important in methods where

the maximum height value is an essential variable in the

growth estimation. In the present study, we did not use the

maximum values for this reason and because the maximum

value tend to be less stable than many of the other laser-

derived height metrics. The precision of the maximum values

also seems to be less improved by increasing size of the

target area (cf. Tables 4 and 5). In single-tree based methods,

however, the individual trees are usually derived from

canopy surface models created from local maxima. Growth

studies based on this approach as demonstrated by St-Onge

and Vepakomma (2004) and Yu et al. (2004), are probably

more dependant on stable laser sampling densities over time

to perform well than statistically based methods like the one

demonstrated in our study. In the present study, the average

laser sampling densities in 1999 and 2001 were 1.18 and

0.87 m2 (Table 3), respectively. The effects of suchmoderate changes in data density on laser-based predictions

of mean height, basal area, and stand volume using height

percentiles and measures of canopy density as predictor

variables are probably neglectable (Holmgren, 2004).

A major consideration in the study by St-Onge and

Vepakomma (2004) was the fact that they used different

sensors on the two occasions. The sensor-dependent effects

are probably the most difficult ones to control in multi-

temporal laser studies, especially for longer time intervals,

because under such conditions it is very likely that different

sensors will be used due to rapid technological develop-

ment. Another sensor-dependent source of uncertainty,

which has not yet received any attention is the fact that all

sensors are subject to changing physical properties over

their life-time. Although the ranging device is calibrated to

perform well when it is used for ranging of solid surfaces

such as terrain surfaces, effects of changed properties when

measuring an irregular and penetrable surface like a tree

canopy is unknown.

of Environment 96 (2005) 453465 463The most important concern regarding data processing is

the selection of a proper ground reference level that all the

procedure. Yu et al. (2004), however, used both separate and

common terrain models when they compared laser data for a

sing2-year growth period. They demonstrated that in certain

cases canopy height changes attributed to the use of

different terrain models were larger than the changes

attributed to canopy height growth.

In this study, we assessed the effects of growth over a

very short growth period. For boreal conifer species, it is

quite common to use 5-year periods in growth projec-

tions. Over the 2-year period assessed in the present

study, the height growth, for example, ranged from 1.2%

to 6.6% (cf. Tables 4 and 5). It is therefore a risk that

effects of imperfections in the computational procedures

and actual growth are confounded. In the present study,

we used the same equations to predict the three

biophysical variables from the laser data on the two

occasions. If different prediction models are used, it is

always a risk that different model properties may

influence on the predictions.

To conclude, the present study has indicated that forest

growth over a short growth period may affect laser-derived

metrics such as height percentiles and other canopy height

related metrics and canopy density. The effects are more

pronounced for the first pulse reflection than for the last

pulse reflection. These metrics can be used to predict a

significant growth in stand height, stand density, and

volume, even for a short growth period, at least if the site

productivity and thus the growth rate are high. However, for

short growth periods, the precision of the laser-derived

growth estimates is low.

If airborne lasers are to be considered as a useful

technology in large-area monitoring, a careful planning is

needed to control external factors across time such as data

acquisition parameters and data processing routines. A

major obstacle for detecting growth over short time periods

are probably the sensor-specific properties that affect how

the laser beams depict the various parts of a forest canopy.

Sensor-specific effects of canopy measurements by airborne

lasers and calibration of laser-derived canopy measures

across sensors are therefore important aspects that need

careful consideration prior to operational use of airborne

laser in forest monitoring.

Acknowledgments

This research has been funded by the Research Council

of Norway, the Norwegian University of Life Sciences, and

the Norwegian Institute of Land Inventory. Thanks to Blompulse measurements can be related to when the height

values of each pulse is computed. St-Onge and Vepakomma

(2004) argue that the same terrain model should be used for

both years to avoid terrain differences causing false canopy

height changes. In the present study, we followed this

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E. Nsset, T. Gobakken / Remote Sensing of Environment 96 (2005) 453465 465

Estimating forest growth using canopy metrics derived from airborne laser scanner dataIntroductionMaterials and methodsStudy areaSample plotsStand inventoryLaser scanner dataComputations

ResultsHeight percentilesHeight maximum, mean, and variabilityCanopy densityGrowth predictions

Discussion and conclusionsAcknowledgmentsReferences

estimating forest growth using canopy metrics derived from airborne laser scanner data

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