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PredictingforeststandvariablesfromLiDARdataintheGreatLakes–St.LawrenceforestofOntario

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NOVEMBER/DECEMBER 2008, VOL. 84, NO. 6 — THE FORESTRY CHRONICLE 827

Predicting forest stand variables from LiDAR data in the Great Lakes – St. Lawrence forest of Ontario

by M. Woods1, K. Lim2 and P. Treitz3

ABSTRACTModels were developed to predict forest stand variables for common species of the Great Lakes – St. Lawrence forest ofcentral Ontario, Canada from light detection and ranging (LiDAR) data. Stands that had undergone various ranges of par-tial harvesting or initial spacing treatments from multiple geographic sites were considered. A broad forest stratificationwas adopted and consisted of: (i) natural hardwoods; (ii) natural conifers; and (iii) plantation conifers. Stand top height(R2 = 0.96, 0.98, and 0.98); average height (R2 = 0.86, 0.76, and 0.98); basal area (R2 = 0.80, 0.80, and 0.85); volume (R2 =0.89, 0.81, and 0.91); quadratic mean diameter (R2 = 0.80, 0.68, and 0.83); and density (R2 = 0.74, 0.71, and 0.73) werepredicted from low density (i.e., 0.5 point m-2) LiDAR data for these 3 strata, respectively.

Key words: light detection and ranging, LiDAR, airborne laser scanning, forest modelling, remote sensing, forest standvariables, Great Lakes – St. Lawrence forest

RÉSUMÉDes modèles ont été élaborés afin d’effectuer des prédictions sur les variables des peuplements forestiers associées aux espècescommunes des forêts des Grands Lacs et du Saint-Laurent dans le centre de l’Ontario au Canada, à partir des données de détec-tion de la lumière et de calcul de la distance (LiDAR). Les peuplements ayant subi des coupes partielles de diverses intensitésou des traitements préliminaires d’espacement et établis sur diverses stations géographiques ont été retenus pour fins d’étude.Une stratification forestière générale a été mise en place et faisait référence (i) aux peuplements feuillus naturels, (ii) aux peu-plements résineux naturels et, (iii) aux plantations de résineux. Les hauteurs maximales des peuplements (R2 = 0,96, 0,98 et0,98); la hauteur moyenne (R2 = 0,86, 0,76 et 0,98); la surface terrière (R2 = 0,80, 0,80 et 0,85); le volume (R2 = 0,89, 0,81 et0,91); le diamètre de la tige de surface terrière moyenne (R2 = 0,80, 0,68 et 0,83) et la densité (R2 = 0,74, 0,71 et 0,73) ont étéprédites respectivement à partir de données LiDAR à faible densité (c’est-à-dire, 0,5 point m-2) pour ces trois strates.

Mots clés : détection de la lumière et calcul de la distance, LiDAR, numérisation par laser aéroporté, modélisationforestière, télédétection, variables de peuplement forestier, forêt des Grands Lacs et du Saint-Laurent.

1Ontario Ministry of Natural Resources, 3301 Trout Lake Rd, North Bay, Ontario P1A 4L7. E–mail: murray.woods@ontario.ca2Lim Geomatics Inc., 264 Catamount Court, Ottawa, Ontario K2M 0A9.3Department of Geography, Queen’s University, Kingston, Ontario K7L 3N6.

M. Woods K. Lim

IntroductionEvolving strategic- and operational-scale modelling activitiesrequires the development of natural resource inventories withan increased spatial resolution of forest stand metrics anddetailed terrain attributes. Forest modelling trends are shift-ing towards spatially explicit tools requiring increased accu-racy of the location, accessibility, quantity (e.g., stand vol-ume), and size (e.g., average piece size) to help formulatepotential scenarios to be considered in developing forest

management plans. Accurateestimates of inventory vari-ables at the stand level becomemuch more crucial when eval-uating short- and long-termmanagement decisions andalternatives with the use ofspatially explicit models.

Current forest inventoriesare derived through airphotointerpretation and photogram-metric techniques that deter-mine forested polygons andassign a species list, average

height, site occupancy measure (i.e., stocking or crown clo-sure) and a coarse estimate of age. With an interpreted heightand estimated age, stand site productivity is derived (i.e., siteclass or site index). In Ontario, normal and empirical yieldtable estimates for an aggregated forest community are usedto assign an average basal area and volume to a group of sim-ilar stand conditions based on an assessment of site produc-tivity and species composition. Today, forest managementmodelling and operational planning require more accurateand precise estimates of these inventory variables.

P. Treitz

Airborne light detection and ranging (LiDAR) for forestapplications has been studied since 1982 (Arp et al. 1982).Over the past decade, improvements in global positioningsystems (GPS), inertial navigation systems (INS), computerhardware, LiDAR processing software, and reduced acquisi-tion costs have permitted LiDAR technology to evolve from aresearch tool to operational status in forestry (Næsset 2004a,Stephens et al. 2007). Current acquisition costs, includingclassification of LiDAR points, breakline collection, deriva-tion of digital elevation models (DEMs) and digital surfacemodels (DSMs), has become an operationally affordablealternative when development of a precision inventory is con-sidered.

Recent work in Ontario has focused on estimating forestinventory and biophysical variables for tolerant northernhardwoods (Lim et al. 2001, 2002, 2003; Todd et al. 2003, Limand Treitz 2004), boreal mixedwoods (Thomas et al. 2006,2008) and conifer plantations (Chasmer et al. 2006). Otherinternational studies have also clearly demonstrated the appli-cation of LiDAR to forest inventory (Nilsson 1996; Lefsky etal. 1999a, b; Means et al. 1999; Holmgren 2003; Gobakkenand Næsset 2004; 2007; Hyyppä et al. 2004; Næsset 2004b;Bollandsås and Næsset 2007; Breidenbach et al. 2007;Stephens et al. 2007).

The objective of this study was to explore the utility of air-borne LiDAR data to estimate stand-level forest variables,which included stand top height (TOPHT), average height(AVGHT), stem density (DENSITY), quadratic mean diame-ter (QMDBH), basal area (SUMBA), and gross total volume(SUMGTV), for Great Lakes – St. Lawrence forest specieswith the goal of implementing these methods in operationalinventories. This study is unique in comparison to previousstudies in that it considers stands that have undergone variousranges of partial harvesting, which comprise much of the for-est management activities for the Great Lakes – St. Lawrenceforest, or initial spacing treatments, and are distributed acrossmultiple geographic sites.

Material and MethodsStudy areaThe study area consisted of multiple research forest sitesthroughout central Ontario with the 2 primary sites consistingof the Swan Lake and Petawawa Research Forests (Fig. 1).Additional research plots, which were located in the NipissingForest, are representative of other Great Lakes – St. Lawrenceforest types and silvicultural systems of central Ontario (Fig. 1).

Swan Lake Research Forest (SLRF)The Swan Lake Research Forest is located 250 km north ofToronto and east of Huntsville, Ontario, within AlgonquinProvincial Park. The 2000-ha site situated in Peck Townshipis located at 45° 28′ N, 78° 45′ W and ranges in elevation from412 m to 587 m above sea level (asl). This site lies on the Pre-cambrian Shield and is characterized by rolling hills and highrocky ridges that are separated by valleys scoured by glacia-tion. Outwash flats, ablation moraines, and drumlinoiddeposits provide soil deposits ranging from coarse to mediumtexture. The Algonquin Dome, due to its elevation, has a cli-mate that is generally cooler and wetter than its surroundingareas (Cole and Mallory 2005).

The site is within the Great Lakes – St. Lawrence ForestRegion and comprises mature stands of shade- and mid-

tolerant hardwoods (sugar maple [Acer saccharum Marsh.],American beech [Fagus grandifolia Ehrh.], soft maple [Acerrubrum L.], yellow birch [Betula alleghaniensis Britt.], iron-wood [Ostrya virginiana (Mill.) K. Koch]), conifers (easternhemlock [Tsuga canadensis (L.) Carrière], white pine [Pinusstrobus L.], white spruce [Picea glauca (Moench) Voss], redspruce [Picea rubens Sarg.], eastern larch [Larix laricina (DuRoi) K. Koch], eastern white cedar [Thuja occidentalis L.],balsam fir [Abies balsamea (L.) Mill.]), and minor propor-tions of mid-tolerant and intolerant hardwoods (i.e., whitebirch [Betula papyrifera Marsh.], black cherry [Prunusserotina Ehrh.], white ash [Fraxinus americana L.], black ash[Fraxinus nigra Marsh.], and trembling aspen [Populustremuloides Michx.]).

Petawawa Research Forest (PRF)The Petawawa Research Forest (PRF) is located approxi-mately 200 km west of Ottawa and 180 km east of NorthBay, just east of Chalk River, Ontario (46° 00′ N, 77° 26′ W).The research forest encompasses 10 000 ha of mixed maturenatural and plantation forest that is representative of the GreatLakes – St. Lawrence Forest Region and is characterized byeastern white pine, red pine, trembling aspen, and whitebirch. Red oak (Quercus rubra L.) dominates many poor, drysoils. Boreal forest species from the north and shade-toleranthardwoods from the south exist on suitable sites.

PRF lies on the southern edge of the Precambrian Shieldwith its topography strongly influenced by glaciation andpost-glacial outwashing. There are 3 types of terrains charac-terizing the site including extensive sand plains of mostlydeltaic origin; imposing hills, shallow, sandy soils, andbedrock outcrops; and gently rolling hills with moderatelydeep, loamy sand containing numerous boulders. Elevationsrange from 140 to greater than 280 m asl within the forest.Mean annual precipitation for the research forest is around 82cm per year. Approximately 25% of the precipitation falls assnow. The mean annual temperature is 4.4°C. The area aver-ages 136 growing season days with an average of 100 daysbeing frost-free.

Nipissing Forest (NF)Nipissing Forest is an actively managed forest in CentralOntario. The Crown-managed forested area of 621 000 ha iscentered on North Bay, Ontario (46° 18′ N, 79°27′ W). Theforest is characterized as one of transition between the GreatLakes – St. Lawrence Forest Region and the Boreal ForestRegion to the north. The main forest species include whitepine, red pine, sugar maple, soft maple, red oak, yellow birch,trembling aspen and balsam fir.

Field dataGround reference data were collected for the 3 study sites dur-ing the period of July 2005 and August 2006. Aside from estab-lishing new plots for measurements, existing research plotswere also used, which resulted in a network of plots that var-ied in shape (i.e., circular, square, and rectangular) and area(Table 1). The minimum plot area was 400 m2. Conversely,there were a few large plots that ranged from 0.1 to 0.5 ha.

Each plot had all trees larger than or equal to 10 cm meas-ured for diameter at breast height (DBH) with a diametertape. Each tree was assessed for species, status (live or dead),crown class (dominant, co-dominant, etc.) and visual quality.

828 NOVEMBRE/DÉCEMBRE 2008, VOL. 84, No 6 — THE FORESTRY CHRONICLE

NOVEMBER/DECEMBER 2008, VOL. 84, NO. 6 — THE FORESTRY CHRONICLE 829

Fig. 1. Project study areas in Ontario.

Table 1. Field plots by research site and forest type

Natural Natural Plantation Research Site Plot area (m2) hardwoods conifers conifers Total

Swan Lake Research Forest 400 12 4 1 17800 6 – – 6

1000 4 – – 4

Subtotal 22 4 1 27

Petawawa Research Forest 400 9 15 18 42506 – – 1 1675 – – 1 1

1000 – 1 4 51012 – – 2 21350 – – 1 12500 – 8 – 6

Subtotal 9 24 27 60

Nipissing Forest 400 6 3 – –1000 9 – – –

Subtotal 15 3 – 18

Total 46 31 28 105

A Vertex™ hypsometer was used to measure height to base oflive crown and total tree height for every tree. Heights ofhardwood species were measured in the leaf-off period dur-ing fall 2005 and spring 2006.

The centre of each circular plot or corner post of eachsquare or rectangular plot was geo-referenced with a TrimblePro XT™ kinematic GPS unit connected to a Hurricane™antenna, which was mounted on a tripod (Fig. 2). A mini-mum of 300 points was collected for each post position andlater post-processed against a base station to achieve sub-meter accuracy. In cases where not all corner posts could begeo-referenced with GPS due to dense overhead canopy lim-iting the incoming signal, a compass was used to sightbetween plot posts to measure the bearing of the plot line anda fibreglass tape used to measure plot size.

The 3 research forests chosen for this study offered differ-ent forest ecosystems and silvicultural systems from which tosample and predict forest variables. An effort was made tosample extreme differences in density or basal area conditionsin order to test the capability of LiDAR to penetrate the asso-ciated canopy conditions and its potential to model theseranges of density and basal area conditions.

SLRF offered tolerant hardwood forest conditions fromno-harvest (i.e., natural old-growth areas) to stands that hadundergone silvicultural treatment using single-tree selection

methods. Additional conifer plots were also establishedwithin the SLRF.

The PRF offered plantation, natural unharvested, and sil-viculturally treated conifer stands. Plantations of differentspecies and initial planting densities, along with natural standcontrols and white and red pine stands treated with the uni-form shelterwood system were sampled.

Three different site conditions were sampled within NFincluding: (i) the Olrig site consisting of young yellow birchstands exhibiting a range of residual basal area conditions; (ii)the Phelps site consisting of an unharvested red oak conditionand a red oak uniform shelterwood treatment area; and (iii)natural white pine conditions at Samuel de ChamplainProvincial Park.

The plot data were pooled for the 3 research sites, strati-fied, and analyzed according to 3 different forest speciesgroups that included: (i) natural hardwoods, (ii) naturalconifers; and (iii) plantation conifers. These coarse groupingswere based primarily on species crown similarity (i.e., ran-dom oval, random conical, and orderly conical) with theassumption that LiDAR pulses would intercept each group ina unique way. Species statistics for these groupings are pre-sented in Table 2. Plot data consisting of individual tree datawere compiled to per hectare (ha) values using equations pre-sented in Table 3.

830 NOVEMBRE/DÉCEMBRE 2008, VOL. 84, No 6 — THE FORESTRY CHRONICLE

Fig. 2. Acquiring sub-metre plot centre position.

NOVEMBER/DECEMBER 2008, VOL. 84, NO. 6 — THE FORESTRY CHRONICLE 831

Tabl

e2.

Fiel

dda

tast

atis

tics

byfo

rest

spec

ies

grou

p

Nat

ural

hard

woo

ds

Top

heig

ht(m

)D

ensit

y(s

tem

s/ha

)Ba

sala

rea

(m2 /h

a)G

ross

tota

lvol

ume

(m3 /h

a)

Lead

ing

spec

ies

NM

ean

Min

Max

Std

Dev

Mea

nM

inM

axSt

dD

evM

ean

Min

Max

Std

Dev

Mea

nM

inM

axSt

dD

ev

Suga

rMap

le27

24.1

16.8

27.3

2.9

389.

220

0.0

630.

010

3.0

22.3

11.6

36.1

6.9

201.

576

.634

1.1

72.4

Yello

wBi

rch

918

.915

.825

.23.

241

7.8

340.

053

0.0

69.4

11.1

6.1

18.8

4.5

84.0

40.1

166.

246

.4Re

dO

ak3

24.7

23.4

25.7

1.2

275.

075

.060

0.0

284.

016

.85.

535

.616

.415

5.3

52.7

319.

714

3.9

Trem

blin

gA

spen

525

.120

.728

.33.

692

0.0

525.

014

75.0

359.

024

.417

.628

.84.

423

4.2

144.

927

4.1

52.7

Am

eric

anBe

ech

125

.9–

––

425.

0–

––

23.1

––

–21

8.0

––

–W

hite

Birc

h1

23.0

––

–52

5.0

––

–25

.4–

––

210.

7–

––

All

4623

.215

.828

.33.

544

8.8

75.0

1475

.022

6.2

20.1

5.5

36.1

8.2

179.

640

.134

1.1

84.4

Nat

ural

coni

fers

Top

heig

ht(m

)D

ensit

y(s

tem

s/ha

)Ba

sala

rea

(m2 /h

a)G

ross

tota

lvol

ume

(m3 /h

a)

Lead

ing

spec

ies

NM

ean

Min

Max

Std

Dev

Mea

nM

inM

axSt

dD

evM

ean

Min

Max

Std

Dev

Mea

nM

inM

axSt

dD

ev

Red

Pine

1128

.322

.433

.23.

432

5.0

68.0

775.

024

5.1

32.5

13.1

60.3

14.8

368.

316

5.3

724.

117

2.7

Whi

tePi

ne9

28.5

21.4

34.1

3.8

442.

120

.085

0.0

291.

730

.65.

048

.314

.633

4.1

66.1

625.

217

3.0

E.H

emlo

ck4

25.2

21.4

28.3

2.9

431.

375

.075

0.0

294.

733

.320

.251

.413

.330

3.7

172.

449

8.8

147.

0Bl

ack

Spru

ce2

22.5

22.1

23.0

0.6

787.

550

0.0

1075

.040

6.6

25.5

19.6

31.4

8.4

208.

015

8.6

257.

569

.9Ba

lsam

Fir

216

.313

.319

.34.

211

02.5

730.

014

75.0

526.

820

.516

.324

.75.

912

5.1

117.

713

2.5

10.5

E.W

hite

Ced

ar2

22.6

22.0

23.2

0.8

662.

555

0.0

775.

015

9.1

39.5

26.2

52.8

18.8

301.

419

1.7

411.

015

5.1

Jack

Pine

124

.2–

––

350.

0–

––

19.9

––

–19

4.0

––

–

All

3126

.313

.334

.14.

547

4.5

20.0

1475

.033

3.8

30.9

5.0

60.3

13.5

314.

166

.172

4.1

160.

9

Con

iferp

lant

atio

ns

Top

heig

ht(m

)D

ensit

y(s

tem

s/ha

)Ba

sala

rea

(m2 /h

a)G

ross

tota

lvol

ume

(m3 /h

a)

Lead

ing

spec

ies

NM

ean

Min

Max

Std

Dev

Mea

nM

inM

axSt

dD

evM

ean

Min

Max

Std

Dev

Mea

nM

inM

axSt

dD

ev

Larc

h2

25.8

22.8

28.8

4.2

507.

534

0.0

675.

023

6.9

29.5

28.5

30.6

1.5

275.

324

0.2

310.

449

.7Ja

ckPi

ne5

15.0

10.3

21.7

5.4

739.

832

0.0

1200

.042

5.8

16.0

6.6

25.1

8.2

109.

734

.521

2.6

84.8

Red

Pine

328

.227

.728

.90.

611

08.7

742.

015

02.0

380.

767

.966

.669

.91.

878

6.9

764.

480

3.0

20.1

Blac

kSp

ruce

414

.612

.716

.42.

014

81.3

1050

.019

00.0

350.

825

.916

.130

.76.

614

9.4

76.7

193.

352

.6Re

dSp

ruce

216

.615

.417

.81.

711

37.5

1125

.011

50.0

17.7

37.0

26.2

47.8

15.2

264.

316

8.9

359.

813

5.0

Whi

teSp

ruce

1217

.910

.825

.23.

210

75.0

340.

027

00.0

648.

630

.017

.144

.28.

619

8.3

87.6

292.

568

.7

All

2818

.510

.328

.95.

410

40.7

320.

027

00.0

541.

431

.46.

669

.915

.924

8.8

34.5

803.

020

6.2

LiDAR dataLiDAR data were collected in September 2005 using anupgraded Leica ALS40 airborne laser scanner mounted in aKing Air 90 aircraft. The base mission was flown at 9000 feetwith a 20° field of view, scan rate of 30 Hz, and a maximumpulse repetition frequency of 32 300 Hz. This configurationresulted in a cross track spacing of 2.87 m, an along-trackspacing of 2.4 m, an average sampling density of 0.46 pointsm-2, and a swath width of approximately 1 km. The LiDARpoint cloud data were classified as ground or vegetation by thevendor using proprietary algorithms. LiDAR returns thatwere classified as ground were normalized to the terrain usinga Triangulated Irregular Network (TIN). For each return clas-sified as vegetation, the z-value on the TIN matching its x–ycoordinate was subtracted from the return’s z-value resultingin a normalized height measure (metres above ground).These normalized data were in turn used to generate variousLiDAR-based statistical, canopy height, and canopy densitypredictors

LiDAR-based predictorsThree types of predictors, which included statistical, canopyheight, and canopy density predictors, were derived from allLiDAR returns (i.e., classified ground and vegetation returns).No height threshold was used to filter any of the point data.The statistical group of predictors included mean height andstandard deviation, absolute deviation, skew, and kurtosis ofthe distribution of LiDAR height measurements. The canopyheight predictors consisted of deciles of LiDAR canopy height(i.e., p1 … p9; with p1 and p9 corresponding to the 1st and 9th

deciles, respectively) and the maximum LiDAR height. Adecile is any of the 9 values that divide sorted data into 10equal parts with each part representing 1/10th of the sampleor population. For example, the 5th decile, also referred to asthe 50th percentile, 2nd quartile, or median, of LiDAR canopyheight would correspond to the height value where 50% of theobservations are found below and above it.

Eleven canopy density metrics were derived. For each plot,the range of LiDAR height measurements was divided into 10equal intervals and the cumulative proportion of LiDAR

returns found in each interval, starting from the lowest inter-val (i.e., d1), was calculated. Since the last interval always sumto a cumulative probability of 1, it was excluded resulting in 9 canopy density metrics (i.e., d1 … d9). The remaining 2 canopy density metrics were calculated as the proportion offirst returns divided by all returns intersecting a sample plot(Da) and the proportion of first returns classified as vegeta-tion (i.e., non-ground) divided by all returns intersecting a sample plot (Db).

Statistical analysesBest subsets regression, a model-building technique thatidentifies subsets of variables that best predict responses on adependent variable by linear or non-linear regression, wasused in this study. For each forest variable, the 4 best modelswere identified for models that were based on 1 up to 10 pre-dictors. For example, for a model based on 5 predictors, the 4“best” predictors were identified and assessed.

A diagnosis of each model was performed to determine ifparametric statistical assumptions were satisfied. TheShapiro–Wilk’s W Test was used to determine if residualswere normally distributed, whereas the Modified Levene’sTest was used to check for the presence of heteroschedasticity(i.e., unequal error variance). In many instances, dependentvariables were transformed using a natural log transforma-tion in order to satisfy these assumptions. Back transforma-tions were based on the method described by Baskerville(1972) where 1/2 of the squared residual standard error isadded to the estimate before taking the inverse log.

As LiDAR predictors have been reported to be highly cor-related, the variance inflation factors (VIF) for the predictorsused in a model were examined (Neter et al. 1996). Candidatemodels where predictors exhibited VIF greater than 10 werediscarded, as values above 10 suggest the presence of multi-collinearity in the predictor data (Neter et al. 1996). The finalmodels (Table 4), in addition to the individual predictors usedin each model, were tested at the 0.05 significance level.

The cross-validation prediction of sum of squares (PRESS)procedure (Myers 1986) was used to validate the models, sincenot enough observations were available to permit the splitting

832 NOVEMBRE/DÉCEMBRE 2008, VOL. 84, No 6 — THE FORESTRY CHRONICLE

Table 3. Ground metrics calculated from field data

Ground metric Description

TOPHT (m) Calculated as the average of the largest 100 stems per hectare

AVGHT (m) Calculated as the average height of all trees 10.0cm and larger.

DENSITY (stems ha-1) Number of live trees 10.0cm and larger expressed per hectare

QMDBH (cm) where n is stems per plot

SUMBA (m2 ha-1) DBH2 * .00007854 Per hectare value calculated by summing each tree per plot.

SUMGTV (m3 ha-1) = ß1 * DBH2*(1-0.04365* ß2)2/( ß3+(0.3048 * ß4/Ht))(Honer et al. 1983) Individual tree volume equation.

Coefficients varies by species Per hectare value calculated by summing each tree per plot.

NOVEMBER/DECEMBER 2008, VOL. 84, NO. 6 — THE FORESTRY CHRONICLE 833

Tabl

e4.

Mod

elre

sults

for

the

natu

ralh

ardw

oods

,nat

ural

coni

fers

and

plan

tatio

nco

nife

rsfo

rest

grou

ping

Shap

iro–

Wilk

’sM

odifi

edLe

vene

’sTe

stTe

stPR

ESS

RM

SER

MSE

Vari

able

Equa

tion

R2

R2 (a

dj)

p(%

)W

pt L

p(%

)N

atur

alha

rdw

oods

SUM

BASU

MBA

=69

.0-3

.88

abs_

dev

-65.

0D

a+

1.51

p70

+29

.7d6

-25.

2d8

0.82

0.80

<0.

001

3.46

0.98

0.74

0.12

0.90

3.99

(m2

ha-1

)(1

7.2)

(19.

9)SU

MG

TVln

(SU

MG

TV)=

6.56

-0.1

56ab

s_de

v-3

.44

Da

+0.

128

p70

+1.

85d7

-1.9

0d8

0.90

0.89

<0.

001

39.3

50.

970.

251.

540.

1352

.03

(m3

ha-1

)(2

1.9)

(29.

0)D

ENSI

TYln

(DEN

SITY

)=4.

22-3

.65

Da

+5.

57D

b-0

.036

3p7

0+

3.04

d1-2

.27

d40.

770.

74<

0.00

119

6.03

0.97

0.38

1.81

0.08

214.

98(s

tem

sha-1

)(4

3.7)

(47.

9)Q

MD

BHln

(QM

DBH

)=2.

93-0

.141

abs_

dev

-1.3

5D

b+

0.10

1p7

0+

1.58

d50.

820.

80<

0.00

13.

070.

970.

290.

020.

994.

17(c

m)

(12.

4)(1

6.8)

AVG

HT

AVG

HT

=2.

41+

1.18

std_d

ev-1

.91

skew

-0.3

63p6

0+

0.73

8p7

00.

870.

86<

0.00

11.

100.

960.

121.

600.

121.

25(m

)(5

.7)

(6.4

)TO

PHT

ln(T

OPH

T)=

2.13

+0.

0242

p70

+0.

0225

max

+0.

191

d40.

960.

96<

0.00

10.

800.

970.

220.

110.

920.

89(m

)(3

.5)

(3.8

)N

atur

alco

nife

rsSU

MBA

ln(S

UM

BA)=

2.17

+0.

0576

p50

+0.

0859

p80

-0.0

887

max

+1.

22d8

0.82

0.80

<0.

001

7.23

0.97

0.54

0.74

0.47

11.4

6(m

2ha

-1)

(23.

4)(3

7.1)

SUM

GTV

ln(S

UM

GTV

)=2.

63+

0.17

5ab

s_de

v-0

.466

skew

+1.

74D

b0.

830.

81<

0.00

172

.96

0.97

0.64

0.73

0.47

106.

84(m

3ha

-1)

(23.

2)(3

4.0)

DEN

SITY

ln(D

ENSI

TY)=

8.54

+0.

250

abs_

dev

+0.

0783

p50

-0.2

11m

ax0.

740.

71<

0.00

122

2.27

0.99

0.94

0.17

0.87

611.

10(s

tem

sha-1

)(4

6.8)

(128

.6)

QM

DBH

ln(Q

MD

BH)=

2.27

+0.

207

mea

n+

0.28

7sk

ew-0

.091

9p5

00.

710.

68<

0.00

16.

930.

980.

880.

090.

9310

.51

(cm

)(2

0.1)

(30.

5)AV

GH

TAV

GH

T=

13.4

-0.5

46p5

0+

1.01

max

-15.

6d7

0.78

0.76

<0.

001

2.54

0.96

0.24

0.70

0.49

2.85

(m)

(11.

5)(1

2.9)

TOPH

TTO

PHT

=18

.8+

0.10

4p5

0+

0.75

1m

ax-1

4.5

d90.

960.

96<

0.00

10.

890.

940.

110.

950.

350.

99(m

)(3

.4)

(3.8

)Pl

anta

tion

coni

fers

SUM

BAln

(SU

MBA

)=1.

95+

0.11

5p4

0-1

.81

d4+

1.42

d70.

870.

85<

0.00

15.

330.

970.

650.

490.

637.

46(m

2ha

-1)

(17.

0)(2

3.7)

SUM

GTV

ln(S

UM

GTV

)=2.

28-0

.467

skew

+0.

156

p50

+1.

66d7

0.92

0.91

<0.

001

40.1

80.

990.

960.

200.

8459

.69

(m3

ha-1

)(1

6.2)

(24.

0)D

ENSI

TYln

(DEN

SITY

)=6.

82+

0.48

4std

_dev

+0.

173

p30

-0.2

14m

ax0.

760.

73<

0.00

125

7.08

0.98

0.79

0.82

0.42

486.

99(s

tem

sha-1

)(2

4.7)

(46.

8)Q

MD

BHln

(QM

DBH

)=0.

259

+1.

23D

a-0

.033

6p3

0+

0.06

00m

ax+

1.02

d90.

860.

83<

0.00

12.

340.

930.

070.

740.

473.

17(c

m)

(11.

4)(1

5.4)

AVG

HT

AVG

HT

=3.

97+

0.38

8ku

rtos

is-0

.294

p30

+0.

950

p90

0.98

0.98

<0.

001

0.59

0.96

0.36

0.12

0.90

0.71

(m)

(3.7

)(4

.5)

TOPH

TTO

PHT

=4.

27+

0.97

7p9

00.

980.

98<

0.00

10.

.65

0.97

0.60

1.03

0.31

0.75

(m)

(3.5

)(4

.1)

of the data into separate model development and validationdatasets. This approach to model validation is similar to apply-ing the equation to an independent sample because the PRESSresidual is obtained for the observations that are not includedin the data when the equation is derived (Sun et al. 2003).

The procedure for calculation of the PRESS statistic isundertaken by: (1) fitting a regression model through the dataminus 1 observation, 2) obtaining the predicted value of theexcluded observation, 3) calculating the residual for the pre-dicted value (observed–predicted), 4) repeating steps 1 to 3for the remaining observations, 5) calculating the sum ofsquares of all residuals, and 6) deriving the PRESS statistic,herein referred to as the PRESS RMSE, by calculating thesquare root of the sum of squares of the residuals divided bythe total number of observations (Myers 1986).

Results and DiscussionResults indicate that LiDAR statistically based, canopy height,and density predictors are suitable predictors of stand levelvariables for enhanced inventory development for forestgroupings within the Great Lakes – St. Lawrence forest (Fig.3–8 and Table 4). In addition, it appears that adequate modelscan be developed from plot data covering a range of silvicul-tural treatments and spanning large geographies even whenlow sampling density LiDAR data (i.e., 0.5 hits m-2) are used.

An evaluation of low-density to high-density LiDAR datafor the prediction of boreal mixedwood stand attributes wasreported by Thomas et al. (2006). Results of the validationefforts concluded that low- and high-density LiDAR modelswere highly correlated with key forest structural attributes,mean dominant height, basal area, and average abovegroundbiomass (low density: R2 = 0.90, 0.91, and 0.92; and high den-sity: R2 = 0.84, 0.89, and 0.91). Næsset (2004c) also found thatLiDAR density, as a function of flying height, had no statisti-cal significance on the prediction of biophysical stand charac-teristics derived from regression equations.

The broad species models developed for this study identifythe potential for further refinement of model predictionsbased on more rigorous stratification and field sampling. Theresults reported here are based on field data that were pooledfrom across many geographic sites into strata arranged bygeneral species crown shapes. Field data were collected acrosslarge gradients of age, height, basal area, density, species, andsilvicultural treatment to identify the capability of LiDAR topenetrate various crown closure levels and to determine thesuccess of generalized forest variable predictive models.Operational application of LiDAR for forest inventory wouldinvolve more rigorous stratification of field sampling effortswithin a single forest being investigated (Næsset 2004a). As aresult, it is assumed that model predictions presented belowcould be further improved within an operational inventorycontext.

Top height and average heightSimple predictive models for TOPHT (i.e., the height of thelargest 100 trees ha-1) were developed for each of the 3 forestgroupings. The TOPHT model for all groupings performedvery well and as anticipated given that LiDAR pulses firstintercept the top (or near the top) of crowns within a plot(Table 4; Fig. 3). The coefficients of determination (R2) fornatural hardwoods and natural conifers were 0.96, whereas a

value of 0.98 was obtained for plantation conifers. The rangeof root mean square error (RMSE) values across all forestgroupings ranged from 0.70 m to 0.89 m (3%–4%). Theresults reported here are consistent with those that have beenreported in the literature (e.g., Lim et al. 2003, Holmgren andJonsson 2004, Næsset 2004a, Rooker Jensen et al. 2006,Thomas et al. 2006).

The larger error in the prediction of TOPHT for the natu-ral conifer grouping (i.e., RMSE = 0.89) is assumed to be dueto the fact that TOPHT was calculated from field plot data instands that had undergone a uniform shelterwood silviculturaltreatment. TOPHT calculated from field data biased theexpression of TOPHT by utilizing the largest trees that wereleft on site to be a residual seed source and as such, werespaced around the experimental block. In some cases, largetrees were removed for the purpose of crown spacing, result-ing in smaller trees being used to calculate an average TOPHT.In general, TOPHT was over-estimated on these sites.

The prediction of AVGHT was generally poorer than thatfor TOPHT (i.e., R2 values for natural hardwoods, naturalconifers, and plantation conifers were 0.87, 0.78, and 0.98,respectively) (Table 4; Fig. 4). In many respects, these resultsare expected given the variability in vertical structure charac-terizing the various forest groups considered. The exception isconifer plantations where the RMSE for the prediction ofAVGHT is comparable to TOPHT (0.59 m and 0.65 m,respectively). Conifer plantations, differing from the otherspecies groups investigated, have a simple single-tier verticalstructure profile. The natural hardwood and natural coniferconditions sampled in this study have a multi-tier structureprofile owing to their natural adaptive recruitment strategy(i.e., gap phase replacement in a tolerant hardwood standdeveloping a mixed-age and height cohort) or their humanmanipulated structure from silvicultural activities (i.e., single-tree selection or uniform shelterwood treatments). The rela-tively low LiDAR sampling density (Fig. 9) may also havecontributed to the poorer performance of this model giventhat there are fewer ground samples in stands with mixed-species, mixed-height structures (Thomas et al. 2006).

Although larger than the RMSE values reported forTOPHT, the reported RMSE values for AVGHT predictionswe are still deemed acceptable for stand inventory purposes.The reported RMSE of 1.10m (6%) for hardwoods providedsan indication of the range of vertical structure found nor-mally in these multi-tiered unenven-aged stands (i.e., saplingsthrough to sawlog-sized trees). Natural conifers, weightedheavily in the dataset by the influence of 10-year, post-treat-ment white pine shelterwood plots with a large amount ofregeneration, reported a large RMSE of 2.54 m (12%). Thisresult is not surprising as these types of stand conditions(refer to Fig. 9) consist of tall overstory trees and advancedregeneration that will intercept LiDAR pulses. Conifer plan-tations reported the lowest RMSE of 0.59 m (4%) as expectedwith their simpler canopy structure. Researchers from otherjurisdictions have reported similar RMSE values for averageheight model predictions (Holmgren 2003, Holmgren andJonsson 2004, Næsset 2004a).

Stocking (basal area and density)The prediction of stand stocking attributes (i.e., density andbasal area) based on LiDAR predictors has proven more dif-

834 NOVEMBRE/DÉCEMBRE 2008, VOL. 84, No 6 — THE FORESTRY CHRONICLE

NOVEMBER/DECEMBER 2008, VOL. 84, NO. 6 — THE FORESTRY CHRONICLE 835

Fig. 3. Top height (TOPHT) field observed values vs. predictedmodel values for the natural hardwoods, natural conifers andplantation conifers forest groupings.

Fig. 6. Density (number of trees) field observed values vs. pre-dicted model values for the natural hardwoods, natural conifersand plantation conifers forest groupings.

Fig. 4. Average height (AVGHT) field observed values vs. pre-dicted model values for the natural hardwoods, natural conifersand plantation conifers forest groupings.

Fig. 7. Volume (SUMGTV) field observed values vs. predictedmodel values for the natural hardwoods, natural conifers andplantation conifers forest groupings.

Fig. 5. Basal area (SUMBA) field observed values vs. predictedmodel values for the natural hardwoods, natural conifers andplantation conifers forest groupings.

Fig. 8. Quadratic mean diameter (QMDBH) field observed valuesvs. predicted model values for the natural hardwoods, naturalconifers and plantation conifers forest groupings.

ficult than predicting height metrics (Stephens et al. 2007).Basal area models developed for this study exhibit R2 valuesof 0.80, 0.79, and 0.85 with associated RMSE values of 3.46 m2

ha-1 (17%); 7.23 m2 ha-1 ( 23%); and 5.33 m2 ha-1 (17%) fornatural hardwoods, natural conifers, and conifer plantations,respectively (Table 4; Fig. 5). These values fall within therange of RMSE values reported by other authors, such as

Drake et al. (2002) (7.15 – 7.88 m2ha-1), Holmgren (2003)(4.8 m2 ha-1), Holmgren and Jonsson (2004) (3.0 m2 ha-1),Næsset (2004a) (2.38 – 4.88 m2 ha-1), Rooker Jensen et al.(2006) (3.1 m2 ha-1), and Stephens et al. (2007) (8.0 m2 ha-1).

Many forest management activities are driven by knowl-edge of stand basal area. These include the selection of anappropriate silvicultural system in combination with a pre-

836 NOVEMBRE/DÉCEMBRE 2008, VOL. 84, No 6 — THE FORESTRY CHRONICLE

Fig. 9. Comparison of raw LiDAR hits of different densities for various forest stand conditions. Green dots indicate classified vegetationhits. Purple dots indicate classified ground hits.

Natural tolerant hardwood Natural conifer shelterwood Conifer plantation

Photographic image

LiDAR density of 0.5 hits/m2

LiDAR density of 3 hits/m2

scribed thinning regime development. The performance of thebasal area model may be a function of the broad speciesgroupings combined with the wide range of stand spacing andtreatments sampled. The hardwood grouping includes toler-ant hardwood conditions with a wide range of basal area con-ditions along with varied structures (i.e., managed to oldgrowth). Many of the stands sampled were uneven-aged andconsisted of a wide range of size classes. This grouping alsoincluded mid-tolerant hardwood plots (i.e., red oak and yellowbirch) some of which had recently undergone spacing anduniform shelterwood treatments within 2 years of the LiDARacquisition. Plots dominated by intolerant trembling aspenand white birch species were also included in this grouping.Although the crown shapes of these species are consideredsimilar (i.e., random oval), measurable stand attributes, suchas basal area, diameter distribution and stand density, can bevery different for these tolerant, mid- and intolerant speciesgroups. These intolerant stands tend to exhibit a normal distri-bution of stem sizes versus the inverse J-shaped curve of sizeclasses commonly associated with tolerant species. As a result,variable potential for low- and mid-storey stems to be sampledby LiDAR pulses in the tolerant species plots may be causingdifferent patterns than found in the intolerant-dominatedspecies plots with no significant understory.

Whereas volume predictions have been successful in anumber of studies, prediction of stem density has been shownto be more problematic (Maltamo et al. 2004). The reason forthe discrepancy between volume and stem density predictionhas been attributed to the fact that the majority of the volumeis accounted for in the dominant tree layer (Vuokila 1980;from Maltamo et al. 2004), which accounts for the dominantcomponent of the LiDAR data distribution. In this study, pre-diction of stem density from LiDAR predictors was the leastsuccessful application. RMSE values ranged from 196 stemsha-1 (44%) for hardwoods, 222 stems ha-1 (47%) for naturalconifers, and 257 stems ha-1 (25%) for plantation conifers(Table 4; Fig. 6).

Maltamo et al. (2003) addressed the problem of estimatingstem density by calibrating the estimates using theoreticaldiameter distributions to describe small trees. However, thismodification for estimating stem density was applied to high-resolution optical and LiDAR data in a single-tree approach.Here, with the application of low-sampling-density LiDARdata, a large RMSE for the natural hardwoods group may bea result of the inclusion of trembling aspen plots. These plotsexhibit densities uncommon for the tolerant and mid-tolerantspecies comprising the rest of the grouping, perhaps furtherbiasing the predictive model. A potential reason for the natu-ral conifer model results may be the excessive variation inspecies and/or vertical crown distribution. Many of the plotshad been silviculturally treated and now have a dense under-story of regeneration present in the plots. Their associatedLiDAR canopy height and canopy density predictors alongwith unharvested plot conditions may have caused noise inthe model development. It is anticipated that model perform-ance could be improved given more dense LiDAR point data(i.e., higher sampling point density).

VolumeVolume estimation for forest stands is a critical piece of infor-mation required for strategic and operational modelling ofwood supply. Predictions of gross total volume resulted in

RMSE values of 39.4 m3 ha-1 (22%), 73.0 m3 ha-1 (23%), 40.2m3 ha-1 (16%) for natural hardwoods, natural conifers, andplantation conifers, respectively (Table 4; Fig. 7). The R2 val-ues for the natural hardwoods, natural conifers, and planta-tions conifers were 0.90, 0.83, and 0.92, respectively. Theseresults are in agreement with those reported by others (Holm-gren 2003 [55 m3 ha-1], Holmgren and Jonsson 2004 [28 m3

ha-1], Næsset 2004a [13.9 – 45.9 m3 ha-1], Rooker Jensen et al.2006 [23.7 m3 ha-1]).

Quadratic mean diameterIn addition to basal area and volume, knowledge of a standsQMDBH (cm) provides key information to forest plannersand operational forest managers as it relates directly to hori-zontal structure for habitat, expected product size distribu-tions and associated harvesting efficiencies. Favourableresults from this study (RMSE values of 3.1 cm (12%), 6.9 cm(20%), and 2.3 cm (11%) for natural hardwoods, naturalconifers and plantation conifers, respectively) supportLiDAR’s predictive ability to enhance inventories with keyattributes not normally found in current inventories (Table 4;Fig. 8). Results from other studies support the ability ofLiDAR to predict QMDBH within this range (Drake et al.2002 (RMSE = 3.74 cm to 3.84 cm), Holmgren and Jonsson2004 (RMSE = 1.9 cm), Rooker Jensen et al. 2006 (RMSE =9.3 cm)). As identified earlier in the discussion of the otherpredicted forest variables, a more refined stratification andmodest increase in LiDAR density are expected to reduce theRMSE values presented in this study.

ValidationAs expected, the model validation resulted in an increase inthe resultant PRESS RMSE values when compared to themodel RMSE values (Table 4). Not surprisingly, only minordifferences were found through the validation of the heightestimation model for all forest groupings. Generally, the nat-ural hardwood model validation effort demonstrated reason-able stability in each of the derived models. The exception tothis is the density model in the hardwoods and also in theother forest groupings. This result is not unexpected as thisequation represented the poorest model fits of this study. Bet-ter estimates of density for all forest groupings may requirerefined stratification or increased LiDAR sampling densities.The natural conifer and the plantation conifer groupings val-idation results showed similar trends to those of the naturalhardwood except that larger increases in RMSE generallywere observed. These increases are a function of using broadforest groupings for model development and the extremerange of density conditions targeted for plot establishment.

ConclusionIn the past 5 years, LiDAR has moved from the research arenato operational reality in the area of forest resource inventory.LiDAR has proven an efficient and accurate means to spa-tially estimate stand height and forest structure (i.e., DEN-SITY, SUMBA, QMDBH and SUMVOL) in support of statis-tically based model predictions across a broad range of foresttypes. Decreased acquisition costs, increased sampling densi-ties, and enhanced inventory variable estimation have nowmade this technology attractive to operational forest invento-ries across a range of conditions. This enhanced capacity iscritical to decision makers for sustainable forest management.

NOVEMBER/DECEMBER 2008, VOL. 84, NO. 6 — THE FORESTRY CHRONICLE 837

The results of this study clearly support the contribution ofdiscrete-return LiDAR data for the enhancement of forestinventories for species groups in the Great Lakes – St. Lawrenceforest. It has been demonstrated that low sampling densityLiDAR data (0.5 hits m-2) provide acceptable levels of accuracyfor forest level attributes such as TOPHT, AVGHT, SUMBA,SUMGTV, DENSITY, and QMDBH. In addition, the modelsand results were based on a stratification of broad forest crownshapes and field plots from multiple geographical locations.Future studies will focus on developing improved models formore precise forest groupings and identifying appropriateranges of LiDAR sampling densities to best predict this suite offorest variables.

AcknowledgementsThis study was made possible through the financial partner-ship of the Forest Research Partnership (Tembec Inc., OntarioMinistry of Natural Resources, and Canadian Forest Service)and the Enhanced Forest Science Productivity Fund. Specialthanks to Paul Courville, Dave Nesbitt, John Pineau, and KenDurst for their leadership, vision, support, and constantenthusiasm.

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