Calculation system for large-scale forest inventory

CALCULATION SYSTEM FOR LARGE-SCALE FOREST INVENTORY

KariT.

Korhonen

Metsäntutkimuslaitoksen

tiedonantoja

⁵⁰⁵

CALCULATION SYSTEM FOR LARGE-SCALE FOREST INVENTORY

Kari T. Korhonen

Metsäntutkimuslaitoksen

tiedonantoja

⁵⁰⁵

tiedonantoja

Calculationsystem for

large-scale

^forest

inventory

Kari T. Korhonen

Joensuu 1994

Korhonen, system

large-scale inventory.

Metsäntutkimuslaitoksen

tiedonantoja

^{505. The Finnish Forest Research} Institute, ^Research Papers505.36pp.ISBN951-40-1371-9,ISSN0358-4283.

Summary:

^Thispaperdescribesa calculationsystem ^for

large-scale

^forest

inventory.

^National Forest

Inventory

^datafromthe

Forestry

^{BoardDistrictofKainuuare usedfor}

demonstrating

^the calculationsystem. ^{Mixedestimationis usedfor}

estimating

^{localizedvolumes functionsfrom} the

sample

^{tree data measuredinthe}

inventory

^{anddatameasuredin} a

previous inventory.

Ordinary

^least_squares

-technique

^isusedfor

estimating growth

modelsandvolumefunctions

by

timber assortments. Estimated models and _some basic statistics calculated for the testarea are

presented.

Keywords:

^forest

inventory,

^mixedestimation, models,volume,

growth

Author'saddress: Korhonen, ^{KariT. TheFinnishForestResearch} Institute, ^{JoensuuResearch} Station, P.0.80x 68, FIN-80101 Joensuu, Finland.

Publisher:TheFinnishForestResearchInstitute,

Department

^{ofForestResources,}

project

^3001.

Accepted by:

^AameReunala,

professor,

^24.5.1994

Distributor:TheFinnishForestResearch Institute, ^{JoensuuResearch} Station, ^P.0.80x 68, ^FIN -80101 Joensuu, Finland.

Data used in this

study

were collected

by

^{the field}groups of the

project

^National Forest

Inventory

^{of Finland. Several} persons

working

^{in the same}

project

^{in the Finnish Forest} ResearchInstitutehavedonevaluableworkinfurther

processing

^{oftheHelddata.}

Especially

^the workofMr.

Alpo

^{Aarnio,Mr.ArtoAhola,Mr.Matti}

Kujala

^{andMs. HelenaMäkelähavemade} it

possible

^to carry ^out this

study.

Discussions with

people

^{mentionedaboveand with Ms.}

HelenaHenttonen,^{Mr. Antti}Ihalainen,^{Mr. Juha}

Lappi,

^{Mr. SakariSalminenand Mr. Erkki}

Tomppo

^have

helped

ⁱⁿ

solving

^several

problems

^meat

during

^{the research work. Mr. Juha}

Lappi,

^{Mr.SakariSalminenandMr.Erkki}

Tomppo

^havereadthe

manuscript

^and

given

^valuable criticalcomments. Ms.Joann_von

Weissenberg

^{hasrevisedthe}

English

^{text.Theauthorwishes}

to thankallthese

people

^{for theirefforts.}

Joensuu 1.6.1994 Kari T. Korhonen

1. BACKGROUND 8

2. MATERIAL AND METHODS 9

2.1

Study

^{material 9}

2.2Methods 11

3. DESCRIPTIONOF SYSTEM 12

3.1

Processing sample

^{treedata 12}

3.1.1Estimationofvolumes 12

3.1.2 Estimation of volume increment 13

3.2Estimationofvolumesandincrementfor

tally

^{trees 15}

3.2.1 Volume functions 15

3.2.2 Growth models 18

3.3

Generating

reports 19

4. APPLICATION OF THE SYSTEM FOR KAINUU DISTRICT 22

4.1 Estimated models 22

4.2

Examples

^{ofcalculatedresultsforKainuudistrict 23}

5. DISCUSSION 25

APPENDICES 29

Concepts

^andNotation

The

following

concepts ^relatedtothe measurementsof thefielddata_areusedinthispaper.

sample point

^{= a}

point

^wherea

relascope plot

^{is measured}

relascope plot

⁼ a set of concentric circles with each circle

having

^{a fixedradius for each}

diameter

(the

^{radiusis afunctionofthecross sectional areaofthe}

tree)

restricted

relascope plot

^=a

relascope plot having

^{amaximumradius; treeswith distancefrom}

the

sample point

greater^{thanthemaximumradiusarenot tallied}

plot

^{section=sectionof}a

plot,

^whenthe

plot

^{isnear aland-class}

boundary

plot

^{factor=relativesize of} a

plot;

^whena

plot

^{is located}neara land-class

boundary

^{and the}

center

point

^ofthe

plot

^ison

forestry

^land,the

plot

^{factorindicatesthe}

proportion

^{ofthe whole}

plot

^{circle made}

by

^the

plot

^sectionon

forestry

^land

plot

^stand=stand

containing

^{trees tallied}on a

relascope plot, usually

a

plot

^{containstrees from}

only

^onestand; delineationofstandsisbased_onthecharacteristics ofthesite andthe

growing

stock

tally

^{tree =a tree}

belonging

^{to the}

(restricted) relascope plot

sample

^{tree =a}

tally

^{tree forwhichmore detailed}measurements aretaken

timber_{tree =}

tally

tree

containing high enough

^timber

quality

^foratleastone saw

log

non-timbertree ⁼

tally

^{tree whose dimensionsand/or}

quality

^{are not}

enough

^forany ^saw

logs

The

following

^{notationsforthemost}common treeandstandvariables_are usedinthispaper.

1. BACKGROUND

In

large-scale

^forestinventories

sampling

^{methodsare usedtoobtaina}

representee sample

^of

the

population.

^Inmanycases it is_not

possible

orrational_tomeasure

directly

^{thosevariables}

that _{we are} interested in. Therefore, mathematicalmethods

(also

^{methodsotherthan}

simple

summation)

are needed_toderivethestatisticsoffinalinterestfromthecharacteristicsmeasured

forthe sample.

A

complete

calculationsystem ^of

inventory

^{resultsshouldinclude}

following

components:

1.

checking

^offielddata,

2. derivationof volumes, ^volume

growth

^{etc. for}

sample

^trees

using existing

^modelsand

measured data,

3.

generalization

^{ofvolumesandother}characteristics for

tally

trees,

4. summationofstatistics for

any chosen calculationstratum,and

5. estimationof

reliability

^{oftheresults.}

Theaimofthis

study

^wasto

develop

^a system^ofcalculationfor theNationalForest

Inventory

ofFinland(NFI).^Thesystem ^{shouldbe based}ontestedanddocumentedmethodsandshould

cover estimationof areas of different strata

(e.g.

^forest

types),

^{mean volume,}

growth

^and

percentages ^oftimber assortments. Estimationsoffuture

growth

^and

cutting possibilities

are, however,^{excludedfromthe} system. ^Norare

procedures

^for

detecting

errors inthe fielddata_nor

estimationof

sampling

^{error withinthe}scope ofthis

study.

Thecalculationsystem ^{is tested}

using

^{Kainuudistrictasa}

study

^area.

2. MATERIAL AND METHODS

2.1Studymaterial

Datafromthe7^thNationalForest

Inventory

^ofFinland

(NFI7)

^{forthe whole}countryanddata

fromtheBth8^thNationalForest

Inventory

^{ofFinland(NFI8) forKainuudistrict(see}

Fig.

^{1) were}

usedin this

study.

^{The NFI7wascarriedout}

during

^1977-1984

(Kuusela

^{& Salminen}

1991).

The NFIB data for Kainuu district were measured in 1992.

In both inventoriesthe

sampling

^methodwas

systematic

^cluster

sampling.

^{In the NFI7 the}

distance between clusters _was 8 km andeach clusterconsistedof 21

relascope plots.

^{In the}

NFIB in the Kainuu district the distance between clusters was 7 km and each cluster consisted

of15 restricted

relascope plots.

Figure

^{1. LocationofKainuudistrict.}

Inbothinventories,severalvariables

describing

^thesiteand

growing

^stockofthe

plot

^stand(s)

wererecorded. Talliedtreeswereselectedwith_a

relascope.

^{Inthe NFI7}a

relascope

^withabasal

areafactorof2was used.IntheNFIBinKainuudistrictarestricted

relascope plot

^withabasal

area factor of 1.5 and _a maximum radius of 12.45 _m was used. In both sets of data the

following

^variableswererecorded foreverytalliedtree:

tree

species

diameter

quality

^class

describing

the

quality

^ofthestem,latercalled

'tally

tree

quality

^class'

crown class.

IntheNFI7data,the

living

treesweredividedinto3

quality

^{classes: non-timber}trees

(based

^on

the dimensionsofthe stem), ^non-timbertrees(basedondefects_on thestem),^{and timbertrees.}

In theNFIBdataamoredetailedclassificationwasused todescribe,_e.g. whetheratimbertree

is of

good

^orpoor

quality.

In theNFI7,

tally

^{treesmeasuredatfour}

plots

ⁱⁿeveryclusterwere used as

sample

^trees.Inthe NFIB every7^thtalliedtree was measured _{as a}

sample

^{tree. In bothsetsofdatathe}

following

variableswere

registered

^for

sample

^trees:

height

-

age

length

^{andlocationofdifferenttimber}assortments

(=saw log quality

^{classesA,B, andC;}

pulp

wood;

cull)

diameterincrementfor thepast

5-year period

height

^{incrementforthe}past

5-year period (only

^forconifers).

Inaddition_toabovementionedvariables,diameteratsixmeters

height

^{andthicknessofbarkat}

breast

height

were

registered

^forall

sample

^{trees in the NFI7data andfor} a

sub-sample

^of

sample

^{treesin theNFIB data.}

In the NFIB dataavariablecalled

'sample

tree

quality

^class' was alsorecorded. This variable

describes the cruisers

opinion

^ofthe

quality

^{ofthe stemafter}measurementofthe

sample

^tree.

The

'tally

^tree

quality

^{class'describes thecruiser's}

opinion

^aboutthe

quality

^beforethe

sample

tree was measured. The cruiser may

change

^his

opinion

^{about the}

quality during

^detailed

examinationofthestem when

measuring

^thecharacteristicsof the

sample

^tree.

2.2 Methods

The first

phase

^{in the} calculations is to derive volume,

growth

^and percentages ^oftimber

assortments forevery

sample

tree measured.Thevolumesof the_trees were calculated

using

volumefunctionsofLaasasenaho

(1982).

^{Volumesoftimber}assortments werecalculated

using

thetaper ^{curve modelsof}Laasasenaho

(1982)

^{asa functionofd,}

d«,

^{andh.Volumeincrement}

ofthe

sample

^treeswas estimated

according

^{to themethodsdescribed}

by

^Salminen

(1978)

^and

Kujala (1980).

Regression analysis (Ordinary

^Least

Squares, OLS)

^{andmixedestimationwereusedtoestimate} thevolumeandincrementof

tally

^{trees.Mixedestimationis}

widely

^usedin

problems requiring

combinationoftwo_ormoredatasets

(Teräsvirta 1981).

^Korhonen

(1992, 1993)

^hasshownthat

mixedestimationisefficientfor

combining sample

^{treedatafromtwo} inventories.

SAS statistical software was usedfor

studying

^the

relationships

^{betweendifferentmeasured}

variables inorder to determinethe correct formof thenecessary models

(SAS

^{InstituteInc.}

1989).Theparameters^{ofthemodelswereestimatedwith}

Fortran-programs

^made

by

^theauthor.

IMSL-routines_were usedfor matrix

operations (such

as

inversion)

^{in these}programs

(IMSL

library...

^{1982). The reason for}

selecting Fortran-programs

^{instead of available} statistical software was that

Fortran-programs

^makesit

possible

^{to simulate}

sampling

^andthus test the

methodsusedinthecalculationsystem.

Fortran-programs

werealso usedtoderivethevolumes ofdifferenttimberassortments for

sample

^{trees measured.}

Volumeand

growth

^of

tally

^{trees were estimatedwith}

Fortran-programs developed by

^the

author. The treewisecharacteristics _were summed upinto statistics forthe wholecalculation

area with SAS statistical software.

3. DESCRIPTION OF THE SYSTEM

3.1

Processing sample

^treedata

3.1.1 Estimation of volumes

IntheNFIB data,^dandhwere measuredforevery

sample

^tree.

Upper

diameter,

dg,

however,

was measured

only

^fora

sub-sample

^ofthe

sample

trees. The first

phase

^inthecalculationof volumeswas toconstructmodelsfor

estimating

^the upperdiameterofall

sample

^trees

(higher

than8

meters).

^Function

(1)

was

applied

asthe model

(Kolhonen 1992)

^butwasusedinitsfull

form

only

^for

pine

^and spruce. For other

species, only

^{variables d}2,

h

2, d/t, and were

significant

regressors; therest ofthe variables_wereexcludedfromthemodel.

Theparameters^ofthemodel

(1)

^{foreach tree}

species

^{wereestimated}

using

^mixedestimation.

In the first stage ^{of theestimation}process, first-levelestimates ofparameters ^{were obtained}

using

^{NFI7dataforthewholecountry.Inthesecondstage,}second-levelestimatesofparameters

a,^-as^wereobtained

using

^{NFIBdatafromKainuudistrict(Korhonen}

1992).

^{Parametersrelated}

tothecoordinates_arenotestimetedinthesecondstage^{becausethedatameasuredinthis}stage

are

quite

^{few and}

geographically

^not

representative.

In

(dj

=ao⁺

a,*d

^{2+ a3*h2+ +a}3*ln(d6L)⁺

a«*ln(G)

^+a7

*YC+

a,*YC

²⁺

a,*XC

^+alO

*XC²+

+

a„*YC*XC,

⁽¹⁾

Whenall

sample

^{treeshavemeasuredvalues forvariablesdandh andalltrees}

higher

than 8

meters haveameasuredorestimatedvalueforvariable thestemvolume

(from

^theestimated

stump

height

^{to the} top ^{of the}

tree)

can be estimated with the functions

presented by

Laasasenaho (1982).

Estimationoftimber assortments is based on thedimensionsof thestem

(d, d«, h)

^andthe

measured

lengths

^ofdifferent

quality

^{classes. These}measurements wereusedtodividethestem

intosaw

logs

^{thatfulfilledthedimension}

(top

^diameterand

length) requirements.

^Thestemwas

divided into saw

logs by maximizing

^{the value of the stem witha}

'complete

enumeration' method.Inthismethod,^all

possible

^solutions

(combinations

^ofsaw

logs

^ofdifferent

lengths)

are testedandthe solutionthat

gives

^{thebestvalueischosen.Thistimber}

ruling

^wasmadewith

a

Fortran-program

^{in whichthedimension}

requirements (minimum

^andmaximum

lengths

^and minimumdiameters)and relativevaluesofdifferentassortments are

optional

^{parameterssothat}

they

can

easily

^be

changed.

3.1.2 Estimation of volume increment

The

sample

treevariables that_arerelatedtotheestimationof

growth

arediameterand

height

increment

during

^thepast

5-year period

^{and thickness ofthebark. Thebark is measured}

only

for_some ofthe

sample

^trees.Therefore,a

regression

^modelwas constructedfor

estimating

^the

thicknessofthebark.Function

(2)

was found_asa suitablemodelfor

pine.

where b = thickness of bark.

For other

species

a

logarithmic

^model

(Function 3)

was foundto be necessary ^to solve the

problem

^of

heteroscedasticity.

Fordecidious_treesheight^incrementwas notmeasured.Therefore,^{this variable} was estimated

b =&o+

a,*d

+

(2)

ln(b) ⁼a„+

a,*ln(d)

+

(3)

using

^{thetablesofIlvessalo}

(1948,

see

Kujala 1980),

^{in which}

height,

age,and_crown classof

the _treeare

independent

^variables.

Whenthebark modelsare estimated,each

sample

^{tree havemeasuredorestimatedvaluesfor} variablesrelatedtovolume

growth:

^diameterand

height

^{incrementandthicknessofthebark.No} characteristics _aremeasured_to

directly

^{describe the}

changes

ⁱⁿ stem formand inthicknessof

thebark

during

^thepast

5-year period.

^When

calculating

^{thevolumeincrementthese}

changes

can betakenintoaccountwiththe method

presented by

^Salminen

(1978)

^and

Kujala (1980).

^In this methodit is assumed thatthe

change

ⁱⁿ

v/gj (ratio

^{ofvolumeand cross sectional}

area)

during

^thepast

5-year period

^{canbeestimatedwith}

help

^ofafunction

(v/g,=f(h))

^{estimatedfrom}

thepresentv,g(

andhofthe trees.

Todescribe themethodofSalminen

(1978)

^and

Kujala (1980),

^{letus note that:}

r(h)

⁼afunctionthatestimates_{r asa} functionof

height,

(Vu^{istheunitvolumeof}a

sample

^{tree=volumeofthetreedivided}

by

^{itscross sectionalarea),} and

(SVu

^{is 'seedvolume'ofa}

relascope

^{tree =the volumeofthe tree 5} years agodivided

by

^its

presentcross sectional

area)

r

=v/g„

⁽⁴⁾

Vu =

v/g (5)

SVu= Vj/g (6)

Formula (6) ^{for SVu} can befurtherwritten_as follows:

Using

^{notationVufor}

v/g,

^{r(h) forestimated}

v/g„

^and

f(h

s

)

^{forestimated Function (7)can} be written:

Afterthe 'seedvolume' ofatreeisestimated

using

^Function

(8)

^{andareasin cross sectionand}

heights

now and5 years ago are measured, ^{the volume5} years agocan be calculated with

Formula (9):

3.2 Estimationofvolumesandincrement for tallytrees

3.2.1 Volume functions

Functionsfor

estimating

^{thevolumeof the wholestem from}stump^tothe top^{of thetreewere}

constructed

using sample

^{trees measured in the NFI7 and the NFIB. The two data} were

combined

using

^{mixedestimation}

(Korhonen 1993).

^Atthefirststage^oftheconstructionofthe

volume functions, ^{NFI7 data} were used for

determining

^{the form of the models andfor}

obtaining

first-levelestimatesoftheparameters. ^Ina

previous study (Korhonen 1993)

^Function 10_was shown to workwellfor

pine.

SVu =gis

/g

^*

(vj/g

i3)

<=>

SVu =gi3

/g

^*

(v/gi

^-

(y/g-,

^-

v,/g

i

5))

<=>

SVu = *

v/g,

^- gis

/g

^*

(V/&

^-

Vj/g

i

5)

<=>

SVu ⁼_gis

/g

^*

(g/g,

^*

v/g

^-

(v/g,

^-

Vj/gi,)) (7)

SVu =

gis

/g

^*

(g/

^{gi *Vu -}

(f(h)

^-

?(h

5

)). (8)

v 5 =

_g ^{* SVu}

(9)

whereRDIST=relativedistancefromthe _seacoast

(see 'Concepts

^and

Notation').

Function

(10)

was alsofoundtobe

satisfactory

^forspruce andbirches. Forother

species,

^the variable RDIST _was excluded from the model.

Atthesecondstage ^intheconstructionofthevolumefunctions,^{mixedestimation}was usedfor

obtaining

second-level estimates of the parameters

(Korhonen 1993). Only

^{data from the} calculation_area

(typically

onedistrictoftheCentralBoardof

Forestry

ⁱⁿ

Finland)

wereusedfor

there-estimation.Becausethe numberof

sample

^{treesmeasuredwas}

quite high

^for

pine,

spruce

and birches, ^modelswereestimated

separately

^{foreachsiteclass.}

Only

^{constant and}parameters

ofvariablesd, d

2,and

ln(G)

wereestimatedatthe second stage;^forothervariables, first-level estimates were used (Korhonen 1993).

Regression

^{models were also} constructed for

estimating

^{the volumes of different timber}

assortments: timberandcull.Thevolumeof

pulp

^wood

quality

wasestimated

by subtracting

^the estimatedvolumesoftimberandcull fromtheestimatedstemvolume.Afunctionwithaform

of

Equation (11)

^{was foundtobesuitable.}

BecausetheformoftheFunction

(11)

^fortimberassortmentwisevolumesdiffers

markedly

^from

theFunction

(10)

^{forwhole-stem}volume,^itwasalso necessary^toestimate_amodelof_aform

similarto

Equation

^{(11)forstemvolume.Otherwise,allerrors duetothe formofthefunctions}

wouldhavebeensummedupin thevolumeestimatefor

pulp

^wood.In somecases thiscould

evenhaveledto

negative

^{estimates for}

pulp

^{wood.Finalestimates} for,_e.g. ^thesaw

log

volume ofa

tally

^{treewerethenobtainedwithformula}

(12).

v/d₂=ao+ a l

*d₊

a^d

²+ a₃*RDIST₊

04*111(0

⁺

a,*YC

⁺

a^YC

²⁺

a,*XC

⁺

a^XC

²+

a,*YC*XC, (10)

v_t/d

2

=a„⁺

a,*ln(d)

^{+ (11)}

Because

logging

^ruleshave

changed

^{since theNFI7,itwas not}

possible

^{touse theNFI7dataas}

prior

information.Timberassortmentwise models_were estimated

using

^{OLS and}

sample

^tree data measured from the calculation _area.

Naturally,

^the

proportions

^{of timber}assortments vary

markedly by

^{tree class.} Therefore, ^the

sample

^treedatawere

grouped by

^{treeclasses asfollows.}

1 ⁼ non-timber tree

2 =a

good

saw

log

^tree

3 ⁼apoor ^saw

log

^tree.

As mentionedinSection 2.1, ^inthefieldmeasurements two differentcodesfor treeclass _were

recorded forthe

sample

^{trees. The firstof these describes the}

quality

^{'at first}

glance',

^which

refers tothe way itiscodedfor

tally

^trees(later ^called

'tally

^tree

quality

class'). ^{The second}

one is coded

according

^{to moredetailed}

sample

^tree measurements

(later

^called

'sample

^tree

quality class'). Usually,

^{thecodes match,butin}somecases thecruiser

may

change

^the

quality

code when

taking sample

^tree measurements. Thus,a

sample

^{tree with}

tally

^{tree class code}

'non-timbertree' _can include_saw

log quality,

^{and vice}versa.

Only

^{trees with the}

sample

^tree

quality

^{class code}

'good

^saw

log

^tree'or

'poor

saw

log

^tree'

were usedin

estimating

^{theabove mentioned}

regression

^{modelsfortimberassortment} volume.

Atthe

application

stage

tally

^treeswere

grouped

^intothe

respective quality

^classes

according

^to

the

tally

^tree

quality

^{class. To avoid}

possible

^{bias caused}

by

differencesin thetwo

quality

classifications _an

adjustment

was made _as follows. For all

sample

^{trees the mean of the}

measuredtimbervolumeand the _meanoftheestimatedtimbervolume_were calculated

by

^tree

species.

^{Thetimbervolumeestimateof a}

single

^{tree was then}

multiplied by

^{theratio ofthese} V,⁼

v/v

2

*

v, _,

(12)

where v,⁼finalestimateforv„

vt=estimateforv,obtainedwiththe modelfortheformof

Equation (11)

v, ⁼estimatefor vobtainedwiththe modelforthe formof

Equation (10),

and

v2

=estimatefor vobtainedwiththe modelfortheformof

Equation

^(11).

two means. Asimilar

adjustment

^{wasmadefortheestimatesofcull volume.}

3.2.2 Growth models

Model

(13)

^{was selectedas a basic modelfor}

estimating

^{thevolumeincrementofthe}past^5-

year

period.

^{For some}

species

^{notallthe variablesinthe}

equation

^were

significant

rcgressors.

Inthesecases,

only significant

^{variableswere used}

(see

^Section

4.1).

whereSI, S2,

S 3 are dummy

^{variablesfordifferentsiteclasses, andSOILis a}

dummy

^variable

to separate^{mineralsoils form}

peatlands.

When the

growth

^models were estimated, trees

growing

^on

poorly productive

^{land were}

separated

^fromtrees

growing

on forestlandfortwo reasons:

1. the

growth

^{of trees}

growing

^on

poorly productive

^landis

markedly

^{different from the}

growth

^{oftrees onforestland,and}

2. mostofthevariables

describing

^the

growing

^{stockare not measuredon}

poorly productive

land.

Equation (14)

^{was usedasa}

growth

^{modelfortreeson}

poorly productive

^land.

The natural

logarithm

^of

i^d

^{2is usedas an}

dependent

^{variable inmodels}

(13)

^and

(14).

^In

applications,

^{unbiasedestimatesfor}

i^d

^{2 inthearithmetic scale are needed.Themostcommon}

way tocorrectthebiasduetothenon-lineartransformationistoaddtheterm 1/2*MSEtothe

logarithmic

^{estimate. This correction is based on the}

assumption

^{that theresiduals of the}

logarithmic

^modelare

normally

distributed.Ifthisdoesnot holdtrue,

following

^estimatorcan

be

justified according

^toSnowdon

(1991):

ln(iyd

^{2) =}a<>⁺

a,*d

⁺

aj*ln(d)

⁺

aj*G

⁺

a^*DD

+ + +

a,*S2

⁺

ag*S3

⁺

a,»SOIL

⁽¹³⁾

ln(i/d

²

)

⁼a,,⁺

a,*d

⁺

a2*ln(d) (14)

y, ⁼measuredvalueforobservationi,and

ft

^=estimated

logarithmic

^valueforobservationi.

Estimator

(15)

wasusedinthis

study

^{to correctthebias duetothenon-linear}transformationin

growth

^models.

3.3

Generating

reports

Using

^{the modelsdescribedinSection3.3, theHelddataare} transformedinto_a file, which is suitableforfurther

processing

^{with SAS}statistical

package.

^Inthisfile,^each

plot

^standhasone

recordforcharacteristics

describing

^{the locationofthe}

plot

^{andsiteandthe}

growing

^{stock of}

the stand; ^{and one record for each measured}

tally

^{tree. The recordof} a

tally

^{tree contains}

following

data:

- tree

species

-

tally

^tree

quality

^class -d

- v/d²

-tyd

²

-OJd

2

-

U

²

.

(Volumes

^andand

growth

^{are divided}

by d 2 before they

are stored in the file in order to decreasethe _errorsdueto

rounding off).

When_areaestimates_are calculatedfordifferentstrata,e.g. site classes, ^the

sample point

^isused

asone observation.Areaestimates_areobtainedwithFormula(17)(Salminen1993).

ft

⁼

c*exp(p

i

), (15)

2y.

where c⁼ _,

S exp(pi)

Volume sum and mean statistics for a calculation area or different strata of the area are

compiled by summing

^{thevolumesand}

plot

^factorsofthe

plots

^{overthestratain}

question.

^The

meanvolumeis calculated

by dividing

^thevolumesum

by

^thesumofthe

plot

^{factors.Nomean} volumesfor

single

^standsof a

relascope plot

are needed.Infact, ^itis

impossible

^tocalculate

suchmeanvolumesin theNFIdatafor standsthatdonot coverthewhole

relascope plot.

In the _case of _a restricted

relascope plot

^{with maximumradius of 12.45} m (as ^{inNFIB in}

Kainuudistrict) thevolume_sumof_a

plot

(section)^iscalculatedasfollows.

It should be noted, that Formula

(17)

^{does not} differentiatebetween whole

plots

^and

plots

sections. Thesizeof _a

plot

^{is takenintoaccount laterwhenthe}means or sums are calculated

for the calculation strata.

Afterthe volume_{sums are}calculatedforeachpart

plot,

mean volumeestimates fordifferent

strata ofa

inventory

^{areaare obtainedwithFormula}

(18).

Äj

⁼

m/M

^* AREA,

(16)

V=

X

_n,^• _V,,

(17)

IV,

Vi

⁼ _,

(18)

iFi

4.APPLICATION OF ^{THE SYSTEMFORKAINUU DISTRICT}

4.1 Estimated models

Theupperdiameterfunctionsestimated

using sample

^{treesfromKainuudistrictarein}

Appendix

2.

Separate

^{modelswereestimatedfor}

following species: pine

^(Pinus

sylvestris),

spruce

(Picea

abies),

^whitebirch

(Betula pendula),

^silverbirch

(B. pubescens),

aspen

(Populus tremuloides),

alder (Alnus incanaand A.

glutinosa).

^{As described earlier, NFI7 data were used} as

prior

informationfor_someoftheparameters ^and

only

asinformationforotherparameters

(Korhonen

1992).

Thebark modelsfor

sample

^{trees of Kainuudistrictare in}

Appendix

^3.

Separate

^modelsfor

pine,

^birches

(no

^{differencebetweenwhiteand silver}

birch),

aspenandalder_wereused. The models_were estimated

using

^{NFI7 andNFIB}

sample

^{tree datafromKainuudistrict.}

Volumefunctionsestimatedfordifferent

species

^{forKainuudistrict}arein

Appendix

^4.For

pine,

spruce and birches the final

parameter^{estimates were calculated}

separately

^{for 4 site class}

groups.For aspen,alderandthe groupofother

species

^the

sample

^{tree data}were too few _to

distinguish

^{betweensiteclasses.Themodels}

presented

ⁱⁿ

Appendix

⁴are not

logical

^forsmall sized _trees.Therefore,generalvolumefunctionswere usedfor treeswithd <3 cm.

The

regression

^{modelsfor timber}assortmentwise volumes_are

presented

ⁱⁿ

Appendix

^{5. The}

datafor

pine

^andspruce^weredividedintotwosite classgroups.

Separate

^{modelsfortimberand}

cull volume models_wereestimatedforthe two groups.Thedataforbirches _were too few to

makeadistinctionbetweensiteclasses. For aspen

only

^few

sample

^{trees were codedas timber}

quality

^{trees,andthereforenomodelfortimbervolume}wereestimated.Atthe

application

stage, timbervolumemodelofbirches _were usedfor thoseaspens that_were coded_as timber

quality

trees.For other

species,

^{no timbertreeswere measured;modelswere estimated}

only

^{for cull} volume.The correctionfactorsfortimberassortmentwisevolumes

(see

^Section

3.2.1)

are also

given

ⁱⁿ

Appendix

^5.

Theestimatedmodelsfor thepast

5-year

^volume

growth

^ofdifferent

species

are in

Appendix

6.

Separate

^{modelsfortrees}

growing

^{atforestlandand}

poorly productive

^{landwereestimated.}

For forest land separate ^{models for}

pine,

spruce,birches and aspenwere used. For

poorly

productive

^{landbirchesand}aspen^were combinedtothegroupofother

species.

^{Thecorrection}

terms

(see Equation (16))

are also

given

ⁱⁿ

Appendix

^6.

4.2

Examples

^{ofcalculatedstatistics forKainuudistrict}

According

^{to thestatisticsoftheNationalBoardof}

Survey,

^{thetotallandareaofKainuudistrict} is2 156690ha. Estimatedareaof forestlandis 1 664015ha.

Figures

^{2and 3}present ^two

examples

^ofestimatedpercentages ^{ofdifferent strata.In}

Figure

^{2 is} thedistributionofforest

land

by

^dominant

species. Figure

³ presents ^the age class distributionon the forestland in

Kainuu district.

Theestimated_meanandtotalvolumesandtimberassortmentwise _meanand totalvolumes

by

species

^{onforestlandand}

poorly productive

^{land are}

given

ⁱⁿ Table1. The

growth

^statistics obtained

using

^thecalculationsystem ^are

presented

^inTable2.

Figure

^{2.Dominanceoftree}

species

^{onforestland.}

Figure

^3.

Age

structure on forestland

Table 1.Meanandtotalvaluesofstemvolumeand timberassortmentwisevolumes

by species

for forestand

poorly productive

^land.

Table2.Meanandtotalvalueestimates for

growth by species

^forforestand

poorly productive

land.

Meanvolumes, m 3

/ha ^Totalvolumes, ¹⁰⁰⁰m

3

saw

log pulp

^total saw

log pulp

^total

Pine 13.3 21.9 37.7 25089 41288 71062

Spruce

^{6.1 9.8 16.9 11427 18427 31947}

Birches 0.2 6.2 8.7 414 11763 16382

Others 0.0 0.7 1.1 29 1273 2009

All 19.8 44.8 64.4 36959 72750 121401

Pine

Spruce

^{Birches Others All}

m

3/ha 1.35 0.41 0.38 0.06 2.20

1000m

3 2552 782 715 104 4153

5. DISCUSSION

Thesystem^ofcalculation

presented

^inthispaperdiffersfromthepresentcalculationsystem^for

NFIin the

following

^ways:

1. Stemvolumeandthe timberassortmentwise volumesare

generalized

^for

tally

^trees

using

regression

^{modelsinsteadofclasswise} meanvalues.

2. Growthestimates_arecalculatedfor

tally

^{trees with}amethodsimilarto thatfor

estimating

the timber assortmentwise volumes. In the

present calculation

system

growth

^{is not}

generalized

^for

tally

^trees

(growth

^isestimated

using growth

percentages^{estimatedfromthe}

sample

treedataanddiameterdistributionsestimatedfromthe

tally

tree

data).

Theabove-mentionedsolutionsmakethe system ^flexible.Area,volumeand

growth

^estimates

can

easily

^{becalculatedfor}anysub-classofthedata.Plotwisevolumeand

growth

^estimatescan

easily

^beusedasa

'ground

^{truth' for}

processing

^satellite

images (Tomppo 1992).

Charactericsof'final

interest',

^suchastimberassortmentwisevolumesandvolume

growth,

were

usedas

dependent

^{variableswhenthemodelswereestimatedfromthe}

sample

^{treedata.Another}

possibility

^{wouldhavebeento} use variables

describing

^{thedimensions}

(d,

h,b, ⁱ_d,

ij

^and

quality (lengths

^ofdifferent

quality

classes) as

independent

^{variables.The modelswouldthen}

give

^{estimatesofall}

sample

^{treevariablesfor}every

tally

^{tree.Theseestimatescouldbe usedas}

independent

^{variables for further} estimations, _e.g. of the volume or

growth

^of

tally

trees.

Variousmodificationsofthismethoddescribed

by

^Kilkki (1979)are

widely

^usedin

inventory

systems. ^{The method hasone serious} drawback, ^{however: residual varianceof thedifferent}

models mustbe taken into account when, _e.g.,

using

^estimatedh,

i,,,

^{and i}h as

independent

variablesin

estimating

^{volumeincrement}

(Kilkki 1979).

^The

joint

distributionsofthe_errorsof

the different models are difficulttoestimate. Therefore, aftersome trials this

approach

^was

rejected.

As stated, in this system ^ofcalculation

sample

^{treevariables such as}

height

^and age ^{are not}

generalized

^for

tally

^trees.

Therefore,

^thedata

generated

^for

tally

^{treescannotbeused to}

predict

the future

development

^{of forests with simulation} systems ^{like the Finnish}

Mela-system

(Siitonen 1983).

^{Furtherstudies}areneeded

if,

^for

example,

^the

grid

^method

(Holm

^etal.

1979)

is

applicaple

^for

generalizing

^the

sample

^treecharacteristicsfor

tally

^{treesinsuch a}waythatthe

results can be used as a basis both for

calculating

^unbiased

inventory

^{statistics and for}

simulating

^thefuture

development

^ofthetrees.

LITERATURE

Holm,S.,

Hägglund,

^B.&Märtensson,A.Amethodfor

generalization

^of

sample

^treedatafrom the Swedish National Forest

Survey.

^Swedish

University

^of

Agricultural

^Sciences.

Department

^{of Forest}

Survey. Report

^{25. 94}pp.

IMSL

library

^{reference manual.Edition9. 1982.IMSLInc. Houston,Texas.}

Kilkki, P. 1979. Outline for a data

processing

system ^{in forest}mensuration. SilvaFennica

13(4):368-384.

Korhonen,K.T. 1993.Mixedestimationincalibrationofvolumefunctionsof Scots

pine.

^Silva Fennica 27(4):269-276.

Korhonen,K.T. 1992.Calibrationofupperdiametermodelsin

large-scale

^forest

inventory.

^Silva Fennica 26(4) ^{:23 1-239.}

Kujala,

^{M. 1980.}

Runkopuun

kuorellisen tilavuuskasvun laskentamenetelmä.

Summary:

^A calculation method for

measuring

^{the volume}

growth

over bark of stemwood. Folia Forestalia441. 18pp.

Kuusela,^K.& Salminen,^{S. 1991.Suomenmetsävarat 1977-1984}

ja

^niiden

kehittyminen

^1952- 1980.Forestresources ofFinlandin 1977-1984and their

development

^{in 1952-1980.Acta} ForestaliaFennica220.84pp.

Laasasenaho, J. 1982.

Taper

^{curve and volume functions for}

pine,

_spruce and birch.

CommunicationesInstitutiForestalisFenniae 108.74pp.

Salminen,S. 1993.EteläisimmänSuomenmetsävarat1986-1988.

Summary:

^Forestresourcesof SouthernmostFinland.FoliaForestalia825. 11l pp.

Salminen,S. 1978. Incrementcalculationsonthe basis of

relascope sampling

^{in theFinnish} NationalForest

Inventory. Paper presented

^{in lUFRO}

Meeting

^{of June} 18-25, ^{1978 in} Bucharest, Romania.

Subject Group

^{54.02. 7} p. The Finnish Forest Research Institute.

Helsinki, ^Finland.

SASInstituteInc.,SAS/STATUser's

quide,

^{Version6,FourthEdition, Volumes1and2,}

Cary,

NC: SAS Institute Inc., ^1989.

Siitonen,

^{M. 1983.A}

long

^term

forestry planning

system^{basedondatafromtheNationalForest}

Inventory

^{ofFinland. In:Forest}

inventory

^for

improved

management.

Proceedings

^ofthe lUFRO

Subject Group

^4.02

Meeting

^{in Finland,}

September

^{5-9, 1983.}

University

^of Helsinki.

Department

^ofForestMensurationand

Management.

^{ResearchNotes} 17:195-207.

Snowdon, P. 1991. Aratio estimatorforbias correction in

logarithmic regression.

^Canadian JournalofForestResearch 21(5):720-724.

Teräsvirta,T. 1981.Someresultson

improving

^{the least}squaresestimationoflinearmodels

by

mixed estimation. Scandinavian Journal of Statistics 8:33-38.

Tomppo,

^{E. 1992.} Multi-source NationalForest

Inventory

^{of Finland. In:}

Proceedings

^of Ilvessalo

Symposium

on National Forest Inventories. Finland 17-21

August

^1992.

Nyyssönen,

^{A.,Poso,S.&Rautala, J.(ed.).TheFinnishForestResearchInstitute.Research}

Papers

^444:52-59.

Valtakunnanmetsien 8. inventointi.

Kenttätyöohjeet,

^Kainuun

ja Pohjois-Pohjanmaan

^veriso.

1992.

[Field

instructionsforthe fieldworkof the8"NationalForest

Inventory

^ofFinland

atKainuuand

Pohjois-Pohjanmaa

^{districts. InFinnish.]}

Manuscript

⁶⁷ pp ⁺

appendices.

TheFinnishForestResearchInstitute. Helsinki, ^Finland.

Valtakunnanmetsieninventoinnin

kenttätyöohjeet

^{VMI7. 1978.}

[Field

instructionsforthefield work of the 7^th NationalForest

Inventory

^{of Finland. In}

Finnish.] Manuscript.

⁵⁹ pp ⁺

appendices.

^{The FinnishForestResearchInstitute.Helsinki, Finland.}

Appendix

^{1. for ratio of volume} over bark and _cross sectional area inside bark (r = v/gj (Kujala 1980)

.

r(h) ⁼ 0.39 +

0.39* h +

2/(h.l-3) +

o.77*V(h-1.3)

r(h) = 0.44 +

0.355* h +

2/(h.l-3) +

o.6s*V(h-1.3)

r(h) = 0.48 + 0.48* h + 3.5/(h.l-3)