Integrated Stand Growth Model (ISGM)

Hong LingXia 2006-06-28The research institute of forest resource information

techniques,

Chinese Academy of Forestry (CAF)

Abstract-1 Integrated Stand Growth Model (ISGM) is a

group of correlated equations which include:

1) basal area growth model

2) density index definition

3) basal area equation

4) Self-thinning model

5) dominant tree growth model

6) average tree growth model

7) form height model

8) stand volume model

Abstract-2

The statistical algorithm of nonlinear error-in-variable simultaneous equations is used to estimate the parameters of correlated equations to ensure that the parameter estimation of the group of correlated equations in ISGM is unbiased and the equations are compatible. ISGM can be used to simulate the even age stand growth and can out put different kinds of growth tables with different site index, stand density, thinning method and draw stand density control graph by ForStat (Chinese,CAF) or Capsis(English,CIRAD,Amap) software.

1.basal area growth model

b1,b2,b3,b4,b5 : parameters

G: total basal area

S: density index

age: the age of even-aged stand

352 ))]()10000

(exp(1[ 041bbb tage

SbLbG

2.density index definition

S: density index

N: number of trees per hectare

D: average diameter at breast height

β: parameter—self thinning rate

)D(NS

20

3.basal area equation

G: total basal area

N: number of trees per hectare

D: average diameter at breast height

)40000

(2 DNG

4.self-thinning model

a: a constant , for a given stand, the constant is decided by afforestation density (initial density )

sf: parameter--maxim density index

β: parameter--self thinning rate

γ: parameter

aD

N

sf )

20()(

5.dominant5.dominant tree growth model

b,c: parametersL: site indexage: the age of even-aged standbaseage: basic Site index age (in China,20)

)exp(baseage

b

age

bLUH

c)]agebexp([LUH 1

Schumacher

Richards

6.average tree growth model

a1,a2: parametersa1,a2: parameters

UH: dominantUH: dominant tree height

PH: average tree height

2

1

a

aUHPH

7.form height model

c1 ,c2 : parameters

PH: average tree height

PHPH

ccfH

)

2( 2

1

8.stand volume mode

fH: form height

G: total basal area

GfHM

ISGM model in ForStat software (Chinese)

Two main parts :

1. From the measurement data to calculate all the parameters in ISGM model .

2. To simulate the normal stand growth , thinning growth and draw the DensityControlGraph.

1-1.Measurement data

Site type Plot number age Number of trees per hectare

breast height diameter

Dominant tree height

Average tree height

volume

1-2.Measurement data requirement

1.For each site type must have several plot data, which include different age, different density and some maximum density plot .

2.For each plot must have some serial measurement data of different age.

3.If one plot have been thinned, before thinning and after thinning is treated as two plot ( have the same site type and different plot number ).

1-3.parameters calculation (ForStat)

1-4.out put window (ForStat)

parameters

2. To simulate the normal stand growth , thinning growth and draw the DensityControlGraph.

ForStat software ----Chinese

Capsis platform----Isgm model----English

Capsis platform--Isgm model--English

1.Normal growth simulation:

1)From plantation

2)From current situation

2.Thinning simulation:

Thinning procedure( selection )

3.DensityControlGraph

This kind of graph is originate in Japan.

2-1. Normal growth simulation--From plantation

give evolution selection:

Results—1.stand growth table

Results—2.dbh growth curve

Results—3.density index curve

Results—4.number of trees curve

Results—5.total basal area growth curve

Results—6.tree height growth curve

Results—7.volume growth curve

Results—8.volume growth rate

2-2. Normal growth simulation--From current

2-3. thinning simulation--From planted

2-4. DensityControlGraph

References: 1.Tang Shouzheng, Meng ZhaoHe, Meng FanRui.1994.A growth and self-thi

nning model for pure even-aged stands theory and applications. Forest Ecology and Management 70(1994): 67~73.

2.Tang Shouzheng, Meng FanRui, Meng ZhaoHe.1995.The impact of initial stand density and site index on maximum stand density index and self-thinning index in a stand self-thinning model. Forest Ecology and Management 70(1995): 61~68.

3. Tang ShouZheng, Li Yong.1996.An Algorithm for Estimating Multivariate Non-liner error-in-measure Models. Journal of Biomathematics. 11(1): 23~27.

4.Tang SZ， Li Y，Wang YH, 2001， Simultaneous equations, error-in-variable models, and model integration in systems ecology Source:ECOLOGICAL MODELLING, 142 (3): 285-294

5.Tang SZ， YH Wang， 2002， A parameter estimation program for the error-in-variable model， 156(23):225-236

6. Li YongCi, 2004,Study on Parameter Estimate of Growth and Harvest Models Based on the Methods of Mixed Model and Measurement Error Model. Doctor Thesis (Chinese with English abstract ).

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