Allometric Models for Estimating Growth and Yield of Eucalyptus

grandis at the Industrial Timber Estate North Sumatera - Indonesia

Siti Latifah

, Teodoro Reyes Villanueva

, Myrna Gregorio Carandang

Nathaniel Cena Bantayan

, Leonardo M.

Forestry Program Study, Sumatera Utara University, Medan, Indonesia

Forest Resources Management, University of the Philippines Los Banos, Los Banos, Philippines

Environmental Science, University of the Philippines Los Banos, Los Banos, Philippines

Keywords: Forest plantation, mercahtable volume, Eucalyptus grandis, growth, Yield

Abstract: The suitability of allometric models for tree merchantable volume predictions in stands of Eucalyptus grandis

at the Industrial Timber Estate North Sumatera, Indonesia was established in this study. Field observation was

conducted to gather stands and geographic data from 49 observation of PsP (permanent sample plots) and 52

inventory plots. Multiple linear regression analyses were used to determine the contribution of the predictor

parameters to the variation in growth rates. Model 1was found to be more suitable and fit for merchantable

volume prediction.

1 INTRODUCTION

Growth and yield prediction models are abstract or

simplified representations of some aspect of reality

used primarily to estimate the future growth and yield

of forest stands ( Lucca ,2002). A stand growth

model represents an abstraction of the natural

dynamics of a forest stand, and depicts growth,

mortality and other changes in stand composition and

structure. Growth modelling of plantation timber

species is a vital tool for the prediction of yield from

future harvesting and estimating financial returns

(Davis et.al 2001). According Vanclay, 2003

modeling is also good for decision making regarding

buying, selling, and trading in forest resources

(Vanclay2003).

Forest management implies performing series of

treatments in complex productive systems. The

purpose of management planning is to provide a basis

for the allocation of these treatments so that the

desired result can be obtained. In order to do this,

management goals must be formulated, effective

treatment options capable of producing the desire

results must be found and outcome of treatment in the

productive system (predicting the result of various

management activities) must be described

(Mof,2005)

Foresters need to know every detail about the

forest they are managing in terms of location, size,

quantity and quality of forest resources available and

how these resources are changing over time (

Medhurst et al.2001). This information can be

obtained through proper resource modeling. Growth

and yield modeling are very useful tools for managing

forest properties either large or small. They are used

for operational and strategic planning in nations that

own and manage forest lands

2 MATERIAL AND METHOD

2.1 Study Site

The study was conducted in Aek Nauli sector of the

Industrial Timber Estate (Hutan Tanaman Industri -

HTI) North Sumatera, Indonesia, which is

geographically situated between 02° 40’00” to 02°

50’00” north latitude and 98° 50’00” to 99° 10’00”

east longitude. It is in the territorial jurisdiction of

Pores subdistric, Simalungun District, North

Sumatera Province, Indonesia

424

Latifah, S., Villanueva, T., Carandang, M., Bantayan, N. and M., L.

Allometric Models for Estimating Growth and Yield of Eucalyptus grandis at the Industrial Timber Estate North Sumatera - Indonesia.

DOI: 10.5220/0010044104240427

In Proceedings of the 3rd International Conference of Computer, Environment, Agriculture, Social Science, Health Science, Engineering and Technology (ICEST 2018), pages 424-427

ISBN: 978-989-758-496-1

2.2 Data Collection and Analysis

Data collection for primary data was done through a

field survey the primary data and secondary data were

digitally encoded. Field observation was conducted to

gather stands and geographic data. Stands features

referred to diameter, height, merchantable volume,

age, species, spacing, site index, basal area, and

density of E. Grandis. Geographical features referred

to slope, elevation, rain fall and soil of the study area

The data in this study used 49 observation of PsP

(permanent sample plots) and 52 inventory plots.

The total area of the plots in this study site is 3.11 ha.

Sample plot was located in an area where the stand

was of even age, uniformly spaced, and disease free.

Multiple Regression analysis was used for the

modeling and analysis of numerical data consisting of

values of a dependent variable (response variable)

and independent variables (explanatory variables).

The dependent variable in the regression equation is

modeled as a function of the independent variables,

corresponding parameters, and an error term

Regression analyses were done to derive the yield

equation of Eucalyptus at stand level using SAS.

Generally, yield (V) is considered to be a function

of basal area, height, age, site index, stand density,

spacing, top soil, rain fall, slope, elevation, , and type

of soil. These can be expressed as :

Vi = f ( BA, TH, Age, SI, SD, SP, TS, R, SL, E,N,

DA, DB, DC, DD) (1)

where :

Vi= merchantable volume of stand for i group

species in cubic meter per hectare

BAi= basal area of i group species in square

meters per hectare

TH = total height in meter

Age= stand age in years from the year of stand

establishment to the year of data

measurement

SI = site index in meter

SD = stand density in tree/ha

SP = original spacing in square meters; their

values are the products of original

spacing ( e.g., for a stand of original

spacing 3 x 2 m., SP has value of 6 )

TS = depth of top soil in centimeter (cm)

R = rain fall monthly (mm)

SL = slope in percent (%)

E = elevation in msal

N = density of upper canopy trees in trees/ha

DA=dummy variable for group of soil

dystrandepts, hydrandepts, 1 if type of

soil DA, 0 otherwise

DB=dummy variable for group of soil

dystropepts, dystrandepts, 1 if type of soil

DB, 0 otherwise

DC=dummy variable for group of soil

dystropepts, hapludults, 1 if type of soil

DC, 0 otherwise

DD= dummy variable for group of soil

dystropepts, humitropepts, 1 if type of

soil DC, 0 otherwise

bij = regression coefficients

ei= error terms

The volume models were assessed with the view of

recommending those with good fit for further uses.

The following statistical criteria were used:

a. The largest coefficients of determination

) and coefficients of correlation (r),

smallest mean square error (MSE) and

values of Mallow’s C(p) and Variance

Inflation Factor (VIF). VIF (βi) < 4

indicates no multicollinerity, if VIF (βi) > 4

indicates a problem of multicollinearity.

There is a possible problem of

multicollinearity if VIF (βi) > 15 and there

is a serious problem of multicollinearity if

VIF (βi) > 30. (Catahan, 2008)

b. Significant F–values as computed in the

analysis of variance (ANOVA) that test the

overall regression given the intercept term;

he critical value of F (i.e., F-tabulated) at

p<0.05 level of significance will be

compared with the F-ratio (F-calculated).

Where the variance ratio (F-calculated) is

greater than the critical values (F-tabulated)

such equation is therefore significant and

can be accepted for prediction

c. Consider the significance of each the

independent variables;

d. Randomness of the residual as shown in the

graph of the residual error values versus

fitted merchantable volume values;

3 RESULT AND DISCUSSION

3.1 Descriptive Statistic of Stand and

Geographic Variables

The summary descriptive statistics of the actual stand

variables to develop the models are shown in Table 1,

Allometric Models for Estimating Growth and Yield of Eucalyptus grandis at the Industrial Timber Estate North Sumatera - Indonesia

425

while descriptive statistics of geographic are shown

in table2. Merchantable volume, basal area, diameter,

height averages for E.grandis, are 60.965 m

/ha,

10.076 m

/ha, 11.213cm;15.5m respectively.

Table 2 indicates that geographic variables were

top soil, monthly rainfall, slope, and elevation with

average 22.287cm; 201.457mm/month; 15.296% and

1225.52 msl respectively.

Table 1. Descriptive statistics of stand variables E. grandis,

Descriptive

statistics

Volume

/ha)

Basal

area

/ha)

Age

(year)

Diameter

(cm)

Height

(m)

Site

index

(m)

Density

(tree/ha)

Spacing

)

Max 152.307 20.277 6.12 16 25.4 25.004 1280 9

Min 0.3159 0.483 1.08 2.3948 2.619 4.632 575 6.75

Average 60.965 10.076 3.119 11.213 15.514 15.747 925.532 8.928

Variance 0.282 0.067 1.585 12.47 0.047 0.04 0.006 0.158

Standard Deviation 0.531 0.259 1.259 3.531 0.216 0.2 0.079 0.398

Table 2. Descriptive statistics of geographic in studi site

Descriptive

statistics

Top soil

(cm)

Rain fall

(mm/month)

Slope (%)

Elevation

(masl)

Max 35 361 45 1400

Min 15 105 4 350

Average 22.287 201.457 15.298 1225.532

Variance 17.669 0.029 0.098 0.016

Standard

Deviation

4.203 0.17 0.313 0.125

3.2 Selecting the Best Models

The plot volumes were obtained by adding the

volumes of all the trees in the plot (Up) while mean

plot volume was obtained by dividing the total plot

volume by number of sample plots.

Forest growth models in this study involving the

logarithm of merchantable volume are the dependent

variable. The use of the logarithm of yield as

dependent variable is a convenient way to

mathematically express the interaction of the

independent variables in their effect on yield.

The assessment criteria revealed that for E.

grandis model 1was discovered best to have good fit

and very suitable for stand volume estimation in the

study area. The result suggests that all the models

with good fit are suitable for volume estimation

within the context of the field data used. Model 1 was

selected as the best model for E.grandis because it

had, R

= 0.9830 and r = 0.9915, and the lowest

MSE = 0.0341, and C(p) = 2.5881, 4/5 of the

independent variables are significant, and not

multicollinerity (Table 3). The final model for

E.grandis is:

V = exp [0.30190 + 1.38912 ln BA -0.40322

ln (A

-1

) + 0.02682 ( SI) -0.00054 (N)]

(2)

It means that there is an increase in volume by

1.38921 per unit increase in multiple basal area

holding other independent variables constant.

There is a decrease in volume by 0.40322 per unit

increase in reciprocal age holding other independent

variables constant. Villar (2005) studied the yield of

Yemane plantation on forest product unit in

Bukidnon, Philippines. There was positive

correlation between yield of yemane on average age.

Site index is the total height of the dominant trees

in a stand at specified ages. There is an increase in

volume by 0.02682 per unit increase in site index

holding other independent variables constant.

Stand density is a measure of how many trees are

growing per unit area. There is a decrease in volume

by 0.00054 per unit increase in density of tree holding

another independent variables constant. Lu ( 2000),

studied population density of 5.6 years old

Eucalyptus urophylla plantation. The results showed

that the population density remarkably affected DBH,

individual standing volume, crown width, live branch

height, stand volume and wood fiber width; but did

not affect tree height, basic density of wood, and

length of wood fibers

Aswandi (2000) reported that the prediction

equation for Eucalyptus grandis in North Sumatera,

Indonesia including age, site index and basal area

were fitted. These models fitted were also found to be

good enough to predict growth and yield in E. grandis

in central Western region of Minas Gerais Brazil,

(Pereira et al, 2006)

ICEST 2018 - 3rd International Conference of Computer, Environment, Agriculture, Social Science, Health Science, Engineering and

Technology

426

Table 3. Coefficients of determination (R2), coefficients of correlation (r), mean square error (Mse), Mallow's C(p), P-value

and Vif using original ages for E.grandis group

Selection

Procedure

Model

Adequate Precision

Test of

Hypotheses

on Β’s

Multi

Collinear

(mc)

Selection

Procedure Model

r Mse C(p) p-value Vif

Full model 1 0.9844 0.9922 0.0347 11.9911 significant not mc

2 0.9225 0.9605 0.1685 14.0000 significant not mc

3 0.9314 0.9651 0.1529 11.9981 significant not mc

Stepwise 1 0.9830 0.9915 0.0341 2.5881 significant not mc

selection 2 0.9202 0.9593 0.1617 2.4451 significant not mc

3 0.9286 0.9636 0.1464 3.2993 significant not mc

4 CONCLUSIONS

Regression models for volume estimation was

develop and validated for Eucalyptus grandis . The

stand growth data was collected from permanent

sample plot and temporary sample plot in the study

area. Based on the evaluation of the models examined

in this study model 1can be applied to accurate

growth and yield at study site. Dependent variables

that significantly affect the volume are basal area,

age, site index and stand density.

ACKNOWLEDGEMENTS

First, we would like to thank people of village

surround Industrial Timber Estate system who had

been incredibly supporting us during this study.

Sincerely appreciation is also extended to anonymous

reviewer for correction and comments. Gratitude is

also extended to PT. Toba Pulp Lestari which gave

permission to conduct this research in its area.

REFERENCES

Aswandi, 2000. Growth and Yield of Eucalyptus grandis

Hill ex Maiden at Aek Nauli Simalungun. North

Sumatera.

CATAHAN, L. 2008. Lectures Notes: Applied regression

and correlation Analysis. Statistic 151 Course. Collage

of Statistic. University of the Philippines Los Banos.

Philippines

Davis, L.S., K.N. Johnson, P.S. Bettinger and T.E. Howard.

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York. NY 10020. 804 pMoore, R., Lopes, J., 1999.

Paper templates. In TEMPLATE’06,

Pereira Aj, Helio G.L, Joao C.C.C, And Agostinho L.S.

2006. Use Data from Permanent Sampling Point in

Growth and Yield Modeling.

Http://www.scielo.br/scielo.php

Vanclay, J.K. 2003. Growth Modeling and Yield Prediction

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the ITTO Workshop on Growth and Yield, 24-28th June

2002. Kuala Lumpur, Malaysia.

http://jkv.50megs.com/R083_mf.pdf

Villar, R. G. 2005. Optimization Model Based on

Geographic Information System for a Forest Production

Unit in Bukidnon, Philippines. PhD Dissertation

Institute of Renewable Natural Resources. University

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Lucca, M. D. 2002. Growth and Yield Modeling.

www.for.gov.bc.ca/hre/gymodels.

Medhurst, J.L., C.L. Beadle And W.A. Neilsen. 2001.

Early- Age and Later-Age Thinning Affects Growth,

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Forestry Research. 31 (2): 187-196

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