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, ·R E SE lia R (H PAP ERN o .. 23 . '

VOLUME EQUATIONS FOR SIX EUCALYPTUS SPECIES ON THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES

By Huiquan Bi

S TAT E

FORESTS RESEARCH DIVISION

l

VOLUME EQUATIONS FOR SIX

EUCALYPTUS SPECIES ON THE

SOUTH-EAST TABLELANDS OF

NEW SOUTH WALES

by

HUIQUANBI

RESEARCH DIVISION STATE FORESTS OF NEW SOUTH WALES

SYDNEY 1994

Research Paper No. 23 June, 1994

The Author:

HtP-quan Bi, Research Officer, Silviculture Section, Research Division, State Forests of New South Wales

Published by:

Research Division,

State 'Forests of New South Wales,

27 Oratava Avenue, West Pennant Hills, 2125

P.O. Box 100, Beecroft 2119

Australia.

Copyright © 1994 by State Forests of New South Wales

DDC 634.9285 ISSN 0729-5340 ISBN 0 7305 9653 2

CONTENTS

SUMMARY

INI'RODUCI'ION

THE STUDY AREA

DATA

MEI'HODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENI'S

REFERENCES

Table 1. Descriptive statistics of the data used for modelling and validation

Table 2. Mean dbhob, mean height and site characteristics of the forty regrowth stands

Table 3. Regression coefficients of combined variable underbark stem volume equations for the six species and the validation statistics for the equations

Figure 1. The distribution of sample stands within Glenbog State Forest

The forest types of these stands are messmate, brown barrel-messmate messmate-gum, brown barrel, brown barrel-gum and mountain/manna gum

Figure 2. Bias and percentage bias and precision of undertark stem volume prediction within dbhob classes for E.fastigata

VOLUME EQUA nONS FOR SIX EUCALYPTUS SPECIES ON THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES

ill

1

1

2

6

8

10

10

11

2

4

8

3

9

SUMMARY

Using data from more than 1,900 sample trees, combined variable (lYH) underbarlc volume equations were developed and validated for six species, Eucalyptus/astigata, E. obliqua, E. radiata, E. nitens, E. viminalis and E. cypellocarpa, on the south-easttablelands of New South Wales. Average bias in volume prediction varied from -0.009335 m3 for E. cypellocarpa to 0.013521 m3 for E./astigata, with -0.001404 m3 for E. viminalis being the closest to zero. Mean absolute deviation in volume prediction ranged from 0.012126 m3 for E. viminalis to 0.043568 m3 for E.fastigata. Root mean squared deviation in volume prediction was generally less than 0.10 for the equations, with the exception of the equation for E. nitens. A further evaluation within DBHOB classes for E./astigata showed that percentage bias was not greater than five percent for all DBHOB classes and percentage precision was mostly smaller than 15 percent. Volume equations for species other than E.fastigata are provisional at this stage. They will be updated when more data become ava~able in two years' time.

VOLUME EQUA nONS FOR SIX EUCALYPTUS SPECIES ON THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES iii

INTRODUCTION

The tableland forests of south-east New South Wales cover approximately 85,000 ha and represent more than thirty percent of the total area of native forests under the management of the State Forests of New South Wales in the region. Pulp wood and sawlogs have been harvested in these forests for many years (Anon. 1982). Regrowth forests from logging and/or fire now constitute a substantial proportion of the tableland forests. They have become increasingly important in wood production as large areas of old growth forests in the region, previously available for logging, have become unavailable to forestry. With a reduced resource base, more intensive management of these regrowth forests seems to be the inevitable way of maintaining an adequate level of wood production.

Accurate stem volume prediction is a prerequisite for intensive forest management It is also a basic step in building forest growth and yield models to support forest planning and decision making. However, volume equations have not previously been available for any species in the tablelands area to aid forest management. As a part of the south-east regrowth forests growth and yield modelling project, this report describes the development of volume equations for six major commercial species in the tableland forests.

THE STUDY AREA

The tableland forests in south-east New South Wales consist of a diversity of forest types of mostly wet sclerophyll forest. Eucalyptus /astigata is the most important commercial species on the tablelands. It can occur in pure stands in some areas, but often grows in association with other eucalypts such as E. obliqua, E. nitens, E. viminalis, E. data, E. cypellocarpa and E. radiata in other areas. 1b.e mean annual rainfall in these forest areas ranges from 700 mm to 1100 mm. 1b.e mean maximum temperature for the hottest month is in the range of 23° to 28°C and the mean minimum for the coldest month is -40 to 3°C.

Wildfire, being a frequent event in the region, has had a pronounced effect on the age structure of the forests. High intensity fire can destroy all trees in a stand, while low intensity fire damages some trees more than others. Relatively even-aged regrowth stands usually develop after high intensity fires; mixed-aged stands often emerge after low intensity ones. Even-aged stands tend to occur on more sheltered aspects which are burnt less frequently but more intensely. whilst mixed-aged stands often occur in more exposed positions which are burnt more frequently but less intensely. In general the regrowth forests after fire are a mosaic of even-aged and mixed-aged stands. Wildfire has also resulted in a substantial number of coppice trees in the forests. These trees grew mainly from the base of old stumps after fire with double or multiple leaders with a thicker base than trees originated from seedlings.

VOLUME BQUA nONS FOR SIX EUCALYP7TJS SPBCIES ON THE SOUTIl-BAST T ABLBLANDS OF NEW SOUTII WALES 1

DATA

The south-east regrowth forests growth and yield modelling project has been collecting taper data from the tableland forests for two years. Field measurements of sample trees included dbhob (diameter at breast height over bark), height and diameters along the stems at 1.5 m intervals. Also two measurements of bark thickness were taken at each point where diameter was measured. 1be data set for this work represented more than 1,900 trees of six species - E.jastigata. E. ob/iqua, E. nitens, E. viminaiis, E. cype/locarpa and E. radiata (Table 1). 1bese sample trees were selected from 40 regrowtb stands which represented a range of growth conditions on the tablelands (Table 2). Most of these stands are distriooted within Glenbog State Forest where the bulk of the field work of the project has been canied out (Figure 1). About two-thirds of the sample trees were selected for developing volume equations and the remainder used for validation. The selection was done systematically by including every third tree in the validation group from a list of trees sorted by dbhob in each stand.

Table 1. Descriptive statistics of the data used for modelling and validation.

• Standard Deviation

VOLUME EQUA nONS FOR SIX EUCALYP7TJS SPECIES ON 2 TIlE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES

.!:: c: :J c. ca E c: ca ca ... .-Cl)

:J <:{

Cl c: :2 .-... 0

2

5960000

5955000

5950000

5945000

5940000

5935000

5930000

Forest Type 150 0

151 6

152 0 154 • 155 A 159 •

5925000

707000 712000

• •

0 • •• • • • 0 • • • o o.

A .·0 • en

6

717000 722000 727000 732000

Easting (Australian map unit)

Figure 1. The distribution of sample stands within Glenbog State Forest The forest types of these stands are messmate (150). brown barrel-messmate (151). messmate-gum (152). brown barrel (154). brown barrel-gum (155) and mountain/manna gum (159).

VOLUME EQUA nONS FOR SIX EUCALYPTUS SPECIES ON THE SOUTH·EAST TABLELANDS OF NEW SOUTH WALES 3

~

mCl

~~ ~: ,I:) ~c:: ~~ ~~ ~CIl

~~ ~~

~~ ~~ ~ril n

Table 2. Mean dbhob, mean height and site characteristics of the forty regrowth stands.

- ------ -

~< t:<lF! ~~ ~t:<l ,I:)

~~ ~g ~z ~CIl ~~

~; O~ '!j~

~~ ~~

!~ ~~ v.

Table 2. (cont.)

Plot State' ':': ::: Forest: rAng1tude Latltpd~ <:;~Jtim4~'::" ::Raihiau:::: ,:"AS~~;: )!::'$Jope Number Stand density

Forest Ty~e· ,::::: :::: ,,:::H::f:;g:(,:'::':::::::::::::}:}: ",;:::::":i!,::: ~il- " '!:~"::::'::::'~~::: ":,}'~~~~!=l,,,::'e~gtee) bUrees (treeslha)

29, :.:.:.; ... :. 30 31 32 33 ~ 35 36 37 38: 39 40

::::;::::

Olenbog ' 152 149~27'19" Glenbog ',' 151 149°27'00" Glenoog ,': 154 149"Z6*10-t

Glenbog ,:': 1S1 149O'

272(Y' Glenbog " 154 149°27'3Q" Olenbog 154 149°2718" Glenbog 159 149°26·43~~ Glenbog .. 154 1;491>2SlSQ" Olenbog 154 j49f2~;S2" Glenbog 154' '. 1.49;z.r-1S,f GlenbOg 154 : 149"28.m-f

GlenbOg 154 149CtZSiOlft .. - ..

::::::::.::;::.:,:::::.:.;. " ,' ',' "", ',-','

3640'34""":,910 ::: : 36°41'38" ',:940

·11 .····.·· . '.',: 3637'4511 '/ ,:950 36"41'2Q" :::: .'940 1> .. 'cc::·

364O'22't "":: 910 ' 36~2'JO" :::: 940 ' " :~ 36~39!27~~ .::::: i900 :::::

36"34'OO~: ::i::f9ob /: :

S~~:'~I~j';; 'lE 36~j7'S7~ ::r:'j03O ) l()()()

.. ':::::;::' -r :<".:.:.:.;.~.:.;.;.;.;.;:;:;.;.;~.::.:.:.:. .., ....

• A. defmed in Forestry Commission of New South Wales Research Note 17.

' 199' 200,

6S 194

::: 100 ·:: 222 :

ti:111!!~ .. ·· 261

:;

o 2 7 1

11 3 r: 8"::

'::: 7 ·

"::,::: 8

1,8 23

:-: ..... :<.: ::;: .::-::"

\ 86 }77

114 86 53 19 93 79 95

110 92 89

7S9 464 150

1211 468 571 474 403 386 518 374 362

Mean Mean dbbob (cm) beight (m)

13.9 19.0 21.5 15.2 20.4 19.8 15.2 23.6 22.4 17.9 19.0 19.6

METHODS

Because the diameter measurement inteIVals were relatively short. Smalian's formula was used to calculate underbark sectional volumes (m') for each tree, apart from the tip volume which was calculated as a cone. Underbarlc diameters used in the calculation were taken as the corresponding overbark diameters minus the sum of the two bark thickness figures. The sum of sectional volumes of each tree was taken as the 'true' stem volume of the tree, although it may still differ from the real volume as would be obtained through water displacement methods (Dargavel and Ditchbume 1971, Martin 1984).

The two most common forms of volume equation were examined to select the equation form for the six species. The first was Spurr's (1952) combined variable equation:

V=a+bIYH (1)

where V is underbark stem volume, D is dbhob, H represents tree height The second was the logarithmic volume equation of Schumacher and Hall (1933):

(2)

Spurr's combined variable equation was fitted at first using least squares regression for each species. A few anomalous points were deleted after their DFFIT statistics were examined. These anomalous points might be due to measurement or recording errors or they might represent measurements from abnormal trees. Since the least squares method assumes homogeneous error variance, a test for heteroscedasticity was carried out using the method of White (1980). Because of the presence of heteroscedasticity the equation was fitted again using weighted least squares regression with a series of four weights, these being (lYH).l/l, (lYH)-l, (lYH)-2 and (lYH)-3f:l. The statistics ofFurnival's (1961) index of fit were calculated for the equations fitted for each species. Furnival's index provides a relative measure of the departures from linearity, normality and homoscedasticity of residuals simultaneously, with a smaller value indicating a smaller departure and a large value indicating a greater departure. Indices of equations fitted using different weights for each species were compared and the equation with the smallest value of Furnival's (1961) index was selected as the combined variable volume equation for each species.

The logarithmic equation of Schumacher and Hall (1933) was also fitted for each species after taking logarithms on both sides of the equation to satisfy the assumption of homoscedasticity in least squares regression. Following the fitting, Furnival's (1961) index was calculated and compared with that of the combined variable equation to determine which equation form was the closest to the assumptions ofleast squares method for each species. Values of Furnival's index for the combined variable equation were 3% to 34% (16% on average) smaller than that of the logarithmic equation for four species. For the remaining species, E./astigata and E. nitens, it was vice versa, with Furnival's index for the logarithmic equation being 12% smaller than that of the combined variable equation.

The two equation forms were further compared in terms of bias and precision of their predictions against the validation data. Several bias and precision statistics were calculated:

VOLUME EQUA nONS FOR SIX EUCALYPTUS SPEClES ON 6 THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES

11

Average bias = .~ (v(V)IN; 1=1

11

Mean percentage bias = ~ (V fV - l)IN; i=1 '

n Mean absolute deviation of volume prediction (MADV' = .~ I V( V IIN;

p' 1=1 ' n

Root mean squared deviation of volume prediction (RMSDV) = ( .~ (V( V l/N)lIl; 1=1

where VI is the stem volume of tree i and V, is the predicted volume of that tree.

Because volume estimation involving logarithmic transfonnationmay introduce bias when back transfonned from logarithmic values (Flewelling and Pienaar 1981), the predicted stem volume from the logarithmic equation was corrected for log transfonnation bias before being tested against the validation data. The correction was perfonned by multiplying the predicted values with Snowdon's (1990) bias correction factor which is simply the ratio between the mean observed stem volume and the mean predicted stem volume of trees calculated from data used in regression for each species.

Comparisons of the validation statistics of the two equation fonns showed that the values of average bias and mean absolute deviation for the logarithmic equations were smaller than that for the combined variable equation for half of the species, while for the remaining species it was the reverse. However, the logarithmic equations for four species had greater values of root mean squared deviation of volume prediction than the combined variable equations, indicating their volume predictions being less precise than that of the combined variable equations for these species, although they had one more coefficient in the equations as well as corrections for log transfonnation bias. Considering the values of Fumival 's index of fit and the validation statistics and, in addition, the principle of parsimony, the combined variable equations were chosen for stem volume prediction for all species.

Because the combined variable equations were fitted through weighted least squares regression with different weights and weighted least squares regression involved fitting the weighted equation without an intercept tenn, a generalized fonn of Rl was calculated to compare the percentage of variation in stem volume explained by the regression equations:

11 11

Rl= l-.r.(V(Vll.r.(VrV,,/ 1=1 1=1

where Vi is the observed volume of tree i; V, is the predicted volume of tree i and V ID the mean volume of all trees.

Bias and percentage bias and precision of stem volume prediction were further evaluated for E.fastigata by dbhob classes using 2-5 cm intervals since this species had a large number of sample trees in the validation data set. Bias and percentage bias were first calculated for each tree as follows:

Bias = (VrV)

and

Percentage bias = (V( V) x lOON,

The standard deviation of bias and percentage bias were then taken as precision and percentage precision respectively.

VOLUME EQUA nONS FOR SIX EUCALYPTIlS SPECIES ON THE SOUTIl-EAST TABLELANDS OF NEW SOUTII WALES 7

RESULTS

The volume equations for underbark stem volume and the results of validation for the six species are presented in Table 3. The generalized Rl was greater than 0.97 for all equations. Average bias in volume prediction varied from -0.009335 m'for E. cype/locmpa to 0.013521 m' for E.fastigata, with -0.001404 m' for E. viminalis being the closest to zero. Mean absolute deviation in volume prediction (MADV p) ranged from 0.012126 m' for E. viminalis to 0.043568 m' for E.fastigata. Although the equation for E.fastigata had the largest values of average bias andMADVp, mean percentage bias was relatively small in comparison withequationsforotherspecies. Root mean squared deviation in volume prediction (RMSDVp) was generally less than 0.10 for the equations with the exception of that for E. mtens.

Bias and percentage bias and precision in underbark stem volume prediction within dbhob classes were shown in Figure 2 for E.fastigata. As expected, bias and precision increased with dbhob classes. While values of bias were close to zero for smaller dbhob classes, they became greater for larger dbbob classes and reached 0.12 m' for the largest dbhob class. However, percentage bias and precision did not follow the same trend. Percentage bias was not greater than five percent for all dbhob classes, whilst percentage precision was mostly smaller than 15 percent

Table 3. Regression coefficients of combined variable underbarkstem volume equations (V=a+b02H) for the six species and the validation statistics for the equations. MADV p denotes mean absolute deviation in volume prediction; RMSDV p denotes root mean squared deviation in volume prediction. Standard errors of the regression coefficients are in brackets.

:.:.

E.raib'aia

E. viminalis

i63S, '.:.

(O.sl~) ·

O.421~S180 (U~44) ·«ig74)

.. 1.208 " .. ~04b4 <9.820) (O.~S).

3.256 (1.486)

0.902 (l.m)

:;:;. .

2.4633 (0.054)

2.7026 (Q.~)

VOLUME EQUA nONS FOR SIX EUCALYP7VS SPEOES ON 8 THE SOUTII-EAST TABLELANDS OF NEW SOUIH WALES

0.30

0.25

5 0.20

..... '" l 0.15

~ 0.10

0.05

-0.05

12.5 15 17.5 20 22.5 25 27.5 30 32:5 35 37.5 40 42.5 45 50

DBHOB classes (cm)

20

-5

12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 50

DBHOB class (cm)

Figure 2. Bias and percentage bias (columns) and precision (lines) of underbark stem volume prediction within dbhob classes for E.fastigata. Numbers attached to the horizontal axis indicate the upper boundaries of the dbhob classes. except for the smallest dbhob class which included all trees with dbhob smaller or equal to 12.5 cm and the largest dbhob class which included all trees with dbhob greater than 45 cm. The number attached to each bar indicates the number of trees in the corresponding dbhob classes used in validation.

VOLUME EQUA nONS FOR SIX EUCALYPTUS SPECIES ON THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES 9

DISCUSSION

The volume equations developed in this study were based on the data currently available, which consist of more than one thousand samples of regrowth E. jastigata, but considerably fewer samples of other species (Table 1). The bias and precision ofvo~ume prediction withi~ diameter classes for these species could not be reasonably examined because the sample size would be too small for many diameter classes. Volume equations for these species are provisional at this stage. They will be updated when more taper data become available in two years' time.

The data used to develop the volume equations were from trees originated from seedlings, coppice and double leaders. More precise volume prediction would have been achieved if trees originated from seedlings were separated from coppices and double leaders. However, unless forest management routinely categorises trees in such a way, it is oflitUe practical value to develop separate volume equations for trees of different origins.

ACKNOWLEDGEMENTS

The study was funded in part by a grant from the Commonwealth Department of Primary Industry and Energy. I am indebted to Mr V. Jurskis for co-ordinating the field work and to Mr I. Rolfe and other workers for collecting the data in the field. Dr R. Gittins provided helpful comments on the manuscript

VOLUME EQUA nONS FOR SIX EUCALYPTUS SPECIES ON 10 THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES

REFERENCES

Anon. (1982). Eden native forest management plan. For. Comm. N.S.W., Sydney. 82 pp.

Dargavel, J.B. and Ditchbume, N. (1971). A comparison of the volumes of tree stems obtained by direct measurement and by water displacement. Aust. For. 35: 191-.198.

F1ewelling, J.W. and Pienaar, L.V. (1981). Multiplicative regression withlognormalerrors. For. Sci. 27: . 281-289.

Furnival, G.M. (1961). An index for comparing equations used in constructing volume tables. For. Sci. 7: 337-341.

Martin, A.J. (1984). Testing volume equation accuracy with water displacement. For. Sci. 30: 41-50.

Schumacher, F.X. and Hall, F.S.D. (1933). Logarithmic expression of timber tree voiume. J. Agric. Res. 47: 719-734.

Snowdon, P. (1990). A ratio estimator for bias correction in logarithmic regressions. Can.J. For. Res. 21: 720-724.

Spurr, S.S. (1952). Forest inventory. Ronald Press, New York. 476 pp.

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica48: 817-838.

VOLUME EQUATIONS FOR SIX EUCALYPTUS SPECIES ON THE SOUTH-EAST TABLELANDS OF NEW SOUTH WALES 11

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