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Evaluation of stem taper models fitted for
Japanese cedar (Cryptomeria japonica) in the
subtropical forests of Jeju Island, Korea
Roscinto Ian C. Lumbres, Yeon Ok Seo, Sung-Hyun Joo & Sung Cheol Jung
To cite this article: Roscinto Ian C. Lumbres, Yeon Ok Seo, Sung-Hyun Joo & Sung Cheol Jung
(2017) Evaluation of stem taper models fitted for Japanese cedar (Cryptomeria japonica) in the
subtropical forests of Jeju Island, Korea, Forest Science and Technology, 13:4, 181-186, DOI:
10.1080/21580103.2017.1393018
To link to this article: http://dx.doi.org/10.1080/21580103.2017.1393018
© 2017 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Group.
Published online: 10 Nov 2017.
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Evaluation of stem taper models fitted for Japanese cedar (Cryptomeria japonica)
in the subtropical forests of Jeju Island, Korea
Roscinto Ian C. Lumbres
a
, Yeon Ok Seo
b
, Sung-Hyun Joo
c
and Sung Cheol Jung
d
a
College of Forestry, Benguet State University, La Trinidad, Benguet, 2601, Philippines;
b
Warm Temperate and Subtropical Forest Research Center,
Korea Forest Research Institute, Seogwipo, Jeju, 679-050, Republic of Korea;
c
Forest Sciences and Landscape Architecture, Kyungpook National
University, Daegu 41556, Republic of Korea;
d
Forest Policy Division, Korea Forest Service, Daejeon, 35208, Republic of Korea
ARTICLE HISTORY
Received 8 July 2017
Accepted 12 October 2017
ABSTRACT
This study was conducted to evaluate the performance of the five stem taper models in predicting the
diameter over bark at any given height (d) and total volume of Japanese cedar (Cryptomeria japonica
D.Don) in the subtropical forests of Korea. The four fit statistics used in this study were standard error
of estimate (SEE), mean bias (E), mean absolute bias (MAB), and coefficient of determination (R
2
). For
the lack-of-fit statistics, SEE,MAB, and Eof the five models in predicting din the different relative
height classes and in predicting the total volume in the different diameter at breast height (D) classes
were determined. Results of the model evaluation indicated that the Kozak88 stem taper model had
the best performance in most of the fit statistics followed by Kozak02 stem taper model. The Kozak88
model also provided the best performance in the lack-of-fit statistics having the best SEE,MAB, and E
in predicting din most of the relative height classes. This model consistently performed well in esti-
mating the total volume of Japanese cedar in the different Dclasses as compared to other stem taper
and volume models. These stem taper equations could serve as a management tool for forest manag-
ers to accurately predict the d, merchantable stem volumes, and total stem volumes of the standing
trees of Japanese cedar in the southern plantation of Korea.
KEYWORDS
Diameter outside bark; Jeju
province; kozak model;
model evaluation; stem
volume estimation
Introduction
Japanese cedar (Cryptomeria japonica D.Don) is native to
Japan (Cheng et al. 2009) and considered as one of the most
commercially important conifers in Asia (Yoon et al. 2009).
It is the most common plantation species in Japan, covering
approximately 45% of the total plantation area and 20% of
the total forested area (Japan FAO Association 1997;
Kon^
opka et al. 2007; Yashiro et al. 2010). This species was
introduced in the different countries in East Asia such as
Taiwan and Korea. In Taiwan it covers 10% of the total plan-
tation area and is thus considered one of the most important
coniferous species in forest plantations (Cheng et al. 2013).
In Korea Japanese cedar was one of the species used for the
afforestation in 1920 and was also planted in the southern-
most province, Jeju, during the 1970s’afforestation. Approxi-
mately 40,000 ha were planted using Japanese cedar in Korea
(Korea Forest Research Institute 2006). Furthermore, accord-
ing to Lim et al. (2013), it is one of the most used coniferous
species in the southern forest plantation of Korea along with
Korean pine (Pinus koraiensis), Japanese cypress (Chamaecy-
paris obtusa), and Japanese larch (Larix leptolepis). To sus-
tainably manage the Japanese cedar forest in the southern
part of Korea, an accurate tool in acquiring merchantable
and total volume estimates is needed.
Several authors (Figueiredo-Filho et al. 1996; Kozak 2004;
Sharma and Zhang 2004; Jiang et al. 2005, Rojo et al. 2005;
Trincado and Burkhart 2006; Yang et al. 2009; Li and
Weiskittel 2010; Ozcelik et al. 2011, Subedi et al. 2011;Li
et al. 2012) recommended a stem taper equation as one of the
most useful tools to accurately predict the stem diameter at
any given height (d), merchantable and total volume. Most of
the stem taper models use total height (H), diameter at breast
height (D), and height of dabove the ground (h) as predictor
variables (Berhe and Arnoldsson 2008; Hjelm 2013) because
these are commonly measured during forest inventories
(Brooks et al. 2008). The most commonly used stem taper
equations are usually classified into segmented polynomial
and variable exponent (Berhe and Arnoldsson 2008;Lietal.
2012;G
omez-Garc
ıaetal.2013). The former uses different
sub-functions for various parts of the stem (Kozak 1988;Rojo
et al. 2005) with an assumption that a tree has three geometric
shapes (a neiloid frustum at the bottom, a paraboloid frustum
at the middle, and cone frustum at the top) (Husch et al. 1982;
Corral-Rivas et al. 2007; Yang et al. 2009; Li and Weiskittel
2010) while the latter assumes that the form of the tree changes
continuously along the stem (Corral-Rivas et al. 2007;Yang
et al. 2009; Li and Weiskittel 2010; Heidarsson and Pukkala
2011;Lietal.2012;Hjelm2013). In comparison to the tradi-
tional stem volume models, Kozak (2004) explained that a stem
taper equation is better because it can estimate d,merchantable
height to any top diameter and from any stump height, volume
of a stem log at any length and at any height from ground in
addition to merchantable and total stem volume.
In Korea there are limited studies that deal with stem
taper equation modeling. Stem taper models were fitted for
the major Korean tree species which are Pinus koraiensis,
Pinus densiflora,Pinus rigida,Larix kaempferi,Quercus accu-
tissima, and Quercus mongolica (Son et al. 2002). However,
prior to this study, a stem taper equation has not been devel-
oped specifically for Japanese cedar grown in Korea. One of
CONTACT Sung Cheol Jung scjungkr@korea.kr
© 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
FOREST SCIENCE AND TECHNOLOGY, 2017
E–ISSN 2158-0715, VOL. 13, NO. 4, 181–186
https://doi.org/10.1080/21580103.2017.1393018
Downloaded by [179.61.162.119] at 16:35 10 November 2017
the major limitations of the stem taper model is that it is spe-
cies specific (Sharma and Zhang 2004; Subedi et al. 2011;Li
et al. 2012); thus, using a stem taper model developed for
other species will have an inaccurate estimate of dand vol-
ume for Japanese cedar. Furthermore, most of the stem taper
studies in Korea focused only on evaluating the accuracy of
stem taper models in predicting dand did not evaluate the
predictive capability of stem taper models in estimating total
stem volume. Developing stem taper models for this com-
mercially important species could help forest managers
develop a more efficient forest inventory, which is essential
for sustainable forest management.Thus, the objective of this
study was to develop stem taper models for Japanese cedar in
Korea and to evaluate the performance of these stem taper
models in predicting dand total stem volume.
Materials and methods
Study site
This study was conducted in the southernmost province of
South Korea, between 126
o
08'43"–126
o
58'20"E and 33
o
11'27"–
33
o
33'50"N (Lee et al. 2009). Jeju province has a total land
area of 184,840 ha and c. 48% (88,874 ha) of this island has
forest cover (Korea Forest Service 2012). The mean annual
temperature (MAT) is 15.40 C. In addition, the minimum
annual temperature is 3.20 C and the maximum annual tem-
perature is 29.80 C. The mean annual precipitation (MAP) is
1560.80 mm (Korea Meteorological Administration 2014).
Stem taper models
A total of 120 Japanese cedar trees were harvested for the
measurement of D(in cm), H(in m), d(in cm), and h(in m).
Before felling, Dand din 0.2 m (stump height) were mea-
sured for each tree while Hand dfrom 2.3 m up to the top of
the tree with 1 m interval were measured after felling. Fur-
thermore, Dand dwere measured using standard diameter
tape and Hand hwere measured using meter tape. The mean
Hwas 20.40 m with a range of 9.00 to 26.80 m and the mean
Dwas 32.60 cm with a range of 9.80 cm to 55.90 cm, as
shown in Table 1. The scatter plot of relative diameter (d/D)
against relative height (h/H) was created as shown in Figure 1
to visually examine the data as suggested by Corral-Rivas
et al. (2007) and G
omez-Garc
ıa et al. (2013).
The stem taper models used in this study were the models
published by Kozak in 1988 (referred hereafter as Kozak88)
and in 2004 (referred hereafter as Kozak01 and Kozak02).
Furthermore, the stem taper model developed by Lee et al.
(2003) for Pinus densiflora in Korea (referred hereafter as
Lee03) and a modification of the Lee03 model (referred here-
after as Mod Lee03) published by Berhe and Arnoldsson
(2008) for Cupressus lusitanica plantations in Ethiopia were
also used. The mathematical forms of these candidate models
are shown in Table 2. The parameters of these models were
estimated using the Statistical Analysis System Non-linear
(SAS NLIN) procedure (SAS Institute Inc. 2004).
Model evaluation
Kozak (2004) recommended the following fit statistics: stan-
dard error of estimate (SEE), mean bias (E), mean absolute
bias (MAB), and coefficient of determination (R
2
), to be used
for evaluation and comparison of stem taper models. These
were determined as follows:
SEE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Xn
i¼1ðYi^
YiÞ2
nk
s(1)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Relative diameter
Relative height
Figure 1. Scatter plot of the relative diameter (diameter outside bark/diameter
at breast height) over relative height (stem height/total height) for Japanese
cedar in Korea.
Table 2. Five stem taper equations selected as candidate models for Japanese cedar in southern Korea.
Model code Mathematical form
1
Reference
Kozak88 ^
d¼a1Da2a3DXb1Z2þb2lnðZþ0:001Þþb3Z162þb4expZþb5ðD6HÞKozak 1988
where: X¼ð1Z162Þ
ð1p162Þ
,
Kozak01 p= proportional height of the inflection point
2
Kozak 2004
^
d¼a1Da2Xb1þb2ð16expD6HÞþb3DXþb4XD6H
where: X¼ð1Z164Þ
ð10:010164Þ
Kozak02 ^
d¼a1Da2Ha3Xb1Z4þb2ð16expD6HÞþb3X0:100þb4ð16DÞþb5HQþb6XKozak 2004
where: Q¼ð1Z163Þ
,
X¼Q
ð1ð1:36HÞ163Þ
Lee03 ^
d¼a1Da2ð1ZÞb1Z2þb2Zþb3Lee et al. 2003
Mod Lee03 ^
d¼a1Da2ð1ffiffiffi
Z
pÞb1Z2þb2Zþb3Berhe and Arnoldsson 2008
Notes:
1
Dis diameter at breast height (cm), His the tree total height (m), his the height from the ground (m), Zis proportional height from the ground (h /H),
^
d
is the predicted diameter outside bark at h(cm), and a
i
,b
i
are the estimated parameters.
2
The pfor Japanese cedar in this study was 0.22, which is within the range of the suggested value (0.1–0.3) given by Kozak (2004).
Table 1. Summary of observed statistics of the data used in the development of
stem taper models for Japanese cedar in southern Korea.
Variable nMean Minimum Maximum SD
Total height 120 20.40 9.00 26.80 4.20
DBH 120 32.60 9.80 55.90 9.80
Note: SD = standard deviation; n= number of sampled trees.
182 R. I. C. LUMBRES ET AL. E-ISSN 2158-0715
Downloaded by [179.61.162.119] at 16:35 10 November 2017
E¼Xn
i¼1ðYi^
YiÞ
n(2)
MAB ¼Xn
i¼1jYi^
Yij
n(3)
R2¼1Xn
i¼1ðYi^
YiÞ2
Xn
i¼1ðYiYÞ2
"#
(4)
where Yi= observed variable;
^
Yi= predicted variable; Y=
observed mean of the variable; k= the number of estimated
parameters; and n= number of observations.
To determine further which model is most suitable, Kozak
and Kozak (2003) recommended using lack-of-fit statistics.
In this evaluation, one or more evaluation statistics must be
determined for the various subgroups of the independent
variable. In this study, the SEE,E, and MAB of the candidate
models in predicting din the different relative height classes
(0.10 interval) were determined. This study also assessed the
applicability of stem taper models in accurately estimating
stem volume (m
3
). According to Li and Weiskittel (2010), a
stem taper model should not only predict dbut it must also
estimate stem volume accurately. Thus, the performance of
five stem taper models in estimating the total volume of
Japanese cedar was also evaluated. Both the observed and
predicted total volumes were calculated using the Smalian
formula (Clutter et al. 1983) as done in the different stem
taper studies (Kurinobu et al. 2007; Berhe and Arnoldsson
2008; Li and Weiskittel 2010; Li et al. 2012). For the observed
volume, the measured dwere used to calculate the volume of
the different log sections and these were summed up to deter-
mine the total stem volume of each tree. For the predicted
volume, the dwere first predicted starting from 0.2 m up to
the top of the tree at 1 m intervals, and the volumes in each
log section were determined and summed up to acquire the
total volume. Finally, the SEE,E, and MAB of the five models
in the different Dclasses (10 cm intervals) were determined.
Results and discussion
Stem taper models (Kozak88, Kozak01, Kozak02, Lee03, and
Mod Lee03) were fitted to Japanese cedar in the southern
part of Korea and their parameters were estimated as shown
in Table 3. The overall performance of these models was eval-
uated using four statistical criteria (SEE,E,MAB, and R2)as
shown in Table 3. To determine the best model, rank analysis
was employed. In this method, the model that had the lowest
values for SEE and MAB had the best rank while a value near-
est to 0 and 1 was considered best forEand R2, respectively.
The ranks of each model in the four performance criteria
were summed and the model with the lowest value was con-
sidered the best stem taper model for Japanese cedar in
Korea. Results of rank analysis indicated that the Kozak88
model had the overall best performance in predicting d, hav-
ing the best SEE (1.5126), MAB (1.0460 cm), and R2
(0.9959), and having the second best E(–0.0160 cm). This
model was followed by the Kozak02 model having the best E
with –0.0060 cm and having the second rank for SEE
(1.5234), MAB (1.0490 cm), and R2 (0.9958). The Lee03
model was considered the poorest among the candidate mod-
els in this study having the lowest rank in three statistical cri-
teria (SEE: 2.1822, MAB: 1.5170 cm, and R2: 0.9914).
To evaluate further, lack-of-fit statistics were used and the
results indicated that the Kozak88 model provided the best
performance in predicting d, having the best SEE,E, and
MAB in most of the relative height classes (Table 4). This
model was followed by Kozak02 and Mod Lee03, respectively,
while the Lee03 model consistently provided the poorest per-
formance in predicting d. Furthermore, the performance of
the candidate stem taper models to accurately predict total
stem volume of Japanese cedar was also assessed using lack-
of-fit statistics, as shown in Table 5. The Kozak88 model
showed again its superiority among the candidate models
having the best SEE,E, and MAB in most of the Dclasses in
predicting the total stem volume. The Kozak02 model again
Table 3. Estimated parameters and fit statistics of the five candidate stem taper
models for Japanese cedar in Korea.
Parameter
and fit
statistics Kozak88 Kozak01 Kozak02 Lee03
Mod
Lee03
a
1
0.7683 1.3946 0.9769 1.9034 2.2673
a
2
1.2363 0.9892 0.8589 0.8885 0.8896
a
3
0.9922 0.1767
b
1
2.1374 0.5105 0.3628 3.7015 1.6992
b
2
¡0.9214 ¡0.2523 ¡0.6183 ¡5.5723 ¡2.3628
b
3
2.9157 0.0418 0.3388 2.8764 1.4579
b
4
¡1.6652 ¡0.2028 3.2012
b
5
0.0949 0.1055
b
6
¡0.2497
SEE 1.5126 1.8596 1.5234 2.1822 1.7785
MAB 1.0460 1.3420 1.0490 1.5170 1.2590
E¡0.0160 ¡0.1350 ¡0.0060 0.0540 0.0210
R
2
0.9959 0.9938 0.9958 0.9914 0.9943
Rank 1425 3
Table 4. Lack-of-fit statistics in the different relative height classes of the five
stem taper models in estimating the diameter outside bark (cm) of Japanese
cedar in Korea.
Statistics
Relative
height
classes Kozak88 Kozak01 Kozak02 Lee03
Mod
Lee03
SEE <0.1 2.8054 3.0924 1.0534 1.2402 1.2232
0.1–0.2 1.2114 1.4534 1.8183 2.1495 1.9606
0.2–0.3 1.2453 1.2838 1.6258 2.3902 1.8843
0.3–0.4 1.2369 1.4374 1.4154 2.0438 1.5948
0.4–0.5 1.3507 1.7208 1.2449 2.0611 1.5407
0.5–0.6 1.2684 1.5839 1.6773 2.5353 1.9685
0.6–0.7 1.3001 1.5154 1.3763 2.4058 1.7791
0.7–0.8 1.3898 1.4144 2.1303 2.9759 2.5601
0.8–0.9 1.3381 1.6351 1.6866 2.4920 1.9726
>0.9 1.2567 2.5899 1.2960 1.2754 1.1694
E<0.1 ¡0.1847 ¡0.3902 ¡0.2667 ¡0.4042 ¡0.4229
0.1–0.2 0.0979 ¡0.8304 ¡0.2715 ¡0.3672 ¡0.4001
0.2–0.3 0.3415 0.0397 0.0284 0.0475 0.0096
0.3–0.4 ¡0.0405 0.4491 0.1048 0.2605 0.2247
0.4–0.5 ¡0.1742 0.8687 ¡0.2179 0.0381 ¡0.0205
0.5–0.6 ¡0.3100 0.8691 ¡0.1061 0.2074 0.1579
0.6–0.7 ¡0.0578 0.6893 0.1550 0.4223 0.3839
0.7–0.8 0.1748 0.0819 0.2676 0.2420 0.1986
0.8–0.9 0.2475 ¡0.8527 0.0320 0.2998 0.2598
>0.9 ¡0.4687 ¡2.1801 0.2782 ¡0.1190 ¡0.1525
MAB <0.1 1.7593 2.0273 0.7289 0.8992 0.8618
0.1–0.2 0.8924 1.0697 1.1905 1.5627 1.4006
0.2–0.3 0.9032 0.9258 1.1461 1.6371 1.3193
0.3–0.4 0.8837 1.0749 0.9924 1.4899 1.1900
0.4–0.5 0.9870 1.3669 0.9553 1.5836 1.2531
0.5–0.6 0.9747 1.2183 1.1276 1.8160 1.4321
0.6–0.7 0.9750 1.1219 0.9701 1.6555 1.2592
0.7–0.8 1.0332 1.0552 1.3645 1.9736 1.7350
0.8–0.9 0.9758 1.2247 1.0819 1.6386 1.3250
>0.9 0.9789 2.2268 0.9963 1.0082 0.8790
Sum 60 120 76 147 113
Overall
rank
14253
E-ISSN 2158-0715 FOREST SCIENCE AND TECHNOLOGY 183
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came second in accurately predicting the total stem volume
of Japanese cedar.
Several studies have shown that the Kozak88 stem taper
model can provide accurate estimate of dfor various species
in different countries. Huang et al. (2000) developed a stem
taper model for Picea glauca in Alberta, Canada using this
model in the different ecoregions and found that the data fit-
ted quite well based on the evaluation. Furthermore, Huang
et al. (2000) concluded that the Kozak88 stem taper model is
flexible, easy to use, and readily adaptable to any species.
This was proven by Klos et al. (2007) who also used the
Kozak88 model for the five major commercial trees (Populus
balsamifera,Populus tremuloides,Picea glauca,Picea
mariana, and Pinus banksiana) in Manitoba, Canada. They
concluded that the Kozak88 model provided a good fit for
these five species as the model explained more than 97% of
the total variation in d. In Sweden Hjelm (2013) also con-
cluded that the Kozak88 model had the best performance for
Populus maximowiczii £P. trichocarpa compared to five
other stem taper models based on the different evaluation
statistics. In Korea, the Kozak88 model had the best perfor-
mance compared to other stem taper models for Pinus kor-
aiensis,Pinus densiflora,Pinus rigida,Larix kaempferi,
Quercus accutissima,Quercus mongolica (Son et al. 2002),
Quercus acuta (Chung et al. 2010), Pinus thunbergii (Son
et al. 2013), and Larix kaempferi in the southern region
(Kang et al. 2014).Moreover, Son et al. (2012) concluded
that the Kozak88 model fitted well for Robinia pseudoacacia
and this model was used for the development of a stem vol-
ume table. In tropical countries, Kozak88 had a better predic-
tive capability in estimating dfor Acacia mangium and
Eucalyptus pellita in Kalimantan, Indonesia (Son et al. 2009)
and Pinus kesiya in the Philippines (Lumbres et al. 2013). In
Ethiopia, Berhe and Arnoldsson (2008) concluded that
Kozak88 was the best overall model for Cupressus lusitanica
as compared to six other stem taper models, especially for
predicting merchantable and total volume. Rojo et al. (2005)
evaluated the performance of 31 stem taper equations for
Pinus pinaster in Galicia, northwestern Spain. Based on the
results of their study, Kozak88 and Kozak02 were recom-
mended as the most suitable taper models for volume
estimation.
The predictive capability of the second best model of this
study (Kozak02) to accurately estimate dhas been demon-
strated in the research literature. In a comprehensive study,
Kozak (2004) concluded that Kozak02 was the overall best
among four models based on 38 species groups consisting of
53,603 trees. Heidarsson and Pukkala (2011) also selected
Kozak02 as the best stem taper model for Pinus contorta and
Larix sibirica in Iceland. Among the 10 stem taper models
that were developed for Picea rubens and Pinus strobus,Li
and Weiskittel (2010) concluded that the Kozak02 model
was the most accurate in predicting d.
The stem taper models in this study can be applied in the
estimation of stem form and volume of Japanese cedar. Using
the best three stem taper models in this study (Kozak88,
Kozak02, and Mod Lee03), the stem profiles of three Japanese
cedar trees were predicted and compared to the observed
stem profile (Figure 2). Another application of this study is
in the volume prediction of Japanese cedar. The din the dif-
ferent hshould be predicted first using the best model
(Kozak88) in this study. Using the Smalian formula, the vol-
ume of the different log section can be determined and
summed up for the total stem volume estimation. For
instance, the total stem volume of a Japanese cedar with a
DBH of 32 cm and total height of 20 m can be estimated.
The dstarting from the stump height (0.20 from the ground)
to the Hwith intervals of 0.50 m can be predicted as follows:
Z1¼0:20620 ¼0:01 (5)
X1¼ð10:01162Þ
ð10:22162Þ¼1:01 (6)
d1¼0:7683 321:2363 0:992232
1:01½2:13740:012þ½0:9214lnð0:01þ0:001Þþ½2:91570:01162þ½1:6652exp0:01þ½0:0949ð32 620Þ
d1¼44:10 cm
(7)
The dof the next height position (h
2
= 0.70 m) can also be
predicted as follows:
Z2¼0:70620 ¼0:04;(8)
X2¼ð10:04162Þ
ð10:22162Þ¼0:91;(9)
d2¼0:7683 321:2363 0:992232
0:91½2:13740:042þ½0:9214lnð0:04þ0:001Þþ½2:91570:04162þ½1:6652exp0:04þ½0:0949ð32 620Þ
d2¼35:67 cm
(10)
Table 5. Lack-of-fit statistics in the different DBH classes of the five stem taper
models in estimating the total stem volume (m
3
) of Japanese cedar in Korea.
Statistics
DBH
class Kozak88 Kozak01 Kozak02 Lee03
Mod
Lee03
SEE <15 0.0146 0.0153 0.0164 0.0126 0.0119
15–25 0.0174 0.0216 0.0231 0.0155 0.0148
25–35 0.0505 0.0505 0.0534 0.0493 0.0497
35–45 0.0900 0.0924 0.0934 0.0921 0.0942
>45 0.1521 0.1558 0.1499 0.2121 0.2066
E<15 0.0061 ¡0.0064 ¡0.0025 ¡0.0072 ¡0.0065
15–25 0.0069 0.0000 0.0023 ¡0.0053 ¡0.0036
25–35 ¡0.0092 0.0030 ¡0.0024 ¡0.0023 0.0025
35–45 0.0121 0.0340 0.0245 0.0161 0.0240
>45 0.0017 ¡0.0373 ¡0.0368 ¡0.1116 ¡0.0998
MAB <15 0.0071 0.0097 0.0073 0.0077 0.0073
15–25 0.0119 0.0155 0.0153 0.0106 0.0101
25–35 0.0358 0.0392 0.0405 0.0364 0.0367
35–45 0.0600 0.0626 0.0604 0.0659 0.0662
>45 0.1094 0.1098 0.1078 0.1741 0.1653
Sum 35 55 46 47 47
Overall rank 1 5 2 3 3
0
10
20
30
40
50
60
0.0 0.2 0.4 0.6 0.8 1.0
Diameter (cm)
Relative height
Kozak88 (Predicted)
Kozak02 (Predicted)
Mod Lee03 (Predicted)
Observed (D=42.8, H=24.1)
Observed (D=31.3, H=17.9)
Observed (D=16.5, H=12.8)
Figure 2. Observed and predicted tree stem profiles of different sizes of
Japanese cedar using the three best stem taper models.
184 R. I. C. LUMBRES ET AL. E-ISSN 2158-0715
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This process must be done at every 0.5 m height position
until the 19.70 m. After estimation of d, the volume for each
log section can now be determined using the Smalian formula
as follows:
Volume1¼0:00007854 d12þd22
62
L (11)
Volume1¼0:00007854 44:102þ35:672
62
0:5(12)
Volume1¼0:0632 m3(13)
By summing up the volumes from the different sections,
the total stem volume of this tree is 0.7272 m
3
. This process
can be done with the aid of a spreadsheet or other computer
program as it is relatively easier than a pocket calculator (Li
et al. 2012).
The performance of the Kozak88 model in volume estima-
tion was compared to the volume model developed for
Japanese cedar by Lee et al. (2001) and to a computer pro-
gram called Forest Resources Evaluation and Prediction Pro-
gram (FREPP) developed by the Korea Forest Research
Institute to estimate the stem volume of the different tree spe-
cies in Korea, including Japanese cedar. The MAB in the dif-
ferent Dclasses were determined for the three models as
shown in Figure 3. Results indicated that the Kozak88 model
had the lowest MAB in the different Dclasses, but most espe-
cially in the higher Dclasses. This only shows that stem taper
models provide better estimates of stem volume, which is
more important than destimates.
Conclusion
Based on the fit statistics and lack-of-fit statistics, the perfor-
mance of the five stem taper models was evaluated. The
Kozak88 model provided the best performance in accurately
predicting dof Japanese cedar in the southern part of Korea.
This model was followed by the Kozak02 and Mod Lee03
model, respectively. The results of this study also indicated
that stem taper models can be used to accurately estimate the
total stem volume of Japanese cedar. The Kozak88 model
also showed its superiority in total volume estimation as
compared to the other stem taper models. This model was
also superior when compared to the FREPP computer pro-
gram and volume model developed by Lee et al. 2001 in
accurately estimating the total stem volume of Japanese
cedar; thus, this model is recommended for the estimation of
d, log volume at any given length, merchantable and total
volume of Japanese cedar in Jeju island, Korea.
Acknowledgements
This study was carried out with the support of the Warm Temperate and
Subtropical Forest Research Center, Korea Forest Research Institute.
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