Abstract. Measurements were made of 101 Kandelia obovata Liu & Yong trees
growing in Giao Lac Commune, Giao Thuy District, Nam Dinh Province, and,
based on the diameter (cm) at 30 cm above the widening of the trunk base,
allometric regressions were done to estimate the biomass (kg) of the entire tree,
above-ground biomass, trunk biomass, leaf biomass and below-ground biomass,
found to be W = 0.10316D1.85845(R2 = 0, 86), W = 0.09012D1.78752(R2 =
0, 84), W = 0.04975D1.94748(R2 = 0, 79), W = 0.00899D1.7643(R2 = 0, 63)
and W = 0.01420D2.12146(R2 = 0, 73), respectively. Compared to regressions
obtained using the traditional logarithmic transformation method, the above
regressions had a much better fit. The original biomass data of the sample trees
were also used to calculate the proportion of total biomass apportioned to trunk,
branches, leaves and roots. While for small trees (D ≤ 4 cm), 20% is leaves, 20%
is branches, 35% is trunk and 25% is roots, for larger trees (D ≥ 10 cm), only
about 5% is leaves, 5% is branches, 65% is trunk and 25% is roots. The allometric
equations and biomass partition obtained in this study could be used effectively to
account for biomass and carbon in Kandelia obovata Liu & Yong mangroves.

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JOURNAL OF SCIENCE OF HNUE
Chemical and Biological Sci., 2013, Vol. 58, No. 9, pp. 91-103
This paper is available online at
ALLOMETRIC RELATIONSHIP AND BIOMASS PARTITION
OF Kandelia obovata LIU & YONG PLANTED IN NAM DINH PROVINCE
Pham Hong Tinh1 and Mai Sy Tuan2
1Mangrove Ecosystem Research Center, Hanoi National University of Education
2Faculty of Biology, Hanoi National University of Education
Abstract. Measurements were made of 101 Kandelia obovata Liu & Yong trees
growing in Giao Lac Commune, Giao Thuy District, Nam Dinh Province, and,
based on the diameter (cm) at 30 cm above the widening of the trunk base,
allometric regressions were done to estimate the biomass (kg) of the entire tree,
above-ground biomass, trunk biomass, leaf biomass and below-ground biomass,
found to be W = 0.10316D1.85845(R2 = 0, 86),W = 0.09012D1.78752(R2 =
0, 84),W = 0.04975D1.94748(R2 = 0, 79),W = 0.00899D1.7643(R2 = 0, 63)
and W = 0.01420D2.12146(R2 = 0, 73), respectively. Compared to regressions
obtained using the traditional logarithmic transformation method, the above
regressions had a much better fit. The original biomass data of the sample trees
were also used to calculate the proportion of total biomass apportioned to trunk,
branches, leaves and roots. While for small trees (D ≤ 4 cm), 20% is leaves, 20%
is branches, 35% is trunk and 25% is roots, for larger trees (D ≥ 10 cm), only
about 5% is leaves, 5% is branches, 65% is trunk and 25% is roots. The allometric
equations and biomass partition obtained in this study could be used effectively to
account for biomass and carbon in Kandelia obovata Liu & Yong mangroves.
Keywords: Allometric relationship, Kandelia obovata Liu & Yong, Biomass,
Vietnam.
1. Introduction
Mangrove forest is an important ecosystem in tropical and subtropical coastal
regions. However, this ecosystem is being degraded and damaged at an alarming rate by
human activites, e.g. land use change, unsustainable exploitation and human population
increase [6]. Moreover, the value of mangrove forests in terms of carbon accumulation
and other factors are not well understood.
Received September 26, 2013. Accepted December 18, 2013.
Contact Pham Hong Tinh, e-mail address: phamtinhsp@yahoo.com
91
Pham Hong Tinh and Mai Sy Tuan
Kandelia obovata Liu & Yong is a key species that has been planted in coastal
areas of Northern Vietnam, mainly Quang Ninh, Nam Dinh and Thai Binh Provinces.
In a natural development and ecological succession of mangrove forest, this species
and others grow together in national mangrove forests [2]. Therefore understandings
ecological characteristics of this species such as biomass and carbon accumulation could
significantly contribute to sustainable management of the mangrove forests.
Scientists have developed a number of methods to estimate biomass (dry weight)
of both inland and mangrove forest. These methods are divided into three categories: 1)
the harvest method, 2) the mean-tree method and 3) the allometric method. The harvest
method is not practical for measuring mature forests of the large amount of time and
manpower needed. Moreover, the harvest method is not reproducible because the trees are
destroyed. The mean-tree method is utilized only in forests that are relative homogeneous
in terms of tree size. The allometric method uses allometic equations to estimate the
whole and partial weight of a tree referring to measured tree dimensions, including
trunk diameter and height. This method is useful for estimating temporal changes in
forest biomass by subsequent measurements (Komiyama et al.) [5]. However, allometric
equations are site- and species-specific.
Little research done using allometric equations to determine Kandelia obovata Liu
& Yong biomass has been published or cited. The research presented in this paper is one
of the first studies in Vietnam that makes use of allometric equations to determine the
total and component biomass of Kandelia obovata Liu & Yong. In addition, we compared
two ways of building allometric equations, i.e. determining parameters of equations.
In term of carbon accumulation, the roots of mangrove trees are probably the most
important component. However, an understanding of carbon accumulation in roots as well
as in other components is limited because very few studies have been done on biomass
proportion of mangrove trees. Ong et al. [7] have shown that in 20-year-old Rhizophora
apiculata mangrove trees, carbon is accumulated in the roots at a rate of 0.42 tC/ha/year,
whereas accumulation in the canopy is at a rate of 0.52 tC/ha/year. We have not found
published data on carbon accumulation and biomass proportion of Kandelia obovata Liu
& Yong. Therefore, in this paper we are the first to announce the biomass proportion of
Kandelia obovata Liu & Yong in Vietnam.
The results of this study are expected to significantly contribute to biomass and
carbon accounting for Kandelia obovata Liu & Yong mangroves in Nam Dinh Province
as well as other areas of Northern Vietnam.
2. Content
2.1. Methodology
2.1.1. Study site
The present study was carried out onKandelia obovata Liu &Yong that was planted
10 - 20 years ago in Giao Lac Commune, Giao Thuy District, in Nam Dinh Province. Giao
92
Allometric relationship and biomass partition of Kandelia obovata...
Lac is located at 20013’-20015’ North, 106015’-106030’ East (Figure 1) and is one of the
buffer zones of Xuan Thuy National Park. It is the first Ramsar Site in Vietnam. In Giao
Lac there are about 407.7 hectares of mangrove forest. The Giao Lac mangrove trees
received a lot of sediment from the Ninh Co and Red River and it is a relatively flat area
with a thick layer of alluvial sediment. Mangrove plantations may also be grown in clay
mud and sand. Giao Lac has a diurnal tide with sea level of 0.1 - 3.9 m, a temperature
of 240C, rainfall of nearly 1500 mm/year, air humidity of about 82% and salinity 18.0 -
28.3%.
Figure 1. Location and map of the study site
2.1.2. Materials
A sampling of 101 trees was chosen in the study site having diameters ranging from
0.5 to 15 cm. The trees were cut down and the roots dug out in 2008, 2009 and 2013 to
measure trunk diameter, total and component dry weight (above ground, stem, branch, leaf
and below ground). All sample trees was selected using the stratified sampling method: 1)
divide the study area into sections corresponding to the year the trees were planted (from
1998 to 2009); 2) randomly select two or three sample plots (10 × 10 m) within each
compartment (a total of 34 sample plots were established) and 3) select three sample trees
(smallest, largest and average) within each sample plot.
Before felling the sample trees, we measured and recorded the diameter at 30 cm
above the widening at the base of the trunk. The sample trees were cut and separated into
four components: stems, branches, leaves and roots. Then we weighed and recorded the
fresh weight of each component. We took about 5 - 10 g samples of each component, and
weighed and recorded the exact fresh weight of each sample. The samples were then taken
to the laboratory and dried to a constant weight. The dry samples were weighed again to
get the dry weight of each sample. The ratio of fresh weight to dry weight of each sample
was used to calculate the dry weight of each component. The total dry weight of the stems,
branches and leaves is the above ground biomass. The total biomass of a tree is the sum of
the dry weights of all four components. The diameter and dry weight of the sample trees
are presented in Table 1.
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Pham Hong Tinh and Mai Sy Tuan
Table 1. Diameter and dry weight of sample trees
No.
Diamter
D (cm)
Dried weight W (kg)
Total
Above -
ground
Trunk Branches Leaves
Below -
ground
(roots)
1 0.7 0.02 0.02 0.01 0.01 0.01
2 0.7 0.55 0.51 0.01 0.46 0.05 0.04
3 0.7 0.03 0.02 0.01 0.01 0.01
4 0.7 0.08 0.04 0.01 0.04 0.04
5 0.8 0.02 0.01 0.01 0.00 0.01
6 0.8 0.02 0.02 0.01 0.00 0.01
7 1.5 0.02 0.02 0.01 0.01 0.01
8 2.7 1.41 0.83 0.19 0.03 0.60 0.58
9 2.7 0.23 0.13 0.08 0.04 0.10
10 2.9 0.67 0.59 0.10 0.43 0.05 0.08
11 3.1 0.30 0.21 0.12 0.01 0.08 0.09
12 3.1 0.15 0.14 0.14 0.00 0.01
13 3.2 0.19 0.18 0.17 0.01 0.01
14 3.3 0.29 0.24 0.19 0.02 0.03 0.05
15 3.5 0.39 0.29 0.17 0.07 0.05 0.10
16 3.7 0.49 0.32 0.21 0.03 0.08 0.17
17 3.8 1.24 0.73 0.51 0.04 0.18 0.47
18 3.8 1.21 0.76 0.33 0.01 0.42 0.44
19 3.8 0.99 0.90 0.28 0.59 0.04 0.09
20 3.9 0.92 0.75 0.23 0.29 0.23 0.17
21 4.1 1.68 1.14 0.59 0.23 0.32 0.52
22 4.3 0.87 0.77 0.45 0.28 0.05 0.10
23 4.4 1.21 0.90 0.51 0.32 0.07 0.30
24 4.4 1.58 1.13 0.62 0.36 0.14 0.43
25 4.6 2.13 1.60 0.88 0.45 0.27 0.50
26 4.8 3.07 1.55 0.81 0.40 0.34 1.49
27 5.2 1.76 1.24 0.70 0.32 0.22 0.49
28 5.2 2.85 1.61 0.93 0.49 0.19 1.21
29 5.2 1.17 1.11 1.08 0.04 0.06
30 5.3 2.45 1.74 1.40 0.18 0.16 0.69
31 5.3 3.19 1.72 1.03 0.15 0.54 1.43
32 5.3 3.87 3.27 2.64 0.33 0.30 0.57
33 5.3 0.57 0.47 0.33 0.04 0.10 0.10
34 5.4 2.78 2.15 1.81 0.16 0.18 0.60
35 5.4 2.14 1.70 1.44 0.13 0.13 0.41
36 5.6 3.25 2.37 1.90 0.18 0.29 0.87
37 5.6 2.25 1.79 1.01 0.60 0.19 0.44
38 5.6 2.92 2.20 1.01 0.78 0.40 0.71
39 5.7 1.92 1.57 1.08 0.29 0.20 0.35
40 5.7 3.46 2.58 1.66 0.50 0.41 0.82
41 5.7 2.81 2.28 1.15 0.76 0.37 0.53
42 5.7 2.43 2.00 1.51 0.36 0.13 0.38
43 5.7 3.15 2.22 1.41 0.58 0.23 0.91
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Allometric relationship and biomass partition of Kandelia obovata...
44 5.7 0.63 0.43 0.25 0.04 0.14 0.20
45 5.9 4.33 2.48 1.64 0.24 0.60 1.84
46 6.0 3.43 2.89 2.08 0.65 0.16 0.49
47 6.0 2.23 1.84 1.49 0.20 0.16 0.37
48 6.0 2.46 1.93 1.62 0.06 0.25 0.52
49 6.0 2.92 1.86 1.17 0.19 0.51 1.02
50 6.0 1.00 0.73 0.51 0.08 0.14 0.28
51 6.1 3.37 2.69 2.26 0.09 0.33 0.62
52 6.1 2.37 1.84 1.36 0.27 0.21 0.52
53 6.1 2.98 2.28 1.24 0.50 0.54 0.64
54 6.4 3.32 2.90 2.33 0.30 0.28 0.42
55 6.4 3.02 2.48 2.03 0.15 0.30 0.52
56 6.4 3.78 2.31 1.35 0.40 0.56 1.45
57 6.4 3.49 2.32 2.09 0.23 1.18
58 6.4 3.03 1.80 1.58 0.21 1.23
59 6.5 3.24 2.33 1.69 0.30 0.34 0.90
60 6.7 2.92 1.90 1.59 0.16 0.16 0.98
61 6.7 2.45 2.07 1.60 0.22 0.24 0.38
62 6.7 2.83 2.13 1.79 0.02 0.32 0.71
63 6.7 2.78 2.24 2.19 0.05 0.54
64 6.8 4.09 3.14 2.13 0.73 0.28 0.94
65 7.0 3.37 2.61 2.06 0.25 0.30 0.70
66 7.0 3.45 2.45 1.97 0.22 0.26 0.99
67 7.0 3.38 2.08 1.82 0.27 1.30
68 7.1 2.64 2.16 1.70 0.24 0.22 0.46
69 7.2 3.91 2.65 1.68 0.63 0.34 1.24
70 7.2 1.69 1.40 1.18 0.06 0.16 0.22
71 7.3 4.97 3.61 2.77 0.47 0.37 1.36
72 7.5 4.75 3.92 3.13 0.24 0.54 0.82
73 7.7 4.28 3.49 3.05 0.16 0.27 0.78
74 7.8 3.39 2.58 2.45 0.13 0.80
75 7.9 5.05 2.76 2.49 0.09 0.18 2.26
76 7.9 4.89 4.22 3.72 0.17 0.32 0.65
77 8.0 4.66 3.21 2.40 0.25 0.55 1.37
78 8.0 3.57 1.83 1.16 0.36 0.32 1.68
79 8.0 2.32 1.99 1.66 0.02 0.31 0.33
80 8.3 5.94 5.01 4.61 0.24 0.16 0.81
81 8.3 6.04 4.52 3.97 0.24 0.31 1.48
82 8.4 4.65 3.90 3.08 0.41 0.41 0.73
83 8.6 7.99 6.61 5.36 0.74 0.50 1.30
84 8.6 3.20 2.31 1.62 0.40 0.30 0.82
85 8.6 2.51 1.73 1.22 0.31 0.21 0.77
86 8.8 7.82 6.37 5.16 0.74 0.47 1.37
87 8.8 7.46 6.26 5.51 0.28 0.47 1.12
88 8.8 7.56 6.44 5.51 0.46 0.47 1.12
89 8.9 7.87 6.67 5.61 0.31 0.75 1.16
90 9.0 5.03 4.55 4.14 0.28 0.13 0.46
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Pham Hong Tinh and Mai Sy Tuan
91 9.1 8.28 6.76 5.80 0.46 0.51 1.48
92 9.2 8.46 5.90 5.29 0.30 0.32 2.52
93 9.2 6.57 5.25 4.64 0.13 0.48 1.31
94 9.3 4.74 3.54 2.91 0.28 0.35 1.20
95 9.4 3.47 2.76 2.32 0.27 0.18 0.67
96 9.6 5.52 4.23 3.52 0.31 0.40 1.22
97 10.5 9.73 5.94 5.39 0.26 0.29 3.79
98 12.1 12.64 7.90 7.07 0.34 0.49 4.72
99 13.0 11.22 9.61 8.39 0.25 0.96 1.59
100 13.7 13.33 8.44 7.52 0.34 0.59 4.85
101 13.7 8.66 6.50 5.37 0.53 0.60 2.14
2.1.3. Allometry and variables of allometric equations
Allometry is based on the fact that there is proportionality between the relative
growth rates of two different parts of the plant [3]. The relationship between the two
variables can be expressed by the following equation:
(
dy
ydt
) : (
dx
xdt
) = k (1)
where x is the independent variable (e.g. stem diameter, tree height or both), y is the
dependent variable (e.g. biomass) and b and k are the allometric constants. The equation
can be simplified as follows:
(1)⇔
dy
y
= k
dx
x
⇔
∫
dy
y
= k
∫
dx
x
⇔ ln y + c1 = k (lnx+ c2)
⇔ ln y = ln xk + ln b
⇔ y = bxk (2)
In this study, we used diameter at 0.3 m height (D) as the independent variable because
it is easy to measure in the field by using a caliper or tape measure. Tree height was
not used in the equation because measuring the height of mangrove trees does not in
an accurate and it is time consuming. In the latest guidelines on carbon assessment of
mangroves, CIFOR (Center for International Forestry Research) recommended that the
allometric equation should be developed and used with one independent variable – the
diameter [4].
2.1.4. Allometric constant determination
As the allometric equation form and variables of equations were determined, we
used the statistical analysis software JMPIN with the input data presented in Table 1 to
96
Allometric relationship and biomass partition of Kandelia obovata...
find the allometric constants b and k. The equations obtained by JMPIN were compared
with the corresponding equations developed using the traditional approach.
For the traditional method, the equation (2) was represented on logarithmic
coordinates as a linear relationship of the form: lny = klnx + b (3). The measured date
(Table 1) was also converted from arithmatic to logarithmic form in order to correspond
with the equation (3). Then the least squares method was used to find the equation
parameters b and k.
2.1.5. Allometric equation evaluation
The obtained allometric equations were evaluated using the the coefficient of
determination (R2), sum squared error of estimate (SE) and mean error of estimate
(bias) of the allometric equations developed by both approaches. Bias, R2 and SEE
were calculated by equation (4), (5) and (6) respectively. R2 is a statistic that would give
information about the goodness of fit of the allometric equations (i.e. R2 is a statistical
measure of how well the regression curve/line approximates the real data points). An R2
of 1 indicates that the regression curves/lines fit the data perfectly. SSE and bias are
errors of estimates when using allometric equations compared with the true values.
R2 = 1−
N∑
i=1
(yi − y
,
i)
2
N∑
i=1
(
yi −
1
N
N∑
i=1
yi
)2
(4)
SSE =
N∑
i=1
(yi − y
,
i)
2
(5)
bias =
N∑
i=1
(yi − y
,
i)
N
(6)
where yi is biomass of i
th tree measured in the field, y′i is biomass of i
th tree using the
allometric equation and N is total number of sample trees.
2.2. Results and discussions
2.2.1. Total biomass allometry
Table 2. Allometric equations for total biomass
Log -
transformed
Equation D (cm) N R2 SSE bias
Yes
lnW = 2.31487lnD – 3.26991
(W = 0.03801D2.31487)
0 – 15 101 0.82 154.49 0.13
No W = 0.10316D1.85845 0 – 15 101 0.86 113.43 -0.07
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Pham Hong Tinh and Mai Sy Tuan
Table 2 presents the allometric regressions obtained for total biomass with
log-transformation and non-transformation.
The coefficients of determination (R2) for both equations are greater than 0.8. They
indicate that a large proportion (over 80%) of the total biomass could be determined when
referring to a diameter at a height of 0.3 m. However, the errors of estimates (SE and
bias) show that the non-transformed equation fits the data better than the log-transformed
equation because their SSEs are 113.43 and 154.49 respectively, and their biases are -0.07
and 0.13 respectively.
Moreover, the non-transformed and log-transformed regressions fitting the actual
data shown in Figure 2 also indicate that the fit was better with the non-transformed data
than with the log-transformed data. For trees with a diameter less than 5 cm, two equations
overestimate the actual biomass. For trees with a diameter greater than 10 cm, the
log-transformed equation also overestimates the actual biomass, but the non-transformed
equation yields a better estimate.
Figure 2. Total biomass against diameter
of actual and two fitted models
Figure 3. Total above-ground biomass against
diameter of actual and two fitted models
2.2.2. Above-ground allometry
Total above-ground biomass
The allometric regressions developed for total above-ground biomass with
log-transformation and non-transformation are presented in Table 3.
Table 3. Allometric equations for total above-ground biomass
Log -
transformed
Equation D (cm) N R2 SSE bias
Yes
lnW = 2.33585lnD – 3.59103
(W = 0.02757D2.33585)
0 – 15 101 0.76 111.82 0.09
No W = 0.09012D1.78752 0 – 15 101 0.84 76.28 -0.06
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Allometric relationship and biomass partition of Kandelia obovata...
The coefficient of determination (R2) for a non-transformed equation is 0.84 and
for a log-transformed equation it is 0.76. This indicates that their proportions of total
above-ground biomass when referring to a diameter at 0.3 m height are 84% and 76%
respectively. On the other hand, SSE and bias for the log-transformed equation are
111.82 and 0.09 while the values for the non-transformed equation are 76.28 and -0.06,
respectively. Thus, it is clear that the non-transformed equation fits the data better than
the log-transformed equation. A detailed consideration of the graphs of total above-ground
biomass against the diameter of the actual and two fitted models (Figure 3) also indicates
that for trees with a diameter greater than 5 cm, the non-transformed equation fits the data
better than the other.
Trunk biomass
The allometric regressions developed for trunk biomass with log-transformation
and non-transformation are presented in Table 4.
Table 4. Allometric equations for trunk biomass
Log -
transformed
Equation D (cm) N R2 SSE bias
Yes
lnW = 2.22714lnD – 4.26584
(W = 0.01404D2.22714)
0 - 15 101 0.76 67.66 0.19
No W = 0.02485D2.04924 0 - 15 101 0.80 60.83 -0.04
Figure 4. Trunk biomass versus diameter
of actual and two fitted models
Figure 5. Branch biomass versus diameter
of actual and two fitted models
Both equations have a coefficient of determination (R2) of around 80% indicating
that about 80% of the trunk biomass could be determined referring to the diameter.
However, SSE and bias show that the non-transformed equation fits the actual data better
than the log-transformed equations because SSE and bias for the log-transformed equation
are 67.66 and 0.19 while the values for non-transformed equation are 60.83 and -0.04,
respectively. The graphs of trunk biomass against diameter of the actual and two fitted
models (Figure 4) also indicate this for trees with a diameter that is greater than 10 cm. For
99
Pham Hong Tinh and Mai Sy Tuan
trees with a diameter less than 10 cm, both equations have an almost equivalent goodness
of fit.
Branch biomass
Branches were not separated from the total biomass in 15 of the 101 trees sampled.
The allometric regressions developed for branch biomass with log-transformation and
non-transformation are presented in Table 5.
Table 5. Allometric equations for branch biomass
Log -
transformed
Equation D (cm) N R2 SSE bias
Yes
lnW = 1.35289lnD – 3.17169
(W = 0.02429D1.35289)
0 - 15 86 0.57 2.56 1.40
No W = 0.00209D2.56871 0 - 15 86 0.73 1.83 -0.38
The calculations of coefficient of determination (R2) and errors of estimates (SSE
and bias) indicate that the non-transformed equation fits the actual data much better than
the log-transformed equation. The values for the non-transformed equation are 0.73, 1, 83
and -0.38, respectively, while the values for the log-transformed equation are 0.57, 2.56
and 1.40, respectively. The graph of branch biomass against diameter of the actual and
two fitted models (Figure 5) also clearly shows that the log-transformed equation does