Biomass Equations For Tropical Tree Plantation Species Using
Secondary Data From The Philippines
Ma. Regina N. Banaticla^{1,3} , Renezita F. Sales^{1} and Rodel D. Lasco^{2,3}
^{1 }College of Forestry, Leyte State University, Visca, Baybay, Leyte, Philippines
^{2} Institute of Renewable Natural Resources, College of Forestry and Natural Resources,
U.P. Los Baños, College, Laguna, Philippines
^{3 }now at: World Agroforestry Centre (ICRAF) Philippines, 2/F Administration Building, College of Forestry and Natural Resources, U.P. Los Baños, College, Laguna, Philippines
ABSTRACT
Estimation of the magnitude of sinks and sources of carbon requires reliable estimates of the biomass of forests and of individual trees. Equations for predicting tree biomass have been developed using secondary data involving destructive sampling in plantations in several localities in the Philippines. These equations allow estimates of carbon sequestration to be made at much lower cost than would be incurred if detailed stand inventories were undertaken. The species included in the study reported here include Gmelina arborea, Paraserianthes falcataria, Swietenia macrophylla and Dipterocarp species in Mindanao; Leucaena leucocephala from Laguna, Antique, Cebu, Iloilo, Rizal, and Ilocos Sur, and Acacia mangium, Acacia auriculiformis and G. arborea in Leyte. Nonlinear regression was used to derive speciesspecific, sitespecific and generic equations between yield and diameter of the form y = aD^{b}. Equations were evaluated based on the correlation coefficient, standard error of the estimate and residual plots. Regressions resulted to high r values (>0.90). In some cases, nonhomogeneous variance was encountered. The generic equation improved estimates compared with models used in previous studies.
Keywords: allometric equation, fastgrowing species, nonlinear estimation, power fit
INTRODUCTION
Climate change is of major community concern, the most recent Intergovernmental Panel on Climate Change (IPCC) assessment report concluding that there is strong evidence that anthropogenic activities have affected the world’s climate (IPCC 2001). The rise in global temperatures has been attributed to emission of greenhouse gases, notably CO_{2} (Schimell et al. 1995). Deforestation and change in land use result in a high level of emissions of CO_{2} and other greenhouse gases. Presently, it is estimated that the world’s tropical forests emit about 1.6 Gt of CO_{2}C per year (Watson et al. 2000). Landuse and forestry also have the potential to mitigate carbon emissions through the conservation of existing carbon reservoirs (i.e. by preventing deforestation and forest degradation), improvement of carbon storage in vegetation and soils and wood products, and substitution of biomass for fossil fuels for energy production (Brown et al. 1993). Estimation of the magnitude of these sinks and sources of carbon requires reliable estimates of the biomass of forests and of individual trees.
Direct measurement of tree biomass involves felling an appropriate number of trees and estimating their field and ovendry weights, a method that can be costly and impractical, especially when dealing with numerous species and large sample areas. Rather than performing destructive sampling all the time in the field, an alternative method is to use regression equations (developed from a previously felled sample of trees) that predict biomass given some easily measurable predictor variable, such as tree diameter or total height. Such equations have been developed for many species (Parde 1980), including fastgrowing tropical species (Lim 1988, Fownes and Harrington 1991, Dudley and Fownes 1992, Stewart et al. 1992). These equations allow estimates of carbon sequestration to be made at much lower cost than would be incurred if detailed stand inventories were undertaken.
Biomass is typically predicted using either a linear (in the parameter to be estimated) or nonlinear regression model, of the following forms:
Linear: Y = X + (Equation 1)
Nonlinear: Y = X^{} + (Equation 2)
where Y = observed tree biomass
X = predictor variable (diameter, height)
= model parameter
= error term
The nonlinear model can be subdivided into two types: ‘intrinsically linear’ and ‘intrinsically nonlinear’. A model that is intrinsically linear can be expressed by transformation of the variables into standard linear form. If a nonlinear model cannot be expressed in this form, then it is intrinsically nonlinear. An example of an intrinsically linear model is the power function:
y = aD^{b}e (Equation 3)
where y = tree biomass (or total height)
D = diameter at 1.30 m (dbh)
a, b = model parameters
e = error term
Taking the natural logarithms of both sides of the equation yields the linear form:
ln y = ln a + b ln D + ln e (Equation 4)
In this form, the regression model can be fitted to biomass (or height) data using standard linear regression and least squares estimation. In earlier attempts to develop biomass equations for trees, logarithmic transformation was traditionally employed as a means of linearising nonlinear relationships, mainly because of the difficulty of solving nonlinear relationships without the aid of highspeed computers (Payandeh 1981). However, there are disadvantages in using logarithmic transformations, including the assumption of a multiplicative error term in the model (Baskerville 1972) and difficulties in evaluating usual measures of fit such as R^{2} and the standard error of estimate (SEE) in terms of the original data. In the case of biomass equations, nonlinear models usually produce a better fit than both the logarithmic and multiple linear regression models (Payandeh 1981).
Many works on mathematical models for biomass show the superiority of the power function (Equation 3 above), notably for estimation of the stems and roots of trees (Parde 1980, Fownes and Harrington 1991, Ketterings et al. 2001). The model also expresses the longrecognised allometry between two parts of the plant (Parde 1980), i.e. proportionality in the relative increment between the two parts (e.g. stem biomass and girth of a tree).
A generic equation for predicting individual aboveground tree biomass using dbh as predictor variable was developed by Brown (1997) using data on 170 trees of many species harvested from the moist forest zone of three tropical regions. This equation has been used in previous studies to determine indirectly the biomass and C storage of forest ecosystems n the Philippines (Lasco et al. 2002a and b, Lasco et al. 2004) because of the scarcity of local species or sitespecific biomass equations. However, generic equations applied to local data tend to overestimate the actual biomass of trees (Ketterings et al. 2000, Van Noordwijk et al. 2002, Macandog and Delgado 2002), which highlights the need to develop speciesspecific and sitespecific equations that produce estimates that more closely reflect the characteristics of species and conditions in the Philippines.
RESEARCH METHOD
For this study, no destructive sampling of trees was done; instead existing data from studies involving destructive sampling for biomass determination of trees conducted in several localities in the Philippines by Kawahara et al. (1981), Tandug (1986) and Buante (1997) were reanalysed. A general description of the study sites from these sources is provided in Table 1.
The data sets consisted of individual tree measurements for dbh, total height and total aboveground biomass of tropical tree species, majority of which are fastgrowing plantation species (Tables 24). Tandug (1986) and Buante (1997) both developed biomass regression equations with dbh and height as predictor variables. Nevertheless, both data sets were still analysed in order to develop simpler equations (i.e., those with fewer parameters and would not require prior transformation of data).
Table 1. Description of sampling sites from various data sources
Locality

Climate Type

Species

Forest type

Age (yr)

Stand density
(stems/ha)

Source

Arasasan, Mindanao

IV

Paraserianthes falcataria(L.) Nielsen

Plantation (timber)

4.9,
8.3

1085, 315

Kawahara et al. 1981



Swietenia macrophylla King

Plantation (timber)

15.3

1147




Gmelina arborea Roxb.

Plantation (timber)

9.3

1191




Dipterocarpaceae

Natural forest

unknown

1144


Laguna

I

Leucaena leucocephala de Wit

Plantation

9

459

Tandug 1986

Antique

III

L. leucocephala

Plantation

4

10742


Cebu

III

L. leucocephala

Plantation

10

1500


Ilocos Sur

I

L. leucocephala

Plantation

7

8140


Iloilo

IV

L. leucocephala

Plantation

5

648


Rizal

I

L. leucocephala

Plantation

24

8926


Leyte

II

Acacia auriculiformis A. Cunn. ex Benth

Plantation (fuelwood)

4

2500

Buante 1997



Acacia mangium Willd.

Plantation (fuelwood)

4

2500




G. arborea

Plantation (fuelwood)

4

2500


Table 2. Summary data of trees sampled by Kawahara et al. (1981)
Species

Number of trees

Dbh
(cm)

Total height (m)

Total aboveground biomass (kg/tree)

Paraserianthes falcataria (5yr old)

7

5.4 – 20.5

9.3  18.3

2.865  104.845

Paraserianthes falcataria (8yr old)

13

4.1 – 36.1

4.3  33.6

2.682  533.299

Gmelina arborea

7

8.0 – 31.4

7.3  25.0

9.384  306.008

Swietenia macrophylla

5

6.7 – 26.0

5.6  18.9

7.247  314.610

Dipterocarpaceae

7

7.3 – 34.0

7.9  26.9

6.85  472.822

Table 3. Summary data of L. leucocephala trees sampled by Tandug (1986)
Locality or province

Number of trees

Dbh
(cm)

Total height (m)

Total aboveground biomass
(kg/tree)

Laguna

18

5.4 – 21.0

5.7  10.5

5.141  151.368

Antique

13

4.5  14.1

9.0  12.7

7.4896  72.8962

Cebu

21

10.0  31.8

12.3  19.0

35.995  534. 973

Ilocos Sur

18

5.2  20.8

10.1  21.0

11.093  287.349

Iloilo

14

5.1  13.8

8.3  10.3

8.7576  75.7346

Rizal

27

4.0 16.2

5 .5  16.1

3.274  100.984

Table 4. Summary data of trees sampled by Buante (1997)
Species

Number of trees

Dbh
(cm)

Total height (m)

Total aboveground biomass
(kg/tree)
 Acacia auriculiformis 
30

7.2  12.9

6.48  9.50

15.708  49.080

Acacia mangium

30

7.1  12.5

6.20  8.90

11.775  48.827

Gmelina arborea

30

4.2  15.9

3.94  8.21

9.177  68.579

A preliminary screening was done for each data set by plotting biomass vs dbh to check for the Jshape associated with the power fit. Next, nonlinear regression analysis of the data was performed with CurveExpert v.1.3 (Hyams 1997) software using the LevenbergMarquardt algorithm. Practical experience in the field has shown the difficulty of obtaining accurate measurements of the height of standing trees, especially in natural forest stands. Bearing this in mind, priority has thus been given to a model with only diameter as predictor variable. Separate biomass equations of the form y = aD^{b}, with Y = total aboveground biomass of tree, D = diameter at breast height, and a,b = parameter estimates, were derived for each species and each site in the data sets. Pooled biomass data were also analysed to obtain generic equations with potential wider applicability. In the analysis, the effect of species and site differences on biomass was not considered. Speciesspecific, sitespecific as well as generic equations were evaluated based on the correlation coefficient (r), standard error of the estimate (SEE) and residual plots.
RESULTS AND DISCUSSION
Scatter plots of Buante’s data for Acacia mangium, Acacia auriculiformis and Gmelina arborea (Figure 3) show no apparent relationship between biomass and dbh, which was not the case with the other two data sets (Figures 1 and 2). Because the expected functional relationship between dbh and total aboveground biomass was not exhibited, it was decided to exclude this (secondary) data set from further analysis.



a. Biomass vs. Dbh: P. falcataria

b Biomass vs. Dbh: G. arborea

c. Biomass vs. Dbh: S. macrophylla




d. Biomass vs. Dbh: Dipterocarp species

e. Biomass vs. Dbh: all species


Figure 1. Scatter plots of biomass vs. dbh from Kawahara et al. (1981)



a. Biomass vs. Dbh: : L. leucocephala  Laguna

b. Biomass vs. Dbh: : L. leucocephala  Antique

c. Biomass vs. Dbh: L. leucocephala  Cebu




d. Biomass vs. Dbh: : L. leucocephala  Ilocos Sur

e. Biomass vs. Dbh: : L. leucocephala  Iloilo

f. Biomass vs. Dbh: : L. leucocephala – Rizal




g. Biomass vs. Dbh: : L. leucocephala – all sites



Figure 2. Scatter plots of biomass vs. dbh from Tandug (1986)



a. Biomass vs. Dbh: A. auriculiformis

b. Biomass vs. Dbh: A. mangium

c. Biomass vs. Dbh: G. arborea




d. Biomass vs. Dbh: all species



Figure 3. Scatter plots of biomass vs. dbh from Buante (1997)
Estimates for the parameters of the power function fitted to individual species and sites and the pooled biomass data are presented in Table 5. All analyses resulted in high r values (>0.90), although the SEE are variable.
When Tandug (1986)’s sitespecific equations for L. leucocephala are compared with the equations generated in this study, Figure 4 shows that in the absence of height data, the new equations can adequately approximate the observed biomass values with diameter at breast height as sole predictor variable. The generic (pooled sites) equations for L. leucocephala (Figure 5) and Tandug’s and Kawahara et al.’s data combined (Figure 6) – indicate a good fit to the lower range of the data, but greater uncertainty in predicting biomass with greater diameters (> 20 cm). Despite this, as seen in Figure 7, the use of the power function y = 0.342D^{2.073}, improved estimates compared with applying the generic equation by Brown (1997) used in previous studies.
Examination of residual plots (Figure 810) revealed that in some cases (L. leucocephala in Laguna and Ilocos Sur, and the generic equations), nonhomogeneous error variance was encountered, i.e. increases as dbh increases. Future work should address this problem to improve the predictive ability of the equations. One remedy discussed in Ballard et al. (1998) is the application of a weighting scheme for the nonlinear fitting.
Table 5. Summary of regression parameter estimates and statistics for biomass equations for five species using model: y = aD^{b} , where y = total aboveground tree biomass (kg), D = dbh (cm) and a,b = model parameters
Species

n

Min D

Max D

a

b

SEE

r
 Paraserianthes falcataria 
20

4.1

36.1

0.049

2.591

19.766

0.991
 Gmelina arborea 
7

8.0

31.4

0.153

2.217

13.831

0.994

Swietenia macrophylla

5

6.7

26.0

0.022

2.920

17.616

0.993

Dipterocarpaceae

7

7.3

34.0

0.031

2.717

24.374

0.992
 Leucaena leucocephala 







Laguna

18

5.4

21.0

0.132

2.316

11.424

0.972

Antique

13

4.5

14.0

0.477

1.937

5.412

0.975

Cebu

21

10

31.8

0.753

1.921

32.151

0.981

Ilocos Sur

18

5.2

20.8

0.112

2.580

14.860

0.982

Iloilo

14

5.1

13.8

0.225

2.247

5.710

0.967

Rizal

25

4.0

16.2

0.182

2.296

4.149

0.992

All sites combined

111

4.0

31.8

0.206

2.305

26.468

0.973

All species/sites

148

4.0

36.1

0.342

2.073

41.964

0.938



a. L. leucocephala Laguna

b. L. leucocephala Antique



c. L. leucocephala  Cebu

d. L. leucocephala  Ilocos Sur



e. L. leucocephala  Iloilo

f. L. leucocephala  Rizal

Figure 4. Observed vs. predicted biomass values of trees sampled by Tandug (1986),
‘Power Fit’ refers to allometric equation specific to a site and ‘Tandug’ = biomass equations by Tandug with dbh and height as predictors (Y= aD^{b1}H^{b2}).
Figure 5. Observed vs. predicted biomass values of trees sampled by Tandug (1986)
These are estimated using the power function y = 0.206D^{2.305 }fitted to the pooled L .leucocephala data (‘Power Fit Leucaena’)
Figure 6. Observed vs. predicted biomass values of the pooled TandugKawahara et al. data
These are estimated using the power function y = 0.342D^{2.073}fitted to the pooled data (‘Power Fit Gen’)
Figure 7. Observed vs. predicted biomass values using the generic equation y = 0.342D^{2.073} (‘Power FitGen’), and Brown's (1997) equation y = exp(2.134+2.530ln(D))


a. P. falcataria

b.G. arborea



c.S. macrophylla

d.Dipterocarps

Figure 8. Residuals from the regressions for speciesspecific equations from Kawahara et al. (1981)’s data


a. L. leucocephala –Laguna

b. L. leucocephala Antique



c. L. leucocephala –Cebu

d. L. leucocephala Ilocos Sur



e. L. leucocephala –Iloilo

f. L. leucocephala –Rizal

Figure 9. Residuals from the regressions for sitespecific equations for L. leucocephala from Tandug’s (1986) data


a. Pooled sites Tandug (1986) data set

b. Pooled Kawahara et al. (1981) and Tandug (1986) data sets

Figure 10. Residuals from the regressions for generic equations from the pooled Kawahara et al. (1981) and Tandug (1986) data
SUMMARY AND CONCLUSIONS
Allometric equations for predicting tree biomass were developed using secondary data from studies involving destructive sampling and conducted in the Philippines. Biomass data were taken from studies conducted independently by Kawahara et al. (1981) for timber plantations of Gmelina arborea, Paraserianthes falcataria, Swietenia macrophylla and Dipterocarp species in Mindanao; Tandug (1986) for Leucaena leucocephala plantations (mainly for dendrothermal power plants) from Laguna, Antique, Cebu, Iloilo, Rizal, and Ilocos Sur, and Buante (1997) for Acacia mangium, Acacia auriculiformis and G. arborea in Leyte. Nonlinear estimation was used to fit the data to the power function Y = aD^{b} , with Y = total aboveground biomass of tree, D = diameter at breast height, and a,b = parameter estimates.
Regression equations based solely on diameter appear to estimate adequately tree biomass, with a correlation coefficient of more than 0.90, although the inclusion of height as predictor variable was not explored. A problem encountered with the regressions is that in some cases tested, errors in prediction tend to increase with increasing diameter (nonhomogeneous variance).
It is emphasised that the biomass regression equations presented in this study are deterministic in nature, i.e. parameter estimates are single fixed numbers at any given time and applying them on trees under different growing conditions and to diameters outside the range of the measurements of the sampled trees is not advised.
Future efforts in equation development should consider including large trees whenever possible, because the analysis reported here shows greater variability in tree biomass among groups at larger diameters ( 30 cm dbh). The variability in biomass of the different speciessites in the pooled data precludes the development of a generalised biomass equation of potential wider applicability. It is still recommended that species and sitespecific equations be used whenever possible.
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