Formulating biomass allometric model for Paraserianthes falcataria (L) Nielsen (Sengon) in smallholder plantations, Central Kalimantan, Indonesia

Figures & data

Figure 1. Study area.

Table 1. Candidate models for biomass allometric equation development.

Model no.	Type	Expression
MD1	Straight line	$Y=b_0+b_1\times D^2$
MD2	Power	$Y=b_o\times D^{b_1}$
MD3	Logarithmic	$Y=b_0+b_{1}ln(D)$
MD4	Quadratic polynomial	$Y=b_0+b_1\times D+b_2{\times D}^2$
MD5	Exponential	$Y=b_o\times e^{b_{1}D}$
MDH1	Straight line	$Y=b_0+b_1\times {(D}^{2}H)$
MDH2	Power	$Y=b_o\times D^{b_1}\times H^{b_2}$
MH1	Exponential	$Y=b_o\times e^{b_{1}H}$
MH2	Logarithmic	$Y=b_0+b_1\ln \left(H\right)$

Y: biomass (kg); D: DBH (cm); H: total height (m); b₀, b₁, and b₂: regression coefficients.

Table 2. Considered models for comparison.

Source	Models	Forest type	Remarks
AGB
Brown (1997)	$\mathit{TAGB}=\exp (-2.134+2.530\times ln(\mathit{DBH}))$	Moist Forest	Pantropical
Pearson et al. (2005)	$\mathit{TAGB}=\exp (-2.289+2.649\times ln(\mathit{DBH})-0.021\times ln({\mathit{DBH}}^2))$	Moist Forest	Pantropical
Chave et al. (2005, 2014)	$\mathit{TAGB}=0.0559\times (WD\times {\mathit{DBH}}^2\times TH)$	Moist Forest	Pantropical
Rusolono (2006)	$\log (\mathit{TAGB})=-1.239+2.561\times \log (\mathit{DBH})$	Plantation	Jateng, Indonesia
Siregar (2007)	$\mathit{TAGB}=0.3196\times {\mathit{DBH}}^{1.9834}$	Plantation	Jatim, Indonesia
Merchantable volume
Siswanto (2008) (A)	$\log (V)=-3.702+2.423\times \log (\mathit{DBH})$	Plantation	Jatim, Indonesia
Siswanto (2008) (B)	$\log (V)=-3.991+2.071\times \log (\mathit{DBH})+0.636\times \log (TH)$	Plantation	Jatim, Indonesia

TAGB: total above-ground biomass (kg); TH: total height (m); WD: wood density (g cm⁻³); DBH: diameter at breast height: 1.3 m (cm); V: merchantable volume (m³).

Figure 2. Observed vs predicted plots of the AGB candidate models.

Figure 3. Residuals’ distribution of the AGB candidate models.

Table 3. Computed coefficients and comparative statistics of the AGB candidate models.

Model	b0	b1	b2	AIC	BIC	RMSE	MPE (%)
MD1	−7.102651**	0.269022***	–	156.98	160.38	6.44	36.58
MD2^a	0.08062***	2.36816***	–	138.84	142.24	4.34	6.52
MD3	−119.46***	71.31***	–	231.23	234.64	32.38	159.07
MD4	9.43071*	−2.72977***	0.35812***	142.02	146.56	4.46	−9.04
MD5	8.2587321***	0.1183898***	–	172.46	175.86	9.02	−74.69
MDH1	3.9191112**	0.0136124***	–	140.66	144.07	4.52	−14.82
MDH2	0.04346 ^ns	2.06760***	0.53853 ^ns	138.91	143.45	4.17	6.87
MH1	1.292994***	0.253516***	–	175.50	178.90	9.64	−27.74
MH2	−219.31***	109.77***	–	235.11	238.51	35.22	146.37

^aIndicates the best-fit model identified in this study.

***Significant at α = 0.001, **significant at α = 0.01, *significant at α = 0.05.

ns: not statistically significant at α = 0.05.

Figure 4. Identified AGB allometric model: MD2 (power function).

Figure 5. Graphical representation of the predictive accuracy of the allometric model identified in this study (MD2) against those considered from the literature.

Figure 6. Illustration of the statistical significances among the AGB allometric models under consideration (*significant at α = 0.05, ns: not statistically significant at α = 0.05).

Table 4. Predictive accuracy metrics of the model identified in this study (MD2) and the models considered from the literature.

Model	RMSE	ME	MPE (%)
This study (MD2)	4.34	0.99	6.52
Brown (1997)	111.77	−3.18	−107.70
Chave et al. (2005, 2014)	10.07	0.97	7.29
Pearson et al. (2005)	129	−4.57	−117.21
Rusolono (2006)	24.64	0.80	−9.66
Siregar (2007)	18.03	0.89	−43.12

Figure 7. Illustration of the statistical significances among the indirect methods of AGB estimation in comparison to this study model (MD2).

Table 5. Descriptive statistics of BEF, WBD and stem bole volume, and the AGB estimation using BEF-biomass method and this study model (MD2).

Variable	Description
	Mean	SE (Standard Error)	Range
BEF	1.69	0.05	1.20–2.25
WBD (kg m^−3)	282.52	12.39	256.85–307.69
Volume
Smalian (stem bole volume) (m^3)	0.11	0.022	0.0020–0.35
Siswanto (2008) (A) (stem bole volume) (m^3)	0.16	0.034	0.0026–0.65
Siswanto (2008) (B) (stem bole volume) (m^3)	0.17	0.037	0.0024–0.70
AGB
This study (MD2) (kg)	55.11	11.68	1.00–221.06
Siswanto (2008) (A) (BEF-Biomass) (kg)	76.22	16.46	1.25–312.33
Siswanto (2008) (B) (BEF-Biomass) (kg)	82.03	17.73	1.17–336.49
Smalian (BEF-Biomass) (kg)	51.22	10.31	0.98–167.62

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Data availability statement

Dataset used during this study are available from the corresponding author on plausible request.