Improved allometric equations for tree aboveground biomass estimation in tropical dipterocarp forests of Kalimantan, Indonesia

Tropical dipterocarp forest (TDF) is one of the most important tropical ecosystems in the Indonesian archipelago. The forest harbours a high diversity of plant and animal species as well as a high density of carbon stock (MacKinnon 1996; Kartawinata 2005; Paoli et al. 2008). Over the last three decades, unsustainable management practices coupled with pressures from illegal logging, fires and plantation expansion have led to substantial rates of deforestation and degradation of natural forests (Hansen et al. 2009; Miettinen et al. 2011). This has greatly contributed to national greenhouse gas emissions (MoEF 2015).

To halt further forest losses, a performance-based incentive mechanism to reduce emissions from tropical deforestation and forest degradation (known as REDD+) has been discussed at a global forum (UNFCCC 2015). This mechanism, however, relies on accurate estimations of biomass stocks in forests (Asner 2011). Credible estimations on aboveground biomass (AGB) stocks and emission factors are essential data required for REDD+ reference emission levels, which is the benchmark for evaluating the performance of activities under the REDD+ framework (IPCC 2006).

Most studies on forest biomass in tropical regions have been carried out using remote sensing technology, which provides wall-to-wall and consistent estimates across spatial, temporal and ecological variations (Avitabile et al. 2016; Halperin et al. 2016). However, this approach requires validation through ground measurement and appropriate allometric equations to convert tree metrics derived from field measurements into tree biomass. Many plot-level-based studies on AGB stock have been carried out for TDFs in Borneo (Berry et al. 2010; Griscom et al. 2014), mostly without destructive sampling efforts to validate existing or develop new equations. Some studies used existing local equations which developed from relatively small samples (Hiratsuka et al. 2006; Krisnawati et al. 2014). Unbiased allometric equation is essential for accurate estimates of forest AGB stocks and carbon emissions associated with deforestation and forest degradation activities at landscape level (van Breugel et al. 2011; Johnson et al. 2014).

Traditionally, AGB equations rely on the relationship between AGB and tree diameter, wood density and tree height (Chave et al. 2014), as well as the crown size (Henry et al. 2010; Goodman et al. 2014) as predictor variables. A large-scale tropical forest inventory campaign requires a simple and robust method to be implemented in a cost-effective and consistent way. Because of optical obstruction of the multi-layered canopies of dipterocarp forest, total tree height or crown measurements are relatively difficult, time consuming and subject to measurement errors. Several authors have suggested more practical solutions, including the use of the tree height-diameter model (Feldpausch et al. 2012) or bole height measurement, instead of total height measurement (Basuki et al. 2009).

The number of local or site-specific allometric studies in Indonesia is high compared with studies in other countries in South-East Asia (Yuen et al. 2016), including studies in the TDFs of Indonesian Borneo (Kalimantan) by Yamakura et al. (1986a), Basuki et al. (2009) and Hashimoto et al. (2004). The first two studies are the most well known and were conducted on TDFs with relatively large samples and a wide range of trunk diameter. Basuki et al. (2009) compared the locally developed equations with the pantropical equations and found that the mean percentage errors of the pantropical equations were more than 40% when applied to the local dataset. Yamakura’s equations were constructed for each tree component rather than for the total tree, and thus can introduce bias if simply added together for estimating total tree AGB. Hashimoto et al. (2004) developed species-specific and mixed-species biomass equations for pioneer trees in a secondary forest in East Kalimantan. Although Hashimoto et al. (2004) study involved large sample size was (N = 108), the diameter range of the trunk was limited to a maximum of only 20.3 cm. In addition, some pantropical equations were developed and widely used for estimating AGB in tropical regions, e.g. Brown (1997) and Chave et al. (2014). Both studies used large samples and a wide range of tree diameter compiled from tropical region, including Indonesia. Before the use of existing equations, a validation for the selection of the best allometric equation is required to assess the model bias and precision (Pearson et al. 2005).

Our interest lies in the validation and improvement of existing equations for more credible AGB estimations in TDFs. The study has three objectives: (1) to evaluate the validity of existing equations; (2) to develop new allometric equations in estimating tree AGB for TDFs in Kalimantan; and (3) to validate the new equations using independent datasets.

The dataset used for developing and validating AGB models covered a wide range of diameter, height, wood density and tree species (Additional file 1). A total of 108 sample data were collected from destructive harvesting in East, Central and West Kalimantan. The largest tree had a diameter of 172 cm and a total height of 75 m. Fifty per cent of the samples were trees with D > 50 cm, while trees with D > 100 accounted for 10% of the total samples (n = 11). The dataset consisted of 80 species from 27 families. Thirty per cent of total felled trees were from the dipterocarp family.

Accuracy of the existing equations

We evaluated the precision and bias of previously published local AGB equations using our dataset. Most of the previously published equations had an MRE and MARE of more than 0.21 and 0.31, respectively. Only DH _Yam had an MRE of less than 0.1 and a slope close to 1 (Table 1). The pantropical equations performed better than the existing local equations. The MRE of all pantropical equations were less than 0.1. DGH _Cha had the smallest MARE among the existing equations. However, only D _Bro2 had the deviation of less than 5% (slope of 0.964).

The regression analysis between the log-transformed measured AGB and the log-transformed predicted AGB of existing local equations showed an underestimated trend, especially the DG _Bas and D _Has models (Fig. 2). The D _Has model, which was developed from a low range of tree diameter from secondary succession, failed to accurately estimate the tree AGB from primary TDFs. D _Has showed a systematic bias at all diameters. The regression lines of LnD _Bas and LnDĤ _Bas depicted underestimation of small trees and overestimation of large trees, with the points of intersection at 5.15 and 5.24, respectively.

Model validation

We validated our equations using datasets from independent datasets. We found significantly different results between our models and most of the existing local models. Our models outperformed local models considerably. Both D _Bas and DG _Bas equations showed underestimation trends, even when applied to their own dataset, in particular for the large trees (Fig. 3). Although both models have relatively normal precisions, the biases of the models are very large (Table 3). For example, DG _Bas has MRE and MARE of −0.042 and 0.304, respectively, with the slope of the regression between observed and predicted AGB close to two. Slopes of two indicate large bias, whereas the estimates are twice smaller than the predicted, if the intercepts are zero. D _Bas, D _Bro and DH _Yam had negative intercepts that significantly different to zero, suggesting the overestimation of small trees. In contrast, DG8 and DGH9 had intercepts that were not significantly different to zero and slope more than 0.95, indicating bias of less than 5%.

Model ID	Adj.r 2	RMSE (kg)	MRE	MARE	Intercept (SE)	Slope (SE)
D1	0.935	1220	0.025	0.265	−123 (123)	1.201b (0.030)
DH3	0.971	819	0.069	0.240	−142 (83)	1.133b (0.019)
DG8	0.941	1157	−0.084	0.202	113 (115)	0.955b (0.023)
DGH9	0.993	395	0.049	0.142	66 (39)	0.954b (0.008)
D Bas	0.915	1392	0.056	0.383	−438a (144)	2.349b (0.069)
D Has	0.932	1253	−0.486	0.507	−202 (127)	2.890b (0.075)
D Bro	0.908	1453	0.053	0.289	−437a (150)	1.669b (0.051)
D Bro2	0.935	1221	0.043	0.272	−125 (123)	1.295b (0.033)
DG Bas	0.937	1197	−0.042	0.304	−206 (121)	1.946b (0.048)
DH Yam	0.988	514	−0.025	0.217	−137 (52)a	1.243b (0.013)
DGH Cha	0.993	395	0.005	0.146	71 (39)	0.889b (0.007)

^aand ^bdenote significant difference to 0 and 1, respectively

Only the DH _Yam model that had lower MRE and MARE than our model that has the same predictor variables (Table 3, Fig. 3). The reason could be that the dataset used for developing DH _Yam was the validation dataset in this study. However, the deviation of the estimated AGB using DH _Yam was larger than the deviation from our DH3 model, indicated by the intercept that was different from zero and the greater slope. This large deviation was mainly due to the underestimation of large trees and overestimation of small trees (Fig. 3). DH _Yam used a complex model form because it was originally developed for estimating biomass of tree components (Table 1). Similarly, DGH _Cha and our DGH9 model had comparable MRE and MARE values, with deviation from the actual estimates 11.1 and 4.6% respectively.

Our new AGB equations outperformed all existing local equations. Most of the local models tended to have a systematic errors, potentially due to field measurement errors or biased samples. The existing pantropical equations performed only slightly worse than our new equations. The DGH _Cha in particular, performed consistently well when applied to our dataset and the validation data. DGH _Cha was developed using large number of samples from Borneo, including the validation dataset used in this study (Chave et al. 2014). Therefore previous studies on forest aboveground biomass stocks in TDF of Kalimantan or Borneo using DGH _Cha should be valid.

Our DGH9 model performs better than other models, with lower bias and better precision. Individual tree height measurements in closed-canopy TDFs are difficult and thus have high uncertainty. In that case, the DG8 should be used. However, due to a very high diversity of tree species in the TDF, identification of tree taxonomy could be problematic. Tree taxonomy identification during forest inventory for large area creates logistical and financial burden for the collection, shipment and identification of the herbarium specimens. For timber extraction planning purpose, tree identification was commonly carried out only using local names without involving botanist, and thus difficult to obtain accurate wood density values from the existing wood databases. Therefore, for estimating AGB from existing timber inventory dataset, we suggested to use the D1 or DĤ5 (if the bole height is available).

AGB models developed from a small number of samples and limited tree diameter range have the potential risk to be biased, especially when applied beyond their sample characteristic as well as geographical, biophysical and forest boundaries (van Breugel et al. 2011; Manuri et al. 2014). However, although the samples used by Basuki et al. (2009) were sufficient in number and diameter range, their models were not able to predict AGB accurately, even using the dataset they partly used for the models development. We suspect these inaccuracies are due to differences in sampling strategy (e.g., sample selection), assumptions in model development (e.g., correction factor) or approach in AGB field measurements (e.g., assumptions of regular shapes of stems and branches with diameter more than 15 cm).

In contrast with the dataset used by Basuki et al. (2009), which used only 40 species, our total number of species was doubled. The percentage of dipterocarp trees in the Basuki et al. (2009) dataset was more than 50%, while we had only 30%. Our dataset composition seems to be more similar to the floristic composition in the primary dipterocarp forests, with a percentage of total trees of about 25% (Sist and Saridan 1999). In Danum Valey, the dipterocarps population accounted for only 16% of total trees sampled in the primary dipterocarp forests. Nevertheless, they dominated the forest, representing about 50% of the basal area owing to their large and emergent trees (Newbery et al. 1992).

Basuki et al. (2009) calculated the biomass of stems and branches, which diameter greater than 15 cm, using volume-based measurement, while we weighed all stems and branches that had a diameter of less than 30 cm or had irregular shapes, other than a cylindrical shape. Therefore, we also weighed most of the irregular stumps. The kernel smoother line representing the error distribution of D _Bas model across Ln AGB, intersected at the value of 4.7 with the zero line (Fig. 3) which equals 110 kg of AGB or 14.3 cm of tree diameter. This suggested that the D _Bas equation tend to underestimate the AGB of trees with diameter of more than 14.3 cm. This supports our supposition regarding the possible error of biomass measurement of trunks or branches with diameters greater than 15 cm. Such different approaches or assumptions in field measurement might introduce bias. Differences in the destructive sampling method used in independent research are unavoidable (Manuri et al. 2014, under review), which may lead to incomparable tree biomass datasets. Thus, standardised methods for principal measurement components are required to ensure the measured datasets are valid. Such related initiatives have been carried out globally (Picard et al. 2012) and nationally (BSN 2011).

Some of our wood samples have exceptionally large values of wood density (>1 gr∙cm⁻³) compared to the existing wood density databases. For example the 45 cm-diameter Dipterocarpus stellatus has wood density of 1.3 gr∙cm⁻³, which is greater than any records from Dipterocarpus genus. We checked the field and laboratory records, and did not find any inconsistencies in the measurements. This species is endemic to Borneo. We did not find any record of the wood density from this species from the existing wood density databases. Soerianegara and Lemmens (1993) and Zanne et al. (2009) recorded the highest wood density from Dipterocarpus genus were 1.07 and 0.89, respectively. There are two possible main reasons that explain this. First, wood density variation occurs among individual within species (Henry et al. 2010), which influenced by tree diameter size and guild status (Henry et al. 2010; Iida et al. 2012), climatic variables (Onoda et al. 2010) and soil fertility (Muller‐Landau 2004). Second, there are some differences in the method for wood density measurement between tree biomass and wood characteristic studies. Our wood density measurement involves wedge or pie-shaped samples, which include barks, from various trunk sections and tree compartments. This is to ensure that the measured wood densities are closed to the actual values of tree wood densities (Williamson and Wiemann 2010).

A validation of existing AGB models is essential before the use of the models. We found that the use of MRE and MARE are not sufficient for evaluating the AGB model performance, since they only represent the mean errors, not the trend of the residuals. To address this gap, a simple linear regression analysis between the observed and predicted values of the models is required to quantify the general tendency of the residuals (Piñeiro et al. 2008). The r ² and RMSE indicate the precision of the estimates, while the slope and the intercept of the fitted line describe the bias of the estimates.

Most of the existing local AGB equations tend to be biased and imprecise. Local models developed from small samples tend to systematically biased. We recommend to not using the local models for estimating AGB or to validate prior their use especially if the models were developed from other region outside the study site, even within the same forest type. We developed new allometric equations for tree AGB estimation in the TDFs of Kalimantan using a relatively large dataset with a maximum tree diameter of 175 cm. Through a validation using independent datasets, we found that our equations improve the precision and reduce the bias of AGB estimates.