This study was done in community woodlands at Srobyong village, Jepara district, Central Java province, Indonesia (Figure 1), one of the key zones for the biomass pool in supporting the National Co-Fairing. Its coordinates are 110°9′48.02″ and 110°58′37.40″ East and 5°43′20.67″ to 6°47′25.85″ N. It is near the power plants generating electricity for Java and Bali. The topography of the land consists primarily of flat regions characterized by a gradient ranging from 0 to 8% and an elevation between 70 and 150 meters above sea level. The average daily temperature is 29°C, accompanied by a mean air humidity of 84%. Annual rainfall is 2,446 mm year^–1, with dry intervals for 4 months from May to August. The soil is categorized as alfisols, with a pH range of 5.5–6.0. Approximately 52% of the land cover in the research site was largely community forests, with an approximate size of 19.516 ha (Central Java Provincial Statistics Bureau, 2022).

The forest inventory was conducted utilizing the quadrat method, employing a sampling plot size of 25 m × 25 m (Wirabuana et al., 2021). A total of 64 units of permanent plots were randomly dispersed over the study site for the inventory, as depicted in Figure 2. Thus, this inquiry covered a sampling area of 4 hectares. Data was collected from each plot, encompassing the landowner’s name, tree species, diameter at breast height (DBH), and tree height (H). The DBH was measured at a height of 1.3 meters above the ground using a phi band, while the H was measured from the ground to the top of the tree crown using a spiegel. Each tree within every sampling plot was assigned a unique numerical tag to simplify the identification of specific tree samples for the purpose of sampling through complete tree removal. Upon completion of the forest inventory, all the data were merged into a single DBH, which was divided into four distinct groups: 0-10 cm, 11-20 cm, 21-30 cm, and ≥ 31 cm (Altanzagas et al., 2019; Wirabuana et al., 2020; Setiahadi, 2021). The goal was to determine the abundance of trees spanning from small number to abundance. Previous studies frequently utilized this approach to get tree samples that precisely represented the variation in growth (Chave et al., 2014; Mulyana et al., 2020; Sadono et al., 2021). The number of tree samples in our study was limited to 45 due to resource restrictions and the necessity for permission from landowners. However, an equal number of samples were assigned to each species. Previous research, with much smaller sample sizes (Youkhana and Idol, 2011; Stas et al., 2017; Sadono et al., 2022) have shown that our modest sample sizes were enough for generating the allometric models.

The process of cutting the whole tree was conducted and the GPS was used to record the coordinates of each tree sample (Figure 2). Once the chosen tree was cut down, its parts were divided into trunks, branches, and leaves. The weight of each component of the tree was measured using a suspended scale. Subsequently, around 500 g of subsample was obtained from each component and subjected to drying in the laboratory using a forced-air over at 70°C for 48 h for biomass determination. The total biomass in every component (Equation 1) and at the individual tree level (Equation 2) were calculated following these equations:

where W_c is the biomass of tree component (kg), DW_s is a dry weight of subsample (g), FW_s is a fresh weight of subsample (g), FW_c is the total fresh weight of tree component (kg), W_t is the total biomass at the individual tree level (kg), W_s is the stem biomass (kg), W_b is the branches biomass (kg), and W_f is the foliage biomass (kg).

The desiccated subsamples were examined utilizing the standard of the American Society for Testing and Material (ASTM E-711-87) to measure the calorific value of each individual tree component. The energy stock of each component (Equation 3) and the total energy stock (Equation 4) were calculated using these formulas:

where ES_c is an energy stock of tree component (MJ), W_t is the total biomass at the individual tree level (kg), HHV_c is a calorific value of tree component (kcal kg^–1), f is a constant of 4.184 × 10^–3, ES_t is the total energy stock at the individual tree level (MJ), ES_s is an energy stock in stem (MJ), ES_b is an energy stock in branches, and ES_f is an energy stock in foliage.

This study also calculated the energy expansion factor (EEF) and energy harvesting index (EHI). EEF is the ratio between the total energy stock at the individual tree level and the energy stock in stem (Equation 5). EEF can be used as a constant to convert the energy stock in the stem component to the total individual tree. Meanwhile, EHI is the ratio between the allowable total energy harvested and the total energy produced from the individual tree (Equation 6). Woody components like stem and branches are generally classified as the allowable harvested. Both parameters were calculated using the following equations:

where EEF is an energy expansion factor of species, ES_t is the total energy stock at the individual tree level (MJ), ES_s is an energy stock in stem (MJ), ES_b is an energy stock in branches (MJ) and EHI is an energy harvesting index of species.

Data screening was conducted using the Boxplot method to identify the existence of outliers in the dataset. Then, the normality of the data was examined using the Shapiro–Wilk test. Scatter diagrams were also constructed to recognize the pattern of relationships between independent and dependent variables. The DBH and H were selected as the independent variables, while the ES in each tree component and in total were considered as the dependent variables. The scatter plot method was frequently used in previous studies before developing the allometric models (Vega-Nieva et al., 2015; Lisboa et al., 2018; Ogana and Ercanli, 2022).

Two allometric models were examined in this study. Both models differed in the number of independent variables. The first model used DBH as the predictor (Equation 7), while the second applied DBH and H as the predictors (Equation 8). The allometric models were developed in two steps, namely specific species, and the combination of all species. For details, both formulas are shown below:

where Y is the energy stock in tree component or in total (MJ), DBH is the diameter at breast height (cm), H is tree height (m), and a, b, and c are fit coefficients.

The allometric models were evaluated in several stages, i.e., (1) assessing the model fitting; (2) testing the model validation; and (3) checking the significance of predictor addition. There are five things that were used to judge how well the model fit: the ANOVA test result, the fitted parameters (a, b, and c) result, the adjusted coefficient of determination (R²_adj) (Equation 9), the residual standard error (RSE) (Equation 10), and the Akaike information criterion (AIC) (Equation 11). Meanwhile, two criteria were selected to examine the validation, such as mean absolute error (MAE) (Equation 12) and root mean square error (RMSE) (Equation 13). We used the leave-one-out cross-validation (LOOCV) method for validating the model due to the small sample size. Previous studies also applied LOOCV when developing models with a small sample size (Altanzagas et al., 2019; Tetemke et al., 2019; Wirabuana et al., 2020; Sadono et al., 2021). High R²_adj, small RSE, AIC, MAB, MAE, and RMSE indicate high model precision (Altanzagas et al., 2019). Detailed formula for calculating these criteria is presented below:

where Y_i is the observed energy stock, Y¯ is the average observed energy stock, Yi^ is the estimated energy stock from the fitted model, R² is the coefficient of determination, n is the sample size, RSS is the residual sum of squares from the fitted model, k is the number of parameters, and p is the number of terms in the model.

We used the Extra Sums of Square (ESS) to verify the significant contribution of additional H in the allometric models. This method is reliable to check whether the addition of other predictors provides a substantial effect on improving the model’s reliability (Hector et al., 2016; Wirabuana et al., 2021; Sadono et al., 2022). When the result is insignificant, using a single predictor in the allometric equation is sufficient to obtain a good estimation.

The number of sample trees differed for each species within the DBH class (Table 1). Fifteen trees classified most tree samples into the DBH class of 0–10 cm. There was a total of nine trees in the DBH class, ranging from 11 to 20 cm and 21 to 30 cm. F. moluccana and T. grandis had the most tree samples in the smallest DBH class (0–10 cm), whereas S. macrophylla had a majority in the greatest DBH class (31 cm). Our investigation observed that each species had an equal number of tree samples within the DBH range of 21–30 cm, specifically three trees. Meanwhile, T. grandis had the smallest sample size in DBH class of 11–20 cm, with only two trees. The restrictions imposed by landowners’ permission are the main cause for the variation in the distribution of tree samples among various species and the DBH classes. Owners of trees only permitted destructive sampling of trees that met the criteria.

The calorific value varied significantly among each component of the tree (Table 2). The mean calorific value for all species was highest in foliage (5,021.24 ± 39.37 kcal kg^–1), then stems (4,352.8 ± 32.07 kcal kg^–1), and finally branches (4,200.11 ± 33.54 kcal kg^–1). Across all species, it was consistently observed that the foliage had a larger calorific value compared to other components. Additionally, this study found that the calorific value of T. grandis was comparatively greater than that of F. moluccana and S. macrophylla for every component of the tree. Meanwhile, S. macrophylla exhibited the lowest calorific value among all the species’ components.

Our analysis revealed that while the leaves had the highest calorific value, the stem of each species contained the maximum energy store (Table 2). The energy allocation in stocks showed a consistent decrease from the stem to the foliage in all species, as shown in Table 2. The stem of the individual tree had almost fifty percent of the energy supply since it had the highest biomass accumulation compared to other tree components (Table 3).

Notably, each tree component of all species exhibited a distinct pattern of energy distribution as the DBH class increased (Figure 3). The energy distribution in the stems of F. moluccana and S. macrophylla improved as the DBH class increased. Conversely, it demonstrated a decreasing pattern in T. grandis. The stem exhibited a greater dispersion of energy, but the foliage showed a lesser concentration of energy.

The findings also revealed a significant variation in the total energy stock among species, with S. macrophylla exhibiting the highest average of 5,877.1 ± 1,309.57 MJ, followed by T. grandis with 3,366.27 ± 1,160.64 MJ, and F. moluccana with 1,133.28 ± 344.44 MJ (Table 3). The species exhibited the highest average energy of 2,109.00 ± 687.23 MJ in the year. Further, the branches were with an average energy of 981.27 ± 341.73 MJ and leaves with an average energy of 368.61 ± 130.42 MJ. So that the wood constituents amassed a greater amount of energy compared to the non-woody components.

The study found that the EEF was almost the same across different species, ranging from 1.66 to 1.69 (Figure 4). Concurrently, the EHI for all species varied between 0.88 and 0.94. This shows that over 85 percent of the energy generated at the level of each individual tree in every species may be collected to facilitate the advancement of renewable energy. T. grandis had a greater EHI compared to F. moluccana and S. macrophylla, with a difference of 0.94 ± 0.01; which demonstrated that T. grandis had a higher energy stock yield compared to other species.

The cumulative energy reserves of each species exhibited a progressive increase as the DBH and H increased (Figure 5). These results highlighted that DBH and H have the capability to serve as predictor factors for evaluating the energy stock. The outcomes of constructing allometric models also demonstrated a strong fit for each individual model (Table 4). Furthermore, allometric models were used to explain about 80% of the variations in energy stocks across different parts of the tree and the entire tree for each species. General allometric models can be developed for all species. As shown in Table 4, this model estimates high degree of the energy stock for each individual component of a tree with a precision of up to 90%.

The estimation of the total energy stored at the level of individual trees was determined to be dependable. It was noted that incorporating H as a separate variable in the regression model did not consistently yield a statistically significant enhancement in the model’s predictive precision, as demonstrated in Table 5. The addition of H has significantly improved the precision of the model in determining the energy content in the stems of S. macrophylla and T. grandis, encompassing all species. Additionally, the incorporation of this variable was essential in improving the reliability of the overall allometric models used to calculate the total energy storage. Therefore, the most efficient models for each individual part within each species displayed significant differences.

The allometric models underestimated the energy stock value for S. macrophylla and T. grandis compared to the real value. Conversely, it yielded a greater estimate when assessing the energy reserves for F. moluccana (Figure 6). While F. moluccana and T. grandis, the biggest error in estimation was seen in the DBH category of 31 cm, and in S. macrophylla, it was seen in the DBH category of 21–30 cm (Figure 7). However, the overall allometric model remains adequate for estimating energy storage in all species.

The key factor contributing to the greater energy content of foliage compared to stems and branches is outlined in Table 2. Trees typically harness solar energy through the process of photosynthesis, with foliage playing a crucial part in controlling this function. It regulates the transfer of energy between trees and the atmosphere (de Mattos et al., 2020). The energy is stored by foliage through the process of photosynthesis (Ellison et al., 2017). Furthermore, the size of the leaf’s surface area has an impact on the quantity of solar radiation that is absorbed by the foliage (Lee et al., 2019). Trees possessing greater leaf surface areas will assimilate a bigger amount of solar radiation compared to those with smaller leaf surface areas. Due to its larger leaf size compared to S. macrophylla and F. moluccana, T. grandis possessed a higher caloric content.

The fact that the foliage of the three species had a higher calorific value than the other components suggests that the abundant species’ leaves available as waste could be used for co-firing biomass. Further, because community people commonly collect teak leaves from the ground during the dry season for traditional food packages, they can be used as a biomass replacement for co-firing. So, once appropriate plantations of faster growing species for co-firing wood biomass are established, the species remain beneficial, especially when the trees are returned to their original use as a supply of lumber. Given that T. grandis had a higher calorific value than F. moluccana and S. macrophylla for all components of the tree, this important information reinforces the importance of planting this easily planted teak tree in any less fertile soil between unused community lands. This is especially helpful since teak can be coppiced for harvesting without having to replant.

Trees, along with other autotrophic organisms, have the natural capacity to transform solar energy into biomass through photosynthesis (Lee et al., 2019; de Mattos et al., 2020). This process contributes to the net primary productivity. Thus, an increased quantity of tree biomass indicates a better capacity for energy storage. The energy distribution pattern inside a single tree has resemblances to biomass allocation, with the stem containing the highest proportion of leaves and branches. This phenomenon can occur because the stem serves a vital function in maintaining the stability of trees and facilitating the process of translocation (Wirabuana et al., 2020). Therefore, it can be deduced that the stem has a larger store of energy in comparison to other components. Pruning and leaf abscission can also lead to a reduction in the formation of energy reserves in the branches and leaves (Suchocka et al., 2021). These occurrences occur at regular intervals over an organism’s existence and result in a decrease in the total amount of living matter. Although the stem of all species contains the most energy, for co-firing wood biomass energy that does not require a beautiful shape, the ability to be harvested from the coppice on a regular basis is required, which T. grandis and F. moluccana possess that coppicing ability but S. macrophylla does not. Meanwhile, F. moluccana, which grows relatively quickly, may be favored over S. macrophylla, which has the lowest calorific value of all the species’ components (Table 2).

The correlation between energy levels and tree age is evident through the growth of energy reserves in all species and the enhancement of DBH class. The DBH normally rises over time due to the gradual growth of biomass (Wirabuana et al., 2022). Trees having a larger DBH typically indicate a more advanced level of maturity in comparison to trees with smaller DBH measurements. Prior studies have also recorded comparable results, suggesting that a larger DBH is a reliable indicator of a more advanced age of the tree (Kirongo et al., 2012; Sumida et al., 2013). With these findings, an assessment of the diameter and allometric models for coppice, particularly for T. grandis and F. moluccana, is required, especially when both species are included as selected species for the next specific co-firing plantations.

The energy harvesting index in T. grandis demonstrated a superior level in comparison to other species, as illustrated in Figure 4. As stated by reference Gutiérrez-Soto et al. (2008), the plant consistently sheds its leaves during the dry season as a tactic to minimize transpiration. At this point, the focus will be on the allocation of energy toward the woody constituents. T. grandis had a less dense canopy compared to F. moluccana and S. macrophylla. As a result, this species shows a greater distribution of biomass toward its stem and branches to ensure its survival. The reason for exclusively harvesting stems and branches for renewable energy materials was confirmed.

DBH and H are frequently employed as the independent variables for constructing allometric models. In addition to their ease of measurement in the field, the variables are strongly correlated with the plant development mechanism, specifically photosynthesis (Zhang et al., 2016). The increase in DBH and H is a direct consequence of greater biomass storage in the stems (Köhl et al., 2017). Hence, using allometric models that incorporate both variables ensures a high degree of accuracy in estimating the energy store of each tree component as well as the overall total for each species (R²_adj = 0.88–0.99; Table 4). Therefore, this is in line with the first hypothesis that the allometric models can accurately estimate the energy stock of those species in a community forest. It also confirmed that the best models are expected to predict more than 70% of the energy stock variation in each tree component and the total energy stock of each tree. Furthermore, the unique patterns of allometric models for each species were confirmed.

Furthermore, other research investigations also utilize these factors of DBH and H as independent variables when creating allometric models for other tree parameters, including biomass, carbon storage, and crown features (Chave et al., 2005; Zahabu et al., 2018; Pretzsch, 2019; Shi et al., 2019). For species in this study, adding H only showed a significant role in improving the model’s reliability for estimating the energy stock in the stem of S. macrophylla and T. grandis. Meanwhile, this variable of H was essential to increase the reliability of general allometric models for estimating the total energy stock. Therefore, the best-fit models for every component in each species were relatively different, which is in accordance with our second hypothesis.

While the allometric models show satisfactory reliability, it is important to consider many factors before employing this model. For instance, the utilization of the species-specific model in forest inventory may yield the most precise estimation, but at the cost of increased time consumption. The technician should modify the equation whenever they encounter distinct species. However, utilizing allometric models with two predictors is likewise wasteful in terms of time and cost, albeit providing improved precision. When gathering data, measuring tree height presents a greater level of difficulty compared to measuring tree diameter due to the limitation imposed by canopy overlap between trees, which can potentially introduce errors (Magalhães, 2017; Dey et al., 2021; Kafuti et al., 2022). Hence, employing a universal model with a solitary predictor (DBH) is more advantageous for facilitating the estimation of energy stock in tree species within the community forest in the study site. This predictor can provide accurate estimation approximately more than 80% (Table 4). Prior research has also demonstrated that a straightforward using DBH as a solitary predictor for facilitating forest inventory is more effective when it is used to estimated energy stock for many species in large area (Lumbres et al., 2015; Forrester et al., 2017; Romero et al., 2020).

Our observations indicate that the overall model, using DBH as the sole predictor, has demonstrated sufficient dependability. Therefore, we can confidently suggest it as a tool for landowners or local governments to assess the energy stock of tree species in community forests. Therefore, using a general model with a single predictor (DBH) is better to facilitate the energy stock estimation supports of community forest tree species in the study site. This also support our third hypothesis, that the general allometric models can be developed for all species, using DBH as the sole predictor both in every component and for the total individual tree.

Furthermore, it is crucial to recognize the constraints of our research, which encompass the utilization of a rather small sample size including only 45 trees, representing merely three unique species. The investigation was constrained to a singular location, hence precluding the assessment of the equation’s dependability across several sites and forest ecosystems. Further investigation is required to validate the reliability of allometric equations in accurately estimating energy reserves, especially when applied to a broader array of species and bigger sample numbers. Moreover, it is preferable that future research endeavors to include many sites to evaluate the overall validity of this approach.

The current local government is discussing about constructing a specific biomass plantation for co-firing raw materials. To reduce the setup costs, it is worthwhile to investigate species that yield high-quality biomass for energy while also producing coppices without the need to plant new trees. T. grandis and F. moluccana are two species that may be included, as well as many other fast-growing species that have been genetically improved for high-volume and quality wood for energy (Hendrati and Nurrohmah, 2018; Hendrati et al., 2022). F. moluccana has also been genetically improved for high biomass and gall tolerance, making it an appealing alternative for inclusion (Baskorowati et al., 2017). These species are legumes, and they can not only be harvested annually from close-spacing plantations, but they also improve soil and land quality and prevent erosion. T. grandis with a MAI (Mean Annual Increment) of 6.9 m³ha^–1year^–1 and S. macrophylla 19.71 m³ha^–1year^–1 (Hiratsuka et al., 2005; Krisnawati et al., 2011), which were used in this study, may produce much less wood biomass for co-firing, compared to the above-mentioned legume trees with a range MAI of 43–65 m³ha^–1year^–1. In 2021, the approximate requirement of biomass for generating electricity was estimated to be around 570,000 metric tons (Economic Research Institute for ASEAN and East Asia, 2022), while there are 19,516 ha of community forests in Jepara. Of these, half can still be planted with trees for timber for fulfilling the community needs of lumber, and the other half, or about 10,000 ha, can produce 430,000 m³ha^–1year^–1 (258,000 metric tons) of wood biomass when genetically improved legume species are grown for co-firing plantations. With a year of rotation, this only area in Jepara is estimated to be adequate to meet 25% of the requirement wood biomass for co-firing.