Individual Biomass and Carbon Equations for Mimosa scabrella Benth. (Bracatinga) in Southern Brazil

Mimosa scabrella Benth. is an important native species of southern Brazil widely used for energy and promising for reforestation carbon offsets. Quantification of biomass and carbon stock is valuable for both purposes. From a forest inventory conducted in southern Brazil, data of M. scabrella were analyzed. Thirty sample trees were felled, excavated and weighed in the field and brought to laboratory for biomass and carbon determination. The total aboveground biomass represented 85% of the tree biomass, while roots corresponded to 15%. Correlation matrix of diameter at 1.3 m height (D), tree height (H) versus total and compartment biomass (P) indicated strong association between tree dimensions and biomasses. Five regression models were tested and equations were fitted to data of five biomass compartments and total tree biomass. The best fitting model for total biomass was P = –0.49361 + 0.034865 × D2H whereas for the partial biomass of the compartments was lnP = β0 + β1 × ln(D) + β2 lnH. Carbon concentration was statistically significantly different in foliage than in other compartments. Three approaches of calculating carbon stocks were evaluated and compared to actual data: 1) Estimated total biomass × weighted mean carbon concentration; 2) Estimated partial (compartment) biomass × compartment average carbon concentration; and 3) Carbon regression equations. No statistical difference was detected among them. It was concluded that biomass equations fitted in this study were accurate and useful for fuelwood and carbon estimations.


Introduction
Biomass represents 10.9% of the world´s offer of energy (IEA 2008).In turn, Brazil has a consolidated and growing use of this energy source in its matrix, comprised of 27.3% of biomass, of which 9.6% correspond to wood sources, mainly firewood and charcoal (BEN 2011).
Mimosa scabrella Benth.(bracatinga) is key native species in southern Brazil.This N 2 -fixing legume tree is fast-growing (MacDicken 1994), produce sawntimber, honey, animal forage, besides of providing excellent firewood to use in a wide range of small and medium size factories.It is distributed naturally in southern and southeastern Brazil, within 23°05' and 29°04'S and 48°05' to 53°50'W, where a great number of small-scale farmers use its wood from generation to generation for various purposes.Just in the neighborhood of Curitiba (the Parana State capital), over 60 thousand hectares of bracatinga are cultivated and managed, especially through the traditional family agroforestry (EMBRAPA 1988).The usual rotation for firewood management regime is 4-7 years, with 2200 plants per hectare (Carvalho 1994).
Besides the economic and social importance of M. scabrella as energy wood, it is also important for projects that combine forest restoration and carbon sequestration (Urbano 2007).This species is valuable for small-scale reforestation projects and also as a substitute of fossil fuels and electricity.Hence, it has a remarkable potential to the development of projects aiming at CO 2 removal and reducing greenhouse gas emissions, such as CDM (Clean Development Mechanism), voluntary carbon offsets as well as carbon neutral initiatives.There is a remarkable interest of farmers in using this species for low carbon agriculture projects supported by the Brazilian government.
The establishment of reforestation and forest management projects with M. scabrella for fuelwood purposes requires quantification of biomass.At the same time, carbon offset projects and low carbon plans need suitable techniques for quantification of carbon stocks.However, direct methods imply in tedious and expensive destructive procedures.Regression models are very useful to obtain indirect estimation of biomass and carbon (Somarriba and Kass 2001).The aim of this study was to test regression models and fit equations for using in total and partial biomass and to evaluate different approaches of quantifying carbon stock of individual trees of the species M. scabrella in southern Brazil.

Study Site
In a circle of 30 km around the União da Vitória municipality, 30 trees of Mimosa scabrella were sampled in native forests of the states of Santa Catarina and Paraná (Fig. 1).The region has extensive areas of native forests with pure stands of this species or forests where it occurs in significant volumes alongside other tree taxa.Most of these forests are owned by small farmers that produce firewood or charcoal from the woody parts of M. scabrella.

Forest Inventory
Pure and mixed stands of Mimosa scabrella were selected according to their age class (3-5 years = 5 sample trees, 5-8 years = 11 sample trees and >8 years = 14 sample trees).The mixed stands with M. scabrella are generally older and richly structured native forests whereas the pure stands are younger and established under highly perturbed ecosystems.
The inventory plots were selected randomly using LANDSAT satellite imagery, where pure and mixed stands of M. scabrella could be distinguished with good precision.This could be evaluated by several "ground true" activities of the authors, which were involved in the inventory.The sampled trees were taken from forest inventory plots consisting of 70 units of a size of 20 m × 20 m.Tree biomass weighting in the field was carried on trees close to the forest inventory plots.
The data collection for determining the biomass of M. scabrella has to consider some particularities of the species.M. scabrella is considered a pioneer species.It occurs in native stands as well as in plantation-like homogeneous stands.Some provenances of the species tend to have bifurcation, whereas others show straight growth.The 30 sampled trees were selected according to the morphological characteristics of the distinct age classes.The selected trees fulfilled the following characteristics: -no open grown single trees; -no bifurcations below 3 m height allowed; -no excess of dead or broken branches; or -no dying trees or of unsound appearance.
Of the 70 analyzed inventory units, 30 trees fulfilling these criteria were randomly selected.GPS coordinates were taken for each tree and the diameter at a 1.3 m height and crown diameter were measured.After felling, tree length and crown length were measured.Tree height was difficult to measure at standing trees, because of intensive understory in the mixed stands.In this study, tree length was taken as an estimator for tree height, even both are not always identical.Exact tree age was determined by stem disc analysis.For details on sample trees see Table 1.

Biomass Measurements in the Field
After felling the sample trees were divided into the following biomass compartments: stem, bark, branches (living and dead), foliage, and roots.The fresh masses of the different compartments were measured directly after felling by a simple beam balance.The stemwood was completely measured with bark.Fresh mass of bark was taken directly after the measurement by cutting stem discs of 5 cm thickness at 0.5 m, 50% of tree height and at height of crown base.Bark was removed from the discs and separately analyzed.Branches were defined as thick branches (diameter ≥ 4 cm) and thin branches (diameter < 4 cm).Wood after a bifurcation was always considered as branchwood.To determine the fresh mass of  the branches, they were separated into living and dead and all of them measured.From all sample trees, an estimated 25% of the leaves were removed for fresh mass determination, since the leaves of M. scabrella are very fine and difficult to remove.To analyze the fresh mass of the root system, the growing space of the individual tree was estimated according to its crown size.According to Köstler et al. (1968), this method may be applied in field work, being the crown area a rough estimator for root system expansion.All roots with a diameter ≥ 0.5 cm were dug out and weighted.The tree stump remaining after felling was considered as stemwood and added to this compartment.Splitting of the root system starting directly below ground level was added to the root compartment.All fresh mass was measured using a mechanical balance with a maximum capacity of 100 kg and a precision of 10 g.

Dry Mass and Carbon Determination in the Laboratory
The biomasses of the sample tree were estimated by applying ratio estimation methods based on the moisture content of the sub-samples and the measured fresh mass of the tree compartments.
From each compartment of the sampled trees, a sample of 500 g was taken immediately after fresh mass determination and packed in a plastic bag.These sub-samples were used to determine dry matter and carbon concentration in the laboratory.With a balance of a precision of 10 mg, fresh mass of the sample was measured again.After that, samples were oven-dried at 70°C until reaching constant mass and moisture content.Percentage of dry matter for each compartment was calculated by using the following equation: where: W dry = dry mass (g); W fresh = fresh mass (g).
The oven-dried sub-samples were ground in a mill and used for determining carbon concentration.Using a LECO-144 combustion chamber, based on infrared gas detection, samples of 350 mg were analyzed.In this method samples are burned at ca. 1350°C in an oxygen-rich environment (99.7%).

Biomass Modeling Approaches
The modeling approaches applied were based on former studies about biomass and carbon modeling (Sanquetta 2002, Tobin et al. 2006).In these studies, it could be shown that the variables diameter at 1.3 m (D) and tree height (H), as well as logarithmic transformation and interaction of diameter and height are highly applicable for predicting biomass and carbon concentration of individual trees.The variables, their transformations and interactions used for testing the different model equations were taken from Mello (2004).
Only simple tree measurement variables were used in this study because age and crown size are usually difficult to determine in ordinary forest inventories.
A correlation matrix of the tree measurement variables and total and partial biomass was constructed and analyzed.For estimating the biomass of the whole tree as well as its compartments, the following equations were tested using the software Statistica ® : where H = total tree height (m); D = diameter at a 1.3 m height (cm); and P = biomass (dry matter -kg) for the total biomass and respective compartments.
The ordinary goodness of fit statistics, e.g.coefficient of determination (R²), standard error of the model (S yx %), and the graphical residual analysis (Schlittgen 2009) were used as indicators of the quality of adjustment.Correction of the logarith-mic discrepancy was made by multiplying the estimated values of each tree by the correction factor of Meyer (after Machado et al. 2002): M = e 0.5 Syx 2 (7) where: M = Meyer´s correction factor; e = 2.718281828; S yx = Standard error of estimation.

Approaches to Calculate Individual Carbon Stock
Three approaches for calculating individual carbon stock were compared to the control by means of pair-wise t-tests.It was assumed that the control can be obtained from the sum of partial carbon stocks (compartments), which in turn is calculated from the biomass of a specific compartment multiplied by the respective carbon concentration.The first and simplest one consisted of using the estimated biomass from the best fitting regression equation previously fitted for the total biomass multiplied by the medium weighted carbon concentration of the species (0.4426).The second multiplied the biomass of each compartment by the respective average carbon concentration and resuming the total estimated carbon stock per tree by summing the compartment estimates.
The third involved the directly fitting individual carbon stock from diameter at 1.3 m height (D) and height, in which the carbon concentration of each tree individually is used, as follows: where: As stated before, these approaches were compared to the control, which is the actual individual carbon stock calculated by multiplying the biomass by the carbon concentration.The objective of this analysis was to analyze whether the three carbon stock approaches produce statistically different results and to propose the use of one in individual carbon stock quantification of the studied species.

Biomass Determination
Individual biomass of a M. scabrella tree is distributed in accordance with Fig. 2. Aboveground biomass accounts for roughly 85% of the total dry mass, whereas belowground (roots) for 15%.Stem with bark represents three fourths of the aboveground biomass and crown (foliage+branches) for one fourth.The usual firewood biomass includes stem and branches over 4 cm of diameter, but it has been changed nowadays due to the strong demand and scarce biomass supply in the region.Therefore, even twigs (thin branches) have been converted to fuel and charcoal.Hence, fuelwood (stem+bark+branches) corresponds to ca. 82% of the total biomass.As stated before, M. scabrella is a broadleaved species with sympodial branching, in this specific case often leading to crooked growth or bifurcation.Though the sampled individuals represent the typical growth of the species in stands, the main stem (below the main bifurcation) accounts for only 56% of the total biomass.

Correlation Matrix
Correlations of all variables used in the present study are shown in Table 2.It is noteworthy that all of them were statistically significant.Diameter

Biomass Equations
The best fitting regression equations for the total and partial (compartments) biomass of M. scabrella are presented in Table 3.It is noticed that for the total biomass Eq. ( 4) gave the best fit and for all partial biomass compartments Eq. ( 6) showed the best performance in terms of adjustment.
The best fitting equations (showing the lowest standard error, the highest coefficient of determination, and the most adequate residual distribution) were obtained for the total biomass, followed by the stemwood.It is expected to happen due to less variability and size stability of these variables in comparison to the particular compartments.Models for roots, branches, bark, and foliage also fitted fairly well to the actual data, providing equations of good performance.Fig. 3 also indicates that estimates are more stable for large-sized trees and residuals are more scattered for the smaller size individuals.

Determination of Carbon Concentration
The carbon concentrations of the sampled trees were analyzed separately for the different biomass compartments.It can be noted that of all compartments analyzed foliage has the highest carbon concentration, followed by roots, bark, branches, and stemwood (Table 4).ANOVA carried out  on the carbon concentration indicated a statistically significant difference among compartments (p < 0.001), confirmed by a Tukey´s test that also showed that foliage presented higher carbon concentration than any other compartment.

Individual Carbon Stock Quantification
Pair-wise t-tests indicated no statistically significant differences between the three individual carbon estimation approaches and the control.This is also denoted by Fig. 4 that shows no trend on the estimates by the three approaches of estimating individual carbon stock of M. scabrella.Therefore, if the purpose is exclusively to estimate total carbon stock, more simple approaches may be used satisfactorily, e.g. by multiplying the total biomass estimate from a regression equation by the mean carbon concentration the species.Nevertheless, it is noteworthy that the weighted mean shall be used instead of the simple arithmetic mean in order to not lead to unreliable estimation.Since total biomass is much more stable and easy-to-fit than the partial compartment estimates, reliable figures of individual carbon stock can be provided by this robust approach.

Discussion
According to official inventory data, significant areas of M. scabrella exist in southern Brazil, chiefly in Parana and Santa Catarina States (FAO 2010).Besides Araucaria angustifolia (Bertol.)Kuntze, which is under protection, the studied species is the most important native species in the region that shows the potential for commercialization.Belonging to the leguminous plants with the ability of nitrogen fixation, the species offers a high potential to be planted in poorer soils and by rural populations with no access to technology for soil amelioration (MacDicken 1994).There is strong evidence that the species will be promoted in the next decades and that area as well as volumes of M. scabrella will increase (Carvalho 2003).This also is a key species for promoting the so-called low-carbon agriculture through fuelwood substituting fossil fuels and electricity and for degraded land restoration (carbon sequestration).In this case, knowledge about biomass allocation and carbon storage will play a more important role in the future.The percentage distribution of the biomass in the analyzed trees showed that more than 50% is located in the stem, followed by branches, roots, bark, and foliage.The portion corresponding to fuelwood corresponds to 85% of the total biomass in this species.Similar results were found elsewhere (Urbano 2007), for trees growing in pure and mixed stands of the species on the metropolitan region of Curitiba, the state capital, where firewood of M. scabrella is the preferred one for cooking and wooden poles.Depending on the market, part of the wood may supply the demand of the civil construction (sawnwood and roundwood) sector that generally pays a higher price.In such a case farmers must extend the management rotation up to 17 years (Weber 2007).Since the age range of the sample trees covered younger and older trees (2-19 years), the equations fitted may be applied for fuelwood (short rotation periods) or sawnwood (long rotation period) management regimes.
The biomass distribution in the different tree compartments (stemwood and branches are the most important for fuelwood) was also discussed by various authors.Deciduous tree species deviate significantly from each others in terms of biomass allocation (Bastien-Henri et al. 2010).According to the same authors, site conditions influenced significantly on biomass allocation among the different tree compartments.
However, for foliage the fit was only reasonable, due to the fact that the usual tree measurable variables (i.e.D and height) included in the models explain poorly the variability of foliage biomass, demonstrating that perhaps other variables (as age, site conditions, etc.) might also play a role.This can also be seen in Fig. 3 that plots the graphical residual analysis of the fitting equations.For the coniferous species Picea abies (L.) H. Karst., Pajtik et al. (2008) found that the needles and branches contribute more than 50% to the biomass.Another important factor for biomass partitioning within a tree species is tree age.With increasing age the proportion of stemwood in the biomass becomes more important (Peichl and Arain 2007, Nogueira et al. 2008, Sanquetta et al. 2011).For the material in the study, a higher variation could be observed in biomass produced in the smaller diameter classes, being the variance more constant with bigger diameters.For predicting the biomass, most studies have used the variables D, basal diameter, tree height or a combination.In many cases, quadratic terms and the logarithmic or square root transformation of the predicting variables were also conducted (Zianis and Mencuccini 2003, Zianis et al. 2005, Peichl and Arain 2007, Nogueira et al. 2008, Zianis 2008, Basuki et al. 2009, Bastien-Henri et al. 2010).In the regression equations used in this study, tree diameter and tree height also showed up as being important for predicting the biomass.The goodness of fit of the regression equations for individual biomass of M. scabrella was surprisingly satisfactory.Since most broadleaved subtropical trees belong to species with sympodial branching, often linked with crooked growth and bifurcation, it would be expected a somewhat weak correlation of tree measurement variables and biomass, especially for partial compartment biomass.Hence, poor fitting would be expected in some cases.However, for M. scabrella it did not occur.The fitted equations could be used safely in all cases, even for foliage.
Mimosa scabrella carbon concentration, related to 1 kg of biomass, is the highest in foliage, followed by roots, bark, branches, and stemwood.Statistical analyses showed that only the mean value of the carbon concentration of foliage is significantly different from those of other compartments.Anyhow, for reliable carbon flow and carbon balance calculations as well as for life cycle assessment and substitution effects such information is important.Ganeshaiah et al. (2003) analyzed carbon concentration in different compartments of several tropical tree species.Compared with other broadleaved tree species the carbon concentration of bark was similar, whereas the carbon stored in the leaves was between 5 to 10% higher in M. scabrella (Ganeshaiah et al. 2003).Conversely, the carbon stored in stemwood is at a low level compared with other species.Detailed analysis on carbon allocation in eucalypt stands was also completed by Ryan et al. (2010) and Madeira et al. (2002), showing that management, water, light and nutrient availability significantly influenced the carbon allocation in different tree compartments.Bert and Danjon (2006) with Pinus pinaster Aiton, Kraenzel et al. (2003) with Tectona grandis L., Stape et al. (2008) with a clonal Eucalyptus sp. and Vallet et al. (2009) for Quercus and Pinus spp.showed that among species, among trees of the same species, among different compartments of the same tree, and also at different tree heights the carbon concentration can be significantly different.
Three different approaches of quantifying individual carbon stock were tested for the studied species.No statistical difference was noticed from the statistical analyses.Therefore, no matter if biomass multiplied by carbon concentration or directly carbon equations are used for carbon quantification.However, as stated by Koehler et al. (2002), who analyzed the deviations and accuracy of carbon stock estimates, the indiscriminate application of 0.5 as a universal carbon fraction is a fallacy and may lead to serious overestimates of carbon stocks.According to the authors, this assumption combined with other generalization frequently adopted in carbon inventories may lead to inaccuracy of 20 to 53%.
The Intergovernmental Panel on Climate Change (IPCC) (2003,2006) has defined five carbon pools for greenhouse gas inventory, which were also included in the so-called Marrakesh Accord of the United Nations Framework on Climate Change (UNFCCC) (Ravindranath and Ostwald 2008).They are: aboveground and belowground biomass (roots), litter, dead wood, and soil organic carbon.In this study, necromass and soil were not taken into account because they are not individual tree variables and require specific methodological procedures.For this purpose, the user shall use the compartment-specific equations for foliage, branches, stem, and bark and sum the estimates to get the individual aboveground biomass and the root equation to calculate belowground biomass.At this place the assumption that expansion of root system is equal to the area covered by the crown must be discussed.In native forests, tree roots may extend to a much wider area than the crown.In many cases, the aboveground competition leads to asymmetric crown development, which does not correspond to belowground root expansion (Kutschera and Lichtenegger 2002).However, when digging out the roots for weighting, it could be observed that the approach used represented the root system well.Even so, the estimate of the distribution of tree biomass between above-and belowground compartments may be biased because of the root sampling method.
For the purpose of estimation biomass or carbon from firewood or wood debris after harvesting, for instance, the user shall use the biomass equations in separate and integrate them accordingly, as also stated by Urbano (2007).

Conclusions
The study was a first attempt to attain realistic data for the biomass and carbon storage of M. scabrella, which is available at significant volumes in southern Brazil in both mixed and pure stands (Weber 2007).That makes the species interesting for broad commercial uses and also for ecological restoration purposes, including carbon sequestration.
The developed equation for estimating individual biomass and carbon of different tree compartments with the help of the easily available variables diameter at the height of 1.3 m and tree height allow predictions with a high precision.The models can be used to estimate the fuelwood, quantify carbon stocks for greenhouse gas inventories, carbon offsets and or even compare the different harvesting forms and uses of M. scabrella.Life cycle assessment from the biomass produced in the forest until the final product for the carbon flows is also possible.
Even not considering the influence of different growth and site conditions, which are important parameters for carbon allocation in different tree compartments, the allometric functions for estimating biomass and carbon showed a high predictability.

Fig. 1 .
Fig. 1.Location of the area where the Mimosa scabrella trees were sampled, at a circle of 30 km around the União da Vitória municipality.

Fig. 3 .
Fig. 3. Graphical residual analyses of the best fitting regression equations of individual biomass of Mimosa scabrella.

Fig. 4 .
Fig. 4. Actual (Control) and predicted individual carbon stock of Mimosa scabrella by different quantification approaches.

Table 1 .
Characteristics of the sample trees used in the study (D = diameter at 1.3 m height, H = tree height).

Table 2 .
Correlation matrix for measurement and biomass variables of Mimosa scabrella (D = diameter at 1.3 m height, H = tree height).

Table 3 .
Fitting statistics of the regression equations to estimate biomass of Mimosa scabrella (S yx % = standard error of estimation, %; st.error = standard error).