Species-Specific Allometric Equations, Biomass Expansion Factor, and Wood Density of Native Tree Species in the Dry Afromontane Forest of Ethiopia

. A forest is a storehouse of carbon released from diferent sources when the activities of sustainable forest management, planting, and rehabilitation exist. However, few allometric equations are present to determine its contribution to carbon reduction. Te target of the study was to develop species-specifc allometric equations and establish a database for biomass expansion factor and wood density for fve tree species grown in the dry Afromontane forest of Ethiopia. A direct or destructive sampling method was used on 62 trees from diferent diameter classes. Te diameter at breast height and the total height of selected trees ranged from 7 to 48cm and 6.7 to 23.4 m, respectively. Trees were felled and divided into various biomass sections. Stem and big branch discs were sampled to determine the wood density and volume of the trees. Sample wood and foliage were oven-dried for three days and two days at 105 ° C and 70 ° C, respectively, to get their dry weight. Total above-ground biomass was regressed using diameter at breast height, total height, wood density, and average crown diameter as independent variables. R software version 4.0.1 was used to ft the biomass equations. Te best biomass models were determined to have lower AIC and RSE and highest adj. R 2 . Te biomass expansion factor and wood density of fve tree species ranged from 1.19 to 1.40 and 0.53 to 0.74g/cm − 3 , respectively. Species-specifc allometric equations were better than both mixed species and pan tropical models for the assessment of above-ground biomass in the Chilimo dry Afromontane forest of Ethiopia.


Introduction
Forests are considered the storehouse of carbon released from fossil fuels, industry, and land use change emissions if and only if the activities of sustainable forest management, planting, and rehabilitation exist [1].Forests on all the continents accumulate 283 gigatonnes of carbon in their biomass alone.As a result, 229 to 263 petagrams of carbon are stored by tropical forests in various pools [2,3].According to FRA [4], there are fve carbon pools in forest ecosystems: above-and below-ground biomass, dead wood, litter, and soil organic carbon.
Te amount of carbon stored by the forest decreases from time to time due to deforestation and forest degradation.Tis led to an increase in the concentration of greenhouse gases in the atmosphere [5], which in turn caused climate change, one of the major challenges to human society and the environment in the world.Tis also brought critical challenges to Ethiopia [6].
To address the challenges of climate change, Ethiopia has developed and applied REDD + strategies for the last 10 years [6].Accordingly, measurement, reporting, and verifcation (MRV) for greenhouse gas emissions, including greenhouse gases from deforestation and forest degradation, have been adopted.Te estimation of the contribution of the forestry sector to REDD + activities requires accurate biomass estimation methods [5].
Most of the time, both direct and indirect methods can be used to assess tree biomass [7].Te direct approach entails cutting down the tree and determining the precise masses of each of its components [8,9].Although it is quite accurate, it is expensive and time-consuming to cut down trees and separate them into diferent components [10].In contrast, indirect methods are less expensive and take less time to estimate tree biomass since they use allometric models and biomass expansion factors that have already been developed [11].In addition, when employing developed allometric equations, basic wood density, which is computed as the dry weight of wood divided by the green volume of wood, can be utilized to forecast biomass or estimates derived from volume and biomass expansion factors [12].
Allometric models for biomass estimation are scarce in the tropics compared to the species diversity of the area [10].Te majority of biomass models are created for tree species in South Africa and Latin America.Ethiopia in particular and sub-Saharan Africa in general have seen some studies seeking to build biomass equations [12][13][14][15][16][17][18][19].
Pan tropical allometric equations developed by many researchers may overestimate or underestimate the biomass since diferent tree species have very diferent tree architecture and wood density [7].To reduce the estimation problem, both species-specifc and mixed-species allometric equations for Ethiopia are required for forest biomass and carbon stock estimation.But the country lacks appropriate standard biomass tables and equations to calculate speciesspecifc or mixed tree biomass.So, local allometric equations may solve this problem due to their ability to accurately estimate the amount of biomass in the forest and enable the country to beneft from the carbon market opportunity.It is also used by a country to report accurate and consistent data that meet international standards and to create a favorable policy on the environment [5].
Terefore, this study was aimed at developing speciesspecifc allometric equations and establishing a database for biomass expansion factor and wood density for Apodytes dimidiata, Cassipourea malosana, Celtis africana, Ilex mitis, and Myrica salicifolia tree species in the Chilimo dry Afromontane forest of Ethiopia.

Study Site Location.
Te Chilimo dry Afromontane forest belongs to the state-owned Oromia Forest and Wildlife Enterprise.With an elevation range of 2,470 to 2,900 meters above sea level, the forest may be found at latitudes 038 °08′ 679″ to 038 °10′ 283″ east and longitudes 09 °04′ 038″ to 09 °05′ 765″ north, respectively.Te region's mean annual temperature varied between 15 and 20 degrees centigrade, and it averaged 1000 to 1264 mm of precipitation per year [20].Te climate of Chilimo forest might be described as warm temperate climate I (CWB) type following Köppen's classifcation system [21].Te forest has a total area of about 2500 hectares and is located 97 kilometers west of Addis Ababa, the capital of Ethiopia [22].

Vegetation Description of the Study Site.
Chilimo forest is one of the few remnant forests located in the central highlands of Ethiopia and is composed of mixed broadleaved tree species such as Podocarpus falcatus, Olea europaea subsp.cuspidata, Scolopia theifolia, Rhus glutinosa, Olinia rochetiana, Allophylus abyssinicus, and Juniperus procera [23,24].Soromessa and Kelbessa [22] reported that 213 diferent woody species, which belong to 83 families, and 18 plant species are registered as endemic to the Chilimo forest, of which one is endangered and three are considered vulnerable.Shumi [20] investigated 42 species, made up of 27 tree and 15 shrub species, in the forest.In addition, 33 diferent indigenous woody species (22 trees and 11 shrubs) were registered for Chilimo by Tesfaye et al. [19] in three forest sections.

Data Collection and Sampling.
For the development of above-ground biomass equations, tree species such as A. dimidiata, C. malosana, C. africana, I. mitis, and M. salicifolia were chosen based on the importance value index (IVI).Ten, based on previously collected tree data by Tesfaye et al. [25], diameter distributions at 10 cm were done on sample trees in each diameter class, and the number of harvestable trees from each diameter class was determined.Moreover, the basal area of each tree in each diameter class, the total basal area of all species in diferent classes, and the total number of trees harvested in each diameter class were calculated.Te sampled tree diameter intervals ranged from 5 to 55 cm (Table 1).Trees with a broken crown, excessive branching, or less branching were not cut [26].A total of 62 sampled trees were cut and portioned into diferent biomass sections.For C. malosana 14 trees were selected; 13 trees were selected for A. dimidiata, C. africana, M. salicifolia; and 9 trees forI.mitis were selected and cut (Table 1).

Biomass Data Collection.
Before cutting down the chosen trees, environmental information like slope (%), altitude, and UTM coordinates (using a Garmin 72-channel GPS) were recorded.Additionally, DBH (cm) and average crown diameter (m) were measured.Ten, using a chainsaw, test trees were cut down nearly to the ground.Diameter at a 2 m interval, total height (H), and commercial height (Hc) (height up to a top stem diameter of ≥7 cm) were measured using diameter tape and measuring tape.Ten branches and foliage were removed.Te felled trees were divided into four categories: stems (from the ground base to the top diameter of ≥7 cm), big branches (diameter ≥7 cm), small branches (diameter <7 cm up to 2 cm), and foliage (diameter <2 cm) [27].Te total fresh weights of all components were determined, and 200-gram subsamples were taken from small branches and foliage using a sensitive mass balance.Tree and two discs, respectively, were taken from the stem and big branch for the purposes of determining the volume and density of the wood [26].

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International Journal of Forestry Research Te following formula was used to determine each component's total dry weight: Total dry weight of the small branches �  total fresh weight of the small branches × sample dry weight sample fresh weight , Total dry weight of the foliage �  total fresh weight of the foliage × sample dry weight sample fresh weight . ( Te biomass of stems and big branches was estimated by using wood density times volume.Te volume of the stem and big branch section was derived using Smalian's formula as cited by De Gier [28].Finally, the following is used to get the dry weight of the total above-ground biomass: �  total dry weight of stem +  total dry weight of big branches +  total dry weight of small branches +  total dry weight of foliages. (2) 2.5.Biomass Expansion Factor Data Collection.Bimass expansion factor was calculated using the total biomass and stem biomass of particular tree species (biomass was calculated using the log section stem volume and the corresponding log section's wood density) (M = WD * V) where M is estimated biomass, WD disc wood density, and V is tree log volume.

Data Collection and Sampling for Wood Density.
Tree discs from the stem were cut at the base, middle, and top with a thickness of 5 cm to measure the density of the wood.Two discs from the base and top of the big branch were taken.Te Central Ethiopia Environment and Forest Research Center laboratory received fresh weights that had been measured in the feld and transferred there.After that, they were oven-dried at 105 °C and 70 °C for three days and two days, respectively, for wood and foliage, until a steady weight was achieved.Te water displacement method was used to estimate each disc's volume (Figure 1).

Biomass Equations.
Allometric equations were developed for selected tree species and validated following appropriate procedures.First of all, descriptive and scatter plot analyses were carried out in order to determine the biomass and see its relationships with dendrometric variables.Te Spearman method is used in order to identify the best predictor variables.Ten the best dendrometric variables tested for each total biomass were ftted individually using Statistical R version 4.0.1.A comparison was made using AIC, residual standard error, adj.R squared, and p value.Finally, the results were compared with [12,[30][31][32][33].

Data Analysis and Model Validation
Te statistical analysis was conducted with R statistical software (https://www.r-project.org/versions/R-4.0.1),SAS version 9.2, and Microsoft Ofce Excel 2007 and decided at a signifcant level of 0.05 based on feld and laboratory data.Transformed regression techniques were applied to develop allometric models to predict total biomass using independent variables including diameter at breast height, total height, wood density, and average crown diameter.
Te model selection and validation were calculated based on the statistical signifcance of model parameter estimates: AIC, adjusted coefcient of determination (adj.R 2 ), relative bias in percent, mean prediction error (MPE), and RMSE [31].Te Akaike information criterion (AIC) was estimated from the following equation: where L is the likelihood of the ftted model; p is the total number of parameters in the model; and ln is the natural Te adjusted R 2 value indicates the variation explained by the model from total variation.It is a value between 0 and 1, and the closer it is to 1, the better the quality of the ft is.
Te mean prediction error was calculated by Te root mean square error was calculated using the following equation: where y i is the observed above-ground biomass in kg, y l is the predicted above-ground biomass in kg, y j is the mean observed biomass in kg, n is the number of observations, and p is the number of parameters.

Allometric Biomass Models.
Many species-specifc and general allometric equations have been developed based on nonlinear regression model techniques [13,27,30,31].To avoid heteroscedasticity, a logarithmic transformation was applied [34,35].Te correction factor (CF) formula was developed by Sprugel [36] and used to adjust for underestimation of biomass [31,37].Tus, the correction factor was computed using the residual standard error of the regression (RSE) for each allometric model.
Tested models: Where TAGB (in kg) is the total above-ground biomass of trees as a response and DBH is the diameter at breast height (cm), H is height (m), WD is wood density (g•cm −3 ), CD average crown diameter (m) as independent variables, exp is an exponential function, ln is natural logarithmic, ais intercept, andb, c, d, and e are model parameter estimates.

Biomass Expansion Factor Determination.
Te average ratio of all of the harvested trees' dry weights and stem weights was used to compute the BEF using the following equation: where BEF is the biomass expansion factor (unit less); tDWi (kg tree −1 ) is the total dry weight of each individually sampled tree (stem, branches, and foliage); tSi (kg tree −1 ) is the total dry weight of the stem alone and of each individually sampled tree; and n is the total number of sampled trees for each species [42].

Wood Density Determination.
Wood density is calculated using the following formula [43]: where WD is the wood density in grams per cubic centimeter, M is the oven-dry mass of wood in grams, and V is the green volume of wood in cubic centimeters.

Validation and Evaluation of Models.
Model comparison was done by using our dataset to select a pan tropical model and tested by a paired t-test for comparison of actual total biomass with predicted total biomass by general models.

Wood sample Water
Figure 1: Sample volume measurement by water displacement [29].

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Correlations between Above-Ground Biomass and Tree
Variables. A. dimidiata tree species' total above-ground biomass had a stronger correlation with total tree height than DBH but a weaker correlation with the average crown diameter (CD) and was negatively correlated with WD of their total biomass (Table 2).Although the total biomass of C. malosana was weakly connected with the average (CD) and negatively correlated with WD, it was strongly correlated with DBH rather than H (Table 2).DBH, average (CD), and total tree height were highly linked with C. africana's total biomass and weakly correlated with WD (Table 2).In contrast to average (CD) and WD, the total biomass of M. salicifolia and I. mitis was substantially linked with total tree height after DBH (Table 2).

Species-Specifc Allometric Equations for Studied Tree
Species.Te relationship between above-ground biomass and dendrometric predictor variables such as DBH, H, WD, and average CD was formulated for A. dimidiata, C. malosana, C. africana, I. mitis, and M. salicifolia.Te prediction accuracy and validation potential of ftted allometric equations for total above-ground biomass are presented in Table 3 and supplemental material.Te selected models had a high adjusted coefcient of determination (>89%), a p value less than 0.01, and a relatively low standard residual error (Table 3).
(1) Observed versus Predicted Total Biomass.Te dotted line shows the adjusted line to the residuals, and the continuous line is the 1 : 1 line.Te results of the paired t-test did not show a signifcant diference between observed and predicted total biomass for the developed models (Table 3 and Figure 2).Te validation of observed and predicted values showed a linear relationship for all the targeted tree species.Based on the hypothesis, a oneto-one relationship between the observed and predicted above-ground biomass showed the better prediction accuracy of the model (Figure 2).Te mean diference between the observed and predicted total biomass of the studied tree species ranged between 0.14 and −11.03 (Table4).Overestimation of above-ground biomass was seen in all studied tree species except A. dimidiata.

Fitted Allometric Equations for Mixed Tree Species.
From ftted allometric equations for mixed tree species, the best model is the combination of (diameter at breast height, total tree height, wood density, and average crown diameter) exhibiting the highest adjusted R 2 value (Table 5).Te lowest model explanation is seen when only using diameter at breast height; it explains variation by 84% of total aboveground biomass.However, the combination of diameter with other tree variables explained more than 85% of the variability of total above-ground biomass.Te combination of wood density with diameter and height in diferent forms explains variability well (Table 5).

Biomass Expansion Factor and Wood Density of
Studied Tree Species.Te biomass expansion factor (BEF) of selected tree species ranged from 1.02 to 1.95, and the results demonstrate that the mean of BEF difered among species.Te highest BEF was found for C. malosana and A. dimidiata, while the lowest was found for C. africana (Table 6).Te mean wood density (WD) values for chosen tree species are summarized, and the values ranged from 0.53 to 0.74 g•cm −3 .Te mean wood density of selected tree species ranged from 0.53 to 0.74 g•cm −3 and varied among the targeted species.Te highest mean WD was recorded in A. dimidiata, while the lowest was recorded by I. mitis (Table 6).

Comparison of Species-Specifc and Pan Tropical
Models.Tere is no signifcant diference between the species-specifc model and the observed above-ground biomass for A. dimidiata (p > 0.05).Te total aboveground biomass of relative bias in A. dimidiata ranged from −0.17 to 2.44 kg, while the root mean square error ranged from 14 to 195.61 kg.While for all generalized models, p < 0.05 showed a signifcant diference between observed and predicted biomass.Positive mean prediction error values are signifcantly diferent from zero, implying an underestimation of the total above-ground biomass of selected tree species and vice versa (Table 4).While the root mean square error ranged from 4.34 to 285.7 kg, the species-specifc allometric equations were more precise for C. malosana than generic ones.Tere was no discernible diference between the total biomass observed and predicted for C. malosana according to the species-specifc allometric equations, Brown and Lugo [30]; and Chave et al. in [31,32].While the majority of studies overestimate biomass, Brown and Lugo [30] and Djomo et al. [33] both understate it (Table 4).For C. africana, the species-specifc allometric equations were more precise than the generic ones.Te observed and predicted total biomass by the species-specifc allometric model and generalized model [30][31][32] had no signifcant diference for I. mitis at p ≤ 0.05 (Table 4).Te species-specifc allometric equation was more accurate for M. salicifolia than the generalized model, with the lowest value of relative bias in percent ranging from 0.37 to 4.1 and the root mean square ranging from 39.78 to 438.Tere is no signifcant diference between the total above-ground biomass predicted by the speciesspecifc allometric equation [33] and the observed biomass for M. salicifolia (Table 4).But there is a signifcant diference between observed and predicted biomass by other generalized models.

Species-Specifc Allometric Equations for Above-Ground Biomass.
For the quantifcation of carbon storage, which is crucial for the carbon market credit, appropriate allometric equations are needed.Te residual standard error is reduced when estimating total biomass International Journal of Forestry Research     Overman et al. [46]; and Tesfaye et al. [19] who found that combining diameter and height as independent variables led to more accurate results.But in contrast to our fndings, the addition of height did not improve the models [47] or raise the coefcient of determination [48].
According to Ogawa's [49] fndings, the prediction accuracy increased when the squared diameter and height were combined.Tey disagreed with the conclusions of the earlier studies [13,33,50] and discovered that dbh 2 ht was a suitable predictor of total above-ground biomass.Most of the time, the wood density to total biomass spearman correlation was weak and statistically insignifcant (p > 0.05).Te residual standard error for C. africana, I. mitis, and M. salicifolia decreased when wood density was added to diameter and height for total biomass (supplemental material (available here)).Tis is consistent with the reports from Ali et al. [44], Chave et al. [32], and Goodman et al. [41] and is in contrast with those of other research studies conducted elsewhere    [52]; and Tetemke et al. [47], these results are consistent.Crown diameter was crucial for biomass estimation, increasing the coefcient of determination for M. salicifolia from 0.89 to 0.94 (supplemental material (available here)).Our fndings concur with those of Hofstad [48] and Conti et al. [53].According to Tetemke et al. [47], diameter and crown width make for superior independent variable pairings when compared to the more common diameter and height.Tis is due to the diameter of the crown being the easiest feld measurement variable [54], and species might have the same architecture and branching patterns, which disagrees with the report of Ali et al. [44], who discovered that diameter and height are more crucial for determining the above-ground biomass than crown factors.
Depending on the availability of data from forest inventory, any model with substantial model parameter estimates (supplemental material (available here)) may be used to estimate total above-ground biomass.

Biomass Expansion Factor.
Te biomass expansion factor (BEF) for the targeted tree species ranged from 1.19 to 1.40 (Table 6).Te fndings of Levy [55], who reported a BEF of 1.31 to 1.69 for 129 conifer species in Great Britain, were consistent with our fndings.Tis resemblance may result from the estimation technique used.Te results of A. dimidiata and those of Giri [56] were very similar.He mentioned that the species of Aillanthus excels had a biomass expansion factor of 1.23.Our results fell short of the IPCC's estimated biomass expansion factor for tropical forest stands, which is 3.4.Te diference may be explained by the strong correlations between basal area, volume, tree height, and biomass expansion parameters [57].Our results are higher than those of Momba and Bux [58] who discovered 0.8731 tropical dry trees in eastern Sinaloa, Mexico.Tis was caused by biomass expansion factors that depend on the size of the tree or are directly proportional to the total biomass of trees [59].Te results of Iranmanesh et al. [57], who reported a BEF for single stem vegetation of Brant's Oak species at 2.37, are very diferent from ours.

Wood Density.
Te mean wood density of the sampled tree species varied between 0.53 and 0.74 g•cm −3 (Table 6).Tis outcome was comparable to that reported by Olale et al. [60] who found mean wood density of 0.42 to 0.73 g•cm −3 for a few diferent tree species in Western Kenya.While Tesfaye et al. [25] researched the Chilimo forest for the prominent native tree species (0.44 to 0.67 g•cm −3 ), their fndings difer greatly from ours.According to Gartner and Meinzer [61], this diference may be explained by the diameter range and species characteristics.In comparison to the chosen tree species, Apodytes dimidiata, Cassipourea malosana, and Celtis africana had higher wood densities (Table 6).Tis may be caused by variation in foristic composition [62].According to our fndings, Apodytes dimidiata and Ilex mitis had wood densities of 0.74 and 0.53 g•cm −3 , respectively (Table 6).But this result is far from the reports of Merti et al. [63] of 0.53 and 0.45 g•cm −3 , respectively.Tese variations may result from the type of vegetation and the estimating technique (the semidestructive technique).
Cassipourea malosana has a basic wood density of 0.71 g•cm −3 .Tis outcome difers signifcantly from the Genus average, which was reported as 0.673 g•cm −3 .Te number of trees we sampled and the stem positions we sampled may be to blame for this discrepancy.Te basic wood density of Celtis africana is 0.74 g•cm −3 which is in line with the report of https://db.wordagroforestry.org//wd/species/Celtisafricana and Getachew et al. [64].Ilex mitis has a basic wood density of 0.53 g•cm −3 , which is much lower than the fndings of Vreugdenhil et al. [65].Finally, Myrica salicifolia's basic wood density was 0.55 g•cm −3 , which was much less than the number given by https://db.wordagroforestry.org//wd/species.
Te overall average wood density for the studied tree species was 0.656 g•cm −3 .Tis outcome is comparable to that of Chave et al. [62] who discovered that the average weight of 2456 Central and South American tree species was 0.645 g•cm −3 .

Species-Specifc Comparison with the Pan Tropical
Model. Brown and Lugo [30][31][32][33] discovered that the actual biomass and general model were comparable to, but not identical to, the actual mean value.Tis similarity is probably due to the allometry of the trees in the Brown and Lugo [30][31][32][33] sample, which may have included trees with similar allometry to the trees in our study area.Te result is similar to that of Ares and Fownes [66].When the equations of Brown and Lugo [30]; Chave et al. [31,32]; Djomo et al. [33]; and Asrat et al. [12] were applied to our dataset, the predicted values were over-and underestimated (Table 4).Te numerical diferences in the results might arise because of agro-ecology and diameter range.

Conclusions and Recommendations
Te incorporation of a diverse set of independent tree variables including diameter at breast height, total tree height, wood density, and average crown diameter signifcantly improved the precision of the models.Te coefcients of determination were greater than or equal to 84% for both species-specifc and mixed tree species for total biomass estimation.Among selected tree species, the maximum biomass expansion factor was recorded for C. malosana tree species, and wood density was recorded for A. dimidiata.Speciesspecifc allometric equations were better than both pan tropical and mixed allometric equations for the estimation of total above-ground biomass.Generally, the selected models and computed wood density and biomass expansion factors in this study are believed to be applied by both government and nongovernment organizations to estimate the total biomass and carbon stock of selected tree species.To use the developed allometric equations, we have to consider the species composition and type of the forest ecosystem.

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Figure 2 :
Figure 2: Observed versus predicted total biomass for studied tree species.

Table 1 :
Sample trees selected corresponding to tree size distribution.

Table 2 :
Correlation between total above-ground biomass and tree variables.

Table 3 :
Te best regression species-specifc allometric equations for TAGB for studied tree species.

Table 4 :
Comparison of species-specifc model with pan tropical model.

Table 5 :
Te best regression equations for total above-ground biomass for mixed tree species.Model performance information should be put on the top of Adj.R 2 , AIC, CF, RSE, P value, and Rank.

Table 6 :
Mean and range of biomass expansion factor and wood density (mean ± SD) for studied tree species.

Table 4 :
[51]inued.For the species C. malosana, wood density did not make the model more accurate.According to Baker et al.[51]; Njana et al.