Allometric equations for determining volume and biomass of Acer monspessulanum L. subsp. cinerascens multi-stemmed trees

Document Type: Research Paper

Authors

1 Department of Forest Sciences, Faculty of Natural Resources, Yazd University, Yazd, Iran

2 Department of Forest Sciences, Faculty of Natural Resources, Tehran University, Tehran, Iran

Abstract

Due to the importance of Acer monspessulanum in Iranian mountain forests, a study was carried out to reliably estimate its woody biomass and growing volume via allometric equations. Four transects, five trees in each were chosen randomly. The characteristics of standing trees including: diameter at root collar, height, number of stems and crown width were measured, then trees were finally cut down. Trunk and branches were separated and weighed. Some disks were taken and moved to the laboratory to determine the dry/fresh weight ratio and wood specific gravity and subsequently to calculate the dry weight of trunk, branch as well as aboveground biomass. Linear regression analysis was conducted to create allometric equations. Results showed that there was a strong and significant correlation between volume/biomass of Acer monspessulanum and quantitative characteristics of standing trees. The most robust predictors of volume and aboveground biomass were found to be crown width and crown area (R2 = 0.83) followed by equivalent diameter at root collar (R2 = 0.81). The normalized root-mean-square error amounts were found to be under 20% for most models especially for predicting biomass of branches. Tree height combined with equivalent diameter at root collar (EDRC) explained 87% of the variations in volume and biomass, creating precise models. It is concluded that crown diameter and EDRC can predict biomass and the volume of A. monspessulanum as a multi-stemmed tree with high accuracy and precision. 

Keywords


[Research]

 

Allometric equations for determining volume and biomass of Acer monspessulanum L. subsp. cinerascens multi-stemmed trees

 

Afroonde A.1, Kiani B.*1, Attarod P.2

1. Department of Forest Sciences, Faculty of Natural Resources, Yazd University, Yazd, Iran

2. Department of Forest Sciences, Faculty of Natural Resources, Tehran University, Tehran, Iran

 

* Corresponding author’s E-mail: bnkiani@yazd.ac.ir                          (Received: Dec. 23. 2017 Accepted: April 25. 2018)

ABSTRACT

Due to the importance of Acer monspessulanum in Iranian mountain forests, a study was carried out to reliably estimate its woody biomass and growing volume via allometric equations. Four transects, five trees in each were chosen randomly. The characteristics of standing trees including: diameter at root collar, height, number of stems and crown width were measured, then trees were finally cut down. Trunk and branches were separated and weighed. Some disks were taken and moved to the laboratory to determine the dry/fresh weight ratio and wood specific gravity and subsequently to calculate the dry weight of trunk, branch as well as aboveground biomass. Linear regression analysis was conducted to create allometric equations. Results showed that there was a strong and significant correlation between volume/biomass of Acer monspessulanum and quantitative characteristics of standing trees. The most robust predictors of volume and aboveground biomass were found to be crown width and crown area (R2 = 0.83) followed by equivalent diameter at root collar (R2 = 0.81). The normalized root-mean-square error amounts were found to be under 20% for most models especially for predicting biomass of branches. Tree height combined with equivalent diameter at root collar (EDRC) explained 87% of the variations in volume and biomass, creating precise models. It is concluded that crown diameter and EDRC can predict biomass and the volume of A. monspessulanum as a multi-stemmed tree with high accuracy and precision. 

Key words: Allometric equations, Biomass, Modeling, Multi-stemmed, Prediction.


INTRODUCTION

Volume and biomass estimation of forest trees is very important in forest resource planning. Calculating the volume in standing trees is more difficult than in fallen trees with lower accuracy. Therefore, we have to find a reliable method to estimate standing volume. Several methods have been used by different researchers to estimate the volume of forest trees. However the accuracy of these methods highly depends on the type of forest (Pourshakoori & Hassanzad 2007). Calculating the volume of multi-stemmed trees using simple formulas is nearly impossible since most of the stems have small diameter with collections of about ten stems forking from the ground. Therefore, introducing the allometric equations to estimate their volume would be helpful. The most accurate method to estimate biomass of trees is a method in which the tree is entirely cut and divided to separate organs, dried and weighted (Basuki et al. 2009). Then allometric equations showing the relation between weight and size of each organ can be derived (JICA, 2005). Allometric equations are tools for estimating total weight of tree or tree parts by measuring diameter at breast height (DBH), tree height and other variables (Komiyama et al. 2008). Allometric equations are regression-based equations directly convert measurements of diameter and sometimes height to the total tree biomass (Losi et al. 2003). As a brief literature, in a study carried out by Panahi et al. (2011) in Iran National Phytology Garden, biomass and leaf carbon reserve were investigated using allometric equations in Pistacia atlantica forests considering crown width as the most effective variable on leaf biomass and carbon reserve. Zhou et al. (2007) improved two sets of allometric equations for predicting biomass of multi-stemmed Eleagnus angustifilia trees in Montana. Sohrabi & Shirvani (2012) also investigated the allometric relations for estimating crown and trunk biomass for Pistacia atlantica trees. Williams & Gresham (2006), Bakhtiarvand Bakhtiari (2011) and Parsapour et al. (2013) also employed allometric equations and introduced the best correlation and the most proper model for different parts of trees. Zewdie et al. (2009) calculated aboveground biomass of a coppice forest in central mountains of Ethiopia using allometric relations. The results showed that aboveground biomass had a linear relation with age of coppicing. Fu & Wu (2011) found a nonlinear regression equation based on tree height and crown width that was very suitable for estimating aboveground biomass of multi-stemmed mangrove trees in Quanzhou Bay, China. Cienciala et al. (2013) indicated that equivalent diameter at breast height predicts 98.8% of variations in aboveground biomass of Prosopis spp. in Santo Antano islands, West Africa. Miller (2016) found that total basal area was a suitable predictor to estimate biomass of multi-stemmed poplar trees in Mishigan. The purpose of this study was to introduce allometric equations for reliable estimation of volume and biomass in multi-stemmed trees of Acer monspessulanum. The equations would possibly make precise estimation of standing volume and aboveground biomass in this valuable species that can be regarded in forest management.

MATERIALS AND METHODS

Study site

This research was carried out in Baghe-Shadi protected forest is managed by Iranian Institute of Environmental Protection (11665 ha, 29º 42' 50'' - 29º 50' 41'' N, 54º 05' 35'' - 54 º 14’ 35'' E, 1840-2664 m a.s.l.). The forest is located in South Yazd Province (240 km south of Yazd city) and belongs to Iran-Touran biogeoclimatic zone. The main forest species were Pistacia atlantica (F. & M.), Acer monspessulanum subsp. cinerascens (Boiss.), Amygdalus scoparia (Spach.) and Amygdalus eleagnifolia (Spach.). The slope was gentle in most area, with a mean inclination of about 20%. The area has a semi-arid climate with mean annual temperature and precipitation of about 17.4 ºC and 285 mm, respectively.

Sampling Strategy

Habitat of A. Monspessulanum trees was firstly positioned in the topography map of study area with scale 1:80000. Transect sampling method was selected for the area and several transects were determined randomly in specified zones. Starting points coordinates were recorded along with azimuth. Five trees with different dimensions were selected randomly in four transects (totally 20 trees in study area) in November 2015. Characteristics of trees including trees height (with Sunnto clinometer), stem numbers, crown width (with tape measure), crown area and diameter of stems at root collar (with caliper) were measured prior to cutting the trees. Equivalent diameter at root collar (EDRC) for each tree was calculated by equation 1.

 

                                               (1)

where d1 to dn are stem diameters (d ≥ 2.5 cm) and EDRC is equivalent tree diameter at root collar (Junior et al. 2014). The trees were ultimately harvested and then trunks and branches were separated. Noteworthy, leaves biomass was not calculated as trees were cut during leafless period (we could not get permission to cut trees in growth season, as the study site was located in a protected area). All trunks and branches were weighted separately for each tree (by digital balance with an accuracy of ± 0.05 g). Discs were taken from trees at root collar and DBH points to determine the specific gravity of wood.

 

Lab measurements

Dry weight of samples was measured by a digital scale (with an accuracy of ± 0.05 g) after keeping in oven (80 ºC for 48 h). The coefficient derived from the ratio of dry weight to fresh weight of the samples was considered as an expansion factor, employing for measuring dry weight of all trunks and branches. The water displacement method was applied to obtain trunk volume. This method provides a better estimation of volume for species that have big hollow sections (Cornelissen et al. 2003). After determining the volume, specific gravity of woods was calculated as below (Vahedi & Metaji 2013):

 

ρ = M / V                                                       (2)

Where ρ is specific gravity (kg m-3), M is sample dry weight (kg) and V is sample volume (m3). As wood dry weight and specific gravity were given, trunk volume of each tree was calculated. Also woody biomass of trees was determined for branches and trunks (aboveground biomass except leaves).

 

Statistical analysis

The validity of the models was evaluated by illustrating normality graphs and error value distribution. The normalized root means squared error (NRMSE) and coefficient of determination (R2) were calculated to determine the best model. The more close the NRMSE to zero, the more precise the model (Andrei 2014). So, NRMSE in ranges of 10 - 20 and 20 - 30 shows the proper and the average precision of the model respectively, while the values more than 30%, show model unreliability (Singh et al. 2008).

The best models with the highest R2 and the least NRMSE were selected. Error independency and normality were tested by Durbin-Watson and Shapiro-Wilks tests respectively to assure model reliability.

In the case of logarithmic transformation, a bias Correction factor (SE2/2) proposed by Baskerville (1972) was used to calculate model errors. All analysis were conducted using SPSS version 21 except the scattergram that was created using Excel 2013.

 

RESULTS

Correlation analysis showed that there was a linear relation between all dependent and independent variables. With respect to the multiplicity of graphs, only two graphs regarding crown area-aboveground biomass and EDRC-tree volume were illustrated (Fig. 1). The results of modeling for estimating dependent variables (trunk dry weight, branch dry weight, tree and trunk volume) against EDRC as independent variable showed that EDRC is suitable estimator for aboveground biomass (R2 = 0.81) and as shown in Table 1 for the tree volume (R2 = 0.81).

Results showed that the least NRMSE was related to branch dry weight (10.93), explaining this independent variable provided the most precise model. Results of modeling for estimating the volume and biomass of A. monspessulanum trees with crown width are presented in Table 2. Crown width was found to be a suitable predictor for branch dry weight (R2 = 0.85) and also for trunk volume and aboveground biomass (R2 = 0.83). Model for branch dry weight had the least NRMSE value and was the most precise one.

Tree height as independent variable was a proper predictor for tree volume (R2 = 0.7) and also for branch dry weight (R2 = 0.68).

The most precise model was found to be appropriate for tree volume estimation (Table 3). Obviously models for height were less strong than crown width and EDRC.

It seems that a combination between tree height and other specifications could improve prediction capability.

 

 

 

Fig. 1. Scattergram for reviewing the linear relation of variables: EDRC against tree volume (left) and crown area vs. tree aboveground biomass (right).

 

Table 1. Models for predicting dependent variables based on EDRC.

Dependent

Model

R2

SE

RMSE

NRMSE

Trunk DW

Log Y= -1.59 + 2.22 log X

0.684

0.271

28.14

20.61

Tree DW

Log Y= -1.38 + 2.38 log X

0.816

0.203

40.65

14.16

Branch DW

Y= -53.04 + 4.72 X

0.792

20.83

19.76

10.93

Tree V

Log Y= -4.38 + 2.41 log X

0.807

0.212

0.044

14.10

Trunk V

Log Y= -4.59 + 2.25 log X

0.676

0.280

0.030

20.27

                                    * D.W. = Dry Weight                 V= Volume

 

Table 2. Models for predicting dependent variables based on crown width.

Dependent   

Model

R2

SE

RMSE

NRMSE

Trunk DW

Log Y = 0.44 + 1.66 log X

0.688

0.269

28.97

21.25

Tree DW

Log Y = 0.79 + 1.8 log X

0.837

0.191

43.89

15.25

Branch DW

Log Y = 0.45 + 2.008 log X

0.857

0.197

20.87

11.55

Tree V

Log Y= -2.18 + 1.83 log X

0.834

0.197

0.047

15.06

Trunk V

Log Y= -2.53 + 1.69 log X

0.686

0.276

0.032

21.62

 

Table 3. Models for predicting dependent variables based on height.

Dependent

          Model

R2

SE

RMSE

NRMSE

Trunk DW

Y = -78.43 + 27.18X

0.623

22.88

21.70

15.91

Tree DW

Y = -159.99 + 58.94X

0.679

43.88

41.63

14.5

Branch DW

Log Y=-0.67 + 3.59logX

0.685

0.292

29.86

16.52

Tree V

Y = -0.18 + 0.06X

0.703

0.046

0.044

14.10

Trunk V

Y =-0.08 + 0.03X

0.641

0.024

0.023

15.54

 

As shown in Table 4, stem number was a proper estimator for tree volume and biomass.  Model for trunk volume had the most accuracy and lowest NRMSE value (13.59). Generally, it seems that the number of stems could estimate 70% of variations in aboveground biomass and volume of A. monspessulanum trees. Models fitted on data for estimating volume and biomass by tree crown area were shown in Table 5.  Results showed that crown area was a suitable predictor for tree volume and biomass (R2 = 0.83).

This variable also estimated branch dry weight accurately (R2 = 0.85). Multivariate models created by stepwise linear regression were presented in Table 6. Tree height and EDRC were significant to present in models. Two-variable models could improve prediction capability from 2% to 14% in contrast to simple ones and increased precision considerably.

 

 

Table 4. Models for predicting dependent variables based on stem numbers.

Dependent

Model

R2

SE

RMSE

NRMSE

Trunk DW

Y= -8.41 + 9.089X

0.726

19.53

18.53

13.59

Tree DW

 Log Y = 1.11 + 1.12 log X

0.734

0.244

42.12

14.67

Branch DW

Log Y = 0.84 + 1.198 log X

0.690

0.290

31.02

17.16

Tree V

Log Y = -1.84 + 1.124 log X

0.708

0.261

0.048

15.38

Trunk V

 Y = -0.008 + 0.01X

0.685

0.023

0.022

14.86

Table 5. Models for predicting dependent variables based on crown area.

Dependent

Model

R2

SE

RMSE

NRMSE

Trunk DW

Log Y = 0.53 + 0.83 log X

0.688

0.269

28.91

21.20

Tree DW

Log Y = 0.88 + 0.90 log X

0.837

0.191

41.13

14.32

Branch DW

Log Y = 0.55 + 1.004 log X

0.857

0.197

17.28

9.56

Tree V

Log Y= -2.08 + 0.91 log X

0.834

0.197

0.045

14.42

Trunk V

Log Y = -2.44 + 0.84 log X

0.686

0.276

0.032

21.62

 

Table 6. Multivariate models for predicting dependent variables.

Dependent

Model

R2

SE

RMSE

NRMSE

Tree DW

Y= - 130.07 + 6.03 EDRC + 18.57 H

0.87

26.2

28.41

9.9

Branch DW

Y= -84.8 + 3.67 EDRC + 3.2 H

0.85

18.1

14.76

9.2

Tree V

Y= -0.149 + 0.007 EDRC + 0.023 H

0.87

0.028

0.014

9.9

 

DISCUSSION

All independent variables in this paper had a significant correlation with aboveground biomass and volume, providing high accurate models. In most cases, logarithmically converted data had better fit than untransformed ones especially in data sets that include outlying observations (Feng et al. 2014). This situation probably occur frequently when sample size is small (as in our study).   In this case a correction factor was applied to adjust model errors that increased amount of errors a little. The most accurate models for estimating dry weight of branches were related to crown area. Crown area and width were found to be suitable predictors for estimating the volume and biomass of A. monspessulanum trees. It was in consistent with the study of Conti et al. (2013)  once estimating shrubs biomass in Argentina, and also with that of Kuyah et al. (2012) on trees in farmlands of Kenya, as well as that of  Goodman et al. (2014) in tropical forests of Peru. Conversely Zhou et al. (2007) found that crown diameter is not a suitable predictor for multi-stemmed Eleagnus Angustifoilia L. because of its ununiformed crown distribution.

Parsapour et al. (2013) found that diameter at breast height (DBH) provided a high accurate model to predict biomass of four poplar species (R2 = 0.95). Therefore, it was expected that the equivalent diameter at root collar (EDRC) presented a superior model for biomass estimation.  Also Cienciala et al. (2013) found that equivalent diameter at breast height is a suitable predictor for biomass of Prosopis spp. in Santo Antao islands, West Africa. Our results

 

 

showed that EDRC was a suitable predictor for the biomass of A. monspessulanum trees, where the variables of crown area and crown width were not available. Considering the method of calculating EDRC higher amounts of this variable relates to thicker stems. It can be concluded that higher EDRC has a clear effect in volume and consequently biomass increscent. However we applied equivalent diameter at root collar instead of EDBH and found it suitable. Whereas in the studies of Mitsopoulos & Dimitrakopoulos (2007) on Pinus halepensis Mill., that of Litton (2008) on Metrosideros polymorpha and that of Cai et al. (2013) on ten tree species in Northeast China, diameter at breast height was the most significant determinant of crown fuel biomass, total biomass and aboveground live biomass respectively. 

Top height of trees could predict 70% of variations in volume and biomass.  Hierro et al. (2000) showed that the diameter of the highest stem was the best estimator for determining the biomass of Condalia erinacea. In the present study, it was not possible to accurately determine the highest stem as the crowns were entangled. Stem numbers showed significant relation to biomass and volume of A. Monspessulanum trees, estimating 70% of variations with acceptable precision. Noteably, all stems of A. Monspessulanum showed sufficient growth, whereas in some species such as Haloxylon ammodendron (C A Mey) with increasing the number of stems, their diameter decreased. So that, the number of stems could not be a well predictor for biomass and volume estimation, particularly in young shrubs.

In the present study, we found that EDRC (for multi-stemmed trees regarded as DBH) in combination with tree height could predict 87% of variations in aboveground biomass and volume. However multivariate models were not suitable in prediction capability, whereas provided more precise results than simple models. According to the study of Ebuy et al. (2011), tree height and diameter at breast height provided predicting up to 77 % of variations in above ground biomass of 12 trees belonging to three species at Yangmbi in Congo.  Cole & Evel (2006) showed also that the allometric equations generally fit well to the data. So that, in most cases, over 50% of the observed variations in biomass could be explained by diameter and height. Tree height and crown width were also suitable predictors for biomass of mangrove trees (Fu & Wu 2011).

Ketterings et al. (2001) found that regression parameters for exponential models varied in different sites. It should be pointed out that estimates of aboveground biomass and their changes over the time extremely depends on the source of allometric data. Allometric studies often rely on samples that are too small to selecte in a statistically valid manner from the population of interest (Brown et al. 1999). There are some limitations, however, in tree cut as we were encountered in this study. Other potential errors in estimation may also result from differences in biomass allocation or morphology from one forest system to another.

Multi-stemmed trees form an important component of the woody vegetation in forest ecosystems (Matula et al. 2015). However, lack of a clear methodology for reliable measurement and estimation of their woody biomass is evident. In this research we found that the volume and aboveground biomass of multi-stemmed A. monspessulanum can be predicted accurately and precisely according to standing tree specifications. Allometric equations provided in this study can be used as a non-destructive method to estimate the amount of wood per unit area and are considered to be valuable tools in managing mountain forests. They make great assistance to forest managers for planning forest yield and quantifying wood production obtained from this species.

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