ESTIMATE THE COMMERCIAL VOLUME OF Anadenanthera colubrina ( Vell . ) Brenan

This work aimed to evaluate the use of traditional models, profile and relative height method, for estimating the commercial volume of Anadenanthera colubrina (Vell.) Brenan. Data were obtained from scaling of separate lengths of the stem of 22 trees, using Smalian’s method. Tree stems were measured 0.1m, 0.30m, 0.70m, 1.0m, 1.30m above the ground and then every 1m. For purposes of method assessment and comparison, statistics were used that include percent standard error, bias, standard deviation of differences, in addition to graphic interpretation of residuals. Assessments showed that Stoate’s model is the most accurate, followed by Schumacher’s model. They also showed that the linearized Schumacher’s model reduced accuracy by an average 0.32% and that the relative height method was biased in this study.


INTRODUCTION
The growing demand for timber for a wide variety of purposes also brings the imminent danger of timber shortage.This growing demand intensifies pressures on native forests, leading to increasingly predatory exploration which, in most cases, lacks the use of suitable measurement and management techniques.
Belonging to the Leguminosae-Mimosoideae family, s Anadenanthera colubrina (Vell.)Brenan, also known as angico, is a native species with multiple uses, including building construction, hydraulic systems, railroad crossties, floor boards, wood structures etc., on account of its inherent characteristics of high density (0.93g/cm³), compaction and thick, reverse grain composition, which confer high durability on products.It can reach 12 to 15 m in high, and 30 to 50 cm in diameter (LORENZI 2002).
Obtaining timber volume can be crucial in forestry, particularly for time and cost reduction but also for accuracy reasons.There are several ways of obtaining this volume in both standing and felled trees, with studies demonstrating that Huber's method is the most accurate for felled trees (MACHADO et al. 2006).
It is a common practice to estimate volume via quantitative methods, using stochastic models.In forest management and mensuration, models are used to estimate volume with limited data from each plot, as obtained from field observations (SPATHELF & NUTTO 2000).The most popular volumetric models in forestry CARVALHO, S. de P. C. e et al.
Another highly accurate, very applicable procedure to obtain tree volume is by using profile or taper models which, according to Lima (1986), are a mathematical way of describing stem profile.These models are based on solid of revolution techniques that derive volume within a finite bound of integration.
A currently used methodology for describing stem profile is the geometric or relative height method.According to Andrade (2001), this method is based on the postulate that 'there is a specific point between the diameter 1.30m above ground (DBH) and total height of a tree which, after dividing the tree into two intervals, allows minimizing taper estimate errors, a point known as relative height'.This point, according to Andrade (2001) Studies being scarce on the species in question, and considering its high yield and use potential, this work aims to evaluate three different methodologies for estimating the commercial volume of Anadenanthera colubrina (Vell.)Brenan.

Study site
The study site is about 2.36 ha in area and lies in the campus of the Federal University of Lavras (MG).It comprises a heterogeneous stand with trees at different ages, with predominance of species Anadenanthera colubrina (Vell.)Brenan.
Historically, species Anadenanthera colubrina was introduced by way of an experiment attempting to verify the effect of shading on coffee plantations.About thirty-five years ago, after verifying that where coffee plantations were fully exposed to the sun the yield was 40% higher than yield in shaded areas, the experimental area was abandoned.Then natural regeneration followed, with predominance of Anadenanthera colubrina, and according to Nascimento et al. (2009), the area has now 25 families divided into 66 vegetal species.The local climate according to Köppen classification is 'Cwb' type (temperate with mild summers and dry winters).The average annual precipitation is 1,493.2mm and the average annual temperature is 19.3ºC, with 66% of the precipitation occurring between November and February (VILELA & RAMALHO 1979).

Data collection and analysis
22 trees were cubed using Smalian's method.Stems were measured 0.1m, 0.30m, 0.70m, 1.0m, 1.30m above the ground, and then every 1m.Additionally, measurements were taken of the commercial height, which is the height of a stem up until the first bifurcation, and also of the total height.
The number of cubed trees by diameter class and height is illustrated in Table 1.
Statistical software R was used for data analysis.
The variation in diameter according to height, characterizing tree tapering, is illustrated in Figure 1.
According to Figure 1, a great variation is noted in data and in shape for the species in question.Some of the

Methodologies applied to estimate commercial volume
Volumetric models, taper functions and the relative height method were evaluated, in order to estimate the commercial volume of species Anadenanthera colubrina.

Volumetric models a) Schumacher & Hall's model
where: V i = commercial volume of i-th tree (m³); DBH i = diameter 1.30m above ground of i-th tree (cm); Hc i = commercial height of i-th tree (m); ln = natural logarithm; â is = parameters to be estimated; i = random error. .(SCHOEPFER 1966) where: d ij = diameter of i-th tree in j-th position h ij (cm); h ij = commercial height of i-th tree in j-th position (m); H i = total height of i-th tree (m); DBH i = diameter 1.30m above ground of i-th tree (cm).With the polynomial, volume was derived by integrating the following equation:  Andrade (2001) developed the relative height method in his formulation of AC (angular coefficients), as follows: The following 'taper' equations were generated: For 0.1 < h i < 1.3m; 2 2.6 For 1.3 < h i < hr; For hr <h i <ht; where: AC ki = angular coefficient of straight line passing by k-th interval I, II, III in the i-th tree; ) 0 , 0 ( h hi d diameter at h i-th desired height (cm); h 0,1 = stump height, corresponding to 0.1 m; h i = commercial height (m); hr 2 refers to commercial height for this study as the method was adapted to the specific situation.
Relative height is determined by the expression: 2 ) 2 (ht hr Different strategies to estimate the commercial volume ...
Table 2 -Parameter estimates for each proposed model in order to estimate volume, with their respective significance levels.
After estimating diameters at different portions of the stem, trees were cubed using Smalian's method.

Method diagnosis
Each methodology was tested for accuracy using the following statistics:  where: Based on test results, methodologies were ordered by degree of accuracy, attributing scores 1 to 6 (LIMA 1986, MENDONÇA et al. 2007).The most accurate method is the one presenting the lowest aggregate score.
A visual analysis of residual dispersion was also carried out.

RESULTS AND DISCUSSION
Table 2 presents parameter estimates for each proposed model, in order to estimate the commercial volume of Anadenanthera colubrina.
From Table 2 it is noted that all fitted parameters were significant at the 5% significance level, being therefore indispensable for estimating volume.It can be noted that virtually every method presented good residual distribution, with mean errors tending to zero and identically distributed, except for the relative height method, which tended to underestimate volume values.Despite being applied only to Pinus and Eucalyptus stands before, the relative height method proved applicable in this study, according to statistics in Table 3.

Graphic residual analysis
Stoate's and Schumacher's models, in original and linearized forms, presented better residual distribution, with errors being overall distributed randomly around zero.Chichorro et al. (2003) concluded that the linearized Schumacher's model presents a good residual distribution, normally distributed and with a high R² value.

Methodology accuracy
Table 3 presents statistical results for the proposed methodologies to estimate the commercial volume of Anadenanthera colubrina.
When percent standard error is analyzed, which is a commonly applied statistic in modeling works, the most suitable methodology is Stoate's linear model, followed by Schumacher's model.
Figure 2 indicates volume trend as a function of input variables diameter and commercial height.2.3.2Taper functions a) Polynomial of degree 5(SCHOEPFER 1966)

Figure 2 -
Figure 2 -Tendency of diameter and height variables as a function of commercial volume.

Figure 3
Figure3presents a graphic residual analysis of volume estimation, as a function of percent error.

Figure 3 -
Figure 3 -Graphic distribution of percent residuals for different methodologies in volume estimation.

Table 1 -
Tree distribution by diameter class and height.Distribuição por classe de diâmetro e altura das árvores amostradas.

strategies to estimate the commercial volume ...
models and methods capable of capturing such variations are addressed in this work.