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ŠUMARSKI LIST 9-10/2019 str. 32     <-- 32 -->        PDF

developing the individual volume methods and models that could be combined with other forest simulators in forest operations (Clutter et al. 1983; van Laar and Akça 2007).
As the individual trees have no recognizable geometric shape, such as a cylinder, paraboloid, cone, and neyloid, it is not possible to directly calculate tree volume using analytical methods without falling tree. The unique practical solution to this inventory procedure, including felling tree that can be a time consuming and costly operation is the use of allometric relationships between the individual tree volume and other tree attributes such as diameter at breast height, dbh, and height that could be easily and practically measured in forest inventory and could be dendrometrically correlated with the tree volume. These allometric models are statistical equations that can be used to estimate the stem volume or commercial volume of a tree from certain independent variables such as diameter at breast height (dbh) or total height. When included the dbh as independent variables, these equations are called as “Single Entry Tree Volume Equations, while the equations comprised together the dbh and height are called as “Double Entry Tree Volume Equations”. In addition, the equations prepared based on three or more variables such as dbh, tree height and stem diameter at a certain point on a tree (e.g. at 30% of the tree length) or trunk diameter at 7 meters above the ground is called as “Multiple Entry Tree Volume Equations”.
Because of this practical usability of the volume equations in forest inventory, numerous volume equations have been presented and developed by using the statistical techniques in forestry literature over the past several decades. However, these single or double entry volume equations cannot predict the tree volume to any merchantable height or diameter limits and become impracticable to produce the predictions for tree volume by assortments of tree log sizes if stem merchantable standard alter in the forest stand harvesting and yield operations (Reed and Green 1984; Gal and Bella 1995). Alternatively, the stem taper equations that can provide the predictions of diameter at any height of the stem, the height to any specific diameter, merchantable volume and merchantable height to any top diameter and ant stump diameter can be used to obtain the total individual tree volume predictions. Although there are two major categories of taper equations, the segmented polynomial taper equations that were firstly represented by Max and Burhart (1976) has been regarded to most precise for predicting the individual tree volume to any merchantable limits (Jiang et al. 2005). Max and Burhart (1976), Clark et al. (1991), Fang et al. (2000), Jiang et al. (2005) developed the segmented polynomial taper and compatible volume equations that predicted individual tree volume by basing on this compatible taper equation.
While developing these single or double entry volume equations and taper-based equations, the tree data that collected through individual tree measurements are fitted by using the Linear Regression Analysis or Nonlinear Regression Analysis, which are subject to statistical methods. However, these linear or nonlinear equations developed through regression analysis methods can provide accurate and reliable estimations only if certain statistical fundamental assumptions have been assured, which can be listed as a normal distribution of model errors, homogeneity of error variances, no correlation between errors (autocorrelation), and no correlation between independent variables (multicollinearity). Recently, Artificial Neural Networks (ANNs) have gained prominence in the area of forest biometricians, since such networks are able to provide successful predictions without any requirement for the assumptions of statistical assumptions. Artificial Neural Networks (ANNs) are widely used in the estimation-based processes of several fields of engineering, such as aircraft, automobiles, electronics, production, robotics, communications, and civil engineering. ANNs can be a very useful tool in engineering practices and can be a strong tool in data modeling (Esteban et al. 2009; Atkinson and Tatnall 1997; Ashraf et al. 2013; Buğday 2018; Doğan and Buğday 2018). However, there are only a limited number of studies on the use of ANN in the forest applications about modeling individual tree volume predictions. Diamantopolou et al. (2005), Diamantopolou (2006), Özçelik et al. (2010), Soares et. al. (2011), Görgens et al. (2009), Silva et al. (2009), Binoti et al., (2014), Bhering et al. (2015), Miguel et al. (2016) and Sanquetta et al. (2018) found the best predictive volume by using ANN with respect to other prediction methods. In addition to these studies, it is particularly necessary to conduct more studies on artificial neural networks that can be defined as a member of artificial intelligence and ANN as the new technique may probably provide an opportunity to obtain more accurate and predictive volume predictions in the field of forestry beyond classical regression models. Thus, the objectives of the present study are (1) to develop Artificial Neural Network Models for predicting of individual tree volumes of Crimean Black Pine trees within the Çankırı Forests and (2) to evaluate various ANN having different neuron contents and transfer functions for the volume predictions with the single and double entry volume equations and Fang et al. (2000)’s compatible volume equation.
Material and Method
Materijal i metoda
In this study, 360 tree samples that were selected from different diameters and heights to reflect the variability in volume were used to model the individual tree volume of