Volume equations of Pinus brutia Ten. in Zawita Forest, Duhok Province, Iraq

Planning for forest management depends upon the forest dynamics, which includes integration of all forest disciplines and understanding of forest resource characteristics including its growth dynamics. The forest growth and yield modeling can provide valuable information about forestry, which can be used to determine harvest levels or allowable cut and to analyze alternative stand treatments. The lack of technical information on forests in the Zawita region is one of the main obstacles to the development of growth and yield, environmental policy and forest evaluation indicators. The Zawita plantation forest needs more information on yield models using volume equations for P. brutia growing under the conditions of the Kurdistan Region of Iraq which will contribute to providing valuable information in the planning and sustainable management of the forest plantations in the region. Hence, this work has been carried out to apply volume equations for P. brutia that can explicitly state the relationship between tree volume and diameter and provide more information for the development of more systematic forest management prescriptions at the Zawita region in future. This study consists of four parts. For the first part, a large number of mathematical models, which have been used by various authors in the development of volume-tables and volume equation construction, were analyzed in searching for suitable volume equations for P. brutia plantations. Overall, we have used eight unweighted volume equations including two logarithmic transformed equations and seven weighted forms of volume equations for volume data of a 25 – 30 year old P. brutia plantation. In the second part, the study used the method of least squares for the construction of volume equations, because the most common problem in volume table construction has been the variation in tree forms or commonly referred to as heteroscedasticity of residuals. This is because the larger tree volumes tend to deviate from the regression line more than the smaller ones, and therefore the weighted least squares was used to correct the heteroscedasticity in volume table construction. The least squares method was used to fit the construction of volume equations for both over bark and under bark volumes. The third part discussed the statistical method to find the best-fit equation. A more suitable index for comparing regression equations has been devised by Furnival, which is based on the concept of maximum likelihood. The index was used to determine the best-fit equation, in choosing the final equations for both over and under bark equations. Finally, the study conducted validation to compare the true volume calculated using Newton’s formula with the predicated volume derived from the equation. The actual and estimated volume per hectare was compared and tested using the t-test. In conclusion, the study developed the following equations for estimating under bark (VI) and over bark (VO) volume, equations: VI = 0.0003378 * D1.21342 * H1.18863 , VO =0.0002722 * D 1.40425 * H1.06470, where VI and VO are (merchantable tree volumes m3 up to 10 cm) breast height diameter (cm), and H is the total log length (m). The equations were found to estimate merchantable tree volumes. As usual, a test of applicability of these equations is needed if they are to be applied elsewhere