Woodland Tree Volume 

 Estimation: A Visual 

 Segmentation Technique 



J. David Born 

 David C. Chojnacky 



INTRODUCTION 



In the arid Rocky Mountain regions, vast acreages of 

 trees once ignored by foresters are now drawing atten- 

 tion as a source of wood fiber. Of interest are the vari- 

 ous species of piny on, juniper, mountain-mahogany, 

 mesquite, and the evergreen and deciduous oaks. Lowe 

 (1972) grouped these trees in an ecological community 

 known as woodland. In order to assess the wood fiber 

 resource of woodland trees, simple cost-effective volume 

 measurement methods are needed. 



Estimating tree volume is a standard concept for 

 foresters, but the shrublike multiple-stem character of 

 woodland species creates new problems that were not 

 considered in the development of volume mensuration 

 methods. Traditional volume measurements, designed for 

 commercial timber species, have focused on the main 

 bole. But a large percentage of the wood in a woodland 

 tree is found in the branches, and frequently a main bole 

 is not well defined. 



A cubic measure of wood for all stems and branches is 

 a reasonable approach to assessment of woodland spe- 

 cies. In this approach, all linear segments of stem and 

 branch wood are identified, and then volume is calcu- 

 lated for each segment with the appropriate geometric 

 solid formula. Summing the segment volumes produces a 

 volume per tree. However, measuring the necessary 

 diameters and length of each segment is a costly, time- 

 consuming task. For example, a single large juniper tree 

 can have more than 100 1- to 6-foot wood segments. 



Rather than measure each tree, sample trees are 

 usually measured for use in constructing volume equa- 

 tions. This then leads to the question of how sample tree 

 volume data can be obtained in an efficient and timely 

 manner for the vast areas of woodlands in the Rocky 

 Mountain States. 



BACKGROUND 



In previous woodland tree studies, some researchers 

 have estimated wood volume indirectly by first weighing 

 a tree and then converting the weight to volume through 

 specific gravity factors (Felker and others 1983; Weaver 

 and Lund 1982; Miller and others 1981; Storey 1969). 

 Others have cut trees into segments to measure segment 

 diameters and length needed to calculate volume (Howell 

 1940; Gholz 1980). Weighing trees and cutting trees into 

 sections are suitable techniques for research work where 

 motorized equipment access is good and where the land 

 owner will allow trees to be destroyed for use in a study. 



Clendenen (1979) developed volume equations using 

 volume data collected using a method adapted from 

 Cost's (1978) work for measuring volume of standing 

 trees without cutting them down. This method, known 

 as "visual segmentation," does not require a physical 

 measurement of each stem segment (Born and Clendenen 

 1975). Instead, each segment in a tree is classified into a 

 2-inch midpoint diameter (outside bark) by 2-foot mid- 

 point length class (since this study, the procedure has 

 been changed to 1-foot length classes). The appendix has 

 a full description of the procedure. 



After classification, volumes are computed from the 

 segment diameter class and length class values instead 

 of exact dimensions. Each segment is assumed to be a 

 paraboloid frustum, and Huber's formula (Husch and 

 others 1982, p. 101) is used to compute the volume of 

 each segment: 



Vj = 0.005454 HiD.2 

 where 



Vj = volume of the ith segment (cubic feet) 



Hj = length class of the ith segment (feet) 



Dj = diameter class of the ith segment (inches). 



Success of visual segmentation is dependent upon (1) 

 correct classification of the segments and (2) the length 

 and diameter class values underestimating and overes- 

 timating the actual dimensions in an equal proportion. 

 The following algebraic manipulation of Huber's formula 

 (using class dimensions) illustrates the second point: 



V = i; 0.005454 (H. + h.)(D +d )2 (1) 



i=i 1111 



= L (0.005454 H D.'l 

 i=i ' ' 



+ i; |d.[0.005454 (2D H +dH.)] 



i=i ' 1111 



+ h,[0.005454 (D, + di)']| (2) 



where 



V = volume of a tree (cubic feet) 

 H| + h| = actual length of the ith segment (feet) 

 D^ + dj = actual diameter of the ith segment (inches) 

 h^ = ± deviation (up to 1 foot) of actual segment 

 length from H^ 



d, = ± deviation (up to 1 inch) of actual segment di- 

 ameter from D . 



1 



The second summation (E) in equation (2) must sum to 

 zero, if the volume of a tree is properly represented by 



1 



