to indicate that the merchantable top diameter was a fixed function of a tree's diameter 

 breast height and not to indicate that the top diameter was an independent variable in 

 the volume equation. The latter type of equation can be converted to the former by 

 defining the functional relationship between d.b.h. and top diameter.) 



The purpose of this study was to develop gross and net tree volume equations for 

 forked and unforked trees of the major tree species found in Arizona and New Mexico. 

 Species-National Forest (sp-NF) specific equations were developed for the following 

 units of measure--total stem cubic foot volume, merchantable cubic foot volume for any 

 top diameter between 3 and 8 inches, and International 1/4-inch and Scribner board foot 

 volumes to a 6.0-inch top. The resulting equations and methodology used to derive these 

 equations are described in this paper. Volume tables for use in the field appear in a 

 companion piece, "Comprehensive tree volume equations for major species of New Mexico 

 and Arizona: II. Tables for unforked trees." 



The present study provides a complete set of standardized gross and net volume 

 equations for the major species, forked or unforked, in Arizona and New Mexico. In 

 addition, all equations are derived from a common data base. Further, modeling proce- 

 dures were adopted to ensure that (a) net volumes do not exceed gross volumes, 

 (b) reasonable board foot-cubic foot ratios prevail, and (c) Scribner board foot volumes 

 do not exceed International 1/4-inch board foot volumes. Merchantable cubic foot volume 

 equations for any top diameter between 3 and 8 inches also are provided, thus permitting 

 users of the equations to adapt to changing merchantability standards. 



SOURCE AMD NATURE OF DATA 



The data were collected from five National Forests of Arizona and New Mexico by 

 field crews of the Division of Timber Management, Southwestern Region, Forest Service, 

 Albuquerque, New Mexico (table 1). 



The data for the Coconino, Tonto, and Lincoln National Forests are the same as used 

 by Hann and McKinney (1975) in the development of surface area equations. On the Santa 

 Fe and Carson National Forests, the measurement trees were selected by line sampling 

 with a 40 basal area factor angle. The lines were located and trees designated by 

 inventory field crews traveling to randomly selected continuous forest inventory plots. 

 Later, a second crew felled and measured as many of the designated trees as could be 

 finished in one working day, using procedures similar to those described by Stage and 

 others (1968). 



Tree volumes were computed using a modified version of the NETVSL computer program 

 (Stage and others 1968) . Merchantable volumes were determined to various top diameters 

 and to a 1-foot stump on all National Forests except the Lincoln, where stump height 

 was 1.2 feet. 



2 



