Early volume formulas, taper, implicit volume ratio, and auxiliary information: A new system of volume equations invariant to silvicultural practices, site, and genetic pedigree

Abstract

This article returns to the Hossfeldt and Pressler volume formulas that were developed in the 19th century and uses them as predictor variables for total volume equations of species in North and South America. Both the Hossfeldt and Pressler formulas require an upper-stem measurement and are exact equations for the geometric shapes of a cone or paraboloid. Rarely is a direct measurement of the Hossfeldt diameter or Pressler height made on a stem, and a taper function is employed to indirectly obtain these values. A Kozak-type taper function is expanded to include routine auxiliary information of an inventory, such as age, dominant height, relative spacing, and a ranking variable that indicates position of the subject tree to a tree of average size. Using the Hossfeldt diameter and Pressler height, it is demonstrated how a merchantable volume ratio equation is indirectly derived. With the aid of one lower-stem measurement of diameter and height, such as the height at 5 m, vastly enhanced estimates of total stem volume are possible. These new volume equations imply that form factor is dependent upon the ratio of Pressler height to total tree height, and Hossfeldt diameter to diameter breast height (dbh). Therefore, the costly method of destructive tree sampling for making new volume equations can be obviated, since changes in form can be detected easily and less expensively by monitoring changes to the ratios of Pressler height to total tree height, and Hossfeldt diameter to dbh.