Accurately Measuring the Height of (Real) Forest Trees

Abstract

Q uick and accurate tree height measurement has always been a goal of foresters. The techniques and technology to measure height were developed long ago—even the earliest textbooks on mensuration showcased hypsometers (e.g., Schlich 1895, Mlodziansky 1898, Schenck 1905, Graves 1906), and approaches to refine these sometimes remarkable tools appeared in the first issues of Forestry Quarterly, Proceedings of the Society of American Foresters, and the Journal of Forestry. For example, one such hypsometer based on the geometric principle of similar triangles (top of Figure 1) employed rotary mirrors to allow the user to simultaneously see the top and bottom of the tree in “proper parallax” (Tieman 1904). Other early hypsometers applied different approaches that used angles and distance (e.g., Graves 1906, Detwiler 1915, Noyes 1916, Krauch 1918). Of these trigonometric hypsometers, those that calculated total tree height (HT) as a function of the tangent of the angles to the top (B2) and bottom (B1) of the tree and a baseline horizontal distance (b) to the stem were most common (Figure 1). Because they are easy to apply and required only simple technology, these approaches (hereafter, the similar triangles and tangent methods) have dominated tree height measurement. That is not to say the challenge of accurate tree height measurement was solved— many early foresters reported problems with getting consistent data in uneven terrain or dense understories or with the use of different types of hypsometers. Good measurement practices usually mitigated these issues and became standard components of forester training programs. Others addressed these challenges by designing new techniques based on different trigonometric relationships. As an example, Haig (1925) proposed a slide rule solution that calculated tree height using the sine law and slope distance from the observer to the tree base (s1)