# Knowledge reference for national forest assessments - modeling for estimation and monitoring

# 3. Volume estimation

Wood volume is a cubic measure of the amount of wood, or wood plus bark, present in an individual tree, group of trees, or stand. Volume is usually measured in cubic meters, but may be measured in other units specific to intended commercial products. |

Volume is the most widely used measure of wood quantity and is usually estimated for the assessment of economic value or commercial utilization potential. The wood volume of a tree includes stem, branches, stump, and roots. For standing trees, aboveground volume production is generally based on stem wood volume for conifers, but may include branch volume for broad-leaved tree species.

Depending on measurement objective and local traditions, measurements or predictions of wood cubic volume may refer to, for example, total stem volume, total tree volume (stem and branches), or volume above a certain merchantable limit. Volume estimates may include or exclude bark and, for aboveground estimates, include or exclude the stump.

Volume is always a cubic measure, and usually expressed in cubic meters. Merchantable volume, however, is sometimes expressed in other units related to commercial use (Skovsgaard 2004).

Volume is usually estimated for standing trees from such measurements as diameter, or diameter plus merchantable height, using a volume equation or a log rule. Volume may be measured directly on felled trees or logs, but is often estimated from dimensions such as minimum diameter or piece length. Direct measurement of volume is usually done by sectioning the tree into smaller pieces assumed to be cylinders. Volume may be estimated for stacks of logs or processed products by measuring dimensions. In these cases, local knowledge is often needed for appropriate estimation of volume.

## 3.1 Volume Equation Forms

Volume is usually expressed quantitatively as a function of diameter, or diameter and height or merchantable length. Occasionally, other variables such as clear bole length are used to estimate volume. An important consideration is that any variables needed to predict volume should be observed during field data collection.

Volume may be estimated from dimensional variables such as diameter and height. Classical volume models include the so-called combined-variable equation: And the more general model: where, in both cases, α, β and γ are coefficients, D refers to diameter (usually measured at 1.3 m above ground level), and H refers to total height, merchantable height, or merchantable length as defined for a given application. The latter model is often used after logarithmic transformation: where estimates of β often approach 2 while estimates of γ approach 1. For simplicity, height may be omitted in applications of these models. Choice of model may depend on modeling objective, data used in the estimation of coefficients, and error structure (Skovsgaard 2004). These basic equations implicitly assume a single-stemmed form and may require modification or replacement for species with a more complex form. In addition, when equations are used to estimate the logarithm of a variable, a negative bias is introduced when the predicted logarithm is converted back to arithmetic units. This bias is approximately the order of magnitude of one-half of the residual variance of the equation. |

In the absence of local equations, it is possible to utilize geometric relationships to approximate volume. The volume of a cylinder is simply the area of the base times the height, and the volume of a cone is one-third of the volume of a cylinder with the same area of the base and height. Trees are neither cones nor cylinders, but empirical analyses often indicate that the volume of a single-stemmed tree is between that of a cone and a cylinder, with tree volume often lying between 0.40 and 0.45 times that of an equivalent cylinder. Using a value of 0.42, for example, an equation can be developed to estimate cubic volume of wood in the absence of local equations as given below. This equation will often overestimate volume of open-grown trees with more conic form, underestimate the volume of trees with more cylindrical form, and may need to be modified for species with more complex forms. Nevertheless, it does provide a first approximation that can subsequently be modified following local experience.

In the absence of local equations, cubic volume of wood for standing trees may be estimated by the following equation: where B is tree basal area at breast height and H is tree merchantable height. |