Volume Calculations and Rules, Part 2: Individual Tree Volume Calculation Methods (and Why We Don’t use Form Classes)

In our previous post, we reviewed the four primary logrules and explained the strengths, drawbacks, and best uses for each method.

Today, we’re going to explore the differences between estimating tree volume based on form classes and calculating the volume of trees with individual tree equations.

Some of the log rules we discussed in our last post can be easily converted into tables that will give an estimate of volume based on the diameter and length of the tree - no math required. For these tables, height is typically measured in bolts (8-foot length of tree stem) or logs (16- or 32-foot length of tree stem); however, more exact units (paired with more precise tables) may also be used. The log scaling tables themselves are often included on cruiser sticks for making fast and easy estimates while on a cruise.

Form classes:
As we discussed in the last post, some logrules take tree taper into account, while others do not. For the logrules that do account for taper, ‘form classes’ have been developed to estimate volume based on typical tree taper for that region. The form class, also called a form quotient, is a ratio. Typically this is the ratio of dbh (diameter at breast height, 4.5 feet above ground) to inside-bark diameter at the top of the first 16-foot log, usually measured at 17.3 feet above the ground.

FunkyTree
Photo credit: Travis Pond

Girard form class values (also called Girard-Mesavage, or Mesavage-Girard), the most commonly used in the US, were first developed in the 1940s by James Girard and Clement Mesavage of the US Forest Service. In order to use a Girard form class correctly, one must first estimate the total diameter of the tree at the end of the first log (the aforementioned 17.3 feet above ground), and then estimate how thick the bark is. Even the correct usage of Girard form classes are, at best, an estimate based on an estimate and are therefore inadequate.

This problem is amplified because the actual trees in any particular stand may deviate from the regional form classes, especially when comparing trees of different ages or species. Furthermore, volume measurements calculated by a combination of logrule and form class are based on the unfounded assumption that all stems will taper the same way above 17.3 feet. That is seldom the case. When these problems are taken together, it’s easy to see how significant errors can slip into volume estimates based on form class.

Individual tree equations:
In an effort to combat the errors that creep in using form classes, much research has been done over the past seventy years into equations that can describe the taper of individual trees, rather than assuming they are all alike. This trend has increased as technology has made the computations easier. Many of these individual tree equations use the same predictors as the lookup tables described previously- dbh and total height, but may also include height at the merchantable limit, diameter at 17.3 feet, and crown class. ‘Segmented’ equations are the best and most versatile of the individual tree equations because they break the tree into multiple sections that taper at different rates. This results in even more accurate calculations.

These individual tree taper equations are so useful because of their flexibility. In this paradigm, volume tables are based on a pre-determined set of merchantability requirements. As markets change, so do merchantability specs. It may become necessary, for example, to incorporate the grade of lumber, or mill output reductions due to log defects, in a calculation. This type of consideration could require several different tables to estimate, but a flexible taper equation is a lot more helpful in this endeavor than a form class equation. For example, it can return an estimate of length at a set minimum diameter, or be used in conjunction with an individual tree volume equation to determine a more precise volume estimate for a stem by taking size, species, and local market requirements into consideration.

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SilviaTerra’s volume system leverages large amounts of publicly available forestry data in conjunction with local cruise data to develop species and stand-specific volume coefficients which we can use to accurately estimate stem volume in any units required. These estimates may not match the values from a Form Class table, but, for all the reasons listed above, our numbers are more in tune with local variability and, therefore, more accurate.

That’s the basics of the differences between form classes and individual tree volume calculations. But there’s still so much to cover! Be sure to check back soon for our next blog post, in which we will go into more detail about the SilviaTerra volume calculation method.