Jenkins (2003): Simple, robust, and, well, a little too simple

The Jenkins equations have been used in the forest carbon community for over 20 years. They were built from a meta-analysis of many biomass studies across the US. They predict biomass using species and diameter at breast height (DBH), where species are collapsed into one of 10 species groups. So, there are only 10 sets of coefficients, which makes the equations easy to implement in a spreadsheet. Biomass can also be estimated by component (stem wood, stem bark, and so on). Carbon is usually inferred by assuming it’s 50% of biomass.

What’s good

• They’re easy to implement. You need species and DBH, nothing else.
• They work with nearly any forest inventory, because almost every ground-based inventory records species and DBH.
• That robustness is why they remain so popular in forest carbon projects.

What’s not

• They don’t incorporate tree height. The model form is exponential in DBH, so predicted biomass and carbon increase as diameter increases. This goes against what we know about trees, as we know each species has its own size limitations. Using the Jenkins equations, a 20-inch tree that’s 60 feet tall will have the same biomass estimate as a 20-inch tree that’s 90 feet tall.
• They work well across large areas, but aren’t meant for local scales.

CRM (2010–2023): A new framework for volume, biomass, and carbon

The CRM was developed by the US Forest Service around 2010. Its idea was to bring tree volume, biomass, and carbon under a single estimation framework. It’s a multi-step process: volume is estimated first, followed by biomass and then carbon. Gross and sound volume are estimated and converted to biomass and carbon with a component proportion approach built on the Jenkins equations.

The CRM is also regional. Look at a map of CRM regions and you’ll see boundaries that follow state lines and other administrative units. For example, one set of equations applies from Ohio to Maine (the Northeast), whereas the Southeast has its own set of equations.

What’s good

• Volume, biomass, and carbon come from a single framework, which matters because most forestry applications need more than just biomass.
• It’s regionally specific.
• It uses more than species and DBH. For example, in the Northeast it also uses bole height and percent cull. In the Southeast, it also uses total tree height and percent cull.

What’s not

• It’s nationally consistent in design but not necessarily in practice. Every region uses its own volume equations, and those equations call for different variables (e.g., DBH, height, bole height, site index, or basal area).
• The regions generally follow administrative boundaries, not ecological differences. This is especially true in the Eastern US. There’s no biological reason a pine tree grows differently on one side of a state line than on the other.

To summarize how CRM performed relative to Jenkins, Domke et al. (2012) is an excellent reference. It showed that nationally, CRM produced lower biomass and carbon estimates compared to Jenkins. (Figure 6 is a particularly stark one showing the impacts of not using tree height in predicting biomass.)

NSVB (2023–today): The current standard

The NSVB equations (Westfall et al. 2024) are what the US Forest Service currently uses in the Forest Inventory and Analysis program. They predict volume, biomass, and carbon simultaneously, and the models were refit to a compiled national database so the system is compatible across all three.

What sets NSVB apart is that it follows ecological divisions instead of political boundaries. The equations are also species-specific, and a few intensively managed species, such as loblolly pine and Douglas-fir, have separate coefficients for planted versus natural stands.

NSVB also implements species-specific carbon fractions, which Jenkins and CRM don’t. So, no longer relying on the default 0.5 fraction to convert biomass to carbon.

What’s good

• It’s ecologically grounded and uses the latest science in its application.
• It’s species-specific, with carbon fractions to match.

What’s not

• It requires more tree measurements as inputs: DBH, total height, crown ratio, percent cull, and crown ratio. Most inventories don’t measure height and crown ratio on every tree. If you want to apply the NSVB equations to inventories without these measurements, you need to estimate the missing values through imputation or predicting them with another equations.

Restrepo et al. (2025) and Westfall et al. (2024) both compare NSVB with CRM. Merchantable bole estimates were fairly similar between the two, so tree volume changed little. The noted difference was in tops and limbs, where NSVB predicted more biomass and carbon. This suggests that the CRM approach was underestimating biomass and carbon in tree tops. There is also an online tool that shows differences between NSVB and CRM approaches by state and National Forests.

To summarize, here is what each equation requires. Note the CRM implementation is for the Northeast region, and each region differs:

User thoughts on the three equations

1. Jenkins is still robust and widely used, but it overestimates biomass for large trees. Without a height variable, it keeps adding biomass and carbon as diameter increases, which is a problem for large trees.
2. Hard to see a future for the CRM. It isn’t endorsed by the Forest Service, you can’t really find the older estimates anywhere, and NSVB has replaced this approach. It may have a use for comparison to other methods, though.
3. NSVB represents the latest science, but it’s hard to implement. Few inventories have all the variables it needs, so you end up imputing them or estimating them with other equations.

In an ideal world, I’d like to see a version of the Jenkins equations that includes height. One could refit the current Jenkins models with height as an additional predictor. The result is a system that still works for most inventories but is more realistic: it uses diameter and height, and height is often measured in forest inventories or can be inferred using a canopy height model. The NSVB equations are a great system, but to use them outside of Forest Inventory and Analysis data, variables like height and crown ratio need to be estimated with other equations.

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