Methods for Estimating Carbon Within Forests

Introduction

Trees contain up to half the carbon in a forest and can be more strategically managed compared to the carbon stored belowground. Estimating how much carbon is in a tree or stand is useful for informing decisions about forests and climate stewardship. 

It is unlikely that a private forest owner will be responsible for measuring the carbon in their forest if they want to manage for it or sell the carbon to an offset project developer. However, the information provided here can help owners get a sense of what is typically involved and, if they have forest stand inventory data available, come up with some rough estimates of their own. 

Estimating Carbon is a Prediction

Carbon in a forest is not an obvious feature, so it is difficult to measure carbon directly. Instead, carbon amounts are predicted for a tree or stand (a collection of trees managed together as a unit) using simplified mathematical relationships.

Allometric equations are standard practice in forestry and can be used to estimate the amount of carbon in a tree or stand. It works by determining how the tree variables that are easy to measure (e.g., diameter of a tree) are proportionally related to another tree variable that may be more difficult to measure (e.g., metric tons of carbon).

Changes in the amount of carbon sequestered in a stand over time are done by doing repeated stand inventories. This procedure helps verify how much carbon was likely stored in the same stand between two time periods. "Additional" carbon is produced when there is a change in management activities that leads to more living biomass on the landscape than there would have been otherwise.

Estimating Carbon in a Tree

Estimating carbon in a tree involves two basic steps: (1) determine the dry weight of the wood, and (2) determine how much of that wood is carbon. The following is a simple allometric equation form for predicting the dry weight of a loblolly pine tree growing in the southeastern United States. More specifically, it estimates the dry weight of wood in the above-ground part of the tree (i.e., stem) and only requires that you know the tree’s diameter (in centimeters) at 4.5 feet above the ground (i.e., diameter at breast height or dbh). This equation is shown here:

   dbh^2.77x 0.021=Stem biomass for loblolly pine (dry weight in kilograms)    [1]

Example calculation for a loblolly pine tree:

Step 1: Let's say that you have a loblolly pine tree that is 12 centimeters in dbh. Using equation [1], the dry weight of the above-ground wood would be,

   12^2.77x 0.221 = 21.46 kilograms of dry wood

Step 2: Once you have estimated the dry weight of the wood, it is typically assumed that the amount of carbon in a tree is approximately half the dry weight. In this example, the amount of carbon would be,

    21.46 kilograms of dry wood / 2 = 10.73 kilograms of carbon

Most allometric equations are developed for tree species that have a market value. Species-specific equations are generally preferred for their accuracy, but in many cases, a generalized composite equation may be used because it is assumed to be representative of many tree species.

Estimating Carbon in a Stand

In forestry, data describing many individual trees is collected to describe the whole stand. You can use allometric equations, such as the one above, along with other metrics (e.g., number of trees per unit area) to estimate the amount of carbon within a stand. 

Initially, an inventory of the trees needs to be conducted of the trees that you want to manage. The inventory can include all the trees, or alternatively, only the trees within designated plots, which are then used to make predictions about the whole stand. Steps 1 and 2, described above in the "Estimating Carbon in a Tree" section, can be used to predict the dry weights and amount of carbon in each of the measured trees. The amount of carbon in each of the trees would then be summed to estimate the total amount of carbon in a plot. The plot-level data is then "expanded" or "blown-up" to a per-unit area basis, say an acre or hectare. At this point, you would have the information needed to estimate the total amount of carbon in a forest of a known size or the average amount of carbon per acre.

Estimating Carbon in a Forest

Within forests, carbon sequestration is not just limited to the merchantable living stems of trees. Carbon is also sequestered in the different parts of the tree (e.g., crown, branches, roots), dead trees and leaves lying on the forest floor, understory vegetation (i.e., groundcover), and forest soils. Managing for these parts of the forest can also provide climate regulation benefits, especially if you plan to harvest and remove some trees from time to time.

In 1987, Baldwin presented an allometric equation that has a slightly different form compared to equation [1]. This equation can be used to estimate the dry weight of the foliage in the crown of a loblolly tree as a function of dbh (inches) and total tree height (feet).

    16.38dbh^2.91x Height^-1.47 = Dry weight of crown foliage in pounds     [2]

Sometimes managers need equations so they can better understand the biological trade-offs between understory and overstory vegetation and the impact to carbon pools. In this case, non-allometric equations may be used, in part because they need to include non-tree-related variables, such as rate of fertilization and precipitation. We can also see how forest management actions, such as thinning, impact the number of trees and site resources to the understory vegetation. The following example is more technical, but is a good illustration of how well-designed equations can help make predictions about forest carbon in all types of contexts.

Equation to estimate total understory vegetation dry weight in loblolly pine plantations by VanderSchaaf et al. (2010):

    InTotal = -20.0312 + 0.000177Fert x Precip + 6.656713InPrecip - 0.02987InPrecip X SDI^1/2
      -0.00015(SDI^1/2 x Fert x InPrecip)     [3]

Explanation of equation 3.
Natural logarithmic transformations, represented by the "ln" term in equation, are often required when estimating various carbon pools. Total refers to what vegetative forms or types are actually being estimated and here it refers to the dry weight biomass of grasses and grass-likes, forbs, woody vines, and shrubs in mid to late August, measured in kilograms on a per-hectare basis. As you can see, it is assumed that understory biomass is a function of precipitation amounts and fertilization rates. The positive sign in front of the fertilization and precipitation term (Fert x Precip) represents the synergistic effect of fertilization with greater amounts of precipitation – thus, nutrients and precipitation are more available to the understory. Additionally, understory vegetation production is greater as precipitation increases, as shown by the positive sign in front of the precipitation (lnPrecip) term. SDI refers to Reineke's stand density index, a metric that represents the amount of site resources being utilized by the overstory tree component.  Generally, a larger SDI results from more trees. Site resources such as light, moisture, and nutrients at some point become limited to the understory vegetation. The negative sign in front of the terms that contain SDI (SDI^1/2 x Fert x lnPrecip and lnPrecip x SDI^1/2) represents the negative relationship between overstory trees and understory vegetation, the competition for limited resources.  Further, the negative sign in front of the SDI terms implies that fertilization and precipitation not only benefit the understory vegetation, but also the overstory vegetation. Fertilization, along with greater precipitation, actually deters understory vegetation production at an accelerated rate because of the greater amount of overstory tree production.

Closing Thoughts

• The forest carbon sold on an offset market is not the carbon already in the stand, but the promise that additional carbon will be stored in the future, due to changes in forest management. Learn more about how to manage for additional carbon in the links below.
• To measure the carbon potential in your stand, it is best to work with a professional forester and identify which management practices can help enhance carbon storage based on the condition of your forest.

Additional Resources

Raju Pokharel at Michigan State University has developed a Forest Carbon Calculator Tool that helps to calculate the carbon stocks on your land and the potential economic value! 

This article was produced by the Forest Owner Carbon and Climate Education Program. What do you think? Please take this short survey.

If you have any questions or are interested in collaborating with FOCCE, please reach out to Melissa Kreye at mxk1244@psu.edu.

Related Articles and Resources 

• Carbon Accounting in Forest Management
• Forest Carbon Pools
• How Much Should I be Paid to Manage Forest Carbon?
• Long-Term Financial Planning for Timber and Carbon

Article Information Sources

• Baldwin, V.C., Jr.  1987.  Green and dry-weight equations for above-ground components of planted loblolly pine trees in the West Gulf Region.  South. J. Appl. For. 11: 212-218.
• Gonzalez-Benecke, C.A., S.A. Gezan, T.J. Albaugh. H.L. Allen, H.E. Burkhart, T.R. Fox, E.J. Jokela, C. A. Maier, T.A. Martin, R.A. Rubilar, L.J. Samuelson.  2014.  Local and general above-stump biomass functions for loblolly pine and slash pine trees.  Forest Ecology and Management 334: 254-276.
• Jenkins, J.C., Chojnacky, D.C., Heath, L.S., Birdsey, R.A., 2003. National-scale biomass estimators for United States tree species. Forest Sci. 49, 12–35.
• Lenhart, J.D., T.L. Hackett, C.J. Laman, T.J. Wiswell, and J.A. Blackard.  1987.  Tree content and taper functions for loblolly and slash pine trees planted on non-old-fields in East Texas.  South. J. Appl. For. 11: 147-151.
• VanderSchaaf, C.L.; McKnight, Ryan W.; Fox, Thomas R.; Allen, H. Lee. 2010. A model for estimating understory vegetation response to fertilization and precipitation in loblolly pine plantations. In: Stanturf, John A., ed. 2010. Proceedings of the 14th biennial Southern Silvicultural Research Conference. Gen. Tech. Rep. SRS–121. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 601-607.