United States

Department of 

Agriculture

Forest Service

Northern 

Research Station

General Technical

Report NRS-18

Measurement Guidelines 

for the Sequestration of 

Forest Carbon 

Timothy R.H. Pearson

Sandra L. Brown

Richard A. Birdsey
Visit our homepage at: http://www.nrs.fs.fed.us/

Published by: For additional copies:

USDA FOREST SERVICE USDA Forest Service 

11 CAMPUS BLVD SUITE 200 Publications Distribution

NEWTOWN SQUARE PA 19073-3294 359 Main Road

 Delaware, OH 43015-8640

November 2007 Fax: (740)368-0152

Abstract

Measurement guidelines for forest carbon sequestration were developed to support 

reporting by public and private entities to greenhouse gas registries. These guidelines are 

intended to be a reference for designing a forest carbon inventory and monitoring system by 

professionals with a knowledge of sampling, statistical estimation, and forest measurements. 

This report provides guidance on defining boundaries; measuring, monitoring, and estimating 

changes in carbon stocks; implementing plans to measure and monitor carbon; and 

developing quality assurance and quality control plans to ensure credible and reproducible 

estimates of the carbon credits. Expected users include entities, e.g., individual landowners, 

industrial forestry companies and managers of utility company lands, within the United States 

who are interested in implementing forestry activities and projects designed to generate 

carbon credits that could be traded as an offset, or for registering carbon dioxide reductions 

using the U.S. Department of Energy 1605(b) voluntary reporting registry.

The Authors

TIMOTHY R.H. PEARSON and SANDRA L. BROWN are scientists with Winrock 

International, Washington, D.C.

RICHARD A. BIRDSEY is a program manager with the Northern Research Station at 

Newtown Square, Pennsylvania.

This publication was sponsored by the USDA Forest Service’s Northern Global Change 

Research Program. We thank David Shoch, Matt Delaney, Mike Amacher, David Chojnacky, 

Coeli Hoover, and Greg Reams for contributions to an earlier version of this report that is part 

of the guidelines for the United States Voluntary Reporting of Greenhouse Gases Program. 

We also thank Jennifer Jenkins, John Stanovick, Jim Cathcart, and Raymond Czaplewski for 

helpful comments and suggestions. Material presented here does not represent the policy of 

the sponsoring agency. 

Manuscript received for publication 19 March 2007

Cover Photo

Forest measurement in Lake County, Oregon, used with permission from Winrock 

International.
CONTENTS

Introduction and Scope of Guidelines......................................................1

Monitoring Design....................................................................................4

 Boundaries ...........................................................................................4

 Stratifi cation of Land Area ....................................................................4

 Type and Number of Sampling Plots ...................................................6

 Frequency of Monitoring ....................................................................10

Sampling Design ...................................................................................12

 Plot Layout .........................................................................................12

 Size and Shape of Sample Plots .......................................................12

 Selection of Carbon Pools to Measure and Monitor ..........................13

Measurement and Data Analysis Techniques ........................................15

 Living Above-Ground Biomass...........................................................15

 Below-Ground Biomass .....................................................................23

 Dead Organic Matter..........................................................................24

 Soil Organic Carbon...........................................................................27

Estimating Net Change and Uncertainty ...............................................31

 Activities on Nonforested Lands ........................................................32

 Activities on Forested Lands ..............................................................35

Quality Assurance and Quality Control ..................................................38

 QA/QC for Field Measurements.........................................................38

 QA/QC for Laboratory Measurements ...............................................39

 QA/QC for Data Entry ........................................................................39

 QA/QC for Data Archiving ..................................................................39

Literature Cited ......................................................................................40
1

INTRODUCTION AND SCOPE OF GUIDELINES

Measurement guidelines for forest carbon sequestration were developed to support reporting by 

public and private entities to greenhouse gas registries. Although developed primarily for reporting 

about forestry “activities”—the categories of actions comprising forestry—rather than “projects”, 

which are specifi c carbon management undertakings, the guidelines are based on experience with 

methods for the latter and thus are broadly useful for carbon estimation. The national greenhouse gas 

registry, known as 1605(b) in reference to the original authorizing language contained in the Energy 

Policy Act of 1992, accepts reports by entities about their forestry activities as a bundle (Birdsey 

2006). Other greenhouse gas registries, such as that maintained by the state of California, accept 

reports about specifi c forestry projects.

These guidelines are intended to be a reference for designing a forest carbon inventory and 

monitoring system, and are based on the authors’ experience and the literature. Users should 

carefully review the material presented here and adapt the recommended procedures to their specifi c 

circumstances using local knowledge of forest conditions and practices, and location-specifi c data 

where possible. The guidelines are designed for “average” or typical conditions, so your results might 

not be as precise as described in this report. For example, although our guidelines recommend using 

generalized biomass equations that represent average national conditions, these equations may not 

perform well for populations of forest trees that deviate signifi cantly from the average.

These guidelines are designed for use by professionals with a knowledge of sampling, statistical 

estimation, and forest measurements. Users also should be familiar with specifi c protocols required by 

the registry to which the forest-carbon estimates will be reported. We cannot guarantee that a specifi c 

application will be accepted by a greenhouse gas registry. Nonetheless, by carefully referencing these 

guidelines and other sources of information, reporters can meet targeted levels of precision.

Expected users include entities, e.g., individual landowners, industrial forestry companies and 

managers of utility company lands, within the United States who are interested in implementing 

forestry activities and projects designed to generate reductions in atmospheric carbon dioxide (CO2

) 

that could be traded as an offset, or reported to the U.S. Department of Energy 1605(b) voluntary 

reporting registry. This report provides guidance on defi ning boundaries; measuring, monitoring, 

and estimating changes in carbon stocks; implementing plans to measure and monitor carbon; and 

developing quality assurance and quality control plans to ensure credible and reproducible estimates 

of the carbon credits.

Forestry activities primarily affect the exchange of CO2

 between the land and atmosphere. Techniques 

and methods for measuring and monitoring terrestrial carbon pools that are based on commonly 

accepted principles of forest inventory, soil sampling, and ecological surveys are described in the 

sections that follow.

Although the primary purpose of forestry activities for greenhouse gas reduction is to increase carbon 

stocks, these activities also can result in changes in non-CO2

 greenhouse gas emissions and removals. 
2

Examples include burning biomass; applying synthetic and organic fertilizers to soils; cultivating 

nitrogen-fi xing trees; and peat fl ooding and drainage activities. In addition, land-use activities that 

disturb soils, e.g., site preparation during afforestation, may affect non-CO2

 emissions and removals 

from soils. It is likely that these are insignifi cant in the forest sector, and practical and cost-effi cient 

methods for measuring non-CO2 greenhouse gases for forestry activities are less well developed. We 

do not provide guidelines for monitoring, estimating, or reporting signifi cant fl uxes of non-CO2

 gases 

for forestry.

For forestry activities it is not always necessary to measure all carbon pools (Brown et al. 2000). 

Selective or partial accounting systems may be appropriate so long as all pools for which emissions 

are likely to increase as a result of the activity (loss in carbon or emission) are included. The selection 

of which pools to measure and monitor depends on factors such as the expected rate of change, 

magnitude and direction of the change, availability and accuracy of methods to quantify change, 

and cost to measure. All pools that are expected to decrease must be measured and monitored. Pools 

that are expected to increase by a small amount need not be estimated if costs are high relative to the 

magnitude of the increase. For example, in the case of afforestation, understory herbaceous vegetation 

rarely is a signifi cant factor in the ecosystem carbon budget.

Our guidelines focus on forest ecosystem carbon only and include only the carbon pools on the land, 

e.g., live and dead above- and below-ground biomass and soil. The following steps are needed to 

produce credible and transparent estimates of net changes in carbon stocks:

A monitoring plan, including delineation of boundaries, stratifi cation of project area, type 

and number of sample plots, duration of project, and frequency of monitoring.

Sampling procedures for carbon stocks.

Methods for estimating carbon stocks and techniques for analyzing the results.

Methods for estimating net change in carbon stocks.

A quality assurance/quality control plan.

The primary focus is on fi eld measurements designed to produce accurate estimates of net changes 

in carbon stocks to known levels of precision. A suggested target for the precision for forest-carbon 

accounting is a suffi cient sample of measurements to conclude that with 95-percent confi dence, the 

true population value lies within plus or minus 10 percent of the sample estimate.

Many reporting entities with large tracts of forests have good records on types of management, timber 

stock, harvest rates, and related information. Such records can be used to develop estimates of net 

changes in carbon stocks from forestry activities. It is good practice to compare per-acre or perhectare (ha) estimates with similar estimates from regional databases. For other entities where such 

data are not available, e.g., for owners of non-industrial forest land, there are numerous national to 

regional databases that can be downloaded from the internet. Although estimates based on these data 

likely will be less accurate and less precise than those based on fi eld measurements, such data used 

in combination with the methods in this report can provide better estimates than those based on 

default values alone. The following list of web sources are useful for verifying that measurements and 

calculations are within the ranges reported at national and regional scales.

1.

2.

3.

4.

5.
3

Internet Sites Available for Carbon Estimation

Internet site: Organization Relevant content

http://fia.fs.fed.us/ USDA Forest Service 

Forest Inventory and 

Analysis

Forest statistics of the U.S.

Forest statistics by state

Sample plot and tree data

Forest inventory methods and 

basic definitions

http://www.fhm.fs.fed.us/ USDA Forest Service 

Forest Health Monitoring

Forest health status

Regional data on soils, dead 

wood stocks 

Forest health monitoring methods 

http://www.usda.gov/oce/global_

change/gg_inventory.htm

USDA Greenhouse Gas 

Inventory

State-by-state forest carbon 

estimates

http://www.fs.fed.us/ne/

durham/4104/index.shtml

USDA Forest Service, U.S. 

carbon budget project

On-line carbon estimation

Forest carbon estimation 

methods

U.S. and regional forest carbon 

statistics 

http://www.fs.fed.us/pnw/

sev/rpa/ 

USDA Forest Service 

resources planning act

Timber resource statistics and 

projections

http://unfccc.int/

http://www.ipcc.ch/

United Nations Framework 

Convention on Climate 

Change and IPCC

International guidance on carbon 

accounting and estimation

http://www.wri.org/ World Resources Institute Greenhouse gas mitigation 

projects

Accounting, measuring, and 

reporting procedures

http://nature.org/initiatives/

climatechange/

The Nature Conservancy Greenhouse gas mitigation 

projects

Accounting and reporting 

procedures

http://www.winrock.org/

Ecosystems/

Winrock International Greenhouse gas mitigation 

projects

Developments in baseline and 

leakage analyses

Accounting, measuring, and 

reporting procedures
4

MONITORING DESIGN

Boundaries

Forestry activities and the land base for an entity can vary in size (from tens to hundreds of 

thousands of ha) and can be confi ned to a single or several geographic areas. The area may be one 

contiguous block of land with a single owner or many small blocks of land spread over a wide 

area with numerous small or several large landowners. The spatial boundaries of the land need to 

be clearly defi ned to facilitate accurate measuring, monitoring, accounting, and verifi cation. The 

spatial boundaries can be in the form of permanent boundary markers, e.g., fences; clearly defi ned 

topographic descriptions, e.g., rivers/creeks, mountain ridges; spatially explicit boundaries (identifi ed 

with a Global Positioning System, GPS); and/or other methods. Ground-based surveys that delineate 

property boundaries are an accurate means of documenting land boundaries. Many methods and 

tools are available for identifying and delineating land boundaries, including remote sensing, e.g., 

satellite images from optical or radar sensor systems, aerial photos, GPS, topographic maps, and land 

records. Larger areas across the landscape can be defi ned by specifi c boundary descriptions using 

GPS-based coordinates on topographic maps or other suitable means.

Boundaries must be documented properly from the start (mapped and described) and preferably not 

subject to changes for the duration of the estimation period. Boundary changes must be noted and 

inclusions and/or exclusions of physical land area must be surveyed using the methods described. This 

would require adjusting the estimated net emissions or removals of greenhouse gases attributable to 

the activity or entity.

Stratifi cation of Land Area

Stratifi cation Before Activities Begin

Once the land area has been delineated, it is useful to collect basic information such as landuse history as well as maps of soil, vegetation, and topography. The land for the project can be 

georeferenced and mapped onto a base map. A geographic information system (GIS) is useful for 

such an activity. Maps can then be used to stratify the area into more or less homogeneous units 

(relative to carbon stocks and rates of change in carbon) to increase sampling effi ciency.

To facilitate fi eld work and increase the accuracy and precision of measuring and monitoring, divide 

the area (population of interest) into subpopulations or strata that form relatively homogenous units. 

Useful tools for defi ning strata include ground-truthed maps from satellite imagery, aerial photos, and 

maps of vegetation, soils, or topography. Many of these products are available as GIS data layers, e.g., 

STATSGO soil maps, USGS Digital Elevation Model, 1992 National Land Cover map, that can be 

overlain in a GIS to identify possible strata. The key to stratifi cation is to ensure that measurements 

are more alike within each stratum than in the sample frame as a whole. A GIS can automatically 

determine stratum size and the size of exclusions or buffer zones.
5

The size and spatial distribution of the land area does not infl uence site stratifi cation. One large, 

contiguous block of land or many small parcels can be considered the population of interest and are 

stratifi ed in the same manner. When an area is not homogeneous, stratifi cation generally reduces 

monitoring costs, e.g., the amount of sampling required is reduced due to the smaller variation in 

carbon stocks in each stratum. Stratifi cation should be carried out using criteria that are directly 

related to the variables to be measured and monitored, for example, the carbon pools in trees for 

afforestation. For afforestation, the strata can be defi ned on the basis of variables such as the tree 

species (if several), age class (as generated by delay in practical planting schedules), initial vegetation 

(totally cleared versus cleared with patches or scattered trees), and site factors (soil type, elevation, 

slope, etc.). However, there is a tradeoff between the number of strata and sampling intensity. Strata 

should be suffi ciently large to enable adequate sampling within each stratum but not so large as to 

incur higher costs.

Site visits to the project area and nearby areas with existing vegetation that will be the target of the 

activity will aid in stratifying the area. Field assessments and measurements of key variables such as 

general soil type, topography, and nearby existing vegetation aid in stratifi cation and contribute to 

cost-effective monitoring.

Post-Stratifi cation

For some areas, it may not be possible to prestratify because the site appears to be homogeneous. 

However, it is possible that after the fi rst monitoring period, the estimated change in carbon stocks is 

highly variable within a stratum, and that the original stratum can be subdivided into homogeneous 

areas (post-stratifi cation).

Remote Sensing Data

Data on remote sensing are useful in designing and implementing measuring and monitoring plans for 

forest-based carbon activities, for example a land-use map for the area, stratification of the area, landuse history, monitoring of overall performance, and verification that the carbon pool exists.

Selected High Resolution Data Sources for Monitoring Carbon Sequestration Projects

Sensor/

satellite

Spatial 

resolution

Spectral 

resolution Revisit time Owner Data

Landsat 5 TM 30 m VNIR/SWIR 16 days NASA/USGS http://edc.usgs.gov

Landsat 7 ETM+ 30 m VNIR/SWIR 17 days NASA/USGS http://edc.usgs.gov

EO-1 ALI 30 m VNIR/SWIR 18 days NASA http://edc.usgs.gov

EO-1 Hyperion 30 m VNIR/SWIR 19 days NASA http://edc.usgs.gov

IKONOS 1- 4 m VNIR/SWIR 2 – 5 days Space Imaging http://www.spaceimaging.

com

Quickbird 0.6 – 3 m VNIR/SWIR 1 – 4 days DigitalGlobe http://www.digitalglobe.

com

TM = Thematic Mapper; ETM+ = Enhanced Thematic Mapper Plus; ALI = Advanced Land Imager; VNIR = Visible 

to Near Infrared; SWIR = Shortwave Infrared
6

Type and Number of Sampling Plots

Plot type

For forestry activities, permanent or temporary sampling plots can be used for sampling over time 

to estimate changes in the relevant carbon pools. Permanent plots are applicable only where both 

the trees and the plots are permanently marked. For all other pools, temporary plots are used. For 

trees, both methods have advantages and disadvantages. Permanent sample plots in which trees are 

tagged generally are regarded as statistically more effi cient for estimating changes in forest-carbon 

stocks than temporary plots because there is high covariance between observations at successive 

sampling events (Avery and Burkhart 1983). Moreover, the use of permanent plots allows effi cient 

verifi cation at relatively low cost. A verifying organization can fi nd and measure permanent plots at 

random to verify the design and implementation of the carbon monitoring plan in quantitative terms. 

Disadvantages of permanent plots are that their location might be known and they might be treated 

differently, e.g., fertilized or irrigated to enhance the carbon stocks, tags can become dislocated from 

trees, or they can be destroyed or lost by disturbances over the measurement interval. Advantages of 

temporary plots are that they can be established more cost-effectively to estimate the carbon stocks 

of the relevant pools, their location changes at each sampling interval, and they would not be lost to 

disturbances. The primary disadvantage of temporary plots is related to the precision in estimating 

the change in forest-carbon stocks. Because individual trees are not tracked (see Clark et al. 2001), the 

covariance term is nonexistent so it will be more diffi cult to attain the targeted precision level without 

measuring more plots. Thus, any time advantage gained by using temporary versus permanent forest 

plots may be lost by the need to install additional temporary plots to attain the targeted precision.

If permanent sample plots are used it is necessary to mark or map the trees to measure the growth of 

individuals at each time interval so that growth of survivors, mortality, and ingrowth of new trees can 

be tracked. Changes in carbon stocks for each tree are then estimated and summed per plot. Statistical 

analyses are performed on net carbon accumulation per plot, including ingrowth and losses due to 

mortality. Because permanent plots also track mortality, they can be used to track the major changes 

in dead wood (both on the ground and standing) after the initial inventory of this component.

Tagging Trees in Permanent Plots

When estimating change in carbon stocks, an important consideration is accounting for ingrowth 

and mortality. Not understanding where, when, and how to include these components can result in 

erroneous estimates of changes in the carbon stocks of trees. Here we emphasize why it is important 

to tag and track individual surviving trees as well as new ingrown trees. For measuring the live-tree 

pool, there is no requirement to track mortality (measured as part of dead wood pool) but there must 

be an estimate of trees growing into the plots, i.e., exceeding the minimum measurement size only at 

time 2.

Figure 1 shows the same trees being measured in a plot that tags and tracks individual trees and in a 

plot that does not tag or track trees. The change in biomass stock for ingrowth trees is the biomass of 

the new tree at time 2 minus the minimum biomass required for a tree to be measured (assume four 

units of biomass in Figure 1).

It is clear that the two methods produce widely different results. Although in this example the 

untagged plot gives a negative change in stock, it could just as readily give a larger positive change 
7

than the tagged plots. Because individual trees are not tracked in the untagged plots, there is no 

way of knowing that the 7-unit tree at t2

 was ingrowth or that the 13-unit tree at t1 died during the 

interval.

Prism Plots

The alternative to fi xed-area plots is point sampling using basal area prisms (point sampling). When 

a prism from a fi xed point is used, trees are tallied according to size. Tree stems at diameter at breast 

height (d.b.h.) that are close enough to completely fi ll the sighting angle are tallied. Stems that are too 

small or too distant are ignored.

The primary advantage of point sampling is the speed with which data are collected, i.e., no fi xedplot boundary is involved. However, errors in the tallies arising from point sampling are more serious 

than those arising from fi xed-area plots. Because point sampling preferentially samples large trees, it is 

well suited to commercial forestry and to rapid reconnaissance sampling, though sampling with fi xedarea plots generally is more precise (Avery and Burkhart 1994) and representative of the full range of 

trees that contribute to carbon estimation.

Number of Plots, Precision, and Sample Size

Because the level of precision required for a carbon inventory has a direct effect on inventory costs, 

it must be carefully chosen by users of inventory results. A reasonable estimate of the net change in 

Figure 1.—Illustration of the methods for calculating change in above-ground biomass stocks for trees 

that are or are not tagged and tracked in permanent plots. AGB = above-ground biomass of live trees; 

AGB of a minimum-size tree is set arbitrarily to 4 units (based on Clark et al. 2001).

Time: t1 t2

AGB: 10 12 13 12 15.2 7 

Trees tagged and tracked: 

Stand Increment = (Σ Increments of surviving trees) + (Σ Increment(s) of ingrowth) 

 = ((12 - 10) + (15.2 - 12)) + (7 - 4) 

 = (2 + 3.2) + (3) 

 = 8.2 

Trees not tagged and tracked: 

Stand Increment = (ΣAGB at t2 - ΣAGB at t1)

= ((12 + 15.2 + 7) – (10 + 12 + 13)) 

= (34.2 – 35)

= - 0.8 
8

carbon stocks that can be achieved at a reasonable cost is to target within 10 percent of the true value 

of the mean at the 95-percent confi dence level (see Brown 2002).

When the level of precision has been chosen, sample sizes must be determined for each stratum in 

the project area. Each carbon pool will have a different variance (amount of variation around the 

mean). However, focusing on the variance of the tree component for forestry activities captures most 

of the total variance. Although the variance in other pools may be high, it often contributes little to 

the net change in carbon stocks or it can reduce the total variance when the net change in all pools is 

estimated. For example, the understory in forests can be highly variable but it usually is a negligible 

component of the net change. By contrast, dead wood, though highly variable, often reduces the 

overall variability of the net change in carbon. Soils often are the exception. Soil-carbon stocks are 

highly variable and are less closely associated with tree carbon stocks than the other measurement 

pools. It is advisable to have a sampling scheme specifi cally for soils if they are an important 

component of the anticipated carbon benefi ts.

The sample size for monitoring in each stratum must be calculated on the basis of the estimated 

variance of the carbon stock (between separate measurement plots) in each stratum, and the 

proportional area of the stratum. Typically, to estimate the number of plots needed for monitoring 

at a given confi dence level, one must fi rst obtain an estimate of the expected variance of the carbon 

stock in each stratum. This can be accomplished from existing data of the type of activity to be 

implemented, e.g., a forest inventory in an area representative of the proposed activity, or by 

taking measurements on an existing area that represents the proposed activity. For example, if the 

activity is to afforest agricultural lands and it will last for 20 years, a measure of the carbon stocks of 

approximately 15 plots of an existing 20-year forest would suffi ce. If the project area comprises more 

than one stratum, repeat this procedure for each one. Such measurements will provide estimates of 

the variance in each stratum and, along with the area of the stratum, the total number of plots per 

stratum can be estimated by standard statistical methods.

As sampling plots cannot always be relocated or reoccupied for a variety of reasons, for example, if 

plot markers are overgrown or removed by people, plots are burned, or records are lost, it is prudent 

to increase the number of plots beyond the minimum in the initial sampling design. Increasing 

the number of plots to some percentage over the calculated minimum number of samples provides 

a cushion that helps meet minimum precision requirements despite missing plots in subsequent 

inventories. The minimum sample size should be increased by at least 10 percent to allow for plots 

that cannot be relocated or are lost due to unforeseen circumstances.

Managers who contemplate progressive plantings over time must develop an open-ended monitoring 

framework that can accommodate the progressive addition of plantings to the area over time. This 

can be done by predicting the eventual size of the area at year X and progressively assigning distinct 

stand-age cohorts to separate strata within the overall population, anticipating that a full contingent 

of permanent sample plots would be installed by year X. No more than two or three age classes 

should be combined into one cohort class.
9

Using Forest Inventory and Analysis Data to Estimate Coefficient of 

Variation and Number of Sampling Plots

Download data (http://ncrs2.fs.fed.us/4801/fiadb/) and apply biomass equations 

and expansion factors (see section 4.1) for the specific area and forest type of 

interest. Sum to obtain plot level results.

Calculate mean carbon stocks across the dataset or optionally across strata of 

interest, then calculate standard deviation and the coefficient of variation.

The minimum number of plots required for monitoring is calculated by solving 

for n in the formula for the confidence interval (CI). Target ± 7 to 8 percent of the 

mean as a reasonable level of precision (this accounts for the sampling error 

only; sources of error such as measurement error and model error likely will 

account for 10 to 20 percent of total error thus, a target of ± 7 to 8 percent CI 

of the mean for sampling will result in a total error for the confidence interval of 

about 10 percent of the mean).

n = (s x 2.1)/(mean x 0.08)2 (where s = standard deviation)

The 95 percent CI becomes the ±8 percent precision chosen—i.e. we can be 95 percent 

confident that the true mean is covered by the determined sampling precision.

If the activity is planned to run for 50 to 70 years, use the large FIA size class (one 

method of sorting FIA data) where variation and consequently minimum number 

of plots is low. Variation is highest in young or small size-class plots regardless of 

whether regeneration was natural or artificial.

The minimum number of plots can be decreased by stratification of study area, 

for example, by slope, soil type, or site index. 

Coefficients of variation ([standard deviation * 100] / mean) and minimum 

number of sampling plots at 95 percent confidence level calculated for 

specific forest types in three regions using FIA data.

Number of plots

Region Forest type FIA size 

class

Percent 

C.V.

(95 percent)

Ohio Oak-hickory Large 27 45

Medium 33 65

Small 63 237

Illinois Oak-hickory Large 41 99

Medium 35 74

Small 74 325

Lower Mississippi 

Valley

Bottomlands Large 29 50

Medium 33 66

Small 80 384

•

•

•

•

•
10

At the simplest level, the number of plots required should be calculated using the following equation:

2

ts

n

E

 ¬ = ­

 ­  ­  ®

Where

E = allowable error or the desired half width of the confi dence interval. Calculated by multiplying the 

mean carbon stock by the desired precision, i.e., mean carbon stock * 0.1 (for 10-percent precision) 

or 0.2 (for 20-percent precision),

t = the sample statistic from the t-distribution for the 95-percent confi dence level; t usually is set at 2 

as sample size is unknown at this stage, 

s = standard deviation of stratum 

Where the project is composed of strata, a more complex equation should be used:

For L strata, the number of plots needed (n) =

2

1

2 2

2

2

1

*

*

*

L

h h

h

L

h h

h

N s

n

N E N s

t

=

=

 ¬  ­

 ­

 ­­  ® =  ¬

+ ­  ­

 ­­  ®





This equation can be simplifi ed as:

For a single stratum: For two strata:

( )2

2 2

2

2

*

*

*

N s

n

N E N s

t

=

+ 

( )

2

11 2 2

2 2

2 2

2 11 2 2

* ( *)

*

* *

Ns N s

n

N E Ns N s

t

+ =

+ +

Where

E = allowable error or the desired half width of the confi dence interval. Calculated by multiplying the 

mean carbon stock by the desired precision, i.e., mean carbon stock * 0.1 (for 10-percent precision) 

or 0.2 (for 20-percent precision),

t = the sample statistic from the t-distribution for the 95-percent confi dence level; t usually is set at 2 

as sample size is unknown at this stage, 

Nh = number of sampling units for stratum h (= area of the stratum, in ha/area of the plot, in ha),

N = number of sampling units in the population ( ) N N = h ,

s

h = standard deviation of stratum h

Frequency of monitoring

The frequency of monitoring is related to the rate and magnitude of change. The smaller the expected 

change, the greater the potential that frequent monitoring will not detect a signifi cant change. This 

becomes a cost-benefi t analysis so that the frequency of monitoring should be determined by the 

magnitude of expected change. Less frequent monitoring is applicable only if small changes are 

expected.
11

Increasing the interval between sampling events should increase the magnitude of the change that 

takes place which, where variance around the means is constant, increases the percentage and 

magnitude of the change resolved (Fig. 2). This is an important consideration because small changes 

expected with short sampling intervals may be undetectable, even with high sampling intensity.

Frequency of monitoring should consider the carbon dynamics of the activity and costs involved. 

Given the dynamics of forest processes, they generally are measured at intervals of 5 years. For carbon 

pools that respond more slowly, e.g., soil, even longer periods can be used -- perhaps even 20 years 

between sampling events. Thus for carbon accumulating in the trees, the frequency of measuring 

and monitoring should be defi ned in accordance with the rate of change of the carbon stock, or in 

accordance with the rotation length in the case of plantations.

A disadvantage of long periods between sample events is the risk of natural or anthropogenic 

disturbance, the effects of which will not be captured with widely spaced monitoring intervals. This 

needs to be taken into account when deciding on the frequency of monitoring.

Independent checks of the monitoring system are recommended to ensure data quality. Monitoring 

changes in carbon stocks in the permanent sampling plots does not always provide information 

that the changes in carbon stocks are the same across the entire area and/or that the purpose of 

the activity is accomplished, e.g., to establish several thousand hectares of trees. Repeated visits to 

the carbon-monitoring plots reveal that the carbon in those plots, which were located randomly 

and purportedly represent the population, is accumulating with known accuracy and precision. 

To determine that the plots are representative of the entire project area, periodic checks should be 

made to ensure that the overall activity is performing in the same way as the plots. This is done by 

fi eld checking indicators of carbon stock changes, e.g., tree height for afforestation activities. Thus, 

indicators can be produced that can readily be fi eld-checked across the area. High-resolution satellite 

imagery also can be used to accomplish this task, at least with respect to the area treated. Periodic 

acquisition of such imagery or even aerial imagery might be a relatively inexpensive way to monitor 

overall performance.

Figure 2.—Example of how 

percent absolute change in 

the mean (with 95 percent 

confi dence) soil carbon for 

afforestation activities varies in 

relation to the sampling interval 

and sample size (n), assuming 

constant coeffi cient of variation 

(30 percent), constant rate of soil 

carbon accumulation of 0.5 t C/ha/

yr, and initial soil carbon 50 t/ha.

0

20

40

60

0 5 10 15 20 25 30

Sampling Interval (years since forest initiation)

Absolute Change in Means (%) 

n=100

n=90

n=80

n=70

n=60

n=50
12

SAMPLING DESIGN

Plot Layout

Permanent plot locations can be selected randomly or systematically (plot grid). If plot values are 

distributed irregularly in a random pattern, both approaches are about equally precise. If some parts 

of the strata have a higher carbon content than others, systematic selection usually results in greater 

precision than random selection. Systematic sampling also may appear more credible. The risk is that 

a map of random sample locations might seem like the plots were selected to monitor only highcarbon areas. Systematic samples are incontrovertible. Sample locations can be readily defi ned by GIS 

for either approach.

Size and Shape of Sample Plots

The size and shape of the sample plots is a tradeoff among accuracy, precision, and time (cost) of 

measurement. Sample plots containing smaller subunits of various shapes and sizes are cost effective 

depending on the variables to be measured. For example, for afforestation, all trees are measured in 

the entire sample plot, whereas data on nontree vegetation, litter, and soil are collected in a smaller 

sub-plot. The FIA standard plot consists of a cluster of four subplots, each containing smaller nested 

plots for sampling understory vegetation and soils, of relatively small radius.

Unlike fi xed-area plots (Fig. 3), nested plots are better suited to stands with a wide range of tree 

diameters or to stands with changing diameters and stem densities. The optimum area for nested 

plots can be anticipated by predicting changes in stem density and mean stem diameter over time, 

or by direct measurements of proxy stands of known age. A nested plot design is effi cient when it it 

likely that individual trees will grow at different rates resulting in uneven size distribution. However, if 

the forest is likely to remain even-sized, a single-size plot would suffi ce. For example, limited-duration 

afforestation or highly managed short rotation plantations require only a single-size plot.

Nested plots are composed of several full circular or rectangular plots; each nested plot should be 

viewed separately. The number of nested circles or rectangles depends on forest structure and the 

length of the activity. Where the activity is to plant trees but to track only for 20 years, a single-size 

plot likely would suffi ce. However, additional nested circles or rectangles should be added beyond this 

duration; a diverse mature forest might require four plot sizes. When trees attain the minimum size 

for one of the nested circles, they are measured and included. When they exceed the maximum size, 

measurement of the tree in that nest stops and begins in the next larger nest. If ingrowth into a new 

nest occurs between censuses, the growth up to the maximum size is included with the smaller nest. 

Growth in excess of this size is accounted for in the larger nest.

Large plot:

radius 20 m, 

trees > 50 cm d.b.h. 

Intermediate plot:

radius 14 m, 

trees 20-50 cm d.b.h. 

Small plot:

radius 4 m, 

trees 5-20 cm d.b.h. 

Figure 3.—Schematic of nested, fi xed area circular sample plots. The radius and diameter limits for 

each circular plot would be a function of local conditions and expected size of the trees through time.
13

Plot Size

Time and effort spent on field measurements depends on sample size (number of plots) 

and plot area. Although increasing sample size increases precision, increasing plot area 

reduces variability between plots roughly following the relationship derived and discussed 

by Freese (1962). By increasing plot area, variation between plots is reduced, allowing for 

a smaller sample size while achieving the same precision level. For example, pilot studies 

can provide an estimate of the CV and plot area (e.g., from FIA plots). Then a plot size can 

be selected to achieve the desired precision and cost considerations. However, calculating 

a new plot size for each strata is an added cost and introduces a complexity that can result 

in additional measurement errors. It is common to select a standard constant plot size (see 

Figure 3), which balances measurement effort and variability of plot-level results.

Plots are extrapolated to the full-hectare area to produce carbon-stock estimates. Extrapolation by 

use of expansion factors occurs by calculating the proportion of a hectare that is occupied by a given 

plot. For example, if a series of nested circles measuring 4, 14, and 20 m in radius were used, their 

areas equal 50, 616 and 1,257 m2

 respectively. The expansion factors for converting the plot data 

to a hectare basis are 198.9 for the smallest, 16.2 for the intermediate, and 8.0 for the largest nested 

circular plot (1 ha = 10,000 m2

).

Selecting Carbon Pools to Measure and Monitor

The key pools included in forestry activities are defi ned in Table 1. Selecting which pool to measure 

and monitor depends on several factors, including expected rate of change, magnitude and direction 

of the change, availability and accuracy of methods to quantify change, and cost to measure. All 

pools that are expected to decrease signifi cantly due to activities must be measured and monitored. 

The 1605(b) process includes a de minimis criterion whereby any emission that is equal to or less 

than 3 percent of the total need not be monitored. Moreover, it generally is not cost effective to 

monitor pools that are expected to change by a small amount relative to the overall rate of change, 

e.g., understory herbaceous vegetation in the case of an afforestation project. The decision matrix in 

Table 1.—Key carbon pools for forests and their definition

Carbon Pool Defi nition

Live trees Live trees: above ground

Live trees: below ground

Understory vegetation Tree seedlings

Shrubs, herbs, forbs, grasses

Standing dead trees Standing dead trees: above ground

Standing dead trees: below ground

Down dead wood Down dead wood

Stumps and dead roots

Forest fl oor Fine woody debris

Litter

Humus

Soil carbon Soil carbon

Wood products Harvested wood mass
14

Table 2 shows the primary carbon pools for forests and which ones should be (Y), might be (M), or 

should not be (N) measured for each type of forestry activity.

Clearly, it makes sense to measure and monitor the carbon pool in live trees and their roots for all 

activity types. Above-ground nontree biomass or understory vegetation might require measuring if 

this is a signifi cant component, e.g., where shrubs are dominant or codominant with other forms of 

vegetation. Measuring might not be required if the understory is dominated by herbaceous material as 

this likely would account for negligible changes over the duration of the activity (less than 3 percent). 

The forest fl oor should be measured for most activity types, particularly where the forest likely will be 

dominated by conifers, as this can be a signifi cant component of the total carbon pool.

Dead wood consists of standing dead trees and downed dead wood. For changes in management for 

timber, this must be measured as this pool often decreases as a result of a project. For example, the 

change from more intensive to less intensive harvesting causes the dead-wood pool to decrease (less 

timber is removed and less slash is left behind).

Table 2.—Decision matrix illustrates selection of pools to measure and monitor in forestry projects that can 

be implemented in the United States (modified from Brown et al. 2000)

Activity

Living biomass Dead organic 

matter 

Soil

Wood 

productsa Above-ground 

tree

Above-ground 

nontree 

BelowgroundForest 

fl oor

Dead 

wood 

Afforestation Y1 M2 Y3 M4 M5 Y6 M

Forest

 restoration

Y1 M2 Y3 M4 M5 Y6 N

Forest

 management

Y1 N Y3 M4 Y5 N Y

Agroforestry Y1 M2 Y3 M4 N Y6 M

Short-rotation

 biomass 

 energy

 plantations

Y1 N Y3 M4 N Y6 Y

Mine-land

 reclamation

Y1 M2 Y3 M4 M5 Y6 M

Forest

 preservation

Y1 M2 Y3 M4 M5 M6 Y

a

 No methods are provided for measuring this pool as the focus of this report is on ecosystem carbon; 

see http://treesearch.fs.fed.us/pubs/22954 for methods for estimating change in stocks of wood products.

Letters in table refer to the need for measuring and monitoring carbon pools

Y = Yes: the change in this pool likely will be large and should be measured.

N = No: the change likely will be small to none so it is not necessary to measure this pool.

M = Maybe: the change in this pool might require measuring depending on the forest type and/or management

 intensity of the project.

Numbers in table refer to different methods for measuring and monitoring carbon pools:

1 = See methods of carbon-stock measurement for above-ground biomass of trees.

2 = See methods described for above-ground biomass of nontree vegetation.

3 = See methods for measuring/estimating the carbon stock in below-ground biomass.

4 = See methods for measuring carbon stock in forest fl oor. 

5 = See methods for measuring dead wood.

6 = See methods for measuring carbon pool in soils.
15

For the preservation of mature forests, it can be expected that substantial emissions will result in the 

baseline. Soil organic carbon likely will change signifi cantly for afforestation, forest restoration, and 

mine-land reclamation as the initial amount of soil carbon likely will be low. However, changes in 

forest management or even forest preservation (from harvesting to preservation) likely will produce 

very small or undetectable changes in soil carbon, and the cost to measure this pool might exceed the 

value of the carbon.

The decision to monitor wood products depends on whether the project will be harvested. For shortrotation biomass energy plantations, monitoring would be required as the product is the primary 

purpose of the activity. Activities related to changes in forest management also require monitoring 

of wood products as harvesting often changes the live carbon pool. The same is true for forest 

preservation if the original activity was timber production. In other words, all of the live biomass that 

is “protected” by the activity (as preservation or reduced logging intensity) cannot be claimed as a 

savings for the atmosphere because some biomass went into long-term wood products.

MEASUREMENT AND DATA ANALYSIS TECHNIQUES

Measurements of net carbon fl ows for forests generally lend themselves to the stock-change method, 

that is, the amount of carbon sequestered is estimated as the net change in carbon stocks over time. 

Much of the previous discussion focused on the design required to estimate changes in carbon stocks 

precisely. Although the stock change method is applicable for most components, the fl ow method 

may be appropriate for some components. For example, changes in the dead wood pool often are 

estimated from the difference between inputs from slash (estimated from the difference between total 

tree biomass and mass of timber removed) and outputs from decomposition of the dead wood. In the 

sections that follow, both the stock and fl ow approaches are described where applicable.

These methods are based on measurements and models resulting in estimates of biomass except for 

soil, which can be measured directly in units of carbon. Biomass always is oven dried and generally is 

converted to units of carbon by multiplying biomass by 0.5 (the 1605b and Intergovernmental Panel 

on Climate Change default), unless more specifi c data are available.

Living Above-ground Biomass

Trees

The carbon stocks of trees are estimated most accurately and precisely by direct methods, e.g., 

through a fi eld inventory, where all the trees in the sample plots above a minimum diameter are 

measured. The minimum diameter often is 5 cm in d.b.h., but it can vary depending on the expected 

size of trees. For arid environments in which trees grow slowly, the minimum d.b.h. may be as small 

as 2.5 cm; for humid environments in which trees grow rapidly, the minimum d.b.h. may be up to 

10 cm. Biomass and carbon stock are estimated using appropriate allometric equations applied to 

the tree measurements. Tree biomass often is estimated from equations that relate biomass to d.b.h. 

only. Although the combination of d.b.h. and height as the independent variables is often superior to 

d.b.h. alone, measuring tree height can be time consuming and will increase the cost of a monitoring 

program. Further, the empirical database of trees in the United States shows that highly signifi cant 

biomass regression equations can be developed using d.b.h. only (Tables 3 - 4).

Biomass equations often are reported for individual species or groups of species, but the literature is 

inconsistent and/or incomplete for all U.S. tree species. However, recent analyses have shown that 
16

Table 3.—Parameters and equationsa for estimating total above-ground biomass for hardwood 

and softwood species grouped in 10 classes in the United States. (Jenkins et al. 2004.)

Species group

Parameter Data

pointsb

Maxc

β d.b.h. 0 β1 RMSEd R2

cm log units

 Hardwood

Aspen/alder/

Cottonwood/ willow

-2.2094 2.3867 230 70 0.507441 0.953

Soft maple/birch -1.9123 2.3651 316 66 0.491685 0.958

Mixed hardwood -2.4800 2.4835 289 56 0.360458 0.980

Hard maple/oak/

Hickory/ beech

-2.0127 2.4342 485 73 0.236483 0.988

 Softwood

Cedar/larch -2.0336 2.2592 196 250 0.294574 0.981

Douglas-fi r -2.2304 2.4435 165 210 0.218712 0.992

True fi r/hemlock -2.5384 2.4814 395 230 0.182329 0.992

Pine -2.5356 2.4349 331 180 0.253781 0.987

Spruce -2.0773 2.3323 212 250 0.250424 0.988

 Woodlande

Juniper/oak/mesquite -0.7152 1.7029 61 78 0.384331 0.938

a

Biomass equation:

 y = Exp (β0 + β1 Ln x)

Where

y = total aboveground biomass (kg) for trees 2.5 cm and larger in d.b.h.,

x = d.b.h. (cm),

Exp = “e” to the power of,

Ln = natural log base “e” (2.718282). b

Number of data points generated from published equations (generally at intervals of 5-cm d.b.h.) for parameter 

estimation.

c

Maximum d.b.h. of trees measured in published equations; beyond this maximum diameter equations should only 

be used with caution.

d

Root mean squared error or estimate of the standard deviation of the regression error term in natural log units.

e

Woodland group includes both hardwood and softwood species from dry-land forests.

Table 4.—Parameters and equationsa for estimating above-ground biomass for southern and 

eastern hardwood and softwood species in the United States (from Brown and Schroeder 1999)

Species class

Parameter Number of 

data points

Max 

d.b.h. R2 β0 β1 β2 β3

cm

Hardwood 0.5 25000 2.5 246872 454 85.1 0.990

Pine 0.887 10486 2.84 376907 137 56.1 0.980

Fir-spruce 0.357 34185 2.47 425676 83 71.6 0.980

a

Biomass equation:

2

2

1

0

3

x

y

x

C

C

C C C = +

+

Where

 y = above-ground biomass (kg),

 x = d.b.h. (cm).
17

equations based on multi-species groupings can work well for U.S. forests (Schroeder et al. 1997; 

Jenkins et al. 2004).

Jenkins et al. (2004) compiled all available diameter-based allometric regression equations for estimating 

total above-ground and component biomass, defi ned in terms of dry mass, for U.S. trees. More than 

1,700 biomass equations were assembled for more than 100 species from 177 sources. Using a subset of 

318 equations from 104 sources, Jenkins et al. (2003) developed generalized equations appropriate 

for estimating tree biomass from d.b.h. at large scales. This approach for generalized equations included 

a method for generating “pseudodata” (Pastor et al. 1984) by calculating biomass values for a range of 

diameters within bounds of raw data for each equation. These pseudodata were used to refi t new equations 

for 10 broad species groups (Table 3). See Jenkins et al. (2003) for details on species in each group.

When using allometric equations, note carefully the given maximum diameter used in the regression. 

The equations for trees that exceed the maximum diameters should be used only after considering 

the functional form of the equation. In particular, caution should be used for equations based on an 

exponential function beyond the range of diameters used to develop the equation, e.g., the equations 

in Table 3. Equations with more sigmoidal form, where biomass is constrained at large diameters, 

can be used with confi dence, even beyond the given maximum bounds (Brown et al. 1989). The 

general equations of Schroeder et al. (1997) and Brown and Schroeder (1999) with this sigmoidal/

constrained form are shown in Table 3. The estimated biomass per tree for a given diameter based on 

the exponential and sigmoidal models is compared in Figure 4. Up to about 75 cm in diameter, the 

models give the same estimated biomass per tree. Beyond this size, the exponential models show an 

increasingly larger estimated biomass while the sigmoidal model is more conservative. The maximum 

diameter used by the authors to create the exponential curve is 73 cm; this is approximately where the 

two curves diverge signifi cantly.

The equations of Jenkins et al. (2003) exhaustively cover U.S. tree fl ora, but they are dominated by 

western species in the softwood category. Western softwoods are unique in stature and thus do not 

adequately represent southern pines or eastern fi r-spruce species. By contrast, the equations of Brown 

and Schroeder (1999) for pines and fi r-spruce (Table 4) are calculated specifi cally for these species 

groups. In the following example, above-ground tree biomass is calculated for a plot using allometric 

regression equations.

0

5

10

15

20

25

0 15 30 45 60 75 90 105 120 135

Biomass (t/tree)

Diameter (cm)

exponential

sigmoidal

Figure 4.—Comparison of the 

relative treatment of large trees 

by equations with an exponential 

form, e.g., the hard maple/oak/

hickory/beech equation; Table 

3, and those with a limiting 

function, e.g., the eastern 

hardwoods equation; Table 4.
18

Calculating Carbon Stock and its Change in Above-ground Trees 

from Allometric Regression Equations

In this example, a single plot from an oak-hickory forest is examined. The plot consists of three 

nested subplots:

5-m radius for trees 2.5 to < 10 cm d.b.h. expansion factor: 198.9

14-m radius for trees ≥ 10 to < 50 cm d.b.h. expansion factor: 16.2

20-m radius for trees ≥ 50 cm d.b.h. expansion factor: 8.0

The allometric regression equation of Jenkins et al. (2003) is used for hard maple/oak/hickory/

beech to convert from d.b.h. to biomass.

The following shows measurements over two periods using permanent plots in which all trees 

are tagged. At time 2, note the ingrowth of trees too small to be measured at time 1 (trees 101 

and 102 in the small nest and 103 in the intermediate nest) and the outgrowth from one plot size 

and ingrowth into the next size when the max/min thresholds are passed (trees 004, 005 small to 

intermediate, tree 009 intermediate to large). That is, a tree’s growth during a given period can be 

split as follows: outgrowth is accounted for in the plot in which it is growing to the point where its 

diameter moves it to the larger nested plot, —i.e. where the tree’s remaining growth is accounted 

for as ingrowth for the large plot into which it moved.

•

•

•

In the figure above the three nested plots are shown at time 1 and time 2. The numbers/stars 

indicate the position of trees. At time 2, numbers in dark circles indicate trees that remained in the 

same size class as at time 1. Numbers in other circles indicate trees that have grown into the next 

class. Stars are trees that have exceeded the measurement minimum for that plot for the first time. 

The number indicates the tag number in the following table.

Time 1 

Time 2 

n

o

p

r

q

n

o

p

g

f

s

t

s

t

v

k

u

w

w

103 

101

102 
19

Time 1 Time 2

tag Nest D.b.h. Biomass tag Nest D.b.h. Biomass 

cm kg cm kg

001 Small 2.6 1.37 001 Small 3.1 2.10

002 Small 5.3 7.74 002 Small 5.8 9.64

003 Small 6.1 10.90 003 Small 6.8 14.20

004 Small 6.2 11.34 004 Intermediate 10 36.32

005 Small 8.1 21.74 005 Intermediate 12.1 57.76

006 Intermediate 10.2 38.11 006 Intermediate 10.9 44.79

007 Intermediate 12.3 60.11 007 Intermediate 13.3 72.71

008 Intermediate 38.6 972.67 008 DEAD DEAD 972.67

009 Intermediate 48.2 1670.20 009 Large 51 1916.30

010 Large 57.0 2512.15 010 Large 58 2620.79

101 Small 2.5 1.24

102 Small 2.8 1.64

103 Intermediate 10.3 39.03

Change in biomass stocks in each subplot = (Σ biom. increments of trees remaining in subplot size class) + (Σ biom. 

increments for outgrowth trees [= Σ max biomass for size class – biomass at time 1]) + (Σ biom. increments for ingrowth 

trees [= Σ biomass at time 2 – min biomass for size class]).

(The numbers in dark circles and squares indicate the tree tag numbers for each increment)

Small subplot = [n (2.1-1.37) + o (9.64-7.74) + (p14.20-10.9)] + 

 [q (36.32-11.34) + r (36.32-21.74)] + [ 101 (1.24-1.24) + 102 (1.64-1.24)]

 = (0.73 + 1.90 + 3.30) + (24.98 + 14.58) + (0 + 0.49) = 45.89 kg

Intermediate subplot = [s (44.79-38.11) + t (72.71-60.11)] + [v (1826.12-1670.20)]

 + [q (36.32-36.32) + r (57.76-36.32) + 103 (39.03-36.32)]

 = (6.68 + 12.60) + (155.92) + (0 + 21.44 + 2.71) = 199.35 kg

Large subplot = (w (2620.79-2512.15)) + ((0)) + (v (1916.30-1826.12))

 = (108.64) + (0) + (90.18) = 198.82 kg

Change in biomass = Σ Δbiomass in each subplot x expansion factor for that subplot

Small = 45.89 x 127.32 = 5,842.71 kg/ha

Int. = 199.35 x 16.24 = 3,237.44 kg/ha

Large = 198.82 x 7.96 = 1,582.13 kg/ha

Sum = 10,662.28 kg/ha = 10.7 t/ha or 5.35 t C/ha (biomass * 0.5) for the time interval
20

All allometric equations are estimating biomass and as such will have an uncertainty associated with 

them. The broader the equation in geographic scope and species included, the greater the uncertainty. 

The uncertainty is indicated by the r2

 value and can be included in the total uncertainty using the 

root mean square error.

To ensure that there is no systematic bias from the use of regional equations at a local scale, it is good 

practice to roughly estimate the volume of approximately 10 trees and apply a wood density to obtain 

biomass, which in turn, should be compared with biomass calculated using an allometric equation. 

Volume can be estimated by calculating the volume of the trunk of the tree (volume = 1/3π x h x 

[r1

2

 + r2

2

 + r1 x r2] where h is the height of the tree, r1 is the radius at the base of the tree, and r2 is 

the estimated radius at the top of the tree), and multiplying this by 1.2 to approximately account for 

branches and leaves. Biomass is determined by multiplying volume by density.

An alternative approach for estimating the biomass of forests is using the volume of the commercial 

component of the tree. This volume is estimated with standard forestry techniques. This method 

is commonly used with temporary plots. The estimated volume must be converted to total aboveground biomass, which includes the other tree components, e.g., branches, twigs, and leaves. The 

volume method is based on factors developed at the stand level for closed canopy forests. It cannot be 

used for estimating biomass of individual trees.

There are two potential methods. The fi rst calculates biomass directly from stand volume for different 

vegetation types in different regions. The second includes the additional step of calculating a biomass 

expansion factor (BEF). Neither method has a statistical advantage with respect to end results. In 

both methods, growing-stock volume (GSV) is defi ned as the net outside bark volume of growingstock trees at least 12.5 cm in d.b.h. to a minimum of 10 cm in diameter at treetop or the point at 

which the central stem breaks into limbs (defi nition used by FIA). Other defi nitions of volume could 

be used but the BEFs reported here could not be applied—new ones would have to be developed for 

local conditions.

Direct Method

Smith et al. (2003) used FIA data on growing-stock volume and the biomass equations of Jenkins et 

al. (2003) to develop regression equations of the form:

Above-ground biomass (t/ha) = F x (G + (1-exp(-GSV (m3

/ha) /H))

Where

GSV = growing-stock volume,

F, G, H = regression coeffi cients

Fifty-seven variants of this equation were developed for a variety of forest types across 10 regions in 

the continental United States. See Smith et al. (2003) for details on the coeffi cients for each of the 

variants of the equation (http://www.fs.fed.us/ne/newtown_square/publications/technical_reports/

index.shtml ). Schroeder et al. (1997) also used this approach for eastern U.S. hardwood and 

softwood forests, but developed equations of a different form based on a smaller subset of the FIA 

database.
21

Biomass Expansion Factor Method

This method is expressed as (Brown and Schroeder 1999):

Above-ground biomass (t/ha) = GSV (m3

/ha) x BEF (t/m3)

Where

GSV = growing-stock volume,

BEF = [total above-ground biomass of all living trees above a minimum d.b.h. of 2.5 cm]/[growingstock volume]

The BEF is signifi cantly related to the GSV for most forest types, generally starting high at low 

volumes and then declining at an exponential rate to a constant low value at high volumes. Thus, 

using one value for the BEF for all values of GSV is incorrect. This general relationship applies to 

many of the world’s forests, including tropical forests (Brown 1997) and forests in China (Fang et al. 

1998).

Schroeder et al. (1997) and Brown and Schroeder (1999) provided methods for calculating the BEF 

(t/m3

) for all hardwood and softwood forest types and regions across the Eastern United States.

Hardwoods: BEF = exp(1.912 – (0.344 x ln GSV))

 If GSV > 200 m3

/ha use a constant BEF of 1.0

Spruce-Fir: BEF = exp(1.771 - (0.339 x ln GSV))

 If GSV > 160 m3

/ha use a constant BEF of 1.0.

Pines: GSV < 10 m3

/ha BEF = 1.68 t/m3

 GSV 10 – 100 m3/ha BEF = 0.95 t/m3

 GSV > 100 m3/ha BEF = 0.81 t/m3

where GSV = growing stock volume in m3/ha 

In the following example, both the direct and the BEF methods are used to calculate biomass for 

two forest types. The two methods differ by less than 5 percent for both forest types and thus can be 

considered as giving equivalent results.
22

Calculating Biomass from Stand Volume Data

Example 1: An oak-hickory forest in Wisconsin with a growing-stock volume of 180 m3/ha.

A. Direct Method

Smith et al. (2003) listed the following coefficients for calculating above-ground biomass 

(AGB) of oak-hickory in the Northern Lake States:

 F = 307.5 G = 0.0748 H = 186.9

Therefore, AGB = F x (G + (1 – exp(-volume/H)))

 = 307.5 x (0.0748 + (1 – exp(-180/186.9)))

 = 213.1 t/ha

B. BEF Method

As growing-stock volume is < 200 m3

/ha, we must calculate the BEF. Oak-hickory is a 

hardwood forest type.

Therefore, BEF = exp(1.912 – (0.344 x ln GSV))

 = exp(1.912 – (0.344 x ln(180)))

 = 1.134

Therefore, AGB = GSV x BEF

 = 180 x 1.134

 = 204.1 t/ha

Example 2: A loblolly pine plantation in Georgia with a growing stock volume of 120 m3/ha.

A. Direct Method

Smith et al. (2003) listed the following coefficients for calculating above-ground biomass 

(AGB) of planted pine in the Southeastern States:

 F = 187.3 G = 0.0662 H = 184.9

Therefore AGB = F x (G + (1 – exp(-volume/H)))

 = 187.3 x (0.0662 + (1 – exp(-120/184.9)))

 = 101.8 t/ha

B. BEF Method

Growing stock volume is > 100 m3

/ha and the forest type is pine the BEF is 0.81 t/m3.

Therefore, AGB = GSV x BEF

 = 120 x 0.81

 = 97.2 t/ha
23

Nontree Vegetation

Herbaceous plants in the forest understory can be measured by simple harvesting techniques in small 

subplots (about two per tree plot are recommended) for each sample plot. A small frame (circular or 

square), usually encompassing about 0.25 m2

, can be used. The material inside the frame is cut to 

ground level, pooled by plot to give a composite sample, and weighed. Well-mixed subsamples are 

oven-dried to determine dry-to-wet mass ratios. These ratios are used to convert the entire sample to 

oven-dry mass.

For shrubs and other large nontree vegetation, it is desirable to measure the biomass by destructive 

harvesting techniques. A small subplot (0.25-4 m2

 depending on the size of the vegetation) is 

established and all the shrub vegetation is harvested and weighed

If the shrubs are large, an alternative approach is to develop biomass regression equations for local 

shrubs based on variables such as crown area and height or diameter at base of plant, or another 

relevant variable, e.g., number of stems in multistemmed shrubs. The equations would then be based 

on regressions of biomass of the shrub versus a logical combination of the independent variables. This 

approach is more ambitious and may not be practical for the average inventory.

Below-ground Biomass

Measuring above-ground biomass is relatively established and simple. Measuring below-ground 

biomass (coarse and fi ne roots) is time consuming so it is more effi cient to apply a regression model 

to estimate below-ground biomass (living and dead) as a function of above-ground biomass. The 

following regression models can be used to estimate below-ground biomass (Cairns et al. 1997):

Boreal:

BGB = exp(-1.0587 + 0.8836 x ln ABD + 0.1874)

Temperate:

BGB = exp(-1.0587 + 0.8836 x ln AGB + 0.2840)

Tropical:

BGB = exp(-1.0587 + 0.8836 x ln AGB)

where BGB = below-ground biomass density in tons/hectare (t/ha) and AGB = above-ground biomass 

density (t/ha)

n = 151; r2

 = 0.84

Estimating Change in Below-ground Biomass

The correct use of these equations is important when calculating the increase in carbon in belowground biomass. For tagged trees in permanent plots, it is not possible to simply calculate the total 

above-ground biomass at time 1 and time 2, apply the equations, and then divide by the number 

of years. This approach does not account for ingrowth or mortality trees. Instead, change in belowground biomass carbon stocks should be calculated by the following method:
24

Calculate above-ground biomass at time 1 using allometric equations and appropriate 

expansion factors.

Calculate increment of biomass accumulation above ground between time 1 and time 2 and 

add to time 1 to estimate the biomass stock at time 2.

Apply the appropriate equation to estimate below-ground biomass at each time interval.

Calculate the annual change in stock of biomass below ground as (time 2 below ground 

- time 1 below ground)/number of years).

Dead Organic Matter

Forest Floor

The forest fl oor (Table 2) can be sampled directly by simple harvesting techniques in small subplots 

within each permanent plot (Fig. 3). A circular or square frame, usually encompassing an area of 

about 0.25 m2

, can be used. If the forest fl oor is particularly deep as often is the case in western U.S. 

forests, a smaller frame (0.06 m2

) can be used. If herbaceous material is collected, the forest fl oor 

can be collected from the same frames at the same locations. All live vegetation from the sample 

area is removed carefully with a pair of clippers. Living mosses should be clipped at the base of the 

green, photosynthetic material. The forest fl oor along the inner surface of the frame is cut through 

to separate it from the frame and surrounding soil. The entire volume of the forest fl oor must be 

removed carefully from within the confi nes of the sampling frame down to the top of the mineral soil 

layer (to distinguish the bottom of the forest fl oor from the top of the mineral soil, see section on soil 

organic carbon). All litter within the frame is collected and all samples from the subplots are pooled 

and weighed. A well-mixed subsample is then collected and placed in a marked bag. The subsample is 

used to determine oven-dry-to-wet mass ratios to convert the total wet mass to oven-dry mass. Forestfl oor samples can be sent to a professional laboratory for drying and weighing.

For the forest fl oor, amounts of biomass per unit area are given by:

(forest-fl oor oven-dry weight (g) / sampling frame area (cm2

)) x 100

Where multiplying by 100 converts the units to metric t/ha. Multiplying by 0.5 gives the amount of 

carbon.

Dead Wood

Dead wood, both standing and on the ground, correlates poorly with any index of stand structure 

(Harmon et al. 1993). Methods developed for measuring biomass of dead wood and tested in many 

forest types generally require no more effort than measuring live trees (Harmon and Sexton 1996; 

Delaney et al. 1998).

A time-effi cient method for sampling down dead wood is the line intersect. At least 100 m length 

of line per plot must be used (Harmon and Sexton 1996). Placing two 50-m sections of line at right 

angles across the plot center also is a time-effi cient approach, though the line can be established as 

readily as one 100-m length through the plot center. To allow remeasurement of the same “dead 

wood plot”, it is important to accurately record where the line was placed. The diameters of all pieces 

of wood that intersect the line are measured and the density class noted. A minimum diameter for 

1.

2.

3.

4.
25

measurement must be defi ned—typically 10 cm (Harmon and Sexton 1996). Each piece of dead 

wood is assigned one of several density classes. The volume per unit area calculated for each density 

class is: 

Volume (m3

/ha) =π

2

 * [(d12 + d22.......dn2)/8L]

Where d1, d2, dn = diameter (cm) of each of the n pieces intersecting the line, and L = the length of 

the line (100 m recommended; Harmon and Sexton 1996).

Density measurements. Three density classes—sound, intermediate, and rotten—are suffi cient. 

Common practice in the fi eld is to strike the wood with a strong sharp blade. If the blade bounces 

off, it is sound, if it enters slightly, it is intermediate, if the wood falls apart, it is rotten. Samples of 

dead wood in each class are then collected to determine their density. Mass of dead wood is then the 

product of volume per density class (from previous equation) and the wood density for that class. 

Thus, a key step in this method is classifying the dead wood into its correct class and then sampling 

a suffi cient number of logs in each class to represent the wood densities present. It is advisable 

to sample at least 10 logs for each density class. In forests with unique plant forms, e.g., early 

successional species and palms as in tropical forests, it is advisable to treat these as separate groups and 

sample them in the same way.

The simplest method for estimating the density of dead wood is to obtain a value for the proportion 

of undecomposed density that each density classes represents. Undecomposed wood densities are 

widely available in the literature (e.g., U.S. Forest Products Laboratory 1974). Biomass is calculated 

by multiplying the initial density value by the decomposed proportion by the volume. Heath and 

Chojnacky (2001) calculated the proportions as 90 percent (sound), 70 percent (intermediate), and 

40 percent (rotten) for forests in the Northeast. These proportions can be used, but several samples 

must be collected to test their validity.

For forest areas with few species and where the rate of decomposition of wood is well known for a 

given species or forest type, simple decomposition models can be developed locally for estimating 

the density of the dead wood at different stages of decomposition (Beets et al. 1999). The volume of 

wood still must be estimated, but density can be estimated based on the model of decomposition. In 

the following example, the biomass density of dead wood is calculated.
26

Standing dead wood can be measured as part of the tree inventory. Standing dead trees should be 

measured by the same criteria used for live trees. However, measurements that are taken and data that 

are recorded differ slightly from those for live trees. For example, if the standing dead tree contains 

branches and twigs and resembles a live tree (except for leaves), this would be indicated on fi elddata records. From the measurement of its d.b.h., the amount of biomass can be estimated using 

the appropriate biomass regression equation and subtracting the biomass of leaves (2 to 3 percent of 

above-ground biomass). However, a dead tree can contain only small and large branches, or only large 

branches, or no branches. These conditions must be recorded in the fi eld measurements. Branches 

must be classifi ed in proportion to the size of the standing dead tree so that the total biomass can be 

reduced accordingly to account for less of the dead tree remaining. When a tree has no branches and 

is only the bole, its volume can be estimated from measurements of its basal diameter and height and 

an estimate of its top diameter. The tree’s biomass can be estimated using the appropriate density 

class. In the following examples, the biomass of standing dead wood is calculated.

Calculating Biomass Density of Dead Wood

In this example, dead wood is sampled along a 100-m line (line-intersect method) 

to determine the biomass stock. Diameters and density classes are recorded and a 

subsample collected to determine density in each of the three density classes (sound, 

intermediate, and rotten). The following numbers represent the hypothetical results:

13.8 cm: sound

10.7 cm: sound

18.2 cm: sound

10.2 cm: intermediate

11.9 cm: intermediate

56.0 cm: rotten

Densities of subsamples: Sound: 0.43 t/m3

 Intermediate: 0.34 t/m3

 Rotten: 0.19 t/m3

Volume of sound wood: π 2 x [d12 + d22.....dn2/8L]

 π 2

 x [13.82 + 10.72 + 18.22/800]

 7.85 m3

/ha

Volume of intermediate wood: π 2 x [10.22

 + 11.92/800]

 3.03 m3

/ha

Volume of rotten wood: π 2 x [56.02

/800]

 38.7 m3

/ha

Biomass stock = (7.85 x 0.43) + (3.03 + 0.34) + (38.7 x 0.19) = 11.8 t/ha

Carbon stock = 11.8 * 0.5 = 5.9 t C/ha
27

Soil Organic Carbon

To obtain an accurate inventory of organic carbon stocks in the mineral soil1 or organic soil,2 three 

types of variables must be measured: soil depth, soil bulk density (calculated from the oven-dry 

weight of soil from a known volume of sampled material), and concentrations of organic carbon 

within the sample. General guidance on sampling and analyzing forest and agricultural soils for 

estimating carbon stocks are found in Lal et al. (2001) and Robertson et al. (1999).

Calculating Biomass of Standing Dead Wood

1. A tree with no leaves in a mixed hardwood forest with a d.b.h. of 25 cm in sound 

density class

Use the equation of Jenkins et al. (2003) for mixed hardwood forests with a 3 percent 

deduction due to the absence of leaves.

y = exp (–2.4800 + 2.4835 x ln(25)) = 248.16 kg x 0.97 = 240.72 kg

As this is the only dead tree measured in a 14-m plot, the mass is multiplied by an expansion 

factor of 16.24 plots/ha, giving a biomass of 3.91 t/ha (1.96 t C/ha).

2. A sugar maple tree with missing branches (estimated as 15 percent of above-ground 

biomass). The d.b.h. is 51 cm and the tree is sound.

Use the equation of Jenkins et al. (2003) for hard maple/oak/hickory/beech with a 15 percent 

deduction for the lack of biomass.

y = exp (–2.0127 + 2.4342 x ln(51)) = 1,916.3 * 0.85 = 1,628.9 kg

As this is the only dead tree measured in a 20-m plot, the mass is multiplied by an expansion 

factor of 7.96 plots/ha, giving a biomass density of 12.97 t/ha (6.49 t C/ha).

3. A bole with no branches, the height is 15 m, basal diameter is 40 cm, and top diameter 

is 25 cm. Analysis of a cored sample reveals a wood density of 0.49 g/cm3

.

The volume of a truncated cone = 1/3π x h x (r1

2

 + r2

2

 + r1 x r2)

 = 1/3π x 1500 x (202

 + 12.52 + 20 x 12.5)

Biomass density = 1,266,455 cm3

 x 0.49 g/cm3

 = 620,563 g = 0.62 tons 

As this is the only dead tree measured in a 14-m plot the mass is multiplied by an expansion 

factor of 16.24 plots/ha, giving a biomass density of 10.08 t/ha (5.04 t C/ha).

1

Mineral soil: soil consisting predominantly of and having its properties determined predominantly by mineral 

matter. Usually contains less than 200 g/kg organic carbon (less than 120-180 g/kg if saturated with water), but 

may contain an organic surface layer up to 30 cm thick.

2

Organic soil: soil material that is saturated with water and has 174 or more g/kg organic carbon if the 

mineral fraction has 500 g/kg or more clay, 116 g/kg organic carbon if the mineral fraction has no clay, or has 

proportional intermediate contents. If these materials never were saturated with water, they would have 203 or 

more g/kg organic carbon. Defi nitions from Technical Guidelines for Voluntary Reporting of Greenhouse Gases 

1605(b) Program: http://www.pi.energy.gov/pdf/library/TechnicalGuidelines_March2006.pdf
28

Tracking changes in soil carbon over time requires that the same equivalent mass of soil is measured 

from one monitoring event to another. Sampling to a fi xed depth (equal volumes) can underestimate 

carbon gains via forestation. As the bulk density generally decreases over time, the same sampled 

volume contains less of the original soil-mass equivalent. Therefore, rates of accrual estimated from 

sampling to a fi xed depth should be considered conservative estimates of soil-carbon accretion.

Where there are no additions of new carbon at greater depth, sampling to greater depth reduces the 

detectability of change by diluting additions that occur in the upper layers of the soil column. For 

example, after monitoring 35 years of forest regrowth of loblolly pine in the Calhoun Experimental 

Forest in South Carolina, Richter et al. (1999) found no signifi cant increase in soil carbon below 7.5 

cm. Likewise, in contrasting formerly cultivated and never tilled sites under longleaf pine, Markewitz 

et al. (2002) found the most notable carbon difference in the upper 10 cm of soil. As hardwood leaf 

litter is likely to break down and become incorporated into the soil more quickly, and hardwood trees 

typically produce more roots than pines, inputs of soil carbon are expected to a greater depth—to 40 

or 50 centimeters (MacDonald 1999; unpublished data) (Fig. 5).

The forest fl oor is sampled as described earlier, i.e., exposing the top of the mineral or organic soil. 

For some soils, it is diffi cult to distinguish between the bottom of the forest fl oor and the top of the 

mineral soil. In such cases, one can refer to standard soil sampling methods, e.g., in Robertson et al. 

(1999), for tips on how to distinguish the top of mineral soil. Coring tools and liners are available to 

hold the soil cores of varying lengths, but it often is impractical to use a manually operated, impactdriven, soil-coring tool below about 30 cm. Simple soil corers are effective in many soils, particularly 

in the deeper soils of the central and southern regions of the United States. Shallow soil pits to about 

30 cm also work well and are cost effective. The impact-driven soil coring tool is impractical for 

collecting deep cores, nor is the use of a truck or trailer-mounted, hydraulically driven soil coring tool 

practical or cost effective in most forest areas.

Composite sampling is effective in reducing intersample variability. This is done by aggregating a 

predetermined number of samples (often four) from each collection site in the fi eld, from which 

one sample is derived for analysis. The resulting composite sample captures more of the range of 

intermicrosite variability in soil carbon.

Figure 5.—Mineral soil carbon, 

forest = 50- to 70-year-old 

bottomland hardwoods on 

clay soil, bars = 95 percent 

confi dence intervals.

0

20

40

60

80

100

120

140

0-10 0-20 0-30 0-40 0-50

Depth of Sample (cm)

t C/ha

agriculture

(n=8)

forest (n=8)
29

Sampling Mineral Soil

Concentrations of soil chemicals generally are measured in air-dried soils, while bulk density must 

be measured in oven-dried soils (to 105 oC). It often is easier to take separate sets of cores when 

determining bulk density and carbon because the sample preparation differs for each. Fewer cores 

may be required to accurately estimate bulk density, which generally is less variable than soil-chemical 

properties.

Using the core sampler method, mineral soil samples are collected from within the area of the 

sampling frame after the forest fl oor has been removed. Because the carbon concentration of forestfl oor materials is much higher than that of the mineral soil, including even a small amount of surface 

organic material can result in a serious overestimation of mineral-soil carbon stocks.

Once the soil corer has been inserted into the soil to the desired depth, it is removed from the ground 

by pulling upward in a smooth vertical motion. The top and bottom (or bottom only depending 

on the coring tool used) of the core should be trimmed even with the rims. When taking cores 

for measurements of bulk density, care should be taken to avoid any loss of soil from the cores; 

if any material is lost, a second sample is needed. All material in the corer should be placed into 

appropriately labeled sample bags.

The excavation method entails digging a pit that is wide enough to collect the soil to the depth 

desired. A hand shovel can be used to collect material. The volume of soil from the sides of the pit 

must approximately equal the volume of a soil corer. It is important to collect material from the entire 

depth to avoid biasing the sample. Uniform rings can be used to sample the sides of the pit for bulk 

density, taking care not to compress the soil.

As with forest-fl oor samples, soil samples can also be sent to a professional lab for analysis. It is 

important that the selected laboratory follows standard procedures with respect to sample preparation 

(sieving at 2-mm mesh, grinding, etc.), drying temperatures, method for carbon analysis (dry 

combustion) and machine calibration and duplicate samples.

In determining bulk density, samples are dried in an oven at 105 o

C for a minimum of 48 hr. If the 

soil contains coarse, rocky fragments, the fragments should be retained and weighed and the weights 

recorded.

In determining soil carbon, the material is sieved (2-mm sieve) and then mixed thoroughly. In the 

dry combustion method, a controlled-temperature furnace, e.g., LECO CHN-2000 or equivalent, is 

used3

. This method is recommended for determining total carbon in the soil (Nelson and Sommers 

1996). Where carbonate minerals may be present, a dry-combustion method that includes use 

of a LECO RC-412 multicarbon analyzer is preferred (Amacher et al. 2003). Both organic and 

inorganic forms of carbon can be measured on the same mineral soil sample in one analytical run. An 

alternative is to remove any carbonates through acid treatment beforehand.

3

The use of trade, fi rm, or corporation names in this report is for the information and convenience of the 

reader. Such use does not constitute an offi cial endorsement or approval by the U.S. Department of Agriculture 

or Forest Service of any product or service to the exclusion of others that may be suitable.
30

As an alternative to the multicarbon analyzer, the dichromate oxidation method with heating, is 

acceptable for measuring organic carbon (Nelson and Sommers 1996). The pressure calcimeter 

method is effective in determining soil carbonates (Sherrod et al. 2002). The classic Walkley-Black 

method is unacceptable for determining organic carbon in soil due to incomplete wet combustion 

and other inaccuracies.

The bulk density of the mineral soil core is calculated by:

CV (RF / PD)

b ODW

−

ρ =

Where 

b S = Bulk density of the < 2mm fraction, (g/cm3

)

ODW = Oven-dry mass of fi ne fraction (<2 mm) in g

CV = Core volume (cm3

)

RF = Mass of coarse fragments (> 2 mm) in g

PD = Density of rock fragments (g/cm3

). This often is given as 2.65 g/cm3, though the 

actual value can be determined by submerging a known mass of coarse fragments in a known volume 

of water; the displacement gives an estimate of rock volume, which can be used to calculate density.

Data on bulk density and carbon concentrations are used to compute amounts of carbon per unit 

area. 

For the mineral soil, amounts of carbon per unit area are given by:

3 C t ha soil bulk density g cm soil depth cm C ( / ) [( , ( / ) ( ) % ) ] 100 = × ××

In this equation %C must be expressed as a decimal fraction; for example, 2.2 %C is expressed as 

0.022. In the following example, the mass of soil carbon per unit area is calculated.
31

Estimating Net Change and Uncertainty

The type of activity infl uences how each carbon-stock component (Table 1) is integrated into an 

estimate of the net change in carbon stock at each monitoring interval. The activities listed in Table 

2 can be grouped into two classes. The fi rst class includes those that typically would be implemented 

on nonforested lands (afforestation, forest restoration, agroforestry, short-rotation biomass energy 

plantations, and mine-land reclamations). The other class includes activities implemented on existing 

forested land (forest management and forest preservation). This grouping has implications with 

respect to how measurements and estimations are integrated to obtain an estimate of the net change 

in total carbon stocks in the time interval.

Calculating Mass of Soil Carbon per Unit Area

Mass of carbon per unit volume is calculated by multiplying carbon concentration (reported 

as percent mass) times bulk density (g/cm3

). Bulk density equals the oven-dry weight of 

the soil core divided by the core volume. For example, a core of volume 94.2 cm3

 (1-cm 

radius x 30-cm length cylinder) with a dry weight 144.06 yields a bulk density of 1.53 

g/cm3

. Referencing the sample depth, mass per unit area is calculated, which represents a 

corresponding volume of soil. Thus, 

 Volume/ha = 100 m x 100 m x 0.3 m (sample depth) = 3 x 109

 cm3 = 3,000 m3

 Mass/ha = 3 x 109 cm3 x 1.53 g/cm3 (bulk density) = 4.586 x 109 g = 4,586 tons 

A portion of this volume is occupied by tree roots, which are accounted for separately. 

However, this fraction tends to be insignificant and is ignored here.

From within the same plot, the corresponding aggregate core analyzed for carbon 

concentration yields 0.8 percent mass carbon. Mass per unit area, 4,586 t/ha, calculated 

previously, multiplied by 0.8 percent yields equivalent 36.7 tons of soil carbon/ha. A series 

of sample calculations of mass soil carbon is tabulated as follows:

Sample weight Volume Bulk density Volume/ha Mass/ha Carbon conc. Mass soil C

g cm3 g/cm3 cm3 tons % mass t/ha

144.06 94.2 1.53 3.E+09 4586 0.80 36.7

126.48 94.2 1.34 3.E+09 4026 0.82 33.0

146.95 94.2 1.56 3.E+09 4678 0.72 33.7

132.20 94.2 1.40 3.E+09 4208 0.90 37.9

147.39 94.2 1.56 3.E+09 4692 0.53 24.9

131.96 94.2 1.40 3.E+09 4200 1.39 58.4

115.95 94.2 1.23 3.E+09 3691 1.22 45.0

133.96 94.2 1.42 3.E+09 4264 1.09 46.5

115.59 94.2 1.23 3.E+09 3679 1.20 44.2

139.03 94.2 1.48 3.E+09 4425 0.76 33.6

Mean 39.4

95% CI 6.7
32

Activities on Nonforested Lands

All activities on nonforested lands typically begin on land that initially has low carbon stocks in 

vegetation (generally less than 2 tons/ha) and variable amounts in the soil. In each case, a sampling 

regime would be implemented that monitors each carbon-stock component. The task is then 

combining all the estimates of the carbon stock for each component to obtain an estimate of the net 

change in total carbon.

Using permanent plots, the carbon stock for living and standing dead trees above and below ground 

and downed dead wood of individual plots can be monitored through time. Therefore, the change in 

carbon stocks can be estimated directly at the plot level. In this case, the change in carbon stocks for 

the different components should be summed within plots to give a per-plot change in carbon stock 

(t C/ha). Plot-level results are then averaged to obtain the mean and 95-percent confi dence intervals. 

The mean change in carbon stocks per unit area is then multiplied by the area of the project activity 

to produce an estimate of the total change in carbon. If stratifi cation is used, this approach is repeated 

for each stratum and then all strata are summed to estimate the total. This total is converted to t CO2

equivalent by multiplying by 3.67 (the value of 3.67 refl ects the ratio of molecular weights between 

carbon [12] and carbon dioxide [44]).

Soils, forest-fl oor and nontree vegetation are calculated separately as the statistics, number of 

sampling plots, and even the sampling interval may differ from the other components. The results 

from these measurements are analyzed to produce an estimate of the mean and the 95-percent 

confi dence interval. This estimate is added to create a system level mean and 95-percent confi dence 

interval. The total confi dence interval is calculated as:

Total 95% CI = √( [95%CIveg]

2

 + [95%CIsoil]

2

 + [95%CIforest fl oor]

2

 +[95%CInon-tree vegetation]

2

 )

Where

[95%CIveg] = 95-percent confi dence interval for vegetation, [95%CIsoil] = 95-percent confi dence 

interval for soil, etc.

If part of the afforested area is harvested, the sampling plots theoretically would monitor the change 

in live and dead biomass, but they would not monitor the amount going into wood products. As 

mentioned previously, wood products must be considered because the decrease in live biomass from 

harvesting does not mean that the equivalent amount of carbon went into the atmosphere—some of 

it could go into long-lived wood products. To correctly estimate the effects of harvesting on the net 

change in carbon stocks, the amount of wood biomass going into long-term wood products must be 

determined. This quantity and its estimated 95-percent confi dence interval would then be added to 

the total change. In the following example, the integration of all the components from permanent 

plots is given where the initial carbon stocks are of former cropland.
33

If temporary plots are used to measure changes in carbon stocks, the mean and 95-percent confi dence 

interval of the carbon stock in each component across all plots is calculated at time 1 and time 2. The 

total carbon stock at each time interval is then estimated by summing the means for each component 

and the total error is estimated as:

Total 95% CI = √( [95%CIc1]

2

 + [95%CIc2]

2

 +.......... [95%CIcn]

2

 )

Where

[95%CIc1] = 95-percent confi dence interval for component 1, e.g., above-ground biomass, 

component 2, and so on for all components measured in the plots.

Calculating Net Change for the System

In this example of afforestation activity on 500 ha of former cropland, the baseline for 

carbon stocks is cropland with an average carbon stock in vegetation of 0.9 t C/ha. The 

following shows the change in carbon stock between years 1 and 10.

Plot 

number

 Change in carbon stocks 

SUM Living biomass Dead organic matter 

Above-ground: trees Below-ground Dead wood

t C/ha t C/ha t C/ha t C/ha

Plot 1 12.1 2.4 0.1 14.6

Plot 2 11.5 2.3 0.0 13.8

.... ... ... ... ...

.... ... ... ... ...

Plot 31 12.6 2.5 0.1 15.1

Plot 32 10.9 2.2 0.1 13.2

Mean 13.9

95% CI 2.4

+ Nontree Vegetation 1.8

N-T V 95% CI 0.1

+ Forest Floor 0.2

F.F. 95% CI 0.1

 + Soil 0.5

Soil 95% CI 0.1

- Baseline Stock on Cropland 0.9

Baseline 95% CI 0.1

NET Change in Carbon Stock 15.5
34

The change in carbon stock is calculated by subtracting the mean carbon stock at time 2 from that at 

time 1. The confi dence interval is calculated as:

Total 95% CI = √( [95%CItime1]

2

 + [95%CItime2]

2

 )

Where

[95%CItime1] = 95-percent confi dence interval for time 1 and [95%CItime2] = 95-percent confi dence 

interval for time 2.

The net change is calculated similarly for permanent plots by subtracting the initial carbon stocks 

(nearly zero if afforestation occurs on former cropland) from the carbon stocks that accrued at the 

time of measurement. Finally, the total carbon-stock change per unit area is multiplied by the total 

area to produce the estimated total change in carbon and confi dence interval for the area.

In this section we have focused on an activity with a single stratum. If the activity contained 

multiple strata, each would be calculated separately as described. Once the area-based carbon dioxide 

equivalents and confi dence levels are calculated for each stratum, the values can be combined to 

obtain total carbon stock or stock change for all carbon pools in all strata. The new confi dence 

interval for the combined strata would be estimated as:

Total 95% CI = √( [95%CIs1]

2

 + [95%CIs2]

2

 +.......... [95%CIsn]

2

 )

Where

[95%CIs1] = 95-percent confi dence interval for strata 1, strata 2, and so on for all strata measured in 

the project).

The methods presented here for calculating uncertainty in reported values are known as “error 

propagation.” Error propagation is simple and robust. However, these methods should be used with 

caution where there are:

Strong correlations between datasets (there is a signifi cant covariance), or

Uncertainties exceed 100 percent

In such cases it is statistically more appropriate to use a Monte Carlo analysis .

4

 In practice the 

difference in results attained through the two methods are small unless correlations and/or 

uncertainties are very high.

Guidance on analyzing uncertainty and propagating errors is found in Annex 1 of the “IPCC Good 

Practice Guidance and Uncertainty Management in National Greenhouse Gas Inventories” (2000; 

http://www.ipcc-nggip.iges.or.jp/public/gp/english/).

•

•

4

The principle of Monte Carlo analyses is to perform the summing of uncertainties many times each time with 

the uncertain stocks or increments chosen randomly by Monte Carlo software from within the distribution 

of uncertainties input initially by the user. Examples of Monte Carlo software include Simetar, @Risk, and 

Crystal Ball (www.simetar.com, www.palisade.com/html/risk.asp, www.crystalball.com).
35

Activities on Forested Lands

Forest management consists of alternating periods of harvest and regrowth such that carbon stocks 

in forest biomass vary over time (Fig. 6). Changes in management practices also can increase carbon 

storage by changing the timing or intensity of harvest, reducing damage to the residual stand through 

more effi cient logging practices, switching from clearcutting to selective harvesting, or by creating or 

widening riparian buffer zones.

Initially, it is important to consider which carbon pools are important in forest management. Live 

vegetation, dead wood, and wood products are obvious examples. With the examples in Figure 6, 

the amount of dead wood could increase over time with a subsequent harvest. The amount of dead 

wood that accumulates through time is a function of the amount of slash left behind and the rate of 

decomposition of that slash. The larger the amount of slash and the slower the rate of decomposition, 

the larger the amount that accumulates. For preservation of mature forests, the dead-wood carbon 

stock can be highly signifi cant. Measuring soil organic carbon is marginally benefi cial at best in 

forest management. Soil carbon may be reduced slightly immediately following harvest (Laiho et al. 

2002, Carter et al. 2002), though any losses will be regained as the succeeding forest regrows with 

accompanying soil organic-matter inputs (Carter et al. 2002). The relative difference in postharvest 

Figure 6.—Carbon stocks associated with (top) complete harvest of forest 

followed by 25-year even-age management and (bottom) selective harvest of 

a similar forest.
36

effects on soil carbon among different harvest intensities is slight and often undetectable (Carter et al. 

2002). As a result, additional soil sampling on projects on forested lands is not recommended.

An important additional consideration is storage of carbon in long-term wood products. Timber 

extracted from the forest is not immediately emitted to the atmosphere but is stored in wood 

products, often for many years. Guidance on wood products is included in the appendix to the 

technical guidelines for the 1605(b) process and in a publication by Smith et al. (2006).

Differences in the effects of clearcutting versus selective harvests on forest-ecosystem carbon stocks 

(Figure 6) affects the accuracy and precision of measuring and monitoring changes over time. There 

are two alternative methodologies for monitoring changes in carbon stocks: direct and indirect 

measurement.

Direct Measurement

Where the activity includes clearcutting, the simplest approach is to install sample plots and monitor 

the changes in carbon stocks as described previously. As shown in Figure 6, there will be periods 

of carbon accumulation and a period of carbon loss resulting in positive and negative changes in 

carbon stocks. With a well designed sampling regime, remeasurements will reveal shifts of preharvest 

living biomass to the dead wood pool (logging slash and collateral mortality) and subsequent 

decomposition over time, as well as regrowth, after harvest. Mean total carbon stocks and 95-percent 

confi dence intervals are calculated in the same way as for activities on nonforested lands.

Indirect Measurement

For selective cutting where harvest intensity per hectare is low, the required number of plots to 

capture the variation in harvested areas could be so large as to make measurement neither practical 

nor cost effective. In this case, it is possible to use targeted measurements plus the statistics of 

the relevant logging activity. It is more appropriate to measure the change in live biomass due to 

harvesting directly. The change in live biomass caused by logging is a result of the extraction of 

timber and damage to residual trees. Calculating carbon gains and losses by indirect measurement 

typically requires information on:

Total volume removed.

Area damaged (converted from living to dead biomass) per cubic meter removed.

Amount of slash and damage to residual stand per volume removed.

Rate of regrowth in the harvested areas relative to nonharvested areas (relative rate of carbon 

accumulation).

Decomposition rates of slash.

The change in carbon stocks using this approach is calculated as:

Δ live biomass C + Δ dead biomass C

•

•

•

•

•
37

Where 

Δ is the change in carbon of live biomass and dead biomass caused by timber harvesting. Estimates of 

each term can be made annually or over longer periods.

The change in live biomass caused by logging is a result of the extraction of timber, slash from the 

harvested tree, and damage to residual trees, all of which will reduce live biomass or represent a 

negative quantity after harvest.

Δ live biomass C = ([biomass C from logging damage + C in timber extracted])

An additional component of the analysis is the relative rate of carbon accumulation during regrowth 

that applies to areas affected by timber extraction. This could be faster or slower in a logged than in 

an unlogged area. A stand is thinned to enhance the growth rate of the desired trees. However, from 

a stand perspective, the rate of carbon accumulation can be slower, faster, or the same because trees 

have been removed and damaged in the logged gaps. The default assumption is equal growth rates 

between logged and unlogged areas. For example, in a mixed tropical forest in Bolivia, measurements 

of nearly 100 paired logged and unlogged plots over 4 years showed no signifi cant difference in 

carbon accumulation rates between the two sets of plots (unpublished data).

In estimating the amount of damaged and dead biomass produced in the logging operations, fi eld 

plots are established around a harvested tree(s). The plot usually has dimensions equivalent to the gap 

of the harvested tree, which can be estimated by GPS. Data are collected on the initial diameter and 

height of the harvested tree, and the amount of volume removed is measured, as is the diameter of all 

trees that were severely damaged (snapped or uprooted) and presumed dead. Measurements in 100 

logged tree gaps ensure adequate precision. The measurements are then combined to produce a ratio 

of total amount of live biomass converted to dead biomass per unit mass of timber extracted.

The carbon in extracted timber enters wood products where it can remain fi xed for a prolonged 

period. Guidance is available for tracking carbon in wood products (Smith et al. 2006).

Δ dead biomass C = (dead biomass from logging damage and slash times the decomposition rate)

The slash and damaged wood are assumed to enter the dead wood pool, where they begin to 

decompose. Each year, dead wood is added from harvesting, though some is lost each year due to 

decomposition and resulting carbon emissions. Decomposition of dead wood is modeled as a simple 

exponential function based on mass of dead wood and a decomposition coeffi cient (proportion 

decomposed per year). Decomposition coeffi cients for major U.S. forest types are given in Table 

5. The change in carbon stocks of the slash and damaged wood can be measured in the fi eld, but 

this tends to be time consuming and costly. Mean total changes in carbon stocks and 95-percent 

confi dence intervals can be calculated in the same way as described earlier.
38

Table 5.—Decomposition rate constants and half lives for down dead wood, 

by region and forest type

Region Forest type Decomposition 

ratea Half life

Year -1 Years

Pacifi c Northwest Douglas-fi r 0.022 31.5

Spruce-fi r 0.028 24.8

Hemlock-spruce 0.031 22.4

Lodgepole pine 0.041 16.9

Hardwoods 0.082 8.5

Ponderosa pine 0.017 40.8

Redwoods 0.014 49.5

Rocky Mountains Douglas-fi r 0.022 31.5

Ponderosa pine 0.017 40.8

Spruce-fi r 0.014 49.5

Larch 0.022 31.5

Lodgepole pine 0.023 30.1

South Oak-hickory 0.075 9.2

Oak-pine 0.060 11.6

Bottomland hardwood 0.112 6.2

Natural pine 0.056 12.4

Planted pine 0.056 12.4

Northeast White/red pine 0.042 16.5

Spruce-fi r 0.042 16.5

Oak-hickory 0.075 9.2

Maple-beech-birch 0.062 11.2

North Central White/red pine 0.042 16.5

Spruce-fi r 0.042 16.5

Maple-beech 0.082 8.5

Aspen-birch 0.082 8.5

Bottomland hardwood 0.112 6.2

Oak-hickory 0.060 11.6

a

From Turner et al. 1993.

QUALITY ASSURANCE AND QUALITY CONTROL (QA/QC)

Measuring and monitoring requires provisions for quality assurance (QA) and quality control (QC) 

to be implemented via a QA/QC plan to ensure that the reported carbon units are reliable and meet 

minimum measurement standards. The plan should become part of the documentation and include 

procedures for: (1) collecting reliable fi eld measurements; (2) verifying laboratory procedures; (3) 

verifying data entry and analysis techniques; and (4) data maintenance and archiving.

QA/QC for Field Measurements

Collecting reliable fi eld measurements is an important step in the QA plan. Those responsible for the 

carbon measurement should be fully trained in all aspects of fi eld data collection and data analyses. It 

is wise to prepare Standard Operating Procedures (SOP) for each step of fi eld carbon measurements. 

These SOPs should detail all phases of the fi eld measurements so that the measurements can be 
39

repeated. A document should be produced and fi led with the project documents verifying that all 

QA/QC steps have been taken.

Field crews should receive extensive training and be fully cognizant of all procedures and the 

importance of collecting accurate data. An audit program for fi eld measurements and sampling 

should be established. A typical audit program consists of three types of checks. During a hot check, 

auditors observe members of the fi eld crew during data collection on a fi eld plot (this is primarily 

for training purposes). Cold checks occur when fi eld crews are not present for the audit. Blind checks

represent the complete remeasurement of a plot by the auditors. Hot checks allow the correction of 

errors in techniques. Measurement variance can be calculated through blind checks. When fi eldwork 

is completed, about 10 percent of the plots should be checked independently. Field data collected at 

this stage can be compared with the original data, and errors should be corrected and recorded. Errors 

can be expressed as a percentage of all plots that have been rechecked to provide an estimate of the 

measurement error.

QA/QC for Laboratory Measurements

The SOPs also should be prepared by the operating entity and followed for each part of the analyses. 

Typical steps for the SOP for laboratory measurements include calibrating combustion instruments 

for measuring total carbon or carbon forms using commercially available certifi ed carbon standards. 

Similarly, all balances for measuring dry weights should be calibrated periodically against known 

weights. Fine-scale balances should be calibrated by the manufacturer. Where possible, 10 to 20 

percent of the samples should be reanalyzed/reweighed to produce an error estimate. If a laboratory 

perform these steps, be sure to obtain a record of the procedure(s).

QA/QC for Data Entry

The proper entry of data into analysis spreadsheets is required. This step may be redundant if the fi eld 

data are collected in an electronic format. Ongoing communication between all personnel involved 

in measuring and analyzing data is critical for resolving apparent anomalies before fi nal analysis of the 

monitoring data is completed. If there are any anomalies that cannot be resolved, the plot should not 

be used in the analysis. Errors can be reduced if entered data are compared with independent data.

QA/QC for Data Archiving

Because of the relatively long-term nature of forestry activities, data archiving (maintenance and 

storage) is important and should include the following steps:

Original copies of the fi eld measurement (data sheets or electronic fi les) and laboratory data 

should be maintained in original form, placed on electronic media, and stored in a secure 

location.

Copies of all data analyses, models, the fi nal estimate of the amount of carbon sequestered, 

GIS products, and a copy of the measuring and monitoring reports also should all be stored 

in a secure location (preferably offsite).

Given the period for reporting and the pace of production of updated versions of software and new 

hardware for storing data, electronic copies of the data and report should be updated periodically or 

converted to a format that can be accessed by new or updated software.

•

•
40

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Printed on Recycled Paper

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on 

the basis of race, color, national origin, age, disability, and where applicable, sex, marital status, familial 

status, parental status, religion, sexual orientation, genetic information, political beliefs, reprisal, or because 

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of Civil Rights, 1400 Independence Avenue, S.W., Washington, DC 20250-9410, or call (800)795-3272 

(voice) or (202)720-6382 (TDD). USDA is an equal opportunity provider and employer. 

Pearson, Timothy R.H.; Brown, Sandra L.; Birdsey, Richard A. 2007. Measurement 

guidelines for the sequestration of forest carbon. Gen. Tech. Rep. NRS-18. 

Newtown Square, PA: U.S. Department of Agriculture, Forest Service, Northern 

Research Station. 42 p.

Measurement guidelines for forest carbon sequestration were developed to support 

reporting by public and private entities to greenhouse gas registries. These guidelines 

are intended to be a reference for designing a forest carbon inventory and monitoring 

system by professionals with a knowledge of sampling, statistical estimation, 

and forest measurements. This report provides guidance on defining boundaries; 

measuring, monitoring, and estimating changes in carbon stocks; implementing plans 

to measure and monitor carbon; and developing quality assurance and quality control 

plans to ensure credible and reproducible estimates of the carbon credits. Expected 

users include entities, e.g., individual landowners, industrial forestry companies and 

managers of utility company lands, within the United States who are interested in 

implementing forestry activities and projects designed to generate carbon credits that 

could be traded as an offset, or for registering carbon dioxide reductions using the 

U.S. Department of Energy 1605(b) voluntary reporting registry.

KEY WORDS: greenhouse gas registries, carbon sequestration, forest measurements, 

carbon monitoring.
www.nrs.fs.fed.us

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integrated, cohesive, landscape-scale research program