United States 

Department of 

Agriculture

Forest Service

Northern 

Research Station

General Technical

Report NRS-22

Sampling Protocol,

Estimation, and Analysis

Procedures for the Down

Woody Materials Indicator 

of the FIA Program 

Christopher W. Woodall 

Vicente J. Monleon
The Forest Inventory and Analysis (FIA) program of the USDA Forest Service

conducts a national inventory of forests of the United States. A subset of FIA

permanent inventory plots are sampled every year for indicators of forest health

such as soils, understory vegetation, and down woody materials (DWM). The

DWM indicator provides estimates of down and dead woody materials in forest

ecosystems. Estimates of DWM are used in assessments of forest-ecosystem

attributes such as fuel loadings, carbon stocks, and structural diversity. As defined

by the FIA program, DWM comprises fine and coarse woody debris, slash piles,

duff, litter, and shrub/herbs cover and height. Components of DWM are sampled

using the line-intersect method, point sampling, and fixed-radius sampling. 

DWM data analyses are an integral part of national inventory reports, multi-scale 

forest-health reports, and wildlife-habitat, and fuel-loading assessments. The

DWM inventory began in 2001 and currently is implemented in 46 states 

and two territories. In this report we provide the rationale and context for a

national inventory of DWM, describe woody material components sampled by the

DWM indicator, discuss the sampling protocol used to measure the DWM

components and corresponding estimation procedures, and provide guidance on

managing and processing DWM data and incorporating that information into

pertinent inventory analyses and research projects.

Abstract

Manuscript received for publication

August 2007

Published by:

USDA Forest Service

Northern Research Station

11 Campus Blvd, Suite 200

Newtown Square, PA 19073-3294

January 2008

For additional copies:

USDA Forest Service

Publications Distribution

359 Main Road

Delaware, OH 43015-8640

Fax: 740-368-0152

Visit our website: www.nrs.fs.fed.us
1

The DWM indicator was developed in 1999-2000 as part of a joint pilot program

by the USDA Forest Service’s Forest Health and Monitoring and FIA programs.

Rick Busing, Kelly Rimar, Ken Stolte, Tom Stohlgreen, and Karen Waddell

implemented this initial work. In 2001, FIA implemented a national DWM

indicator program. Karen Waddell was the first national indicator advisor for this

program. We thank regional trainers, field crews, QA staff, database programmers,

and analysts who collect, manage, and disseminate down woody materials

inventory data and products. As this was a blind peer-reviewed publication, the

authors would like to thank James Westfall for serving as editor and three

anonymous reviewers for their constructive comments.

Acknowledgments
2

A previous publication by Woodall and Williams (2005), “Sampling, estimation,

and analysis procedures for the down woody materials indicator” (Gen. Tech.

Rep. NC-256) did not explicitly describe procedures for estimating DWM 

currently used by the national inventory program. This publication includes these

procedures, supporting materials, and refined analytical examples. Finally, this

edition has been blind peer-reviewed.

Foreword
3

1.0 INDICATOR OVERVIEW........................................................................................................................... 5

1.1 FIA Inventory and Forest-Health Indicators.................................................................................... 5

1.2 Down Woody Materials Indicator..................................................................................................... 6

2.0 PLOT-BASED SAMPLING PROTOCOLS.............................................................................................. 13

2.1 Coarse Woody Debris ....................................................................................................................... 14

2.2 Fine Woody Debris............................................................................................................................. 15

2.3 Duff, Litter, and Fuelbed.................................................................................................................... 15

2.4 Fuel Loading on Microplot (Shrubs, Herbs, Litter Cover) ........................................................... 15

2.5 Slash Piles........................................................................................................................................... 16

3.0 ESTIMATING POPULATION ATTRIBUTES ......................................................................................... 17

3.1 Computating Attribute of Interest for Each Plot .......................................................................... 17

3.2 Estimating Population Totals and Variances................................................................................. 24

3.3 Estimating Ratios ............................................................................................................................... 25

3.4 Estimating DWM for Individual Plots or Portion of Plots............................................................ 27

3.5 Change Estimation............................................................................................................................. 31

4.0 DWM ANALYTICAL GUIDELINES........................................................................................................ 33

4.1 Field Data............................................................................................................................................. 33

4.2 Analyses at Plot/Condition Level..................................................................................................... 34

4.3 Core Tables ......................................................................................................................................... 34

4.4 Graphical Summaries........................................................................................................................ 37

4.5 Maps .................................................................................................................................................... 38

4.6 Science Areas .................................................................................................................................... 41

5.0 LITERATURE CITED................................................................................................................................ 43

6.0 GLOSSARY .............................................................................................................................................. 48

7.0 APPENDICES .......................................................................................................................................... 49

7.1 Line-Intersect Sampling of Coarse and Fine Woody Debris...................................................... 49

7.2 Examples ............................................................................................................................................. 54

7.3 Bulk Density by Tree Species ......................................................................................................... 62

7.4 Estimation Constants of Fine Woody Debris, Litter, and Duff by Forest-type Group ............. 66

7.5 Down Woody Material Sample Designs, 1999-2001 .................................................................... 67

7.6 Down Woody Material Field Datasheet......................................................................................... 68

Contents

About the Authors:

Christopher W. Woodall

is a research forester with

the Forest Inventory and

Analysis (FIA) program at

the Northern Research

Station in St. Paul,

Minnesota. He earned a B.S.

degree in forest resource

management from Clemson

University and M.S. and

Ph.D. degrees in forest 

science from the University

of Montana. He joined the

North Central Research

Station in 2001 and has

served as the national 

indicator advisor of FIA’s

Down Woody Materials

inventory since 2002.

Vicente J. Monleon is a

research mathematical 

statistician with the FIA 

program at the Pacific

Northwest Research Station

in Portland, Oregon. He

earned a B.S. degree in 

forest engineering from the

University of Madrid, and an

M.S. degree in forest 

science and a Ph.D. degree

in statistics from Oregon

State University. He joined

the Pacific Northwest

Research Station in 2006. 
4
5

1.1 FIA Inventory and Forest-Health

Indicators

Forest ecosystems are more than assemblages 

of trees. They often are associations of flora 

(e.g., trees, shrubs, herbs, and mosses), fauna (e.g.,

mammals, amphibians, and soil microbes), and

abiotic entities (e.g., decaying organic material,

mineral soil, and water). In recognition of this fact,

the Forest Inventory and Analysis (FIA) program of

the USDA Forest Service conducts an inventory of

the Nation’s forest ecosystems not only measuring

tree components, but also numerous nontimber

ecosystem attributes (Gillespie 1999, McRoberts et

al. 2004, USDA For. Serv. 1999). Estimating a

variety of forest ecosystem attributes, rather than

focusing solely on live trees, may better indicate

the status and trends in forest-health. The

nontimber ecosystem attributes estimated by FIA

are collectively referred to as forest-health

indicators and currently include tree damage,

crown conditions, ozone injury, lichen

communities, down woody materials (DWM),

vegetation structure and diversity, and soil

conditions (McRoberts et al. 2004). 

The DWM indicator is sampled in conjunction

with FIA’s national sampling protocol and occurs

on a subset of FIA’s regular forest inventory plots.

The sampling protocol for all phases of inventory

except forest health indicators is described in

Bechtold and Patterson (2005). Briefly, FIA’s

national program consists of three phases of data

collection (these phases are not equivalent to

three-phase sampling, see Cochran 1977,

Chapter 12). During phase 1, auxiliary

information is collected to poststratify forest

inventory ground plots into a minimum of two

strata: forest and nonforest. Stratification can be

based on “wall to wall” satellite imagery, which

divides the region of interest into strata of known

area, or on a dense sample of photo plots that

allows estimates of stratum size. Stratified

estimation is used in the former case and double

sampling for stratification in the latter (Scott et

al. 2005). This stratification of inventory sample

plots is used to improve the precision of

estimates of population totals. 

In phase 2 of the FIA inventory, information is

gathered from a network of permanent ground plots,

with a spatial sampling intensity of approximately

one plot per 6,000 acres (Fig. 1.1). Each phase 2

plot consists of four, 24-foot, fixed-radius subplots

arranged in a clustered formation (Fig. 1.2). On

each subplot, stand and site information such as

standing live/dead tree height/diameter and

physiographic class/ownership is collected. In

special situations, the sample intensity of phase 2

plots can be increased (e.g., one plot per 2,000

acres). Examples of such situations include

widespread disturbance events (e.g., hurricanes) or

when additional inventory funding is obtained.

Standing live and standing dead trees (snags) are

inventoried on phase 2 plots; DWM are

inventoried during phase 3 of the inventory.

Phase 3, the final phase of the FIA inventory,

entails sampling forest-health indicators such as

DWM. The DWM sampling protocol is applied to

a subset of phase 2 plots (approximately 1/16 of

all phase 2 plots, one plot per 96,000 acres) (Fig.

1.1). The first two phases of the FIA sampling

1.0 INDICATOR OVERVIEW

Figure. 1.1. – Approximate hexagonal panel grid for FIA phase 2 (6,000 acre hexagons)

and phase 3 (96,000 acre hexagons) inventories in Minnesota.

Phase 2 Phase 3
6

protocol are detailed in Bechtold and Patterson

(2005); separate sampling design and estimation

documents for each indicator collectively

describe the third inventory phase (see O’Neill et

al. 2005 for soils example). In this publication

we describe sampling protocol and estimation

procedures for the DWM indicator in the context

of FIA’s national sampling protocol.

1.2 Down Woody Materials

Indicator

The DWM indicator estimates dead organic

materials (resulting from plant mortality and leaf

turnover) and fuel complexes of live shrubs and

herbs. Specifically, components estimated by the

DWM indicator are downed fine woody debris

(FWD), downed coarse woody debris (CWD),

litter, duff, fuelbed, slash piles, live/dead shrubs,

and live/dead herbs. Definitions, sample designs,

and estimation procedures for each DWM

component are included in subsequent sections. 

1.2.1 Fire, Wildlife, and Carbon Modeling

Sciences

DWM data can be used by scientists – foresters,

wildlife biologists, ecologists, fuel specialists, and

carbon/climate-change modelers – to quantify

the carbon pools, fuels, structure, and wildlife

habitat within the Nation’s forest ecosystem.

Such information also benefits policymakers,

state officials, and interested citizens.

The FWD and CWD components of the DWM

indicator were designed to match the components

defined by the National Fire Danger Rating

System (Burgan 1988, Deeming et al. 1979).

This system divides FWD and CWD into size

classes that are equivalent to the lag-time fuelclass system (1, 10, 100, and 1,000+ hours)

used by many fire scientists (Table 1.1).

Additionally, litter and duff depths are sampled

for estimates of forest floor fuel loadings, and

estimates of microplot shrub/herb heights and

coverage provide information on forest ladder

fuels. Estimates of dead and down woody

material, duff/litter, and shrub/herb fuel ladders

are integral to numerous fire behavior models (see

Albini 1976, Burgan and Rothermal 1984; Finney

1998; Reinhardt et al. 1997, and Rothermal

1972). Along with the entire FIA inventory, the

DWM inventory can be used to estimate fuel

loads and fire dangers at strategic scales across the

United States (Woodall et al. 2005).

The United States, mirroring efforts by other

countries (Woldendorp et al. 2002, Kukeuv et al.

1997, Fridman and Walheim 2000), is

attempting to quantify forest-ecosystem carbon

pools (criterion 5, criteria and indicators for the

conservation and sustainable management of

temperate and boreal forest; United Nations

Framework Convention on Climate Change) (J.

For. 1995, Can. For. Serv. 1997, McRoberts et al.

2004). This quantification of the carbon budget

can aid in understanding climate change and the

role of forest-carbon dynamics in climate-change

scenarios. The DWM indicator will increase the

Figure 1.2. – FIA phase 2

sampling design. Each

subplot has a fixed radius

of 24 feet, with the 

centers of three subplots

arranged around the 

center of one subplot at a

distance of 120 feet at

azimuths of 0, 120, and

240, respectively. The

microplot is a 6.8-foot

fixed-radius plot located

12 feet from each subplot

center at a 90-degree

azimuth.

Transect diameter DWM class Fuel-hour class 

0.00-0.24 Small FWD 1 hr

0.25-0.99 Medium FWD 10 hr

1.00-2.99 Large FWD 100 hr

3.00+ CWD 1,000+ hr

Table 1.1. – Transect diameters (inches) of fine woody debris and their relation to timelag fuel-hour classes
7

accuracy of estimates of carbon stock across the

United States. Estimates of DWM components,

such as FWD and CWD, can be coupled with

phase 3 estimates of soil organic carbon content

and phase 2 estimates of standing tree carbon to

create comprehensive carbon estimates in forest

ecosystems (O’Neill et al. 2005a, O’Neill et al.

2005b). The FIA program, with all phases

contributing toward a comprehensive assessment

of total forest carbon, maintains the only national

public database for estimating and providing

continuous monitoring of forest carbon pools in

the United States (Heath and Birdsey 1997).

DWM components such as CWD serve as critical

habitat for numerous flora and fauna. From

“nurse logs” in the Pacific Northwest to black

bear dens in the Southeast, many species find

their ecological niche in the shelter of DWM.

Flora use the microclimate of moisture, shade,

and nutrients provided by CWD to establish

regeneration (Harmon et al. 1986). CWD

provides structural diversity (stages of decay, size

classes, and species) of habitat for fauna ranging

from large mammals to invertebrates (Bull et al.

1997, Harmon et al. 1986, Maser et al. 1979).

Due to the possibility of dwindling habitat for

many native species across the Nation,

inventories of DWM are important for habitat

assessments and wildlife conservation (see

Ohmann and Waddell 2002, Tietje et al. 2002).

1.2.2 Detection and Evaluation Monitoring

Besides providing estimates and associated

variances for DWM components at various

spatial scales, the DWM indicator serves in the

broader context as a monitoring tool of forest

ecosystem health. Data from other phases and

forest-health indicators of the FIA program have

been used to evaluate the annual status and

changes in forest health conditions across all

ownerships (Keyes et al. 2003, Woodall et al.

2005). Forest-heath monitoring typically entails

detection, evaluation, and intensive site

monitoring (Keyes et al. 2003). The baseline

down woody inventory provided by the DWM

indicator can be used to detect regional

disparities in wildlife habitats or prominent fire

hazards. Once possible forest-health hazards are

detected, these areas can be further evaluated

with additional phase 3 plots (plot

intensification) or through additional studies

(intensive site monitoring) (Tkacz 2002). For

example, through analysis of baseline DWM

inventory for Minnesota, it might be observed

that fuel loadings for the Boundary Waters

Canoe Area are relatively high compared to that

for the entire Great Lakes region (e.g., Fig. 1.3).

Because this might constitute a forest-health

hazard, phase 3 plots might be intensified to

refine both fuel-loading estimates and mapping. 

1.2.3 Current and Expected Outputs

DWM play a varied role in many ecosystem

processes. As such, data analysis varies according

to the specific issue being addressed. The DWM

inventory can be used to address the following

primary issues:

• Estimation of DWM attributes per unit area

for individual plots. These values can be

mapped to determine spatial patterns in

DWM, linked to standing live-tree data for

modeling efforts, or monitored over time to

indicate changes in the DWM resource. 

• Estimation of population totals, means, 

and ratios of DWM attributes, which, in turn,

can be used for regional/national DWM

assessments. 

Estimation techniques for classifying plots and

estimating population parameters are based on

the same general principles. However, the

techniques differ when specific subpopulations

are estimated. FIA recognizes two types of

subpopulations (domains) depending on whether

membership is determined by characteristics of

the individual piece of DWM or characteristics of

the land on which the piece is located. Examples

of domains determined by the status and/or

attributes of individual pieces of DWM include

species, decay status, or piece size. Condition class

is used to denote area-based subpopulations that

can be mapped on the ground (e.g., forest type 

or ownership). 
8

Current outputs from the DWM indicator can be

grouped into the following categories: field data,

core tables, graphical summaries of population

estimates, and maps. Field data are organized

into tables according to the DWM component

(e.g., FWD or CWD) and the sampling protocol

that facilitates its estimation. The six tables

containing DWM field data are coarse woody

debris (Table 1.2), fine woody debris (Table 1.3),

duff/litter (Table 1.4), transect (Table 1.5), piles

(Table 1.6), and shrub/herbs (Table 1.7). See

USDA For. Serv. (2007) for additional

information on the preceding tables.

FIA uses the term core tables to refer to standard

tabular summaries of inventory data. For phase

2, core tables typically consist of total amounts

or estimates per unit area of standing timber

volume and number of trees (e.g., total

sawtimber volumes on timberland by county for

a particular state). Thus, DWM core tables

include population-level estimates of totals (e.g.,

total tons of FWD in the state of Maine) or ratios

(e.g., mean 100-hr fuel loading per acre of

loblolly pine forest types in South Carolina) for

example, see Table 1.8.

Graphical summaries of core tables or

population estimates provide more user-friendly

outputs for interpreting DWM estimates.

Because the phase 3 inventory typically has

sample intensities less than that of the phase 2

inventory, analysts should be more cognizant of

couching interpretation of DWM estimates in

terms of associated sampling errors (Fig. 1.4).

The DWM indicator uses a sampling intensity

sufficient to indicate the current status and

trends in DWM components across large

regions of the United States. However, care

should be taken when interpreting DWM

estimates at smaller scales.

Maps of DWM component estimates allow

analysts to estimate not only the amount but

also the spatial distribution of DWM

components across forest landscapes, for

example, forest duff mass across the Upper

Midwest. DWM maps may be created through

full analytical integration of all three phases of

the FIA inventory. Due to the relative low

sample intensity of the DWM indicator,

modeling efforts often are associated with phase

2 plots and with remotely sensed imagery

(Woodall et al. 2004). 

Figure 1.3. – Spatial interpolation of coarse woody debris fuel loadings (tons/acre) for forests in northern Minnesota based on FIA DWM plots, 2001-2003.
9

To enable analysts to fully utilize DWM data/

estimates, research is under way to develop new

mapping methodologies, more sophisticated data

processing algorithms, seamless integration with

other FIA inventory phases, and integration into

state/regional reports. 

Plot Subplot Transect Slope Species Transect Small Large Piece Decay Hollow CWD 

distance diameter diameter diameter length class History

xxxx x xxx xxx.y (ft) xxx xxx (in) xxx (in) xxx (in) xxx (ft) x x x

1 1 030 3.5 317 3 3 5 6 2 N 1

1 1 030 4.0 316 11 5 12 22 3 N 1

1 2 030 22.7 316 7 5 8 19 4 N 1

1 3 150 11.1 317 5 4 5 12 1 N 1

1 3 150 2.2 802 9 7 11 37 3 N 1

1 3 270 7.0 316 7 28 5

1 3 270 15.6 802 3 3 4 24 2 N 1

1 4 270 21.0 802 17 15 18 57 3 Y 1

1 4 270 2.9 202 7 5 7 42 2 N 1

Table 1.2. – FIA coarse woody debris (CWD) field data table with example data

Plot Subplot Condition FWD Reason Residue 

class Small Medium Large high pile

xxxx x x xxx xxx xxx x x

1 1 1 0 02 0 0

1 2 1 8 63 0 0

1 3 2 3 11 0 0

1 4 1 0 31 0 0

Table 1.3. – FIA’s fine woody debris (FWD) field data table with example data

Plot Subplot Transect Sample Duff Litter Fuelbed 

taken depth depth depth

xxxx x xxx x xx.y (in) xx.y (in) xx.y (ft)

1 1 30 Y 0.2 0.9 2.2

1 1 150 Y 0.8 1.9 4.5

1 1 270 N 0 0 0

1 2 30 Y 0.2 2.0 1.9

1 2 150 Y 1.1 1.7 1.0

1 2 270 Y 0.5 0.8 0.5

Table 1.4. – FIA’s duff, litter, and fuelbed field data table with example data
10

Plot Subplot Condition Azimuth Shape Length1 Length2 Width1 Width2 Height1 Height2 Density

class

xxxx x x xxx (°) x xx (ft) xx (ft) xx (ft) xx (ft) xx (ft) xx (ft) xx (%)

15 3 1 112 1 9 16 10

27 3 2 127 2 10 11 7 20

35 4 1 50 3 14 4 10 3 6 20

45 1 1 15 3 20 9 15 2 5 30

46 3 3 30 2 21 8 5 10

Table 1.6. – FIA’s slash/residue pile field data table with example data

Plot Subplot Transect Cond. Class Slope Pct Distance xxx.y (ft)

xxxx x xxx x xxx (%) Begin slope End slope Horizontal

1 1 30 1 10 0.0 24.1 24.0

1 1 150 1 5 0.0 24.0 24.0

1 1 270 1 0 0.0 24.0 24.0

1 2 30 1 0 0.0 24.0 24.0

1 2 150 1 0 0.0 24.0 24.0

1 2 270 1 0 0.0 24.0 24.0

1 3 30 2 5 0.0 24.0 24.0

1 3 150 2 0 0.0 24.0 24.0

1 3 270 2 0 0.0 11.5 11.5

1 3 270 1 0 11.6 24.0 12.5

1 4 30 1 10 0.0 24.1 24.0

1 4 150 1 15 0.0 24.3 24.0

1 4 270 1 10 0.0 24.1 24.0

Table 1.5. – FIA’s transect field data collection table with example data, 2002 to present

Plot Subplot Live Live Dead Dead Live Live Dead Dead Litter 

shrub shrub shrub shrub herb herb herb herb cover

cover HT cover HT cover HT cover HT

xxxx x xx (%) xx.y (ft) xx (%) xx.y (ft) xx (%) xx.y (ft) xx (%) xx.y (ft) xx (%)

1 1 30 6.1 0 0.0 60 1.2 1 1.2 60

1 2 60 5.7 0 0.0 30 1.9 0 0.0 30

1 3 40 4.0 1 3.1 20 1.5 0 0.0 80

1 4 0 6.3 0 0.0 1 2.0 0 0.0 100

Note: HT=tallest height

Table 1.7. – FIA’s microplot fuel loading (shrubs and herbs) field data table
11

Forest-type group Down and dead woody fuels Slash Forest floor fuels

1 hr 10 hr 100 hr 1000+ hr Duff Litter

Maple/beech/birch 1.11 2.45 4.44 6.72 2.22 12.22 3.55

Oak/hickory 2.02 4.32 4.21 5.34 4.21 8.84 3.67

Oak/pine 1.97 3.44 5.69 7.54 0.00 13.54 2.64

Elm/ash/cottonwood 3.12 2.17 4.87 8.54 4.87 18.21 5.24

Loblolly/shortleaf pine 1.25 4.11 3.61 6.89 3.61 9.87 2.33

White/red/jack pine 2.33 3.21 5.21 12.11 0.00 11.46 1.34

Other groups 2.22 3.34 3.33 10.54 3.33 7.78 2.43

All forest-type groups 2.33 3.21 5.21 12.11 3.33 11.46 1.34

Table 1.8 – Mean fuel loadings by forest type group and fuel class on forest land (tons/acre), State X, Year 1 to Year 2

0

5

1 0

1 5

2 0

GA NC SC TN VA

Fine Woody Debris 

Coarse Woody Debris 

Duff

Litter Mean Forest land (tons/acre) 

Figure 1.4. – Population

estimates of DWM 

component data for

selected states.
12
13

In this section we present an overview of field

protocols for the DWM indicator as currently

implemented by FIA. For a detailed description

of the protocols implemented by field crews, see

USDA For. Serv. (2004) and Appendix 7.6 (field

datasheet). The DWM protocols described here

have been used by FIA since 2002. For

information on historical DWM sample designs

used by the Forest Health Monitoring (1999-

2000) and the FIA programs (2001), see

Appendix 7.5. The Pacific Coast states began

sampling CWD in the 1990s (Waddell 2002).

For information on organizing field data into a

database structure and definitions see USDA For.

Serv. (2007). The DWM protocols share

components and measurements with phase 2

plots (Bechtold and Patterson 2005).

The diversity of ecosystem attributes estimated

by the DWM indicator requires a variety of

sampling techniques (Fig. 2.1). FIA field crews

cannot efficiently count the number of pine

needles, down twigs, and measure the duff depth

across an entire plot. Hence, the DWM sampling

protocol is distinctly different from phase 2

sampling techniques used to estimate

populations of standing trees. The sampling

protocol for DWM components includes: 

1. Line-intersect sampling for CWD and FWD. 

2. Systematic point sampling for duff, litter, and

fuelbed depths.

3. Fixed-area plot sampling for cover and height

of shrubs and herbs.

4. Fixed-area plot sampling, with shape and

packing ratio estimation, for slash/residue

piles.

As numerous ecological disciplines may have

different definitions for forest ecosystem

components sampled by the DWM indicator,

N

4 30°

150°

270°

30°

150°

270°

30°

150°

270°

30°

150°

270°

3

2

1

Distancebetweensubplots(2,3,and4)andsubplotcenter(1):120ftatangles(deg.)

0,120,and240respectively,distancebetweensubplotcenterandmicroplotcenter:12

ft.;shrubs/herbssampledonmicroplot.Duff/littersampledat24-ftslopedistanceon

eachCWDtransect.

Transect Information

FWD < 0.25”&

0.26”-0.99”

FWD 1.00”-2.99”

6 ft. s.d.

10 ft. s.d.

24 ft. h.d.

s.d.=slopedist.,h.d.=horizontaldist.

Key

Subplot

Microplot

CWD Tran.

FWD Tran.

CWD

> =

3.00”

Figure 2.1. – DWM

indicator sampling design

on FIA plot (inventory

years 2002 to present).

2.0 PLOT-BASED SAMPLING PROTOCOL
14

the indicator includes a population definition for

each component. As a result, users are cautioned

to be fully aware of DWM component definitions

that may differ from those used in other

disciplines/studies. 

2.1 Coarse Woody Debris

FIA considers CWD as dead and downed pieces

or portion of pieces of wood that meet the

following criteria:

1. Diameter of at least 3 inches along a length of

at least 3 feet for decay classes 1-4, and at

least 5 inches above the duff layer along a

length of at least 5 feet for decay class 5.

2. Detached from the bole of a standing

live/dead tree. If still partially rooted, the lean

angle must be more than 45 degrees from

vertical. Standing dead trees with a lean angle

less than 45 degrees from vertical are tallied

as snags during the phase 2 inventory. 

3. Branched and forked pieces are separated 

into individual CWD pieces and tallied

accordingly. For each piece, a main bole is

determined as the fork with the largest

diameter, with all branches and secondary

forks considered separate CWD pieces that

must meet minimum size specifications.

4. If CWD pieces become fractured, whether

lengthwise or in broken sections, each

portion is treated as a separate piece. 

CWD pieces are selected into the sample if the

piece’s centerline intersects any of three 24-foot

horizontal distance transects emanating from the

center of each FIA subplot (azimuths of 30, 150,

and 270 degrees) (Fig. 2.1). CWD pieces are 

tallied with each transect intersection as many

times as intersected, regardless of the number of

intersections. The decay class of each CWD piece

is rated according to a 5-class scale (Maser et al.

1979, Sollins 1982) (Table 2.1). Information on

decay class allows the determination of mass and

habitat condition for CWD pieces. Recorded for

pieces in decay classes 1-4 are the slope 

distance to subplot center, diameter at the point

of transect intersection, large-end diameter,

small-end diameter (or the minimum 3 inches,

whichever is greater), species, decay class, length

between the large- and small-end diameters,

presence/absence of butt-end cavity, and history.

Due to the highly decayed state of class 5, only

slope distance, transect diameter, total length

Decay Structural Texture of Color Invading Branches 

class integrity rotten portions of wood roots and twigs

1 Sound, freshly fallen, Intact, no rot; conks of stem; Original color Absent Branches are present,

intact logs decay absent fine twigs still are attached

and have tight bark.

2 Sound Mostly intact; soft (starting to Original color Absent Branches are present, many 

decay) but cannot be pulled fine twigs are absent with 

apart by hand those remaining have peeling

bark

3 Heartwood sound; Hard, large pieces; sapwood Reddish-brown Sapwood Branch stubs will not pull out

piece supports its can be pulled apart by or original only

own weight hand or sapwood absent color

4 Heartwood rotten; Soft, small blocky pieces; Reddish or Throughout Branch stubs pull out

piece does not support metal pin can be pushed light brown

its own weight, but into heartwood

maintains its shape

5 None; piece no longer Soft; powdery when dry Red-brown to Throughout Branch stubs and pitch

maintains its shape; dark brown pockets have usually rotted 

it is spread out on down

the ground

Table 2.1. – Attributes of coarse woody debris pieces used in determining decay classes
15

with diameter greater than 5 inches, and decay

class are recorded for CWD pieces.

To determine the length of transect in each

mapped condition class and attribute estimates

of DWM components to condition classes, the

beginning and ending distance of each condition

class along each CWD transect is recorded. This

process is called transect-line segmenting. Rather

than calculating horizontal distances in the field,

crews record slope distances and the slope of

each segment. The condition classes mapped by

the DWM indicator match those recorded 

during phase 2 sampling. Because CWD, FWD,

and duff, litter, and fuelbed depth are measured

along CWD transects, segmenting on these

transects allows estimation of DWM attributes by

condition class. 

CWD pieces are assigned to a condition class

based on the point of intersection between the

piece and transect. For pieces that straddle

condition classes, the entire length of the piece is

measured, rather than only the portion of the

length within the mapped condition class. 

This may result in a slight underestimation when

results are reported by condition class for 

some attributes (when estimators require a

measurement of the length of the piece).

However, the potential bias is thought to be

minimal compared with the errors associated

with determining, measuring and recording the

length of the piece within each condition class.

2.2 Fine Woody Debris

The DWM indicator defines FWD as down

woody pieces with diameter less than 3 inches.

In practice, pieces are tallied if the diameter at

the point of intersection with the transect is less

than 3 inches. FWD does not include dead

branches attached to standing trees or shrubs,

dead foliage, bark fragments, or small pieces of

decomposed wood. Because it would be

impractical for field crews to measure the

diameter of hundreds of small FWD pieces, they

tally the number of FWD pieces by three size

classes related to the time-lag fuel classes often

referenced by fire scientists (Table 1.1). The three

classes of FWD are sampled on each of the four

FIA subplots using 6- and 10-foot slope-distance

transects collocated on the 150 degree CWD

transect and starting at 14-foot slope distance

from subplot center (Fig. 2.1). The 6-foot slope

distance transect is used to tally the small (0.01

to 0.24 inch) and medium (0.25 to 0.99 inch)

classes of FWD; the 10-foot slope-distance

transect is used to tally large (1.00 to 2.99 inch)

FWD. The slope (percent) of each transect is

recorded for use in FWD estimators. If a FWD

transect straddles two mapped condition classes,

separate tallies are recorded for each condition.

2.3 Duff, Litter, and Fuelbed

The DWM indicator defines litter as a forest-floor

layer of freshly fallen leaves, needles, twigs,

cones, bark chunks, dead moss, dead lichens,

dead herbaceous stems, and flower parts. Duff is

defined as an organic forest-floor layer, just

below litter, consisting of well decomposed

leaves and other organic material. Individual

plant parts should not be recognizable in the

duff layer. The fuelbed is the accumulated mass

of all woody DWM components above the top of

the duff layer (excluding live shrubs/herbs). The

DWM indicator measures the depth of duff,

litter, and fuelbed at 12 points, located at the 24-

foot slope distance on each of the 12 CWD

transects (Fig. 2.1). If a large obstruction (e.g.,

boulder or slash pile) is present at the sample

locations, crews do not measure duff/litter depths

and indicate such in the field data. If the

obstruction is a log, only the depth of the

fuelbed is measured. Errors in duff, litter, and

fuelbed measurements can occur when crews are

not trained properly in identifying the duff layer

from mineral soils and the litter layer. Crews also

must be trained on how to measure the depth of

the fuelbed. Fuelbed measurements are not used

to estimate fuel loadings (i.e., mass), but to

describe the dispersion of fuels from the forest

floor up toward the canopy (the fuel complex). 

2.4 Fuel Loading on Microplot

(Shrubs, Herbs, Litter Cover)

The DWM indicator samples five fuel

components on each FIA microplot if its center
16

is an accessible forested condition: dead herbs,

live herbs, dead shrubs, live shrubs, and litter

coverage (Fig. 2.1). Microplots are 6.8-foot,

fixed-radius plots located 12-feet from subplot

center at an azimuth of 90 degrees. Within each

microplot, the cover and maximum height of

each shrub/herb component is estimated visually

and recorded. The DWM indicator defines

shrubs as vascular plants with woody stems that

are not defined as trees by phase 2. Herbs are

defined as nonwoody vascular plants including

but not limited to ferns, moss, lichens, sedges,

and grasses. The cover from 0 to 100 percent in

10-percent classes is estimated for each of the

five fuel categories. The tallest height within the

microplot of all fuel categories (excluding litter)

is also estimated. To produce estimates of mass

and/or volume of live/dead shrub/herbs, detailed

information on species and form must be

collected. Because the vegetation structure and

diversity indicator collects this information, the

DWM indicator does not collect the data

necessary for input to shrub/herb prediction

equations. However, data from phase 2 and the

vegetation indicator (i.e., shrub species and

forest type) can be combined with DWM

height/coverage data to estimate shrub/herb

volumes/mass (see Brown and Marsden 1976 for

an example of calculations of shrub weight).

The entire microplot is assigned to the condition

of its center. If a microplot straddles a

nonforested condition, fuel loading is

determined only in the accessible portion of

forest land. If it straddles several forested

conditions, one value is recorded for all forested

conditions combined. The condition at the

center of the microplot is thought sufficient for

subsequent estimation, because there is little

likelihood of a microplot falling on a condition

boundary. Thus, any bias associated with the

lack of condition-class mapping on the microplot

is thought to be minimal. 

2.5 Slash Piles

Slash or residue piles are defined as CWD in

piles created directly from human activity or

from natural events that prohibit safe

measurement by CWD transect. Slash piles are

conglomerations of woody debris for which

transect sampling would be impractical or

hazardous. The sampling protocol for estimating

slash pile volume/mass is based on Hardy

(1996). A pile is included in the sample if its

center is within the accessible forest land area

sampled by any FIA subplot (24-foot radius).

The shape of each tallied slash pile is classified

according to a shape code (Fig. 2.2). Depending

on a pile’s shape code, certain dimensions of the

pile are measured to the nearest foot along with

an estimate of the pile’s packing ratio. The

packing ratio, otherwise termed density, is the

ratio of wood volume to total volume within any

defined shape. Typically, the packing ratio should

not exceed 40 percent. The forest condition class

of the center of the slash pile is recorded.

Figure 2.2. – Shape codes for slash/reside piles sampled by FIA.
17

Scott et al. (2005) described general procedures used by FIA to estimate population parameters. In this

section, we adapt those principles, methods, and estimators to DWM indicator variables (readers are

referred to that publication for additional detail and justification). The components of the DWM

indicator are sampled using different protocols. As a result, specific DWM estimators differ substantially

from each other and from estimators for attributes of standing trees as described in Scott et al. (2005).

However, the general estimation process is the same for all estimators. First, an estimate of the attribute

of interest in the domain of interest is computed for each plot and adjusted for plots that overlap the

population boundary (section 3.1). Most of the differences in estimation procedures of DWM attributes

occur at this step. Second, estimates from all of the plots within a stratum are combined to yield a

stratum average and estimated variance (section 3.2). Third, the estimated total for the population is

calculated as a weighted average of the strata means using stratum weights (section 3.2). Ratios, such as

values per forested acre, are estimated using a ratio-of-means estimator and associated variances

(section 3.3). Estimators for individual plots for purposes such as classification, modeling or mapping

are described in section 3.4. 

Estimation units for phase 2 traditionally have been counties or a combination of counties. However,

phase 3 estimation units differ due to different user groups and the less intensive number of sample

points per unit area. DWM estimation units may be based on broad ecological classifications, such as

Bailey’s (1995) ecological provinces and sections, or large administrative or geographic units. Because of

the less intensive sample of phase 3 plots, the same strata used for phase 2 estimation may not be

appropriate. At a minimum, a forest/nonforest stratification is advisable and currently is used in

standard estimation procedures. It should be stressed that users must determine both the appropriate

stratification and estimation units for the DWM indicator regardless of what is done for phase 2

estimation. However, a phase 3 stratification can be defined by combining phase 2 strata for a region.

3.1 Computing Attribute of Interest for Each Plot

The first step in estimating population parameters is computing an estimate of the attribute of interest

in the domain of interest for each plot. This estimate is corrected for plots that straddle the population

boundary. In general, these are plots that straddle international boundaries (Canada or Mexico), are

partially left unsampled due to problems related to accessibility (e.g., access denied by owner or

hazardous conditions) (see Scott et al. 2005: 48). Nonforested conditions are a domain and part of the

population, so they are not included in the correction factor. The computed variables presented here

should be considered intermediate steps for obtaining estimates of population totals and averages. To

estimate DWM for individual plots or portion of plots for classifying, modeling or mapping, use the

estimators described in section 3.4. 

3.1.1 Coarse Woody Debris

In each plot, CWD is measured along twelve, 24-foot-long transects. The theory behind line-intersect

sampling (LIS) for segmented transects and logs of arbitrary shape is discussed in Appendix 7.1. The

LIS estimator is computed for each straight-line transect and then averaged over the three transects per

subplot and four subplots per plot (Appendix 7.1.4). From equation 7.10 in Appendix 7.1, the LIS

estimator for an attribute of interest in domain of interest d for plot i assigned to stratum h, on a perunit-area basis, is: 

3.0 ESTIMATING POPULATION ATTRIBUTES
18

(3.1)

where

is the attribute of interest measured in piece t intersected by transect m of subplot j of plot i

assigned to stratum h. Recall that a piece is recorded as many times as interested by the transect. 

(ft) is the length of piece t intersected by transect m of subplot j of plot i assigned to stratum h.

domain indicator variable which is 1 if piece t intersected by transect m of subplot j of plot i

assigned to stratum h belongs to the domain of interest d and 0 otherwise.

L (ft) length of the transect, 24 ft. Because there are 12 transects per plot, the total length is 12 L.

c constant to convert to proper units

mean proportion of stratum h observed transect lengths falling within the population. Dividing by

adjusts the length of the transect to account for any portion of stratum h plots falling outside the

population (Scott et al. 2005: 48). This correction factor is simply the ratio of the total length of transect

segments actually observed

to the length that would had been observed if all plots had fallen

entirely within the population (12Lnh): 

(3.2)

where 

(ft) is the horizontal length of the transect segment within condition class k on transect m of

subplot j of plot i assigned to stratum h.

indicator variable which is 1 if condition k on transect m of subplot j of plot i assigned to stratum

h is within the boundaries of the population.

nh number of phase 3 plots in stratum h. Plots that are entirely nonsampled are excluded.

number of conditions intersected by transect m of subplot j of plot i assigned to stratum h. 

The attribute of interest in eq. 3.1, , could be any attribute measured or calculated in each piece.

Table 3.1 includes some of the attributes that can be calculated from FIA data and the corresponding

LIS estimator equations. For volume estimation, eq. 3.1 requires an estimate of the volume of each

piece. Currently, FIA uses Smalian’s formula to calculate the volume of pieces in decay classes 1-4 and
19

Table 3.1. – Equations for estimating attributes of coarse woody debris from FIA data (Eq. 3.1)
20

the diameter at the intersection for pieces in class 5. Smalian’s formula assumes that the shape of the

piece is a fustrum of paraboloid and, to the extent that this assumption is not met, a bias will be

introduced. Husch et al. (2003:122) and Fraver et al. (2007) reported biases of 12 percent when using

Smalian’s formula, and the latter examined other formulae that may result in less bias. Alternatively,

volume can be estimated from the diameter at the intersection for all pieces. While this method does

not require assumptions about the shape of the piece, it is likely to result in greater variance. Since eq.

3.1 can be applied to any method to estimate the volume of individual pieces, users are advised to use

the method that they consider most appropriate.

The LIS estimator is derived under the assumption that CWD pieces lie horizontally on the ground. If

this is not the case, due to the slope of the terrain or because the piece is partially hanging, the length

of each piece in eq. 3.1 must be multiplied by the cosine of the angle between the piece and the

horizontal plane. The resulting correction factor ranges from 1 (no correction) for horizontal pieces to

a maximum of 1.41 for a 45-degree lean angle. The correction factor always is greater than or equal to

1, so ignoring it results in underestimating the target parameter. For small to moderate piece

inclination, the correction factor is relatively small: 1.015 (1.5 percent) for an inclination of 10 degrees

and 1.064 (6.4 percent) for an inclination of 20 degrees. FIA does not measure piece inclination and

the correction factor is set to 1 by default.

3.1.2 Fine Woody Debris

FWD is measured by tallying the number of pieces in each of three diameter classes within each

condition class crossed by the transect. Four transects are measured in each plot, with length varying

with the diameter of the pieces. Not recorded are the actual diameter, species, or other attributes of

individual pieces. Thus, estimation of FWD is limited to total volume and weight and the only

possible domains are those based on mapped condition classes. An additional complication is that the

length of the transect is not corrected for slope during field measurements, so slope correction must

be incorporated into the FWD estimator. 

The LIS estimator of the total volume of fine woody debris (ft3

/acre), for each size class, is obtained

from eq. 7.9 in Appendix 7.1:

(3.3)

where

is the slope correction factor for the segment in condition class k of subplot j of plot i assigned

to stratum h :

Decay class Species group

Softwoods Hardwoods

1 1.00 1.00

2 0.84 0.78

3 0.71 0.45

4 and 5 0.45 0.42

Table 3.2. – Decay-class reduction factors for coarse woody debris by decay class and species group (from Waddell 2002)
21

(3.4)

(ft) is the slope-length of the transect segment in condition class k of subplot j of plot i assigned

to stratum h.

is the number of FWD pieces tallied in the diameter class of interest in condition class k of

subplot j of plot i assigned to stratum h.

(in) is the quadratic mean diameter of the diameter class of interest in condition class k of

subplot j of plot i assigned to stratum h (Appendix 7.4).

domain indicator variable which is 1 if condition class k of subplot j of plot i assigned to

stratum h is in the condition classes of interest d and 0 otherwise.

mean proportion of stratum h observed transect lengths falling within the population:

(3.5)

where 

indicator variable which is 1 if condition k on transect m of subplot j of plot i assigned 

to stratum h is within the boundaries of the population.

L (ft) length of the FWD transect: 6 ft for the small (0.01 to 0.24 inch) and medium (0.25 to 0.99

inch) diameter classes and 10 ft for the large (1.00 to 2.99 inches) diameter class.

To estimate biomass, volume estimates are multiplied by the bulk density of FWD and an assumed

decay-reduction factor of 0.80 (Appendix 7.4). As with CWD decay reduction factors, if refined FWD

decay reduction factors are available for a FWD class and forest-type group, they should be used

rather than the default constant. An estimate of the total amount of FWD for the plot can be obtained

by computing eq. 3.3 for each diameter class and then adding the three estimates at the plot level. 

The FWD estimator is affected by the same problem described for nonhorizontal pieces. However, the

underestimation may be much greater for FWD than for CWD. First, the inclination of FWD pieces

may be greater that than of CWD pieces, particularly for fresh slash and when FWD is still attached to

fallen branches (Brown and Roussopoulos 1974). Second, FWD tilt angle is not limited to a maximum

inclination of 45 degrees. Brown and Roussopoulos (1974) examined this issue with a large sample of

FWD pieces from conifer forests. The average correction factor for naturally fallen braches ranged

between 1.09 and 1.21 depending on forest type and piece size class. For slash, the correction factors

were as high as 1.38 for recent slash and 1.25 for older slash. FIA sets the correction factor to 1.13 by

default (Brown 1974), but analysts are encouraged to use specific correction factors where available.

The LIS estimator in eq. 3.3 requires measurement of the quadratic mean diameter (QMD) of the

pieces tallied. However, FIA tallies only the number of pieces within each class, not individual
22

diameters. In many instances, the midpoint diameter of the size class has been used a surrogate for the

QMD. However, the distribution of piece size is not uniform (smaller pieces are more abundant) and

the QMD tends to be smaller than the midpoint diameter of the size class. For example, the QMD of a

sample of ponderosa pine FWD pieces in the 1- to 3-inch class was 1.77 inches, but the midpoint of

the interval is 2 inches (Brown and Roussopoulos 1974). Using 2 rather than 1.77 inches in eq. 3.3

would overestimate the volume of FWD by 28 percent. Several authors have published estimated QMD

for selected species or forest types (e.g., Brown and Roussopoulos 1974, Ryan and Pickford 1978,

Nalder et al. 1997, 1999), but most regions lack estimates. Van Wagner (1982) proposed a method for

estimating QMD without additional field work or the need to identify the species of individual pieces.

This method is based on the assumption that the distribution of piece diameters follows a power

function. The default QMD values included in Appendix 7.4 are based on this method (Woodall and

Monleon, in press).

3.1.3 Duff, Litter, and Fuelbed

Duff, litter, and fuelbed depth are estimated at 12 points per plot, located systematically at the 24-foot

slope-distance location on each CWD transect. In addition to average depth, duff and litter mass are

calculated. For each attribute, the depth in domain (condition class) of interest d for plot i assigned to

stratum h, is:

(3.6)

where

(in) is the depth of the duff, litter, or fuelbed at the end of transect m of subplot j of plot i

assigned to stratum h.

domain indicator variable which is 1 if the point at the end of transect m of subplot j of plot i

assigned to stratum h belongs to the domain of interest d and 0 otherwise.

mean proportion of stratum h observed points falling within the population:

(3.7)

where 

domain indicator variable which is 1 if the points at the end of transect m of subplot j of plot i

assigned to stratum h is within the boundaries of the population.

To compute litter and duff weights per unit area, the depth ( in eq. 3.6) is multiplied by bulk

density (lb/ft3

, Appendix 7.4) and a unit-conversion factor. If the depth is measured in inches, the

unit-conversion factor that yields tons per acre is 1.815. 

3.1.4 Fuel Loading on Microplot (Shrubs, Herbs, Litter Cover)

The maximum height and total cover of dead and live shrubs and herbs are measured in each of the
four microplots. The entire microplot is assigned to the condition class at its center. The height or

cover in the domain (condition class) of interest d for plot i assigned to stratum h, is:

(3.8)

where

is the depth (ft) or cover (expressed as a proportion) of herbs, shrubs, or litter at microplot j of

plot i assigned to stratum h.

domain indicator variable which is 1 if microplot j of plot i assigned to stratum h belongs to the

domain of interest d and 0 otherwise.

mean proportion of stratum h observed microplots falling within the population:

(3.9)

where 

indicator variable which is 1 if microplot j of plot i assigned to stratum h is within the

boundaries of the population.

3.1.5 Slash Piles

A slash pile is tallied if its center falls within the subplot boundary. The volume of the pile is 

determined based on the pile’s shape and associated sampled dimensions (Fig 2.2) using equations

from Table 3.3. 

The weight of an individual pile is estimated by multiplying the pile’s net volume by a slash bulkdensity constant (Appendix 7.4) and a unit conversion constant (0.0005 to convert to tons). Then,

pile volume (ft3

/acre) or weight (tons/acre) in domain of interest d for plot i assigned to stratum h, is:

(3.10)

where

is the volume (ft3

) or weight (tons) of pile t in subplot j of plot i assigned to stratum h.

domain indicator variable which is 1 if pile t in subplot j of plot i assigned to stratum h belongs

to the domain of interest d and 0 otherwise.

(acres) area of the subplot (1/24 acre). There are four subplots, so is the total area

sampled in the plot.

23
24

mean proportion of stratum h observed plot areas falling within the population:

(3.11)

where 

area of subplot covering condition class k on subplot j of plot i assigned to stratum h.

domain indicator variable which is 1 if condition k on subplot j of plot i assigned to stratum h is

within the boundaries of the population.

It should be noted that the biomass of CWD in slash piles can be reduced by incorporating a decay

reduction factor, as occurred in the CWD estimator. Because there is no species or decay information

for slash piles, the decay reduction factor would implicitly be based on expert opinion. Starting values

for slash pile decay reduction factors may be based on forest type and decay classes of 1 or 2.

3.2 Estimating Population Totals and Variances

Once attributes are calculated at the plot level, the estimation of stratum averages and population

totals proceeds as described in Scott et al. (2005: 54-55). Those equations are included here for

completeness. First, calculated plot values are averaged within each stratum:

(3.12)

where

is the plot estimated value from eqs. 3.1, 3.3, 3.6, 3.8, or 3.10.

is the number of observed plots in the stratum.

The variance estimator of eq. 3.12 is:

Shape code Net volume equation

1 – Paraboloid

2 – Half-elliptical cylinder

3 – Half-frustum of an elliptical cone

4 – Irregular solid

Note: P is the packing ratio, and h, w and l are size measurements according to the pile’s shape code (Fig 2.2). 

Table 3.3. – Equations for determining the net volume of slash piles based on its shape (adapted from Hardy 1996)
25

(3.13)

Estimated population totals for the domain of interest are weighted averages of the stratum means

multiplied by the total population area. For stratified estimation and double sampling for stratification,

respectively, the estimators are

(3.14)

where

(acres) total area of the population. 

weight for stratum h, calculated as the proportion of the area of stratum h to that of the

population .

number of phase 1 plots classified as belonging to stratum h.

total number of phase 1 plots sampled in the population.

H total number of strata in the population. 

For variables such as those involving estimates of depth, height or cover, the population total is not a

meaningful parameter. The parameter of interest typically the mean, which can calculated by dividing

equation (3.14) by the total area or, more appropriately, by the forested area or area in the

condition class of interest (see ratio estimation, section 3.3). 

An approximate variance of the estimated total for stratified sampling and double sampling for

stratification, respectively, is given by:

(3.15)

where n is the total number of observed plots, .

3.3 Estimating Ratios

In many instances, users are not interested in estimated population totals but in estimates of the

attribute expressed on a per-acre or per-piece basis. For example, a user may be interested in the

average volume of CWD per acre of ponderosa pine forest, or the per-acre average number of pieces

larger than 20 inches in Douglas-fir forests of western Oregon. This is accomplished by dividing an
26

estimate of the total of the attribute in the domain of interest (i.e., total number of CWD pieces greater

than 20 inches in Douglas-fir forest of western Oregon) by an estimate of the area covered by the

domain of interest (Douglas-fir forest of western Oregon). In general, most attributes are reported in a

per-forested-acre basis rather than total area of the population. In such cases a ratio estimator with the

estimated number of forested acres in the denominator would be used.

3.3.1 Ratio Estimator

The ratio estimator and its approximate estimated variance are (Scott et al. 2005: 55):

(3.16) 

where and are estimators of the population total for two attributes in the domains of interest d

and d’, respectively. Typically, would be an estimator of total area or total number of pieces.

(3.17)

For stratified sampling, the covariance is estimated as (terms defined in section 3.2):

(3.18)

(3.19)

For double sampling for stratification, the covariance is estimated as:

(3.20)

(3.21)

3.3.2 Area Estimation 

Area estimation per se is not of interest for the DWM indicator. FIA produces area estimates such as the

number of acres of forest land from the mapped phase 2 plots. However, for estimating ratios of DWM

attributes on a per-acre basis, eq. 3.16 requires an estimator of total area in the domain on interest. For

this purpose, area can be estimated in two ways: directly from phase 3 variables, such as the proportion 

of transect length in the domain of interest, or from the proportion of the mapped plot area in the

domain of interest. Estimates calculated directly from phase 3 variables may be advantageous. First, the
27

covariance between the estimator of the attribute of interest and the estimator of area may be greater

if area is estimated from the DWM indicator data than from mapped data. As a result, the variance

of the ratio estimator (eq. 3.17) may be reduced. Second, estimating both the numerator and

denominator from DWM indicator data may simplify calculations since extraneous data need not be

considered. However, estimating area from the much larger phase 2 sample may result in a more

precise estimator of area and, as a result, reduced variance of the ratio estimator. The development of

methods that combine phase 2 and 3 data to improve the precision of phase 3 estimation is an active

area of research within FIA. Interested users should follow those developments and apply those

estimators as they become available.

For each plot, the proportion of the plot in the domain of interest is calculated as:

for CWD (3.22)

for FWD (3.23)

for duff, litter, and fuelbed measurements (3.24)

for fuel-loading (shrubs and herbs) variables (3.25)

for slash piles (3.26)

where the indicator variable is 1 if the transect segment, point, microplot or plot area is within the

condition class of interest and 0 otherwise, and the remaining symbols are described in their

respective sections.

The total area in the domain of interest is calculated following the estimators in section 3.2,

substituting for in equation 3.12 and 3.13. The estimated total area is then used in the

denominator of the ratio estimator (eq. 3.16). 

3.4 Estimating DWM for Individual Plots or Portion of Plots

For uses such as modeling, classifying plots, or mapping, it may be of interest to estimate DWM

attributes for individual plots or for condition classes within plot. When calculating separate estimates

per condition class within a plot, caution should be used when the transect length or number of

points in the condition class is small. In this situation, unreliable estimates may result. This situation is

relatively rare with FIA data, and the appropriate solution may depend on the intended use. In

general, we recommend that the transect length or number of points equivalent to those of an entire

subplot should be the minimum for plot-level calculations (Bechtold and Scott 2005: 40).
28

3.4.1. Coarse Woody Debris

From eq. 7.7 in Appendix 7.1, the LIS estimator for an attribute of interest in domain of interest d for a

plot, on a per-unit-area basis, can be computed as: 

(3.27)

where

is the attribute of interest measured in piece t intersected by transect m of subplot j. A piece is

recorded as many times as intersected by the transect.

(ft) is the length of piece t intersected by transect m of subplot j.

domain indicator variable which is 1 if piece t intersected by transect m of subplot j belongs to

the domain of interest d and 0 otherwise.

(ft) length of the segment of transect m of subplot j in the condition class of interest d’.

c constant to convert to proper units.

The attribute of interest in equation 3.27, , could be any attribute measured or calculated in each

piece. Table 3.4 lists some of the attributes that can be calculated from FIA data and the corresponding

estimator equations.

3.4.2. Fine Woody Debris

The estimator of the total volume of fine woody debris (ft3/acre), for each size class, is obtained from eq.

7.9 in Appendix 7.1:

(3.28)

where

(ft) slope-length of the transect segment on subplot j in the condition class of interest d’.

is the slope correction factor for the segment in the condition class of interest d’ of subplot j (eq.

3.4).

is the number of FWD pieces tallied in the diameter class of interest in condition class k of subplot j.

(in) is the quadratic mean diameter of the diameter class of interest in condition class k of

subplot j (Appendix 7.4).
29

Table 3.4. – Equations to estimate coarse woody debris attributes from individual plots (eq. 3.27)
30

domain indicator variable which is 1 if condition class k of subplot j is the condition classes of

interest d and 0 otherwise.

To compute FWD mass per unit area, the volume of FWD ( ) must be multiplied by bulk density

and the decay-reduction factor as presented in eq. 3.5.

3.4.3 Duff, Litter, and Fuelbed

Duff, litter, and fuelbed depth in domain of interest d is:

(3.29)

where

(in) is the depth of the duff, litter, or fuelbed at the end of transect m of subplot j.

domain indicator variable which is 1 if the point at the end of transect m of subplot j belongs to

the condition class of interest d and 0 otherwise.

To compute litter and duff mass per unit area, the depth ( in eq. 3.29) is multiplied by bulk

density (Appendix 7.4) and a unit-conversion factor. If the depth is measured in inches, the unitconversion factor to obtain tons per acre is 1.815. 

3.4.4 Fuel Loading (Shrubs, Herbs, and Litter Cover)

The average maximum height and cover of dead and live shrubs, herbs in the domain of interest d,

is:

(3.30)

where

is the depth (ft) or cover of herbs, shrubs or litter at microplot j. 

domain indicator variable which is 1 if microplot j is in the domain of interest d and 0 otherwise.

3.4.5 Slash Piles

Pile volume (ft3/acre) or weight (tons/acre) in domain of interest d, is:
31

(3.31)

where

is the volume (ft3

) or weight (tons) of pile t at subplot j.

domain indicator variable which is 1 if pile t in subplot j belongs to the domain of interest d and

0 otherwise.

area of subplot j in the condition class of interest d’.

3.5 Change Estimation

Through the process of remeasuring the same CWD transects there is a moderate likelihood that the

same CWD pieces will be remeasured in forest ecosystems with minimal disturbance and slow decay

rates, albeit not the case for rapidly decaying FWD pieces. Despite this occurrence, few crews

permanently mark CWD or FWD pieces. Therefore, unlike phase 2 standing-tree protocols that track

individual trees over time, it is assumed that individual woody pieces will not be relocated and

measured during remeasurement activities. Thus, it will not be possible to estimate components of

change, but it will be possible to estimate net changes over large areas by comparing estimates of

DWM components at two points in time or by combining information from different panels.

Estimating change is currently an area of active research by FIA. 
32
To facilitate efficient and effective analysis of

DWM data, forest-inventory analysts should be

well versed in the sampling protocol, estimators,

and management of DWM field data. Analysis of

DWM data follows a hierarchy based on level of

sophistication and required effort: field data,

plot/condition level analyses, core tables,

graphical summaries of population estimates, and

maps. Analysis of DWM data also depends on

access to actual data, with FIA analysts having

access to actual plot locations. Users of external

FIA data may have reduced access to plot

locations and less ability to link DWM data to all

phases of FIA’s inventory program. However,

most of the analysis in this section should be

available to all.

4.1 Field Data

Although field data provide the base of any

analytical exploration of DWM, analysts will only

infrequently deal with raw data. Field data are

organized into one of six tables (1.2-1.7).

Researchers engaged in specific DWM studies can

use these datasets where their investigations

require unique processing and/or summarization

of field data. An example of such an analysis is

the relationship between CWD large-end

diameters and total length on forest land in

Maine (Fig. 4.1). In such instances, individual

pieces or plots can be assumed to be a simple

random sample in forest land to assess ecological

dynamics, not a population estimate following

procedures detailed in section 3. Alternatively,

more complex models that incorporate the

clustered structure of the data can be used.

Otherwise, analysts may want to focus their

resources on provided plot/condition and

population estimates.

Although section 3.0 deals primarily with

estimation of total variability including 

both sampling variability and measurement

error, analysts should be aware of measurement

errors and their potential impact on

interpretation/application of field data. An 

initial examination of DWM measurement errors

(Westfall and Woodall, in press) indicates 

poor repeatability of most DWM variables with

some instances of bias, particularly for FWD.

Given the highly disturbed and transitory nature

of DWM, these repeatability results may be

expected. However, it was further found that

despite possible measurement errors, overall

33

Figure 4.1. – Relationship

between coarse woody

debris large-end diameter

and total length in Maine,

2001-2005.

4.0 DWM ANALYTICAL GUIDELINES
34

plot-level estimates of DWM resources were not

substantially affected.

4.2 Analyses at Plot/Condition Level

Most analysts will have access to estimates of

DWM components at the plot and/or conditionclass level. These outputs are not considered

population estimates of a defined domain (e.g.,

red oak forests in Missouri). Instead, these

estimates typically are expressed in per-unit-area

values for individual plots or conditions (e.g.,

CWD cubic-foot volume/acre for plot x,

condition class x) and are critical to modeling

and mapping efforts (see section 3.4 and

Appendix 7.2.3). For example, quantifying the

relationship between standing dead trees (snags)

and downed dead trees is critical to refining

understanding of the ecological process of tree

mortality contributions to the carbon cycle (Fig.

4.2). Another example is comparing the standing

live-tree forest-type to the species composition of

CWD pieces to evaluate forest change over long

periods (Woodall and Nagel 2006). A final

example is the mapping of individual plot-level

estimates of CWD carbon stocks across the

United States (Fig. 4.3). Such an analysis allows

examination of spatial trends in carbon stocks

across large scales.

4.3 Core Tables

Core tables provide population estimates of

DWM attributes of interest for specified

domains. The domains of core tables typically

are forest-type groups in individual states. Core

tables can be created using estimation

procedures for population totals (e.g, total CWD

tons in a region, see section 3.2 and Appendix

7.2.1) or ratio-estimation procedures (e.g., CWD

tons per forest land acre in a region, see section

3.3 and Appendix 7.2.2). A series of core tables

has been suggested for the DWM indicator based

on the estimation procedures defined in this

document (Tables 1.8, 4.1, 4.2, and 4.3). As

estimation procedures are implemented in

database procedures and provided to users, these

core tables may be revised. These tables can

serve as the basis of DWM investigations for

most inventory analysts wishing to present userfriendly output to the public. 

A fire science-oriented core table (Table 1.8)

contains ratio estimates of fuel loadings

(tons/acre) by forest-type group in a particular

state. Holistic assessments of fire hazard can be

made by combining the fire core table with other

datasets such as phase 2 stand information and

ancillary data (e.g., standing dead tree biomass,

meteorological data, fuel-ladder estimates, and

wildland-urban interface information). 

Figure 4.2. – Relationship

between standing dead

trees biomass (tons/acre)

and downed woody 

biomass (CWD+FWD)

(tons/acre) on FIA 

inventory plots in the

North-central United

States, 2001-2005.
35

Carbon-oriented core tables contain estimates

desired by the carbon and greenhouse gasaccounting scientific community (Table 4.1). The

core table contains population estimates of

DWM component total carbon stocks on forest

land in individual states. Because the soils

indicator collects information on duff, litter, and

small FWD, all DWM carbon components are

delineated to avoid overlap of carbon pools (e.g.,

separation of FWD size classes). These

delineations also match widely accepted carbon

conventions: duff, forest floor, FWD, and CWD

(Intergov. Panel on Clim. Change 1997).

Analysts can use the carbon core tables in

combination with other phases of the FIA

inventory (e.g., phase 2 tree inventory, phase 3

soils, and phase 3 vegetative diversity indicator)

to assess and monitor carbon pools of forest

ecosystems for specified domains. 

CWD core tables provide information about the

quantity and quality of habitat for fauna with

CWD niches (Table 4.2). CWD estimates also aid

in assessing structural diversity in forest

ecosystems. Therefore, the CWD core table

contains ratio estimates of CWD attributes per

unit of forest land by forest-type group in a

particular state. The CWD attributes include

large-end diameter distribution, decay-class

distribution, CWD volume, and CWD cover. The

distributions of CWD size and decay classes are

represented by the estimated mean number of

CWD pieces per acre. 

The most appropriate core table for fuel loading

information (shrubs and herbs) contains mean

height and cover of shrubs and herbs by foresttype group for an individual state (Table 4.3).

The mean cover of litter and fuelbed depth also

is included in this core table which provides

analysts with estimates that describe the fuel

ladders for a given domain. It can be assumed

that with all other environmental factors held

constant the greater cover and heights of these

fuel ladders indicate increased fire hazard.

4.4 Graphical Summaries

The estimates from DWM core tables and/or

population estimation procedures can be 

displayed in numerous ways (Figs. 4.1, 4.2). The

number of DWM plots in a defined domain

determines which DWM summaries are possible.

Analysis may not be possible if an analyst wishes

to examine fuel loadings in an infrequent forest

type in a state with a relatively small amount of

Figure 4.3. – Individual 

plot-level estimates of

coarse woody debris 

carbon stocks (tonnes/ha)

across the United States,

2001-2004 (plot values

matched to EMAP 

hexagons).
36

Forest-type group Forest floor Fine woody debris Coarse woody Slash

Duff Litter Small Medium Large debris

Maple/beech/birch 12.22 3.55 12.22 3.55 12.22 3.55 0.00

Oak/hickory 8.84 3.67 8.84 3.67 8.84 3.67 2.22

Oak/pine 13.54 2.64 13.54 2.64 13.54 2.64 6.00

Elm/ash/cottonwood 18.21 5.24 18.21 5.24 18.21 5.24 0.00

Loblolly/shortleaf pine 9.87 2.33 9.87 2.33 9.87 2.33 5.55

White/red/jack pine 11.46 1.34 11.46 1.34 11.46 1.34 3.55

Other types 7.78 2.43 7.78 2.43 7.78 2.43 0

All forest-type groups 81.92 21.20 81.92 21.20 81.92 21.20 2.22

Table 4.1. – Carbon stocks by forest-type group and down woody component on forest land (million tons), State X, Year 1 to Year 2 

Forest-type group Large-end diameter distribution (inches) Decay-class distribution CWD CWD 

3.0 – 7.9 8.0 – 12.9 13.0 – 17.9 18.0 + 1 2 3 4 5 volume cover

Maple/beech/birch 100.0 55.0 22.0 1.1 3.0 34.0 66.0 88.0 67.0 3.55 7.1

Oak/hickory 120.0 44.0 21.0 2.3 5.0 55.0 75.0 90.0 54.0 3.67 6.5

Oak/pine 233.0 35.0 23.0 4.0 7.0 45.0 67.0 98.0 56.0 2.64 8.9

Elm/ash/cottonwood 432.0 65.0 13.0 5.0 4.0 72.0 45.0 70.0 75.0 5.24 3.1

Loblolly/shortleaf pine 233.0 45.0 16.0 3.0 8.0 46.0 64.0 110.0 75.0 2.33 2.9

White/red/jack pine 244.0 76.0 31.0 7.0 9.0 75.0 79.0 87.0 58.0 1.34 6.6

Other types 234.0 75.0 24.0 2.1 2.2 44.0 97.0 96.0 77.0 2.43 5.4

All forest-type groups 265.0 45.0 12.0 1.3 7.8 65.0 76.0 86.0 78.0 1.34 4.9

Table 4.2. – Mean attributes of coarse woody debris by forest-type group and attribute on forest land, State X, Year 1 to Year 2

Table 4.3. – Mean attributes of shrub, herb, litter, and fuelbed by forest-type group on forest land, State X, Year 1 to Year 2

Note: diameter and decay distribution units are CWD pieces/acre, CWD volume is cubic feet/acre, CWD cover is percent of acre covered by CWD

Forest-type group Mean cover (percent) Mean height (feet) Fuelbed

Live Dead Live Dead Litter Live Dead Live Dead depth 

shrub shrub herb herb shrub shrub herb herb (feet)

Maple/beech/birch 60.5 5.5 77.6 3.3 96.0 3.1 0.9 0.4 0.1 2.2

Oak/hickory 44.3 7.2 59.0 5.4 89.7 2.3 0.7 0.3 0.2 1.8

Oak/pine 77.9 11.1 93.1 7.8 94.3 1.9 0.4 0.9 0.1 4.5

Elm/ash/cottonwood 69.4 3.6 88.4 2.2 95.1 2.2 0.2 0.6 0.2 2.1

Loblolly/shortleaf pine 78.4 5.9 83.1 2.7 89.6 1.1 0.8 0.1 0.3 3.7

White/red/jack pine 91.0 7.5 79.9 7.3 92.0 1.7 1.1 0.2 0.3 1.1

Other types 66.7 13.2 85.3 8.8 93.1 1.6 0.9 0.3 0.1 1.2

All forest type groups 75.6 8.8 81.7 5.4 91.0 1.9 0.8 0.4 0.2 1.6
37

forest land (e.g., hemlock types in Maryland). In

this case, the domain needs to be more inclusive

of DWM plots due to the sparse sample intensity

of phase 3 plots (e.g., hemlock types in New

England states). Analysts also must determine

the sampling errors associated with DWM

estimates to determine which scale is appropriate

for summary. A logical scale for summary of

DWM data collected at the national base

sampling intensity often is at the state or supercounty level (Fig. 4.4a). DWM data summaries at

scales smaller than a state might be permissible

in states with extensive forest areas or when

sample intensification occurs. Ratio estimates of

population means (tons/acre) also can be

displayed by broad forest-type groups within a

state (Fig. 4.4b). Beyond ratio estimates,

population totals can be displayed for a defined

domain (Fig. 4.5). Defined areas again will

depend on the sample size. If variances allow,

analysts can produce a summary chart at supercounty scales. 

0

2

3

4

5

6

7

ILINIAKSMIMNMONENDSDWI

Coarse Woody Debris

Fine Woody Debris

0

5

10

15

20

25

PinePine/HardwoodHardwood

Forest-type Group

Fine Woody Debris

Coarse Woody Debris

Duff

Litter

A

B Mean Tons/Acre Mean Forest Land Tons/Acre

Figure 4.4. – Possible

DWM summaries using 

population ratio estimates

(with associated sampling

errors) by two domains

(A) states in a region and

(B) forest-type groups in

an individual state.
38

4.5 Maps

Maps of DWM components can be created

several methods requiring various data inputs

and levels of sophistication. At the very least,

perturbed spatial locations of phase 3 inventory

plots and associated estimates of DWM

components are necessary to create maps.

Ancillary datasets that aid the DWM map

creation include but are not limited to ecological

provinces, phase 2 data (e.g., live-tree volumes),

and remotely sensed imagery (e.g.,

forest/nonforest maps). Estimates at the

plot/condition (see section 3.4) are the primary

data source for map creation.

The most basic type of map is one of perturbed

plot locations with associated estimates of DWM

components (Fig. 4.6). An analyst can use GIS

software to display plot locations that are colored

according to the associated DWM component.

Although limited in creative scope, this basic

map can be tailored to specific user requests,

such as answering the rhetorical question, “What

is the spatial distribution of FWD biomass in my

area of interest based on FIA plots?” 

A second type of DWM map can be created by

linking ancillary datasets that are spatial in

nature with the DWM inventory (Fig. 4.7).

Typically, a population-ratio estimate (e.g., mean

CWD volume per acre of forest land) can be

mapped to defined domains (e.g., ecological

province, Fig. 4.7). Mean values of DWM

components can be estimated for any spatial data

layer using procedures for estimating total

population (section 3.3) and mapping results to

domains defined in GIS layers (e.g., ecological

provinces).

Estimates at the plot/condition level estimates

can used to create “wall to wall” estimates of

DWM attributes using interpolation techniques

(Fig. 4.8). Interpolation entails predicting the

values of DWM components between all sample

points to create a continuous map of predicted

DWM values (Woodall et al. 2004). DWM maps

can be created in one of two ways by using

interpolation methodologies. An analyst can

constrain interpolation to forested areas as

defined by FIA phase 1 stratification imagery, or

an analyst can overlay an interpolated map of

DWM values on that of a forest/nonforest map,

thus masking out all nonforest areas (Fig. 4.8).

Maps can be created by intensive modeling based

on FIA phase 2 data (Fig. 4.9). This process uses

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

North Northeast Southeast Interior Coastal

Survey Unit Thousand Tons

Coarse Woody Debris

Fine Woody Debris

Litter

Duff

Figure 4.5. – Population

total estimates of DWM

components for an entire

state by inventory surveyunit domain.
39

Figure 4.6. – Plot-level 

estimates of fine woody

debris (tons/acre) in U.S.

forest land, 2001-2005.

Figure 4.7. – Mean

estimates of coarse

woody debris volumes for

North Central ecological

province sections (Bailey

1995), 2001-2002.
40

Figure 4.8. – Example of

inverse distance 

weighting interpolation

technique for creating

regional maps of DWM

estimates.

+

Forest/nonforest NLCD coverage for North Central states

Inverse distance weighting of coarse woody debris plot-level estimates, FIA phase 3

DWM plots, 2001-2003
41

both phase 2 and 3 data to create models such

that DWM components are estimated for every

phase 2 plot. Once satisfactory models are

created, DWM components can be estimated for

every phase 2 plot and mapped (Fig. 4.9).

Although the sampling intensity is much greater

for phase 2 plots, the efficacy of this methodology

depends on the explanatory power of the models

established between phase 2 and 3 plots. 

Finally, although DWM attributes (e.g., CWD

biomass) may be both correlated and directly

modeled with phase 2 attributes (e.g., standing

live tree basal area), there are numerous 

non-parametric methods that serve as an

interesting alternative. Non-parametric methods

may predict DWM attributes as a weighted

average of the values of neighboring observations.

In this process, neighbors are chosen from a

database of previously measured observations

(known pairs of phase 2 and phase 3 attributes).

Often these non-parametric methods are referred

to as imputation techniques where values are

assigned to observations that lack such data.

Given the relatively sparse sample intensity of

DWM plots relative to the diversity of forest

ecosystem components they estimate, nonparametric methods may offer several advantages

compared to using parametric regression models

to predict mean values.

The mapping of DWM indicator data is a

relatively recent analytical undertaking that

allows maximum freedom for analysts. Every

method for producing maps of DWM estimates

has advantages and disadvantages, and it is

suggested that analysts explore all options and

be aware of recent scientific developments.

4.6 Science Areas

There are numerous knowledge gaps in the study

of DWM ecology in forest ecosystems that may

help direct DWM research and inventory

reporting. Knowledge gaps can be broadly

summarized by discipline: wildlife, fire/fuels,

carbon, snags, structure, and nutrient cycles. With

regard to wildlife sciences, there are numerous

knowledge gaps in the effect of CWD decay and

size distributions on habitat, particularly for

specific wildlife species. Particularly with respect

to the DWM indicator, there has been a lack of

analysis of hollow codes inventoried by the FIA

program. With respect to the fire and fuel

sciences, there is both a great public need and a

significant knowledge gap in the following areas:

Figure 4.9. – Interpolation

of predicted down fuels

for Michigan, Minnesota,

and Wisconsin FIA phase

2 plot attributes based on

phase 2/phase 3 fuel

model (McRoberts et al.

2004).
42

mapping of fuel loadings, population summaries

by state/region, linkage between the FIA inventory

and models of fire behavior, comprehensive

assessments of fire danger by FIA plot, and

linkages between phase 2 and DWM plots. With

regard to assessments of carbon stocks, there are

numerous knowledge gaps both in the estimation

procedures and basic analyses. Carbon content

and bulk density of DWM components are not

measured, but calculated using volume-tobiomass-to-carbon conversion constants.

Increasing our understanding of how bulk density

and carbon content vary by species, tree size, and

decay class would, in turn, refine DWM carbonpopulation estimates. We also need to understand

how DWM carbon stocks such as CWD vary by

stand structure, management activities, and

change over time. With respect to standing dead 

trees, there has been a lack of analysis of both snag

and CWD (as defined by FIA) attributes

collectively. Because snags often are precursors of

CWD recruitment, increasing our understanding

of the relationship between DWM and snags could

be beneficial in predicting DWM attributes based

on the phase 2 inventory. With regard to

assessments of stand structure, DWM is a critical

component of the overall structure of stands but

often is omitted in most assessments of structure.

Including DWM attributes in assessments of stand

structure probably would require new structure

indices. Finally, there has been a lack of analysis of

DWM inventory data with respect to nutrient

cycling. The DWM inventory can be used to

increase our understanding of nutrient cycles in

forest ecosystems at the landscape scale.
43

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Department of Agriculture, Forest Service. 
Coarse Woody Debris (CWD): Pieces or portion

of pieces of down dead wood with a minimum

small-end diameter of at least 3 inches and a length

of at least 3 feet (excluding decay class 5). CWD

pieces must be detached from a bole and/or not be

self-supported by a root system with a lean angle

more than 45 degrees from vertical. 

Decay Class: Rating of individual coarse woody

debris according to a 5-class decay scale defined

by the texture, structural integrity, and appearance

of pieces. Scale ranges from freshly fallen trees

(class 1) to totally decomposed cubicle rot heaps

(class 5).

Down Woody Materials (DWM): Collective

attributes estimated by the DWM indicator.

Consists primarily of the following down and

dead forest materials: fine woody debris, coarse

woody debris, duff, litter, slash, live and dead

herb and shrubs, and fuelbed depths.

Duff: Organic forest-floor layer consisting of

decomposing leaves and other organic material in

which individual plant parts are not recognizable. 

Fine Woody Debris (FWD): Pieces or portion of

pieces of down woody debris with a diameter less

than 3 inches at the point of transect intersection;

excludes dead branches attached to standing trees,

dead foliage, bark fragments, and cubicle rot.

Fuelbed: Accumulated mass of all DWM

components above the top of the duff layer

(excluding live shrubs/herbs).

Herbs: Nonwoody vascular plants including but

not limited to ferns, mosses, lichens, sedges, and

grasses.

Line-Intersect Sampling (LIS): Sampling

technique by which sampling planes are installed

in defined areas of interest whereby the

intersection of down woody debris with sampling

planes is used to estimate attributes of coarse and

fine woody populations.

Litter: Forest-floor layer of freshly fallen leaves,

needles, twigs, cones bark chunks, dead moss,

dead lichens, dead herbaceous stems, and flower

parts.

Pile Density: Density of coarse woody debris in

slash piles within the volume defined by the

shape code and dimensions estimated by field

crews; also known as packing ratio.

Shrubs: Vascular plants with woody stems

exclusive of plants defined as trees by FIA.

Slash: Otherwise known as residue piles, coarse

woody debris in piles created directly from

human activity or from natural events that

prohibit safe measurement by transects.

Time-Lag Fuel Classes: Fuel classes defined by

the amount of time it takes for moisture conditions

to fluctuate. Larger coarse woody debris takes

longer to dry out than smaller fine woody pieces

(small FWD=1 hour, medium FWD=10 hours,

large FWD=100 hours, CWD=1,000+ hours). 

Transect Diameter: Diameter of coarse woody

pieces at the point of intersection with sampling

planes.

Transect Segment: Sections of transects that lie

entirely within one condition class whereby one

24-foot transect that lies across two condition

classes will have two transect segments.

Y Transect: Spatial arrangement of sampling

transects on FIA subplots whereby they radiate

out from the subplot center at obtuse angles of

120 degrees from each other.

48

6.0 GLOSSARY 
49

7.1. Line-intersect Sampling of Coarse and Fine Woody Debris

Line-intersect sampling (LIS) differs from the fixed-area plots used in phase 2 of the FIA inventory. It

may be a novel concept for some analysts, so we present background on its development and

application. The fundamental concept of LIS, also known as line-intercept and planar-intercept

sampling, is that sampling of down woody debris occurs along transect lines. Before LIS was

introduced, down woody debris was sampled by tallying down woody pieces within a defined area.

Warren and Olsen (1964) introduced the first application of the LIS technique for estimating logging

residue in New Zealand. On the basis of this work, there have been a number of refinements and

alterations of LIS that are reflected in the FIA methods. Van Wagner (1968) introduced a method for

requiring only field measurements of the diameter of each piece at transect intersection for

determining volume, discussed potential sources of bias when using LIS, and suggested the use of Lor Y-shape transects. de Vries (1973) and de Vries and van Eijnsbergen (1973) expanded LIS theory,

including populations of linear particles of arbitrary shape, and proposed various LIS estimators,

many of which are used by FIA. One of the most widely used manuals based on this work is Brown’s

(1974) handbook on inventorying DWM. It remains a key reference for determining fuel loadings

across the Western United States. Hazard and Pickford (1986) and Bell et al. (1996) examined transect

shape and the effect of the orientation of the pieces of wood in estimation, and concluded that a Yshape transect is the most efficient transect design. Kaiser (1983) generalized LIS for particles of any

shape and provided a comprehensive treatment from a design-based perspective. The most detailed

treatment of LIS theory for CWD estimation is in de Vries (1986, chapter 13). Recent reviews include

Marshall et al. (2000) and Waddell (2002), the latter from an FIA perspective. 

7.1.1. Background and Notation

Here we derive the LIS estimator specifically for estimating coarse and fine woody debris. For the

purpose of sampling woody debris, each log is reduced to its centerline axis. Therefore, we consider

a population of discrete lines of arbitrary shape, possibly branched, distributed over a region A of

area equal to A. We do not make assumptions about the characteristics of the lines or their location

or orientation. However, we ignore edge effects so that the estimators apply only to pieces in the

interior of A. The definition of the region of interest and the treatment of edges by FIA is described

in Scott et al. (2005). 

Let yt be any fixed, measurable attribute of the t-th piece (e.g., volume). We are interested primarily in

estimating the total amount of the attribute of interest in the region A, defined as the sum of yt over all

the pieces in the population, 

, where N is the number of pieces in A. Other parameters, such as values per unit area,

follow directly by dividing the total by the area A, or by using ratio estimators (section 3.3).

The population is sampled with a straight-line transect of length L. A piece is included in the sample

if its centerline is intersected by the transect, and the number of intersections is recorded. Then, an

unbiased estimator of the total is:

(7.1)

7.0 APPENDICES
50

where the sum is over the pieces intersected by the transect, n is the number of intersected pieces, zt is

a random variable that counts the number of intersections between the transect and the piece, and

E(•) is the expectation, or mean, operator. 

To prove that the estimator 7.1 in unbiased, we need to show that its expected value is the parameter

of interest, that is, . First note that if a piece is not intersected by the transect, the number

of intersections zt = 0. Therefore, the sum in equation 7.1 can be extended from the pieces included in

the sample, n, to all the pieces in the population, N:

(7.2)

The only random variable in equation 7.2 is zt , and the expectation is a linear operator, so

unbiasedness follows:

Therefore, to obtain an unbiased estimator of the total , all that is needed is the ability to calculate

the expected number of intersections, E(zt

), for those pieces intersected by the transect. 

7.1.2. Expected Number of Intersections Between Transect and Piece of Wood

The derivation of the expected number of intersections between the transect and a piece of wood of

arbitrary shape follows three steps. First, it is derived for a hypothetical population of straight-line

pieces. Then, as an intermediate step, it is extended to a population of pieces formed by connected,

straight-line segments. Finally, it is generalized to a more realistic population of continuous lines of

arbitrary shape, such as log centerlines. A different derivation is found in de Vries (1986, chapter 13)

and Kaiser (1983, example 2d).

The population is sampled uniformly at random with a straight-line transect of length L, specifically:

(1) the transect midpoint might lay anywhere in A with equal probability, so that the probability that

the midpoint falls in any subset, B, is the area of B divided by the area of A; (2) the transect azimuth,

, can take any value between 0 and 180 degrees ( radians) with equal probability, so that the

probability distribution of is uniform in the interval [0, ]; (3) the location and azimuth of the

transect are determined independently. 

Population of straight lines

Consider a population of discrete, straight-line pieces. Figure 7.1(a) shows an example of a portion of

the region of interest A, highlighting an arbitrary piece. Figure 7.1(b) shows a possible location of the

transect, in which the t-th piece is intersected. Because both the transect and the piece are straight

lines, there can be only one intersection at most. Therefore, zt is an indicator variable, that is, 1 if the

piece is intersected, or 0 otherwise. By definition, the expected value of the random variable zt is the

probability of intersection, . 

To derive the probability that the transect intersects the t-th piece, we first fix the transect azimuth to

an arbitrary angle . The transect intersects the piece if and only if its center falls in the area shaded in
51

Figure 7.1(c). This area is , where lt is the length of the piece and t is the angle between the

piece and the transect. Therefore, conditional on the value , and because of condition (1), the probability

that the transect intersects the piece is the area divided by the area of A:

(7.3)

The azimuth of the piece is fixed and constant. t

, the angle between the piece and the transect, is 

calculated as the azimuth of the piece, a constant, minus . Thus, the distribution of t also is uniform on

the interval [0, ] (condition (2)), with probability density . We can apply the law of total 

probability to obtain the probability of intersection, unconditional of transect orientation, as the conditional

probability [7.3], averaged over all possible values of :

(7.4)

Population of segmented lines

Consider a population of lines composed of an arbitrary number St of connected, straight-line segments,

each of length lts. We do not make assumptions about how the segments are arranged or whether the piece

is branched or a single line. Define a random variable, zts, that takes the value of 1 if the s-th segment of the

t-th piece is intersected by the transect and 0 otherwise. Let 

be a random variable that counts the number of intersections between the t-th piece and the

transect, and 

the total length of the piece. Then, from equation 7.4 and the linear properties of the expectation

operator,

(7.5)

Population of lines of arbitrary shape

The generalization to continuous linear pieces of finite length and arbitrary shape follows by taking the limit

of a segmented piece as . The t-th piece is divided into S+1 points, which define S segments of

length . In the limit, this segmented line approaches the arbitrarily shaped line. Then, substituting

equation 7.5, the expected number of intersection is:

(7.6)

Therefore, the expected number of intersections between a piece and the transect is exactly the same

whether the piece is straight line or a line of arbitrary shape. It depends only on the piece’s length, not its

shape (de Vries 1986: 272, Kendall and Moran 1963: 71).

7.1.3. Line-intersect Sampling Estimator: Straight-line Transect

From eqs. 7.1 and 7.6, the LIS estimator of the population total of a measurable attribute, , for linear
52

pieces of arbitrary shape is:

(7.7)

where the sum is over the pieces intersected by the transect (n). In this equation, zt is the number of

times that the t-th piece is intersected by the transect. To facilitate data recording in the field rather

than tallying the number of intersections, FIA tallies each piece as many times as intersected by the

transect. Then, the equation can be written as:

(7.8)

where the last sum is over the number of intersections, , not the number of pieces. 

If the attribute of interest is the total volume of down wood, then yt is the volume of the t-th piece.

This volume can be estimated by realizing that the diameter at the intersection is a random sample of

the diameter of the piece (De Vries 1986: 258), so that 

where DI is the diameter at the intersection, is an estimate of the volume of the piece.

Substituting in eq. 7.8, 

(7.9)

where is the estimated total volume and the quadratic mean diameter at the intersection.

This is the equation used by FIA to estimate fine woody debris. 

7.1.4. Line-intersect Sampling estimator: Segmented Transects

Extension to a Y-shape transect, or to a cluster of M lines arranged in any shape, is straightforward:

the estimator is applied to each arm of the transect, and the estimates averaged (Van Wagner 1968).

Let be the estimator in eq. 7.7, unbiased for a straight-line transect, applied to the m-th arm of the

transect. Then, the average over M arms, regardless of transect configuration, always is unbiased:

(7.10)

where the last sum is over the pieces intersected by any branch of the transect, ML is the total transect

length, znt is the number of the number of intersections between the t-th piece and the m-th branch of

the transect, and 

is the total number of intersections between the t-th piece and any branch of the transect.

Note that eqs. 7.7 and 7.10 have the same form. Therefore, the estimator is exactly the same whether

a single-line or a cluster of lines is used. 
53

7.1.5. Orientation Bias

The derivation discussed in section 7.1.2 for populations of

straight-line pieces was proposed by Buffon in 1777 and generally

is known as Buffon’s “needle” problem. It concerns the probability

that two straight lines intersect — one fixed at an arbitrary location

and orientation within a region, and one randomly thrown into 

that region (needle). This is simply a probability exercise and does

not specify whether the needle should be the transect or the piece

of wood. If the transect is the needle then inference is based on the

sampling design and the expectation in eq. 7.4 is valid for any

location and orientation of the pieces. Alternatively, the transect

may be set at a fixed position and orientation and the pieces of

wood are assumed to be randomly distributed in A. If this

distribution follows the conditions listed in section 7.1.2, i.e., that

any piece location and orientation are equally likely, then eq. 7.4

gives the expected value of the number of intersections. It is

important to note that those conditions are only sufficient, not

necessary for eq. 7.4 to be valid. Most of the initial work on LIS

for estimating down wood was developed under the assumption of

a population of pieces distributed at random (e.g., Warren and

Olsen 1964, Van Wagner 1968, de Vries 1973). Both Kaiser (1983)

and de Vries (1986) discussed estimation in a fixed population of

arbitrary pieces.

If the conditions under which an estimator is derived are not met,

bias is possible. Orientation bias, which can occur if the actual

orientation (of pieces or transect) is not uniformly at random, has

received much attention. Van Wagner (1968) suggested the use of

transects oriented in various directions to minimize this bias.

Although he was working under the assumption of a randomly

oriented population of pieces, the same conclusion applies when a

random orientation of the transect is postulated but not fully met.

For a Y-shape transect, maximum bias occurs if all the pieces are

oriented in exactly the same direction and the angle between the

pieces and any branch of the transect is 30 or 0 degrees. Then,

upper and lower bounds for the bias are +5 and -9 percent,

respectively. Obviously, in a real population not all pieces are

oriented exactly in those directions so that, even if there is a

dominant orientation, the actual bias likely will be negligible. The

primary issue with respect to transect configuration is efficiency

(both statistical and practical). Without knowledge of the actual

distribution of the pieces of wood in the study population, any

discussion of the relative statistical efficiency of straight-line versus

Y-shape transects is speculation. Bell et al. (1996) and Hazard and

Pickford (1986), using a series of simulation studies to examine

transect configuration and concluded that, under their simulation

assumptions, a Y-shape configuration is the most efficient in both

variance and field implementation.

Figure 7.1. – Line-intersect sampling: the process used

to calculate a piece’s inclusion probability. 
54

7.2. Examples

In this section the estimation procedures described in section 3.0 are illustrated with three examples.

The first concerns estimating the total biomass of coarse woody debris in a population. The first of

three steps is to compute the total biomass in each plot, corrected for plots partially outside of the

population (section 3.1.1). In the second step, the computed plot values are averaged to the stratum

level (section 3.2). Finally, the averages for each stratum are combined to arrive at an estimate of the

total for the population (section 3.2). Because the total amount of biomass is the parameter of interest

regardless of species or any other attribute, all pieces are included and the domain indicator variable is

always 1 (domain restrictions are considered in the second example). 

The second example illustrates a ratio estimator with domain restrictions. We estimate the mean

number of large pieces of woody debris per acre of Douglas-fir forest. Estimating a ratio requires

estimating the population total of both the numerator (number of large pieces) and denominator

(acreage in Douglas-fir forest type), following the steps in the first example. The domain for the

numerator is based on both an attribute of the piece (defined here as large end diameter greater than

20 inches) and the forest condition in which it is located (Douglas-fir forest type), while the domain of

the denominator is singly defined by a forest condition (Douglas-fir type). The total acreage in

Douglas-fir forest can be estimated from phase 2 mapped plots; however, we recommend and will use

transect data as described in section 3.3.2.

The third example illustrates the estimation of a DWM attribute for a portion of a plot. We estimate the

biomass of CWD in accessible forest land for one plot, following procedures described in section 3.4.

We illustrate the estimation procedures using a hypothetical stratum composed of four plots. Each

plot represents a different situation that may be encountered when analyzing FIA DWM data. One

plot could not be measured because the property owner denied access and a second plot was only

partially measured because a portion was too hazardous to be sampled (e.g., cliff or meth lab). The

other two plots straddle two condition classes: one was partially nonforested while the other straddled

two forest types. Each of those situations is treated differently as is seen in the examples. 

7.2.1. Estimating Population of Total Biomass in Coarse Woody Debris

Compute values at plot level

The first step is computing the adjustment factor for partial plots outside the population, ,

following eq. 3.2. Table 7.2.1 shows the plot and condition class data that are needed to compute this

equation. The stratum contains four plots, but the owner denied access to one of them. Thus, the

number of observed plots in the stratum (nh) is three and the total length of transect that could

potentially be observed is 864 ft (3 plots * 12 transects per plot * 24 ft per transect). The length of

transect actually measured in the stratum is calculated using information provided in Tables 7.2.1 and

7.2.2. Field crews record the slope and slope distance of each transect segment, from which the

horizontal length of each segment, , is calculated. The horizontal distance is provided by default

in the standard FIA tables, but can be calculated as:

where and are the length and slope of the transect, respectively.
55

Each segment also is assigned to a condition class. From Table 7.2.1, the only condition class outside

of the population is that labeled 2 in plot 3. This portion of the plot was considered hazardous and

could not be accessed. Note that condition class 2 in plot 1 is not forested. However, although

nonforested land never is a domain of interest, nonforested conditions are part of the population and

are observed. Therefore, the indicator variable, takes the value of 1 for all segments except those

in condition class 2 of plot 3. The length of transect measured,

, can be calculated by simply summing column in Table 7.2.2. 

Based on these calculations, is:

The next step entails computing eq. 3.1 for each observed plot in the stratum. Table 7.2.3 provides

the information for each intersected piece of down wood. To compute the total biomass, we first

calculate the piece’s volume using equation 1 or 2 in Table 3.1, as appropriate. Next, the piece’s

biomass is calculated by multiplying the volume by the bulk density of the species’ wood (Appendix

7.5), a decay-class mass-reduction factor (Table 3.2), and a constant to convert to proper units (eqs. 3

and 4, Table 3.1). Table 7.2.3 shows the computed volume and biomass of each piece in cubic feet

and pounds, respectively. Plot biomass is computed from equation 3.1, where is the biomass of

each piece and the unit conversion factor to tons per acre is 43560/2000. Because we are interested in

total biomass, all pieces are in the domain of interest and always is 1. Example 2 illustrates the

case when domain restrictions are imposed in the pieces of wood and, as a consequence, is not

1 for all the pieces. Eq. 3.1 can now be computed for each plot:

Plot 1: 

Plot 2: 

Plot 3: 

Computed stratum mean and variance 

The next step combines the data from each plot to yield an average for the stratum (eq. 3.12):

with estimated variance (eq. 3.13):
56

Total biomass and its variance 

The estimated total biomass is obtained by combining information from all the strata in the

population. Table 7.2.4 provides the stratum data from a hypothetical population, where stratum 1 is

the stratum illustrated in this example. For stratified sampling, the estimated total biomass is

calculated from eq. 3.14:

with estimated variance (eq. 3.15)

The standard error is estimated as the square root of the variance:

7.2.2 Number of Large Pieces of Woody Debris per Acre of Douglas-fir Forest

In this example we estimate the total number of pieces of CWD with a large-end diameter greater

than 20 inches per acre of Douglas-fir forest type. The first task when estimating a ratio involves

computing the population total for both the numerator and denominator, as described in the first

example. However, because of the domain restrictions, we use indicator variables to select the

pieces and transect segments that meet the criteria of the domains of interest. 

Compute values at plot level

In the first example, we calculated . The next task is to compute the estimated

number of large pieces of CWD for each plot in the stratum, applying eq. 3.1. In this case, 

always is 1 (eq. 5, Table 3.1). is an indicator variable that takes the value of 1 if the piece of

wood belongs to the domain (large-end diameter greater than 20 inches and in a Douglas-fir forest

type condition class), and 0 otherwise. To calculate , we first assign each piece to a condition

class, based on the slope distance from subplot center to the point of intersection of each piece

(Table 7.2.3) and the transect segment beginning and ending slope distance (Table 7.2.2). Only
57

pieces in the Douglas-fir forest type are included, that is, pieces in condition class 1 in plot 1, 2 in

plot 2, and 1 in plot 3 (Table 7.2.1). Next, is assigned a value of 1 for the large pieces in this

condition class. Eq. 3.1 can then be computed:

Plot 1:

Plot 2: 

Plot 3: 

The next step requires estimating the proportion of each plot’s transect length in Douglas-fir forest

type adjusted for partial plots outside the population (section 3.3.2). is again a domain

indicator that takes the value of 1 if a transect segment falls within the Douglas-fir forest type

condition class, or 0 otherwise (Table 7.2.2). Then, eq. 3.20 is computed for each plot using the

column labeled as :

Plot 1: 

Plot 2 

Plot 3 

Computed stratum means, variances and covariance 

The estimated strata means and variances for each of the two variables (number of large pieces and

proportion of Douglas-fir forest type) are calculated as described in the first example, yielding:

Stratum mean Stratum variance

Number of large pieces per acre, 7.51 6.98

Proportion in Douglas-fir forest, 0.6145 0.0286
58

Estimating the variance of a ratio requires an estimate of the covariance between the two variables,

following eq. 3.19:

Population totals

The total number of large pieces and acreage of Douglas-fir forest type are estimated following the

process described in the first example, using data from Table 7.2.4: 

Total Variance

Number of large pieces, 3,236,354 (1,062,388)2

Acreage of Douglas-fir forest, (acres) 367,443 (104,102)2

Therefore, we estimate that there are approximately 3.2 million pieces of large CWD in Douglas-fir

forest type, and that this forest type covers 367,400 acres. 

The estimated population covariance is calculated from eq. 3.18 as:

Estimated ratio and its variance 

The final step is dividing the estimated total number of large pieces of CWD in the population by the

estimated acreage of Douglas-fir forest (eq. 3.16):

with estimated variance (eq. 3.17):

The standard error, estimated as the square root of the variance, is 3.05 pieces per acre. Assuming that

the sampling distribution of the estimator can be approximated by a normal distribution, an

approximate 95 percent confidence interval for the average number of large CWD pieces per acre of
59

Douglas-fir forest is 2.27 to 15.34 ( , where is the 97.5 percentile of a tdistribution with n-1 = 14 degrees of freedom).

7.2.3. CWD Biomass in Individual Plot 

In this example, we illustrate the estimation of the CWD biomass in accessible forest land in plot 1

(Table 7.2.3) using eq. 3.27. First, from Table 7.2.2 we estimate the length of transect in accessible

forest land, denoted by condition class code 1. There are 58.38 ft of forest-land subplot 1, 72 ft in each

of subplots 2 and 3, and none in subplot 4, for a total of 202.8 ft of transect in forest land.

The volume of each piece was calculated in the first example and is included in Table 7.2.3. There are

no domain restrictions in the pieces because we are interested in the biomass of all CWD pieces

present. Therefore, eq. 3.27 can be computed: 

Note the difference in the estimated CWD biomass for plot 1 in example 1 (25.17 tons per acre) and

example 3 (32.33 tons per acre). In the first example, the objective was to estimate the total biomass in

the population, which includes nonforest conditions. The amount of CWD biomass in nonforested

conditions is 0 but those conditions actually are sampled. Further, in the first example, we needed to

account for the portion of plots in the stratum that are not sampled. In this example, the interest is in

describing what was found in the observed plot only, not the population. Therefore, only the condition

of interest is included in the estimator as information from other plots in the population is not

required. Users should be aware of this difference and interpret plot-level estimators accordingly. 

Plot Condition class Land class Forest type

1 1 Accessible forest land Douglas-fir

1 2 Nonforest land ---

2 1 Accessible forest land Red alder

2 2 Accessible forest land Douglas-fir

3 1 Accessible forest land Douglas-fir

3 2 Hazardous ---

4 ------ Access denied by owner ------

Table 7.2.1. – Plot and condition class information in a stratum
60

Measured variables Computed variables

Example 1 Example 2

Begin End Segment 

slope slope length

Condition dist. dist. Slope

Plot Subplot Transect Segment class (ft) (ft) (%) (ft)

1 1 30 1 1 0 32.3 90 24.0 1 24.0 1 24.0

1 1 150 1 1 0 31.5 85 24.0 1 24.0 1 24.0

1 1 270 1 1 0 11.0 20 10.8 1 10.8 1 10.8

1 1 270 2 2 11 24.5 20 13.2 1 13.2 0 0.0

1 2 30 1 1 0 31.5 85 24.0 1 24.0 1 24.0

1 2 150 1 1 0 29.3 70 24.0 1 24.0 1 24.0

1 2 270 1 1 0 24.5 20 24.0 1 24.0 1 24.0

1 3 30 1 1 0 27.4 55 24.0 1 24.0 1 24.0

1 3 150 1 1 0 25.4 35 24.0 1 24.0 1 24.0

1 3 270 1 1 0 24.0 0 24.0 1 24.0 1 24.0

1 4 30 1 2 0 28.0 60 24.0 1 24.0 0 0.0

1 4 150 1 2 0 27.4 55 24.0 1 24.0 0 0.0

1 4 270 1 2 0 24.1 10 24.0 1 24.0 0 0.0

2 1 30 1 1 0 24.5 20 24.0 1 24.0 0 0.0

2 1 150 1 1 0 24.1 10 24.0 1 24.0 0 0.0

2 1 270 1 1 0 24.5 20 24.0 1 24.0 0 0.0

2 2 30 1 2 0 24.3 15 24.0 1 24.0 1 24.0

2 2 150 1 2 0 24.3 15 24.0 1 24.0 1 24.0

2 2 270 1 2 0 24.5 20 24.0 1 24.0 1 24.0

2 3 30 1 1 0 26.8 50 24.0 1 24.0 0 0.0

2 3 150 1 1 0 24.1 10 24.0 1 24.0 0 0.0

2 3 270 1 1 0 25.8 40 24.0 1 24.0 0 0.0

2 4 30 1 1 0 24.5 20 24.0 1 24.0 0 0.0

2 4 150 1 1 0 24.1 10 24.0 1 24.0 0 0.0

2 4 270 1 1 0 24.5 20 24.0 1 24.0 0 0.0

3 1 30 1 1 0 28.0 60 24.0 1 24.0 1 24.0

3 1 150 1 1 0 24.0 0 24.0 1 24.0 1 24.0

3 1 270 1 1 0 14.3 40 13.3 1 13.3 1 13.3

3 1 270 2 2 14.3 --- --- 10.7 0 0.0 0 0.0

3 2 30 1 2 --- --- --- 24.0 0 0.0 0 0.0

3 2 150 1 2 --- --- --- 24.0 0 0.0 0 0.0

3 2 270 1 2 --- --- --- 24.0 0 0.0 0 0.0

3 3 30 1 1 0 25.1 30 24.0 1 24.0 1 24.0

3 3 150 1 1 0 24.3 15 24.0 1 24.0 1 24.0

3 3 270 1 1 0 28.6 65 24.0 1 24.0 1 24.0

3 4 30 1 1 0 24.1 10 24.0 1 24.0 1 24.0

3 4 150 1 1 0 24.0 0 24.0 1 24.0 1 24.0

3 4 270 1 1 0 28.0 60 24.0 1 24.0 1 24.0

Table 7.2.2. – Transect segmentation data
61

Measured data Calculated data Calculated data

Small- Large- (Example 1) (Example 2)

Slope end end 

dis- Transect diam- diamSub- tance Decay diameter eter eter Length Volume Biomass Cond. 

Plot plot Transect (ft) Species class (in) (in) (in) (ft) (ft3) (lb) class

1 1 30 15 Douglas-fir 2 3 3 5 9 0.83 19.7 1 0

1 2 30 20.4 Douglas-fir 1 28 20 28 98 316.43 8889.6 1 1

1 2 150 6.7 Douglas-fir 4 14 11 21 70 107.28 1356.3 1 1

1 3 30 12.2 Douglas-fir 2 33 12 33 139 467.39 11029.6 1 1

2 1 150 1.5 Red alder 4 7 6 7 4 0.93 9.0 1 0

2 1 270 9.9 Red alder 1 3 3 4 9 0.61 14.2 1 0

2 2 30 2.4 Red alder 3 4 3 4 10 0.68 7.1 1 0

2 2 30 4.8 Red alder 3 5 4 5 14 1.57 16.3 1 0

2 2 30 5.5 Red alder 3 7 3 7 48 7.59 78.9 1 0

2 2 30 7.6 Red alder 3 6 4 7 25 4.43 46.1 1 0

2 2 30 14.8 West. hemlock 3 4 3 4 7 0.48 8.9 1 0

2 2 150 4.5 Red alder 3 5 4 5 15 1.68 17.4 1 0

2 2 150 10.7 West. hemlock 2 6 3 6 15 1.84 40.5 1 0

2 2 150 23.9 West. hemlock 2 8 3 8 21 4.18 92.1 1 0

2 3 150 7.6 West. hemlock 4 6 8 9 10 3.95 46.7 2 0

2 3 150 20.5 West. hemlock 4 4 3 4 3 0.20 2.4 2 0

2 3 270 16.4 Douglas-fir 3 17 13 25 102 220.86 4405.4 2 1

2 3 270 20.5 Douglas-fir 3 8 7 11 19 8.81 175.7 2 0

3 1 30 10.3 Douglas-fir 3 11 3 18 87 79.01 1575.9 1 0

3 1 150 18.7 West. hemlock 2 9 5 10 48 16.36 360.4 1 0

3 3 30 6 Douglas-fir 4 20 13 30 44 128.27 1621.6 1 1

3 3 30 17.7 Red alder 4 3 3 5 16 1.48 14.4 1 0

3 3 150 6.2 Douglas-fir 3 28 24 33 87 395.03 7879.4 1 1

3 3 150 8.9 West. hemlock 2 6 6 7 11 2.55 56.2 1 0

3 3 150 17.3 Douglas-fir 2 20 15 25 100 231.80 5470.2 1 1

3 4 30 3.7 Unknown 5 20 --- --- 21 45.81 579.2 1 ---

3 4 30 18.2 Douglas-fir 4 15 17 18 32 53.49 676.3 1 0

3 4 150 22.3 West. Hemlock 2 4 3 4 4 0.27 6.0 1 0

3 4 270 12.6 Douglas-fir 3 3 3 4 6 0.41 8.2 1 0

Table 7.2.3. – Coarse woody debris piece data

Observed variables Calculated variables

Example 1 Example 2

Proportion Biomass Number of large pieces Proportion in 

Observed area in Mean Variance Mean Variance Douglas-fir forest

Area plots strata (tons/ (tons/ (pieces/ (pieces/

Stratum (acres) (nh) (Wh) acre) acre)2 acre) acre)2 Mean Variance Covariance

1 403,200 3 0.2517 23.36 52.03 7.51 6.98 0.6145 0.0286 0.4193

2 470,400 5 0.2936 0.98 0.96 0.00 0.00 0.0000 0.0000 0.0000

3 728,400 7 0.4547 11.4 2.87 0.286 0.082 0.1643 0.0109 0.0279

Total 1,602,000 15

Table 7.2.4. – Stratum data
62

Species Bulk Species Bulk 

number Genus Species density number Genus Species density

10 Abies spp. 21.22 476 Cercocarpus montanus 62.40

11 Abies amabilis 24.96 479 Cercocarpus intricatus 62.40

12 Abies balsamea 21.22 481 Cladrastis lutea 32.45

14 Abies bracteata 22.46 490 Cornus spp. 39.94

15 Abies concolor 23.09 491 Cornus florida 39.94

16 Abies fraseri 21.22 492 Cornus nuttallii 36.19

17 Abies grandis 21.84 500 Crataegus spp. 38.69

19 Abies lasiocarpa 19.34 510 Eucalyptus spp. 41.81

20 Abies magnifica 22.46 521 Diospyros virginiana 39.94

21 Abies magnifica var.

shastensis 22.46 531 Fagus grandifolia 34.94

22 Abies procera 23.09 540 Fraxinus spp. 33.70

41 Chamaecyparis lawsoniana 24.34 541 Fraxinus americana 34.32

42 Chamaecyparis nootkatensis 26.21 542 Fraxinus latifolia 31.20

43 Chamaecyparis thyoides 19.34 543 Fraxinus nigra 28.08

50 Cupressus spp. 27.46 544 Fraxinus pennsylvanica 33.07

60 Juniperus spp. 27.46 545 Fraxinus profunda 33.70

64 Juniperus occidentalis 27.46 546 Fraxinus quadrangulata 33.07

69 Juniperus monosperma 28.08 551 Gleditsia aquatica 37.44

70 Larix spp. 27.46 552 Gleditsia triacanthos 37.44

71 Larix laricina 30.58 555 Gordonia lasianthus 23.09

72 Larix lyallii 29.95 571 Gymnocladus dioicus 31.20

73 Larix occidentalis 29.95 580 Halesia spp. 19.97

81 Calocedrus decurrens 23.09 591 Ilex opaca 31.20

90 Picea spp. 23.71 600 Juglans spp. 31.82

91 Picea abies 23.71 601 Juglans cinerea 22.46

92 Picea breweriana 20.59 602 Julglans nigra 31.82

93 Picea engelmannii 20.59 611 Liquidambar styraciflua 28.70

94 Picea glauca 23.09 621 Liriodendron tulipifera 24.96

95 Picea mariana 23.71 631 Lithocarpus densiflorus 36.19

96 Picea pungens 23.71 641 Maclura pomifera 47.42

97 Picea rubens 23.71 650 Magnolia spp. 28.08

98 Picea sitchensis 23.09 660 Malus spp. 38.06

101 Pinus albicaulis 23.09 680 Morus spp. 36.82

102 Pinus aristata 23.09 681 Morus alba 36.82

103 Pinus attenuata 23.09 682 Morus rubra 36.82

104 Pinus balfouriana 23.09 691 Nyssa aquatica 28.70

105 Pinus banksiana 24.96 692 Nyssa ogeche 28.70

106 Pinus edulis 31.20 693 Nyssa sylvatica 28.70

107 Pinus clausa 28.70 701 Ostrya virginiana 39.31

108 Pinus contorta 23.71 711 Oxydendrum arboreum 31.20

109 Pinus coulteri 23.09 712 Paulownia tomentosa 23.71

Appendix 7.3. Bulk density (lbs/ft3) by tree species for the United States (USDA Forest Service 1999)
63

110 Pinus echinata 29.33 721 Persea borbonia 31.82

111 Pinus elliotti 33.70 731 Platanus occidentalis 28.70

112 Pinus engelmannii 23.09 740 Populus spp. 23.09

113 Pinus flexilis 23.09 741 Populus balsamifera 19.34

114 Pinus strobiformis 21.84 742 Populus deltoides 23.09

115 Pinus glabra 25.58 743 Populus grandidentata 22.46

116 Pinus jeffreyi 23.09 744 Populus heterophylla 23.09

117 Pinus lambertiana 21.22 745 Populus deltoides 23.09

118 Pinus leiophylla 23.09 745 Populus sargentii 23.09

119 Pinus monticola 21.84 746 Populus tremuloides 21.84

120 Pinus muricata 23.09 747 Populus balsamifera 19.34

121 Pinus palustris 33.70 748 Populus fremontii 21.22

122 Pinus ponderosa 23.71 749 Populus angustifolia 21.22

123 Pinus pungens 30.58 752 Populus alba 23.09

124 Pinus radiata 23.09 755 Prosopis spp. 36.19

125 Pinus resinosa 25.58 760 Prunus spp. 29.33

126 Pinus rigida 29.33 761 Prunus pensylvanica 22.46

127 Pinus sabiniana 23.09 762 Prunus serotina 29.33

128 Pinus serotina 31.82 763 Prunus virginiana 22.46

129 Pinus strobus 21.22 765 Prunus nigra 29.33

130 Pinus sylvestris 25.58 766 Prunus americana 29.33

131 Pinus taeda 29.33 800 Quercus spp. 36.19

132 Pinus virginiana 28.08 801 Quercus agrifolia 43.68

133 Pinus monophylla 31.20 802 Quercus alba 37.44

133 Pinus nigra 25.58 803 Quercus arizonica, grisea 43.68

134 Pinus discolor 31.20 804 Quercus bicolor 39.94

135 Pinus arizonica 23.09 805 Quercus chrysolepis 43.68

202 Pseudotsuga menziesii 28.08 806 Quercus coccinea 37.44

211 Sequoia sempervirens 21.22 807 Quercus douglasii 31.82

212 Sequoiadendron giganteum 21.22 808 Quercus durandii 37.44

221 Taxodium distichum var. 

nutans 26.21 809 Quercus ellipsoidalis 34.94

231 Taxus brevifolia 37.44 810 Quercus emoryi 43.68

241 Thuja occidentalis 18.10 811 Quercus engelmannii 43.68

242 Thuja plicata 19.34 812 Quercus falcata var. falcata 32.45

251 Torreya californica 21.22 813 Quercus falcata var. pagodaefolia 38.06

260 Tsuga spp. 23.71 814 Quercus gambelii 39.94

263 Tsuga heterophylla 26.21 815 Quercus garryana 39.94

264 Tsuga mertensiana 26.21 816 Quercus ilicifolia 34.94

299 softwood 23.71 817 Quercus imbricaria 34.94

300 Acacia spp. 37.44 818 Quercus kelloggii 31.82

310 Acer spp. 30.58 819 Quercus laevis 32.45

Species Bulk Species Bulk 

number Genus Species density number Genus Species density

Appendix 7.3. (Continued)
64

311 Acer barbatum 33.70 820 Quercus laurifolia 34.94

312 Acer macrophyllum 27.46 821 Quercus lobata 39.94

313 Acer negundo 27.46 822 Quercus lyrata 35.57

314 Acer nigrum 32.45 823 Quercus macrocarpa 36.19

315 Acer pensylvanicum 27.46 824 Quercus marilandica 34.94

316 Acer rubrum 30.58 825 Quercus michauxii 37.44

317 Acer saccharinum 27.46 826 Quercus muehlenbergii 37.44

318 Acer saccharum 34.94 827 Quercus nigra 34.94

319 Acer spicatum 27.46 828 Quercus nuttalli 34.94

321 Acer glabrum 27.46 829 Quercus oblongifolia 43.68

322 Acer grandidentatum 27.46 830 Quercus palustris 36.19

330 Aesculus californica 23.71 831 Quercus phellos 34.94

330 Aesculus spp. 20.59 832 Quercus prinus 35.57

341 Ailanthus altissima 23.09 833 Quercus rubra 34.94

350 Alnus spp. 23.09 834 Quercus shumardii 34.94

355 Amelanchier spp. 41.18 835 Quercus stellata 37.44

361 Arbutus menziesii 36.19 837 Quercus velutina 34.94

367 Asimina triloba 29.33 838 Quercus virginiana 49.92

370 Betula spp. 29.95 839 Quercus wislizeni 43.68

371 Betula alleghaniensis 34.32 840 Quercus incana 34.94

372 Betula lenta 37.44 843 Quercus hypoleucoides 43.68

373 Betula nigra 34.94 901 Robinia pseudoacacia 41.18

374 Betula occidentalis 33.07 902 Robinia neomexicana 41.18

375 Betula papyrifera 29.95 920 Salix spp. 22.46

376 Betula papyrifera var. 

commutata 29.95 925 Sapium sebiferum 29.33

379 Betula populifolia 28.08 931 Sassafras albidum 26.21

381 Bumelia lanuginosa 29.33 935 Sorbus americana 26.21

391 Carpinus caroliniana 36.19 945 Tamarix spp. 24.96

400 Carya spp. 38.69 950 Tilia spp. 19.97

401 Carya aquatica 38.06 951 Tilia americana 19.97

402 Carya cordiformis 37.44 952 Tilia heterophylla 19.97

403 Carya glabra 41.18 970 Ulmus spp. 31.20

404 Carya illinoensis 37.44 971 Ulmus alata 35.57

405 Carya laciniosa 38.69 972 Ulmus americana 28.70

406 Carya myristicaeformis 34.94 973 Ulmus crassifolia 35.57

407 Carya ovata 39.94 974 Ulmus pumila 28.70

408 Carya texana 33.70 975 Ulmus rubra 29.95

409 Carya tomentosa 39.94 976 Ulmus serotina 35.57

421 Castanea dentata 24.96 977 Ulmus thomasii 35.57

422 Castanea pumila 24.96 980 Aleurites fordii 29.33

423 Castanea ozarkensis 24.96 981 Umbellularia californica 31.82

Species Bulk Species Bulk 

number Genus Species density number Genus Species density

Appendix 7.3. (Continued)
65

430 Castanopsis spp. 26.21 981 Vaccinium arboreum 29.33

450 Catalpa spp. 23.71 983 Melia azedarach 29.33

460 Celtis spp. 30.58 984 Planera aquatica 33.07

461 Celtis laevigata 29.33 985 Cotinus obovaus 29.33

462 Celtis occidentalis 30.58 990 Olneya tesota 62.40

471 Cercis canadensis 36.19 998 hardwood 31.82

475 Cercocarpus ledifolius 62.40 999 unknown 28.70

Species Bulk Species Bulk 

number Genus Species density number Genus Species density

Appendix 7.3. (Continued)
66

Forest- Fine Woody Debris FWD and Litter 

type (squared diameter, inches) slash bulk bulk Duff bulk 

group density density density 

code Forest Type Group Small Medium Large (lbs/ft3) (lbs/ft3) (lbs/ft3)

100 White/red/jack pine 0.017 0.254 3.043 23.71 5.14 13.21

120 Spruce/fir 0.018 0.256 3.058 22.46 1.85 4.76

140 Longleaf/slash pine 0.020 0.310 3.457 33.70 5.14 13.21

160 Loblolly/shortleaf pine 0.019 0.286 3.279 29.33 5.33 13.72

180 Pinyon/juniper 0.018 0.257 3.062 28.70 3.34 8.59

200 Douglas-fir 0.016 0.233 2.879 28.80 1.85 4.76

220 Ponderosa pine 0.019 0.293 3.330 23.09 3.34 8.59

240 Western white pine 0.018 0.262 3.101 21.84 3.34 8.59

260 Fir/spruce/mountain hemlock 0.017 0.247 2.987 22.46 1.85 4.76

280 Lodgepole pine 0.017 0.248 2.993 23.71 3.34 8.59

300 Hemlock/Sitka spruce 0.018 0.258 3.072 26.21 1.85 4.76

320 Western larch 0.018 0.272 3.175 29.95 3.34 8.59

340 Redwood 0.018 0.267 3.141 21.22 3.34 8.59

360 Other western softwoods 0.019 0.277 3.210 24.34 3.34 8.59

370 California mixed conifer 0.018 0.271 3.172 24.34 3.34 8.59

380 Exotic softwoods 0.018 0.262 3.101 31.20 3.34 8.59

400 Oak/pine 0.019 0.280 3.238 37.44 5.24 13.48

500 Oak/hickory 0.018 0.272 3.179 28.70 4.47 11.51

600 Oak/gum/cypress 0.019 0.286 3.282 32.45 4.46 11.46

700 Elm/ash/cottonwood 0.019 0.280 3.238 33.07 3.06 7.87

800 Maple/beech/birch 0.018 0.265 3.124 23.09 4.37 11.24

900 Aspen/birch 0.019 0.279 3.226 23.09 4.77 12.27

910 Alder/maple 0.018 0.274 3.192 23.09 4.37 11.24

920 Western oak 0.017 0.249 3.005 31.82 4.47 11.51

940 Tanoak/laurel 0.017 0.247 2.986 39.31 4.47 11.51

950 Other western hwds 0.015 0.206 2.661 39.31 4.47 11.51

980 Tropical hardwoods 0.018 0.262 3.101 31.20 4.40 11.31

990 Exotic hardwoods 0.018 0.262 3.101 31.20 4.40 11.31

999 Nonstocked 0.018 0.262 3.101 28.08 4.41 11.33

Appendix 7.4. Estimation constants of fine woody debris, litter, and duff by forest-type group

Note: All constants are subject to revisions as additional information is available. Users are strongly cautioned to use their own

local-regional values where available. FWD constants are based on Woodall and Monleon (in press); FWD and slash bulk density

are based on averaging the bulk densities of individual species in each forest-type group (see Appendix 7.3); duff/litter constants are

based on bulk densities measured by FIA’s phase 3 soils inventory (O’Neill et al. 2005a) and will be updated as future information

is available.
67

Appendix 7.5 Down Woody Material Sample Designs, 1999-2001
68

Appendix 7.6 Down Woody Material field datasheet
Woodall, Christopher W.; Monleon, Vicente J. 2008. Sampling protocol, estimation, and

analysis procedures for the down woody materials indicator of the FIA program.

Gen. Tech. Rep. NRS-22. Newtown Square, PA: U.S. Department of Agriculture, Forest

Service, Northern Research Station. 68 p.

The USDA Forest Service’s Forest Inventory and Analysis program conducts an inventory

of forests of the United States including down woody materials (DWM). In this report

we provide the rationale and context for a national inventory of DWM, describe the

components sampled, discuss the sampling protocol used and corresponding estimation

procedures, and provide guidance on managing and processing DWM data and

incorporating that information into inventory analysis and research projects.

KEY WORDS: down woody material, forest inventory, line-intersect sampling, coarse

woody debris, fine woody debris

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the

basis of race, color, national origin, gender, religion, age, disability, political beliefs, sexual orientation, and

marital or family status. (Not all prohibited bases apply to all programs.) Persons with disabilities who

require alternative means for communication of program information (Braille, large print, audiotape, etc.)

should contact USDA’s TARGET Center at (202) 720-2600 (voice and TDD).

To file a complaint of discrimination, write USDA, Director, Office of Civil Rights, Room 326-W, Whitten

Building, 14th and Independence Avenue, SW, Washington, DC 20250-9410, or call (202) 720-5964 (voice or

TDD). USDA is an equal opportunity provider and employer.
“Capitalizing on the strengths of existing science capacity

in the Northeast and Midwest to attain a more integrated,

cohesive, landscape-scale research program”