Analyzing

Forest Health Data

William D. Smith and Barbara L. Conkling

United States

Department of

Agriculture

Forest Service

Southern

Research Station

General Technical

Report SRS-77
Jennifer D. Knoepp, Research Soil Scientist, and

James M. Vose, Project Leader, U.S. Department of

Agriculture, Forest Service, Southern Research Station,

Coweeta Hydrologic Laboratory, 3160 Coweeta Lab Road,

Otto, NC 28763.

The Authors:

William D. Smith, Research Scientist, U.S. Department of Agriculture

Forest Service, Southern Research Station, Research Triangle Park, NC

27709; and Barbara L. Conkling, Research Assistant Professor, North

Carolina State University, Department of Forestry, Raleigh, NC 27695.

March 2005

Southern Research Station

P.O. Box 2680

Asheville, NC 28802

The use of trade or firm names in this publication is for reader information and does not

imply endorsement of any product or service by the U.S. Department of Agriculture or other

organizations represented here.

Cover:

The top photo shows the first detection of sudden oak death caused by

Phytophthora ramorum near Plaskett Creek, Los Padres National Forest

(Monterey County, CA) in the fall of 2003. (Photo by Jeff Mai, USDA

Forest Service)

The bottom photo shows an area of severe sudden oak death, primarily on

tanoak, in the Big Sur area (Monterey County, CA) in the fall of 2004.

(Photo by Susan Frankel, USDA Forest Service)
i

Analyzing Forest Health Data

William D. Smith and

Barbara L. Conkling
ii

Contents

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The FHM Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The Santiago Criteria and Indicators of Sustainable Forest Management . . . . 5

Assessment of Forest Health . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

FHM Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Scale of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Analytical Procedures for Estimation from FHM Data . . . . . . . . . . . . . . . . . . . . 7

Estimating Change Over Time Within Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Testing for Differences in Change Over Time Among Groups . . . . . . . . . . . . . . . 9

Estimating Change Using Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Estimating Plot Values for Unmeasured Years . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Estimating Heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Assessment of Forest Health Based on the Santiago Criteria . . . . . . . . . . . . . . . 16

Santiago Criterion 1—

Conservation of Biological Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Santiago Criterion 2—

Maintenance of Productive Capacity of Forest Ecosystems . . . . . . . . . . . . . . . 16

Santiago Criterion 3—

Maintenance of Forest Ecosystem Health and Vitality . . . . . . . . . . . . . . . . . . . 17

Santiago Criterion 5—

Maintenance of Forest Contribution to Global Carbon Cycles . . . . . . . . . . . . . 27

Summary and Future Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Appendix A: Interpreting FHM Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Appendix B: Measures of Tree Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1

Analyzing Forest Health Data

William D. Smith and Barbara L. Conkling

Abstract

This report focuses on the Forest Health Monitoring Program’s development and use of analytical procedures for monitoring changes in forest

health and for expressing the corresponding statistical confidences. The

program’s assessments of long-term status, changes, and trends in forest

ecosystem health use the Santiago Declaration: “Criteria and Indicators

for the Conservation and Sustainable Management of Temporate and

Boreal Forests” (Montreal Process) as a reporting framework. Procedures

used in five aspects of data analysis are presented. The analytical

procedures used are based on mixed estimation procedures. Examples

using the indicators are included, along with a clear link to the analytical

procedures used (1) estimating change over time within groups—estimation of growth, harvest, mortality, and crown condition; (2) testing for

differences in change over time among groups—foliar transparency;

(3) estimating change using covariates—impact of drought on change in

foliar transparency; (4) estimating plot values for unmeasured years—

comparison of observed and predicted (Best Linear Unbiased Predictions)

values of foliar transparency, dieback, and total volume; and (5) estimating tree heights—examples of using estimated tree heights to estimate

tree volume.

Keywords: Assessment, BLUP, change estimation, mixed models,

monitoring, tree height.

Executive Summary

In this report we focus primarily on the Forest Health

Monitoring (FHM) Program’s development and use of

analytical procedures for monitoring changes in forest

health and for expressing the corresponding statistical

confidences. FHM’s assessments of long-term status,

changes, and trends in forest ecosystem health are based

on the Santiago Declaration: “Criteria and Indicators for

the Conservation and Sustainable Forest Management

of Temporate and Boreal Forests” (U.S. Department of

Agriculture Forest Service 1995). The Santiago criteria and

indicators characterize the components of sustainable forest

management. The FHM forest health indicators are a subset

of the Santiago indicators, which are used as an

organizational framework for reporting.

Procedures used in five aspects of data analysis are

presented in this report: (1) estimating change over time

within groups, (2) testing for differences in change over

time among groups, (3) estimating change using covariates,

(4) estimating plot values for unmeasured years, and (5)

estimating tree heights. Example analyses using FHM

indicators are then presented with a clear link to the

analytical procedure used. Estimates of the annual change

in FHM indicators are based on the measurements

collected from 1991 through 1996 from the FHM plot

grid. Measurements from 1997 for six Colorado plots

measured out of sequence are also included.

Estimates of change can be made using a procedure that

accounts for the fact that FHM data are often correlated

over time. This model is used to estimate change for different groupings, i.e., ecoregion section and forest type, over

time. Example analyses include the estimation of growth,

harvest, mortality, and crown condition. A specific example

is the mixed-conifers forest type in California. The annual

net growth of this forest type from 1992 to 1996 was -96.4

cubic feet per acre per year, and mortality was 125.3 cubic

feet per acre per year. Drought- and insect-induced mortality has been observed in this forest type, primarily in white

(Abies concolor) and red fir (Abies magnifica) (Dale 1996),

which contributed to the negative net growth rate.

By testing for differences among regions or forest types

that have distinct attributes (climate, soils, species, etc.) or

exposure to stressors, we gain insight into likely causal

mechanisms behind the observed changes. Although the

estimate of mean change provides this insight, it is essential

that the significance of the estimated differences over time

and among ecoregions or forest types be tested. Otherwise

differences due to random sampling error only can be

interpreted as real change. The rate of change in softwood

transparency among four sections of the Southern Rocky

Mountains Steppe Province in Colorado illustrates this type

of analysis. In addition to providing information about

transparency changes over time and among sections, the

analysis results provide direction for future analyses

integrating data such as climate and land use.

Estimating change using covariates provides the analysis

needed to integrate data such as climate, precipitation, and

ozone exposure. These data are covariates with time.

Assessing the impact of drought on change in foliar

transparency in California illustrates this procedure. The

Palmer Drought Severity Index (PDSI)—an empirically

derived index based on total rainfall, the periodicity of the

rainfall, and soil characteristics such as water-holding

capacity—data are the drought data used. The example

analysis suggests that year, and the interaction between

year and PDSI, are significant factors in foliar transparency

change. However, the demonstrated power of the procedure

is most important in this report because it suggests the

utility of the procedure in analyzing more subtle factors

such as ozone and other pollutants.
2

In addition to estimating change, making annual assessments of forest health status is a major requirement of FHM.

The procedures described result in estimates that can be

used to predict the plot or tree values for unmeasured years.

These predicted values are referred to as Best Linear

Unbiased Predictions (BLUP). In this report, comparing

observed and predicted values of transparency, dieback,

and total volume illustrates the validity of this process.

Tree height is one of the measures of forest vertical structure that is important in addressing many of the Santiago

criteria. Although FHM did not measure tree heights across

all diameter classes, the heights of one or two dominant or

codominant trees (site trees) were measured on most plots.

Until height data are available for all trees, regional height/

diameter equations of various forms can be used to estimate individual tree heights. Greater accuracy in estimation is obtained by conditioning the equations through the

measured heights of dominant/codominant trees (Clutter

and others 1983). Conditioning reparameterizes the equation such that the predicted value calculated using the

equation is equal to the measured values. In this report,

height estimates used to estimate tree volume for productivity and carbon content were calculated using the siteindex-species conversion factors to adjust all heights.

Estimates of plot volume were then calculated, with tree

heights estimated using the conditioning procedures.

Introduction

Assessing the susceptibility of forests to disturbance from

pollution, insects, diseases, climatic change, and other

stressors, and the capacity of forests to recover is the cooperative responsibility of several programs within the U.S.

Department of Agriculture Forest Service (USDA Forest

Service) and other Federal and State agencies. Because a

forest is an ecosystem of floral, faunal, and abiotic processes, forest health assessment requires regional expertise

in ecology, plant physiology, plant pathology, entomology,

and many other disciplines that use data from numerous

sampling grids and surveys.

The National FHM Program has been established by

several Federal and State agencies to monitor, assess, and

report on the long-term status, changes, and trends in

forest ecosystem health with known confidence on regional

and national scales. National FHM assessments are based

on the Santiago Declaration: “Criteria and Indicators for

the Conservation and Sustainable Management of

Temporate and Boreal Forests” (U.S. Department of

Agriculture Forest Service 1995), an international

agreement signed by 12 nations that characterizes the

components of sustainable forest management. Sustainable

forest management requires that the capacity to produce

forest products and services, including key ecosystem

functions, be maintained. The Santiago criteria have been

endorsed by the Chief of the Forest Service, the National

Association of State Foresters, the American Forest &

Paper Association, and the Ecological Society of America.

This report focuses primarily on FHM’s development and

use of analytical procedures for monitoring changes in

forest health and for expressing the corresponding statistical confidences. The forest health indicators measured by

FHM since 1990 are a subset of the indicators presented in

the Santiago Declaration. Estimates of the annual change

in FHM indicators are based on the measurements collected

from 1991 through 19961 from the FHM plot grid. Only

the States that have completed at least one repeat measurement visit to the plots are included. The FHM plot measurements presented in this report include crown dieback

and damage, foliar transparency, diameter at breast height

(d.b.h.), and tree species. FHM measurements and published equations were used to derive volume, mortality,

and carbon sequestration. Non-FHM plot data, i.e., climate

data, and how they fit into the assessment process are

discussed.

The FHM Program

The FHM Program was originally established by merging

the forest component of the U.S. Environmental Protection

Agency’s (EPA) Environmental Monitoring and Assessment

Program (EMAP Forests), the Vegetation Survey Project

of the USDA Forest Service’s Forest Response Program,

and the emerging forest health initiative of the USDA

Forest Service’s Forest Health Protection (FHP) Program.

Currently within the USDA Forest Service, data are

collected for monitoring forest health by the National Forest

Inventory and Analysis (FIA) Program in Research and

Development, and the national Forest Health Monitoring

(FHM) Program in State and Private Forestry. Analytical

procedures for analyzing forest health data are developed

by the National Forest Health Monitoring Research Unit

(FS-SRS 4803) and cooperating scientists at North

Carolina State University. These procedures are shared

with regional and State forest health analysts. The National

Association of State Foresters provides essential program

1 Measurements from 1997 for six Colorado plots that were

measured out of sequence are included in the analysis.
3

support, guidance, and assistance. The EPA; the U.S.

Department of the Interior, Bureau of Land Management;

the Tennessee Valley Authority; the USDA Natural

Resources Conservation Service; and several universities

participated in the development of FHM.

The FHM Program from 1991 through the 1999 field

season comprised three interrelated monitoring activities:

detection monitoring (plot and survey components), evaluation monitoring, and intensive site ecosystem monitoring.

Each activity provided a different level of information and

had specific, complementary goals. A fourth related activity

was research on monitoring techniques.

In 1999, the ground plot activities of detection monitoring

were integrated with the USDA Forest Service, FIA Program. A systematic grid was adopted by the enhanced FIA

Program that includes some, but not all, former FIA plots.

This is the phase 2 grid—the annual survey plots that are

designed to be measured on a 5-year rotation such that

one-fifth of the plots are measured each year. Most former

FHM plot indicators became phase 3 indicators, measured

on a subset of phase 2 plots. At least one FHM indicator

(damage) became part of the phase 2 measurements.

Through 1999, detection monitoring was the most extensive of FHM’s three monitoring activities. The objectives of

this activity were to collect information annually on the condition of forest ecosystems, to estimate baseline (current)

conditions, and to detect short- and long-term changes.

Data from FHM plots and surveys were analyzed with other

forest data to determine if changes were within normal

bounds, indicated improving conditions, or were cause for

concern and warranted additional evaluation. Detection

monitoring covered all forested lands (with the exception of

riparian forests < 100 feet wide) and had two components:

(1) the plot component, a network of permanent plots

(approximately 4,600 forested plots for the 50 States); and

(2) the survey component, primarily an aerial survey of

insect, disease, and other disturbances. Each year a systematic sample of one-third of the permanent plots was

measured and most forested acres were aerially surveyed.

Figure 1 shows the States participating in both the plot and

survey components of detection monitoring through 1997.

The plot component was a systematic sample of permanent,

fixed-area plots on a hexagonal base grid, located approximately 22 miles apart. The plots were measured on a 4-year

cycle such that one-fourth of the plots systematically

Figure 1—States in which both the plot and survey components of detection monitoring were implemented in 1997;

approximately 52 percent of the forest area in the lower 48 States was systematically sampled (States have been

added since 1997).

Plot and survey components

implemented in 1997

Implemented in 1997, but

data not used in this report

Alaska

Hawaii
4

covering the entire State (called a panel) were measured

every year. In addition, one-third of the plots systematically covering the entire State in the previous year’s panel

(called the overlap) were remeasured. This overlap was

one-twelfth of the base grid. The rotating panel with

overlap was referred to as the FHM rotating panel design.

When the design was implemented in a new State, all

plots were established and measured the first year. Figure

2 illustrates the year-to-year sampling design.

The objective of the FHM design was to provide precision

in estimates of change over short time intervals (temporal)

rather than in estimates of change for small geographic

areas (spatial). Two to four years was considered a short

time interval, and a small geographic area was considered

to be < 2 million acres. In making annual assessments, the

capacity to update (predict plot values for unmeasured

plots) was of particular importance. The overlapping

design was developed to allow this updating process.2

Each FHM plot had four fixed-area, circular subplots as

shown in figure 3. Subplot centers were spaced 120 feet

apart. All subplots were 1/24-acre in size and contained a

microplot offset 12 feet from the subplot center. The

microplots were 1/300-acre in size. The basic plot design

could be augmented to meet regional requirements. For

example, the West Coast region used a 2.47-acre (1-ha)

plot encircling the four subplots to increase the sample of

large trees.

The survey component provided a record (location and

extent) of disturbances from forest insects, diseases, and

other change agents. This information was an indicator of

forest health, and provided a context for interpreting plot

data and for identifying likely factors that contribute to

forest health changes. Damage to individual plot trees was

indicated and insects, diseases, and other disturbances were

identified from the aerial surveys. Without the survey data,

Figure 2—Year-to-year sampling design.

2 Smith, W.D.; Gumpertz, M.L.; Catts, G.C. 1996. An analysis of the

precision of change estimation of four alternative sampling designs

for forest health monitoring. For. Health Monit. Tech. Rep. Ser. (10/

96). Research Triangle Park, NC: U.S. Department of Agriculture,

Forest Service, Southern Research Station. 25 p. Administrative

report. On file with: Forestry Sciences Laboratory, Southern

Research Station, P.O. Box 12254, Research Triangle Park, NC

27709.

Figure 3—Forest Health Monitoring field plot (drawn to scale).

Year 1 2 3 4 5 6 7 8

Panel

0

1

2

3

X X

X X

⇒

⇓ X

X X X/

3

X/

3

X X/

3

X X/

3

X/

3

X X/

3

X/

3

X

Subplot

24.0–foot radius

(7.32 m) Annular plot

58.9–foot radius

(17.95 m)

Microplot

6.8–foot radius

(2.07 m)

2

1

4 3
5

the ability to interpret and make management decisions in

response to the observed changes in plot variables would be

very limited. National standards for the survey component

of detection monitoring were developed to address the

accuracy of other data associated with digitized, polygonal

aerial survey data, e.g., species, damage severity, and causal

agent, implement consistent training, quality assurance, and

reports across regions, and more fully integrate the plot

and survey components, exploiting the strengths of each.

The Santiago Criteria and Indicators of

Sustainable Forest Management

Under the Santiago Declaration (U.S. Department of

Agriculture Forest Service 1995), a criterion is a category

of conditions or processes by which sustainable management can be assessed. It is characterized by a set of indicators that are monitored periodically to assess change.

Indicators are quantitative or qualitative variables that can

be measured and that demonstrate trends when observed

periodically. Changes in the status of forests and related

conditions over time, and the direction of those changes,

are relevant to assessing sustainability. Given the dynamic

nature of forests, it is essential that indicators be assessed

as trends over time (U.S. Department of Agriculture Forest

Service 1995).

The seven Santiago criteria are:

Criterion 1—Conservation of biological diversity

Criterion 2—Maintenance of productive capacity of

forest ecosystems

Criterion 3—Maintenance of forest ecosystem health

and vitality

Criterion 4—Conservation and maintenance of soil and

water resources

Criterion 5—Maintenance of forest contributions to

global carbon cycles

Criterion 6—Maintenance and enhancement of longterm multiple socioeconomic benefits to meet the needs

of societies

Criterion 7—Legal, institutional, and economic

framework for forest conservation and sustainable

management.

Criterion 6 addresses socioeconomic issues that FHM does

not assess directly; criterion 7 addresses infrastructure and

other factors that FHM cannot or does not address. Sixtyseven indicators are currently associated with the 7

Santiago criteria.

Initially, most of the Santiago criteria and indicators (U.S.

Department of Agriculture Forest Service 1995) were stated

in terms of change in “area and percent of forest land.” For

example, the first indicator being addressed by FHM under

criterion 3 is:

Area and percent of forest affected by processes or

agents beyond the range of historic variation, e.g.,

by insects, diseases, competition from exotic

species, fire, storm, land clearance, permanent

flooding, salinization, and domestic animals (U.S.

Department of Agriculture Forest Service 1995).

FHM uses available data to answer questions that reflect the

temporal aspects of the indicators. Examples of this type of

questions are as follows:

• What is the annual change in crown dieback by

ecoregion section and forest type?

• What is the annual change in foliar transparency by

ecoregion section and forest type?

• What is the annual change from forest to nonforest use

by ecoregion section and forest type?

Assessment of Forest Health

The National FHM assessment process begins with the

development of questions relevant to ecological, economic,

and political concerns. These issues are addressed in the

context of the Santiago criteria. FHM data are being

evaluated to determine which FHM measurements can be

used to address these criteria and related issues. Analytical

procedures for estimating change and the corresponding

confidence are currently being applied to FHM plot data.

Inferences from the changes observed on the FHM plots

are supported with qualitative data from insect and disease

surveys. Future developments in the program will include

data applications that more explicitly exploit the spatial

aspects of plot, survey, and other data sources.

FHM Data Analysis

FHM detection monitoring data and other data are reviewed

each year to determine whether forest health conditions of

concern are emerging. This review may include analyses of

FHM data; other USDA Forest Service data such as FHP

survey and plot data, FIA data, National Forest System

(NFS) Continuous Vegetation Survey (CVS) data; and data

from other agencies such as weather and air quality data.

These analyses corroborate whether or not apparent
6

indicator changes are significant and provide insight into

problem extent, severity, and likely causal relationships. If

these analyses do not satisfactorily explain a situation, an

evaluation monitoring project may be needed. Meaningful

evaluation requires an integration of FHM plot and survey

data, FIA data, NFS data, and other data by biometricians,

pathologists, entomologists, plant physiologists, ecologists,

and silviculturists knowledgeable about each specific State

or region. Because causal agents or stressors are not

identified on the plot, the plot data must be related to other

information to make meaningful interpretations. Through

1999 in FHM, the survey component of the program

Figure 4—Analysis groupings of California

ecoregion sections. In some cases, small ecoregion

sections or sections with a small number of plots are

combined with contiguous section(s) with similar

characteristics.

Northern California Coast

American Semi-Desert and Desert

Intermountain Semi-Desert

Klamath Mountains

Northern California Coast Ranges

Northern CA Interior Coast Ranges, Valleys, and Foothills

Southern Cascades

Sierra Nevada

Modoc Plateau

Central California Coast Ranges

Southern California Coast and Ranges

Salto Lake (in southern California)

Lake Tahoe (in northern California)

California Ecoregion Sections
7

determined the stress or damaging agent and the plot

component determined the magnitude and direction of the

forest’s response to stresses or damaging agents.

Scale of Analysis

For analyses in this report, FHM plot data were aggregated

spatially [plots that are in proximity to one another based

on some geographic characteristic such as State or Bailey’s

(1995) ecoregion section] or by condition (plots are not

proximal to one another but are grouped by some common

characteristic such as forest type, age, or seral stage). In

general, stresses or damaging agents, such as pollution and

storms, affect forests on a spatial basis while insects and

diseases affect forests on a condition basis (such as host or

forest type). The minimum level of analysis in this report is

the mean plot value of each variable or indicator by species

or species group within some contiguous or noncontiguous

grouping of approximately 2 million acres (see footnote 2).

In some cases, small ecoregion sections are combined with

contiguous sections with similar characteristics. These

groupings are presented in figure 4 for California, figure 5

for Colorado, and figure 6 for eastern ecoregions. Some

indicators, such as crown dieback, are evaluated by the

mean change per plot within each group (ecoregion or

forest type), while other indicators, such as tree species

richness, are meaningful only over a large geographic area

(ecoregion, administrative region, or State).

Analytical Procedures for Estimation

from FHM Data

Procedures used in five aspects of data analysis are

presented in this section: (1) estimating change over time

within groups, (2) testing for differences in change over

time among groups, (3) estimating change using

covariates, (4) estimating plot values for unmeasured

years, and (5) estimating heights. Included with the

analytical procedures described are the indicators used as

example analyses and a reference to where the analytical

results can be found in this report.

Figure 5—Analysis groupings

of Colorado ecoregion

sections. In some cases, small

ecoregion sections or sections

with a small number of plots

are combined with contiguous

section(s) with similar

characteristics.

Colorado Plateau Semi-Desert

Palouse Dry Steppe

Southern Parks and Rocky Mountain Ranges

South-Central Highlands

North-Central Highlands and Rocky Mountain

Northern Parks and Ranges

Colorado Ecoregion Sections
8

Estimating Change Over Time Within Groups

The analysis for change is based on the general linear

model:

 model (1)

where

yij = the value of the indicator on plot i at time j

b0 = estimated mean of the value of all plots at year 0

b1 = estimated change in y over time

t

j = time of measurement j

t

0 = time of initial measurement

= plot effect (spatial) variability

= within-plot (temporal) variability

The measurement error, δ, is assumed to be normally

distributed with a mean = 0 and variance = σ2

. This

assumption is critical to detecting change. This requirement

can be relaxed if it can be assumed that a nonzero

measurement error (bias) does not change with time. For

example, if the error in measurement is of a consistent

direction and magnitude, the measurement of change is

minimally affected by the measurement error. Because the

current analysis method does not partition measurement

error from random variation, all standard error, probability

estimates, and R2

 statistics reflect both sources of error.

Both Y and b are estimated using a procedure that accounts

for the fact that FHM data are often correlated over time

(the value of measurements at time 2 are influenced by the

values at time 1). For example, if in response to some stress

factor a tree has significant crown dieback at time 1, the

same tree is more likely to have crown dieback at time 2

than similar trees not exhibiting crown dieback at time 1

(see footnote 2).

This model is used to estimate mean change of plots within

different groupings, such as ecoregion section and forest

type, over time. An example of this procedure is presented

in the sections “Assessment of Forest Health Based on the

Santiago Criteria, Santiago Criterion 2—Maintenance of

Productive Capacity of Forest Ecosystems, Estimation of

Growth, Harvest, and Mortality” and “Assessment of Forest

Health Based on the Santiago Criteria, Santiago Criterion

3—Maintenance of Forest Ecosystem Health and Vitality,

FHM Measures of Crown Condition.”

Figure 6—Analysis groupings of eastern ecoregion sections. In some

cases, small ecoregion sections or sections with a small number of

plots are combined with contiguous section(s) with similar

characteristics.

Aroostook Hills and Lowlands

Maine and New Brunswick Foothills and Eastern Lowlands

Fundy Coastal and Interior

Central Maine Coastal and Interior

Lower New England and Hudson Valley

Upper Atlantic Coastal Plain

Northern Appalachian Piedmont

Southern Appalachian Piedmont

Cumberland Plateau

Coastal Plains, Middle

Middle Atlantic Coastal Plain

Coastal Plains and Flatwoods

White Mountains

New England Piedmont

Green, Taconic, Berkshire Mountains

Cumberland and Allegheny Mountains

Blue Ridge Mountains

Eastern Ecoregion Sections

ij ε

ηi

ij j i ij y = b + b (t −t )+η +ε 0 1 0
9

Testing for Differences in Change Over Time

Among Groups

Insight into likely causal mechanisms behind the observed

changes can be obtained by testing for differences among

regions or forest types that have distinct attributes

(climate, soils, species, etc.) or exposure to stressors. The

differences in change over time among ecoregions or

forest types can be tested using the following model:

model (2)

where

Yi,j,k = the value of Y at measurement i for plot j in

group k

t

i,j,k = the year of measurement i on plot j in group k

n = the interval between measurements

b0 = the initial value of Y

b1 = the annual change in Y

b1, j = the change in Y per change in unit x

sj = group effect

= random variation among plots

= random error over time within plots

An example of this procedure is presented in “Assessment

of Forest Health Based on the Santiago Criteria, Santiago

Criterion 3—Maintenance of Forest Ecosystem Health

and Vitality, Testing for Equality of the Changes in

Transparency Among Ecoregion Sections in Colorado.”

Estimating Change Using Covariates

In analyses, the FHM Program uses data other than the plot

component data, i.e., climate, precipitation, and ozone exposure. Data such as these are covariates to time. A covariate

is a variable whose change influences the change in another

variable. Adding these data to model 1 can provide insight

into the causal mechanism underlying the estimated

change in Y and a more precise estimate of the change:

model (3)

where

Yij = the value of Y at measurement i for plot j

t

i,j = the year of measurement i on plot j

xij = the value of a covariate at measurement i for plot j

i j

i n j i j i n j i j i j

i n j i n j i j i n j i j

b t t x x

Y b b t t b x x

,

3 ( ), , ( ), , ,

( ), 0 1 ( ), , 2 ( ), ,

( )( )

( ) ( )

ε

η

+

+ − − +

= + − + −

+ +

+ + +

n = the interval between measurements

b0 = the initial value of Y

b1 = the annual change in Y over time

b2 = the change in Y per change in unit x

b3 = the interaction between the change in x and the

change in Y

= random variation among plots

= random error over time within plots

In model 3, the value of x is a continuous variable rather

than a class variable as in model 2. Examples of continuous

variables are precipitation and ozone exposure that change

over time. In model 2, S is a discrete class such as

ecoregion, State, or forest type.

Model 1 is used to test whether Y changes over time. Model

2 is used to test whether the change over time is different

among groups such as ecoregions or forest types. Model 3

is used to test whether the change over time is affected by

other factors such as climate, precipitation, or ozone

concentration. An example of analysis using model 3 is

presented in “Assessment of Forest Health Based on the

Santiago Criteria, Santiago Criterion 3—Maintenance of

Forest Ecosystem Health and Vitality, Including Climatic

Factors in Estimates.”

Estimating Plot Values for Unmeasured Years

The parameter estimates resulting from the previous models

can be used to predict plot or tree values for unmeasured

years. This is particularly useful for displaying data

spatially. As more mechanistic models are developed, the

procedure can also be used to develop predictive models

for future years based on current conditions.

In addition to estimating change, a major requirement of

FHM is to make annual assessments of forest health status.

Although FHM plots were measured on a 4-year interval,

a benefit of the general least squares estimation procedure

(model 1) and the FHM rotating panel design is the

capacity to estimate plot values for unmeasured years.

Although this facilitates spatial display and analysis,

predicted values are never used in estimation. An example

of this procedure is presented in “Assessment of Forest

Health Based on the Santiago Criteria, Santiago Criterion

3—Maintenance of Forest Ecosystem Health and Vitality,

Including BLUPs in Spatial Analysis.” In addition to

estimating plot values for unmeasured years, the procedure

can be used to estimate the value of missed trees based on

subsequent measurements.

i, j η

i, j

ε

i, j, k η

i, j, k

ε

j i n j k i j k i j k i j k

i n j k i n j k i j k j

b t t

Y b b t t s

1, ( ), , , , , , , ,

( ), , 0 1 ( ), , , ,

( )

( )

+ − +η +ε

= + − +

+

+ +
10

i s

where

The weight increases as the number of measurements

increases and/or the correlation over time increases. This

reflects the statistical confidence in the estimate. If the

estimate is based on very few measurements or the

correlation over time is small, the weight approaches 0

and the best estimate of the plot value is the mean of the

population.

This procedure contrasts with traditional regression

estimates in that the plot factor ( ) accounts for spatial

variation between plots, and the within-plot error ( )

reflects the variation over time as well as the mean ( ) of

all plots within the ecoregion or forest type. The BLUP is

composed of two components: (1) an estimate of the mean

value of all plots within the group, in this case ecoregion

section or forest type; and (2) a component that reflects

where the plot fits within the distribution of plots in the

group. The procedure can be better understood by

examining a few simple numerical examples.

For example, a plot was measured in years 1 and 4 and an

estimate of the plot value at year 5 is needed. Assuming the

model is , the estimate for year 0 is 10

and change over the 5-year interval is 2 units per year.

Then the mean value of all plots in the section is 10 + 2(5)

or 20. If, in addition, correlation with time is 0.7, and

observed and predicted values for the plot are:

Year 0 1 2 3 4 5 mean

Observed • 3 • • 5 • 4

Fitted • 5 • • 12 • 8.5

then the average deviation from the observed value is 4 -

8.5 = - 4.5; that is, in years when plot i was measured, its

average was 4.5 units less than the mean of the fitted

values. Therefore, the BLUP for year 5 is 20 + weight

(-4.5). For this illustration the appropriate weight can be

determined from figure 7. A correlation of 0.7 with two

measurements gives a weight of 0.8. The best estimate of

the value of plot i in year 5 is 20 + 0.7(-4.5) = 16.85.

The behavior of this estimate can be better understood by

considering some other possible conditions relating to this

example:

These predicted values are referred to as BLUPs. BLUPs are

best in that they have the minimum mean square error,

linear in that they are linear functions of the data,

unbiased in that the average value of the estimate is equal

to the average value of the quantity being estimated, and

predictors in that they are predictors of random effects

(Robinson 1991). In this report they are used to predict the

value of particular plot attributes; i.e., transparency and

volume, from a population of random effects. This procedure maximizes the efficiency of unbalanced designs, such

as those where not all samples are measured every year

(Gregoire and others 1995). BLUPs are commonly used in

quantitative genetics, statistical quality control, time

series, and geostatistics (Christensen 1991, Robinson

1991). Given linear model 1, the BLUP for predicting the

value of plot i at time k is:

model (4) where

= the value of plot i at time k

= the fitted value for plot i at time k, i.e., the

expected value of all plots within an ecoregion

= the number of measurements on plot i

= the value of plot i at time j

= the mean of all measurements of plot i

= the between-plot variance

= the residual within-plot (temporal) variance

The BLUP consists of the mean value of all plots within

the group measured in year k, plus the mean deviation of

the predicted values of plot i from the actual value in the

years the plot was measured. Mean deviation is multiplied

by a weight term, which reflects the number of times the

plot was measured, and the plot and residual variance.

Figure 7 illustrates the relationship between the weight

with number of measurements and plot variance. To

facilitate understanding, weight is plotted against

correlation, rho,

mean weight mean deviation

2 σ ε

ni

y

ij y

k yˆ

( ) j j o yˆ =10 + 2 t − t

ij ε

ik yˆ

ik y

2 σ ρ

( )  ̧

 ̧

1

·

 ̈

 ̈

©

§ − + = + ¦=

ni

j

ij

i

i

i

i

ik ik y

n

y

n

n

blup y y 1

2 2

2

ˆ 1 ˆ

ε ρ

ρ

σ σ

σ

( ) ̧

 ̧

1

·

 ̈

 ̈

©

§ − + = + ¦=

ni

j

ij ij

i i

i

ik y y

n n

n

y 1

2 2

2

ˆ 1 ˆ

ε ρ

ρ

σ σ

σ

ε ρ

ρ

σ σ

σ

+

rho =
11

1. When predicting the value of a plot that has never been

measured, mean deviation is 0 and the best estimate is

the mean of all plots in the group (20).

2. If the plot value in the first measurements was 5 greater

than the mean, and at the second measurement the

value was 5 less than the mean, then mean deviation is

0 and the best estimate for year 5 is again 20, the mean

estimate of all plots in the group. The mean deviation of

0.0 indicates that the within-plot variability is probably

due to measurement error or seasonal variability, in

contrast to the initial example where the plot was

consistently lower (-4.5) than the mean of all plots.

3. If the correlation over time was 0.3 instead of 0.7, the

weight would be approximately 0.45 instead of 0.8

(fig. 7). This would indicate a high degree of within-plot

variability due to measurement error or seasonal

variability, and the best estimate is 20 + 0.45(-4.5) = 18.0.

The precision of BLUP estimation was evaluated on FHM

plots using data collected in the Northern region from 1991

through 1996. Figure 8 shows the sequence of measurements taken in that region. Prior to 1996, every plot was

measured every year in that region. The parameters for

model 4 were estimated using FHM data, but omitting the

plots measured in 1995, indicated by a “Y” in the figure.

The values for those plots were predicted using the BLUP

equation described, and compared with the actual values

from the plots. This procedure independently tested the

precision of the estimates. Table 1 and figure 9 present the

results of the test. The goodness-of-fit of the BLUP values

is comparable to that when the actual values are used. For

Figure 7—Relationship between correlation over time and number of times a plot has been

measured with weight of Best Linear Unbiased Predictions adjustment. The numerical

annotation on the graph is the number of times the plot was measured.

1.0

0.8

0.4

0.2

0.6

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Correlation over time

Weight

5

4

3

2

1
12

example, the R2 of hardwood dieback for all forest types

was 0.65 (table 1) for the BLUPs compared to R2

s that

ranged from 0.06 (oak-hickory) to 0.79 (natural yellow

pine) for the actual data (table 2). The R2 of volume was

0.99 (table 1) for the BLUPs compared to R2

s of 0.98 to

0.99 for the actual data (table 3).

Estimating Heights

Addressing many of the Santiago criteria requires a measure

of forest vertical structure. This requirement ranges from

tree heights for estimating productivity and carbon

sequestration, to vertical structure for estimating wildlife

habitat suitability, e.g., the presence of a midstory in a

forest’s vertical structure lowers pine warbler habitat

Figure 8—Sequence of measurements for the Forest Health Monitoring (FHM)

North region. Measurement years consistent with the FHM sampling design

(1997–99) are indicated with an “X.” The “Y” indicates the years and plots used

to test the Best Linear Unbiased Predictions.

Table 1—Results of BLUP evaluation using Forest Health Monitoring northern

data from 1991 through 1996

BLUP Mean Measured

Indicators R2 deviation Mean Deviation R2

percent

Hardwood dieback 0.49 0.61 9.92 6.15 0.65

Hardwood transparency 0.20 0.65 13.56 4.82 0.36

Softwood dieback 0.29 0.29 5.79 4.95 0.53

Softwood transparency 0.38 0.61 9.92 6.14 0.48

Volume (ft3

 per acre) 0.99 -12.7 2,217.2 -0.57 0.99

Mortality (ft3

 per acre) 0.16 16.34 129.1 12.66 0.41

Carbon sequestration

(pounds per acre) 0.95 740.9 66,702.9 1.11 0.95

BLUP = Best Linear Unbiased Predictions; R2 = a measure of goodness-of-fit of the estimate.

Year 1991 1992 1993 1994 1995 1996

Panel

0

1

2

3

Y X

X

X X

⇒

⇓ X

X

X X/

3

Y
13

Figure 9—Plots of observed vs. predicted values for northeastern forest types: (A) softwood transparency, (B) hardwood dieback, and (C)

total volume. Observed values are actual values for 1995 that would not have been measured under the Forest Health Monitoring design

starting in 1997. Predicted values were estimated using the 1997 design, i.e., plots that would not have been measured were deleted for the

estimation.

35

30

25

20

15

10

5

0

0 5 10 15 20 25 30 35

(A) Softwood transparency (percent)

8,000

6,000

0

Observed

(C)

4,000

2,000

0

Predicted

2,000 4,000 6,000 8,000

Total volume (cubic feet per acre)

70

60

50

40

30

20

10

0

(B)

0 10 20 30 40 50 60 70

Hardwood dieback (percent)

Predicted Predicted

Observed

Observed
14

suitability. Although FHM did not measure tree heights

across all diameter classes, the heights of one or two

dominant or codominant trees (site trees) were measured

on most plots. Since 2000, colocation with FIA/CVS plots

has eliminated this limitation.

However, using FHM data through 1999, individual tree

heights can be estimated using published, regional height/

Table 2—Dieback of northeastern hardwood by forest type

Estimate Standard

of value in Estimate error of Degrees of Value

Forest type n 1991 of change estimate R2 freedom of t Pr > t

White-red-jack pine 115 6.21 1.12 0.32 0.667 91 3.51 0.001

Spruce-fir 245 9.56 0.86 0.31 0.669 195 2.80 0.006

Natural yellow pine 20 7.40 0.71 0.44 0.792 15 1.61 0.128

Oak-pine 60 6.24 0.58 0.37 0.167 47 1.58 0.122

Oak-hickory 52 6.29 0.19 0.36 0.059 40 0.53 0.600

Bottomland hardwood 20 7.09 -0.65 0.57 0.089 15 -1.14 0.272

Birch-beech-maple 445 7.47 0.82 0.14 0.754 355 6.06 0.000

Aspen-birch 35 6.68 0.16 0.47 0.109 27 0.33 0.742

n = Total number of measurements over time, including repeat measurements; estimate of value in 1991 = average value at the initial

year of measurement; estimate of change = annual change over the time interval; standard error of estimate = a measure of the

variability of the data; R2

 = a measure of goodness-of-fit of the estimate; degrees of freedom = number of repeat measurements -2;

value of t = a measure of the variability of the data relative to the mean; Pr > t = probability that the estimated change was due to

random chance and that the true change over the interval was 0.

Table 3—Volume growth of softwood and hardwood by forest type in the Northeast

Standard

Estimate error of Degrees of Value

Forest type n of change estimate R2 freedom of t Pr > t

cubic feet per acre

White-red-jack pine 71 67.4 12.5 0.987 41 5.38 0.000

Spruce-fir 148 46.1 7.8 0.982 83 5.94 0.000

Natural yellow pine 12 41.8 31.7 0.983 6 1.32 0.235

Oak-pine 35 25.6 18.2 0.996 20 1.40 0.175

Oak-hickory 30 50.4 20.7 0.995 15 2.43 0.028

Bottomland hardwood 9 19.8 37.6 0.997 4 0.53 0.626

Birch-beech-maple 224 45.6 6.6 0.985 127 6.91 0.000

Aspen-birch 20 24.8 26.4 0.977 10 0.94 0.370

n = Total number of measurements over time, including repeat measurements; estimate of change = annual

change over the time interval; standard error of estimate = a measure of the variability of the data; R2

 = a measure

of goodness-of-fit of the estimate; degrees of freedom = number of repeat measurements -2; value of t = a

measure of the variability of the data relative to the mean; Pr > t = probability that the estimated change was due

to random chance and that the true change over the interval was 0.

diameter equations of various forms, e.g., (Bechtold and

Zarnoch in an unpublished report4 ), Ek and others (1984),

Garman and others (1995), Moore and others (1996).

4 Bechtold, W.A.; Zarnoch, S.J. 1996. FHM mensuration engine.

Version 1.5. [Not paged]. On file with: U.S. Department of

Agriculture Forest Service, Southern Research Station, P.O. Box

2680, Asheville, NC 28802.
15

Greater accuracy in estimation is obtained by conditioning

the equation through the measured heights of dominant

(codominant) trees. This conditioning approach is

commonly used in growth and yield models (Clutter and

others 1983).

The simplest regional height/diameter equation is of the

form:

where

H = total height

D = d.b.h. (4.5 feet above the ground)

a = species- and region-specific estimate of the

intercept

b = species- and region-specific estimate of the slope

This can be conditioned through the dominant height of

the stand since

where

= the average total height of the dominant trees

= the average d.b.h. of the dominant trees

Combining the two equations results in the following

equation:

where

= the predicted height of the i

th tree

= the measured diameter of the i

th tree

Figure 10 provides an example of this procedure. The

model is plotted in the exponential form,

In this example the tree heights relative to the tree

diameters are greater than the regional average, probably

reflecting better site quality or the influence of

management. The procedure described adjusts the heights

to reflect those differences.

When species occur on the plot that are not represented by

a site tree of the same species, the procedure is modified.

In this case the height is estimated using dominant heights

and diameters of species present on the plot, and then is

Figure 10—Regional height/diameter model conditioned through measured height (*).

Conditioned Original

80

60

40

20

0

0 5 10 15 20

D.b.h. (inches)

Height (feet)

*

log( ) H = a + b / D

( ) Hd a b Dd log = + /

Hd

Dd

() ( ) ( ) Hi Hd b Di Dd log = log + 1/ −1/

Hi

Di

( ) Di Dd Hi Hd e1/ −1/ =
16

adjusted using site-index-species conversion factors, e.g.,

Ek and others (1984). For example, if the site index for the

site-tree species is 100 and the equivalent site index of the

subject tree is 80, then the height of the subject tree is

reduced by 20 percent. Height estimates, used to estimate

tree volume for the productivity and carbon content in the

sections “Assessment of Forest Health Based on the

Santiago Criteria, Santiago Criterion 3—Maintenance of

Forest Ecosystem Health and Vitality, FHM Measures of

Crown Condition” and “Assessment of Forest Health

Based on the Santiago Criteria, Santiago Criterion 5—

Maintenance of Forest Contribution to Global Carbon

Cycles, Sequestration of Atmospheric Carbon in Trees”

were calculated using site-index-species conversion factors

to adjust all heights.

Estimates of plot volume were calculated with tree heights

estimated using the conditioning procedures, and were

used in the section “Assessment of Forest Health Based on

the Santiago Criteria, Santiago Criterion 2—Maintenance

of Productive Capacity of Forest Ecosystems, Estimation

of Growth, Harvest, and Mortality.” Although harvested

trees are recorded on FHM plots, harvest estimates were

not included in this report due to lack of robustness in

making estimates from severely discontinuous data with

small sample sizes.

Assessment of Forest Health Based

on the Santiago Criteria

The following sections are organized using the Santiago

criteria; they present the results of analyses using the five

techniques previously discussed.

Santiago Criterion 1—Conservation of Biological

Diversity

Introduction—Biological diversity is considered a key

attribute of ecosystem sustainability (Anon. 1995). Both

the number of species (richness) and the relative abundance

of species (evenness) are of interest when evaluating plant

diversity. Overall plant biological diversity is expressed

differently in different forest types and seral stages; there

may be different woody and nonwoody understory and

midstory species as well as different overstory trees. This

report focuses on the tree component of biodiversity as

expressed by number of tree species.

Number of tree species by ecoregion—Plant diversity,

like many other aspects of forest health, is dynamic both

temporally and spatially. For example, stand development

causes changes in species composition over time, and stand

disturbances—including management—can cause changes

spatially. For the most part, this dynamic process can be

stopped only by urbanization, soil loss through erosion, or

physical damage such as compaction.

Table 4 presents the maximum numbers of tree species per

plot present in the overstory and the understory, and total

tree species richness for each ecoregion section. Richness

is defined here as the number of unique species irrespective of structure location (overstory or understory). For

example, the Southern Appalachian Piedmont Ecoregion

Section (in the South) has 16 species in the overstory, 9 in

the understory, and a tree species richness of 20, indicating

that 5 species occur in both the understory and overstory.

Figure 11 spatially presents tree species richness within

ecoregion sections. Comparisons of richness among

regions are not as meaningful as richness comparisons

over time for individual regions, because climatic and

edaphic factors differ among regions. For example, diversity among tree species is expected to be greater in the

Southeast than in the West; within the Southeast, tree

species diversity is expected to be greater in the mountains

than on the coastal plain due to the history of periodic

fires on the coastal plain. Diversity changes over time

within each region are indicative of relative states of forest

health. For example, evidence of changes in plant communities due to climate change is reflected first in woody

and nonwoody vegetation in the understory (Devall and

Parresol 1994).

Santiago Criterion 2—Maintenance of

Productive Capacity of Forest Ecosystems

Introduction—The ultimate measure of health in an

ecosystem is its ability to support and sustain plant

growth. In the absence of inherent poor site quality, poor

plant growth invariably indicates the presence of some

biotic or abiotic constraint (Pankhurst 1994).

Estimation of growth, harvest, and mortality—The

definition of growth used in this analysis is traditionally

used in calculating growth from permanent plots (Beers

1962, Meyer 1953, Society of American Foresters 1984).

For a further discussion on the growth calculations used,

see appendix B. In this report, net growth is referred to as

growth.

Table 5 presents the estimates of growth and mortality for

each forest type by FHM region. In California, for

example, mixed conifers (last entry in table 5) experienced

an annual growth from 1992 to 1996 of -96.4 cubic feet
17

Table 4—Maximum number of tree species in the overstory and understory, and total tree species richness by province

or ecoregion section for each Forest Health Monitoring region in 1997

Tree species

FHM region Province or ecoregion section Overstory Understory richness

 - - - - - - - - - - - - - - number - - - - - - - - - - - - - - 

North Aroostook Hills and Lowlands Section 12 3 15

Maine and New Brunswick Foothills and Eastern

Lowlands Section 11 4 12

Fundy Coastal and Interior Section 9 2 9

Central Maine Coastal and Interior Section 9 6 15

Lower New England and Hudson Valley Sections 13 6 16

Upper Atlantic Coastal Plain Section 6 2 7

Northern Appalachian Piedmont Section 12 1 12

White Mountains Section 13 8 14

New England Piedmont Section 11 8 14

Green, Taconic, Berkshire Mountains Section 12 5 12

South Southern Appalachian Piedmont Section 16 9 20

Coastal Plains, Middle Section 16 6 16

Southern Cumberland Plateau Section 17 7 20

Middle Atlantic Coastal Plain Section 14 5 15

Coastal Plains and Flatwoods Sections 14 8 15

Cumberland and Allegheny Mountains Sections 13 5 15

Blue Ridge Mountains Section 13 6 17

Interior West Palouse Dry Steppe Province 3 1 4

Southern Parks and Rocky Mountain Ranges Section 4 1 5

South-Central Highlands Section 5 1 5

North-Central Highlands and Rocky Mountain Sections 5 1 5

Northern Parks and Ranges Section 6 1 6

Colorado Plateau Semi-Desert Province 4 0 4

West Coast Northern California Coast Section 7 1 7

Intermountain Semi-Desert and Desert Province 3 0 3

Klamath Mountains Section 6 4 9

Northern California Coast Ranges Section 6 3 6

Northern California Interior Coast Ranges, Valleys, and

Foothills Section 6 2 6

Southern Cascades Section 5 2 6

Sierra Nevada Section 8 2 8

Modoc Plateau Section 4 1 5

Southern California Coast and Ranges Section 3 1 3

FHM = Forest Health Monitoring.

per acre per year and mortality of 125.3 cubic feet per acre

per year. Drought- and insect-induced mortality has been

observed in this forest type, primarily in white and red fir

(Dale 1996), which contributed to the negative growth

estimate.

Santiago Criterion 3—Maintenance of Forest

Ecosystem Health and Vitality

Introduction—An insightful definition of tree health and

vitality is presented by Shigo (1996):

• Vitality—the ability to grow under the dynamic

conditions present
18

• Stress—a condition wherein a system begins to operate

near the limits of its design

• Strain—disruption in a system operated beyond the

limits of stress

• Health—the ability to resist strain

Applying these definitions to forests, a healthy and vital

forest ecosystem has the capacity to function and grow

within the range of historic variation. In response to

normal stresses, such as drought, trees have developed

adaptations such as dieback and precocious loss of

foliage. Pushed beyond stress conditions considered

normal, a forest may become unhealthy and lack vitality.

For example, a forest that has evolved under a fire

disturbance regime can grow with endemic levels of

insects and diseases. If fire exclusion results in a dramatic

change in tree species composition, the ecosystem balance

can be affected. If the fire-resistant species are encroached

by fire-susceptible species that are also susceptible to

insects and diseases, the insect and disease population can

reach epidemic levels. Even resistant tree species can be

susceptible at epidemic levels. Similarly, anthropogenic

pollutants are by definition beyond the level of historic

variation and may affect the forest’s capacity to grow or

reproduce.

Forest health and vitality were measured on FHM plots

using crown dieback, transparency, mortality (dead tree

d.b.h./live tree d.b.h. ratio), tree damage, and evidence of

specific insect, disease, and abiotic stressors from FHM

and FHP survey data.

FHM measures of crown condition—The predominant

measure for assessing forest health worldwide has been

based on visual assessment of tree crowns and foliage

(Innes 1993). Crown dieback is branch mortality that

begins at the terminal and proceeds toward the stem in

response to biotic or abiotic stressors. In many cases this is

an adaptation to local or temporal stressors such as

drought or root damage. When the stress is alleviated, the

tree grows normally with only a structural change such as

Figure 11—Number of unique tree species by Forest Health Monitoring plot in 1997.

Tree species richness

1 – 2

2 – 5

5 – 10

10 – 15

15 +
19

Table 5—Annual growth and mortality of softwood and hardwood by Forest Health Monitoring region

or State and forest type from 1992 to 1996

FHM region Standard error Standard error

or State Forest type Growth of growth Mortality of mortality

 - - - - - - - - - - - - - - - - ft3

per acre - - - - - - - - - - - - - - -

Northeasta White-red-jack pine 55.5 10.2 28.9 4.3

Spruce-fir 36.6 6.3 30.1 3.4

Natural loblolly-shortleaf 35.8 17.3 5.4 1.1

Oak-pine 18.5 6.0 19.7 3.3

Oak-hickory 42.6 6.1 14.6 4.0

Bottomland hardwood -0.2 11.5 60.8 12.7

Birch-beech-maple 39.9 5.5 29.8 2.4

Aspen-birch 16.0 18.7 52.7 16.4

Southb White-red-jack pine 92.55 74.02 20.14 14.24

Natural slash-longleaf pine 63.45 12.63 11.05 5.95

Planted slash-longleaf pine 75.66 25.72 4.04 1.78

Natural loblolly-shortleaf pine 55.39 13.55 29.89 8.14

Planted loblolly-shortleaf pine 173.1 20.57 7.86 2.10

Oak-pine 54.71 7.04 22.29 4.13

Oak-hickory 37.96 5.12 20.59 3.70

Bottomland hardwood 49.28 8.12 15.74 5.00

Colorado Douglas-fir 30.80 3.22 13.9 9.4

Lodgepole pine 6.71 8.63 14.9 5.3

Ponderosa pine 21.54 9.05 0.0 0.0

Englemann spruce 48.86 14.08 1.6 0.8

Quaking aspen 16.01 6.65 9.8 2.5

Gambel oak 13.60 2.98 0.0 0.0

Pinyon-juniper 0.90 1.21 0.1 0.1

California Douglas-fir 50.6 36.1 34.31 12.45

Lodgepole pine 53.3 3.3 0.38 0.29

Jefferey pine 17.7 10.1 2.41 1.53

Ponderosa pine 29.3 26.3 25.22 13.38

White fir 43.4 34.6 73.89 24.55

California red fir 47.0 22.0 1.00 0.65

Tanoak 141.8 27.0 10.24 4.07

Oak–decidious 28.6 27.8 10.32 4.83

Blue oak 48.3 23.3 5.52 2.74

Oak–evergreen 35.8 11.8 0.0 —

Pinyon-juniper 2.3 2.2 0.0 —

Mixed conifers -96.4 100.1 125.3 61.97

FHM = Forest Health Monitoring.

— = No mortality occurred in this forest type.

a

 States include: Connecticut, Delaware, Maine, Maryland, Massachusetts, New Hampshire, New Jersey, Rhode Island, Vermont,

and West Virginia.

b

 States include: Alabama, Georgia, and Virginia.

the development of crook or forking. Although these

structural changes can result in severe loss of a tree’s value

as a timber product, other ecological processes proceed

unabated.

A FHM field measurement related to dieback is loss of

apical dominance, dead terminal. If dieback progresses to

the point where no branches on the dead part of the stem

are < 1 inch, the condition is no longer classified as
20

dieback but as a dead terminal. In this analysis, when trees

initially identified with dieback show declining dieback

and increasing dead terminal over the same time period,

the value assigned to dieback is the maximum of the two

measures. In figure 12, the tree on the left represents the

initial measurement with no crown dieback. The middle

tree represents the same tree with 20 percent dieback at

the first remeasurement. The tree on the right represents

the same tree at the second remeasurement, and because

all the dead branches have dropped off, it would be

recorded as having a dead terminal at 20 percent and no

dieback. The dieback value alone erroneously implies that

the tree recovered from dieback when it had actually

worsened. In the analysis for this report, the dieback value

remained at 20 percent.

Foliar transparency is the percentage of light visible

through the normally foliated portion of the crown. Like

dieback, this can be a normal adaptation to climatic stress.

An example of an adaptation is needle cast in response to

drought or as the result of insect, diseases, or anthropogenic pollutants. Specific stressors related to both dieback

and transparency are described in Stolte (1997).5

Examples of crown dieback and transparency are in tables 2

and 6. Determining whether specific values represent a

problem is a function of the magnitude of the change,

which is very species specific, and the confidence in the

estimate. Although the FHM Program has established a

significance probability level of 0.10 as the sampling

objective, changes with a lower probability level, e.g., FIA

uses 0.33, may be important given the specific forest

health issue, value, location, etc., addressed.

Testing for equality of the changes in transparency

among ecoregion sections in Colorado—Analyzing the

differences in rate of change in softwood transparency

among four sections of the Southern Rocky Mountains

Steppe Province in Colorado provides an example of how

testing among groups can give insight into probable causal

mechanisms behind changes over time resulting from

differences in climate, soils, species, or exposure to

stressors. Table 7 presents the analysis using model 2,

while figure 13 graphically illustrates the initial condition

and change between 1992 and 1996.

The test of fixed effects in table 7 indicates that a

significant change in foliar transparency occurred over

time and that the change over time differed among

ecoregion sections (indicated by “a” and “b” in figure 13).

The Pr > F of 0.0001 in the test of fixed effects means that

the probability was 1 in 10,000 that the estimated change

was a result of random chance and not some causal

mechanism. The CONTRAST statement results (table 7)

indicate that the annual increase in the North-Central

Figure 12—Relationship between dieback and dead terminal.

5 Stolte, K.W. 1997. 1996 national technical report on forest health.

[Research Triangle Park, NC]: U.S. Department of Agriculture,

Forest Service, Southern Research Station. 47 p. Administrative

report FS–605. On file with: Forestry Sciences Laboratory,

Southern Research Station, P.O. Box 12254, Research Triangle

Park, NC 27709.

Dieback = 0 Dieback = 20 percent Dieback = 0

Dead terminal = 20 percent
21

Table 6—Foliar transparency of Colorado softwood by province or ecoregion section

Estimate Standard

of value in Estimate error of Degrees of Value

Province or ecoregion section n 1992 of change estimate R2 freedom of t Pr > t

Palouse Dry Steppe Province 15 6.30 1.19 0.14 0.985 1 8.39 0.076

Southern Parks and Rocky Mountain

Ranges Section 10 4.93 3.12 0.30 0.797 1 10.33 0.061

South-Central Highlands Section 52 6.29 1.36 0.34 0.251 14 4.04 0.001

North-Central Highlands and

Rocky Mountain Sections 17 3.92 2.49 0.20 0.919 2 12.54 0.006

Northern Parks and Ranges Section 56 7.02 1.79 0.11 0.908 13 16.50 0.000

Colorado Plateau Semi-Desert

Province 18 6.34 1.70 0.63 0.353 3 2.71 0.073

n = Total number of measurements over time, including repeat measurements; estimate of value in 1992 = average value at the initial year of

measurement; estimate of change = annual change over the time interval; standard error of estimate = a measure of the variability of the data;

R2

 = a measure of goodness-of-fit of the estimate; degrees of freedom = number of repeat measurements -2; value of t = a measure of the

variability of the data relative to the mean; Pr > t = probability that the estimated change was due to random chance and that the true change over

the interval was 0.

Table 7—Results of analysis of variance to test the

equality of the change in foliar transparency in

Colorado softwood among ecoregion sections [PROC

MIXED (SAS Institute 1996)]

Type

Sourcea NDF DDF III F Pr > F

Tests of fixed effects

Year 1 35 92.28 0.0001

Year * ecosection 3 35 3.22 0.0342

CONTRAST statement results

Section A * section B 1 35 1.05 0.3122

Section A * section C 1 35 0.12 0.7341

Section A * section D 1 35 0.56 0.4594

Section B * section C 1 35 3.21 0.0819

Section B * section D 1 35 9.29 0.0044

Section C * section D 1 35 0.21 0.6477

a

 Section A = Southern Parks and Rocky Mountain Ranges; section

B = South-Central Highlands; section C = North-Central Highlands

and Rocky Mountains; section D = Northern Parks and Ranges.

Highlands and Rocky Mountain (2.49) and Northern Parks

and Ranges (1.79) Sections was significantly greater than

the increase of 1.36 in the South-Central Highlands

Section (table 6). Several characteristics about the sections

provide direction for future analysis. Of these three

sections, the North-Central Highlands and Rocky Mountain

Section showed the greatest increase in transparency, i.e.,

foliage is getting sparser. A large power plant is located in

this section. In addition to increased transparency, a

decrease in lichen diversity has been observed. The section

with the smallest, although increasing, change of these three

sections was the South-Central Highlands, the section with

the highest rainfall. The Northern Parks and Ranges Section

had the highest population and associated pollution

(industry, fireplaces, etc.). As stated earlier, this insight6

provides direction for future analysis and mitigating

measures.

Including climatic factors in estimates—The FHM

Program also uses non-USDA Forest Service data in

analyses. For example, the PDSI is used in model 3 to

assess the impact of drought on change in foliar

transparency in California. The PDSI is an empirically

derived index based on total rainfall, the periodicity of the

rainfall, and soil characteristics such as water-holding

capacity. Figure 14 presents the PDSI for seven climatic

regions in California and the corresponding values of

foliar transparency for the years 1992 and 1996. The foliar

transparency was intersected with PDSI to test to what

degree the observed change in crown condition can be

attributed to the change in PDSI (tables 8 and 9).

6 Personal communication. 1998. Michael Schomaker, Colorado

State Forest Service, 203 Forestry Building, Colorado State

University, Fort Collins, CO 80523–5060.
22

Analysis suggests that year and the interaction between year

and PDSI may be significant factors in the change in foliar

transparency. Table 8 indicates that transparency decreased

over time, decreased with increasing PDSI, and the

Year*PDSI interaction was significant. Table 9 shows that

blue oak, oak–evergreen, and mixed-conifer forest types

had a significant decrease in transparency over time and

with increasing PDSI.

In contrast, Douglas-fir and ponderosa pine decreased in

transparency, but the relationship with increasing PDSI

was not significant. A cursory analysis suggests that the

initial poor transparency in 1992 was not drought related

as is indicated in the blue oak, oak–evergreen, and mixedconifer types. Although this simple analysis does not

explain the process itself, it demonstrates the power in the

procedure and suggests its usefulness in analyzing more

subtle factors such as ozone and other pollutants.

Figure 13—Change in softwood foliar transparency for four ecoregion sections located in

the Southern Rocky Mountains Steppe Province in Colorado (1997). Sections with letters

in common were not significantly different at the 0.10 probability level.

18

16

14

12

10

8

6

4

2

1992 1996

Year

Southern Parks and Rocky Mountain Rangesab

South-Central Highlandsb

North-Central Highlands and Rocky Mountaina

Northern Parks and Rangesa

Foliar transparency

G

H

I

F
23

Figure 14—Comparison of Palmer Drought Severity Index and foliar transparency in

California in (A) 1992 and (B) 1996.

Extreme drought

Moderate drought

Normal

Moist

Very moist

Palmer Drought Severity Index Foliar transparency

 5 – 10

10 – 20 

20 +

(A)

(B)
24

Table 9—Results of analysis of variance to test significance of change in foliar

transparency by forest type in California to change in Palmer Drought

Severity Index [PROC MIXED (SAS Institute 1996)]

Standard Degrees of Value

Parameter Estimate error freedom of t Pr > t

Douglas-fir

Intercept 16.78766120 0.93546449 9 17.95 0.0001

Year -4.42007989 0.72100990 1 -6.13 0.1029

PDSI -1.08510212 0.34923821 1 -3.11 0.1982

Year * PDSI 0.80593644 0.17486038 1 4.61 0.1360

Lodgepole pine

Intercept 10.43072545 1.61618715 4 6.45 0.0030

Year -0.14547244 0.45234293 0 -0.32 —

PDSI 0.13923832 0.57031957 0 0.24 —

Year * PDSI -0.01091106 0.16474579 0 -0.07 —

Jeffrey pine

Intercept 11.19010980 3.41683302 5 3.27 0.0221

Year 3.51280668 1.94643187 0 1.80 —

PDSI -1.31407184 1.49945396 0 -0.88 —

Year * PDSI -0.20290791 0.53965409 0 -0.38 —

Ponderosa pine

Intercept 14.40996203 1.09218854 12 13.19 0.0001

Year -2.33336064 0.93585584 4 -2.49 0.0672

PDSI -0.16755919 0.41990673 4 -0.40 0.7103

Year * PDSI 0.28029481 0.20574172 4 1.36 0.2447

White fir

Intercept 6.23110158 1.65610312 11 3.76 0.0031

Year 1.56456571 0.85272008 0 1.83 —

PDSI 0.82073571 0.72994874 0 1.12 —

Year * PDSI -0.41380309 0.26623328 0 -1.55 —

(continued)

Table 8—Results of analysis of variance to test significance of change in foliar

transparency in California to change in Palmer Drought Severity Index

[PROC MIXED (SAS Institute 1996)]

Solution for fixed effects

Standard Degrees of Value

Parameter Estimate error freedom of t Pr > t

Intercept 13.93981621 0.50116905 168 27.81 0.0001

Year -1.27370858 0.25366039 53 -5.02 0.0001

PDSI - 0.42381249 0.26584618 53 -3.30 0.0017

Year * PDSI 0.23836641 0.10288753 53 3.22 0.0022

PDSI = Palmer Drought Severity Index; degrees of freedom = number of repeat measurements -2;

value of t = a measure of the variability of the data relative to the mean; Pr > t = probability that

the estimated change was due to random chance and that the true change over the interval was 0.
25

Table 9—Results of analysis of variance to test significance of change in foliar

transparency by forest type in California to change in Palmer Drought

Severity Index [PROC MIXED (SAS Institute 1996)] (continued)

Standard Degrees of Value

Parameter Estimate error freedom of t Pr > t

California red fir

Intercept 11.87348178 1.48086567 7 8.02 0.0001

Year -1.63858286 2.53061496 2 -0.65 0.5837

PDSI -0.72063537 0.52523306 2 -1.37 0.3037

Year * PDSI 0.38342295 0.50636533 2 0.76 0.5280

Tanoak

Intercept 13.53924557 1.43523951 6 9.43 0.0001

Year -0.46545367 3.31550260 5 -0.14 0.8938

PDSI -0.97943545 0.72869723 5 -1.34 0.2367

Year * PDSI 0.21083092 0.70546794 5 0.30 0.7771

Oak–deciduous

Intercept 17.12126497 2.68575164 6 6.37 0.0007

Year -2.83476979 1.64234355 1 -1.73 0.3343

PDSI -1.96286207 1.77768703 1 -1.10 0.4685

Year * PDSI 0.77370159 0.61230748 1 1.26 0.4262

Blue oak

Intercept 17.06350213 1.34180898 19 12.72 0.0001

Year -3.03316617 1.03607430 5 -2.93 0.0327

PDSI -1.78170568 0.68448076 5 -2.60 0.0481

Year * PDSI 0.67541451 0.25963152 5 2.60 0.0482

Oak–evergreen

Intercept 16.89438632 1.77780313 24 9.50 0.0001

Year -1.61712203 0.57863387 3 -2.79 0.0682

PDSI -1.46727088 0.73019200 3 -2.01 0.1381

Year * PDSI 0.47978064 0.22267746 3 2.15 0.1202

Pinyon-juniper

Intercept 10.73759529 1.73602316 16 6.19 0.0001

Year -0.58961533 0.70256678 2 -0.84 0.4897

PDSI 0.64492988 0.65147120 2 0.99 0.4265

Year * PDSI -0.23278898 0.22062881 2 -1.06 0.4020

Mixed conifers

Intercept 13.53400976 0.65617231 30 20.63 0.0001

Year -1.34167446 0.37345714 5 -3.59 0.0157

PDSI -0.77074669 0.28249972 5 -2.73 0.0414

Year * PDSI 0.33028711 0.12580859 5 2.63 0.0468

PDSI = Palmer Drought Severity Index; degrees of freedom = number of repeat measurements -2;

value of t = a measure of the variability of the data relative to the mean; Pr > t = probability that the

estimated change was due to random chance and that the true change over the interval was 0.

— = Insufficient sample size.
26

Figure 15—Status of hardwood dieback in the Forest Health Monitoring (FHM) North region using only measured plots

compared with the status of hardwood dieback in the FHM North region including the predicted values [Best Linear

Unbiased Predictions (BLUP) estimation procedure of all nonmeasured plots].

Including BLUPs in spatial analysis—In figure 15, a

display of the status of hardwood dieback using only the

measured plots (panel 0 and overlap from panel 3) is

compared with a display that includes the predicted values

of all unmeasured plots (panels 1, 2, and 3) in addition to

the measured plots. The comparison illustrates the benefit

of using the BLUP procedure. In figure 15 the map on the

left displays only the plots measured in 1995. All the plots

in New Jersey are in the 0 to 5 dieback class. By random

chance the plots measured in that year had minimal

dieback, implying good health. In contrast, the map on the

right includes the predicted values of all plots not measured

in 1995. Four of the 14 plots in the State are in the 2 most

severe dieback classes, which implies that approximately

one-third of the State is in poor health (concentrated in the

southern part).

Mortality—Tree mortality is a natural and essential

process in normal stand dynamics. In fact, the absence of

mortality can be a useful indicator of poor stand vigor,

which often leads to catastrophic conditions of forest

health.

Measured values for panel 0 and

overlap from panel 3 in 1995

0 – 5

5 – 10

10 – 15

15 +

0 – 5

5 – 10

10 – 15

15 +

BLUPs for panels 1, 2, and 3

in 1995
27

Figure 16—Spatial pattern of the ratio of the diameter of trees that died from 1992 to 1996 to the diameter of trees still living in 1996.

An informative indicator of mortality relative to forest

health is the ratio of the diameter of dead trees to the

diameter of live trees (MD/LD). The dead trees in this

ratio are the trees that have died since the previous diameter

measurement. A low ratio (much less than 1) indicates that

the mortality observed is composed primarily of smaller

trees that are probably part of the natural self-thinning

development of the forest. A higher ratio (much greater

than 1) indicates that mortality is due to senescence or

some external factor such as insects or diseases. Figure 16

illustrates the plot level average of MD/LD. In California,

the Sierra Nevada Section shows an MD/LD ratio of 1.4.

Although FHM did not identify causal agents on the plots,

the mortality of large trees [red fir (A. magnifica)] in that

section was associated with attacks by fir engravers

(Scolytus ventralis) (Dale 1996).

Santiago Criterion 5—Maintenance of Forest

Contribution to Global Carbon Cycles

Introduction—It is widely suggested that the increased

concentration of greenhouse gases, including carbon

dioxide, will result in climate change in most regions of

the World. There are many ways of mitigating this effect

that relate to trees and forests. Tree- and forest-based

methods include increasing forest growth, planting trees,

minimizing loss of carbon to the atmosphere through

catastrophic mortality, and making efficient use of

harvested material and salvaged mortality.

Sequestration of atmospheric carbon in trees—Carbon

storage is an important factor affecting the increase of

carbon dioxide concentrations in the atmosphere and the

0 – 0.5

Mortality d.b.h./live d.b.h.

0.5 – 1

1 – 1.5

1.5 – 2

2 +
28

resulting global warming. Trees use carbon from the

atmosphere as they grow. Dead trees lose carbon to the

atmosphere as they decay. Approximately one-half of the

carbon harvested as biomass is stored for long periods as

wood products. The amount of carbon stored or lost

annually from FHM plots was estimated for variable time

periods from 1990 to 1996. Carbon sequestration rates are

determined using tree volume data from FHM plots and

estimates of other carbon (belowground, downed woody

debris) from published information (Birdsey 1996).

Carbon storage was estimated by determining the biomass

of the living boles and roots of all trees and saplings and

then subtracting (1) the biomass of the trees that died, and

(2) approximately one-half of the biomass of the trees that

were harvested over the same time period. This one-half

represents the proportion of harvested biomass that is used

in a durable form, e.g., bound books, wooden structures,

etc. (Birdsey 1996). A net gain is the result of increased

stand growth and the efficient utilization of harvest trees

and salvaging of mortality. Figure 17 presents the spatial

distribution of estimated net annual carbon sequestration

or storage for each FHM plot.

Several regions showed significant losses in carbon. In

California most of the losses were in the Sierra Nevada

Section, where mortality was substantial due to drought

and other contributing factors (table 10). The Coastal

Plains and Flatwoods Section of the Southeast showed a

net gain in carbon, primarily in planted loblolly pine (P.

taeda) (table 11).

Figure 17—Rate of carbon sequestration in all tree species from 1992 to 1996 by ecoregion section.

Tree carbon sequestration

Net loss

No change

Net gain
29

Table 10—Tree carbon of softwood and hardwood by province or ecoregion section in California

Standard Degrees

Estimate error of of Value

Province or ecoregion section n of change estimate R2 freedom of t Pr > t

- - - pounds per acre - - -

Northern California Coast Section 21 4,050.74 1,184.75 0.9974 5 3.42 0.019

American Semi-Desert and Desert Province 10 180.07 170.37 0.9999 1 1.06 0.482

Klamath Mountains Section 34 -1222.5 1,683.78 0.9901 8 -0.73 0.488

Northern California Coast Ranges Section 17 2,363.43 596.45 0.9995 3 3.96 0.029

Northern California Interior Coast Ranges,

Valleys, and Foothills Section 26 253.07 360.79 0.9968 5 0.70 0.514

Southern Cascades Section 24 206.29 430.75 0.9987 6 0.48 0.649

Sierra Nevada Section 74 -1776.7 1,530.35 0.9825 16 -1.16 0.263

Modoc Plateau Section 17 164.06 151.47 0.9998 3 1.08 0.358

Central California Coast Ranges Section 13 2,417.45 1,143.97 0.9908 2 2.11 0.169

Southern California Coast and Ranges

Section 9 873.51 678.38 0.9998 1 1.29 0.420

n = Total number of measurements over time, including repeat measurements; estimate of change = annual change over the time interval;

standard error of estimate = a measure of the variability of the data; R2

 = a measure of goodness-of-fit of the estimate; degrees of freedom =

number of repeat measurements -2; value of t = a measure of the variability of the data relative to the mean; Pr > t = probability that the

estimated change was due to random chance and that the true change over the interval was 0.

Table 11—Tree carbon of softwood and hardwood by province or ecoregion section in the East

Standard Degrees

Estimate error of of Value

Province or ecoregion section n of change estimate R2 freedom of t Pr > t

- - - pounds per acre - - -

Aroostook Hills and Lowlands Section 28 318.2 772.7 0.961 14 0.41 0.687

Maine and New Brunswick Foothills

and Eastern Lowlands Section 66 889.6 604.5 0.942 37 1.47 0.150

Fundy Coastal and Interior Section 15 335.3 973.1 0.985 7 0.34 0.741

Central Maine Coastal and Interior Section 45 -1,128.2 746.9 0.945 25 -1.51 0.144

Lower New England and Hudson Valley

Sections 106 -413.1 610.5 0.949 60 -0.68 0.501

Upper Atlantic Coastal Plain Section 27 849.2 284.7 0.994 14 2.98 0.001

Northern Appalachian Piedmont Section 7 -3,814.8 3,606.6 0.808 3 -1.06 0.368

White Mountains Section 164 -1,210.7 475.7 0.951 93 -2.54 0.013

New England Piedmont Section 44 3,094.7 673.4 0.978 24 4.60 0.000

Green, Taconic, Berkshire Mountains Section 47 -1,196.0 1,132.7 0.897 27 -1.06 0.300

Southern Appalachian Piedmont Section 218 -166.4 661.3 0.927 108 -0.25 0.802

Coastal Plains, Middle Section 124 336.4 737.2 0.883 61 0.46 0.650

Cumberland Plateau Sections 72 237.7 897.8 0.922 35 0.26 0.793

Middle Atlantic Coastal Plain Section 58 -300.6 1,006.6 0.973 30 -0.30 0.767

Coastal Plains and Flatwoods Sections 165 701.2 525.8 0.970 81 1.33 0.186

Cumberland and Allegheny Mountains

Sections 56 771.2 850.5 0.948 27 0.91 0.373

Blue Ridge Mountains Section 40 1,019.3 1,185.4 0.952 19 0.86 0.401

n = Total number of measurements over time, including repeat measurements; estimate of change = annual change over the time interval;

standard error of estimate = a measure of the variability of the data; R2

 = a measure of goodness-of-fit of the estimate; degrees of freedom =

number of repeat measurements -2; value of t = a measure of the variability of the data relative to the mean; Pr > t = probability that the

estimated change was due to random chance and that the true change over the interval was 0.
30

Summary and Future Assessments

After completing at least one 4-year cycle measurement in

some regions, the FHM Program can reliably estimate

change in forest health. National FHM assessments are

based on the Santiago Declaration: “Criteria and Indicators

for the Conservation and Sustainable Forest Management

of Temporate and Boreal Forests.” Through 1999, FHM

measured indicators that contribute information to address

four of the seven Santiago criteria: (1) conservation of

biological diversity, (2) maintenance of productive

capacity of forest ecosystems, (3) maintenance of forest

ecosystem health and vitality, and (5) maintenance of

forest contributions to global carbon cycles.

In addition to data collected directly as part of the plot and

survey components of detection monitoring, FHM uses

data from other sources such as other FHP data, FIA data,

NFS data, and other related weather and air quality data.

These ancillary data are vital to the interpretation of plot

data and the assessment process.

The data and data analysis procedures presented in this

report show that FHM data are useful in assessing the

status and change of forest health. Several data gaps that

must be addressed are also identified. The lack of

complete vegetative structure information or plant counts

in all height components of the forest ecosystem

represents a vital data gap. Although collocation of FHM,

FIA, and NFS/CVS plots has helped fill this data gap that

could be used to assess biodiversity, both FIA (phase 2)

and NFS must measure plots during all seasons, increasing

the difficulty in detecting and identifying nonwoody

plants. As of 1999, FHM was the only program that

logistically could measure only during the growing season.

In addition to the tree species diversity information

collected by FHM, other indicators, such as lichen

communities, contributed plant biodiversity information.

More complete tree-height data from ground plots are also

needed to improve determination of growth. Growth information is important to assessing the maintenance of forest

ecosystem productive capacity. Although at present, tree

volumes must be calculated using estimated tree heights,

the resulting growth information is useful on a regional

scale.

Other FHM data that contribute to the productive capacity

assessment are tree mortality, crown dieback, and crown

foliar transparency. The data on these indicators can also

be used in the procedures presented in this report to

predict plot values for unmeasured years. These prediction

procedures highlight one of the benefits of the FHM

rotating panel sampling design.

FHM assessments are at the point of integrating nonplot

data and the data collected as part of the ground plot

system. An example of nonplot data presented in this

report is climate data (PDSI). In addition, preliminary

inferences on causal agents and processes are suggested

from insect and disease survey reports (Dale 1996). This

step provides the framework for more meaningful

interpretation of information. Other kinds of ancillary

data, such as remotely sensed landscape data, are being

investigated for inclusion in future assessments.

Carbon sequestration is an important part of monitoring

the forest contribution to global carbon cycles. FHM data

used to determine tree volume could be combined with

published information to estimate carbon sequestration

rates.

Acknowledgments

The authors thank Marcia Gumpertz, North Carolina State

University, Department of Statistics, for her assistance in

statistical derivations. The authors also thank Mark

Ambrose, North Carolina State University, Department of

Forestry, for his assistance with the final revision of the

sections pertaining to models. The authors thank John Pye,

Noel Cost, and Stan Zarnoch, U.S. Department of

Agriculture Forest Service, Southern Research Station, for

their thorough and insightful reviews. Additional thanks go

to the many others in the FHM Program who provided

review comments. This work was funded in part by the

USDA Forest Service under a cooperative agreement with

North Carolina State University.

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Christensen, Ronald. 1991. Linear models for multivariate time-series

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Central Forest Experimental Station. 5 p.

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height-diameter equations for twenty-four tree species in western

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irregularly spaced, unbalanced, longitudinal data from permanent-plot

measurements. Canadian Journal of Forest Research. 25: 137-156.

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United Kingdom: CAB International. 677 p.

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productivity. In: Greenland, D.J.; Szabolcs, I., eds. Soil resilience and

sustainable land use. Wallingford, United Kingdom: CAB

International. 561 p.

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 ed. New

York: John Wiley. 1,335 p.

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sustain_dev/sd/sfmsd.htm. [Date accessed: unknown].
32

All estimates for the following tables were derived using PROC MIXED (SAS Institute 1996).

Definitions of table output:

Dieback branch mortality that begins at the terminal and proceeds toward the stem

Foliar transparency percentage of light visible through the normally foliated portion of the crown

Volume growth increase in volume of trees living at the initial measure, including those harvested

plus ingrowth

Tree mortality volume of trees living at the initial measurement that were dead at the following

measurement

Tree carbon total aboveground and belowground carbon sequestered since the initial

measurement, including that utilized into durable products.

Ecoregion the ecoregion section based on Bailey’s (1995) ecoregions

n the total number of measurements over time, including repeat measurements

Estimate of value in 1991 the average value at the initial year of measurement

Estimate of change annual change over the time interval

Standard error of estimate a measure of the variability of the data

R2 a measure of goodness-of-fit of the estimate

Degrees of freedom n - 2

Value of t a measure of the variability of the data relative to the mean

Pr > t the probability that the estimated change was due to random chance and that the

true change over the interval was 0

Interpretation—The significance of an estimate of change is a function of the magnitude of the change and the

confidence in the estimate. For example, in the Aroostook Hills and Lowlands Ecoregion Section, the mean

change in dieback was 0.93 with a standard error of 0.26. The probability is 0.001 of a greater t value if the true

change is 0.0. This means the odds are 1 in 1,000 that the FHM plots had a change in dieback by random chance

equal to 0.93, even though the mean change of all trees in the section was 0.0. Therefore, the change probably

occurred.

Appendix A

Interpreting FHM Tables

Appendix table A.1—Example of dieback of eastern softwoods by ecoregion

Estimate Standard Degrees

of value Estimate error of of Value

Ecoregion n in 1991 of change estimate R2 freedom of t Pr > t

Aroostook Hills and Lowlands 55 2.51 0.93 0.26 0.556 43 3.63 0.001

Maine and New Brunswick Foothills

and Eastern Lowlands 120 3.27 0.54 0.20 0.721 95 2.74 0.007

Fundy Coastal and Interior 35 4.88 3.54 1.12 0.600 27 3.16 0.004
33

Appendix B

Measures of Tree Growth

Three measures of growth relevant to forest health follow:

Gross growth = (V2

 + M + C - V1 ) / (t2 - t1 )

Net growth = (V2

 + C - V1 ) / (t2 - t1 )

Net change = (V2

 - V1 ) / (t2 - t1 )

where

V1 = volume of trees at initial measurement

V2

 = volume of trees at remeasurement

M = initial volume of trees that died since initial measurement

C = initial volume of trees removed since initial measurement

t

1 = year of initial measurement

t

2

 = year of remeasurement

Consistent with common usage (Beers 1962), the inclusion of ingrowth, i.e., trees that were below the threshold

diameter at time t

1

, in V2 is implied.

Gross growth is the change in volume from period t

1

 to t

2

 including trees that died during the interval. Net growth is

the change in volume from period t

1

 to t

2 minus the initial volume of trees that died during the interval. Both gross

growth and net growth include volume harvested during the period. Gross growth and net growth are measures of

productivity. Net growth is commonly, and in this document, referred to as simply growth.

A related term that can be confused with net growth is net change. Net change is sometimes referred to as net

increase or actual change in growing stock (Beers 1962). Net change is equal to growth minus cut.
34
Smith, William D.; Conkling, Barbara L. 2004. Analyzing forest health data. Gen. Tech. Rep.

SRS–77. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research

Station. 33 p.

This report focuses on the Forest Health Monitoring Program’s development and use of analytical

procedures for monitoring changes in forest health and for expressing the corresponding statistical

confidences. The program’s assessments of long-term status, changes, and trends in forest

ecosystem health use the Santiago Declaration: “Criteria and Indicators for the Conservation and

Sustainable Forest Management of Temporate and Boreal Forests” (Montreal Process) as a

reporting framework. Procedures used in five aspects of data analysis are presented. The analytical

procedures used are based on mixed estimation procedures. Examples using the indicators are

included, along with a clear link to the analytical procedures used (1) estimating change over time

within groups—estimation of growth, harvest, mortality, and crown condition; (2) testing for

differences in change over time among groups—foliar transparency; (3) estimating change using

covariates—impact of drought on change in foliar transparency; (4) estimating plot values for

unmeasured years—comparison of observed and predicted (Best Linear Unbiased Predictions)

values of foliar transparency, dieback, and total volume; and (5) estimating tree heights—examples

of using estimated tree heights to estimate tree volume.

Keywords: Assessment, BLUP, change estimation, mixed models, monitoring, tree height.
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