U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2013–1222

National Water-Quality Assessment Program

Prepared in cooperation with the U.S. Environmental Protection Agency

Design Tradeoffs for Trend Assessment in 

Aquatic Biological Monitoring Programs

Design Tradeoffs for Trend Assessment in 

Aquatic Biological Monitoring Programs

By Martin E. Gurtz, John Van Sickle, Daren M. Carlisle, and Steven G. Paulsen

National Water-Quality Assessment Program

Prepared in cooperation with the U.S. Environmental Protection Agency

Open-File Report 2013–1222

U.S. Department of the Interior 

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Gurtz, M.E., Van Sickle, J., Carlisle, D.M., and Paulsen, S.G., 2013, Design tradeoffs for trend assessment in

aquatic biological monitoring programs: U.S. Geological Survey Open-File Report 2013–1222, 15 p. plus 1 app.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope .......................................................................................................................................2

Methods...........................................................................................................................................................2

Study Area and Sampling Methods...................................................................................................2

Sample Processing and Metric Calculation.....................................................................................5

Estimation of Variance Components and Minimum Detectable Trend ........................................6

Trend Design Choices ..........................................................................................................................7

Major Findings................................................................................................................................................7

Metrics....................................................................................................................................................7

Design Elements....................................................................................................................................8

Sampling Period...........................................................................................................................8

Number of Samples Per Year.....................................................................................................8

Sampling Interval.........................................................................................................................9

Number of Sites in Multiple-Site Designs ...............................................................................9

Balancing the Tradeoffs.....................................................................................................................10

Design [1]: Site-Specific Trend................................................................................................10

Design [2]: Multiple Sites—Same Sites Resampled............................................................10

Design [3]: Multiple Sites—New Sites Sampled..................................................................11

Discussion.....................................................................................................................................................12

Acknowledgments.......................................................................................................................................13

References Cited..........................................................................................................................................13

Appendix 1. Variance Component Equations.......................................................................................16

Design [1]: Site-Specific Trend.........................................................................................................16

Design [2]: Trend in Multiple Sites—Same Sites Resampled......................................................16

Design [3]: Trend in Multiple Sites—New Sites Sampled............................................................17

Figures

1. Locations of 32 streams and rivers sampled in this study.....................................................3

2. Variance components as a percentage of total variance for 17 metrics and 

indices commonly used in bioassessments.............................................................................7

3. Minimum detectable trend at a site in Total Richness or MMI for designs 

with annual sampling and one, two, or three samples per year...........................................8

4. Minimum detectable trend at a site in Total Richness and MMI for 10-year,

 20-year, and 30-year sampling periods and different sampling intervals ..........................9

5. Minimum detectable trend for multiple sites in Total Richness and MMI 

for different numbers of sites and sampling intervals............................................................9
iv

6. Percentage decrease in minimum detectable trend for an individual site, 

resulting from a 100-percent increase in sampling effort for different design 

choices and different metrics...................................................................................................10

7. Percentage reduction in minimum detectable trend for multiple sites, 

resulting from a 100-percent increase in sampling effort for different 

design choices and different metrics......................................................................................11

8. Percentage reduction in minimum detectable trend for multiple sites, 

resulting from a 100-percent increase in sampling effort for different 

design choices and different metrics......................................................................................11

Tables

1. Watershed characteristics of the 32 sites in this study.........................................................3

2. Terms used in this report.............................................................................................................5

3. Invertebrate metrics and indices, with mean and range for all samples, 

grouped by type of data. .............................................................................................................6
v
Design Tradeoffs for Trend Assessment in 

Aquatic Biological Monitoring Programs 

By Martin E. Gurtz1, John Van Sickle2, Daren M. Carlisle1, and Steven G. Paulsen3

1

 U.S. Geological Survey, National Water-Quality Assessment Program.

2 Oregon State University, Department of Fisheries and Wildlife

3 U.S. Environmental Protection Agency, Office of Research and Development

Abstract

Assessments of long-term (multiyear) temporal trends 

in biological monitoring programs are generally undertaken 

without an adequate understanding of the temporal variability of biological communities. When the sources and levels 

of variability are unknown, managers cannot make informed 

choices in sampling design to achieve monitoring goals in a 

cost-effective manner. We evaluated different trend sampling 

designs by estimating components of both short- and longterm variability in biological indicators of water quality in 

streams. Invertebrate samples were collected from 32 sites—

9 urban, 6 agricultural, and 17 relatively undisturbed (reference) streams—distributed throughout the United States. 

Between 5 and 12 yearly samples were collected at each 

site during the period 1993–2008, plus 2 samples within a 

10-week index period during either 2007 or 2008. These data 

allowed calculation of four sources of variance for invertebrate 

indicators: among sites, among years within sites, interaction among sites and years (site-specific annual variation), 

and among samples collected within an index period at a site 

(residual). When estimates of these variance components are 

known, changes to sampling design can be made to improve 

trend detection. Design modifications that result in the ability 

to detect the smallest trend with the fewest samples are, from 

most to least effective: (1) increasing the number of years in 

the sampling period (duration of the monitoring program), 

(2) decreasing the interval between samples, and (3) increasing the number of repeat-visit samples per year (within an 

index period). This order of improvement in trend detection, 

which achieves the greatest gain for the fewest samples, is 

the same whether trends are assessed at an individual site or 

an average trend of multiple sites. In multiple-site surveys, 

increasing the number of sites has an effect similar to that of 

decreasing the sampling interval; the benefit of adding sites is 

greater when a new set of different sites is selected for each 

sampling effort than when the same sites are sampled each 

time. Understanding variance components of the ecological 

attributes of interest can lead to more cost-effective monitoring designs to detect trends.

Introduction

Long-term monitoring studies contribute valuable 

information toward understanding the condition of our natural 

resources and how they respond to human influences and 

natural variation (Hirsch and others, 2006; Jackson and Füreder, 2006; Peterson and others, 2011). Such studies are rare, 

however, and are susceptible to budget constraints that may 

jeopardize the continuity of monitoring networks. Because of 

limited data on the sources of variation in trends and factors 

affecting the variability of ecological attributes of interest, 

design choices are often made primarily to reduce costs, with 

minimal consideration of effects on the goals of trend detection. This study estimated temporal components of variance in 

long-term biological monitoring data to evaluate how different 

monitoring design choices affect the ability to detect trends.

Biological monitoring programs that assess the ecological 

condition of streams and rivers typically focus on macroinvertebrates, although sometimes supplemented by collections 

of fish or algae. Long-term studies of freshwater invertebrates are uncommon, particularly those that span 10 or more 

years—with a few notable exceptions, including Robinson 

and others (2000); Beche and others (2006); Mazor and others 

(2009); Ormerod and Durance (2009); Webb and King (2009); 

Peterson and others (2011). Even fewer studies have used a 

common approach and methods over time at more than a local 

scale (Davies-Colley and others, 2011; Kennen and others, 

2012; Miller and others, 2012). More long-term investigations 

are needed to enable researchers and resource managers to 

relate changes in stream health to local, regional, and global 

phenomena, including climate change (Daufresne and others, 

2004; Durance and Ormerod, 2007; Mazor and others, 2009; 

Lawrence and others, 2010). Such data also would provide 

information about sources of temporal variation that could be 

used in the design of long-term monitoring programs. 

Monitoring programs—whether intended to assess 

status and change at individual sites or a group of sites—can 

be designed in several ways that influence trend detection, 
2 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

with tradeoffs in the program cost (number of samples) and 

duration (number of years in the sampling period) required 

to achieve the program’s objectives. These design choices 

include: (1) increasing the sampling period (the total elapsed 

time, in years, over which samples are collected), (2) decreasing the sampling interval (number of years between sampling 

efforts), and (3) increasing the number of samples collected 

each year. When the goal is to assess the average trend 

throughout a stream network, a fourth design element—the 

number of sites to be sampled—can be adjusted. This report 

focuses on these four elements of the sampling design—the 

allocation of sampling effort within and among years and 

across sites (Stevens and Urquhart, 2000; Larsen and others, 

2001). 

Sampling design decisions for monitoring programs are 

ideally founded on an understanding of the temporal variability of biological communities and other ecological endpoints 

of interest. Program designers should consider sources of variation that affect the ability of the sampling program to detect 

change in some attribute of interest over time. One framework 

for understanding these sources of variation (Urquhart and 

others, 1998; Larsen and others, 2001) identifies four major 

variance components: (1) site-to-site geographic variation, (2) 

coherent (or synchronous) year-to-year variation expressed by 

all of the sites together, (3) site-by-year interaction with differing temporal patterns across sites, due to site-specific factors, 

and (4) residual variation, composed of temporal variation 

within the sampling season as well as sampling error. If coherent temporal variation is large, the only option is to sample 

over a longer time period; however, other sources of variation can be managed through design and sample size choices 

(Kincaid and others, 2004). 

Information about how variance components influence 

design tradeoffs—for example, number of replicates, number of sites, and number of times to sample—is often limited 

(Philippi and others, 1998). Estimation of variance components for trend assessments requires data collection that is 

designed to incorporate both short-term (for example, within 

year) and long-term (among years) temporal sampling. Such 

studies have been done for evaluating trends in the ecological 

condition of lakes (Larsen and others, 1995; Urquhart and others, 1998; Larsen and others, 2001; Kincaid and others, 2004); 

related studies of streams have been limited to a small number 

of sites (Mazor and others, 2009). Most studies that have 

estimated variance components in monitoring programs have 

examined how these components affect statistical power for 

detecting trends (Wagner and others, 2007; Al-Chokhachy and 

others, 2011; Anlauf and others, 2011). The emphasis in this 

report is not on statistical power but on the magnitude of trend 

that can be detected, so that the findings can be more directly 

applied to management decisions on the design of monitoring 

programs. 

Purpose and Scope

This report presents the research and findings of a joint 

effort of the U.S. Geological Survey National Water-Quality 

Assessment (USGS NAWQA) Program and the U.S. Environmental Protection Agency (EPA) National Rivers and Streams 

Assessment. The objective of this study was to evaluate how 

different monitoring program designs affect trend detection 

in invertebrate communities in streams throughout the United 

States at sites sampled by the NAWQA Program. We follow an 

approach similar to Larsen and others (1995, 2001) and estimate spatial and temporal variance components to quantify the 

magnitude of trend that could be detected for different monitoring designs—varying the number of samples collected, the 

number of years over which the monitoring was conducted, 

and the number of sites—and evaluate tradeoffs associated 

with different trend design choices.

Methods

Study Area and Sampling Methods

We selected 32 sites that were sampled as part of the 

NAWQA Program (http://water.usgs.gov/nawqa/), distributed 

across a broad range of geographic regions and a wide range 

of human influences (fig. 1, table 1). Seventeen sites represented least-disturbed conditions, referred to in this paper as 

“reference” sites, 9 sites were dominated by urban land use, 

and 6 sites represented agricultural land use. All sites were 

wadeable, draining19 to 3,204 km2, with mean annual discharge ranging from 0.1 to 14.5 m3

/s (table 1).

Invertebrate community samples were collected during 

1993–2008 during a 6-week index period specified for each 

site, generally during summer low flow. Index periods were 

selected so that annual sampling was conducted under similar 

seasonal conditions from one year to the next (“index period” 

and other terms used in this report are defined in table 2). During either 2007 or 2008, two samples were collected at each 

site within an extended 10-week index period to allow estimation of variation within the index period; for that year, the time 

between samples at a site ranged from 27 to 64 days, with 

one exception—a site with only 11 days between samples. 

The span of calendar days at any site, across all sample years, 

ranged from 36 to 67. The number of samples at a site ranged 

from 6 to 13, representing from 5 to 12 distinct years; 24 of 

32 sites had at least 8 years of biological data.
Methods 3

Land use category

Agriculture

Urban

Reference

16 1

2 4 5

6

7

8

9

10

12 11

13

14 15

17

18

19

20

21

22

23

24

25

26

27

28 29

30

31

32

3

EXPLANATION

Figure 1. Locations of 32 streams and rivers sampled in this study (6 agriculture, 9 urban, and 

17 reference sites). Land use refers to the dominant land use in the watershed as defined by 

Gilliom and others (2006).

Table 1. Watershed characteristics of the 32 sites in this study.—Continued

[Site locations are shown in figure 1. Ecoregions are Omernik Level III (Omernik, 1987). km2, square kilometers; m, meters; m3/s, cubic meters per second]

Site Station

number Station name Land use

Drainage 

area

(km2

)

Elevation

(m)

Mean annual 

discharge

(m3/s)

Ecoregion at sampling 

reach

1 01170100 Green R nr Colrain, MassachusettsReference 107 133 2.6 Northeastern Highlands

2 01403900 Bound Brook at Middlesex, New 

Jersey

Urban 125 8 2.2 Northern Piedmont

3 01464907 Little Neshaminy Cr nr Neshaminy, PennsylvaniaUrban 69 58 1.5 Northern Piedmont

4 01472157 French Cr nr Phoenixville, PennsylvaniaReference 153 49 2.6 Northern Piedmont

5 01610400 Waites Run nr Wardensville, 

West Virginia

Reference 33 378 0.5 Middle Atlantic Coastal 

Plain

6 01621050 Muddy Cr at Mount Clinton, 

Virginia

Agriculture 37 402 0.3 Ridge and Valley

7 02087580 Swift Cr nr Apex, North Carolina Urban 54 89 0.7 Southeastern Plains

8 02335870 Sope Cr nr Marietta, Georgia Urban 80 269 1.4 Piedmont

9 02338523 Hillabahatchie Cr nr Franklin, 

Georgia

Reference 44 277 0.6 Piedmont

10 0242354750 Cahaba Valley Cr at Pelham, 

Alabama

Urban 66 134 1.2 Ridge and Valley

11 03267900 Mad R nr Springfield, Ohio Agriculture 803 276 9.3 Eastern Corn Belt Plains
4 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

Table 1. Watershed characteristics of the 32 sites in this study.—Continued

[Site locations are shown in figure 1. Ecoregions are Omernik Level III (Omernik, 1987). km2, square kilometers; m, meters; m3/s, cubic meters per second]

Site Station 

number Station name Land use

Drainage 

area 

(km2

)

Elevation 

(m)

Mean annual 

discharge 

(m3/s)

Ecoregion at sampling 

reach

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

03357330

03361650

04161820

04175600

06324970

07053250

07060710

08057200

08178800

08195000

08227000

09505800

10172200

11051500

11335000

12056500

12464770

12505450

13092747

14205400

14206950

Big Walnut Cr nr Roachdale, 

Indiana

Sugar Cr at New Palestine, 

Indiana

Clinton R at Sterling Heights, 

Michigan

River Raisin nr Manchester, 

Michigan

Little Powder R nr Weston, 

Wyoming

Yocum Cr nr Oak Grove, Arkansas

North Sylamore Cr nr Fifty Six, 

Arkansas

White Rock Cr at Dallas, Texas

Salado Cr at San Antonio, Texas

Frio R at Concan, Texas

Saguache Cr nr Saguache, 

Colorado

West Clear Cr nr Camp Verde, 

Arizona

Red Butte Cr nr Salt Lake City, 

Utah

Santa Ana R nr Mentone, California

Cosumnes R at Michigan Bar, 

California

North Fork Skokomish R nr 

Hoodsport, Washington

Crab Cr nr Ritzville, Washington

Granger Drain at Granger, Washington

Rock Cr at Twin Falls, Idaho

East Fork Dairy Cr nr Meacham 

Corner, Oregon

Fanno Cr at Durham, Oregon

Reference

Agriculture

Urban

Reference

Reference

Agriculture

Reference

Urban

Urban

Reference

Reference

Reference

Reference

Reference

Reference

Reference

Reference

Agriculture

Agriculture

Reference

Urban

339

243

800

342

3,204

137

150

172

490

1,008

1,541

624

19

544

1388

148

995

161

671

88

82

244

240

184

274

1,039

305

133

122

161

367

2,448

1106

1646

594

51

232

506

219

1106

88

35

5.1 

3.1

7.8

3.0

0.6

1.4

1.4

2.5

1.3

3.5

1.8

1.7

0.1

0.7

14.1

14.5

1.3

1.0

3.1

 2.4

1.2

Eastern Corn Belt Plains

Eastern Corn Belt Plains

Southern Michigan/

Northern Indiana Drift 

Plains

Southern Michigan/

Northern Indiana Drift 

Plains

Northwestern Great 

Plains

Ozark Highlands

Ozark Highlands

Texas Blackland Prairies

Texas Blackland Prairies

Edwards Plateau

Southern Rockies

Arizona/New Mexico 

Mountains

Wasatch and Uinta 

Mountains

Southern California 

Mountains

Southern and Central 

California Chaparral 

and Oak Woodlands

Coast Range

Columbia Plateau

Columbia Plateau

Snake River Plain

Willamette Valley

Willamette Valley
Methods 5

Table 2. Terms used in this report.

Term Definition

Index period Interval of time such as 6 weeks or 10 weeks within which sampling 

occurs during a calendar year; for example, June 1–July 15.

Variance components Sources of variability.

SITE Site-to-site geographic variation.

YEAR Coherent (or synchronous) year-to-year variation expressed by all 

sites together.

SITE:YEAR Year-to-year variation that differs among sites due to site-specific 

factors (site-by-year interaction).

WITHIN INDEX PERIOD Temporal variation within the sampling (index) period; this variance 

component includes sampling error—for example, due to differences in field crews and measurement error in field and laboratory 

analyses (residual variation).

Minimum Detectable Trend (MDT) Smallest trend that can be detected within a defined confidence interval; for example, 95%.

Sampling period Total elapsed time (years) over which samples are collected; for 

example, a 10-year sampling period.

Sampling interval Number of years between sampling efforts (Index Periods); for 

example, a 1-year sampling interval is the same as annual sampling, although multiple samples may be collected within a given 

year (Index Period).

Number of samples per year Number of (repeat-visit) samples collected within the same year 

(within the Index Period).

Multiple-site designs Trend monitoring designs for estimating average trends among multiple sites over a period of time (sampling period).

Same sites resampled A trend monitoring design in which each site is sampled during each 

sampling effort; for example, each site is sampled (“revisited”) 

every year.

New sites sampled A trend monitoring design in which a new set of sites is selected for 

each sampling effort.

Invertebrate samples were collected following the 

Richest-Targeted Habitat (RTH) method of the NAWQA Program (Cuffney and others, 1993; Moulton and others, 2002). 

Five discrete collections of 0.25 m2

 each were taken from riffle 

habitat with a Slack sampler equipped with 500-μ mesh within 

a predefined reach. Collections were composited into a single 

sample, passed through a 500-μ-mesh sieve, preserved in a 

10-percent buffered formaldehyde solution in the field, and 

transported to the laboratory.

Sample Processing and Metric Calculation

All samples were processed at the USGS National WaterQuality Laboratory in Denver, Colorado, according to standard procedures (Moulton and others, 2000). Most taxa were 

identified to genus, but some non-insect taxa were identified to 

family or higher levels of taxonomic resolution. All pupae and 

non-aquatic taxa or lifestages were removed from the dataset. 

Taxonomic identifications, mostly at the genus level or 

higher, were made at the USGS laboratory and harmonized 

with operational taxonomic units (OTUs) used by EPA’s 

Wadeable Streams Assessment (WSA) (U.S. Environmental 

Protection Agency, 2006; Yuan and others, 2008); this ensured 

that individual taxa were consistently counted as a single 

taxonomic level across all samples. We standardized samples 

to a computerized 300 count by randomly resampling (without 

replacement) individuals in each sample. 

Decisions on ambiguous taxa (identifications that were 

not made to the resolution of the OTU; Cuffney and others, 

2007) were made independently for each site. Specimens 

that could not be identified to the target level were assigned a 

taxon only if the assignment could be made unambiguously 

(for example, when only one taxon was found in any of the 

samples from that station); otherwise these specimens were 

removed from the dataset. 

We examined a set of invertebrate metrics and indices 

commonly used in monitoring programs (table 3). Metrics—

including functional, structural, and tolerance characteristics 

of invertebrate communities—were all candidates for the 

national-scale Multimetric Index (MMI) used in the WSA 

(U.S. Environmental Protection Agency, 2006; Stoddard and 

others, 2008).
6 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

Table 3. Invertebrate metrics and indices (from Stoddard and others, 2008), with mean and range for all samples, grouped by 

type of data. 

[EPT=Ephemeroptera, Plecoptera, Trichoptera; MMI=Multimetric Index; PTV=Pollution Tolerance Value (values range from 0 to 10 and were assigned 

to categories); WSA=Wadeable Streams Assessment]

Metric Definition Mean Range

Richness

EPT Richness Number of EPT taxa 9.0 0–28

Scraper Richness Number of scraper taxa 4.9 0–14

Clinger Richness Number of clinger taxa 13.9 5–29

Mayfly Richness Number of mayfly taxa 4.3 0–11

Shredder Richness Number of shredder taxa 3.5 0–8

Intolerant Richness Number of intolerant taxa 5.1 0–20

Total Richness Total number of taxa 26.0 11–46

Percent taxa

% EPT Taxa Percentage of EPT taxa 33.8 0–68

% Mayfly Taxa Percentage of mayfly taxa 16.0 0–38

% Chironomid Taxa Percentage of chironomid taxa 25.9 0–61

% Non-Insect Taxa Percentage of non-insect taxa 18.9 0–59

% Clinger Taxa Percentage of clinger taxa 53.3 24–78

% Burrower Taxa Percentage of burrower taxa 11.9 0–30

% Taxa with PTV 0–5.9 Percentage of taxa with PTV 0–5.9 66.1 31–89

% Taxa with PTV 8–10 Percentage of taxa with PTV 8–10 7.4 0–32

Percent individuals

% EPT Individuals Percentage of EPT individuals 44.3 0–91

% Non-Insect Individuals Percentage of non-insect individuals 16.9 0–91

% Individuals Top 3 Taxa Percentage of individuals in the three mostdominant (most-abundant) taxa53.9 25–95

% Individuals Top 5 Taxa Percentage of individuals in the five mostdominant (most-abundant) taxa67.5 38–97

% Tolerant Individuals Percentage of tolerant individuals 10.4 0–75

Indices

Shannon Diversity Shannon diversity index 2.4 0.7–3.3

MMI WSA National Multi-Metric Index 46.7 5.6– 90.1

Estimation of Variance Components and 

Minimum Detectable Trend

We estimated four components of variance for each metric, using restricted maximum likelihood estimation (REML; 

Littell and others, 2006): (1) among SITEs, (2) among 

YEARs within sites, (3) the SITE:YEAR interaction, and (4) 

among samples collected within the index period of 1 year at 

each site (WITHIN INDEX PERIOD) (Larsen and others, 

2001). The YEAR component represents the “coherent” (or 

concordant) annual variability that is common to all sites; this 

is the degree to which a dry year that occurs nationwide would 

affect invertebrates similarly at all sites. The SITE:YEAR

interaction expresses any additional YEAR effects that differ 

among sites, such as wet or dry years that occur in different 

parts of the country. The WITHIN INDEX PERIOD component is the residual variance among multiple samples collected 

at one site within the index period and year, including other 

local sources of error such as differences in field crews and 

measurement error in field and laboratory analyses. We also 

tested whether each variance component differed from zero 

(P<0.05; Littell and others, 2006). Components are expressed 

as proportions of their sum, defined as the total variance. 

REML estimation occasionally yields negative estimates for 

small components, which we set equal to zero prior to calculating totals and proportions.

We assume that the goal is to detect a linear trend of 

the form Y = A + B*YEAR, where Y is an invertebrate index 
Major Findings 7

or metric score, and the trend slope (B) has units of change 

per year in the invertebrate score. If b is the estimate of B

based on sample data, then its variance, Var(b), determines 

the magnitude of trend that would be declared significantly 

(P<0.05) different from zero. Specifically, a 95 percent confidence interval (CI) for B is centered on b, with a half-width 

of 1.96*sqrt(Var(b)). Thus, the estimated Minimum Detectable Trend (MDT, the slope of the linear trend line) is MDT = 

1.96*sqrt(Var(b)), because the 95 percent CI centered on any 

trend estimate that exceeds MDT will not include the value 

B=0 and thus will be declared significant (Larsen and others, 

1995).

Trend Design Choices

We calculated Var(b) and MDT for different scenarios 

to illustrate tradeoffs of alternative design choices for detection of a trend at a single site and an average trend of multiple 

sites. For a single site (Design [1]), we examined the effect 

of changing the sampling period (increasing the number 

of years), the sampling interval (number of years between 

sampling efforts), and the number of samples collected at a 

site each year (within the restricted index period). For multiple 

sites, we also examined the effect of changing the number 

of sites for two designs: all sites revisited for each sampling 

effort (Design [2]: “same sites”), and a new set of different sites selected for each sampling effort (Design [3]: “new 

sites”). Equations adapted from Larsen and others (1995, 

2001) for calculating Var(b) from variance components for 

these three trend designs are included in Appendix 1.

Major Findings

Metrics

Of the 22 metrics and indices for which variance components were calculated, 5 were eliminated from further 

analysis because of nonnormal distributions (determined by 

visual inspection): Mayfly Richness, % Non-Insect Individuals, Intolerant Richness, % Tolerant Individuals, and % Taxa 

with a Pollution Tolerance Value (PTV) of 8–10. Of the 4 

variance components, SITE represented the highest percentage (39–75 percent) of total variance for 15 of the 17 metrics 

(fig. 2); because these data are from sites that span the entire 

United States and different land uses, SITE variance estimates 

0

10

20

30

40

50

60

70

80

90

100

Percentage of total variance

Site

Year

Site:Year

Within Index

Period

Richness counts % Taxa measures %

individuals Indices

EXPLANATION

EPT richness

Scraper richness

Clinger richness

Shredder richness

Total richness

% EPT taxa

% Mayfly taxa

% chironomid taxa

% non-insect taxa

% clinger taxa

% burrower taxa

% taxa with PTV 0–5.9

% EPT individuals

% individuals top 3 taxa

% individuals top 5 taxa

Shannon diversity

MMI

Figure 2. Variance components as a percentage of total variance for 17 metrics and indices 

commonly used in bioassessments. (EPT, Ephemeroptera, Plecoptera, Trichoptera; PTV, Pollution 

Tolerance Value; MMI, Multimetric Index).
8 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

are probably much larger than would be observed in any sing

region or basin. WITHIN INDEX PERIOD accounted for 

7–63 percent of total variance. SITE:YEAR interaction was 

higher proportion of total variance for metrics that were base

on percent individuals than for other metric categories. Variance due to YEAR was zero or negligible for nearly all metrics, which is not surprising, because this variance componen

represents consistent annual variation for all sites, and sites 

were distributed among diverse settings throughout the Unite

States. Other than YEAR variance, at least two of the remain

ing three variance components were significantly greater tha

zero for all metrics; significance levels may be overestimated

because we did not do familywise corrections for these tests. 

Two commonly used measures—Total Richness and the

MMI—were selected for examining responses to changes in 

trend design elements. Responses of selected other metrics ar

contrasted to highlight the effects of different relative propor

tions of variance components. Our goal is not to ascertain 

the “best” metric; we assume that choice of metrics for trend 

monitoring is based on the objectives of the program. 

Design Elements

Design elements that can be modified to improve trend 

detection, such as a reduction in the minimum detectable 

trend, include the sampling period, the number of samples 

collected each year, the sampling interval, and, for multiplesite designs, the number of sites. These design choices affect 

the MDT in different ways that depend on a combination of 

mathematical relations, ecological attributes that are measure

and characteristics of the sites.

Sampling Period

Sampling period affects trend detection in mathematical

predictable ways, according to the equations of Larsen and 

others (2001; see Appendix 1). Only the term for the sum of 

squares in each of the three equations is affected by sampling

period, and this term (the denominator) does not contain any 

variance components. Thus, the proportional effect of a chan

in period on the variance of trend slope is the same, regardles

of variance component values. Data from our study provide 

context to these equations to demonstrate how trend detectio

changes when certain design elements are altered.

As predicted by the variance slope equations, the sitespecific MDT for Total Richness (fig. 3A) and MMI (fig. 3B) 

declined sharply as the sampling period increased. Based on 

our estimated variances, the rates of reductions in MDT were

much lower after about 10 years. The change in metric that is

detectable over the sampling period can be obtained by multi

plying the MDT (trend slope) by the number of years; thus, t

change in the number of taxa that is detectable after 4 years i

very large at 34 (8.6*4), but the number falls to 11 taxa after 

10 years (1.1*10), 7 taxa after 20 years, and 6 taxa after 

30 years.

le 

a 

d 

t 

d 

-

n 

e 

-

d, 

ly 

ge 

s 

n 

-

he 

s 

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Sampling period, in years

A

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

MDT, in MMI units per year MDT, in number of taxa per year

Sampling period, in years

B

1/year

2/year

3/year

EXPLANATION

Figure 3. Minimum detectable trend (MDT) 

at a site in Total Richness (A) or MMI (B) for 

designs with annual sampling and one, two, or 

three samples per year. Units for the Y-axis are 

number of taxa per year (A) and MMI units per 

year (B). (MDT, Minimum Detectable Trend; MMI, 

Multimetric Index).

Number of Samples Per Year

Increasing the number of samples per year (collected 

within the index period) strongly reduced the MDT at a 

site, but only for short sampling periods (fig. 3). The results 

showed that the MDT for Total Richness for a single-site trend 

with a 4-year sampling period dropped sharply from nine to 

four taxa/year as the number of samples/year increased from 

one to two, with a smaller decline in MDT to three taxa/

year if three samples/year were collected; reductions in MDT 

were negligible after about 10 years (fig. 3A). MMI showed a 

similar pattern with increasing samples/year (fig. 3B). Reductions in MDT for all trend designs from increasing the number 

of samples/year are higher for metrics with relatively high 

WITHIN INDEX PERIOD variance, and(or) low YEAR

variance, according to the equations of Larsen and others 

(2001; see Appendix 1). 
Major Findings 9

Sampling Interval

As with sampling period, declines in MDT as the sampling interval decreases are also predicted by the variance 

slope equations of Larsen and others (2001; see Appendix 1). 

Based on our data, the reduction in MDT for a site-specific 

trend was lower for longer sampling periods (fig. 4). For 

example, a decrease in sampling interval from 5 years to 

annual for a 10-year sampling period, which increases the 

number of samples from 4 to 20, reduced the MDT for Total 

Richness from 4.2 to 0.8 taxa/year (fig. 4A). However, over a 

30-year sampling period, which provided an increase from 12 

to 60 samples, MDT was reduced much less, decreasing from 

0.4 to 0.2 taxa/year. The pattern was the same for MMI (fig. 

4B). As with sampling period, a decrease in sampling interval has the same proportional effect on MDT for all metrics, 

because only the denominator in the equation for the variance 

of trend slope is modified (see equations in Appendix 1).

Number of Sites in Multiple-Site Designs

Multiple-site designs have the additional option to 

modify the number of sites. For our data and a same-site 

design (same sites resampled for each effort), the MDT for 

Total Richness decreased 68 percent as the number of sites 

in the sampling design was increased from 10 to 100 sites, 

regardless of the sampling interval (fig. 5A). The MDT is the 

average trend slope for the total number of sites; the magnitude of change that can be detected in multiple-site designs is 

lower than for single sites—for example, 2.2 taxa (0.11*20) 

for 10 sites with annual sampling for 20 years. The pattern was 

the same for MMI (fig. 5B), with a corresponding decrease of 

50 percent. In general, MDT decreased as the number of sites 

increased for both same-site and new-site designs, with proportional differences in reductions in both designs dependent 

on variance components of the metrics.

4

0

1

2

3

4

5

6

7

8

9

10

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

10 year 20 year 30 year

MDT, in number of taxa per year MDT, in MMI units per year

Sampling period, in years

10 year 20 year 30 year

Sampling period, in years

5 year

4 year

Biennial

Annual

A

B 

10

20 40

5

10

20

12 15

60

8

30

4

10

20 40

5

10

20

12 15

60

8

30

EXPLANATION

Figure 4. Minimum detectable trend (MDT) at a site 

in Total Richness (A) and MMI (B) for 10-year, 20-year, 

and 30-year sampling periods and different sampling 

intervals; all cases assume two samples in each 

sampled year. Total numbers of samples collected 

over the sampling period are shown above each 

bar. (MDT, Minimum Detectable Trend; MMI, 

Multimetric Index).

Figure 5. Minimum detectable trend (MDT) for 

multiple sites (same sites resampled) in Total 

Richness (A) and MMI (B) for different numbers 

of sites and sampling intervals (all designs with 1 

sample/year and a 20-year sampling period). (MMI, 

Multimetric Index).

10 sites

25 sites

50 sites

100 sites

EXPLANATION

0

0.1

0.2

0.3

0.4

0.5

0.6

5 year 4 year Biennial Annual

Sampling interval

B

0

0.05

0.10

0.15

0.20

0.25

5 year 4 year Biennial Annual

Sampling interval

A

MDT, in number of taxa per year MDT, in MMI units per year
10 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

Balancing the Tradeoffs

Any design change to improve trend detection incurs a 

cost, in terms of sampling effort (number of samples), or time 

(sampling period), or both. For example, increasing the sampling interval from annual to biennial can reduce the sampling 

effort in half for each year, but achieving the same level of 

trend detection would require extending the sampling period 

for twice as long, thus incurring a cost in terms of time or a 

delay in trend detection. Although tradeoffs can be evaluated 

in terms of the proportional gain in trend detection (in other 

words, reduction in MDT) relative to the increase in sampling 

effort, the actual MDT should determine the merit of any particular design for meeting program goals. 

Design [1]: Site-Specific Trend

Tradeoffs among design choices can be expressed as 

the proportional reduction in MDT for a specified increase 

in sampling effort. The results show that the greatest reduction in MDT from a doubling of sampling effort is achieved 

by increasing the sampling period, followed by reducing the 

sampling interval, with the least reduction from increasing the 

number of samples/year (fig. 6). Given a starting design of 

biennial sampling and 1 sample/year for 10 years, doubling the 

sampling period yielded a 74-percent reduction in MDT for 

Total Richness. In contrast, doubling the number of samples 

by reducing the interval in half from biennial to annual yielded 

only a 49-percent reduction in MDT, and doubling the number 

of samples/year resulted in a 44-percent reduction in MDT.

For reasons given earlier, increasing the sampling period, 

or decreasing the sampling interval, yields the same proportional reductions in MDT at an individual site for all metrics 

(fig. 6). In contrast, increasing the number of samples per year 

affects MDT differently among metrics, depending on their 

variance component characteristics. The greatest reduction in 

MDT from increasing the number of samples per year occurs 

for metrics with high WITHIN INDEX PERIOD variance 

(relative to other metrics), particularly if YEAR variance 

is also relatively low (for example, % Burrower Taxa). The 

reduction in MDT is least for metrics with low WITHIN 

INDEX PERIOD (% EPT Individuals) and(or) high YEAR

variance (for example, % Individuals Top 3 Taxa).

Design [2]: Multiple Sites—Same Sites 

Resampled

The order of greatest reduction in MDT is the same for 

multiple sites as for an individual site for the same design 

options: the greatest reduction is achieved by increasing the 

sampling period, then by decreasing sampling interval, and 

least by increasing the number of samples per year; increasing 

the number of sites yields reductions between the latter two 

design elements (fig. 7). Doubling the sampling effort from the 

initial design of biennial sampling, 1 sample/year, 10 years, 

0

10

20

30

40

50

60

70

80

Total

richness

MMI EPT

richness

% 

burrower

taxa

% 

individuals

top 3 taxa

% EPT

individuals

Percentage reduction in MDT

Increase sampling period

Reduce sampling interval

Increase number of samples

per year

EXPLANATION

Figure 6. Percentage decrease in minimum 

detectable trend for an individual site, resulting 

from a 100-percent increase in sampling effort for 

different design choices and different metrics. 

Each bar represents a design change that doubles 

the total number of samples collected at a site, 

from 5 to 10; the starting design sampling period 

is 10 years, the interval is biennial, and 1 sample/

year is collected. Metrics shown represent 

different relative contributions of the variance 

components. (MDT, Minimum Detectable Trend; 

MMI, Multimetric Index; EPT, Ephemeroptera, 

Plecoptera, Trichoptera).

and 10 sites by increasing the sampling period to 20 years 

yielded a 65-percent reduction in MDT for Total Richness, 

whereas reducing the sampling interval to annual or increasing the number of sites to 20 sites yielded only a 29-percent 

reduction. Increasing the number of samples/year yielded the 

least reduction in MDT of 23 percent. These reductions from 

a doubling of effort are proportionally less than those for an 

individual site, because of the additional variance component 

of SITE:YEAR interaction for multiple sites (see equations in 

Appendix 1). 

The percentage reductions resulting from changes in 

sampling period or sampling interval are the same for all 

metrics, as predicted by the variance equations (see Appendix 

1). However, increasing the number of sites yields reductions 

in MDT that vary among metrics. Least proportional reduction 

occurs for metrics that have relatively high YEAR variance 

(for example, MMI and % Individuals in Top 3 Taxa); the 

number of sites affects the terms for SITE:YEAR interaction 

and WITHIN INDEX PERIOD variance, but not YEAR

variance (see Appendix 1, equation 2). Doubling the number 

of samples per year yielded reductions in MDT from 10 to 
Major Findings 11

0

10

20

30

40

50

60

70

Total

richness

MMI EPT

richness

% 

burrower

taxa

% 

individuals

top 3 taxa

% EPT

individuals

Percentage reduction in MDT

Increase sampling period

Reduce sampling interval

Increase number of sites

Increase number of samples

per year

EXPLANATION

Figure 7. Percentage reduction in minimum 

detectable trend for multiple sites (same sites 

resampled each year), resulting from a 100-percent 

increase in sampling effort for different design 

choices and different metrics. Each bar represents 

a design change that doubles the total number 

of samples collected, from 50 to 100; the starting 

design sampling period is 10 years, the interval is 

biennial, 10 sites are sampled, and 1 sample/year 

is collected. Metrics as in figure 6. (MDT, Minimum 

Detectable Trend; MMI, Multimetric Index; EPT, 

Ephemeroptera, Plecoptera, Trichoptera).

29 percent among six metrics; the greatest reduction was for 

% Burrower Taxa, because of the negligible variance due to 

YEAR, and relatively high WITHIN INDEX PERIOD variance, for this metric.

Design [3]: Multiple Sites—New Sites Sampled

A multiple-site trend monitoring program in which a 

new set of sites is selected for each sampling effort (“newsite” design) has the same relative importance among design 

choices as one in which each site is sampled during each effort 

(“same-site” design). Thus, the sampling period has the greatest effect on trend detection for same-site design, followed 

by the sampling interval, the number of sites, and the number 

of samples per year (fig. 8). The principal difference in these 

designs is that SITE variance contributes more to the trend 

slope variance in the new-site design, causing MDTs to be 

higher than a comparable same-site design (Larsen and others, 

2001; see equations in Appendix 1). The proportional reduction in MDT resulting from reducing the sampling interval or 

increasing the sampling period is the same for both designs, 

because both of these changes affect only the denominator of 

the variance equation (Appendix 1). However, an increase in 

the number of samples per year yields a greater proportional 

reduction in MDT for all metrics for same-site than for newsite designs (fig. 8), because the SITE variance contributes to 

total variance only when different sites are sampled each time.

Differences in the effect of increasing the number of 

sites on MDT between the two types of multiple-site designs 

depend on the variance components of the metric. For example, for metrics with negligible YEAR variance, such as Total 

Richness and EPT Richness, the effect on MDT of increasing 

the number of sites is the same for either type of network. 

However, for metrics with a larger YEAR variance, such as 

MMI, a “new-site” network will have a greater reduction in 

MDT from increasing the number of sites than a “same-site” 

network; this is because the number of sites affects two terms 

in the slope variance equation for new sites, but only one term 

for same sites (see Appendix 1, equations 2 and 3). Similarly, 

new-site designs benefit more than do same-site networks 

from increasing the number of sites for metrics with relatively 

high SITE variance, such as MMI. 

0

10

20

30

40

50

60

70

Percentage reduction in MDT

Total

richness

MMI EPT

richness

% 

burrower

taxa

% 

individuals

top 3 taxa

% EPT

individuals

Increase sampling period

Reduce sampling interval

Increase number of sites

Increase number of samples

per year

EXPLANATION

Figure 8. Percentage reduction in minimum detectable 

trend for multiple sites (new sites sampled each year), 

resulting from a 100-percent increase in sampling effort 

for different design choices and different metrics. 

Each bar represents a design change that doubles the 

total number of samples collected, from 50 to 100; the 

starting design sampling period is 10 years, the interval 

is biennial, 10 sites are sampled, and 1 sample/year 

is collected. Metrics as in figure 6. (MDT, Minimum 

Detectable Trend; MMI, Multimetric Index; EPT, 

Ephemeroptera, Plecoptera, Trichoptera).
12 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

Discussion

 Most previous studies comparing the effects of different 

design choices on trend detection have focused on statistical 

power for detecting trends—in other words, the probability 

of detecting a trend if one is present (Wagner and others, 

2007; Dauwalter and others, 2009; Al-Chokhachy and others, 

2011; Anlauf and others, 2011). While statistical properties 

are crucial for understanding temporal variations in ecological characteristics, managers of environmental monitoring 

programs typically have an interest in practical questions, such 

as the magnitude of trend that can be detected, the length of 

time or the number of sampling visits required before a trend 

can be detected, or the cost or sampling effort required to 

achieve some trend detection objective. In this report, we followed an approach similar to that of Larsen and others (1995, 

2001), and derived the minimum detectable trend (MDT) from 

components of variance for ecological attributes of interest and evaluated tradeoffs associated with different trend 

design choices. This approach can be applied to any response 

attribute used in long-term monitoring, including indices and 

metrics of biological communities, habitat, or chemistry, and 

can be applied to terrestrial as well as aquatic systems.

The results of this study support the conclusions of 

Larsen and others (1995)—that extending the sampling period 

of a consistent long-term monitoring program is the most 

cost-effective way to improve trend detection at a site, that is, 

to reduce the magnitude of trend that can be detected. Delays 

in trend detection, however, are not always consistent with 

monitoring program goals; to achieve results sooner, a reduction in sampling interval—for example, from once every 4 or 

5 years to biennial or annual—yields the next best reduction 

for a given increase in sampling effort. To further reduce the 

detectable trend, the effects of within-year variation must be 

reduced by increasing the number of samples collected within 

the index period—perhaps in combination with minimizing 

measurement errors (for example, through improved training 

or sampling protocols), or redefining the index period to a narrower temporal window. 

Although site-specific trends provide insight into ecological patterns and relations to changes in land use and specific 

stressors at the watershed scale, multiple-site trends address 

questions about larger systems such as a regional population 

(Urquhart and others, 1998). The order of improvement in 

trend detection is the same for both site-specific and multiplesite trends: increasing the sampling period is most effective, 

decreasing the sampling interval is the next best option, and 

increasing the number of samples per year is least effective. 

Although the order of improvement is the same, there is less 

gain from decreased sampling interval for regional trends than 

for an individual site. Multiple-site trend monitoring has the 

additional option of increasing the number of sites, the benefits 

of which depend on the regional scale. Adding sites yields 

greater improvement in trend detection for networks that 

encompass broad heterogeneous areas such as the NAWQA 

Program national network, which may have larger variance 

due to site and site-specific annual variation (site-year interaction) components than networks that cover a smaller region; 

for example, a single state or ecoregion. Costs associated with 

expanding the number of sites, however, go beyond the additional costs of sample collection and include reconnaissance, 

obtaining landowner permissions, and establishing a sampling 

reach.

A monitoring design with repeated visits of the same sites 

over time is often considered the preferred design for regional 

trends (Philippi and others, 1998; Al-Chokhachy and others, 

2011) because of the reduced influence of site-to-site variation 

on trend detection. Although regional trends can be inferred 

from a network of fixed sites, any bias in the selection of those 

sites reduces their representativeness of the regional population. Networks in which new sites are selected for each sampling effort—or “panel” combinations of repeat-visit and new 

sites—are used when trends representing a population of sites 

are desired; (for example, Urquhart and others, 1998). The 

effect of the additional site variation in a network of new sites 

is reduced only by increasing the number of sites. Increasing 

the number of samples per year yields a better reduction in 

MDT for same-site than new-site networks.

The choice of metrics affects detection and interpretation of trends and the characteristics of monitoring design 

required to detect a change (Ferris and Lehman, 2008). There 

are substantial differences in variance components among the 

metrics examined herein, as has been found in other studies 

(Mazor and others, 2009); the effect of these differences on 

trend detection depends on the design. Although the effects on 

trend detection of two design options—sampling period and 

sampling interval—are the same for all metrics, other options 

vary among metrics. The number of samples per year can be 

increased to reduce the MDT for those metrics with relatively 

high within-index period variance. For multiple-site networks, 

increasing the number of sites reduces the MDT for metrics 

where among-year variance is low.

Benefits in trend detection from increasing the number 

of years of monitoring have other complementary advantages. 

Long-term monitoring data contribute to understanding of 

natural temporal variation, which is influenced by climatic 

variations in temperature and flow (Durance and Ormerod, 

2007; Kaushal and others, 2010; Lawrence and others, 2010; 

Kennen and others, 2012), and species-specific characteristics 

such as life history and traits that can vary seasonally; for 

example, Beche and others (2006). Long-term data, therefore, 

are needed so that changes due to anthropogenic influence can 

be distinguished from those due to natural variability (Jackson 

and Füreder, 2006). Some sources of natural variation can be 

minimized in trend monitoring by restricting sampling to a 

seasonal temporal window (index period) or by scheduling 

annual sampling to match an annual population cycle (Larsen 

and others, 2001). Variance is expected to increase as length 

of monitoring continues because of the increased likelihood 

of encountering stochastic changes or disturbance events 

(Al-Chokhachy and others, 2011). Other considerations in 

design for long-term monitoring include the need for more 
References Cited 13

frequent sampling if the goals include distinguishing effects of 

multiple factors, particularly in dynamic systems where natural and human factors are rapidly changing. Changes in water 

quality and biological diversity may not be linear (Magurran 

and others, 2010), but rather reflect short-term increases and 

decreases that are a function of both natural factors such as the 

proportion of wet years to dry years, cool years to warm years, 

or differences in antecedent seasonal conditions, and humancaused factors such as changes in rates of chemical application to the land, changes in management policies, or stream 

restoration efforts.

Future research needs for improving the design of trend 

monitoring programs include evaluating variance components 

for reference sites to better characterize natural variability 

for commonly measured ecological attributes; such a study 

should be tailored to the appropriate geographic scope for the 

program. Although the present study characterized variance 

components for sites representing a broad range of natural 

and anthropogenic characteristics over a large geographic 

area, studies of sites in more homogeneous regional networks 

would be useful to compare variance components and to select 

metrics appropriate for different monitoring objectives. 

The approach presented here provides managers with 

tools for adjusting the design of trend monitoring programs in 

the most cost-effective manner. Studies to quantify sources of 

variability are particularly valuable when conducted early in a 

trend monitoring program. Tradeoffs among design elements 

can be evaluated so that monitoring goals can be achieved 

with the lowest cost (fewest samples) or within the expected 

duration of the monitoring program. The potential benefits of 

improving understanding of long-term consequences of human 

activities on aquatic ecosystems are increased when managers 

have the tools to design cost-effective monitoring programs.

Acknowledgments

This research was a collaboration between the U.S. 

Geological Survey and the U.S. Environmental Protection 

Agency; the authors thank Charlie Crawford, Alan Herlihy, 

Phil Kaufmann, Tony Olsen, Dave Peck, John Stoddard, and 

Ian Waite for contributing to the design of this study. We are 

especially grateful to the many biologists in the National 

Water-Quality Assessment (NAWQA) Program who collected 

the samples for this study and whose hard work and dedication 

over the past 2 decades has made this long-term study possible, and to Keith Slack, who designed the original Slack samplers that helped create a basis for NAWQA’s use of nationally 

consistent methods. We also thank Pete Ruhl for assisting with 

data retrievals and the data management structure of BioTDB 

and BioData, and James Falcone, who provided ancillary data 

and cartographic assistance. 

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16 Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs

Before the variance components were calculated, metric 

scores were first “detrended” by regressing all scores on 

YEAR; only one metric had a significant (and numerically 

small) trend, and all other metrics had essentially zero trend. 

Variance components were then estimated for the residuals 

from this regression. Contributions of the variance components to the uncertainty of the estimated trend slope, b, can be 

expressed in the linear trend model Y = A + B*YEAR, where 

Y is the value of a metric in different years (Larsen and others, 

2001), A is a constant (y-axis intercept), and B is the trend 

slope with units of change per year in the invertebrate score. 

Specific equations for estimating trends at a single site, trends 

for multiple sites when the same sites are sampled each year, 

such as a regional trend, and trends for multiple sites when 

a new set of sites is selected each year are described below 

(Larsen and others, 1995, 2001).

Design [1]: Site-Specific Trend

For simplicity, assume that invertebrates are sampled at 

regular yearly intervals over a sampling period and that each 

yearly sample has the same number (Nseas) of repeat-visit 

samples within the sampling season (index period). Then the 

variance of the estimated trend slope, b, is given by:

 (1)

In equation 1, Var(YEAR) and Var(WITHIN INDEX 

PERIOD) are the YEAR and WITHIN INDEX PERIOD

variance components. For trends at a single site, the variance 

of the trend slope decreases as the number of samples within a 

season (Nseas) increases, or as the number of annual samples, 

which affects SSQ, increases. The SSQ in the denominator is 

the sum of squares of the (centered) years over the entire sampling period (the sum of squared deviations of each sampling 

year from the mean year of the whole period). SSQ can be 

expressed in terms of sampling period and sampling interval, 

as follows:

SSQ = p2

k(k2–1)/12 , 

where

p = sampling interval (years)=number of years 

between samples, and

k = number of years in the sampling period in 

which samples are collected.

For example, for biennial sampling for a 20-year period, k is 

10 (samples collected every other year), and p is 2.

Because equation 1 is for trends at a single site, 

Var(YEAR) is equal to the sum of the YEAR and SITE:YEAR

components. Thus, for trends at a single site, the variance of 

the trend slope decreases as the number of samples within a 

season (Nseas) increases, or as the number of annual samples, 

which affects SSQ, increases.

Design [2]: Trend in Multiple Sites—Same Sites 

Resampled

For a monitoring program of multiple sites in which all 

sites are visited for each sampling effort (“same sites”), a separate linear time trend can be estimated at each site, based on its 

own multiyear data. The trend slope, B, then can be defined as 

the average of these site-specific trend slopes. The estimation 

uncertainty of b is given by Larsen and others (1995, 2001):

 (2)

In equation 2, Nsites is the number of (same) sites, and 

Var(SITE:YEAR) is the SITE:YEAR interaction variance 

component. The interaction variance component appears 

because it represents differential variation in YEAR effects at 

different SITEs, leading to greater variability in the estimated 

trend. There is no Var(SITE) component in equation 2 because 

temporally consistent, between-site differences (SITE effects) 

have been removed by estimating the trends separately for 

each site using only that site’s data, essentially treating sites 

as “blocks” as in an analysis of variance. Equation 2 shows 

that Var(b) is reduced by increasing Nseas or the number of 

annual samples, strategies that are also effective for monitoring a single site. However, Var(b) can now also be reduced by 

increasing the number (Nsites) of monitored sites. 

Appendix 1. Variance Component Equations

Var b

Var YEAR

Var WITHIN INDEX PERIOD

Nseas

SSQ sampl ( ) =

( ) + ( ) 

( ) ing period

( ) ( ) ( ) ( )

( )

 : 

 

Var WITHIN YEAR

Var SITE YEAR

Nseas Var YEAR

Nsites Var b

SSQ sampling period

+

+

=
Appendix 1 17

Design [3]: Trend in Multiple Sites—New Sites 

Sampled

For a monitoring program of multiple sites in which a 

new set of sites is selected each year, a mean metric value 

can be estimated in Year 1 across the sites that are chosen in 

that year. As new sets of sites are chosen in Years 2, 3, 4, etc., 

mean metric values are estimated using only the data for the 

sites sampled in each year. The trend slope, B, is then defined 

as the slope of the linear time regression fitted to these yearly 

means.

For this sampling and estimation approach, the estimation 

uncertainty of b is given by:

  (3)

This is the same Var (b) as for equation 2 (same sites), 

plus a substantial term of new uncertainty due to Var(SITE)/

Nsites. This term appears because now only new sites are 

sampled each year, thereby losing the “blocking” advantages 

of resampling the same sites over multiple years. To reduce 

the effect of Var(SITE), the number of sites can be increased, 

or metrics can be chosen for which the Var(SITE) variance 

component is relatively low. The effects of all variance components, other than Var(YEAR), can be reduced by increasing 

Nsites. 

( )

( ) ( ) ( ) ( )

( )

 : 

 

 

Var WITHIN YEAR

Var SITE YEAR Var SITE Nseas Var YEAR

Nsites Nsites Var b

SSQ sampling period

+

+ +

=
For additional information about this report write to:

Martin E. Gurtz

Daren M. Carlisle

U.S. Geological Survey, MS 413

National Water-Quality Assessment Program

12201 Sunrise Valley Drive

Reston, VA 20192

John Van Sickle

Department of Fisheries and Wildlife

Oregon State University

Corvallis, OR 97331

Steven G. Paulsen

U.S. Environmental Protection Agency

200 SW 35th Street

Corvallis, OR 97330

Gurtz, Van Sickle, Carlisle, and Paulsen—Design Tradeoffs for Trend Assessment in Aquatic Biological Monitoring Programs—Open-File Report 2013–1222