EPA 600/R-04/023

August 2005

The EMPACT Beaches Project

Results from a Study on Microbiological Monitoring in 

Recreational Waters

Larry J. Wymer

Kristen P. Brenner

John W. Martinson

Walter R. Stutts

Stephen A. Schaub*

Alfred P. Dufour 

U.S. Environmental Protection Agency

Offi ce of Research and Development

National Exposure Research Laboratory

Cincinnati, OH 45268

*

 U.S. EPA, Offi ce of Water, Health and Ecological Criteria Division, Washington, DC

Recycled/Recyclable

Printed with vegetable-based ink on

paper that contains a minimum of

50% post-consumer fi ber content

processed chlorine free
ii

Disclaimer: This document has been reviewed by the U.S. Environmental Protection Agency (EPA) 

and approved for publication. Mention of trade names or commercial products does not constitute 

endorsement or recommendation of their use.
iii

Acknowledgements

We convey our gratitude to the following local offi cials for allowing us to conduct the fi eldwork 

in beaches under their jurisdiction and for their enormous help in the logistics of conducting the 

fi eldwork: Donald Hamel, Detroit Health Department, Environmental Health Services, Detroit, MI; 

Rick Amador, San Diego County Department of Environmental Health; Kenneth Wilde, Diagnostic and 

Public Health Microbiology, Maryland Department of Health and Mental Hygiene, Baltimore, MD; 

Dale B. Engquist, U.S. National Park Service, Indiana Dunes National Lakeshore, Porter, IN; Andrea 

Rex, Environmental Quality Department, Massachusetts Water Resources Authority, Charlestown 

Navy Yard, Boston, MA.

We especially thank the following two individuals who, through their extensive experience and 

knowledge, helped overcome problems associated with logistics and site selection: Steve Weisberg, 

Director, Southern California Coastal Water Research Program, Westminster, CA; Richard Whitman, 

Field Station Supervisor, U.S. Geological Survey, Lake Michigan Ecological Research Station, Porter, 

IN.

Other individuals that we are indebted to for their participation and contributions during the conduct 

of the study are Abdel El-Shaarawi of the National Water Research Institute, Burlington, Ontario, 

Canada; Richard O. Gilbert, independent consultant, Rockville, MD; Molly Leecaster, formerly of 

the Southern California Coastal Water Research Program, Westminster, CA, and currently at Idaho 

National Engineering and Environmental Laboratory, Idaho Falls, ID; David F. Parkhurst, Professor, 

School of Public and Environmental Affairs, Indiana University, Bloomington, IN; William F. (Rick) 

Hoffman, Offi ce of Water, Offi ce of Science and Technology, Washington, DC; Robin Oshiro, Offi ce 

of Water, Offi ce of Science and Technology, Washington, DC; Mimi Dannel, Offi ce of Research and 

Development, Offi ce of Science Policy, Washington, DC; Daniel Lewis, formerly of OAO Corporation 

(now Lockheed Martin Information Technology), Cincinnati, OH; Sherie Brown, Shawn C. Siefring, 

and Frederick P. Williams, U.S. EPA/National Exposure Research Laboratory, Cincinnati, OH.

The fi eldwork was organized and conducted by two contractors, Battelle Research Institute and 

Lockheed Martin. We are grateful to their staff for their skill, cooperation, and diligence in this 

study. The microbiological assays of water samples during this study were performed by contract 

laboratories at various sites across the nation. We thank the staffs of these laboratories for their 

diligent work and extraordinary cooperation: Battelle Research Institute Laboratory, Duxbury, MA; 

Battelle Research Institute Laboratory, Edgewood, MD; City of San Diego Laboratory, San Diego, 

CA; Huron Valley Laboratory, Romulus, MI; Severn Trent Laboratory, Valparaiso, IN. Finally, 

we thank Katherine Loizos of Computer Sciences Corporation for preparing this document for 

publication.
iv
v

Table of Contents

Overview of the Study Results ______________________________________________ 1

Factors found to infl uence indicator levels ________________________________________ 1

Introduction ____________________________________________________________ 3

Study Design ____________________________________________________________ 5

Sites _______________________________________________________________________ 5

Sampling design _____________________________________________________________ 6

Sampling schedule ___________________________________________________________ 7

Data collection _______________________________________________________________ 8

Microbiological analysis _____________________________________________________________ 8

Other data ________________________________________________________________________ 9

Factors Affecting Water Quality at a Beach _______________________________________ 13

Introduction ________________________________________________________________ 13

Statistical methods ___________________________________________________________ 13

Criterion variable ___________________________________________________________________ 14

Design variables ___________________________________________________________________ 14

Covariates ________________________________________________________________________ 14

Spatial factors _______________________________________________________________ 15

The physical signifi cance of spatial factors _________________________________________________ 15 

Findings from the EMPACT Beaches study with regard to spatial factors _________________________ 17

Variation in target density associated with zones ________________________________________ 17

Variation in target density associated with distance along the shoreline ______________________ 17

Sampling depth __________________________________________________________________ 22

Temporal factors _____________________________________________________________ 24

The signifi cance of temporal factors in sample design ______________________________________ 24

Findings from the EMPACT Beaches study with regard to temporal factors _____________________ 24

Day-to-day variability ____________________________________________________________ 24

Variation between morning and afternoon results _______________________________________ 28

Environmental and bather effects _______________________________________________ 35

Statistical evaluation ________________________________________________________________ 36

Tides __________________________________________________________________________ 39

Weather _______________________________________________________________________ 39

Bather density ___________________________________________________________________ 43

Sampling Variance _______________________________________________________ 45

Sources of variation __________________________________________________________ 45

Populations, sampling, variance, and components of variation _______________________________ 45

Sampling distribution _______________________________________________________________ 45

Components of spatial variation _______________________________________________________ 46

Components of temporal variation _____________________________________________________ 47
vi

Estimates of variance components for the EMPACT beaches ______________________ 48 

Spatial components of variation _______________________________________________________ 48

Small-scale (replicate) variance _____________________________________________________ 48

Variance among sampling depths ____________________________________________________ 49

Variance among zones ____________________________________________________________ 50

Variance among locations within zone (among transects) _________________________________ 50

Temporal components of variation _____________________________________________________ 52

Hourly variation _________________________________________________________________ 52

Variance among days _____________________________________________________________ 52

Variance of the change over a 24-hour period __________________________________________ 52

Designing a Beach Monitoring Program _____________________________________ 54 

The DQO approach __________________________________________________________ 54

Defi ning the boundaries of the study: the population _______________________________________ 55

Sampling depth __________________________________________________________________ 55

Distance from shore (Depth zone) ___________________________________________________ 56

Distance along the beachfront ______________________________________________________ 56

Time __________________________________________________________________________ 58

Specifying tolerable limits on decision errors _____________________________________________ 58

A rationale for setting tolerance intervals ______________________________________________ 60

Optimizing the design for obtaining data ________________________________________________ 61

Stratifi cation along the shoreline ____________________________________________________ 64

Summary_______________________________________________________________ 68

References _____________________________________________________________ 71
vii

Index of Figures

Figure 1. EMPACT study beaches _________________________________________ 5

Figure 2. Beach sampling grid _____________________________________________ 6

Figure 3. Cross-section of beach sampling area ______________________________ 7

Figure 4. Freshwater beach sampling schedules _____________________________ 10

Figure 5. Point-in-time geometric mean indicator density per 100 mL by zone ____ 18

Figure 6. Indicator density per 100 mL by zone and transect ___________________ 20

Figure 7. Geometric mean density of surface samples vs. depth samples__________ 23

Figure 8. Time series plots of geometric mean morning (9:00 am) indicator levels _ 26

Figure 9. Change in mean log10 indicator density between the morning (9:00 am ) 

sampling and afternoon (2:00 pm) sample ___________________________________ 30

Figure 10. Geometric mean indicator density for morning (9:00 am) samples and 

afternoon (2:00 pm) samples, by whether afternoon was sunny (<50% cloud cover) 

or not sunny ____________________________________________________________ 32

Figure 11. Geometric mean (GM) indicator density by time-of-day (9:00 am – 6:00 

pm) for samples collected on hourly sampling days – ratio of GM on the hour to 

overall GM for the day. Average ratio for each hour is shown by the heavy line ___ 34

Figure 12. Geometric mean enterococci density by tide stage at marine beaches ___ 40

Figure 13. Geometric mean indicator density for various weather conditions _____ 41

Figure 14. Geometric mean indicator organism density by number of bathers on 

the beach and in the water ________________________________________________ 44
viii

Figure 15. The Data Quality Objectives Process (from “Guidance for the Data 

Quality Objectives Process”, U.S. EPA [2000b]) ______________________________ 54

Figure 16. Variance of indicator density per 100 mL vs. average separation among 

sampling locations _______________________________________________________ 57

Figure 17. Correspondence between health effects criteria and indicator density __ 60

Figure 18. Operating characteristic curves __________________________________ 65
ix

Index of Tables

Table 1. Number of sampling visits and total number of samples collected _______________ 8

Table 2. Summary of laboratory methods _________________________________________ 9

Table 3. Data Collected at each sampling visit (in addition to microbial data). ____________ 12

Table 4. Comparisons of point-in-time geometric mean indicator density by zone _________ 17

Table 5. Percentage of total samples collected that exceed the single sample limit as 

recommended in EPA guidelines [U.S. EPA, 1986] ___________________________________ 19

Table 6. Percentage of samples collected in knee-deep water that exceeded the single sample 

limit as recommended in EPA guidelines [U.S. EPA 1986] (9:00 am samples) _____________ 21

Table 7. Comparison of geometric mean density1 of indicator densities by depth of water 

from which the sample was collected. ______________________________________________ 22

Table 8. Percentage of total samples collected that exceeded the single sample limit as recommended in 

EPA guidelines [U.S. EPA, 1986] ____________________________________________________ 23

Table 9. Ratio to the previous day of the geometric mean (GM) of all knee- and chest-depth 

samples taken at the 9:00 am visit _________________________________________________ 27

Table 10. Serial correlations between log means separated by 1,2, or 4 days _____________ 28

Table 11. Percentages of total samples collected that exceed the single sample limit [U.S. 

EPA, 1986], classifi ed by whether the sample from the same location was above or below the 

limit 1, 2, or 4 days earlier ______________________________________________________ 29

Table 12. Comparison of geometric mean density of respective indicator organisms at each 

study beach between morning and afternoon visits — sunny vs. cloudy days _____________ 31

Table 13. Percentage of knee-deep samples collected at 2:00 p.m. that exceeded the single 

sample limit as recommended in EPA guidelines [U.S. EPA, 1986], by whether the sample 

from the same location was above or below the limit at 9:00 am. _______________________ 33
x

Table 14. Percentage of knee-deep samples that exceeded the single sample limit [U.S. EPA, 1986], 

by time-of-day. Only hourly sampling results are used. For all but Belle Isle, there were 14 hourly 

sampling days and 39-42 valid knee-deep observations (for Belle Isle there were 23 or 24 observations 

over 8 days). ____________________________________________________________________ 35 

Table 15. Environmental characteristics and bather densities of EMPACT 

study beaches __________________________________________________________________ 36

Table 16. Results of regression analysis on log10 density of indicator organisms __________ 38

Table 17. Comparisons of geometric mean entercocci density per 100 mL at low, mid, and 

high water levels for marine beaches (based on 25th and 75th percentiles of water level). __ 39

Table 18. Comparisons of geometric mean indicator density per 100 mL for various 

weather-related variables ________________________________________________________ 42

Table 19. Comparisons of geometric mean indicator density per 100 mL. vs number 

of bathers in the water and on the beach, for the afternoon (2:00 pm) sampling visits _____ 44

Table 20. Standard deviation and variance component estimates for the EMPACT beaches 

______________________________________________________________________________ 49

Table 21. Standard deviation among locations (transects) within each separate dept zone 

______________________________________________________________________________ 51

Table 22. Variance and standard deviation of 24-hour change in log10 indicator density and 

of 24-hour change in log10 indicator density when modeled as in Table 16 _______________ 53

Table 23. Sample size requirements based on estimated overall sampling variance for the 

geometric mean within a single depth zone in the water _______________________________ 62

Table 24. Width of tolerance intervals for various sample sizes based on sample variances 

within depth zone at the study beaches _____________________________________________ 63

Table 25. Comparison of sample size requirements for equivalent precision with and 

without compositing. ____________________________________________________________ 67
1

Overview of the Study Results

Quantitative guidelines with respect to indicator organism densities in recreational waters that have 

been established by the U. S. EPA have been supported by human health studies, notably those 

performed in the late 40’s and early 50’s by the U.S. Public Health Service, and in the 70’s and early 

80’s by the U.S. EPA. Upper limits of 35 enterococci per 100 mL in marine water and 33 enterococci 

per 100 mL in freshwater were recommended for the geometric mean of at least fi ve samples taken over 

a 30-day period [U.S. EPA, 1986]. An upper limit on the geometric mean of 126 E. coli per 100 mL 

was recommended for freshwater environments only, since E. coli failed to show a good relationship 

to swimming-associated illnesses in marine waters. A recommendation was also made that, for a 

designated public beach, no single sample exceed the 75th percentile of a lognormal distribution with 

these respective geometric means. Lacking site-specifi c log standard deviations, this implied an upper 

limit on any single sample of 104 enterococci per 100 mL in marine water (log standard deviation of 

0.7), and 98 enterococci or 235 E coli per 100 mL in freshwater (log standard deviation of 0.4).

Providing numerical guidelines that are supported by scientifi c data was a great advance. Lacking, 

however, was scientifi c data of comparable quality to support monitoring schemes that would 

provide the most meaningful information about whether the guidelines are being met. The EMPACT 

(Environmental Monitoring for Public Access and Community Tracking) Beaches project has attempted 

to identify those characteristics of a beach environment that have signifi cant impact on monitoring. 

This project examined fi ve beach environments to determine the factors that most infl uence the 

measurement of beach water quality. Two ocean beaches, an estuarine beach, a Great Lakes beach, 

and a riverine beach were selected to provide as broad a representation of beach environments as 

possible. This approach was used to develop model protocols that can be applied to similar beaches.

Factors found to infl uence indicator levels

For each of the fi ve study beaches, the greatest single determinant of microbial indicator level was 

found to be the depth zone, or, roughly, distance from the shoreline at which the sample was collected. 

Bacterial densities became substantially lower as one moved from ankle-deep to knee-deep to chestdeep water. This fact has important implications for sample design as well as for public health.

In contrast, this study found no signifi cant difference in indicator level among samples that were 

taken at different depths below the surface, such as between those taken the standard 0.3 M from the 

surface and those taken from near the bottom. At three of the fi ve beaches, no substantial systematic 

differences were found among samples taken at different points parallel to the beachfront, which 

spanned a distance of 60 M, as long as they came from water of the same depth. Minor “hot spots” 

and “cold spots” were found at two of the beaches, although the differences were not dramatic and 

were not consistently found at all times.

Signifi cant declines in indicator densities from the morning to the afternoon (9:00 a.m. to 2:00 p.m.) 

were observed at four of the study beaches. This effect was seen only on sunny days at one freshwater 

beach, but was observed to be independent of sunshine at three others, a freshwater beach and two 

marine beaches. Indicator levels at the remaining beach, a West Coast marine environment, tended to 

be very low at all times.

From one day to the next, the geometric mean indicator density among all samples that were collected 

changed by a factor of 2 (doubling or halving) or more about half the time at each studied beach. 
2

There was virtually zero correlation between the indicator level on any given day and the indicator 

level more than two days later. The geometric mean of fi ve samples taken over a 29-day period (that 

is, on the same day of the week) did not accurately represent actual conditions on any given day during 

the 29-day period.

Findings from this study with regard to spatial and temporal variation suggest the following implications 

for a beach monitoring program:

• Time and location of sampling must be carefully considered.

o Depth zones from which samples are collected are likely to have great effect on the 

resulting estimate of indicator density. Sampling in knee- to waist-deep water would 

seem to offer a reasonable, but still conservative, approach to estimating water quality, 

particularly given that health effects are based on quality of water at waist-depth or 

deeper.

o Sampling at 0.3 M below the surface is justifi ed based on exposure considerations. This 

study failed to discern differences at lower collection depths.

o Sampling in the morning will likely be a conservative practice, in addition to perhaps 

being a convenient time to sample.

o Sampling should be performed as close as practical to the day on which a decision is to 

be made regarding beach closure or advisement. Preferably this should be the day before, 

given current conditions of a one day turnaround for the results.

• A number of samples should be collected from different points in knee- to waist-deep water.

o Results from the EMPACT Beaches Study can be used as a guideline for the initial 

determination of sample size requirements. For the beaches in this study, sample sizes of 

from 3 to 6 would be adequate to allow for 95% certainty of detecting a 0.3 log exceedence 

from the action level for the geometric mean, equivalent to a health risk of 3 to 3.5 cases 

of HCGI per 1000 swimmers.

o As data are gathered, the sampling plan should be refi ned and ultimately based on a 

variance estimate that is uniquely associated with the subject beach.

• “Hot spots” within the bathing area, which may be known a priori or discovered as a result of 

sampling, should be considered as separate strata for sampling purposes.

o These should be sampled independently and weighted appropriately in the fi nal result.

o If indicator density within the problem area is very different from that elsewhere, sampling 

should be limited to this area. A proposed rule-of-thumb is a two-fold difference.

o Lesser differences would warrant a combined, stratifi ed estimate, weighting the “hot 

spot” in proportion to its extent relative to the rest of the beachfront.

• Composite sampling may be used as a cost-effi cient technique, enabling better sample coverage at 

minimally increased cost.

o In the initial stages of a monitoring program, composite sampling should not be used in 

order to develop data that is necessary in estimating the appropriate sampling variance for 

a particular beach.

o A composite sample estimates an arithmetic mean, which would require adjustment in 

order to equate this to standards based on a geometric mean.

o If resources are available to collect the data necessary for developing a predictive model 

for the change in indicator density over a 24 hour period, this will likely result in muchimproved assessment of water quality, given the 1-day lag in obtaining results from 

membrane fi ltration assays.
3

Introduction

Protecting the health of swimmers who use surface waters for recreation has been of interest to public 

health offi cials in the United States since 1930. It was well recognized at that early date that human 

excreta discharged to surface waters posed a health hazard to those who used the water for recreation. 

Although the relationship between swimming-associated health effects and feces-contaminated water 

used for swimming had not been defi ned, microbial limits based on coliform bacteria were used in 

many states, particularly when there was physical evidence of sewage contamination. The limiting 

values selected by responsible authorities were based more on attainment rather than on risk of illness. 

Thus, there was little uniformity among states regarding what level of coliforms constitute waters safe 

for swimming. Several states chose 1,000 coliforms per 100 ml as a measure of good quality water, 

but there was not much uniformity among states regarding what level of coliforms was a safe level. 

There was, however, a general understanding that fecal contamination of surface water posed a risk to 

those exposed to the water, and that the risk might be limited by setting a level of fecal contamination 

above which exposure would be unacceptable. The manner in which water samples were taken, the 

frequency of sampling, and the number of samples were usually not described in the early literature. 

It is probable, however, that multiple samples from several points along a beach were not taken. 

Early monitoring schemes seldom involved several samples. Even now the Environmental Protection 

Agency (EPA) recommends at least 5 samples taken over a 30-day period, a sampling scheme that 

was fi rst suggested in 1968. That number of samples will not characterize a body of water as to its 

true quality. Similarly, weekly sampling, no matter how accurate, is an unlikely scheme to alert risk 

managers of poor quality water between sample dates. Taking one daily sample might solve the latter 

problem, but still would not provide an accurate characterization of the water.

In the late 1940’s and early 1950’s a series of studies were carried out by the U.S. Public Health Service 

to determine the relationship between swimming-associated health effects and bathing water quality. 

The results of those studies were reported by Stevenson (1953). This data was used by the National 

Technical Advisory Committee (NTAC), commissioned by the Federal Water Pollution Control 

Administration in 1968 to establish guidelines for recreational waters. The NTAC recommended 

that a geometric mean of 200 fecal coliforms per 100 ml from 5 samples collected over a 30-day 

period be used as an upper limit which was believed to be protective of public health for swimmers 

[NTAC, 1968]. In the early 1970’s the U.S. Environmental Protection Agency initiated a series of 

epidemiological studies to determine the relationship between swimming-associated illness and water 

quality as measured with multiple microbial indicators that are commonly found in feces [Cabelli, 

1983; Dufour, 1984]. These studies showed that, of all the microbes examined, enterococci had the 

best relationship to swimmers’ illness in marine waters. Thus, as the water quality became poorer, 

i.e., the enterococci density increased, the swimming-associated illness rate increased. In fresh waters 

E. coli and enterococci were found to be effective for relating water quality to swimmer illness. EPA 

recommended an upper limit on geometric mean enterococci density of 35 per 100 ml for marine 

waters and 33 per 100 ml for fresh waters [U.S. EPA, 1986]. The means were to be calculated from at 

least 5 samples taken over a 30-day period. E. coli was not effective in marine waters, but did show 

a good relationship to swimmer-associated illness in freshwater environments. An upper limit of 

126 E. coli per 100 ml was recommended for fresh waters [U.S. EPA, 1986]. These epidemiological 

studies conducted by the U.S. Public Health Service and the U.S. Environmental Protection Agency 

resulted in guidelines that limited the number of fecal indicator bacteria in a water body and, thereby, 

the number of swimming-associated illnesses to a tolerated level.

Providing numerical guidelines that are supported by scientifi c data was a great advance; however, 

these guidelines cannot stand alone. Monitoring schemes that will provide meaningful information 
4

about whether the guidelines are being met must also be available. The manner in which monitoring 

is carried out at any particular beach is not likely to be the same for a marine beach with tidal cycles as 

for a freshwater beach, where other factors will signifi cantly affect the level of indicator bacteria.

Since microbes almost universally have been recommended as the measure of water quality for 

recreational waters some of the characteristics that limit their usefulness should be addressed. 

Bacterial indicators frequently die off more rapidly than some of the pathogens found in feces [Fattal 

et al., 1983]. When this happens, potential pathogens associated with feces might be present and pose 

a health hazard. Another issue with indicator microbes is that they usually take up to 24 hours to grow 

to visible colonies on solid media or turbidity in liquid media. This lengthy time lag creates a situation 

where exposed individuals are informed of risk of illness long after the fact [Bartram, 1999]. 

Physical factors may affect the measurement of water quality in ways that are not controllable. For 

instance, microbial indicators are affected by solar radiation, which cause many indicators to die off 

at variable rates [Fujioka and Narikawa, 1982], and neither the amount nor the intensity of sunlight 

is constant. These have a tendency to change from hour to hour and day to day. Rainfall is another 

factor that signifi cantly infl uences the measurement of indicator microbes in beach waters [Olivieri et 

al., 1977], but it is more predictable than other variables. Wind direction may also affect the quality 

of beach waters either by driving contamination toward the beach or away from the beach. Swimmer 

density can infl uence the quality of beach water as well. Swimmers shed high numbers of indicator 

bacteria from their bodies. Tub experiments have shown the millions of indicator bacteria are shed in 

very short periods of time [Smith and Dufour, 1993]. In marine waters, tides signifi cantly affect the 

measurement of indicator bacteria, in addition to other factors mentioned [Cabelli et al., 1974].

It is diffi cult to determine which of the above factors has the greatest effect on the monitoring of beach 

waters. It is likely that each beach will have its own characteristics based on predominant factors 

active at any one time. The EMPACT (Environmental Monitoring for Public Access and Community 

Tracking) Beaches project has attempted to defi ne which characteristics are most signifi cant with 

regard to monitoring approaches. This project examined fi ve beach environments to determine the 

factors that most infl uence the measurement of beach water quality. Two ocean beaches, an estuarine 

beach, a Great Lakes beach, and a riverine beach were selected to provide as broad a representation 

of beach environments as possible. This approach was used to develop model protocols that can be 

applied to similar beaches.
5

Study Design

Sites

Beaches selected for this study are all located in or near partner cities in the Environmental Monitoring 

for Public Access and Community Tracking (EMPACT) grants program. The study was jointly 

conducted by the EPA Offi ce of Water, Offi ce of Science and Technology, and Offi ce of Research 

and Development with the goal of helping communities collect, manage, and present environmental 

information to their residents. The following were the participating sites in this study (see Figure 1):

• West Beach, Indiana Dunes National Lakeshore, Ogden Dunes, Indiana, a freshwater beach 

on the shores of Lake Michigan. The EMPACT partner city is Gary.

• Belle Isle Park, Detroit, Michigan, a freshwater beach on the Detroit River between Lake St. 

Clair and Lake Erie.

• Wollaston Beach, Quincy, Massachusetts, a marine beach in Quincy Bay. The EMPACT 

partner city is Boston.

• Imperial Beach, Imperial Beach, California, a marine beach on the Pacifi c Ocean. The 

EMPACT partner city is San Diego.

• Miami Beach Park, Bowley’s Quarters, Maryland, an estuarine beach on Chesapeake Bay 

near Middle River. The EMPACT partner city is Baltimore.

Figure 1. EMPACT study beaches.
6

Sampling design

Samples were collected from each of nine locations within the limits of the beach=s bathing area, each 

location being determined by an associated transect and zone, as illustrated in Figure 2. A transect 

is defi ned as an imaginary line through a fi xed point on the beach and forming a right angle with 

the shoreline. A zone is defi ned as a contour line of equal water depth. As illustrated in Figure 2, 

each sampling location is defi ned by the intersection of transect and zone on a grid comprising three 

transects and three zones projected on the water=s surface. A random point along the shoreline within 

the recognized beach area was selected to defi ne the fi rst transect (the leftmost transect in Figure 2). 

The middle transect was, then, determined as the parallel to the fi rst transect at a distance of 20 meters, 

and the remaining transect, as the parallel to the middle transect at an additional distance of 20 meters, 

or 40 meters from the fi rst transect. 

Figure 2. Beach sampling grid.

Intersections of sampling zones with these transects were determined by the depth of the water at 

the time of sampling. Zone 1 was determined at each transect as the point at which the water fi rst 

attained a depth of 0.15 meters (“ankle-deep”); zones 2 and 3 were determined as those points along 

each of the transects where the water fi rst attained depths of 0.5 meters (“knee-deep”) and 1.3 meters 

(“chest-deep”), respectively. Buoys demarcating the swimming area in Belle Isle were so located that 

the water within this boundary never attained a depth of 1.3 meters; at this beach, therefore, the buoys 

themselves, at which the water was approximately 1 meter deep or about waist level, demarcated zone 

3. The bathing area at Miami Beach Park was similarly restricted, the water depth along zone 3 being 

about 1.1 meter. Low tide at Wollaston Beach resulted in shallows extending quite far out from the 

beach. A 100 meter limit was established on the distance an individual would go to collect samples, 

resulting in waist-deep water at zone 3 at these times.
7

Water samples were collected from a depth of 0.075 meters below the surface in ankle deep water and 

0.3 meters below the surface in knee-deep and chest-deep water. These sampling depths are shown 

schematically in Figure 3. Note that the actual sample locations (1-9 in Figure 2) may vary from one 

visit to the next, in terms of both absolute geographical location and relative distance from shore, 

in accordance with variations in water level and/or changing contour of the fl oor, particularly at the 

marine beaches.

 

Figure 3. Cross-section of beach sampling area.

Water samples were collected in 500-mL pre-sterilized, polypropylene bottles. Care was taken 

in collecting samples near the bottom to avoid introducing additional sand or other solids into the 

samples. Following collection, samples were maintained on ice until analysis.

Sampling schedule 

On each day, one of four sampling plans, referred to as “basic”, “hourly”, “replicate”, and “depth” 

sampling, was followed according to the schedules shown in Figures 4a and 4b. The actual schedule 

at West Beach most closely followed the planned schedule, which was to have been identical at all 

fi ve beaches. It was anticipated, and was, in fact, the case in all cities, that events such as inclement 

weather and rough water would force revision of the schedules. At Belle Isle and Imperial Beach, 

major activities necessitated changes in schedule and cancellation of certain sampling visits. The 

total number of sampling visits and total samples collected under each of these plans is summarized 

in Table 1 for each beach. Following are descriptions of each sampling plan.

Basic sampling

On each basic sampling day, samples were collected on two separate visits, at 9:00 a.m. and 

2:00 p.m. A single sample was collected at each of the nine sampling locations (1 through 9 

in Figure 2) on each sampling visit.

Hourly sampling

On each hourly sampling day, sampling was performed on ten separate occasions, hourly on 

the hour, the fi rst set being collected at 9:00 a.m. and the last at 6:00 p.m. A single sample was 

collected at each of the nine sampling locations on each occasion.
8

 Replicate sampling

On each replicate sampling day, samples were collected on two separate visits, at 9:00 a.m. 

and 2:00 p.m. On each sampling visit, ten replicate water samples were collected at the 

central sampling location (location 5 in Figure 2), and two replicate samples were collected 

at each of the eight remaining locations. Initially, because it was anticipated that its location 

on a river would make the collection of true replicates diffi cult, Belle Isle was to be an 

exception to the general replicate sampling scheme, with two samples being collected at all 

nine sampling points. However, after the fi rst two replicate sampling visits, ten replicates 

were taken from the central location at this beach as well, when it became apparent that water 

fl ow was negligible within the protected confi nes of the bathing area.

 Depth sampling

On each depth sampling day, samples were collected on two separate visits, at 9:00 a.m. and 

2:00 p.m., with samples being collected at each of the nine sampling locations in Figure 2, the 

same as on a basic sampling visit. In addition to the standard sampling depths (0.3 m for knee 

and chest deep water), a sample was collected at a depth of 0.425 meters (0.075 meters, or 3 

inches, from the bottom) at each of the three sampling points in the knee-deep zone. At each 

of the three chest deep zone sampling points, two additional samples were collected, one from 

mid-depth (normally, 0.65 meters from the surface) and another at a depth of 0.075 meters, or 

3 inches, from the bottom. Thus, a total of nine additional samples were collected beyond the 

nine samples collected in the basic sampling plan.

Table 1. Number of sampling visits and total number of samples collected.

Location

Basic sampling Hourly Replicate Depth

Visits Samples Visits Samples Visits Samples Visits Samples

West Beach 69 610 139 1162 16 416 8 144

Belle Isle 75 671 80 705 16 334 8 138

Wollaston 71 638 138 1242 16 407 8 144

Imperial 

Beach 68 612 140 1254 16 416 8 144

Miami Beach 

Park 72 643 140 1257 16 416 8 144

Data collection

Microbiological analysis

Freshwater samples, collected at Belle Isle and West Beach were assayed for Escherichia coli by the 

modifi ed mTEC agar membrane fi lter method [U.S. EPA 2000a], while the marine and estuarine water 

samples, collected at Imperial Beach, Wollaston Beach, and Miami Beach Park, were analyzed for 

enterococci by the mEI agar membrane fi lter method (Method 1600) [Messer and Dufour, 1998 U.S. 

EPA 1997b, U.S. EPA 2000a]. The methods are summarized in Table 2. Using volumes of 100, 10, and 

1 mL of each sample, fi ltrations were begun within six hours of collection and completed within eight 

hours of collection [Code of Federal Regulations 2000]. When concentrations were very high on the 

previous day’s sample(s), 0.1 mL volumes of the water samples were also analyzed. Bacterial counts, 
9

volumes, and other critical information, such as analysis start time and incubation start and completion 

times, were recorded on specially-designed data sheets, faxed daily to EPA (NERL-Cincinnati), and 

entered into the EMPACT database for subsequent audits of data quality and data analysis.

Table 2. Summary of laboratory methods.

 

Method

Used

Medium

Used Incubation Time and 

Temperatures ( °C)

Detection Limits 

(Colonies

Per Plate)

Ideal # of 

Colonies Per 

Membrane

E. coli

(EPA 1603)

mTEC2

agar

2 hours @ 35 + 0.5

20-22 hours @ 44.5 + 0.2 1 - 200 20 - 80

Enterococci

(EPA 1600)

mEI

agar 24 + 2 hours @ 41 + 0.5 1 - 200 20 - 60

The general microbiology laboratory quality control procedures used in this study have been 

previously described [American Public Health Assoc. 1998, Bordner et al. 1978, U.S. EPA 1997a, 

U.S. EPA 2000a]. In addition, each preparation of modifi ed mTEC agar and mEI agar was pre-tested 

for performance with known positive (target) and negative (non-target) cultures, and membrane fi lter, 

phosphate-buffered dilution water, and agar controls were performed with each set of samples that 

was analyzed (For example, all of the samples taken at the nine locations on the three transects for a 

specifi c time and date would be considered a set of samples.)

Other data

Other data that were collected at each sampling visit are shown in Table 3. Hourly and high and 

low water tidal data were obtained from the National Ocean Service of the National Oceanic and 

Atmospheric Administration for the reference station nearest to each respective study beach.
10

Figure 4a. Freshwater beach sampling schedules.
11

Figure 4b. Marine and estuarine beach sampling schedules.

 
12

 Table 3. Data collected at each sampling visit (in addition to microbial data).

Measurement Description & units of measurement Units

Date and time Date and time of day.

Air temperature Measured by thermometer at a fi xed location every 

visit. C

Water temperature Measured by thermometer at the central sampling 

location at appropriate depth for thermometer. C

Cloud cover

Sunny, Mostly Sunny (20-50% cloud cover), 

Cloudy (50-70% cover), Mostly Cloudy (70-99% 

cover), Overcast 

S, MS, C, MC, O

Rainfall since last 

visit

Measured by rain gauge; collected each sampling 

visit. Inches

Wind speed Sustained speed measured by wind gauge. Miles per hour 

Wind direction Compass direction to nearest semi-quadrant leeward 

on wind gauge. N, NE, E, etc.

Current direction Described in relation to shoreline facing out. Descriptive:

(onshore, right, etc.)

Wave height Meter stick measurement at central sampling point. Meters

Bather density in 

the water

Number of bathers in the water, within the sampling 

area.

Categorical: <20, 20-100, 

100-200, >200

Bather density on 

the beach Number of bathers on beach, within outer transects. Categorical: <20, 20-100, 100-200, >200

Boats Number of boats in the water within 500 m of 

sampling area.

Categorical:

 <20, 20-100, 100-200, >200

Animals

Animals within 20M of the sampling area in the 

water or on the beach; also includes number of fowl 

or other birds in the air near the sampling area.

Type & number of animals

Debris Description of debris fl oating in the water or 

washed on shore within the sampling area.

Categorical; “None,” “Very 

Little,” “Little,” “Lots;” and 

description

Total Suspended 

Solids (TSS)

Measured from the sample taken at the central 

sampling location, per Standard Methods (APHA, 

1998).

mg/L

pH Each sample measured after microbiological 

analysis, per Standard Methods (APHA, 1998). pH units

Turbidity

Each sample measured by nephlometer after 

microbiological analysis processing, per Standard 

Methods (APHA, 1998).

NTU
13

Factors Affecting Water Quality at a Beach

Introduction

In this section, we will discuss various factors that were seen to have some association with the 

indicator density that was observed in our samples. This will provide answers to questions such as:

 At what locations in the water, if any, does one tend to see higher or lower levels of indicator 

organisms?

 Are any temporal cycles evident, such as a time of the day or a day of the week when indicator 

levels tend to be higher or lower than they are at other times?

 Can we expect generally higher or lower sample results under certain weather conditions? 

What about tidal infl uences at marine beaches?

These refer to systematic variability, as opposed to random variability, which will be discussed in the 

next section. Systematic variability implies predictable differences, albeit with a degree of uncertainty 

as indicated in the phrasing of these questions. The variability that is left unexplained, the uncertainty 

in our prediction, is random variability. 

Knowledge about systematic variability is important for two reasons:

 Systematic differences that are found to exist may be exploited in the sample design, suggesting 

where and when to take samples.

 Because results from sampling are not available until the next day, a predictive model must 

be used to assess the current “state of the beach” (Of course, one possible model is to assume 

that nothing has changed). Even if results could be obtained instantaneously, it would still be 

desirable to have some lead-time for informing the public of the results.

Results from each of the fi ve study beaches are considered individually. Any observed spatial, 

temporal, and environmental relationships with indicator density strictly apply only to that beach. 

While we have found similarities among the study beaches with regard to certain parameters, this 

should not be construed to mean that these relationships would apply to all beaches in general. Nor 

should relationships found to exist at a particular study beach be assumed to apply to a general class 

of which it is representative, such as an estuarine, Great Lakes, or west coast marine beach. Certainly, 

however, a relationship found to exist at any of these study beaches may apply to other beaches, and 

some of these characteristics may be true for many or most of a given class of beach. In the course 

of a regular beach monitoring program ample data can be generated to enable one to verify these 

relationships and even to discover factors that are unique in one’s own environment.

Statistical methods

A distinction is made between design variables and covariates. Design variables are those factors 

over which we have control and were specifi cally accounted for in the design of the study. Samples 

were specifi cally collected in ankle-, knee-, and chest-deep water, thus, “zone” is a design variable. 

Likewise, three fi xed transects were employed to defi ne locations at each depth zone where samples 

were to be taken, so that the variable of “transect”, position along the shoreline, is also designed into 

the study. Another design variable is time-of-day, mainly being either 9:00 a.m. or 2:00 p.m. on a 

given day, but also hourly from 9:00 a.m. to 6:00 p.m. on selected days. Depth below the surface from 
14

which the sample was collected is also a design variable, since we occasionally sampled from depths 

below the standard 0.3 meters from the surface.

“Covariates” include all factors that were outside of our control which were not a part of our sampling 

plan, such as rainfall, cloud cover, tidal movements, currents, and bather load. In general, these 

constitute a “messier” set of observations than do design variables. We may not be able to attribute an 

effect due to one of these variables at a given beach simply because there was too little variability in 

that factor at that beach. Such was the case at Imperial Beach, for example, where rainfall occurred 

only twice during the course of our study. In addition, many of these covariates may be interrelated 

(“co-linear” or “confounded” variables), a potential example being temperature, cloud cover, prior 

rainfall, and bather load. Are the increased counts due to the greater number of bathers at the beach 

or are they due to the high temperatures that bring these bathers out? Do we fail to see an increase 

in indicator density with greater numbers of bathers simply because there are more bathers on sunny 

days when, at the same time, the sunlight increases the rate of bacteria die-off?

Criterion variable

Log10 indicator density per 100 mL is used as the criterion variable (the “dependent” or “response” 

variable) in the analyses that follow, thus having a direct correspondence with models that relate 

mean log10 indicator density to swimming-related health effects [Cabelli et al., 1982; Cabelli, 1983; 

Dufour, 1984]. Existing U.S. EPA guidelines [1986], based on these models, specify limits for the 

geometric mean - the antilog of the mean log10 density. The implications of these health effect models 

with respect to a sampling will be discussed later, in the section Designing a Beach Monitoring 

Program.

Single sample limits

Another criterion recommended by the EPA [U.S. EPA, 1986] is the single-sample limit. Over 

1500 samples were collected at each of the study beaches (see Table 1), giving us a multitude 

of “case studies” for evaluating the performance of the single-sample limit vis-à-vis any given 

factor. These case studies will be presented in parallel to the analyses on log means in a boxed 

format such as this.

Design variables

Relationships between log10 indicator densities per 100 mL and design variables were investigated 

via an analysis of variance (ANOVA) model. Factors used in the ANOVA were zone (ankle-, knee-, 

and chest-deep), transect (labeled 1-3, as in Figure 2), time-of-day (9:00 a.m. through 6:00 p.m.), and 

weekend (Friday through Sunday).

Covariates

The initial analysis of the dependencies of log10 indicator density per 100 mL on the ancillary variables 

recorded in this study (Table 3) was conducted via a stepwise regression. Because these variables, 

such as air temperature, cloud cover, etc., apply to the entire sampling visit, the dependent variable 

is the average log density for the respective visit. This is calculated as a weighted average, by fi rst 

averaging replicate observations, if any, within a location, then averaging over transects within a zone, 

and fi nally averaging over zones. Only samples taken from the usual sampling depth of 0.3 M below 

the surface are used in this average. So that whatever conditions happen to exist on hourly sampling 
15

days do not disproportionately infl uence the results, only data from the 9:00 a.m. and 2:00 p.m. visits 

are used.

Some ancillary data were transformed before being used as candidate covariates. In some cases, a 

single variable was expressed in more than one form in the search for best predictor. Many were 

expressed as dummy variables, that is, variables that can take on only two values, zero and one, 

where one indicates the presence of some condition and zero, the absence of that condition. For 

example, cloud cover determined the value of a dummy variable, “Sunny?”, which took on the value 

1 when cloud cover was coded as “Sunny” or “Mostly Sunny”, and 0 when cloud cover was coded as 

“Cloudy”, “Mostly Cloudy”, or “Overcast.” Some of the variations on covariate that were considered 

are:

 Temperature (air and water) was used in °C, as originally measured. In addition, this was 

expressed as a high-temperature dummy variable (greater than the median for the respective 

time-of-day) and as 1st quartile and 4th quartile dummy variables (among lowest/highest 25% 

for the respective time-of-day).

 Rainfall was used in inches, as originally measured, and in the form of dummy variables 

indicating whether it had rained in the past 24 hours or in the past 3 days.

 Wind speed and wind direction were combined to produce a wind vector variable (the 

component of wind velocity that is onshore, which is negative if the wind is blowing away 

from the shore). Also, dummy variables indicate onshore wind and offshore wind.

 Wave height was used in meters, as originally measured, and as a “high wave” dummy 

variable.

 Bather densities (on the beach/in the water) were considered as dummy variables (1=less than 

20, 0=20 or more). They were also combined in order to consider cases where there were 

more than 20 bathers both on the beach and in the water. (Note: Categories of “100-200” and 

“over 200” were too infrequently observed to be considered.)

One covariate that was included in all models was the previous day’s log10 indicator density at the 

same time-of-day. This was either considered as an independent variable or subtracted from the 

current day’s log10 indicator density to create a dependent variable equal to the change in log density.

Several regression model-building techniques were attempted, including stepwise and best R2 searches, 

along with considerable trial-and-error. In the end, however, it was a matter of judgment among 

several competing models, each of which was as good as the other in terms of degree of complexity 

and the percentage of variation explained (R2

). A model for a given beach that is presented here is only 

one of several possible models, any of which may be a reasonable alternative. In general, however, 

these models do tend to be similar in that some form of a major effect is common to all models with 

only minor contributions being made by disparate effects. For example, rainfall and tidal stage, in one 

form or another, may be common to all the models, while some models may include a bather density 

effect, others, a temperature effect.

Spatial factors

The physical signifi cance of spatial factors

We defi ned the physical location from which a sample is collected in terms of transect, zone, and 

sampling depth.
16

Transect – an imaginary line extending at a right angle to the beach’s orientation from 

a given point along the shoreline, and the water column below it. Specifying transect 

fi xes a location with respect to its distance along the shoreline.

Zone – the water column above a contour line on the fl oor of the bathing area, 

corresponding to constant water depth, that is, ankle-deep, knee-deep, or chest-deep 

water. Where the water depth is constant or decreases as one moves away from shore, 

as when the fl oor is level or undulates, our zones refer to the fi rst occurrence of the 

specifi ed depth. Roughly, “zone” means “distance from shore”, at least in the sense 

that going from ankle-deep to chest-deep water takes one farther from shore. The 

actual distance from shore, however, may vary between two locations that are in the 

same zone.

Sampling depth – the depth below the surface of the water from which a sample is 

collected.

For this study, samples were collected along parallel transects located 20 meters apart, each transect 

being defi ned by two points on the shore that were fi xed for the duration of the study. Samples were 

collected in zones described as “ankle-deep”, “knee-deep”, and “chest-deep” water, but in actuality 

fi xed by measurement to determine where the mean water depth was 0.15, 0.5, and 1.3 M, respectively. 

Samples were collected from approximately 0.3 M below the surface (0.075 M in ankle-deep water), 

and, on certain days, additional samples were collected at greater depths.

Barring some rather unusual beach topography, there are several common factors that ought to 

differentially affect water quality among depth zones in qualitatively the same way at practically any 

beach:

• Contamination on the shore or in the swash zone ought to have, if anything, a greater impact 

on water quality in ankle-deep water than in chest-deep water.

• The shallower the water, the more the water quality at or near the surface will be affected by 

any disturbance of the sediment, such as might be caused by bathers or wave action.

• Indicator organisms that come directly from bathers, not from sewage contamination, should 

be more common in shallower water due to children and a higher bather density in general.

• Deeper water, on the other hand, may be exposed to any offshore point source of contamination 

to a greater degree than shallower water.

In contrast, there are few, if any, such generalities one can make with regard to transects-different 

locations along a shoreline. Currents along or near the shoreline may have negative or positive 

effects on contamination levels downstream, and may have signifi cant impact at some beaches and be 

negligible at others. Their impact may vary even at the same beach. A physical barrier in or near the 

bathing area, such as a sandbar, reef, or pier, may effect a gradient in the level of contamination parallel 

to the shoreline at some beaches, but such effects will be absent at others. Lacking such generalities, 

systematic variability along the shoreline must be evaluated with respect to a specifi c beach.
17

Findings from the EMPACT Beaches study with regard to spatial factors 

Major fi ndings on spatial variation are:

• In every case, the zone from which the sample was collected was found to have the greatest 

predictable impact on microbial indicator densities of all factors investigated in this study, 

spatial or temporal. Bacterial densities become progressively lower as one moves from ankledeep to knee-deep to chest-deep water.

• Two of the study beaches, Belle Isle and Miami Beach Park, exhibited some form of systematic 

spatial variation that was not adequately accounted for by zones alone. It may or may not be 

a coincidence that both of these beaches are associated with river systems.

Variation in target density associated with zones

For each of the fi ve study beaches, the greatest single determinant of microbial indicator level is the 

zone, or, roughly, distance from the shoreline at which the sample was collected. Bacterial densities 

become substantially lower as one moves from ankle-deep to knee-deep to chest-deep water. Figure 

5 and Table 4 illustrate the relative magnitudes of measurements taken 0.3 meter (0.075 M for ankledeep water) from the surface in these respective depth zones during the 9:00 a.m. and 2:00 p.m. visit 

for each beach. Although the effect appears to be relatively small at Imperial Beach, even here this 

was the single most important infl uence on sample indicator density.

 Table 4. Comparisons of point-in-time geometric mean indicator 

density by zone.

 Location 

9:00 a.m. 2:00 p.m.

Ankle Knee Chest Ankle Knee Chest 

 West Beach 34 19 14 41 19 9

 Belle Isle 2113 487 11 754 224 4

 Wollaston 43 24 12 36 12 7

 Imperial Beach 654643

 Miami Beach Park 426 221 15 231 67 4

The relationship between distance from shore and indicator density is important in terms of its 

implication for sample design. First, if the bather population exposed to contamination in one zone 

essentially differs from those exposed to the contamination in another zone, then an overall estimate 

that combines indicator densities from both zones may not adequately refl ect exposure for either 

population. Given that the usual route of exposure for gastrointestinal effects is through ingestion, 

an example of two different bather populations would be small children, who are likely to be exposed 

to contamination only in shallow water, and adults and older children, who are most likely to be 

exposed only in deeper waters. Second, if combining indicator densities from different depth zones 

is appropriate for a given bather population, then the sampling scheme should take these known 

systematic differences between zones into account.

Variation in target density associated with distance along the shoreline

In contrast to indicator densities from samples taken at different distances out from the 

shoreline, samples that were collected in water of the same depth but at different locations 

relative to the beach front (that is, on different transects) generally are not that different 
18

from one another. This is evident in Figure 6, which shows, by depth zone for each of the 

study beaches, the geometric mean densities along each transect at 9:00 a.m. and 2:00 p.m. 

Any systematic differences that may exist along the parallel-to-shore dimension are minor, 

particularly in comparison to the obvious differences between depth zones, as seen previously 

in Figure 5.

Figure 5. Point-in-time geometric mean indicator density per 100 mL by zone.

There are, however, two instances in which we note a statistically signifi cant “transect effect” 

– a persistent difference in microbial density along one transect relative to another. The more 

pronounced of these is at Belle Isle, where E. coli densities in knee-deep water are consistently 

lower along the leftmost transect (Transect 1 in Figure 6), than in the other two knee-deep 

sampling locations. At Miami Beach Park, where the other transect-related difference is indicated, 

the situation is not so clear and the relationship is comparatively weak. Furthermore, analysis of 

variance reveals an interaction between sampling location and time-of-day, indicating that any 

such difference varies between the 9:00 a.m. and 2:00 p.m. visits. As seen in Figure 6, values in 

ankle-deep water were somewhat higher along one transect, the leftmost transect in the morning, 

but the rightmost transect in the afternoon. We can also discern an increasing trend, particularly 

in the morning, as one moves left to right (i.e., from Transect 3 to Transect 1) in chest-deep water.
19

Whether these observed differences in indicator levels among transects have any practical signifi cance 

can be determined only by a detailed sanitary survey of these respective beaches. It may be noted, 

however, that at Belle Isle, where we see the only truly substantial transect effect, a drainage ditch 

empties very near the vicinity of the rightmost transect from an area adjacent to a water park and 

bathhouse. This might be hypothesized as a point source capable of affecting

Single sample limits and depth zones

Zones (“distance from shore”) from which to collect samples will be a critical consideration in 

designing a monitoring program. How far from shore should one go? Two important points:

• If zones are not accounted for, it may be impossible to compare monitoring results from two 

different days, or even to interpret the results of a single sample.

• Our current knowledge of human health effects is based on studies that have measured 

indicator levels in approximately waist-deep water.

Among the fi ve study beaches, those samples taken in ankle-depth water were the most likely to 

exceed single-sample criteria [U.S. EPA, 1986], and, except at Imperial Beach where only one 

sample failed the criterion, samples taken in chest-deep water were least likely to do so.

 

Table 5. Percentage of total samples collected that exceeded 

the single sample limit as recommended in EPA 

guidelines [U.S. EPA, 1986]

Location

% of samples exceeding the single sample limit: 

Number of exceedences / total number of samples

 (total number of samples in parentheses)

Ankle Knee Chest

West Beach 21.9 (183) 12.0 (183) 9.3 (172)

Belle Isle 97.0 (167) 88.5 (174) 2.3 (174)

Wollaston Beach 24.0 (183) 14.2 (183) 6.6 (183)

Imperial Beach 1.6 (183) 0.0 (183) 0.5 (183)

Miami Beach Park 80.1 (186) 61.2 (185) 12.9 (186)

contamination levels in a manner consistent with observations. Mainly, we might see higher levels 

in the knee depth zone at the rightmost and middle transects, which are upstream in this riverine 

environment, simply because the plume is more concentrated at these points. Other features of the 

observed pattern at Belle Isle are consistent with this hypothesis - particularly the elevated microbial 

levels in chest-deep water at the leftmost transect (downstream from the ditch), and in ankle-deep 

water near the outlet of the ditch at transects 2 and 3 (although this is clear only in the afternoon).
20

Figure 6. Indicator density per 100 mL by zone and transect.

The Public Health Laboratory Service (PHLS) Water Surveillance team (PHLS, 1995) examined 

multiple parameters in eight inland recreational waters. Water samples were collected at 10 

predetermined sites on each water body on four consecutive weeks. Unlike the results in the current 

study, the PHLS study results showed signifi cant differences between results from the ten sites even 

when the sites were very near each other. The sampling sites in the PHLS studies were, in general, 

further apart than the 20 meter distances in our study and, in addition, some of the sampling sites 

were at the inlet and outlet points of the lakes. However, on two of the lakes, six of the sampling 

points were in a grid one meter apart and the results from these points showed differences greater than 

random variation. The differences between our data and the PHLS data probably indicate that transect 

parameter cannot be generalized from one location to another.
21

Single sample limits and shoreline location

We offer two suggestions with regard to where to sample along the beach. The fi rst is obvious. 

The other may entail extra effort (and funding) to implement.

• Naturally, we want to sample in areas where bathers tend to congregate.

• Other than this, “hot spots” that deserve special consideration may exist. These may only be 

determined by knowledge of peculiarities at a particular beach or by exploratory sampling.

Consider the exceedences found in the fi ve study beaches among samples taken in knee-deep 

water, again based on the 1986 single-sample criteria [U.S. EPA, 1986]. We chose the knee-depth 

zone since this is likely to be an area that is sampled and yields a fair number of exceedences 

among our study beaches (with the exception of Imperial Beach, where few exceedences were 

seen among any of the samples).

Table 6. Percentage of samples collected in knee-deep 

water that exceeded the single sample limit as 

recommended in EPA guidelines [U.S. EPA, 

1986] (9:00 a.m. samples)

Location

% of samples exceeding the single sample 

limit:

Total # of exceedences/total # of samples

 (total number of samples in parentheses)

Transect 1 Transect 2 Transect 3

Belle Isle 81.0 (58) 93.1 (58) 91.4 (58)

West Beach 11.5 (61) 13.1 (61) 11.5 (61)

Wollaston Beach 14.8 (61) 11.5 (61) 16.4 (61)

Imperial Beach 0.0 (61) 0.0 (61) 0.0 (61)

Miami Beach Pk. 61.3 (62) 64.5 (62) 57.4 (61)

Belle Isle 

p.m. samples 54.4 (57) 73.7 (57) 82.5 (57)

For the most part, there are no meaningful differences in the rate of exceedence among the three 

transects. A possible exception is Belle Isle, where fewer exceedences were observed at the 1st

(leftmost) transect. While the p-values for the observed differences among transects for the other 

three beaches that had exceedences were all greater than 0.70, indicating that the magnitude of the 

differences shown in Table 6 could very likely result from simple random variation, the p-value 

for Belle Isle’s inter-transect differences in exceedence was 0.08, indicating a somewhat unlikely 

result unless there are truly systematic differences among these locations. As further evidence 

of some transect effect at this beach, afternoon results for Belle Isle only are shown (afternoon 

results for the other beaches do not indicate any different variability than the morning results). 

The difference in the afternoon is even more dramatic for Belle Isle, with a p-value of less than 

0.01. Managers at Belle Isle would be well advised to pay particularly close attention to the area 

defi ned by transects 2 and 3, and to investigate the cause for this phenomenon with an eye toward 

possible remediation.
22

Sampling depth

One of the more interesting outcomes of these beach studies was the lack of a clear gradient in the 

indicator density with respect to the depth from the surface at which the sample was collected (Table 

7). Such a difference with depth might be expected from the fact that water near the bottom is 

more likely to contain suspended particles from the sediment, which is presumably relatively rich in 

bacteria. Others have observed depth effects [Public Heath Laboratory Service Water Surveillance 

Group, 1995].

Bottom samples (0.075 m from the bottom) were collected in knee-deep and chest-deep water and 

mid-depth samples (0.65 m from the bottom) were collected in chest-deep water. Geometric mean 

densities over the duration of the study and over all transects for each type of depth sample are 

compared to corresponding surface densities (from only those samples collected at the same time as 

depth samples) in Figure 7.

The effect of depth on indicator density results was examined in one other study [PHLS, 1995]. 

The fi ndings of that study indicated that paired comparisons between surface, 30 cm and 100 cm 

depth samples, showed a signifi cant tendency for higher fecal streptococci counts at the surface. A 

similar trend was shown for E. coli, but the differences were not statistically signifi cant. Although the 

procedure for taking surface samples was not described, an accumulation of microbes at the water-air 

interface could have accounted for the differences observed in the PHLS studies.

Table 7. Comparison of geometric mean density1 of indicator densities 

by depth of water from which the sample was collected. “P0

” 

is the “p-value” for the difference (log10 means) between the 

surface and respective depth means.

Location

Knee deep water Chest deep water

Surface2 Bottom3 P0

4 Surface5 Bottom P0 Surface5 Middepth6 P0

West 

Beach 32 36 0.237 19 22 0.229 20 21 0.954

Belle Isle 154 142 0.324 3 4 0.082 3 4 0.331

Wollaston 

Beach 31 47 0.040 18 16 0.732 18 14 0.315

Imperial 

Beach 3 3 0.716 2 2 0.673 2 3 0.292

Miami 

Beach Park 79 87 0.499 2 3 0.478 3 4 0.045

1 Geometric means are over all transects and sampling visits. For surface samples, only those samples for 

which a corresponding depth sample was taken at the same time are considered. Numbers of samples range 

from 18 to 30. 2 Samples collected 0.3 m below the surface. 3 Samples collected 0.075 m from the bottom. 4

 “P-value” for difference in mean log10 values between surface and the respective depth (paired samples). 

Generally, a value less than 0.05 is considered “signifi cant” 5 The two values for surface samples from 

chest-deep water may differ slightly due to missing data among the depth samples. 5 Samples collected 

midway between surface and bottom.
23

Figure 7. Geometric mean density of surface samples vs. depth samples.

Single sample limits and sampling depth

We see little difference between samples collected near the surface and those collected near the 

bottom with respect to the rate at which they exceeded the single-sample criteria [U.S. EPA, 

1986]. Lest Table 8 lead one to believe that the closeness of the exceedence rates indicates 

agreement between samples taken from different depths, we note that, overall, the results were in 

disagreement 44% of the time when an exceedence was recorded in at least one of the two samples 

from different depths.

 

Table 8. Percentage of total samples collected 

that exceeded the single sample limit as 

recommended in EPA guidelines [U.S. EPA, 

1986]

Location

% of samples exceeding the single sample limit 

in knee-deep water, top vs. bottom samples

Top Bottom Total #

Belle Isle 42.9 33.3 21

West Beach 11.1 11.1 27

Wollaston Beach 41.7 41.7 24

Imperial Beach 0.0 0.0 24

Miami Beach Park 20.8 25.0 24
24

Temporal factors

The signifi cance of temporal factors in sample design

Current EPA guidelines refer to limits on indicator organisms based on the geometric mean of “not less 

than 5 samples equally spaced over a 30-day period” and further specify that, for designated bathing 

beaches, no single sample exceed the 75th percentile of the corresponding log-normal distribution 

[U.S. EPA, 1986]. Based on health studies conducted by the EPA in the 1970’s and early 1980’s 

[Dufour, 1984; Cabelli, 1983], the time-averaged recommended maximum geometric means of 126 E. 

coli per 100 mL in freshwater and 35 enterococci per 100 mL in marine water correspond to marginal 

illness rates of 8 and 19 cases of gastroenteritis per 1000 swimmers, respectively.

In current practice, a reasonable scenario for a beach monitoring authority might be to collect a sample 

every, say, Tuesday morning. This would allow adequate time to obtain the results from that sample 

and, if necessary, take corrective action and resample before the weekend, or give suffi ciently advanced 

notice to the public that the beach will be closed the following weekend. Closure, or action to avoid 

closure, would be based on the above 30-day geometric means or single sample limits.

Bearing this in mind, the daily, and sometimes hourly, collection of samples in both the morning and 

afternoon in this analysis will give insight into the following questions on sampling strategy:

• How well does a 30-day mean characterize recreational water quality on a given day?

• How does an observed exceedence (or non-exceedence) in today’s sample correspond to 

water quality four (or three, two, one) days in the future?

• When is a good time of day to sample?

Findings from the EMPACT Beaches study with regard to temporal factors 

Major fi ndings on temporal variation are:

• From one day to the next, the geometric mean indicator density over all sampling locations 

changed by a factor of 2 (doubling or halving) or more about half the time at each studied 

beach.

• There was a limited statistical relationship observed between levels on the sampling day and 

the following day at three out of the fi ve beaches studied.

• Indicator densities tended to decline from morning to afternoon at three of the beaches. This 

was true for both freshwater and marine indicators. Early morning results were fairly indicative 

of afternoon water quality, realizing that the density may be lower as the day progresses.

Day-to-day variability

Time series plots of geometric mean indicator densities over all sampling locations in knee-deep and 

chest-deep water at 9:00 a.m. are shown in Figure 8 for each of the fi ve beaches. From the analysis 

of spatial factors, depth zone was seen to have a substantial impact on indicator densities. These plots 

are representative of samples from zones in which adult swimmers would be exposed.

The time series plots of Figure 8 afford us a rather accurate daily “snapshot” of each beach. At 

the same time, we may simulate a realistic beach monitoring scenario. For illustration, we will use 

scenario described in the previous section – a single Tuesday morning sample. Having examined 
25

other scenarios, however, we can offer assurance that the conclusions apply to a single-sample scheme 

for any day of the week or time of day, although specifi c details in the behavior of the simulated 

monitoring results will, of course, vary.

Based on this scenario, the four-week moving geometric mean is superimposed on these graphs for a 

sample collected on Tuesday morning, approximating a monitoring result based on 5 samples collected 

over a 30-day period (actually a 29-day period) as specifi ed in U.S. EPA guidelines. Naturally, a four 

week moving average cannot be calculated until August 1, four weeks from the fi rst Tuesday of the 

study. From then on, the running geometric mean is based on an idealized Tuesday sample result – a 

single sample that matches the geometric mean of six knee- and chest-deep samples.

In the fi rst of these graphs, which is for West Beach, note that the only occasion during August when 

the point-in-time geometric mean for the morning exceeded 126 was on Sunday the 27th. On this day, 

the geometric mean reached 446, well above the single-sample limit of 235 E. coli per 100 mL in fresh 

water. Not only does the 29-day geometric mean fail to predict this event, it is, in fact, at its lowest 

level of the study. There appears to be very little possibility that any single sample that had been 

collected on the preceding Tuesday would have itself exceeded the single-sample limit (235), given 

that the highest single value actually obtained on that Tuesday morning of August 22 was 11 E. coli

per 100 mL. Even the day before August 27, the highest observed single density was 23. In fact, there 

is nothing from these data that would indicate this high indicator levels on Sunday, August 27 at West 

Beach, other than the monitoring results from that very day. The last rainfall prior to this day had been 

observed about four days earlier, and was fairly light (0.3”). There was a brisk on-shore wind on this 

particular Sunday, a factor which will be shown to have an impact at this beach, but stronger winds 

that were observed nine to eleven days prior to this failed to exhibit such a strong effect.

This is just one contradiction of many that can be gleaned from these plots. For example, at Wollaston 

Beach, the only beach at which there was not a preponderance of results on one side or the other of 

the recommended limit, only fi ve out of eleven exceedences were captured by the 29-day Tuesday 

moving geometric mean.

Aside from the geometric mean over 29 days, it is obvious that variations in the geometric mean at 

a point in time can be quite large in themselves from one day to the next. In fact, for each of these 

beaches and considering the 9:00 a.m. results only, on at least half of the days during this study the 

change in geometric mean indicator level from the previous day was by a factor of 2 or more, that 

is, it more than doubled or halved from the previous day (Table 9). Day-to-day changes in indicator 

density in this study were large enough that the geometric mean over fi ve Tuesdays, or, for that matter, 

any geometric mean of fi ve observations over a 30-day period, will often not refl ect true conditions at 

a beach at a given time.
26

Figure 8. Time series plots of geometric mean morning (9:00 a.m.) indicator levels. 

Heavy line indicates the 4-week geometric mean for samples collected on 

Tuesday morning of each week.
27

Table 9. Ratio to the previous day of the geometric mean (GM) of all 

knee- and chest-depth samples taken at the 9:00 a.m. visit. 

Interquartile range (25th and 75th percentiles) and frequency 

with which the geometric mean changes by a factor of 2 or more 

(ratio<0.5 or ratio>2) and 5 or more (ratio<0.2 or ratio>5).

Location Number

Interquartile range 

for change in GM

Percent of days that the 

ratio to previous GM is:

25th %-ile 75th%-ile <0.5 or >2 <0.2 or >5

West Beach 54 0.32 1.99 67% 20%

Belle Isle 56 0.55 2.34 43 21

Wollaston 

Beach 59 0.39 2.50 66 25

Imperial Beach 60 0.50 2.00 55 13

Miami Beach 61 0.33 2.64 69 28

Table 10 compares the serial correlation between indicator densities at each beach using a 1-day, 2-day, 

and 4-day time lag. This is simply the correlation between two time-related variables, the log mean 

indicator density over all samples on a given day at 9:00 a.m. and the corresponding log mean at 9:00 

a.m. 1, 2, or 4 days later. The higher this correlation, a perfect correlation being +1 (or -1), the better 

will be our ability to predict results 1, 2, or 4 days in the future based on “today’s” results. While none 

of these correlation values are particularly impressive, at least a positive relationship is indicated at 

most of the beaches between one day and the very next day. Correlation becomes markedly weaker 

when the lag is two days, and negligible at four days. These results do not support a scenario whereby 

water is sampled on Tuesday for a decision on whether it will be acceptable to swim next Saturday.

Signifi cant day-to-day, week-to-week, or month-to-month variation has been observed in several 

studies (Seyfried, 1973, Cheung, 1990, Brenniman, 1981, PHLS, 1995). The differences were as 

great as two orders of magnitude between days, weeks, or months. Similar differences were observed 

in the current study.
28

Table 10. Serial correlations between log means separated by 1, 2, or 4 days

Location

Time lag between samples

1-day lag 2-day lag 4-day lag

Correlation coeffi cients1

:

West Beach 0.27 0.04 -0.03

Belle Isle 0.18 0.06 0.17

Wollaston Beach 0.44 0.18 0.13

Imperial Beach 0.45 0.28 -0.09

Miami Beach Pk. 0.40 0.30 0.18

P-values2

:

West Beach 0.039 0.789 0.805

Belle Isle 0.191 0.644 0.233

Wollaston Beach 0.001 0.176 0.329

Imperial Beach <0.001 0.031 0.514

Miami Beach Pk. 0.001 0.021 0.180

1

Correlations greater than about 0.24 are statistically signifi cant 

(α=0.05). Sample sizes are in the range of N=50-60 (days). 2

Probability associated with the sample correlation under the null 

hypothesis that the true correlation is zero.

Variation between morning and afternoon results

A phenomenon that was observed to occur in three of the fi ve beaches studied was a tendency for 

indicator levels to decrease between the morning (9:00 a.m.) and afternoon (2:00 p.m.) sampling 

events (Figure 9). We use log10 of the indicator density per 100 mL as the y-axis in these plots, since 

there are problems with scale in attempting to show the changes in geometric mean or percentage 

changes. Note that the predominant effect seen at Miami Beach Park, Wollaston Beach, and Belle 

Isle, the three beaches where indicator levels were relatively high, was a decline in the 2:00 p.m. 

reading as compared to the 9:00 a.m. value.
29

Consider the scenario of taking one Tuesday morning sample for a decision whether to close the 

beach on Saturday and those instances when a Tuesday sample from knee-deep water exceeds the 

EPA recommended limit for a single sample of 235 E. coli or 104 enterococci per 100 mL [1986]. 

Had that sample been collected on Saturday instead, would the decision to close the beach or 

not, have been the same? How well does the Tuesday sample discriminate between acceptable 

and unacceptable Saturday results? Does an exceedence on Tuesday indicate a higher risk of 

exceedence the following Saturday?

The fi rst part of Table 11 examines each single sample from knee-deep water in terms of whether 

it exceeds the EPA limit and whether that sample taken from the very same location four days 

earlier had exceeded the limit. In effect, this gives the probability of exceedence four days from 

now when (in column 1) today’s sample does not exceed the limit or (in column 2) today’s sample 

does exceed the limit. One would hope that the probability of exceedence four days hence is 

substantially higher when today’s sample exceeds the limit than when it does not. That is, column 

2 should be substantially higher than column 1. 

This is not the case. In fact, for the four-day time lag, the percentages in both columns are remarkably 

similar except at Wollaston Beach. It may well be that the validity of this sampling scenario varies 

by beach, and has merit at Wollaston. However, note that the difference at Wollaston is not 

statistically signifi cant (p-value = 0.31).

What about sampling on Friday morning, the day before a decision must be made? We can see 

from Table 11 that a sample was generally more likely to exceed the limit if that same sample 

had exceeded the limit the previous day (“1 day earlier”). Sampling two days earlier may be 

somewhat, but not much, better than sampling four days earlier. In fact, note that all exceedences 

at Wollaston, the only beach where the four-day lag appeared to hold promise, are missed by the 

two-day sampling lag.
30

Figure 9. Change in mean log10 indicator density between the morning (9:00 a.m.) 

sample and afternoon (2:00 p.m.) sample.
31

Previous studies [Sieracki, 1978] have demonstrated the die-off of E. coli after exposure to sunlight, 

an effect supported by these data when cloud cover at the time of the afternoon sample is considered. 

As seen in Table 12, and illustrated by Figure 10, indicator levels tended to be lower in the afternoon 

relative to the same morning on sunny afternoons (i.e. less than 50% cloud cover) at both freshwater 

beaches. At West Beach, lower E. coli densities were observed in sunny or mostly sunny afternoons, 

but higher levels were seen in the afternoon on cloudy days. E. coli at Belle Isle generally dropped in 

the afternoon even on overcast days, but decreased even more on those occasions when cloud cover 

was less than 50%.

Table 12. Comparison of geometric mean density of respective indicator 

organism at each study beach between morning and afternoon 

visits – sunny vs. cloudy days.

Location

Cloudy days

(Greater than 50% cloud cover)

Sunny days

(Less than 50% cloud cover)

Number 9:00 a.m. 2:00 p.m. Number 9:00 a.m. 2:00 p.m.

West 

Beach 19 24 31 41 22 17

Belle

Isle 19 202 125 41 235 60

Wollaston 

Beach 32 27 14 25 21 15

Imperial 

Beach 30 7 4 31 4 4

Miami 

Beach 32 149 80 30 84 20

Although enterococci have been shown to be relatively more resistant to solar radiation than are E. 

coli [Sieracki 1978], signifi cantly lower densities of this indicator were noted at Miami Beach Park in 

the afternoon relative to corresponding morning levels on days when there was less than 50% cloud 

cover at the time of the afternoon visit. Neither of the other two saltwater beaches exhibited this effect 

to a signifi cant degree. In our evaluation of changes between morning and afternoon, other effects, 

such as tidal stage, rainfall, air and water temperature, and bather load were included as co-variable 

with cloud cover, but failed to account for the apparent effect of sunlight at the Miami Beach Park 

location. Of course, this research only indicates association between indicator levels and cloud cover, 

not causation of die-off of either E. coli or enterococci because of exposure to sunlight. There may be 

other, unmeasured associations with cloud cover that infl uence indicator levels at any of the beaches.

Some studies in the literature have reported signifi cant differences between the indicator densities 

obtained in the morning when compared with results obtained in the afternoon [Seranno et al., 1998; 

Brenniman, 1981; Seyfried, 1973]. Indicator densities were generally highest in the early morning 

and lowest in the mid-afternoon. These authors point out that this time interval is closely related 

to the period of greatest solar radiation intensity. What we may be seeing is a confi rmation of this 

phenomenon. 
32

Figure 10. Geometric mean indicator density for morning (9:00 a.m.) samples and 

afternoon (2:00 p.m.) samples, by whether afternoon was sunny (< 50% 

cloud cover) or not sunny.

Results from the hourly sampling that was performed on several days at each study beach are also 

available for ascertaining whether there were any predominant diurnal patterns in indicator density. 

We can make at least a qualitative assessment of this by examining Figure 11, in which indicator levels 

observed on the hour (9:00 a.m. through 6:00 p.m.) relative to the overall geometric mean indicator 

level for that day are shown. The heavy lines in these graphs indicate the average (geometric mean) 

of this ratio for each hour.

With exception of West Beach, the tendency is for elevated indicator levels during the fi rst sampling 

event of the day, at 9:00 a.m. This is particularly evident at Miami Beach Park, where average values 

for the fi rst two hours were substantially higher than the overall daily mean, after which values tended 

to be much lower. As can be seen from the actual hourly results, deviations from this overall trend can 

be substantial in any case. These data are quite noisy; the best indication of overall trend still comes 

from the normal 9:00 a.m. and 2:00 p.m. daily sample results, which cover the entire two-month 

period.
33

Single sample limits and time of day

Again, consider the single-sample exceedence rate for those samples taken at 9:00 a.m. from kneedeep water, using the EPA limits of 235 E. coli or 104 enterococci per 100 mL. On those occasions 

when the morning sample exceeded the limit, at three of the study beaches a sample taken from 

the same location in that same afternoon was much more likely also to be in exceedence, when 

compared to those occasions when the morning sample did not exceed the limit. This is illustrated 

in Table 13. At West Beach, for example, of the 22 knee-depth samples that were over the 235 per 

100 mL standard for E. coli at 9:00 a.m., 40.9% were also higher than this limit at 2:00 p.m., as 

compared to 7.3% of the “acceptable” 9:00 a.m. samples that exceeded 235 by 2:00 p.m.

 

Table 13. Percentage of knee-deep samples collected at 

2:00 p.m. that exceeded the single sample limit as 

recommended in EPA guidelines [U.S. EPA,1986], 

by whether the sample from the same location 

was above or below the limit at 9:00 a.m.

Location

Percent of samples above the EPA recommended 

single sample limit at 2:00 p.m.

(total number of samples in parentheses)

< Limit at 9:00 am > Limit at 9:00 am

West Beach 7.3 (164) 40.9 (22)

Belle Isle 21.9 (32) 74.8 (151)

Wollaston Beach 7.5 (160) 11.5 (26)

Imperial Beach 1.1 (186) - (0)

Miami Beach Park 19.2 (73) 52.2 (113)

% above the limit:

At 9:00 a.m. At 2:00 p.m.

West Beach 11.8 (186) 11.3 (186)

Belle Isle 82.5 (183) 65.6 (183)

Wollaston Beach 14.0 (186) 8.1 (186)

Imperial Beach 0.0 (186) 1.1 (186)

Miami Beach Park 60.8 (186) 39.2 (186)

In total, single sample exceedences were much more likely to occur in the morning at both Belle 

Isle and Miami Beach Park. At West Beach, the relative number of exceedences was about the 

same at the morning and afternoon visits. Considering both parts of Table 13, it can be seen that a 

morning sample from a given location in the water that exceeds the recommended limit is nearly 

four times as likely also to exceed that limit in the afternoon compared to what may be expected 

by chance (40.9% compared to 11.3%).
34

Figure 11. Geometric mean (GM) indicator density by time-of-day (9:00 a.m. – 6:00 

p.m.) for samples collected on hourly sampling days - ratio of GM on the 

hour to overall GM for the day. Average ratio for each hour is shown by 

the heavy line.
35

Single sample limits by the hour

Hourly single-sample exceedence rates among knee-deep water samples are shown in Table 14. 

Exceedences were lower by mid-afternoon at Wollaston and Miami, confi rming what we saw 

earlier when comparing only 9:00 a.m. and 2:00 p.m. results. Belle Isle, which showed a tendency 

to decline between 9:00 a.m. and 2:00 p.m. when all data were considered, does not show this 

tendency when hourly results alone are considered. Then too, because of logistic problems, only 

eight days of hourly sampling were completed at this beach, compared with a full two weeks at 

the other sites.

Table 14. Percentage of knee-deep samples that exceeded the single 

sample limit [U.S. EPA, 1986], by time-of-day. Only hourly 

sampling results are used. For all but Belle Isle, there 

were 14 hourly sampling days and 39-42 valid knee-deep 

observations (for Belle Isle there were 23 or 24 observations 

over 8 days).

Time of 

day

Percent of knee-deep samples that were in exceedence

West Beach Belle Isle

Wollaston 

Beach

Imperial 

Beach

Miami 

Beach Park

09:00 2.4 79.2 23.8 0 78.6

10:00 4.8 52.2 16.7 0 63.4

11:00 4.8 39.1 14.3 0 52.4

12:00 7.1 54.2 33.3 0 45.2

13:00 0 58.3 26.2 0 40.5

14:00 2.6 75.0 7.1 4.8 35.7

15:00 4.8 58.3 14.3 0 26.2

16:00 0 75.0 5.1 0 51.2

17:00 0 66.7 20.5 0 38.1

18:00 2.4 79.2 19.0 2.4 50.0

Environmental and bather effects

A summary of environmental and bather density data collected reveals some striking differences 

among the study beaches (Table 16). West Beach was by far the most heavily used, followed by 

Imperial Beach. The water at Wollaston Beach was particularly turbid in comparison to the other 

beaches with an average of 56 NTU. Note that turbidity at any of the study beaches was highly 

variable, with the standard deviation of the turbidity values approximately equal to its mean in every 

case (data not shown).

Particularly noteworthy is that weather conditions at Imperial Beach were fairly uniform throughout 

the period of the study. Most of the afternoons were sunny or mostly sunny, only trace amounts of 

rainfall were recorded, and the onshore wind was ever present. This constancy obviously limits any 

conclusions that may be made regarding weather related effects at Imperial.
36

Table 15. Environmental characteristics and bather densities of 

EMPACT study beaches.

West 

Beach Belle Isle Wollaston Beach

Imperial 

Beach

Miami 

Beach 

Park

Sunny/mostly sunny days 1 67% 44% 50% 71% 48%

Avg. air temperature (oC) 1 25.0 24.7 26.6 22.5 27.5

Avg. water temperature(oC) 1 23.6 24.1 22.2 19.8 27.4

Total rainfall (in.) 9.9 13.2 14.2 < 0.1 13.7

# days with rain 14 17 14 2 22

Offshore winds 1,2

- Frequency 31% 47% 26% 0% 24%

- avg. wind speed (mph) 4.1 4.5 3.0 - 3.3

Onshore winds 1,2

- Frequency 59% 25% 39% 81% 56%

- avg. wind speed (mph) 8.3 6.3 5.8 4.9 4.6

Avg. wave height (M) 0.30 0.02 0.11 0.36 0.13

Avg. turbidity (NTU) 3 6 4 56 1 7

Avg. tide range (ft.) 4 - - 9.9 4.2 0.6

# bathers on the beach 1

- < 20 6 34 52 19 50

- 20-100 21 21 10 37 11

- 101-200 20 1 0 2 1

- > 200 14 1 0 1 0

# bathers in the water 1

- < 20 19 37 62 30 52

- 20-100 31 18 0 29 10

- 101-200 9 2 0 0 0

- > 200 2 0 0 0 0

1

 at 2:00 p.m. 2 Wind at a direction of at least 45o with respect to shoreline 3

 as measured from the central sampling location in the water (9:00 a.m. & 2:00 p.m.)

4

 average difference in water level between succeeding low and high tides 

Statistical evaluation

In evaluating environmental and bather effects, the goal was to develop a model for each beach that 

might be used in predicting log mean indicator density 24 hours later based on its current value, since 

with the culture methods used, “current” values are not known until the next day. Thus, the previous 

day’s log10 density is present in all of these models, even though it proves to be non-signifi cant in 

one case. A stepwise regression procedure [Draper and Smith, 1981] was utilized on the potential 

predictor variables, with the signifi cance level (“p-value”) for entry or removal from the equation 

set at 0.10. Trial and error was involved in selecting the “best” regression as well. In some cases, 

forcing one or two variables into the equation, in addition to the previous day’s density, resulted in 
37

some improvement in its explanatory power with little or no increase in its complexity (number of 

independent variables in the model).

These analyses are exploratory, indicating variables which might be useful predictors of log microbial 

densities. There is a tendency for any technique designed to select a “best” regression model to 

overstate the fi t, with regard to signifi cance levels, partial or total R2, or any other measure. To the 

extent that the same variables are suggested as being good predictors in a number of different beaches, 

this suggests that these variables really are important. Several variables show up consistently in these 

models: rainfall, bathers on the beach, etc. There is good theoretical rationale to believe that these 

variables make a difference in water quality. Consequently further examination of these variables in 

more detail will be presented.

Potential explanatory factors considered in this section are not “design variables”, in contrast to 

the time-of-day, day-of-week, depth zone, and transect of the previous section. Rather, we take 

environmental and human factors as they occur. Often, these variables may be correlated with one 

another, and, thus, we do not observe an effect that is purely a result of a single factor. For example, 

it is probable that bather density at a beach, the occurrence of rain in the past 24 hours, whether it is 

sunny or not, and the temperature are all interrelated. We cannot isolate their effects, because we did 

not, for example, prevent bathers from going to the beach on warm, sunny days. Therefore, some 

variables may be surrogates for others or may mask the effects of other variables.

In addition, if some condition never occurred, or happened only infrequently, in the study, we cannot 

infer an effect from that condition. Such was the case for offshore winds and rainfall at Imperial 

Beach. Rainfall was observed on only two occasions at this location. It may well be that rainfall 

has an overwhelming effect on conditions at Imperial Beach, but, if so, we were not afforded the 

opportunity to observe this effect.

Relationships found at the study beaches are specifi c to the respective location during the time period 

of the study; blindly generalizing these results to other beaches should be avoided. Such correlates 

with indicator levels as found in this section, however, may serve as a general guideline for related 

research at other sites.

Table 16 summarizes the results of modeling for each of the study beaches. The regression models 

shown are not the only models possible, but are representative of a group of models, any of which 

might be appropriate.

The corresponding log density of indicator organisms 24 hours earlier is included as a covariate in all 

models in Table 16. In one case, that of Miami Beach Park, the relationship is seen to be non-signifi cant. 

In this case, there is a highly signifi cant relationship between the 1-day lagged log indicator densities 

by themselves (Table 10 shows this), but the inclusion of other variables is suffi cient to account for 

this relationship.

The last column of Table 16 gives the coeffi cient of determination, R2

, for each model. This is the 

proportional of total variation (sum of squared deviations from predicted value) of the dependent 

variable that is accounted for by the regression. A “partial R2

” is also listed, which indicates the 

extra proportion of variation accounted for by the other covariates over that which is accounted for 

by knowledge of the previous day’s log density alone. The partial R2

 is a critical consideration in 

improving our prediction of water quality based on the previous day’s microbial levels, as will be 

discussed in the next section, Sources of Sampling Variance.
38

Table 16. Results of regression analysis on log10 density of indicator organism.

Factor Coeffi cient P-value1 R2

West Beach (N=120) 2 Int.=1.0322

Sunny?3

Wind vector4

Rain in past 3 days? 3

PM & rain in past 24 hrs.?3

Previous day log10 density

-0.329

0.029

0.229

-0.326

0.280

<

<

<

0.001

0.001

0.024

0.032

0.001

R2

 = 0.345

Partial R2 = 0.24 6

Belle Isle (N=113) Int.=1.769

Sunny?3

2:00 p.m.?3

Rain in past 24 hrs.? 3

<20 bathers on beach?3

Previous day log10 density

-0.180

-0.281

0.173

0.148

0.212

<

0.005

0.002

0.016

0.076

0.010

R2

 = 0.42

Partial R2 = 0.28

Wollaston Beach 

(N=121) Int.=0.928

2:00 p.m.?3

Rain in past 24 hrs.? 3

Low air temperature?3,7

Onshore wind?3

<20 bathers on beach?3

Water level8

Previous day log10 density

-0.259

0.396

0.239

0.195

-0.334

0.043

0.234

0.007

0.001

0.029

0.049

0.051

0.003

0.005

R2

 = 0.37

Partial R2 = 0.24

Imperial Beach (N=118) Int.=0.236

<20 bathers in water?3

Water level

- if 9:00 a.m. sample9

- if 2:00 p.m. sample9

Previous day log10 density

-0.246

0.158

0.102

0.221

<

0.005

0.001

0.00710

0.010

R2

 = 0.31

Partial R2 = 0.21

Miami Beach 

Park(N=122) Int.=1.326

Rain in past 24 hrs.? 3

Wind vector

Water level8

PM & sunny?3

Water temp. > median?3

 - if 2:00 p.m. sample11

Previous day log10 density

0.258

0.041

0.290

-0.111

-0.387

0.071

<

0.009

0.004

0.001

0.031

0.004

0.371

R2

 = 0.42

Partial R2

 = 0.37

1

 “Signifi cance level” of the variable – required to be < 0.10 for stepwise selection. 2

 N=# of observations, Int.=intercept 3 Dummy variable: value = 1 if the condition is true, 0 

if false. 4 Wind speed x direction vector, where the direction vector is +1 for a wind blowing 

straight onshore, -1 for offshore. 5 Proportion of variation explained by the regression. 6

Additional proportion of variation explained by environmental and bather factors over that 

explained by previous day’s log density alone. 7

 Air temperature less than the 25th percentile 

for the respective time-of-day. 8 Water level in feet above mean lower-low tide mark. 9 Effect 

differs between morning and afternoon. 10 P-value for the difference between morning and 

afternoon effects. 11 Water temperature higher than the median (for that time of day) is a 

signifi cant effect only at 2:00 p.m.
39

Tides

Among the three beaches in this study subject to tidal movement, tide stage is seen to be a signifi cant 

determinant of enterococci density within the swimming area; in fact, in terms of the p-values of Table 

16, tide stage has the strongest association with microbial contamination of all the environmental 

factors examined at these beaches. We note that the water level, measured in feet above the mean 

lower-low tide mark (the lower of the two low tides in a 24-hour tidal cycle), was found to have a 

stronger association with bacteria densities than the actual tide stage itself, which we defi ned as high 

or low when samples were collected within 1.5 hours of the actual event. Neither did it seem to 

matter whether the tide was incoming or outgoing. Figure 12, data for which are shown in Table 17, 

illustrates the observed water level effect, comparing geometric mean enterococci levels for times 

when the water level was in the lower and upper quartiles of its range at each particular beach for 

both the morning and afternoon visits. Ranges of water level, at least over the times when sample 

collection took place at that beach, are also indicated in Table 17.

Table 17. Comparisons of geometric mean enterococci density per 100 mL 

at low, mid, and high water levels for marine beaches (based on 

25th and 75th percentiles of water level).

Location

9:00 a.m. 2:00 p.m.

Water level: Water level:

Low Mid High Low Mid High

Wollaston Beach 12 28 37 11 12 22

Imperial Beach 2 5 11 4 3 6

Miami Beach Park 85 101 140 20 49 228

In each case, enterococci densities are seen to be higher when the water level was in its upper quartile 

compared to densities obtained during lower quartile water stages; this is so even at the estuarine 

beach, Miami Beach Park, where tidal variations were relatively low. The fact that water level 

shows a stronger association with microbial levels than does tidal stage itself or whether the tide is 

incoming or outgoing suggests that suspension of sediment or debris from the beach may contribute 

to contamination, perhaps in tandem with waste washing in from deeper waters. Shoreline sediment, 

of course, would constantly mix with bathing waters, and may ultimately affect water of swimming 

depths whether the tide is coming in or going out, but sediment higher on the beach is more exposed 

to humans and animals as well as to air and may be richer in microbial content.

Weather

We had previously discussed the apparent effect of sunlight on afternoon readings. Other weather 

factors are also seen to play important roles in determining microbial contamination. These vary 

among the beaches of this study, and include wind, particularly whether the wind is blowing onshore 

or offshore, the occurrence of rain in the hours prior to sampling, and air or water temperature. Rainfall 

exhibited a strong association with water quality in three of the study beaches, as did wind velocity 

and direction, while association with air or water temperature was found in two of the beaches.
40

Figure 12. Geometric mean enterococci density by tide stage at marine beaches. 

These various weather effects are illustrated in Figure 13 and summarized in Table 18. Signifi cant 

rain effects were observed at Miami Beach Park, Wollaston Beach, and Belle Isle. In all three cases, 

as might be expected, the occurrence of rainfall within the past 24 hours is associated with higher 

indicator levels at the beach. Note that measurable rainfall occurred on only two occasions at Imperial 

Beach; thus, we have no real opportunity to discern rain effects due to rain at this location. While 

previous 24-hour rainfall fails to be a signifi cant factor at West Beach, there is an evident rainfall effect 

when we consider rain in the past three days, as indicated in Table 18. In essence, then, rainfall was 

observed to have an effect on water quality in all cases where we had the opportunity to observe this 

effect. A 24-hour window is arbitrary; in truth, rain effects on recreational water quality may likely 

vary from beach to beach, depending on such factors as the size and gradient of the drainage area.

Wind vector at the beach, which takes into account the wind direction as well as wind speed, is a 

signifi cant factor at Miami Beach Park, Wollaston, and West Beach, in each case resulting in higher 

geometric mean indicator densities with a relatively strong onshore wind component and lower 

densities with an offshore component. Once again, we do not have the opportunity to gauge an 

effect at Imperial Beach, because offshore winds never occurred at this site; its graph in Figure 13 

compares light or calm onshore wind conditions with moderate onshore winds. At Belle Isle, E. 

coli levels were actually somewhat lower, but not signifi cantly so, when winds were onshore in the 

morning, but virtually zero difference with wind vector is seen in the afternoon.
41

Figure 13. Geometric mean indicator density for various weather conditions.

Elevated water or air temperatures might be predicted to result in an increase in microbial counts at 

a beach. However, either may also be associated with increased sunshine. Even when cloud cover 

at the time of sampling is accounted for, there may have been occasions on which cloud cover was 

more than 50%, at the time of sampling, yet water temperature was relatively high because of earlier 

sunshine. This is one possible explanation for both cases where either water or air temperature was 

associated with decreased densities of indicators organisms, at Miami Beach Park (water temperature) 

and Wollaston (air temperature), as indicated by Figure 13. Note that E. coli levels were generally 

higher at Belle Isle when water temperature was relatively high compared to those occasions when 

water temperature was on the low side, but only on the afternoon visits. The opposite was true for 

this beach on morning visits, and this is a statistically signifi cant difference between morning and 

afternoon effects of temperature at this particular beach. Whether changes in water temperature have 

an effect on growth of these organisms may also be supposed to depend on the range of temperatures 

involved; water temperatures at Imperial Beach were generally the lowest among these study beaches, 

reaching a high of only 23o C, possibly still too low to promote bacterial growth.
42
43

Bather density

Bather density at a beach was recorded in order to ascertain whether the presence of bathers itself 

infl uences microbial contamination. Both bathers on the beach and bathers in the water at the time 

of sample collection were categorized as fewer than 20, 20-100, 101-200, and more than 200. These 

are further condensed for our purposes into two categories, 0 to 19 and 20 or more, since occasions on 

which over 100 bathers were recorded at any of the beaches are rare. Figure 14 compares indicator 

densities at the 2:00 p.m. sample collection for each of the beaches with regard to whether there were 

fewer than 20 bathers either on the beach or in the water, data for this fi gure being shown in Table 

19.

Bather effects were found to be signifi cant at Wollaston and Imperial Beaches, where an increase in 

numbers of bathers was found to result in a corresponding increase in enterococci levels. At Wollaston 

Beach, few bathers were ever observed to be in the water at any given moment, but the presence of 

substantial numbers of bathers on the beach was adequate to trigger the increase in microbial levels 

in the water. People on the beach in greater numbers implies the possibility that there are more actual 

bathers in the water, whether more than 20 or not, or that there had been more bathers in the water 

prior to the time of sampling.

Three studies looked at the potential for bather load to affect indicator density [Sekla, 1987; Cheung et 

al., Seranno et al., 1998]. Sekla indicated that in spite of bather numbers varying between 0 and 3000, 

there was no related variation in indicator densities. Seranno et al., on the other hand, clearly showed 

that as the number of bathers increased the density of indicator bacteria decreased. Cheung et al. 

were able to observe a correlation between indicator density and number of bathers at only one beach 

out of nine beaches and only on one day. These differences in observed results may be related to the 

location of the study sites and to the type of dispersion of contamination at any one site. Locations 

with very little water movement may result in data where indicator densities increase with number 

of bathers. At locations where there is signifi cant wave action, indicators shed into the water may be 

dispersed very rapidly and the relationship between indicator and bather density cannot be developed. 

It appears that the effect of bather load on water quality measurement will have to be determined on 

a case-by-case basis.
44

Figure 14. Geometric mean indicator organism density by number of bathers on 

 the beach and in the water.

 Table 19. Comparisons of geometric mean indicator density per 100 

mL. vs. number of bathers in the water and on the beach, for 

the afternoon (2:00 p.m.) sampling visits.

Location

Bathers on the beach Bathers in the water

0-19 20 or more 0-19 20 or more

West Beach 23 20 18 22

Belle Isle 114 65 115 58

Wollaston Beach 14 18 14 --

Imperial Beach 3 5 3 5

Miami Beach Park 40 43 41 39
45

Sampling Variance

Sources of variation

Populations, sampling, variance, and components of variation

Sampling variance is a measure of the variability of a measurement, and is calculated from a sample 

as

 

in which n is the sample size, , the sample mean, and xi is the ith sample value for the measurement 

(i=1 to n). The xi

 are assumed to be results that have been realized from a random sampling of 

somepopulation encompassing all of the possible individual x values that might be obtained.

By the term “population,” we mean the aggregate from which samples are collected and to which 

the variance given by Formula 1 applies. It is the population to which any inferences derived from 

sampling apply. Later, we will discuss in detail the Data Quality Objectives (DQO) Process [U.S. EPA 

2000b], which is a formal framework for considering study objectives (the inferences and decisions 

to be made), population, and sampling. For now, we wish simply to emphasis the importance of the 

concept of a population to sampling and appropriate variance components for various population 

concepts.

In the context of water sampling, the population might be, for example, daily values of the indicator 

density in waist-deep water midway along the designated beachfront at 9:00 a.m. In this case, a 

random sample of days would enable one to make an inference such as “the geometric mean density 

was X over the last thirty days.” Another example of a population could be the entire stretch of 

waist-deep water within the “bather area” at noon on a specifi ed date. The inference becomes “the 

geometric mean density was Y in waist-deep water at noon on the 23rd of July.”

If day-to-day variability (at the same point in the water and time-of-day) is greater than betweenlocations variability (at the same point in time and water depth), then Equation 1 is expected to give a 

higher value for V for samples that have been collected among different days than for those collected 

among different locations. “Among days” and “among locations” are two sources of variation, or 

variance components, that can be thought of as arising from two different, independent populations, 

as in this example. Sources of variation relevant to the EMPACT Beaches Study are discussed next. 

For each source, the variance component due to that source is calculated with all other sources, spatial 

and temporal, held fi xed.

Sampling distribution

Estimates of variance components are used to assess the accuracy of a mean derived from sampling 

based on a model of the sampling distribution, which gives the underlying probabilities of obtaining 

a sample value within a given range. We hope to be able to utilize fairly small sample sizes in beach 

monitoring – current EPA guidelines [1986] specify a single sample - a worthy goal of any sample 

design, and, therefore, cannot rely upon some large sample theory. Some assurance is needed that 

normality applies, or else we need to determine the sampling distribution that does apply.
46

Previous research has indicated that log10 indicator densities from environmental samples tend to 

be approximately normally distributed [Fleisher and McFadden, 1980; Gannon and Busse, 1989; 

Mujeriego et al., 1980]; that is, valid inferences regarding the means of such data can be made in 

using normal theory. Suffi cient data have been collected in this study to enable an evaluation of the 

consequences of using a normal model. This evaluation indicates that this is a reasonable model of 

the log10 densities, resulting in probability statements that are in error by only +/-1% (i.e., a 95% 

confi dence interval may actually be a 96% confi dence interval). Given that a normality assumption 

is appropriate for indicator sampling, this allows us to construct confi dence limits for the log mean 

density based on the sample log mean, log variance, and sample size using “z” (standard normal 

distribution) values and to perform z tests in comparing the sample log mean to some critical value.

Components of spatial variation

On eight days at each of the fi ve beaches that participated in this study, replicate samples were 

collected at each location in the water during both the 9:00 a.m. and 2:00 p.m. sampling visits. On 

these occasions, ten samples were collected from the central location (Location 5, knee-deep water 

at Transect 2) and two samples, at the remaining eight locations. These samples yield information 

on the small-scale variability inherent in measuring recreational water quality. Only if the water of 

the bathing area were perfectly mixed, by defi nition, would the variability of water quality between 

different locations in the water equal this small-scale value. Otherwise, between-locations variability 

will always be higher.

The study design used explicitly accounted for all three physical dimensions. Locations in the water 

at which samples were collected varied in directions parallel to the beachfront, at right angles to the 

beachfront, and vertically from different depths within the water column.

We have seen that the zone from which the sample was collected has the greatest predictable impact 

on microbial indicator densities of any factor considered in this study. In each of the study beaches, 

bacterial densities become progressively lower as one moves from ankle-deep to knee-deep to chestdeep water.

On the other hand, as long as the sample came from the same depth zone, there were only minor 

consistent differences among transects at two of the beaches. Therefore, given a sample of water, it 

makes a great deal of difference in our ability to assess overall water quality to know how deep the 

water was where that sample was collected, but makes little or no difference to know what where 

along the beachfront it was collected.

Likewise, we found no consistent differences among the various sampling depths. Recall that, on four 

days, samples were taken from two depths in knee-deep water (0.3 and 0.425 M from the surface) and 

from three depths in chest-deep water (0.3, 0.75, and 1.425 M from the surface), whereas a standard 

sampling depth of 0.3 M was used on all other days.

In evaluating their respective variances, the different zones, transects, and sampling depths from which 

sample are taken are regarded as having been randomly selected. In reality, however, these dimensions 

were fi xed at the start of the study. Thus, the sampling plan is similar to a systematic sample (with the 

exception that a random starting point is not determined each time). Given the observed differences 

among zones, it is apparent that the value for the variance among zones will be dependent on exactly 

how these zones are defi ned. Had waist-deep been used instead of knee-deep, the resulting variance 

may have been much different. Likewise, for different transect spacing or sampling depths. We shall 
47

see, however, that this is not so great a concern – zone and sampling depth variance are not relevant, 

and a way of accounting for transect separation is shown in the next section.

How is the population defi ned spatially?

• If we consider the population to consist of water 0.3 M below the surface within one zone, then 

variation in sampling depth or between zones are not considerations in our sample design.

• Variance between zones is important when we expand the population to include all of a given 

area of water. This may be beyond limits of practicality, and is possibly not even desirable 

since health studies themselves were based on approximately waist-deep water results.

• We may not have to consider them in sample design, but knowledge of the magnitude of interzone and depth variances is useful in describing the indicator levels that may be experienced 

along these dimensions.

Components of temporal variation

We estimate the variance of indicator density among days for samples collected at the same location 

in the water and at the same time of day. This estimates the variance among, for example, samples 

collected in knee-deep water along the leftmost transect at 9:00 in the morning, where a single sample 

is taken on each of several days. Because the duration of this study was 62 days, from July 1 to August 

31, the variance thus estimated is appropriate for a set of random dates chosen out of a sixty-two day 

period of time.

Another temporal component is the intra-day variability, the variation in indicator levels throughout 

a day. The eight to fourteen days of sampling at each beach during which samples were collected on 

the hour from 9:00 a.m. through 6:00 p.m. will enable us to determine an hourly variance.

How is the population defi ned temporally?

• EPA criteria refer to a geometric mean over 30 days. The population implied by this consists 

of microbial water quality during those 30 days. Are samples collected at the same time in the 

morning? Then the population is further limited to water quality at that time in the morning 

over 30 days.

• We have shown that a mean over 30 days does not refl ect water quality at any given point 

in time except by chance. An estimate of water quality at a point-in-time is needed. Our 

population is, then, the water quality at that point in time, and temporal variation ceases to be 

a concern.

• Unfortunately, given the state of the art of recreational water assessment, even though we may 

base a sample design on a population that consists of the water quality indicator at 9:00 a.m. 

on Friday, the population of concern is the water quality at noon on the following day.

o Temporal variation is again a concern, but now affects our ability to predict.

o No amount of sampling will reduce this type of uncertainty. This takes us into the realm 

of modeling in an attempt to reduce the unexplained part of temporal variability.
48

Estimates of variance components for the EMPACT beaches

The various components of spatial and temporal variance, and standard deviations (simply the square 

root of the variance), as estimated for each of the fi ve study beaches are presented in Table 20. Two 

kinds of variance are given for each component. One is a “pure” factor variance for each component, 

that is, the variance that would be seen if we had “perfect” knowledge of the indicator density at each 

sampling location. This is added to the variance within sampling location (that is, the variance among 

the replicate samples taken on occasion at each location), to derive the variance that would actually 

be observed when a single sample is collected at each location and many such samples are taken from 

different transects, zones, days, etc. The pure and observed variances for a given spatial or temporal 

factor apply to the situation in which all of the other factors are held fi xed; for example, the variance 

among zones is applicable to samples that are taken along the same transect at the same time.

Statistical tests would reveal signifi cant differences among the different variance components for any 

individual beach, and, likewise, signifi cant differences among the different beaches for any individual 

variance component for most comparisons. There is, however, no reason to suspect that they should 

be the same.

Note that the incremental factor variance components, except for replicates variance, are the lowest, or 

among the lowest, at Imperial Beach and among the highest at Belle Isle. Variance among replicates, 

the “pure error” component, however, follows the opposite trend, being lowest at Belle Isle and highest 

at Imperial Beach. This implies that, on a large scale, the distribution of indicator organisms is the 

most uniform at Imperial Beach, the least so at Belle Isle.

Spatial components of variation

Small-scale (replicate) variance

This variance is a result of the variation among different samples taken at the same time from the same 

location in the water from a depth of 0.3 M from the surface. There are two components that may 

contribute to the small-scale variation:

1. Method variance is likely negligible for both methods. Precision (standard deviation) for 

method 1600 is on the order of +/-0.02 [U.S. EPA, 1997b], implying a log10 standard deviation 

of about 0.01, affecting only the least signifi cant digit of small-scale standard deviation 

displayed in Table 20.

2. This leaves true variation among replicates as the only real contributor to small-scale variance. 

Although we describe replicate samples as being collected from the same location at the same 

time, they, of course, are not. They are as close to one another, temporally and spatially, as 

we can get.
49

Table 20. Standard deviation and variance component estimates for the 

EMPACT beaches.

Location

Source of variation

Replicate 

Samples1

Sampling

Depth2

Depth 

Zones

Location

Within 

Zone3

Hourly

9:00am -

6:00pm)

Among

Days

Pure factor variances4

West Beach 0.055 - 5 0.078 0.031 0.091 0.234

Belle Isle 0.037 0.021 1.480 0.103 0.182 0.168

Wollaston Beach 0.096 0.052 0.203 0.036 0.190 0.339

Imperial Beach 0.138 0.010 0.017 0.032 0.118 0.114

Miami Beach Pk. 0.039 0.047 0.911 0.169 0.329 0.432

Total variances6

West Beach 0.055 0.045 0.133 0.086 0.147 0.289

Belle Isle 0.037 0.058 1.517 0.140 0.219 0.205

Wollaston Beach 0.096 0.147 0.299 0.132 0.285 0.434

Imperial Beach 0.138 0.147 0.155 0.169 0.256 0.252

Miami Beach Pk. 0.039 0.086 0.950 0.208 0.368 0.471

Standard deviations

West Beach 0.235 0.212 0.365 0.294 0.383 0.538

Belle Isle 0.193 0.241 1.232 0.375 0.468 0.453

Wollaston Beach 0.309 0.384 0.547 0.363 0.534 0.659

Imperial Beach 0.371 0.384 0.394 0.412 0.506 0.502

Miami Beach Pk. 0.198 0.293 0.975 0.456 0.607 0.686

1

 Samples collected at the same point in the water 0.3 M from the surface. 2 Samples collected at 

the same position in the water, but at different depths below the surface. 3 Samples collected from 

water of the same depth & from the same depth below the surface, but at different points in water. 

4

 Variance attributable solely to its respective factor. 5 Estimate of this variance component was 

negative, so is assumed to be zero. 6 Total variance = pure factor variance + replicate sample 

variance (except in the case of replicate samples themselves, where it is identical to pure factor 

variance). 

Replicate variance represents the least variability that we may expect among any set of water samples, 

even if the water comprising the bathing area were “well-mixed” prior to our collection of the samples. 

This small-scale variability is a component of every other variance shown in Table 20.

Variance among sampling depths

In addition to samples that were collected at a depth of 0.3 M from the surface, on occasion samples 

also were collected at 0.075 M from the bottom in both knee- and chest-deep water, and at 0.75 M from 

surface (mid-depth) in chest-deep water. Variance among sampling depths represents the variation 

among these samples (including the 0.3 M sample). In most cases, we note that the contribution to 

replicate variance is relatively small, being at most on the same order as the magnitude of the replicate 

variance itself.
50

In one case (West Beach), the estimate of pure variance due to different sample depths is negative, 

leading to a total variance for this factor that is smaller than the corresponding replicate variance. 

That this should be true is not believable, but that this might occur for one of these estimates is not 

particularly surprising. This simply implies that the variance due to sampling depth is suffi ciently 

small that such a result is likely to occur.

We had previously shown that there were no consistent differences among the various sampling depths. 

Additionally, the human health studies that are the basis for recreational water criteria (Dufour, 1984; 

Cabelli, 1983) are based on water samples taken at a depth of 0.3 M from the surface. For these 

reasons, there is little reason for collecting samples at any other than the standard depth of 0.3 M. 

Thus, the variation in sampling depth is not a relevant consideration in recreational water sampling.

Variance among zones

We have divided the remaining spatial variation into two components, variation among zones (outward 

from the beach) and variance among locations within depth zone (parallel to the beachfront) for 

reasons mentioned earlier, mainly, that variation among zones was shown to be substantial and, to a 

large degree, predictable. The consistent differences in indicator levels among zones can be exploited 

by the technique of stratifi cation – sampling within each zone and then combining the individual zone 

means using a weighting scheme to account for their relative importance.

Variance among depth zones as given in Table 20, however, represents variation that would be 

encountered if one were to randomly select sampling locations (i.e., ankle-, knee-, chest-deep and 

locations) along a fi xed transect. Variance among zones is seen to have the largest component of 

spatial variation at all but Imperial Beach, a fact that is particularly evident when unique, pure factor 

variances are examined. At Imperial Beach, all components of spatial variation seem to result in 

virtually the same total variance, whether we look down through the water column, across the beach, 

or outwards from the beach.

This variance, though, is avoidable because of the consistent ordering of indicator levels, decreasing as 

one goes out from the shoreline from ankle-deep to chest-deep water. Besides the technique of sample 

stratifi cation, it seems reasonable that water of a particular depth be a separate population of study 

in itself, given that, as previously mentioned, epidemiological models for swimmers’ illnesses have 

relied on indicator values from waist- to chest-deep water. Additionally, contamination in shallow 

water is likely to affect different bather sub-populations.

Variance among locations within zone (among transects)

This leaves the variation within depth zone, or “transect” variance, to contend with. Variance among 

locations within the same depth zone in Table 20 represents an inescapable source of sampling variation. 

This source of variation must be considered in any sampling plan because rarely, if ever, would we 

be interested in the indicator level at a single point in the water. Even if we limit our sampling to one 

such location, the question remains, “How ‘representative’ is this of the water quality in general?”

We can use between locations variance to estimate how much we might expect a single sample taken 

in, say, knee-deep water to differ from the true mean for knee-deep water along that stretch of beach. 

Using a normal distribution model for log indicator density the half-width of the 95% confi dence 

interval is calculated as two times the standard deviation among locations by 2. At West Beach, for 
51

example, this gives a 95% confi dence interval of 2 x 0.294=0.588 logs. The interpretation is that 95% 

of the time the value from a single sample will be within 0.588 logs of the actual geometric mean 

density in knee-deep water. This is equivalent to a factor of nearly 4 (100.588=3.9), so that our 95% 

confi dence interval implies that the density of a single sample may range from about 1⁄4 of the true 

mean to 4 times the true mean value.

It may be more interesting to consider what kind of difference might be expected between single 

samples, such as two samples taken in knee-deep water but at somewhat different locations. At 

West Beach, we would expect the two samples to differ from one another by more than 0.28 

logs 50% of the time, based on the normal distribution. This means that if one relies on a single 

sample, half of the time a different sample would have given a result more than about twice 

(100.28=1.9) or less than half (1/1.9) the value.

Replication, sampling from several different locations, is the means of reducing the impact of this 

variance on the uncertainty of the sample estimate. If V represents the variance of single samples 

among locations, or transects, the variance of the mean of n samples taken from different locations 

within the same zone is V/n.

A valid concern is whether variance among sampling locations itself varies from one zone to another. 

In fact, this question may be asked of all sources of variation. On theoretical grounds, if these data 

are log-normally distributed, and this does appear to be at least a reasonable model, this implies 

proportionality between mean and standard deviation. Their logs (base 10 or any other base), then, 

will follow a normal distribution with constant variance. In particular, the variance, or, equivalently, 

standard deviation, within the zone will be the same value for each zone. When separate variances 

are computed for ankle, knee, and chest depth zones, as they were for Table 21, there is no evidence 

to refute that this is the case. This is found to be true for other factors of variation as well, even in 

the case of day-to-day variation where one may suppose that whatever environmental factors may 

affect this sort of variation, the magnitude of their effects close to shore may differ from that in deeper 

water.

Table 21. Standard deviation among 

locations (transects) within 

each separate depth zone.

Location 

Depth zone

Ankle Knee Chest

West Beach 0.329 0.275 0.270

Belle Isle 0.389 0.361 0.369 

Wollaston Beach 0.360 0.336 0.393 

Imperial Beach 0.410 0.423 0.402

Miami Beach Pk. 0.458 0.428 0.470
52

Temporal components of variation

Hourly variation

At least for the period from 9:00 a.m. to 6:00 p.m., we can determine the variance that takes place 

from hour to hour within a day. Variation on this time scale might be of interest if one were to collect 

samples at random times during the day in order to estimate some daily average.

In our case, however, it is interesting to compare the variance hour-by-hour with that on the larger 

day-to-day time scale. Despite this difference in time scale, the hourly variation is equal to the daily 

variation, or approximately so, at three of these beaches. At two of these beaches, Miami and Belle 

Isle, we had previously noted a pronounced tendency for indicator levels to drop between the early 

morning and mid-afternoon visits (specifi cally, between the normal visit times of 9:00 a.m. and 2:00 

p.m.). This may explain some of the apparent “excess variance” among hourly results at these two 

beaches, just as the drop off in indicator levels from shallow to deep water accounts for much of the 

inter-zone variance we saw earlier. While we could not discern a substantial decline between morning 

and afternoon at Imperial Beach, its hourly graph in Figure 11 does show a generally U-shaped curve, 

which may account for its relatively high hourly variance as well. We do note, also, that all of the 

variance components there, spatial and temporal, appear to be much more like one another than at any 

of the other beaches studied.

Variance among days

This source of variation refers to single samples that are collected at the same time of day at the same 

relative location in the water (e.g., along transect 1 in knee-deep water) at a depth of 0.3 M from the 

surface. This, in fact, is the variance referred to in the EPA criteria document [Dufour and Ballantine, 

1986] in relation to single sample limits in recommending “a one-sided confi dence limit ... based on a 

site specifi c standard deviation” (emphasis added). In the absence of such information, recommended 

log standard deviations are given – 0.4 for E. coli in freshwater and 0.7 for enterococci in marine water 

– which appear to be entirely reasonable based on the standard deviation results among days given in 

Table 20.

The total variance among days would also be used in assessing the precision of the log mean of 5 

samples over a thirty-day period, as recommended in the criteria document. Letting V represent the 

variance among days, the corresponding variance of the log mean is V/5, and we could construct 

confi dence intervals or upper bounds for the true mean. Here, the “true mean” refers to the actual log 

mean value at the same (relative) location in the water at the same time of day over the entire 30-day 

period.

Variance of the change over a 24-hour period

Current technology for monitoring recreational water quality results in a one-day lag between the 

time that the samples are collected and the time that results from these samples are known. Therefore, 

another source of temporal variability that we must be concerned about is that of the change in indicator 

levels that occur over approximately a 24-hour period. This variance component refl ects how good a 

prediction of today’s water quality based on yesterday’s samples will be.
53

That a prediction is being made implies that a model exists for making that prediction. The simplest, 

and probably most often used, such model is that of status quo - that there will be no change over 

the 24 hours. Lacking any other information, this would be as good a model as any. In this case, the 

variance of the error in our predictions is that of the raw change in log mean density, tomorrow’s log 

mean density minus today’s.

Earlier, in examining environmental and bather effects on indicator levels, we developed a linear 

regression for each EMPACT study beach that predicted what the log mean density will be 24 hours 

later based on various weather, tide, and bather density information along with the current day’s 

sample value (see Table 16). If these models are used in place of the status quo, the error variance for 

our predictions becomes the difference between the true log mean density and our predicted value.

These two variances are given in Table 22 for each of the EMPACT Study beaches. With remarkable 

consistency, the variance of predictions based on the regression models of Table 16 is about one-half 

that of the raw change (the “status quo” model). Variances for predictions based on the regression 

models are likely understated in Table 22, simply because of the amount of “data mining” that went 

into the development of these models, leaving plenty of opportunity for over-fi tting the regressions. 

Nevertheless, the benefi t of basing the assessment on information in addition to yesterday’s samples 

is apparent.

Table 22. Variance and standard deviation of 24-hour change 

in log10 indicator density and of 24-hour change in 

log10 indicator density when modeled as in Table 16.

Location

Raw change in mean 

log10 density

Modeled change in mean 

log10 density

Variance

Standard 

Deviation Variance

Standard 

Deviation

West Beach 0.397 0.631 0.201 0.448

Belle Isle 0.205 0.452 0.100 0.316

Wollaston Beach 0.423 0.651 0.213 0.462

Imperial Beach 0.195 0.442 0.108 0.329

Miami Beach Park 0.540 0.735 0.225 0.474
54

Designing a Beach Monitoring Program

The preceding sections have led us through an examination of the spatial, temporal, and environmental 

factors that infl uence recreational water quality to the description of potential sources of spatial and 

temporal variance and estimation of their respective magnitudes. The concept of a population as it 

relates to sampling, how it affects which variance components come into play, and the importance of 

the sampling distribution have been emphasized. These, together with what we know about human 

health effects, are all factors to be considered in developing an optimal sampling strategy.

A standard for systematically planning for the collection of environmental data have been established 

by the U.S. Environmental Protection Agency by its Data Quality Objectives (DQO) Process [U.S. 

EPA 2000b]. Implications from the EMPACT Beaches study with respect to monitoring recreational 

waters will be given in the context of this standard.

The DQO approach

The DQO Process [U.S. EPA 2000b] addresses the requirements for systematic planning to “ensure 

that data collected for the characterization of environmental processes and conditions are of the 

appropriate type and quality for their intended use ...” enumerating seven steps to be taken in planning 

for data collection projects that support environmental decision-making. These seven steps are shown 

in Figure 15. The reader is encouraged to refer to the U.S. EPA DQO Guidance document, which 

presents in a readable fashion a formal framework for planning any environmental sampling program, 

and can be downloaded from the Internet at http://www.epa.gov/quality1/qs-docs/g4-fi nal.pdf.

 Figure 15. The Data Quality Objectives Process (from “Guidance for the 

Data Quality Objectives Process”, U.S.EPA [2000b])

Step 1. State the Problem

Defi ne the problem; identify the planning team; examine budget, 

schedule.

Step 2. Identify the Decision

State decision; identify study question; defi ne alternative actions.

Step 3. Identify the Inputs to the Decision

Identify information needed for the decision (information sources, 

basis for Action Level, sampling/analysis method).

Step 4. Defi ne the Boundaries of the Study

Specify sample characteristics; defi ne spatial/temporal limits and 

units of decision-making.

Step 5. Develop a Decision Rule

Defi ne statistical parameters (mean, median); specify Action Level; 

develop logic for action

Step 6. Specify Tolerable Limits on Decision Errors

Set acceptable limits for decision errors relative to consequences 

(health effects, costs).

Step 7. Optimize the Design for Obtaining Data

Select resource-effective sampling and analysis plan that meets the 

performance criteria.
55

Results from the EMPACT Beaches Study will be related primarily to steps 4 and 7 of the DQO Process. 

Step 6 will be discussed in some detail in order to present concepts that are useful in understanding the 

rationale behind sample size determination. Some brief comments on the remaining steps are:

 State the problem. Fecal contamination at a recreational beach poses a threat to human health 

and because of this, water quality must be monitored. Questions to be answered at a local 

level are: Who is to be involved in the monitoring program? What is our budget? What is the 

timeframe for developing the program?

 Identify the decision. At a minimum, results from monitoring will lead to the decision to 

close the beach or not, depending on whether contamination is found to be at an unacceptable 

level. Additional actions may be identifi ed, for example, public posting of microbial counts 

or posting a warning when contamination levels are in a questionable range.

 Identify the inputs to the decision. The very purpose for conducting the EMPACT Beaches 

Study itself was to provide this input. Other studies on sampling recreational beaches have 

been published [Brenniman et al., 1981; Cheung et al., 1990; Churchland and Kan, 1982; 

Noble et al., 2000; Pande et al., 1983; Van Ess and Harding, 1999]. The World Health 

Organization (WHO) has published a series of guidelines for beach monitoring [1975, 1977, 

1998]. A good starting point for Internet resources is the U.S. EPA’s Beach Watch website at 

http://www.epa.gov/OST/beaches/. Other resources may be available locally.

 Develop a decision rule. Examples of decision rules are given in current EPA guidelines 

[Dufour and Ballentine, 1986; U.S. EPA, 1986] and are based on limits of acceptable illness 

rates among swimmers of 8 per 1000 in freshwater and 19 per 1000 in marine waters. Beach 

monitoring programs using federal grants authorized by the BEACH Act must use the water 

quality standards (decision rules) adopted by the state [U.S. EPA, 2004].

Defi ning the boundaries of the study: the population

The concept of a population in its statistical sense was discussed earlier in the section on sources of 

variation. We defi ned the term “population” as “the aggregate from which samples are collected and 

to which inferences and, ultimately, decisions are made.” The phrase “defi ne the boundaries of the 

study” tells us to identify this population in detail. What should the target population, the body of 

water, be in terms of sampling depth, distance from shore, distance along the beachfront, and time?

Sampling depth

We have used 0.3 meters from the surface as the standard depth at which to collect water samples in 

water that is of swimming depth [APHA, 1998]. Sampling at this depth, at which a swimmer is likely 

to be exposed to pollution, is recommended in the WHO approach to monitoring [1998] and was 

the depth used for microbial sampling in the U.S. EPA epidemiological studies [Cabelli et al., 1982; 

Dufour, 1984], upon which United States recreational water quality standards have been based.

While this study found little in the way of systematic differences among samples collected at different 

depths, this does not mean that there may not be meaningful differences at other beaches. Regardless, 

sampling from different depths below the surface would seem to introduce an additional component 

of variance, unnecessary in light of the lack of interpretability in regard to human health for sample 

results that come from depths other than 0.3 meters from the surface.
56

Distance from shore (Depth zone)

This study has demonstrated that the depth zone from which samples are to be collected will likely be 

a critical decision to be made in a beach sampling plan. At all of the study beaches, indicator levels 

were seen to fall off substantially as one goes from ankle-deep to chest-deep water, to such a degree 

that the likelihood that a beach met current U.S. EPA guidelines (1986) at any point in time was highly 

dependent upon the depth zone from which samples were taken.

Depth zones in a bathing area can be associated with particular usage patterns and segments of the 

human population that are likely to be affected by the water quality in that zone. Infants and toddlers, 

given their activities at the beach, are most likely to ingest water in the “ankle zone” as defi ned by this 

study. For adults, exposure to contamination from immersing one’s head in water seems most likely 

to occur in waist-deep or deeper water, given that substantial swimming activity probably does not 

occur until one reaches this depth. It is advisable that a sampling plan account for these differences in 

the affected population, and be capable of yielding separate estimates of indicator density for shallow 

water and water of swimming depth.

Epidemiological studies have concentrated on adults, and have measured indicator densities in water 

of swimming depth. U.S. EPA guidelines for beach water quality (1986) are based on these studies, 

and, thus, on fecal contamination levels in deeper waters. Unfortunately, epidemiological data that 

would enable quantitative evaluations of the risks inherent to infants and toddlers with respect to 

exposure to sewage-contaminated water are not available.

Distance along the beachfront

We defi ne the beach itself in setting the boundaries for this fi nal spatial dimension, the shoreline 

to be encompassed by a monitoring program. This expanse comprises the beach with regard to 

which decisions will be made. One will need to determine areas that may be exposed to pollution, as 

determined by the locations of point sources on the shore or in the water. Conversely, other areas may 

be shielded from contamination. Usage is another consideration. Where do bathers tend to congregate 

and when? What areas are used primarily by surfers or by swimmers? Answers to these questions 

can help to defi ne unique recreational areas of the beach. In some cases, political boundaries or the 

authority responsible for managing the beach may come into play in determining what constitutes 

a beach. Public perception of the beach area will need to be considered, regardless of the offi cially 

recognized boundaries of the beach. Those responsible for communicating the quality of recreational 

waters to the public, along with reporting the results of the day’s sample, must unambiguously state 

the area of the beach to which the results apply, that area decided upon in this phase of the design 

process.

The World Health Organization, in its recommendations for beach monitoring [1998], addresses 

the issue of defi ning a beachfront for sampling purposes through its “primary microbiological 

categorization protocol”. This protocol entails a sanitary survey to determine sources of contamination 

and a preliminary sampling phase to determine if “signifi cant variation” along the beach is indicated. 

The term “signifi cant variation”, as used in the WHO report, connotes systematic variation in which 

a section of the beach is consistently more, or less, contaminated than other sections of the same 

beach. We have found “signifi cant variation” to exist at each of the fi ve study beaches in the statistical 

meaning of this term, mainly that there is a between-locations variance component, over and above 

the variance we see from replicate sampling at the same location in the water. This variation, however, 
57

is not systematic, as seen from the lack of any apparent consistent differences among transects (with 

possible exceptions at Belle Isle and Miami Beach Park).

The length of shoreline that one decides upon to defi ne the monitoring area may itself affect the 

magnitude of the variance encountered in the process of sampling. Sampling variances shown in 

Table 20 apply to the forty-meter, centrally located expanses of beach that comprised the sampling 

area at each of the study beaches. If sampling had encompassed larger sections of the beaches, these 

variances would likely be higher. This is so because values obtained from two points separated by 

a relatively large distance are likely to be less correlated than values obtained from two points that 

are closer together. The effect can be illustrated by considering only those points along transects 1 

and 3, the two extreme transects, in our variance calculation, yielding a variance between sampling 

locations that are separated by 40 meters. Variances computed from all the data, as they are in Table 

20, refl ect an average separation of 26.7 meters (40 m separation for one pair of points, and 20 m for 

each of the two other pairs). In addition, “pure error” variance is available, refl ecting zero separation 

between sampling points (replicate samples from the same location). Respective variances calculated 

for average separations of 0, 26.7, and 40 meters are plotted in Figure 16, and joined by a smooth 

curve to show hypothetical relationships 

Figure 16. Variance of log10 indicator density per 100 mL vs. average separation 

among sampling locations.
58

between average distance separating the sampling locations and the corresponding sampling variance. 

Stratifying the beach along shoreline segments is a potential counter to this trend, as discussed later, 

in the section “Optimize the design for obtaining data.”

Time

A geometric mean calculated from fi ve values over a four-week period did not accurately represent 

actual conditions on any given day at any of our fi ve study beaches. Figure 8 in the section on 

temporal variation clearly illustrates this fact. A point-in-time estimate of indicator levels is needed.

The water quality measurement from which decisions will be made should be the contaminant level in 

the swimming area at a time when beachgoers will be exposed, and, unfortunately, current membrane 

fi ltration and culture methods do not allow us to obtain the sample results any earlier than about 24 

hours after the samples have been collected. A scenario was introduced earlier, in which the beach 

manager sampled on a Tuesday in order to make decisions for the next weekend. Results from a 

Tuesday sample were shown to have little bearing on conditions that exist the following Saturday. 

Correlations between indicator levels on one day and those four days later (see Table 10) were seen to 

be negligible, while serial correlations for a one-day lag were, if not impressive, at least positive.

Collecting samples the day before one must make a decision with regard to public safety at a beach 

may not be convenient, but it appears that data obtained earlier than this may have little or no relevance 

to such a decision.

The time of day when sampling is performed is also likely to be governed by practical considerations 

- one would prefer to collect samples in the morning in order to assure ample time for transporting the 

samples to the lab and for the labs to process the samples and start incubation. In addition, the earlier 

the sampling time, the more timely the results from the analysis. This study has demonstrated that, 

for the fi ve beaches studied, contamination levels in the afternoon were, if anything, likely to be lower 

than in the morning. Thus, morning sampling would tend to err on the safe side.

To summarize, this study indicates appropriate spatial and temporal boundaries for beach 

sampling to be:

 0.3 M from the surface

 in water of swimming depth

 along a pre-determined beachfront

 in the morning

 of the day before

Monitoring in shallow (ankle-deep) water may be performed as an adjunct to, and viewed 

separately from, monitoring in deeper waters, although results with respect to children’s health 

effects may be diffi cult to interpret without further health studies

Specifying tolerable limits on decision errors

The U.S. EPA’s DQO guidance document [EPA, 2000b] uses the concept of a power curve to defi ne 

tolerable limits on decision errors. In our case, a power curve gives the probability of rejecting a 

beach as unfi t for bathing as a function of the true (log) indicator level at that beach. This probability 

will be the complement of what is commonly known as the “Type II” or “” (beta) error in those cases 

in which the true indicator level exceeds a given standard but a sample fails to detect this exceedence, 
59

and equal to the “Type I” or “α” (alpha) error when the true indicator level falls below this standard. 

We may also view this in terms of acceptance sampling(see box), in which the beach is considered a 

product that we wish to accept or reject as suitable for use.

For either the power function or the operating characteristics curve, it is necessary and suffi cient to 

specify two points on that curve, the shape of the curve being given by the normal (usually) probability 

density function. The DQO guidance document illustrates this by showing a true value equal to the 

“action level” for the decision variable and another true value equal to an upper limit specifi ed by 

the user. Figure 18 emphasizes two true density levels that determine the producer and consumer 

points.

Meaningful producer and consumer points or action levels can be determined based on the relationship 

between implied risk and indicator level. Health studies conducted by the EPA give these relationships 

in terms of extra cases of “highly credible gastrointestinal illness” (HCGI) per 1000 swimmers as

-11.9 + 9.5·log10(E.coli per 100 mL) (2)

in freshwater [Dufour, 1984], and

0.1+ 12.3·log10(enterococci per 100 mL) (3)

in marine water [Cabelli, 1983]. At EPA recommended limits for the 30-day geometric mean, 126 per 

100 mL for E. coli and 35 per 100 mL for enterococci in marine water, the implied illness rates are 

about 8 and 19 per thousand swimmers, respectively.

As an example to be used for sample size estimation in the following section, “Optimizing the design 

for obtaining data”, consider the freshwater case and assume that we would desire a low probability 

of accepting a beach as safe for swimming if the swimming-related illness (HCGI) rate is 10 per 1000 

or higher. Somewhat arbitrarily, based on custom more than anything else, we set this probability 

at 0.05 (5%), and this represents our consumer’s point, as in Figure 18. Conversely, should the 

swimming-related illness rate be 6 per 1000 or less, we consider this to be an acceptable risk, and 

want a high probability of accepting this beach, i.e., declaring it to be suitable for swimming. We set 

this probability at 0.95 (again, based on a commonly accepted value for what we mean by a “high 

probability”), to obtain the producer’s point in Figure 18.

Equation 2 can be used to determine the values of the log10 E. coli density per 100 mL that correspond 

to each of these decision points. An incidence of 6 cases of HCGI per 1000 is seen to correspond to 

about 1.9 logs, and of 10 cases per 100, to 2.3 logs. Whenever the beta risk at the consumer’s point 

is equal to the complement of the alpha risk at the producer’s point, the action level will lie exactly 

halfway between the two corresponding illness rates, or log densities for the indicator organisms. These 

decision points are centered about an illness rate of 8 per 1000, corresponding to 2.1 log density per 

100 mL, the current EPA-recommended action level for a geometric mean over time (log10126=2.1).

This is not to be construed to advocate the retention of current EPA recommendations, which, after 

all, apply to a geometric mean over 30 days (or to single samples). The EPA recommended action 

level simply offers a convenience reference point for this presentation of a rationale for determining 

an appropriate action level based on the acceptance sampling concepts of consumer and producer’s 

points and an operating characteristics curve. Indeed, as far as sample size requirements are concerned, 
60

what is important is the width of the interval between the log10 indicator values at the producer and 

consumer’s points (the tolerance interval). In our case, this width is 0.4 logs, or +/- 0.2 logs with 

respect to the action level (the half-width of the tolerance interval). A different action level may be 

selected, but as long as our decision points remain +/- 0.2 logs from this value (corresponding to +/- 

2 illnesses per 1000 swimmers in fresh water), the operating characteristics of the sampling plan, as 

exemplifi ed by the curve in Figure 18, do not change.

 Figure 17. Correspondence between health effects criteria and indicator density.

A rationale for setting tolerance intervals

We may choose a tolerance interval to be as narrow as we wish. The narrower this interval is, that 

is, the closer the producer and consumer points are to each other, the more precise our sampling plan 

becomes, and the better we are able to “pinpoint” the condition of the beach.

Is there a point at which increased precision, and the associated expense, is wasted? The ultimate 

purpose of sampling is to determine if a beach is safe for recreational use. Measurements of indicator 

organisms help to make this determination through what we know about their relationship to human 

health, as given in Equations 2 and 3. Thus, uncertainty in water quality assessment should be viewed 

not only in terms of sampling precision, but also in terms of the precision of our knowledge of health 

effects.

The +/-0.2 log tolerance interval that we have described corresponds to a 90% confi dence interval for 

the estimated mean log density, because of the 5% tail regions at each end of the interval. This spread 

for log densities was shown to be equivalent to +/-2 HCGI cases per 1000 swimmers. Available data 

from the freshwater health studies [Dufour, 1984] indicate a 90% confi dence interval for the expected 

health effect of about +/-4 HCGI cases per 1000 swimmers at 126 E. coli per 100 mL (this will be 
61

dependent to a degree on the actual indicator density). Thus, the uncertainty due the estimated density 

is substantially less than the uncertainty in its health effect, at least based on the EPA studies alone.

In fact, the square of the total uncertainty will be equal to the sum of the squares of the individual 

components, leading to the conclusion that the total uncertainty will increase by only 12%, from 

4 to 4.5, when the sampling error alone is equivalent to +/-2 illnesses. For marine waters [Cabelli, 

1983], the 90% confi dence interval for the expected illness rate is about +/- 3 HCGI cases per 1000 

at 35 enterococci per 100 mL. In this case, a sampling error equivalent to +/-2 illnesses per 1000 

contributes about 20% over the uncertainty in the health effect itself.

Another component of uncertainty in recreational water quality assessment unfortunately comes into 

play when we consider the 24 hour lag in information from a membrane fi ltration assay. Using 

ancillary data collected at the study beaches, we were able to achieve a meaningful reduction in the 

standard deviation of the change in indicator density (Table 22). However, the residual standard 

deviation, which represents the uncertainty in our ability to project today’s values based on what they 

were yesterday, is still on the order 0.4 logs. This is equivalent to +/- 6 illnesses per 1000 swimmers for 

a 90% confi dence interval, larger than even the uncertainty in the health effect itself, and underscores 

the need for refi ned predictive models and rapid methods for assessing water quality.

Optimizing the design for obtaining data

We have described appropriate spatial and temporal boundaries to encompass sampling from within 

a single depth zone (say knee- to chest-deep water), at a point in time (the morning before), from the 

same depth below the surface (0.3 M). The only difference among samples, then, is the locations 

(transects) along the beachfront from which they have been collected. The appropriate sampling 

variance for such a design is given by “total variance between locations” in Table 20 as experienced 

in each of the individual EMPACT study beaches.

One possible specifi cation for tolerance requirements of a sampling was given in the previous section, 

mainly, that the sampling plan should be capable of correctly classifying the beach 95% of the time 

when the true mean indicator density at the beach is 0.2 logs removed in either direction from our 

action level. This was derived from a consideration of the implied health effects at these indicator 

densities specifi cally for a freshwater beach, where +/-0.2 logs is equivalent to +/-2 illnesses (HCGI) 

per 1000 swimmers. In the case of marine beaches, a 0.2 log increase in indicator (enterococci) 

density has a somewhat greater predicted effect on illness due to exposure, being equivalent to an 

increase of 2.5 illnesses per 1000 swimmers per Equation 3. However, rather than basing freshwater 

and marine designs on equivalent illness rates, we will use the +/-0.2 log range for each so that each 

has the same precision with respect to the decision variable itself. In practice, one might choose to 

consider the same marginal illness rates for each type of beach, or, perhaps, choose a wider interval 

for marine beaches, given that their expected illness rate is more than twice that of freshwater beaches 

at existing recommended indicator levels.

Sample sizes in Table 23, the number of samples to be collected in a single visit, are based on the 

respective sampling variances within depth zone at each of the study beaches using the tolerance 

requirements of a 95% probability for correctly identifying +/-0.2 log deviations from the action 

level. In addition, we show sample size requirements for +/-0.3 log deviations (equivalent to a health 

effect of about 3 illnesses per 1000 swimmers in freshwater and 3.7 illnesses per 1000 swimmers at 

marine beaches). Note that, because the tolerance interval is expressed in terms of a log scale, the 

effect is that, in terms of the raw indicator densities, the lower and upper limits of this interval will 
62

be a constant factor of the action level. For instance, 0.2 logs over the action level is about 1.6 times 

the action level and the log action level -0.2 logs is about 1/1.6, or about 0.6, times the action level. 

Likewise, +0.3 logs and -0.3 logs from the log of the action level are equivalent to twice and one-half 

the action level, respectively.

Any given beach, after a routine monitoring program has been in place for some time, will have data 

approaching the quality we have from this study upon which to base a sampling program. At the 

outset, one necessarily will have to make assumptions about sampling variances. Results from the 

EMPACT studies may serve as a guideline to some provisional estimate of the appropriate sampling 

variances, but these provisional estimates will soon be superseded by experience. Because monitoring 

will be an ongoing process, once data is obtained this serves as a feedback to further data obtainment. 

The feedback addresses earlier steps in the DQO process as well, for example, defi ning the boundaries 

of the monitoring program, which may change as heretofore-unknown “hot spots” are discovered.

Table 23. Sample size requirements based on 

estimated overall sampling variance for the 

geometric mean within a single depth zone 

in the water.

Location

Sample size required for a 

95% tolerance limits of:

+/-0.2 logs1 +/-0.3 logs1

West Beach 6 3

Belle Isle 9 4

Wollaston Beach 9 4

Imperial Beach 11 5

Miami Beach Park 14 6

1

 Specifi es a range centered on the action level such that 

there is a 95% probability of accepting the beach as safe for 

swimming when the true log mean indicator density per 100 

mL is at the lower end of the range and a 95% probability of 

rejecting the beach when the true log mean indicator density 

is at the upper end of the range.

Because estimates of spatial variance are critical to evaluating precision and, subsequently, determining 

sample size requirements, samples should be analyzed individually during the initial phases of a 

monitoring program so that microbial density can be established for each location in the water from 

which a sample was collected. This procedure should be followed at least until enough samples have 

been collected over a number of days to enable a reliable estimate of the underlying variances. After 

that, one may consider compositing samples prior to analysis (see the box on composite sampling), 

with the benefi t of potential cost savings. Even so, whole samples should be assayed periodically in 
63

order to monitor and update sampling variances.

Sample size requirements, when individual samples are assayed, may be calculated using the same 

formula as was used to create Table 23. The sample size, n, required is given by

Here, V is the variance within the zone, Δx is the half-width of the desired tolerance interval for log10

indicator density per 100 mL, and z0.05 represents the upper 5th percentile of the standard normal 

distribution (=1.645). Again, the value of V will be a rough estimate at fi rst, perhaps based on these 

EMPACT beach study results. As more data are collected, a more appropriate value for V will be 

obtained.

Given the common practice of collecting a single water sample at the beach, we are interested in 

knowing the sampling properties of a sample size of one. In this case, the only estimate of spatial 

variance would necessarily come from prior knowledge, since at least two samples are required 

in order to derive a variance estimate. Corresponding tolerance intervals for a sample size of 

one are shown for each of the study beaches are shown in Table 24, based on their respective 

variances within depth zone. The effects of more intensive sampling are illustrated by considering 

the width of this tolerance interval as the sample size increases. Log indicator density tolerance 

intervals are translated into equivalent health effect tolerances in the second part of Table 24 

based on the relationships between incidence of HCGI among swimmers and indicator organism 

density given in Equations 2 and 3.

 

Table 24. Width of tolerance intervals for various 

sample sizes based on sample variances 

within depth zone at the study beaches.

Location

Width of tolerance interval in log10 indicator 

density per 100 mL for sample size =

1 2 4 8 16

West Beach +/- 0.45 +/- 0.32 +/- 0.22 +/- 0.16 +/- 0.11

Belle Isle 0.60 0.42 0.30 0.21 0.15

Wollaston Beach 0.60 0.42 0.30 0.21 0.15

Imperial Beach 0.68 0.48 0.34 0.24 0.17

Miami Beach Park 0.74 0.52 0.37 0.26 0.18

Location Width of tolerance interval in terms of equivalent 

health effect (cases of HCGI per 1000 swimmers) 

for sample size =

1 2 4 8 16

West Beach +/- 4.3 +/- 3.0 +/- 2.1 +/- 1.5 +/- 1.1

Belle Isle 5.7 4.0 2.9 2.0 1.4

Wollaston Beach 7.4 5.2 3.7 2.6 1.8

Imperial Beach 8.3 5.9 4.2 3.0 2.1

Miami Beach Park 9.1 6.4 4.5 3.2 2.3
64

Composite sampling, while reducing analysis costs, will necessitate collecting additional samples 

beyond the requirements of Equation 4 in order to achieve the same precision in terms of a fi xed 

tolerance interval. There also must be consideration of the fact that a composite sample yields an 

estimate of an arithmetic mean rather than a geometric mean (the geometric mean being the antilog of 

the log mean which we have used thus far in describing sampling strategy). See the boxed discussion 

on composite sampling and its effects on sample size requirements and equivalent action levels.

Stratifi cation along the shoreline

Study areas limited to a beachfront of forty meters resulted in variances among locations within depth 

zone as shown in Table 20. In practice, the shoreline comprising a beach may be much longer than 

this, and division of the beach into “shoreline strata” may be indicated in order to maintain variance 

within each such stratum at levels comparable to those given in Table 20. Stratifi cation along the 

shoreline may be based on a priori considerations, for example, the locations of point sources of 

pollution into the beach area or of physical barriers that may serve to isolate an area of the beach 

from contamination. Stratifi cation also may be decided upon as a result of continued sampling that 

reveals systematic differences between different sections of beachfront. In any event, strata need not 

be contiguous - an area affected by drainage may comprise one stratum while the expanses of beach 

on each side together comprise another single stratum.

Table 21 shows there to be no substantial differences among standard deviations within different depth 

zones. Because these standard deviations pertain to log densities, this tells us that the coeffi cient of 

variation, or “percent standard deviation,” is roughly the same for each zone. Assuming that the same 

holds true for shoreline strata, one would substitute a common (log) variance for V in Equation 4 in 

calculating the total sample size requirement. The total sample size would then be allocated among 

the various shoreline strata in proportion to the total length of each respective shoreline. If composite 

sampling is to be used, only samples collected from the same stratum (i.e., segment of shoreline) 

should be composited, and the results from different strata combined via a weighted geometric mean 

(antilog of the weighted mean of log densities), the weights being the proportion of beach represented 

by each stratum.

Large systematic differences may warrant special consideration. Depending on the magnitude of 

the difference, one may want to limit sampling to known “problem areas.” For example, in the 

knee-deep zone at Belle Isle, densities between transects 2 and 3 were observed to be over twice 

that of transects 1. If this holds true for waist-deep water as well, we would limit sampling to 

the area within transects 2 and 3. Cut this difference by one-half, and we would be inclined to 

combine all three transects.
65

Acceptance sampling

EPA’s guidance document on the DQO process discusses the decision process, and 

decision errors in particular, in terms of a “decision performance curve”, which describes 

the probability of deciding that the decision parameter exceeds some allowable level based 

on a sample given the true value of that parameter. Similar in concept is the operating 

characteristics (OC) curve, an example of which is shown in Figure 18.

Figure 18. Operating characteristics curves

For every possible value that the true geometric mean indicator density at a beach might be (on the 

horizontal axis), the OC curve indicates the probability of not declaring beach to be unacceptable 

(the vertical axis) based on a sample result. The producer’s point and the consumer’s point, 

as labeled on the OC curve, are concepts of acceptance sampling, a statistical quality control 

technique used in industry to accept or reject a lot (batch) of some product based on a sample. The 

consumer’s point specifi es the probability of accepting a “bad” lot, and the producer’s point, the 

probability of accepting a “good” lot. Usually, “good” and “bad” are defi ned in terms of percent 

defective. When this percent is truly some specifi c, acceptably low value, we want the probability 

of acceptance to be high (commonly, 95%), thus specifying the producer’s point. Conversely, for 

some unacceptably high value for percent defectives, we want the probability of acceptance to 

be low (e.g., 5%), giving the consumer’s point. The producer’s risk, corresponding to the Type I 

() error, is 100% minus the probability of acceptance at the producer’s point, and the consumer’s 

risk, the Type II or  error, is the probability of acceptance at the consumer’s point.
66

Composite Sampling, Part I

Composite sampling is a commonly used technique in environmental monitoring [Lancaster and KellerMcNulty, 1998] and may be a cost-effective practice for monitoring recreational water quality. For our 

purposes, we will defi ne composite sampling as follows.

Composite sampling involves thoroughly mixing together equal volumes from various samples collected 

from different locations in the water and subsequently assaying a subsample of the resulting mixture. 

For example, ten 100 mL samples are combined and mixed, and a single 100 mL aliquot of this 1 L 

mixture is selected for analysis. Two or more composites may be formed from a like number of distinct 

sets of samples, such as those drawn from knee-deep and those drawn from chest-deep waters and 

combined to create knee-deep and chest-deep composites.

However, an indicator density obtained from a composite sample differs in a fundamental way from the 

geometric mean of the individual samples; namely, a composite sample result will almost always be higher. 

This is purely a mathematical artifact arising from the fact that, for any series of non-negative numbers, the 

geometric mean is always less than the arithmetic mean (unless all the values are identical). Consider the 

following hypothetical counts obtained from fi ve 100 mL samples:

11, 24, 68, 56, 16

The geometric mean of this series is 27.6. If, instead, these samples had been combined and a single 100 

mL of the resulting composite assayed, the expected count would the arithmetic mean of this series, 35. 

Of course, because of additional sampling variation introduced by subsampling, the actual count may be 

greater or less than 35; however, there is a 90% probability that the count will be greater than the geometric 

mean, 27.6 (we know this from the Poisson distribution, which describes the distribution of possible counts 

from “well-mixed” samples).

The use of the geometric mean is based on well-founded principles, as stated elsewhere in this report. There 

is, however, a correspondence between geometric and arithmetic means that results if densities among the 

original samples follow a lognormal distribution, and we have shown that our data is reasonably described 

by such a distribution. Given lognormal data, a geometric mean estimates the median of those data (actually, 

the geometric mean is biased on the high side, but this bias becomes negligible as the sample size increases). 

The median of a lognormal distribution is related to its mean by:

 

Here, V is the variance of the log10 densities, as in Table 20 for example. Multiplying the count per 100 mL 

obtained from a composite sample by the factor 10 -1.15V yields an estimate that is approximately equivalent 

to that of the geometric mean of the individual samples. Alternatively, one could use the inverse relationship 

to express a mean in terms of the corresponding median, and infl ate the decision level for the indicator 

density accordingly. In that case, the equivalent decision level for a composite sample mean becomes 35 x 

10 1.15V enterococci or 126 x 10 1.15V E. coli per 100 mL.

Note that the preceding assumes we know the value of V. We also need to know this variance in order to 

properly evaluate precision of the composite sample estimate, as discussed in Composite Sampling Part 

II. The appropriate value for V can be known only from suffi cient historical results based on assays of 

individual samples. We recommend that this variance estimate be based on individual analyses of at least 

50 samples (from each depth zone when multiple zones are sampled); this precludes composite sampling 

during an initial start-up phase of a monitoring program. More samples may be required for an adequate 

estimate of V if the sampling variance is greater than about 0.3 for the log10 densities. Additionally, assays 

of individual samples should be performed periodically, on the order of every 2-4 weeks, thereafter in order 

to verify and update this variance estimate.
67

Composite Sampling, Part II

Having addressed the problem of non-equivalence between geometric means and arithmetic means, we 

must face another problem inherent in composite sampling. As briefl y mentioned in Part I, subsampling 

from a composite adds another layer of estimation; a single aliquot is used to estimate the indicator 

density over all samples, which, in turn, are used to estimate the indicator level at the entire beach. The 

extra step in the estimation process, naturally, adds additional sampling error to the fi nal estimate. This 

may be illustrated using the example in Part I; the expected value of the composite count is 35, which is 

the average of the individual counts, but, 95% of the time, will range between 23 and 47.

However, what about collecting more samples than we otherwise would have and then compositing these 

samples? Say, in the above example, we collect ten samples instead of fi ve and take a 100 mL composite 

from these ten samples. Certainly, ten samples are superior to fi ve, and this may offset the additional 

uncertainty of subsampling from a composite.

In order to evaluate sampling errors resulting from compositing samples compared to that of complete 

analysis, simulation studies were performed under the assumptions that (1) individual 100 mL samples 

follow a lognormal distribution with known variance of log densities, and (2) samples are composited 

and well-mixed so that the number of CFU captured in a 100 mL aliquot follows a Poisson distribution. 

Conclusions from this, in terms of sample size requirements with and without composite sampling, are 

shown below. Note that the additional sampling required when compositing is utilized increases rapidly 

when variance exceeds about 0.20 or so – another reason for stratifying the beach front into relatively 

homogeneous sections.

Table 25. Comparison of sample size requirements for equivalent

precision with and without compositing.

Sampling variance1

Number of samples to collect for equivalent precision

Individually

analyzed Composited

0.10 3 5

0.15 5 8

0.20 6 9

0.25 8 14

0.30 9 17

0.40 12 32

0.50 15 43

 1 Variance of log10(indicator density per 100 mL)
68

Summary

Several factors have been identifi ed in this study as correlates of microbial indicators in recreational 

water. These include:

• Spatial factors

o Zone – Indicator levels decreased the farther one goes from shore into deeper water 

(not to be confused with the depth from which a sample is taken, which was not found 

to be an important factor in this study)

o Distance along the shoreline (“transect”) – There were only minor systematic effects 

at two of the fi ve beaches that were monitored for this study.

• Temporal factors

o Morning to afternoon (9:00 a.m. to 2:00 p.m.) - Indicator levels generally decreased 

by the afternoon at three of the beaches (2 marine and one freshwater). Afternoon 

levels at the other freshwater beach tended to be lower on sunny days, but higher on 

overcast days. Only Imperial Beach in Southern California, where indicator densities 

were very low at all times, failed to show this effect.

o Fecal indicator levels were found to vary signifi cantly from day to day. There was a 

limited statistical relationship observed between levels on the sampling day and the 

following day at three out of the fi ve beaches studied.

• Environmental & bather factors

o Rain – Resulted in increased indicator levels at the four beaches where substantial 

rainfall occurred (there was very little rain at Imperial Beach). The relationship may 

be complicated; at West Beach, there was no apparent effect unless rainfall in the past 

days was considered, in contrast to the others, where rainfall in the past 24 hours was 

suffi cient.

o Wind – Associated with increased indicator levels when blowing onshore at three of 

the beaches. No effects were observed at Belle Isle, and Imperial Beach experienced 

too little variation, as its winds were constantly onshore.

o Cloud cover – Under mostly sunny conditions, both freshwater beaches tended to 

have lower indicator densities. This effect is in addition to its association with the 

morning to afternoon change at West Beach, mentioned above, since levels were 

lower on sunny mornings also. At Miami Beach Park, the estuarine beach, sunshine 

tended to enhance the decrease that was observed in the afternoon.

o Tides – Tidal effects on water quality were observed. Absolute water level, rather 

than the tide stage per se, was found to be a predictor of water quality, high water 

being associated with increased microbial counts at the two East Coast beaches (very 

much so at Miami Beach Park), and with lower counts at the West Coast beach.

o Temperature – Only Miami Beach Park yielded a relationship with air or water 

temperature. The tendency here was for counts to be lower with increased water 

temperature. While this may seem counterintuitive, this relationship does not 

necessarily imply causation, and may indicate the common infl uence of some 

unmeasured factor, such as deep-water currents, on both water temperature and 

indicator levels.

o Bather density – Lower bather density was associated with lower indicator density 

at two of the beaches, but higher density at another. However, relationship of bather 

density to microbial counts may be infl uenced by conditions that bring bathers to the 

beach (or keep them away) in the fi rst place.
69

Spatial and temporal components of variation have been identifi ed and estimated. These are:

• Spatial sources of variation

o Replicate variance (“Pure error”) – A factor at any level of analysis that represents the 

smallest attainable variation in sampling (standard deviation=0.235).

o Sampling depth – Adds to sampling variability, but is not a constraining factor, since 

all samples should be taken from the same depth below the surface.

o Variance between zones – Would add considerably to sampling variance if not 

accounted for in the design. This variability can be eliminated by restricting sampling 

to water of the same depth.

o Variance within zone (variance between transects) – The key component of variance 

for a point-in-time estimate. May be able to reduce this variance if the beach can be 

stratifi ed along its length into “hot” and “clean” regions.

• Temporal sources of variation

o Variance among days

 Equivalent to the standard deviation that is referred to in the EPA criteria 

document [Dufour and Ballentine, 1986] in its recommendations for singlesample limits.

 Would be the principal source of variability in a sample estimate over time 

for the same location at the beach each time, e.g. a 30-day geometric mean.

 Not a source of sampling variability for a point-in-time estimate, but must be 

considered when using such an estimate to project results to future days.

o Hourly variation – based on hourly sampling that was performed over several days at 

each beach, hour-to-hour variability was not much less than day-to-day variability.

The following points would be included in a protocol for sampling recreational waters for indicators 

of fecal contamination:

• Time and location of sampling must be carefully considered.

o Depth zones from which samples are collected are likely to have great effect on the 

resulting estimate of indicator density. Sampling in knee- to waist-deep water would 

seem to offer a reasonable, but still conservative, approach to estimating water quality, 

particularly given that health effects are based on quality of water at waist-depth or 

deeper.

o Sampling at 0.3 M below the surface is justifi ed based on exposure considerations. 

This study failed to discern differences at lower collection depths.

o Sampling in the morning will likely be a conservative practice, in addition to perhaps 

being a convenient time to sample.

o Sampling should be performed as close as practical to the day on which a decision is 

to be made regarding beach closure or advisement. Preferably this should be the day 

before, given current conditions of a one day turnaround for the results.

• A number of samples should be collected from different points in knee- to waist-deep water.

o Results from the EMPACT Beaches Study can be used as a guideline for the initial 

determination of sample size requirements. For the beaches in this study, sample 

sizes of from 3 to 6 would be adequate to allow for 95% certainty of detecting a 0.3 

log exceedence from the action level for the geometric mean, equivalent to a health 

risk of 3 to 3.5 cases of HCGI per 1000 swimmers.

o As data are gathered, the sampling plan should be refi ned and ultimately based on a 

variance estimate that is uniquely associated with the subject beach.
70

• “Hot spots” within the bathing area, which may be known a priori or discovered as a result of 

sampling, should be considered as separate strata for sampling purposes.

o These should be sampled independently and weighted appropriately in the fi nal 

result.

o If indicator density within the problem area is very different from that elsewhere, 

sampling should be limited to this area. A proposed rule-of-thumb is a two-fold 

difference.

o Lesser differences would warrant a combined, stratifi ed estimate, weighting the “hot 

spot” in proportion to its extent relative to the rest of the beachfront.

• Composite sampling may be used as a cost-effi cient technique, enabling better sample 

coverage at minimally increased cost.

o In the initial stages of a monitoring program, composite sampling should not be used 

in order to develop data that is necessary in estimating the appropriate sampling 

variance for a particular beach.

o A composite sample estimates an arithmetic mean, which would require adjustment 

in order to equate this to standards based on a geometric mean.

• If resources are available to collect the data necessary for developing a predictive model for 

the change in indicator density over a 24 hour period, this will likely result in much-improved 

assessment of water quality, given the 1-day lag in obtaining results from membrane fi ltration 

assays.
71

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