U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2006-5192

In cooperation with Ohio Water Development Authority, Ohio Lake Erie Office, 

Northeast Ohio Regional Sewer District, and Cuyahoga County Board of Health

Models for Predicting Recreational Water Quality at 

Lake Erie Beaches
COVER PHOTOGRAPH: Edgewater Park, Main Beach, looking east to downtown Cleveland, Ohio. (Photo by Ken Frame, 

 U.S. Geological Survey.)
Models for Predicting Recreational Water 

Quality at Lake Erie Beaches 

By Donna S. Francy, Robert A. Darner, and Erin E. Bertke 

In cooperation with Ohio Water Development Authority, Ohio Lake Erie Office, 

Northeast Ohio Regional Sewer District, and Cuyahoga County Board of Health

Scientific Investigations Report 2006-5192

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

P. Patrick Leahy, Acting Director

U.S. Geological Survey, Reston, Virginia: 2006

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Suggested citation:

Francy, D.S., Darner, R.A. and Bertke, E.E., 2006, Models for predicting recreational water quality at Lake Erie 

beaches: U.S. Geological Survey Scientific Investigations Report 2006-5192, 13 p.

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U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted material contained within this report.
iii

Contents

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

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

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

Data Collection......................................................................................................................................2

Quality Assurance and Quality Control .............................................................................................3

Data Analysis and Development and Testing of Predictive Models ............................................3

Relations Between Escherichia coli Concentrations and Environmental or 

Water-Quality Variables ..................................................................................................................4

Development and Validation of Beach-Specific Predictive Models.....................................................7

Determination of Model Output Values.............................................................................................7

Model Validation ...................................................................................................................................7

Future Work ..................................................................................................................................................10

Summary and Conclusions.........................................................................................................................11

Acknowledgments.......................................................................................................................................12

References Cited..........................................................................................................................................12

Figures

1. Map showing locations of the five Lake Erie beaches used for studies of 

predictive modeling......................................................................................................................2

2. Graphs showing Escherichia coli concentrations in water by wave height and 

24-hour wind direction, Villa Angela, 2004–2005 .....................................................................6

3. Graph showing establishment of the threshold probability for Huntington 

2000–2004 model ...........................................................................................................................9

Tables 

1. Summary statistics of Escherichia coli (E. coli) concentrations at five Lake Erie 

beaches, 2000–2005......................................................................................................................5

2. Pearson’s r correlations between log10 Escherichia coli (E. coli) concentrations 

and explanatory variables at five Lake Erie beaches, 2000–2005.........................................6

3. Variables and regression statistics for beach models ........................................................................8

4. Numbers of correct responses and the sensitivities and specificities of model 

responses with indicated thresholds and predicted Escherichia coli (E. coli)

concentrations compared to previous day’s E. coli concentrations 

(current method for assessing recreational water quality)...................................................9

5. Responses of the Huntington model 2000–2004 in 2005 and comparison to responses 

obtained with previous day’s Escherichia coli (E. coli) concentrations (current 

method for assessing recreational water quality)................................................................10
iv

Conversion Factors and Abbreviations

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

milliliter (mL) 0.06102 cubic inch (in3)

Bacteria concentrations are given as either Colony Forming Units per 100 milliliters (CFU/100 mL) 

or colonies per 100 milliliters (col/100 mL). 
Abstract

Data collected from four Lake Erie beaches during the 

recreational seasons of 2004–05 and from one Lake Erie beach 

during 2000–2005 were used to develop predictive models for 

recreational water quality by means of multiple linear regression. The best model for each beach was based on a unique 

combination of environmental and water-quality explanatory 

variables including turbidity, rainfall, wave height, water 

temperature, day of the year, wind direction, and lake level. 

Two types of outputs were produced from the models—the 

predicted Escherichia coli concentration and the probability 

that the bathing-water standard will be exceeded. The model 

for one of beaches, Huntington Reservation (Huntington), was 

validated in 2005. For 2005, the Huntington model yielded 

more correct responses and better predicted exceedance of the 

standard than did current methods for assessing recreational 

water quality, which are based on the previous day’s E. coli

concentration. Predictions based on the Huntington model 

have been available to the public through an Internet-based 

“nowcasting” system since May 30, 2006. The other beach 

models are being validated for the first time in 2006. The 

methods used in this study to develop and test predictive 

models can be applied at other similar coastal beaches. 

Introduction

Swim advisories or closings issued by beach managers 

in the United States are based on standards for concentrations 

of fecal-indicator bacteria, such as Escherichia coli (E. coli)

or enterococci. Concentrations may change between the time 

of sampling and the reporting of results (18–24 hours). For 

example, in Ohio, the current practice is to use results from the 

previous day’s E. coli to assess whether to post a recreational 

water-quality advisory (Ohio Department of Health, 2005). 

This time lag can lead to beach advisories and closures that 

cause unwarranted loss of valuable recreation access or to permit swimming when conditions present an unacceptable level 

of risk. Recognizing this problem and other inadequacies in 

beach monitoring, the U.S. Environmental Protection Agency 

(USEPA) initiated the Beaches Environmental Assessment, 

Closure, and Health (BEACH) Program to reduce the health 

risks for users of U.S. recreational waters (U.S. Environmental 

Protection Agency, 1999a). 

One goal of the USEPA BEACH Program is development 

of mathematical models for real-time forecasting. Real-time 

forecasting may help resolve the delayed notification problems 

inherent with the present approach to recreational monitoring. 

In cases where fecal contamination to a beach is point-source 

dominated, hydrodynamic mixing and transport models can 

be applied (U.S. Environmental Protection Agency, 1999b). 

At many Ohio beaches and elsewhere, however, nonpoint or 

unidentified sources dominate, and multiple linear regression 

(MLR) models may be more appropriate. MLR models typically make use of easily measured environmental and waterquality variables to estimate bacterial indicator concentrations 

or the probability of exceeding target concentrations. 

Models based on environmental and water-quality variables have been shown to be useful predictors of recreational 

water quality. They include advisory systems based on rainfall 

amounts (Ackerman and Weisberg, 2003; Hose and others, 

2005) or more complicated models that employ real-time sensors to measure several explanatory variables (Olyphant and 

others, 2003; Whitman, 2005; Olyphant and Pfister, 2005). 

Beach-specific models were previously developed for Ohio 

Lake Erie beaches using MLR techniques and 1 or 2 years of 

data (Francy and Darner, 2002; Francy and others, 2003). The 

explanatory variables included wave height, number of birds 

on the beach, lake-current direction, rainfall, turbidity, and 

wind direction and speed. 

The U.S. Geological Survey (USGS), in cooperation with 

Ohio Water Development Authority, Ohio Lake Erie Office, 

Northeast Ohio Regional Sewer District, and Cuyahoga 

County Board of Health, developed and tested MLR predictive 

models during a 2-year study. Data were collected to identify 

and compare the explanatory variables that best described 

E. coli concentrations at five Ohio Lake Erie beaches. This 

study was also done to compare the performance of predictive models to the current method for assessing recreational 

water quality and determine whether model results were good 

enough to be used for future public notifications. At Huntington Reservation, because of 6 years of data collection, investiModels for Predicting Recreational Water Quality at 

Lake Erie Beaches

By Donna S. Francy, Robert A. Darner, and Erin E. Bertke
gations were further along than at other beaches, so this model 

was assessed during an independent (validation) year. The best 

model for each beach was based on a unique combination of 

explanatory variables including wave height, antecedent rainfall, turbidity, lake level, water temperature, wind direction, 

and day of the year. Although the models performed better 

than the current method to assess recreational water quality, 

work is ongoing to improve their accuracies. 

Methods

Studies were done at five popular Ohio Lake Erie beaches 

(fig. 1). At the beaches studied, breakwaters and (or) groins 

restrict water circulation, and large populations of waterfowl 

frequent the swimming areas. At Lakeview, in Lorain, Ohio, 

the sources of fecal contamination are largely unknown, but 

bird excrement may be a major cause of the degradation of 

water quality. At Huntington Reservation (Huntington), in Bay 

Village, a western suburb of Cleveland, two outfalls discharge 

stormwater runoff from a parking lot into the lake, and a creek 

to the east of Huntington drains a heavily populated area. 

Potential sources of E. coli to Edgewater and Villa Angela, 

two urban beaches in Cleveland, are stormwater runoff and 

combined-sewer overflows. At Lakeshore, in the small city 

of Ashtabula, sources of fecal contamination may include 

septic-system and wastewater effluents and runoff from gravel 

parking lots. 

Data Collection 

Data collection included analysis of daily water samples 

for E. coli and measurement of explanatory variables for 

model development and testing. Data were collected during 

the recreational seasons (May through September) of 2004–

2005. At Huntington, data from past studies (2000–2003) also 

were included. At Edgewater and Villa Angela, samples were 

collected Monday through Friday; sampling at the other three 

beaches was done Monday through Thursday. Samples were 

collected between 8 and 11 a.m. in areas of the beach used for 

swimming where the water was 2 to 3 ft deep. All water-sample bottles were filled about 1 ft below the water surface using 

a grab-sampling technique (Myers and Wilde, 2003). Because 

of spatial variability of E. coli concentrations, samples were 

collected at two or three well-spaced sampling points at each 

beach. 

Figure 1. Locations of the five Lake Erie beaches used for studies of predictive modeling.

 Models for Predicting Recreational Water Quality at Lake Erie Beaches
Water samples were kept on ice until analyzed for 

concentrations of E. coli and turbidity locally by each agency 

within 6 hours of collection. Samples from Huntington were 

analyzed by use of the mTEC method (U.S. Environmental 

Protection Agency, 2000); samples from the other beaches 

were analyzed by use of the modified mTEC membrane-filtration method (U.S. Environmental Protection Agency, 2002). 

Turbidity was determined in water samples with laboratory 

turbidimeters. 

Data on explanatory variables were collected by field 

crews or compiled from a variety of sources. Upon arrival, 

field crews counted the number of birds on the beach, and they 

estimated wave-height categories at the time of sample collection. Wave heights were placed into categories based on minimum and maximum heights in each wave train: (1) 0 to 2 ft, 

(2) 1 to 3 ft, (3) 2 to 4 ft, and (4) 3 to 6 ft or greater. If there 

were only a few observations in category 4, categories 3 and 4 

were combined. Lake-level data were obtained from National 

Oceanic and Atmospheric Administration (NOAA) station in 

Fairport Harbor, Ohio, for Lakeshore (NOAA ID 9063053) 

and the station in Cleveland for the other four beaches (NOAA 

ID 9063053) (National Oceanic and Atmospheric Administration, 2005a). 

Rainfall and wind-direction data were compiled from the 

National Weather Service local climatology data stations at 

Hopkins International Airport for Huntington, Villa Angela, 

and Edgewater; from Lorain County Regional Airport for 

Lakeview; and from Ashtabula County Airport for Lakeshore (National Oceanic and Atmospheric Administration, 

2005b). “Rd-1” was the amount of rain, in inches, that fell in 

the 24-hour period (9 a.m. to 9 a.m.) preceding the morning 

sampling. Similarly, “Rd-2” and “Rd-3” were amounts of rain 

that fell in 24-hour periods 2 days and 3 days preceding the 

morning sampling, respectively. Additional rainfall variables 

were computed as follows:

Rainfall weighted 72 hours (Rw72) = 

(3* Rd-1 + 2* Rd-2 + Rd-3) 

Rainfall weighted 48 hours (Rw48) = (2* Rd-1 + Rd-2)

“Wind direction 24” was calculated by summing hourly 

wind vectors for the 24-hour period preceding sampling and 

determining the direction of the resultant vector. Wind directions were then placed into categories by examining patterns in 

plots of E. coli concentrations as a function of wind direction 

24; processes affecting E. coli were also considered to ensure 

that the wind direction 24 categories could reasonably be 

explained by physical processes. 

Quality Assurance and Quality Control

Because models are only as good as the data used to 

develop them, strict quality-assurance and quality-control 

(QA/QC) practices were implemented. Written protocols were 

distributed to all personnel. The USGS did several onsite 

QA/QC checks of procedures performed by field and laboratory personnel throughout the recreational season, and any 

needed corrective actions were immediately taken. Approximately 10 percent of E. coli samples were QC samples 

including split replicates, interagency replicates, field blanks, 

and positive control reference cultures, described elsewhere 

(Francy and others, 2005). For turbidity, duplicate aliquots 

were measured from the same bottle, and measurements that 

did not agree within 10 percent were repeated. Turbidity 

reference standards were sent to all laboratories. Results from 

QC samples were carefully monitored; retests were done and 

corrective measures were taken when needed. 

Data Analysis and Development and Testing of 

Predictive Models

A daily E. coli concentration was calculated by averaging 

results from multiple sampling points at each beach. Averages 

were used instead of medians so as not to downweight the 

influence of extreme measurements. Bacterial concentrations 

were log10 transformed before data analysis. Because, in previous studies (Francy and others, 2003), relations were shown 

to differ from year to year at the same beach, at least 2 years 

of data from each beach were examined and used for model 

development.

Statistical tests were done and plots were constructed 

to determine the strength of associations between E. coli 

and explanatory variables measured during the study. These 

included calculations of correlation coefficients and construction of scatterplots for continuous variables. Box plots were 

used to understand the distribution of E. coli concentrations 

as a function of categorical variables, such as wave height 

and wind direction. Analysis of variance (ANOVA) was used 

to determine the relations between categorical variables and 

E. coli concentrations. The Tukey-Kramer multiple comparison test was used to determine which groups differed from 

each other (Helsel and Hirsch, 2002, p. 198). 

Explanatory variables that showed significant relations to 

E. coli concentrations were used to produce a list of possible 

MLR models using the Mallows Cp test (Mallows, 1973). The 

MLR models were ordered so that the coefficient of determination (R2

) was maximized and the Mallows’ Cp statistic 

was minimized. The R2 of each model is the fraction of the 

variation in E. coli concentrations that can be explained by 

a combination of explanatory variables. The Cp statistic is a 

measure of the error in a model with a subset of explanatory 

variables, relative to the error in a model that incorporates all 

potential explanatory variables. Models with explanatory variables strongly related to each other (collinear), such as those 

with multiple rainfall variables, were omitted from the list. 

Models were then selected for further examination on the basis 

of the Mallows’ Cp ranking. Model statistics were examined 

and diagnostic tests were done to identify the model(s) for 

each beach that provided the best linear, unbiased estimator 

of E. coli concentrations (Helsel and Hirsch, 2002, p. 228). 

These included determination of parameter estimates, Cook’s 

Methods 
D values, partial residual plots, and residuals plots. Performing 

well on model diagnostic tests and having a set of explanatory 

variables that seemed reasonable and were relatively easy to 

collect were the criteria for choosing the “best” model for each 

beach. 

Two types of output were produced by the models. The 

first and obvious output was the predicted E. coli concentration. Because prediction intervals were shown to be fairly 

wide in earlier studies (Francy and Darner, 1998; Francy and 

others, 2003), a second output variable was developed in the 

hope of providing a more accurate prediction—the probability 

of exceeding the Ohio single-sample bathing water standard 

for E. coli of 235 colony-forming units per 100 milliliters 

(CFU/100 mL). The probability that the predicted value with 

n-p degrees of freedom was greater than 235 CFU/100 mL 

was computed as prob (t>x), where x = (log10 (235) – \Ö ) / sep, 

t is student’s t, \Ö is the regression estimate of the log10 E. coli, 

sep is the standard error of prediction of y, n is the number of 

observations used in the regression, and p is the number of 

regression coefficients estimated in the regression equation.

 For each selected model, a threshold probability associated with too great a risk to allow swimming was determined 

retrospectively. Threshold probabilities were determined by 

taking the dataset used to develop the model and finding the 

probability that provided a reasonable balance between achieving a high number of correct responses and a low number of 

false negative responses. 

Model specificities and sensitivities for the threshold 

probability technique and predicted E. coli concentrations 

were reported and compared to specificities and sensitivities 

associated with the current method used to assess recreational 

water quality. The sensitivity is the proportion of actual 

exceedances (concentrations > 235 CFU/100 mL) that were 

predicted correctly. The specificity is the proportion of nonexceedances that were predicted correctly. 

For model validation, data were collected during an 

independent year (a year whose data were not used for model 

development) to compare the model’s performance with 

the current method for assessing recreational water-quality. 

The model developed with data collected in 2000–2004 at 

Huntington was validated with data collected in 2005. After 

validation tests, new parameter estimates were determined 

based on data collected at Huntington from 2000–2005. At the 

other beaches, model validation will be done in 2006 for data 

collected during 2004–05. 

Relations Between Escherichia coli

Concentrations and Environmental or 

Water-Quality Variables

Annual summary statistics for E. coli concentrations at 

the five Lake Erie beaches are listed in table 1. Annual median 

concentrations of E. coli were highest at Lakeview and Lakeshore, ranging from 130 to 380 CFU/100 mL. The percentage 

of days that the bathing-water standard was exceeded ranged 

from 8.1 percent at Edgewater in 2004 to 61.2 percent at 

Lakeview in 2005. 

For Huntington, correlations between E. coli concentrations and potential explanatory variables were determined for 

data collected during 2000–2004 (table 2, left side of the solid 

line). Rd-1, turbidity, and log10 turbidity were positively and 

significantly related to E. coli for 2000–2004 combined and 

for each of the 5 years examined separately (data not shown). 

Number of birds, day of the year, Rd-3, water temperature, and 

lake level were weakly or not significantly related to concentrations of E. coli. Because both Rd-1 and Rd-2 (daily rainfall 

variables) were significantly related to E. coli, Rw48 was 

included as an additional variable. Rw48 was more highly correlated with E. coli than the single-day rainfall variables. 

For Edgewater, Villa Angela, Lakeshore, and Lakeview, 

correlations between E. coli concentrations and potential 

explanatory variables were determined for data collected during 2004–2005 (table 2). Rd-1, Rw48, and log10 turbidity were 

positively and significantly related to E. coli at all beaches. 

The strongest relations between number of birds or day of the 

year and E. coli were found at Lakeview. At Edgewater, Villa 

Angela, and Lakeshore, but not at Lakeview, weighted rainfall 

variables (Rw48 or Rw72) were more highly correlated with 

E. coli than single-day rainfall variables. Water temperature 

was a significant variable for all beaches except Edgewater. 

Lake level was negatively and significantly related to E. coli at 

all beaches except Lakeshore. 

The relations between categorical explanatory variables 

and E. coli were examined graphically and statistically. At 

all beaches, median E. coli concentrations increased with 

increasing wave height, and statistically significant differences 

were found among most of the wave-height categories. For 

example, at Villa Angela, statistically significant differences 

in E. coli concentrations were found between wave-height 

category 0 to 2 ft and other categories (fig. 2). Wind direction 

was found to be significantly related to E. coli concentrations 

at Lakeview and Villa Angela, but not at Huntington, Lakeshore, or Edgewater. At Villa Angela, southwesterly winds 

(173–254°) were associated with significantly higher E. coli

concentrations than other wind directions (fig. 2). Because 

no physical factors seemed to explain this phenomenon, wind 

direction 24 was not used in model development at Villa 

Angela. At Lakeview, southerly winds (91–270°) were associated with the highest E. coli concentrations (data not shown). 

Southerly winds tend to calm the beach waters and may lead 

to more birds in the area. 

 Models for Predicting Recreational Water Quality at Lake Erie Beaches
Table 1. Summary statistics of Escherichia coli (E. coli) concentrations at five Lake Erie beaches, 

2000–2005. 

[CFU/100 mL is colony-forming units per 100 milliliters]

Beach Number of 

samples

Daily E. coli concentrationsa, 

in CFU/100 mL

Number (percent) of days bathingwater standardb Median Minimum Maximum was exceeded

Edgewater

2004 99 51 5 890 8 (8.1)

2005 93 58 2 1,900 16 (17.2)

Villa Angela

2004 99 49 1 6,900 19 (19.2)

2005 89 110 2 4,200 32 (36.0)

Huntington

2000 51 110 8 6,600 12 (23.5)

2001 50 44 3 1,200 10 (20.0)

2002 52 43 4 1,800 11 (21.2)

2003 54 58 2 730 6 (11.1)

2004 54 31 3 1,500 7 (13.0)

2005 58 34 1 2,400 8 (13.8)

Lakeview

2004 46 280 54 4,200 27 (58.7)

2005 49 380 11 3,500 30 (61.2)

Lakeshore

2004 44 130 18 14,000 16 (36.4)

2005 45 240 9 5,200 23 (51.1)

a The daily concentrations of E. coli were determined by calculating the average of two or three point samples.

b Days the concentration of E. coli exceeded the single-sample maximum bathing-water standard of 235 CFU/100 mL.

Relations Between Escherichia coli Concentrations and Environmental or Water-Quality Variables 
Table 2. Pearson’s r correlations between log10 Escherichia coli (E. coli) concentrations and explanatory variables at 

five Lake Erie beaches, 2000–2005. 

[Relations that were significant at p < 0.05 are in italics and bold]

Variable Huntington Edgewater Villa Angela Lakeshore Lakeview Huntington

2000-2004 2004-2005 2004-2005 2004-2005 2004-2005 2000-2005

Birds, number at time of 

sampling -0.10 0.15 0.21 -0.18 0.33 0.03

Day of the year 0.09 0.15 -0.13 0.26 0.43 0.15

Rd-1

 a 0.34 0.30 0.36 0.35 0.29 0.36

Rd-2

 a 0.20 0.22 0.09 0.20 -0.02 0.22

Rd-3

 a 0.08 0.10 0.09 0.31 -0.04 0.08

Rw48

 b 0.37 0.37 0.37 0.40 0.24 0.40

Rw72

 b -- 0.38 -- 0.46 -- --

Turbidity 0.51 0.40 0.38 0.37 0.18 0.48

Log10 turbidity 0.54 0.44 0.31 0.52 0.31 0.51

Water temperature 0.13 0.09 0.34 0.36 0.49 < 0.01

Lake level -0.11 -0.25 -0.16 -0.12 -0.30 -0.16

a

Rd-1 was the rainfall amount, in inches, in the 24-hour period preceding sampling; Rd-2 and Rd-3 were the rainfall amounts 2 and 3 days, 

respectively, before sampling.

b

Rw48 and Rw72 were the rainfall amounts, in inches, in the 48- and 72-hour periods, respectively, before sampling, with the most recent 

rainfall receiving the most weight.

(146) A (20) B (19) B (73) A (115) B

10,000.0

1,000.0

100.0

10.0

1.0

0.1

10,000.0

1,000.0

100.0

10.0

1.0

0.1

0-2 1-3 3-6 173 to 254 Other

Wave height, in feet 24-hour wind direction

Escherichia coli, in CFU/100 mL

235 235

25th percentile

lower whisker

number of values (146)

outlier2

upper whisker1

75th percentile

average

median

Explanation

1

The whiskers span the

largest and smallest values within

1.5 times the interquartile range.

2

Outliers are defined as values

outside the whisker span.

Figure 2. Escherichia coli concentrations in water by wave height and 24-hour wind direction, Villa Angela, 2004–2005. 

Results of Tukey’s test are presented as letters; concentrations with at least one letter in common do not differ significantly. 

The Ohio single-sample maximum bathing-water standard of 235 colony-forming units per 100 milliliters (CFU/100 mL) is 

indicated by dotted lines and used as a benchmark.)

 Models for Predicting Recreational Water Quality at Lake Erie Beaches
Development and Validation of BeachSpecific Predictive Models

A list of possible models was produced for each beach, 

along with their Mallow’s Cp statistic and R2 values. From 

the list, one best model for each beach was selected; R2 values 

ranged from 0.35 for Lakeshore to 0.44 for Lakeview (table 3, 

above the solid line). All of the best beach models incorporated log10 turbidity as an explanatory variable, and four out 

of five models incorporated a rainfall variable. Lake level was 

used only at Edgewater, and wind direction and day of the year 

only at Lakeview. Wave height and water temperature were 

used in three and two beach models, respectively.

Determination of Model Output Values

The MLR models were used to predict output values for 

the data used to develop the models. For the output as predicted E. coli, no further calculations were needed because the 

threshold is, by default, set at 235 CFU/100 mL. The output as 

the probability requires determination of a threshold probability—the lowest (most conservative) probability that produces 

the most correct responses and (or) fewest false negative 

responses (Francy and others, 2003). This concept can be 

best explained by examining the plot for the Huntington 

2000–2004 best model with a 29 percent threshold (fig. 3) and 

then explaining the process used to determine the 29 percent 

threshold. The plot is divided into four quadrants by a vertical 

line through 2.37 (log10 of 235 CFU/100 mL) on the x-axis 

and a horizontal line through the threshold probability of 29. 

By raising or lowering the horizontal probability line, one can 

determine the best threshold probability. This determination 

is somewhat subjective. For example, a threshold of 50 would 

have produced the highest number of correct responses (215) 

but would also have produced a high number of false negatives (28). Thresholds between 35 and 45 do little to reduce 

the number of false negatives. Selecting a threshold of 29, 

however, still maintains a high number of correct responses 

(210) but reduces the false negatives to a more acceptable level 

(18) and represents a compromise between false negative and 

false positive responses. In addition, setting the threshold to a 

lower value such as 29 enables the beach manager to err on the 

safe side. Thresholds, determined for the other beaches in this 

manner, ranged from 29 to 38 percent (table 4, above the solid 

line). 

The responses from models that predict E. coli concentrations and threshold probabilities were compared to use of the 

previous day’s E. coli (table 4). For all beaches, the percentages of correct predictions were higher using the model than 

using the previous day’s E. coli. For Huntington 2000–2004 

and Edgewater, model specificities using threshold probabilities were relatively high (90.2 and 94.9 percent), but model 

sensitivities (59.1 and 59.3 percent) were the lowest among the 

threshold probability responses for all beaches. The specificities may be high at Huntington and Edgewater because the 

E. coli concentration did not exceed the standard for most of 

the days sampled (table 1). In contrast, at Lakeview and Lakeshore, model specificities using the threshold probability were 

less than those found using the current method and were relatively low (52.6 and 68 percent), but model sensitivities using 

the threshold probability were high (92.9 and 92.3 percent). 

The sensitivities may be high at Lakeview and Lakeshore 

because the standard was frequently exceeded in the datasets 

used to develop the models (table 1). In comparing the two 

model output values, use of predicted E. coli concentrations 

resulted in higher specificities, and use of threshold probabilities resulted in higher sensitivities. In fact, at all beaches, 

sensitivities were substantially higher using the threshold 

probability than using the predicted E. coli or the previous 

day’s E. coli. 

Model Validation

Models perform fairly well when predicting responses to 

data used for their development. A better test of a model is to 

predict responses for an independent period. The 2000–2004 

Huntington model was tested in 2005, and model responses 

were compared to use of the previous day’s E. coli (table 5). 

The percentages of correct predictions and specificities using 

either model output were in the same range as those found 

using the previous day’s E. coli. However, use of the previous 

day’s E. coli provided fewer predictions (41) than the model 

(50) because no samples were collected on Sundays. The difference between the model responses and the current method 

responses is most pronounced when examining the sensitivities. Using both output values from the model, four out of 

eight exceedances (50 percent sensitivity) during 2005 were 

correctly predicted. Using the previous day’s E. coli, none of 

the exceedances was predicted, resulting in a sensitivity of 

zero.

The data collected at Huntington during 2005 were added 

to the 2000–2004 dataset, and a new model was developed. 

Correlation coefficients that describe the relations between 

explanatory variables and E. coli for Huntington 2000–2005 

are listed in table 2 (right side of solid line). As in 2000–2004, 

the relations between E. coli and Rd-1, Rd-2, Rw48, turbidity, 

and log10 turbidity were significant for the 2000–2005 dataset. With the additional year, day of the year and lake level 

were significantly related to E. coli for 2000–2005 and were 

therefore added as possible explanatory variables during the 

2000–2005 model-development process.

Development and Validation of Beach-Specific Predictive Models 
Table 3. Variables and regression statistics for beach models.

[The adjusted R2 indicates the fraction of the variation in Escherichia coli concentration explained by the model, adjusted for number of variables in the model]

Beach Time period of data for 

model development

Adjusted R2

of model Variables in model Parameter estimates

Significance of 

variable

Huntington 2000 -2004 0.38 y-intercept 0.914 <0.0001

Wave height 0.144 0.0018

Rw48

b 0.301 <0.0001

Log10 turbidity 0.563 <0.0001

Edgewater 2004-2005 0.40 y-intercept 1.817 <0.0001

Lake level -0.407 <0.0001

Rw72

b 0.084 0.0013

Wave height 0.240 <0.0001

Log10 turbidity 0.318 0.0004

Villa Angela 2004-2005 0.38 y-intercept -1.279 0.0031

Water temperature 0.114 <0.0001

Rd-1

a 0.555 0.0011

Wave height 0.236 0.0026

Log10turbidity 0.410 0.0051

Lakeshore 2004-2005 0.35 y-intercept 0.613 0.1725

Water temperature 0.054 0.0089

Rw72

b 0.137 0.0271

Log10 turbidity 0.476 0.0011

Lakeview 2004-2005 0.44 y-intercept -0.167 0.6279

Wind direction 0.100 0.0001

Day of the year 0.010 <0.0001

Log10 turbidity 0.406 <0.0001

Huntington 2000-2005 0.42 y-intercept -0.219 0.3482

Wave height 0.134 0.0016

Rw48

b 0.292 <0.0001

Log10 turbidity 0.592 <0.0001

Day of the year 0.006 <0.0001

a

 Rd-1 was the rainfall amount, in inches, in the 24-hour period preceding sampling.

b

 Rw48 and Rw72 were the rainfall amounts, in inches, in the 48- and 72-hour periods, respectively, before sampling, with the most recent 

rainfall receiving the most weight.

 Models for Predicting Recreational Water Quality at Lake Erie Beaches
Probability Total correct False + False -

50 215 5 28

45 213 9 26

40 211 12 25

35 208 16 24

31 210 19 19

30 210 19 19

29 210 20 18

28 207 23 18

27 207 24 17

26 205 27 16

29-percent threshold 0

10

20

30

40

50

60

70

80

90

100

1 10 100 1,000 10,000

Measured Escherichia coli , in CFU/100mL

Probability

of exceeding 235

CFU/100 mL based on m

odel

Bathing-water standard

29-percent threshold

Correct

nonexceedance

(184)

False positive (20)

Correct exceedance (26)

False negative

(18)

(20) Number of responses

Figure 3. Establishment of the threshold probability for Huntington 2000–2004 model. (CFU/mL is colony-forming units per 

100 milliliters.)

Table 4. Numbers of correct responses and the sensitivities and specificities of model responses with indicated thresholds and predicted Escherichia coli (E. coli) concentrations compared to previous day’s E. coli concentrations (current 

method for assessing recreational water quality).

Beach model Threshold probability Number of

samples

Response (percent)

Correct

predictions Specificitya Sensitivityb

Huntington 2000-2004 29 248 84.7 90.2 59.1

Predicted E. coli 248 86.7 97.5 36.4

Previous day’s E. coli 171 76.6 86.5 30.0

Edgewater 2004-2005 29 185 89.7 94.9 59.3

Predicted E. coli 185 88.1 98.7 25.9

Previous day’s E. coli 142 79.6 90.6 28.0

Villa Angela 2004-2005 31 183 78.7 85.0 62.0

Predicted E. coli 183 79.8 97.0 34.0

Previous day’s E. coli 139 64.0 75.3 38.1

Lakeview 2004-2005 38 94 76.6 52.6 92.9

Predicted E. coli 94 74.5 63.2 82.1

Previous day’s E. coli 67 68.6 72.7 66.7

Lakeshore 2004-2005 32 89 78.6 68.0 92.3

Predicted E. coli 89 76.4 86.0 64.1

Previous day’s E. coli 65 69.2 78.8 59.4

Huntington 2000-2005 27 306 85.9 90.9 61.5

Predicted E. coli 306 85.6 96.4 32.7

Previous day’s E. coli 213 76.5 87.0 25.0

a

 Specificity was the proportion of nonexceedance responses that were correctly predicted as safe for swimming.

b

 Sensitivity was the proportion of exceedance responses that were correctly predicted as unsafe for swimming.

Development and Validation of Beach-Specific Predictive Models 
A list of possible models was developed for Huntington 

based on 2000–2005 data along with Mallow’s Cp statistics 

and R2 values. The best model contained the variables wave 

height, Rw48, log10 turbidity, and day of the year with an R2 of 

0.42 (table 3). The predicted E. coli and threshold probability 

from the Huntington 2000–2005 model (table 4, below the 

solid line) yielded similar responses as those for the Huntington 2000–2004 model. The 2000–2005 Huntington model will 

be validated in 2006; it will also be used a predictive tool by 

beach managers. 

Future Work

During exploratory data analysis, and later in development of MLR models for five Lake Erie beaches, it was 

evident that there was a unique set of explanatory variables 

for each beach. Similarly, in an investigation of four Lake 

Michigan beaches in Illinois and Indiana, Olyphant (2005) 

found that the method used to develop predictive models 

was transferable, but the form of each model was unique and 

required site-specific calibration. The important explanatory 

variables in the Indiana study were wind speed and direction, 

waves, lake stage, rainfall, sunshine, and temperature. The 

explanatory variables used in Lake Erie beach models were 

turbidity (five beaches), rainfall (four beaches), wave height 

(three beaches), water temperature (two beaches), day of the 

year (two beaches), wind direction (one beach), and lake level 

(one beach). 

The current study suggests that MLR predictive models 

can do better than use of the previous day’s E. coli in assessing current recreational water-quality conditions, even during 

an independent year. Both the predicted E. coli concentration 

and probability outputs did considerably better at predicting 

exceedance of the E. coli standard than the current method. 

Because probability output thresholds are set by beach managers or modelers, however, they can be adjusted to minimize 

false negative responses and thus may provide more protection 

for public health than use of predicted E. coli concentrations. 

Regardless of which model output is used, at Huntington, the 

current method failed to accurately predict any of the eight 

exceedances, whereas the model accurately predicted four of 

them during an independent year. Consequently, predictions 

based on the Huntington 2000–2005 model and the threshold 

probability have been presented to the public through an Internet-based “nowcasting” system since May 30, 2006. Because 

validation was done for only a single year at a single beach, 

the Huntington model again and the other beach models for 

the first time are being validated in 2006. 

As the models are validated in 2006, steps may be taken 

to further refine and improve them. One possible improvement, tested at several beaches during 2005, is to replace 

categorical wave heights with a less subjective measuring 

method. During 2005, a survey rod was placed in the water at 

the sampling location for 1 minute, during which field crews 

noted the minimum and maximum heights. Additionally, 

during 2005 at Edgewater, a pressure transducer was installed 

on a buoy placed in the bathing area. The hourly nearshore 

wave heights collected with the buoy showed site-specific 

wave fluctuations not evident in offshore data and were more 

accurate than categorical wave heights. Because turbidity is an 

important variable at five beaches, plans call for installation 

of probes at each beach to obtain continuous turbidity measurements instead of one measurement at the time of sample 

collection. Data from a local rain gage may also improve the 

predictive ability of the model at Lakeshore because in previous studies, fecal contamination at Lakeshore was identified to 

be primarily local in origin. Lastly, a rapid detection method 

for E. coli that involves an antibody-antigen binding mechanism (Lee and Deininger, 2004) is being tested at Edgewater 

and Villa Angela to determine whether the results may be useful in a predictive model. 

Combining hydrodynamic modeling with MLR modeling may improve the predictive ability of models at beaches 

with identified point sources. In an Australian study, sewage 

plumes that were predicted to surface were coded as 1 because 

of possible dispersal by wind and surface movements; sewage 

plumes that were predicted to remain below the surface were 

Table 5. Responses of the Huntington 2000–2004 model in 2005 and comparison to responses 

obtained with previous day’s Escherichia coli (E. coli) concentrations (current method for assessing 

recreational water quality).

Prediction based on Number of 

samples

Response (percent)

Correct

predictions Specificity Sensitivity

Model threshold, 29 percent 50 82.0 88.1 50.0

Model-predicted E. coli 50 88.0 95.2 50.0

Previous day’s E. coli 41 75.6 88.6 0.00

10 Models for Predicting Recreational Water Quality at Lake Erie Beaches
coded as 0 (Krogh and Robinson, 1996). This “plume entrapment” variable generated by near-field oceanographic models 

was found to be a significant variable in regression models. 

The procedures detailed in this report can be used by others to develop predictive models at coastal beaches; all that is 

needed is an existing monitoring program and a basic knowledge of statistics and computer software. Equipment costs for 

data collection are minimal because most of the data required 

for predictive models are available from other agencies or are 

easily measured at the beach. As a model proves to be a useful tool at a particular beach, beach managers may decide to 

invest in more expensive equipment to measure environmental 

conditions in real time. If validation tests are successful, beach 

managers may also decide to develop an Internet-based system 

that provides model predictions to the beach-going public 

7 days a week. Currently, weekend estimates are not commonly available because most laboratories are not staffed on 

weekends. 

Predictive models are meant to augment existing beach 

monitoring programs, not to replace them, and must be continuously tested and refined. For example, if changes are made 

to improve water quality at the beach (for example, bird-deterrent devices are installed, leaking sewerlines are repaired), 

new models can be developed using data collected after the 

improvements have been initiated. Additional data and refined 

variables can be added to models to improve predictions and 

to better protect public health. 

Summary and Conclusions

A goal of the U.S. Environmental Protection Agency 

(USEPA) Beaches Environmental Assessment, Closure, and 

Health (BEACH) Program is development of mathematical 

models for real-time forecasting to help resolve the delayed 

notification problems inherent with the present approach to 

recreational monitoring. At many beaches where nonpoint 

or unidentified sources dominate, multiple linear regression 

(MLR) models based on easily measured environmental and 

water-quality variables may be the most appropriate type of 

model for estimating bacterial indicator concentrations or the 

probability of exceeding target concentrations. 

The U.S. Geological Survey (USGS), in cooperation with 

Ohio Water Development Authority, Ohio Lake Erie Office, 

Northeast Ohio Regional Sewer District, and Cuyahoga 

County Board of Health, developed and tested MLR predictive models for E. coli concentrations at five Ohio Lake Erie 

beaches—Lakeview (Lorain, Ohio), Huntington Reservation 

(Bay Village, Ohio), Edgewater and Villa Angela (Cleveland, Ohio), and Lakeshore (Ashtabula, Ohio). At one beach, 

Huntington Reservation (Huntington), investigations were 

further along than at other beaches, so the Huntington model 

was assessed during an independent or validation year (a year 

whose data were not used for model development). 

Data collection included analysis of daily water samples 

for E. coli and measurement of explanatory variables for 

model development and testing. Data were collected during 

the recreational seasons (May through September) of 2004–05. 

At Huntington, data from past studies (2000–2003) also were 

included. Among the environmental variables were single-day 

and weighted rainfall variables. Single-day variables included 

rainfall that fell in a previous 24-hour period; weighted rainfall 

included rainfall that fell in the 48- or 72-hour antecedent 

period, with the most recent rainfall receiving the most weight 

(Rw48 and Rw72, respectively). Wind direction was calculated by summing hourly wind vectors for the 24-hour period 

preceding sampling and determining the direction of the resultant vector. Wave height was visually estimated and placed 

into one of four categories. 

A daily E. coli concentration was calculated by averaging 

results from multiple sampling points at each beach. Bacterial 

concentrations were log10 transformed before data analysis. At 

least 2 years of data from each beach were examined and used 

for model development. Explanatory variables that showed 

significant relations to E. coli concentrations were used to 

produce a list of possible MLR models using the Mallows Cp 

test. The MLR models were ordered so that the coefficient 

of determination (R2) was maximized and the Mallows’ Cp 

statistic was minimized. Model statistics were examined and 

diagnostic tests were done to identify the model(s) for each 

beach that provided the best linear, unbiased estimator of 

E. coli concentrations. 

The two types of output produced by the models were 

predicted E. coli concentration and the probability of exceeding the Ohio single-sample bathing water standard for E. coli

of 235 colony-forming units per 100 milliliters 

(CFU/100 mL). For each selected model, a threshold probability associated with too great a risk to allow swimming 

was determined retrospectively. Threshold probabilities were 

determined by taking the dataset used to develop the model 

and finding the probability that provided a reasonable balance 

between achieving a high number of correct responses and a 

low number of false negative responses. 

From a list of possible models, one best model for each 

was selected; R2 values ranged from 0.35 for Lakeshore to 

0.44 for Lakeview. All of the best beach models incorporated 

log10 turbidity as an explanatory variable, and four out of five 

models incorporated a rainfall variable. Weighted rainfall 

variables (Rw48 and Rw72) were used in three beach models 

instead of single-day rainfall variables. Lake level was used 

only at Edgewater, and wind direction and day of the year only 

at Lakeview. Wave height and water temperature were used in 

three and two beach models, respectively. 

The responses from models that predict E. coli concentrations and threshold probabilities were compared to use of 

the previous day’s E. coli (current method). Model threshold 

probabilities ranged from 29 to 38 percent. For all beaches, the 

percentages of correct predictions were higher using the model 

than using the previous day’s E. coli. 

Summary and Conclusions 11
The model developed with data collected in 2000–2004 

at Huntington was validated with data collected during an 

independent period (2005). Using either model output, the 

percentages of correctly predicting nonexceedance of the 

bathing-water standard (specificity) were in the same range 

as the percentage found using the previous day’s E. coli. 

The difference between the model responses and the current 

method responses was most pronounced when examining the 

percentages of correctly predicting exceedance of the bathingwater standard (sensitivity). Using both output values from the 

model, four out of eight exceedances (50 percent sensitivity) 

during 2005 were correctly predicted. Using the previous day’s 

E. coli, none of the exceedances was predicted. 

Principal conclusions and implications for future work 

are the following:

It was evident that there was a unique set of explanatory variables for each beach. The explanatory variables used in Lake Erie beach models were turbidity 

(five beaches), rainfall (four beaches), wave height 

(three beaches), water temperature (two beaches), day 

of the year (two beaches), wind direction (one beach), 

and lake level (one beach). 

This study suggests that MLR predictive models can 

do better than use of the previous day’s E. coli in 

assessing current recreational water-quality conditions, 

even during an independent year. Because validation 

was done for only a single year at a single beach, the 

Huntington model and other beach models are being 

validated in 2006. 

As the models are validated in 2006, steps may be 

taken to further refine and improve them. Possible 

improvements include obtaining more accurate 

measurements of wave heights, measuring continuous 

turbidity, obtaining data from local rain gages, and 

incorporating rapid analytical methods for E. coli into 

the models. Combining hydrodynamic modeling with 

MLR modeling also may improve the predictive ability 

of models at beaches with identified point sources. 

The procedures detailed in this report can be used by 

others to develop predictive models at coastal beaches. 

Through an Internet-based system, models can be useful tools that provide predictions to the beach-going 

public 7 days a week. 

If changes are made to improve water quality at a 

beach, new models can be developed using data collected after the improvements have been initiated. 

Additional data and refined variables can be added to 

models to improve predictions and to better protect 

public health. 

•

•

•

•

•

Acknowledgments

The authors thank Lester Stumpe, Mark Citriglia, and 

Eva Hatvani of the Northeast Ohio Regional Sewer District; Jill Lis of the Cuyahoga County Board of Health; Jack 

Kurowski of the Lorain City Health Dept.; Brenda Stephens 

of the Ashtabula Township Park Commission; and students 

Timothy Roberts and Paula Carver. 

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