In cooperation with the Erie County Health Department

Modeling to Predict Escherichia coli at Presque Isle Beach 2, 

City of Erie, Erie County, Pennsylvania

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2008-5039

Modeling to Predict Escherichia coli at 

Presque Isle Beach 2, City of Erie, Erie 

County, Pennsylvania

By Tammy M. Zimmerman

In cooperation with the Erie County Health Department

Scientific Investigations Report 2008-5039

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

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Suggested citation:

Zimmerman, T.M., 2008, Modeling to predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania: U.S. Geological Survey Scientific Investigations Report 2008-5039, 13 p.
iii

Contents

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

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

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

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

Quality Control.......................................................................................................................................3

Model Validation, Data Analysis, and Model Refinement..............................................................3

Model Validation ............................................................................................................................................4

Relations Between Escherichia coli Concentrations and Data Variables ...........................................4

Modeling to Predict Escherichia coli .........................................................................................................8

Summary and Conclusions...........................................................................................................................9

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

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

Figures

1. Map showing location of Presque Isle beaches, City of Erie, Erie County, 

Pennsylvania .................................................................................................................................3

2-5. Graphs showing—

2. Log10 Escherichia coli concentrations by wind direction, Presque Isle Beach 2,

City of Erie, Erie County, Pennsylvania ..............................................................................7

3. Log10 Escherichia coli concentrations by water-current direction, Presque Isle

Beach 2, City of Erie, Erie County, Pennsylvania .............................................................7

4. Log10 Escherichia coli concentrations by wave height, Presque Isle Beach 2,

City of Erie, Erie County, Pennsylvania ..............................................................................8

5. Observed log10 Escherichia coli concentrations and probability of exceeding

235 col/100 mL to achieve optimum threshold probability for the combined

2005–2006 model for Presque Isle Beach 2, City of Erie, Erie County,

Pennsylvania........................................................................................................................10

Tables

1. Comparison of responses of the Presque Isle (Beach 2) 2004-2005 model in 2006

and responses using current method of assessing bacteriological quality of

recreational waters......................................................................................................................5

2. Summary of Spearman’s rho correlations between log10 Escherichia coli

concentrations in water and selected water-quality or environmental variables at

Presque Isle Beach 2, Erie, Pennsylvania, 2004–2005............................................................6

3. Summary of tobit regression model explanatory variables, statistics, and

performance with selected threshold probabilities in predicting exceedances of

the Escherichia coli single-sample bathing-water standard of 235 col/100 mL for

Presque Isle Beach 2, 2004–2006...............................................................................................9

4. Comparison of responses of Presque Isle Beach 2 models and responses using

current method of assessing bacteriological quality of recreational waters ..................11
iv

Conversion Factors

Multiply By To obtain

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

cubic inch (in3

) 1.639 milliliter (mL)

Concentrations of bacteria in water are reported in colonies per 100 milliliters (col/100 mL)
Modeling to Predict Escherichia coli at Presque Isle 

Beach 2, City of Erie, Erie County, Pennsylvania

By Tammy M. Zimmerman

Abstract

The Lake Erie beaches in Pennsylvania are a valuable 

recreational resource for Erie County. Concentrations of 

Escherichia coli (E. coli) at monitored beaches in Presque Isle 

State Park in Erie, Pa., occasionally exceed the single-sample 

bathing-water standard of 235 colonies per 100 milliliters 

resulting in potentially unsafe swimming conditions and 

prompting beach managers to post public advisories or to 

close beaches to recreation. 

To supplement the current method for assessing recreational water quality (E. coli concentrations from the previous 

day), a predictive regression model for E. coli concentrations 

at Presque Isle Beach 2 was developed from data collected 

during the 2004 and 2005 recreational seasons. Model output 

included predicted E. coli concentrations and exceedance 

probabilities—the probability that E. coli concentrations 

would exceed the standard. For this study, E. coli concentrations and other water-quality and environmental data were 

collected during the 2006 recreational season at Presque Isle 

Beach 2. The data from 2006, an independent year, were used 

to test (validate) the 2004–2005 predictive regression model 

and compare the model performance to the current method. 

Using 2006 data, the 2004–2005 model yielded more correct 

responses and better predicted exceedances of the standard 

than the use of E. coli concentrations from the previous day. 

The differences were not pronounced, however, and more 

data are needed. For example, the model correctly predicted 

exceedances of the standard 11 percent of the time (1 out of 9 

exceedances that occurred in 2006) whereas using the E. coli

concentrations from the previous day did not result in any correctly predicted exceedances.

After validation, new models were developed by adding the 2006 data to the 2004–2005 dataset and by analyzing the data in 2- and 3-year combinations. Results showed 

that excluding the 2004 data (using 2005 and 2006 data 

only) yielded the best model. Explanatory variables in the 

2005–2006 model were log10 turbidity, bird count, and wave 

height. The 2005–2006 model correctly predicted when the 

standard would not be exceeded (specificity) with a response 

of 95.2 percent (178 out of 187 nonexceedances) and correctly 

predicted when the standard would be exceeded (sensitivity) 

with a response of 64.3 percent (9 out of 14 exceedances). In 

all cases, the results from predictive modeling produced higher 

percentages of correct predictions than using E. coli concentrations from the previous day. Additional data collected each 

year can be used to test and possibly improve the model. The 

results of this study will aid beach managers in more rapidly 

determining when waters are not safe for recreational use and, 

subsequently, when to close a beach or post an advisory.

Introduction

Approximately 7 mi of Lake Erie shoreline lies within 

Presque Isle State Park in Erie, Pa. Monitored public bathing beaches at Presque Isle make up less than 1 mi (Natural Resources Defense Council, 2007). Previous studies 

conducted by the Erie County Health Department (ECHD) 

and other agencies (Erie County Health Department, 2007) 

identified sources of fecal contamination at the Presque Isle 

beaches that included stormwater runoff and combined sewer 

overflows. These same types of sources likely continue to 

influence concentrations of fecal-indicator bacteria at Presque 

Isle beaches, especially during periods of heavy rainfall. 

According to the Natural Resources Defense Council (2007), 

the number of beach advisories or closings for permitted public bathing beaches at Presque Isle rose from 39 days in 2005 

to 53 days in 2006. Nine of the 12 public bathing beaches 

that are permitted at Presque Isle State Park had at least one 

advisory or closing in 2006 (U.S. Environmental Protection 

Agency, 2007). Most of the closings or advisories in 2006 (51 

of 53 days) were due to elevated bacteria concentrations; a 

small percentage of the advisories or closings (2 of 53 days) 

was related to a rainfall advisory system (Natural Resources 

Defense Council, 2007). 

Beach advisories or closings are issued by beach managers on the basis of recreational water-quality standards 

for fecal-indicator bacteria. In 2004, Pennsylvania adopted 

bacteriological criteria recommended by the U.S. Environmental Protection Agency that use Escherichia coli (E. coli)

as the indicator to assess the recreational water quality of all 

public bathing beaches in the Commonwealth (U.S. Environmental Protection Agency, 1986). The regulations estab-
2 Modeling to Predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania 

lish the single-sample bathing-water standard for E. coli as 

235 col/100 mL and also state that the geometric mean for 

E. coli concentrations in multiple samples collected during 

any 30-day period during the recreational season should not 

exceed 126 col/100 mL (Pennsylvania Code, 28 PaCode § 

18.28). Concentrations of E. coli in recreational waters may 

change substantially from the time of sample collection until 

the sample is processed and analyzed and the results are 

reported (18-24 hours). This presents a delay in posting closings or issuing advisories for Pennsylvania beaches because 

the current practice is to use the E. coli concentrations from 

the previous day to determine if an advisory should be posted 

or a beach should be closed. Such a delay may cause recreational users of the beaches to be exposed to potential health 

risks when the risks are the greatest (bacteria concentrations 

are high and exceed the standard). Conversely, a delay may 

prohibit access to recreational areas or prohibit swimming 

when the health risk is reduced or no longer present (bacteria 

concentrations have declined from the value on the previous day and are below the standard by the time the beach is 

closed or advisories are posted). Because of the drawbacks 

of using the E. coli concentrations from the previous day as 

the only method to assess the recreational quality of Presque 

Isle beaches and the fact that concentrations of bacteria in 

beach waters continue to frequently exceed the single-sample 

bathing-water standard of 235 col/100 mL, other methods of 

assessing the water quality of the beaches are being initiated 

to reduce the potential health risks to recreational users of the 

beaches. 

Predictive modeling can supplement the use of measured 

E. coli concentrations for indicating if fecal contamination 

has occurred at Presque Isle beaches. Environmental and 

water-quality variables that are easily measured can be used 

in regression models to predict, or forecast, when concentrations of fecal-indicator bacteria will exceed recreational 

standards. This regression approach to modeling is appropriate 

for Presque Isle beaches where dominant sources of bacterial 

contamination are nonpoint or unidentified. More complicated 

models (that incorporate hydrodynamic mixing and transport) are appropriate in cases where bacterial contamination 

is dominated by point sources. Examples of selected predictive-modeling studies that have used the above-mentioned 

approaches to determine exceedances of recreational waterquality standards are referenced in Francy and Darner (2006). 

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

the ECHD, validated and refined beach-specific predictive 

regression models at Presque Isle Beach 2 near Erie, Pa. Data 

initially were collected during two recreational seasons (2004 

and 2005), and a model was developed (Zimmerman, 2006). 

This report presents the results of testing (validating) the 

2004–2005 regression model for E. coli using data collected 

during 2006. In addition, this report presents the results of new 

models developed by adding the 2006 data to the 2004–2005 

dataset. The new models consisted of combinations of data 

(2004 and 2006 data combined; 2005 and 2006 data combined) in order to determine the “best” model for Presque Isle 

Beach 2. Finally, this report describes the results of comparing 

the performance of predictive models to the current method of 

assessing recreational water quality (using E. coli concentrations from the previous day) for determining beach closings/

advisories. 

Methods

This study was done at Presque Isle Beach 2 in Erie, Pa. 

(fig. 1). Data were collected during the summer of 2006 recreational swimming season. The following sections describe the 

methodology of data-collection efforts, quality control, model 

validation, data analysis, and model refinement.

Data Collection

Data were collected during the 2006 summer recreational 

season (May through September) at Presque Isle Beach 2. 

Sampling each week involved the collection of water samples 

daily from Sunday through Wednesday at two locations in the 

swimming area. Water samples were collected using grabsample techniques described in Myers and others (2007). To 

maintain sterile conditions, grab samples were collected in 

sterile 125-mL polypropylene bottles in at least 3 ft of water at 

approximately 12 in. below the water surface. Water samples 

were kept on ice prior to processing and were analyzed for 

E. coli bacteria using modified mTEC membrane-filtration 

techniques (U.S. Environmental Protection Agency, 2002). 

Water samples were processed by ECHD staff in their laboratory within 6 hours of sample collection.

Ancillary data for explanatory variables used in the 

regression equations were collected at the time of water 

sampling or compiled from other sources as described in 

Zimmerman (2006). Data that were collected at the time of 

sampling include water temperature, specific conductance, 

pH, dissolved oxygen, and turbidity. Other data collected at 

the time of sampling included number of birds (bird count) on 

the beach and wave heights that were categorized into one of 

five groups with heights ranging from 0 to 2 ft, 1 to 3 ft, 2 to 

4 ft, 3 to 5 ft, and 4 to 6 ft. Data compiled from other sources 

included streamflow data from the nearest USGS streamflowgaging station, Brandy Run near Girard, Pa. (04213075), to 

determine instantaneous streamflow to the nearest 30 minutes 

of when water samples were collected (Siwicki, 2005, 2006; 

U.S. Geological Survey, 2007). Brandy Run is a tributary to 

Elk Creek, a creek that discharges to Lake Erie approximately 

15 mi from the Presque Isle Beaches. Speed and direction 

of water currents (model-derived for the Presque Isle Beach 

2 location) were obtained from the National Oceanic and 

Atmospheric Administration (NOAA) Great Lakes Coastal 

Forecasting System (Greg Lang, National Oceanic and Atmospheric Administration, written commun., 2005, 2006). Wind 

speed, wind direction, and rainfall data were obtained from 
Methods

a weather station at the Erie International Airport, Erie, Pa. 

(Pennsylvania State Climatologist, 2007). 

Quality Control

Quality-control measures were practiced in this study to 

ensure data quality met project objectives. These measures are 

the same as those described in detail in Zimmerman (2006) 

and include quality control in the field and quality control in 

the laboratory. Quality control in the field included the collection of a field blank approximately once each month and 

the collection of duplicate field measurements of turbidity, 

specific conductance, pH, dissolved oxygen, total dissolved 

solids, and water temperature with each sample. Measurements that did not agree within 10 percent were repeated. 

Quality-control measures in the laboratory included the 

processing of membrane-filtration equipment blanks and 

membrane-filtration procedure blanks with every sample. No 

bacteria colonies were detected in any of the equipment blanks 

or procedure blanks. Other quality-control measures in the 

laboratory included the processing of positive and negative 

control reference cultures.

Model Validation, Data Analysis, and Model 

Refinement

Model validation tests the performance of a model in predicting responses from data collected in an independent year 

that were not used in the development of the model. For this 

study, the 2004–2005 model (Zimmerman, 2006) was validated using data collected during 2006, and responses were 

compared to using the E. coli concentrations from the previous 

day—the current method of assessing recreational water quality. After validation testing, 2- and 3-year combinations of data 

were analyzed, and new models were developed to determine 

the “best” model for Presque Isle Beach 2.

Water-quality and ancillary data collected during 2006 

were compiled and statistically analyzed in various combinations with data collected previously (2004 and 2005) using the 

methodology described in Zimmerman (2006). Scatterplots for 

continuous data and boxplots for categorical data were used 

as graphical screening tools to examine the relation between 

E. coli concentrations and ancillary variables measured during 

the study. Continuous data included water temperature, dissolved oxygen, turbidity, bird count, rain, streamflow, wind 

speed, and water-current speed. Categorical data were wind 

direction, water-current direction, and wave height. After 

graphical analysis of the data, statistical tests were used to 

determine the strength of the associations between E. coli

concentrations and possible explanatory variables. The SpearFigure 1. Location of Presque Isle beaches, City of Erie, Erie County, Pennsylvania (modified from Pennsylvania Department of 

Conservation and Natural Resources, 2006). 

City of Erie

Presque Isle Harbor

Lake Erie

Barracks Beach

Beach 2

Beach 6

Breakwalls

P r e s q u e I s l e

P e n i n s u l a

Study Area

PENNSYLVANIA

0

0

1 MILE

1 KILOMETER

80°10’ 80°05’

42°

10’

42°07’30”
4 Modeling to Predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania 

man’s rho statistical test was used to determine the relations 

between E. coli concentrations and continuous variables. 

Correlations at the 95-percent confidence interval (probabilites less than 0.05) were considered statistically significant. 

The Kruskal-Wallis test was used to determine the relations 

between E. coli concentrations and three or more groups of 

data (categorical variables). If results of the Kruskal-Wallis 

test showed statistically significant differences between 

groups of data, the Tukey-Kramer multiple-comparison test 

was used to determine which groups differed from each other. 

The groups with the highest medians were assigned a letter 

“A,” the groups with the next highest medians were assigned 

a letter “B” or an “AB” combination, and so on. Any groups 

assigned the same letter (or combination of letters) designations were not statistically different from each other.

All variables found to be statistically related to E. coli 

concentrations were considered as potential explanatory 

variables in tobit regression models using 2- and 3-year 

combinations of data. Tobit regression was chosen because 

of the capability it has to handle multiple-censored data, and 

regression models were developed by methods documented 

in Zimmerman (2006) using the LIFEREG procedure using 

SAS statistical software (SAS Institute, 1990). Tobit regression models were evaluated using likelihood-ratio chi-square 

statistics and generalized R2 values (generalized coefficient of 

determination). Models were chosen such that the combination and number of variables explaining the concentrations of 

E. coli in the model were significantly better, as determined 

using likelihood-ratio chi-square statistics, than simpler, 

nested models with fewer variables. Models also were selected 

to maximize the generalized R2. The generalized R2 for tobit 

regression models is a number between 0 and 1 that is larger 

when the explanatory variables are more strongly associated with the dependent variable (Allison, 1995). Evaluation 

criteria for the best models also included ensuring model-variable estimates were statistically significant at the 95-percent 

confidence level (probabilities = 0.05 or less) and graphically 

evaluating model fit by creating plots of the residuals from the 

tobit regression models.

The regression models produced two types of output. 

First, a predicted E. coli concentration was computed for 

each observation used in the regression. Then, the predicted 

values for E. coli were used to determine the probabilities 

(exceedance probabilities) that the predicted E. coli concentrations would exceed the E. coli standard of 235 col/100 mL. 

Using an equation modified from Allison (1995, p. 264), 

exceedance probabilities were calculated as 1 – Probnorm 

(log(235) - lp) / sep where probnorm is a SAS function (SAS 

Institute, 1990) that computes the probability that an observation from a standard normal distribution falls below the given 

value for x—in this case x = (log(235)-lp)/sep where lp is the 

predicted E. coli concentration and sep is the standard error of 

the prediction.

Once exceedance probabilities were computed for 

each observation, a threshold probability was determined. 

Computed exceedance probabilities above this threshold are 

considered to be associated with waters of poor bacteriological 

quality that present an unacceptable risk level for swimming. 

A threshold probability is selected by analyzing a scatterplot 

of actual E. coli concentrations and predicted exceedance 

probabilities for the corresponding predicted E. coli concentrations. The exceedance probability that maximizes the number 

of correct responses (correct exceedances and correct nonexceedances) and minimizes the number of incorrect responses 

(false positives and false negatives) is chosen as the threshold 

probability. Determinations of whether beach closings/advisories should be issued can be made if values meet or exceed the 

established threshold probability.

The responses of the best models using the threshold 

probability method and predicted E. coli concentrations were 

compared to responses of the current method that uses the 

E. coli concentrations from the previous day to assess recreational water quality. The responses of each method included 

specificities, sensitivities, and total correct predictions. Specificity is the proportion of nonexceedances that were predicted 

correctly and sensitivity is the proportion of exceedances (concentrations greater than 235 col/100 mL) that were predicted 

correctly.

Model Validation

The 2004-2005 model was used to predict responses during an independent period (2006) for model validation. Model 

responses were compared to use of E. coli concentrations from 

the previous day—the current method of assessing recreational 

water quality (table 1). Model output (predicted E. coli concentrations and predicted exceedance probabilities) produced 

slightly higher percentages of correct predictions than the use 

of E. coli concentrations from the previous day. The differences between model responses and responses using E. coli

concentrations from the previous day were not pronounced. 

For example, the response of the model in correctly predicting 

when the standard would be exceeded and waters would not 

be safe for swimming (sensitivities) was only slightly better at 

11.1 percent (1 out of 9 correct) than using E. coli concentrations from the previous day (zero correct responses). 

Relations Between Escherichia coli

Concentrations and Data Variables

The bacteriological quality of waters at Presque Isle 

Beach 2 in Erie, Pa., was generally good as determined by 

analyzing E. coli concentrations in 291 water samples collected during the 2004, 2005, and 2006 recreational seasons. 

E. coli was not detected in 52 of 291 samples (18 percent)—

37 samples were reported at a detection limit of less than (<) 

4 col/100 mL, and 15 samples were reported at a detection 
Relations Between 

limit of <10 col/100 mL. The maximum concentration of 

E. coli was 852 col/100 mL following a storm in July 2006. 

For the days sampled during this study at Presque Isle Beach 

2, the single-sample bathing-water standard of 235 col/100 mL 

was exceeded 4 of 31 days in 2004, 5 of 58 days in 2005, and 

7 of 57 days in 2006 (a total of 11 percent of the days sampled 

over the 3 years). 

The Spearman’s rho statistical test was used to determine 

if there were relations between E. coli concentrations and 

other continuous variables. The variables tested against E. coli

concentrations are shown in table 2 in a summary of Spearman’s rho correlations for this study.

Statistically significant correlations were found between 

log10 E. coli concentrations and several continuous variables 

in the Presque Isle Beach 2 datasets. Log10 turbidity, rain24, 

wind speed, and water-current speed were positively and 

significantly related to log10 E. coli for each dataset or combination of datasets analyzed (table 2). The strongest correlations were observed between log10 E. coli and log10 turbidity 

with Spearman’s rho values of 0.577 in the combined 2005-

2006 dataset and 0.539 in the combined 2004–2006 dataset. 

Weaker correlations exist between log10 E. coli concentrations 

and other variables as indicated by smaller values of Spearman’s rho (statistically significant at the 95-percent confidence 

level). The bird count variable was statistically correlated to 

log10 E. coli in all datasets analyzed for this study (Spearman’s rho value of 0.342 in the 2006 dataset, for example) 

although it was not found to be statistically correlated to 

log10 E. coli in a previous study (Zimmerman, 2006). One 

streamflow variable was weakly correlated to log10 E. coli in 

the combined 2004–2006 dataset with a Spearman’s rho value 

of 0.142 (log10 Q_inst). None of the streamflow variables were 

statistically correlated to log10 E. coli in the 2006 or combined 

2005–2006 datasets. Variables that were statistically correlated 

to log10 E. coli were used in model development.

The Kruskal-Wallis test and Tukey-Kramer multiplecomparison test were used to determine if there were relations 

between log10 E. coli concentrations and categorical variables. 

The categorical variables were wind direction, water-current 

direction, and wave height. Statistical relations were found 

between log10 E. coli and wind direction. The log10 E. coli data 

were grouped according to wind direction with fewer than five 

observations for any particular wind direction being combined 

with a logically similar wind direction. Significantly higher 

median concentrations of log10 E. coli were observed when 

winds were blowing from the north/northeast direction than 

when winds were from the east, southeast/south, or northwest 

directions (fig. 2). High concentrations of log10 E. coli usually 

were observed when winds were parallel with the shoreline, 

keeping the contamination in the swimming area. 

Statistically significant differences were observed 

between log10 E. coli concentrations and water-current direction categories using the Kruskal-Wallis test and TukeyKramer multiple-comparison test. Log10 E. coli data were 

grouped according to water-current direction with fewer than 

five observations for any particular water-current direction 

being combined with a logically similar water-current direction. Although most water currents (approximately 77 percent) 

were from the northeast or east, the median concentrations of 

log10 E. coli when water currents were from those directions 

were similar to when they were from any other direction. 

Median log10 E. coli concentrations were significantly higher 

when water currents were from the southwest than when water 

currents were from southeast or northwest/north directions. 

Water currents were from the northeast/east or southwest 

directions when concentrations of log10 E. coli exceeded the 

single-sample bathing-water standard (fig. 3). High concentrations of log10 E. coli usually were observed when water currents were parallel to the shoreline (northeast and southwest), 

keeping the contamination in the swimming area.

Wave height was another categorical variable analyzed 

using the Kruskal-Wallis test and Tukey-Kramer multiplecomparison test. Wave heights were categorized as 0 to 2 ft, 1 

to 3 ft, 2 to 4 ft, 3 to 5 ft, or 4 to 6 ft, and log10 E. coli concentrations were grouped by wave-height category. Only 6 out of 

291 observations had wave heights in the 4- to 6-ft category 

so the 3- to 5-ft and 4- to 6-ft categories were combined. 

The analyses showed that median log10 E. coli concentrations 

increased as wave height increased (fig. 4) and all wave-height 

categories were statistically different from each other (as indicated by different Tukey-Kramer letter designations assigned 

to each category). Significantly higher median concentrations 

Table 1. Comparison of responses of the Presque Isle (Beach 2) 2004–2005 model in 2006 and responses using current method of 

assessing bacteriological quality of recreational waters.

Assessment method Number of 

samples

Response (percent)

Total correct Specificity1 Sensitivity2

2004-2005 Model (using 2006 data)

Exceedance probability

(threshold 27 percent)

111 90.1 97.0 11.1

Predicted E. coli 111 92.8 100 11.1

Current E. coli from the previous day 83 83.1 89.6 0.

1

 The specificity is the percentage of responses that were correctly predicted as not exceeding the standard (safe for swimming).

2

 The sensitivity is the percentage of responses that were correctly predicted as exceeding the standard (not safe for swimming).
6 Modeling to Predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania 

Table 2. Summary of Spearman’s rho correlations between log10 Escherichia coli concentrations in water and selected water-quality 

or environmental variables at Presque Isle Beach 2, Erie, Pennsylvania, 2004–2005.

[bold type denotes variables statistically correlated to log10 Escherichia coli at the 95-percent confidence level (probabilities of 0.05 or less); <, less than]

Variable

Spearman’s rho correlation coefficient

(probability)

Number of samples

2006 2005–2006 combined 2004–2006 combined

Water temperature

0.117

(.2184)

113

0.111

(.0942)

229

0.108

(.0677)

287

Dissolved oxygen

.078

(.4125)

113

-.012

(.8635)

221

.003

(.9544)

279

Log10 turbidity

.514

(<.0001)

113

.577

(<.0001)

221

.539

(<.0001)

279

Bird count

.342

(.0002)

112

.186

(.0063)

214

.174

(.0040)

272

Rain24 1

.302

(.0011)

113

.378

(<.0001)

229

.344

(<.0001)

291

Rain48 1

-.023

(.8063)

113

.035

(.6016)

229

.025

(.6708)

291

Rain72 1

-0.034

(.7238)

113

.012

(.8580)

229

-.040

(.4986)

291

Rain weight 2

.129

(.1734)

113

.258

(<.0001)

229

.203

(.0005)

291

Log10 Q_inst 3

.000

(.9986)

113

.112

(.0904)

229

.142

(.0153)

291

Log10 Q_prev 4

-.062

(.5149)

113

.072

(.2783)

229

.100

(.0879)

291

Wind speed 5

.370

(<.0001)

113

.359

(<.0001)

229

.281

(<.0001)

291

Water-current speed 6

.352

(.0001)

113

.213

(.0012)

229

.249

(<.0001)

291

1

Rain24, rain48, and rain72 were the amounts of rain that fell at Erie International Airport, Erie, Pa., in the 24-, 48-, and 72-hour period, respectively, before 

the sample was collected at Presque Isle Beach 2.

2

Rain weight is the sum of weighted rainfall amounts from the past 24-, 48-, and 72-hour period giving the most weight to amounts closest to sampling.

3

Q_inst is the instantaneous streamflow measurement (nearest 30-minute measurement to time of sampling) from the U.S. Geological Survey streamflowgaging station at Brandy Run near Girard, Pa. (04213075).

4

Q_prev is the mean daily streamflow at Brandy Run near Girard station, Pa., the day prior to sampling.

5

Wind speed was obtained from a weather station at the Erie International Airport, Erie, Pa. (Pennsylvania State Climatologist, 2007).

6

Water-current speed was obtained from the National Oceanic and Atmospheric Administration (NOAA) Great Lakes Coastal Forecasting System (Greg 

Lang, National Oceanic and Atmospheric Administration, written commun., 2005, 2006).
Relations Between 

Figure 2. Log10 Escherichia coli concentrations by 

wind direction, Presque Isle Beach 2, City of Erie, 

Erie County, Pennsylvania. 

[Results of the Tukey-Kramer test are designated 

with letters; categories with at least one letter in 

common are not significantly different]

LOG10 ESCHERICHIA COLI CONCENTRATIONS,

IN COLONIES PER 100 MILLILITERS

1

10

100

1,000

NORTH,

NORTHEAST

EAST

SOUTHEAST,

SOUTH

NORTHWEST

A B B AB B

(21) (16) (86) (158) (10)

EXPLANATION

Outlier

90th percentile

75th percentile

Median

25th percentile

10th percentile

B Tukey-Kramer letter designation

(10) Number of samples

Single-sample bathing-water 

standard

SOUTHWEST,

WEST

Figure 3. Log10 Escherichia coli concentrations by watercurrent direction, Presque Isle Beach 2, City of Erie, Erie 

County, Pennsylvania. 

[Results of the Tukey-Kramer test are designated with 

letters; categories with at least one letter in common are not 

significantly different]

LOG10 ESCHERICHIA COLI CONCENTRATIONS,

IN COLONIES PER 100 MILLILITERS

1

10

100

1,000

NORTHEAST,

EAST

SOUTHEAST

SOUTHWEST

NORTHWEST,

AB B A B

(224) (6) (45) (16)

EXPLANATION

Outlier

90th percentile

75th percentile

Median

25th percentile

10th percentile

B Tukey-Kramer letter designation

(10) Number of samples

Single-sample bathing-water 

standard

NORTH
8 Modeling to Predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania 

of log10 E. coli concentrations were observed when waves 

were from 3 to 6 ft than when wave height was in any other 

category. Wave heights from 0 to 2 ft had significantly lower 

median concentrations of log10 E. coli than observed in any 

other wave-height category. Concentrations of log10 E. coli

exceeded the standard nearly 50 percent of the time when 

waves were from 3 to 6 ft. 

Modeling to Predict Escherichia coli

Variables statistically related to E. coli as determined by 

Spearman’s test or the Kruskal-Wallis and Tukey-Kramer tests 

were considered as explanatory variables in the development 

of models using tobit regression-analysis techniques. The 

models were used to predict concentrations of E. coli and to 

predict the probability that the E. coli single-sample bathingwater standard of 235 col/100 mL would be exceeded. Predicted exceedance probabilities as output by the best models 

produced from 2- and 3-year combinations of data analyzed 

were used to determine a threshold probability, above which 

the fewest number of false positives and false negatives and 

the greatest number of correct exceedances and correct nonexceedances for E. coli concentrations would be observed. 

A new model was developed after model validation using 

the data collected during 2006 and adding it to the 2004–2005 

dataset. The best 2004–2006 model (model with all 3 years 

of data combined) contained the variables log10 turbidity, 

bird count, and wave height. Combining the 2005 and 2006 

datasets (omitting 2004 data) produced the best model overall 

with the same explanatory variables as when all 3 years of data 

were combined (log10 turbidity, bird count, and wave height) 

and the highest number of correct exceedances (9 out of 14 or 

64.3 percent).

The summary of model output in table 3 shows variables 

and regression statistics for the “best” models produced from 

2- and 3-year combinations of data. The threshold probabilities ranged from 27 in the 2004–2005 (2-year) model 

and 2004–2006 (3-year) model to 26 in the 2005–2006 

(2-year) model; generalized R2 values ranged from 0.66 in the 

2005–2006 model to 0.62 in the 2004–2006 model. All the 

best models included the explanatory variables log10 turbidity and wave height. The best combined 2004–2005 model 

also included the explanatory variables rain weight and wind 

direction, whereas the best 2005–2006 and 2004–2006 models 

included the explanatory variable bird count. 

The regression models were used to predict output 

values for each observation used to develop the models. First, 

models were used to predict E. coli concentrations, and then 

the predicted values for E. coli were used to determine the 

exceedance probabilities—the probability that the predicted 

E. coli concentrations would exceed the standard. A scatterplot 

of observed E. coli concentrations and predicted exceedance 

probabilities for the corresponding predicted E. coli concentrations helps determine a threshold probability for each model 

Figure 4. Log10 Escherichia coli concentrations by wave 

height, Presque Isle Beach 2, City of Erie, Erie County, 

Pennsylvania. 

 [Results of the Tukey-Kramer test are designated with 

letters; categories with at least one letter in common are 

not significantly different]

LOG10 ESCHERICHIA COLI CONCENTRATIONS,

IN COLONIES PER 100 MILLILITERS

1

10

100

1,000

D C B A

(173) (57) (26) (19)

EXPLANATION

Outlier

90th percentile

75th percentile

Median

25th percentile

10th percentile

B Tukey-Kramer letter designation

(10) Number of samples

Single-sample bathing-water 

standard

0-2 1-3 2-4 3-6

WAVE HEIGHT, IN FEET
Summary and Conclusions

that is associated with too great a risk to allow swimming. The 

combined 2005–2006 model results are shown in figure 5. 

The plot is divided into four sections using the E. coli singlesample bathing-water standard to divide the plot vertically 

(2.37=log10 of 235 col/100 mL) and the chosen threshold probability of 26 to divide the plot horizontally. Moving the threshold-probability line up or down on the plot changes the number of observations in each of the four sections. The goal in 

establishing a threshold probability is to maximize the number 

of correct responses showing E. coli concentrations (1) above 

the E. coli standard of 235 col/100 mL and having a predicted 

probability of exceedance above the established threshold 

probability (correct exceedance—upper-right quadrant), and 

(2) meeting the standard by being less than 235 col/100 mL 

and having a predicted probability of exceedance below the 

established threshold probability (correct nonexceedance—

lower-left quadrant). Minimizing the number of incorrect 

responses is another goal in establishing the threshold probability. False negatives (lower-right quadrant) result when the 

standard was, in fact, exceeded but the predicted probability of 

exceedance was below the established threshold probability. 

False positives (upper-left quadrant) result when the standard 

was not exceeded but the predicted probability of exceedance 

was above the established threshold probability. Determinations of whether to close the beach or post an advisory can be 

made if predicted exceedance probabilities exceed the established threshold probability. 

The performance of each model was evaluated by comparing model responses in predicting E. coli concentrations 

and exceedance probabilities to the use of E. coli concentrations from the previous day (table 4). In all cases, responses 

from the models yielded higher percentages of correct predictions than E. coli concentrations from the previous day. The 

overall best model for Beach 2 was produced by excluding 

the 2004 dataset; it is unclear why omitting the 2004 data 

produced a better model. The 2005–2006 model correctly 

predicted when the standard would not be exceeded (specificity) with a response of 95.2 percent (178 out of 187 nonexceedances) and correctly predicted when the standard would 

be exceeded (sensitivity) with a response of 64.3 percent (9 

out of 14 exceedances).

Summary and Conclusions

This report describes a study done during the 2006 recreational season by the U.S. Geological Survey, in cooperation 

with the Erie County Health Department, to validate and refine 

regression models designed to predict E. coli concentrations 

used to determine the probability of exceeding the E. coli

single-sample bathing-water standard at Presque Isle Beach 

2 in Erie, Pa. The results of this study will provide a supplemental method for determining the recreational water quality 

of Presque Isle Beach 2 that will aid beach managers in more 

rapidly determining when waters are not safe for recreational 

use and when to close a beach or post an advisory.

The 2004–2005 model was validated with data collected 

during 2006. Model output (predicted E. coli concentrations 

and predicted exceedance probabilities) produced higher 

percentages of correct predictions than the use of E. coli

concentrations from the previous day. All assessment methods 

produced similar percentages of correctly predicting when the 

standard would not be exceeded (specificities); those percentTable 3. Summary of tobit regression model explanatory variables, statistics, and performance with selected threshold 

probabilities in predicting exceedances of the Escherichia coli single-sample bathing-water standard of 235 col/100 mL for 

Presque Isle Beach 2, 2004–2006.

[Generalized R2, a number between 0 and 1 that is larger when the explanatory variables are more strongly associated with the dependent variable 

(Allison, 1995); threshold probability, exceedance probability chosen for a model on the basis of the E. coli standard of 235 col/100 mL being met 

or exceeded].

Summary

Combined 

2004–2005 model

(2-year dataset)

Combined 

2005–2006 model

(2-year dataset)

Combined 

2004–2006 model

(3-year dataset)

Number of observations 166 201 255

Generalized R2 .64 .66 .62

Explanatory variables in model

log10 turbidity

rain weight

wave height

wind direction

log10 turbidity

bird count

wave height 

log10 turbidity

bird count

wave height 

Threshold probability 27 26 27

Number of correct exceedances 6 9 9

Number of correct nonexceedances 150 178 226

Number of false positives 4 9 10

Number of false negatives 6 5 10
10 Modeling to Predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania 

Figure 5. Observed log10 Escherichia coli concentrations and probability of exceeding 

235 col/100 mL to achieve optimum threshold probability for the combined 2005–2006 model for 

Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania.

[2005–2006 model explanatory variables for determining bacteria concentrations include 

log10 turbidity, bird count, and wave height]

0

PREDICTED PROBABILITY OF EXCEEDING 235 COLONIES PER 100 MILLILITERS

FALSE POSITIVES

CORRECT

NONEXCEEDANCES

100

90

80

70

60

50

40

30

20

10

0

1 2 3

OBSERVED LOG10 ESCHERICHIA COLI CONCENTRATIONS, IN COLONIES PER 100 MILLILITERS

CORRECT

EXCEEDANCES

THRESHOLD PROBABILITY = 26 

S I N G L E - S A M P L E B A T H I N G - W A T E R S T A N D A R D

FALSE

NEGATIVES
Summary and Conclusions

ages were slightly higher in the responses from the model. 

There were differences between the model and the current 

assessment method in percentages of correctly predicting 

when the standard would be exceeded and waters would not be 

safe for swimming (sensitivities). The model responses were 

11.1 percent for predicted E. coli concentrations and predicted 

exceedance probabilities. No correct responses (zero percent) 

were observed for sensitivity using E. coli concentrations from 

the previous day. 

Correlation tests were conducted to determine the continuous variables that were related to log10 E. coli concentrations. In each of the datasets analyzed, log10 turbidity, rain24, 

wave height (calculated), wind speed, and water-current speed 

were found to be correlated to log10 E. coli concentrations. 

The strongest correlations were observed between log10 E. coli 

and log10 turbidity in the combined 2004–2005 dataset and the 

combined 2005–2006 dataset with Spearman’s rho correlation 

coefficients 0.662 and 0.577, respectively. Weaker correlations 

exist between log10 E. coli concentrations and the streamflow 

variables, the rain variables, and number of birds (bird count) 

as indicated by smaller values of Spearman’s rho (statistically significant at the 95-percent confidence level). Variables 

that were statistically correlated to E. coli were considered in 

model development.

The Kruskal-Wallis and Tukey-Kramer multiple-comparison tests were used to determine if there were relations 

between E. coli concentrations and categorical environmental variables. Statistical relations were observed between 

log10 E. coli and wind direction. Significantly higher median 

concentrations of log10 E. coli were observed when winds were 

blowing from the north/northeast direction than when winds 

were from the east, southeast/south, or northwest directions. 

Statistical relations also were observed between log10 E. coli

and direction of water currents. The single-sample bathing-water standard was exceeded when water-current directions were 

northeast/east or southwest. Wave heights were categorized 

into one of five groups—0 to 2 feet, 1 to 3 feet, 2 to 4 feet, 3 

to 5 feet, and 4 to 6 feet. All categories of wave height were 

significantly different from each other. Significantly higher 

log10 E. coli concentrations were observed when wave heights 

were from 3 to 6 feet than any other wave-height category. 

Statistically lower log10 E. coli concentrations were observed 

when wave heights were from 0 to 2 feet than any other wave 

height category.

Models were developed at Presque Isle Beach 2 using 

combinations of data collected from 2004 to 2006. All waterquality and environmental variables that were found to be 

related to log10 E. coli concentrations were considered in the 

tobit regression models. All the “best” models included the 

explanatory variables log10 turbidity and wave height. Rain 

weight and wind direction were explanatory variables in 

the 2004–2005 model; bird count was an explanatory variable in the 2005–2006 and 2004–2006 models. Combining 

the 2005 and 2006 datasets produced a model with the same 

explanatory variables as when all 3 years of data were combined (2004–2006). Using only 2005 and 2006 data produced 

a model with the highest number of correctly predicted 

exceedances (9 out of 14 or 64.3 percent). The explanatory 

Table 4. Comparison of responses of Presque Isle Beach 2 models and responses using current method of assessing bacteriological 

quality of recreational waters.

Dataset Assessment method Number of 

samples

Response (percent)

Total correct Specificity1 Sensitivity2

2004–2005

Model

Exceedance probability 

(threshold 27 percent) 166 94.0 97.4 50.0

Predicted Escherichia coli 166 92.8 98.7 16.7

Current Escherichia coli from the 

previous day 114 88.6 95.2 11.1

2005–2006

Model

Exceedance probability 

(threshold 26 percent) 201 93.0 95.2 64.3

Predicted Escherichia coli 201 92.5 98.4 14.3

Current Escherichia coli from the 

previous day 161 87.6 94.0 0.

2004–2006

Model

Exceedance probability 

(threshold 27 percent) 255 92.2 95.8 47.4

Predicted Escherichia coli 255 92.2 98.7 10.5

Current Escherichia coli from the 

previous day 197 86.3 92.8 6.67

1

 The specificity is the percentage of responses that were correctly predicted as not exceeding the standard (safe for swimming).

2

 The sensitivity is the percentage of responses that were correctly predicted as exceeding the standard (not safe for swimming).
12 Modeling to Predict Escherichia coli at Presque Isle Beach 2, City of Erie, Erie County, Pennsylvania 

variables in the best predictive models for E. coli at Presque 

Isle Beach 2 could indicate that E. coli concentrations from 

birds are being washed into the lake during storms and then 

lakebed sediments harboring bacteria are being resuspended 

when winds produce high waves. In all cases, the results from 

predictive modeling produced higher percentages of correct 

predictions than using E. coli concentrations from the previous 

day.

Further study could focus on improving the predictive 

ability of the model by adding data from new weather stations 

and a streamflow-gaging station closer to the Presque Isle 

beaches. Two new weather stations have been installed—one 

on the tower of the Tom Ridge Environmental Center and one 

near Presque Isle Beach 2 in Presque Isle State Park. These 

weather stations collect various data including rainfall, wind 

speed, and wind direction. Wind and rainfall variables are 

among the explanatory variables that have been shown to 

explain the distribution in E. coli concentrations at Presque 

Isle Beach 2 and collecting data in close proximity to the 

beach might improve the model results. Similarly, streamflow 

is a variable that has been weakly correlated to E. coli concentrations at Beach 2. The installation of a steamflow-gaging 

station on Walnut Creek is planned for the fall of 2007. The 

new gaging station will be closer (about 20 miles) than the 

gaging station from which data were compiled for this study. 

Data from a gaging station closer to the Presque Isle beaches 

may improve the predictive ability of the model. 

Acknowledgments

The author thanks Scott White from the Erie County 

Health Department for his asssistance throughout all phases of 

the project. The author also acknowledges the assistance that 

Linda Zarr of the U.S. Geological Survey provided in helping 

with data compilation and processing.

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