Appendix D.2: Predictive Modeling at Beaches Volume II: Predictive Tools 

for Beach Notification, EPA-600-R-10-176

COMPLETION NOTICE

Pilot test Virtual Beach model for beach notification and advisories/closures (P23).

Refine and validate existing water quality models for freshwater beach notification and 

advisories/closures (P24).

Refine and validate other existing water quality models for marine beach notification and 

advisories/closures (P25).

Summary of the Study 

The study refined and evaluated the Virtual Beach software tool which is designed to build 

multiple linear regression (MLR) models that can predict fecal indicator bacteria (FIB) densities 

measured by culturable and quantitative polymerase chain reaction (qPCR) techniques in both 

freshwater and marine settings. EPA developed and pilot tested the initial version of Virtual 

Beach (Virtual Beach 1.0) using existing data from the Great Lakes. Virtual Beach 1.0 included 

Model Builder to construct beach-specific models, and Beach Advisor as a user-friendly tool for 

acquiring and inputting data to refine beach-specific models and for data visualization. In 2008 

other modeling approaches (SAS, Minitab, and R) were evaluated using site-specific data (e.g., 

UV attenuation, spectral, and DOC measurements, and microbial, meteorological, water quality, 

UV, and current data) from South Shore Beach WI, La Monserrate Beach PR and Hobie Beach 

FL. In 2009, by collecting modeling data from Boqueron Beach PR and Surfside Beach SC, sitespecific modeling predictions were evaluated and Virtual Beach 1.0 was redesigned to become 

Virtual Beach 2.0. This refinement involved an updating of its programming language, including 

all functionality of Virtual Beach 1.0 Model Builder and Beach Adviser, as well as additional 

modeling, visualization and statistical capabilities. The updated version, Virtual Beach 2.0, was 

further evaluated and modified using data from EPA epidemiological studies (from Huntington 

Beach OH, Silver Beach MI, Washington Park Beach IN, West Beach IN, Fairhope Beach AL, 

Goddard Beach RI, and Edgewater Beach MS). The current version, VB 2.1, facilitates the use of 

multiple approaches for evaluating model performance (e.g., comparing observed versus 

predicted FIB densities and/or examining correctly-predicted exceedances and non-exceedances 

of FIB criteria). 

Summary of Findings 

The summary of results from this study is: 

Taking into account time lags and time windows can significantly improve MLR model 

results. 

Model predictions of observed FIB densities were generally more accurate for the 

freshwater beaches than for the marine beaches. 

Models developed using VB 2.0 more closely predicted FIB densities measured by 

culture methods than densities measured by qPCR techniques. 

Turbidity and antecedent rainfall were among the most influential variables for prediction 

of culture at both freshwater and marine beaches. 

The number of swimmers at both freshwater and marine beaches was another influential 

variable, especially at sites and times where large numbers of people were present. 
The effectiveness of environmental variables for prediction of FIB levels was dependent 

on factors such as the method used to measure the FIBs and site specific factors. 

Chlorophyll was most influential for cultured data but UV absorption coefficient was 

most influential for qPCR. 

Chlorophyll and dissolved oxygen were most influential for freshwaters but turbidity, 

salinity, UV absorption coefficients and bird abundance were the most influential for 

marine beaches. 

This study has been completed as of December 15, 2010
Predictive Modeling at 

Beaches

Volume II: Predictive Tools 

for Beach Notification

Richard G. Zepp, Mike Cyterski, Rajbir Parmar, Kurt Wolfe, Emily M. White, and Marirosa Molina

U.S. Environmental Protection Agency

National Exposure Research Laboratory

EPA-600-R-10-176

November 22, 2010

Predictive Modeling at Beaches—Volume II November 22, 2010

i 

Contents

Executive Summary ..................................................................................................................... xi

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

2 Virtual Beach ............................................................................................................................5

2.1 Introduction ...................................................................................................................... 5

2.2 Multiple Linear Regression Model Development ............................................................ 6

2.2.1 Automated Retrieval of Data over the Internet ......................................................... 7

2.2.2 Model Development.................................................................................................. 8

2.2.3 Improving MLR Models Using VB 2.0 Software .................................................... 9

2.2.4 Best Model Selection .............................................................................................. 11

2.2.5 Using MLR Models to Provide Nowcast and Forecast of FIB Concentrations ...... 13

2.3 Features Comparison: VB 2.0 Versus VB 1.0 ................................................................. 13

3 Model Evaluation Strategies .................................................................................................17

3.1 Introduction .................................................................................................................... 17

3.2 Methods .......................................................................................................................... 19

3.3 Results at Various Sample Sizes .................................................................................... 20

3.4 Results within a Sample Size ......................................................................................... 24

3.4.1 Small Sample Size .................................................................................................. 25

3.4.2 Intermediate and Large Sample Sizes ..................................................................... 25

3.4.3 Effect of Response Levels on Predictions .............................................................. 27

4 Study Sites and Data Acquisition .........................................................................................29

4.1 Introduction .................................................................................................................... 29

4.2 Freshwater Beaches (Great Lakes) ................................................................................. 32

4.2.1 South Shore Beach, Milwaukee, Wisconsin ........................................................... 32

4.2.2 West Beach, Porter, Indiana.................................................................................... 33

4.2.3 Washington Park Beach, Michigan City, Indiana ................................................... 33

4.2.4 Silver Beach, St. Joseph, Michigan ........................................................................ 34

4.2.5 Huntington Beach, Bay Village, Ohio .................................................................... 34

4.3 Marine Beaches .............................................................................................................. 35

4.3.1 Goddard Beach, West Warwick, Rhode Island ...................................................... 35

4.3.2 Surfside Beach, Surfside Beach, South Carolina .................................................... 36

4.3.3 Edgewater Beach, Biloxi, Mississippi .................................................................... 36

4.3.4 Fairhope Beach, Fairhope, Alabama ....................................................................... 37

4.3.5 Hobie Beach, Miami, Florida .................................................................................. 37

4.3.6 La Monseratte Beach, Luquillo, Puerto Rico .......................................................... 38

4.3.7 Boquerón Beach, Cabo Rojo, Puerto Rico.............................................................. 38
Predictive Modeling at Beaches—Volume II November 22, 2010

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4.4 Methods and Data Acquisition ....................................................................................... 39

4.4.1 Sample Collection ................................................................................................... 39

4.4.2 Dependent Variables ............................................................................................... 40

4.4.3 Independent (Explanatory) Variables ..................................................................... 41

5 Predictive Modeling of Beaches ............................................................................................47

5.1 Freshwater Sites ............................................................................................................. 47

5.1.1 Data Sources and Methods...................................................................................... 47

5.1.2 MLR Model Results ................................................................................................ 47

5.2 Marine Sites.................................................................................................................... 48

5.2.1 Data Sources and Methods...................................................................................... 48

5.2.2 MLR Model Results ................................................................................................ 48

5.3 Comparison of MLR Modeling Results Across Freshwater and Marine Sites .............. 53

6 Evaluation of Dynamic Modeling and Forecasts of Biological Contamination ...............59

6.1 Materials and Methods ................................................................................................... 59

6.2 Results and Discussion ................................................................................................... 59

6.2.1 Various Approaches to Developing MLR Models for Nowcasts ........................... 59

6.2.2 The Performance of Dynamic Nowcast Models of Variable Duration................... 60

6.2.3 Dynamic Forecasting Models ................................................................................. 62

7 Evaluating the Predictive Capabilities of Models for E. coli Levels at Huntington 

Beach, Ohio, Using Varying Amounts of Historical Data ..................................................63

7.1 Introduction .................................................................................................................... 63

7.2 Methods .......................................................................................................................... 64

7.3 Results and Discussion ................................................................................................... 65

7.4 Conclusions .................................................................................................................... 68

8 The Importance of Site-Specific Environmental Data for Modeling Enterococci 

Densities at South Shore Beach, Wisconsin .........................................................................69

8.1 Introduction .................................................................................................................... 69

8.2 Materials and Methods ................................................................................................... 69

8.2.1 Site Details .............................................................................................................. 69

8.2.2 Data Management ................................................................................................... 69

8.2.3 Model Development................................................................................................ 71

8.2.4 Model Validation/Evaluation .................................................................................. 71

8.3 Results ............................................................................................................................ 72

8.3.1 PA Analysis ............................................................................................................ 72

8.3.2 Combined PA + SS Analysis .................................................................................. 72

8.3.3 Model Comparisons ................................................................................................ 73
Predictive Modeling at Beaches—Volume II November 22, 2010

iii

8.4 Discussion ...................................................................................................................... 75

8.5 Conclusions .................................................................................................................... 76

9 Advanced Techniques to Refine MLR Model Results ........................................................77

9.1 Introduction to Temporal Synchronization .................................................................... 77

9.2 Temporal Synchronization at South Shore Beach.......................................................... 78

9.2.1 Methods................................................................................................................... 78

9.2.2 Results ..................................................................................................................... 79

9.3 Advanced Modeling Techniques at Hobie Beach, Miami ............................................. 84

9.3.1 Introduction ............................................................................................................. 84

9.3.2 Temporal Synchronization Analysis ....................................................................... 84

9.3.3 Data Sub-Setting ..................................................................................................... 84

10 Acknowledgements ................................................................................................................87

11 References ...............................................................................................................................89

Appendix A. Additional Site Details

Appendix B. Additional Data Collection Details 

Appendix C. Regression Modeling Results
Predictive Modeling at Beaches—Volume II November 22, 2010

iv

Tables

Table 4.1. Summary of beach sites (i.e., water type and climate) and field studies that 

served as a source of data for modeling studies .......................................................................41

Table 5.1a. Results of MLR modeling on freshwater beach sites .................................................49

Table 5.1b. Summary statistics for the MLR models for freshwater beach sites. .........................50

Table 5.2a. Results of MLR modeling on marine beach sites .......................................................51

Table 5.2b. Summary statistics for the MLR models for marine beach sites. ...............................52

Table 5.3. Summary of variables used for modeling beach sites...................................................55

Table 5.4. Importance ratings for IVs at freshwater versus marine sites. ......................................56

Table 5.5. Importance ratings for IVs for culturable (CFU) versus qPCR data. ...........................57

Table 6.1. Statistics for the predictions made by models of five temporal durations (seven 

models were fit in each duration category and each one made seven predictions, thus n 

= 49 for each category). ...........................................................................................................60

Table 7.1. The matrix for recording MSE of models developed using a variable number of 

previous years’ data (M1prev–M9prev) applied to each single year of data (Y2001–Y 2009). .........64

Table 7.2. The matrix for recording MSEs of models developed using a single year of data, 

then applying that model to all other years of observations. ...................................................65

Table 7.3. Results of modeling the MSEs of Table 7.1. ................................................................66

Table 7.4. Results of modeling the MSEs of Table 7.2. ................................................................67

Table 8.1. Environmental variables used in model development ..................................................70

Table 8.2. Results of the threshold analysis for the PA and PA+SS models. ................................75

Table 9.1. Statistics for the 500 MEF and MEP values obtained from models developed 

using temporally synchronized data (both PRESS-selected IV aspects, PRS, and 

correlation coefficient-selected IV aspects, PCC) and unsynchronized data (UNS) ...............80

Table A.1. Historical water quality monitoring details and criteria exceedances for 

freshwater beaches based on publicly available data from local monitoring agencies ......... A-4

Table A.2. Historical water quality monitoring details and criteria exceedances for 

temperate and subtropical marine beaches ......................................................................... A-12

Table A.3. Historical water quality monitoring details and criteria exceedances for tropical 

marine beaches based on data provided by the local monitoring agency, PREQB ............ A-20

Table C.1. Regression model for South Shore Beach enterococci qPCR data ............................C-2

Table C.2. Regression model for South Shore Beach enterococci culturable data......................C-2

Table C.3. Regression model for Huntington Beach, Ohio, enterococci qPCR data. .................C-3

Table C.4. Regression model for Huntington Beach, Ohio, enterococci culturable data. ...........C-3

Table C.5. Regression model for Huntington Beach, Ohio, E.coli culturable data, 2003. ..........C-3
Predictive Modeling at Beaches—Volume II November 22, 2010

v 

Table C.6. Regression model for Huntington Beach, Ohio, E.coli culturable data,

2000–2009..............................................................................................................................C-3

Table C.7. Regression model for Washington Park enterococci qPCR data ...............................C-4

Table C.8. Regression model for Washington Park enterococci culturable data.........................C-4

Table C.9. Regression model for Silver Beach enterococci qPCR data. .....................................C-4

Table C.10. Regression model for Silver Beach enterococci culturable data ..............................C-4

Table C.11. Regression model for West Beach enterococci qPCR data .....................................C-5

Table C.12. Regression model for West Beach enterococci culturable data ...............................C-5

Table C.13. Regression model for Boquerón enterococci qPCR data .........................................C-5

Table C.14. Regression model for Boquerón enterococci culturable data ..................................C-5

Table C.15. Regression model for Edgewater Beach enterococci qPCR data. ............................C-6

Table C.16. Regression model for Edgewater Beach enterococci culturable data. .....................C-6

Table C.17. Regression model for Fairhope Beach enterococci qPCR data ...............................C-6

Table C.18. Regression model for Fairhope Beach enterococci culturable data. ........................C-6

Table C.19. Regression model for Goddard Beach enterococci qPCR data. ...............................C-7

Table C.20. Regression model for Goddard Beach enterococci culturable data .........................C-7

Table C.21. Regression model for Surfside Beach enterococci qPCR data ................................C-7

Table C.22. Regression model for Surfside Beach enterococci culturable data ..........................C-7

Table C.23. Regression model for Hobie Beach enterococci qPCR data. ...................................C-8

Table C.24. Regression model for Hobie Beach enterococci culturable data. ............................C-8

Table C.25. Regression model for La Monseratte Beach enterococci qPCR data ......................C-8

Table C.26. Regression model for La Monseratte Beach enterococci culturable data ................C-8
Predictive Modeling at Beaches—Volume II November 22, 2010

vi 

Figures

Figure 2.1. The VB 2.0 Beach Location interface showing a Google Hybrid map. Beach 

orientation is marked by the blue rectangle at the top of the screen. .........................................7

Figure 2.2. VB 2.0 wind and current data decomposition dialog. ...................................................9

Figure 2.3. Pearson scores dialog for transformation of IVs. ........................................................10

Figure 2.4. Response and IV plots. ................................................................................................11

Figure 2.5. Model selection interface. ...........................................................................................12

Figure 2.6. Prediction interface showing populated input data grid, prediction grid, and 

seasonal data grid. ....................................................................................................................13

Figure 3.1. Plot of predictions versus observations for a regression model. .................................18

Figure 3.2. Increasing sample size leads to more significant parameters in the chosen 

model........................................................................................................................................21

Figure 3.3. The mean squared error of fitting (MEF) increases with increasing sample size. ......21

Figure 3.4. The adjusted R2 declines as sample size increases. .....................................................22

Figure 3.5. Declining mean squared errors of prediction with increasing sample size. ................23

Figure 3.6. Sample size effect on the MEP/MEF ratio. .................................................................23

Figure 3.7. Effect of sample size on MEP/MEF for sample sizes greater than 50. .......................24

Figure 3.8. Predictive errors increase with increased adjusted R2. Each of the 150 points 

represents the predictive errors of a testing data set of size = 20 observations. ......................25

Figure 3.9. Relationship between adjusted R2

 and MEP for 150 samples of size 75 ....................26

Figure 3.10. Relationship between adjusted R2 and MEP for 150 samples of size 200. ...............26

Figure 3.11. No clear relationship between the mean Y value in a training data set

(ntrain = 35) and the resultant MEP of the testing data set. .......................................................27

Figure 3.12. No clear relationship between the standard deviation of Y values in a training 

data set (ntrain = 35) and the resultant MEP of the testing data set. ..........................................28

Figure 4.1. Processes considered in collecting IVs for predictive modeling studies. ....................29

Figure 4.2. Location of (A) freshwater and (B) marine beach sites ..............................................31

Figure 4.3. Location of 2008 PREMIER studies at (A) South Shore Beach in Milwaukee, 

Wisconsin; (B) Hobie Beach, Miami, Florida; (C) La Moserrate beach, Luquillo, 

Puerto Rico...............................................................................................................................43

Figure 4.4. Location of 2009 PREMIER/NEEAR study at (A) Boquerón Beach, Puerto 

Rico; (B) Surfside beach, South Carolina. ...............................................................................44

Figure 6.1. Results of models built by VB 1.0 using data at Huntington Beach, Ohio, during 

2006..........................................................................................................................................61

Figure 8.1. Plotting model predictions versus observations for the PA and PA+SS data sets. .....73
Predictive Modeling at Beaches—Volume II November 22, 2010

vii 

Figure 8.2. Plotting the probability that a predicted bacteria count will exceed a threshold 

value (log[61] CFU/100 mL) versus actual observations. .......................................................74

Figure 9.1. A comparison between the MEF values of model developed using temporally 

synchronized data (IV aspects selected using correlation coefficients) and 

unsynchronized data.................................................................................................................80

Figure 9.2. A comparison of the 500 MEP values for the PRS data and the UNS data. ...............81

Figure 9.3. A comparison of the 500 MEP values for the PCC data and the UNS data. ...............82

Figure 9.4. The comparison between the 500 MEP values for the models developed using 

the two different temporal synchronized data, PRESS-selected IV aspects and 

correlation-coefficient-selected IV aspects. .............................................................................83

Figure 9.5. Effects on the regression adjusted R2 and the significance of the residual 

normality test when successively removing observations based on the largest remaining 

DFFIT value in the data set. .....................................................................................................85

Figure A.1. Location of 2008 PREMIER study at South Shore Beach in Milwaukee, 

Wisconsin .............................................................................................................................. A-3

Figure A.2. Locations of (A) Lake Michigan NEEAR studies including (B) 2003 study at 

West Beach in Porter, Indiana, (C) 2004 study at Washington Park Beach in Michigan 

City, and (D) 2004 study at Silver Beach in St. Joseph, Michigan....................................... A-8

Figure A.3. Location of 2003 NEEAR study at Huntington Beach in Bay Village, Ohio. ........ A-9

Figure A.4. Location of 2007 NEEAR study at Goddard Beach in West Warwick, 

Rhode Island ....................................................................................................................... A-11

Figure A.5. Location of 2009 NEEAR/ PREMIER study at Surfside Beach in Surfside 

Beach, South Carolina ........................................................................................................ A-13

Figure A.6. Location of 2005 NEEAR study at Edgewater Beach in Biloxi, Mississippi. ...... A-15

Figure A.7. Location of 2007 NEEAR study at Fairhope Beach in Fairhope, Alabama .......... A-16

Figure A.8. Location of 2008 PREMIER study at Hobie Beach in Miami, Florida. ................ A-17

Figure A.9. Location of 2008 PREMIER study at La Monserrate Beach in Luquillo, 

Puerto Rico.......................................................................................................................... A-19

Figure A.10. Location of 2009 NEEAR study at Boquerón Beach in Cabo Rojo, 

Puerto Rico.......................................................................................................................... A-20
Predictive Modeling at Beaches—Volume II November 22, 2010

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Abbreviations and Acronyms

ADCP acoustic Doppler current profiler

AIC Akaike Information Criterion

AICC Corrected Akaike Information Criterion

BEACH Act Beaches Environmental Assessment and Coastal Health Act

BIC Schwarz Bayesian Information Criterion

CCE calibrator cell equivalents

CDOM colored dissolved organic matter 

CFU colony forming units 

Cp Mallows’ Cp

cm centimeter(s)

CSO combined sewer overflow 

DOC dissolved organic carbon 

EC Escherichia coli or E. coli

EPA U.S. Environmental Protection Agency 

FIB fecal indicator bacteria

GA Genetic Algorithm

IV independent variable 

km kilometer(s)

m meter(s)

MEF mean squared error of fitting 

MEP mean squared error of prediction 

mL milliliter(s)

MLR multiple (or multivariable) linear regression

MSE mean squared error

μm micrometer

nm nanometer

NEEAR EPA National Epidemiological and Environmental Assessment of Recreational 

Water study
Predictive Modeling at Beaches—Volume II November 22, 2010

x 

NOAA National Oceanic and Atmospheric Administration

PA publicly available

PREQB Puerto Rico Environmental Quality Board 

PREMIER Predictive Modeling of Indicator Exposure Research

PRESS Predicted Residual Sum of Squares 

qPCR quantitative Polymerase Chain Reaction

R2 coefficient of determination

RMSE root mean square error

RMSEP root mean square error of prediction 

SS site-specific

TSA temporal synchronization analysis 

TSC target sequence copies

USGS U.S. Geological Survey 

UV ultraviolet

VB Virtual Beach Manager Toolset or Virtual Beach

VIF variance inflation factor 

WWTP wastewater treatment plant
Predictive Modeling at Beaches—Volume II November 22, 2010

xi

Executive Summary

The U.S. Environmental Protection Agency (EPA) is in the process of developing new or revised 

recreational water quality criteria as required in the Beaches Environmental Assessment and 

Coastal Health (BEACH) Act of 2000. Microbial contamination is often assessed by monitoring 

for indicator bacteria such as fecal coliforms, Escherichia coli or fecal enterococci. 

Epidemiological studies have demonstrated a correlation between the levels of those bacteria in

water and rates of gastrointestinal and other illnesses in swimmers. Those fecal indicator bacteria 

(FIB) generally are not a significant cause of illness, but their presence at levels exceeding 

certain criteria indicates that health effects are likely to occur from pathogenic bacteria, viruses, 

or protozoans that are associated with fecal matter. One means to supplement, not replace, 

monitoring results and to make same-day public health decisions is to use predictive tools such 

as statistical models to evaluate beach water quality by providing estimates of FIB densities on 

the basis of current environmental conditions. 

Pioneering studies at beaches on the West Coast and Great Lakes showed that site-specific 

predictive models can be used to determine beach closure notifications. This report supplements 

those earlier studies by refining and evaluating modeling tools for building multiple linear 

regression (MLR) models that can predict FIB densities measured by culturable and quantitative 

Polymerase Chain Reaction (qPCR) techniques at freshwater and marine beaches. The Great 

Lakes component of the research was linked to EPA’s Advanced Monitoring Initiative. The 

research detailed here also was guided by a panel of experts who met in Airlie, Virginia in 2007 

to discuss and recommend critical research needs for developing new or revised recreational 

water quality criteria {USEPA, 2007 #121. 

This document is Volume II of a two-volume report. Volume I summarizes current uses of 

predictive tools that provide beach managers with basic concepts to develop predictive tools 

for same-day beach notifications at coastal, Great Lakes, and inland waters. 

Volume II provides results of research conducted by EPA’s Office of Research and 

Development to develop statistical predictive models at research sites. It also presents Virtual 

Beach—a software package that builds statistical multiple linear regression (MLR) predictive 

models. 

A highlight of the report discussed in Chapter 2 is the development of a user-friendly 

software tool (Virtual Beach [VB]) that can be used to build and evaluate predictive MLR 

models. VB uses a collection of culturable and qPCR microbial FIB data, referred to in the 

report as dependent variables, and concurrently collected parameters that quantified 

environmental conditions at the beach sites. Such parameters are called independent variables

(IVs) in the report. The software systematically relates FIB densities to the IVs to produce an 

optimal fit, i.e., a predictive model. The software’s other capabilities include improving MLR 

modeling by creating interaction terms, transforming variables to maximize response linearity, 

and filtering out highly correlated IVs. The software chooses models (i.e., selects IVs) by 

optimizing metrics such as Root Mean Square Error (RMSE), Akaike Information Criterion, 

Bayesian Information Criterion, and Predicted Residuals Sum of Squares (PRESS) and includes 
Predictive Modeling at Beaches—Volume II November 22, 2010

xii

a genetic search algorithm for handling a large number of IVs. In any endeavor involving 

predictive modeling, variability and uncertainty is associated with the model output. Such

uncertainty arises from a variety of factors that are impossible to completely eradicate from the 

modeling exercise. VB addresses the uncertainty issue by providing a probability of exceedance 

for any regulatory standard that the user wishes to investigate. Even so, there is no guarantee that 

every model prediction will be correct, and a situation where the model predicts water quality to 

be good enough for public recreation could be erroneous. Decisions to open or close the beach 

must be made, however, and in the best case scenario, the regression models developed using VB

will outperform less rigorous predictive efforts. 

VB facilitates the use of different approaches to evaluate model performance. On the basis 

of analyses of data obtained at a freshwater beach using VB, we recommend having at least 

50 observations for model development but, having 100 or more is preferable. However, 

shorter-term dynamic models might still provide useful guidance for beach managers as 

the longer term data sets are obtained. That conclusion should be evaluated using longterm data sets from other locations, especially from coastal marine beaches. Chapter 3 of 

this report discusses several different approaches that are used to evaluate model performance. 

Volume I and other parts of this report includes discussion of the use of model builders such as 

VB version 2.0 to select the best model for a given data set. The VB tool can be used to examine 

techniques for evaluating the performance, or trustworthiness, of this best model. Among other 

approaches to evaluate whether a chosen model is good in an absolute sense rather than best in a 

comparison to other potential models (see Chapter 3 on model evaluation methods), we used the 

model’s adjusted coefficient of determination (adjusted R2

) and the RMSE to evaluate the fit 

achieved in regression of predicted versus observed values. Another approach involves 

evaluating a model’s ability to predict observations known as exceedances, i.e., observations that 

are greater than a given value (e.g., an EPA regulatory threshold for FIB levels at freshwater 

beaches). Another assessment of a model’s goodness-of-fit uses a process called crossvalidation, in which the data set is split into a training data set and a testing data set. A model 

built by fitting the former is used to make predictions for the latter. Analysis of a decade-long 

data set collected by the U.S. Geological Survey (USGS) at Huntington Beach, Ohio, indicated 

that the ratio of predictive to fitting errors moves toward unity as the sample size increases.

To provide the data needed for refining and evaluating statistical models, we developed a 

program designed to enhance the predictive modeling of indicator exposure research

(PREMIER). Using automated instruments to obtain data enhanced modeling results by 

facilitating application of new modeling techniques such as temporal synchronization 

analysis (Chapter 9). The dependent variables and IVs obtained in those studies were used for 

model refinement at selected freshwater beaches on the Great Lakes and at coastal marine 

beaches of the eastern United States and in the tropics. That part of the research is discussed in 

Chapter 4 and the appendices. We chose culturable enterococci and enterococci qPCR as the 

dependent variables because previous studies have shown that enterococci are the best FIB for 

assessing risk at both freshwater and marine beaches. We deliberately patterned the spatial and 

temporal sampling patterns of those studies after those used in EPA’s National Epidemiological 

and Environmental Assessment of Recreational Water (NEEAR) studies. At the PREMIER 

beach sites, we used automated techniques for IV measurements that were not used in most 

NEEAR studies or in other modeling studies. We also used data provided by EPA’s NEEAR 

epidemiological studies team.EPA data from a total of five freshwater and seven marine beaches 
Predictive Modeling at Beaches—Volume II November 22, 2010

xiii

were used in the studies. In addition, our model evaluation studies used the extensive data set 

obtained over 10 years by USGS and collaborators at Huntington Beach, Ohio. 

Comparisons of the MLR modeling results provided in Chapter 5 indicate that, on the 

basis of adjusted R2 values for predicted versus observed levels of the FIB, model 

performance was better for the freshwater beaches than for the marine beaches 

(freshwater average adjusted R2 = 0.5, marine average adjusted R2 = 0.39). Also, modeling 

results for the culturable FIB data are somewhat better than for the qPCR data (colony 

forming units [CFU] average adjusted R2

 = 0.46, qPCR average adjusted R2 = 0.42). The 

lower values for marine beaches likely reflect the interplay of several factors. Those factors 

include the effects of currents and tides at the beaches, sunlight-induced inactivation, and inputs 

of FIB from bird and dog droppings, bather shedding, runoff, groundwater and desorption from 

sand and decaying vegetation. Waves also can be an important factor that reduces model 

performance; however, all but one of the marine beaches examined in the study were enclosed 

bays or estuaries that had subdued wave action. 

Another general finding of Chapter 5 is that the models are much more accurate in 

predicting non-exceedances than exceedances at the beaches included in the study. On the 

other hand, on the basis of general ability of the models to predict observed FIB densities 

throughout the data sets (judged by the adjusted R2

), little evidence was apparent of a 

relationship between FIB densities and model performance, although we had expected that 

there might be. One contributing factor to the findings, especially in regards to the marine sites 

we studied, is that the data sets include very few exceedances. Accurately predicting phenomena 

(such as exceedances) that are rarely seen in the training data set is a very difficult task for a 

statistical model. In the case of freshwater beaches modeled in the study, CFU modeling results 

for the two cleanest beaches, South Shore Beach and West Beach, were among the best. 

Likewise, satisfactory modeling results were obtained at marine beaches such as Surfside Beach 

where almost no exceedances were observed. Although comparisons of results using culturable 

enterococci or E. coli were limited, we did find that model performance was about the same for 

both indicators, e.g., at Huntington Beach, Ohio, during 2004. 

The VB tool was successfully used to evaluate the effectiveness of various IVs in predicting 

culturable-based and qPCR-based observations of enterococci at freshwater and marine 

beaches (Chapter 5). The analysis showed that 

1. Turbidity and antecedent rainfall were top IVs for culturable enterococci at both 

freshwater and marine beaches. This conclusion reinforces the findings of earlier 

studies.

2. The number of swimmers is an important IV, perhaps in part because part of our 

data sets were obtained at the NEEAR sites that were selected to ensure that large 

numbers of people were present for epidemiological studies at the beaches. 

Presumably, shedding could have contributed to this finding. 

3. The effectiveness of IVs was dependent on factors such as the method used to 

measure the FIBs and site-specific factors. For example, chlorophyll was the top IV for 

culturable measurements of FIB, but water UV absorption coefficient was the top IV for 

qPCR measurements. Chlorophyll and dissolved oxygen were top IVs for freshwaters, 

but turbidity, salinity, absorption coefficients, and bird abundance were the top variables 
Predictive Modeling at Beaches—Volume II November 22, 2010

xiv

for marine beaches. Additional process-based research is required to understand the 

various factors that underlie the results of the statistical models.

Models developed using the VB tool can provide useful analyses of (1) the effect of the data 

set’s length on model performance (Chapters 6 and 7). It could be valuable for optimizing 

and updating dynamic models based on short-term data sets.; (2) effects of data source 

location on the accuracy of models developed for a freshwater beach (Chapter 8); and 

(3) sub-grouping of data sets to help improve modeling results (Chapter 9).

Taking into account time lags and time windows using a temporal synchronization analysis

can significantly improve MLR model results. Analyses of data from a freshwater and 

marine beach (Chapter 9) showed that temporal synchronization analysis is a noteworthy 

modeling technique that should be pursued. That methodology computes mean values of the 

IVs over temporal windows and lags relative to the time at which the response variable is 

measured. That is done to improve the statistical relationship between the IVs and the response. 

Applying the technique at a freshwater beach in the Great Lakes (South Shore Beach, 

Milwaukee) produced better MLR models compared to models using IVs measured at the time of 

FIB sampling.
Predictive Modeling at Beaches—Volume II November 22, 2010

1 

1 Introduction

Contamination of recreational waters and drinking water supplies by pathogenic microorganisms 

has attracted the attention of environmental groups, public health officials, and water resource 

managers in coastal areas. Microbial contamination is often assessed by monitoring for indicator 

bacteria such as fecal coliforms, E. coli or fecal enterococci. Epidemiological studies have 

demonstrated a correlation between the levels of those bacteria in water and rates of 

gastrointestinal and other illnesses in swimmers. Those fecal indicator bacteria (FIB) generally 

are not a significant cause of illness, but their presence at levels exceeding certain criteria 

indicates that health effects are likely to occur from pathogenic bacteria, viruses, or protozoans 

that are associated with fecal matter. Fecal contamination originates from many sources, 

including coastal and shoreline development, wastewater collection and treatment facilities, 

septic tanks, urban runoff, disposal of human waste from boats, bathers themselves, animal 

feeding operations, and natural animal sources like wildlife and pet wastes.

State and local public health agencies use beach advisories and closings to communicate to the 

public that the level of pathogens in the water could be unsafe for swimming or other body 

contact recreation. The advisories and closings are based on water quality information and 

typically occur when monitoring results show that fecal bacteria levels exceed an applicable 

water quality criterion. The model can be very effective in locations where conditions change 

slowly, i.e., where conditions persist. But FIB densities often are highly uncorrelated with those 

of the previous day. 

The Beaches Environmental Assessment and Coastal Health (BEACH) Act of 2000 requires 

coastal states to submit to the U.S. Environmental Protection Agency (EPA) monitoring, 

notification, and other information concerning their beaches. Recreational water quality 

assessments are based primarily on enumerating FIB; such measurements can take up to a day to 

complete. When beach advisories rely on sampling techniques that require about a day to 

analyze, a closure decision is made using a persistence model, which assumes that the last 

measured FIB density accurately reflects current contamination levels. Microbial densities can be 

highly dynamic because they are sensitive to factors such as changing meteorological conditions, 

water hydrodynamics, solar irradiance and in-water composition such as temperature and salinity 

(Boehm et al. 2007; Boehm 2003; Whitman et al. 2004). Thus, water-quality advisories based on 

the persistence model are likely of limited relevance to current bacterial densities (Kim and 

Grant 2004). The emerging use of rapid monitoring techniques such as quantitative Polymerase 

Chain Reaction (qPCR) techniques can help reduce that time lag (Haugland et al. 2005), but up 

to 4 hours or more are still required to use such techniques. An alternative approach for 

evaluating beach water quality uses models to predict indicator densities in recreational waters. 

Predictive models can provide useful and timely estimates that have been the basis for advisories 

at several locations in the Great Lakes and coastal marine beaches. The utility of predictive 

models is reflected by the fact that the BEACH Act included a Beach Action Plan that calls for 

research on developing predictive models to assess recreational water quality. 

An overview of tools that have been used to develop predictive models is provided in Volume I 

of this report. It emphasizes statistical models and provides background information on (1) types 

of predictive models and tools that can be used to make beach notification decisions; 

(2) influences that different hydrologic environments have on biological contamination of 
Predictive Modeling at Beaches—Volume II November 22, 2010

2 

beaches and how consideration of those influences affect model development; (3) predictive 

tools that health departments and other responsible agencies are using to make timely decisions 

on beach notifications; (4) procedures for developing statistical predictive models such as MLR 

models, rainfall thresholds, and notification protocol; and (5) trends in predictive tools for beach 

notifications, including deterministic tools.

In Volume II, we present specific considerations of research on how to improve and evaluate 

tools for creating statistical models that predict FIB levels at freshwater and marine beaches. The 

research was fostered initially through interactions with EPA Region 5 and scientists from the 

U.S. Geological Survey (USGS), National Oceanic and Atmospheric Administration (NOAA) 

and other partners in a Great Lakes project sponsored by EPA’s Advanced Monitoring Initiative. 

That project focused on exchanging information and comparing modeling approaches at selected 

beaches of the Great Lakes. With that information in hand, a pilot study was conducted to 

improve and evaluate the statistical component of a model-building tool called Virtual Beach 

(VB). The results of that effort are described partly in Section 2.2 of this report. After software 

improvements, VB version 1.0 (VB 1.0) was created. Communicating VB 1.0 to end users was 

accomplished through several workshops conducted by the Wisconsin Department of Natural 

Resources, which was doing its own extensive testing of the software. Monitoring personnel 

from across the Great Lakes attended its two hands-on training workshops, which provided direct 

technical assistance to potential end users (Mednick and Watermolen 2009). The effort resulted 

in a number of recommendations for enhancing VB from a local operations perspective. 

Modifications made to version 1.0 before the 2009 beach season enabled a successful use case at 

Upper Lake Park Beach in Ozaukee County, Wisconsin 

(http://dnr.wi.gov/org/es/science/pdf/OzaukeeCountyWisconsin.pdf). Feedback from workshop 

participants and end users has informed the development of VB version 2.0 (VB 2.0). Personnel 

at other agencies, such as the USGS, NOAA and local governments, such as Lake County, 

Illinois, have been helpful in developing and refining the tool. 

The research detailed here also was guided by a panel of experts who met in Airlie, Virginia, in 

2007 to discuss and recommend critical research needs for developing new or revised 

recreational water quality criteria {USEPA, 2007 #121}. A sub-group of the panel met to discuss 

modeling applications for FIB prediction. The group’s recommendations that are relevant to the 

research reported here are the following:

• Developing and testing simple (heuristic statistical) notification models on different 

recreational water types with a wide range of sources and geographical locales. 

• Training recreational water managers. 

• Creating a user-friendly portable package for developing local models. 

• Investigating the effect of meteorological factors (e.g., rainfall, evapotranspiration) on 

nonpoint sources. 

• Conducting modeling studies concurrently with planned epidemiological studies to help 

link statistical models to health effects.

A key aspect of predictive modeling involves collecting the data used to create the models. MLR

models are the main statistical model used for making beach closure or advisory decisions. 

Building such models requires relevant microbial data (the dependent variable in MLR models) 
Predictive Modeling at Beaches—Volume II November 22, 2010

3 

and other concurrently observed hydrometeorological and biogeochemical data (independent 

variables or IVs) that characterize the beach. Although monitoring data for culturable FIB have 

become more abundant in recent years, citable information involving qPCR measurements of 

FIB densities in recreational waters are scarce. Because qPCR data provide useful information 

about the sources and health impacts of fecal contamination, developing predictive model 

techniques for this type of measurement is also of interest. Compared to the amount of microbial 

data now available for beaches, it is difficult to find beach studies in which microbial data and 

relevant IVs have been concurrently observed. When these studies were initiated, predictive 

models had been developed primarily at beaches of the West Coast and Great Lakes (Boehm 

2007; Francy et al. 2006b; Nevers and Whitman 2005). Although those pioneering studies 

showed that statistical models were quite useful for beach notifications, the predictive approach 

needed to be evaluated using culturable- and qPCR-based data from other types of recreational 

waters, including data collected as part of epidemiological studies.

Our objectives in this study were the following: 

1. Develop a user-friendly software tool for building and evaluating predictive MLR 

models that can be used for beach notifications. 

2. Use various strategies for model evaluation, e.g., cross-validation or exceedances of 

regulatory criteria, to assess the effects of differing data set sizes on model 

performance.

3. Refine and evaluate the capabilities of this modeling tool using concurrently collected 

culturable- and qPCR-based data and IVs from selected freshwater and marine beaches 

in the Great Lakes, eastern and southeastern United States, and the tropics (Puerto 

Rico).

4. Use data from epidemiological study sites to refine and evaluate the modeling tool. 

5. Collect IVs using automated techniques to provide sufficient data to evaluate the 

dependence of model performance on the period over which the IVs are collected. 

6. Use data from objective 4 above, evaluate the dependence of model performance on the 

period over which the IVs are collected (going beyond a focus on precipitation only). 

7. Evaluate the relationship between the degree of contamination at a beach and model 

performance.

8. Compare model performance and the most important IVs at both freshwater and marine 

beaches in which similar or the same types of microbial and IV data were obtained.

9. Compare model performance for culture-based and qPCR-based methods that were 

used to measure beach contamination.

10. Provide model results that can be used to help evaluate the variability of model 

performance at a beach over differing periods of data collection.

11. Compare the results of models constructed using IV data obtained from sources that are 

varying distances from a beach, i.e., at the beach or several miles away from the beach.

12. Evaluate the use of data sub-grouping to improve model performance. 
Predictive Modeling at Beaches—Volume II November 22, 2010

4 

Chapter 2 of the report provides a general discussion of the VB software. The software and its 

user guide are provided on the Web separately from this report. Chapter 3 discusses several 

different approaches used to evaluate model performance and applies the approaches in an 

assessment of sample size on model performance. In Chapter 4 and the appendices, we provide 

information about characteristics of the various beaches that were the subjects of the modeling 

efforts and approaches used in predictive modeling of indicator exposure research (PREMIER) 

to acquire the data for the modeling studies. Chapter 5 presents and discusses MLR modeling 

results for the various freshwater and marine beaches in this report where the data were collected 

by EPA (PREMIER and NEEAR [National Epidemiological and Environmental Assessment of 

Recreational Water] research). The discussion includes evaluation of the performance of VB 2.0 

at the various beaches and identifies the most effective IVs for the beaches. The results are 

compared with results from other regions, and possible impacts of beach conditions on the 

results are discussed. The remainder of the report details efforts that have been pursued in this 

study to improve statistical modeling techniques. Chapter 6 provides results on the variability of 

model performance at a beach over differing periods of data collection. We provide evidence that 

short-term dynamic models—those that are re-fit periodically to new data as they become 

available—can provide satisfactory short-term predictions (nowcasts) of FIB densities and that 

predictive models can be structured to provide 24-hour forecasts of FIB levels. Chapter 7 

presents evidence that models built from extensive long-term data for a freshwater beach provide 

results superior to those based on short-term data sets. Chapter 8 shows the utility of the 

modeling approach by providing comparisons of models constructed using IV data obtained from 

sources that are varying distances from a beach, i.e., at the beach or several miles away from the 

beach (or both). Chapter 9 introduces the concept of temporal synchronization to refine MLR 

model results. That technique was used to improve modeling results at both a freshwater beach in 

Milwaukee and a marine beach in Miami. Chapter 10 summarizes and discusses the modeling 

results detailed in Volume II.
Predictive Modeling at Beaches—Volume II November 22, 2010

5 

2 Virtual Beach

2.1 INTRODUCTION

VB 2.0 is a software package designed to construct site-specific MLR models to predict 

pathogen indicator levels at recreational beaches. The VB 2.0 modeling interface is designed to 

help find the best model amongst a large number of candidate models, based on criteria selected 

by the user. As the number of IVs increases, the number of possible models in the solution space 

increases exponentially. The user is able to select all, or a subset of, the IVs for consideration in 

the model to reduce the size of the solution space. 

A pilot study for developing the VB tool was conducted using historical data for E. coli and 

various relevant IVs for Huntington Beach, Ohio (Frick et al. 2008). The site and data collection 

techniques are described in Section 4.2.5 of this report and in Francy et al. (2006a; Francy and 

Darner 2007). The data were collected by the USGS Ohio Water Science Center and its partners, 

the Cuyahoga County Board of Health, and others. 

The early version of the VB tool(VB 1.0) was designed to help develop statistical models 

(equation 2.1) for predicting beach FIB densities (denoted by EC):

i

p

i

i E EC ∑ x =

+=

1

0 )][ln( ββ , (equation 2.1) 

where E[ln(EC)] represents the expected value of the natural logarithm of the mean of the 

dependent variable (EC), β0 and βi are the regression coefficients, xi the IVs and p the number of 

variables used in the model. MLR analysis is based on the least squares method to fit models and 

is subject to several considerations, notably variable interactions, multi-collinearity and model 

selection. Their relevance to beach bacteria modeling was described further by Ge and Frick (Ge 

and Frick 2007). VB 1.0 used a backward elimination process, described in the parsimonious 

model section below, to help the user select the most promising model from a number of 

candidates that rapidly increase with the number of IVs in the analysis. That process offered a 

way to rank the usefulness of the selected IVs, with the best variable being the last recommended 

for elimination.

By definition, MLR equations (equation 2.1) are linear. That property can limit the value of IVs 

if the response variable is not a linear function of the variable. Often, variable transformations 

are used to overcome this limitation. In fact, the response variable itself is routinely natural logtransformed, a transformation that, alone, substantially increased the adjusted coefficient of 

determination (adjusted R2

) value of the model. VB 1.0 offered a number of common 

transformations, including square root, square, and others that, when selected, automatically 

transform the values of the IVs. Transformations can greatly increase the predictive value of 

vector quantities, such as wind and current (Nevers et al. 2007). For example, wind speed and 

direction are two IVs that, untransformed, often rank low as MLR IVs (Olyphant and Whitman 

2004). The problem is that wind and current are vector quantities, and direction is a harmonic 

function. By transforming vector variables into their components, however, e.g., into along-shore 

and cross-shore, their value often is enhanced. VB 1.0 included the trigonometric 

transformations for converting wind (or current) speed and direction into their vector 
Predictive Modeling at Beaches—Volume II November 22, 2010

6 

components, including axis rotation. It also offered asymmetric transformations, because, for 

example, the effects of wind speed can be completely different for onshore winds than offshore 

winds. Thus, the offshore component might be square-root transformed, while the onshore 

component remains unchanged. 

Most importantly, VB 1.0 helped to identify the best IVs from the suite of potential variables 

available for fitting. In a typical study, dozens of candidate variables might be considered 

(Olyphant 2005; Olyphant and Whitman 2004). Each variable tended to increase the explained 

variance but, in successively smaller increments, compared the best variables. Fit to noise or to 

chance occurrences present in the data, and risking multi-collinearity, the marginal variables can 

degrade prognostic performance, and model maintenance also can increase. In practice, a smaller 

set of variables from which a parsimonious model is finally selected is preferred. In this work, 

the number of variables recommended for the parsimonious model ranged from two to five, but, 

for uniformity and comparability, four variables were retained. To help the user identify the most 

significant variables, VB 1.0 offered an automated model selection facility. VB 1.0 used 

backward elimination with Mallows’ Cp (Frick et al. 2008)

22 2 /))(( p full full npC p −−+= σσσ (equation 2.2) 

as the selection criterion, where n is the number of samples, p is the number of included 

variables, and σ

2

 and σfull

2 are the residual variances of the reduced and full models. The 

parsimonious model is defined as the one with the minimum Cp value among the full (all 

variables) and the reduced (fewer variables) models. The automated model selection command

of VB 1.0 computed the Cp statistic for all possible models and ranked the variables for 

elimination. If the default parsimonious model recommended by VB 1.0 is not selected, a 

process of guided variable elimination based on other factors that might influence variable 

selection, can be performed to arrive, stepwise, at the final model.

VB 1.0 offered other features, such as warnings when the data matrix is singular and when

residuals demonstrate significant serial correlations. Users could also check for influential cases

(i.e., those that greatly influence the values of the regression coefficients) and data outliers. 

Although VB 1.0 provided a useful tool for building MLR models, it did not have the full range 

capabilities of VB 2.0 described in Section 2.3.

2.2 MULTIPLE LINEAR REGRESSION MODEL DEVELOPMENT

Variability and uncertainty are intrinsically associated with the model output of any predictive 

modeling endeavor. . Such uncertainty arises from a variety of factors that are impossible to 

completely eradicate from the modeling exercise. VB addresses the uncertainty issue by 

providing a probability of exceedance for any regulatory standard that the user wishes to 

investigate. Even so, there is no guarantee that every model prediction will be correct, and a 

situation where the model predicts water quality to be good enough for public recreation might 

be erroneous. Decisions to open or close the beach must be made, however, and in the best case 

scenario the regression models developed using VB will outperform less rigorous predictive 

efforts.

VB 2.0 is a software package designed to construct site-specific (SS) MLR models to predict 

pathogen indicator levels at recreational beaches. MLR has been shown to outperform 
Predictive Modeling at Beaches—Volume II November 22, 2010

7 

persistence models (using only FIB concentrations at time t-1 to predict FIB levels at time t) 

beaches where conditions such as weather, hydrology, and human and animal traffic levels 

change significantly day to day (Frick et al. 2008). On the basis of direct user input and 

participants’ feedback at the VB1 workshops conducted by Wisconsin’s Department of Natural 

Resources, several enhancements were made to VB 1.0. For example, VB 1.0 was written in a 

computer language called Delphi; VB 2.0 has been written in Microsoft.NET language C# which 

makes it more inter-operable with other open source and commercial software libraries. Other 

improvements in VB 2.0 include better data import/export, improved data preparation methods, 

enhanced user interface, more model selection criteria, better reporting of modeling results, 

handling of larger number of IVs, improved prediction capabilities once a model has been 

developed, and new project management functions. 

2.2.1 Automated Retrieval of Data over the Internet

VB 2.0 automatically retrieves geospatial data from the Internet and displays it on a map. That 

allows the user to locate the beach of interest and determine its orientation, which is important 

when processing wind and current data (Figure 2.1). Cross-shore and along-shore wind and 

current components affect pathogen indicator levels in some beach waters. Locating the beach on 

a map also allows VB 2.0 users to identify meteorological and water quality monitoring stations 

in the vicinity of the beach. 

Figure 2.1. The VB 2.0 Beach Location interface showing a Google Hybrid map. Beach orientation 

is marked by the blue rectangle at the top of the screen.
Predictive Modeling at Beaches—Volume II November 22, 2010

8 

2.2.2 Model Development

VB 2.0 uses a multilinear regression technique to relate a dependent variable (FIB densities) to 

IVs such as meteorological conditions, hydrological and water variables. The user can provide 

data for any number of potential model IVs. VB 2.0 allows the user to import data from 

Microsoft Excel spreadsheets. FIB concentration values can vary from 0 to several million or 

more. Such a large variation in dependent variable values often violates the assumption of linear 

relationship between the dependent and IVs in MLR. To make the relationship between 

dependent variables and IVs a linear one, it is recommended that the FIB concentration values be 

transformed, using a log transformation. The dependent variable values can be transformed either 

before or after importing data into VB 2.0. 

VB 2.0 alerts the user for missing values of IVs. The user can then decide whether to exclude 

data with missing values from the analysis or enter estimates for missing values. VB 2.0 ensures 

that sufficient data points are available before a model can be developed. To develop a 

meaningful model, it requires a minimum ratio of 1:5 (although 1:10 is preferable) between the 

number of IVs and FIB concentration values. 

Processing wind and current data also is facilitated by VB 2.0. Using beach orientation (beach 

angle), VB 2.0 processes wind and current data into cross-shore and along-shore components 

(Figure 2.2). Two new data columns corresponding to the two components are automatically 

added to the data table. Beach orientation is automatically calculated if the beach is defined using 

the mapping interface in VB 2.0. Otherwise, the user must specify the beach orientation using the 

rules given in VB 2.0 user’s guide. 

The user can opt to develop a model with any subset of IVs. The user also specifies model 

evaluation (goodness of fit) criteria. In addition, the user specifies the maximum value of 

variance inflation factor (VIF) to be tolerated. VIF measures multi-collinearity in MLR. From 

the user’s choices, VB 2.0 develops and ranks models by the specified model selection criterion. 

The top models are presented with various types of model statistics and graphs for each, allowing 

users to decide on the best model for their application. 
Predictive Modeling at Beaches—Volume II November 22, 2010

9 

Figure 2.2. VB 2.0 wind and current data decomposition dialog.

2.2.3 Improving MLR Models Using VB 2.0 Software

VB 2.0 presents many ways to improve MRL modeling. Decomposition of wind and current data 

into cross-shore and along-shore parts, interactions between IVs, transformation of dependent 

and IVs, and filtering out highly correlated IVs all help to improve MLR modeling exercises. 

Creating Interaction Terms. The user is presented with an option to include two-way interactions 

between IVs. Interaction between two IVs implies that the relationship between the first IV and 

the dependent variable is influenced by the second IV. If the user believes there are no 

interactions between the IVs, this step can be skipped. 
Predictive Modeling at Beaches—Volume II November 22, 2010

10 

Transforming Variables to Maximize Response Linearity. If a relationship between the response 

variable and an IV is nonlinear, the IV can be transformed to make the relationship linear. VB 

2.0 provides five types of IV transformations: polynomial, square root, inverse, natural log, and 

log to the base 10. For a comparison of the response variable to each IV, a univariate correlation 

statistic (Pearson Correlation Coefficient) is calculated for each transformation (Figures 2.3 and 

2.4). By default VB 2.0 uses the transformation with the highest value of Pearson Correlation 

Coefficient, but the user can accept any other transformation or to pick a transformation based on 

univariate relationship plots. 

Figure 2.3. Pearson scores dialog for transformation of IVs.
Predictive Modeling at Beaches—Volume II November 22, 2010

11 

Figure 2.4. Response and IV plots.

Filtering out highly correlated IVs. MLR has an underlying assumption that the IVs are not 

highly correlated with each other. VB 2.0 uses VIF to filter out highly correlated IVs. The higher 

the value of the VIF, the stronger the correlation between the variables:

VIF = 1 / (1 – Ri

2

) (equation 2.3) 

where Ri

2

 is the coefficient of determination of a regression where the IV in question is used as 

the dependent variable, and all other IVs in the model are used as predictors. As such, a VIF 

value is calculated for every IV in the regression model. The user specifies the maximum value 

of VIF, and VB 2.0 drops any model with an IV whose VIF value exceeds that threshold.. 

2.2.4 Best Model Selection

VB 2.0 uses two methods to develop possible MLR models. If the number of IVs is not large, an 

exhaustive search method is used. In the exhaustive method, MLR models are developed with all 

possible combinations of the IVs. Invalid models, such as those including highly correlated IVs, 

are dropped. The remaining models are then ranked, on the basis of user-specified model 

selection criterion such as Akaike Information Criterion (AIC), Corrected AIC (AICC), Bayesian 

Information Criterion (BIC), R Squared, Corrected R Squared, Predicted Residual Sum of 

Squares (PRESS) Statistics, Root Mean Square Error (RMSE), number of true positives 

(Sensitivity), number of true negatives (Specificity), and overall correct number of positives and 

negatives (Accuracy). The top models are then presented to the user along with various model 

statistics. Users can then examine the statistics to select the best model for their application. The 

user has the following statistics available for each IV in a model: standard error, t-statistics, and 

p-value. Although models are ranked by a single user-specified criterion, the following statistics 
Predictive Modeling at Beaches—Volume II November 22, 2010

12 

available for each ranked model help the user pick the model best suited to his or her application: 

R Squared, Adjusted R Squared, AIC, AICC, RMSE, BIC, PRESS statistics, Sensitivity, 

Specificity, and Accuracy. A graph of observations versus predictions can be used to further 

assist model selection (Figure 2.5). 

Figure 2.5. Model selection interface.

As the number of IVs increases, the number of possible models to be developed increases 

exponentially. VB 2.0 uses an artificial intelligence technique called Genetic Algorithms (GAs) 

to reduce the number of models developed when the number of IVs is large. GAs are search 

methods inspired by evolutionary biology. They are based on genetic processes such as 

inheritance, selection, crossover, and mutation that are seen in nature for species evolution. 

While GAs cannot be used directly for modeling beach pathogens, they can be used to evaluate 

and select models developed by other modeling techniques. Rather than developing and 

evaluating every possible model, GAs intelligently select IVs to be used, resulting in fewer 

models that need development and evaluation. GAs often result in finding the near-best model, 

as opposed to finding the best model. 

The user specifies GA performance parameters such as initial population size, stopping criterion, 

crossover and mutation rates, random number generator seed, and the like. The model ranking 

and selection criteria remain the same as the exhaustive search method. GAs and exhaustive 

methods can also be combined to achieve better models for situations with a large number of 

IVs. First, the user takes a collection of all IVs represented in the top few (five or so) models 

ranked by GAs then selects the exhaustive method using the IVs collection from step one. In 

other words, GAs are used to select a set of potential IVs to be used in the exhaustive search 

method. 
Predictive Modeling at Beaches—Volume II November 22, 2010

13 

2.2.5 Using MLR Models to Provide Nowcast and Forecast of FIB 

Concentrations

Once a suitable model has been selected as described in the previous sections, VB 2.0 can be 

used to make FIB concentration predictions. Two types of predictions can be made with a model: 

predictions based on current and recently observed values of IVs (nowcast), and prediction based 

on forecasted values of IVs (forecast). VB 2.0 lets the user either directly enter values of IVs or 

import data from an Excel spreadsheet. Interactions and transformations, if required, are 

calculated automatically in the background. Predicted values of the response variable, and the 

probability of exceedance, are presented to the user. Predictions can be made for a single set or 

multiple sets of IVs. Predictions can be exported to Microsoft Excel. Predictions also can be 

appended to existing predictions for recordkeeping (Figure 2.6). 

Figure 2.6. Prediction interface showing populated input data grid, prediction grid, and seasonal 

data grid.

2.3 FEATURES COMPARISON: VB 2.0 VERSUS VB 1.0

VB1.0 and VB 2.0 are SS pathogen-predictor software packages designed to explore and analyze 

users’ data sets to produce a best-fit MLR model and employ such a model for estimating future 

pathogen levels using environmental data collected at the beach site. Both versions use 

regression methodologies to measure the appropriateness of variables for inclusion in models.
Predictive Modeling at Beaches—Volume II November 22, 2010

14 

VB 1.0 can be characterized as an MLR model building tool that supports a primarily manual 

analysis of data sets by visual inspection of data plots and manipulation of variables (e.g. 

transformations, creating interaction terms), followed by an iterative process of testing, 

comparing and evaluating models. The fitness of developed models is computed and tracked, 

allowing for comparison and eventual selection of a best model for the data set under 

consideration. This model can then be used to produce estimates of pathogen levels with current 

or forecasted environmental data from the site.

VB 2.0 enhances the functionality of its predecessor. VB 2.0 performs similar functions as VB 

1.0 (visual inspection of univariate data plots, manual transformations of individual variables, 

MLR model building, prediction, and such) but also automates and extends the functionality in 

several ways:

• The Map component provides access to localized data sources (NOAA/NCDC data) 

through the map interface. Such data sources can provide recently collected or forecasted 

data, or both, for generating predictions using a chosen MLR model. 

• The Map component provides a convenient method for defining the beach orientation by 

overlaying the beach on shore-line layers (satellite images, Google Maps, MS Virtual 

Earth, and the like). Given the orientation, VB 2.0 can calculate wind or current 

components (one component is parallel to shore, and one is perpendicular to the beach), 

which can be important predictor variables. 

• Although the manual processing and analysis of imported data (visual inspection of 

univariate data plots and the transformations/interactions of variables) has been retained, 

the Data Processing component of VB 2.0 provides automated generation of all possible 

second-order interaction terms among IVs, as well as automated testing of a suite of 

variable transformations for improved model linearity. That functionality increases the 

number of models to evaluate during later model selection routines and removes the 

burden/difficulty of manual assessment placed on a user of VB 1.0. 

• Multi-collinearity among predictor variables is handled automatically in the Model 

Building component; any model containing an IV with a high degree of correlation with 

other IVs (as measured by a large VIF; the threshold value is user-specified, but defaulted 

to 5) is removed from consideration during the model selection process. 

• During the model selection process, MLR models are ranked by a user-selected 

evaluation criterion. Possible criteria include R2

, adjusted R2, AIC, AICC, PRESS, BIC, 

Accuracy, Sensitivity, Specificity, or the model’s RMSE. Regardless of what criterion is 

chosen, the software records the ten best models in terms of that criterion. In comparison, 

VB 1.0 had only a single comparative criterion, Mallows’ Cp. 

• As the number of IVs in a data set increases, the number of possible MLR models 

increases factorially (considering transforms/interactions) resulting in trillions of possible 

models from a modest number (12–13) of IVs. VB 2.0 implements a GA to effectively 

and efficiently search for the best possible MLR model. Instead of using the GA, VB 2.0 

users can optionally perform an exhaustive calculation in which all possible combinations 

of IVs are used and tested (if the number of possible models is reasonably small). Both 

the GA and exhaustive approaches greatly expands the modeling building capabilities 

compared to VB 1.0. 
Predictive Modeling at Beaches—Volume II November 22, 2010

15 

• Users no longer have to enter data values in transformed, interacted, or componentdecomposed form to make a prediction with a chosen MLR model. On the VB 2.0 

Prediction tab, a user-selected model is coded into an input grid with data entry columns 

matching the model’s main effects. Any mathematical manipulation of the IVs is then 

automatically performed before making predictions.

VB 1.0 was written in Object Pascal (Delphi) for DotNet frameworks usable on Windows-based 

PC systems. Excel v4.0 data files and text files with conforming data organizational 

specifications can be imported into the application.

VB 2.0 is written in C# for the DotNet framework 3.5 and is targeted for Windows desktop 

computers. VB 2.0 reads and writes Excel 2003, Excel 2007, and text-formatted data files. VB 

2.0 uses several open-source, licensed and custom-written components: Extreme Numerics 

mathematical and statistical library, ZedGraph for plotting and charts, WeifenLuo’s Windows 

Docking UI as a basis for the application’s user interface, GMap.Net and Google’s GeoCoding 

network services for the map interface, EPA’s D4EM for NOAA/NCDC station locations, and an 

OLEDB library for Excel file access.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Predictive Modeling at Beaches—Volume II November 22, 2010

17 

3 Model Evaluation Strategies

3.1 INTRODUCTION

Many statistical metrics (AIC, BIC, PRESS, and such) allow a model developer to choose the 

best model from a large suite of potential models; they are discussed in Section 6.6 of Volume I 

of this report. This section focuses on a different, but important, question regarding modeling 

FIB densities at beaches: is the best model good enough? We know the chosen model is best in a 

relative sense, but how trustworthy are its predictions in an absolute sense? Several approaches 

can provide information that allows us to make such a determination. 

Among other approaches to evaluate whether a chosen model is good in an absolute sense rather 

than best in a comparison to other potential models (see Chapter 3 on model evaluation methods), 

we used the model’s adjusted R2 and the RMSE to evaluate the fit achieved in regression of 

predicted versus observed values. Adjusted R2 is similar to R2

, which is the proportion of 

variability in the response variable that can be explained by the model. However, in a model with 

more than one parameter, the adjusted R2 is always lower than the R2, as it incorporates a penalty 

for additional parameters (see Section 5.6, Volume 1). The RMSE is the square root of the sum of 

the squared residuals of the model, divided by the degrees of freedom for error in the model:

RMSE = [Σ(yi – ŷi)

2 / (n – p)]0.5 (equation 3.1) 

where yi is the ith observation in the data set; ŷi is the fitted value of the ith observation (found 

using the regression model); n is the number of observations in the data set; and p is the number 

of estimated parameters in the regression model. The adjusted R2 and the RMSE are amenable to 

comparison between models derived from different data sets. However, in the case of the RMSE, 

comparisons should be made only if the response variable is the same in each data set. 

One statistical method depends on classifying observations and predictions as exceedances, 

meaning they are greater than a given value (e.g., an EPA regulatory threshold for FIB levels at 

freshwater beaches). In Figure 3.1, the x axis shows observed values of the FIB response 

variable, and the y axis is corresponding predicted values (made with a regression model) of 

those observations. The interior of the plot is broken into four quadrants on the basis of two 

values. The regulatory standard is a vertical line that denotes a value above which water quality 

is considered to be out of compliance for human recreational use. The horizontal line (often set at 

the same value of the regulatory standard) represents a decision threshold marking the place on 

the y axis above which predicted values will be considered exceedances; below that line, 

predicted values will be considered non-exceedances. Therefore, the regulatory standard defines 

exceedances for observations, while the decision threshold defines exceedances for predictions. 

The upper-right quadrant of the graph is where correct positives are found. Both the observation 

and the prediction are exceedances. Given that result, a beach manager rightfully would close the 

beach to the public. The lower-left quadrant denotes correct negatives. Both predictions and 

observations are non-exceedances, so the beach correctly could be opened for public use. Errors 

occur in the other two quadrants: the upper left quadrant indicates false positives. The model 

makes a prediction above the decision threshold, but the actual observation is below the 

regulatory standard, so the beach might be closed in error when no danger existed. The bottom-
Predictive Modeling at Beaches—Volume II November 22, 2010

18 

left quadrant indicates false negatives, when predictions fall below the threshold, but 

observations are actually above the standard. If the beach were open in such cases, public health 

would be threatened. 

Figure 3.1. Plot of predictions versus observations for a regression model.

To assess how well a model is performing, three statistics have been developed on the basis of 

the data in Figure 3.1 (Francy and Darner 2006, 2007; Frick et al. 2008). 

Specificity describes how well the model predicts non-exceedances:

Specificity = Number of Correct Negatives / (Number of Correct Negatives + Number of 

False Positives)

Sensitivity defines how well the model predicts exceedances:

Sensitivity = Number of Correct Positives / (Number of Correct Positives + Number of False 

Negatives)

Accuracy is the total percentage of correct predictions:

Accuracy = (Number of Correct Positives + Number of Correct Negatives) / Total Number of 

Observations 

All three metrics are fractions that can vary from 0 to 1, with 1 being ideal. It would be up to the 

analyst or beach manager to decide if a model’s specificity, sensitivity, and accuracy are high 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1

Observed Log(Enterococci CFU)

Predicted Log(Enterococci CFU)

False

Negatives

Correct

Negatives

False

Positives

Correct

Positives

Regulatory

Standard

Decision Threshold
Predictive Modeling at Beaches—Volume II November 22, 2010

19 

enough to be considered good. Note that analysts can choose to raise or lower the decision 

threshold to alter the sensitivity and specificity of the model. They might do that after 

considering the relative costs of false positives (lost economic revenue from the beach being 

closed) to false negatives (public health endangered). For example, they might decide to close 

the beach if the model makes a prediction above 1.5 instead of above 1.8, as in Figure 3.1. That 

would take some observations out of the false negative quadrant and put them into the correct 

positive quadrant. However, it would also take observations out of the correct negative quadrant 

and put them into the false positive quadrant. In such a scenario, a manager has to decide 

whether to sacrifice specificity for improved sensitivity. VB 2.0 allows for the use of specificity, 

sensitivity, and accuracy as decision criteria in model selection.

We note that when a data set is composed of many FIB measures that fall below an instrument 

detection limit, it might be advisable to reformulate the response variable as a binary exceedance 

measure, and then use other statistical techniques designed for that purpose (e.g., binary logistic 

regression). However, modeling exceedances at a beach with only a small percentage of 

exceedances is extremely difficult. For statistical modeling, it is ideal for a beach to have 

between 25 and 75 percent exceedances.

We investigated another way to assess model goodness-of-fit using a process called crossvalidation in which a data set is split into two groups. One is called the training data set, and the 

analyst will choose a model (using a model selection approach of choice) that best fits the 

training data. It will then be used to make predictions for the second group, termed the testing

data set. Doing so easily shows how well the best model makes predictions for data it has not 

seen before. If done hundreds of times by randomly splitting the data into training and testing 

sub-groups, one can develop robust statistics that quantify the predictive capabilities of the 

chosen model. Our objective was to investigate relationships between the errors seen in the 

training data set, errors seen in the testing data set, the measured goodness-of-fit, sample size 

considerations, and other characteristics of a data set to see if useful generalizations could be 

drawn. The fundamental question is whether characteristics of a data set (and the best model for 

that data set) exist that will determine if that model will provide good predictions.

3.2 METHODS

We define the mean squared error of fitting (MEF) for a training data set as

MEF = Σ(yi – yifit)

2 / ntrain (equation 3.2) 

where the sum is over all observations in the training data set, yi is the ith observation in that data 

set, yifit is the fitted value for the ith observation, and ntrain is the number of observations in the 

training data set. The MEF is similar to the commonly used mean squared error, or MSE, except 

that the denominator of the MSE is ntrain minus the number of parameters in the regression 

model. We define the MSE of a testing data set as MEP (mean squared error of prediction): 

MEP = Σ(yi – yipred)

2 / ntest (equation 3.3) 

where the sum is over all observations in the testing data set, yi is the ith observation in that data 

set, yipred is the predicted value for the ith observation, and ntest is the number of observations in 

the testing data set.
Predictive Modeling at Beaches—Volume II November 22, 2010

20 

Because of its large sample size, we performed our analysis on the Huntington Beach, Ohio, 2000–

2009 data set. The response variable was E. coli colony forming units (CFU) measurements taken 

by Ohio (for a site description, see Section 4.2.5). The data set has many more observations (709) 

than IVs (11). When that is not the case, MLR techniques might not be the most appropriate; 

instead, Partial Least Squares regression techniques are often implemented(Haenlein and Kaplan 

2004; Hou et al. 2006). For our study, we performed the following steps:

1. Take a random sample of size j (j varied from 30 to 700) from the original data set. 

2. Randomly split the subsample into training (50 percent) and testing (50 percent) data sets.

3. Use a backwards-stepwise model selection routine (based on minimizing the AIC 

statistic) to choose a linear regression model that best fits the training data.

4. Record the MEF, AIC, adjusted R2

, and number of parameters for the model.

5. Use the model to make predictions on the testing data, and record the MEP of the 

predictions. 

6. Go back to step 1. 

For each value of j, we performed the steps a total of 150 times and then examined the output. 

Note that by making the number of observations in the training and testing data sets equal, the 

denominators of equations 3.2 and 3.3 are equivalent so, essentially, we compared the sum of 

squared errors within both data sets. Code written in the R statistical language was used to generate 

the results because VB 2.0 does not have the required functionality to produce the desired output.

3.3 RESULTS AT VARIOUS SAMPLE SIZES

As might be expected, the single most important factor in determining sample statistics such as 

the MEF, MEP, and adjusted R2 was the size of the sample taken from the data set. Figures 3.2 

through 3.7 demonstrate those relationships. The x axis in the graphs refers to the size of the 

training (and testing) data set. It is important to note that, for all following graphs, studies done 

with data sets from other sites would display very similar trends. What would change are the 

values on the y axis, which are site-dependent. In Figure 3.2, we see that taking larger samples 

from the population leads to an increase in the number of significant parameters in the final 

model. That increase seems to level off at a sample size of 350, and there is great variability in 

the smallest sample sizes (n = 15 and n = 20). For another site, number of parameters could vary 

between 2 and 6, or 12 and 18; however, the upward trend of more significant parameters with 

increasing sample size would hold. 

The MEF increases with increasing sample size (Figure 3.3), meaning small samples are easier to 

fit than large samples. That is supported by Figure 3.4, which shows that the adjusted R2 declines 

as sample size increases. Both statistics leveled off at a sample size of around 100. Those 

findings are important for interpreting later results that detail modeling efforts across many 

marine and freshwater sites. We found a wide range of adjusted R2 values between sites, and 

some of that variability is due to differences in the complexities of water quality dynamics at the 

various beaches; however, some of the variability in model goodness-of-fit must be attributed to 

sample size differences in the data sets: a small data set is expected to have a higher adjusted R2

compared to a much larger data set.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure 3.2. Increasing sample size leads to more significant parameters in the chosen model.

Figure 3.3. The mean squared error of fitting (MEF) increases with increasing sample size.

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0 50 100 150 200 250 300 350

Sample Size

Number of Model Parameters

0.00

0.05

0.10

0.15

0.20

0.25

0 50 100 150 200 250 300 350

Sample Size

MEF (Mean Squared Error of Fitting)
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure 3.4. The adjusted R2 declines as sample size increases.

The MEP declines as sample size increases (Figure 3.5). That statistic is close to leveling off at a 

sample size of about 50. Prediction errors are expected to be much higher for samples sizes less 

than about 20. Again, at another site, the magnitude of prediction errors would differ depending 

on the complexity of FIB dynamics at the site; however, the pattern shown in Figure 3.5 should 

be the same.

The effect of the sample size on the ratio of MEP to MEF is shown in Figure 3.6. As sample size 

increases, the ratio moves toward 1.0, meaning that predictive errors are about equal to fitting 

errors. Figure 3.7 zooms into a small portion of the y axis to show in greater detail how the ratio 

is changing for samples sizes greater than 50. At a sample size of 50, the MEP is approximately 

90 percent greater than the MEF. At the largest sample size we could examine (350), the MEP is 

about 10 percent larger than the MEF. 

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0 50 100 150 200 250 300 350

Sample Size

Adjusted R-Squared
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure 3.5. Declining mean squared errors of prediction with increasing sample size.

Figure 3.6. Sample size effect on the MEP/MEF ratio.

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 50 100 150 200 250 300 350

Sample Size

MEP (Mean Squared Error of Prediction)

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0 50 100 150 200 250 300 350

Sample Size

Ratio of MEP/MEF
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure 3.7. Effect of sample size on MEP/MEF for sample sizes greater than 50.

3.4 RESULTS WITHIN A SAMPLE SIZE

Increasing sample size has an observed effect on the various model statistics, but how do those 

quantities vary within a sample of a certain size? These results, because of sample variability, are 

more representative of what can be expected when models across many different beach sites are 

examined. Results are presented for a small training sample (n = 20), an intermediate-sized 

training sample (n = 75), and a large training sample (n = 200). For each of the sample sizes, 

150 random samples of size 40, 150, and 300 were drawn from the population of more than 700 

observations, and then randomly and equally split into training and testing subgroups. A model 

was fit to the training data, and then predictive errors were calculated for the testing data. The 

adjusted R2 for the model fit to the training data was plotted against the MEP for the 

corresponding testing data. That enables evaluation of whether a model’s level of fit to the 

training data can be used to indicate its expected success in making predictions.

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

50 100 150 200 250 300 350

Sample Size

Ratio of MEP/MEF
Predictive Modeling at Beaches—Volume II November 22, 2010

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3.4.1 Small Sample Size

For the smallest sample size, as the adjusted R2 of the model fit to the training data increased, 

prediction errors and their variability increased (Figure 3.8). That result is somewhat 

counterintuitive and deserves restating: for a small sample size, the better the model fit the training 

data, the greater was the probability that prediction errors from using that model could be very 

high. Indeed, the greatest prediction error was seen in a sample with an adjusted R2 over 0.9. How 

can such a counterintuitive result be explained? Basically, when such a small sample size is taken 

from the population, there is a possibility that members of that sample can be fit very well to a very 

specific model. However, those individuals can be very different from others in the population, 

meaning that when that model is used for predictive purposes, large errors are found.

Figure 3.8. Predictive errors increase with increased adjusted R2. Each of the 150 points 

represents the predictive errors of a testing data set of size = 20 observations.

3.4.2 Intermediate and Large Sample Sizes

For intermediate-sized and large samples, no discernible relationship exists between adjusted R2

and the MEP (Figures 3.9 and 3.10). Thus, at those sample sizes, the fit of the model to the 

training data provides no information about how well the model will make predictions.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Adjusted R-Squared

MEP
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure 3.9. Relationship between adjusted R2 and MEP for 150 samples of size 75.

Figure 3.10. Relationship between adjusted R2 and MEP for 150 samples of size 200.

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70

Adjusted R-Squared

MEP

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

0.30 0.35 0.40 0.45 0.50 0.55 0.60

Adjusted R-Squared

MEP
Predictive Modeling at Beaches—Volume II November 22, 2010

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3.4.3 Effect of Response Levels on Predictions

Finally, we used a relatively small training sample size (n = 30) to examine if any relationship 

existed between the magnitude and variability of the response (the mean and standard deviation 

of the FIB levels in the sample) in the training data and the magnitude of the predictive errors. In 

other words, do models developed for beaches with greater FIB levels (or less variable FIB 

levels) make better predictions than models developed for beaches with low FIB levels? If such 

relationships exist, they might lead to guidelines for determining if regression models are 

appropriate for a specific beach site.

Unfortunately, Figures 3.11 and 3.12 show no strong relationships between either the mean value 

or the standard deviation of the response variable and the mean errors of prediction. That 

indicates that a manager presented with a data set could not infer much about the predictive 

ability of a model developed using the data set from the mean or variation of the FIB levels in 

that data set.

Figure 3.11. No clear relationship between the mean Y value in a training data set (ntrain = 35) 

and the resultant MEP of the testing data set.

0

0.5

1

1.5

2

2.5

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Mean Y Value

MEP
Predictive Modeling at Beaches—Volume II November 22, 2010

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95

Figure 3.12. No clear relationship between the standard deviation of Y values in a training data 

set (ntrain = 35) and the resultant MEP of the testing data set.

In the end, there is no substitution for careful monitoring of the predictions made by statistical 

models. As predictions are made, it is important to go back later and validate them against real 

data to see if the model is performing adequately. A few weeks’ worth of MEP values at least 

twice as large as the MEF values, or more than a handful of false negatives or false positives 

(or both) over a month’s time, can be sufficient to mandate developing a new empirical 

model/alternative modeling approach, or at the very least ceasing to rely on the current one. On 

the basis of the data in Figures 3.5 and 3.7, we recommend that at least 50 observations be used 

for model development, but 100 or more are preferable. 

0

0.5

1

1.5

2

2.5

0.35 0.45 0.55 0.65 0.75 0.85 0.

Standard Deviation of Y

MEP
Predictive Modeling at Beaches—Volume II November 22, 2010

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4 Study Sites and Data Acquisition

4.1 INTRODUCTION

To provide the data for our modeling research, we developed a program designed to enhance the 

predictive modeling of indicator exposure research (PREMIER). PREMIER includes a 

concurrent collection of culturable and qPCR microbial data, as well as IVs for model refinement 

at selected freshwater beaches on the Great Lakes and at coastal marine beaches of the eastern 

United States and in the tropics. Several of the beaches have nonpoint sources of fecal 

contamination, but most were contaminated by nearby publicly owned treatment works. We 

deliberately patterned the spatial and temporal sampling patterns of the studies after those used in 

EPA’s National Epidemiological and Environmental Assessment of Recreational Water 

(NEEAR) studies (Haugland et al. 2005; Wade et al. 2006). At PREMIER beach sites in 

Milwaukee, Wisconsin; Surfside Beach, South Carolina; Miami, Florida; Luquillo, Puerto Rico; 

and Boquerón, Puerto Rico, we used automated techniques for IV measurements that were not 

used in most NEEAR studies or in other modeling studies. Such techniques were prompted in 

part by consideration of processes that are known to affect the fate and transport of 

microorganisms (Figure 4.1) (Boehm 2007; Haugland et al. 2005; USEPA 2007). Examples are 

concurrent measurements of underwater solar ultraviolet (UV) radiation, currents and waves 

(using acoustic Doppler current profilers or ADCPs); meteorological data; and water quality 

parameters, such as turbidity, dissolved organic carbon (DOC), UV-visible spectra, dissolved 

oxygen, salinity, or conductivity. Automated collection of the data permitted subsequent analysis 

of the time-dependence of modeling results (see Section 6.3 on temporal synchronization). 

Figure 4.1. Processes considered in collecting IVs for predictive modeling studies.
Predictive Modeling at Beaches—Volume II November 22, 2010

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During the 2008 and 2009 summer beach seasons, samples were collected at the PREMIER 

recreational water sites to measure culturable and qPCR-based Enterococcus, while automated 

field equipment was deployed to monitor various environmental parameters. The resulting data, 

and existing data sets from the NEEAR studies, were used in the predictive modeling studies 

presented here. Beaches in both the PREMIER and NEEAR studies include six freshwater Great 

Lakes beaches (Figure 4.2A), a temperate marine beach, four subtropical marine beaches, and 

two tropical marine beaches (Figure 4.2B). In addition to differences in water type (fresh versus 

marine) and climate (temperature, rainfall), factors such as tidal change, wave energy, and 

location relative to contamination sources likely will also influence the usefulness of certain IVs. 

The beaches represent a range of different contamination sources and include sites that

potentially are affected by point sources (i.e., treated wastewater effluent) and nonpoint sources 

(e.g., urban runoff, birds) of FIB. 

Descriptions of the freshwater and marine study sites, including location, potential sources of 

fecal contamination, and historical water quality information are given in the following sections 

and Appendix A to provide background and context for the modeling results. Such information 

will help to evaluate and explain the usefulness of certain IVs in predictive statistical models. 

Details regarding the weather stations, ADCPs, water quality sondes, and underwater light 

sensors deployed at the beaches are provided, as are the methods used to determine culturable 

and qPCR-based enterococci.
Predictive Modeling at Beaches—Volume II November 22, 2010

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(A)

(B)

Figure 4.2. Location of (A) freshwater and (B) marine beach sites. Yellow and red pins indicate the 

NEEAR and PREMIER study sites, respectively. Joint NEEAR/PREMIER studies were carried out at 

Surfside Beach and Boquerón (white pins).
Predictive Modeling at Beaches—Volume II November 22, 2010

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4.2 FRESHWATER BEACHES (GREAT LAKES) 

4.2.1 South Shore Beach, Milwaukee, Wisconsin

South Shore Beach is located on the western shore of Lake Michigan (Figure 4.2A) in South 

Shore Park in Milwaukee, Wisconsin. South Shore Beach is a public beach area (~ 0.01 square 

kilometer [km2

]) with 150 meters (m) of sandy shoreline. Its shore is low sloping, and the 

benthic zone is muddy and sandy. The beach is adjacent to the South Shore Yacht Club and a ~ 

0.02 km2 paved parking area that drains into the lake. A 20–m-long rock embankment juts into 

the lake, separating the sandy beach area from a 185-m-long cobble/pebble beach area with a 

high sloping shore (South Shore Rocky Beach). The beach is occupied consistently by large 

flocks of roosting waterfowl and shore birds. Ring-billed gulls are the predominant species, but 

Canada geese, Mallard ducks, and pigeons are also present (McLellan and Salmore 2003; Scopel 

et al. 2006). The entire beach and marina area is partially enclosed by a breakwall ~ 300 m 

offshore, which limits wave action, water circulation and exchange with the outer harbor. Water 

depths within the breakwall are < 5 m, with depths < 2 m within 50 m of shore. The beach is ~ 4 

km south of Milwaukee Harbor, which is the site of the Milwaukee Metropolitan Sewerage 

District Jones Island Water Reclamation Facility. The Milwaukee, Menomonee, and 

Kinnickinnic rivers also discharge to Lake Michigan inside the Milwaukee Harbor breakwall.

Historically, South Shore has poor water quality, with 34 percent of samples collected from 2003 

to 2009 exceeding water quality criteria standards (Appendix A). Potential sources of fecal 

contamination include combined sewer overflows (CSOs); urban/suburban and agricultural 

runoff from the Milwaukee River Basin; runoff from impervious surfaces including parking lots 

and the beach face; and gulls (Scopel et al. 2006). However, high E. coli counts are not always 

attributable to rainfall and CSO events (McLellan et al. 2001; Scopel et al. 2006). A detailed 

spatial assessment found that poor beach water quality was mostly a local phenomenon, with 

contamination originating at the shoreline (McLellan and Salmore 2003). Previous modeling 

efforts at South Shore Beach include hydrodynamic and water quality models developed to 

describe the fate and transport of fecal coliform in Milwaukee Harbor and nearshore Lake 

Michigan. Calibration and validation of the models was accomplished using Milwaukee 

Metropolitan Sewerage District and Great Lakes WATER Institute field data. Modeling results 

indicate that the fecal coliform load from rivers and CSO/sanitary sewer overflow events had 

only slightly more than marginal impact on the beach site, with local sources (e.g., stormwater 

runoff and birds) being more important (MMSD 2005). South Shore Beach was also one of the 

55 beaches included in a regional forecast model for southern Lake Michigan, from Milwaukee, 

Wisconsin, to Michigan City, Indiana (Whitman and Nevers 2005). The City of Milwaukee is 

considering adopting a predictive model. In addition to issuing advisories on the basis of the 

monitoring of E. coli levels (where < 235 CFU/100 milliliters (mL) is acceptable, 235–1,000 

CFU/100 mL results in a water quality advisory, and > 1,000 CFU/100 mL results in a closure 

advisory), a rainfall threshold of 2.5 centimeters (cm) in 24 hours is also used to predict poor 

water quality and issue advisories at South Shore. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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4.2.2 West Beach, Porter, Indiana

West Beach is on the south shore of Lake Michigan (Figure 4.2A), ~ 40 km southeast of Chicago 

Harbor; it is part of the Indiana Dunes National Lakeshore Park in Porter, Indiana. This public 

beach has ~ 2 km of sandy shoreline and contributes to the total 10-km length of contiguous 

swimming beaches along this section of Lake Michigan. The shore has a gradual slope, and 

water depths are < 2.5 m within 250 m of shore. As an open, unprotected, lakefront beach, West 

Beach is subject to moderate wave exposure. The beach area is west of the Portage-Burns 

Waterway (Burns Ditch), a man-made channel that serves as the outfall point for the Little 

Calumet River to Lake Michigan. Discharge from Burns Ditch is directed west by a breakwall 

and then dispersed by lake currents and waves (Appendix A). 

The West Beach and Burns Ditch sites have been the subject of several predictive modeling 

studies. Multiple regression analysis found that a combination of water quality variables could 

account for the observed variability in E. coli at Burns Ditch outlet during storm events 

(Olyphant et al. 2003). Further efforts led developing regression models that predict beach 

E. coli levels from wave and precipitation data, as well as water quality parameters. Because of 

the role of wind direction on the transport of Burns Ditch discharge to the beaches (Nevers and 

Whitman 2005), model performance was improved by separately modeling days with onshore 

and offshore winds. Regional forecast models also were developed for southern Lake Michigan, 

which includes West Beach (Whitman and Nevers 2005; Nevers and Whitman 2008). In addition 

to E. coli, more recent predictive models for beaches affected by Burns Ditch include culturable 

and qPCR-based enterococci as dependent variables. Differences in the models developed for 

each indicator (i.e., IVs identified for culturable compared to qPCR-based enterococci) provide 

evidence of the different processes that determine their fate (Byappanahalli et al. 2010; Telech et 

al. 2009). Beach monitoring practices rely on culturable E. coli where levels > 235 CFU/100 mL 

result in a contamination advisory or closure, as well as on a rainfall threshold. In addition, the 

Project S.A.F.E. (Swimming Advisory Forecast Estimate) predictive model was implemented as 

a USGS pilot study (Whitman 2008) and is used in conjunction with the NOAA/Great Lakes 

Environmental Research Laboratory Indiana Dunes Nowcast hydrodynamic model (Schwab et 

al. 2010) to provide real time E. coli estimates at West Beach.

4.2.3 Washington Park Beach, Michigan City, Indiana

Washington Park Beach is in Michigan City, Indiana on the south shore of Lake Michigan 

(Figure 4.2A). The public beach area is ~ 1.1 km long and is immediately east of a breakwall that 

directs discharge from Trail Creek to the west. Trail Creek is a source of E. coli to the lake with 

the potential to affect water quality at nearby beaches (Nevers et al. 2007). The Trail Creek 

watershed drains urban, agricultural, and residential areas, with a number of human and animal 

nonpoint sources including agricultural field drainage and runoff, cattle/steer grazing, failing 

septic systems, illicit connections, and urban stormwater runoff (Triad Engineering Incorporated 

2003). In addition, the Michigan City Sanitary District Wastewater Treatment Plant (WWTP) 

(~ 3 km upstream of Lake Michigan), which applies chlorine disinfection during the summer 

months, is a major discharger to the creek (Wade et al. 2008), although plant improvements have 

practically eliminated CSO events (Nevers et al. 2007). Water quality at Washington Park Beach 

is poor, with the recreational water quality criteria for E. coli exceeded in 23 percent of the 

samples collected from 2005 to 2009. In addition, pathogens (adenoviruses and enteroviruses) 
Predictive Modeling at Beaches—Volume II November 22, 2010

34 

and a marker for human sewage were detected in samples collected from the swimming area 

during summer 2004 (Wong et al. 2009). 

Predictive modeling of E. coli has not been reported at Washington Park Beach, but work was 

done at another Trail Creek-influenced beach, Mount Baldy Beach, ~ 2.5 km west of the mouth 

of Trail Creek (Nevers et al. 2007). The Mount Baldy site was also incorporated in a southern 

Lake Michigan regional forecast model (Whitman and Nevers 2005; Nevers and Whitman 2008). 

The observed variation in E. coli levels at Mount Baldy was further explained, based on loadings 

from Trail Creek and nearby Kintzele Ditch, using a process-based hydrodynamic model (Liu et 

al. 2006; Thupaki et al. 2009). 

4.2.4 Silver Beach, St. Joseph, Michigan

Silver Beach is in St. Joseph, Michigan, on the southern end of the eastern shore of Lake 

Michigan, ~ 55 km northeast of Washington Park Beach (Figure 4.2A). The ~ 0.6-km-long sandy 

beach area is just south of where the St. Joseph River flows into Lake Michigan. At its mouth, 

the river is lined by two parallel navigational piers that extend into the lake, guiding riverine 

discharge ~ 0.5 km out, roughly perpendicular to the shoreline. 

Possible sources of fecal contamination to the St. Joseph River watershed, which encompasses 

both urban and agricultural areas, include seven WWTPs (that use chlorine disinfection), four of 

which are on the river (Wade et al. 2008), CSOs, stormwater discharges, agricultural inputs, and 

illicit discharges (MDEQ 2003). The river is the receiving water for the St. Joseph-Benton 

Harbor WWTP, which is located ~ 2.7 km upstream of Lake Michigan. Only 1 percent of 

samples collected from 2001 to 2009 exceeded local water quality criteria standards for E. coli

(Appendix A). 

Regression modeling was employed at Silver Beach to investigate relationships between 

culturable and qPCR-based enterococci and various environmental conditions in an effort to 

identify useful predictors of water quality (Telech et al. 2009). Routine water quality monitoring 

at the beach is based on a culturable E. coli criteria of 300 CFU/100 mL and is supplemented by 

the use of a rainfall plus 48-hour health advisory. 

4.2.5 Huntington Beach, Bay Village, Ohio

Huntington Beach is part of Huntington Reservation of Cleveland Metroparks, which is in Bay 

Village, Ohio (a western suburb of Cleveland), on the southern shore of western Lake Erie 

(Figure 4.2A). The swimming area is situated just west of Porter Creek, and the beach is ~ 8 km 

west of the Rocky River mouth. The ~ 0.5-km-long sandy beach area is broken into segments by 

a series of rock jetties (< 100-m long) that run perpendicular to the shoreline (Appendix A). The 

breakwalls limit water circulation in the swimming area.

Huntington Beach is in the Black-Rocky Watershed, within which are 10 sewage discharge 

locations that could affect water quality at the beach. Three of those flow directly into Lake Erie: 

Avon Lake WWTP, ~ 11 km west of the beach; Rocky River WWTP, ~ 6 km east of the beach; 

and Westerly WWTP, ~ 18 km east of the beach. The others are discharged to the Rocky River 

or its tributaries, the closest being Lakewood WWTP (< 3 km from the mouth of the Rocky 

River). The majority of the treatment plants use UV or chlorine disinfection during the summer 
Predictive Modeling at Beaches—Volume II November 22, 2010

35 

(Wade et al. 2008; Wade et al. 2006). Porter Creek, on the east end of the beach, was identified 

as a likely contributor to high E. coli counts at beach (Huang and Sigler 2006). In addition, two 

outfalls discharge storm runoff from the parking lot to the beach (Francy et al. 2003). 

Water quality at Huntington Beach is poor, with 16 percent of samples collected from 2000 to 

2009 exceeding water quality criteria standards for E. coli. During the summer beach season, the 

Cuyahoga County Board of Health and Cuyahoga County Sanitary Engineers Laboratory, 

monitor Huntington Beach water quality (i.e., E. coli). In addition, a number of ancillary 

environmental parameters (i.e., water temperature, turbidity, and wave height) are also measured 

at the time of sample collection. Those data (real-time and historical since 2006) are publicly 

available through the Ohio Nowcast website, along with the associated water quality predictions 

and advisories (http://www.ohionowcast.info/nowcast_huntington.asp). Real-time and historical 

discharge and gage height data are available from the USGS Rocky River gauging station near 

Berea, Ohio (04201500), which is ~ 20 km upstream of Lake Erie 

(http://waterdata.usgs.gov/nwis/uv?04201500).

As a result of ongoing efforts of the USGS Water Science Center and its partners in daily routine 

sampling and data collection, an extensive, multiyear data set is available for Huntington Beach. 

The focus of the work was to develop an MLR model that continues to be tested and refined over 

time by incorporating additional years of data. The Ohio Nowcast predictive model is employed 

to supplement E. coli data (235 CFU/100 mL criteria) when making decisions about swimming 

advisories. 

4.3 MARINE BEACHES

4.3.1 Goddard Beach, West Warwick, Rhode Island

Goddard Beach is in Goddard State Memorial Park in West Warwick, Rhode Island (Figure 

4.2B). The beach stretches ~ 1.2 km along the southern shoreline of Greenwich Bay, just east of 

the mouth of Greenwich Cove. Greenwich Bay is a small (13 km2) estuary on the western side of 

Narrangansett Bay, which is ~ 6.5 km southwest of the mouth of the Providence River. The 

Maskerchugg River discharges to the head of Greenwich Cove, while a number of smaller 

brooks and creeks flow into Greenwich Bay, either directly or through one of the bay’s four 

other coves. Tributary streams that discharge to the cove and bay transport fecal contamination 

and direct stormwater discharge. Those vectors are along the west coast of the cove and include 

the East Greenwich Wastewater Treatment Facility, which discharges treated effluent to the 

middle of the channel about halfway down the cove, < 2 km from the beach. Faulty septic 

systems, waterfowl that gather at the beach, wildlife, and domestic pets are other potential 

sources of contamination at Goddard Beach. Nine percent of samples collected from 2002 to 

2009 exceeded water quality criteria standards for enterococci (Appendix A). To our knowledge, 

formal predictive models have not been previously employed at Goddard Beach. Beach 

management decisions are based on enterococci monitoring (using the 104 CFU/100 mL criteria) 

and consideration of water quality history and other environmental conditions such as rain 

(RIDEM 2005). 
Predictive Modeling at Beaches—Volume II November 22, 2010

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4.3.2 Surfside Beach, Surfside Beach, South Carolina

Surfside Beach is in the town of Surfside Beach, South Carolina, just south of Myrtle Beach in 

Horry County (Figure 4.2B). The beach is 3.4 km long and is only a small fraction of the South 

Carolina coastline that encompasses more than 100 km of uninterrupted, open beachfront known 

as the Grand Strand. The Grand Strand is the northernmost part of the South Carolina Coastal 

Plain. Several impoundments were created in Surfside Beach to serve as retention ponds during 

storm events. The associated watersheds were designed and constructed for stormwater 

management purposes. The Myrtle Basin designed in 2005–2006, with construction starting in 

2007, was followed by lake dredging. Two small lakes (each with an area of ~ 3000 m2) are 

between North Myrtle Drive, North Dogwood Drive, 2nd Avenue North, and 5th Avenue North. 

They are connected by a 120-m-long channel, with another 200-m-long channel running between 

them and the beach. The swash at 5th Avenue North receives runoff from this area, which is then 

discharged directly to the beach. A sign is permanently posted at the swash, stating that 

swimming is not recommended within 30.5 m because stormwater runoff can result in elevated 

levels of bacteria. The Public Works Department digs out the swash outlets on the beach as 

needed (as often as three times per week) to ensure proper water flow.

The Grand Strand Water and Sewer Authority Schwartz WWTP is ~ 8 km northwest of the 

beach. Surfside Beach is not affected by effluent from the WWTP because the effluent is 

discharged to the Intracoastal Waterway where the outlet to the Atlantic Ocean is 50 km from the 

beach. Several campgrounds along the coast north of the beach are within 4 km of Surfside 

Beach. In addition to the swash at 5th Avenue North, which is at the section of the beach 

considered here, additional swashes are up and down the coast. Those closest to the beach area 

include the 11th Avenue North Dogwood Swash (0.6 km north), the Surfside Drive outfall (0.5 

km south by the pier), and the 3rd Avenue South Swash (0.9 km south of the 5th Avenue North 

Swash). Given the lack of known point sources, the most likely source of fecal contamination to 

Surfside Beach is runoff from the surrounding urban areas. Wildlife can also contribute to 

observed fecal indicator levels in the swash as birds (i.e., geese, ducks, gulls) frequent the lake 

and surrounding areas. Water quality at the 5th Avenue North Swash of Surfside Beach has been 

poor, with 29 percent of samples collected from 2005 to 2007 exceeding water quality criteria 

standards for enterococci (Appendix A). However, water quality has improved over time (from 

70 percent in 2005 to 13 percent in 2007) because of improvements made to the stormwater 

management watershed. Beach monitoring practices at Surfside Beach rely on culturable 

enterococci, where levels > 500 CFU/100 mL or repeated measurements > 104 CFU/ 100 mL 

lead to advisories. In addition, preemptive rainfall advisories were issued on the basis of a 

rainfall threshold. More recently, a rain model for advisory predictions has been in development. 

The beach was used for a combined PREMIER-NEEAR study in 2009. 

4.3.3 Edgewater Beach, Biloxi, Mississippi

Edgewater Beach is in Biloxi, Mississippi, on the Mississippi Sound along the Gulf of Mexico 

(Figure 4.2B). The Mississippi Sound is separated from the Gulf by a chain of barrier islands, the 

closest of which is Ship Island, ~ 20 km south of the beach. This lagoon is < 5-m deep in most 

areas and runs 124 km along the southern coasts of Mississippi and Alabama. Beaches in the 

area generally are subject to low energy wave conditions. The beach shore is gently sloped 

(i.e., 5 to 10 degrees) and consists of well- to very-well-sorted medium sand. Major rain events 
Predictive Modeling at Beaches—Volume II November 22, 2010

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form runoff channels (Otvos 1999). Seven Harrison County Utility Authority WWTPs are within 

10 km of the beach. Water quality at Edgewater Beach (near Eisenhower Drive) is poor, with 

16 percent of samples collected from 2004 to 2009 exceeding water quality criteria standards for 

enterococci (Appendix A). Decisions regarding water quality are based on culturable enterococci 

where levels > 104 CFU/100 mL result in beach advisories. 

4.3.4 Fairhope Beach, Fairhope, Alabama

Fairhope Municipal Beach is in Fairhope, Alabama, ~ 22 km southeast of Mobile, on the eastern 

shore of Mobile Bay (Figure 4.2B). The Mobile Bay Estuary is an inlet of the Gulf of Mexico, 

with an average depth of 3 m. The small mouth of the bay is shaped on the east by the Fort 

Morgan Peninsula and the Dauphin Island barrier island on the west. The sandy beach area at 

Fairhope Beach is ~ 0.6 km long. 

The Fairhope WWTP, < 1 km northeast of the beach, serves as a potential source of continuous 

fecal contamination. The facility employs UV disinfection as the final treatment step. Additional 

sources include sanitary sewer overflows, failing septic tanks, and urban runoff (ADEM 2010). 

Water quality at Fairhope Beach is poor, with 17 percent of samples collected from 2006 to 2009 

exceeding water quality criteria standards for enterococci (Appendix A). Decisions regarding 

water quality are based on culturable enterococci, where repeated measurement of levels > 104 

CFU/100 mL result in a public health advisory. 

4.3.5 Hobie Beach, Miami, Florida

Hobie Beach in Miami, Florida is on Virginia Key in the southern part of Biscayne Bay, off the 

east coast of mainland Miami (Figure 4.2B). Biscayne Bay is a subtropical estuary that receives 

freshwater inputs from the Miami River and small creeks, as well as from a network of drainage 

canals. The Miami River is ~ 4 km northwest of the beach, and its freshwater can influence the 

beach under certain conditions. Hobie Beach is ~ 1.6 km long and runs along the south side of 

Rickenbacker Causeway, between the William Powell Bridge and Miami Seaquarium. Hobie is 

also known as Dog Beach because it is the only Miami-Dade County beach where pets are 

allowed; the ratio of dogs to humans at the beach is on the order of 1:6. The beach is narrow, 

with a distance of 5 m and12 m between the water line and the outer edge of the sand line during 

high and low tide, respectively. Vehicles park right along the sand line. The benthic zone is silty 

and muddy, and the shoreline typically is covered with seaweed. The slope is relatively shallow, 

and natural runoff channels form following heavy rainfall events. Hobie Beach is shallow with 

water depths < 2 m at the buoy line, ~ 130 m from the shoreline. Due to its location in a shallow 

cove, water circulation at the beach is poor, and movement near shore is controlled by tidal 

action (with an average tidal height fluctuation of 58 cm) rather than waves (Shibata et al. 2004; 

Wright 2008). During ebb tide (the period in between high and low tide), water flows out of 

Biscayne Bay to the Atlantic through the Norris Cut and Bear Cut inlets. During flooding tide, 

water enters the bay. Flow is parallel to the shoreline with velocities of 0.2 m/s and < 0.1 m/s 

during ebbing and flooding tide, respectively. Easterly winds prevail with a weak southerly 

component in the summer, accompanied by a strong local sea-breeze and thunderstorms 

(Zhu 2009). 
Predictive Modeling at Beaches—Volume II November 22, 2010

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During July 1999 to June 2000 at Hobie Beach an EPA/Florida Department of Environmental 

Health (FDOH) Beach Monitoring Study, indicated that 29 percent of samples exceeded the 

enterococci water quality criteria (Solo-Gabriele et al. 2002). Since that period, however, only 

6 percent of samples collected from 2001 to 2009 exceeded water quality criteria standards for 

enterococci.

There are no known point sources to the beach. No storm drains are at the beach, but other 

suspected sources of enterococci include runoff during heavy rainfall events and animals, 

particularly dogs (Wright et al. 2009). Spatially intensive sampling efforts, including surveys of 

beach sand and water, identified the shoreline as a source of fecal indicators (Shibata et al. 2004; 

Solo-Gabriele et al. 2002). A water quality model developed to evaluate sources of nonpoint 

pollution found runoff to be the most important source of enterococci, followed by dogs, sand, 

birds, and bathers (Elmir 2006). Research efforts also have focused on the associations between

indicator microbes, pathogens, and environmental conditions (Abdelzaher et al. 2010). 

Decisions regarding water quality are based on enterococci and fecal coliform levels, with counts 

> 104 CFU/100 mL resulting in a poor enterococci rating. A process-based predictive numerical 

hydrodynamic water quality model for Hobie Beach is being developed as a tool to improve 

assessing nonpoint source fecal contamination (Zhu 2009). 

4.3.6 La Monseratte Beach, Luquillo, Puerto Rico

La Monserrate public beach, better known as Luquillo Beach, is on the northeast coast of Puerto 

Rico in the town of Luquillo (Figure 4.2B). The public beach is ~ 400 m long and runs along the 

eastern side of the bay. The mouth of the Mameyes River is ~ 2.2 km west of the main 

swimming area at Luquillo. During periods of low flow, the river mouth can be closed off 

completely from the ocean. Two streams fed by stormwater runoff are potential sources of fecal 

contamination to the beach; one is just west of the beach, and the other is east of the beach, along 

the northern shoreline. 

The Puerto Rico Environmental Quality Board (PREQB) monitors enterococci and fecal 

coliform levels at Luquillo Beach twice a month year-round by. Some data for the current year 

are publicly available at the PREQB water quality website (http://www.prtc.net/~jcaagua). 

Historical data indicate that 8 percent of samples collected at Luquillo Beach from 2006 to 2008 

exceeded the water quality criteria standard of 104 CFU/100 mL for enterococci. Decisions 

regarding water quality are based on both culturable enterococci and fecal coliforms, where the 

level of 35 CFU/100 mL is used as the criteria for enterococci. Puerto Rico’s standard is more 

stringent than that recommended by EPA, and its use results in a total of 18 percent exceedances 

for 2006 to 2008.

4.3.7 Boquerón Beach, Cabo Rojo, Puerto Rico

Boquerón Beach is in southwestern Puerto Rico, in the town of Boquerón in Cabo Rojo (Figure 

4.2B). The 1.6-km-long beach is along the eastern shore of Boquerón Bay, on the western coast 

of Puerto Rico. The bay is ~ 4.7-km wide at its mouth and the beach is ~ 4 km from the mouth. 

Potential sources of fecal contamination to the beach include a sewage treatment plant’s outfall 

in the bay ~ 1.3 km northwest of the beach, and two package plants that operate during periods 

of high demand. The two plants discharge treated effluent into the mangrove lagoon south of the 
Predictive Modeling at Beaches—Volume II November 22, 2010

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beach. The mouth of the lagoon is ~ 1.5 km from the beach. A marina and condominium 

complex, just north of the beach, is also a potential source of contamination. Urban runoff is also 

likely because afternoon storms are common during the summer, with heavy rains resulting in 

flooding. The beach was used for a combined PREMIER-NEEAR study in 2009. 

4.4 METHODS AND DATA ACQUISITION

For more details on methods used for data acquisition, see Appendix B of this report. 

4.4.1 Sample Collection

Details regarding the NEEAR study sample collection protocol have been described previously 

(Haugland et al. 2005; Wade et al. 2006). That general approach was taken at all NEEAR study 

sites. Briefly, samples were collected on weekends and holidays during the single summer study 

carried out at each beach. Samples were collected three times a day (8 a.m., 11 a.m., and 3 p.m.) 

at six locations at each beach. The locations included two depths (shin and waist deep) collected 

along three transects, ≥ 60 m apart. Shin-depth samples were collected ~ 0.15 m below the 

surface in 0.3-m-deep water, and waist deep samples were collected ~ 0.3 m below the surface in 

1-m-deep water. Grab samples were collected in sterilized polypropylene bottles in accordance 

with Standard Methods Section 9060 (Clesceri et al. 1998). Samples were mixed to create three 

composite samples per time point: a shin composite, waist composite, and total composite. 

Sample collection for the 2008 PREMIER studies (at South Shore, Hobie, and La Monserrate) 

was designed deliberately to match the NEEAR studies, where possible. However, more frequent 

sampling was performed to provide a larger data set for modeling purposes. Waist-deep samples 

were collected four days a week (Mondays, Wednesdays, Thursdays, and Saturdays), three times 

a day (9 a.m., 11:30 a.m., and 3 p.m.) at South Shore and Hobie. Shin-deep samples were also 

collected on Saturdays at South Shore and on Thursdays and Saturdays at Hobie. No shin-deep 

samples were collected at La Monserrate, and waist-deep samples were collected only once a day 

(10 a.m.), three days a week (Mondays, Thursdays, and Saturdays) over a longer period. At each 

sampling location and time, three 500-mL grab samples were collected and mixed to give 

composite samples for each of the three transects; unlike the NEEAR studies, no beach-wide 

composites were collected. The distance between sampling transects at the beaches ranged from 

125 to 250 m. 

The 2009 PREMIER studies at Surfside Beach and Boquerón were specifically designed to 

complement the concurrent NEEAR studies by expanding the spatial and temporal scale of data 

collection. In addition to the NEEAR sampling scheme (i.e., weekend and holiday samples) 

described previously, waist-deep samples were collected on Fridays (three times per day) as part 

of the PREMIER study. Samples were also collected from two locations outside the beach area 

(at 8 a.m. and 3 p.m. on Fridays, Saturdays, Sundays, and holidays to better evaluate potential 

sources of contamination to the beaches (i.e., runoff and effluent at Surfside and Boquerón, 

respectively). At Surfside Beach, samples were collected from the 3rd Avenue North swash 

channel along North Ocean Boulevard and from the lake at North Dogwood Drive. Boquerón 

samples were collected at the outfall of the WWTP and just outside the mouth of the mangrove 

lagoon. For each sampling event at the sites, three grab samples were collected and composited. 

The distance between sampling transects at both beaches was ~ 150 m.
Predictive Modeling at Beaches—Volume II November 22, 2010

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In addition to the samples collected for microbial analysis (described above), water samples were 

also collected during the PREMIER studies to analyze DOC and colored dissolved organic 

matter (CDOM). The same collection scheme was used for these samples, as detailed above for 

the 2008 sites, without any sample compositing. At Surfside and Boquerón, beach water samples 

for the analyses were collected only at the waist-deep site of the middle transect. Single grab 

samples were also collected from the potential contamination source locations using the 

microbial sampling scheme. The samples were collected in glass bottles, which were cleaned as 

described in Standard Methods Section 5310B (Clesceri et al. 1998). 

Samples collected from EPA’s PREMIER and NEEAR studies provided most of the large data 

set that was used to refine and evaluate predictive modeling tools, discussed later in this report. 

In addition, the unique long-term (10-year) data set from Huntington Beach, Ohio (Section 4.2.5) 

was provided for our use by Donna Francy, USGS. Details regarding the beach field studies that 

generated data for the modeling studies discussed in this report are summarized in Appendix B. 

4.4.2 Dependent Variables

As the dependent variable, FIB density data are the most important component of predictive 

model development. The current acceptable standard by which recreational water quality is 

evaluated is culturable enterococci; E. coli is also acceptable for freshwater only. 

As a result of the BEACH Act of 2000, more than 7 years of monitoring data now exist for many 

beaches in the United States. Most of the data are available on the Internet, providing an 

extensive database of historical information. In the PREMIER and NEEAR studies described 

here, culturable enterococci were enumerated by membrane filtration according to EPA Method 

1600 (USEPA 2006). For that method, the detection limit was 1 CFU/volume filtered (i.e., 0.01 

CFU/mL for 100 mL volumes) and a value of 0.5 CFU/100 mL (one-half the limit of detection) 

was used as the lower limit for data analysis. All culturable data were log-transformed before 

modeling. Given the interest in more rapid monitoring techniques (i.e., qPCR-based enterococci) 

and the paucity of existing qPCR monitoring data that includes the environmental parameters 

required for modeling, a goal of the PREMIER studies was to build on the existing NEEAR data 

set by obtaining qPCR-based enterococci measurements at additional beach sites. Procedures 

used for the qPCR-based enterococci measurements have been detailed elsewhere (Haugland et 

al. 2005; USEPA 2010) and are described in Appendix B. We used the same qPCR data for our 

modeling research that were employed in the NEEAR studies conducted at Boquerón Bay and at 

Surfside Beach.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Table 4.1. Summary of beach sites (i.e., water type and climate) and field studies that served as a 

source of data for modeling studies 

Water Climate Data source

Beach F M TEMP SUB TROP PREMIER NEEAR USGS YEAR 

South Shore X X X X 2008

West X X X 2003

Washington Park X X X 2004

Silver X X X 2004

Huntington-EPA X X X 2003

Huntington-USGS X 2000–2009

Goddard X X X 2007

Surfside X X X X 2009

Edgewater X X X 2005

Fairhope X X X 2007

Hobie X X X 2008

La Monserrate X X X 2008

Boquerón X X X X 2009

Notes: 

Huntington refers to Huntington Beach, Ohio.

F = freshwater, M = marine, TEMP = temperate, SUB = subtropical, TROP = tropical, PREMIER = EPA modeling studies, NEEAR = 

EPA National Epidemiological and Environmental Assessment of Recreational Water studies, USGS = USGS, Ohio Water Science 

Center (provided by D. Francy).

4.4.3 Independent (Explanatory) Variables

Because water quality criteria are based on FIB levels, monitoring data are crucial for beach 

management. However, models can be useful in predicting indicator densities, which is 

increasingly important, given issues associated with capability of monitoring data to reflect 

beach conditions accurately at a given time. More easily measured environmental conditions, 

often obtained with automated techniques, can be used as IVs in statistical models to explain 

observed variability in FIB levels. Those include physical hydrologic measurements (e.g., water 

temperature, turbidity, current, and wave information; tidal phase; and stream discharge); 

chemical and biological parameters (e.g., pH, dissolved oxygen, conductivity, salinity, and 

chlorophyll); meteorological conditions (e.g., rainfall, solar radiation, air temperature, and wind 

information); and ancillary beach conditions (e.g., number of bathers and birds). A variety of 

such parameters were measured concurrently with FIB measurements during the NEEAR and 

PREMIER studies. While measurements were taken at the time of sample collection and in 

discrete samples during the NEEAR studies, one purpose of the PREMIER studies was to obtain 

more detailed IV data by deploying automated instruments at the beach sites to monitor ambient 

conditions. Those measurements were also supplemented with variables mined from public 

databases, where available.

Details about collecting environmental data during the NEEAR studies were previously 

discussed for the four freshwater sites (Heaney et al. 2009); the same procedures were followed 

for the subsequent marine studies. Measurements recorded at each sampling event included the 

following parameters: air and water temperature; percent cloud cover; UV irradiance; wave 

height; current direction; wind speed and direction; number of bathers on the beach and in the 

water; total number of birds and animals within 20 m of the sampling area; number of boats 

within 500 m of the sampling area; and the presence of debris. Rainfall data for the study period 
Predictive Modeling at Beaches—Volume II November 22, 2010

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were obtained from weather stations at nearby airports and from on-site weather stations 

installed at some of the beaches. Turbidity, pH, salinity, and conductivity were measured in 

collected water samples. Limited ancillary data were collected during the 2008 PREMIER 

studies because efforts were focused on in situ measurements. Local water and beach conditions 

were noted, including wave conditions (South Shore and Hobie), presence of birds (South Shore) 

or dogs (Hobie), and number of people and dogs within 50 m of the sampling transects (Hobie). 

IV data at South Shore Beach, Milwaukee; Hobie Beach, Miami; Surfside Beach, SC; 

La Monserrate Beach, Luquillo, Puerto Rico; and Boquerón Beach, Cabo Rojo, Puerto Rico were 

obtained using procedures and equipment, which are listed with more detail in Appendix B. 

Field equipment was deployed at the PREMIER and NEEAR/ PREMIER beach sites to obtain 

more detailed and beach-relevant IVs from which to develop predictive water quality models. 

Field equipment locations are indicated in Figure 4.3 for the PREMIER beaches at Milwaukee, 

Miami, and Luquillo. Figure 4.4 provides locations of the equipment locations for the combined 

PREMIER/NEEAR studies at Boquerón and Surfside Beach. In addition to using automated field 

instruments, a unique aspect of the PREMIER studies was measuring underwater UV radiation 

with the analysis of DOC and CDOM (i.e., UV-visible absorption spectra). By characterizing the 

optical properties of beach waters, the amount of light to which bacteria are exposed in the water 

column was more accurately determined in investigating the effects of light on the inactivation of 

FIB.

Meteorological conditions were monitored by installing HOBO (U30 NRC, Onset Computer 

Corporation) weather stations at or near each beach site. Weather stations were equipped with 

sensors to measure air temperature; relative humidity; dew point (determined from temperature 

and relative humidity); barometric pressure; wind speed and direction; gust speed (i.e., highest 

3-second wind recorded during logging interval); rain; photosynthetically active radiation , solar 

radiation (silicon pyranometer); and UV radiation (Apogee instruments sensors were used in 

2009 only) approximately every 15 or 30 minutes. Data were routinely downloaded in the field 

by connecting a laptop to the weather station data logger. Wind speed and direction were used to 

determine cross-shore (u-component) and along-shore (v-component) winds at each beach site. 

The on-site weather data were supplemented with other available meteorological data 

(http://cdo.ncdc.noaa.gov/ulcd/ULCD).

Current and wave information was obtained by deploying Nortek Aquadopp Profilers (2 MHz, 

right angle sensor head) at each beach site. The ADCPs were installed on the lake or sea floor 

using a weighted cross-frame with a mounting height of ~ 0.3 m (Mooring Systems, Inc.). With 

the exception of the studies at Boquerón Bay, where we deployed two ADCPs, one ADCP was 

deployed at each beach. A University of Puerto Rico-Mayagüez ADCP was also installed at the 

Boquerón Bay site. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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A B 

C 

Figure 4.3. Location of 2008 PREMIER studies at (A) South Shore Beach in Milwaukee, Wisconsin; 

(B) Hobie Beach, Miami, Florida; (C) La Moserrate beach, Luquillo, Puerto Rico Yellow pins 

indicate locations of the beach and sampling transects; red pins show locations of the field 

equipment.
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A B 

Figure 4.4. Location of 2009 PREMIER/NEEAR study at (A) Boquerón Beach, Puerto Rico; 

(B) Surfside beach, South Carolina. Yellow pins indicate the locations of the beach and sampling 

transects; red pins show locations of the field equipment.

Multi-parameter water quality sondes (YSI 6600V2-2) were deployed at each beach site for the 

duration of the studies. The sondes were deployed at fixed locations at a depth of < 2 m. 

Although actual sonde depths varied at most sites because of tidal changes, sonde readings were 

taken to represent surface conditions. Water temperature, specific conductance, salinity, 

dissolved oxygen (using a Clark oxygen electrode), pH, turbidity, and chlorophyll (as relative 

fluorescence) were measured every 15 minutes. The sondes were typically retrieved every one to 

two weeks for cleaning, calibration, and data retrieval. Fouling was significant and, in some 

cases, could be identified as having influenced data quality, specifically for optical 

measurements (i.e., turbidity and chlorophyll). Fouling of the optical sensors results in high 

turbidity and chlorophyll readings with a high frequency of spikes. Real (i.e., event-driven) 

spikes in data progress in a natural upward trend and are short in duration. Examples of bad data 

from fouling (available from the instrument manufacturer) were used to help identify 

questionable data during manual review by an experienced individual. 

Underwater downwelling solar irradiance (Ed) was measured at each beach using pairs of 

Satlantic multispectral radiometers (OCR-504 ICSW) with 305, 325, 340, and 380 nanometer 

(nm) channels. The sensors were placed at two depths to evaluate the attenuation of UV radiation 

in the water column. The top sensor was < 0.5 m below the water surface (at low tide), and the 

bottom sensor was placed ~ 0.6 m to 1.5 m below the top sensor, depending on water clarity. To 

reduce biofouling, each sensor was equipped with a copper Satlantic Bioshutter. In addition to 

the sensors and Bioshutters, each UV sensor instrument package was equipped with a data 

logger, battery pack (51Ah), wireless telemetry system with GSM modem, and dual band 

marine-grade cellular antenna. The equipment was deployed on temporarily installed tower 

structures. UV irradiance data were processed using the Satlantic SatCon data conversion 

software. The rate at which irradiance at a given wavelength decreases as a function of depth can 

be described by a diffuse attenuation coefficient for downwelling irradiance (Kd(λ)). Kd values 

were estimated from the irradiance measured at the top and bottom sensors, assuming 

exponential decrease with increasing depth. The Kd(λ) value is the slope of a natural log plot of 

irradiance versus depth. 
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DOC was measured in filtered water samples as non-purgeable organic carbon by high 

temperature combustion using a Shimadzu 5050A or TOC-V Total Organic Carbon Analyzer. 

UV-visible absorption spectra were determined from 200 to 800 for 0.2-micrometer (μm) filtered 

water samples, using a Perkin-Elmer LAMBDATM 35 UV/Vis Spectrophotometer. Measured Aλ

were used to calculate absorption coefficients (i.e., aλ = 2.303(Aλ/L) where L is the path length in 

m) at 350 nm. 
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5 Predictive Modeling of Beaches

5.1 FRESHWATER SITES

5.1.1 Data Sources and Methods

We used MLR analyses to examine data sets from five freshwater beaches. At most sites, the 

response variable was either Enterococcus CFU or qPCR values, but we also had E. coli CFU 

data for 2000–2009 from Huntington Beach, Ohio (Section 4.2.5). FIB data are primarily lognormally distributed, so we always log10 transformed the raw FIB measurements (CFU and 

qPCR) before model development. Site characteristics, the collection of water samples, 

laboratory bacterial measurement methods, and deployment of on-site instrumentation to collect 

environmental data are described in Chapter 4, and Appendices A and B of this report. 

VB 2.0 was used for developing MLR models for each of the data sets. As described in Chapter 

2, VB 2.0 performs data preprocessing to improve the predictive capabilities of MLR models. 

IVs are tested to see if transformations (logarithm, polynomial, inverse, square root) can induce a 

more linear relationship to the response variable. Later, as model selection is occurring, VB 2.0 

automatically checks for large correlations between IVs (using the VIF), thus avoiding problems 

associated with multi-collinearity among IVs. When selecting MLR models, many different 

metrics can be used to choose a best model from a large number of candidates (see Section 5.6, 

Volume I). For the data sets and analyses, we used the AICC (McQuarrie and Tsai (1998). 

Model evaluation techniques used here are discussed in Chapter 3. 

5.1.2 MLR Model Results

Tables 5.1a (significant IVs) and 5.1b (summary model statistics) show the results of our MLR 

modeling on the freshwater beach data sets. In all, 23 significant IVs appeared across the various 

data sets gathered at the five freshwater beach locations. The frequency of occurrence shown in 

Table 5.1a and in Table 5.2a does not account for the fact that not all the IVs were measured at 

all beaches. Results corrected for whether the IV was measured are in Section 5.3. Turbidity and 

antecedent rainfall were most often seen as significant variables. Those were followed by air 

pressure, the number of bathers, and air temperature. Water temperature, across-shore winds, 

wave height, dew point, wind speed, and the number of boats were each seen as significant in 

three of the analyses. Along-shore wind, dissolved oxygen, algae, cloud cover, and chlorophyll 

were significant for two data sets. Excluding the very large data set from Huntington Beach, 

Ohio, the adjusted R2

 values for cultured FIB models (CFU in the table) ranged from 0.32 to 

0.78, with a mean of 0.55. For these data, RMSE values ranged from 0.24 to 0.48, with a mean 

of 0.36. For qPCR values, the adjusted R2

 ranged from 0.2 to 0.69, with an average of 0.46. 

RMSE values for qPCR models ranged from 0.36 to 0.59, with an average of 0.44. The qPCR 

model produced a higher adjusted R2 than the CFU model at two of five sites where both qPCR 

and CFU data were obtained. Details of the regression models chosen for each site are in 

Appendix C. 
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5.2 MARINE SITES

5.2.1 Data Sources and Methods

Data sets from seven different marine beach sites were modeled, using MLR analyses. The 

response variable for the data sets was the logarithm (base 10) of enterococci CFU/qPCR values. 

Site characteristics, the collection of water samples, laboratory bacterial measurement methods, 

and deployment of on-site instrumentation for collecting environmental data are described in 

Chapter 4, and Appendices A and B of this report. VB 2.0 was used to develop MLR models for 

each of the data sets. For a description of our MLR analytical techniques, see Section 5.1. 

because the methodology used was very similar to that for freshwater sites.

5.2.2 MLR Model Results

Tables 5.2a (significant IVs) and 5.2b (summary model statistics) show the results for the marine 

site MLR modeling. Twenty-seven IVs were found to be significant across analyses at the seven 

sites. Water temperature, humidity, and antecedent rainfall (typically cumulative over the past 

48 hours) were most often significant—four analyses for each. Salinity/conductivity, UV 

intensity, the number of birds seen on the beach, turbidity, and absorbance were next with three 

appearances each. The qPCR model’s adjusted R2 exceeded that of the CFU model for only one 

of four data sets where nearly equal numbers of qPCR and CFU observations were taken. 

Comparisons were not made between qPCR and culturable data at Hobie, Boqueron, and 

Surfside because of the wide discrepancy in sample sizes between the two data sets (see Chapter 

3). If we ignore the sample size discrepancies, the mean adjusted R2 values for CFU models 

ranged from 0.19 to 0.48, with a mean of 0.39. For qPCR models, the adjusted R2 ranged from 

0.14 to 0.68, with an average of 0.39. The RMSE values for the qPCR data sets ranged from 0.06 

(although that is for the very small Hobie data set) to 0.7, with a mean of 0.41. For the CFU 

models, the RMSE varied from 0.43 to 0.6, with a mean of 0.52. Details of the regression models 

for each of the marine sites are included in Appendix C. 
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Table 5.1a. Results of MLR modeling on freshwater beach sites. A “+” in the cell means that the regression coefficient for that IV was 

positive. A “-” means the regression coefficient was negative. “P” means the IV was modeled as a second-degree polynomial

(ax2 + bx + c). The response variable is the log10 of enterococci levels except for the E.coli data set for Huntington Beach, Ohio.
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Table 5.1b. Summary statistics for the MLR models for freshwater beach sites. The response variable is the log10 of enterococci levels 

except for the E.coli data set for Huntington Beach, Ohio. Sensitivity is the number of correctly predicted exceedances over the total 

actual number of exceedances; Specificity gives the number of correctly predicted non-exceedances over the total actual number of 

non-exceedances, Accuracy gives the total number of correctly predicted values over the total count of the data set.
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Table 5.2a. Results of MLR modeling on marine beach sites. A “+” in the cell means that the regression coefficient for that IV was 

positive. A “-” means the regression coefficient was negative. “P” means the IV was modeled as a second-degree polynomial (a▪x2 + b▪x 

+ c). The response variable is the log10 of Enterococcus CFU or qPCR measures. 
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Table 5.2b. Summary statistics for the MLR models for marine beach sites. The response variable is the log10 of enterococci levels. 

Sensitivity is the number of correctly predicted exceedances over the total actual number of exceedances; Specificity gives the number 

of correctly predicted non-exceedances over the total actual number of non-exceedances, Accuracy gives the total number of correctly 

predicted values over the total count of the data set.
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5.3 COMPARISON OF MLR MODELING RESULTS ACROSS FRESHWATER 

AND MARINE SITES

Comparisons of the MLR modeling results indicate that, on the basis of adjusted R2 values for 

predicted versus observed levels of the FIB, model performance was better for the freshwater 

beaches than for the marine beaches (Tables 5.1b and 5.2b; freshwater average adjusted R2

 = 0.5, 

marine average adjusted R2 = 0.39). Also, modeling results for the culturable FIB data were 

somewhat better than for the qPCR data (Tables 5.1b and 5.2b; CFU average adjusted R2 = 0.46, 

qPCR average adjusted R2 = 0.42). The lower values for marine beaches likely reflect the 

interplay of several factors that have recently been reviewed by Grant and Sanders (2010). Those 

factors include the effects of currents and tides at the beaches (Grant and Sanders 2010), 

sunlight-induced inactivation (Boehm et al. 2009) and inputs of FIB from bird and dog 

droppings, bather shedding, runoff, groundwater and desorption from sand and decaying 

vegetation (Grant and Sanders 2010; Yamahara et al. 2007). Waves also can be an important 

factor that reduces model performance; however, all but one of the marine beaches examined in 

the study were enclosed bays or estuaries that had subdued wave action. Given the results shown 

in Tables 5.1b and 5.2b, the models were much more accurate in predicting non-exceedances 

than exceedances at the beaches. One contributing factor, especially in regards to the marine sites 

we studied, is that there were very few exceedances in the data sets. Accurately predicting 

phenomena (such as exceedances) that are rarely seen in the training data set is a very difficult 

task for a statistical model. For the calculations of sensitivity and specificity, we used the same 

decision thresholds as the EPA regulatory standards (61 CFU for enterococci in freshwaters, 104 

for enterococci in marine waters, and 235 for E.coli in freshwaters). A beach manager always has 

the option of lowering the decision threshold (i.e., a model predicted value over which the beach 

is closed). Depending on how low the decision threshold is set, the result is fewer false negatives 

(higher sensitivity), but more false positives (lower specificity).

Another general finding was that there was little evidence of a relationship between FIB densities 

and model performance, although we had expected that there might be. In the case of freshwater 

beaches modeled in this study, CFU modeling results (adjusted R2

) for the two cleanest beaches, 

South Shore Beach and West Beach, were among the best. Likewise, satisfactory modeling 

results were obtained at marine beaches such as Surfside Beach where almost no exceedances 

were observed. Although comparisons of results using culturable enterococci or E. coli were 

limited, we found that model performance was about the same for both indicators, e.g., at 

Huntington Beach, Ohio, during 2004. 

Table 5.3 shows the results of examining every available IV for all the freshwater and marine 

sites that were examined. The table indicates variables that were available in each data set, and 

whether they were significant contributors to the empirical modeling of qPCR or CFU responses. 

The top half of the table lists the five freshwater sites, and the seven marine sites are shown in 

the bottom half. The Rating in the last row of the table is the ratio of the number of times an IV 

was found to be significant (filled circles), over the maximum number of times it could have 

been significant (all circles). Take the IV algae as an example. It was present in 12 data sets and 

found to be significant in three instances: Washington Park CFU, West CFU, and Edgewater 

CFU; thus, its overall rating is 3/12 = 0.25. The assumption here is that variables with the highest 
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ratings would be the most worthwhile for measuring because there is a higher likelihood they 

will be significant contributors to an empirical model.

Table 5.4 displays three lists of the IVs sorted by their rating for freshwater sites, their marine 

site rating, and the difference between their freshwater and marine ratings. Variables at the top of 

the (freshwater-marine) list are relatively more important at freshwater sites, while variables at 

the bottom are relatively more important at marine sites. Table 5.5 displays three lists of the IVs 

sorted by their rating for culturable (CFU) data, for qPCR data, and the difference between those 

ratings. Variables at the top of the (CFU-qPCR ) list are relatively more important for modeling 

CFU data, while variables at the bottom are relatively more important for modeling qPCR data. 

The results in Tables 5.4 and 5.5 are combined for both culturable and qPCR enterococci models. 

To further explore the modeling differences between the two measurements of beach water 

quality, we evaluated IV effectiveness in four categories: culturable /freshwater, 

qPCR/freshwater, culturable/marine, and qPCR/ marine. That analysis showed that there were 

distinct differences between culture-based and qPCR-based models. For predictions of culturable 

enterococci at the freshwater beaches, the top IVs were turbidity, number of swimmers, 

barometric pressure, dew point, algae, and antecedent rainfall. The top IVs for qPCR predictions 

at freshwater sites were air temperature, wind speed, boats, turbidity, antecedent rainfall, and 

water temperature. At the marine beaches, the most effective IVs for predicting culturable 

enterococci were salinity, turbidity, bird counts, algae, swimmers, and wave height. For qPCR 

levels at marine beaches, the top IVs were the UV absorption coefficient of the water, antecedent 

rainfall, water temperature, debris on beach, relative humidity, and cloud cover.

The occurrence of turbidity and antecedent rainfall as top IVs for culturable enterococci at both 

freshwater and marine beaches reinforces the findings of earlier studies (Boehm et al. 2007; 

USEPA 2007). The number of swimmers was an important IV, perhaps in part because the 

NEEAR sites were selected to ensure that large numbers of people were present for 

epidemiological studies at the beaches. Presumably, shedding might have contributed to that 

finding. The fact that algal levels in the water also were important IVs suggests that remote 

sensing of chlorophyll could be a useful tool for evaluating beach water quality. Our studies also 

indicate that UV absorption coefficients of the water and, thus, CDOM can be important IVs in 

predicting qPCR levels at marine beaches. That finding is probably related to co-variation of this 

IV with inputs of contaminated waters from nearby streams or wetlands. CDOM also can be 

quantified by remote sensing. Additional process-based research is required to understand the 

various factors that underlie the results of these statistical models.

We acknowledge that the accuracy of the ratings calculated for IVs that appear in only a few data 

sets is suspect, and the robustness of the results can be improved by incorporating information 

from future empirical modeling efforts.
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Table 5.3. Summary of variables used for modeling beach sites. 

Notes:  = an IV was in the data set for a specific site but did not appear in the site’s chosen MLR model; . = the IV did appear in the chosen model; Rating = how often each 

IV, when available, appeared in chosen models (for each column, this is equal to the number of filled circles divided by the total number of circles).
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Table 5.4. Importance ratings for IVs at freshwater versus marine sites. 

Note: In each section of the table, the variables are sorted in descending order by their rating. The last section gives the result of subtracting the marine rating from the freshwater 

rating. Variables at the top of this list are relatively much more important at freshwater sites, while variables at the bottom are relatively much more important at marine sites. A 

variable that is very important (or completely unimportant) at both freshwater and marine sites would appear in the middle of this last list.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Table 5.5. Importance ratings for IVs for culturable (CFU) versus qPCR data. 

Note: In each section of the table, the variables are sorted in descending order by their rating. The last section gives the result of subtracting the qPCR rating from the CFU rating. 

Variables at the top of this list are relatively much more important for CFU data, while variables at the bottom are relatively much more important for qPCR data. A variable that is 

very important (or completely unimportant) for both qPCR and CFU data would appear in the middle of this last list.
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6 Evaluation of Dynamic Modeling and Forecasts 

of Biological Contamination

The utility of the VB tool was demonstrated initially by a pilot study that evaluated and assessed

the feasibility of dynamic models—those that are refit periodically to new data as they become 

available. Relatively short-duration, dynamic models developed using VB 1.0 (see Chapter 2) 

were compared in this pilot study, using the adjusted R2 statistic as a performance measure. A 

second objective of the modeling study using VB 1.0 was to evaluate 24-hour forecasts of 

microbial contamination at beaches. The study also tested the usefulness of publicly available 

data. The results of this section have been presented, in part in a peer-reviewed journal article by 

Frick et al. (2008). 

6.1 MATERIALS AND METHODS

Section 4.2.5 of this report describes the Huntington Beach, Ohio, site used for the study and our 

data collection techniques. The data were collected by the USGS Ohio Water Science Center and 

its partners, the Cuyahoga County Board of Health, and others. 

6.2 RESULTS AND DISCUSSION

6.2.1 Various Approaches to Developing MLR Models for Nowcasts

MLR models can be fit to data sets of durations ranging from a few days (the actual minimum 

number is a function of the number of variables included) to a season or longer. Some authors 

maintain that MLR models should be based on long-term data sets (Francy and Darner 2006; 

Nevers and Whitman 2005), producing models that are referred to as static models in this 

document. With a static MLR model, the regression coefficients are invariant over the period of 

its application. For example, USGS used 2000–2005 summer data to fit a unique MLR model 

that then was used to produce the 2006 beach advisories that are discussed here. In this 

subsection, such a unique model based on several years of data is called static. 

The dynamic modeling approach anticipates that models will likely vary as the regression 

responds to recent trends in the data. Periods as short as 10 days have been used to fit models at 

marine beaches (Hou et al. 2006). Both the model coefficients and best variables can vary over 

time because of changing environmental and other conditions, such as treatment plant flow rates, 

land use changes, storm events, and even climatic fluctuations, which are not well represented by 

static models (Boehm et al. 2002; Hou et al. 2006). In fact, as the database grows, the best 

predictive capacity for beaches with changing conditions over time might be obtained using 

models based on limited subsets of the data record (Hou et al. 2006). A dynamic MLR model can 

be defined as one in which the IVs are updated periodically with data generated within a limited 

recent period—usually on the order of 30 to 60 days. 
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6.2.2 The Performance of Dynamic Nowcast Models of Variable 

Duration

To evaluate the possible use of dynamic nowcast models, VB 1.0 was used to develop a series of 

models for multi-week subsets of 2006 data for Huntington Beach, Ohio (Figure 6.1). The 

models were evaluated by comparing predicted and observed E. coli densities for data subsets 

corresponding to 21, 28, 35, 42 and 49 days of data collection. Those results were compared to 

predictions obtained from the USGS using a model based on the entire 2006 summer season. For 

the 2006 season, the overall adjusted R2 for the USGS model was reported to be 42 percent

(Francy and Darner 2006). The dynamic modeling results (Table 6.1) for the final 49 days of the 

2006 season compared favorably with that result. Like the USGS model, the models built using 

VB 1.0 identified turbidity as one of the most significant IVs.

Table 6.1. Statistics for the predictions made by models of five temporal durations (seven models 

were fit in each duration category and each one made seven predictions, thus n = 49 for each 

category). 

Note: Given is the adjusted R2 value for the training data, the standard error of the predictions (SE), the number of correctly 

predicted exceedances (CE), the number of false negative predictions (FN), and the number of false positive predictions (FP).

Figure 6.1 categorizes models by their duration of fit to the data and best IVs. The IVs used in 

each case are listed across the top of the figure. The rows of the figure show different categories 

of models based on five different fitting durations: 21, 28, 35, 42, and 49 days. The start day

column provides the date of the start of each model’s predictive implementation. For example, 

the 21-day model used to nowcast daily bacteria densities for the 7 days starting July 14 and 

ending July 20 was fitted to the previous 21 days (June 23 to July 13) of known data. That was

followed by the second 21-day model in the category fitted to the 21 days before July 21, and so 

on. Thus, each of the seven 21-day models contributed seven predictions for a total of 49 

predictions (n = 49 for each category). For each duration category, statistics appear in Table 6.1: 

adjusted R2 (%) of the training data, the standard error of the predictions, number of correct 

predictions above the health standard, false negatives, and false positives. 
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Note: The data were collected by the USGS Ohio Water Science Center, and its partners, the Cuyahoga County Board of Health 

and others. Data sets were composed of 21-, 28-, 35-, 42-, and 49-day durations. The significance of the variables: green = most 

significant IV, blue = 2nd most significant IV is based on a model selection process using Cp as the selection criterion (figure 

modified from Frick et al. (2008). 

Figure 6.1. Results of models built by VB 1.0 using data at Huntington Beach, Ohio, during 2006. 
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Figure 6.1 also shows that turbidity, with a few exceptions, was the best IV in 2006. While 

turbidity was a valuable IV in the 2006 nowcast test, useful models were developed 

incorporating off-site IVs. Off-site IVs also were found to be valuable predictors for other 

beaches (Chapter 8). Here at Huntington, Ohio, we found that models incorporating dew point, 

temperature, and cloud cover variables from the Cleveland airport routinely outperformed those 

incorporating on-site water temperature and wave height variables. That is valuable knowledge 

because the off-site data from NOAA weather stations can be obtained with little effort. 

Moreover, adjusted R2 values generally increased as the fitting period for the data sets increased 

from 21 to 35 days but were more or less constant, even decreasing as the duration of fit 

increased further. The standard errors followed a similar, but inverse, relationship. Overall, 

models of limited (35 to 42 days) duration appeared to perform best. Also, models developed 

over the short time frames show great stability; i.e., turbidity, dew point, and cloud cover are 

consistently among the best variables. 

The results of that research suggest that models based on short-term data sets at Huntington 

Beach, Ohio, perform approximately as well as static models that are based on much longer term 

data from the beach. However, a detailed analysis of a more extensive data set (2000–2009) from 

Huntington Beach (Chapter 7) indicates that inclusion of more historic data improved the models 

for the beach. Thus, as suggested in Chapter 7, random climate-driven fluctuations in conditions 

might be the strongest determinant of FIB levels at Huntington Beach over an extended period. 

For other beaches that experience more rapid changes in nearby land use or climate than in 

northern Ohio, it is possible that models based on longer-term data sets would be less reliable 

than those based on more recently observed data (Boehm et al. 2002). 

6.2.3 Dynamic Forecasting Models

The term forecast is defined in this section as making predictions that are typically 24 to 48 

hours into the future, using primarily Cleveland airport forecasts as IVs. More details about this 

procedure are included in Frick et al. (2008). The experimental forecast period covered 42 days 

in the second half of the 2006 beach season. From nowcasting results that showed 5-week 

models performed best, no attempt was made to fit forecast models with data sets of other 

durations. For the 42-day forecast period (July 21 to August 31), the adjusted R2was 42.3 

percent, similar to nowcast results that exclude turbidity. Eight exceedances were correctly 

predicted, and there were six false negatives and no false positives. The 24-hour forecast 

performance compared favorably to the corresponding nowcast performance (omitting turbidity), 

despite the reduction in available IVs. 

The results of the research were an initial indication that the VB tool could facilitate and 

optimize the development of statistical models used for nowcasting and forecasting FIB densities 

at recreational water sites, and it could be valuable for optimizing and updating dynamic models 

based on short-term data sets.
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7 Evaluating the Predictive Capabilities of 

Models for E. coli Levels at Huntington Beach, 

Ohio, Using Varying Amounts of Historical 

Data

7.1 INTRODUCTION

The previous section, which discusses results presented in Frick et al. (2008), raises interesting 

questions about data used for MLR model development. They discuss the concept of dynamic 

modeling, in which the temporal characteristics of the data used to generate FIB models come 

under scrutiny. Using USGS data for 2006 at Huntington Beach, Ohio, they investigated whether 

short-term data sets, such as those spanning from 1 to 7 weeks before the desired prediction date, 

could produce models that outperform models using longer-term data sets, i.e., entire previous 

years of data. They found that short-term data sets could, indeed, produce useful statistical 

models for the site and that it was not necessary to accumulate multiple years of modeling data 

before statistical relationships could be fruitfully explored.

Our objective was to expand on the analyses of Chapter 6. Given a robust 10-year (2000–2009) 

USGS data set documenting environmental conditions and E. coli counts at Huntington Beach, 

Ohio, we set out to record the predictive capabilities of models developed using successively 

longer periods of data. We did not investigate short-term intra-annual data sets as in Frick et al. 

(2008), instead focusing on modeling results for inter-annual data sets ranging from 1 to 9 years 

of observations. Our initial hypothesis was that more data would mean better models, i.e., 

predictions would improve as more historical data were used for model development. However,

if factors that control FIB levels at a site change through time continuously—possibly from land 

use change in the surrounding watershed or climate change—model performance could degrade 

according to the period of data used. If periodic or cyclical environmental conditions affect the 

site, there might be an optimum historic period of record to use for making predictions. When 

forces driving FIB contamination at a site change annually in an unpredictable manner, models 

developed using a prior year’s data could be good or poor, depending on the similarity between 

the historical data period and the current period for which predictions are needed. 

We formalized these issues with the following research questions: 

1. Will using longer historical periods of data lead to better predictive models for E. coli

at Huntington Beach? 

2. If not, is there another period of record that optimizes model predictive performance?

3. Does year-to-year variability in model predictive ability show any discernible patterns?

4. Do the answers to 1, 2, and 3 provide insight about FIB dynamics at Huntington Beach? 
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7.2 METHODS

Huntington Beach, including sampling protocols, is described in detail in Section 4.2.5, 

Appendix A, and in Francy et al. (2003), Francy and Darner (2006), and Haugland et al. (2005). 

E. coli levels were measured during the 2000–2009 swimming seasons (late May through late 

August), along with a suite of potential IVs (water temperature, turbidity, wave height, wind 

speed and direction, solar radiation, and the like). Wind speed and direction were converted into 

along-shore (u) and cross-shore (v) components, as discussed in Frick et al. (2008). Relative to 

each E. coli measurement, raw rainfall data were aggregated into 48-hour antecedent cumulative 

precipitation. Log10 values of E. coli were used as the response variable.

To address our first two questions, we tested the predictions of MLR models, using E. coli levels 

as the response, based on successively longer historic data sets (Table 7.1).

Table 7.1. The matrix for recording MSE of models developed using a variable number of previous 

years’ data (M1prev–M9prev) applied to each single year of data (Y2001–Y 2009).

For example, we developed a model (model selection always done using backwards stepwise 

procedure with AIC as the criterion) with data from 2004, and then used this model to predict the 

E. coli values in 2005. We termed the model M1prev because it was based on one previous years’ 

worth of data. We would then record the MSE of those predictions in row “Y2005,” column 

“M1prev” in Table 7.1. Next, we would construct a model with data from 2003 and 2004, use that

model to predict the E. coli values in 2005, and record the MSE of the predictions in row 

“Y2005,” column “M2prev.” That methodology was used to find all the MSE values in Table 7.1. 

Y2000 values do not appear in the table because it was the first year of our data record.

To address our third research question, we created 10 data sets of IVs (X) and corresponding E. 

coli measurements (Y). Those are labeled as (X2000, Y2000), (X2001, Y2001), ..., (X2009,Y2009). Next, 

we developed MLR models (again using backwards stepwise procedures with AIC as the model 

criterion) using each of these data sets, and denoted those models as M2000, M2001, ..., M2009. 

Next, we fit each of the models to every other year of data during the period of record and noted 

the MSE for that application (Table 7.2). 

M1prev M2prev M3prev M4prev M5prev M6prev M7prev M8prev M9prev

Y2001 MSE1,1 - - - - - - - -

Y2002 MSE2,1 MSE2,2 - - - - - - -

Y2003 MSE3,1 MSE3,2 MSE3,3 - - - - - -

Y2004 MSE4,1 MSE4,2 MSE4,3 MSE4,4 - - - - -

Y2005 MSE5,1 MSE5,2 MSE5,3 MSE5,4 MSE5,5 - - - -

Y2006 MSE6,1 MSE6,2 MSE6,3 MSE6,4 MSE6,5 MSE6,6 - - -

Y2007 MSE7,1 MSE7,2 MSE7,3 MSE7,4 MSE7,5 MSE7,6 MSE7,7 - -

Y2008 MSE8,1 MSE8,2 MSE8,3 MSE8,4 MSE8,5 MSE8,6 MSE8,7 MSE8,8 -

Y2009 MSE9,1 MSE9,2 MSE9,3 MSE9,4 MSE9,5 MSE9,6 MSE9,7 MSE9,8 MSE9,9
Predictive Modeling at Beaches—Volume II November 22, 2010

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Table 7.2. The matrix for recording MSEs of models developed using a single year of data, then 

applying that model to all other years of observations.

For example, using the model developed from X2002,Y2002 data (M2002), plugging in the X2004 IVs 

and taking the MSE of the fit of this model compared to the actual Y2004 observations, would 

produce the MSE5,3 value (the highlighted cell in Table 7.2). 

7.3 RESULTS AND DISCUSSION

The MSEs given in Table 7.3 support the notion that using as much historic data as possible 

leads to better overall predictions, i.e., the mean column values decline from left to right. Within 

any single row, the pattern is not always maintained, but on average, it is clearly seen. Such 

results are consistent with some previous studies (Francy et al. 2006b; Nevers and Whitman 

2005). 

M2000 M2001 M2002 M2003 M2004 M2005 M2006 M2007 M2008 M2009

(X2000,Y2000) MSE1,1 MSE1,2 MSE1,3 MSE1,4 MSE1,5 MSE1,6 MSE1,7 MSE1,8 MSE1,9 MSE1,10

(X2001,Y2001) MSE2,1 MSE2,2 MSE2,3 MSE2,4 MSE2,5 MSE2,6 MSE2,7 MSE2,8 MSE2,9 MSE2,10

(X2002,Y2002) MSE3,1 MSE3,2 MSE3,3 MSE3,4 MSE3,5 MSE3,6 MSE3,7 MSE3,8 MSE3,9 MSE3,10

(X2003,Y2003) MSE4,1 MSE4,2 MSE4,3 MSE4,4 MSE4,5 MSE4,6 MSE4,7 MSE4,8 MSE4,9 MSE4,10

(X2004,Y2004) MSE5,1 MSE5,2 MSE5,3 MSE5,4 MSE5,5 MSE5,6 MSE5,7 MSE5,8 MSE5,9 MSE5,10

(X2005,Y2005) MSE6,1 MSE6,2 MSE6,3 MSE6,4 MSE6,5 MSE6,6 MSE6,7 MSE6,8 MSE6,9 MSE6,10

(X2006,Y2006) MSE7,1 MSE7,2 MSE7,3 MSE7,4 MSE7,5 MSE7,6 MSE7,7 MSE7,8 MSE7,9 MSE7,10

(X2007,Y2007) MSE8,1 MSE8,2 MSE8,3 MSE8,4 MSE8,5 MSE8,6 MSE8,7 MSE8,8 MSE8,9 MSE8,10

(X2008,Y2008) MSE9,1 MSE9,2 MSE9,3 MSE9,4 MSE9,5 MSE9,6 MSE9,7 MSE9,8 MSE9,9 MSE9,10

(X2009,Y2009) MSE10,1 MSE10,2 MSE10,3 MSE10,4 MSE10,5 MSE10,6 MSE10,7 MSE10,8 MSE10,9 MSE10,10
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Table 7.3. Results of modeling the MSEs of Table 7.1. 

Note: The mean MSE values in the last row indicate that using more historic data generally leads to better predictions.

FIB levels at beaches respond to a suite of environmental factors such as storm events, local land 

use, nearby WWTPs, beach attendance, and such. If the set of factors important for determining 

FIB levels at a site changes through time, it would seem that predictions made using short-term 

data sets could, indeed, be more responsive to these changes. However, when using a long-term 

data set, the model is basically averaged over all the data, and representative of many different 

conditions experienced at the site. In other words, predictions from this model will be decent 

over a large range of possible environmental scenarios. With models derived from short-term 

data sets, the likelihood of boom and bust predictions arises. When conditions at the site have not 

changed recently, using the past 5 weeks of data to make predictions should work well. In the 

days following an important change in conditions, however, predictions based on the past several 

weeks of data could be terrible. A third scenario, in which conditions at the site are slowly 

changing along some gradient (global climate change leading to increasing temperatures or 

precipitation, or impervious surfaces in the local watershed continually increasing) could favor 

short-term data sets. In such a case, abrupt changes to the system are not present, and conditions 

in the future will be unlike those seen in the past, so using long, historic data sets could be 

counterproductive. 

The MSE values in Table 7.4 support the notion that random climate fluctuation determined FIB 

levels at Huntington Beach over the period. 

M1prev M2prev M3prev M4prev M5prev M6prev M7prev M8prev M9prev

Y2001 2.39 - - - - - - - -

Y2002 2.99 2.12 - - - - - - -

Y2003 3.21 1.91 1.53 - - - - - -

Y2004 1.64 1.77 1.44 1.60 - - - - -

Y2005 2.84 1.88 2.04 2.02 1.92 - - - -

Y2006 1.92 1.92 1.70 1.82 1.67 1.78 - - -

Y2007 1.23 1.17 1.24 1.28 1.19 1.26 1.20 - -

Y2008 1.62 1.20 1.16 1.02 1.15 1.22 1.13 1.09 -

Y2009 0.77 0.67 0.67 0.66 0.67 0.64 0.64 0.66 0.62

Mean 2.07 1.58 1.40 1.40 1.32 1.22 0.99 0.87 0.62
Predictive Modeling at Beaches—Volume II November 22, 2010

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Table 7.4. Results of modeling the MSEs of Table 7.2. 

Note: The lack of an easily discernible pattern in these data is consistent with a hypothesis that random annual climatic variation 

governs FIB dynamics at Huntington Beach, Ohio. 

Those data show no easily discernible pattern (although no statistical test was performed), other 

than values along the diagonal are the lowest for each row, as would be expected—i.e., the 

model derived from the data of a given year has to fit that same year’s observations better than 

any model developed from another year’s data. The MLR regression coefficients are determined 

by minimizing the sum of the squared error term. Any other set of coefficients mathematically 

could not produce a lower MSE. That does not mean, however, that the value along the diagonal 

has to be the lowest value within any column. For example, the 2004 model fits the 2009 data 

even better than it fits its own 2004 observations. But the 2009 model still fits the 2009 data best 

of all, and the 2004 model fits the 2004 data best (lowest values within each row). 

If a gradient effect reflecting gradually changing conditions existed, the MSE values in Table 7.4 

would rise moving left or right, away from the diagonals within each row, but that pattern is not 

seen. The table makes it clear that certain pairs of years are more alike than other pairs, leading 

to better predictions. For example, the model based on 2006 data fits 2008 observations very 

well, but it does not fit 2002 observations well. Overall, the 10 models had the hardest time 

fitting 2005 observations, and the easiest time fitting 2009 observations, based on the MSE row 

means given in the far right column. The model from 2000 did the poorest job of fitting the 10 

data sets, because of its largest mean value in the last row of the table.

M2000 M2001 M2002 M2003 M2004 M2005 M2006 M2007 M2008 M2009 Mean

(X2000,Y2000) 0.56 2.03 1.97 1.42 2.43 1.79 1.56 1.39 1.07 0.99 1.52

(X2001,Y2001) 2.39 1.26 2.42 1.94 2.64 1.99 1.98 2.62 1.62 1.68 2.05

(X2002,Y2002) 3.49 3.15 1.27 2.44 2.27 2.36 2.70 2.19 2.77 2.06 2.47

(X2003,Y2003) 2.71 1.74 1.76 0.61 1.46 0.83 1.39 1.23 1.67 0.95 1.44

(X2004,Y2004) 2.14 1.82 2.25 1.62 1.26 1.96 2.49 1.64 2.67 1.87 1.97

(X2005,Y2005) 6.79 3.05 2.56 1.97 2.84 1.69 2.22 2.93 2.68 2.34 2.91

(X2006,Y2006) 3.22 2.74 2.11 1.90 2.15 1.92 1.21 1.92 1.77 1.52 2.05

(X2007,Y2007) 4.24 2.19 1.93 1.81 1.54 1.86 1.23 0.77 1.20 1.14 1.79

(X2008,Y2008) 4.84 1.20 3.08 1.50 1.32 1.88 1.13 1.62 0.72 0.93 1.82

(X2009,Y2009) 2.72 0.94 2.24 1.12 0.74 1.09 1.31 1.08 0.77 0.52 1.25

Mean 3.31 2.01 2.16 1.63 1.86 1.74 1.72 1.74 1.70 1.40
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7.4 CONCLUSIONS

Using MLR modeling on a series of annual data sets (2000–2009) for Huntington Beach, Ohio, 

better predictions of E. coli were made as more historic data were used in developing predictive 

models. Also, random annual climatic fluctuations appeared to be driving FIB levels at this site 

because no easily discernible pattern or gradient was found when examining temporal trends 

within model predictions on a year-to-year basis. In other words, a model developed using data 

from year T did not make better predictions for years T-1 and T+1, as compared to predictions 

made for years more temporally removed from T. The temporal positions of good and bad 

predictions between individual years showed no apparent pattern. 

We must note that these results, having been derived from a study at a single site, are not nearly 

robust enough to draw general conclusions regarding other beaches, but they do provide clear 

evidence that in at least this case, more historic data leads to better predictions. FIB dynamics at 

other beaches, driven by different sources, hydrodynamics, and climatic conditions, might react 

quite differently over time and short-term models might be able to provide more effective 

predictions in some cases.
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8 The Importance of Site-Specific Environmental 

Data for Modeling Enterococci Densities at 

South Shore Beach, Wisconsin

8.1 INTRODUCTION

This study focused on comparing the fit and predictive ability of MLR models developed using 

two sets of IVs for a site—one data set containing only publicly available environmental data 

collected near the beach, and a second data set that contains the first, but then adds additional 

environmental data collected at the beach itself. In both cases, on-site microbial data were used 

as the dependent variables in model development. We did not include in this comparison a data 

set consisting of data collected on-site only, because publicly available data could always be 

added at little cost, so the condition itself is not worth examining when costs and benefits are at 

issue. Such a type of analysis can allow a beach manager to make an objective determination of 

whether the resources used for equipment installation and monitoring are worthwhile, as 

measured by improvements in model predictive abilities.

8.2 MATERIALS AND METHODS

8.2.1 Site Details

South Shore Beach’s location is shown in Figure 4.2, and the beach is described in detail in 

Section 4.2.1. Given the history of biological contamination at South Shore, plus the public 

availability of nearby meteorological and other IVs for modeling microbial levels, we decided to 

conduct a detailed modeling study at this beach during the summer of 2008.

In keeping with the objectives of our study, all IVs were categorized into two groups (Table 8.1): 

publicly available (PA) and SS. SS refers to all additional data collected by EPA or the 

University of Wisconsin-Milwaukee’s Great Lakes WATER Institute despite the fact that the 

EPA’s weather station was a mile from the beach. For our response variable (enterococci 

CFU/100 mL), we then developed and compared MLR models that used only the PA variables 

versus a model that used both PA and SS variables. 

8.2.2 Data Management

An important step in MLR analysis is to check for high correlations among the IVs to avoid 

inflated standard errors and instability when estimating regression coefficients. We checked for 

IV collinearity, using Pearson correlation coefficients. Given a pair of highly correlated IVs 

(correlation coefficient above 0.8, (Cohen 1988), collinearity is remedied by dropping one of the 

two from the analysis. The primary criterion for this choice was to choose the IV with fewer 

missing values in the data set. When PA and SS variables were found to be highly correlated, 

and if the missing-value criterion was equivalent, PA variables were retained over SS in 
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Table 8.1. Environmental variables used in model development

Data Collection

Data Source Type Variable Description Duration Frequency

Absorption Coefficient (325 nm)

Dissolved Organic Carbon 7/2 - 9/22 9:00, 11:30, 15:00

Water Temperature

Conductivity

Salinity

Dissolved Oxygen

pH

Turbidity

Chlorophyll

Ammonium

Ammonia

Nitrate

7/17 - 10/18 Every 15 minutes

Current Speed

Current Direction

Water Depth

7/17 - 10/21 Every 10 minutes

Wave Height

EPA Sonde SS

Wave Direction 7/17 – 10/21 Every 60 minutes

Attenuation Coefficient (325 nm) EPA UV Sensor SS Mean Attenuation at 0.3 meters (325 nm) 7/17 - 10/22 Every 60 minutes

Solar Radiation

Photosynthetic Active Radiation

Wind Speed

Wind Direction

Gust Speed

Cumulative 48hr Rainfall

Air Temperature

Humidity

Dewpoint

EPA Weather Station SS

Pressure

7/21 - 10/18 Every 15 minutes

Water Temperature

Conductivity

pH

Dissolved Oxygen

Chloride

UW Sonde SS

Turbidity

7/17 - 10/19 Every 30 minutes

Air Temperature

Cumulative 48hr Rainfall

Wind Speed UW Weather Station SS

Wind Direction

7/17 - 10/19 Every 60 minutes

Visibility

Dry Bulb Temperature

Wet Bulb Temperature

Dewpoint

Humidity

Wind Speed

Wind Direction

Barometric Pressure

Pressure at Sea Level

Cumulative 48hr Rainfall

General Mitchell Airport PA

Altimeter Pressure

7/1 - 9/30 Every 60 minutes

USGS PA Flow at Mouth of Milwaukee River 6/25 - 8/28 Once per day
Predictive Modeling at Beaches—Volume II November 22, 2010

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developing models based on both data sets. If correlated IVs were either both PA or both SS—

and no missing-value advantage was seen—ease of interpretation and measurement was used to 

decide which IV to retain. After that processing, 9 IVs remained for the PA data set, and 21 IVs 

for the PA+SS data set.

As in previous modeling studies (Frick et al. 2008; Hou et al. 2006; Francy and Darner 2006; 

Olyphant and Whitman 2004), the logarithm (base 10) of the Enterococcus count was taken to 

help ensure a more linear relationship to the IVs. Measurements describing wind speed and 

direction, and water current speed and direction, were transformed into an along-shore 

component (u) and perpendicular-to-shore component (v) (Nevers et al. 2007). 

8.2.3 Model Development

After removing missing values from our data set, 79 measurements of enterococci CFUs 

remained for model development. Many metrics allow an analyst to judge the relative merit of 

how well statistical models fit data, such as the AIC, AICC, BIC, adjusted R2, PRESS and 

Mallows’ Cp (Cp). While the adjusted R2, AIC, AICc, BIC and Cp are different measures of the 

fit of a model to a set of training data, with a penalty imposed for over-fitting, PRESS uses oneobservation-at-a-time cross-validation to optimize the out-of-sample prediction performance. 

PRESS sums the prediction residuals of a model, so lower PRESS values mean better models. 

Because of the public health ramifications of not making accurate predictions of fecal indicator 

levels at beaches, we chose the PRESS statistic to define the best predictive model.

Model selection was accomplished using VB 2.0 (see Chapter 2). Because we had 79 

observations, and knowing that 10 observations per IV provide adequate power to estimate 

regression coefficients with precision (Aguinis and Harden 2009), we evaluated only those 

models with seven IVs or fewer. While calculating every possible 1- to 7-parameter regression 

model was possible for the PA data set (a total of 9 IVs), the PA+SS data set had too many IVs 

(21) for this to be done, so we used VB 2.0’s GA instead. 

8.2.4 Model Validation/Evaluation

After the two best models (one using the PA data set and one using the PA+SS data set) were 

identified, they were compared. First, the ability of these models to fit the observed 

Enterococcus counts was evaluated using the model’s adjusted R2 value (Frick et al. 2008; 

Nevers et al. 2007; Francy and Darner 2006). Second, the model’s PRESS values were 

compared. Finally, we examined the sensitivity and specificity of each model (Francy and Darner 

2006); see definitions in Chapter 3) using the 61 CFU/100 mL EPA national advisory level for 

Enterococcus in freshwater as the critical threshold.

Generally, the probability of exceeding a threshold or standard, S, can be calculated as:

Pexceed = Prob (T ≥ [ŷ – log(S)] / sŷ) 

where T has the Student’s t distribution with n–p degrees of freedom (n is the number of 

observations in the data set and p is the number of estimated regression parameters), ŷ is the 

predicted value of the logarithm of the FIB count and sŷ is the standard error of this prediction. 

We could alternatively define a probability threshold (e.g. 30 percent), such that any ŷ whose 

corresponding Pexceed surpasses the threshold (meaning ŷ has a greater than 30 percent chance of 
Predictive Modeling at Beaches—Volume II November 22, 2010

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exceeding log[S]) is considered an unacceptable risk to public health and would lead to beach 

closure. We specified three Enterococcus count thresholds (30, 61 and 100 CFU/100 mL) and 

three probability thresholds (30, 50, and 70 percent) to calculate the specificity and sensitivity of 

each model.

8.3 RESULTS

8.3.1 PA Analysis

The primary objective of this report is to compare the ability of the PA and PA+SS data sets to 

fit observed bacteria counts, and interpretation of significant IVs is beyond the scope of this 

report. Analysis of the PA data set, which included measurements from the General Mitchell 

Airport and the USGS gage on the Milwaukee River, produced the following model:

The adjusted R2 of this model is 0.47, and the PRESS statistic is 11.02. 

8.3.2 Combined PA + SS Analysis

The analysis used the publicly available General Mitchell Airport and USGS data as well as the 

data collected by EPA and the UWM-GLWI at South Shore Beach. The VB 2.0 GA selected this 

model:

Parameter Coefficient Std. Error t-Statistic P-Value

(Intercept) -52.4 9.96 -5.26 < 0.001

Dewpoint 0.020 0.01 2.40 0.019

Wind U-Component -0.018 0.01 -2.91 0.005

Barometric Pressure 1.79 0.33 5.38 < 0.001

Cumulative 48-hr Rainfall 104.7 14.02 7.47 < 0.001

Parameter Data Source Coefficient Std. Error t-Statistic P-Value

Intercept -12.12 2.73 -4.44 < 0.001

Cumulative 48-hr Rainfall PA - Airport 94.38 12.67 7.45 < 0.001

pH SS - EPA Sonde 0.65 0.24 2.70 0.0087

Dissolved Oxygen SS - UW Sonde -0.21 0.03 -6.25 < 0.001

Nitrate SS - EPA Sonde 0.20 0.06 3.43 0.001

Mean Attenuation Coefficient (0.3m) SS - EPA Sensor -0.04 0.01 -3.43 0.001

Wind U-Component PA - Airport -0.02 0.01 -3.00 0.0037

Water Depth SS - EPA Sonde 3.74 0.64 5.83 < 0.001
Predictive Modeling at Beaches—Volume II November 22, 2010

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The adjusted R2 obtained was 0.59, and the PRESS statistic was 9.1 for the model. The PA 

model uses four IVs, while the PA+SS model has seven—five SS and two PA variables. Using 

the PA+SS data set increased the adjusted R2 by 25 percent and decreased the PRESS statistic by 

17 percent over the model that used only PA variables. That indicates that on-site environmental 

data can help predict FIB at South Shore Beach but that publicly available meteorological data 

alone can explain a significant proportion of the variability in FIB levels. 

8.3.3 Model Comparisons

Plots, using a count threshold (Figure 8.1) and a probability threshold (Figure 8.2), of model 

predictions versus actual observations demonstrate a graphical approach to model evaluation.

Note: The colored quadrants are formed by the vertical line (EPA regulatory standard) and the horizontal line (beach manager’s 

decision criterion). The decision criterion can be shifted up and down to meet an objective of minimizing false positives or false 

negatives.

Figure 8.1. Plotting model predictions versus observations for the PA and PA+SS data sets. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Note: As in Figure 8.1, the vertical line is the regulatory standard. The three horizontal lines represent three choices of probability 

threshold (30 percent, 50 percent, and 70 percent).

Figure 8.2. Plotting the probability that a predicted bacteria count will exceed a threshold value 

(log[61] CFU/100 mL) versus actual observations.

Horizontal thresholds, set by the analyst, and vertical standards, typically set by a regulatory 

agency (e.g., EPA’s freshwater Enterococcus standard of 61 CFU/100 mL), separate the space 

into four quadrants: false positives (upper left), correct positives (upper right), correct negatives 

(lower left) and false negatives (lower right). The plots are used to count observations in each 

quadrant directly and provide the summary data entered in Table 8.2. 

In addition, the analyst can determine the impact of changing the decision threshold (horizontal 

line) on the numbers of false negatives and false positives that a model produces. For example, in 

looking at PA predictions in Figure 8.1, lowering the decision threshold to 1.57 would result in 

three fewer false negatives, while not incurring any additional false positives.

Table 8.2 shows that the minimum specificities of both models were near 90 percent, meaning 

actual counts of bacteria below the standard were well-predicted. Some threshold-specific 

sensitivities, however, were much lower, indicating both models had more difficulty 

distinguishing false negatives from correct positives. Upon examination of Table 8.2, we 

conclude that the PA data set produced a model that performed well when compared to the 

PA+SS data set. Sensitivity for the PA model was on average 87 percent as large as sensitivity 

for the PA+SS model, and specificity values for the two models were nearly identical. So, while 

comparisons using adjusted R2 and PRESS statistics definitely favored the PA+SS model, the 

threshold analysis, focusing only on placing prediction/observation pairs into one of four 

quadrants (as in Figure 8.2), showed fewer discrepancies between the two models. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Table 8.2. Results of the threshold analysis for the PA and PA+SS models. 

Notes: 

EPA’s regulatory threshold for Enterococcus is 61 CFU/100 mL. 

CN = number of correct negatives, FP = number of false positives, CP = number of correct positives, and FN = number of false 

negatives. Specificity = CN/(CN+FP), Sensitivity = CP/(CP+FN)

8.4 DISCUSSION

Our preliminary analyses indicate that the best models chosen by metrics that measure fit to 

training data (Mallows Cp, AIC, BIC, and such) are very similar to the models chosen by the 

PRESS statistic. That is not completely unexpected, given that our data are taken from a single 

swimming season. Environmental processes dictating the fate and transport of fecal indicators at 

the beach probably were stable over the period. At beach sites where there are intra-seasonal or 

annual shifts in the processes important to fate and transport of bacterial contaminants, models fit 

to a long-term series of previously collected data might not be best at predicting new 

observations (Frick et al. 2008). For example, if a new bacterial source near the beach is 

introduced (i.e., a breakwall is constructed), hydrologic patterns at the beach might be altered, or 

if an exceptional climatic period occurs, using a weighted regression that emphasizes the most 

recently collected data would be our recommended statistical technique. 

Adopting higher decision thresholds (as shown in Figure 8.2) imposes more risk to public health 

than if lower horizontal thresholds were to be used; however, lowering the horizontal threshold 

can result in more frequent false positives. Such a strategy is more protective of public health, 

but it results in economic losses because of more frequent beach closures. When setting the 

horizontal thresholds, the manager must seek a balance between protection of public health and 

economic concerns. From a health perspective, the consequences of false negatives often are 

seen as more serious than those of false positives; therefore, horizontal count thresholds below 

the regulatory standard (corresponding to probability thresholds lower than 50 percent) are used. 

For example, the model developed for the combined (PA+SS) data set had a sensitivity of about 

Model Threshold Type Threshold CN FP Specificity CP FN Sensitivity

Log(30) 59 7 0.894 10 3 0.769

Log(61) 66 0 1.000 7 6 0.538

Log(100) 66 0 1.000 4 9 0.308

30% 66 0 1.000 8 5 0.615

50% 66 0 1.000 7 6 0.538

70% 66 0 1.000 6 7 0.462

Log(30) 62 4 0.939 11 2 0.846

Log(61) 66 0 1.000 9 4 0.692

Log(100) 66 0 1.000 4 9 0.308

30% 66 0 1.000 9 4 0.692

50% 66 0 1.000 8 5 0.615

70% 66 0 1.000 8 5 0.615

PA

PA+SS

Count

Probability

Count

Probability
Predictive Modeling at Beaches—Volume II November 22, 2010

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70 percent when using a probability threshold of 30 percent. That means, if a manager closed the 

beach whenever the model predicted a greater than 30 percent chance of exceeding the standard 

(61 CFU/100 mL), the standard would actually be exceeded on 70 percent of those days. An 

even lower probability threshold might improve the sensitivity, but it also could cause the 

model’s specificity to decrease. Lower model sensitivities (relative to specificities) in the 

analysis were likely the result of a data set with very few large FIB counts. Regression models 

generally will fit the dominant type of observation well, especially when using the PRESS 

statistic as the selection criterion because it negates the influence of high leverage outliers; in this 

case, the majority of observations were small FIB counts (< 50 CFU/100 mL). A more balanced 

data set of small and large FIB levels would produce a model better suited to fit either type of 

observation. If the analyst is more interested in making good predictions when bacteria levels are 

high, one tactic could be a weighted regression with greater weights given to the larger FIB 

observations. 

Managers attempting to model FIB beach levels with publicly available near-site data must 

consider the distance from the beach site to the monitoring location. In this case, approximately 

4 miles separate South Shore Beach from the General Mitchell Airport. The geographic 

variability of meteorological data depends on the parameter (Rogers and Vanloon 1982; Koprov 

et al. 1998; Grants and Gerbeth 2003; Baigorria et al. 2007), but one would expect the predictive 

capabilities of meteorological data to decline as the distance between the monitoring location and 

beach site increases. Unfortunately, we cannot provide definitive advice on a maximum distance 

that should be considered. 

8.5 CONCLUSIONS

We found that the PA data set could not match the performance of the PA+SS data set at South 

Shore Beach, in terms of the adjusted R2 and PRESS statistics. However, given funding 

constraints or lack of availability of monitoring equipment at the beach of interest, a PA data set 

can provide a feasible alternative for developing an acceptable model. In our study, the PA data 

produced a model that explained about 47 percent of the variability in FIB levels. The predictive 

performance (as measured by the PRESS statistic) of the PA model was 11 versus 9 for the 

PA+SS models. To draw general conclusions about the utility of on-site data, however, more 

studies of this type need to be performed, including at marine and riverine beach sites where 

different processes could control the fate and transport of pathogens. 
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9 Advanced Techniques to Refine MLR Model 

Results

9.1 INTRODUCTION TO TEMPORAL SYNCHRONIZATION

For most IVs used in an MLR analysis, a value is recorded at the moment the water sample for 

FIB levels is taken, but rainfall is an exception. Cumulative precipitation over some period 

before the FIB water sample is often used as an IV in predictive beach bacteria modeling efforts 

(Francy and Darner 2006; Hose et al. 2006; Neumann et al. 2006; Nevers et al. 2009). MLR 

models might be improved if all measured environmental data, not just precipitation, were 

summarized over a longer temporal window rather than relying on the instantaneous value taken 

at the time of FIB sampling. In addition to taking a mean value of an IV over some temporal 

window, a temporal lag might also increase the relationship between an IV and the FIB response. 

For example, consider a water sample collected at 9 a.m. on a Thursday. For the IV water 

temperature, you wish to investigate a window of 24 hours and a lag of 12 hours. That means 

you will select a time 12 hours earlier (the lag) to 9 p.m. on Wednesday, then examine every 

water temperature measurement taken from that point to 24 hours earlier (the window), 9 p.m. on 

Tuesday. You would then compute the average of all the water temperature measurements over 

the window/lag combination. The mean value would become the new value of the water 

temperature for the Thursday 9 a.m. water sample. Note that using a window of zero and a lag of 

zero is equivalent to the traditional approach of using a single instantaneous value of the IV 

measured as the water sample is collected.

We gave this technique a name—Temporal Synchronization Analysis (TSA). Essentially, TSA 

seeks to maximize the correspondence between each IV and the FIB response by examining 

different combinations of temporal windows and lags over which the mean value of the IV is 

calculated. Those windows and lags are defined, relative to when the FIB concentration is 

measured. We set out to test whether a TSA could improve both the ability of an MLR model to 

fit a data set and, more importantly, the ability of an MLR model to make predictions of new 

observations. Such a technique assumes that the potential effects of the IVs on the response are 

hard to detect using single instantaneous measures of each IV, but the examination of mean 

values of IVs over a longer duration at some point in the past will lead to stronger empirical 

relationships between the IVs and the response variable.

Using such methods, one can compute an infinite number of different enumerations, or 

window/lag combinations, for each IV. One area of our research focused on criteria for selecting 

the enumeration that would be the best for empirical modeling. Note that if you begin the 

analysis with 10 IVs and, for each IV you investigate 10 enumerations, after selecting one 

enumeration for each IV, you would still have 10 IVs—but each would be temporally 

synchronized to the response variable. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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9.2 TEMPORAL SYNCHRONIZATION AT SOUTH SHORE BEACH

9.2.1 Methods

One site where we applied TSA methods was South Shore Beach (Figure 4.2A). The period we 

examined was the swimming season of 2009. Site characteristics, laboratory methods, and our 

data collection efforts are detailed in Section 4.2.1. After data preparation, 44 FIB observations 

and 13 IVs remained: water temperature, conductivity, water depth, pH, turbidity, chloride, NH4, 

NO3, dry bulb air temperature, wet bulb air temperature, relative humidity, wind speed and wind 

direction. The last two variables were combined into two wind components: parallel to the shore 

(u component) and perpendicular to the shore (v component).

Cross-Validation. To begin the analysis, we randomly split the raw data into two parts: 75 

percent of the 44 observations (33) were used as training data, and the methods described in the 

following sections were applied. The remaining 25 percent of the observations (11) were set 

aside as testing data. The randomization was done 500 times to create a population of 500 paired 

training/testing data sets that subsequently could be analyzed.

Temporal Synchronization. Each FIB measurement has a time stamp in the data set. That is a real 

number to represent the day and time each observation was collected. For instance, the time 

stamp of an observation made on July 13, 2008, at 9:00 a.m. would have a time stamp of 

39642.375. The integer 39642 is the number of days since day 1 (January 1, 1900, in our 

convention, but it could be any day for calculation purposes.) The decimal 0.375 represents the 

time of day (9/24 hours). The time stamp for every IV measurement was also known. However, 

the IVs were measured much more frequently than the response variable, typically at intervals of 

every 5, 15, or 30 minutes. For our TSA, we wrote code (using the R statistical package) that 

would generate an array of data columns for every IV variable. Within each column, the IV 

would be averaged over a specific temporal window and lag, with respect to the time stamp of 

the response variable. We used four windows (0 days, 0.5 days, 1.5 days and 3 days) and four 

lags (0 days, 1 day, 1.5 days, and 3 days). Note that the 0-day window and 0-day lag correspond 

to traditional FIB regression modeling. We called each window-lag combination an aspect, 

generating 16 aspects (4 windows x 4 lags) of each IV.

Next, we choose a single aspect of the possible 16 for each IV to model the response variable. 

We considered two criteria to determine the aspect selection: a Pearson correlation coefficient 

between the response variable and each aspect, with the highest coefficient indicative of the best 

linear relationship; and the PRESS statistic calculated from a univariate regression of the 

response on each potential IV aspect. The Pearson coefficient emphasizes the best fit of a model 

to the data, while the PRESS statistic emphasizes prediction of observations not seen by the 

model. Lower PRESS values indicate greater predictive accuracy.

Model Selection. At this point, each of the 500 training data sets had been changed into three 

data sets: one where none of the IVs had been synchronized (the UNS data set); one 

synchronized data set that had IV aspects chosen by a Pearson coefficient (the PCC data set); and 

one synchronized data set where IV aspects were chosen using the PRESS statistic (the PRS data 

set). We then used MLR methods to develop predictive models of FIB densities using the three 

data sets. In developing our MLR models, we used two selection procedures: 

1. For the UNS and PCC data sets, we used the AIC as a variable selection criterion. 
Predictive Modeling at Beaches—Volume II November 22, 2010

79 

2. For the UNS, PCC, and PRS data sets, we used the PRESS statistic to perform model 

selection.

For each analysis, we employed a backwards-stepwise variable selection algorithm.

Measuring Model Performance. To measure how well a chosen model fit its corresponding 

training data, we calculated the mean squared error of fitting (MEF) using the 33 training 

observations (which had been natural-log transformed). However, to measure predictive model 

performance, a model was selected using the 33 observations in the training data set, and then an 

MEP was calculated using the 11 observations in the testing data set (again, natural-log

transformed).

To summarize, the following four-step process was repeated 500 times:

1. 75–25 percent randomized splitting of the original raw data into training and testing subgroups 

2. IV aspect selection (both Pearson coefficient and PRESS) using the training data.

3. Model selection (PRESS or AIC) using the training data. 

4. Model performance metrics calculated (MEF for training data, MEP for testing data).

Afterwards, we made the following comparisons: 

A. MEF of UNS versus PCC when AIC was used for model selection

B. MEP of UNS versus PRS when PRESS was used for model selection 

C. MEP of UNS versus PCC when PRESS was used for model selection 

D. MEP of PCC versus PRS when PRESS was used for model selection 

The comparisons allowed us to measure the effectiveness of TSA for improving MLR fitting and 

predictive capabilities of the best-fit models.

9.2.2 Results

Comparison A. Across the 500 data sets (Figure 9.1, Table 9.1), the mean of the MEF for models 

developed using temporally synchronized data (IV aspects chosen using correlation coefficients) 

was 35 percent smaller than the mean of the MEF using unsynchronized data (16.9 versus 26.2, 

p < 0.001). When the statistical objective is fitting a set of training data, rather than prediction of 

new observations, selecting IV aspects using the maximum correlation coefficient should be 

ideal.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure 9.1. A comparison between the MEF values of model developed using temporally 

synchronized data (IV aspects selected using correlation coefficients) and unsynchronized data. 

Five-hundred randomly generated data sets were examined. Each data set had 33 observations. 

Note that we modeled the natural logarithm of Enterococcus CFU measurements in these models.

Table 9.1. Statistics for the 500 MEF and MEP values obtained from models developed using 

temporally synchronized data (both PRESS-selected IV aspects, PRS, and correlation coefficientselected IV aspects, PCC) and unsynchronized data (UNS). The natural logarithm of Enterococcus

CFU measurements were modeled in this study.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 51 101 151 201 251 301 351 401 451

Random Dataset Number

Mean Squared Error (natural logarithm units) 

Synchronized using Correlation

Unsynchronized
Predictive Modeling at Beaches—Volume II November 22, 2010

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Comparison B. Figure 9.2 shows the 500 MEP values for models, using the PRS data (red line) 

and the UNS data (black line). The mean MEP for the PRS data was 1.85, and for the UNS data 

it was 3.67—nearly twice as large (p < 0.001). For many data sets, the UNS data produced a 

MEP similar to that of the PRS data, but there were also many spikes; the MEP for the UNS data 

was much higher than that of the PRS data. We can conclude that temporal synchronization 

helped to improve predictions of new observations when fitting a MLR model.

Figure 9.2. A comparison of the 500 MEP values for the PRS data and the UNS data.

0

10

20

30

40

50

60

1 51 101 151 201 251 301 351 401 451

Random Dataset Number

Mean Squared Error of Prediciton

(natural logarithm units)

Synchronized using PRESS

Unsynchronized
Predictive Modeling at Beaches—Volume II November 22, 2010

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Comparison C. The MEP values produced by models fit to the PCC data sets are also smaller, on 

average, than the mean MEP values for the UNS data sets (Figure 9.3). The mean MEP value for 

the PCC data sets was 2.71 versus 3.67 for the UNS data sets (p < 0.001). 

Figure 9.3. A comparison of the 500 MEP values for the PCC data and the UNS data.

0

10

20

30

40

50

60

1 51 101 151 201 251 301 351 401 451

Random Dataset Number

Mean Squared Error of Prediciton

(natural logarithm units)

Unsynchronized

Synchronized using Correlation
Predictive Modeling at Beaches—Volume II November 22, 2010

83 

Comparison D. Figure 9.4 shows that the MEP values for the PRS data sets were indeed smaller, 

on average, than the MEP values for the PCC data sets (mean of 1.85 versus 2.71, p < 0.001). 

Thus, choosing IV aspects with a method that emphasizes predictive modeling (PRESS) will 

result in better predictions than synchronizing data (choosing IV aspects) with a simple 

correlation coefficient that emphasizes data fitting.

Figure 9.4. The comparison between the 500 MEP values for the models developed using the two 

different temporal synchronized data, PRESS-selected IV aspects and correlation-coefficientselected IV aspects.

Methodological Comments. For simplicity and clarity in this South Shore TSA, we investigated a 

limited number of windows and lags, the longest of which was 72 hours. Expanding to a week or 

more, if the data allow, could produce additional predictive improvements. In addition, we 

computed a mean value of the IV over each window, but other statistics such as the median, 

standard deviation, maximum or minimum value of the IV might be a more potent correlate to 

the response variable.

The TSA can be likened to a type of transformation of each IV, but instead of using a 

logarithmic or square root transformation to linearize the relationship between the IV and the 

response, we temporally transform the IV to discover if windows and lags can improve its 

predictive power. The most useful windows and lags most certainly would be dependent on SS 

relationships of pathogen sources to each individual beach site. The best aspect of each IV might 

even vary annually or seasonally, depending on SS dynamics of pathogen fate and transport. 

0

2

4

6

8

10

12

14

16

1 51 101 151 201 251 301 351 401 451

Random Dataset Number

Mean Squared Error of Prediciton

(natural logarithm units)

Synchronized using PRESS

Synchronized using Correlation
Predictive Modeling at Beaches—Volume II November 22, 2010

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9.3 ADVANCED MODELING TECHNIQUES AT HOBIE BEACH, MIAMI

9.3.1 Introduction

Standard MLR techniques were not able to produce successful models at Hobie Beach, Miami 

(Figure 4.2B) for CFU data collected in the summer of 2008 (adjusted R2 of 20 percent). 

Conditions and historical data for the beach are described in Section 4.3.5. For data collected by 

Florida in 2005–2008, the adjusted R2

 of the best CFU regression model was only 7 percent (see 

Appendix C). We decided to apply more sophisticated techniques to the summer 2008 CFU data 

in hopes of improving the statistical models. The first method was a TSA of the IVs. The second 

technique can be best described as data sub-setting, or a form of hierarchical modeling. 

9.3.2 Temporal Synchronization Analysis

Because we performed TSA before making refinements in the approach, the TSA for Hobie 

Beach data was not as sophisticated as that for South Shore, Milwaukee. For Hobie, we 

examined 14 different windows ranging from one hour to 28 days, but we did not incorporate 

lags. We used the Pearson correlation coefficient for IV aspect selection and did not consider the 

PRESS statistic. After running a MLR analysis with the new IVs, we produced a five-parameter 

model (water depth, air temp, water temp, photosynthetically active radiation, dew point) that 

had an adjusted R2

 of 0.41, twice that of the original adjusted R2 of 0.2 obtained using 

unsynchronized IVs. Thus, even without using lags in the TSA, we saw a large increase in the fit 

achieved by the empirical model.

9.3.3 Data Sub-Setting

As stated, the best regression model fit to 2008 Hobie Beach CFU data (137 observations, no 

TSA used on the IVs), was not very convincing, with an adjusted R2

 of about 0.2 and residuals 

that failed a normality test. In hopes of improving the model, we examined the DFFIT values of 

each observation. The DFFIT value for an observation is a statistic that measures how influential 

a single observation is on a regression model. It is defined as the change in the predicted value 

of an observation (i.e., a comparison of the predicted value when the observation is removed 

from the dataset versus its predicted value when it remains in the dataset), divided by the 

standard deviation of the observation's predicted value when the data point has been excluded. 

DFFIT = (ŷi – ŷ-i) / s-i × hii

0.5

where ŷi is the predicted value of the ith observation, ŷ-i is the predicted value of the ith 

observation computed after removing the ith observation from the data, s-i is the standard error of 

ŷ-i, and hii is the leverage of the ith observation. Observations with large DFFIT values (negative 

or positive) have a large influence on the fitted regression coefficients and are often interpreted 

as outliers.

To improve the model fit, we could remove observations with the largest DFFIT value, one by 

one, re-fitting the model after each removal and then rechecking the remaining DFFIT values. As 

the process is repeated, the adjusted R2 rises and the residuals might become more normally 

distributed (Figure 9.5). However, the analyst must make a decision at some point to stop the 

process. Usually that is done using a general threshold on what exactly constitutes a DFFIT value 
Predictive Modeling at Beaches—Volume II November 22, 2010

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that is too large. The decision, however, might also be made on the basis of a leveling off of the 

adjusted R2—that occurred in our data set after about 65 observations had been removed. 

Alternatively, it could be done when the residuals appear to be normally distributed (when the p 

value for the residual normality test exceeds 0.05)—which for this data set also occurred after 

removing about 65 observations. 

Figure 9.5. Effects on the regression adjusted R2 and the significance of the residual normality 

test when successively removing observations based on the largest remaining DFFIT value in the 

data set. 

Looking at the data set after 65 points had been removed, 72 observations remain. The adjusted 

R2

 is about 0.81, a very impressive fit. However, some questions arise. We now have a 

drastically different data set compared to what we started with. A model using completely 

different IVs fit to the 72 points might be even better. Also, what should be done with the 65 

points that had been removed? It might be possible to achieve a good fit to those observations 

with another regression model, or perhaps no model can be found to fit them well. In our case, 

after removing 5 observations with very large DFFIT values, we had a good regression model for 

the remaining 60 observations (adjusted R2

 = 0.5, residuals normally distributed). Whatever the 

case, we need to answer the following question: when new data are collected and a prediction 

needs to be made, what should we do? Do we use the model for the 72 observations, or do we 

decide that new observation is more similar to the 65 removed observations? 
Predictive Modeling at Beaches—Volume II November 22, 2010

86 

To answer the question, we could use an advanced statistical technique like a discriminant 

analysis, which is a multivariate method whose objective is to find variables that play the most 

significant roles in discriminating between two or more groups of objects. For that analysis we 

would use the same IVs as used for the regression models but focus on finding a combination of 

IVs that can best distinguish if an observation belongs to Group 1 (the 72 observations) or Group 

2 (the 65 observations). For example, such a technique might tell us that one model fits 

observations taken on warm, sunny days and another model should be used for cooler, cloudy 

days. That information would then allow us to choose between the use of various models 

depending on environmental conditions, and we would have added confidence in their 

predictions. Such a technique is related to hierarchical modeling, where subsets of observations 

are analyzed with different models to achieve better results.

After performing a discriminant analysis on the Hobie Beach data, we found a discriminant 

function that used three IVs—water depth, air temperature, and UV radiation—and it was 65 

percent successful in categorizing our observations as belonging to Group 1 or Group 2 (64 

percent successful for Group 1 and 66 percent successful for Group 2). Thus, if any observation 

were chosen from the data set, we would have a decent chance of correctly classifying it as a 

Group 1 or Group 2 observation, on the basis of those three IVs. Without that information (if 

done completely randomly), we would have about a 53 percent chance of success for classifying 

Group 1 observations and a 47 percent chance for Group 2 observations. If a new data point were 

predicted to be in Group 1, we could then apply the Group 1 regression model to achieve a much 

higher adjusted R2

 than if we had attempted to model all 137 observations using a single 

regression function. The danger of the technique is that if we applied that regression model to a 

Group 2 observation, the prediction would be very poor. In general, we would like the 

discriminant function to have a high rate of classification success (85–90 percent) for us to have 

confidence in using the method. 

We should note that the example discussed in this section is not typical of the analysis we 

performed on the other data sets presented in this report. One usually finds only a handful of 

observations with large enough DFFIT values to be considered outliers, and thus possibly 

warrant exclusion from the data set. Indeed, with the Hobie Beach data, only a few observations 

(out of the original 137) actually had DFFIT values large enough to be considered for exclusion 

under normal circumstances. The problem was that after excluding the data points, we were still 

left with a poor regression model (adjusted R2 under 0.2, and non-normal residuals). At that 

point, we wanted to go beyond the typical and demonstrate an analysis that can produce much 

better regression models for a given data set. However, analysts must exercise caution when 

using the technique so as not to completely overlook sound statistical principles. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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10 Acknowledgements

We gratefully acknowledge the assistance of many institutions and individuals in obtaining the 

data, refining and evaluating the predictive models, and communicating the use of the software. 

We especially thank Candida West, U.S. EPA, ORD, National Exposure Research Laboratory 

for her support and many inputs to this research. Bruce Mintz of U.S. EPA, National Exposure 

Research Laboratory assisted in many ways with communicating the research to ORD 

management and the Office of Water. Jim Kitchens, Brenda Kitchens, Lourdes Prieto and 

Carlyn Haley (U.S. EPA, ORD, National Exposure Research Laboratory) all made substantive 

contributions to administrative aspects of the project. We appreciate receiving data from the 

NEEAR epidemiological research team for this project and particularly thank Tim Wade, 

Elizabeth Sams, Al Dufour, Richard Haugland, Kristen Brenner, and Larry Wymer for their 

assistance. Many useful review comments were received from John Wathen and Beth Leamond 

of the U.S. EPA Office of Water.

Analyses of the data at the U.S. EPA, ORD, National Exposure Research Laboratory Ecosystems 

Research Division, were conducted by O’Niell Tedrow, Jack Varner, Shayla Hunter, Eva Duvall, 

Ellen Price, Caitlin Sloan, Chris Fitzgerald, and Anjali Viswakumar. Shuyan Zhang, Jon Wong, 

Walter Frick, and Zhongfu Ge all contributed to the modeling studies. 

We had many fruitful interactions related to the U.S. EPA Advanced Monitoring Initiative 

(AMI). We thank the AMI program for its support of part of this research. Richard Zdanowitz 

from Region 5, Chicago was helpful in many different ways. He helped to coordinate workshops 

and a series of teleconferences with scientists from USGS, NOAA and EPA that provided many 

useful insights into modeling activities in the Great Lakes region. Also, thanks go to Holly 

Wirick of Region 5 for her assistance with developing liaisons with others who were conducting 

beach modeling studies in the Great Lakes region. We also thank Adam Mednick and Dreux 

Watermolen, State of Wisconsin, Dept. of Natural Resources for their outstanding efforts with 

communicating the use of the Virtual Beach software. 

At South Shore Beach, Milwaukee we were assisted by Lindsay Olson (Student Services 

Associate); Sandra McLellan, Sabrina Mueller-Spitz, Robert Paddock, Geoff Anderson, Jack 

Orchard, and Greg Barske of University of Wisconsin- Milwaukee Great Lakes WATER 

Institute; Daniel Feinstein of U.S.G.S.- Madison WI; Richard Henry and Alan Humphrey of U.S. 

EPA, Region 2; Don Conlee of Nortek USA; and ERG with sample collection and analysis and 

equipment maintenance. At Hobie Beach, Miami Diana Aranda, Chris Sinigalliano, and 

Maribeth Gidley of NOAA-Atlantic Oceanographic Marine Laboratory; Erich Bartels of Mote 

Marine Laboratory; Jed Campbell of U.S. EPA, National Health and Environmental Effects 

Laboratory, Gulf Ecology Division; Manuel Collazo, Lora Fleming, John Wang and Helena 

Solo-Gabriele of University of Miami); Samir Elmir of Miami-Dade County Health 

Department); and ERG helped collect and analyze samples and maintain the equipment. 

Likewise, at La Monserrate we were assisted by Maria Vega-Rodriguez(Student Services 

Associate), Milton Carlo of University of Puerto Rico-Mayaguez); Angel Meléndez of PREQB; 

Mildred Matos, Juan Pacheco, and Eddie Nieves of Puerto Rico Department of Natural 

Resources); Jose Font of U.S. EPA, Region 2; and Luquillo lifeguards. At Surfside Beach 

Henry Styron of University of North Carolina at Wilmington; Shannon Berry, Sean Torrens, and 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Ted Ambrose of South Carolina Department of Health and Environmental Control; Micki 

Fellner, Ed Booth, and beach personnel of the Town of Surfside Beach, SC; Carolyn Ross and 

Kellah Webster (Westat subcontractors) and Westat all provided assistance. At Boquerón, able 

assistance was provided by Milton Carlo and Ernesto Otero-Morales of University of Puerto 

Rico- Mayaguez; Angel Meléndez of PREQB; and Eddie Nieves, beach staff and life guards of 

Puerto Rico Department of Natural Resources; Gary Toranzos of University of Puerto Rico; 

Raisha Cornier (Westat sub-contractors), and Westat personnel. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Environmental Management, Indianapolis, IN.

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evaluation of posting errors at Huntington Beach, California. Environmental Science & 

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McQuarrie, A., and C.L. Tsai. 1998. Regression and Time Series Model Selection. World 

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a peninsular beach complex of Lake Michigan. Journal of Environmental Quality

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concentrations for beaches along a 35 km stretch of Southern Lake Michigan. 

Environmental Science & Technology 42:4454-4460. 

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creeks on Escherichia coli concentrations of nearby beaches: Exploration of 

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modeling of bacterial (Escherichia coli) outflows from watersheds that discharge into 

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recreational water quality using multiple microbial indicators in an urban tropical 

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Predictive Modeling at Beaches—Volume II November 22, 2010

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Appendix A. Additional Site Information
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A.1 FRESHWATER BEACHES (GREAT LAKES) 

A.1.1 South Shore Beach, Milwaukee, Wisconsin

South Shore Park in Milwaukee, Wisconsin, is within the residential area of Bayview on the west 

coast of Lake Michigan (Figure 4.2A). The park includes South Shore Beach, a public beach area 

(~ 0.01 square kilometer [km2

]) with 150 meters (m) of sandy shoreline. Its shore is low sloping, 

and the benthic zone is muddy and sandy. The beach is adjacent to the South Shore Yacht Club 

and a ~ 0.02 km2 paved parking area, which drains into the lake. A 20-m-long rock embankment 

juts into the lake, separating the sandy beach area from a 185-m-long cobble/pebble beach area 

with a high sloping shore (South Shore Rocky Beach). Large flocks of roosting waterfowl and 

shore birds consistently occupy the beach. Ring-billed gulls are the predominant species, but 

Canada geese, Mallard ducks, and pigeons are also present (McLellan and Salmore 2003; Scopel 

et al. 2006). The entire beach and marina area is partially enclosed by a breakwall ~ 300 m 

offshore, which limits wave action, water circulation, and exchange with the outer harbor (Figure 

4-2). Water depths within the breakwall are < 5 m, with depths < 2 m within 50 m of shore. The 

beach is ~ 4 km south of Milwaukee Harbor, where the Milwaukee Metropolitan Sewerage 

District Jones Island Water Reclamation Facility is. The Milwaukee, Menomonee, and 

Kinnickinnic rivers also discharge to Lake Michigan inside the Milwaukee Harbor breakwall.

Historically, South Shore has poor water quality, with 34 percent of samples collected from 2003 

to 2009 exceeding water quality criteria standards (Table A.1). Potential sources of fecal 

contamination include combined sewer overflows (CSOs); urban/suburban and agricultural 

runoff from the Milwaukee River Basin; runoff from impervious surfaces including parking lots 

and the beach face; and gulls (Scopel et al. 2006). However, high Escherichia coli counts are not 

always attributable to rainfall and CSO events (McLellan et al. 2001; Scopel et al. 2006). A 

detailed spatial assessment found that poor beach water quality was mostly a local phenomenon, 

with contamination originating at the shoreline (McLellan and Salmore 2003). While CSO and 

sanitary sewer overflow events resulted in increased E. coli levels in the Milwaukee Estuary and 

Harbor (compared to rainfall without overflow), that source of sewage contamination did not 

influence the beach site (McLellan et al. 2007). The Russell Avenue outfall, about 0.5 km north 

of the beach inside the northwest corner of the marina breakwall is a closer source. The influence 

of discharge from the outfall is variable, with wind-driven and along-shore currents being 

important to water exchange in the beach area (Scopel et al. 2006). Antibiotic resistance profiles 

further confirmed that the major sources for E. coli found at the beach were shoreline runoff or 

stormwater, not CSO or sanitary sources (McLellan 2004). In addition, human-specific 

Bacteroides were not found at the beach or the Russell Avenue outfall (McLellan and Jensen 

2005) (Figure A.1). 
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Figure A.1. Location of 2008 PREMIER study at South Shore Beach in Milwaukee, Wisconsin. 

Yellow pins indicate locations of beach and sampling transects and green pins mark possible 

sources of fecal contamination (i.e., WWTP on the Milwaukee River and Russell Avenue outfall). 

Details regarding field equipment (red pins) are given in Section 4.4.3. The beach is on the west 

shore of Lake Michigan (Figure 4.2A).

During the 14-week swimming season (Memorial Day through Labor Day), the Milwaukee 

County Health Department routinely monitors the beach for E. coli. Water quality (water 

temperature, specific conductance, pH, dissolved oxygen, chlorophyll, and turbidity) and 

meteorological conditions (air temperature, rainfall, wind speed, and wind direction) are 

continuously recorded by a sonde and weather station maintained by the University of 

Wisconsin-Milwaukee Great Lakes WATER Institute. Data are transmitted every hour (weather) 

or half hour (water quality) to a website via Ethernet communication. The sonde is deployed just 

northwest of the beach, off the east end of the South Shore Yacht Club dock, and the weather 

station is installed on a post at the beach, near the boat launch. Real-time and historical bacterial 

(since 2003), meteorological, and in-lake sonde data are publicly available through the 

Wisconsin Beach Health website (http://www.wibeaches.us).
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Table A.1. Historical water quality monitoring details and criteria exceedances for freshwater beaches based on publicly available 

data from local monitoring agencies. Great Lakes beaches are sampled during the summer beach season, the start and end of 

which typically corresponds to the Memorial Day (last Monday in May) and Labor Day (first Monday in September) holiday 

weekends, respectively. The number of exceedances is expressed per total number of samples, with the corresponding percentage

given in parentheses.

Data sources: South Shore Beach (http://www.wibeaches.us), Ogden Dunes Beach (https://extranet.idem.in.gov/beachguard), Washington Park Beach 

(https://extranet.idem.in.gov/beachguard), Silver Beach (http://www.deq.state.mi.us/beach), Huntington Beach, Ohio (2000–2005 data are from Francy et al. (2006) (Francy and 

Darner 2006); 2006–2009 data are from http://www.ohionowcast.info/nowcast_huntington.asp).
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Previous modeling efforts at South Shore Beach include hydrodynamic and water quality models 

developed to describe the fate and transport of fecal coliform in Milwaukee Harbor and 

nearshore Lake Michigan. Calibration and validation of the models was accomplished using 

Milwaukee Metropolitan Sewerage District and Great Lakes WATER Institute field data. 

Modeling results indicated that the fecal coliform load from rivers and CSO/sanitary sewer 

overflow events had only slightly more than marginal impact on the beach site, with local 

sources (e.g., stormwater runoff and birds) being more important (MMSD 2005). South Shore 

Beach was also one of the 55 beaches included in a regional forecast model for southern Lake 

Michigan, from Milwaukee, Wisconsin, to Michigan City, Indiana (Whitman and Nevers 2005). 

Milwaukee is considering adopting a predictive model. In addition to issuing advisories on the 

basis of the monitoring of E. coli levels (where < 235 CFU/100 mL is acceptable, 235–1,000 

CFU/100 mL results in a water quality advisory, and > 1,000 CFU/100 mL results in a closure 

advisory), a rainfall threshold of 2.5 cm in 24 hours is also used to predict poor water quality and 

issue advisories at South Shore. 

A.1.2 West Beach, Porter, Indiana

West Beach is on the south shore of Lake Michigan (Figure 4.2A), ~ 40 km southeast of Chicago 

Harbor; it is part of the Indiana Dunes National Lakeshore Park in Porter, Indiana. The public 

beach has ~ 2 km of sandy shoreline and contributes to the total 10-km length of contiguous 

swimming beaches along this section of Lake Michigan. The shore has a gradual slope, and 

water depths are < 2.5 m within 250 m of shore. As an open, unprotected, lakefront beach, West 

Beach is subject to moderate wave exposure. The beach area is west of the Portage-Burns 

Waterway (Burns Ditch), a man-made channel that serves as the outfall point for the Little 

Calumet River to Lake Michigan. Discharge from Burns Ditch is directed west by a breakwall 

and then dispersed by lake currents and waves (Figure A.2B).

E. coli levels in Burns Ditch are typically higher than those in the lake and adjacent beach sites. 

Levels greater than 10,000 CFU/100 mL have been observed at the Burns Ditch outlet following 

storm events, and E. coli levels at the beach were found to be associated with rainfall (Olyphant 

et al. 2003). Outfall from Burns Ditch has the potential to affect water quality in the surf zone of 

the adjacent swimming beaches, particularly when prevailing north winds force the plume 

onshore (Nevers and Whitman 2005). Land use in the surrounding Little Calumet-Galien Basin 

is primarily agricultural with some forested, urban, and industrial areas. Seven wastewater 

treatment plants (WWTPs) are within the river basin and Lake Michigan watershed that provide 

disinfection with chlorine and ultraviolet (UV) radiation during the summer (Wade et al. 2008). 

The Portage, Indiana, WWTP, discharges UV-treated wastewater to the west branch of the Little 

Calumet River, ~ 5 km upstream of Lake Michigan. The Little Calumet River also receives 

inputs from a variety of nonpoint sources, including urban runoff, runoff from farms and 

livestock operations, failing septic systems, and wildlife (IDEM 2004; NIRPC 2005). Coliphage 

was detected in the ditch and at the beaches following heavy rainfall that resulted in CSO, 

providing evidence of sewage sources (Nevers and Whitman 2005). Water quality is good with 

water quality criteria exceeded in 4 percent of the samples collected from 2004 to 2009 at Ogden 

Dunes, and with no exceedances at West Beach in 2008 and 2009 (Table A.1).
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During the Memorial Day to Labor Day summer beach season, the beaches are monitored 

routinely for E. coli, typically by the Indiana Dunes National Lakeshore. Real-time and historical 

bacterial data (since 2008) are publicly available through the Indiana Department of 

Environmental Management’s BeachGuard website (https://extranet.idem.in.gov/beachguard). 

Real-time and historical discharge, gage height, and stream velocity data are available from the 

U.S. Geological Survey (USGS) Burns Ditch gauging station at Portage, Indiana (04095090), 

which is ~ 1.2 km upstream of Lake Michigan (http://waterdata.usgs.gov/nwis/uv?04095090).

The West Beach and Burns Ditch sites have been the subject of several predictive modeling 

studies. Multiple regression analysis found that a combination of water quality variables could 

account for the observed variability in E. coli at Burns Ditch outlet during storm events 

(Olyphant et al. 2003). Further efforts led to developing regression models that predict beach E. 

coli levels from wave and precipitation data, as well as water quality parameters. Because of the 

role of wind direction on the transport of Burns Ditch discharge to the beaches (Nevers and 

Whitman 2005), model performance was improved by separately modeling days with onshore 

and offshore winds. Regional forecast models also were developed for southern Lake Michigan, 

which include West Beach (Whitman and Nevers 2005; Nevers and Whitman 2008). In addition 

to E. coli, more recent predictive models for beaches impacted by Burns Ditch included 

culturable and quantitative polymerase chain reaction (qPCR)-based enterococci as dependent 

variables. Differences in the models developed for each indicator (i.e., IVs identified for 

culturable compared to qPCR-based enterococci) provide evidence of the different processes that 

determine their fate (Byappanahalli et al. 2010; Telech et al. 2009). Beach monitoring practices 

rely on culturable E. coli where levels > 235 CFU/100 mL result in a contamination advisory or 

closure, as well as on a rainfall threshold. In addition, the Project S.A.F.E. (Swimming Advisory 

Forecast Estimate) predictive model was implemented as a USGS pilot study (Whitman 2008) 

and is used in conjunction with the NOAA/Great Lakes Environmental Research Laboratory 

Indiana Dunes Nowcast hydrodynamic model (Schwab et al. 2010) to provide real time E. coli

estimates at West Beach.

A.1.3 Washington Park Beach, Michigan City, Indiana

Washington Park Beach is in Michigan City, Indiana, on the south shore of Lake Michigan 

(Figure 4.2A). The public beach area is ~ 1.1 km long and is immediately east of a breakwall that 

directs discharge from Trail Creek to the west (Figure A.2C). 

Trail Creek is a source of E. coli to the lake with the potential to affect water quality at nearby 

beaches (Nevers et al. 2007). The Trail Creek watershed drains urban, agricultural, and 

residential areas, with a number of human and animal nonpoint sources including agricultural 

field drainage and runoff, cattle/steer grazing, failing septic systems, illicit connections, and 

urban stormwater runoff (Triad Engineering Incorporated 2003). In addition, the Michigan City 

Sanitary District WWTP (~ 3 km upstream of Lake Michigan), which applies chlorine 

disinfection during the summer months, is a major discharger to the creek (Wade et al. 2008), 

although plant improvements have practically eliminated CSO events (Nevers et al. 2007). Water 

quality at Washington Park Beach is poor, with the recreational water quality criteria for E. coli

exceeded in 23 percent of the samples collected from 2005 to 2009 (Table A.1). In addition, 

pathogens (adenoviruses and enteroviruses) and a marker for human sewage were detected in 

samples collected from the swimming area during summer 2004 (Wong et al. 2009). 
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The Michigan City Parks Department or LaPorte County Health Department monitor the beach 

regularly for E. coli during the 14-week beach season (Memorial Day through Labor Day). Realtime and historical bacterial data (since 2005) are publicly available through the Indiana 

Department of Environmental Management’s BeachGuard website 

(https://extranet.idem.in.gov/beachguard). In addition, daily water quality results that lead to 

advisories or closures are posted on the Michigan City Parks & Recreation Current Beach 

Conditions website (http://www.emichigancity.com/cityhall/departments/parks/beach.htm). 

Real-time and historical discharge, gage height, and stream velocity data are available from the 

USGS Trail Creek gauging station at Michigan City Harbor, Indiana (04095380), which is 

< 1 km upstream of Lake Michigan (http://waterdata.usgs.gov/nwis/uv?04095380).

Predictive modeling of E. coli has not been reported at Washington Park Beach, but work was 

done at another Trail Creek-influenced beach, Mount Baldy Beach, ~ 2.5 km west of the mouth 

of Trail Creek (Nevers et al. 2007). The Mount Baldy site was also incorporated in a southern 

Lake Michigan regional forecast model (Whitman and Nevers 2005; Nevers and Whitman 2008). 

The observed variation in E. coli levels at Mount Baldy was further explained, based on loadings 

from Trail Creek and nearby Kintzele Ditch, using a process-based hydrodynamic model (Liu et 

al. 2006; Thupaki et al. 2009). Given the proximity of Washington Park to Mount Baldy, a 

similar type of model will likely apply to both beaches. In work specific to the Washington Park 

site, independent and predictive models were used to investigate the relationship between 

enterococci (culturable and qPCR-based) and environmental conditions (Telech et al. 2009). 

Water quality monitoring at the beach is based on culturable E. coli where levels > 235 CFU/100 

mL result in a contamination advisory or closure when counts ≥ 1,000 CFU/100 mL.

A.1.4 Silver Beach, St. Joseph, Michigan

Silver Beach is in St. Joseph, Michigan, on the southern end of the eastern shore of Lake 

Michigan, ~ 55 km northeast of Washington Park Beach (Figure 4.2A). The ~ 0.6-km-long sandy 

beach area is just south of where the St. Joseph River flows into Lake Michigan. At its mouth, 

the river is lined by two parallel navigational piers that extend into the lake, guiding riverine 

discharge ~ 0.5 km out, roughly perpendicular to the shoreline (Figure A.2D).

Possible sources of fecal contamination to the St. Joseph River watershed, which encompasses 

both urban and agricultural areas, include seven WWTPs (that use chlorine disinfection), four of 

which are on the river (Wade et al. 2008), CSOs, stormwater discharges, agricultural inputs, and 

illicit discharges (MDEQ 2003). The St. Joseph-Benton Harbor WWTP is on the river, ~ 2.7 km 

upstream of Lake Michigan. Water quality at Silver Beach is good, with only 1 percent of 

samples collected from 2001 to 2009 exceeding local water quality criteria standards for E. coli

(Table A.1). As with Washington Park Beach, pathogens (adenoviruses, enteroviruses, and 

rotaviruses) and a human sewage marker were detected in samples collected from the Silver 

Beach swimming area during summer 2004 (Wong et al. 2009). 
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(A) (B)

(C) (D)

Figure A.2. Locations of (A) Lake Michigan NEEAR studies including (B) 2003 study at West Beach 

in Porter, Indiana, (C) 2004 study at Washington Park Beach in Michigan City, and (D) 2004 study 

at Silver Beach in St. Joseph, Michigan. Yellow pins indicate locations of beaches and green pins 

mark possible fecal contamination sources (i.e., WWTPs). Red pins show nearby USGS, NOAA, 

and airport weather stations. The beaches are on southern Lake Michigan (Figure 4.2A).

The Berrien County Environmental Health Department monitors the public beach weekly for 

E. coli during the summer season (from Memorial Day to Labor Day). 

Real-time and historical bacterial data (since 2001) are publicly available through the Michigan 

Department of Environmental Quality BeachGuard website (http://www.deq.state.mi.us/beach).

Real-time and historical discharge and gage height data are available from the USGS St. Joseph 

River gauging station at Elkhart, Indiana (04101000), which is ~ 100 km upstream of Lake 

Michigan (http://waterdata.usgs.gov/nwis/uv?04101000).
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Regression modeling was employed at Silver Beach to investigate relationships between 

culturable and qPCR-based enterococci and various environmental conditions in an effort to 

identify useful predictors of water quality (Telech et al. 2009). Routine water quality monitoring 

at the beach is based on a culturable E. coli criteria of 300 CFU/100 mL and the use of a rainfall 

plus 48-hour health advisory. 

A.1.5 Huntington Beach, Bay Village, Ohio

Huntington Beach is part of Huntington Reservation of Cleveland Metroparks, which is in the 

City of Bay Village, Ohio (a western suburb of Cleveland), on the southern shore of western 

Lake Erie (Figure 4.2A). The swimming area is just west of Porter Creek, and the beach is ~ 8 

km west of the Rocky River mouth. The ~ 0.5-km-long sandy beach area is broken into segments 

by a series of rock jetties (< 100 m long) that run perpendicular to the shoreline (Figure A.3). 

The breakwalls limit water circulation in the swimming area.

Figure A.3. Location of 2003 NEEAR study at Huntington Beach in Bay Village, Ohio. Yellow pin 

indicates location of beach and green pins mark possible sources of fecal contamination 

(i.e., WWTPs). Red pin shows nearby airport weather station. The beach is on Lake Erie 

(Figure 4.2A).

Huntington Beach is in the Black-Rocky watershed, within which are 10 sewage discharge 

locations that could affect the beach. Three of those flow directly into Lake Erie: Avon Lake 

WWTP, ~ 11 km west of the beach; Rocky River WWTP, ~ 6 km east of the beach; and 

Westerly WWTP, ~ 18 km east of the beach. The others are discharged to the Rocky River or its 

tributaries, the closest being Lakewood WWTP (< 3 km from the mouth of the Rocky River). 

The majority of the treatment plants use UV or chlorine disinfection during the summer (Wade et 

al. 2008; Wade et al. 2006). Porter Creek, on the east end of the beach, was identified as a likely 

contributor to high E. coli counts at beach (Huang and Sigler 2006). In addition, two outfalls 

discharge storm runoff from the parking lot to the beach (Francy et al. 2003). Water quality at 

Huntington Beach is poor, with 16 percent of samples collected from 2000 to 2009 exceeding 

water quality criteria standards for E. coli (Table A.1).
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During the 14-week summer beach season, the Cuyahoga County Board of Health and Cuyahoga 

County Sanitary Engineers Laboratory, monitor Huntington Beach water quality (i.e., E. coli). In 

addition, a number of ancillary environmental parameters (i.e., water temperature, turbidity, and 

wave height) are also measured at the time of sample collection. The data (real-time and 

historical since 2006) are publicly available through the Ohio Nowcast website, along with the 

associated water quality predictions and advisories 

(http://www.ohionowcast.info/nowcast_huntington.asp). Real-time and historical discharge and 

gage height data are available from the USGS Rocky River gaging station near Berea, Ohio 

(04201500), which is ~ 20 km upstream of Lake Erie 

(http://waterdata.usgs.gov/nwis/uv?04201500).

Because of ongoing efforts of the USGS Water Science Center and its partners in daily routine 

sampling and data collection, an extensive, multiyear data set is available for Huntington Beach. 

The focus of the work was to develop a multiple linear regression (MLR) model that continues to 

be tested and refined over time by incorporating additional years of data. 

Water quality predictions resulting from the model have been available to the public since 2006 

as a real-time, Internet-based nowcasting system (Francy et al. 2003; Francy et al. 2006b; Francy 

and Darner 2007). The USGS data set (for 2000 to 2004) was used to examine statistical issues 

related to MLR modeling (Ge and Frick 2007). In addition, publicly available data from 2006 

demonstrate the efficacy of VB 1.0 in developing statistical models for predicting E. coli at 

Huntington Beach, while exploring the usefulness of dynamic models and time-frequency 

analysis (Frick et al. 2008; Ge and Frick 2009). Additional pilot studies focusing on developing 

VB 1.0, using Huntington Beach as an example study site, are discussed in more detail in Section 

2.1. Relationships between culturable and qPCR-based enterococci and various environmental 

parameters were investigated at Huntington Beach, using regression modeling to identify 

potentially useful water quality predictors (Telech et al. 2009). The Ohio Nowcast predictive 

model is used to supplement E. coli data (235 CFU/100 mL criteria) when making decisions 

about swimming advisories. 

A.2 MARINE BEACHES

A.2.1 Goddard Beach, West Warwick, Rhode Island

Goddard Beach is in Goddard State Memorial Park in West Warwick, Rhode Island (Figure 

4.2B). The beach stretches ~ 1.2 km along the southern shoreline of Greenwich Bay, just east of 

the mouth of Greenwich Cove (Figure A.4). Greenwich Bay is a small (13 km2) estuary on the 

western side of Narragansett Bay, which is ~ 6.5 km southwest of the mouth of the Providence 

River. The Maskerchugg River discharges to the head of Greenwich Cove, while a number of 

smaller brooks and creeks flow into Greenwich Bay, either directly or through one of the bay’s 

four other coves. 
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Figure A.4. Location of 2007 NEEAR study at Goddard Beach in West Warwick, Rhode Island. 

Yellow pin indicates location of beach, and green pin marks possible source of fecal 

contamination (i.e., WWTP). Red pin shows nearby airport weather station. The beach is on the 

western side of Narragansett Bay (Figure 4.2B).

Greenwich Cove and the south inner Greenwich Bay (just north of the beach) are designated for 

shellfish harvesting and recreational use. As a result, the surrounding waters are held to stricter 

water quality criteria than the swimming standard at the beach. The Greenwich Bay watershed 

includes parts of Warwick, East Greenwich, and West Warwick in central Rhode Island where 

land use is predominantly urban and residential. Potential sources of fecal contamination include 

tributary streams that discharge to the cove and bay, such as the Maskerchugg River, and direct 

stormwater discharges. Those sources are along the west coast of the cove and include the East 

Greenwich Wastewater Treatment Facility, which discharges treated effluent to the middle of the 

channel about halfway down the cove, < 2 km from the beach. However, dye studies showed 

sufficient dilution of fecal coliform that suggest that Greenwich Cove and Bay are not 

significantly affected by the effluent. Faulty septic systems, waterfowl that gather at the beach, 

wildlife, and domestic pets are other potential sources of contamination at Goddard Beach. In 

addition to the swimming beach, the state-owned Goddard Park, which makes up half of the 1.6 

km2

 Potowomut subwatershed, includes golf courses and forested land; the rest of the 

subwatershed is residential. No sewers and few freshwater sources drain the area to Greenwich 

Bay. In the park, culverts direct stormwater from the parking lot onto the beach (RIDEM 2005). 

During the 14-week summer season (Memorial Day through Labor Day), the Rhode Island 

Department of Health routinely monitors Goddard Beach for enterococci. Real-time and 

historical data (since 2002) are publicly available through the Rhode Island Department of 

Health Beach Monitoring Program website 

(http://www.ribeaches.org/beach.cfm?beachID=RI810609). Water quality at Goddard Beach is 

good, with 9 percent of samples collected from 2002 to 2009 exceeding water quality criteria 

standards for enterococci (Table A.2). To our knowledge, formal predictive models have not 

been previously employed at Goddard Beach. Beach management decisions are based on 

enterococci monitoring (using the 104 CFU/100 mL criteria), and consideration of water quality 

history and other environmental conditions such as rain (RIDEM 2005). 
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Table A.2. Historical water quality monitoring details and criteria exceedances for temperate and subtropical marine beaches. 

Number of exceedances is expressed per total number of samples, with the corresponding percentage given in parentheses.

Data sources: Goddard Beach (http://www.ribeaches.org/beach.cfm?beachID=RI810609), Surfside Beach (station 31A, data provided by SCHEC), Edgewater Beach (station 

11A, http://www.coms.usm.edu/msbeach/harbmon.cgi), Fairhope Beach (http://www.adem.state.al.us/programs/coastal/beachMonitoring.cnt), Hobie Beach (1999–2000 is taken 

from Solo-Gabriele et al. (2002); 2001–2009 data are from http://esetappsdoh.doh.state.fl.us/irm00beachwater).
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A.2.2 Surfside Beach, Surfside Beach, South Carolina

Surfside Beach is in the town of Surfside Beach, South Carolina, just south of Myrtle Beach in 

Horry County (Figure 4.2B). The beach is 3.4-km long and is only a small fraction of the South 

Carolina coastline that makes up more than 100 km of uninterrupted, open beachfront known as 

the Grand Strand. The Grand Strand is the northernmost part of the South Carolina Coastal Plain. 

Several lakes were created in Surfside Beach to serve as retention ponds during storm events. 

The associated watersheds were designed and constructed for stormwater management purposes. 

The Myrtle Basin designed in 2005–2006, with construction starting in 2007, was followed by 

lake dredging. Two small lakes (each with an area of ~ 3000 m2) are between North Myrtle 

Drive, North Dogwood Drive, 2nd Avenue North, and 5th Avenue North. They are connected by 

a 120-m-long channel, with another 200-m-long channel running between them and the beach. 

The swash at 5th Avenue North receives runoff from this area, which is then discharged directly 

to the beach (Figure A.5). A sign is permanently posted at the swash, stating that swimming is 

not recommended within 30.5 m because stormwater runoff can result in elevated levels of 

bacteria. The Public Works Department digs out the swash outlets on the beach as needed (as 

often as three times per week) to ensure proper water flow.

Figure A.5. Location of 2009 NEEAR/ PREMIER study at Surfside Beach in Surfside Beach, South 

Carolina. Yellow pins indicate locations of beach and sampling transects and green pins mark 

possible sources of fecal contamination (i.e., swash channel at 5th Avenue North and retention 

pond). Details regarding field equipment (red pins) are given in Section 4.4.3. The beach is on the 

Grand Strand on the southeastern coast of the United States (Figure 4.2B).

The Grand Strand Water and Sewer Authority Schwartz WWTP is ~ 8 km northwest of the 

beach. Surfside Beach is not affected by effluent from the WWTP because it is discharged to the 

Intracoastal Waterway (~ 3.4 km northwest). The outlet to the Atlantic Ocean is 50 km from the 

beach. Several campgrounds along the coast north of the beach are within 4 km of Surfside 

Beach. In addition to the swash at 5th Avenue North, which is at the section of the beach 

considered here, additional swashes are up and down the coast. Those closest to the beach area 

include the 11th Avenue North Dogwood Swash (0.6 km north), the Surfside Drive outfall (0.5 

km south by the pier), and the 3rd Avenue South Swash (0.9 km south of the 5th Avenue North 

Swash). Given the lack of known point sources, the most likely source of fecal contamination to 
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Surfside Beach is runoff from the surrounding urban areas. Wildlife can also contribute to 

observed fecal indicator levels in the swash as birds (i.e., geese, ducks, gulls) frequent the lake 

and surrounding areas. 

The South Carolina Department of Health and Environmental Control (SCDHEC) monitors 

Surfside Beach for enterococci regularly, from May 15 to October (during the 20-week summer 

season). Data from the current year are publicly available through the SCDHEC Beach 

Monitoring Data website (http://www.scdhec.gov/environment/water/beachmondata.aspx). In 

addition, a new GIS-based Integrated Monitoring and Assessment Program web application is 

being developed to provide water quality data and beach status 

(http://gisweb00.dhec.sc.gov/ImapPublic/beach.html). Water quality at the 5th Avenue North 

Swash of Surfside Beach is poor, with 29 percent of samples collected from 2005 to 2007 

exceeding water quality criteria standards for enterococci (Table A.2). However, water quality 

has improved over time (from 70 percent in 2005 to 13 percent in 2007) because of 

improvements made to the stormwater management watershed. Beach monitoring practices at 

Surfside Beach rely on culturable enterococci, where levels > 500 CFU/100 mL or repeated 

measurements > 104 CFU/100 mL lead to advisories. In addition, preemptive rainfall advisories 

were issued on the basis of a rainfall threshold. More recently, a rain model for advisory 

predictions has been in development. 

A.2.3 Edgewater Beach, Biloxi, Mississippi

Edgewater Beach is in Biloxi, Mississippi, on the Mississippi Sound along the Gulf of Mexico 

(Figure 4.2B). The Mississippi Sound is separated from the Gulf by a chain of barrier islands, the 

closest of which is Ship Island, ~ 20 km south of the beach. This lagoon is < 5 m deep in most 

areas and runs 124 km along the southern coasts of Mississippi and Alabama. Beaches in the 

area generally are subject to low energy wave conditions. The beach shore is gently sloped (i.e., 

5 to 10 degrees) and consists of well- to very-well-sorted medium sand. Major rain events form 

runoff channels (Otvos 1999). The beach is about 16 km west of the mouth of Biloxi Bay. There 

is a narrow sand island (Deer Island) to the west of the Biloxi Bay and a system of breakwalls 

direct water from the bay westward along the shoreline toward the beach. The Back Bay of 

Biloxi runs parallel to the coast as a land-locked, westward continuation of Biloxi Bay (Figure 

A.6). 
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Figure A.6. Location of 2005 NEEAR study at Edgewater Beach in Biloxi, Mississippi. Yellow pin 

indicates location of beach and green pins mark possible sources of fecal contamination (i.e., 

WWTPs). Red pin shows nearby airport weather station. The beach is on the Mississippi Sound 

along the Gulf of Mexico (Figure 4.2B).

The Biloxi Bay watershed has a drainage area of ~ 1,600 km2. Land use in the watershed consists 

predominantly of forested and wetland areas. Only a small percentage (<6 percent) is urban, and 

those areas are concentrated around the Back Bay of Biloxi and Biloxi Bay. Biloxi Bay is 

designated for shellfishing and, therefore, is subject to stricter water quality criteria than the 

recreational beach standard. The Coastal Streams Basin is made up of several independent 

watersheds including a number of rivers, streams, creeks, bayous, and bays. Seven Harrison 

County Utility Authority WWTPs are within 10 km of the beach. Treated effluent from the 

facilities is discharged to the Biloxi River, Bernard Bayou (Gulfport Lake), and the Back Bay of 

Biloxi. The Keegan Bayou East Biloxi Wastewater Treatment Facility is closest to Biloxi Bay 

(the bayou is ~ 6 km from the mouth of Biloxi Bay). Two additional treatment facilities are 

closer to the coast ≥ 20 km west of the beach. The Gulfport North Wastewater Treatment 

Facility, which discharges to Gulfport Lake in the Bernard Bayou, employs UV disinfection, 

while all the others use chlorine. Possible nonpoint sources of fecal contamination include failing 

septic systems, wildlife, applied manure, grazing animals, and urban development (MDEQ

2002). 

The beach is monitored year-round for enterococci and fecal coliform by the Mississippi 

Department of Environmental Quality (MDEQ) and the University of Southern Mississippi’s 

Gulf Coast Research Laboratory. Real-time and historical data (since 2004) are publicly 

available from the MDEQ Mississippi Beach Monitoring Program website 

(http://www.coms.usm.edu/msbeach/harbmon.cgi). Water quality at Edgewater Beach (near 

Eisenhower Drive) is poor, with 16 percent of samples collected from 2004 to 2009 exceeding 

water quality criteria standards for enterococci (Table A.2). Decisions regarding water quality 

are based on culturable enterococci where levels > 104 CFU/100 mL result in beach advisories. 
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A.2.4 Fairhope Beach, Fairhope, Alabama

Fairhope Municipal Beach is in Fairhope, Alabama, ~ 22 km southeast of Mobile, on the eastern 

shore of Mobile Bay (Figure 4.2B). The Mobile Bay Estuary is an inlet of the Gulf of Mexico, 

with an average depth of 3 m. The small mouth of the bay is shaped on the east by the Fort 

Morgan Peninsula and the Dauphin Island barrier island on the west. The sandy beach area at 

Fairhope Beach is ~ 0.6 km long. Several piers are perpendicular to the shoreline on the 

southwest end of the beach (Figure A.7). 

The > 115,500 km2 Mobile Bay watershed includes seven river systems, with the Mobile River 

serving as the primary freshwater input to the bay. The seawater portion of Mobile Bay is 

designated for shellfish harvesting and subject to more stringent water quality standards than the 

beach. The Fairhope WWTP, < 1 km northeast of the beach, serves as a potential source of 

continuous fecal contamination. The facility employs UV disinfection as the final treatment step. 

Additional sources include sanitary sewer overflows, failing septic tanks, and urban runoff 

(ADEM 2010). 

Figure A.7. Location of 2007 NEEAR study at Fairhope Beach in Fairhope, Alabama. Yellow pin 

indicates location of beach and green pins mark possible sources of fecal contamination (i.e., 

WWTPs). Red pin shows nearby airport weather station. The beach is on the eastern shore of 

Mobile Bay, an inlet of the Gulf of Mexico (Figure 4.2B).

Enterococci levels are monitored year-round at Fairhope Beach by the Alabama Department of 

Environmental Management (ADEM) and the Alabama Department of Public Health (ADPH) 

with samples collected by the Baldwin County Health Department. In addition, a number of 

ancillary environmental parameters (i.e., water temperature, dissolved oxygen, pH, conductivity, 

salinity, turbidity, and the occurrence of rain) are sometimes measured at the time of sample 

collection. The data (real-time and historical since 2006) are publicly available at the 

ADEM/ADPH Coastal Alabama Beach Monitoring Program website 

(http://www.adem.state.al.us/programs/coastal/beachMonitoring.cnt). Water quality at Fairhope 

Beach is poor, with 17 percent of samples collected from 2006 to 2009 exceeding water quality 

criteria standards for enterococci (Table A.2). Decisions regarding water quality are based on 

culturable enterococci, where repeated measurement of levels > 104 CFU/100 mL result in a 

public health advisory. 
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A.2.5 Hobie Beach, Miami, Florida

Hobie Beach in Miami, Florida is on Virginia Key in the southern part of Biscayne Bay, off the 

east coast of mainland Miami (Figure 4.2B). Biscayne Bay is a subtropical estuary that receives 

freshwater inputs from the Miami River and small creeks, as well as from a network of drainage 

canals. The Miami River is ~ 4 km northwest of the beach, and its freshwater can influence the 

beach under certain conditions. Hobie Beach is ~ 1.6 km long and runs along the south side of 

Rickenbacker Causeway, between the William Powell Bridge and Miami Seaquarium (Figure 

A.8). Hobie is also known as Dog Beach because it is the only Miami-Dade County beach where 

pets are allowed; the ratio of dogs to humans at the beach is on the order of 1:7. The beach is 

narrow, with a distance of 5 m and 12 m between the water line and the outer edge of the sand 

line during high and low tide, respectively. Vehicles park right along the sand line. The benthic 

zone is silty and muddy, and the shoreline typically is covered with seaweed. The slope is 

relatively shallow and natural runoff channels form following heavy rainfall events. Hobie Beach 

is shallow with water depths < 2 m at the buoy line, ~ 130 m from the shoreline. Due to its 

location in a shallow cove, water circulation at the beach is poor and movement near shore is 

controlled by tidal action (with an average tidal height fluctuation of 58 cm) rather than waves 

(Shibata et al. 2004; Wright 2008). During ebb tide (the period in between high and low tide), 

water flows out of Biscayne Bay to the Atlantic through the Norris Cut and Bear Cut inlets. 

During flooding tide, water enters the bay. Flow is parallel to the shoreline with velocities of 

0.2 m/s and < 0.1 m/s during ebbing and flooding tide, respectively. Easterly winds prevail with 

a weak southerly component in the summer, accompanied by a strong local sea-breeze and 

thunderstorms (Zhu 2009). 

Figure A.8. Location of 2008 PREMIER study at Hobie Beach in Miami, Florida. Yellow pins 

indicate locations of beach and sampling transects and green pins mark possible sources of fecal 

contamination (i.e., WWTP). Details regarding field equipment (red pins) are given in Section 4.4.3. 

The beach is on Virginia Key in the southern part of Biscayne Bay (Figure 4.2B).

Hobie Beach was found to have poor water quality during an EPA/Florida Department of 

Environmental Health (FDOH) Beach Monitoring Study, when 29 percent of samples collected 

from July 1999 to June 2000 exceeded the enterococci water quality criteria (Solo-Gabriele et al. 

2002). There are no known point sources to the beach, but the Central District WWTP, 2 km 
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northeast of beach, is a potential source of fecal contamination. Treated, chlorine-disinfected 

effluent is discharged to the Atlantic Ocean through an outfall ~ 4 km east of the plant. No storm 

drains are at the beach, but other suspected sources of enterococci include runoff during heavy 

rainfall events and animals, particularly dogs (Wright et al. 2009). Spatially intensive sampling 

efforts, including surveys of beach sand and water, identified the shoreline as a source of fecal 

indicators. Bacterial counts were higher at the shoreline than offshore. Higher levels were 

observed at the east end of the beach, likely reflecting reduced flushing due to the adjacent 

peninsula. Indicator densities were also higher at high tide compared to low tide, suggesting a 

correlation with tidal stage and pointing to the inter-tidal zone (i.e., the sand area that is wetted 

and dried between high and low tide) as the source of contamination (Shibata et al. 2004; SoloGabriele et al. 2002). A water quality model developed to evaluate sources of nonpoint pollution 

found runoff to be the most important source of enterococci, followed by dogs, sand, birds, and 

bathers (Elmir 2006). Research efforts also have focused on the associations between indicator 

microbes, pathogens, and environmental conditions (Abdelzaher et al. 2010). 

The Miami-Date County Health Department routinely monitors Hobie Beach year-round for 

enterococci and fecal coliform. Real-time and historical data (since 2000) are publicly available 

through the FDOH Beaches website (http://esetappsdoh.doh.state.fl.us/irm00beachwater). Water 

quality at the beach is good, with 6 percent of samples collected from 2001 to 2009 exceeding 

water quality criteria standards for enterococci (Table A.2). Decisions regarding water quality 

are based on enterococci and fecal coliform levels, with counts > 104 CFU/100 mL resulting in a 

poor enterococci rating. A process-based predictive numerical hydrodynamic water quality 

model for Hobie Beach is being developed as a tool to improve assessing nonpoint source fecal 

contamination (Zhu 2009). 

A.2.6 La Monseratte Beach, Luquillo, Puerto Rico

La Monserrate public beach, better known as Luquillo Beach, is on the northeast coast of Puerto 

Rico in the town of Luquillo (Figure 4.2B). The public beach is ~ 400 m long and runs along the 

eastern side of the bay (Figure A.9). The mouth of the Mameyes River is ~ 2.2 km west of the 

main swimming area at Luquillo. During periods of low flow, the river mouth can be closed off 

completely from the ocean. Two streams fed by stormwater runoff are potential sources of fecal 

contamination to the beach; one is just west of the beach and the other is east of the beach, along 

the northern shoreline. 

The Puerto Rico Environmental Quality Board (PREQB) monitors enterococci and fecal 

coliform levels at Luquillo Beach twice a month year-round. Some data for the current year are

publicly available at the PREQB water quality website (http://www.prtc.net/~jcaagua). Water 

quality is good at Luquillo Beach, with 8 percent of samples collected from 2006 to 2008 

exceeding the water quality criteria standard of 104 CFU/100 mL for enterococci (Table A.3). 

Decisions regarding water quality are based on both culturable enterococci and fecal coliforms, 

where 35 CFU/100 mL is used as the criteria for enterococci. Puerto Rico’s standard is more 

stringent than that recommended by EPA and its use results in a total of 18 percent exceedances 

for 2006 to 2008. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure A.9. Location of 2008 PREMIER study at La Monserrate Beach in Luquillo, Puerto Rico. 

Yellow pins indicate locations of beach and sampling transects. Details regarding field equipment 

(red pins) are given in Section 4.4.3. The beach is on the northeast coast of Puerto Rico 

(Figure 4.2B).

A.2.7 Boquerón Beach, Cabo Rojo, Puerto Rico

Boquerón Beach is in southwestern Puerto Rico, in the town of Boquerón in Cabo Rojo (Figure 

4.2B). The 1.6-km-long beach is along the eastern shore of Boquerón Bay, on the western coast 

of Puerto Rico. The bay is ~ 4.7 km wide at its mouth and the beach is ~ 4 km from the mouth. 

Potential sources of fecal contamination to the beach include a sewage treatment plant’s outfall 

in the bay, ~ 1.3 km northwest of the beach, and two package plants that operate during periods 

of high demand (Figure A.10). The plants discharge treated effluent into the mangrove lagoon 

south of the beach. The mouth of the lagoon is ~ 1.5 km from the beach. A marina and 

condominium complex, just north of the beach, is also a potential source of contamination. 

Urban runoff is also likely because afternoon storms are common during the summer, with heavy 

rains resulting in flooding. 

PREQB monitors both enterococci and fecal coliform levels at Boquerón Beach every other 

week during the entire year. Data for the current year are posted on the web 

(http://www.prtc.net/~jcaagua), but we have not yet analyzed the data. Beachgoers at Boquerón 

are advised to avoid direct contact with waters in the 24 hours following heavy rainfall events 

because of the potential risk of exposure to pathogens. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Figure A.10. Location of 2009 NEEAR study at Boquerón Beach in Cabo Rojo, Puerto Rico. Yellow 

pins indicate locations of beach and sampling transects and green pins mark possible sources of 

fecal contamination (i.e., WWTP outfall and package plants). Details regarding field equipment 

(red pins) are given in Section 4.4.3. The beach is on the eastern coast of Puerto Rico 

(Figure 4.2B).

Table A.3. Historical water quality monitoring details and criteria exceedances for tropical marine 

beaches based on data provided by the local monitoring agency, PREQB. Number of exceedances 

is expressed per total samples, with the corresponding percentage given in parentheses.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Environmental Quality, Lansing, MI. 

MMSD (Milwaukee Metropolitan Sewerage District). 2005. Bacteria Source, Transport and 

Fate Study - Phase 1, Milwaukee Harbor Estuary Hydrodynamic & Bacteria Modeling. 

Milwaukee Metropolitan Sewerage District, Milwaukee, WI.

Nevers, M.B., and R.L. Whitman. 2005. Nowcast modeling of Escherichia coli concentrations at 

multiple urban beaches of southern Lake Michigan. Water Research 39:5250-5260. 

Nevers, M.B., and R.L. Whitman. 2008. Coastal strategies to predict Escherichia coli

concentrations for beaches along a 35 km stretch of southern Lake Michigan. 

Environmental Science & Technology 42:4454-4460. 

Nevers, M.B., R.L. Whitman, W.E. Frick, and Z. Ge. 2007. Interaction and influence of two 

creeks on Escherichia coli concentrations of nearby beaches: Exploration of 

predictability and mechanisms. Journal of Environmental Quality 36:1338-1345. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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NIRPC (Northwestern Indiana Regional Planning Commission). 2005. Watershed Management 

Plan for Lake, Porter, and LaPorte Counties. Northwestern Indiana Regional Planning 

Commission, Portage, IN.

Olyphant, G.A., J. Thomas, R.L. Whitman, and D. Harper. 2003. Characterization and statistical 

modeling of bacterial (Escherichia coli) outflows from watersheds that discharge into 

southern Lake Michigan. Environmental Monitoring and Assessment 81:289-300. 

Otvos, E.G. 1999. Rain-induced beach processes; landforms of ground water sapping and surface 

runoff. Journal of Coastal Research 15(4):1040-1054. 

RIDEM (Rhode Island Department of Environmental Management). 2005. Total Maximum Daily 

Load Analysis for Greenwich Bay Waters: Pathogen/Bacteria Impairments. Rhode Island 

Department of Environmental Management, Providence, RI. 

Schwab, D.J., D. Beletsky, and G.A. Lang. 2010. Indiana Dunes Nowcast 2010. . 

<http://www.glerl.noaa.gov/res/glcfs/bd>. Accessed July 2010. 

Scopel, C.O., J. Harris, and S.L. McLellan. 2006. Influence of nearshore water dynamics and 

pollution sources on beach monitoring outcomes at two adjacent Lake Michigan beaches. 

Journal of Great Lakes Research 32(3):543-552. 

Shibata, T., H.M. Solo-Gabriele, L.E. Fleming, and S. Elmir. 2004. Monitoring marine 

recreational water quality using multiple microbial indicators in an urban tropical 

environment. Water Research 38:3119-3131. 

Solo-Gabriele, H., T. Shibata, M. Al-Kendi, Y. St. Fort, L. Fleming, D. Squicciarini, W. Quirino, 

M. Arguello, S. Elmir, and M. Rybolowik. 2002. A Pilot Study Evaluation and Sanitary 

Survey of Microbial Recreational Water Quality Indicators in the Subtropical Marine 

Environment. National Institute of Environmental Health Sciences, Marine and 

Freshwater Biomedical Sciences Center, Rosensteil School of Marine and Atmospheric 

Sciences, Miami-Dade County Department of Health.

Telech, J.W., K.P. Brenner, R. Haugland, E. Sams, A.P. Dufour, L. Wymer, and T.J. Wade. 

2009. Modeling Enterococcus densities measured by quantitative polymerase chain 

reaction and membrane filtration using environmental conditions at four Great Lakes 

beaches. Water Research 43:4947-4955. 

Thupaki, P., M.S. Phanikumar, D. Beletsky, D.J. Schwab, M.B. Nevers, and R.L. Whitman. 

2009. Budget analysis of Escherichia coli at a southern Lake Michigan beach. 

Environmental Science & Technology 44(3):1010-1016. 

Triad Engineering Incorporated. 2003. Trail Creek Escherichia coli TMDL Report. Indiana 

Department of Environmental Management, Indianapolis, IN. 

Wade, T.J., R.L. Calderon, K.P. Brenner, E. Sams, M. Beach, R. Haugland, L. Wymer, and A.P. 

Dufour. 2008. High sensitivity of children to swimming-associated bastrointestinal 

illness: Results using a rapid assay of recreational water quality. Epidemiology 19:375-

383. 
Predictive Modeling at Beaches—Volume II November 22, 2010

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Wade, T.J., R.L. Calderon, E. Sams, M. Beach, K.P. Brenner, A.H. Williams, and A.P. Dufour. 

2006. Rapidly measured indicators of recreational water quality are predictive of 

swimming-associated gastrointestional illness. Environmental Health Perspectives

114(1):24-28. 

Whitman, R. 2010. About Project S.A.F.E. 2008. 

<http://www.glsc.usgs.gov/main.php?content=research_projectSAFE_about&title=Project

%20S.A.F.E.0&menu=research_initiatives_projectSAFE>. Accessed July 2010. 

Whitman, R., and M. Nevers. 2005. Regional and local factors affecting patterns of E. coli 

distribution in southern Lake Michigan. U.S. Geological Survey, Porter, IN. 

Wong, M., L. Kumar, T.M. Jenkins, I. Xagoraraki, M.S. Phanikumar, and J.B. Rose. 2009. 

Evaluation of public health risks at recreational beaches in Lake Michigan via detection 

of enteric viruses and a human-specific bacteriological marker. Water Research 43:1137-

1149. 

Wright, M.E. 2008. Evaluation of enterococci, an indicator microbe, and the sources that impact 

the water quality of a subtropical non-point source recreational beach. University of 

Miami, Civil Engineering, Coral Gables, FL.

Wright, M.E., H.M. Solo-Gabriele, S. Elmir, and L.E. Fleming. 2009. Microbial load from 

animal feces at a recreational beach. Marine Pollution Bulletin In press, corrected proof. 

Zhu, X. 2009. Modeling microbial water quality at a non-point source subtropical beach. 

University of Miami, Applied Marine Physics, Coral Gables, FL.
Predictive Modeling at Beaches—Volume II November 22, 2010

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Appendix B. Additional Data Collection Details 
Predictive Modeling at Beaches—Volume II November 22, 2010

B-2 

B.1 SAMPLE COLLECTION

Details regarding the NEEAR study sample collection protocol have been described previously 

(Haugland et al. 2005; Wade et al. 2006). That general approach was taken at all NEEAR study 

sites. Briefly, samples were collected on weekends and holidays during the single summer study 

carried out at each beach. Samples were collected three times a day (8 a.m., 11 a.m., and 3 p.m.) 

at six locations at each beach. The locations included two depths (shin and waist deep) along 

three transects, ≥ 60 m apart. Shin samples were collected ~ 0.15 m below the surface in 0.3-mdeep water, and waist-deep samples were collected ~ 0.3 m below the surface in 1-m-deep water. 

Grab samples were collected in sterilized polypropylene bottles in accordance with Standard 

Methods Section 9060 (Clesceri et al. 1998). Samples were mixed to create three composite 

samples per time point: a shin composite, waist composite, and total composite. Total composites 

were primarily used for statistical modeling.

Sample collection for the 2008 PREMIER studies (at South Shore, Hobie, and La Monserrate) 

was designed deliberately to match the NEEAR studies, where possible. However, more frequent 

sampling was performed to provide a larger data set for modeling purposes. Waist-deep samples 

were collected four days a week (Mondays, Wednesdays, Thursdays, and Saturdays), three times 

a day (9 a.m., 11:30 a.m., and 3 p.m.) at South Shore and Hobie. Shin-deep samples were also 

collected on Saturdays at South Shore and on Thursdays and Saturdays at Hobie. No shin-deep 

samples were collected at La Monserrate, and waist-deep samples were collected only once a day 

(1000), three days a week (Mondays, Thursdays, and Saturdays) over a longer period (June 

through October 2008). At each sampling location and time, three 500-mL grab samples were 

collected and mixed to give composite samples for each of the three transects; unlike the 

NEEAR studies, no beach-wide composites were collected. The distance between sampling 

transects at the beaches ranged from 125 to 250 m. Because shin- and waist-deep samples were 

not collected with equal frequency, waist-deep composite samples were used for statistical 

modeling purposes. 

The 2009 PREMIER studies at Surfside Beach and Boquerón were specifically designed to 

complement the concurrent NEEAR studies by expanding the spatial and temporal scale of data 

collection. In addition to the NEEAR sampling scheme (i.e., weekend and holiday samples) 

described previously, waist-deep samples were collected on Fridays (three times per day) as part 

of the PREMIER study. Samples were also collected from two locations outside the beach area 

(at 8 a.m. and 3 p.m. on Fridays, Saturdays, Sundays, and holidays to better evaluate potential 

sources of contamination to the beaches (i.e., runoff and effluent at Surfside and Boquerón, 

respectively). At Surfside Beach, samples were collected from the 3rd Avenue North swash 

channel along North Ocean Boulevard and from the lake at North Dogwood Drive. Boquerón 

samples were collected at the outfall of the wastewater treatment plant and just outside the mouth 

of the mangrove lagoon. For each sampling event at these sites, three grab samples were 

collected and composited. The distance between sampling transects at both of these beaches was 

~ 150 m. As stated for the 2008 PREMIER sites, waist-deep composite samples were used for 

statistical modeling purposes.
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In addition to the samples collected for microbial analysis (described above), water samples were 

also collected during the PREMIER studies to analyze dissolved organic carbon (DOC) and 

colored dissolved organic matter. The same collection scheme was used for those samples, as 

detailed above for the 2008 sites, without any sample compositing. At Surfside and Boquerón, 

beach water samples for the analyses were collected at only the waist-deep site of the middle 

transect. Single grab samples were also collected from the potential contamination source 

locations using the microbial sampling scheme. The samples were collected in glass bottles, 

appropriately cleaned as described in Standard Methods Section 5310B (Clesceri et al. 1998). 

Samples collected for the studies provided a large data set that was used to develop predictive 

models, discussed in Chapter 5. Historical monitoring data can also be used for model 

development, but most local beach monitoring programs do not have the resources to carry out 

sampling efforts on the scale of the NEEAR and PREMIER studies. For example, while 

Huntington Beach, Ohio, has been sampled for E. coli daily since 2006, sampling is done only at 

one time (around 9 a.m.) and one location (30 cm below the surface in the surf zone at a depth of 

1 m). Routine E. coli sampling at the Ogden Dunes Beach site is done less frequently (≤ 5 times 

per week), but samples are collected from three different locations, which provides better 

coverage of the larger beach area. Publicly available data from those two beaches were used (as 

were data obtained from the NEEAR and PREMIER studies) in our efforts to refine and evaluate 

the development of predictive models. Details regarding the beach field studies that generated 

data for the modeling studies discussed in this report are summarized in Table 4.1.

B.2 DEPENDENT VARIABLES

As the dependent variable, fecal indicator bacteria (FIB) density data are the most important 

component of predictive model development. The acceptable standard by which recreational 

water quality is evaluated is culturable enterococci; E. coli is also acceptable for freshwaters

only. 

As a result of the BEACH Act of 2000, more than 10 years of monitoring data now exist for 

beaches in the United States. Most of the data are available on the Internet, providing an 

extensive database of historical information. In the PREMIER and NEEAR studies described 

here, culturable enterococci were enumerated on membrane-Enterococcus Indoxyl-B-DGlucoside (mEI) plates according to EPA Method 1600 (USEPA 2006). For that method, the 

detection limit was 1 CFU/volume filtered (i.e., 0.01 CFU/mL for 100 mL volumes) and a value 

of 0.5 CFU/100 mL (one-half the limit of detection) was used as the lower limit for data analysis. 

All culturable data were log-transformed before modeling. Because of the interest in more rapid 

monitoring techniques (i.e., quantitative polymerase chain reaction [qPCR]-based enterococci) 

and the paucity of existing qPCR monitoring data that include the environmental parameters 

required for modeling, a goal of the PREMIER studies was to build on the existing NEEAR data 

set by obtaining qPCR-based enterococci measurements at additional beach sites.

Enterococcus 23S rRNA target sequences were quantified by the TaqMan® qPCR assay, as 

detailed in EPA (2010), with several modifications. Briefly, samples were filtered and total DNA 

was extracted from enterococci collected on the membrane filter by bead beating. PCR 

amplification of the target DNA sequence was quantified on the basis of the increase in 

fluorescence resulting from enzymatic hydrolysis of the fluorogenically labeled probe during 

each amplification cycle. NEEAR samples were analyzed as described in Haugland et al. (2005), 
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B-4 

using the Sketa2 reverse primer for analysis of the Salmon DNA sample processing control 

sequence. That assay has been revised (as of April 2010) and now uses the Sketa22 reverse 

primer (USEPA 2010). qPCR results from the NEEAR studies are reported as calibrator cell 

equivalents (CCE) per 100 mL volume filtered, relative to calibrator samples containing a known 

quantity of Enteroccocus cells. Samples from the 2008 PREMIER studies were analyzed by the 

TaqMan® Fast Mix Entero2 assay described by Siefring et al. (2008) using the Sketa22 reverse 

primer. Reactions were performed in 96-well optical plates in an Applied Biosystems 7500 Fast 

Real-Time PCR instrument, using a thermal cycling program of 20 seconds (s) at 95 degrees 

Celsius (°C), followed by 40 cycles of 3 s at 95 °C and 30 s at 60 °C. Threshold cycles (CT) were 

calculated by the instrument software, using a threshold setting of 0.03. qPCR results from the 

2008 PREMIER studies are reported as Enteroccocus target sequence copies (TSC) per 100 mL 

volume filtered, as described in EPA (2010). Briefly, that involves comparison with TSC 

recovery in a calibrator standard for which TSC can be calculated from CT (using a DNA 

standard curve). The limit of detection for Enterococcus was determined to be 5 TSC (CT ≈ 37).

As outlined in EPA (2010), samples with Salmon CT values that were not within 3 CT units of 

the calibrator were considered inhibited. Samples with higher CT values (suggesting poor DNA 

recovery or PCR inhibition or both) were diluted by an additional factor of 5 (25-fold dilution) 

and reanalyzed to rule out or eliminate inhibition, wherever possible. If the sample was not 

inhibited, poor DNA recovery was corrected for using the ΔCT method (Siefring et al. 2008). 

Samples with CT values below detection or non-detects (i.e., no signal after 45 cycles) were 

assigned a value of one-half the detection limit.

Reporting qPCR results in different units (i.e., CCE versus TSC for the NEEAR and PREMIER 

studies, respectively) will not influence the modeling results. The units can be converted because 

the TSC extracted from a calibrator sample should be directly proportional to the number of 

Enterococcus cells. That is, the extraction efficiency for the calibrator sample should be 

reproducible such that the ratio of TSC to cells is always the same. As with the culturable data, 

CCE and TSC data were log-transformed before modeling.

B.3 INDEPENDENT (EXPLANATORY) VARIABLES

Because water quality criteria are based on FIB levels, monitoring data are crucial for beach 

management. However, models can be useful in predicting indicator densities, which is 

increasingly important, given issues associated with capability of monitoring data to reflect 

beach conditions accurately at a given time. More easily measured environmental conditions, 

often obtained with automated techniques, can be used as independent variables (IVs) in 

statistical models to explain observed variability in FIB levels. Those include physical 

hydrologic measurements (e.g., water temperature, turbidity, current and wave information, tidal 

phase, and stream discharge); chemical and biological parameters (e.g., pH, dissolved oxygen, 

conductivity, salinity, and chlorophyll); meteorological conditions (e.g., rainfall, solar 

irradiation, air temperature, and wind information); and ancillary beach conditions (e.g., number 

of bathers and birds). A variety of such parameters were measured with FIB measurements 

during the NEEAR and PREMIER studies. While measurements were taken at the time of 

sample collection and in discrete samples during the NEEAR studies, the purpose of the 

PREMIER studies was to obtain more detailed IV data by deploying automated instruments at 
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B-5 

the beach sites to monitor ambient conditions. The measurements were also supplemented with 

variables mined from public databases, where available.

Details about collecting environmental data during the NEEAR studies were previously 

discussed for the four freshwater sites (Heaney et al. 2009); the same procedures were followed 

for the subsequent marine studies. Measurements recorded at each sampling event included the 

following parameters: air and water temperature; percent cloud cover; ultraviolet (UV) 

irradiance; wave height; current direction; wind speed and direction; number of bathers on the 

beach and in the water; total number of birds and animals within 20 m of the sampling area; 

number of boats within 500 m of the sampling area; and the presence of debris. Rainfall data for 

the study period were obtained from weather stations at nearby airports and from on-site weather 

stations installed at some of the beaches. Turbidity, pH, salinity, and conductivity were measured 

in collected water samples. Limited ancillary data were collected during the 2008 PREMIER 

studies because efforts were focused on in situ measurements. Local water and beach conditions

were noted, including wave conditions (South Shore and Hobie), presence of birds (South Shore) 

or dogs (Hobie), and number of people and dogs within 50 m of sampling transects (Hobie). 

IV data at South Shore Beach, Milwaukee; Hobie Beach, Miami; Surfside Beach, South 

Carolina; La Monserrate Beach, Luquillo, Puerto Rico; and Boquerón Beach, Cabo Rojo, Puerto 

Rico were obtained, using procedures and equipment that are described in detail in the balance of 

this appendix. 

General. Field equipment was deployed at the PREMIER and NEEAR/ PREMIER beach sites to 

obtain more detailed and beach-relevant IVs from which to develop predictive water quality 

models. Field equipment locations for South Shore, Surfside, Hobie, La Monserrate, and 

Boquerón beaches are shown in Appendix A. In addition to using automated field instruments, a 

unique aspect of the PREMIER studies was measuring underwater UV radiation with the 

analysis of DOC and colored dissolved organic matter (i.e., UV-VIS spectra). By characterizing 

the optical properties of beach waters, the amount of light to which bacteria are exposed in the 

water column was more accurately determined in investigating the effects of light on the 

inactivation of FIB. 

Weather stations. Meteorological conditions were monitored by installing HOBO (U30 NRC, 

Onset Computer Corporation) weather stations at or near each beach site. In Milwaukee, the 

weather station was on the roof of the Great Lakes WATER Institute, 3.3 km northwest of South 

Shore beach. At Surfside Beach, a weather station was installed on the roof of the Surfside Beach 

civic center, ~ 1 km west of the beach. A second, earlier model HOBO station was at the end of 

Surfside Beach pier, ~ 200 m offshore. The pier is 550 m southwest of the 5th Avenue North 

Swash sampling location. The weather station at Hobie Beach was deployed southeast of the 

beach on the grounds of the adjacent Miami Seaquarium property. At Luquillo Beach, the 

weather station was on the roof of a beach snack bar, ~ 200 m from the middle sampling transect. 

The Boquerón Beach weather station was deployed on top of the lifeguard station, just south of 

the handicap-access facilities, ~ 300 m south of the center sampling transect.

Weather stations were equipped with sensors to measure air temperature; relative humidity; dew 

point (determined from temperature and relative humidity); barometric pressure; wind speed and 

direction; gust speed (i.e., highest 3-second wind recorded during logging interval); rain; 

photosynthetically active radiation, solar radiation (silicon pyranometer); and UV radiation 

(Apogee Instruments sensors were used in 2009 only) every 15 or 30 minutes. Data were 
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B-6 

routinely downloaded in the field by connecting a laptop to the weather station data logger. Wind 

speed and direction were used to determine cross-shore (u component) and along-shore (v 

component) winds at each beach site. The on-site weather data were supplemented with other 

available meteorological data (http://cdo.ncdc.noaa.gov/ulcd/ULCD).

Acoustic Doppler current profilers. Current and wave information was obtained by deploying 

Nortek Aquadopp Profilers (2 MHz, right angle sensor head) at each beach site. The acoustic 

Doppler current profilers (ADCPs) were installed on the lake or sea floor using a weighted crossframe with a mounting height of ~ 0.3 m (Mooring Systems, Inc.). At South Shore, the ADCP 

was under the South Shore Yacht Club dock (because of shallow water depths and heavy boat 

traffic), < 200 m northwest of the beach. At Surfside, an ADCP was deployed ~ 200 m from 

shore, roughly in line with the middle transect. The Hobie ADCP was on the northwest end of 

the beach, along the buoy line ~ 300 m northwest of middle sampling transect, 100 m from 

shore. The Luquillo ADCP was ~ 100 m from the beach shore, at the middle transect. Two 

ADCPs were used at Boquerón Beach to better characterize the hydrodynamics of the bay, as 

related to potential contamination sources; one ADCP was deployed at the beach, 55 m from 

shore along the southern sampling transect, and the second was ~ 400 m southeast of the WWTP 

outfall, ~ 1 km from the beach. A University of Puerto Rico-Mayagüez ADCP was also installed 

in the bay, ~ 600 m west of the mouth of the mangrove lagoon. The area immediately beyond the 

swimming area of both beaches in Puerto Rico was buoyed off from a channel for kayaks. It 

provided an excellent location for field equipment that was close to the sampling area and where 

water conditions were likely very representative of water in the swimming area.

Measurement of current velocity by the ADCP is based on the Doppler Effect. Sound waves 

transmitted by the Aquadopp are reflected by small particles in the water that move at the same 

speed as the water. Listening to the echo of the transmitted sound, the Aquadopp determines 

water velocity by measuring changes in frequency. To generate depth profiles of current speed 

and direction, current measurements are taken in cells along three acoustic beams. Current 

measurements were taken every 10 minutes, and velocity and pressure data were collected every 

one or two hours to measure wave bursts; post-processing of the data was done with the Nortek 

Storm software. Current speed and direction for each cell were averaged to obtain current 

information for the overall water column. Depth averaged cross-shore (u component) and alongshore (v component) currents were determined from current speed and direction. Approximate 

water depth (estimated from pressure), temperature, significant wave height, and mean wave 

direction also were acquired from the ADCP data. ADCPs at South Shore and Luquillo were 

deployed with a communication cable (from the Aquadopp to a weatherproof enclosure mounted 

above water on the dock or UV sensor tower) to enable data retrieval in the field with a laptop. 

The Hobie ADCP was routinely recovered from the water, and data were downloaded before 

redeployment in the same location. In Surfside Beach and Boquerón, ADCPs were left 

unattended for the duration of the study period. 

Water quality sondes. Multi-parameter water quality sondes (YSI 6600V2-2) were deployed at 

each beach site for the duration of the studies. At South Shore, Surfside, Luquillo, and Boquerón, 

sondes were deployed on the support frame of the UV sensor instrument package (described 

below), although the Surfside sonde was later relocated to its own buoy. The equipment was 

placed ~ 500 northwest of South Shore Beach, 80 m from shore to avoid boat traffic. At the other 

beaches, sondes (and UV sensors) were adjacent to the ADCP, allowing enough space so as not 

to interfere with the ADCP measurements. At Hobie, the sonde was hung from an existing 
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B-7 

marker buoy (Dade County Public Works Rickenbacker Causeway Buoy 6A) on the northwest 

end of the study area. The sondes were deployed at fixed locations at a depth of < 2 m. Although 

actual sonde depths varied at most sites because of tidal changes, sonde readings were taken to 

represent surface conditions.

Water temperature, specific conductance, salinity, dissolved oxygen (using a Clark oxygen 

electrode), pH, turbidity, and chlorophyll (as relative fluorescence) were measured every 15 

minutes. Nitrate, ammonia, and ammonium were also measured at the freshwater South Shore 

Beach using ion selective electrodes. The sondes were typically retrieved every one to two weeks 

for cleaning, calibration, and data retrieval. Probes were calibrated as follows: conductivity (10 

mS/cm), dissolved oxygen water-saturated air), pH (pH 7 and 10 buffers), ammonium (1 and 100 

mg/L), nitrate (1 and 100 mg/L), chlorophyll (deionized water), and turbidity (deionized water 

and 123 nephelometric turbidity units [NTU]). Fouling was significant and in some cases could 

be identified as having influenced data quality, specifically for optical measurements (i.e., 

turbidity and chlorophyll). Fouling of the optical sensors results in high turbidity and chlorophyll 

readings with a high frequency of spikes. Real (i.e., event-driven) spikes in data progress in a 

natural upward trend and are short in duration. Examples of bad data from fouling (available 

from the instrument manufacturer) were used to help identify questionable data during manual 

review by an experienced individual. Data for periods during which biofouling was suspected 

were manually deleted from the final data set to avoid the use of possibly erroneous data. 

Likewise, data for periods in which calibrations were later found to be unacceptable were 

manually deleted. Regarding treatment of the turbidity data, the correction with an offset of 0.5 

NTU (i.e., adding 0.5 NTU to negative values) was done at the manufacturer’s recommendation. 

Errors resulting in negative values are very common when the sonde is not adequately cleaned 

(before it is calibrated between deployments) and can result in contamination of the blank. In 

addition, a longer calibration cup should have been used to minimize interference during 

calibration when the sonde is to be used in low turbidity waters. While the data could have been 

excluded, it was decided that negative values should be adjusted (to between 0.05 and < 0.5 

NTU) and included because values that low clearly indicate that turbidity was very low 

(regardless of the exact value). A minimum value of 0.05 NTU was used because it is one-half 

the smallest value that the turbidity probe can measure (i.e., 0.1 NTU). Using a small positive 

value rather than 0 prevented the loss of data points following the log-transformation used to 

process the data before modeling.

Underwater UV radiation. Downwelling irradiance (Ed) was measured at each beach using 

pairs of Satlantic multispectral radiometers (OCR-504 ICSW) with 305, 325, 340, and 380 nm 

channels. The sensors were placed at two depths to evaluate the attenuation of UV radiation in 

the water column. The top sensor was < 0.5 m below the water surface (at low tide) and the 

bottom sensor was placed ~ 0.6 m to 1.5 m below the top sensor, depending on water clarity; for 

example, the bottom sensor at Luquillo was placed deeper because UV penetration was deeper in 

the clearer water. To reduce biofouling on the sensor optics, each sensor was equipped with a 

copper Satlantic Bioshutter. The shutters opened for hourly measurements (during daylight 

hours) and data were logged for 60 s. Sensors were cleaned sporadically and, while fouling was 

not a major issue, the lack of routine cleaning resulted in deterioration of data quality over the 

course of the study. 

In addition to the sensors and Bioshutters, each UV sensor instrument package included the 

following Satlantic equipment: a STOR-X data logger, battery pack (51Ah), wireless telemetry 
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B-8 

system with GSM modem, and dual band marine-grade cellular antenna. The modem was housed 

in a weatherproof enclosure, mounted above the water surface, and connected by cable to the 

data logger. All other equipment was deployed underwater on temporarily installed tower 

structures. Irradiance data were transmitted hourly as an email attachment. In some cases, 

problems with signal strength prevented communication, resulting in intermittent data 

transmission. In those cases, data were recovered from the loggers when instruments were 

retrieved at the end of the study. In 2009 surface UV and visible light sensors were also included 

to provide a better reference for surface light levels.

UV irradiance data were processed using the Satlantic SatCon data conversion software. Data 

were averaged over each 60-s logging event and irradiance values ≤ 0.01 μW cm-2 nm

-1 were 

excluded. The rate at which irradiance at a given wavelength decreases as a function of depth can 

be described by a vertical attenuation coefficient for downwelling irradiance (Kd(λ)). Kd values 

were estimated from the irradiance measured at the top and bottom sensors, according to the 

following equation (Smith and Baker 1981): 

12

zd,

zd,

d

zz

)(E

)(E

n

)(K 1

2

−

















−= λ

λ

l

λ (equation B.1) 

where Ed(λ) is the downwelling irradiance measured at each wavelength (λ) by the top (2) and 

bottom (1) sensors, at a given depth (z) below the water surface. Sensor depth varied during each 

logging event due to tidal variations at Hobie and Luquillo. Approximate sensor depths were 

determined as a function of time at each of three beaches, using ADCP pressure readings as a 

measure of total water depth. Available tide and water level data from nearby NOAA/NOS/COOPS stations were also used to relate depths measured during deployment to tidal cycle water 

level. Data were retrieved (www.tidesandcurrents.noaa.gov) for the study dates from the 

following stations: Milwaukee, Wisconsin (Station ID: 9087057); Springmaid Pier, South 

Carolina (Station ID: 8661070); Virginia Key, Florida (Station ID: 8723214); and San Juan, 

Puerto Rico (Station ID: 9755371). In cases where measured irradiance was higher at the bottom 

sensor than the top sensor, likely because of fouling or physical blockage of the top (or both) 

sensors (e.g., seaweed floating over), Kd values were negative. These erroneous data were 

excluded. Irradiance 0.3 m below the water surface (Ed,0.3), the depth at which water was 

sampled for bacterial analyses, was calculated from Kd and top sensor irradiance and depth by 

rearranging equation B.1.

Dissolved organic material. DOC was measured in filtered water samples as non-purgeable 

organic carbon by high temperature combustion using a Shimadzu 5050A or TOC-V Total 

Organic Carbon Analyzer. Samples were acidified to pH ≤ 2 with hydrochloric acid and sparged 

for 8 minutes before injection. The instrument was calibrated with potassium hydrogen phthalate 

standards (0.1 to 1 mM carbon) in NANOpure water. A blank and check standard were included 

with every six samples. Analysis of samples, in triplicate (75 μL injection volume), gave a 

coefficient of variation of ≤ 5 percent.

UV-visible absorption spectra were determined from 200 to 800 nm for 0.2-μm filtered water 

samples, using a Perkin-Elmer LAMBDATM 35 UV/Vis Spectrophotometer equipped with a 

sipper system and a 5-cm long microvolume, flow-through quartz cell (Hellma). Spectra were 
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referenced against NANOpure water (Barnsted) and then baseline-corrected by adjusting the 

absorbance (Aλ) to zero between 690 and 710 nm. Measured Aλ were used to calculate 

absorption coefficients (i.e., aλ = 2.303(Aλ/l) where l is the path length in m) at 350 nm. 
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Appendix C. Regression Modeling Results
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Tables C.1 through C.26 show the MLR models that were chosen for each site and each response 

variable (culturable/qPCR data). The first column in each table is the name of the IV. POLY

means the variable was transformed using a polynomial (ax

2 + bx + c) before regression analysis. 

That was done because such a transformation best linearized the relationship between the IV and 

the response variable, as measured by a Pearson correlation coefficient (see Chapter 2). The 

values of a, b, and c were chosen using an ordinary least squares regression approach. We do not 

show the values of a, b, and c. INV means the inverse transformation of the original parameter 

was instituted for modeling. Columns two through five are the fitted regression coefficient for 

that parameter, its standard error, t-statistic, and significance level. Each table note gives the 

adjusted R2, root mean square error (RMSE) and sample size for each of the models. 

C.1 FRESHWATER SITES

Table C.1. Regression model for South Shore Beach enterococci qPCR data. 

Note: Adjusted R2 = 0.39, RMSE = 0.36, n = 81.

Table C.2. Regression model for South Shore Beach enterococci culturable data.

Note: Adjusted R2 = 0.56, RMSE = 0.33, n = 79.
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Table C.3. Regression model for Huntington Beach, Ohio, enterococci qPCR data.

Note: Adjusted R2 = 0.69, RMSE = 0.42, n = 44.

Table C.4. Regression model for Huntington Beach, Ohio, enterococci culturable data.

Note: Adjusted R2 = 0.62, RMSE = 0.48, n = 45.

Table C.5. Regression model for Huntington Beach, Ohio, E.coli culturable data, 2003.

Note: Adjusted R2 = 0.54, RMSE = 0.38, n = 46.

Table C.6. Regression model for Huntington Beach, Ohio, E.coli culturable data, 2000–2009.

Note: Adjusted R2 = 0.44, RMSE = 0.47, n = 709.
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Table C.7. Regression model for Washington Park enterococci qPCR data.

Note: Adjusted R2 = 0.20, RMSE = 0.59, n = 66.

Table C.8. Regression model for Washington Park enterococci culturable data.

Note: Adjusted R2 = 0.45, RMSE = 0.24, n = 66.

Table C.9. Regression model for Silver Beach enterococci qPCR data.

Note: Adjusted R2 = 0.41, RMSE = 0.41, n = 58.

Table C.10. Regression model for Silver Beach enterococci culturable data.

Note: Adjusted R2 = 0.32, RMSE = 0.36, n = 58.
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Table C.11. Regression model for West Beach enterococci qPCR data.

Note: Adjusted R2 = 0.63, RMSE = 0.41, n = 49.

Table C.12. Regression model for West Beach enterococci culturable data.

Note: Adjusted R2 = 0.78, RMSE = 0.40, n = 49.

C.2 MARINE SITES

Table C.13. Regression model for Boquerón enterococci qPCR data.

Note: Adjusted R2 = 0.23, RMSE = 0.29, n = 79.

Table C.14. Regression model for Boquerón enterococci culturable data.

Note: Adjusted R2 = 0.43, RMSE = 0.43, n = 44.
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Table C.15. Regression model for Edgewater Beach enterococci qPCR data.

Note: Adjusted R2 = 0.14, RMSE = 0.44, n = 55.

Table C.16. Regression model for Edgewater Beach enterococci culturable data.

Note: Adjusted R2 = 0.48, RMSE = 0.56, n = 55.

Table C.17. Regression model for Fairhope Beach enterococci qPCR data.

Note: Adjusted R2 = 0.35, RMSE = 0.49, n = 66.

Table C.18. Regression model for Fairhope Beach enterococci culturable data.

Note: Adjusted R2 = 0.43, RMSE = 0.57, n = 66.
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Table C.19. Regression model for Goddard Beach enterococci qPCR data.

Note: Adjusted R2 = 0.18, RMSE = 0.70, n = 69.

Table C.20. Regression model for Goddard Beach enterococci culturable data.

Note: Adjusted R2 = 0.36, RMSE = 0.60, n = 69.

Table C.21. Regression model for Surfside Beach enterococci qPCR data.

Note: Adjusted R2 = 0.35, RMSE = 0.60, n = 82.

Table C.22. Regression model for Surfside Beach enterococci culturable data.

Note: Adjusted R2 = 0.46, RMSE = 0.43, n = 85.
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Table C.23. Regression model for Hobie Beach enterococci qPCR data.

Note: Adjusted R2 = 0.67, RMSE = 0.06, n = 17.

Table C.24. Regression model for Hobie Beach enterococci culturable data.

Note: Adjusted R2 = 0.19, RMSE = 0.47, n = 97.

Table C.25. Regression model for La Monseratte Beach enterococci qPCR data.

Note: Adjusted R2 = 0.45, RMSE = 0.45, n = 24.

Table C.26. Regression model for La Monseratte Beach enterococci culturable data.

Note: Adjusted R2 = 0.41, RMSE = 0.59, n = 32.