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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 Edge water 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 Boqueron Beach, CaboRojo, Puerto Rico 38
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 forNowcasts 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 CombinedPA + SS Analysis 72
8.3.3 Model Comparisons 73
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 atHobie 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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. la. 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 (CPU) 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 MSB of models developed using a variable number of
previous years' data (Miprev-M9prev) applied to each single year of data (Y2ooi-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.I. 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.I. 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 qPCRdata C-4
Table C.10. Regression model for Silver Beach enterococci culturable data C-4
Table C.ll. 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 forBoqueron enterococci qPCRdata C-5
Table C.14. Regression model forBoqueron 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 qPCRdata C-8
Table C.26. Regression model for La Monseratte Beach enterococci culturable data C-8
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs 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) Boqueron 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 thePCC 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
9
Figure 9.5. Effects on the regression adjusted R 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.I. 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-ll
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 Boqueron Beach in Cabo Rojo,
Puerto Rico A-20
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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
CPU colony forming units
Cp Mallows' Cp
cm centimeter(s)
CSO combined sewer overflow
DOC dissolved organic carbon
EC Escherichia coli or E. coll
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 predict!on
mL milliliter(s)
MLR multiple (or multivariable) linear regression
MSE mean squared error
jim micrometer
nm nanometer
NEEAR EPA National Epidemiological and Environmental Assessment of Recreational
Water study
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November 22, 2010
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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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., & 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
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a genetic search algorithm for handling a large number of TVs. 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 long-
term 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 cross-
validation, 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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
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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
TVs 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 TVs 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 ^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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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)
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Predictive Modeling at Beaches—Volume II November 22, 2010
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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs increases, the number of possible models in the solution space
increases exponentially. The user is able to select all, or a subset of, the TVs 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):
E[\n(EQ] = /?0 + Z fa , (equation 2.1)
where E[\n(EC)] represents the expected value of the natural logarithm of the mean of the
dependent variable (EC), flo and $ are the regression coefficients, xt the IVs andp 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 log-
transformed, 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs 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)
Cp=p + (n-p)(<32 -o-]ull)/G]UII (equation 2.2)
as the selection criterion, where n is the number of samples, p is the number of included
variables, and a2 and OM2 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
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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.
Project Window Help
Data Hf ocessing
Beach Location
Map Controls
B Current Marker Q Grid
0 pjm Drag M*p I Reload I
[ Remove 1sf Beach Marker j
[ Remove 2rsd Beach
| Flea
[ bhowitabonLocabons |
0 NWIG 0 HCDC
Q STORE!
[ Remove Station Locations j
Carant Localiot*
4T6283K858591 1st
-07.137204EJ040G3 Lug
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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
2.2.2 Model Development
VB 2.0 uses a multilinear regression technique to relate a dependent variable (FIB densities) to
TVs 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.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
Wind and Current Components
Use this form to add orthogonal components
(on-shore and across-shore] for either/both wind and
water current to your dataset. U and V data columns
will be added to the dataset.
Wind Data
Specify wind data columns:
Speed
WindS peed
Direction (deg) WindDirection
Current Data
Specify current data columns:
Speed
Direction (deg)
Current
Beach Angle (deg):
-90.56
Ok
Cancel
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.
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Predictive Modeling at Beaches—Volume II
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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.
Peason Univariate Correlation Results - Maximum Pearson Coefficients (signed) in BOLD text
Variables, possible variable
interactions, and their
transforms are shown. Select
variables for further
processing and modeling.
Auto-Select
The variable or one of its
transforms is selected by
maximum Pearson Coefficient.
(This is the default view shown.]
Threshold Select
Select a transformed variable only
if its Pearson Coefficient exceeds
the untransformed variable's
Pearson Coefficient by a
specified threshold.
Thresholld [%) J20 Q
[ Go ]
Manual Select
Mouse-click on a row header to
select or deselect that variable.
At most one member from each
group can be selected.
Ok : [ Print |
>
Variable
turbidity
turbidity
turbidity
turbidity
turbidity
Previous24hrrainfall
Previous24hrrainfall
Previous24hrtainfall
windspeed
windspeed
windspeed
windspeed
windspeed
windspeed
airtemp
airtemp
airtemp
airtemp
airtemp
airtemp
dewpoint
Transform
none
POLY[turbidity]
SQR[turbidity]
LN [turbidity]
INV[turbidity]
LOG [turbidity]
none
POLY[Previous24hrrainfall]
SQR[Previous24hrrainfall]
none
FQLY'I'A'indspeed]
SQR[windspeed]
LN[windspeed]
INV[windspeed]
LOG['A'indspeed]
none
POLY[airtemp]
SQR[airtemp]
LN[airtemp]
INV[airternp]
LOG [airtemp]
none
Pearson
Coefficient
0,4842
0.5142
0.5370
0,5267
-0,4175
0,5267
0,3412
0.3770
0.4Z75
0.2198
0,2130
0,2078
0.2066
-0,1828
0,2066
-0,1421
0.1735
-0,1375
-0,1327
0.1224
-0,1327
0,1983
A
V
Figure 2.3. Pearson scores dialog for transformation of IVs.
10
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Predictive Modeling at Beaches—Volume II
November 22, 2010
Dependent Variable: logEcoli
Transform dependent variable: O LOG base e
O LOG base 10 Q Clear
D Add column in datable with transformed dependent variable.
Select Different Dependent Variable
View Frequency Plots of Dependent Variable
D LOG e 9 * | Go
D LOG 10 Number of Categories
turbidity
Figure 2.4. Response and IV plots.
Filtering out highly correlatedIVs. 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 =11 (I-
(equation 2.3)
where R\ 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
11
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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 TVs 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 TVs 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 TVs 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
TVs. First, the user takes a collection of all TVs represented in the top few (five or so) models
ranked by GAs then selects the exhaustive method using the TVs collection from step one. In
other words, GAs are used to select a set of potential TVs to be used in the exhaustive search
method.
12
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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 TVs (nowcast), and prediction based
on forecasted values of TVs (forecast). VB 2.0 lets the user either directly enter values of TVs 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).
File Window Help
Beach Location Data Processing Modeling ,' "Prediction |
Selected Model prediction = 5 0743e-001 + 17500e-002':[SQR[(iultdih.;(airiPT,F]]] -:-1 1968e^01UOG[[tuibid^][rocl^ei[low]]l +5.5907e-OOBTSQ[[artemp][cloudsl
II wind and/or current IJ,V component are in your mod?! the data :ojrce column: u:ed to general? then apprear in the gilds.
turbidity
2.95
2.6
ncky rive rflow
43.GS
9.950000000000...
Date / T
Stamp
Clear Input
Make Predictions | | Clear Prediciioi
| Append Inpul |
L
Export
L
| Cleat Seasonal Data |
turbidity
rocky rive rflow A
^^^^^^Q
6/2/200712:00:...
6/3/200712:00:...
6/4/200712:00:...
6/5/200712:00:...
6/6/200712:00:...
6/7/200712:00:...
6/6/200712:00:...
6/9/200712:00:...
6/10/200712:00...
6/11/200712:110
6/12/200712:00...
1.230448921
2.933519253
1.204113903
0.903089907
2.416640587
1.631241237
1.447153031
2.62324929
1.986771734
1.079181246
2.748188027
1.53147B917
6/13/200712:00. 2.612783857
1703
1.617
2.065
1.596
1.584
1.528
2.09
1.808
1.418
1.575
1.304
1.538
1.701
2.95
2.6
43.65
9.95
3.7
13.25
40.78
27.53
6.63
22.05
11.85
7.28
3.83
31
78
78
78
73
72
80
83
88
68
73
71
63
226
167
236
151
109
83
49
47
53
50
30
201
303
Variable Transforms; Done,
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
VBl.O 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.
13
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Predictive Modeling at Beaches—Volume II November 22, 2010
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.
14
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Predictive Modeling at Beaches—Volume II November 22, 2010
• Users no longer have to enter data values in transformed, interacted, or component-
decomposed 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 TVs 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 R 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 = [Ifyi -ytf I (n -p)]°'5 (equation 3.1)
where yt is the ith observation in the data set; yt is the fitted value of the ith observation (found
using the regression model); n is the number of observations in the data set; andp is the number
of estimated parameters in the regression model. The adjusted R 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-
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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.
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Observed Log(Enterococci CPU)
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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 cross-
validation 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 = E(y, - yifit)21 ntrain (equati on 3.2)
where the sum is over all observations in the training data set, yt is the ith observation in that data
set, ytfit 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 MSB, except
that the denominator of the MSB is ntrain minus the number of parameters in the regression
model. We define the MSB of a testing data set as MEP (mean squared error of prediction):
MEP = Ł(y, _ylpred)2 / n,es, (equation 3.3)
where the sum is over all observations in the testing data set, yt 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Because of its large sample size, we performed our analysis on the Huntingdon Beach, Ohio, 2000-
2009 data set. The response variable was E. coli colony forming units (CPU) 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 sizey (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 ofj, 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 R
compared to a much larger data set.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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Figure 3.3. The mean squared error of fitting (MEF) increases with increasing sample size.
21
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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Figure 3.4. The adjusted R 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.
22
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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Figure 3.6. Sample size effect on the MEP/MEF ratio.
23
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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.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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.
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Figure 3.8. Predictive errors increase with increased adjusted R . 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
r\
For intermediate-sized and large samples, no discernible relationship exists between adjusted R
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.
25
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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Figure 3.10. Relationship between adjusted R and MEP for 150 samples of size 200.
26
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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.
2.5
a.
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1.9
2.1
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.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
2.5
a.
LU
2
1.5 -
1 -
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•
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0.35
0.45
0.55 0.65 0.75
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0.85
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.
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Predictive Modeling at Beaches—Volume II
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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 Boqueron, 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).
Atmospheric circulation, winds
Plume Transport
Currents, Wind
Figure 4.1. Processes considered in collecting IVs for predictive modeling studies.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
(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 Boqueron (white pins).
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Predictive Modeling at Beaches—Volume II November 22, 2010
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, highE1. 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.
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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 ofE. 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)
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Predictive Modeling at Beaches—Volume II November 22, 2010
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
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Predictive Modeling at Beaches—Volume II November 22, 2010
(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. coif). 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/nwi s/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 km ) 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).
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Predictive Modeling at Beaches—Volume II November 22, 2010
4.3.2 Surf side Beach, Surf side 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 CPU/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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 and!2 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).
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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 Boqueron Beach, Cabo Rojo, Puerto Rico
Boqueron Beach is in southwestern Puerto Rico, in the town of Boqueron in Cabo Rojo (Figure
4.2B). The 1.6-km-long beach is along the eastern shore of Boqueron 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 250m.
The 2009 PREMIER studies at Surfside Beach and Boqueron 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 Boqueron,
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. Boqueron
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.
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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 Boqueron, 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 Boqueron Bay and at
Surfside Beach.
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November 22, 2010
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
Beach
South Shore
West
Washington Park
Silver
Huntington-EPA
Huntington-USGS
Goddard
Surfside
Edgewater
Fairhope
Hobie
La Monserrate
Boqueron
Water
F
X
X
X
X
X
M
X
X
X
X
X
X
X
X
Climate
TEMP
X
X
X
X
X
SUB
X
X
X
X
X
TROP
X
X
Data source
PREMIER
X
X
X
X
X
NEEAR
X
X
X
X
X
X
X
X
X
USGS
X
YEAR
2008
2003
2004
2004
2003
2000-2009
2007
2009
2005
2007
2008
2008
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 TVs 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
41
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 Boqueron 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 Boqueron 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/ul cd/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 Boqueron Bay, where we deployed two ADCPs, one ADCP was
deployed at each beach. A University of Puerto Rico-Mayagiiez ADCP was also installed at the
Boqueron Bay site.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
A
B
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.
43
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Predictive Modeling at Beaches—Volume II
November 22, 2010
A B
Figure 4.4. Location of 2009 PREMIER/NEEAR study at (A) Boqueron 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 (YSI6600V2-2) 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 (51 Ah), 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(X)). Kd values
were estimated from the irradiance measured at the top and bottom sensors, assuming
exponential decrease with increasing depth. The Kd(X) value is the slope of a natural log plot of
irradiance versus depth.
44
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 (|im) filtered
water samples, using a Perkin-Elmer LAMBDA™ 35 UV/Vis Spectrophotometer. Measured AX
were used to calculate absorption coefficients (i.e., ax = 2.303(Ax/Ł) where L is the path length in
m) at 350 nm.
45
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Predictive Modeling at Beaches—Volume II November 22, 2010
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46
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Predictive Modeling at Beaches—Volume II November 22, 2010
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. coll CFU
data for 2000-2009 from Huntington Beach, Ohio (Section 4.2.5). FIB data are primarily log-
normally distributed, so we always logic 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. la (significant IVs) and 5. Ib (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. la 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 R 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.
47
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs) 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 R exceeded that of the CPU model for only one
of four data sets where nearly equal numbers of qPCR and CPU 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 CPU 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.
48
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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
(ax'
+ bx + c). The response variable is the Iog10 of enterococci levels except for the E.coli data set for Huntington Beach, Ohio.
Beach Location Response
qPCR
South Shore Milwaukee, Wl
CFU
Independent Variables
Turbidity
P
'Vrtecedent Rainfall
P
-
CO
arometric Pressure
P
# of Svuimmers
Air Temperature
AVater Temperature
Wave Height
Aflnd V-Component
Wind Speed
Dewpoint
P
Wind U-Component
# of Boats
-
AJgae
Dissolved Oxygen
_
-
Chlorophyll
Cloud Cover
-
-
Debris
Nearby River Flow
# of Dogs
P
!Ł:
ongshore Currents
# of Birds
P
o
D
1
red Organic Carbon
CondLlctivity
+ +
Total Appearances per Independent Variable
'A'ashington Park Michigan Citv. IN
S7444333333222221 1 1 1 1 1
49
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Predictive Modeling at Beaches—Volume II
November 22, 2010
Table 5.1 b. Summary statistics for the MLR models for freshwater beach sites. The response variable is the Iog10 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.
b
CD
s <
Si 2, $••
r o Si
0 (0 CD
" - 3D « m >
— CO , CD T3 P-j
00 < Cfi g Ł| 0
CJ F" S S " " ™
Beach Location
South Shore Milwaukee, Wl
H u ntin gto n B ay Villa ge, 0 H
Washington Park Michigan City, IN
Silver St. Joseph, Ml
West Porter, IN
Response
qPCR
CPU
qPCR
CPU
CPU (2003 Ł. coU )
CFU(Ł.coH}
qPCR
CPU
qPCR
CPU
qPCR
CPU
n
81
79
44
45
46
709
cc
6€
58
58
49
*9
c
2.05
1
.2c
2.25
1
1
1
1
1
1
1
.85
.69
.71
.4?
.41
.45
.48
2.02
O.S7
-
us
C.
C
0.
C.
0.
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75
79
57
63
0.66
C.
0.
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C.
C.
?2
54
44
67
Sc
m
C
C
0
0
0
0
C
C
0
0
C
.:-
.::
42
.48
.35
.47
.69
.24
.41
.36
.41
0.4
3 •<
C
C
.39
.56 7/13
0.69
0.62 22/23
0
0
.54 2/5
.44 35/115
— I J
-=: -?:
_
66/66 73/79
- -
20/22 42/45
39/41 41/46
587/594 622/709
0.2
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.41
0.32 4/14
C
C
.63
.78 1/3
61*1 63J67
40/44 44/58
_
44/46 4 = .'; =
50
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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 Iog10 of Enterococcus CPU or qPCR measures.
Total Appearances per Independent Variable
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Predictive Modeling at Beaches—Volume II
November 22, 2010
Table 5.2b. Summary statistics for the MLR models for marine beach sites. The response variable is the Iog10 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.
Beach
Response n
0
d
55
o
CD
•=:
o
III!
DO
Ł1
m
a
bL
CO
3
Sensi
Speci
curacy
Edge water
Goddard
La Monseratte
SurfskJe
Biloxi, MS
West Warwick, Rl
Puerto Rico
Myrtle Beach, SC
qPCR 55
CPU 55
qPCR 66
CPU 66
qPCR 69
CPU 69
qPCR 17
CPU 97
qPCR 24
CPU 32
qPCR 79
CPU 44
qPCR 40
CPU S5
2-2
0.69
2.09
1.07
1.71
0.55
2.0S
0.33
1.63
C.5
2.05
0.99
1.99
0.72
0.4S
0.7S
0.61
0.75
0.77
0.75
0.11
0.52
0.62
0.76
0.33
O.E-7
0.67
O.ES
0.57
0.49
0.57
0.7
0.6
0.06
0.47
0.59
0.29
0.43
0.43
0.43
0.14
0.43
0.35
0.43
0.1S
0.36
0.67
0.19
0.45
0.41
0.23
0.43
0.6S
0/1
0/1
E2/E2
31/31
0/2
42.>'43
&2./S3.
E3/EE
so/se
96/97
31/32
42/44
S3/SE
52
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Predictive Modeling at Beaches—Volume II November 22, 2010
5.3 COMPARISON OF MLR MODELING RESULTS ACROSS FRESHWATER
AND MARINE SITES
r\
Comparisons of the MLR modeling results indicate that, on the basis of adjusted R values for
predicted versus observed levels of the FIB, model performance was better for the freshwater
beaches than for the marine beaches (Tables 5. Ib 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. Ib and 5.2b; CFU average adjusted R = 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
53
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 (CPU) 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
CPU 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.
54
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Predictive Modeling at Beaches—Volume II
November 22, 2010
Table 5.3. Summary of variables used for modeling beach sites.
Data set
South Shore
^•H
Huntington
Washington Park
Silver
West
Edge water
Fairhope
Goddard
Hobie
La Monseratte
Boqueron
Surfside
Location
Milwaukee, Wl
^^^^H
Bay Village, OH
Michigan City, IN
St. Joseph, Ml
Porter, IN
Biloxi, MS
Mobile, AL
West Warwick, Rl
Miami, FL
Puerto Rico
Puerto Rico
Myrtle Beach, SC
Response
QPCR
CFU
QPCR
CFU
CFU (2003 E. coli)
CFU (E. coli)
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
QPCR
CFU
Independent Variables
/Antecedent Rainfall
Chlorophyll
Turbidity
0 » •
• • •
• »
• «
• c
• •
o o
o o
o c-
• o
•
0
o
0
o
o o o
• • o
o o •
o • o
coo
• o o
• «
0 *
Conductivity /Salinity
•
o
o
o
o
•
o
•
c
•
Swimmers/Bathers
*
*
o
•
o
o
o
o
0
o
0
0
o
*
o
*
Water Temperature
Absorbance
Current Direction
o o o
• O 0
o
0
0
o
*
•
c
0
*
*
*
o
o • o
0 O 0
• • o
o o o
o *
o o
• 0
0 0
Nearby River FlovJ
•
0
o
o
Devipoint
o
•
o
o
o
o
•
•
•
0
0
o
o
o
o
o
o
o
0
^ CO
(t (fl
C 0
C 0
0 0
• c
o
0 O
* o
o o
• 0
0 0
0 •
0 0
c •
•
c
o
'T:
=
nalWlnd Components
c
•
0
0
0
o
t
o
o
o
o
0
o
0
0
o
o
o
o
*
o
o
0
— r
— i
en
ID
o
c
0
0
Q
o
o
•
o
0
o
•
0
0
o
o
o
o
o
o
o
0
Wave Height
Barometric Pressure
o o
• o
o
0
0 •
c »
o o
o o
• 0
o o
• 0
o
0 0
O 0
0 0
0 0
c
o
0
o
o o
c o
o o
• *
CD
o
Ł.
H
•
*
o
o
o
o
•
o
o
o
0
c
0
0
•
o
o
c
•
Wind Speed
o
c
o
c
o
•
•
o
c
0
•
o
c
0
c
o
c
o
0
Relative Humidity
Dissolved Oxygen
* 0
» 0
0
o
o
o
c
0
•
0
o
0 •
0 •
o o
o o
0 O
o o
o •
0 0
c
a
ensity/Solar Radiation
Cloud Cover
c
c
•
0
o c
• o
o
o
o
o
* 0
o •
0 •
o o
0 0
O 0
c »
O 0
o
0
• 0
C 0
O 0
0 0
o
o
U)
0
0
c
•
o
o
o
0
o
0
0
Water Depth/Tides
Debris
o
c
o
*
0
0
o
o
0
c
0
o
0 0
o o
* 0
c •
c
o
o
•
* 0
o o
O 0
0 C
o
H
k) ro ho
to k> ro to to
Notes: O = 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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Predictive Modeling at Beaches—Volume II
November 22, 2010
Table 5.4. Importance ratings for IVs at freshwater versus marine sites.
Independent Variable Freshwater Rating [independent Variable
Chlorophyll 1,00
Dissolved Oxygen 1.00
Turbidity 0.67
Antecedent Rainfall 0.58
Conductivity/Salinity 0.50
Swimmers/Bathers 0.50
Current Direction 0.50
Nearby River Flow 0.50
Dissolved Organic Carbon 0.50
B a ro metric Press u re 0.40
Dewpoint 0.38
Boats 0.38
Wind Speed 0.38
Algae 0.33
Directional Wind Components 0.33
Air Temp 0.33
Water Temperatu re 0.30
Wave Height 0.25
Cloud Cover 0.25
Dogs 0.17
Birds 0.13
Debris 0.13
Absorbance 0.00
Relative Humidity 0.00
UV Intensity/Solar Radiation 0.00
Water Depth/Tides 0.00
pH 0.00
Visibility 0.00
Nitrate/Nitrite 0.00
Jellyfish
Marine Rating
Turbidity 0.38
Conductivity/Salinity 0.38
Absorbance 0.38
Birds 0.38
Chlorophyll 0.33
Relative Humidity 0.33
Antecedent Rainfall 0.29
'Water Temperatu re 0.29
Current Direction 0.25
UV Intensity/Solar Radiation 0.21
Swimmers/Bathers 0.20
Wave Height 0.20
Debris 0.20
Dew point 0.17
Algae 0.17
Cloud Cover 0.17
Dogs 0.17
Water Depth/Tides 0.17
Directional Wind Components 0.14
Air Temp 0.14
pH 0.13
Boats 0.10
Barometric Pressure 0.08
Wind Speed 0.08
Nearby River Flow 0.00
Dissolved Oxygen 0.00
Dissolved Organic Carbon 0.00
Jellyfish 0.00
Visibility
Nitrate/Nitrite
Independent Variables
Fresh - Marine Rating
Dissolved Oxygen 1.00
Chlorophyll 0.67
Dissolved Organic Carbon 0.50
Nearby River Flow 0.50
B a ro metric Press u re 0.32
Swimmers/Bathers 0.30
Antecedent Rainfall 0.30
Wind Speed 0.29
Turbidity 0.29
Boats 0.28
Current Direction 0.25
Dewpoint 0.21
Air Temp 0.19
Directional Wind Components 0.19
Algae 0.17
Conductivity/Salinity 0.13
Cloud Cover 0.08
Wave Height 0.05
Water Temperatu re 0.01
Dogs 0.00
Debris -0.08
pH -0.13
Water Depth/Tides -0.17
UV Intensity/Solar Radiation -0.21
Birds -0.25
Relative Humidity -0.33
Absorbance -0.38
Jellyfish
Nitrate/Nitrite
Visibility
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.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
Table 5.5. Importance ratings for IVs
Independent Variable
for cultivable (CPU) versus qPCR data.
CPU Rating [independent Variable
Chlorophyll 0.75
Turbidity 0.67
Conductivity/Salinity 0.60
Swimmers/Bathers 0.56
Algae 0.50
Barometric Pressure 0.40
Birds 0.3-8
Antecedent Rainfall 0.33
Current Direction 0.33
Dewpoint 0.33
Dogs 0.33
Water Depth/Fides 0.29
Directional Wind Components 0.25
Boats 0.22
Relative Humidity 0.22
Wave Height 0.20
Wind Speed 0.20
Dissolved Oxygen 0.20
Water Temperatu re 0.17
UV Intensity/Solar Radiation 0.11
Debris 0.11
pH 0.11
Cloud Cover 0.10
Air Temp 0.08
Absorbance 0.00
Nearby River Flow 0.00
Dissolved Organic Carbon 0.00
Visibility 0.00
Jellyfish 0.00
Nitrate/Nitrite 0.00
qPCR Rating
Absorbance 0.60
Nearby River Flow 0.50
Antecedent Rainfall 0.42
Water Temperatu re 0.42
Turbidity 0.33
Current Direction 0.33
Air Temp 0.33
Cloud Cover 0.30
Chlorophyll 0.25
Boats 0.22
Relative Humidity 0.22
UV Intensity/Solar Radiation 0.22
Debris 0.22
Conductivity/Salinity 0.20
Wind Speed 0.20
Dissolved Oxygen 0.20
Dissolved Organic Carbon 0.20
D irectio n a I Wind Co mp o nents 0.17
Birds 0.13
S vv immers/B athers 0.11
Dew point 0.11
Wave Height 0.10
Algae 0.00
Barometric Pressure 0.00
Dogs 0.00
Water Depth/Tides 0.00
pH 0.00
Visibility 0.00
Jellyfish 0.00
Nitrate/Nitrite 0.00
Independent Variable
CFU-qPCR Rating
Chlorophyll 0.50
Algae 0.50
Swimmers/Bathers 0.44
Conductivity/Salinity 0.40
Barometric Pressure 0.40
Turbidity 0.33
Dogs 0.33
Water Depth/Tides 0.29
Birds 0.25
Dewpoint 0.22
pH 0.11
Wave Height 0.10
Directional Wind Components 0.08
Current Direction 0.00
Boats 0.00
Wind Speed 0.00
Dissolved Oxygen 0.00
Relative Humidity 0.00
Visibility 0.00
Jellyfish 0.00
Nitrate/Nitrite 0.00
Antecedent Rainfall -O.OS
UV Intensity/Solar Radiation -0.11
Debris -0.11
Cloud Cover -0.20
Dissolved Organic Carbon -0.20
Water Temperatu re -0.25
Air Temp -0.25
Nearby River Flow -0.50
Absorbance -0.60
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 CPU rating.
Variables at the top of this list are relatively much more important for CPU 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 CPU data would appear in the middle of this last list.
57
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Predictive Modeling at Beaches—Volume II November 22, 2010
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Predictive Modeling at Beaches—Volume II November 22, 2010
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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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs.
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).
Model Duration Adj. R2 SE CE FN FP
21-Day Models
28-Day Models
35-Day Models
42-Day Models
49-Day Models
50.0
45.7
61.0
53.0
60.7
1.22
1.08
0.99
1.00
0.89
9
8
12
11
11
6
8
4
5
5
0
1
2
2
2
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 TVs. The TVs 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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Predictive Modeling at Beaches—Volume II
November 22, 2010
Independent Variables
Model Duration
21-Day Models
28-Day Models
35-Day Models
42-Day Models
49-Day Models
Start Day
14-Jul
Zl-Jul
28-Jul
4-Aug
11-Aug
18-Aug
25-Aus
14-Jul
Zl-Jul
ZB-Jul
4-Aug
11-Aug
18-Aug
25-Aus
14-Jul
Zl-Jul
ZB-Jul
4-Aug
11-Aug
18-Aug
25-Aus
14-Jul
Zl-Jul
ZB-Jul
4-Aug
11-Aug
18-Aug
25-Aug
14-Jul
21-Jul
2B-Jul
4-Aug
11-Aug
18-Aug
25-Aug
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.
61
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Predictive Modeling at Beaches—Volume II November 22, 2010
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.
r\
Moreover, adjusted R 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 R was 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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Predictive Modeling at Beaches—Volume II November 22, 2010
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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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs (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. Logic 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 (Y2ooi-Y 2009)-
Miprev M2prev M3prev M4prev M5prev M6prev M7prev M8prev M9prev
Y
Y
Y
Y
Y
Y
Y
Y
Y
2001
2002
2003
2004
2005
2006
2007
2008
2009
MSEU
MSE2;1
MSE3:1
MSE4;1
MSE5;1
MSE6>1
MSE7;1
MSE8;1
MSE91
MSE
MSE
MSE
MSE
MSE
MSE
MSE
MSE
2,2
3,2
4,2
5,2
6,2
7,2
8,2
9,2
MSE
MSE
MSE
MSE
MSE
MSE
MSE
3,3
4,3
5,3
6,3
7,3
8,3
9,3
-
MSE
MSE
MSE
MSE
MSE
MSE
4,4
5,4
6,4
7,4
8,4
9,4
-
-
MSE5;5
MSE6;5
MSE7>5
MSE8;5
MSE95
-
-
-
MSE6>6
MSE7j6
MSE8>6
MSE9>6
-
-
-
-
MSE7>7
MSE8>7 MSE8>8
MSE9;7 MSE98 MSE99
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 Miprev because it was based on one previous years'
worth of data. We would then record the MSE of those predictions in row "Ą2005," column
"Miprev" 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.
Y2ooo 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 TVs (X) and corresponding E.
coli measurements (Y). Those are labeled as (X20oo, Y20oo), (X2ooi, Y20oi), ..., (X2oo9,Y2oo9). 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 M2ooo, M2ooi, ..., M2oo9-
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).
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Predictive Modeling at Beaches—Volume II
November 22, 2010
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.
2000
2001
M9n
M9n
2004
M9n
M9n
2007
M9n
M9n
(X-2000
(X2001
(X2002
(X2003
(X2Q04
(X2005
(X2006
(X2007
(X2008
(X2009
Y2000)
Y200l)
Ą2002)
Y2003)
^2004)
Y2005)
^2006)
^2007)
^2008)
^2009)
MSEU
MSE2J
MSE3)1
MSE4J
MSE5J
MSE6J
MSE7J
MSE8J
MSE9J
MSE10J
MSEU
MSE2,
MSE3)
MSE4)
MSE5)
MSE6^
MSE7)
MSE8)
MSE9)
MSE10
MSE13
MSE2)3
MSE33
MSE43
MSE53
MSE6)3
, MSE7)3
, MSE8)3
i MSE9 3
2 MSE10)3
MSE1)4
MSE2,4
MSE3)4
MSE4)4
MSE5)4
MSE6)4
MSE7)4
MSE8)4
MSE9)4
MSE10)4
MSE1)5
MSE2)5
MSE3)5
MSE4)5
MSE5)5
MSE6)5
MSE7)5
MSE8)5
MSE9)5
MSE10)5
MSE1>6
MSE2,6
MSE3)6
MSE4>6
MSE5)6
MSE6)6
MSE7>6
MSE8)6
MSE9)6
MSE10)6
MSEU7
MSE2J
MSE3J
MSE4J
MSE5J
MSE6J
MSE7J
MSE8J
MSE9J
MSE10J
MSE1)8
MSE2,8
MSE3)8
MSE4)8
MSE5)8
MSE6)8
MSE7)8
MSE8)8
MSE9)8
MSE10)8
MSE1>9
MSE2,9
MSE3)9
MSE4>9
MSE5)9
MSE6>9
MSE7)9
MSE89
MSE99
MSE10)9
MSEUO
MSE2,10
MSE3)10
MSE4)10
MSE5)10
MSE6)10
MSE7)10
MSE8)10
MSE9)10
MSE10JO
For example, using the model developed from X2002, Y2002 data (M2002), plugging in the X2004 IVs
and taking the MSB of the fit of this model compared to the actual Y2oo4 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).
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table 7.3. Results of modeling the MSEs of Table 7.1.
Miprev M2prev M3prev M4prev M5prev M6prev M7prev M8prev M9prev
Y20oi
Y2002
Y2003
Y2004
Y2005
Y2006
Y2007
Y2008
Y2009
2.39
2.99
3.21
1.64
2.84
1.92
1.23
1.62
0.77
-
2.12
1.91
1.77
1.88
1.92
1.17
1.20
0.67
-
-
1.53
1.44
2.04
1.70
1.24
1.16
0.67
-
-
-
1.60
2.02
1.82
1.28
1.02
0.66
-
-
-
-
1.92
1.67 1.78
1.19 1.26
1.15 1.22
0.67 0.64
-
-
-
-
-
-
1.20
1.13 1.09
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
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.
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Predictive Modeling at Beaches — Volume II November 22, 2010
Table 7.4. Results of modeling the MSEs of Table 7.2.
M2000 M2001 M2002 M2003 M2004 M2005 M2006 M2007 M2008 M2009
(X2000>Y2ooo)
(X2001>Y2ooi)
(^2002^2002)
(^2003^2003)
(^2004^2004)
0^2005^2005)
(^2006^2006)
(^2007^2007)
(^2008^2008)
(^2009^2009)
Mean
0.56
2.39
3.49
2.71
2.14
6.79
3.22
4.24
4.84
2.72
3.31
2.03
1.26
3.15
1.74
1.82
3.05
2.74
2.19
1.20
0.94
2.01
1.97
2.42
1.27
1.76
2.25
2.56
2.11
1.93
3.08
2.24
2.16
1.42
1.94
2.44
0.61
1.62
1.97
1.90
1.81
1.50
1.12
1.63
2.43
2.64
2.27
1.46
1.26
2.84
2.15
1.54
1.32
0.74
1.86
1.79
1.99
2.36
0.83
1.96
1.69
1.92
1.86
1.88
1.09
1.74
1.56
1.98
2.70
1.39
2.49
2.22
1.21
1.23
1.13
1.31
1.72
1.39
2.62
2.19
1.23
1.64
2.93
1.92
0.77
1.62
1.08
1.74
1.07
1.62
2.77
1.67
2.67
2.68
1.77
1.20
0.72
0.77
1.70
0.99
1.68
2.06
0.95
1.87
2.34
1.52
1.14
0.93
0.52
1.40
1.52
2.05
2.47
1.44
1.97
2.91
2.05
1.79
1.82
1.25
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 MSB. 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 MSB 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 MSB 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
7.4 CONCLUSIONS
Using MLR modeling on a series of annual data sets (2000-2009) for Huntingdon 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-l and T+l, 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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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs 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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Predictive Modeling at Beaches—Volume II
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Table 8.1. Environmental variables used in model development
Variable Description
Data Source
Type
Data Collection
Duration Frequency
Absorption Coefficient (325 nm) . .
Dissolved Organic Carbon
Water Temperature
Conductivity
Salinity
Dissolved Oxygen
T uH,r.K 7/17-10/18
Turbidity
EPA Sonde SS Chlorophyll
Ammonium
Ammonia
Nitrate
Current Speed
Current Direction 7/17 - 10/21
Water Depth
Wave Height 7/17-10/21
Wave Direction
EPA UV Sensor SS Attenuation Coefficient (325 nm) 7/17 . 10/22
Mean Attenuation at 0.3 meters (325 nm)
9:00, 11:30, 15:00
Every 15 minutes
Every 10 minutes
Every 60 minutes
Every 60 minutes
EPA Weather Station
SS
Solar Radiation
Photosynthetic Active Radiation
Wind Speed
Wind Direction
Gust Speed
Cumulative 48hr Rainfall
Air Temperature
Humidity
Dewpoint
Pressure
7/21-10/18 Every 15 minutes
UW Sonde SS
Water Temperature
Conductivity
pH
Dissolved Oxygen
Chloride
Turbidity
7/17 - 10/19 Every 30 minutes
UW Weather Station SS
Air Temperature
Cumulative 48hr Rainfall
Wind Speed
Wind Direction
7/17 - 10/19 Every 60 minutes
General Mitchell Airport PA
Visibility
Dry Bulb Temperature
Wet Bulb Temperature
Dewpoint
Humidity
Wind Speed
Wind Direction
Barometric Pressure
Pressure at Sea Level
Cumulative 48hr Rainfall
Altimeter Pressure
7/1 - 9/30 Every 60 minutes
USGS
PA
Flow at Mouth of Milwaukee River
6/25 - 8/28 Once per day
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Predictive Modeling at Beaches—Volume II November 22, 2010
developing models based on both data sets. If correlated TVs 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 CPUs
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 one-
observation-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 = P™b (T> \y - log(S)] / Sy)
where Thas the Student's t distribution with n p degrees of freedom (n is the number of
observations in the data set and/? is the number of estimated regression parameters), y is the
predicted value of the logarithm of the FIB count and s_p is the standard error of this prediction.
We could alternatively define a probability threshold (e.g. 30 percent), such that any y whose
corresponding P exceed surpasses the threshold (meaning)) has a greater than 30 percent chance of
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Predictive Modeling at Beaches—Volume II November 22, 2010
exceeding log[<5]) 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 TVs 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:
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept)
Dewpoint
Wind U-Component
Barometric Pressure
Cumulative 48-hr Rainfall
-52.4
0.020
-0.018
1.79
104.7
9.96
0.01
0.01
0.33
14.02
-5.26
2.40
-2.91
5.38
7.47
< 0.001
0.019
0.005
< 0.001
< 0.001
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 Data Source Coefficient Std. Error t-Statistic P-Value
Intercept
Cumulative 48-hr Rainfall
PH
Dissolved Oxygen
Nitrate
Mean Attenuation Coefficient (0.3m)
Wind U-Component
Water Depth
PA- Airport
SS-EPASonde
SS - UW Sonde
SS - EPA Sonde
SS - EPA Sensor
PA- Airport
SS - EPA Sonde
-12.12
94.38
0.65
-0.21
0.20
-0.04
-0.02
3.74
2.73
12.67
0.24
0.03
0.06
0.01
0.01
0.64
-4.44
7.45
2.70
-6.25
3.43
-3.43
-3.00
5.83
< 0.001
< 0.001
0.0087
< 0.001
0.001
0.001
0.0037
< 0.001
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Predictive Modeling at Beaches—Volume II
November 22, 2010
The adjusted R 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.
z.o -
27 -
26 -
2.5 -
2.4 -
-J 0 .
JL.J
2.2 -
2.1 -
— 2 -
2 1.9 -
0 18-
l«:
g 1 .6 -
«j 1.5 -
Ł 1-4 -
'ra 1 3 -
1 1-2"
^ 1 -
=5
Ł 09 -
°- 0.8 -
0.7 -
0.6 -
0.5 -
04 -
0.3 -
0.2 -
0.1 -
n
• PA+SS Predictions
* PA Predictions
False
Positives
Decision Threshold = 1,78
. •
•' * /*%
. f * *
A • , •*
A " • •
• *" ,A*> " •.* .* "**
***" *«A* ^?1 t i **
» " * i**. **
• • * i
• * /»
* . * * i
•
. " *
4
Correct
Negatives
.
i
4
. Coirect
. *• Positives
.•
A
A
• •
* False
Negatives
&
Regulatory
Standard = 1.78
*•-*"
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.B 1.9 2 2.1 2.2 2.3 2.4 2.S 2.6 2.7 2.8 2.8 3 3.1
Observed Log(Errterococci CPU)
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.
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Predictive Modeling at Beaches—Volume II
November 22, 2010
0.9 :
o
'0 o.s g
o
§ 0.7
LU
s 0.6 q
a
o
0.5
0.4 :
LU
o 0.3
0.2 :
0.1 :
0
• PA+SS Predictions
* PA Predictions
False
Positives
Probability Threshold =70%
Correct
Negatives
Correct
Positives
Regulatory
Standard = 1.78
False
Negatives
0.5
1.5 2 2.5
Observed Log(Enterococci CPU)
i.5
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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table 8.2. Results of the threshold analysis for the PA and PA+SS models.
Model Threshold Type Threshold CN FP Specificity CP FN Sensitivity
Log(30)
Count Log(61)
Log(lOO)
p *i
30%
Probability 50%
70%
Log(30)
Count Log(61)
Log(lOO)
PA I *?*?
30%
Probability 50%
70%
59
66
66
66
66
66
62
66
66
66
66
66
7
0
0
0
0
0
4
0
0
0
0
0
0.894
1.000
1.000
1.000
1.000
1.000
0.939
1.000
1.000
1.000
1.000
1.000
10
7
4
8
7
6
11
9
4
9
8
8
3
6
9
5
6
7
2
4
9
4
5
5
0.769
0.538
0.308
0.615
0.538
0.462
0.846
0.692
0.308
0.692
0.615
0.615
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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 R 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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Predictive Modeling at Beaches—Volume II November 22, 2010
9 Advanced Techniques to Refine MLR Model
Results
9.1 INTRODUCTION TO TEMPORAL SYNCHRONIZATION
For most TVs 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
9.2 TEMPORAL SYNCHRONIZATION AT SOUTH SHORE BEACH
9.2.1 Methods
One site where we applied ISA 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, NFL;,
NOs, 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 sub-
groups
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.
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Predictive Modeling at Beaches—Volume II
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1.8
1.6
-Synchronized using Correlation
- Unsynchronized
51 101 151 201 251 301 351
Random Dataset Number
401
451
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 coefficient-
selected IV aspects, PCC) and unsynchronized data (DNS). The natural logarithm of Enterococcus
CFU measurements were modeled in this study.
95% Confidence Interval on the Mean
Metric
MEF
MEP
Dataset
UNS
PCC
UNS
PCC
PRS
Mean
0.795
0.513
3.670
2.710
1.850
St Dev.
0.206
0.137
4.990
1.290
0.940
Lower Bound
0.777
0.501
3.230
2.590
1.760
Upper Bound
0.813
0.525
4.110
2.820
1.930
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Predictive Modeling at Beaches—Volume II
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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.
JD
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60
50
40
30
CO
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-Synchronized using PRESS
• Unsynchronized
1 51 101 151 201 251 301 351 401 451
Random Dataset Number
Figure 9.2. A comparison of the 500 MEP values for the PRS data and the UNS data.
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Predictive Modeling at Beaches—Volume II
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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).
60
50
0) _
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0 E
o Ł
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OJ
TO
40
30
Ł=
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20
10
- Unsynchronized
-Synchronized using Correlation
1 51 101 151 201 251 301 351 401 451
Random Dataset Number
Figure 9.3. A comparison of the 500 MEP values for the PCC data and the UNS data.
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Predictive Modeling at Beaches—Volume II
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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.
•Synchronized using PRESS
-Synchronized using Correlation
51 101 151 201 251 301 351
Random Dataset Number
401
451
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.
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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 CPU 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 ISA of the TVs. 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 TVs, 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 TVs. 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 TVs), 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=(yl-y_[)/S_lxhl?'5
where j); is the predicted value of the rth observation, y.\ is the predicted value of the /'th
observation computed after removing the rth observation from the data, s.[ is the standard error of
j>_i, and Mi is the leverage of the rth 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 R 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
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Predictive Modeling at Beaches—Volume II
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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.
1.2 -i
tt
(0
I
Z
"(3
•o
•«
V
0.8
0.5
O. 0.4 -
(N
v
tn 0.2
* Adjusted R-squared
• P-value
20
40
60
SO
100
120
Number of Observations Removed from the Dataset
Figure 9.5. Effects on the regression adjusted R 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
R 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?
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 TVs as used for the regression models but focus on finding a combination of
TVs 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 TVs—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 TVs. 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.
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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 NO A A-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 Melendez 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
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 Boqueron, able
assistance was provided by Milton Carlo and Ernesto Otero-Morales of University of Puerto
Rico- Mayaguez; Angel Melendez 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.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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Schwab, and J.B. Rose. 2006. Modeling the transport and inactivation of E. coli and
Enterococci in the near-shore region of Lake Michigan. Environmental Science and
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McLellan, S. 2004. Sources ofE. coli at South Shore Beach Final Research Report. Great Lakes
WATER Institute, Milwaukee, WI.
McLellan, S.L., A.D. Daniels, and A.K. Salmore. 2001. Clonal populations of thermotolerant
enterobacteriaceae in recreational water and their potential interference with fecal
Escherichia coli counts. Applied and Environmental Microbiology. 67(10):4934-4938.
McLellan, S.L., EJ. Hollis, M.M. Depas, M. Van Dyke, J. Harris, and C.O. Scopel. 2007.
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McLellan, S.L., andE.T. Jensen. 2005. Identification and Quantification oj'Bacterial Pollution
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McLellan, S.L., and A.K. Salmore. 2003. Evidence for localized bacterial loading as the cause of
chronic beach closings in a freshwater marina. Water Research 37(11):2700-2708.
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Predictive Modeling at Beaches—Volume II November 22, 2010
McQuarrie, A., and C.L. Tsai. 1998. Regression and Time Series Model Selection. World
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2002. Fecal Coliform TMDLfor the Back Bay ofBiloxi andBiloxi Bay. Mississippi
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Mednick, A., and D. Watermolen. 2009. Beach pathogen forecasting tools: Pilot testing,
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Bacterial exceedances in marine and freshwater creeks/outfall samples, October 2002-
April 2005. Marine Pollution Bulletin 52(10): 1270-1277.
Nevers, M.B., D.A. Shively, G.T. Kleinheinz, C.M. McDermott, W. Schuster, V. Chomeau, and
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a peninsular beach complex of Lake Michigan. Journal of Environmental Quality
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multiple urban beaches of southern Lake Michigan. Water Research 39:5250-5260.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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the water quality of a subtropical non-point source recreational beach. University of
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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 [km ]) 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.I). 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 coll 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.I).
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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.
Water Body
Location
Possible Sources
Beach Length
Data Source
Sampling Frequency
South Shore
L. Michigan
Wisconsin
Runoff
Birds
150 m
MCHD
4-7 /wk
Rocky
L. Michigan
Wisconsin
Runoff
Birds
200 m
MCHD
1-4 /wk
West
L. Michigan
Indiana
Effluent
Burns Ditch
2000 m
IDEM
1 /wk
Ogden Dunes
L. Michigan
Indiana
Effluent
Burns Ditch
2000 m
IDEM
3-7 /wk
Washington Park
L. Michigan
Indiana
Effluent
Trail Creek
1100 m
IDEM
3-7 /wk
Silver
L. Michigan
Michigan
Effluent
St. Joseph R.
600 m
MDEQ
1-2 /wk
Huntington
L. Erie
Ohio
Effluent
Porter Creek
Rocky River
500 m
CCBH
3-7 /wk
Year
> 235
Water Quality Criteria for E. coli (CPU / 100 mL) and Number of Exceedances
> 235
> 235
> 235
> 235
> 300
> 235
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TOTAL
36/124 (29)
63/120 (53)
56/117 (48)
27/87 (31)
36/53 (68)
27/54 (50)
16/50 (32)
320/949 (34)
18/114 (16)
18/118 (15)
4/15(27)
11/54 (20)
6/28 (21)
2/15(13)
59/344 (17)
0/10
0/15
0/25
(0)
(0)
(0)
2/104
2/77
1/45
10/73
1/48
0/68
(2)
(3)
(2)
(14)
(2)
(0)
16/415 (4)
18/107
13/49
24/57
(17)
(27)
(42)
7/48 (15)
10/48
72/309
(21)
(23)
1/21(5)
0/13(0)
0/11(0)
0/20 (0)
0/14 (0)
0/15(0)
0/14 (0)
0/15(0)
0/15(0)
1/138 (1)
Data sources: South Shore Beach (http://www.wibeaches.us). Ogden Dunes Beach (https://ext ranet.idem.in.gov/beachauard). Washington Park Beach
(https://ext ranet.idem.in.gov/beachguard). Silver Beach (http://www.deg.state.mi.us/beach). Huntington Beach, Ohio (2000-2005 data are from Francy et al.
Darner 2006); 2006-2009 data are from http://www.ohionowcast.info/nowcast huntington.asp).
12/51 (24)
10/50 (20)
11/52(21)
6/54(11)
7/54 (13)
8/58 (14)
26/96 (27)
15/106 (14)
14/106 (13)
10/113 (9)
119/740 (16)
(2006) (Francy and
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Predictive Modeling at Beaches—Volume II November 22, 2010
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. coll 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.I).
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Predictive Modeling at Beaches—Volume II November 22, 2010
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/uv704095090).
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.I). 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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Predictive Modeling at Beaches—Volume II November 22, 2010
The Michigan City Parks Department or LaPorte County Health Department monitor the beach
regularly for E. coll during the 14-week beach season (Memorial Day through Labor Day). Real-
time 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/uv704095380).
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.I). 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)
(C)
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?04101 OOP).
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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 forE1. coli (Table A.I).
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Predictive Modeling at Beaches—Volume II November 22, 2010
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/nwi s/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.
Goddard Surfside Edgewater Fair-hope Hobie
Water Body
Location
Possible Sources
Climate
Beach Length
Data Source
Sampling Frequency
Sampling Period
Greenwich Bay Estuary
Rhode Island
Effluent
Maskerchugg River
temperate
1200 in
RIDH
2-4 /wk
late May to early September
Atlantic Ocean
South Carolina
Runoff
5th Ave. N. Swash
sub-tropical
3400 m
SCDHEC
1 /wk
mid-May to mid-October
Mississippi Sound
Mississipi
Effluent
sub-tropical
MDEQ
1-4 /wk
year round
Mobile Bay
Alabama
Effluent
sub-tropical
600 m
ADEM
2 /wk
year round
Biscay ne Bay
Florida
Runoff
Dogs, Birds
sub-tropical
1600 m
FDOH
2-4 /mo
year round
Year
Water Quality Criteria for Enterococcus (CFU / 100 mL) and Number of Exceedances
> 104
> 104
> 104
> 104
> 104
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
TOTAL
0/28 (0)
8/35 (23)
1/41 (2)
3/49 (6)
7/50 (14)
0/42 (0)
3/35 (0)
8/52(15)
30/332 (9)
14/20 (70)
7/35 (20)
4/31 (13)
25/86 (29)
Data sources: Goddard Beach (http://www.ri beaches. ora/beach.cfm?beachlD=RI81 0609).
11 A, http://www.coms.usm.edu/msbeach/harbmon.cai), Fairhope Beach (http://www.adem
12/70 (17)
18/64 (28)
8/89 (9)
16/91 (18)
11/61 (18)
3/52(6)
68/427 (16)
13/56 (23)
10/58 (17)
8/60 (13)
10/62 (16)
41/236 (17)
Surfside Beach (station 31A, data provided by SCHEC),
. state. al.us/proarams/coastal/beachMonitorina.cnt), Hobi
from Solo-Gabriele et al. (2002); 2001-2009 data are from http://esetappsdoh.doh.state.fl.us/irmOObeachwater).
7/24 (29)
1/27 (4)
3/40 (8)
4/57 (7)
3/55(5)
6/58 (10)
4/56(7)
4/56(7)
2/55 (4)
5/61 (8)
31/484 (6)
Edgewater Beach (station
e Beach (1999-2000 is taken
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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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Predictive Modeling at Beaches—Volume II November 22, 2010
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://giswebOO.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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Predictive Modeling at Beaches—Volume II November 22, 2010
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
(ADEM2010).
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-Bade 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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Predictive Modeling at Beaches—Volume II November 22, 2010
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; 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).
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/irmOObeachwater). 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.
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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 Boqueron Beach, Cabo Rojo, Puerto Rico
Boqueron Beach is in southwestern Puerto Rico, in the town of Boqueron in Cabo Rojo (Figure
4.2B). The 1.6-km-long beach is along the eastern shore of Boqueron 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 Boqueron Beach every other
week during the entire year. Data for the current year are posted on the web
(http://www.prtc.net/~j caagua), but we have not yet analyzed the data. Beachgoers at Boqueron
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.
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Figure A.10. Location of 2009 NEEAR study at Boqueron 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.
La Monserrate
Boqueron
Water Body
Location
Possible Sources
Climate
Beach Length
Data Source
Sampling Frequency
Sampling Period
Luquillo, Puerto Rico
Streams
Runoff
tropical
400 111
PREQB
2x /mo
year round
Boqueron Bay
Cabo Rojo, Puerto Rico
Effluent
Runoff
tropical
1600 m
PREQB
2x /mo
year round
Water Quality Criteria for Enterococcus (CPU / 100 mL) and Number of Exceedances
Year
>35
> 104
> 35
> 104
2006
2007
2008
2009
TOTAL
7/27(26)
4/31(13)
2/14 (14)
13/72(18)
4/27(15)
1/31(13)
1/14(7)
6/72 (8)
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Elmir, S.M. 2006. Development of a water quality model which incorporates non-point
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of recreational water-quality standards at coastal beaches. U.S. Department of the
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Francy, D.S., A.M. Gifford, and R.A. Darner. 2003. Escherichia coli at Ohio Bathing Beaches -
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Frick, W.E., Z. Ge, and R.G. Zepp. 2008. Nowcasting and forecasting concentrations of
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Huang, X., and V. Sigler. 2006. Population-Based Molecular-Tracking of E. Coli at Lake Erie
Beach andHuntington Beach (Ohio). Paper read at the 49th Annual Conference of the
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IDEM (Indiana Department of Environmental Management). 2004. Little Calumet and Portage
Burns Waterway TMDLfor E. coli Bacteria. Final TMDL Report. Indiana Department of
Environmental Management, Indianapolis, IN.
Liu, L., M.S. Phanikumar, S.L. Molloy, R.L. Whitman, D.A. Shively, M.B. Nevers, DJ.
Schwab, and J.B. Rose. 2006. Modeling the transport and inactivation of E. coli and
Enterococci in the near-shore region of Lake Michigan. Environmental Science and
Technology 40:5022-5028.
McLellan, S. 2004. Sources ofE. coli at South Shore Beach Final Research Report. Great Lakes
WATER Institute, Milwaukee, WI.
McLellan, S.L., A.D. Daniels, and A.K. Salmore. 2001. Clonal populations of thermotolerant
enterobactedaceae in recreational water and their potential interference with fecal
Escherichia coli counts. Applied and Environmental Microbiology. 67(10):4934-4938.
McLellan, S.L., E.J. Hollis, M.M. Depas, M. Van Dyke, J. Harris, and C.O. Scopel. 2007.
Distribution and fate of Escherichia coli in Lake Michigan following contamination with
urban stormwater and combined sewer overflows. Journal of Great Lakes Research
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McLellan, S.L., andE.T. Jensen. 2005. Identification and Quantification of 'BacterialPollution
at Milwaukee County Beaches. Great Lakes WATER Institute, Milwaukee, WI.
McLellan, S.L., and A.K. Salmore. 2003. Evidence for localized bacterial loading as the cause of
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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.
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NIRPC (Northwestern Indiana Regional Planning Commission). 2005. Watershed Management
Plan for Lake, Porter, andLaPorte 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
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Schwab, D.J., D. Beletsky, and G.A. Lang. 2010. Indiana Dunes Nowcast 2010. .
. 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.
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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, DJ. 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.
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Wade, T.I, 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
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Whitman, R. 2010. About Project S.A.F.E. 2008.
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Whitman, R., and M. Nevers. 2005. Regional and local factors affecting patterns ofE. 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 enter ococci, 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.
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Appendix B. Additional Data Collection Details
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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-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. 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 Boqueron 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 Boqueron,
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. Boqueron
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 Boqueron,
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-D-
Glucoside (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 23 S 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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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 (Cx ~ 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 ACT 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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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 Boqueron 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
Boqueron 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 Boqueron 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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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 cross-
frame 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 Boqueron Beach to better characterize the hydrodynamics of the bay, as
related to potential contamination sources; one ADCP was deployed at the beach, 55m 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-Mayagiiez 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 along-
shore (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 Boqueron, ADCPs were left
unattended for the duration of the study period.
Water quality sondes. Multi-parameter water quality sondes (YSI6600V2-2) were deployed at
each beach site for the duration of the studies. At South Shore, Surfside, Luquillo, and Boqueron,
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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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 (51 Ah), wireless telemetry
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 jiW 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(X)). Kd values
were estimated from the irradiance measured at the top and bottom sensors, according to the
following equation (Smith and Baker 1981):
,
7n
Eri
Kd(T) = -- -^ - '- (equation B.I)
z2 -Zj
where E<ŁX) is the downwelling irradiance measured at each wavelength (X) 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/CO-
OPS 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 (Ł40.3), the depth at which water was
sampled for bacterial analyses, was calculated from Kd and top sensor irradiance and depth by
rearranging equation B.I.
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 jiL injection volume), gave a
coefficient of variation of < 5 percent.
UV-visible absorption spectra were determined from 200 to 800 nm for 0.2-|im filtered water
samples, using a Perkin-Elmer LAMBDA™ 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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Predictive Modeling at Beaches—Volume II November 22, 2010
referenced against NANOpure water (Barnsted) and then baseline-corrected by adjusting the
absorbance (Ax) to zero between 690 and 710 nm. Measured AX were used to calculate
absorption coefficients (i.e., ax = 2.303(Ax//) where / is the path length in m) at 350 nm.
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Predictive Modeling at Beaches—Volume II November 22, 2010
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Predictive Modeling at Beaches—Volume II November 22, 2010
Appendix C. Regression Modeling Results
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Predictive Modeling at Beaches—Volume II November 22, 2010
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 (ax2 + 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.
Parameter Coefficient Std. Error t-5tatistic P-Value
(Intercept) -3.227 1.221 -2.643 0.010
Chlorophyll 0.012 0.004 2.615 0.011
POLY[Riverflow] 0.893 0.302 2.960 0.004
Conductivity 0.003 0.001 3.098 0.003
48hr Rainfall - Site 1 -0.192 0.079 -2.431 0.018
Dissolved Oxygen -0.060 0.026 -2.288 0.025
Dissolved Organic Carbon 0.001 0.000 2.376 0.020
POLY[48hr Rainfall - Site 2] 0.808 0.251 3.214 0.002
Note: Adjusted R2 = 0.39, RMSE = 0.36, n = 81.
Table C.2. Regression model for South Shore Beach enterococci cultivable data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept)
DIS02 WS
INV[CHL WS]
POLY[PRESSURE AP]
RAIN AP
POLY[CURRENTU ES]
INV[WINDU AP]
POLY[DEW AP]
PGLY[TURBIDITY ES]
0.245
-0.124
0.023
0.762
112.886
0.910
-0.256
-1.440
1.124
0.921
0.035
0.012
0.377
21.692
0.335
0.078
0.418
0.389
0.266
-3.588
2.381
2.025
5.204
2.715
-3.279
-3.447
2.892
0.791
0.001
0.020
0.047
0.000
0.008
0.002
0.001
0.005
Note: Adjusted R2 = 0.56, RMSE = 0.33, n = 79.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table C.3. Regression model for
Parameter
(Intercept)
Turbidity
POLY[# of Boats]
# of Bathers
Cloud Cover
Antecedent Rainfall
Note: Adjusted R2 = 0.69, RMSE = 0.42, n =
Table C.4. Regression model for
Parameter
(Intercept)
Antecedent Rainfall
POLY[Amount of Debris]
Turbidity
# of Bathers
# of Boats
Note: Adjusted R2 = 0.62, RMSE = 0.48, n =
Table C.5. Regression model for
Parameter
(Intercept)
POLY[Air Temp -Dry Bulb]
Air Temp - Wet Bulb
Wave Height
Antecedent Rainfall
INVTTurbidity]
Note: Adjusted R2 = 0.54, RMSE = 0.38, n =
Table C.6. Regression model for
Parameter
(Intercept)
Wave Height
Air Pressure
Acrossshore Wind
Turbidity
Dewpoint
Antecedent Rainfall
Huntington Beach, Ohio, enterococci qPCR data.
Coefficient Std. Error t-Statistic P-Value
-0.871 0.861 -1.011 0.318
0.007 0.002 2.882 0.007
0.783 0.373 2.103 0.042
0.429 0.086 4.972 0.000
0.262 0.047 5.565 0.000
1.200 0.416 2.883 0.007
= 44.
Huntington Beach, Ohio, enterococci cultivable data.
Coefficient Std. Error t-Statistic P-Value
-0.213 0.517 -0.412 0.683
1.961 0.458 4.285 0.000
0.913 0.278 3.288 0.002
0.010 0.002 4.290 0.000
-0.393 0.119 -3.300 0.002
0.377 0.115 3.278 0.002
= 45.
Huntington Beach, Ohio, E.coli cultivable data, 2003.
Coefficient Std. Error t-Statistic P-Value
-1.177 0.996 -1.181 0.245
0.604 0.271 2.231 0.031
0.026 0.013 2.027 0.049
0.213 0.072 2.967 0.005
21.413 8.386 2.553 0.015
-1.454 0.580 -2.508 0.016
= 46.
Huntington Beach, Ohio, E.coli culturable data, 2000-2009.
Coefficient Std. Error t-Statistic P-Value
14.535 3.790 3.835 0.000
0.147 0.024 6.064 0.000
-0.491 0.129 -3.812 0.000
-0.014 0.003 -4.390 0.000
0.009 0.001 9.346 0.000
0.019 0.003 7.489 0.000
24.702 3.423 7.217 0.000
Note: Adjusted R2 = 0.44, RMSE = 0.47, n = 709.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table C.7. Regression model for Washington Park
Note:
Parameter
(Intercept)
Wave Height
POLY[AirTernp]
POLY[Turbidity]
Adjusted R2 = 0.20, RMSE = 0.59, n = 66.
Coefficient
-0.622
-0.566
0.733
0.824
Table C.8. Regression model for Washington Park
Note:
Parameter
(Intercept)
Cloud Cover
INVfTurbidity]
POLY[# of Bathers]
PQLY[#ofDogs]
Antecedent Rainfall
Acrossshore Wind
Algae
Adjusted R2 = 0.45, RMSE = 0.24, n = 66.
Coefficient
-1.132
0.062
-0.232
1.046
0.765
-0.363
0.160
-0.485
enterococci qPCR data.
Std
0.
0.
0.
0.
. Error
815
229
364
404
t-Statistic
-0.763
-2.471
2.015
2.040
P-Value
0.
0.
0.
0.
enterococci cultivable
Std
0.
0.
0.
0.
0.
0.
0.
0.
. Error
692
023
087
387
316
128
071
145
t-Statistic
-1.636
2.696
-3.252
2.701
2.420
-2.839
2.256
-3.339
448
016
048
046
data.
P-Value
0.
0.
0.
0.
0.
0.
0.
0.
107
009
002
009
019
006
028
002
Table C.9. Regression model for Silver Beach enterococci qPCR data.
Note:
Parameter
(Intercept)
Alongshore Wind
Air Temp
INV[Acrossshore Wind]
Water Temp
Wind Speed
Adjusted R2 = 0.41 , RMSE = 0.41 , n = 58.
Table C.10. Regression model for Silver
Parameter
(Intercept)
# of Birds
POLY[Air Pressure]
Water Temp
POLY[# of Bathers]
Coefficient
1 .021
-0.042
0.035
0.137
-0.042
0.073
Std
0.
0.
0.
0.
0.
0.
. Error
381
012
014
033
013
020
Beach enterococci
Coefficient
-3.879
0.002
1 .472
0.025
1 .694
Std
1.
0.
0.
0.
0.
. Error
010
001
417
011
420
t-Statistic
2.684
-3.567
2.461
4.137
-3.316
3.737
culturable
t-Statistic
-3.839
2.989
3.529
2.272
4.030
P-Value
0.
0.
0.
0.
0.
0.
010
001
017
000
002
001
data.
P-Value
0.
0.
0.
0.
0.
000
004
001
027
000
Note: Adjusted R2 = 0.32, RMSE = 0.36, n = 58.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table C.11. Regression model for West Beach enterococci qPCR data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept)
# of Boats
POLY[Wind Speed]
Water Temp
PQLY[AirTemp]
-2.391
-0.122
0.984
0.032
0.959
0.603
0.059
0.135
0.010
0.257
-3.962
-2.076
7.294
3.264
3.738
0.000
0.044
0.000
0.002
0.001
Note: Adjusted R2 = 0.63, RMSE = 0.41, n = 49.
Table C.12. Regression model for West Beach enterococci cultivable data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept)
Algae
Turbidity
Dewpoint
POLY[Air Pressure]
Wind Speed
-3.611
-0.666
0.053
0.054
0.544
0.098
0.550
0.223
0.007
0.009
0.201
0.040
-6.565
-2.996
7.837
5.877
2.703
2.444
0.000
0.005
0.000
0.000
0.010
0.019
Note: Adjusted R2 = 0.78, RMSE = 0.40, n = 49.
C.2 MARINE SITES
Table C.13. Regression model for Boqueron enterococci qPCR data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept) -2.550 1.617 -1.577 0.119
Water Temp 0.158 0.055 2.856 0.006
Debris 0.081 0.025 3.205 0.002
INV[Acrossshore Wind] -0.128 0.064 -2.013 0.048
INV[Cloud Cover] -0.273 0.121 -2.260 0.027
Note: Adjusted R2 = 0.23, RMSE = 0.29, n = 79.
Table C.14. Regression model for Boqueron enterococci culturable data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept) 5.835 2.181 2.675 0.011
Turbidity 0.029 0.011 2.597 0.013
Specific Conductivity -0.096 0.039 -2.461 0.018
# of Bathers 0.001 0.000 2.113 0.041
Note: Adjusted R2 = 0.43, RMSE = 0.43, n = 44.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table C.15. Regression model
Parameter
(Intercept)
POLY[Antecedent Rainfall]
INV[Cloud Cover]
Note: Adjusted R2 = 0.14, RMSE = 0.44,
Table C.16. Regression model
Parameter
(Intercept)
UV
Wave Height
Alongshore Wind
# of Dogs
Algae
Note: Adjusted R2 = 0.48, RMSE = 0.56,
Table C.17. Regression model
Parameter
(Intercept)
POLY[AirTemp]
POLYJDewpoint]
UV
POLY[WaterTemp]
Note: Adjusted R2 = 0.35, RMSE = 0.49,
Table C.18. Regression model
Parameter
(Intercept)
Water Temp
Humidity
POLY[Dewpoint]
INV[# of Birds]
Air Temp
for Edgewater Beach enterococci qPCR data.
Coefficient Std. Error t-Statistic P-Value
0.393 1.105 0.355 0.724
0.916 0.450 2.037 0.047
-0.039 0.016 -2.381 0.021
n = 55.
for Edgewater Beach enterococci cultivable data.
Coefficient Std. Error t-Statistic P-Value
0.905 0.196 4.613 0.000
-0.001 0.000 -5.722 0.000
2.041 0.777 2.626 0.012
-0.049 0.023 -2.122 0.039
0.825 0.343 2.404 0.020
0.738 0.187 3.957 0.000
n = 55.
for Fairhope Beach enterococci qPCR data.
Coefficient Std. Error t-Statistic P-Value
-7.141 2.680 -2.665 0.010
2.631 1.089 2.417 0.019
0.678 0.321 2.111 0.039
0.000 0.000 -3.912 0.000
1.208 0.433 2.788 0.007
n = 66.
for Fairhope Beach enterococci culturable data.
Coefficient Std. Error t-Statistic P-Value
-0.521 2.196 -0.237 0.813
-0.238 0.052 -4.539 0.000
0.028 0.009 3.227 0.002
0.933 0.308 3.029 0.004
1.579 0.602 2.625 0.011
0.066 0.033 2.031 0.047
Note: Adjusted R2 = 0.43, RMSE = 0.57, n = 66.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table C.19. Regression model for Goddard Beach enterococci qPCR data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept)
POLY [Water Temp, Waist Deep]
Amount of Debris
POLY[WaterTemp, Shin Deep]
2.827
-3.905
0.539
2739
1.625
1 .601
0.149
0.878
1.740
-2.440
3.613
3.119
0.087
0.017
0.001
0.003
Note: Adjusted R2 = 0.18, RMSE = 0.70, n = 69.
Table C.20. Regression model for Goddard Beach enterococci cultivable data.
Parameter Coefficient Std. Error t-Statistic P-Value
(Intercept)
Tide
POLY[Wind Speed]
# of Birds
-0.064
-0.218
2.484
0.008
0.660
0.038
1.179
0.003
-0.097
-5.761
2.107
2.843
0.923
0.000
0.039
0.006
Note: Adjusted R2 = 0.36, RMSE = 0.60, n = 69.
Table C.21. Regression model for Surfside Beach enterococci qPCR data.
Note:
Parameter
(Intercept)
Relative Humidity
Antecedent Rainfall
Turbidity
POLY[Absorbance]
POLY[# of Birds]
Adjusted R2 = 0.35, RMSE = 0.60,
Table C.22. Regression model
Note:
Parameter
(Intercept)
Antecedent Rainfall
POLY [Wave Height]
# of Boats
POLY[Salinity]
Time of Day
pH
Air Pressure
POLY[# of Bathers]
Adjusted R2 = 0.46, RMSE = 0.43,
Coefficient Std. Error t-Statistic P-Value
-4.519 1.121 -4.031 0.000
0.022 0.006 3.570 0.001
0.023 0.005 4.426 0.000
0.125 0.041 3.092 0.004
1.091 0.256 4.267 0.000
0.964 0.370 2.604 0.014
n = 82.
for Surfside Beach enterococci culturable data.
Coefficient Std. Error t-Statistic P-Value
35.322 10.955 3.224 0.002
0.011 0.005 2.526 0.014
0.516 0.279 1.850 0.068
0.055 0.025 2.216 0.030
1.092 0.255 4.284 0.000
-1.723 0.418 -4.122 0.000
0.591 0.224 2.637 0.010
-0.040 0.011 -3.666 0.001
0.993 0.493 2.015 0.048
n = 85.
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Predictive Modeling at Beaches—Volume II November 22, 2010
Table C.23. Regression model
Parameter
(Intercept)
POLY[PAR]
Absorbance
POLY[Relative Humidity]
Note: Adjusted R2 = 0.67, RMSE = 0.06,
Table C.24. Regression model
Parameter
(Intercept)
Turbidity
Chlorophyll
Relative Humidity
Note: Adjusted R2 = 0.19, RMSE = 0.47,
Table C.25. Regression model
Parameter
(Intercept)
Absorbance
Alongshore Current
Antecedent Rainfall
Note: Adjusted R2 = 0.45, RMSE = 0.45,
Table C.26. Regression model
Parameter
(Intercept)
Chlorophyll
Water Depth
Salinity
for Hobie Beach enterococci qPCR data.
Coefficient Std. Error t-Statistic P-Value
-2.221 1.038 -2.140 0.052
0.972 0.314 3.098 0.009
0.029 0.010 3.079 0.009
0.601 0.244 2.463 0.029
n = 17.
for Hobie Beach enterococci cultivable data.
Coefficient Std. Error t-Statistic P-Value
-1.825 0.593 -3.076 0.003
-0.016 0.006 -2.745 0.007
0.759 0.265 2.864 0.005
0.026 0.008 3.271 0.002
n = 97.
for La Monseratte Beach enterococci qPCR data.
Coefficient Std. Error t-Statistic P-Value
3.606 0.322 11.196 0.000
-0.748 0.364 -2.055 0.053
-102.088 44.678 -2.285 0.033
0.005 0.002 2.552 0.019
n = 24.
for La Monseratte Beach enterococci culturable data.
Coefficient Std. Error t-Statistic P-Value
41.548 17.795 2.335 0.027
-10.755 2.939 -3.659 0.001
17.555 6.247 2.810 0.009
-1.264 0.516 -2.448 0.021
Note: Adjusted R2 = 0.41, RMSE = 0.59, n = 32.
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