NOAA Technical Memorandum GLERL-156

BEACH WATER QUALITY DECISION SUPPORT SYSTEM

David Rockwell1

Kent Campbell1

Gregory Lang2

David Schwab2,4

Greg Mann3

Richard Wagenmaker3

1

Cooperative Institute for Limnology and Ecosystems Research, 4840 S. State Rd., Ann Arbor, 

MI 48108

2

NOAA, Great Lakes Environmental Research Laboratory, 4840 S. State Rd., Ann Arbor, MI 

48108

3

NOAA, National Weather Service Forecast Office, Detroit/Pontiac, 9200 White Lake Rd., White 

Lake, MI 48386

4

Retired. Now at University of Michigan, Graham Institute, 214 S. State, Suite 200, Ann Arbor, 

MI 48104

March 2013

Revised June 2014

UNITED STATES

DEPARTMENT OF COMMERCE

Rebecca Blank

Acting Secretary

NATIONAL OCEANIC AND

ATMOSPHERIC ADMINISTRATION

Jane Lubchenco

Under Secretary for Oceans & Atmosphere

NOAA Administrator

NAT OI NAL OCEANIC AND ATMOSPHERIC ADMINISTRAT OI N

U.S.DEPARTMENT OF COMMERCE
2

NOTICE

Mention of a commercial company or product does not constitute an endorsement 

by the NOAA. Use of information from this publication concerning proprietary 

products or the tests of such products for publicity or advertising purposes is not 

authorized. This is GLERL Contribution No. 1652.

This publication is available as a PDF file and can be downloaded from GLERL’s 

web site: www.glerl.noaa.gov. Hard copies can be requested from GLERL

Information Services, 4840 S. State Rd., Ann Arbor, MI 48108.

pubs.glerl@noaa.gov.

NOAA’s Mission – To understand and predict changes in Earth’s environment 

and conserve and manage coastal and marine resources to meet our nation’s 

economic, social, and environmental needs. 

NOAA’s Mission Goals:

• Protect, restore and manage the use of coastal and ocean resources through an 

ecosystem approach to management

• Understand climate variability and change to enhance society’s ability to plan 

and respond

• Serve society’s needs for weather and water information

• Support the Nation’s commerce with information for safe, efficient, and 

environmentally sound transportation

• Provide critical support for NOAA’s Mission 
3

TABLE OF CONTENTS

Abstract .............................................................................................................................................................7

1. Introduction.......................................................................................................................................................8

2. Data Description and Sources...........................................................................................................................9

2.1 Identification of Key Variables.................................................................................................................9

2.2 Beach Locations and Orientations..........................................................................................................12

 2.2.1 Alongshore & Onshore Variable Calculations..................................................................................12

2.3 Hydrodynamic Grid Cell Locations........................................................................................................14

2.4 E. coli Data Sources and Data Processing ..............................................................................................14

2.5 Hydrodynamic Model Data Sources.......................................................................................................15

2.6 Meteorological Data Sources..................................................................................................................15

2.7 USGS River Gauging Station Discharge Data Sources..........................................................................15

 2.7.1 River Runoff Computation ...............................................................................................................15

3. Beach Forecast Program .................................................................................................................................15

4. Virtual Beach 2.3 Software .............................................................................................................................15

5. Beach Water Quality Decision Support System (DSS) ..................................................................................15

5.1 2010 Forecast DSS for 35 Sampling Sites at Twenty-Four Beaches......................................................27

5.2 Key Variables in the Forecast DSS for the 35 Sites................................................................................27

5.3 Comparison of 2010 Forecast DSS with Persistence and Always Open Management Tools.................30

5.4 Comparison of 2010 Forecast DSS for adjacent Hydrodynamic Grid Cells at Three Beaches..............32

6. NOAA Beach Water Quality Experimental Forecasts....................................................................................36

6.1 Five Beaches 2012 Forecast DSS ...........................................................................................................36

6.2 Key Variables in 2012 Forecast DSS Equations.....................................................................................36

 6.2.1 Bay City State Rec. Area Beach 2012 Forecast DSS........................................................................36

 6.2.2 Memorial Beach 2012 Forecast DSS................................................................................................37

 6.2.3 Metro Beach 2012 Forecast DSS......................................................................................................39

 6.2.4 Grand Haven State Park 2012 Forecast DSS....................................................................................41

 6.2.5 North Beach Park Beach 2012 Forecast DSS...................................................................................41

6.3 2012 Forecast DSS Results Compared to Monitoring and Other Management Methods......................43

6.4 Communication Plan for Distribution of Forecasts................................................................................44

7. Discussion and Conclusions ...........................................................................................................................47

8. Acknowledgements.........................................................................................................................................50 

9. References.......................................................................................................................................................50
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LIST OF FIGURES

Figure 2.2.1: Great Lakes Basin Beach Overview Location Map ......................................................................12

Figure 2.2.2: Beach Orientation Diagram...........................................................................................................13

Figure 3.1: Beach Forecast Program Screenshot ................................................................................................16

Figure 5.0.1:VB2.3 Data Processing Screenshot................................................................................................17

Figure 5.0.2: VB2.3 Transform Screenshot ........................................................................................................19

Figure 5.0.3: VB2.3 Data Processing Screenshot after Completion of Transform Variable Selection...............19

Figure 5.0.4: VB2.3 Initial Modeling Screenshot...............................................................................................21

Figure 5.0.5: VB2.3 Modeling Genetic Algorithm Screenshot...........................................................................21

Figure 5.0.6: VB2.3 IVs from Ten Best Fit Genetic Algorithm Models Screenshot..........................................22

Figure 5.0.7: VB2.3 Modeling Manual Tab and Cross Validation Screenshot...................................................22

Figure 5.0.8: VB2.3 Display of FDSS Equation Variable P-Values Screenshot.................................................23

Figure 5.0.9: VB2.3 Display Model of DFFITS Residuals Screenshot..............................................................23

Figure 5.0.10: VB2.3 Residuals, Fitted vs Residuals, Anderson Darling Statistic Screenshot...........................25

Figure 5.0.11: VB2.3 Residuals Fitted vs Observed, Model Statistics, Total Errors Screenshot .......................25

Figure 5.0.12: VB2.3 Residuals Fitted vs Observed, Optimize Decision Criterion Screenshot.........................26

Figure 5.0.13: VB2.3 MLR Prediction Screenshot.............................................................................................26

Figure 5.0.14: VB2.3 2010 Model Predictions vs 2010 Observed Values..........................................................27

Figure 5.3.1 FDSS-MV Errors Compared to PM Errors....................................................................................32

Figure 5.3.2 FDSS-LV Errors Compared to PM Errors......................................................................................34

Figure 5.4.1 Racine Zoo Beach Adjacent Hydrodynamic Grid Cells.................................................................34

Figure 5.4.2 Lake Erie Beach Adjacent Hydrodynamic Grid Cells....................................................................35

Figure 5.4.3 Memorial Beach Adjacent Hydrodynamic Grid Cells....................................................................35

Figure 6.2.1 Plot of POLY(DAYS) for Memorial Beach....................................................................................38

Figure 6.2.2 Plot of POLY(AT24) for Memorial Beach .....................................................................................38

Figure 6.2.3 Plot of POLY(OSWVO) for Memorial Beach................................................................................38

Figure 6.2.4 Plot of POLY(ClintonRD_0d)) for Memorial Beach .....................................................................40

Figure 6.2.5 Plot of POLY(DAYS) for Metro Beach..........................................................................................40

Figure 6.2.6 Plot of POLY(AT240m) for Metro Beach ......................................................................................40

Figure 6.2.7 Plot of POLY(ClintonRD_0d) for Metro Beach.............................................................................42

Figure 6.2.8 Plot of POLY(AT0m)) for Grand Haven State Park.......................................................................42

Figure 6.2.9 Plot of Grand River Discharge and Runoff for Grand Haven State Park.......................................42

Figure 6.2.10 Plot of POLY(OSW0m) for North Beach Park Beach .................................................................43

Figure 6.4.1 NOAA Forecast for Memorial Beach Macomb County MI...........................................................45

Figure 6.4.2 Memorial Beach E. coli Forecasts for swimming season 2012......................................................46
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APPENDIX 1: Hydrodynamic Grid Cell Locations

Figure A1: Bay City State Recreation Area, Bay County, MI and Hydrodynamic Grid Cell Locations...........53

Figure A2: North Beach Park Beach, Ottawa County, MI and Hydrodynamic Grid Cell Locations.................53

Figure A3: Grand Haven State Park Beach, Ottawa County, MI and Hydrodynamic Grid Cell Locations.......54

Figure A4: North Beach, Racine County WI and Hydrodynamic Grid Cell Locations.....................................54

Figure A5: Zoo Beach, Racine County, WI and Hydrodynamic Grid Cell Locations........................................55

Figure A6: Upper Lake Park Beach, Ozaukee County, WI and Hydrodynamic Grid Cell Locations................55

Figure A7: South Shore Beach, Milwaukee County, WI and Hydrodynamic Grid Cell Locations....................56

Figure A8: Bradford Beach, Milwaukee County, WI and Hydrodynamic Grid Cell Locations.........................56

Figure A9: Woodlawn Beach State Park, Erie County, NY and Hydrodynamic Grid Cell Locations ...............57

Figure A10: Hamburg Bathing Beach, Erie County, NY and Hydrodynamic Grid Cell Locations...................57

Figure A11: Evans Town Park Beach, Erie County, NY and Hydrodynamic Grid Cell Locations....................58

Figure A12: Wendt Beach, Erie County, NY and Hydrodynamic Grid Cell Locations......................................58

Figure A13: Lake Erie Beach, Erie County, NY and Hydrodynamic Grid Cell Locations................................59

Figure A14: Bennett Beach, Erie, County, NY and Hydrodynamic Grid Cell Locations...................................59

Figure A15: Presque Isle Beach #2, Erie, County, PA and Hydrodynamic Grid Cell Locations........................60

Figure A16: Presque Isle Beach #10, Erie, County, PA and Hydrodynamic Grid Cell Locations......................60

Figure A17: Villa Angela, Cuyahoga County, OH and Hydrodynamic Grid Cell Locations.............................61

Figure A18: Hammond Marina East Beach, Lake County, IN and Hydrodynamic Grid Cell Locations...........61

Figure A19: Marquette Park Beach, Lake County, IN and Hydrodynamic Grid Cell Locations.......................62

Figure A20: Washington Park Beach, Lake County, IN and Hydrodynamic Grid Cell Locations.....................62

Figure A21: Ogden Dunes, Lake County, IN and Hydrodynamic Grid Cell Locations.....................................63

Figure A22: IDSP West Beach, Lake County, IN and Hydrodynamic Grid Cell Locations...............................63

Figure A23: Memorial Beach, Macomb County, MI and Hydrodynamic Grid Cell Location...........................64

Figure A24: Metropolitan Beach, Macomb County, MI and Hydrodynamic Grid Cell Location......................64

LIST OF TABLES

Table 2.1 Independent Variables and Definitions ...............................................................................................10

Table 2.2 Beach List and Information.................................................................................................................13

Table 2.4 E. coli Data Sources............................................................................................................................14

Table 5.1 2010 Forecast DSS Equations for the 35 sites....................................................................................28

Table 5.2 Key variables in the 2010 Forecast DSS for the Twenty-Four Beaches.............................................31

Table 5.4 2010 Forecast DSS Comparisons at Adjacent Hydrodynamic Grid Cells..........................................33

Table 6.1 2012 Forecast DSS Equations for Five Beaches in the State of Michigan .........................................36

Table 6.3 Summary of 2012 Forecast DSS Results for the Forecast Beaches....................................................44
6

LIST OF ATTACHMENTS

Attachment 2.0 Excel files containing the hourly data for the Independent Variables used by 

Virtual Beach 2.3 to arrive at the forecast decision support system equations in Table 5.1.

Attachment 5.3 2010 Forecast DSS Compared to Always Open & Persistence Beach Management Models

Attachment 5.3.1 Stratification of 2010 Forecast DSS by State Single Sample Regulatory Standard
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Beach Water Quality Decision Support System

D.C. Rockwell

K.B. Campbell

G.A. Lang

D.J. Schwab

G. Mann

R. Wagenmaker

ABSTRACT

The need for rapid assessment of bacterial contamination at beaches is well known. Bacterial concentrations 

change rapidly (Bohm, Whitman et al. 1995, Olyphant and Whitman 2004, Whitman and Nevers 2008). The 

“persistence model” regulates today’s swimming with yesterday’s Escherichia coli (E. coli) measurement. As a 

result, this beach management tool is known to be less protective of human health than desired but was still used 

at over 500 beaches in 2010. 

One method for meeting this problem has been to develop rapid analytical methods taking two hours of laboratory 

analytical time. This approach is becoming operationally available but at higher analytical cost (Setty 2012) than 

the slower cultural methods currently employed. These rapid analytical methods provide beach managers with the 

capability to advise swimmers about E. coli concentrations on the same day, but only if sampling, transportation, 

and data management time components can be completed within four hours, giving an overall time of 6 hours. 

This requires early field sampling and laboratories close to the beaches being sampled. 

Another approach is to use Nowcast predictive models that can provide estimations of E. coli during the same 

day (Francy 2009) by measuring easily determined variables that can be correlated with E. coli bacterial 

concentrations. The Nowcast predictive models were being used at 10 beaches in 2010 (Adam Mednick, personal 

communication). It is expected that Nowcast predictive models will be expanded in 2011 to more than 20 beaches 

because of Great Lake Restoration Initiative funding. 

This technical memorandum is based primarily on the final grant report to Ed Pniak, GLRI Project Officer, 

Michigan Project Lead, U.S. EPA, Region 5, Water Division, State and Tribal Programs Branch for GL00E00658. The grant is titled “60 Hour Beach Forecasting Models.” The principle investigators are Allen Burton, 

Kent Campbell, and David Rockwell.

This technical memorandum provides beach managers with a tool to forecast several days in advance the 

likelihood of E. coli concentrations exceeding the state single sample regulatory standard. This predictive 

beach water quality management tool is the only beach management decision support system (DSS) capable 

of forecasting several days in advance the beach water quality bacterial concentrations because it limits the 

explanatory variables to those variables for which the National Weather Service (NWS) is able to make forecasts.

The forecast DSS was applied to 35 sampling locations at 24 beaches during the 2010 swimming season. The 

results of Grant GL-00E00658 showed the forecast DSS provided the same or better beach management decision 

support than the persistence model at 71% (25 of the 35) of the sampling sites. In addition, the stratification of 

beach sampling sites based on 5% of the samples exceeding the state regulatory standard single sample maximum 

of 235 counts/100 ml improved the forecast DSS. The forecast DSS for the beaches meeting this criteria provided 

better (70%) beach management support or the same (15%) beach management support than the persistence 

model for a total of 85% (23 of the 27) of the sampling sites. The evaluation of the percent of samples exceeding 

the state regulatory standard allows the beach manager to readily determine if the beach is more suitable for the 
8

forecast DSS tool. Forecast DSS has the potential to provide the swimming community with information several 

days in advance, allowing the planning of their water recreational activities and reducing the risk of swimming in 

bacterially contaminated water while maximizing the opportunity to use the water recreational facilities.

Lastly, application of the forecast DSS to all monitored beaches with two or more samples per week in 2010 could 

have led to about a 23% reduction (862 swimming advisory days) of the 3766 reported (NRDC 2011). The lost 

value of swimming for the Great Lake recreational swimmers ranges from $11.3M to $117M for these days when 

swimming is banned (Shaikh 2006 and Rabinovici et al. 2004). 

1. INTRODUCTION

This technical memorandum is based primarily on the final grant report to Ed Pniak, GLRI Project Officer, Michigan 

Project Lead, U.S. EPA, Region 5, Water Division, State and Tribal Programs Branch for GL-00E00658. The grant is 

titled “60 Hour Beach Forecasting Models”. The principle investigators are Allen Burton, Kent Campbell, and David 

Rockwell.

Predictive models have served as a management tool for advisory or closure of swimming at some beaches since 1990 

(Kuntz 1998). Early predictive models were rainfall-based alert curve models, were statistical in nature and did not 

distinguish between point and non-point sources. (DNREC 1997, Kuntz 1998, USEPA 1999). Numerous deterministic 

models explicitly incorporating advection, transport, and decay processes have been used (USEPA 1999) to predict 

water quality parameters as well as E. coli levels. Multiple Linear Regression (MLR) models began to be used in the 

Great Lakes in the late 1990’s (Francy 2009, SwimCast, Whitman et al.). A systematic review of published Nowcasting/

Forecasting studies in the Great Lakes basin employing various predictive models indicated that bona fide unbiased tests 

of predictive ability were almost invariably lacking. (Findlay et al. 2009). Nowcasting models have lower errors in making 

decisions compared to the persistence model. Now/forecasting models achieve moderate predictive accuracy using R2 and 

Cp- statistics as joint criteria (Ge and Frick 2007). Typical adjusted R2 for Nowcast models range from 38 to 44% (Francy 

et al. 2006b).

In the earliest reported scientific studies, (Veley et al. 1998, Francy and Darner 1998) USGS scientists looked at 

using turbidity, rainfall, and wave height in a beach-specific statistical model to estimate E. coli concentrations. Since 

characterization and statistical modeling of bacterial concentrations was introduced in the Great Lakes, mathematical 

modeling for bacterially induced beach closures has become a growing body of published research and scientific 

investigations (Olyphant et al. 2003, Francy and Darner 2003). Application of multiple linear regression (MLR) for single 

beaches (Olyphant and Whitman 2004, Pfister 2004, Francy et al. 2006, Zimmerman 2008, Przybyla-Kelly et al. 2008) has 

expanded to regional approaches (Nevers and Whitman 2005, Nevers and Whitman 2008). Other mathematical models 

have been employed using partial least squares regression (Hou et al. 2006) and neural network models (He and He 2008) 

for marine beaches. Nowcast models frequently use explanatory variables that can be forecasted with some confidence out 

to 60 hours. Most of the nowcast models use hydro-meteorological variables such as rainfall, wind direction and speed, 

and wave height as inputs. The Great Lakes Coastal Forecasting System’s hydrodynamic models can be used for beach 

water quality condition forecasting (Schwab et al. 2006). Combinations of Nowcasting and Forecasting using MLR have 

been advanced (Frick et al. 2008) showing the possibility of “dynamic” forecasting using a moving data set based on 

daily beach recreational water quality measurements and meteorological data collected to update an existing model. If 

there is a tributary in the vicinity of the beach, a potential major source of bacteria could come from tributaries (Olyphant 

et al. 2003, Byappanahalli et al. 2003, Whitman et al. 2006). Process models involving the integration of river models, 

hydrodynamic models, and statistical models have been used (Nevers et al. 2007, Holtschlag et al. 2008, Wong et al. 

2009) to improve the ability to forecast E. coli concentrations. 

The transience of fecal coliform bacteria concentrations at the beach, the episodic nature of their introduction, the 

potential for re-growth, and the expanding understanding of the sources for the E. coli indictor bacteria makes the task 

of predicting safe swimming conditions challenging (Canale et al. 1993, Wilkes et al. 2009). Predictive models are used 
9

to inform the swimming public (Francy et al. 2006, Whitman 2005, Pfister 2004) through an internet-based system. 

Because of cost factors and ease of use, professional judgment models proceeded mathematical models and are still 

commonly used (USEPA 1999). Budget factors, generally good water conditions in the Great Lakes, and the lack of 

evidence of swimmer health impacts (there is no swimmer health data base in the Great Lakes) are moving some beach 

managers towards an always open policy connected with an informational system providing the swimming public E. coli

concentrations and an evaluation of the health risk associated with the E. coli concentration through an Internet-based 

system. This information system, based on using real-time data correlated to E. coli concentrations, provides swimmers 

notification of elevated bacterial levels above the state standard meets Federal reporting requirements. Closing of 

swimming is required only under certain conditions such as high waves, lightning, or heavy rainfall releasing sewage into 

the beach (Breitenbach 2012). There is a weakness in this approach, since the E. coli correlations and weather conditions 

are based on samples collected once per day usually during the week, in the morning before bathers arrive. Application 

of this model outside of the times when samples were collected is an extrapolation to conditions not present during 

sample collection times and may not be warranted. Conditions undoubtedly are different during times when swimmers are 

present. Generally more swimmers are present during the weekend days, which are valued higher by recreational users of 

beaches. 

2. DATA DESCRIPTION AND SOURCES

Factors known to influence the fate and transport of E. coli in the Great Lakes are sunlight, rainfall, waves, wind speed 

and direction, temperature, algae, birds, human bathers, farm animals, and domestic animals. (Boehm et al. 2007). A 

wide range of explanatory variables has been tested. When these explanatory variables could be forecast, they have been 

included as possible explanatory variables for the 24 beaches in this study (see Table 2.1). Parameters fall into three 

categories that are useful for explaining E. coli concentrations and can be forecast. Nearshore Beach Conditions (such 

as wave height, surface and bottom lake current speed and direction, water temperature, lake level), Weather Conditions 

(such as antecedent rainfall, air temperature, wind direction and velocity, dew point, cloud cover), and Tributary Discharge 

and Runoff. Data is available for these categories and can be obtained from NOAA–GLERL Great Lakes Coastal 

Forecasting System’s hydrodynamic model, NWS meteorological stations, and USGS stream gauges.

At present, onshore conditions such as turbidity, presence of algae, number and type of birds, number of human bathers, 

and influence of domestic animals cannot be forecast.

Attachment 2 includes the 35 Excel files containing the hourly data for the Independent Variables used by Virtual Beach 

2.3 to arrive at the forecast decision support system equations in Table 5.1.

2.1 Identification of Key Variables

Multi-linear regression models dominate the modeling landscape during the first decade of the 21st century. The 

determination of the “best” statistical model depends on the metric chosen during the descriptive parameter selection 

process (Boehm et al. 2007). The parameters retained can be a function of the evaluation process. The mathematical 

evaluation criteria employed in this study is the Bayesian Information Criterion available in Virtual Beach as one of 

several evaluation criteria. The decision support system usefulness or success is determined by the accuracy of the 

management decisions. 

Decision support systems have been used at 97 beaches as reported in the literature. Both point and nonpoint sources were 

present at these beaches. Independent variables were selected from the above sources where studies resulted in equations 

to predict E. coli concentrations. The independent variables included as possible variables in our forecast models (see 

Table 2.1) were chosen based on work published in Francy and Darner 1998, Francy et al. 2006b, Francy and Darner 

2007, Frick et al. 2008, Holtschlag et al. 2008, Przybyla-Kelly et al. 2008, Nevers et al. 2007, Nevers et al. 2009, Nevers 

and Whitman 2005a,b, Nevers and Whitman 2008a,b, Olyphant 2005, Olyphant and Whitman 2004, Whitman and Nevers 

2004, Whitman and Nevers 2006, Vermette et al. 2008, Zimmerman 2006, Zimmerman 2008, and USEPA 2010. Table 

2.1 summarizes these variables into several groups. Seven key variables for time were used to observe if Julian date, 
10

Table 2.1. Independent variables and definitions. 

Variable Definition

Date Time (GMT) at which the sample was taken (to the nearest hour) in the format: mm/dd/yyyy hh:mm 

GMT = EDST + 4 hours; GMT = CDST + 5 hours; 1-29 minutes round to hour, 30-59 minutes round to next hour)

ECOLI E. coli measurement at beach sampling site. For Michigan Beaches measurement is a geo. mean of at least 3 samples

Log10Ecoli Log to base 10 of E. coli

Days Count of Days from the first sample to the last sample with first sample day = 0

Q1 Categorical Variable = 1 for the First 25% of the sampling season by year

Q2 Categorical Variable = 2 for the Second 25% of the sampling season by year

Q3 Categorical Variable = 3 for the Third 25% of the sampling season by year

Q4 Categorical Variable = 4 for the Fourth 25% of the sampling season by year

QTR Categorical Variable with 1, 2, 3, and 4 values respectively representing the four quarters of the sampling season

GLCFS Hydrodynamic Model Data Variables

AT0 Air temp at sample hour, n ≤ 1 (°C)

AT4 Air temp previous 4 hour avg., n ≤ 4, (°C)

AT24 Air temp previous 24 hour avg., n ≤ 24, (°C)

AT120 Air temp previous 120 hour avg., n ≤ 120, (°C)

AT240 Air temp previous 240 hour avg., n ≤ 240, (°C)

DP0 Dew point temp at sample hour, n ≤ 1 (°C)

DP4 Dew point temp previous 4 hour avg., n ≤ 4 (°C)

DP24 Dew point temp previous 24 hour avg., n ≤ 24 (°C)

SWT0 Surface water temp at nearest 3 hour, n=1 (°C)

SWT6 Surface water temp at nearest previous 6 hour ave., n=2 (°C)

SWT9 Surface water temp at nearest previous 9 hour ave., n=3 (°C)

CS0 Surface current speed at sample hour, n=1 (m/s)

CD0 Surface current direction at sample hour, n=1 (degrees towards True North)

ASC0 Alongshore current at sample hour, n=1 (m/s, positive clockwise)

OSC0 Onshore current at sample hour , n=1 (m/s, positive towards beach)

CSb0 Bottom current speed at nearest 3 hour, n=1 (m/s) 

CDb0 Bottom current direction at nearest 3 hour, n=1 (degrees toward True North) 

ASCb0 Alongshore bottom current at sample hour, n=1 (m/s, positive clockwise)

OSCb0 Onshore bottom current at sample hour , n=1 (m/s, positive towards beach)

WVH0 Wave height at sample hour, n=1 (m)

WVS0 Wave direction at sample hour, n=1 (degrees towards True North)

WVP0 Wave period at sample hour, n =1 (s)

ASWV0 Alongshore Waves at sample hour (m), positive= clockwise rotation

OSWV0 Onshore Waves at sample hour (m), positive towards shore, negative away from shore

CC0 Cloud Cover at sample hour, n ≤ 1 (fraction, 0-1) 

CC4 Cloud Cover previous 4 hour avg., n ≤ 4 (fraction, 0-1)

CC24 Cloud Cover previous 24 hour avg., n ≤ 24 (fraction, 0-1)

WS0 Wind speed at sample hour, n=1 (m/s)

WD0 Wind Direction at sample hour, n=1 (degrees from True North)

ASW0 Alongshore wind at sample hour , n=1 (m/s, positive clockwise)

OSW0 Onshore wind at sample hour , n=1 (m/s, positive towards beach)

Nearby Meteorological Station (NMS) Data Variables: (denoted by “m” at the end of variable name)

AT0m Air temperature (Dry Bulb Celsius) at NMS at sample hour of measurement n ≤ 1 (°C)

AT4m Air temperature (Dry Bulb Celsius) at NMS previous 4 hour avg. 3 ≤ n ≤ 4 (°C)

AT24m Air temperature (Dry Bulb Celsius) at NMS previous 24 hour avg. 18 ≤ n ≤ 24 (°C)

AT120m Air temperature (Dry Bulb Celsius) at NMS previous 120 hour avg. 90 ≤ n ≤ 120 (°C)

AT240m Air temperature (Dry Bulb Celsius) at NMS previous 240 hour avg. 180 ≤ n ≤ 240 (°C)
11

ATmin24m Minimum Temperature at NMS (based on minimum of the hourly night time temps) 18 ≤ n ≤ 24 (°C)

ATmax24m Maximum Temperature at NMS (based on maximum of the hourly night time temps) 18 ≤ n ≤ 24 (°C)

DP0m Dew Point Celsius from NMS at sample hour, n ≤ 1 (°C).

DP4m Dew Point Celsius from NMS previous 4 hour avg., 3 ≤ n ≤ 4 (°C)

DP24m Dew Point Celsius from NMS previous 24 hour avg., 18 ≤ n ≤ 24 (°C)

CC0m Cloud cover at sample hour from NMS, n ≤ 1 (fraction, 0-1)

CC4m Cloud cover previous 4 hour avg., 3 ≤ n ≤ 4 (fraction, 0-1)

CC24m Cloud cover previous 24 hour avg., 18 ≤ n ≤ 24 (fraction, 0-1)

WSP0m Wind speed at sample time (hour) from NMS, n=1 (m/s)

WSP2m Wind speed previous 2 hour avg., from NMS,1 ≤ n ≤ 2) (m/s)

WSP3m Wind speed previous 3 hour avg., from NMS,2 ≤ n ≤ 3) (m/s)

WSP4m Wind speed previous 4 hour avg., from NMS,3 ≤ n ≤ 4) (m/s)

WG0m Wind Gust at sample hour from NMS, n=1 (m/s)

WG2m Wind Gust previous 2 hour avg., from NMS, 1 ≤ n ≤ 2 (m/s)

WG3m Wind Gust previous 3 hour avg., from NMS, 2 ≤ n ≤ 3 (m/s)

WG4m Wind Gust previous 4 hour avg., from NMS, 3 ≤ n ≤ 4 (m/s)

WD0m Wind Direction at sample hour, n=1 (degrees from True North)

ASW0m Alongshore wind at sample hour from NMS, n=1 (m/s, positive clockwise)

OSW0m Onshore wind at sample hour from NMS, n=1 (m/s, positive towards beach)

ASWG0m Alongshore wind gust at sample hour from NMS, n=1 (m/s, positive clockwise)

OSWG0m Onshore wind gust at sample hour from NMS, n=1 (m/s, positive towards beach)

TP0m Total precipitation at sample hour at NMS, n=1 (inches)

TP4m Total precipitation previous 4 hour total at NMS, 3 ≤ n ≤ 4 (inches)

TP24m Total precipitation previous 24 hour total at NMS, 18 ≤ n ≤ 24 (inches)

TP48m Total precipitation previous 48 hour total at NMS, 36 ≤ n ≤ 48 (inches)

TP72m Total precipitation previous 72 hour total at NMS, 54 ≤ n ≤ 72 (inches)

River Discharge Data: “RvrName” is a place holder for any USGS gauged river. Units=Daily Mean Discharge (ft3/s)

RvrNameRD_0d Same Day River Discharge (ft3/s)

RvrNameRD_1d Previous Day River Discharge (ft3/s)

RvrNameRD_2d Previous 2nd Day River Discharge (ft3/s)

RvrNameRD_3d Previous 3rd Day River Discharge (ft3/s)

RvrNameRD_4d Previous 4th Day River Discharge (ft3/s)

RvrNameRD_5d Previous 5th Day River Discharge (ft3/s)

RvrNameRD_6d Previous 6th Day River Discharge (ft3/s)

RvrNameRD_7d Previous 7th Day River Discharge (ft3/s)

RvrNameRD_8d Previous 8th Day River Discharge (ft3/s)

RvrNameRD_9d Previous 9th Day River Discharge (ft3/s)

RvrNameRO_0d Runoff day of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_1d Runoff previous day of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_2d Runoff two days previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_3d Runoff three days previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_4d Runoff fourth day previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_5d Runoff fifth day previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_6d Runoff sixth day previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_7d Runoff seventh day previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_8d Runoff eighth day previous of sample = Discharge - Baseflow (ft3/s)

RvrNameRO_9d Runoff ninth day previous of sample = Discharge - Baseflow (ft3/s)

NOTE: Averages include sample at time = zero. Four hour average involves previous 3 hours and time of sample.

Table 2.1. Independent variables and definitions (cont.). 
12

calendar date, or seasonal effects were significant for E. coli variation. Thirty-one variables are obtained from a nearby 

meteorological station. These variables are denoted by attaching an “m” e.g. AT0m to distinguish from the same parameter 

obtained from the GLCFS hydrodynamic model. Of the 31 meteorological variables, the four wind gustiness parameters 

and five precipitation parameters are not duplicated by the GLCFS. There are 31 GLCFS independent variables. The 

GLCFS produces readings every hour for all of the parameters. Meteorological stations are not as reliable. In this study, 

except for the unique meteorological observations, GLCFS variables could be used in place of the meteorological 

observations without changing the beach management decision outcomes. However, some loss of statistical significance 

did occur in the Forecast DSS equation. The last group of independent variables is the river discharge and runoff variables 

for those rivers where USGS maintained a gauging site. Twenty parameters were used. Ten variables were used for river 

discharge and 10 variables were used for runoff. These variables included the discharge or runoff for the day of the 

measurement, plus nine lags respectively. The lags were included to see if previous day(s) discharge or runoff affected 

the beach suggesting the source of bacterial contamination was higher up in the watershed. The lagged variables would 

represent the additional time needed for transporting the bacteria from more distant sources to the beach water sampling 

location.

2.2 Beach Locations and Orientations

Each beach’s location (Figure 2.2.1) was determined either by the beach’s manager supplying the latitude and longitude 

coordinates for their beach or by manually locating the beach in Google Earth (Table 2.2). Beach Orientation/Beach Angle 

is determined in accordance with the methodology used by the developers of Virtual Beach and is demonstrated in Figure 

2.2.2. The angle (in degrees) follows compass readings.

2.2.1 Alongshore & Onshore Variable Calculations

The variables winds, currents and waves all had alongshore and onshore variables derived from them. The values derived 

were done using formulae that correspond to those used by the developers of the Virtual Beach Software. Alongshore and 

onshore winds were determined using the following formulae:

Figure 2.2.1. Beach locations.
13

ASW=−wind_speed*cos((wind_direction−beach_

angle)*(π/180))

OSW=wind_speed*sin((wind_direction−beach_angle)*(π/180))

Alongshore & onshore currents were determined using the 

following formulae:

ASC=current_speed*cos((current_direction−beach_

angle)*(π/180))

OSC=−current_speed*sin((current_direction−beach_

angle)*(π/180))

Alongshore & onshore waves were determined using the 

following formulae:

ASWν=−wave_speed*cos((wave_direction−beach_

angle)*(π/180))

OSWν=wave_speed*sin((wave_direction−beach_

angle)*(π/180))

Table 2.2. Beach list and information.

60 Hour Beach Forecasting Model: Beach List

Beach Beach Name Lake Beach Latitude Longitude Primary Secondary USGS Gauge

Number Orientation NMS NMS Number

1 Bay City State Rec. Area Huron -44.71 43.672557 -83.906193 HYX MBS 04157000

2 North Beach Park Michigan 165.82 43.081800 -86.255000 MKG 04119000

3 Grand Haven State Park Michigan 147.60 43.053600 -86.247300 MKG 04119000

4 North Beach Michigan -17.53 42.739783 -87.778314 RAC 04087240

5 Zoo Beach Michigan -2.62 42.749851 -87.780914 RAC 04087240

6 Upper Lake Park Beach Michigan 31.39 43.394475 -87.863171 ETB

7 South Shore Beach Michigan -29.05 42.993389 -87.878818 MKE 04087000

8 Bradford Beach Michigan 37.91 43.060442 -87.873579 MKE 04087000

9 Woodlawn Beach Erie -179.07 42.790245 -78.854552 BUF

10 Hamburg Bathing Beach Erie -143.52 42.765617 -78.879825 BUF

11 Evans Town Park Beach Erie -123.39 42.642016 -79.068108 DKK

12 Erie Beach Erie -160.02 42.631319 -79.086144 DKK

13 Wendt Beach Erie -153.16 42.676947 -79.054067 DKK

14 Bennett Beach Erie 178.28 42.662876 -79.064441 DKK

15 Presque Isle Beach #2 Erie -164.31 42.128252 -80.149890 ERI

16 Presque Isle Beach #10 Erie -82.17 42.173621 -80.087003 ERI

17 Villa Angela Erie -140.45 41.586592 -81.566836 BKL

18 Hammond Marina East Beach Michigan -55.22 41.697817 -87.511261 GYY VPZ

19 Marquette Park Michigan -96.67 41.620769 -87.260131 GYY VPZ

20 Washington Park Beach Michigan -106.96 41.729003 -86.903352 GYY VPZ

21 Ogden Dunes Michigan -101.75 41.628791 -87.191905 GYY VPZ 04095090

22 Indiana Dunes West Beach Michigan -117.04 41.662749 -87.064451 GYY VPZ

23 Memorial Park Beach St. Clair 17.49 42.527245 -82.871297 MTC 04164000

24 Metro Park Beach St. Clair -251.11 42.571055 -82.796232 MTC 04164000

Figure 2.2.2 Beach 

Orientation Diagram.
14

2.3 Hydrodynamic Data Grid Cell Locations

The hydrodynamic grid cells for each beach were determined programmatically by their proximity to each beach 

individually. Beaches whose location was within the bounds of a grid cell used hydrodynamic data from the cell in 

which they were located. Beaches that were not located within the bounds of a grid cell used the closest grid cell to their 

location. The proximity was determined using the distance formula . 

A Google Earth ‘.kmz’ overlay of the latest grids for the Great Lakes and Lake St. Clair can be found at:

http://www.glerl.noaa.gov/res/glcfs/kml/glgrid-regions.kmz. A Google Earth ‘.kmz’ overlay of the 2006-2008 Lake Huron 

grid can be found at: http://www.glerl.noaa.gov/res/glcfs/kml/glgrid-regions-5km.kmz. The Beach Forecast Program (see 

section 3) allows a user to manually select a different grid cell than the one the program selected using arrow buttons to 

move the grid cell marker on a map that is displayed. 

2.4 E. coli Data Sources and Data Processing

The E. coli data for the beaches within this project was provided by beach managers and local health departments (Table 

2.4). To utilize the E. coli data provided, some of the data had to be processed. Where an E. coli value had a “<” (less than 

sign) associated with it, the value used was equal to half of the recorded numeric value. Where an E. coli value had a “>” 

(greater than sign) associated with it, the value used was equal to the recorded numeric value. 

Table 2.4. E. coli data sources.

Beach Beach Name Source of E. coli

Data Organization

No. Name

1 Bay City State Rec. Area Robert Hill Bay County Health Department

2 North Beach Park Adeline Hambley Ottawa County Health Department

3 Grand Haven State Park Adeline Hambley Ottawa County Health Department

4 North Beach Adam Mednick City of Racine Health Department & Lab

5 Zoo Beach Adam Mednick City of Racine Health Department & Lab

6 Upper Lake Park Beach Adam Mednick Ozaukee County Public Health Department

7 South Shore Beach Adam Mednick City of Milwaukee/Wisconsin Water Science Center

8 Bradford Beach Adam Mednick City of Milwaukee/Wisconsin Water Science Center

9 Woodlawn Beach Kristen Husson New York State Office of Parks, Recreation, and Historical 

Preservation

10 Hamburg Bathing Beach John Finster Erie County (NY) Department of Health

11 Evans Town Park Beach John Finster Erie County (NY) Department of Health

12 Erie Beach John Finster Erie County (NY) Department of Health

13 Wendt Beach John Finster Erie County (NY) Department of Health

14 Bennett Beach John Finster Erie County (NY) Department of Health

15 Presque Isle Beach #2 Dr. Doug Range Erie County (PA) Department of Health/Presque Isle State Park, PA

16 Presque Isle Beach #10 Dr. Doug Range Erie County (PA) Department of Health/Presque Isle State Park, PA

17 Villa Angela Mark Citrigilia Northeast Ohio Regional Sewer District/USGS Real Time Database

18 Hammond Marina East Beach Michelle Caldwell Indiana Department of Environmental Management

19 Marquette Park Michelle Caldwell Indiana Department of Environmental Management

20 Washington Park Beach Michelle Caldwell Indiana Department of Environmental Management

21 Ogden Dunes Michelle Caldwell Indiana Department of Environmental Management

22 Indiana Dunes West Beach Michelle Caldwell Indiana Department of Environmental Management

23 Memorial Park Beach Steve Lichota Macomb County Health Department

24 Metro Park Beach Steve Lichota Macomb County Health Department
15

2.5 Hydrodynamic Model Data Sources

The hydrodynamic model data was obtained from two online locations. Data from 2002-2005 for Lakes Erie, Huron, 

Michigan, Ontario and Superior and for 2007-2010 for Lake St. Clair was collected from the GLERL website located at 

http://www.glerl.noaa.gov/res/glcfs/gridded_fields/. Data from 2006-present (except for Lake St. Clair), was accessed 

through GLOS’s point query tool for the Great Lakes Coastal Forecasting System (http://data.glos.us/glcfs/). Lake St. 

Clair data is scheduled to be available through GLOS’s web tool in the near-future.

2.6 Meteorological Data Sources

All meteorological data is retrieved from the National Climatic Data Center (NCDC). The data is collected through 

NCDC’s ftp site located at ftp://ftp.ncdc.noaa.gov/pub/data/noaa/. The selection of meteorological station(s) for a 

given beach was accomplished by calculating the closest surface airway stations as determined by the distance formula 

. The availability of key variable data at the closest surface airway stations then narrowed the list 

for a given beach to a single station. In some cases, a secondary station was identified. A secondary station was used for 

locations where the primary station had insufficient or erratic precipitation data, in these cases the secondary station was 

only used for precipitation data.

2.7 USGS River Gauging Station Discharge Data Sources

Daily mean river discharge values are acquired from USGS through their water data website located at http://waterdata.

usgs.gov/nwis/.

2.7.1 River Runoff Computation

The values for river baseflow are calculated using a USGS computer program developed by A.T. Rutledge called PART. 

The PART computer program uses a method of determining baseflow that is based on antecedent streamflow recession. 

Runoff is calculated by subtracting the calculated baseflow values from the river’s daily mean discharge.

3. BEACH FORECAST PROGRAM

To aggregate the data needed to create the models for each beach using Virtual Beach, a graphically driven program was 

written. The Python programming language was used to write the scripts and Tkinter was used in conjunction with Python 

to provide the graphical user interface. Python and Tkinter were chosen because they are both freely downloadable and 

distributable tools (Figure 3.1).

4. VIRTUAL BEACH 2.3 SOFTWARE

Virtual Beach 2.3 (VB2) series is a software package designed to construct beach sampling site-specific beach decision 

support tools using multiple linear regression. These equations correlate E. coli measurements with independent variables 

(IVs) measured at the beach or from nearby meteorological stations, river gage sites, or Great Lakes Coastal Forecasting 

Hydrodynamic cells. The VB2 modeling interface is designed to help find the best model amongst a large number of 

candidate models, based on criteria selected by the user. As the number of IVs increases, the number of possible models 

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

model to reduce the size of the solution space. For complete user instructions, Virtual Beach User guide (Cyterski et al. 

2012) is found on the web at http://www.epa.gov/ceampubl/swater/vb2/Virtual Beach 2 User Guide.pdf.

5. BEACH WATER QUALITY DECISION SUPPORT SYSTEM (DSS)

The technical and scientific merit of the beach water quality decision support system is based on well-known observations 

that general seasonal, weather, and hydrological conditions greatly influence the physical, chemical, and biological 

characteristics of large water bodies such as the Great Lakes. These factors in turn affect the occurrence, distribution, 
16

and survival of microbiological contaminants in the water. Forecast models using data from deterministic models 

(hydrodynamic and meteorological) quantify influences that are common to a geographical region and at no additional 

analytical expense to the beach manager. 

The development and application of this concept by Whitman and Nevers (2004) demonstrated in a regional model from 

Milwaukee, WI to Indiana Dunes State Park, IN of Southern Lake Michigan that many beaches in a common geographical 

area respond similarly. These large-scale patterns cause simultaneous fluctuations in fecal indicating bacteria at beaches 

throughout a region (Nevers and Whitman 2008). Predictive nowcast models frequently include IVs such as current speed 

and direction, wave height, sunlight, and rainfall (Francy et al. 2006, Francy 2009, Olyphant 2005, Nevers and Whitman 

2005); all of which can be forecasted.

The following description uses Indiana Dunes State Park West Beach (IDSP West) data to demonstrate the process used to 

build a multiple linear regression model for making forecasts predicting E. coli using VB2.

The IDSP West 2006-2009 data (Attachment 2) was assembled as described in section 2. The data processing required to 

arrive at a typical forecast DSS equation follows. All Table 2.1 IVs were computed hourly for each E. coli measurement 

using the nearest hour IVs value. Sample times between 1-29 minutes were rounded back to the hour. Sample times 

between 30-59 minutes were rounded to next hour. All local times were converted to GMT using GMT=EDST+4 hours 

and GMT=CDST+5 hours. The recommended minimum number of samples in a training data set is 100 or more samples 

obtained over a preceding time interval of at least one year. However, data was assembled over years assuming beach 

environmental conditions were stable.

To load the data set into VB2, open VB2 and use the Data Processing Tab to import the data file containing the IVs which 

have been assembled for the beach E. coli sampling times. These values represent the training data set for the forecast 

DSS. Typically, they represent measurements from one or more years prior to the year for which the forecast will be made.

Figure 3.1 Beach 

forecast program 

screenshot.
17

Validate the imported data set and correct any errors detected. VB2.3 identifies categorical variables which cannot be 

transformed and automatically disables them. The response variable (LOG10Ecoli) is in the second column. Sample times 

for the E. coli measurements are in column one. The second column is a LOG10 transform of E. coli and VB2 requires 

manual identification of the transform by right clicking on column 2 and selecting the appropriate transform being used. 

Within define transform, highlight transform needed, which in this case is log10 and hit enter key. See Figure 5.0.1. Note 

ECOLI is highlighted in red. VB2 denotes disabled columns by changing the color of the column of numbers from black 

to red.

In preparing variables for transformation, the next step is to disable IVs which would be correlated. In this study, these 

variables included E. coli (disabled in above screenshot as noted by red numbers) which would be correlated with 

LOG10Ecoli. IVs correlated with onshore and along shore components of the surface and bottom currents, wind, and 

wave were CD0, CDb0, WVD0, WD0, and WD0m. QTR was disabled because individual Q1, Q2, Q3, and Q4 categorical 

variables were retained. WVP0 was disabled.

Meteorological variables duplicate the Great Lakes Coastal Forecasting System (GLCFS) hydrodynamic model except for 

precipitation and gustiness variables. In some cases, individual meteorological data sets have instrument failures resulting 

in missed hourly readings. Meteorological variables representing faulty readings or those with fewer than 15% real 

numbers were disabled if a GLCFS variable could be used instead. VB2 will automatically disable some variables that 

have one value. In this example, eleven meteorological parameters were disabled. Altogether, 30 meteorological IVs were 

disabled. 

In general, wind gustiness and precipitation variables are not disabled, because the hydrodynamic deterministic model 

cannot provide these measurements. However, instrument failure represents a challenge to incorporate wind gustiness and 

precipitation variables in the forecast DSS as occurred in this example.

Figure 5.0.1:VB2.3 Data Processing Screenshot
18

Second order or interaction terms are possible using the Manipulate Tab. VB2 provides the user an option to include twoway interactions between IVs. This study did not employ this option (Figure 5.0.1).

This study employed three transforms when using the Transform Tab. The transforms used were square, square root, and 

polynomial. Other transformations are available (such as Log10, Natural Log, and Inverse) were not used in this study. 

Zero sample values would result in a singularity in these transforms. VB2 avoids these transform singularities by adding a 

small value to a zero sample measurement.

VB2 uses a 20% threshold as a default value for the Transform Tab. The 20% transform was rerun by selecting the 40% 

threshold as shown in Figure 5.0.2. A transformed variable was selected if the Pearson coefficient exceeded the untransformed variable by 40%. In Figure 5.0.2, no transform of OSWO exceeded the un-transformed variable by 40%, but 

the POLY transform of OSWO was selected to have the same transform for both ASWO and OSWO. This process was 

applied for all grouped variables so that a single transform was used to aid in interpretation of the forecast DSS.

The 40% threshold (r=.4) provides a stronger linear relationship with the transformed variable and minimized the 

number of transformations (Cyterski, M personal communication). This choice is arbitrary. This effect size variance 

represents at least 16% (r2=.16) of the dependent variable variance is attributable to the independent variable (Cohen, J. 

1988). The goal was to seek stronger linear relationships with the transformed variables and to minimize the number of 

transformations. This would allow for ease in interpretation of the forecast DSS equation. 

Groups of independent variables (e.g. RvrNameRD_0d, RvrNameRD_1d, RvrNameRD_2d...) may have more than one 

transform. To facilitate interpretation of the decision support system, only one transform was selected for such a data 

group. The transform that had the highest average Pearson coefficient was chosen. This was illustrated in Figure 5.0.2.

Figure 5.0.3 shows the Data Processing Tab after the threshold transformation is completed. Note VB2 allows for 

inclusion of the variable and the transformed variable as illustrated by the DAYS and POLY(DAYS) variables. The 

POLY(DAYS) variable is one of eight transforms added to the data set which will be used in the MLR model. Note 

the column count in Figure 5.0.1 was 71. Figure 5.0.3 has a column count of 79 reflecting the 8 additional transforms 

included in the IV data set.

Click on the Go To Modeling Tab in ribbon above data located on the right hand side of Figure 5.0.3. Figure 5.0.3 shows 

the number of IVs available for the MLR. There were 79 IVs (columns) – 38 disabled IVs (columns) – Dependent 

Variable (LOG10Ecoli) - Time Variable (Date) leaving 39 IVs available for multiple linear regression. In the Modeling 

Tab, all the transformed and un-transformed variables obtained from the Data Processing Tab are selected for multiple 

linear regression evaluation and are moved into the Available Variables (under the Variable Selection sub-tab).

The evaluation criteria used in this study was the Bayesian Information Criterion (BIC). This control criterion was 

selected from eight possible options in the pull down screen. BIC is based, in part, on the likelihood function, and it is 

closely related to Akaike information criterion (AIC). When fitting models, it is possible to increase the likelihood by 

adding parameters, but doing so may result in over fitting. The BIC resolves this problem by introducing a penalty term 

for the number of parameters in the model. The penalty term is larger in BIC than in AIC (Schwarz, G. E. 1978). This is 

expected to minimize the number of key variables identified in the forecast DSS equation. In addition to specification of 

the evaluation criterion, the selection of the Genetic Algorithm is needed. Figure 5.0.4 shows the layout of the Modeling 

Tab.

In Figure 5.0.5, the Genetic Algorithm was selected because the possible models for most beaches exceeded 9.2e18. In 

this case the number of possible models is 5.5e11. The Decision Criterion (235 or 300 counts/100 m) and State Regulatory 

Standard (235 or 300 counts/100 m) appropriate for each state was used. Default control values available in VB2 were 

accepted. Default values were used for VIF (5), mutation rate (0.05) and cross over rate (0.5). This study set the seed 

value to 1 to fix the random number generator. The population number was set to 5000. The number of generations was 
19

Figure 5.0.2: VB2.3 Transform Screenshot

Figure 5.0.3: VB2.3 Data Processing Screenshot after Completion of Transform Variable Selection
20

set at 50. VB2 requires a minimum of 25 generations. It was observed that additional generations often did not improve 

the value of the evaluation criteria, but increased the time to complete the MLR run. Typical run times for the program 

was 1-2 hours on a HP Intel 2 Duo CPU P8400 running at 2.26 GHz with Microsoft Windows XP Professional Version 

2002 Service Pack 3.

Upon completion of the Genetic Algorithm run, click on Clear List Tab to remove all IVs. Highlight each of the 10 BIC 

values representing the best equations in the Model Information Best Fit screen, one at a time and click Add To List Tab. 

This will accumulate all the unique IVs in the ten best fit equations in the Independent Variable Screenshot (Figure 5.0.6). 

Note the BIC value was unchanged after six generations in the Forecast DSS for Indiana Dunes State Park West Beach.

Figure 5.0.7 shows the Modeling Manual Tab and Cross Validation screenshot. The resulting number of IVs will generally 

allow the use of the Manual Tab to search all the possible models for the ten best fits available in the reduced set of IV 

obtained from the Genetic Algorithm. Check box for Run all combinations and click on Run Tab.

This will result in another set of ten best fit equations. Run the cross validation step by clicking on Cross Validation Tab. 

In this study, 25% of the samples were held out for this procedure, rounding to the nearest whole number if the number of 

samples were not divisible by 4. The number of trials in this study was set at 5000. On repeats of the cross validation step, 

5000 trials resulted in less variation in the values for MSEP when repeated runs were attempted.

In the Cross Validation screen, the 10 resulting equations can be ranked by MSEP and number of variables. The best fit 

equation with the most variables has the lowest MSEP. In this study, the equation with the minimum MSEP and most 

variables was selected as the best Forecast DSS. This selection is highlighted in blue in the left most column (fitness) 

of the Cross Validation screen above. The equation with the fewest variables and minimum MSEP was also selected for 

this study. This choice was made to keep the Forecast DSS as simple as possible. However, one of the 34 sites had the 

same number of variables for all 10 best fit equations. In this case, the equation with the maximum MSEP was selected to 

represent the second choice.

The “fitness” column is the value of the evaluation BIC criterion chosen in this study. This allows identification of the 

model in the Modeling Tab. The MSEP column stands for the “mean squared error of prediction.” Across all the random 

cross-validation trials (in this case, 5000), it summarizes the average squared predictive error for all of the testing data. It 

is calculated by taking the difference between the actual observation and the model prediction, square the differences, sum 

them up for all testing data set observations, and then divide by the number of observations to obtain the mean value. The 

equation with the smallest MSEP did the very best at predicting “new” observations – that is the 25% of the observations 

not included in fitting the model’s regression coefficients. Models with the largest MSEP did the worst at making 

predictions. Cross-validation is a means to choose the “best” model to be used in prediction (Figure 5.0.7).

Return to the Modeling Tab we get Figure 5.0.8 by highlighting the BIC value from the Cross Validation screen. Select 

the variable statistics tab and check all IV’s P-values. Note in the Variables Statistics screen, all IV’s have statistically 

significant P-values. In this study when one of the IVs did not have a statistically significant P value, the IV was removed 

and the above steps rerun to get a best fit model with all IVs having significant P values (Figure 5.0.8).

The Residuals Tab allows you to evaluate the normality of the residuals resulting from the model. Note Figure 5.0.9 

has the standard cutoff set at 0.65. This choice was made early in VB2 development. A p/n ratio of 0.1 (10 observations 

for each parameter) was chosen as reasonable. If p/n is 0.1, then 2*√(p/n)=0.632 and was rounded to 0.65. If 2*√(p/n) 

becomes too small, it will often result in too many observations being removed from a normally distributed residuals 

dataset. This happens more frequently when the p/n ratio drops below 0.1.

The Anderson Darling statistical test tests for normality of the residuals can be found by clicking the Predicted vs. 

Residuals tab located in the left most position of the ribbon located to the left of the residuals plot. Anderson Darling 

(A.D.) statistical test <0.05 indicates the distribution of studentized residuals is not normal. See Figure 5.0.10.
21

Figure 5.0.5: VB2.3 Modeling Genetic Algorithm Screenshot

Figure 5.0.4: VB2.3 Initial Modeling Screenshot
22

Figure 5.0.6: VB2.3 IVs from Ten Best Fit Genetic Algorithm Models Screenshot

Figure 5.0.7: VB2.3 Modeling Manual Tab and Cross Validation Screenshot
23

Figure 5.0.9: VB2.3 Display Model of DFFITS Residuals Screenshot

Figure 5.0.8: VB2.3 Display of FDSS Equation Variabale P-Values Screenshot
24

For large data sets, which are typical in this study, the A.D. statistic is sensitive to minor variations in the normality of the 

residuals (Cyterski personal communication) and frequently evaluates the residuals as non-normal. To meet this criterion 

would result in too many samples being discarded by applying the iterative threshold options. However, the loss of more 

than 5% of the samples is not recommended to attain normality as measured by the A.D. statistic. The approach applied 

in this study is to remove outliers that have DFFITS absolute values greater than 0.65 and run the rebuild model resulting 

from the outlier removal.

To find the optimum Decision Control (Horizontal) (DCH) setting that minimizes the total number of errors and the 

number of false negative errors (Type 2) in the training data set, the following procedure is used (Francy et al. 2006b).

A plot of the predictions vs. the observations for the training data is obtained by clicking the Fitted vs. Observed tab 

located in the second left most position of the ribbon located to the left of the residuals plot. Doing this replaces the 

predictions versus the Studentized Residuals plot with the Fitted vs. the Observed in the next screenshot (Figure 5.0.11).

Note the total number of errors are 58 with 56 type 2 errors using DCH=RSV=235. The accuracy of the model is 84.3%. 

By adjusting the DCH to lower values we can reduce the number of type 2 errors at the risk of increasing type 1 errors. 

This process will not improve the accuracy of the model if the results are a one for one trade off. Exposure to higher 

bacterial concentrations increases the risk of greater human health problems. The trade-off between not swimming in 

water with higher bacterial concentrations for not swimming in water when bacterial levels are below the state regulatory 

standard is a tradeoff that county health departments favor despite the loss of economic benefits when swimming is not 

permitted.

In this case you can observe in Figure 5.0.11, a cluster of type 2 errors near the DCH=235. By selection of DCH=155 we 

find the cluster of 4 false negatives errors (type 2) are located above the DCH line without incurring an increase in the 

number of false positive errors (type 1). By re-plotting the Fitted vs. Observed with the DCH=155 we get Figure 5.0.12. 

Note the accuracy of the model has increased to 85.3% with the reduction in total errors to 54.

Having found the optimum DCH for the training data, we move to the MLR Prediction tab to apply the model developed 

from the 2006-2009 training data (Figure 5.0.13).

Using IDSP-West Beach 2010 data we can see in Figure 5.0.13, the Forecast DSS equation under consideration in the 

Model text box at the top. You can navigate to Figure 5.0.13, by clicking on the MLR Prediction tab.

The IVs have been imported. The 2010 E. coli observation data has been imported. After passing VB2’s required data 

validation step, prediction of model values to compare with observations can be done. First the DCH is set to 155 based 

on the optimization determined by the training data. If the environmental conditions in effect during the training data years 

have not been altered, the predictions developed from the model should compare well with the observations taken in 2010. 

The next step is to click the Make Prediction tab. Note the IVs from which the predictions are made are displayed on the 

left. In the middle are the observations. On the right side of Figure 5.0.13 are the model predictions and evaluations of the 

type of errors resulting from the model predictions.

The last step is to plot the model predictions verses the observations. Figure 5.0.14 illustrates the results for the 2010 

observations. The accuracy of the forecast model in this case was 81.1% which is slightly below the training data. This is 

a usual outcome since the validation data set contains new variability which the training dataset did not contain.

The persistence model for 2010 would have had 28 errors evenly divided between type 1 and type 2 errors. The forecast 

model reduced the number of type 1 errors by 13 and increased the number of type 2 errors by 5. The accuracy of the 

persistence model is 78.8%. The forecast DSS accuracy is 81.1% with a total of 20 errors. 
25

Figure 5.0.10: VB2.3 Residuals, Fitted vs Residuals, Anderson Darling Statistic Screenshot

Figure 5.0.11: VB2.3 Residuals Fitted vs Observed, Model Statistics, Total Errors Screenshot
26

Figure 5.0.12: VB2.3 Residuals Fitted vs Observed, Optimize Decision Criterion Screenshot

Figure 5.0.13: VB2.3 MLR Prediction Screenshot
27

It should also be noted that the DCH=155 was an optimal selection for the 2010 data. A lower DCH value would have 

increased type 1 errors (prevented swimming) with no corresponding decrease in type 2 errors (allowing swimming when 

bacterial contamination actually exceeded the state regulatory standard).

5.1 2010 Forecast Decision Support Systems for 35 Sampling Sites at Twenty-Four Beaches

The grant proposed to take predictive modeling to the next step. The grant developed forecast DSS for Twenty-Four 

Beaches. This resulted in 35 forecast DSS equations since some of the beaches were sampled at more than one location. 

Table 5.1 contains the 2010 forecast DSS equations for the 35 sites. The beach managers used these additional sampling 

locations to manage a portion of the beach. Table 5.1 lists the six beaches where this occurred. The key parameters 

identified by the multiple linear regressions are from the complete list of key parameters identified in Table 2.1. Fifty-two 

different key parameters were identified as being explanatory variables for E. coli variation at these 35 locations. 

5.2 Key Variables in the Forecast Decision Support Systems for the 35 Sites

Table 5.2 summarizes the key variables in the Thirty-Five forecast DSS at the Twenty-Four Beaches and the number of 

times they were selected by the MLR. As a group, precipitation was identified most often as a key parameter for these 

beaches. Precipitation variables have been reported in several papers as a key explanatory variable. The physical process 

indicated by precipitation is the flushing of bacterial laden materials into the beach watershed (Francy et al. 2006, 

Holtschlag et al. 2008, Nevers and Whitman 2005). Precipitation key variables averaged over 48 and 72 hours suggest 

watershed areas further from the beach are sources of bacterial contamination. Onshore waves, along shore waves, and 

wave height variables are also identified as explanatory variables. The physical process involves the re-suspension of 

beach sand and release of bacteria in the sand (Nevers and Whitman 2005, Olyphant 2005, Frick et al. 2008). Although 

not identified as frequently, variables relating to tributaries are also important. Those beaches in the study near gauged 

Figure 5.0.14: VB2.3 2010 Model Predictions vs 2010 Observed Values
28

Table 5.1. 2010 Forecast DSS equations for the 35 sites.

Beach Name Training 

Data Years

No. of 

Samples

2010 Decision Support System Equation (Using Minimum MSEP)

Bay City State Rec. Area 2009 50 Log10E.coli = -0.468 + 0.917(POLY(WSP0m,0.484,0.442,-0.0570)) + 

1.01(POLY(SaginawRO_1d,1.18,-0.000347,4.62e-08)) +

0.180(AT0) - 0.214(AT120) - 1.77(OSWV0) + 18.9(OSC0)

Grand Haven North Beach 

Park 

2002-2009 119 Log10E.coli = -1.062 + 0.0786(DP24m) + 0.783(POLY(ASW

0m,1.04,0.00538,0.0173)) + 0.000112(GdRiverRD_5d) - 

0.000296(GdRiverRO_8d)

Grand Haven State Park 

Beach

2002-2009 113 Log10E.coli = -1.37 + 0.104(DP24) + 0.906(POLY(AS

WV0,1.02,0.737,1.46)) + 0.842(POLY(CC

0m,1.02,1.15,-0.905)) -

6.62(√(TP0m)) - 0.103(AT240m) + 0.919(POLY(AT24

0m,3.70,-0.326,0.00975))

Racine North Beach Park 2003-2009 516 Log10E.coli = -0.208 - 0.000186(DAYS) + 0.391(WVH0) + 0.301(ASWV0) 

+ 0.316(CC4) + 0.740(POLY(TP24m,1.43,1.58,-0.705)) +

0.0938(TP72m) + 0.149(Q3) + 0.0295(SWT9) - 1.27(TP0m)

Racine Zoo Beach 2003-2009 517 Log10E.coli = 0.430 - 8.66e-05(DAYS) + 1.37(CS0) - 0.817(POLY(AS

CB0,1.47,0.749,66.1)) + 0.490(WVH0) + 0.426(CC4) + 

0.601(POLY(TP24m,1.38,1.71,-0.611)) +

0.426(POLY(TP72m,1.37,0.543,-0.0711)) + 0.118(Q3) + 

0.0174(SWT9)

Upper Lake Park Beach 2003-2009 539 Log10E.coli = -0.206 + 0.568(POLY(DAYS,1.25,0.00122,-5.47e-06)) + 

0.0618(DP24) + 0.0537(SWT9) + 0.904(WVH0) - 1.95(POL

Y(AT240m,1.53,-0.0183,0.00116)) -

0.0347(DP4m) + 0.569(CC4m) + 0.740(POLY

(TP72m,1.52,0.55,-0.0183)) + 0.654(POLY(TP

0m,1.64,55.2,-679))

South Shore Beach 2003-2009 602 Log10E.coli = -13.6 + 0.693(POLY(DAYS,2.08,0.000597,-2.26e-07)) + 

0.474(WVH0) + 0.486(POLY(ASW0,2.24,0.0267,0.00971)) 

- 0.193(Q1) -

 0.0547(AT24m) + 0.983(POLY(AT12

0m,0.605,0.145,-0.00287)) + 0.0404(DP24m) + 0.501(POLY

(TP24m,2.26,0.966,-0.263)) +

3.85(POLY(MlwkeRD_0d,2.29,1.63e-05,-4.73e-10)) + 

0.526(POLY(TP0m,2.32,11.0,-50.0))

Bradford Beach 2003-2009 604 Log10E.coli = 1.45 - 0.000190(DAYS) + 0.0710(SWT0) + 0.819(CS0) 

+ 0.429(CC4) - 0.100(ATmin24) + 0.0673(DP24m) + 

0.0338(WSP2m)

Woodlawn Beach State 

Park 

2003-2009 468 Log10E.coli = 0.354 + 0.000167(DAYS) + 0.0808(DP24) + 2.88(ASC0) - 

0.785(OSWV0) + 0.206(Q4) + 0.580(TP24m) -

0.0647(AT0) + 0.556(POLY(ASWV0,2.01,-0.445,1.99))

Hamburg Bathing Beach 2003-2009 221 Log10E.coli = 0.438 + 7.50(CS0) - 1.19(OSWV0) + 0.426(POLY(TP2

4m,1.75,1.65,-0.402)) + 0.396(TP72m) - 0.192(Q2)

Evans Town Park Beach 2003-2009 212 Log10E.coli = 0.229 + 0.0474(DP24) - 5.45(OSC0) + 1.31(WVH0) + 

0.346(TP72m)

Wendt Beach 2003-2009 209 Log10E.coli = 0.444 + 0.100(DP24) - 0.0592(SWT0) - 3.30(ASC0) + 

0.110(WS0) + 0.0765(OSW0) + 0.400(TP72m) - 0.194(Q2)

Lake Erie Park Beach 2003-2009 222 Log10E.coli = -2.58 + 0.632(POLY(ASW0,1.52,0.00331,0.0125)) + 

0.665(POLY(OSW0,1.67,0.0582,0.00308)) + 0.685(POLY(T

P24m,1.57,1.51,-0.229)) +

0.437(POLY(TP72m,1.52,0.615,0.0101)) + 2.63(CS0) - 

0.000116(DAYS)
29

Bennett Beach 2003-2009 208 Log10E.coli = -3.24 + 0.964(POLY(ASWV0,1.58,-0.169,2.93)) + 0.957(PO

LY(OSW0,1.56,0.0494,0.00525)) +

0.885(POLY(TP72m,1.44,0.846,-0.105)) - 0.212(Q2) + 

0.0120(AT240m)

Presque Isle Beach 2 - 1 2006-2009 193 Log10E.coli = -1.45 + 17.9(CSb0) + 0.672(POLY(OS

WV0,0.662,-2.17,-0.738)) + 0.0733(WS0) + 0.0649(DP24m) 

+ 0.0809(WSP4m) - 0.223(CC0)

Presque Isle Beach 2 - 2 2006-2009 192 Log10E.coli = -1.75 + 0.000248(DAYS) + 5.69(CS0) + 0.735(POLY(OS

WV0,0.581,-2.17,-0.649)) + 0.0525(AT240m) +

0.217(TP48m) + 0.0415(WSP4m) + 0.0221(DP24m)

Presque Isle Beach 10 - 1 2006-2009 164 Log10E.coli = 1.65 + 0.681(POLY(OSC0,1.11,-1.36,125)) + 1.02(WVH0) + 

0.685(POLY(AT120m,-0.451,0.041,0.00198)) + 0.705(POLY

(DP4m,1.29,-0.0797,0.00500)) -

2.85(POLY(CC4m,1.22,0.408,-0.324)) + 0.315(ASW0m) + 

0.726(POLY(CC24m,0.977,1.35,-0.801)) - 0.0444(DP0) - 

0.349(Q1)

Presque Isle Beach 10 - 2 2006-2009 170 Log10E.coli = -1.47 - 3.86(ASCB0) + 0.710(WVH0) + 0.630(CC24) 

+ 0.740(POLY(AT120m,-0.143,0.00497,0.00266)) + 

0.0848(WSP4m) +

0.584(POLY(DAYS,1.24,-0.000888,8.24e-07)) + 0.264(POL

Y(AT24m,0.983,-0.0663,0.00344))

Presque Isle Beach 10 - 3 2006-2009 171 Log10E.coli = -2.07 - 4.32(ASCB0) + 1.06(WVH0) + 0.528(CC24) + 

0.0828(AT24m) + 0.702(POLY(TP0m,1.11,61.1,-490))

Villa Angela East 2002-2009 852 Log10E.coli = -1.26 + 0.0604(DP24) + 0.323(WVH0) + 0.503(POLY(

OSWV0,1.8,-1.55,-0.440)) + 0.248(CC4) + 0.338(Q1) + 

0.417(Q2) +

0.479(TP24m) + 6.18e-05(DAYS) + 0.351(POLY(A

SW0,1.98,0.0156,0.00662))

Villa Angela West 2002-2009 824 Log10E.coli = 0.722 + 0.0751(DP24) - 3.90(OSC0) + 0.183(ASWV0) + 

0.779(POLY(OSWV0,1.76,-1.77,-0.533)) + 0.0700(WS0) - 

0.374(Q3) - 0.370(Q4) -

0.908(POLY(AT240m,1.94,-0.0152,0.000958)) + 

0.398(TP24m) + 0.306(TP48m) + 0.125(CC4)

Hammond Marina East 

Beach

2006-2009 413 Log10E.coli = -2.75 - 0.0655(AT24) + 0.840(POLY(CC4,1.84,-0.730,0.879)) 

- 0.518(Q4) + 0.0481(SWT9) +

1.45(POLY(DAYS,1.68,0.000502,-3.66e-07)) + 0.0504(DP0) 

- 3.38(ASC0) - 0.492(OSWV0)

Marquette Park Beach - 1 2006-2009 176 Log10E.coli = -6.03 + 0.0576(DP24) + 0.889(POLY(A

SW0,1.66,0.00287,0.00703)) + 0.830(POLY(O

SW0,1.72,0.0541,0.00529)) +

1.10(POLY(TP0m,1.77,-22.5,200)) + 1.12(POLY(TP2

4m,1.71,1.62,-1.35)) - 8.44(OSCB0)

Marquette Park Beach - 2 2006-2009 165 Log10E.coli = -4.74 + 0.0387(DP24) + 3.93(OSC0) + 0.787(POLY(OS

WV0,1.32,-1.54,-0.900)) + 0.199(CC24m) + 0.798(POLY(AS

W0m,1.41,1.74,0.516)) +

1.30(POLY(TP4m,1.43,-0.839,-0.322)) + 0.988(POLY(TP4

8m,1.35,0.912,-0.485))

Marquette Park Beach - 3 2006-2009 157 Log10E.coli = -3.56 + 0.0298(AT120) + 1.542(POLY(A

SW0,1.18,0.0198,0.00811)) + 0.988(POLY(O

SW0,1.27,0.0631,0.00448)) +

0.31(CC24m) + 0.705(POLY(TP48m,1.2,1.1,-0.506))

Marquette Park Beach - 4 2006-2009 163 Log10E.coli = -2.57 + 1.39(POLY(ASW0,1.21,0.0230,0.00569)) + 

0.803(POLY(OSW0,1.25,0.0749,0.00565)) + 0.810(POLY(T

P48m,1.21,0.955,-0.506)) - 9.82(OSCB0)

Table 5.1. 2010 Forecast DSS equations for the 35 sites (cont.).
30

Rivers had key variables identified from the tributaries either as discharge or runoff variables. Tributaries carry bacteria to 

the beach watershed from nearby watersheds (Nevers and Whitman 2005) or from storm or waste water treatment plants 

discharging to the rivers.

5.3. Comparison of 2010 Forecast DSS with Persistence and Always Open Management Tools

The grant proposed to compare the forecast models with the persistence and nowcast models. Only one Nowcast Model 

was found available for 2010. In place of the nowcast model, the other common beach management methods used in the 

Great Lakes is the Always Open (AO) management tool. This tool is used to keep the beach swimming always available 

except during times of physical danger such as high waves, lightning, or known sewage spills. AO is used by default when 

no bacterial water quality monitoring is done. AO is used when swimming at your own risk is permitted irrespective of 

elevated bacterial levels based on real time models. 

Attachment 5.3 contains comparison of 2010 forecast DSS with Always Open (AO) and Persistence Model (PM) 

Beach Management Models for 24 Beaches at 35 locations. VB2 provides 10 best equations during the cross validation 

step described in section 5. For this study, the best equation with the most variables and minimum mean square error 

of prediction was chosen and call FDSS-MV. The second selection from the 10 best equations available in the cross 

validation step was the equation with the fewest variables and minimum mean square error of prediction and called FDSSLV. 

Washington Park Beach -1 2006-2009 201 Log10E.coli = -0.482 + 0.0690(DP24) + 0.193(Q3) - 0.0743(AT24) + 

0.0483(SWT0) + 0.915(POLY(DAYS,2.03,0.000566,-

5.85e-07))

Washington Park Beach -3 2006-2009 199 Log10E.coli = -1.42 + 0.0696(AT120) + 0.495(CC24) - 0.214(Q2) + 

0.967(POLY(TP24m,2.03,0.669,-0.434)) - 0.139(Q4)

Washington Park Beach -5 2006-2009 200 Log10E.coli = -1.90 + 0.0648(AT120) + 0.548(CC24) + 1.19(POLY(TP2

4m,2.05,0.454,-0.369)) - 0.617(ASC0)

OgdenDunes - 1 2006-2009 239 Log10E.coli = -1.50 + 0.934(POLY(DAYS,1.20,-0.00279,2.53e-06)) + 

1.06(POLY(ASC0,0.773,3.01,70.3)) +

0.886(POLY(OSW0,0.879,0.0504,0.00181)) - 

0.0175*(DP24m) + 0.0145(AT4m)

OgdenDunes - 2 2006-2009 240 Log10E.coli = -4.41 + 0.969(POLY(OSWV0,1.28,-0.859,-0.243)) + 

0.872(POLY(TP72m,1.24,0.483,-0.0468)) +

1.04(POLY(BrnsDtchRO_1d,1.27,0.000209,-3.20e-08)) + 

1.38(POLY(BrnsDtchRO_8d,1.40,-9.53e-05,9.83e-09))

OgdenDunes - 3 2006-2009 239 Log10E.coli = -3.68 + 0.824(POLY(DAYS,1.08,-0.00220,2.25e-06)) + 

1.11(POLY(OSWV0,0.862,-1.20,-0.409)) + 1.75(POLY(DP2

4m,1.09,-0.0233,0.000312)) +

0.439(CC24m) + 0.933(POLY(TP72m,0.862,0.784,-0.360)) 

+ 0.000121(BrnsDtchRO_1d) + 0.0150(AT4m)

IDSP West Beach 2006-2009 367 Log10E.coli = 1.14 + 0.0228(DP24) + 0.333(WVH0) + 2.29(ASC0) - 

9.52(OSCB0) + 0.213(CC4)

Memorial Beach 2007-2009 130 Log10E.coli = -3.76 + 0.000424(DAYS) + 0.550(CC24) - 0.491(Q4) + 

6.07e-05(ClintonRD_0d) +

1.42(POLY(AT120m,-0.911,0.310,-0.00806)) + 1.23(POLY(O

SWV0,1.93,0.657,3.62))

Metropolitan Beach 2007-2009 130 Log10E.coli = -1.30 + 0.000809(DAYS) + 0.588(POLY(AT2

4m,-0.472,0.229,-0.00595)) + 0.998(POLY(AS

WV0,1.65,2.09,-4.49))

Poly (IV,a,b,c)= a + b(IV) + c (IV)2 where IV is the independent variable, and a,b,c are coefficients in the equation.

Table 5.1. 2010 Forecast DSS equations for the 35 sites (cont.).
31

Table 5.2. Key variables in the 2010 forecast DSS for the TwentyFour Beaches.

Independent 

Variable

No. of 

Occurrances

Independent 

Variable

No. of 

Occurrances

DAYS 16 WVH0 9

Q1 3 ASWV0 6

Q2 5 OSWV0 13

Q3 4 CS0 7

Q4 5 ASC0 6

AT0 2 OSC0 4

AT4m 2 CSb0 1

AT24/AT24m 6 ASCb0 3

AT120/AT120m 8 OSCb0 3

AT240m 6 SWT0 3

ATmin24m 1 SWT9 4

DP0 2 TP0m 5

DP4m 2 TP4m 1

DP24/DP24m 17 TP24m 12

CC0 1 TP48m 5

CC4/CC4m 9 TP72m 9

CC24/CC24m 9 ClintonRD_0d 1

WSP0/WSP0m 4 MlwkeRD_0d 1

ASW0/ASW0m 9 GDRiverRD_5d 1

OSW0 7 SaginawRO_1d 1

WSP2m 1 BrnsDtchRO_1d 2

WSP4m 3 GDRiverRO_8d 1

BrnsDtchRO_8d 1

In actual practice of forecasting for a beach, evaluation of the 10 best equations might result in another selection using the 

beach manager’s professional judgment. The explanatory variables considered and ultimately used in the forecast DSS 

selected would depended on the type of sources found in the beach watershed and the transport mechanisms by which the 

bacterial contamination is suspected to reach the beach waters.

Attachment 5.3.1 stratifies the comparison of 2010 Forecast DSS with AO and PM into those beaches using the E. coli

standard for Michigan’s single sample maximum state standard of 300 counts/100 ml and the single sample maximum of 

235 counts/100 ml state standard for all the other Great Lakes states.

For the beaches with 5% or fewer samples exceeding the single sample maximum state regulatory standard, the forecast 

DSS system does not do better than the PM. AO beach management control system does have fewer total errors when 

compared to forecast DSS or PM at beaches with 30% or fewer samples exceeding the single sample maximum state 

regulatory standard. However, the AO exposes swimmers to elevated bacterial levels more frequently than PM or forecast 

DSS management control systems.

Figure 5.3.1 uses data from 30 sampling sites from 19 beaches where the single sample E. coli standard is 235 counts/100 

ml. The PM is compared with the FDSS-MV using the equation with the minimum Mean Square Error of Prediction 

(MSEP). For beaches where the percentage of the number of samples above the state regulatory standard are less than or 

equal to 5%, the FDSS-MV has more errors than the PM. For beaches where the percentage of the number of samples 

above the state regulatory standard are greater than 5%, the FDSS-MV had fewer errors in 19 of 27 sampling sites or 70% 

of the sites. FDSS-MV had more errors in 4 of 27 sampling sites or 15% of the sites. At 4 of the 27 sites FDSS-MV had 
32

the same number of errors as PM. FDSS-MV did as well or better in 85% of the sites with more than 5% of the samples 

exceeding the state regulatory standard.

Figure 5.3.2 uses data from 30 sampling sites from 19 beaches where the single sample E. coli standard is 235 counts/100 

ml. The PM is compared with the FDSS-LV using the equation with the minimum Mean Square Error of Prediction 

(MSEP). This option is considered because the FDSS-LV equation generally had 2 fewer variables to forecast. For 

beaches where the percentage of the number of samples above the state regulatory standard are less than or equal to 5%, 

the FDSS-LV has more errors than the PM similar to FDSS-MV. For beaches where the percentage of the number of 

samples above the state regulatory standard are greater than 5%, the FDSS-LV had fewer errors in 18 of 27 sampling sites 

or 67% of the sites. FDSS-LV had more errors in 5 of 27 sampling sites or 18% of the sites. At 4 of the 27 sites FDSS-LV 

had the same number of errors as PM. FDSS-LV did as well or better than the PM at 82% of the sites with more than 5% 

of the samples exceeding the state regulatory standard.

These two approaches result in similar outcomes. FDSS-MV and minimum MSEP performed 3% better in this study 

than the FDSS-LV. This resulted in one additional site with fewer errors than the PM model. Based on this small sample, 

FDSS-MV equations were used for the five 2012 forecast DSS models.

5.4 Comparison of 2010 Forecast DSS for adjacent Hydrodynamic Grid Cells at Three Beaches

A comparison of forecast DSS results for three beaches was done to test the impact of using hydrodynamic model data 

from adjacent grid cells. The object of this test was to determine if adjacent hydrodynamic cells would result in different 

beach management decisions and if a method could be identified to optimize the selection.

The three beaches were selected that fell outside the hydrodynamic grids. These beaches are Racine Zoo Beach 

(Wisconsin, Lake Michigan), Lake Erie Beach (New York, Lake Erie), and Memorial Park (Michigan, Lake St. Clair).

Figures 5.4.1 to 5.4.3 shows the two hydrodynamic grid cells with one of the cells identified as optimal for each of the 

four beaches. The optimal cell was selected based on criteria given in section 2.3. For Racine’s Zoo Beach in Figure 5.4.1, 

Figure 5.3.1. FDSS-MV Errors Compared to PM Errors.
33

Table 5.4 Comparison of Beach 2010 FDSS-MV Equation Results to Always Open & Persistence Beach Management Models at Adjacent Hydrodyamic Grid Nodes.

Training Data for Model 2010 Forecast Decision Support System

Beach

Grid Nodes 

Optimal 

or Other

Variables 

in VB2.2 

Decision 

Support 

System

% 

Accuracy % R2 % adj R2 MSEP

Number 

Training 

Samples 

(Start-End 

YY)

% (Number) 

Data Equal 

or Greater 

than State 

Standard 

% 

Accuracy 

% 

Specificity 

False 

Positives

% 

Sensitivity 

False 

Negatives

Total 

Errors

Zoo Beach Optimal 9 91 44 43 0.246 517 (2003- 2009) 11.4 % (59) 91 99 1 0 4 5

Other 7 91 43 42 0.246 517 (2003- 2009) 11.4 % (59) 91 94 3 33 2 5

Racine County, WI PM 93 96 3 25 3 6

AO 95 100 0 0 4 4

Lake Erie Beach Optimal 6 80 42 41 0.362 222 (2003- 2009) 22.5 % (50) 83 96 1 29 5 6

Other 6 80 44 42 0.353 222 (2003- 2009) 22.5 % (50) 77 93 2 14 6 8

Erie County, NY PM 71 82 5 17 5 10

AO 80 100 0 0 7 7

Memorial Park Beach Optimal 6 82 32 29 0.348 130 (2007- 2009) 20.0 % (26) 46 38 21 86 1 22

Other 7 83 38 35 0.342 128 (2007- 2009) 20.0 % (26) 54 47 18 86 1 19

Macomb County, MI PM 80 88 4 43 4 8

AO 83 100 0 0 7 7

FDSS MV = Forecast Decision Support System using Equations with most variables FDSS LV = Forecast Decision Support System using equations with least variablesPM = Persistence ModelAO = Always Open Model
34

Figure 5.3.2. FDSS-LV Errors Compared to PM Errors.

Figure 5.4.1. Racine Zoo Beach Adjacent Hydrodynamic Grid Cells.
35

Figure 5.4.3. Memorial Beach Adjacent Hydrodynamic Grid Cells.

Figure 5.4.2. Lake Erie Beach Adjacent Hydrodynamic Grid Cells.
36

the difference in the distance calculation from each cell is small. The distance is 1.87 km to grid cell “A” and 1.90 km to 

grid cell “B” (see Figure 5.4.1).

Table 5.4 summarizes the results for FDSS-MV equations for adjacent beach cells. The training data sets for each 

hydrodynamic cell for Racine Zoo Beach and Lake Erie beach have the same accuracy. The accuracy for the Memorial 

Beach training data sets differed by one percent. For the three comparisons, the total errors in the 2010 forecasts were the 

same for Racine’s Zoo beach but differed with respect to type 1 and type 2 errors. The total errors for Lake Erie beach 

were two fewer errors for the optimal cell, but for Memorial Beach the optimal cell had three more errors. Based on this 

small number of cases, it appears the adjacent nearest cells, have some effect on the total number of errors in the forecast, 

but the training data does not clearly indicate which cell would be preferred for developing the forecast DSS. For this 

study, the nearest hydrodynamic cell was used.

6. NOAA BEACH WATER QUALITY EXPERIMENTAL FORECASTS

6.1 Five Beaches 2012 Forecast Decision Support Systems

One forecast DSS was developed for the 2012 swimming season for each of five beaches. The beaches involved are 

located in Michigan. Three of the beaches are in the geographical forecast area of the Detroit Pontiac NWS. Two Ottawa 

County beaches are outside of the Detroit Pontiac Forecast Office geographical domain. The 2012 forecast DSS equations 

for each of the five beaches in the State of Michigan are found in Table 6.1. The beaches are Bay City State Recreation 

Area, Bay County MI, Memorial and Metro Beach, Macomb County, and North Beach Park Beach, and Grand Haven 

State Park Beach, Ottawa County, MI. 

The Detroit Pontiac National Weather Service Office provided four daily forecasts for these five beaches. These forecasts 

were issued at Midnight, 6 am, Noon, and 6 pm. The forecasts were provided to cooperating beach managers via the web 

during the swimming season.

6.2 Key Variables in 2012 Forecast Decision Support System Equations

6.2.1 Bay City State Rec. Area Beach 2012 Forecast DSS

The 2012 forecast DSS equation for the Bay City State Rec. beach based on training data from 2009-2011 is: 

LOG10Ecoli = 0.453 - 0.000422 * DAYS + 6.25 * ASC0 + 0.0993 * WS0 + 0.103 * OSW0 + 4.99e-05 * SaginawRD_9d.

Table 6.1. 2012 forecast DSS equations for five beaches in the State of Michigan.

Beach Name Training 

Data Years 2012 Forecast Decision Support System Equations

Bay City State Rec. Area 2009-2011 LOG10Ecoli = 0.453 - 0.000422*(DAYS) + 6.25*(ASC0) + 0.0993*(WS0) + 

0.103*(OSW0) + 4.99e-05*(SaginawRD_9d)

Memorial Beach 2007-2011 LOG10Ecoli = -9.72 + 0.999*POLY(DAYS,1.61,0.00120,-6.61e-07) + 2.44*POLY(

AT24,1.47,0.0798,-0.00263) +

0.880*POLY(OSWV0,1.89,-0.228,2.56) - 0.568*(Q4) + 1.03*POLY(

ClintonRD_0d,1.623,0.000932,-1.42e-07) + 0.0675*(AT120)

Metro Beach 2007-2011 LOG10Ecoli = -4.88 + 0.996*POLY(DAYS,1.18,0.00130,-6.70e-07) + 0.0351*(AT0) 

+ 2.051*(ASWV0) - 0.269*(Q2) +

 POLY(AT240m,0.578,0.093,-0.00193) + 

1.66*POLY(ClintonRD_0d,1.51,0.000316,-6.93e-08)

Grand Haven State Park 2002-2011 LOG10Ecoli = -0.893 + 0.0393*(DP0) + 0.0632*(WS0) + 0.790*POLY(AT

0m,1.827,-0.141,0.00487) +

9.95e-05*(GdRiverRD_0d) - 0.000118*(GdRiverRO_0d)

North Beach Park Beach 2002-2011 LOG10Ecoli = -0.570 + 0.116*(DP24) - 0.0849*(SWT0) + 2.242*(CS0) + 1.065*PO

LY(OSW0m,1.27,0.0551,-0.00834) + 0.328*(TP48m)
37

The five key variables are: DAYS (Count of Days from the first sample to the last sample with first sample day = 0), 

ASCO(Alongshore current at sample hour, n=1 (m/s, positive clockwise)), WSO(Wind speed at sample hour, n=1 (m/s)), 

OSWO(On-shore wind at sample hour , n=1 (m/s, positive towards beach)), and SaginawRD_9d(Discharge nine days 

prior to sample day (ft3/s)).

The DAYS independent variable has a negative coefficient indicating over time E. coli concentrations are diminishing. 

ASCO has a positive coefficient indicating currents from the south of the beach increase E. coli by bringing higher 

bacterial concentration water towards the beach from the mouth of the Bay where the Saginaw River discharges. WSO 

has a positive coefficient indicating stronger winds increase E. coli concentrations at the beach. OSWO has positive 

coefficient indicating onshore winds increase E. coli concentrations at the beach. SaginawRD_9d has a positive coefficient 

indicating Saginaw River Discharge 9 days previous to the sample day increases E. coli concentration at the beach. 

The combination of ASCO and SaginawRD_9d paint a picture of river discharge into the Saginaw Bay that is gradually 

circulated clockwise to the beach. The other key parameters indicate winds blowing Saginaw Bay water towards the beach 

increase E. coli concentrations. Stronger winds can push water more effectively towards the beach and re-suspend more 

sediment.

6.2.2 Memorial Beach 2012 forecast DSS

The 2012 forecast DSS equation for Memorial Beach based on training data from 2007-2011 is:

LOG10Ecoli = -9.72 + 0.999 * POLY(DAYS, 1.61, 0.00120, -6.61e-07) + 0.0675 * AT120 

+ 2.44 * POLY(AT24, 1.47, 0.0798, -0.00263) + 0.88 * POLY(OSWV0, 1.89, -0.228, 2.56) 

– 0.568 * Q4 + 1.03 * POLY(ClintonRD_0d, 1.623, 0.000932, -1.42e-07).

This forecast DSS involves the Polynomial transformation which is defined in Section 4 VB2 software as POLY(KV,a,b,c) 

and is the following equation P(KV)= a + b(KV) + c (KV)2 where KV stands for Key Variable or IV in this report. This 

transformation is more difficult to interpret because the contribution to LOG10Ecoli can change sign over the time period 

of the training data and the forecast year. Several illustrations will be provided with this forecast DSS.

The six key variables are: DAYS (Count of Days from the first sample to the last sample with first sample day = 0), AT120 

(Air temp previous 120 hour average, n≤120, (°C)), AT24 (Air temp previous 24 hour average, n≤24, (°C), OSWVO 

(Onshore Waves (m) at sample hour, positive towards shore, negative away from shore), Q4 (Categorical Variable for the 

fourth quartile of the sampling season by year), and ClintonRD_0d (Same Day River Discharge ft3/s). 

A plot of 0.999 * POLY(DAYS, 1.61, 0.0012, -6.61e-07) is shown in Figure 6.2.1. Note the inflection point during 

2009. After 2009, this IV of the 2012 forecast DSS equation contributes less to the total LOG10Ecoli. This is signaling 

a declining bacterial load to the beach after 2009. Macomb County has been eliminating bacterial sources to the Clinton 

River after the 2002-2005 USGS study (Holtschlag et al. 2008) identified the Clinton River discharge as a key variable in 

explaining E. coli variation at this beach. 

The contribution to E. coli concentration from this IV is greater for Memorial Beach than Metro Beach. This may be 

due to a cutoff in the Clinton River which takes river water closer to Memorial Beach (see discussion in Metro Beach 

following). 

A plot of 2.44 * POLY(AT24, 1.47, 0.0798, -0.00263) is shown in Figure 6.2.2. All AT24 values contribute to increasing 

LOG10Ecoli. However, the optimal temperature for bacterial growth appears to be about 15°C. 

The other IV for air temperature is the un-transformed variable AT120. The coefficient of AT120 is positive indicating that 

with increasing air temperatures averaged over five days, E. coli bacterial concentrations would be increasing.
38

Figure 6.2.1. 

Plot of 

POLY(DAYS) 

for Memorial 

Beach.

Figure 6.2.2. 

Plot of 

POLY(AT24) 

for Memorial 

Beach.

Figure 6.2.3. 

Plot of 

POLY(OSWO) 

for Memorial 

Beach.
39

The coefficient of Q4 is negative indicating that during the last quarter of the swimming season, E. coli bacterial 

concentrations were declining. The last quarter of the season would include August when air temperatures would be 

highest and reduced rainfall. Diminished rainfall would adversely affect bacterial growth and figure 6.2.2 POLY(AT24) 

graph shows less bacterial growth at higher temperatures.

Figure 6.2.3 POLY(OSWVO) is positive and adds to the E. coli concentration regardless of direction of the waves toward 

or away from shore. Waves during the time of sampling are not large with maximum height near 0.6 meter (under 2 ft).

On the next page Figure 6.2.4 POLY(ClintonRD_0d) shows the discharge of the Clinton River at the time of sampling as 

measured by the USGS gauge 04164000. Increased discharge generally results in higher bacterial concentrations at the 

beach up to 3000 ft3/s. The bacterial concentration declined at the highest discharge rate (between 4000 and 5000 ft3/s).

6.2.3 Metro Beach 2012 FDSS

The 2012 forecast DSS equation for Metro Beach based on training data from 2007-2011 is: 

LOG10Ecoli = -4.88 + 0.996 * POLY(DAYS, 1.18, 0.00130, -6.70e-07) + 0.0351 * AT0 + 

2.051 * ASWV0 - 0.269 * Q2 + POLY(AT240m, 0.578, 0.093, -0.00193) + 

1.66 * POLY(ClintonRD_0d, 1.51, 0.000316, -6.93e-08).

The five key variables are: DAYS (Count of Days from the first sample to the last sample with first sample day = 0), AT0 

(Air temp at sample hour, n≤1 (°C), ASWVO (Along Shore Waves at sample hour (m), positive = clockwise rotation), 

Q2 (Categorical Variable =2 for the second 25% of the sampling season by year), AT240m (Air temperature (Dry Bulb 

Celsius) at Selfridge Airport (MTC) over previous 240 hour average 180≤n≤240 (°C)), and ClintonRD_0d (Same Day 

River Discharge ft3/s). 

Figure 6.2.5 shows a plot of 0.996 * POLY(DAYS, 1.18, 0.00130, -6.70e-07). Note the inflection point in the contribution 

to E. coli for Metro Beach during 2009 similar to Memorial Beach. After 2009, Metro’s POLY(DAYS) contributes less 

to the total LOG10Ecoli. The magnitude of this IV to Metro Beach bacterial concentration is less than its contribution to 

Memorial Beach. There is a cut off in the Clinton River which takes river water near to the Memorial Beach. This may 

account for the lower concentrations at Metro Beach since the source of the bacterial contamination at Memorial Beach 

may not be coming from the main Clinton river outlet into Lake St. Clair. 

The coefficient of AT0 is positive indicating that with increasing air temperatures at the time of sampling, E. coli bacterial 

concentrations would be increasing.

The coefficient of ASWVO (Along Shore Waves at sample hour (m), positive= clockwise rotation) is positive indicating 

that waves approaching the beach from the west would increase bacterial concentrations. A dominant clockwise 

circulation cell is observed near Metro Beach (Anderson et al. 2010, Anderson and Schwab 2011).

The coefficient of Q2 is negative indicating that during the second quarter of the swimming season, E. coli bacterial 

concentrations were declining. The second quarter of the season would include July when air temperatures would be 

increasing, and rainfall declining. Increasing air temperatures would increase bacterial growth while declining rainfall 

would adversely affect bacterial growth. Other factors could be in play such as bacteriaphage increased activity could 

consume bacterial concentrations faster than elevated temperatures could increase the bacterial concentrations. 

In Figure 6.2.6, POLY(AT240m) is plotted. The coefficient of the 240 hour average air temperature is positive indicating 

that increasing average air temperatures over the previous ten days will increase bacterial concentrations at the beach 

resulting in increased E. coli concentrations. From the plot bacterial growth is near its maximum around 25°C.
40

Figure 6.2.5. Plot 

of POLY(DAYS) for 

Metro Beach.

Figure 6.2.6. 

Plot of 

POLY(AT240m) 

for Metro Beach.

Figure 6.2.4 Plot of 

POLY(ClintonRD_0d) 

for Memorial Beach.
41

Figure 6.2.7 POLY(ClintonRD_0d) shows the discharge of the Clinton River at the time of sampling as measured by the 

USGS gauge 04164000. Increased discharge results in increased bacterial concentrations at the beach for all discharge 

volumes up to 2500 ft3/s. Above 2500 ft3/s the bacterial concentration appears to decline. The highest discharge above 

4000 ft3/s contribution to E. coli concentrations declines to levels similar to low flow levels.

6.2.4 Grand Haven State Park 2012 forecast DSS 

The 2012 forecast DSS equation for Grand Haven State Park Beach based on training data from 2002-2011 is: 

LOG10Ecoli = -0.893 + 0.0393 * DP0 + 0.0632 * WS0 + 0.790 * POLY(AT0m, 1.827, -0.141, 0.00487) + 9.95e-05 * 

GdRiverRD_0d - 0.000118 * GdRiverRO_0d.

The five key variables are DP0, Dew point temp at sample hour, n≤1 (°C); WS0, Wind speed at sample hour, n=1 (m/s); 

AT0m, (Air temperature (Dry Bulb Celsius) at Muskegon County Airport (MKG) at sample hour of measurement n≤1 

(°C); GdRiverRD_0d and GdRiverRO_0d, Grand River Discharge and Runoff at same day of sample (ft3/s). 

The coefficient of DP0 is positive indicating that increasing amounts of water vapor in the air lead to increased bacterial 

concentration via impeding solar radiation which induces microbial inactivation. Dew point frequently replaces cloud 

cover which suggests that dew point and cloud cover are moderately collinear or redundant. Dr. Richard Zepp (personal 

communication) believes that air quality and/or poor ventilation in the atmospheric boundary layer may explain dew point 

as a key parameter. Aerosols and other air pollutants such as ozone that are particularly prevalent in stagnant urban air are 

effective attenuators of solar radiation, especially in the UV region which is particularly important in inducing microbial 

inactivation. Here in a non-urban atmospheric environment, we are seeing the same affect with increasing bacterial 

concentrations due to the lack of solar radiation attenuation with increasing dew point (increasing cloud cover). 

The coefficient of WS0 is positive indicating increased wind speed increases bacterial concentrations. 

Figure 6.2.8 POLY(AT0M) plot with increasing air temperature at sample time resulting in increased bacterial 

concentration for all temperatures. The positive coefficient of the second order term results in continuing increased 

bacterial concentrations with temperature rather than an optimal temperature.

Grand River discharge during the day of sampling has a positive coefficient which reflects that increasing discharge 

results in higher levels of E. coli at Grand Haven State Park.

Grand River runoff during the day of sampling has a negative coefficient which indicates that higher runoff decreases E. 

coli concentration at Grand Haven State Park. 

The coefficient for the Grand River discharge is an order of magnitude smaller than the coefficient for Grand River 

Runoff. However, the Grand River discharge is more than an order of magnitude greater than the Grand River runoff. The 

combined effect of these two key parameters is to increase bacterial concentration in all years (see Figure 6.2.9). 

6.2.5 North Beach Park Beach 2012 forecast DSS 

The 2012 forecast DSS equation for North Beach Park Beach based on training data from 2002-2011 is: 

LOG10Ecoli = -0.570 + 0.116 * DP24 - 0.0849 * SWT0 + 2.242 * CS0 + 1.065 * POLY(OSW0m, 1.27, 0.0551, 

-0.00834) + 0.328 * TP48m.

The five key variables are: DP24, Dew point temp previous 24 hour average, n≤24(°C); SWT0, Surface water temp at 

nearest 3 hour, n=1 (°C); CS0, Surface current speed at sample hour, n=1 (m/s); OSW0m, Onshore wind at sample hour 

at Muskegon County Airport (MKG), n=1 (m/s, positive towards beach) and TP48m,Total precipitation previous 48 hour 

total at Muskegon County Airport (MKG), 36 ≤n ≤48 (inches).
42

Figure 6.2.9. Plot 

of Grand River 

Discharge and Grand 

River Runoff for 

Grand Haven State 

Park. 

Figure 6.2.8. Plot of 

POLY(AT0m)) for 

Grand Haven State 

Park.

Figure 6.2.7 Plot 

of POLY(Clinton 

RD_0d) for Metro 

Beach.
43

The coefficient of DP24 is positive indicating increasing bacterial concentrations due to increasing values of the 24 

hour average of dew point. This key variable acts in a similar manner to cloud cover which decreases solar radiation 

attenuation.

The coefficient of SWT0 is negative indicating decreasing bacterial concentrations due increasing water temperature. This 

result is counter intuitive since bacterial concentrations generally increase with increasing temperature. It is possible that 

increasing water temperature stimulates bacteriophage which reduces the bacteria concentrations more rapidly than the 

bacteria can grow due to higher water temperatures (Muruleedhara Byappanahalli personal communication).

The coefficient of CS0 is positive indicating increasing bacterial concentrations due to faster surface currents. 

The coefficient of TP48m is positive indicating increasing bacterial concentrations due to increasing rainfall over the 

previous forty-eight hours. Runoff from the beach watershed would carry E. coli to the beach. The 48-hour average 

indicates the impact at the beach is from portions of the watershed further away from the beach.

Figure 6.2.10 POLY(OSW0m) shows the effect of onshore winds increasing bacterial contamination. Strong offshore 

winds have minimal impact while winds onshore have the maximum impact even at lower velocities.

6.3 2012 Forecast DSS Results Compared to Monitoring and Other Management Methods

Timely accurate forecasts of beach water quality are critical to protect human health against adverse exposure situations. 

The Center of Excellence for Great Lakes and Human Health, Great Lakes Environmental Research Laboratory, the 

National Weather Service, Detroit Pontiac Office, and the Cooperative Institute for Limnology and Ecosystems Research, 

University of Michigan developed and tested beach management forecast DSS at five beaches in Michigan. The NOAA 

Beach Water Quality Experimental Forecasts are possible because Bay, Macomb, and Ottawa County Health Departments 

have provided their E. coli monitoring data. The beaches involved are Bay City State Rec. Area, Bay Co. MI, Metro and 

Memorial Beaches, Macomb Co. MI, and North Beach Park and Grand Haven State Park, Ottawa Co. MI. (Table 6.1) The 

first three beaches were monitored approximately four times per week, and the last two were monitored approximately 

one time per week during the 2012 swimming season between Memorial and Labor Day. The NWS was generally 

successful in being able to run the forecast DSS in forecast mode by finding grid point and values for the forecast IVs. 

In one case, NWS required a different forecast equation because the precipitation independent variable needed to be 

replaced.

The results of the beach water quality forecasts was the ability to accurately forecast null events, i.e. keeping swimming 

available when bacterial counts were low. The accuracy ranged from 83 to 100% (average = 93.4 +/- 6.6%) when 

compared with the County Health Departments E. coli monitoring. The weakness was the inability to forecast any of the 

seven E. coli 2012 events occurring at four of the beaches (Table 6.3).

Figure 6.2.10. Plot 

of POLY(OSW0m) 

for North Beach Park 

Beach.
44

Several graphics are provided for Memorial beach to illustrate the work performed. Similar graphics are available for 

the other beaches. For Memorial beach, the forecast DSS specificity was 98%. Specificity is the percentage of correctly 

forecasting bacterial concentrations lower than 300 counts/100 ml. The forecast DSS sensitivity was zero. Sensitivity 

is the percentage of correctly forecasting bacterial concentrations at or above 300 counts/100 ml. This is the important 

measure for forecasting skill used by the NWS. Although forecast DSS had fewer errors than Macomb County’s presently 

used persistence beach management model, an always open management model would have had 100% specificity. 

The NWS requires skill in forecasting rare events. In beach water quality forecasting the rare event is an elevated E. 

coli concentration. Correctly forecasting at least one high bacterial concentration (sensitivity > 0) is required to exceed 

minimal skill in forecasting (Doswell et al. 1990). Doswell’s 2 x 2 contingency table is directly comparable to VB 

predicted E. coli versus observed E. coli graphic. NWS cannot make forecast DSS available for widespread use because 

sensitivity was zero for all beaches where elevated E. coli events (≥300 counts/100 ml) were observed.

Figure 6.4.2 is used to show the results of the forecasting for Memorial beach. The blue, green, and gold traces are the 

minimum, expected, and high E. coli values generated at 06:00 EDT by the Detroit Pontiac NWS to forecast beach water 

quality for the 8:00 am EDT sampling period. Red dots are observed E. coli values provided by the Macomb County 

Health Department. 

Note that six of the seven forecasted elevated E. coli concentrations occurred on the weekends when sampling was not 

conducted. As a result it is not known if these forecasted E. coli concentrations were correctly forecasted on not correctly 

forecasted.

Beach managers are evaluating the results of the 2012 season. Bay County will continue their four times a week 

monitoring in 2013 and is seeking NWS support to continue Bay City State Rec. Area beach forecast DSS in 2013.

6.4 Communication Plan for Distribution of Forecasts

The National Weather Service Forecast Office in White Lake, Michigan (WFO DTX), executed the beach forecast 

regression models for five Michigan Beaches in Bay, Macomb and Ottawa Counties four times per day through the 2012 

beach and boating season (generally Memorial Day to Labor Day). Forecasts generated at midnight and 6 am EDT on a 

given day will be valid for 8 am expected morning sampling time that day and the 8 am expected morning sampling time 

the following day. Forecasts generated at noon and 6 pm EDT on a given day will be valid for 8 am expected morning 

sampling times the following two days. Forecast output will include a minimum value, a most likely value, and maximum 

expected values, and the likelihood that E. coli counts will exceed 300 parts per ml and 600 parts per ml respectively. 

These forecasts were available to beach managers via the National Weather Service dissemination infrastructure, and 

specifically via specified URLs through the National Weather Service Information Dissemination System (NIDS).

Memorial Park: http://www.crh.noaa.gov/dtx/?n=beachwaterquality_mp is provided as an example of the URL available 

during the 2012 summer. Figure 6.4.1 shows the format and information provided by the NOAA Forecast for Memorial 

Beach Macomb County, MI for July 29, 2012 Midnight forecast at the website. All beach URL sites were taken down after 

the 2012 swimming season. 

Beach Name 

Number 

of 2012 

Samples 

Monitored FDSS 

False Positives

Monitored FDSS 

False Negatives

FDSS Elevated 

Counts No 

Monitoring

% Exceedances 

of State Single 

Sample Maximum

Bay City State Rec Area 54 0 0 0 0

Memorial Beach 55 1 3 6 5.5

Metro Beach 55 0 1 0 1.8

Grand Haven State Park 12 0 2 0 13.3

North Beach Park Beach 15 0 1 0 6.7

Table 6.3. Summary of 2012 FDSS Results for the Forecast Beaches.
45

Figure 6.4.1. NOAA forecast for Memorial Beach, Macomb County, MI.
46

Figure 6.4.2. Memorial Beach E. coli forecasts for swimming season 2012.
47

The NWS color codes for the forecast websites illustrated in part by Figure 6.4.1 are presented in four levels depending on 

the likelihood of exceeding the E. coli threshold values of 300 counts/100 ml and 600 counts/100 ml (Minimal, Moderate, 

High, and Very High). Not all outcomes occur in any one forecast. These likelihood probabilities are calculated using the 

high E. coli value forecast for each time period. The expected value and low value complete the box plot. 

Cross over values for each category:

300 counts/100 ml 600 counts/100 ml

Minimal - High : < 200 Minimal - High : < 300

Moderate - High: ≥ 200 Moderate - High: ≥ 300

High - High: ≥ 300 High - High: ≥ 600

Very High - High: ≥ 400 Very High - High: ≥ 700

The whisker values are based on the 40% chance level and are displayed on the trend graphs. The colors on the trend 

graphics correspond to passing the thresholds of 200, 300, and 600 by the whisker, high value (top half of box) and 

expected value (lower half of box).

The color coding is based on the following:

< 200 - green

200 - 299 - orange (essentially approaching critical levels)

300 - 499 - red (exceeding critical levels)

≥ 500 - magenta (very high levels)

The whiskers are the 40% chance values based on the expected value (this is using the neighborhood in the Weibull 

distribution). The box is the range from the tables low, expected, and high values.

7. DISCUSSION AND CONCLUSIONS

The technical and scientific merit of this proposal is based on well-known observations that general seasonal, weather, and 

hydrological conditions greatly influence the physical, chemical and biological characteristics of large water bodies such 

as the Great Lakes. These factors in turn affect the occurrence, distribution, and survival of microbiological contaminants 

in the water. Forecast DSS equations use data from deterministic models. The NOAA Great Lakes Environmental 

Research Lab’s Great Lakes Coastal Forecasting System (GLERL/GLCFS) hydrodynamic model and NOAA/National 

Weather Service National Digital Forecast Database (NWS/NDFD) meteorological model provide variables which 

quantify influences common to a geographical region. The goal of this study was to develop and operationally test the 

utility of 60 hour forecasting of beach water quality at a variety of beaches using E. coli as the indicator variable of 

bacterial contamination. The developmental goal was accomplished at 24 beaches in Lake Erie, Lake Michigan, Saginaw 

Bay and Lake St. Clair. The operational testing goal was accomplished at five beaches. There are 35 monitoring sites 

at the 24 beaches each of which is used to develop a forecast DSS. Of these 35 forecast DSS equations, 30 are in states 

where the state regulatory single sample maximum for E. coli is 235 counts/100 ml. For the five beaches in Michigan, 

the state regulatory single sample maximum for E. coli is 300 counts/100 ml. The NOAA/NWS Detroit Weather Forecast 

Office ran the 2012 forecast DSS equations successfully in operational forecasting mode for these beaches as part of 

NOAA Beach Water Quality Experimental Forecasting Initiative. The NWS office in Detroit Pontiac MI provided the 

beach managers four daily forecasts for each beach. Demonstration of forecast DSS at these five beaches was partially 

successful in 2012 due to minimal forecasting skill of seven E. coli events. This may be due to the beaches exhibiting a 

low percentage of E. coli events in 2012. In 2010 forecast DSS performed better when exceedances were above 5%. In 

addition, six forecasted elevated E. coli concentrations occurred during the weekends when no monitoring was done to 

verify if the forecast was correct. 
48

CILER, University of Michigan developed and tested MLR predictive decision support equations in cooperation with 

NOAA’s Center for Excellence for Great Lakes and Human Health, the National Weather Service, Bay Co. Health Dept. 

MI, Macomb Co. Health Dept. MI, Ottawa Co. Health Dept. MI, Indiana Dept. of Environmental Management, Northeast 

Ohio Regional Sewer District, Erie Co. (PA) Dept. of Health, Presque Isle State Park PA, Erie Co. (NY) Dept. of Health, 

New York State Office of Parks, Recreation, and Historical Preservation, Cities of Racine & Milwaukee, WI, Ozaukee 

Co. Health Dept. WI and the USGS Columbus Ohio Science Center. 

Virtual Beach provides ten equations for consideration as potential forecast DSS equations during the cross validation 

check. In this study, we found the equation with the minimum square error of prediction (MSEP) produced the best 

accuracy when used to predict E. coli concentrations. This equation also had the most key variables. Each of the 30 

forecast DSS equations represented a sampling site from one of 19 beaches. These sites are located in states using the 

single sample maximum for E. coli regulatory standard of 235 counts/100 m. The 30 FDSS-MV equations were evaluated 

together.

For the 30 sampling sites, we found forecast DSS equations for sites having 5% or fewer samples exceeding the single 

sample maximum, were not as accurate as the persistence model. This observation allows selection of beaches for 

forecasting beach water quality. A forecast DSS is more likely to be successful if the samples have more than 5% of 

the values exceeding the state single sample regulatory standard. Unless a beach has water quality issues exceeding the 

state regulatory standard more than 5% of the time, it does not appear to be a good candidate for forecasting beach water 

quality problems. Francy, 2009 noted that beaches are not good candidates for predictive modeling if fewer than five 

exceedances occur per sampling season. This criterion suggests a higher percentage of elevated E. coli sample results may 

be needed. Most health departments do not collect one hundred samples per swimming season which is approximately 

daily monitoring during the swimming season. 

Similarly, Francy, 2009 noted beaches are also not good candidates for predictive modeling if the observations exceed 

the state regulatory standard for a majority of the samples. In this study we had two beaches with respectively 40% and 

43% of the samples exceeding the state regulatory standard. In both cases the forecast DSS had better accuracy than the 

persistence model. 

For the remaining 27 equations, the forecast DSS was superior to the persistence model at 19 sites (70%) with better 

accuracy, i.e. fewer type 1 and type 2 errors. The forecast DSS averaged 2.4 fewer false positive (type 1) errors and 1 

fewer false negative (type 2) errors than the persistence model. For four sites, the forecast DSS was equivalent to the 

persistence model (15%) in terms of the total number of errors. For the remaining four sites, the forecast DSS had more 

errors than the persistence model.

In developing the key variables, we found the GLERL-GLCFS hydrodynamic model played a key role. Since the 

hydrodynamic model can provide data for all meteorological parameters except rainfall and wind gustiness, a beach 

having clear interaction with the lake would be a good candidate for the forecast DSS. Further, the hydrodynamic model 

provides reliable hourly data. Meteorological station data can have gaps in their records for a variety of reasons, i.e. sensor 

problems, budgetary problems, or data management issues.

This study would recommend not using the forecast DSS equation development for beaches where the GLERL-GLCFS 

hydrodynamic model cannot be used. Thus, beaches in a river system or in a bay away from the main body of the 

adjacent lake would not be good candidates. For a beach with a narrow tea cup opening to the lake may possibly make it 

inappropriate to use the hydrodynamic cell information which may be otherwise adjacent to the beach. For a beach where 

there are no GLERL-GLCFS cells nearby, the hydrodynamic model cannot be used.

A sufficient number of E. coli samples collected over one year or more is essential for forecast DSS development. In this 

study, all sites except one, had 100 or more samples. Frick et al. 2008 showed predictive models could be developed with 
49

fewer than 100 samples. It is generally recommended to have two years of data and around 100 samples (Francy et al. 

2006b). Depending on the frequency of sampling, it will generally take more than one year to accumulate 100 or more 

E. coli samples. In these situations, you are inherently making the assumption that environmental processes are stable 

and the collection of E. coli data are representing the same processes. These assumptions include stable funding to allow 

consistent monitoring at the established frequency, usually on the order of 1-4 times per week using trained personnel (or 

adequately trained new hires) over the entire period of record. 

This study demonstrated that beaches near a major tributary were influenced by the tributary. This suggests that tributary 

and or watershed runoff information should be available for all beaches. 

Lastly, the economic impact of unnecessarily closing swimming at beaches can be large due to the wide spread use of the 

persistence model as the beach management decision support tool. The persistence model averages 2.4 more type 1 errors 

per beach than the forecast DSS. Once a beach is posted, the normal time needed to clear the posting is a minimum of two 

days. The number of days swimming is banned would be twice the number of days the beach has swimming posted. The 

forecast DSS makes one less error when advising people not to swim, i.e. shuts swimming at a beach correctly when the 

persistence model would have permitted swimming. The net number of additional days swimming would be permitted 

is 3.8 per monitored beach if the forecast DSS beach management tool was used in place of the persistence model. If 

the persistence model was replaced at the 227 beaches where monitored occurred two to seven times per week in 2010 

(USEPA 2010b), a total 866 additional days of swimming would have been available in 2010 at Great Lake beaches. This 

represents about 23% of the swimming days banned in 2010 (NRDC 2011).

Rabinovici et al. 2004 estimates the loss of swimming at an Indiana Dunes beach ranged between a low ($18,859) and 

high ($37,030) value when mild swimmer health costs are included. Shaikh 2006 estimated the value of swimming day 

loss in 2004 for Chicago was $135,000. Applying the range of values for the days in 2010 when swimming was prohibited 

in error in the Great Lakes, the loss of value swimmers could have received might be substantial and range from 16M to 

117M.

The elimination of swimming in water with high bacterial contamination would reduce the adverse health impacts for 

those exposed unnecessarily by use of the persistence model. However, there is no swimmer health registry available in 

the Great Lakes to assess adverse swimmer health impacts resulting from swimming in bacterial contaminated waters. 

Rabinovici et al. 2004 estimate individual costs from a mild health effects in (2000 dollars) at $250 to a moderate health 

effects at $1,125. The Center for Disease Control is proposing to track Human Health in the Great Lakes where such 

registries are not currently available. The purpose is to expand Great Lakes-associated state health department capacity 

to 1) detect, investigate, and report waterborne disease outbreaks and HAB events associated with inland and Great Lake 

beach use, 2) connect these data to other environmental data (e.g., beach sanitary surveys) through a unique identifier 

system, and 3) use these data to inform decision making by public health officials, beach managers, environmental 

agencies, researchers, and the general public. This is especially important with the decline in funding for monitoring 

which will result in the swimming public being less informed about the bacterial levels.

Principle conclusions and implications for future work are the following:

● At the sites studied, E. coli variation was influenced by weather patterns. Forecasted IVs explain up to almost 40% of 

the variation in beach E. coli concentrations.

● Using VB software, forecast DSS equations can be developed making fewer errors than the persistence model at 70% 

of the sites.

● This study reinforced the concept that a beach with 5% or fewer samples exceeding the State Regulatory E. coli

standard may not be suitable for predictive modeling. This allows a beach manager to quickly determine if a forecast 

DSS should be attempted. The study also suggests that beaches with samples exceeding the state regulatory standard 

at 40 to 42% are still suitable for forecast DSS development.
50

● Because forecast DSS for all beaches adjacent to USGS gauged tributaries used key variables of river discharge or 

runoff, the development of a Great Lakes wide watershed model would be valuable. Such a model would be capable 

of providing water discharge and bacterial concentrations for all 121 watersheds. 

● The procedures detailed in this report may be used by beach managers to develop predictive models at coastal beaches 

where the GLERL-GLCFS hydrodynamic data are available.

● The economic impact of unnecessarily banning swimming at Great Lake beaches is potentially substantial.

● Federal funding for beach monitoring is potentially ending in 2013. Swimmer health impacts are not currently 

registered in the Great Lakes. Establishment of a Great Lakes-swimmer health registry and associated state health 

department capacity will inform beach management decisions made by public health officials, beach managers, 

environmental agencies, researchers, and the general public. 

● Minimal forecasting skill was observed for E. coli events during 2012 when Michigan’s single sample standard was 

exceeded 7 times in 191 samples. 

8. ACKNOWLEDGMENTS

The authors thank all the personnel involved in collecting, analyzing, and providing the E. coli data from the county health 

departments, state parks, and cities. Without this support there would have been no data. We want to acknowledge the fine 

working relationship with the following personnel who provided the E. coli data to us. This data was received from Robert 

Hill, Joel Strasz, Bay County Health Department, MI; Adeline Hambley, Vijayavel Kannappan, Ottawa County Health 

Department, MI;Steve Lichota, Cole Shoemaker, Stacy Mcfarlane, Laura Pobanz, Macomb County Health Department, 

MI, Michelle Caldwell, Indiana Dept. of Environmental Management, IN; Mark Citrigilia, Northeast Ohio Regional 

Sewer District, OH; Doug Range, Erie Co. Department of Health, and Presque Isle State Park PA; John Finster, Erie Co. 

Department of Health, NY; Kristen Husson, New York State, Office of Parks, Recreation, and Historical Preservation; 

Adam Mednick, Department of Natural Resources, WI. Partial Funding Support for this work came from USEPA’s Great 

Lakes Restoration Initiative Grant GL-00E00658 capably managed by Ed Pniak, GLRI Project Officer, Michigan Project 

Lead, U.S. EPA, Region 5, Water Division, State and Tribal Programs Branch. We thank Holly Wirick for her review.

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53

APPENDIX 1: HYDRODYNAMIC GRID CELL LOCATIONS

Figure A1: Bay City State 

Recreation Area, Bay County, 

MI and Hydrodynamic Grid Cell 

Locations.

Figure A2: North Beach Park 

Beach, Ottawa County, MI 

and Hydrodynamic Grid Cell 

Locations.
54

Figure A3: Grand Haven State 

Park Beach, Ottawa County, 

MI and Hydrodynamic Grid Cell 

Locations.

Figure A4: North Beach, Racine 

County WI and Hydrodynamic 

Grid Cell Locations.
55

Figure A5: Zoo Beach, Racine 

County, WI and Hydrodynamic 

Grid Cell Locations.

Figure A6: Upper Lake Park 

Beach, Ozaukee County, WI 

and Hydrodynamic Grid Cell 

Locations.
56

Figure A7: South Shore 

Beach, Milwaukee County, WI 

and Hydrodynamic Grid Cell 

Locations.

Figure A8: Bradford Beach, 

Milwaukee County, WI and 

Hydrodynamic Grid Cell 

Locations.
57

Figure A9: Woodlawn Beach 

State Park, Erie County, NY 

and Hydrodynamic Grid Cell 

Locations.

Figure A10: Hamburg Bathing 

Beach, Erie County, NY and 

Hydrodynamic Grid Cell 

Locations.
58

Figure A11: Evans Town 

Park Beach, Erie County, NY 

and Hydrodynamic Grid Cell 

Locations.

Figure A12: Wendt Beach, Erie 

County, NY and Hydrodynamic 

Grid Cell Locations.
59

Figure A13: Lake Erie Beach, Erie 

County, NY and Hydrodynamic 

Grid Cell Locations.

Figure 11.14: Bennett 

Beach, Erie, County, NY 

and Hydrodynamic Grid Cell 

Locations.
60

Figure 11.15: Presque Isle 

Beach #2, Erie, County, PA 

and Hydrodynamic Grid 

Cell Locations.

Figure 11.16: Presque 

Isle Beach #10, 

Erie, County, PA and 

Hydrodynamic Grid Cell 

Locations.
61

Figure 11.17: Villa 

Angela, Cuyahoga 

County, OH and 

Hydrodynamic Grid Cell 

Locations.

Figure 11.18: Hammond 

Marina East Beach, 

Lake County, IN and 

Hydrodynamic Grid Cell 

Locations.
62

Figure 11.19: Marquette 

Park Beach, Lake 

County, IN and 

Hydrodynamic Grid Cell 

Locations.

Figure 11.20: Washington 

Park Beach, Lake 

County, IN and 

Hydrodynamic Grid Cell 

Locations.
63

Figure 11.21: Ogden 

Dunes, Lake County, 

IN and Hydrodynamic 

Grid Cell Locations.

Figure 11.22: IDSP 

West Beach, Lake 

County, IN and 

Hydrodynamic Grid Cell 

Locations.
64

Figure 11.23: Memorial 

Beach, Macomb County, 

MI and Hydrodynamic Grid 

Cell Location.

Figure 11.24: Metropolitan 

Beach, Macomb County, 

MI and Hydrodynamic Grid 

Cell Location.