U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2012–5064 

Prepared in cooperation with the Milwaukee Metropolitan Sewerage District 

Use of Real-Time Monitoring to Predict Concentrations of 

Select Constituents in the Menomonee River Drainage Basin, 

Southeast Wisconsin, 2008–9 
Cover. Water-quality sonde deployment at Underwood Creek at Wauwatosa, Wisconsin, October 27, 2009. (Photograph by Austin K. Baldwin, 

U.S. Geological Survey.)
Use of Real-Time Monitoring to Predict 

Concentrations of Select Constituents in 

the Menomonee River Drainage Basin, 

Southeast Wisconsin, 2008–9 

By Austin K. Baldwin, David J. Graczyk, Dale M. Robertson, David A. Saad, and 

Christopher Magruder 

Prepared in cooperation with the Milwaukee Metropolitan Sewerage District 

Scientific Investigations Report 2012–5064 

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012 

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Baldwin, A.K., Graczyk, D.J., Robertson, D.M., Saad, D.A., and Magruder, Christopher, 2012, Use of real-time 

monitoring to predict concentrations of select constituents in the Menomonee River drainage basin, Southeast 

Wisconsin, 2008–9: U.S. Geological Survey Scientific Investigations Report 2012–5064, 18 p., plus six appendixes. 
iii

Acknowledgments

The authors would like to thank the Milwaukee Metropolitan Sewerage District (MMSD) staff 

for their flexibility and tireless effort, particularly Gary Eisenmann, Kurt Spieker, and Joe Leszczynski for field operations; Mary Singer, Matthew Magruder, Mark Eigner, and Mike Benedict for 

data management; Chris Schultz and Bill Farmer for station instrumentation and installation; and 

Sharon Mertens and the entire staff at the MMSD laboratory. 

Special thanks to U.S. Geological Survey employees Troy Rutter for data management and 

integrity; Dave Owens and Peter Hughes for site installation and instrumentation; Michelle Lutz 

and Steve Westenbroek for assistance with report illustrations; and Matt Komiskey and Mandy 

Stone for providing colleague reviews. The development of the regression equations would not 

have been possible without the dedicated field and laboratory staff from both agencies. 
iv

Contents

Acknowledgments........................................................................................................................................iii

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

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

Purpose and Scope ..............................................................................................................................2

Description of the Study Area ............................................................................................................2

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

Continuous Real-Time Data .................................................................................................................2

Discrete Water-Quality Samples ........................................................................................................6

Quality Assurance/Quality Control .....................................................................................................7

Regression Model Development .................................................................................................................7

Regression Model Results............................................................................................................................8

Chloride...................................................................................................................................................8

Total Suspended Solids ......................................................................................................................10

Total Phosphorus ................................................................................................................................11

Indicator Bacteria...............................................................................................................................11

Escherichia coli ..........................................................................................................................13

Fecal Coliform .............................................................................................................................13

Model Predictability ....................................................................................................................................13

Summary and Conclusions .........................................................................................................................17

References Cited..........................................................................................................................................17

Appendix 1. Analytical procedures used for water-quality samples ...............................................19

Appendix 2. Regression analysis results for estimating chloride concentration ..........................21

Appendix 3. Regression analysis results for estimating total suspended solids 

concentration ......................................................................................................................43

Appendix 4. Regression analysis results for estimating total phosphorus concentration ..........65

Appendix 5. Regression analysis results for estimating Escherichia coli (E. coli) 

bacteria concentration ......................................................................................................87

Appendix 6. Regression analysis results for estimating fecal coliform bacteria 

concentration ....................................................................................................................109 
v

Figures

 1A. Map showing location of real-time water-quality monitoring sites and 

drainage basins in the Menomonee River Basin. Dotted line demarcates the 

Milwaukee Metropolitan Sewerage District (MMSD) planning area ..................................3

 1B. Map showing location of real-time water-quality monitoring sites and 

land use in the Menomonee River Basin. Dotted line demarcates the 

Milwaukee Metropolitan Sewerage District (MMSD) planning area ..................................4

 2. Graph showing turbidity duration curve developed from 5-minute data from 

November 2008 to September 2010, with associated samples used in the total 

suspended solids regression model, Menomonee River at Menomonee Falls, 

Wisconsin ......................................................................................................................................6

 3. Graph showing predicted and measured chloride concentrations at the 

U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, Wisconsin, 

December 2008–September 2009 ...............................................................................................9

 4. Graph showing predicted and measured total suspended solids concentrations 

at the U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, 

Wisconsin, December 2008–September 2009 ........................................................................11

 5. Graph showing predicted and measured total phosphorus concentrations at 

the U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, 

Wisconsin, December 2008–September 2009 ........................................................................12

 6. Graph showing predicted and measured Escherichia coli (E. coli) bacteria 

concentrations at the U.S. Geological Survey streamgage on Honey Creek at 

Wauwatosa, Wisconsin, December 2008–September 2009 ................................................14

 7. Graph showing predicted and measured fecal coliform bacteria 

concentrations at the U.S. Geological Survey streamgage on Honey Creek at 

Wauwatosa, Wisconsin, December 2008–September 2009 ................................................15

 8. Graphs showing statistics by constituent and monitoring site in the 

Menomonee River Basin, Wisconsin. A, Adjusted R2

. B, root mean square 

error (RMSE). C, prediction error sum of squares (PRESS) .................................................16 
vi

Tables

 1. Basin characteristics of monitoring sites, Menomonee River Basin, 

Southeast Wisconsin ...................................................................................................................5

 2. Water-quality sonde ratings (as percentages of the record) at the continuous 

water-quality monitoring sites in the Menomonee River drainage basin, 

Southeast Wisconsin ...................................................................................................................5

 3. Regression models and summary statistics for estimating chloride 

concentrations in water at five water-quality monitoring sites in the 

Menomonee River Basin, Southeast Wisconsin, November 2008– 

September 2009 .............................................................................................................................9

 4. Regression models and summary statistics for estimating total suspended 

solids concentrations in water at five water-quality monitoring sites in the 

Menomonee River Basin, Southeast Wisconsin, November 2008– 

September 2009 ...........................................................................................................................10

 5. Regression models and summary statistics for estimating total phosphorus 

concentrations in water at five water-quality monitoring sites in the 

Menomonee River Basin, Southeast Wisconsin, November 2008– 

September 2009 ...........................................................................................................................12

 6. Regression models and summary statistics for estimating Escherichia coli 

(E. coli) bacteria concentrations in water at five water-quality monitoring sites 

in the Menomonee River Basin, Southeast Wisconsin, November 2008– 

September 2009 ...........................................................................................................................14

 7. Regression models and summary statistics for estimating fecal coliform 

bacteria concentrations in water at five water-quality monitoring sites 

in the Menomonee River Basin, Southeast Wisconsin, November 2008– 

September 2009 ...........................................................................................................................15 
vii

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2

) 2.590 square kilometer (km2)

Flow rate

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

Conversion Factors and Abbreviations 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows: 

°F=(1.8×°C)+32

Horizontal coordinate information is referenced to the Wisconsin Transverse Mercator (WTM) 

Projection and the North American Datum of 1983 (NAD 83), with 1991 adjustment.

Concentrations of chemical constituents in water are given in milligrams per liter (mg/L), 

micrograms per liter (μg/L), most probable number per 100 milliliters (MPN/100 mL), or colony 

forming units per 100 milliliters (CFU/100 mL). 

Abbreviations used in this report

ADCP acoustic Doppler current profiler

EPA U.S. Environmental Protection Agency

EWI equal-width increment

MLR multiple linear regression

MMSD Milwaukee Metropolitan Sewerage District

MSPE model standard percent error

NTU nephelometric turbidity units

NWIS National Water Information System

PRESS prediction error sum of squares

PVC polyvinyl chloride

QA/QC quality assurance/quality control

RMSE root-mean-squared error

RPD relative percent difference

SLR simple linear regression

SSE sum of squared error

USGS U.S. Geological Survey 

Abstract

The Menomonee River drainage basin in southeast 

Wisconsin is undergoing changes that may affect water quality. Several rehabilitation and flood-management projects 

are underway, including removal of concrete channels and 

the construction of floodwater retention basins. The city of 

Waukesha may begin discharging treated wastewater into 

Underwood Creek, thus approximately doubling the current 

base-flow discharge. In addition, the headwater basins, historically dominated by agriculture and natural areas, are becoming 

increasingly urbanized. 

In an effort to monitor these and future changes to the 

basin, the U.S. Geological Survey and the Milwaukee Metropolitan Sewerage District initiated a study in 2008 to develop 

regression models to estimate real-time concentrations and 

loads of selected water-quality constituents. Water-quality 

sensors and automated samplers were installed at five sites in 

the Menomonee River drainage basin. The sensors continuously measured four explanatory variables: water temperature, specific conductance, dissolved oxygen, and turbidity. 

Discrete water-quality samples were collected and analyzed 

for five response variables: chloride, total suspended solids, 

total phosphorus, Escherichia coli bacteria, and fecal coliform 

bacteria. Regression models were developed to continuously 

estimate the response variables on the basis of the explanatory 

variables. 

The models to estimate chloride concentrations all used 

specific conductance as the explanatory variable, except for 

the model for the Little Menomonee River near Freistadt, 

which used both specific conductance and turbidity as explanatory variables. Adjusted R2

 values for the chloride models 

ranged from 0.74 to 0.97. Models to estimate total suspended 

solids and total phosphorus used turbidity as the only explanatory variable. Adjusted R2

 values ranged from 0.77 to 0.94 

for the total suspended solids models and from 0.55 to 0.75 

for the total phosphorus models. Models to estimate indicator 

bacteria used water temperature and turbidity as the explanatory variables, with adjusted R2

 values from 0.54 to 0.69 for 

Escherichia coli bacteria models and from 0.54 to 0.74 for 

fecal coliform bacteria models. Dissolved oxygen was not 

used in any of the final models. These models may help managers measure the effects of land-use changes and improvement projects, establish total maximum daily loads, estimate 

important water-quality indicators such as bacteria concentrations, and enable informed decision making in the future. 

Introduction

Increasingly, real-time water-quality monitors are being 

used to estimate continuous concentrations of water-quality 

constituents. Certain water-quality constituents, such as bacteria concentrations, cannot easily be measured in real-time 

because of limitations in cost and sensor technology. However, 

studies have demonstrated that water-quality constituents can 

be estimated based on more easily measured surrogates, such 

as water temperature and turbidity (Christensen and others, 

2000; Rasmussen and others, 2005). Using surrogates allows 

for continuous concentration estimates of the constituent(s) 

of interest and, when combined with discharges, constituent 

loads. 

There are several advantages of load estimation with 

continuous concentration over traditional constituent load estimation methods. Traditional studies rely heavily on discrete 

sampling, which provides only snapshots of water-quality 

concentrations; therefore, the vast majority of the water-quality record is entirely unknown and must be estimated. Traditional estimation methods, such as the Graphical Constituent 

Loading Analysis System (Koltun and others, 2006), can be 

subjective, and results can vary from one estimate to the next. 

Daily, monthly, and annual fluctuations in concentrations, as 

well as concentration changes during a storm event, may not 

be accurately described. By providing a continuous record 

(for example, measurements every 5 minutes) of surrogates, 

real-time monitoring captures the variability in water-quality 

concentrations and reduces estimation errors associated with 

methods that do not use real-time data.

Use of Real-Time Monitoring to Predict Concentrations 

of Select Constituents in the Menomonee River Drainage 

Basin, Southeast Wisconsin, 2008–9 

By Austin K. Baldwin,1 David J. Graczyk,1 Dale M. Robertson,1 David A. Saad,1 and Christopher Magruder 2

1

 U.S. Geological Survey, Wisconsin Water Science Center

2

 Milwaukee Metropolitan Sewerage District 
2 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

In November 2008, the U.S. Geological Survey (USGS) 

and the Milwaukee Metropolitan Sewerage District (MMSD) 

began a cooperative study to develop regression models to 

estimate continuous real-time concentrations of selected 

water-quality constituents. Continuous real-time sensors 

and water-quality samplers were installed at five sites in the 

Menomonee River drainage basin. The real-time sensors measured four explanatory variables as surrogates: water temperature, turbidity, dissolved oxygen, and specific conductance. 

Discrete water-quality samples were collected for a range of 

streamflows and seasons and were analyzed for five response 

variables: chloride, total suspended solids, total phosphorus, 

Escherichia coli (E. coli) bacteria, and fecal coliform bacteria. 

A set of concurrently measured explanatory variables was 

used to develop regression equations for each of the response 

variables. These regressions between explanatory and response 

variables were then used to calculate continuous estimates of 

each of the water-quality constituents of interest.

Real-time water-quality information can be beneficial 

in public and ecosystem health management and facilitate 

water-resource management. For example, managers can use 

real-time estimates of chloride to determine if elevated levels 

are toxic to aquatic organisms (Corsi and others, 2010). Realtime estimates can be used for public health notices, such as 

whether fecal coliform concentrations may be above waterquality standards that may present public health risks (Francy 

and Darner, 2007). Real-time concentration estimates in conjunction with stream discharge data can be used to calculate 

loads of water-quality constituents of interest. Load estimates 

can then be used in the development of total maximum daily 

loads (TMDLs). Long-term continuous monitoring of surrogate explanatory variables and estimation of water-quality 

constituents may be used to evaluate the effects of land-use 

changes, improvement projects, and implementation of bestmanagement practices.

Purpose and Scope

The purpose of this report is to describe the process used 

to create regression models to estimate real-time concentrations and loads of selected water-quality constituents based 

on data from real-time water-quality monitors. The regression 

models presented in this report may help provide MMSD with 

a means to document improvements in water quality related to 

capital projects, assist with basin planning efforts, and provide 

water-quality information to communities served by MMSD 

and the general public. 

Description of the Study Area

The Menomonee River Basin drains 146 square miles 

(mi2) in southeast Wisconsin (fig. 1). The basin is within 

the MMSD planning and service area and includes parts of 

Milwaukee, Waukesha, Ozaukee, and Washington Counties. 

The largest tributaries within the basin include Underwood 

Creek, Honey Creek, and the Little Menomonee River. The 

Menomonee River joins the Milwaukee and Kinnickinnic 

Rivers to form the Milwaukee estuary in Lake Michigan near 

downtown Milwaukee.

The Menomonee River drainage basin is currently (2007) 

64 percent urban, an increase from 51 percent urban in 1970 

(Southeastern Wisconsin Regional Planning Commission, 

2007). Although the northern third of the basin is dominated 

by agriculture (fig. 1B), the area has experienced recent urban 

growth. Between 1990 and 2000, the population in the basin 

remained nearly stable at 322,000, although the number of 

households rose by 3.5 percent (Southeastern Wisconsin 

Regional Planning Commission, 2007). 

Five sites within the basin were monitored and sampled 

as part of this study: the Little Menomonee River near Freistadt, the Menomonee River at Menomonee Falls, Honey Creek 

at Wauwatosa, the Menomonee River at Wauwatosa, and 

the Menomonee River at Milwaukee (fig. 1). General basin 

characteristics upstream of these sites, including land use, are 

listed in table 1. The basin with the smallest urban area is the 

Little Menomonee River (20 percent); the basin with the largest urban area is Honey Creek (96 percent).

Data Collection

Data for the regression model development were collected from November 2008 to September 2009. Types of 

data collected included continuous real-time data and discrete 

water-quality samples. Quality assurance/quality control (QA/

QC) samples were collected, as well.

Continuous Real-Time Data

At four of the five sites, stream stage was measured every 

5 minutes and was used to calculate stream discharge (Rantz 

and others, 1982). These four sites are the Menomonee River 

at Menomonee Falls, Little Menomonee River, Honey Creek, 

and Menomonee River at Wauwatosa. Stream stages were 

measured by a gas-purge-pressure system and recorded on a 

datalogger. Discharge measurements at these sites were made 

according to standard USGS methods (Turnipseed and Sauer, 

2010) every 4 to 6 weeks and more frequently during high 

flows to define the stage-discharge relation for each site. At 

the fifth site, the Menomonee River at Milwaukee (16th Street), 

an acoustic Doppler current profiler (ADCP) was installed to 

measure water velocities because this site is affected by backwater and seiche effects from Lake Michigan. Water velocities and the cross-sectional area were used to determine the 

discharge at this site (Laenen, 1985; Oberg and others, 2005; 

Ruhl and Simpson, 2005). 
Data Collection 3

I-94

I-43

I-894

I-43

I-94 MILWAUKEE

WAUWATOSA

MENOMONEE FALLS

MEQUON

MILWAUKEE

WAUWATOSA

MENOMONEE FALLS

MEQUON

88°10' 87°50'

42°50' 43°10'

Lake Michigan

Menomonee R.

Little Menomonee R.

Honey Cr.

Menomonee R.

Little Menomonee R.

Honey Cr.

Base composited from Southeastern Wisconsin Regional Planning Commission regional base map, 1:2,000, 1995; U.S. Geological Survey 

digital line graph hydrography, 1:100,000, 1989; Wisconsin Department of Natural Resources minor civil divisions, 1:100,000, 1998; Wisconsin 

Department of Natural Resources state trunk highways, 1:100,000, 1998; Wisconsin Department of Natural Resources version 2 hydrography, 

1:24,000, 2002. Wisconsin Transverse Mercator Projection, referenced to North American Datum of 1983, 1991 adjustment.

0 42 Miles

0 42 Kilometers

WISCONSIN

MICHIGAN

ILLINOIS

IOWA

MINNESOTA

MMSD

planning area

Menomonee River

at Menomonee Falls

(04087030)

Honey Creek

at Wauwatosa

(04087119)

Menomonee River

at Wauwatosa

(04087120)

Little Menomonee River

near Freistadt

(04087050)

Menomonee River

at 16th Street

at Milwaukee

(04087142)

Honey Creek

at Wauwatosa

(04087119) Menomonee River

at 16th Street

at Milwaukee

(04087142)

Menomonee River

at Wauwatosa

(04087120)

Menomonee River

at Menomonee Falls

(04087030)

Little Menomonee River

near Freistadt

(04087050)

EXPLANATION

Basin boundary

Stream

Real-time streamsampling site and 

station number

Real-time streamsampling site basin 

boundary

MMSD planning area

Highway

Municipal boundary

Figure 1A. Location of real-time water-quality monitoring sites and drainage basins in the Menomonee River Basin. Dotted 

line demarcates the Milwaukee Metropolitan Sewerage District (MMSD) planning area. 
4 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

I-94

I-43

I-894

I-43

I-94 MILWAUKEE

WAUWATOSA

MENOMONEE FALLS

MEQUON

MILWAUKEE

WAUWATOSA

MENOMONEE FALLS

MEQUON

88°10' 87°50'

42°50' 43°10'

Lake Michigan

Menomonee R.

Little Menomonee R.

Honey Cr.

Menomonee R.

Little Menomonee R.

Honey Cr.

0 42 Miles

0 42 Kilometers

Base composited from Southeastern Wisconsin Regional Planning Commission digital land use 

inventory, 1:4,800, 2000; Southeastern Wisconsin Regional Planning Commission regional base 

map, 1:2,000, 1995; U.S. Geological Survey digital line graph hydrography, 1:100,000, 1989; 

Wisconsin Department of Natural Resources version 2 hydrography, 1:24,000, 2002. Wisconsin 

Transverse Mercator Projection, referenced to North American Datum of 1983, 1991 adjustment.

WISCONSIN

MICHIGAN

ILLINOIS

IOWA

MINNESOTA

MMSD

planning area

04087030

04087050

04087120

04087119

04087142

EXPLANATION

Transportation

Industrial

Residential

Basin boundary

Real-time streamsampling site basin 

boundary

Stream

Real-time streamsampling site 

station number

Agriculture

Open water

Natural areas

Other urban areas

Commercial

MMSD planning area

Land use

Figure 1B. Location of real-time water-quality monitoring sites and land use in the Menomonee River Basin. Dotted line 

demarcates the Milwaukee Metropolitan Sewerage District (MMSD) planning area. 
Data Collection 5

A multiparameter water-quality sonde was installed at 

each site in November 2008. Each sonde was equipped with 

an optical dissolved-oxygen sensor, an optical turbidity sensor, 

and a specific conductivity and temperature sensor. The sonde 

was installed in a polyvinyl chloride (PVC) tube in a fixed 

position in the stream, and water-quality measurements were 

made every 5 minutes. Sonde maintenance, data correction, 

and reporting procedures followed standard USGS protocol 

(Wagner and others, 2006). Sites were visited approximately 

every 2 weeks during the open-water period (March through 

November) and monthly in the winter when the streams were 

usually ice covered. Extensive fouling at some sites during the 

summer necessitated weekly visits. 

Continuous monitoring data for use in the regression 

models was downloaded from the USGS National Water 

Information System database on January 25, 2010. For most 

sites and water-quality measurements, the continuous monitoring record was at least 95 percent complete (table 2). Reasons 

for missing records include equipment malfunctions, flood 

damage to equipment, and excessive fouling. The quality of 

the continuous monitoring data was rated according to criteria 

outlined in Wagner and others (2006). This rating scheme is 

based on the combined fouling and calibration drift corrections 

applied to the data. For example, specific conductance data are 

considered excellent if the combined fouling and drift corrections are less than or equal to +/– 3 percent of the specific 

conductance value. The quality of the continuous monitoring data was mostly considered good to excellent, but varied 

substantially by site and water-quality measurements. The 

water temperature record was considered excellent at all five 

sites. The percentage of the specific conductance record rated 

as either good or excellent ranged from 77 percent at Honey 

Creek to 96 percent at the Little Menomonee River and the 

Menomonee River at Wauwatosa. The percentage of the dissolved oxygen record rated as either good or excellent ranged 

from 67 percent at the Menomonee River at Menomonee Falls 

to 95 percent at Honey Creek. The percentage of the turbidity 

record rated as either good or excellent ranged from 48 percent 

at Honey Creek to 82 percent at the Little Menomonee River. 

Table 1. Basin characteristics of monitoring sites, Menomonee River Basin, Southeast Wisconsin. 

[Periods of record for annual mean discharge range from 4 years at Menomonee River at 16th Street (2008 to present) to 51 years at 

Menomonee River at Wauwatosa (1961 to present). Land use percentages are from 2007 (Southeastern Wisconsin Regional Planning 

Commission); USGS, U.S. Geological Survey; mi2, square mile; ft3/s, cubic foot per second]

Monitoring site

USGS 

station 

number

Drainage 

area 

(mi2

)

Annual 

mean 

discharge 

(ft3

/s)

Percent 

urban

Percent 

agriculture

Percent 

natural 

areas

Menomonee River at Menomonee Falls 04087030 34.7 31.5 35 38 27

Little Menomonee River near Freistadt 04087050 8.0 7.3 20 63 16

Honey Creek at Wauwatosa 04087119 10.3 11.4 96 0 4

Menomonee River at Wauwatosa 04087120 123.0 106.0 60 19 20

Menomonee River at 16th Street at Milwaukee 04087142 146.0 184.5 64 17 19

Table 2. Water-quality sonde ratings (as percentages of the 

record) at the continuous water-quality monitoring sites in the 

Menomonee River drainage basin, Southeast Wisconsin. 

[Ratings based on criteria outlined in Wagner and others, 2006, table 18]

Excellent Good Fair Poor or 

missing

Menomonee River at Menomonee Falls, WI 04087030

Water temperature 99 0 0 1

Specific conductance 50 45 5 1

Dissolved oxygen 43 24 10 24

Turbidity 73 5 0 23

Little Menomonee River near Freistadt, WI 04087050

Water temperature 99 0 0 1

Specific conductance 64 32 0 5

Dissolved oxygen 48 24 19 9

Turbidity 68 14 0 18

Honey Creek at Wauwatosa, WI 04087119

Water temperature 95 0 0 5

Specific conductance 68 9 3 20

Dissolved oxygen 85 10 1 4

Turbidity 35 13 14 39

Menomonee River at Wauwatosa, WI 04087120

Water temperature 95 0 0 5

Specific conductance 82 14 2 2

Dissolved oxygen 75 10 8 7

Turbidity 32 21 13 34

Menomonee River at 16th Street at Milwaukee, WI 04087142

Water temperature 99 0 0 1

Specific conductance 78 11 5 6

Dissolved oxygen 71 15 8 6

Turbidity 57 12 8 23

For dissolved oxygen, turbidity, specific conductivity, and 

temperature, the measured values were within the ranges of 

sensor operation.
6 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Continuous in-stream water-quality monitor data were 

compared to cross-sectional data at the monitor location 

to determine if the continuous data were representative of 

the water-quality conditions across the stream. Four to five 

cross-sectional surveys were conducted at each site during 

both base-flow and stormflow conditions. The cross-sectional 

surveys show that the streams at all sites are generally well 

mixed, with no consistent differences from one side of the 

channel to the other. No corrections were made to the continuous water-quality monitor record. Continuous streamflow and 

water-quality data are available at the USGS Web site at http://

waterdata.usgs.gov/wi/nwis (accessed February 2012). 

Discrete Water-Quality Samples 

Each site was equipped with a stage-activated, refrigerated automated sampler for the collection of water samples 

over a full range of hydrologic conditions. These samplers 

were controlled using dataloggers that were programmed to 

collect a sample with each 0.5 foot (ft) increase in stage once 

the stage reached an initial sampling threshold. The initial 

sampling threshold varied at each site and changed seasonally. After the stage peaked, samples were collected with each 

1.0 ft decrease in stage. This sampling strategy was designed 

to maximize the number of samples collected during each 

event and to collect more samples on the rising limb of the 

hydrograph when water-quality constituents typically change 

the most. At the Menomonee River at 16th Street, the sampler was activated by turbidity rather than stage because of 

backwater and reverse flows from the seiche effects of Lake 

Michigan. Once the turbidity reached a predefined threshold, 

sampling would begin, and samples would be collected at set 

time intervals until the turbidity dropped below the threshold. 

The turbidity threshold was changed as needed depending on 

current turbidity and season. 

For most sites and constituents (chloride, total suspended 

solids, total phosphorus, E. coli bacteria, and fecal coliform 

bacteria), between 50 and 100 samples were collected and 

analyzed. At some of the sites between one and four samples 

were not used in the final regression models because of fouling on the water-quality meter. Fewer samples were collected 

at the Little Menomonee River: 39 samples for chloride, total 

suspended solids, and total phosphorus; 37 samples for E. coli 

bacteria; and 32 samples for fecal coliform bacteria. The Little 

Menomonee River site is the most rural of the sampling sites 

and high-flow events were less frequent. Christensen and others (2000) found that 35 to 55 samples, collected throughout 

90 to 95 percent of the stream’s flow duration, were sufficient 

to define relations between constituents and surrogates for two 

Kansas streams. 

The distribution of samples over the range of observed 

hydrologic conditions is at least as important in creating a 

regression model as is the total number of samples (Rasmussen and others, 2009). To evaluate whether the collected 

samples adequately represent the range of observed hydrologic conditions, the samples were plotted on duration curves 

of associated time-series data for each site and constituent. 

The turbidity duration curve in figure 2 was developed from 

5-minute data from the Menomonee River at Menomonee 

Falls for the period from November 2008 to September 2010. 

The samples plotting on top of the curve are associated total 

suspended solids samples. The plot shows very good sample 

coverage for the observed turbidity values between 10 and 

220 nephelometric turbidity units (NTU) and good coverage 

for turbidity values between 2 and 10 NTU. Duration curves 

showing sample coverage for all sites and constituents are 

provided in the appendixes.

0.1

1.0

10.0

100.0

1,000.0

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units

Frequency of exceedance, in percent

Figure 2. Turbidity duration curve 

developed from 5-minute data 

from November 2008 to September 

2010, with associated samples 

used in the total suspended solids 

regression model, Menomonee 

River at Menomonee Falls, 

Wisconsin. 
Regression Model Development 7

Quality Assurance/Quality Control

Quality-assurance and quality-control (QA/QC) samples 

collected during this study accounted for about 6 percent of 

the water-quality samples. Sampler blanks were collected 

at each site to check for sampler contamination by pumping Milli-Q® water through the entire sample line and into 

a sample bottle. The sample was split into bottles and analyzed at the MMSD laboratory. None of the constituents had 

concentrations above the detection limit except for one total 

suspended solids sample that had a concentration of 2.8 milligrams per liter (mg/L). Splitter blanks were also collected to 

check for contamination from the sample processing equipment. The splitter blanks were collected by running Milli-Q 

water through a decaport sample splitter, then collecting and 

analyzing that water. All of the constituents analyzed for the 

splitter blanks were below the detection limit. 

Multiple pairs of concurrent automated sampler and 

equal-width-increment (EWI) samples were collected at each 

site to evaluate whether the automated sampler samples were 

chemically and physically representative of the stream cross 

section. The EWI sampling method is designed to accurately 

represent the discharge-weighted concentrations of the stream 

(Edwards and Glysson, 1999). Relative percent differences 

(RPDs) were calculated between the EWI and automated 

sampler sample concentrations. Median RDPs for chloride, 

total suspended solids, and total phosphorus were all less 

than 10 percent. Median RDPs for fecal coliform bacteria 

and E. coli bacteria were 36 and 18 percent, respectively. The 

higher variability in the bacteria samples may be the result of 

rapidly changing flows in these urban basins and the inherent 

variability of bacteria concentrations in the stream. No corrections were applied on the basis of the EWI results. 

Preparation and analysis of the water samples were 

performed by the MMSD laboratory. The preparatory steps 

included dividing samples into representative subsamples 

using a splitting device developed for aqueous matrices and 

preserving the subsamples according to U.S. Environmental 

Protection Agency (EPA) protocols. The subsamples were 

analyzed for chloride, total suspended solids, total phosphorus, 

and E. coli and fecal coliform bacteria. The analytical methods used by MMSD are based on procedures described by the 

U.S. Environmental Protection Agency (1993) or by Clesceri 

and others (1998). Specific procedure references are listed 

in appendix 1. The MMSD follows extensive QA/QC guidelines set forth in the 2003 National Environmental Laboratory 

Accreditation Conference NELAC Standard (National Environmental Laboratory Accreditation Conference, 2003). 

Regression Model Development

Simple and multiple linear regression (SLR and MLR) 

models were developed to estimate chloride, total suspended 

solids, total phosphorus, E. coli bacteria, and fecal coliform 

bacteria by using continuous in-stream temperature, specific 

conductance, dissolved oxygen, and turbidity sensor measurements. These models were used to calculate continuous 

(5-minute) estimates of chloride, total suspended solids, total 

phosphorus, E. coli bacteria, and fecal coliform bacteria suitable for evaluating exceedance criteria in the sampled streams. 

A detailed description of the process used to develop the 

regression models using continuously measured sensor data 

can be found in Rasmussen and others (2009). A brief description of the methods used for this study follows.

Regression models were developed using a two-step 

approach: (1) initial model development and (2) final model 

selection. Initial regression models were developed for each 

of the response variables by using stepwise regression with all 

of the continuous in-stream sensor measurements as explanatory variables. Initial models were developed with log10-transformed response variables. Untransformed and log10-transformed explanatory variables, as well as seasonal variables 

(sine Julian day and cosine Julian day), were considered 

during model development by using the SAS software PROC 

REG command (SAS Institute Inc., 2004). An alpha value of 

0.05 was used for the stepwise selection (for both entry into 

and removal from the model). Final models were selected 

manually and typically included a subset of the explanatory 

variables chosen during initial model development. Considerations for selecting the final models included (1) simplicity 

of the model (preference for fewer variables), (2) consistency 

between models (preference for a consistent set of variables), 

and (3) similar fit and explanatory power as the initial model 

while including considerations (1) and (2). For example, in 

the initial models for total suspended solids, one of the five 

models found sine Julian day to be a significant variable, 

and another model found water temperature to be significant. 

Because each of these variables was found to be significant in 

only one of the five models and because they lacked explanatory power, both of these variables were omitted from the final 

regression models.

Initial models used between one and six explanatory 

variables. All final models used one or two variables. Final 

models for chloride included specific conductance as the only 

explanatory variable, except for the Little Menomonee River 

model, which used both specific conductance and turbidity as 

explanatory variables. Final models for both total suspended 

solids and total phosphorus included turbidity as the only 

explanatory variable. Final models for E. coli and fecal coliform bacteria included both water temperature and turbidity as 

explanatory variables. Dissolved oxygen was not used in any 

of the final models. Although dissolved oxygen was significant 

in some of the initial models, it was not included in the final 

models to maintain simplicity and consistency between models, and because it lacked explanatory power. 

Similar fit and explanatory power between the initial and 

final models were compared primarily using plots of observed 

versus computed values and the adjusted coefficient of determination (adj R2

). Plots of observed versus computed values 

appeared to have similar fit. Adj R2

 values of the final models 
8 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

were typically within 5 to 15 percent of the initial models. The 

adj R2 and additional regression model statistics considered 

in model development are described in more detail below. 

Statistics and graphs describing the final models are included 

in the appendixes.

Regression models were evaluated for fit and explanatory power by using graphs and several measures of variance 

between computed and observed values. Plots of observed 

versus computed values were evaluated for fit relative to a 1:1 

line and distribution across the range of observed values. Plots 

of residuals versus computed values, date, and a normal quantile distribution were evaluated for bias and normality. Measures of variance between computed and observed values used 

include the sum of squared errors (SSE), root-mean-squared 

error (RMSE), adjusted coefficient of determination (adj 

R2), and prediction error sum of squares (PRESS). The SSE 

represents the total model error, and the RMSE is a measure of 

the average error between computed and observed values. The 

SSE and RMSE have the same units as the response variable. 

Smaller values of SSE and RMSE indicate better fit for a particular model. The model standard percent error (MSPE) is the 

RMSE expressed as a percentage and allows regression model 

comparison. The adj R2 is adjusted for the number of explanatory variables in the model and represents the fraction of variability in the response variable that is explained by the model. 

Adj R2 ranges from 0 to 1, where 1 represents 100 percent of 

variability explained. PRESS is a validation-type estimator of 

error based on regression with one observation left out of the 

regression and repeated for each observation. 

All models developed in this study were based on log10-

transformed response variables. Retransforming the computed 

values back into the original units introduces a bias because 

regression estimates are the mean of y given x in logarithmic 

units, and retransformation of these estimates is not equal to 

the mean of y given x in linear space. Therefore, the retransformation bias of these models was corrected by applying a 

bias correction factor (Duan, 1983). Bias correction factors 

for each model are included in the appendixes. Also provided 

in the appendixes are 90-percent prediction, or confidence, 

intervals. These confidence intervals can be used for evaluating uncertainty of the computed values. Smaller prediction 

intervals indicate less uncertainty associated with the computed value. 

Regression Model Results

Chloride

Chloride occurs naturally in streams, but at high concentrations chloride poses a significant threat to aquatic ecosystems. According to the EPA, chronic chloride concentrations 

above 230 mg/L, and acute chloride concentrations above 

860 mg/L, pose a potential threat to aquatic life (U.S. Environmental Protection Agency, 1988). Road-salt runoff, caused 

by melting snow and ice that contains road salt, is a common 

source of elevated chloride concentrations in urban areas. 

Samples collected from 7 of 13 streams in the Milwaukee area 

during road-salt runoff periods exhibited toxicity in bioassays 

(Corsi and others, 2010). Chloride increases the conductivity 

of water and is, therefore, directly related to specific conductivity (Christensen and others, 2000). The relation between 

chloride concentrations and specific conductivity should make 

specific conductivity an effective surrogate for estimating 

chloride concentrations in streams. 

Chloride regression models for four of the five sites use 

specific conductance as the only explanatory variable, with 

adjusted R2 values between 0.81 and 0.97 and RMSE values 

between 0.07 and 0.23 (table 3). The model for the fifth site, 

the Little Menomonee River, uses both specific conductance 

and turbidity as explanatory variables, with an R2 of 0.74 

and an RMSE of 0.1. Figure 3 is an example from the Honey 

Creek at Wauwatosa monitoring site, showing predicted chloride values with 90-percent confidence intervals as well as the 

measured chloride values used in the regression model. The 

model-calibration dataset, model summary, summary statistics, 

plots of the explanatory and response variables, and residual 

plots are provided in appendix 2.
Regression Model Development 9

Table 3. Regression models and summary statistics for estimating chloride concentrations in water at five water-quality monitoring 

sites in the Menomonee River Basin, Southeast Wisconsin, November 2008–September 2009. 

[R2, coefficient of determination; RMSE, root mean square error; PRESS, prediction error sum of squares; n, number of discrete samples; mg/L, milligrams 

per liter; SC, specific conductance, in microsiemens per centimeter at 25 degrees Celsius; CL, chloride, dissolved, in mg/L; Turb, turbidity, in nephelometric 

turbidity units]

Monitoring site Regression 

model

Model diagnostics Model inputs

Adjusted 

R2 RMSE PRESS n

Range of values 

in variable 

measurements

Mean Median Standard 

deviation

Menomonee River at 

Menomonee Falls, 

Wis. 04087030

Log10CL = −1.63 + 1.28log10(SC) 0.94 0.07 0.32 59 CL 24–960

SC 252–3,700

171

960

120

784

167

643

Little Menomonee 

River near 

Freistadt, Wis. 

04087050

Log10CL = − 4.16 + 1.99log10(SC) 

 + 0.1511log10(Turb)

.74 .10 .38 39 CL 23–130

SC 384 –1,123

Turb 0.7–290

54

698

72

50

676

46

26

192

78

Honey Creek at 

Wauwatosa, Wis. 

04087119

Log10CL = − 0.984 + 1.12log10(SC) .81 .23 3.88 70 CL 11–1,700 

SC 124 –5,930

297

1,150

235

629

321

1,186

Menomonee River 

at Wauwatosa, 

Wis. 04087120

Log10CL = −1.41 + 1.23log10(SC) .92 .12 1.35 101 CL 29–2,300

SC 235–6,890

334

1,429

190

970

418

1,295

Menomonee River 

at Milwaukee, 

Wis. 04087142

Log10CL = −1.50 + 1.26log10(SC) .97 .07 .44 79 CL 18–1,400

SC 174 –4,763

249

1,180

160

938

254

910

Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

0

5,000

10,000

15,000

20,000

Chloride, in milligrams per liter

Predicted chloride

Predicted chloride 90-percent confidence intervals 

Measured chloride

2008 2009

U.S. Environmental Protection Agency acute 

 water-quality criteria concentration

EXPLANATION

Figure 3. Predicted 

and measured chloride 

concentrations at the 

U.S. Geological Survey 

streamgage on Honey Creek 

at Wauwatosa, Wisconsin, 

December 2008–September 

2009. 
10 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total Suspended Solids

Total suspended solids are a combination of suspended 

sediment and organic matter. Because total suspended solids have numerous adverse effects on stream ecosystems, it 

is often considered a major pollutant (Ritchie, 1972). Total 

suspended solids may be detrimental to stream communities 

by reducing light penetration and oxygen levels, smothering, 

scouring, reducing habitat through deposition, and introduction of absorbed pollutants (Lenat and others, 1981; Alabaster 

and Lloyd, 1982). Effects on fish include mechanical abrasion, 

gill damage, fin rot, reduced survival of eggs, and death by 

clogging gills (Ritchie, 1972). Turbidity, caused by dissolved 

and suspended material such as clay, silt, fine organic material, microscopic organisms, organic acids, and dyes (ASTM 

International, 2003), is often used as a surrogate for total 

suspended solids.

The regression models for total suspended solids at all 

five sites use turbidity as the explanatory variable (table 4). 

The adjusted R2

 ranged from 0.77 at the Menomonee River at 

Wauwatosa to 0.94 at the Little Menomonee River. The RMSE 

ranged from 0.16 at the Menomonee River at Menomonee 

Falls to 0.25 at Honey Creek (table 4). Figure 4 is an example 

from Honey Creek at Wauwatosa, showing predicted total 

suspended solids values with 90-percent confidence intervals as well as the measured total suspended solids values 

used in the regression model. The model-calibration dataset, 

model summary, summary statistics, plots of the explanatory 

and response variables, and residual plots are provided in 

appendix 3.

Table 4. Regression models and summary statistics for estimating total suspended solids concentrations in water at five water-quality 

monitoring sites in the Menomonee River Basin, Southeast Wisconsin, November 2008–September 2009. 

[R2, coefficient of determination; RMSE, root mean square error; PRESS, prediction error sum of squares; n, number of discrete samples; mg/L, milligrams per 

liter; SS, suspended solids; Turb, turbidity, in nephelometric turbidity units] 

Monitoring site Regression 

model

Model diagnostics Model inputs

Adjusted 

R2 RMSE PRESS n

Range of values 

in variable 

measurements

Mean Median Standard 

deviation

Menomonee River at 

Menomonee Falls, 

Wis. 04087030

Log10SS = 0.256 + 0.953log10(Turb) 0.92 0.16 1.54 59 SS 4 –500

Turb 2.3–220

81

47

46

25

95

52

Little Menomonee 

River near 

Freistadt, Wis. 

04087050

Log10SS = 0.334 + 0.910log10(Turb) .94 .17 1.25 39 SS 1.6 –410

Turb 0.7–290

108

72

71

46

121

78

Honey Creek at 

Wauwatosa, Wis. 

04087119

Log10SS = 0.160 + 0.967log10(Turb) .86 .25 4.25 66 SS 1–530

Turb 1.3–390

136

95

73

57

147

91

Menomonee River 

at Wauwatosa, 

Wis. 04087120

Log10SS = 0.567 + 0.779log10(Turb) .77 .22 4.92 95 SS 5.2–390

Turb 1.1–210

105

66

76

53

93

52

Menomonee River 

at Milwaukee, 

Wis. 04087142

Log10SS = 0.108 + 0.974log10(Turb) .85 .21 3.61 79 SS 5 –1,800

Turb 2.9 –530

105

64

35

35

249

88
Regression Model Results 11

Total Phosphorus

Elevated concentrations of nutrients, especially phosphorus, are some of the most common stressors affecting rivers 

and streams throughout the United States (Robertson and others, 2006). High nutrient concentrations may cause excessive 

aquatic plant growth, which may result in low dissolved-oxygen concentrations from respiration and decomposing plants. 

Excessive nutrients may also cause nuisance algal blooms in 

receiving waters. Because phosphorus is likely to adsorb to 

suspended sediment, turbidity is often used as a surrogate for 

the estimation of total phosphorus.

The regression models for total phosphorus at each site 

all used turbidity as the explanatory variable (table 5). The 

adjusted R2 ranged from 0.55 at the Menomonee River at 

Wauwatosa to 0.75 at the Little Menomonee River. The RMSE 

ranged from 0.19 at the Little Menomonee River to 0.22 at 

Honey Creek at Wauwatosa. Figure 5 is an example from 

Honey Creek at Wauwatosa, showing predicted total phosphorus values with 90-percent confidence intervals as well as 

the measured total phosphorus values used in the regression 

model. The model-calibration dataset, model summary, summary statistics, plots of the explanatory and response variables, and residual plots are provided in appendix 4.

Indicator Bacteria

Wastewater may enter surface waters through leaking 

sewage lines or septic tanks, wastewater-treatment plants, or 

runoff from agricultural sources. E. coli and fecal coliform 

are common types of bacteria used as wastewater indicators. 

The presence of these bacteria suggests the presence of fecal 

wastes from either humans or other warm-blooded animals 

(Dufour, 1977). Pathogens that may be present in waters 

contaminated by fecal waste include Cryptosporidium spp., 

Giardia spp., Hepatitis A, enteric adenovirus, Norwalk-like 

viruses, and rotavirus (Craun and Calderon, 1999). Exposure 

to these and other pathogens is a serious human health risk. 

Because suspended material is a medium for bacterial accumulation and transport, turbidity is often used as a surrogate 

for bacteria. In addition to turbidity, water temperature was 

determined to be a significant variable in the indicator bacteria 

regression models, likely because E. coli and fecal coliform 

bacteria grow better in warmer temperatures than in cold 

(Madigan and others, 1997).

Figure 4. Predicted and 

measured total suspended 

solids concentrations at 

the U.S. Geological Survey 

streamgage on Honey Creek 

at Wauwatosa, Wisconsin, 

December 2008–September 

2009. 

Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

1

10

100

1,000

Total suspended solids, in milligrams per liter

2008 2009

Predicted total suspended solids

Predicted total suspended solids 

 90-percent confidence intervals 

Measured total suspended solids

EXPLANATION
12 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

0.0

0.5

1.0

1.5

2.0

Total phosphorus, in milligrams per liter

Predicted total phosphorus

Predicted total phosphorus 90-percent confidence intervals 

Measured total phosphorus

2008 2009

EXPLANATION

Figure 5. Predicted 

and measured 

total phosphorus 

concentrations at the 

U.S. Geological Survey 

streamgage on Honey 

Creek at Wauwatosa, 

Wisconsin, December 

2008–September 2009. 

Table 5. Regression models and summary statistics for estimating total phosphorus concentrations in water at five water-quality 

monitoring sites in the Menomonee River Basin, Southeast Wisconsin, November 2008–September 2009. 

[R2, coefficient of determination; RMSE, root mean square error; PRESS, prediction error sum of squares; n, number of discrete samples; mg/L, milligrams per 

liter; TP, total phosphorus, in mg/L; Turb, turbidity, in nephelometric turbidity units] 

Monitoring site Regression 

model

Model diagnostics Model inputs

Adjusted 

R2 RMSE PRESS n

Range of values 

in variable 

measurements

Mean Median Standard 

deviation

Menomonee River at 

Menomonee Falls, 

Wis. 04087030

Log10TP = −1.55 + 0.492log10(Turb) 0.62 0.21 2.67 59 TP 0.034– 0.78

Turb 2.3–220

0.19

47

0.17

25

0.15

52

Little Menomonee 

River near 

Freistadt, Wis. 

04087050

Log10TP = −1.37 + 0.486log10(Turb) .75 .19 1.75 39 TP 0.038– 0.83

Turb 0.7–290

.30

72

.26

46

.21

78

Honey Creek at 

Wauwatosa, Wis. 

04087119

Log10TP = −1.45 + 0.451log10(Turb) .64 .22 3.35 66 TP 0.03– 0.88

Turb 1.3–390

.28

95

.24

57

.21

91

Menomonee River 

at Wauwatosa, 

Wis. 04087120

Log10TP = −1.42 + 0.431log10(Turb) .55 .20 3.96 91 TP 0.035– 0.66

Turb 1.1–210

.66

65

.23

52

.20

51

Menomonee River 

at Milwaukee, 

Wis. 04087142

Log10TP = −1.51 + 0.462log10(Turb) .61 .19 2.97 77 TP 0.039–1.8

Turb 2.9–530

.21

64

.14

35

.26

88
Model Predictability 13

Escherichia coli 

The regression model for E. coli bacteria for each site 

used water temperature and turbidity as explanatory variables (table 6). The adjusted R2

 ranged from 0.54 at the 

Menomonee River at Milwaukee to 0.69 at Honey Creek. The 

RMSE ranged from 0.45 at the Little Menomonee to 0.56 at 

the Menomonee River at Menomonee Falls. Figure 6 is an 

example from Honey Creek at Wauwatosa, showing predicted 

E. coli values with 90-percent confidence intervals as well as 

the measured E. coli values used in the regression model. The 

model-calibration dataset, model summary, summary statistics, 

plots of the explanatory and response variables, and residual 

plots are provided in appendix 5.

Fecal Coliform

The regression model for fecal coliform bacteria at each 

site used water temperature and turbidity as the explanatory 

variables (table 7). The adjusted R2 ranged from 0.54 at the 

Menomonee River at Milwaukee to 0.74 at Honey Creek 

and Menomonee River at Wauwatosa. The RMSE ranged 

from 0.49 at the Menomonee River at Wauwatosa to 0.65 at 

Menomonee River at Milwaukee. Figure 7 is an example from 

Honey Creek at Wauwatosa, showing predicted fecal coliform 

values with 90-percent confidence intervals as well as the 

measured fecal coliform values used in the regression model. 

The model-calibration dataset, model summary, summary 

statistics, plots of the explanatory and response variables, and 

residual plots are provided in appendix 6.

Model Predictability

The fit of the regression models, on the basis of the 

adjusted R2, RMSE, and PRESS statistics, varies by constituent. This variability in fit is demonstrated by the varied 

width of the confidence limits in each of the time series plots 

(figs. 3–7). The models for chloride, total suspended solids, 

and total phosphorus have better fits (higher adj. R2 values and 

lower RMSE and PRESS values) than those for the indicator 

bacteria (fig. 8). In general, the fits for each of these constituents are comparable to those found in similar regression 

studies (Christensen and others, 2001; Rasmussen and others, 

2009). There is no apparent relation between model fit and 

percentage of urban area in the respective basins, nor between 

model fit and number of samples collected at each site. The 

site with the fewest number of samples, the Little Menomonee 

River, had some of the better fitting models. 

Turbidity was the most frequently used explanatory variable of the continuous variables examined and was used in 21 

of the 25 developed models. This frequency is likely because 

turbidity is a measure of particulates, and indicator bacteria and total phosphorus attach to particulates. All chloride 

models used specific conductance as the only explanatory 

variable, except for the Little Menomonee River model, which 

also included turbidity. This may be related to the fact that the 

Little Menomonee River is the most rural site and, therefore, 

the least affected by road-salt runoff. None of the models 

found season to be a significant factor, but water temperature 

was significant in all of the indicator bacteria models. 
14 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Table 6. Regression models and summary statistics for estimating Escherichia coli (E. coli) bacteria concentrations in water at five 

water-quality monitoring sites in the Menomonee River Basin, Southeast Wisconsin, November 2008–September 2009. 

[R2, coefficient of determination; RMSE, root mean square error; PRESS, prediction error sum of squares; n, number of discrete samples; mg/L, milligrams per 

liter; EC, E. coli, in colonies per 100 milliliters; WT, water temperature in degrees Celsius (°C); Turb, turbidity, in nephelometric turbidity units] 

Monitoring site Regression 

model

Model diagnostics Model inputs

Adjusted 

R2 RMSE PRESS n

Range of values 

in variable 

measurements

Mean Median Standard 

deviation

Menomonee River at 

Menomonee Falls, 

Wis. 04087030

Log10EC = 1.30+ 0.057(WT) 

 + 0.674log10(Turb)

0.60 0.56 17.84 55 EC 10–52,000

WT 0–23.1

Turb 2.3–220

4,778

11

47

520

13

25

9,252

8

52

Little Menomonee 

River near 

Freistadt, Wis. 

04087050

Log10EC = 1.81+ 0.025(WT) 

 + 0.693log10(Turb)

.58 .45 8.17 37 EC 10–25,000

WT 0–18.8

Turb 0.70–290

2,840

6

72

1,100

2

46

4,870

7

78

Honey Creek at 

Wauwatosa, Wis. 

04087119

Log10EC = 1.68+ 0.071(WT) 

 + 0.626log10(Turb)

.69 .48 16.22 66 EC 200–200,000

WT 0–21.9

Turb 1.3–390

19,239

11

95

1,850

9

57

41,203

8

91

Menomonee River 

at Wauwatosa, 

Wis. 04087120

Log10EC = 1.28+ 0.063(WT) 

 + 0.884log10(Turb)

.66 .53 23.37 81 EC 60–200,000

WT 0–22.4

Turb 1.1–190

16,476

10

64

1,700

10

52

40,762

8

50

Menomonee River 

at Milwaukee, 

Wis. 04087142

Log10EC = 1.29+ 0.059(WT) 

 + 0.886log10(Turb)

.54 .54 24.05 76 EC 41–140,000

WT 0–26.0

Turb 2.9–530

7,936

10

64

1,550

10

35

19,897

8

88

Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

10

100

1,000

10,000

100,000

Escherichia coli (E. coli ), in most probable number per 100 milliliters

2008 2009

Predicted E. coli

Predicted E. coli 90-percent 

 confidence intervals 

Measured E. coli

EXPLANATION

Figure 6. Predicted and 

measured Escherichia coli

(E. coli) bacteria concentrations 

at the U.S. Geological Survey 

streamgage on Honey Creek 

at Wauwatosa, Wisconsin, 

December 2008–September 2009. 
Regression Model Results 15

Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept.

10

100

1,000

10,000

100,000

1,000,000

Fecal coliform, in colony forming units per 100 milliliters

2008 2009

Predicted fecal coliform

Predicted fecal coliform 

 90-percent confidence intervals 

Measured fecal coliform

EXPLANATION

Figure 7. Predicted 

and measured fecal 

coliform bacteria 

concentrations at the 

U.S. Geological Survey 

streamgage on Honey 

Creek at Wauwatosa, 

Wisconsin, December 

2008–September 2009. 

Table 7. Regression models and summary statistics for estimating fecal coliform bacteria concentrations in water at five water-quality 

monitoring sites in the Menomonee River Basin, Southeast Wisconsin, November 2008–September 2009. 

[R2, coefficient of determination; RMSE, root mean square error; PRESS, prediction error sum of squares; n, number of discrete samples; mg/L, milligrams per 

liter; FC, fecal coliform, in colonies per 100 milliliters; WT, water temperature in degrees Celsius (°C); Turb, turbidity, in nephelometric turbidity units] 

Monitoring site Regression 

model

Model diagnostics Model inputs

Adjusted 

R2 RMSE PRESS n

Range of values 

in variable 

measurements

Mean Median Standard 

deviation

Menomonee River at 

Menomonee Falls, 

Wis. 04087030

Log10FC = 1.07+ 0.063(WT) 

 + 0.834log10(Turb)

0.68 0.54 14.99 49 FC 10 –46,000

WT 0–23.1

Turb 2.2–220

6,975

13

47

570

15

23

11,911

8

52

Little Menomonee 

River near 

Freistadt, Wis. 

04087050

Log10FC = 1.49+ 0.035(WT) 

 + 0.777log10(Turb)

.58 .51 8.97 32 FC 10 –30,000

WT 0–18.8

Turb 0.70–290

2,912

7

77

740

7

52

5,533

7

80

Honey Creek at 

Wauwatosa, Wis. 

04087119

Log10FC = 1.46+ 0.089(WT) 

 + 0.648log10(Turb)

.74 .50 17.81 65 FC 95 –17,000

WT 0–21.9

Turb 1.3–390

25,116

11

95

1,600

10

57

44,560

7

91

Menomonee River 

at Wauwatosa, 

Wis. 04087120

Log10FC = 1.38+ 0.078(WT) 

 + 0.79log10(Turb)

.74 .49 17.10 68 FC 48 –180,000

WT 0–22.4

Turb 1.1–210

22,956

12

70

3,300

15

62

36,566

8

52

Menomonee River 

at Milwaukee, 

Wis. 04087142

Log10FC = 1.07+ 0.062(WT) 

 + 1.001log10(Turb)

.54 .65 25.56 56 FC 24 –110,000

WT 0–26.0

Turb 2.9–530

12,128

10

64

2,150

10

35

23,421

8

88
Honey Creek at Wawatosa, Wis. 04087119 Little Menomonee River near Freistadt, Wis. Menomonee River at Menomonee Falls, Wis. Menomonee River at Milwaukee, Wis. 04087Menomonee River at Wauwatosa, Wis. 04087

Adjusted R

2

1.0

0.9

0.80.70.60.5

Chloride Escherichia

coli

Fecal 

coliform

Total suspended 

solids

Total 

phosphorus

Root mean square error

0.6

0.40.2

0.0

05

10152025

Predicted error sum of squares

Chloride Escherichia

coli

Fecal 

coliform

Total su

so

Chloride Escherichia

coli

Fecal 

coliform

Total suspended 

solids

Total 

phosphorus

EXPLANATION

A BC

Figure 8. Statistics by constituent and monitoring site in the Menomonee River Basin, Wisconsin. A, Adjusted R2. B, root mean square error (RMSE). 

squares (PRESS). 
References Cited 17

Summary and Conclusions

With increasing headwater urbanization, channel restorations, and implementation of best management practices, 

the Menomonee River drainage basin in southeast Wisconsin 

faces changes which may affect water quality in the coming 

years. In an effort to monitor these and future changes to the 

basin, the U.S. Geological Survey and the Milwaukee Metropolitan Sewerage District (MMSD) initiated a study in 2008 to 

develop regression models to estimate real-time concentrations 

and loads of selected water-quality constituents. Water-quality 

sensors and automated samplers were installed at five sites in 

the Menomonee River drainage basin. The sensors continuously measured four explanatory variables: water temperature, 

specific conductance, dissolved oxygen, and turbidity. Discrete 

water-quality samples were collected and analyzed for five 

response variables: chloride, total suspended solids, total phosphorus, Escherichia coli (E. coli) bacteria, and fecal coliform 

bacteria. 

Regression models were developed to estimate the 

response variables on the basis of the explanatory variables. 

The models to estimate chloride concentrations all used specific conductance as the explanatory variable, except for the 

model for the Little Menomonee River near Freistadt, which 

used both specific conductance and turbidity. Adj. R2 values 

for the chloride models ranged from 0.74 to 0.97. Models to 

estimate total suspended solids and total phosphorus used turbidity as the only explanatory variable. Adj. R2

 values ranged 

from 0.77 to 0.94 for the total suspended solids models and 

from 0.55 to 0.75 for the total phosphorus models. Models to 

estimate indicator bacteria used water temperature and turbidity as the explanatory variables, with adj. R2

 ranges from 0.54 

to 0.69 for E. coli bacteria models and 0.54 to 0.74 for fecal 

coliform bacteria models. Dissolved oxygen was not used in 

any of the final models. Although there was a significant correlation between dissolved oxygen and the modeled constituent 

in a few of the bacteria models, dissolved oxygen was not used 

because it lacked explanatory power and because we wanted 

consistency among the sites. 

The regression models can be used to continuously 

estimate concentrations of chloride, total suspended solids, 

total phosphorus, E. coli bacteria, and fecal coliform bacteria. 

Managers can use the resulting data to estimate important 

water-quality indicators such as bacteria concentrations, 

understand variability in constituent concentrations, develop 

total maximum daily loads, assess the effects of improvement 

projects and land-use changes, provide water-quality information to communities served by MMSD and the general public, 

and focus where future improvement projects could be implemented to maximize benefits. 

Continued periodic sampling will be important to test 

the validity of the models in the future. Annual and longerterm climate variability, changes in land use, and improvements to infrastructure may necessitate making future model 

adjustments. 

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freshwater fish (2d ed.): London, Butterworth Scientific, 

361 p.

ASTM International, 2003, D1889–00 standard test method 

for turbidity of water, in ASTM International, Annual Book 

of ASTM Standards, Water and Environmental Technology: 

West Conshohocken, Pa., American Society for Testing and 

Materials, v. 11.01, 6 p.

Christensen, V.G., Jian, Xiaodong, and Ziegler, A.C., 2000, 

Regression analysis and real-time water-quality monitoring 

to estimate constituent concentrations, loads, and yields in 

the Little Arkansas River, south-central Kansas, 1995–99: 

U.S. Geological Survey Water-Resources Investigations 

Report 2000–4126, 36 p.

Christensen, V.G., Ziegler, A.C., and Jian, Xiaodong, 2001, 

Continuous turbidity monitoring and regression analysis to 

estimate total suspended solids and fecal coliform bacteria 

loads in real time, in Proceedings of the Seventh Federal 

Interagency Sedimentation Conference, March 25–29, 

2001, Reno, Nevada: Subcommittee on Sedimentation, v. 1, 

p. III-94 to III-101.

Clesceri, L.S., Greenberg, A.E., and Eaton, A.D., eds., 1998, 

Standard methods for the examination of water and wastewater (20th ed.): American Public Health Association, Washington D.C. [variously paged].

Corsi, S.R., Graczyk, D.J., Geis, S.W., Booth, N.L., and Richards, K.D., 2010, A fresh look at road salt—Aquatic toxicity 

and water-quality impacts on local, regional, and national 

scales: Environmental Science & Technology, v. 44, no. 19, 

p. 7376–7382.

Craun, G.F., Calderon, R.L., and Craun, M.F., 1999, Waterborne disease outbreaks—Their causes, problems, and challenges to treatment barriers, in Talley, D., and Malgrande, 

M., eds., Waterborne pathogens, 1999: American Water 

Works Association Manual of Water Supply Practices, 

AWWA Manual M48, p. 3–17. 

Duan, Naihua, 1983, Smearing estimate—A nonparametric 

retransformation method: Journal of the American Statistical Association, v. 78, no. 383, p. 605–610.

Dufour, A.P., 1977, Escherichia coli—The fecal coliform, in

Hoadley, A.W., and Dutka, B.J., eds., Bacterial indicators/

Health hazards associated with water: American Society for 

Testing and Materials, ASTM STP635, p. 48–58.

Edwards, T.K., and Glysson, G.D., 1999, Field methods for 

measurement of fluvial sediment: U.S. Geological Survey 

Techniques of Water-Resources Investigations, book 3, 

chap. C2, 89 p.
18 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Francy, D.S., and Darner, R.A., 2007, Nowcasting beach advisories at Ohio Lake Erie beaches: U.S. Geological Survey 

Open-File Report 2007–1427, 13 p.

Koltun, G.F., Eberle, M., Gray, J.R., and Glysson, G.D., 2006, 

User’s manual for the Graphical Constituent Loading Analysis System (GCLAS): U.S. Geological Survey Techniques 

and Methods, 4-C1, 51 p.

Laenen, Antonius, 1985, Acoustic velocity meter systems: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 3, chap. A17, 38 p.

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Madigan, M.T., Martinko, J.M., and Parker, J., 1997, Brock 

biology of microorganisms (8th ed.): Upper Saddle River, 

N.J., Prentice Hall, p. 161–162.

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February 21, 2012, at http://www.nelac-institute.org/

docs/2003nelacstandard.pdf.

Oberg, K.A., Morlock, S.E., and Caldwell, W.S., 2005, 

Quality-assurance plan for discharge measurements using 

acoustic Doppler current profilers: U.S. Geological Survey 

Scientific Investigations Report 2005–5183, 35 p.

Rantz, S.E., and others, 1982, Measurement and computation 

of Streamflow—v. 2, Computation of Discharge: U.S. Geological Survey Water Supply Paper 2175, p. 285–631.

Rasmussen, T.J., Ziegler, A.C., and Rasmussen, P.P., 2009, 

Estimation of constituent concentrations, densities, loads, 

and yields in Lower Kansas River, Northeast Kansas, using 

regression models and continuous water-quality monitoring, January 2000 through December 2003: U.S. Geological 

Survey Scientific Investigations Report 2005–5165, 117 p.

Rasmussen, P.P., Gray, J.R., Glysson, G.D., and Ziegler, A.C., 

2009, Guidelines and procedures for computing time-series 

suspended-sediment concentrations and loads from instream turbidity-sensor and streamflow data: U.S. Geological Survey Techniques and Methods book 3, chap. C4, 53 p.

Ritchie, J.C., 1972, Sediment, fish, and fish habitat: Journal of 

Soil and Water Conservation, v. 27, no. 3, p. 124–125.

Robertson, D.M., Graczyk, D.J., Garrison, P.J., Wang, Lizhu, 

LaLiberte, Gina, and Bannerman, Roger, 2006, Nutrient 

concentrations and their relations to the biotic integrity of 

wadeable streams in Wisconsin: U.S. Geological Survey 

Professional Paper 1722, 139 p.

Ruhl, C.A., and Simpson, M.R., 2005, Computation of discharge using the index-velocity method in tidally affected 

areas: U.S. Geological Survey Scientific Investigations 

Report 2005–5004. Available at http://pubs.usgs.gov/

sir/2005/5004/.

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Cary, N.C. Available at http://support.sas.com/

documentation/onlinedoc/91pdf/index_913.html. 

Southeastern Wisconsin Regional Planning Commission, 

2007, Water quality conditions and sources of pollution in 

the Greater Milwaukee watersheds: Southeastern Wisconsin 

Regional Planning Commission, Technical Report No. 39, 

141 p. 

Turnipseed, D.P., and Sauer, V.B., 2010, Discharge measurements at gaging stations: U.S. Geological Survey Techniques and Methods book 3, chap. A8, 87 p.

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quality criteria for chloride—1988: Washington, D.C., 

EPA 440/5-88-001.

U.S. Environmental Protection Agency, 1993, Methods for 

the determination of inorganic substances in environmental 

samples: Cincinnati, Ohio, EPA/600/R-93/100.

Wagner, R.J., Boulger, R.W., Jr., Oblinger, C.J., and Smith, 

B.A., 2006, Guidelines and standard procedures for continuous water-quality monitors—Station operation, record 

computation, and data reporting: U.S. Geological Survey 

Techniques and Methods 1–D3, 51 p., plus 8 attachments.
Appendix 1 19

Appendix 1. Analytical procedures used for water-quality samples 

Variable Method reference

Chloride SM(20)4500-Cl E, Clesceri and others (1998)

Total suspended solids SM(20)2540D, Clesceri and others (1998)

Total phosphorus EPA 365.1, U.S. Environmental Protection Agency (1993)

Escherichia coli bacteria SM(20)9223B, Clesceri and others (1998)

Fecal coliform bacteria SM(20)9222D, Clesceri and others (1998)

Appendix 2 21

Appendix 2. Regression analysis results for estimating chloride concentration 

All data were collected using U.S. Geological Survey 

(USGS) protocols and are stored in the USGS National Water 

Information System (NWIS) database (http://waterdata.usgs.

gov/nwis). The regression models are based on measurements 

of specific conductance and turbidity and concurrent chloride 

samples collected from November 2008 to September 2009. 

Continuous water-quality data were collected at 5-minute 

intervals using a YSI model 6920 V2 multiparameter waterquality monitor with a 6560 specific conductance and water 

temperature sensor, and a 6136 optical turbidity sensor. 

Specific conductance and turbidity values are instantaneous 

unit values temporally corresponding to the collection of the 

chloride samples. Samples were collected throughout the 

range of continuously observed hydrologic conditions. Summary statistics and the complete model-calibration dataset 

are provided. A comparison of cross-section mean and corresponding time-series monitor readings is archived at the 

Wisconsin Water Science Center and is available by request to 

Austin Baldwin (akbaldwi@usgs.gov). 
22 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Chloride at Little Menomonee River near Freistadt, WI (04087050)

Sample data on 2/16/2009 were not used in the regression development because there was a 

program change and the sonde data were lost. 

MODEL SUMMARY—Summary of final regression results for estimating chloride concentrations 

at Little Menomonee River near Freistadt, WI.

Log10 (Chloride) = -4.16 +1.99 log10 (SC) + 0.1511 log10 (Turb), 

Where:

Chloride = chloride concentration in mg/L

SC = Specific Conductance in μS/cm at 25o C; and

Turb = Turbidity (YSI 6136) in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 39,

Root-mean-squared error (RMSE) = 0.10

Model standard percentage error (MPSE) = +25 and -20 percent

90-percent prediction intervals (based on units in mg/L) = +/- 39 percent 

Adjusted coefficient of determination (Adj R2

) = 0.74

Sum of squared error = 0.34

PRESS = 0.38

Coefficients: 

Coefficient Standard t p-value

 error statistic 

Intercept -4.16 0.662 -6.28 <0.0001

Log 10 (SC) 1.99 0.218 9.11 <0.0001

Log10 (Turb) 0.151 0.037 4.04 0.0003

Correlation matrix of coefficients:

Intercept log10 (SC) log10 (Turb)

Intercept 1 -0.998 -0.831

Log10 (SC) -0.998 1 0.802

Log10 (Turb) -0.831 0.802 1 

Duan’s bias correction factor = 1.02
Appendix 2 23

Date Time Chloride

(mg/L)

Turbidity

(NTU)

Specific 

conductance

(μS/cm at 25 °C)

11/20/2008 9:45 44 1.2 877

12/17/2008 11:30 85 2.1 1,060

12/27/2008 13:05 130 11.2 1,123

12/28/2008 1:05 120 52.3 838

12/28/2008 7:15 110 45.0 749

1/20/2009 10:55 57 0.7 963

2/7/2009 18:50 80 19.7 822

2/9/2009 22:40 85 11.3 937

2/10/2009 10:45 69 38.0 697

2/10/2009 14:40 50 113.3 556

2/10/2009 20:40 42 46.0 520

2/11/2009 2:40 49 21.3 599

3/2/2009 7:10 62 4.2 935

3/7/2009 12:55 77 130.0 762

3/7/2009 18:05 52 220.0 538

3/8/2009 7:05 51 62.0 613

3/8/2009 19:00 26 210.0 384

3/9/2009 0:30 33 140.0 455

3/10/2009 3:20 43 68.0 570

3/10/209 8:15 34 94.0 454

3/10/2009 20:15 32 51.0 485

3/24/2009 10:40 57 2.8 844

4/23/2009 9:45 63 2.1 875

4/25/2009 15:10 53 100.0 676

4/26/2009 5:30 35 180.0 517

4/26/2009 19:30 23 200.0 413

Date Time Chloride

(mg/L)

Turbidity

(NTU)

Specific 

conductance

(μS/cm at 25 °C)

4/27/2009 1:30 24 80.0 447

5/9/2009 7:25 41 81.0 638

5/9/2009 13:30 30 54.0 573

5/9/2009 19:30 33 15.0 636

5/14/2009 2:30 24 270.0 485

5/20/2009 9:00 48 4.5 787

6/8/2009 5:20 35 120.0 569

6/16/2009 8:45 50 12.0 805

6/19/2009 2:50 28 290.0 510

6/19/2009 8:50 34 89.0 605

7/16/2009 10:05 51 19.0 786

8/19/2009 10:00 46 8.8 786

9/15/2009 9:30 44 10.0 799

MINIMUM 23 0.7 384

MAXIMUM 130 290.0 1,123

MEAN 53 73.8 684

MEDIAN 48 51.0 638

STANDARD 

DEVIATION 26 79.0 188

Table 2-1. Model-calibration dataset for Little Menomonee River near Freistadt, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units; μS/cm, microsiemens per centimeter; °C, degrees Celsius]
24 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 2-1. Duration curves for specific conductivity and turbidity (November 2008–September 2010) and corresponding values 

associated with chloride concentration samples collected November 2008 to September 2009 at U.S.Geological Survey streamgage on 

Little Menomonee River near Freistadt, Wisconsin. 

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70 80 90 100

Specific conductance, in microsiemens per centimeter 

Frequency of exceedance, in percent 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 2 25

1.4 1.6 1.8 2.0

2.01.81.61.4

Measured log10(chloride)

) chloride( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Chloride, in milligrams per liter

1 2 5 10 20 50 100 200

 80 60 40

120100

B

Specific conductance, in microsiemens per centimeter

Chloride, in milligrams per liter

400 600 800 1000

120100

 80 60 40

C

Discharge, in cubic feet per second

Chloride, in milligrams per liter

0.2 0.5 1.0 2.0 5.0 20.0 50.0 200.0

 80 60 40

120100

D

1.4 1.6 1.8 2.0

−0.1

0.20.10.0

Predicted log10(chloride)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.1

0.20.10.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.1

0.20.10.0

Theoretical quantiles

Residuals quantiles

G

Chloride at Little Menomonee River near Freistadt, Wisconsin, November 2008−September 2009

Figure 2-2. U.S. Geological Survey streamgage on Little Menomonee River near Freistadt, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (chloride 

concentration). B, Relation between turbidity and chloride concentration in log10 space. C, Relation between specific conductance and chloride concentration in log10 space. D, Relation between discharge 

and chloride concentration in log10 space. E, Relation between predicted log10 (chloride concentration) 

and regression residuals. F, Relation between time and chloride regression residuals. G, Probability plot of chloride regression residuals. 
26 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Chloride at Menomonee River at Menomonee Falls, WI (04087030)

Summary of final regression results for estimating chloride concentrations at Menomonee River 

at Menomonee Falls, WI.

Log10 (Chloride) = -1.63 +1.28 log10 (SC), 

Where:

Chloride = chloride concentration in mg/L

SC = Specific Conductance in μS/cm at 25o C 

Model Information (in log units unless otherwise specified): 

Number of measurements = 59,

Root-mean-squared error (RMSE) = 0.073

Model standard percentage error (MPSE) = +18 and -15 percent

90-percent prediction intervals (based on units in mg/L) = +/- 29 percent 

Adjusted coefficient of determination (Adj R2

) = 0.94

Sum of squared error = 0.30

PRESS = 0.32

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.63 0.120 -13.56 <0.0001

Log 10 (SC) 1.29 0.041 31.20 <0.0001

Correlation matrix of coefficients:

Intercept log10 (SC) 

Intercept 1 -0.997 

Log10 (SC) -0.997 1 

 

Duan’s bias correction factor = 1.01
Appendix 2 27

Date Time Chloride

(mg/L)

Specific conductance

(μS/cm at 25 °C)

11/20/2008 9:15 130 1,130

12/17/2008 12:00 250 1,450

12/27/2008 0:35 840 3,487

12/27/2008 6:15 960 3,700

12/27/2008 14:20 560 2,347

12/27/2008 20:20 400 1,873

12/28/2008 8:20 300 1,320

1/20/2009 9:55 190 1,270

2/16/2009 11:00 160 1,110

2/26/2009 15:05 370 1,860

2/26/2009 18:15 280 1,370

2/27/2009 0:15 250 1,180

3/2/2009 7:15 190 1,170

3/7/2009 9:30 180 976

3/7/2009 15:30 190 969

3/8/2009 10:30 150 848

3/8/2009 14:00 140 745

3/9/2009 2:00 120 708

3/24/2009 10:00 160 1,010

3/25/2009 5:25 210 1,070

4/19/2009 23:00 150 866

4/20/2009 11:15 210 1,090

4/20/2009 23:15 200 1,120

4/23/2009 9:15 150 1,050

4/25/2009 10:50 110 756

4/25/2009 11:00 80 642

4/26/2009 5:00 120 749

4/26/2009 16:00 96 671

4/27/2009 4:00 90 657

5/9/2009 1:05 94 744

5/9/2009 1:15 72 654

5/9/2009 10:25 110 749

5/9/2009 22:25 120 839

Date Time Chloride

(mg/L)

Specific conductance

(μS/cm at 25 °C)

5/10/2009 10:25 110 810

5/13/2009 23:00 60 703

5/20/209 9:30 110 901

6/8/2009 3:15 71 547

6/8/2009 3:25 41 354

6/8/2009 9:35 110 670

6/16/2009 10:15 140 990

6/19/2009 0:10 72 529

6/19/2009 0:50 24 252

6/19/2009 2:00 42 361

6/20/2009 2:00 110 758

7/16/2009 9:30 180 984

8/7/2009 19:35 83 573

8/8/2009 9:05 46 327

8/19/2009 9:00 190 1,090

8/25/2009 18:20 120 600

8/25/2009 18:45 46 314

8/26/2009 1:30 88 523

8/26/2009 1:55 53 340

9/15/2009 9:30 190 1,120

9/22/2009 13:15 110 685

9/22/2009 14:05 33 308

9/22/2009 15:20 120 733

9/27/2009 19:25 120 658

9/27/2008 21:30 95 583

9/28/2009 5:55 100 592

MINIMUM 24 252

MAXIMUM 960 3,700

MEAN 171 957

MEDIAN 120 758

STANDARD DEVIATION 167 636

Table 2-2. Model-calibration dataset for Little Menomonee River at Menomonee Falls, Wisconsin.

[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; °C, degrees Celsius]
28 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 2-3. Duration curve for specific conductivity (November 2008–September 2010) and corresponding values associated with 

chloride concentration samples collected November 2008 to September 2009 at U.S.Geological Survey streamgage on Menomonee 

River at Menomonee Falls, Wisconsin. 

100

1000

10000

0 10 20 30 40 50 60 70 80 90 100

Specific conductance, in microsiemens per centimeter 

Frequency of exceedance, in percent 
Appendix 2 29

1.5 2.0 2.5 3.0

3.02.52.01.5

Measured log10(chloride)

) chloride( 10 Predicted log

A B

Specific conductance, in microsiemens per centimeter

Chloride, in milligrams per liter

500 1000 2000

 50

1000

 500 200 100

C

Discharge, in cubic feet per second

Chloride, in milligrams per liter

2 5 10 20 50 100 200

 500 200 100

 50

1000 D

1.5 2.0 2.5 3.0

−0.1−0.2

0.10.0

Predicted log10(chloride)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.1−0.2

0.10.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.1−0.2

0.10.0

Theoretical quantiles

Residuals quantiles

G

Chloride at Menomonee River at Menomonee Falls, Wisconsin, November 2008−September 2009

Figure 2-4. U.S. Geological Survey streamgage on Menomonee River at Menomonee Falls, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (chloride 

concentration). B, No plot. C, Relation between specific conductance and chloride concentration in log10

space. D, Relation between discharge and chloride concentration in log10 space. E, Relation between 

predicted log10 (chloride concentration) and regression residuals. F, Relation between time and chloride 

regression residuals. G, Probability plot of chloride regression residuals. 
30 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Chloride at Honey Creek at Wauwatosa, WI (04087119)

Sample data from 5/20/2009 through 6/19/2009 were not used in the regression development 

because of excessive fouling of the YSI data sonde, followed by damage to the sonde and 

sampler line during an extreme flood event. 

MODEL SUMMARY—Summary of final regression results for estimating chloride concentrations 

at Honey Creek at Wauwatosa, WI.

Log10 (Chloride) = -0.984 +1.12 log10 (SC),

Where:

Chloride = chloride concentration in mg/L

SC = Specific Conductance in μS/cm at 25o

 C 

Model Information (in log units unless otherwise specified): 

Number of measurements = 70,

Root-mean-squared error (RMSE) = 0.23

Model standard percentage error (MPSE) = +71 and -42 percent

90-percent prediction intervals (based on units in mg/L) = +/- 121 percent 

Adjusted coefficient of determination (Adj R2

) = 0.81

Sum of squared error = 3.70

PRESS = 3.88

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -.984 0.186 -5.29 <0.0001

Log 10 (SC) 1.99 0.218 9.11 <0.0001

Correlation matrix of coefficients:

Intercept log10 (SC) 

Intercept 1 -0.989 

Log10 (SC) -0.989 1 

Duan’s bias correction factor = 1.19
Appendix 2 31

Date Time Chloride

(mg/L)

Specific 

conductance 

(μS/cm at 25 °C)

12/17/2008 13:45 1,100 4,360

1/20/2009 11:55 1,700 5,910

2/10/2009 10:10 540 2,253

2/10/2009 13:25 380 1,687

2/10/2009 19:25 500 2,097

2/11/2009 1:25 740 2,937

2/11/2009 11:25 1,000 3,660

2/11/2009 12:00 650 2,930

2/11/2009 15:30 380 1,610

2/12/2009 2:25 670 2,647

2/16/2009 12:20 980 3,737

3/7/2009 9:25 1,100 3,460

3/7/2009 10:25 400 1,300

3/7/2009 12:10 320 727

3/7/2009 16:05 270 520

3/7/2009 22:05 260 518

3/8/2009 14:25 170 354

3/9/2009 1:00 260 477

3/10/2009 0:50 610 704

3/10/2009 5:30 190 377

3/10/2009 9:30 240 354

3/10/2009 12:10 270 411

3/10/2009 12:15 280 411

3/24/2009 11:40 690 3,110

3/25/2009 1:20 240 809

3/25/2009 3:45 660 518

3/31/2009 16:15 510 2,110

3/31/2009 17:05 250 1,160

4/19/2009 17:10 430 2,050

4/19/2009 18:15 150 667

4/20/2009 2:30 86 429

4/20/2009 17:20 260 1,460

4/23/2009 10:45 460 2,340

4/25/2009 10:50 510 2,380

4/25/2009 12:40 34 196

4/25/2009 21:25 230 1,010

4/26/2009 2:25 74 391

4/26/2009 11:10 92 559

4/26/2009 15:30 69 417

4/26/2009 17:20 32 258

4/26/2009 20:25 90 591

Date Time Chloride

(mg/L)

Specific 

conductance 

(μS/cm at 25 °C)

5/13/2009 20:30 310 1,580

5/13/2009 20:50 59 281

5/13/2009 21:10 26 181

5/14/2009 0:55 17 190

5/14/2009 2:40 46 124

7/16/2009 11:00 190 1,050

8/7/2009 17:10 180 938

8/7/2009 20:20 27 241

8/7/2009 23:05 41 305

8/8/2009 9:10 24 179

8/8/2009 9:30 17 150

8/8/2009 19:55 140 715

8/10/2009 1:50 30 153

8/10/2009 4:10 11 181

8/19/2009 12:40 200 1,120

8/25/2009 20:55 270 1,360

8/28/2009 22:05 65 390

8/26/2009 4:05 34 276

9/15/2009 10:45 250 1,670

9/20/2009 20:20 240 1,240

9/20/2009 21:55 140 724

9/21/2009 3:55 59 431

9/22/2009 13:25 260 1,350

9/22/2009 14:05 31 237

9/22/2009 22:40 57 378

9/27/2009 20:20 120 533

9/27/2009 21:00 16 134

9/27/2009 23:35 23 182

9/28/2009 2:30 47 323

MINIMUM 11 124

MAXIMUM 1,700 5,910

MEAN 297 1,150

MEDIAN 235 629

STANDARD DEVIATION 321 1,185

Table 2-3. Model-calibration dataset for Honey Creek at Wauwatosa, Wisconsin.

[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; °C, degrees Celsius]
32 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 2-5. Duration curve for specific conductivity (November 2008–September 2010) and corresponding values associated with 

chloride concentration samples collected November 2008 to September 2009 at U.S.Geological Survey streamgage on Honey Creek at 

Wauwatosa, Wisconsin. 

10

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100

Specific conductance, in microsiemens per centimeter 

Frequency of exceedance, in percent 
Appendix 2 33

1.0 1.5 2.0 2.5 3.0

3.02.52.01.5

Measured log10(chloride)

) chloride( 10 Predicted log

A B

Specific conductance, in microsiemens per centimeter

Chloride, in milligrams per liter

200 500 1000 2000 5000

 50 20 10

20001000

 500 200 100

C

Discharge, in cubic feet per second

Chloride, in milligrams per liter

1 5 10 50 500

 500 200 100

 50 20 10

20001000

D

1.5 2.0 2.5 3.0

−0.2−0.4

0.80.60.40.20.0

Predicted log10(chloride)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4

0.80.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4

0.80.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Chloride at Honey Creek at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 2-6. U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (chloride 

concentration). B, No plot. C, Relation between specific conductance and chloride concentration in log10

space. D, Relation between discharge and chloride concentration in log10 space. E, Relation between 

predicted log10 (chloride concentration) and regression residuals. F, Relation between time and chloride 

regression residuals. G, Probability plot of chloride regression residuals. 
34 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Chloride at Menomonee River at Wauwatosa, WI (04087120)

MODEL SUMMARY—Summary of final regression results for estimating chloride concentrations 

at Menomonee River at Wauwatosa, WI.

Log10 (Chloride) = -1.41 +1.23 log10 (SC),

Where:

Chloride = chloride concentration in mg/L

SC = Specific Conductance in μS/cm at 25o

 C 

 

Model Information (in log units unless otherwise specified): 

Number of measurements = 101,

Root-mean-squared error (RMSE) = 0.115

Model standard percentage error (MPSE) = +30 and -23 percent

90-percent prediction intervals (based on units in mg/L) = +/- 47 percent 

Adjusted coefficient of determination (Adj R2

) = 0.92

Sum of squared error = 1.30

PRESS = 1.35

Coefficients: 

Coefficient Standard t p-value

 error statistic 

Intercept -1.41 0.111 -12.65 <0.0001

Log 10 (SC) 1.23 0.036 33.63 <0.0001

Correlation matrix of coefficients:

Intercept log10 (SC) 

Intercept 1 -0.995 

Log10 (SC) -0.995 1 

Duan’s bias correction factor = 1.03
Appendix 2 35

Date Time Chloride

(mg/L)

Specific 

conductance 

(μS/cm at 25 °C)

11/20/2008 10:30 180 1,250

12/17/2008 12:30 450 2,120

12/27/2008 1:15 2,300 6,520

12/27/2008 3:45 2,100 6,890

12/27/2008 5:50 1,800 6,126

12/27/2008 6:05 1,900 6,100

12/27/2008 10:15 1,300 4,640

12/27/2008 14:00 820 3,040

12/27/2008 14:45 580 2,350

12/28/2008 7:45 480 1,960

1/20/2009 12:10 470 2,370

2/7/2009 11:25 920 3,520

2/7/2009 13:25 990 3,620

2/7/2009 13:40 1,000 3,590

2/7/2009 19:40 670 2,616

2/8/2009 13:40 640 2,593

2/9/2009 1:40 480 2,163

2/9/2009 19:40 460 2,110

2/9/2009 22:00 520 2,320

2/9/2009 23:15 460 2,100

2/10/2009 7:20 440 2,080

2/10/2009 11:00 470 2,190

2/10/2009 17:05 410 1,913

2/10/2009 23:25 350 1,753

2/16/2009 12:45 320 1,770

2/26/2009 14:35 620 2,840

2/26/2009 19:00 630 1,610

2/26/2009 19:45 630 1,320

2/26/2009 22:50 330 1,160

2/27/2009 4:50 280 1,590

3/2/2009 7:20 270 1,670

3/10/2009 0:15 260 1,220

3/10/2009 5:50 210 981

3/10/2009 11:45 200 958

3/10/2009 14:50 200 938

3/11/2008 1:10 180 892

3/24/2009 11:55 280 1,460

3/25/2009 1:30 280 1,350

3/31/2009 17:00 330 1,720

3/31/2009 17:35 310 1,620

4/1/2009 5:35 280 1,520

4/19/2009 19:10 270 1,350

4/20/2009 5:05 190 899

4/21/2009 5:05 270 1,300

4/23/2009 11:00 250 1,320

4/25/2009 11:15 240 1,250

4/25/2009 12:40 160 813

4/25/2009 21:35 140 735

4/26/2009 2:35 120 637

4/26/2009 14:35 130 725

4/26/2009 16:00 80 498

4/26/2009 17:10 63 430

4/27/2009 0:30 86 564

Date Time Chloride

(mg/L)

Specific 

conductance 

(μS/cm at 25 °C)

5/9/2009 0:30 180 992

5/9/2009 9:30 150 825

5/9/2009 15:50 150 807

5/13/2009 20:40 140 816

5/13/2009 21:05 110 673

5/13/2009 22:00 85 513

5/14/2009 3:15 85 525

5/20/2009 11:15 190 1,150

6/8/2009 3:10 210 1,090

6/8/2009 4:00 150 944

6/8/2009 4:15 150 778

6/8/2009 6:45 46 288

6/8/2009 10:15 80 481

6/9/2009 4:15 130 734

6/16/2009 11:50 240 1,320

6/19/2009 9:15 110 319

6/19/2009 18:15 39 361

6/19/2009 21:20 35 269

6/20/2009 3:10 54 496

7/16/2009 11:45 220 1,160

8/7/2009 18:00 240 1,180

8/7/2009 20:40 230 1,230

8/8/2009 0:55 120 699

8/8/2009 8:50 100 598

8/8/2009 9:45 62 402

8/8/2009 19:50 77 485

8/9/2009 19:50 170 861

8/10/2009 2:00 130 739

8/10/2009 4:20 68 457

8/19/2009 12:20 47 1,370

8/25/2009 20:50 82 623

8/25/2009 21:25 99 643

8/25/2009 21:30 150 944

8/26/2009 3:30 95 577

8/27/2009 3:35 94 587

9/15/2009 11:00 290 1,520

9/20/2009 21:40 210 1,080

9/21/2009 3:40 140 740

9/22/2009 13:30 140 889

9/22/2009 13:40 82 848

9/22/2009 21:50 120 470

9/22/2009 23:10 120 675

9/27/2009 20:35 100 666

9/27/2009 21:05 140 758

9/27/2009 21:20 96 508

09/28/209 0:05 29 235

9/28/2009 2:35 57 386

9/28/2009 20:35 100 584

MINIMUM 29 235

MAXIMUM 2,300 6,890

MEAN 334 1,449

MEDIAN 190 992

STANDARD DEVIATION 418 1,308

Table 2-4. Model-calibration dataset for Menomonee River at Wauwatosa, Wisconsin.

[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; °C, degrees Celsius]
36 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 2-7. Duration curve for specific conductivity (November 2008–September 2010) and corresponding values associated with 

chloride concentration samples collected November 2008 to September 2009 at U.S.Geological Survey streamgage on Menomonee 

River at Wauwatosa, Wisconsin. 

100

1000

10000

0 10 20 30 40 50 60 70 80 90 100

Specific conductance, in microsiemens per centimeter 

Frequency of exceedance, in percent 
Appendix 2 37

1.5 2.0 2.5 3.0

3.02.52.01.5

Measured log10(chloride)

) chloride( 10 Predicted log

A B

Specific conductance, in microsiemens per centimeter

Chloride, in milligrams per liter

500 1000 2000 5000

 50

20001000

 500 200 100

C

Discharge, in cubic feet per second

Chloride, in milligrams per liter

5 10 20 50 100 500 2000 5000

 500 200 100

 50

20001000

D

1.5 2.0 2.5 3.0

−0.2−0.4−0.6−0.8

0.40.20.0

Predicted log10(chloride)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4−0.6−0.8

0.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4−0.6−0.8

0.40.20.0

Theoretical quantiles

Residuals quantiles

G

Chloride at Menomonee River at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 2-8. U.S. Geological Survey streamgage on Menomonee River at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (chloride 

concentration). B, No plot. C, Relation between specific conductance and chloride concentration in log10

space. D, Relation between discharge and chloride concentration in log10 space. E, Relation between 

predicted log10 (chloride concentration) and regression residuals. F, Relation between time and chloride 

regression residuals. G, Probability plot of chloride regression residuals. 
38 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Chloride at Menomonee River at 16th Street at Milwaukee, WI (04087142)

MODEL SUMMARY—Summary of final regression results for estimating chloride concentrations 

at Menomonee River at 16th Street at Milwaukee, WI.

Log10 (Chloride) = -1.50 +1.26 log10 (SC),

Where:

Chloride = chloride concentration in mg/L

SC = Specific Conductance in μS/cm at 25o C 

 

Model Information (in log units unless otherwise specified): 

Number of measurements = 79,

Root-mean-squared error (RMSE) = 0.074

Model standard percentage error (MPSE) = +18 and -16 percent

90-percent prediction intervals (based on units in mg/L) = +/- 29 percent 

Adjusted coefficient of determination (Adj R2

) = 0.97

Sum of squared error = 0.42

PRESS = 0.44

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.50 0.078 -19.25 <0.0001

Log 10 (SC) 1.26 0.026 47.86 <0.0001

Correlation matrix of coefficients:

Intercept log10 (SC) 

Intercept 1 -0.994 

Log10 (SC) -0.994 1 

Duan’s bias correction factor = 1.01
Appendix 2 39

Date Time Chloride

(mg/L)

Specific 

conductance 

(μS/cm at 25 °C)

11/20/2008 11:45 110 942

12/17/2008 14:15 520 2,480

12/27/2008 9:35 1,100 4,033

12/27/2008 12:35 1,400 4,763

12/27/2008 15:35 700 2,340

12/27/2008 21:35 510 2,053

12/28/2008 0:35 540 2,200

12/28/2008 6:35 520 2,130

1/20/2009 12:40 150 1,740

2/7/2009 11:40 250 1,493

2/7/2009 20:40 920 3,476

2/8/2009 5:40 730 2,880

2/8/2009 14:40 680 2,843

2/8/2009 23:40 690 2,753

2/9/2009 17:40 520 2,300

2/10/2009 5:40 480 2,210

2/11/2009 17:40 320 1,570

2/16/2009 13:40 360 1,873

2/26/2009 16:00 420 2,090

2/26/2009 19:00 480 2,110

2/26/2009 22:00 280 1,090

2/27/2009 4:00 300 1,240

2/27/2009 12:00 370 1,550

2/28/2009 12:00 320 1,860

3/7/2009 11:10 300 1,710

3/7/2009 14:10 270 1,420

3/7/2009 23:10 290 1,290

3/8/2009 12:10 280 1,300

3/8/2009 18:10 160 743

3/9/2009 0:10 240 1,100

3/10/2009 8:15 200 938

3/10/2009 12:55 210 1,020

3/10/2009 13:00 210 1,030

3/10/2009 20:30 200 991

3/11/2009 4:30 190 984

3/24/2009 12:25 270 1,334

4/1/2009 1:40 240 1,220

4/20/2009 3:05 180 866

4/20/2009 4:50 160 714

4/23/2009 11:15 240 1,220

4/25/2009 13:20 240 1,190

4/25/2009 20:00 120 611

Date Time Chloride

(mg/L)

Specific 

conductance 

(μS/cm at 25 °C)

4/26/2009 8:00 120 639

4/26/2009 14:00 120 680

4/26/2009 16:25 100 601

4/26/2009 17:10 74 450

4/26/2009 19:30 59 411

4/26/2009 19:35 59 414

5/13/2009 22:05 160 895

5/14/2009 0:35 51 374

5/14/2009 1:45 42 326

5/14/2009 3:35 49 378

5/20/2009 11:45 170 1,080

6/8/2009 12:40 66 395

6/8/2009 15:30 79 478

6/9/2009 2:35 95 566

6/9/2009 5:00 100 600

6/16/2009 13:00 150 974

6/19/2009 0:55 50 307

6/19/2009 1:10 18 174

6/19/2009 1:45 20 174

6/19/2009 9:35 47 379

6/19/2040 20:45 39 315

6/20/2009 2:25 56 471

7/16/2009 12:30 150 883

8/8/2009 22:30 56 361

8/9/2009 10:30 82 508

8/19/2009 13:30 120 775

8/26/2009 7:05 69 413

8/26/2009 17:00 84 522

8/26/2009 23:45 90 547

9/15/2009 11:30 96 725

9/23/2009 7:10 100 750

9/24/2009 7:00 110 710

9/28/2009 12:05 39 294

09/28/209 18:05 76 472

9/29/2009 0:05 72 481

9/29/2009 3:05 75 492

9/29/2009 5:00 72 541

MINIMUM 18 174

MAXIMUM 1,400 4,763

MEAN 249 1,180

MEDIAN 160 938

STANDARD DEVIATION 254 910

Table 2-5. Model-calibration dataset for Menomonee River at 16th Street at Milwaukee, Wisconsin.

[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; °C, degrees Celsius]
40 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 2-9. Duration curve for specific conductivity (November 2008–September 2010) and corresponding values associated with 

chloride concentration samples collected November 2008 to September 2009 at U.S.Geological Survey streamgage on Menomonee 

River at 16th Street at Milwaukee, Wisconsin. 

100

1000

10000

0 10 20 30 40 50 60 70 80 90 100

Specific conductance, in microsiemens per centimeter 

Frequency of exceedance, in percent 
Appendix 2 41

1.5 2.0 2.5 3.0

3.02.52.01.5

Measured log10(chloride)

) chloride( 10 Predicted log

A B

Specific conductance, in microsiemens per centimeter

Chloride, in milligrams per liter

200 500 1000 2000 5000

 50 20

1000

 500 200 100

C

Discharge, in cubic feet per second

Chloride, in milligrams per liter

5 10 50 500 5000

 500 200 100

 50 20

1000 D

1.5 2.0 2.5 3.0

−0.1−0.2−0.3−0.4

0.10.0

Predicted log10(chloride)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.1−0.2−0.3−0.4

0.10.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.1−0.2−0.3−0.4

0.10.0

Theoretical quantiles

Residuals quantiles

G

Chloride at Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008−September 2009

Figure 2-10. U.S. Geological Survey streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (chloride 

concentration). B, No plot. C, Relation between specific conductance and chloride concentration in log10

space. D, Relation between discharge and chloride concentration in log10 space. E, Relation between 

predicted log10 (chloride concentration) and regression residuals. F, Relation between time and chloride 

regression residuals. G, Probability plot of chloride regression residuals. 

Appendix 3 43

Appendix 3. Regression analysis results for estimating total suspended solids 

concentration 

All data were collected using U.S. Geological Survey 

(USGS) protocols and are stored in the USGS National Water 

Information System (NWIS) database (http://waterdata.usgs.

gov/nwis). The regression models are based on measurements 

of turbidity and concurrent total suspended solids samples collected from November 2008 to September 2009. Continuous 

water-quality data were collected at 5-minute intervals using 

a YSI model 6920 V2 multiparameter water-quality monitor with a 6560 specific conductance and water temperature 

sensor, and a 6136 optical turbidity sensor. Turbidity values 

are instantaneous unit values temporally corresponding to 

the collection of the total suspended solids samples. Samples 

were collected throughout the range of continuously observed 

hydrologic conditions. Summary statistics and the complete 

model-calibration dataset are provided. A comparison of crosssection mean and corresponding time-series monitor readings 

is archived at the Wisconsin Water Science Center and is available by request to Austin Baldwin (akbaldwi@usgs.gov). 
44 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total suspended solids at Little Menomonee River near Freistadt, WI 

(04087050)

Samples collected on 2/26/2009 were not used in the regression analysis. From inspection of 

the scatter plots, these samples appear to be outliers. 

MODEL SUMMARY—Summary of final regression results for estimating total suspended solids

concentrations at Little Menomonee River near Freistadt, WI.

Log10 (Suspended Solids) = 0.334 + 0.910 log10 (Turb),

Where:

Suspended Solids = total suspended solids concentration in mg/L

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 39,

Root-mean-squared error (RMSE) = 0.17

Model standard percentage error (MPSE) = +46 and -32 percent

90-percent prediction intervals (based on units in mg/L) = +/- 74 percent 

Adjusted coefficient of determination (Adj R2

) = 0.94

Sum of squared error = 1.01

PRESS = 1.25

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 0.334 0.063 5.31 <0.001

Log 10 (Turb) 0.910 0.038 23.84 <0.001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.908

Log10 (Turb) -0.908 1 

Duan’s bias correction factor = 1.08
Appendix 3 45

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

11/20/2008 9:45 2 1.2

12/17/2008 11:30 2 2.1

12/27/2008 13:05 13 11.2

12/28/2008 1:05 100 52.3

12/28/2008 7:15 42 45.0

1/20/2009 10:55 7 0.7

2/7/2009 18:50 37 19.7

2/9/2009 22:40 18 11.3

2/10/2009 10:45 67 38.0

2/10/2009 14:40 220 113.3

2/10/2009 20:40 92 46.0

2/11/2009 2:40 31 21.3

3/2/2009 7:10 5 4.2

3/7/2009 12:55 180 130.0

3/7/2009 18:05 410 220.0

3/8/2009 7:05 84 62.0

3/8/2009 19:00 320 210.0

3/9/2009 0:30 170 140.0

3/10/2009 3:20 100 68.0

03/10/209 8:15 160 94.0

3/10/2009 20:15 44 51.0

3/24/2009 10:40 9 2.8

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

4/23/2009 9:45 6 2.1

4/25/2009 15:10 130 100.0

4/26/2009 5:30 330 180.0

4/26/2009 19:30 310 200.0

4/27/2009 1:30 100 80.0

5/9/2009 7:25 110 81.0

5/9/2009 13:30 75 54.0

5/9/2009 19:30 24 15.0

5/14/2009 2:30 410 270.0

5/20/2009 9:00 14 4.5

6/8/2009 5:20 220 120.0

6/16/2009 8:45 18 12.0

6/19/2009 2:50 360 290.0

6/19/2009 8:50 160 89.0

7/16/2009 10:05 17 17.0

8/19/2009 10:00 10 17.0

9/15/2009 9:30 13 17.0

MINIMUM 2 0.7

MAXIMUM 410 290.0

MEAN 113 74.2

MEDIAN 75 51.0

STANDARD DEVIATION 123 78.7

Table 3-1. Model-calibration dataset for Little Menomonee River near Freistadt, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]
46 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 3-1. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total suspended 

solids concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Little Menomonee 

River near Freistadt, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 3 47

0.5 1.0 1.5 2.0 2.5

2.52.01.51.00.5

Measured log10(total suspended solids)

) total suspended solids( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total suspended solids, in

milligrams per liter

1 2 5 10 20 50 100 200

 50 20 10

 5 2

500200100

B C

Discharge, in cubic feet per second

Total suspended solids, in

milligrams per liter

0.2 0.5 1.0 2.0 5.0 20.0 50.0 200.0

 50 20 10

 5 2

500200100

D

0.5 1.0 1.5 2.0 2.5

−0.2

0.60.40.20.0

Predicted log10(total suspended solids)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2

0.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2

0.60.40.20.0

Theoretical quantiles

Residuals quantiles

Total suspended solids at Little Menomonee River near Freistadt, Wisconsin, November 2008−September 2009

G

Figure 3-2. U.S. Geological Survey streamgage on Little Menomonee River near Freistadt, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total suspended 

solids concentration). B, Relation between turbidity and total suspended solids concentration in log10

space. C, No plot. D, Relation between discharge and total suspended solids concentration in log10 space. 

E, Relation between predicted log10 (total suspended solids concentration) and regression residuals. 

F, Relation between time and total suspended solids regression residuals. G, Probability plot of total suspended solids regression residuals. 
48 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total suspended solids at Menomonee River at Menomonee Falls, WI 

(04087030)

MODEL SUMMARY—Summary of final regression results for estimating total suspended solids

concentrations at Menomonee River at Menomonee Falls, WI.

Log10 (Suspended Solids) = 0.256 + 0.953 log10 (Turb),

Where:

Suspended Solids = total suspended solids concentration in mg/L

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 59,

Root-mean-squared error (RMSE) = 0.16

Model standard percentage error (MPSE) = +43 and -30 percent

90-percent prediction intervals (based on units in mg/L) = +/- 69 percent 

Adjusted coefficient of determination (Adj R2

) = 0.92

Sum of squared error = 1.40

PRESS = 1.54

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 0.256 0.058 4.41 <0.0001

Log 10 (Turb) 0.953 0.038 25.19 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.936

Log10 (Turb) -0.936 1 

Duan’s bias correction factor = 1.07
Appendix 3 49

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

11/20/2008 9:15 6 3.6

12/17/2008 12:00 5 2.7

12/27/2008 0:35 18 18.0

12/27/2008 6:15 36 49.0

12/27/2008 14:20 110 100.7

12/27/2008 20:20 66 39.7

12/28/2008 8:20 37 45.3

1/20/2009 9:55 11 2.5

2/16/2009 11:00 5 3.1

2/26/2009 15:05 130 86.0

2/26/2009 18:15 110 81.0

2/27/2009 0:15 36 30.0

3/2/2009 7:15 22 3.2

3/7/2009 9:30 47 31.0

3/7/2009 15:30 48 29.0

3/8/2009 10:30 39 26.0

3/8/2009 14:00 130 69.0

3/9/2009 2:00 52 34.0

3/24/2009 10:00 9 4.1

3/25/2009 5:25 24 16.0

4/19/2009 23:00 46 23.0

4/20/2009 11:15 14 12.0

4/20/2009 23:15 13 11.0

4/23/2009 9:15 4 3.8

4/25/2009 10:50 120 71.0

4/25/2009 11:00 350 170.0

4/26/2009 5:00 44 27.0

4/26/2009 16:00 50 34.0

4/27/2009 4:00 38 23.0

5/9/2009 1:05 110 83.0

5/9/2009 1:15 210 110.0

5/9/2009 10:25 21 12.0

5/9/2009 22:25 24 14.0

5/10/2009 10:25 12 8.2

5/13/2009 23:00 120 81.0

05/20/209 9:30 11 6.3

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

6/8/2009 3:15 180 91.0

6/8/2009 3:25 500 220.0

6/8/2009 9:35 51 28.0

6/16/2009 10:15 20 13.0

6/19/2009 0:10 250 160.0

6/19/2009 0:50 200 110.0

6/19/2009 2:00 110 66.0

6/20/2009 2:00 28 21.0

7/16/2009 9:30 5 5.0

8/7/2009 19:35 76 46.0

8/8/2009 9:05 150 80.0

8/19/2009 9:00 4 3.2

8/25/2009 18:20 250 210.0

8/25/2009 18:45 120 85.0

8/26/2009 1:30 20 30.0

8/26/2009 1:55 50 48.0

9/15/2009 9:30 6 2.8

9/22/2009 13:15 88 62.0

9/22/2009 14:05 270 130.0

9/22/2009 15:20 36 21.0

9/27/2009 19:25 100 81.0

9/27/2008 21:30 99 51.0

9/28/2009 5:55 10 12.0

MINIMUM 4 2.5

MAXIMUM 500 220.0

MEAN 81 49.8

MEDIAN 46 30.0

STANDARD DEVIATION 95 50.9

Table 3-2. Model-calibration dataset for Menomonee River at Menomonee Falls, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]
50 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 3-3. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total suspended 

solids concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Menomonee River 

at Menomonee Falls, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 3 51

1.0 1.5 2.0 2.5

2.52.01.51.0

Measured log10(total suspended solids)

) total suspended solids( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total suspended solids, in

milligrams per liter

5 10 20 50 100 200

 50 20 10

 5

500200100

B C

Discharge, in cubic feet per second

Total suspended solids, in

milligrams per liter

2 5 10 20 50 100 200

 50 20 10

 5

500200100

D

1.0 1.5 2.0 2.5

−0.2−0.4

0.60.40.20.0

Predicted log10(total suspended solids)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4

0.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4

0.60.40.20.0

Theoretical quantiles

Residuals quantiles

Total suspended solids at Menomonee River at Menomonee Falls, Wisconsin, November 2008−September 2009

G

Figure 3-4. U.S. Geological Survey streamgage on Menomonee River at Menomonee Falls, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total suspended 

solids concentration). B, Relation between turbidity and total suspended solids concentration in log10

space. C, No plot. D, Relation between discharge and total suspended solids concentration in log10 space. 

E, Relation between predicted log10 (total suspended solids concentration) and regression residuals. 

F, Relation between time and total suspended solids regression residuals. G, Probability plot of total suspended solids regression residuals. 
52 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total suspended solids at Honey Creek at Wauwatosa, WI (04087119)

Sample data from 4/25/2009 at 12:40 through 4/26/2009, and sample data from 6/8/2009 were 

not used in the regression development because of excessive fouling of the data sonde. Sample 

data on 6/19/2009 were not used because of damage to the sonde and sampler line during an 

extreme flood event. 

MODEL SUMMARY—Summary of final regression results for estimating total suspended solids

concentrations at Honey Creek at Wauwatosa, WI.

Log10 (Suspended Solids) = 0.160 + 0.967 log10 (Turb),

Where:

Suspended Solids = total suspended solids concentration in mg/L

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 66,

Root-mean-squared error (RMSE) = 0.25

Model standard percentage error (MPSE) = +77 and -44 percent

90-percent prediction intervals (based on units in mg/L) = +/- 128 percent 

Adjusted coefficient of determination (Adj R2

) = 0.86

Sum of squared error = 3.94

PRESS = 4.25

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 0.160 0.085 1.88 0.0643

Log 10 (Turb) 0.967 0.047 20.39 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.934

Log10 (Turb) -0.934 1 

Duan’s bias correction factor = 1.16
Appendix 3 53

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

12/17/2008 13:45 1 1.8

1/20/2009 11:55 3 1.7

2/10/2009 10:10 31 46.0

2/10/2009 13:25 130 123.3

2/10/2009 19:25 100 82.0

2/11/2009 1:25 36 41.3

2/11/2009 11:25 12 21.3

2/11/2009 12:00 220 97.0

2/11/2009 15:30 230 210.0

2/12/2009 2:25 27 32.7

2/16/2009 12:20 41 53.3

3/7/2009 9:25 13 74.0

3/7/2009 10:25 310 210.0

3/7/2009 12:10 350 140.0

3/7/2009 16:05 110 71.0

3/7/2009 22:05 70 46.0

3/8/2009 14:25 180 140.0

3/9/2009 1:00 75 32.0

3/10/2009 0:50 36 40.0

3/10/2009 5:30 60 50.0

3/10/2009 9:30 46 55.0

3/10/2009 12:10 23 33.0

3/10/2009 12:15 21 31.0

3/24/2009 11:40 5 1.8

3/25/2009 1:20 230 280.0

3/25/2009 3:45 60 183.3

3/31/2009 16:15 75 61.0

3/31/2009 17:05 300 390.0

4/1/2009 3:00 24 27.0

4/19/2009 17:10 30 17.0

4/19/2009 18:15 200 117.5

4/20/2009 2:30 50 34.3

4/20/2009 17:20 10 18.5

4/23/2009 10:45 3 1.6

4/25/2009 10:50 37 21.0

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

5/13/2009 20:30 62 54.0

5/13/2009 20:50 440 280.0

5/13/2009 21:10 530 260.0

5/14/2009 0:55 170 130.0

5/14/2009 2:40 170 120.0

5/20/2009 11:00 5 2.7

6/16/2009 11:00 4 2.7

7/16/2009 11:00 8 4.0

8/7/2009 17:10 37 27.0

8/7/2009 20:20 340 170.0

8/7/2009 23:05 77 28.0

8/8/2009 9:10 460 240.0

8/8/2009 9:30 490 300.0

8/8/2009 19:55 29 59.0

8/10/2009 1:50 490 210.0

8/10/2009 4:10 170 100.0

8/19/2009 12:40 10 1.3

8/25/2009 20:55 120 63.0

8/28/2009 22:05 330 206.7

8/26/2009 4:05 120 34.0

9/15/2009 10:45 2 1.6

9/20/2009 20:20 53 44.0

9/20/2009 21:55 210 190.0

9/21/2009 3:55 41 34.0

9/22/2009 13:25 130 84.0

9/22/2009 14:05 370 210.0

9/22/2009 22:40 44 44.0

9/27/2009 20:20 140 110.0

9/27/2009 21:00 450 272.5

9/27/2009 23:35 280 99.0

9/28/2009 2:30 80 88.0

MINIMUM 1 1.3

MAXIMUM 530 390.0

MEAN 136 94.8

MEDIAN 73 57.0

STANDARD DEVIATION 147 91.3

Table 3-3. Model-calibration dataset for Honey Creek at Wauwatosa, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]
54 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 3-5. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total suspended 

solids concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Honey Creek at 

Wauwatosa, Wisconsin. 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 3 55

0.0 0.5 1.0 1.5 2.0 2.5

2.52.01.51.00.5

Measured log10(total suspended solids)

) total suspended solids( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total suspended solids, in

milligrams per liter

2 5 10 20 50 100 200

 50 20 10

 5 2 1

500200100

B C

Discharge, in cubic feet per second

Total suspended solids, in

milligrams per liter

1 5 10 50 500

 50 20 10

 5 2 1

500200100

D

0.5 1.0 1.5 2.0 2.5

−0.5

0.50.0

Predicted log10(total suspended solids)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5

0.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5

0.50.0

Theoretical quantiles

Residuals quantiles

G

Total suspended solids at Honey Creek at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 3-6. U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total suspended 

solids concentration). B, Relation between turbidity and total suspended solids concentration in log10

space. C, No plot. D, Relation between discharge and total suspended solids concentration in log10 space. 

E, Relation between predicted log10 (total suspended solids concentration) and regression residuals. 

F, Relation between time and total suspended solids regression residuals. G, Probability plot of total suspended solids regression residuals. 
56 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total suspended solids at Menomonee River at Wauwatosa, WI 

(04087120)

Samples collected on 6/8-6/9 2009 were not used in the regression analysis because the 

turbidity sensor readings were spiking excessively and the data quality was thought to be poor. 

MODEL SUMMARY—Summary of final regression results for estimating total suspended solids

concentrations at Menomonee River at Wauwatosa, WI.

Log10 (Suspended Solids) = 0.567 + 0.779 log10 (Turb),

Where:

Suspended Solids = total suspended solids concentration in mg/L

Turb = Turbidity (YSI 6136), in NTU

 

Model Information (in log units unless otherwise specified): 

Number of measurements = 95,

Root-mean-squared error (RMSE) = 0.22

Model standard percentage error (MPSE) = +67 and -40 percent

90-percent prediction intervals (based on units in mg/L) = +/- 110 percent 

Adjusted coefficient of determination (Adj R2

) = 0.77

Sum of squared error = 4.59

PRESS = 4.92

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 0.567 0.074 7.67 <0.0001

Log 10 (Turb) 0.779 0.044 17.88 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.951

Log10 (Turb) -0.951 1 

Duan’s bias correction factor = 1.15
Appendix 3 57

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

11/20/2008 10:30 5 1.9

12/17/2008 12:30 5 6.8

12/27/2008 1:15 56 25.0

12/27/2008 3:45 78 46.0

12/27/2008 5:50 87 66.0

12/27/2008 6:05 94 63.0

12/27/2008 10:15 150 89.0

12/27/2008 14:00 260 180.0

12/27/2008 14:45 260 190.0

12/28/2008 7:45 51 36.0

1/20/2009 12:10 20 1.5

2/7/2009 11:25 92 72.3

2/7/2009 13:25 120 105.0

2/7/2009 13:40 230 110.0

2/7/2009 19:40 65 46.3

2/8/2009 13:40 22 26.0

2/9/2009 1:40 13 12.0

2/9/2009 19:40 140 64.0

2/9/2009 22:00 210 140.0

2/9/2009 23:15 110 140.0

2/10/2009 7:20 47 45.7

2/10/2009 11:00 230 100.0

2/10/2009 17:05 110 70.7

2/10/2009 23:25 42 41.3

2/16/2009 12:45 80 4.8

2/26/2009 14:35 36 66.0

2/26/2009 19:00 38 140.0

2/26/2009 19:45 130 170.0

2/26/2009 22:50 210 130.0

2/27/2009 4:50 230 70.0

3/2/2009 7:20 6 7.3

3/10/2009 0:15 31 34.0

3/10/2009 5:50 46 38.0

3/10/2009 11:45 38 38.0

3/10/2009 14:50 51 41.0

3/11/2008 1:10 28 45.5

3/24/2009 11:55 11 1.1

3/25/2009 1:30 57 38.0

3/31/2009 17:00 19 14.0

3/31/2009 17:35 38 33.0

4/1/2009 5:35 33 20.0

4/19/2009 19:10 26 17.0

4/20/2009 5:05 48 24.0

4/21/2009 5:05 12 7.1

4/23/2009 11:00 6 1.4

4/25/2009 11:15 41 22.0

4/25/2009 12:40 370 160.0

4/25/2009 21:35 100 77.0

4/26/2009 2:35 87 68.0

4/26/2009 14:35 50 36.0

4/26/2009 16:00 300 150.0

4/26/2009 17:10 360 190.0

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

4/27/2009 0:30 94 76.0

5/9/2009 0:30 66 37.0

5/9/2009 9:30 37 17.0

5/9/2009 15:50 21 15.0

5/13/2009 20:40 120 68.0

5/13/2009 21:05 250 150.0

5/13/2009 22:00 250 140.0

5/14/2009 3:15 110 86.0

5/20/2009 11:15 11 4.8

6/16/2009 11:50 17 9.6

6/19/2009 9:15 150 84.0

6/19/2009 18:15 75 52.0

6/19/2009 21:20 190 150.0

6/20/2009 3:10 120 45.0

7/16/2009 11:45 9 3.5

8/7/2009 18:00 57 32.0

8/7/2009 20:40 110 60.0

8/8/2009 0:55 59 37.0

8/8/2009 8:50 120 74.0

8/8/2009 9:45 390 210.0

8/8/2009 19:50 66 48.0

8/9/2009 19:50 51 39.0

8/10/2009 2:00 150 110.0

8/10/2009 4:20 77 99.0

8/19/2009 12:20 13 2.7

8/25/2009 20:50 120 68.0

8/25/2009 21:25 140 110.0

8/25/2009 21:30 170 96.0

8/26/2009 3:30 76 47.0

8/27/2009 3:35 20 18.0

9/15/2009 11:00 7 2.8

9/20/2009 21:40 120 69.0

9/21/2009 3:40 46 51.0

9/22/2009 13:30 97 56.0

9/22/2009 13:40 280 71.0

9/22/2009 21:50 260 56.0

9/22/2009 23:10 76 53.0

9/27/2009 20:35 160 100.0

9/27/2009 21:05 270 150.0

9/27/2009 21:20 330 180.0

09/28/209 0:05 110 70.0

9/28/2009 2:35 65 62.0

9/28/2009 20:35 55 25.0

MINIMUM 5 1.1

MAXIMUM 390 210.0

MEAN 105 65.9

MEDIAN 76 53.0

STANDARD DEVIATION 93 52.1

Table 3-4. Model-calibration dataset for Menomonee River at Wauwatosa, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]
58 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 3-7. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total suspended 

solids concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Menomonee River 

at Wauwatosa, Wisconsin. 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 3 59

1.0 1.5 2.0 2.5

2.01.51.0

Measured log10(total suspended solids)

) total suspended solids( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total suspended solids, in

milligrams per liter

1 2 5 10 20 50 100 200

 50 20 10

 5

200100

B C

Discharge, in cubic feet per second

Total suspended solids, in

milligrams per liter

5 10 20 50 100 500 2000 5000

 50 20 10

 5

200100

D

1.0 1.5 2.0

−0.5

0.50.0

Predicted log10(total suspended solids)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5

0.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5

0.50.0

Theoretical quantiles

Residuals quantiles

G

Total suspended solids at Menomonee River at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 3-8. U.S. Geological Survey streamgage on Menomonee River at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total suspended 

solids concentration). B, Relation between turbidity and total suspended solids concentration in log10

space. C, No plot. D, Relation between discharge and total suspended solids concentration in log10 space. 

E, Relation between predicted log10 (total suspended solids concentration) and regression residuals. 

F, Relation between time and total suspended solids regression residuals. G, Probability plot of total suspended solids regression residuals. 
60 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total suspended solids at Menomonee River at 16th Street at 

Milwaukee, WI (04087142)

MODEL SUMMARY—Summary of final regression results for estimating total suspended solids

concentrations at Menomonee River at 16th Street at Milwaukee, WI.

Log10 (Suspended Solids) = 0.108 + 0.974 log10 (Turb),

Where:

Suspended Solids = total suspended solids concentration in mg/L

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 79,

Root-mean-squared error (RMSE) = 0.21

Model standard percentage error (MPSE) = +62 and -38 percent

90-percent prediction intervals (based on units in mg/L) = +/- 100 percent 

Adjusted coefficient of determination (Adj R2

) = 0.85

Sum of squared error = 3.39

PRESS = 3.61

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 0.108 0.078 1.49 0.1416

Log 10 (Turb) 0.974 0.046 21.32 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.946

Log10 (Turb) -0.946 1 

Duan’s bias correction factor = 1.12
Appendix 3 61

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

11/20/2008 11:45 6 3.1

12/17/2008 14:15 7 7.3

12/27/2008 9:35 22 20.0

12/27/2008 12:35 50 52.3

12/27/2008 15:35 260 153.3

12/27/2008 21:35 95 77.3

12/28/2008 0:35 84 58.7

12/28/2008 6:35 49 44.0

1/20/2009 12:40 8 5.4

2/7/2009 11:40 5 3.6

2/7/2009 20:40 68 78.7

2/8/2009 5:40 22 34.7

2/8/2009 14:40 16 28.3

2/8/2009 23:40 17 28.0

2/9/2009 17:40 30 12.7

2/10/2009 5:40 36 98.0

2/11/2009 17:40 78 69.3

2/16/2009 13:40 10 8.1

2/26/2009 16:00 12 8.2

2/26/2009 19:00 220 200.0

2/26/2009 22:00 170 130.0

2/27/2009 4:00 85 85.0

2/27/2009 12:00 13 51.0

2/28/2009 12:00 35 19.0

3/7/2009 11:10 97 19.0

3/7/2009 14:10 97 89.0

3/7/2009 23:10 58 54.0

3/8/2009 12:10 34 35.0

3/8/2009 18:10 120 90.0

3/9/2009 0:10 66 61.0

3/10/2009 8:15 60 47.0

3/10/2009 12:55 35 41.0

3/10/2009 13:00 38 42.0

3/10/2009 20:30 38 41.0

3/11/2009 4:30 23 29.0

3/24/2009 12:25 11 4.0

4/1/2009 1:40 30 34.0

4/20/2009 3:05 12 12.0

4/20/2009 4:50 12 14.0

4/23/2009 11:15 7 5.7

4/25/2009 13:20 26 30.0

4/25/2009 20:00 57 61.0

Date Time

Total 

suspended 

solids 

(mg/L)

Turbidity 

(NTU)

4/26/2009 8:00 48 48.0

4/26/2009 14:00 31 39.0

4/26/2009 16:25 190 82.0

4/26/2009 17:10 460 210.0

4/26/2009 19:30 340 210.0

4/26/2009 19:35 320 190.0

5/13/2009 22:05 42 35.0

5/14/2009 0:35 73 67.0

5/14/2009 1:45 93 93.0

5/14/2009 3:35 71 70.0

5/20/2009 11:45 11 5.0

6/8/2009 12:40 37 42.0

6/8/2009 15:30 37 50.0

6/9/2009 2:35 29 32.7

6/9/2009 5:00 24 31.3

6/16/2009 13:00 11 5.3

6/19/2009 0:55 1,800 530.0

6/19/2009 1:10 1,000 400.0

6/19/2009 1:45 820 340.0

6/19/2009 9:35 110 95.0

6/19/2040 20:45 230 160.0

6/20/2009 2:25 95 84.0

7/16/2009 12:30 12 4.9

8/8/2009 22:30 36 24.0

8/9/2009 10:30 19 17.0

8/19/2009 13:30 9 4.7

8/26/2009 7:05 15 15.0

8/26/2009 17:00 12 13.0

8/26/2009 23:45 15 14.0

9/15/2009 11:30 6 2.9

9/23/2009 7:10 12 7.1

9/24/2009 7:00 11 9.2

9/28/2009 12:05 22 28.0

09/28/209 18:05 22 30.0

9/29/2009 0:05 14 30.0

9/29/2009 3:05 11 17.0

9/29/2009 5:00 14 16.0

MINIMUM 5 2.9

MAXIMUM 1,800 530.0

MEAN 105 63.8

MEDIAN 35 35.0

STANDARD DEVIATION 249 88.4

Table 3-5. Model-calibration dataset for Menomonee River at 16th Street at Milwaukee, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]
62 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 3-9. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total suspended 

solids concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Menomonee River 

at 16th Street at Milwaukee, Wisconsin. 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 3 63

1.0 1.5 2.0 2.5 3.0

2.52.01.51.00.5

Measured log10(total suspended solids)

) total suspended solids( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total suspended solids, in

milligrams per liter

5 10 20 50 100 200 500

 5

 500 200 100

 50 20 10

20001000

B C

Discharge, in cubic feet per second

Total suspended solids, in

milligrams per liter

5 10 50 500 5000

 5

 500 200 100

 50 20 10

20001000

D

0.5 1.0 1.5 2.0 2.5

−0.2−0.4−0.6

0.60.40.20.0

Predicted log10(total suspended solids)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4−0.6

0.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4−0.6

0.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Total suspended solids at Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008−September 2009

Figure 3-10. U.S. Geological Survey streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total 

suspended solids concentration). B, Relation between turbidity and total suspended solids concentration in log10 space. C, No plot. D, Relation between discharge and total suspended solids concentration in log10

space. E, Relation between predicted log10 (total suspended solids concentration) and regression residuals. 

F, Relation between time and total suspended solids regression residuals. G, Probability plot of total suspended solids regression residuals. 

Appendix 4 65

Appendix 4. Regression analysis results for estimating total phosphorus 

concentration 

All data were collected using U.S. Geological Survey 

(USGS) protocols and are stored in the USGS National Water 

Information System (NWIS) database (http://waterdata.usgs.

gov/nwis). The regression models are based on measurements 

of turbidity and concurrent total phosphorus samples collected 

from November 2008 to September 2009. Continuous waterquality data were collected at 5-minute intervals using a YSI 

model 6920 V2 multiparameter water-quality monitor with a 

6560 specific conductance and water temperature sensor, and 

a 6136 optical turbidity sensor. Turbidity values are instantaneous unit values temporally corresponding to the collection of the total phosphorus samples. Samples were collected 

throughout the range of continuously observed hydrologic 

conditions. Summary statistics and the complete model-calibration dataset are provided. A comparison of cross-section 

mean and corresponding time-series monitor readings is 

archived at the Wisconsin Water Science Center and is available by request to Austin Baldwin (akbaldwi@usgs.gov). 
66 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total phosphorus at Little Menomonee River near Freistadt, WI 

(04087050)

MODEL SUMMARY—Summary of final regression results for estimating total phosphorus 

concentrations at Little Menomonee River near Freistadt, WI.

Log10 (Total Phosphorus) = -1.37 + 0.486 log10 (Turb),

Where:

Total Phosphorus = total phosphorus concentration in mg/L

Turb = Turbidity, (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 39,

Root-mean-squared error (RMSE) = 0.19

Model standard percentage error (MPSE) = +56 and -36 percent

90-percent prediction intervals (based on units in mg/L) = +/- 94 percent 

Adjusted coefficient of determination (Adj R2

) = 0.75

Sum of squared error = 1.40

PRESS = 1.75

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.37 0.074 -18.49 <.0001

Log10 (Turb) 0.486 0.045 10.82 <.0001 

Correlation matrix of coefficients:

Intercept log10 (Turb)

Intercept 1.00 -0.908

Log10 (Turb) -0.908 1.00

Duan’s bias correction factor = 1.13
Appendix 4 67

Table 4-1. Model-calibration dataset for Little Menomonee River near Freistadt, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

11/20/2008 9:45 0.042 1.2

12/17/2008 11:30 0.044 2.1

12/27/2008 13:05 0.26 11.2

12/28/2008 1:05 0.52 52.3

12/28/2008 7:15 0.43 45.0

1/20/2009 10:55 0.21 0.7

2/7/2009 18:50 0.24 19.7

2/9/2009 22:40 0.12 11.3

2/10/2009 10:45 0.36 38.0

2/10/2009 14:40 0.57 113.3

2/10/2009 20:40 0.41 46.0

2/11/2009 2:40 0.28 21.3

3/2/2009 7:10 0.049 4.2

3/7/2009 12:55 0.37 130.0

3/7/2009 18:05 0.83 220.0

3/8/2009 7:05 0.35 62.0

3/8/2009 19:00 0.77 210.0

3/9/2009 0:30 0.56 140.0

3/10/2009 3:20 0.3 68.0

3/10/209 8:15 0.43 94.0

3/10/2009 20:15 0.25 51.0

3/24/2009 10:40 0.043 2.8

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

4/23/2009 9:45 0.038 2.1

4/25/2009 15:10 0.24 100.0

4/26/2009 5:30 0.55 180.0

4/26/2009 19:30 0.56 200.0

4/27/2009 1:30 0.32 80.0

5/9/2009 7:25 0.26 81.0

5/9/2009 13:30 0.23 54.0

5/9/2009 19:30 0.11 15.0

5/14/2009 2:30 0.68 270.0

5/20/2009 9:00 0.076 4.5

6/8/2009 5:20 0.32 120.0

6/16/2009 8:45 0.11 12.0

6/19/2009 2:50 0.56 290.0

6/19/2009 8:50 0.37 89.0

7/16/2009 10:05 0.14 19.0

8/19/2009 10:00 0.085 8.8

9/15/2009 9:30 0.066 10.0

MINIMUM 0.04 0.7

MAXIMUM 0.83 290.0

MEAN 0.31 73.8

MEDIAN 0.28 51.0

STANDARD DEVIATION 0.21 79.0
68 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 4-1. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total phosphorus 

concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Little Menomonee River 

near Freistadt, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 4 69

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2

−0.2−0.4−0.6−0.8−1.0−1.2−1.4

Measured log10(total phosphorus)

) total phosphorus( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total phosphorus, in milligrams

per liter

1 2 5 10 20 50 100 200

0.500.200.100.05

B C

Discharge, in cubic feet per second

Total phosphorus, in milligrams

per liter

0.2 0.5 1.0 2.0 5.0 20.0 50.0 200.0

0.500.200.100.05

D

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2

−0.2

0.80.60.40.20.0

Predicted log10(total phosphorus)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2

0.80.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2

0.80.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Total phosphorus at Little Menomonee River near Freistadt, Wisconsin, November 2008−September 2009

Figure 4-2. U.S. Geological Survey streamgage on Little Menomonee River near Freistadt, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total phosphorus 

concentration). B, Relation between turbidity and total phosphorus concentration in log10 space. C, No plot. 

D, Relation between discharge and total phosphorus concentration in log10 space. E, Relation between 

predicted log10 (total phosphorus concentration) and regression residuals. F, Relation between time and 

total phosphorus regression residuals. G, Probability plot of total phosphorus regression residuals. 
70 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total phosphorus at Menomonee River at Menomonee Falls, WI 

(04087030)

MODEL SUMMARY—Summary of final regression results for estimating total phosphorus 

concentrations at Menomonee River at Menomonee Falls, WI.

Log10 (Total Phosphorus) = -1.55 + 0.492 log10 (Turb),

Where:

Total Phosphorus = total phosphorus concentration in mg/L

Turb = Turbidity, (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 59,

Root-mean-squared error (RMSE) = 0.207

Model standard percentage error (MPSE) = +61 and -38 percent

90-percent prediction intervals (based on units in mg/L) = +/- 101 percent 

Adjusted coefficient of determination (Adj R2

) = 0.62

Sum of squared error = 2.45

PRESS = 2.67

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.55 0.077 -20.20 <0.0001

Log 10 (Turb) 0.492 0.050 9.83 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.936

Log10 (Turb) -0.936 1 

 

Duan’s bias correction factor = 1.14
Appendix 4 71

Table 4-2. Model-calibration dataset for Menomonee River at Menomonee Falls, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

11/20/2008 9:15 0.041 3.6

12/17/2008 12:00 0.036 2.7

12/27/2008 0:35 0.23 18.0

12/27/2008 6:15 0.27 49.0

12/27/2008 14:20 0.42 100.7

12/27/2008 20:20 0.35 39.7

12/28/2008 8:20 0.33 45.3

1/20/2009 9:55 0.24 2.5

2/16/2009 11:00 0.054 3.1

2/26/2009 15:05 0.22 86.0

2/26/2009 18:15 0.24 81.0

2/27/2009 0:15 0.17 30.0

3/2/2009 7:15 0.068 3.2

3/7/2009 9:30 0.13 31.0

3/7/2009 15:30 0.17 29.0

3/8/2009 10:30 0.18 26.0

3/8/2009 14:00 0.27 69.0

3/9/2009 2:00 0.2 34.0

3/24/2009 10:00 0.038 4.1

3/25/2009 5:25 0.057 16.0

4/19/2009 23:00 0.1 23.0

4/20/2009 11:15 0.043 12.0

4/20/2009 23:15 0.038 11.0

4/23/2009 9:15 0.034 3.8

4/25/2009 10:50 0.18 71.0

4/25/2009 11:00 0.38 170.0

4/26/2009 5:00 0.1 27.0

4/26/2009 16:00 0.12 34.0

4/27/2009 4:00 0.11 23.0

5/9/2009 1:05 0.17 83.0

5/9/2009 1:15 0.35 110.0

5/9/2009 10:25 0.077 12.0

5/9/2009 22:25 0.066 14.0

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

5/10/2009 10:25 0.053 8.2

5/13/2009 23:00 0.2 81.0

5/20/209 9:30 0.063 6.3

6/8/2009 3:15 0.32 91.0

6/8/2009 3:25 0.78 220.0

6/8/2009 9:35 0.096 28.0

6/16/2009 10:15 0.071 13.0

6/19/2009 0:10 0.55 160.0

6/19/2009 0:50 0.2 110.0

6/19/2009 2:00 0.1 66.0

6/20/2009 2:00 0.55 21.0

7/16/2009 9:30 0.082 5.0

8/7/2009 19:35 0.2 46.0

8/8/2009 9:05 0.21 80.0

8/19/2009 9:00 0.094 3.2

8/25/2009 18:20 0.36 210.0

8/25/2009 18:45 0.28 85.0

8/26/2009 1:30 0.11 30.0

8/26/2009 1:55 0.14 48.0

9/15/2009 9:30 0.06 2.8

9/22/2009 13:15 0.18 62.0

9/22/2009 14:05 0.4 130.0

9/22/2009 15:20 0.12 21.0

9/27/2009 19:25 0.23 81.0

9/27/2008 21:30 0.2 51.0

9/28/2009 5:55 0.088 12.0

MINIMUM 0.03 2.5

MAXIMUM 0.78 220.0

MEAN 0.19 49.8

MEDIAN 0.17 30.0

STANDARD DEVIATION 0.15 50.9
72 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 4-3. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total phosphorus 

concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Menomonee River at 

Menomonee Falls, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 4 73

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2

−0.4−0.6−0.8−1.0−1.2

Measured log10(total phosphorus)

) total phosphorus( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total phosphorus, in milligrams

per liter

5 10 20 50 100 200

0.500.200.100.05

B C

Discharge, in cubic feet per second

Total phosphorus, in milligrams

per liter

2 5 10 20 50 100 200

0.500.200.100.05

D

−1.2 −1.0 −0.8 −0.6 −0.4

−0.2−0.4

0.60.40.20.0

Predicted log10(total phosphorus)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4

0.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4

0.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Total phosphorus at Menomonee River at Menomonee Falls, Wisconsin, November 2008−September 2009

Figure 4-4. U.S. Geological Survey streamgage on Menomonee River at Menomonee Falls, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total phosphorus 

concentration). B, Relation between turbidity and total phosphorus concentration in log10 space. C, No plot. 

D, Relation between discharge and total phosphorus concentration in log10 space. E, Relation between 

predicted log10 (total phosphorus concentration) and regression residuals. F, Relation between time and 

total phosphorus regression residuals. G, Probability plot of total phosphorus regression residuals. 
74 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total phosphorus at Honey Creek at Wauwatosa, WI (04087119)

Sample data from 4/25/2009 at 12:40 through 4/26/2009, and sample data from 6/8/2009 were 

not used in the regression development because of excessive fouling of the data sonde. Sample 

data on 6/19/2009 were not used because of damage to the sonde and sampler line during an 

extreme flood event.

MODEL SUMMARY—Summary of final regression results for estimating total phosphorus 

concentrations at Honey Creek at Wauwatosa, WI. 

Log10 (Total Phosphorus) = -1.45 + 0.451 log10 (Turb),

Where:

Total Phosphorus = total phosphorus concentration in mg/L

Turb = Turbidity, (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 66,

Root-mean-squared error (RMSE) = 0.22

Model standard percentage error (MPSE) = +66 and -40 percent

90-percent prediction intervals (based on units in mg/L) = +/- 108 percent 

Adjusted coefficient of determination (Adj R2

) = 0.64

Sum of squared error = 3.08

PRESS = 3.35

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.45 0.075 -19.21 <.0001

Log10 (Turb) 0.451 0.042 10.74 <.0001 

Correlation matrix of coefficients:

Intercept log10 (Turb)

Intercept 1.00 -0.934

Log10 (Turb) -0.934 1.00

Duan’s bias correction factor = 1.14
Appendix 4 75

Table 4-3. Model-calibration dataset for Honey Creek at Wauwatosa, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

12/17/2008 13:45 0.04 1.8

1/20/2009 11:55 0.26 1.7

2/10/2009 10:10 0.28 46.0

2/10/2009 13:25 0.37 123.3

2/10/2009 19:25 0.26 82.0

2/11/2009 1:25 0.18 41.3

2/11/2009 11:25 0.12 21.3

2/11/2009 12:00 0.37 97.0

2/11/2009 15:30 0.4 210.0

2/12/2009 2:25 0.15 32.7

2/16/2009 12:20 0.14 53.3

3/7/2009 9:25 0.074 74.0

3/7/2009 10:25 0.47 210.0

3/7/2009 12:10 0.41 140.0

3/7/2009 16:05 0.26 71.0

3/7/2009 22:05 0.22 46.0

3/8/2009 14:25 0.28 140.0

3/9/2009 1:00 0.22 32.0

3/10/2009 0:50 0.1 40.0

3/10/2009 5:30 0.15 50.0

3/10/2009 9:30 0.15 55.0

3/10/2009 12:10 0.12 33.0

3/10/2009 12:15 0.12 31.0

3/24/2009 11:40 0.041 1.8

3/25/2009 1:20 0.37 280.0

3/25/2009 3:45 0.14 183.3

3/31/2009 16:15 0.16 61.0

3/31/2009 17:05 0.39 390.0

4/1/2009 3:00 0.078 27.0

4/19/2009 17:10 0.081 17.0

4/19/2009 18:15 0.36 117.5

4/20/2009 2:30 0.12 34.3

4/20/2009 17:20 0.045 18.5

4/23/2009 10:45 0.03 1.6

4/25/2009 10:50 0.064 21.0

5/13/2009 20:30 0.17 54.0

5/13/2009 20:50 0.67 280.0

5/13/2009 21:10 0.66 260.0

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

5/14/2009 0:55 0.3 130.0

5/14/2009 2:40 0.28 120.0

5/20/2009 11:00 0.035 2.7

6/16/2009 11:00 0.051 2.7

7/16/2009 11:00 0.13 4.0

8/7/2009 17:10 0.3 27.0

8/7/2009 20:20 0.83 170.0

8/7/2009 23:05 0.27 28.0

8/8/2009 9:10 0.71 240.0

8/8/2009 9:30 0.7 300.0

8/8/2009 19:55 0.13 59.0

8/10/2009 1:50 0.49 210.0

8/10/2009 4:10 0.21 100.0

8/19/2009 12:40 0.086 1.3

8/25/2009 20:55 0.28 63.0

8/28/2009 22:05 0.51 206.7

8/26/2009 4:05 0.28 34.0

9/15/2009 10:45 0.054 1.6

9/20/2009 20:20 0.14 44.0

9/20/2009 21:55 0.88 190.0

9/21/2009 3:55 0.3 34.0

9/22/2009 13:25 0.33 84.0

9/22/2009 14:05 0.7 210.0

9/22/2009 22:40 0.16 44.0

9/27/2009 20:20 0.35 110.0

9/27/2009 21:00 0.6 272.5

9/27/2009 23:35 0.4 99.0

9/28/2009 2:30 0.16 88.0

MINIMUM 0.03 1.3

MAXIMUM 0.88 390.0

MEAN 0.28 94.8

MEDIAN 0.24 57.0

STANDARD DEVIATION 0.21 91.3
76 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 4-5. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total phosphorus 

concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Honey Creek at 

Wauwatosa, Wisconsin. 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 4 77

−1.5 −1.0 −0.5 0.0

−0.4−0.6−0.8−1.0−1.2−1.4

Measured log10(total phosphorus)

) total phosphorus( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total phosphorus, in milligrams

per liter

2 5 10 20 50 100 200

1.000.500.200.100.05

B C

Discharge, in cubic feet per second

Total phosphorus, in milligrams

per liter

1 5 10 50 500

1.000.500.200.100.05

D

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4

−0.2−0.4

0.80.60.40.20.0

Predicted log10(total phosphorus)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4

0.80.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4

0.80.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Total phosphorus at Honey Creek at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 4-6. U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total phosphorus 

concentration). B, Relation between turbidity and total phosphorus concentration in log10 space. C, No plot. 

D, Relation between discharge and total phosphorus concentration in log10 space. E, Relation between 

predicted log10 (total phosphorus concentration) and regression residuals. F, Relation between time and 

total phosphorus regression residuals. G, Probability plot of total phosphorus regression residuals. 
78 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total phosphorus at Menomonee River at Wauwatosa, WI (04087120)

Total phosphorus samples collected on 12/27/2008 at 06:05, 10:15, and 14:45, and on 

12/28/2008 at 07:45 were not used in the regression analysis because the MMSD laboratory 

reported a qualified total phosphorus concentration of < 1.4 mg/L. Samples collected on 6/8-

6/9 2009 were not used in the regression analysis because the turbidity sensor readings were 

spiking excessively and the data quality was thought to be poor. 

MODEL SUMMARY—Summary of final regression results for estimating total phosphorus 

concentrations at Menomonee River at Wauwatosa, WI.

Log10 (Total Phosphorus) = -1.42 + 0.431 log10 (Turb),

Where:

Total Phosphorus = total phosphorus concentration in mg/L

Turb = Turbidity, (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 91,

Root-mean-squared error (RMSE) = 0.204

Model standard percentage error (MPSE) = +60 and -38 percent

90-percent prediction intervals (based on units in mg/L) = +/- 97 percent 

Adjusted coefficient of determination (Adj R2

) = 0.55

Sum of squared error = 3.72

PRESS = 3.96

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.42 0.068 -20.70 <0.0001

Log 10 (Turb) 0.431 0.041 10.63 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.950

Log10 (Turb) -0.950 1 

 

Duan’s bias correction factor = 1.12
Appendix 4 79

Table 4-4. Model-calibration dataset for Menomonee River at Wauwatosa, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

11/20/2008 10:30 0.046 1.9

12/17/2008 12:30 0.053 6.8

12/27/2008 1:15 0.31 25.0

12/27/2008 3:45 0.34 46.0

12/27/2008 5:50 0.39 66.0

12/27/2008 14:00 0.66 180.0

1/20/2009 12:10 0.23 1.5

2/7/2009 11:25 0.33 72.3

2/7/2009 13:25 0.4 105.0

2/7/2009 13:40 0.54 110.0

2/7/2009 19:40 0.31 46.3

2/8/2009 13:40 0.22 26.0

2/9/2009 1:40 0.13 12.0

2/9/2009 19:40 0.34 64.0

2/9/2009 22:00 0.45 140.0

2/9/2009 23:15 0.3 140.0

2/10/2009 7:20 0.18 45.7

2/10/2009 11:00 0.39 100.0

2/10/2009 17:05 0.28 70.7

2/10/2009 23:25 0.17 41.3

2/16/2009 12:45 0.18 4.8

2/26/2009 14:35 0.093 66.0

2/26/2009 19:00 0.097 140.0

2/26/2009 19:45 0.26 170.0

2/26/2009 22:50 0.29 130.0

2/27/2009 4:50 0.36 70.0

3/2/2009 7:20 0.068 7.3

3/10/2009 0:15 0.13 34.0

3/10/2009 5:50 0.14 38.0

3/10/2009 11:45 0.15 38.0

3/10/2009 14:50 0.14 41.0

3/11/2008 1:10 0.13 45.5

3/24/2009 11:55 0.046 1.1

3/25/2009 1:30 0.11 38.0

3/31/2009 17:00 0.053 14.0

3/31/2009 17:35 0.092 33.0

4/1/2009 5:35 0.058 20.0

4/19/2009 19:10 0.085 17.0

4/20/2009 5:05 0.064 24.0

4/21/2009 5:05 0.042 7.1

4/23/2009 11:00 0.035 1.4

4/25/2009 11:15 0.082 22.0

4/25/2009 12:40 0.48 160.0

4/25/2009 21:35 0.17 77.0

4/26/2009 2:35 0.18 68.0

4/26/2009 14:35 0.098 36.0

4/26/2009 16:00 0.35 150.0

4/26/2009 17:10 0.37 190.0

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

4/27/2009 0:30 0.14 76.0

5/9/2009 0:30 0.15 37.0

5/9/2009 9:30 0.083 17.0

5/9/2009 15:50 0.065 15.0

5/13/2009 20:40 0.28 68.0

5/13/2009 21:05 0.46 150.0

5/13/2009 22:00 0.37 140.0

5/14/2009 3:15 0.2 86.0

5/20/2009 11:15 0.11 4.8

6/16/2009 11:50 0.089 9.6

6/19/2009 9:15 0.35 84.0

6/19/2009 18:15 0.17 52.0

6/19/2009 21:20 0.22 150.0

6/20/2009 3:10 0.18 45.0

7/16/2009 11:45 0.082 3.5

8/7/2009 18:00 0.26 32.0

8/7/2009 20:40 0.29 60.0

8/8/2009 0:55 0.2 37.0

8/8/2009 8:50 0.23 74.0

8/8/2009 9:45 0.56 210.0

8/8/2009 19:50 0.14 48.0

8/9/2009 19:50 0.19 39.0

8/10/2009 2:00 0.25 110.0

8/10/2009 4:20 0.16 99.0

8/19/2009 12:20 0.11 2.7

8/25/2009 20:50 0.3 68.0

8/25/2009 21:25 0.34 110.0

8/25/2009 21:30 0.37 96.0

8/26/2009 3:30 0.2 47.0

8/27/2009 3:35 0.11 18.0

9/15/2009 11:00 0.067 2.8

9/20/2009 21:40 0.41 69.0

9/21/2009 3:40 0.26 51.0

9/22/2009 13:30 0.31 56.0

9/22/2009 13:40 0.56 71.0

9/22/2009 21:50 0.49 56.0

9/22/2009 23:10 0.19 53.0

9/27/2009 20:35 0.37 100.0

9/27/2009 21:05 0.49 150.0

9/27/2009 21:20 0.54 180.0

09/28/209 0:05 0.22 70.0

9/28/2009 2:35 0.17 62.0

9/28/2009 20:35 0.16 25.0

MINIMUM 0.04 1.1

MAXIMUM 0.66 210.0

MEAN 0.23 64.6

MEDIAN 0.20 52.0

STANDARD DEVIATION 0.15 51.4
80 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 4-7. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total phosphorus 

concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Menomonee River at 

Wauwatosa, Wisconsin. 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 4 81

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2

−0.4−0.6−0.8−1.0−1.2−1.4

Measured log10(total phosphorus)

) total phosphorus( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total phosphorus, in milligrams

per liter

1 2 5 10 20 50 100 200

0.500.200.100.05

B C

Discharge, in cubic feet per second

Total phosphorus, in milligrams

per liter

5 10 20 50 100 500 2000 5000

0.500.200.100.05

D

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4

−0.2−0.4

0.60.40.20.0

Predicted log10(total phosphorus)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4

0.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4

0.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Total phosphorus at Menomonee River at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 4-8. U.S. Geological Survey streamgage on Menomonee River at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total phosphorus 

concentration). B, Relation between turbidity and total phosphorus concentration in log10 space. C, No plot. 

D, Relation between discharge and total phosphorus concentration in log10 space. E, Relation between 

predicted log10 (total phosphorus concentration) and regression residuals. F, Relation between time and 

total phosphorus regression residuals. G, Probability plot of total phosphorus regression residuals. 
82 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Total phosphorus at Menomonee River at 16th Street at Milwaukee, WI 

(04087142)

MODEL SUMMARY—Summary of final regression results for estimating total phosphorus 

concentrations at Menomonee River at 16th Street at Milwaukee, WI.

Log10 (Total Phosphorus) = -1.51 + 0.462 log10 (Turb),

Where:

Total Phosphorus = total phosphorus concentration in mg/L

Turb = Turbidity, (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 77,

Root-mean-squared error (RMSE) = 0.192

Model standard percentage error (MPSE) = +56 and -36 percent

90-percent prediction intervals (based on units in mg/L) = +/- 89 percent 

Adjusted coefficient of determination (Adj R2

) = 0.61

Sum of squared error = 2.76

PRESS = 2.97

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept -1.51 0.067 -22.46 <0.0001

Log 10 (Turb) 0.462 0.042 10.93 <0.0001

Correlation matrix of coefficients:

Intercept log10 (Turb) 

Intercept 1 -0.946

Log10 (Turb) -0.946 1 

 

Duan’s bias correction factor = 1.11
Appendix 4 83

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

4/26/2009 14:00 0.095 39.0

4/26/2009 16:25 0.26 82.0

4/26/2009 17:10 0.52 210.0

4/26/2009 19:30 0.38 210.0

4/26/2009 19:35 0.38 190.0

5/13/2009 22:05 0.14 35.0

5/14/2009 0:35 0.17 67.0

5/14/2009 1:45 0.21 93.0

5/14/2009 3:35 0.16 70.0

5/20/2009 11:45 0.12 5.0

6/8/2009 12:40 0.1 42.0

6/8/2009 15:30 0.12 50.0

6/9/2009 2:35 0.087 32.7

6/9/2009 5:00 0.088 31.3

6/16/2009 13:00 0.11 5.3

6/19/2009 0:55 1.8 530.0

6/19/2009 1:10 1.2 400.0

6/19/2009 1:45 0.96 340.0

6/19/2009 9:35 0.2 95.0

6/19/2040 20:45 0.27 160.0

6/20/2009 2:25 0.19 84.0

7/16/2009 12:30 0.1 4.9

8/8/2009 22:30 0.14 24.0

8/9/2009 10:30 0.1 17.0

8/19/2009 13:30 0.076 4.7

8/26/2009 7:05 0.11 15.0

8/26/2009 17:00 0.099 13.0

8/26/2009 23:45 0.1 14.0

9/15/2009 11:30 0.074 2.9

9/23/2009 7:10 0.11 7.1

9/24/2009 7:00 0.095 9.2

9/28/2009 12:05 0.11 28.0

09/28/209 18:05 0.12 30.0

9/29/2009 0:05 0.11 30.0

9/29/2009 3:05 0.1 17.0

9/29/2009 5:00 0.11 16.0

MINIMUM 0.04 2.9

MAXIMUM 1.80 530.0

MEAN 0.21 62.9

MEDIAN 0.14 34.7

STANDARD DEVIATION 0.25 88.9

Table 4-5. Model-calibration dataset for Menomonee River at 16th Street at Milwaukee, Wisconsin.

[mg/L, milligrams per liter; NTU, Nephelometric turbidity units]

Date Time

Total 

phosphorus

(mg/L)

Turbidity 

(NTU)

11/20/2008 11:45 0.051 3.1

12/17/2008 14:15 0.061 7.3

12/27/2008 9:35 0.26 20.0

12/27/2008 12:35 0.28 52.3

12/27/2008 21:35 0.38 77.3

12/28/2008 0:35 0.35 58.7

1/20/2009 12:40 0.26 5.4

2/7/2009 11:40 0.094 3.6

2/7/2009 20:40 0.34 78.7

2/8/2009 5:40 0.24 34.7

2/8/2009 14:40 0.19 28.3

2/8/2009 23:40 0.2 28.0

2/9/2009 17:40 0.18 12.7

2/10/2009 5:40 0.23 98.0

2/11/2009 17:40 0.28 69.3

2/16/2009 13:40 0.073 8.1

2/26/2009 16:00 0.096 8.2

2/26/2009 19:00 0.38 200.0

2/26/2009 22:00 0.3 130.0

2/27/2009 4:00 0.21 85.0

2/27/2009 12:00 0.12 51.0

2/28/2009 12:00 0.19 19.0

3/7/2009 11:10 0.1 19.0

3/7/2009 14:10 0.2 89.0

3/7/2009 23:10 0.17 54.0

3/8/2009 12:10 0.14 35.0

3/8/2009 18:10 0.25 90.0

3/9/2009 0:10 0.19 61.0

3/10/2009 8:15 0.15 47.0

3/10/2009 12:55 0.15 41.0

3/10/2009 13:00 0.14 42.0

3/10/2009 20:30 0.14 41.0

3/11/2009 4:30 0.12 29.0

3/24/2009 12:25 0.057 4.0

4/1/2009 1:40 0.083 34.0

4/20/2009 3:05 0.046 12.0

4/20/2009 4:50 0.044 14.0

4/23/2009 11:15 0.039 5.7

4/25/2009 13:20 0.073 30.0

4/25/2009 20:00 0.097 61.0

4/26/2009 8:00 0.1 48.0
84 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 4-9. Duration curve for turbidity (November 2008–September 2010) and corresponding values associated with total phosphorus 

concentration samples collected November 2008 to September 2009 at U.S. Geological Survey streamgage on Menomonee River at 

16th Street at Milwaukee, Wisconsin. 

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 
Appendix 4 85

−1.0 −0.5 0.0

−0.4−0.6−0.8−1.0−1.2

Measured log10(total phosphorus)

) total phosphorus( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Total phosphorus, in milligrams

per liter

5 10 20 50 100 200 500

2.001.000.500.200.100.05

B C

Discharge, in cubic feet per second

Total phosphorus, in milligrams

per liter

5 10 50 500 5000

2.001.000.500.200.100.05

D

−1.2 −1.0 −0.8 −0.6 −0.4

−0.2−0.4

0.60.40.20.0

Predicted log10(total phosphorus)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.2−0.4

0.60.40.20.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.2−0.4

0.60.40.20.0

Theoretical quantiles

Residuals quantiles

G

Total phosphorus at Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008−September 2009

Figure 4-10. U.S. Geological Survey streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (total 

phosphorus concentration). B, Relation between turbidity and total phosphorus concentration in log10

space. C, No plot. D, Relation between discharge and total phosphorus concentration in log10 space. 

E, Relation between predicted log10 (total phosphorus concentration) and regression residuals. F, Relation 

between time and total phosphorus regression residuals. G, Probability plot of total phosphorus regression residuals. 

Appendix 5 87

Appendix 5. Regression analysis results for estimating Escherichia coli

(E. coli) bacteria concentration 

All data were collected using U.S. Geological Survey 

(USGS) protocols and are stored in the USGS National Water 

Information System (NWIS) database (http://waterdata.usgs.

gov/nwis). The regression models are based on measurements 

of turbidity and water temperature and concurrent E. coli

bacteria samples collected from November 2008 to September 2009. Continuous water-quality data were collected at 

5-minute intervals using a YSI model 6920 V2 multiparameter 

water-quality monitor with a 6560 specific conductance and 

water temperature sensor, and a 6136 optical turbidity sensor. 

Turbidity and water temperature values are instantaneous unit 

values temporally corresponding to the collection of the E. coli 

bacteria samples. Samples were collected throughout the range 

of continuously observed hydrologic conditions. Summary 

statistics and the complete model-calibration dataset are provided. A comparison of cross-section mean and corresponding time-series monitor readings is archived at the Wisconsin 

Water Science Center and is available by request to Austin 

Baldwin (akbaldwi@usgs.gov). 
88 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Escherichia coli (E. coli) bacteria at Little Menomonee River near Freistadt, WI 

(04087050)

Sample data on 2/16/2009 were not used in the regression analysis because there was no sonde data. 

Sample data on 2/26/2010 was not used because it was believed the samples at 09:50 and 15:20 were 

switched and the concentration may be in error. 

MODEL SUMMARY—Summary of final regression results for estimating E. coli concentrations at Little 

Menomonee River near Freistadt, WI.

Log10 (E. coli) = 1.81 + 0.025 (WT) + 0.693 log10 (Turb),

Where:

E. coli = Most Probable Number of E. coli per 100 ml (MPN/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 37,

Root-mean-squared error (RMSE) = 0.45

Model standard percentage error (MPSE) = +182 and -65 percent

90-percent prediction intervals (based on units in MPN/100ml) = +/- 573 percent 

Adjusted coefficient of determination (Adj R2

) = 0.58

Sum of squared error = 6.90

PRESS = 8.17

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.81 0.182 9.91 <.0001

WT 0.025 0.012 2.12 0.041

Log10 (Turb) 0.693 0.106 6.57 <.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb)

Intercept 1.00 -0.296 -0.821

WT -0.296 1.00 -0.125

Log10 (Turb) -0.821 -0.125 1.00

Duan’s bias correction factor = 2.05 
Appendix 5 89

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

11/20/2008 9:45 51 1.2 1.6

12/17/2008 11:30 120 2.1 0.0

12/28/2008 1:05 1,100 52.3 0.1

1/20/2009 10:55 10 0.7 0.1

2/7/2009 18:50 860 19.7 0.0

2/9/2009 22:40 1,700 11.3 0.2

2/10/2009 10:45 1,300 38.0 0.3

2/10/2009 14:40 830 113.3 0.5

2/10/2009 20:40 1,600 46.0 0.3

2/11/2009 2:40 15,000 21.3 0.2

3/2/2009 7:10 230 4.2 0.0

3/7/2009 12:55 400 130.0 1.8

3/7/2009 18:05 1,500 220.0 1.3

3/8/2009 7:05 760 62.0 1.0

3/8/2009 19:00 2,600 210.0 0.2

3/9/2009 0:30 1,500 140.0 0.3

3/10/2009 3:20 570 68.0 1.9

3/10/209 8:15 840 94.0 1.1

3/10/2009 20:15 610 51.0 2.2

3/24/2009 10:40 110 2.8 4.0

4/23/2009 9:45 610 2.1 6.4

4/25/2009 15:10 860 100.0 10.7

Table 5-1. Model-calibration dataset for Little Menomonee River near Freistadt, Wisconsin.

[MPN/100 mL, most probable number per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

4/26/2009 5:30 4,500 180.0 7.1

4/26/2009 19:30 4,000 200.0 9.7

4/27/2009 1:30 2,200 80.0 9.6

5/9/2009 7:25 3,400 81.0 11.7

5/9/2009 13:30 8,700 54.0 11.6

5/9/2009 19:30 2,200 15.0 12.0

5/14/2009 2:30 6,000 270.0 13.8

5/20/2009 9:00 140 4.5 14.0

6/8/2009 5:20 3,800 120.0 11.5

6/16/2009 8:45 260 12.0 14.0

6/19/2009 2:50 9,600 290.0 17.4

6/19/2009 8:50 25,000 89.0 17.4

7/16/2009 10:05 1,100 19.0 16.2

8/19/2009 10:00 250 8.8 16.0

9/15/2009 9:30 730 10.0 16.5

MINIMUM 10 0.7 0.0

MAXIMUM 25,000 290.0 17.4

MEAN 2,839 76.3 6.3

MEDIAN 1,100 52.3 2.2

STANDARD 

DEVIATION

4,870 80.3 6.4
90 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 5-1. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with Escherichia coli (E. coli) concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Little Menomonee River near Freistadt, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 5 91

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

4.03.53.02.52.0

Measured log10 (Escherichia coli)

) Escherichia coli( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

1 2 5 10 20 50 100 200

 500 100

 50 10

10000

 5000 1000

, in most probable Escherichia coli

number per 100 milliliters

B

Water temperature, in degrees Celsius

0 5 10 15

 500 100

 50 10

 5000 1000

10000

, in most probable Escherichia coli

number per 100 milliliters

C

Discharge, in cubic feet per second

0.2 0.5 1.0 2.0 5.0 20.0 50.0 200.0

 50 10

 500 100

10000

 5000 1000

, in most probable Escherichia coli

number per 100 milliliters

D

2.0 2.5 3.0 3.5 4.0

−0.5

1.51.00.50.0

Predicted log10 (Escherichia coli)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5

1.51.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5

1.51.00.50.0

Theoretical quantiles

Residuals quantiles

G

Escherichia coli at Little Menomonee River near Freistadt, Wisconsin, November 2008−September 2009

Figure 5-2. U.S. Geological Survey streamgage on Little Menomonee River near Freistadt, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (Escherichia coli 

(E. coli) concentration). B, Relation between turbidity and E. coli concentration in log10 space. C, Relation 

between water temperature and E. coli concentration in log10 space. D, Relation between discharge 

and E. coli concentration in log10 space. E, Relation between predicted log10 (E. coli concentration) and 

regression residuals. F, Relation between time and E. coli regression residuals. G, Probability plot of E. coli

regression residuals. 
92 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Escherichia coli (E. coli) bacteria at Menomonee River at Menomonee Falls, WI 

(04087030)

MODEL SUMMARY—Summary of final regression results for estimating E. coli concentrations at 

Menomonee River at Menomonee Falls, WI.

Log10 (E. coli) = 1.30 + 0.057 (WT) + 0.674 log10 (Turb),

Where:

E. coli = Most Probable Number of E. coli per 100 ml (MPN/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 55,

Root-mean-squared error (RMSE) = 0.556

Model standard percentage error (MPSE) = +259 and -72 percent 

90-percent prediction intervals (based on units in MPN/100ml) = +/- 768 percent 

Adjusted coefficient of determination (Adj R2

) = 0.60

Sum of squared error = 16.05

PRESS = 17.84

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.30 0.213 6.13 <0.0001

WT 0.057 0.010 5.75 <0.0001

Log 10 (Turb) 0.674 0.143 4.73 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.250 -0.771

WT -0.250 1 -0.326

Log10 (Turb) -0.771 -0.326 1 

Duan’s bias correction factor = 1.84
Appendix 5 93

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

11/20/2008 9:15 63 3.6 1.1

12/17/2008 12:00 230 2.7 0.0

12/27/2008 14:20 490 100.7 0.1

1/20/2009 9:55 41 2.5 2.0

2/16/2009 11:00 50 3.1 0.2

2/26/2009 15:05 300 86.0 0.1

2/26/2009 18:15 730 81.0 0.2

2/27/2009 0:15 550 30.0 0.0

3/2/2009 7:15 70 3.2 0.0

3/7/2009 9:30 160 31.0 1.9

3/7/2009 15:30 160 29.0 2.0

3/8/2009 10:30 150 26.0 0.7

3/8/2009 14:00 370 69.0 0.8

3/9/2009 2:00 260 34.0 0.0

3/24/2009 10:00 190 4.1 4.1

3/25/2009 5:25 130 16.0 5.1

4/19/2009 23:00 410 23.0 10.5

4/20/2009 11:15 100 12.0 8.4

4/20/2009 23:15 200 11.0 8.3

4/23/2009 9:15 150 3.8 7.3

4/25/2009 10:50 750 71.0 14.6

4/25/2009 11:00 850 170.0 14.3

4/26/2009 5:00 410 27.0 8.9

4/26/2009 16:00 520 34.0 9.8

4/27/2009 4:00 520 23.0 10.2

5/9/2009 1:05 160 83.0 16.9

5/9/2009 1:15 1,000 110.0 16.7

5/9/2009 10:25 1,200 12.0 14.0

5/9/2009 22:25 400 14.0 13.5

5/10/2009 10:25 350 8.2 11.9

5/13/2009 23:00 2,300 81.0 15.8

5/20/209 9:30 10 6.3 16.5

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

6/8/2009 3:15 1,800 91.0 14.0

6/8/2009 3:25 12,000 220.0 13.5

6/8/2009 9:35 4,600 28.0 13.4

6/16/2009 10:15 70 13.0 19.1

6/19/2009 0:10 4,000 160.0 21.2

6/19/2009 0:50 4,000 110.0 21.1

6/19/2009 2:00 8,800 66.0 20.9

6/20/2009 2:00 3,600 21.0 20.1

7/16/2009 9:30 5,200 5.0 20.4

8/7/2009 19:35 20,000 46.0 20.2

8/8/2009 9:05 12,000 80.0 20.5

8/19/2009 9:00 430 3.2 20.1

8/25/2009 18:20 8,100 210.0 23.1

8/25/2009 18:45 34,000 85.0 23.1

8/26/2009 1:30 8,600 30.0 22.3

8/26/2009 1:55 6,300 48.0 22.4

9/15/2009 9:30 140 2.8 18.8

9/22/2009 13:15 18,000 62.0 18.9

9/22/2009 14:05 52,000 130.0 19.3

9/22/2009 15:20 19,000 21.0 18.4

9/27/2009 19:25 11,000 81.0 18.0

9/27/2008 21:30 12,000 51.0 17.1

9/28/2009 5:55 3,900 12.0 15.2

MINIMUM 10 2.5 0.0

MAXIMUM 52,000 220.0 23.1

MEAN 4,778 50.7 11.9

MEDIAN 520 30.0 14.0

STANDARD 

DEVIATION

9,252 52.6 8.0

Table 5-2. Model-calibration dataset for Menomonee River at Menomonee Falls, Wisconsin.

[MPN/100 mL, most probable number per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
94 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 5-3. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with Escherichia coli (E. coli) concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Menomonee River at Menomonee Falls, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 5 95

1 2 3 4

4.03.53.02.52.01.5

Measured log10 (Escherichia coli)

) Escherichia coli( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

5 10 20 50 100 200

 500 100

 50 10

5000010000

 5000 1000

, in most probable Escherichia coli

number per 100 milliliters

B

Water temperature, in degrees Celsius

0 5 10 15 20

 500 100

 50 10

 5000 1000

5000010000

, in most probable Escherichia coli

number per 100 milliliters

C

Discharge, in cubic feet per second

2 5 10 20 50 100 200

 50 10

 500 100

5000010000

 5000 1000

, in most probable Escherichia coli

number per 100 milliliters

D

1.5 2.0 2.5 3.0 3.5 4.0

−0.5−1.0−1.5

1.00.50.0

Predicted log10 (Escherichia coli)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0−1.5

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0−1.5

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Escherichia coli at Menomonee River at Menomonee Falls, Wisconsin, November 2008−September 2009

Figure 5-4. U.S. Geological Survey streamgage on Menomonee River at Menomonee Falls, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (Escherichia coli 

(E. coli) concentration). B, Relation between turbidity and E. coli concentration in log10 space. C, Relation 

between water temperature and E. coli concentration in log10 space. D, Relation between discharge 

and E. coli concentration in log10 space. E, Relation between predicted log10 (E. coli concentration) and 

regression residuals. F, Relation between time and E. coli regression residuals. G, Probability plot of E. coli

regression residuals. 
96 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Escherichia coli (E. coli) bacteria at Honey Creek at Wauwatosa, WI (04087119)

Sample data from 4/25/2009 at 12:40 through 4/26/2009, and sample data from 6/8/2009 were not 

used in the regression development because of excessive fouling of the data sonde. Sample data on 

6/19/2009 were not used because of damage to the sonde and sampler line during an extreme flood 

event. 

MODEL SUMMARY—Summary of final regression results for estimating E. coli concentrations at Honey 

Creek at Wauwatosa, WI.

Log10 (E. coli) = 1.68 + 0.071 (WT) + 0.626 log10 (Turb),

Where:

E. coli = Most Probable Number of E. coli per 100 ml (MPN/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 66,

Root-mean-squared error (RMSE) = 0.480

Model standard percentage error (MPSE) = +202 and -67 percent

90-percent prediction intervals (based on units in MPN/100ml) = +/- 610 percent 

Adjusted coefficient of determination (Adj R2

) = 0.69

Sum of squared error = 14.50

PRESS = 16.22

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.68 0.177 9.50 <0.0001

WT 0.071 0.008 9.12 <0.0001

Log 10 (Turb) 0.626 0.092 6.77 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.367 -0.816

WT -0.367 1 -0.124

Log10 (Turb) -0.816 -0.124 1 

Duan’s bias correction factor = 1.98
Appendix 5 97

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

12/17/2008 13:45 640 1.8 0.2

1/20/2009 11:55 500 1.7 0.0

2/10/2009 10:10 3,300 46.0 1.7

2/10/2009 13:25 1,400 123.3 2.5

2/10/2009 19:25 580 82.0 1.2

2/11/2009 1:25 750 41.3 1.9

2/11/2009 11:25 530 21.3 2.7

2/11/2009 12:00 1,100 97.0 2.9

2/11/2009 15:30 1,200 210.0 3.3

2/12/2009 2:25 690 32.7 2.3

2/16/2009 12:20 270 53.3 0.0

3/7/2009 9:25 1,200 74.0 3.2

3/7/2009 10:25 1,300 210.0 2.9

3/7/2009 12:10 680 140.0 3.0

3/7/2009 16:05 530 71.0 3.7

3/7/2009 22:05 400 46.0 3.0

3/8/2009 14:25 570 140.0 2.0

3/9/2009 1:00 600 32.0 2.0

3/10/2009 0:50 620 40.0 3.3

3/10/2009 5:30 260 50.0 2.6

3/10/2009 9:30 450 55.0 2.8

3/10/2009 12:10 1,300 33.0 3.1

3/10/2009 12:15 910 31.0 3.1

3/24/2009 11:40 310 1.8 4.6

3/25/2009 1:20 17,000 280.0 7.1

3/25/2009 3:45 9,200 183.3 7.1

3/31/2009 16:15 2,800 61.0 5.0

3/31/2009 17:05 2,400 390.0 5.0

4/1/2009 3:00 720 27.0 4.1

4/19/2009 17:10 2,300 17.0 9.1

4/19/2009 18:15 3,800 117.5 8.8

4/20/2009 2:30 310 34.3 8.3

4/20/2009 17:20 740 18.5 8.5

4/23/2009 10:45 250 1.6 7.6

4/25/2009 10:50 520 21.0 12.3

5/13/2009 20:30 3,900 54.0 14.0

5/13/2009 20:50 9,800 280.0 16.6

5/13/2009 21:10 11,000 260.0 16.9

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

5/14/2009 0:55 7,300 130.0 16.2

5/14/2009 2:40 9,800 120.0 15.2

5/20/2009 11:00 250 2.7 14.6

6/16/2009 11:00 620 2.7 15.4

7/16/2009 11:00 200 4.0 18.6

8/7/2009 17:10 24,000 27.0 18.3

8/7/2009 20:20 24,000 170.0 19.6

8/7/2009 23:05 24,000 28.0 19.5

8/8/2009 9:10 24,000 240.0 20.4

8/8/2009 9:30 10,000 300.0 20.7

8/8/2009 19:55 17,000 59.0 21.4

8/10/2009 1:50 24,000 210.0 21.9

8/10/2009 4:10 24,000 100.0 21.5

8/19/2009 12:40 300 1.3 18.9

8/25/2009 20:55 10,000 63.0 21.0

8/28/2009 22:05 21,000 206.7 21.9

8/26/2009 4:05 16,000 34.0 21.5

9/15/2009 10:45 510 1.6 19.0

9/20/2009 20:20 11,000 44.0 17.8

9/20/2009 21:55 87,000 190.0 17.8

9/21/2009 3:55 200,000 34.0 18.2

9/22/2009 13:25 98,000 84.0 17.0

9/22/2009 14:05 160,000 210.0 19.7

9/22/2009 22:40 46,000 44.0 19.4

9/27/2009 20:20 160,000 110.0 18.0

9/27/2009 21:00 130,000 272.5 17.4

9/27/2009 23:35 39,000 99.0 17.1

9/28/2009 2:30 17,000 88.0 16.4

MINIMUM 200 1.3 0.0

MAXIMUM 200,000 390.0 21.9

MEAN 19,240 94.8 10.8

MEDIAN 1,850 57.0 9.0

STANDARD 

DEVIATION

41,203 91.3 7.7

Table 5-3. Model-calibration dataset for Honey Creek at Wauwatosa, Wisconsin.

[MPN/100 mL, most probable number per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
98 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 5-5. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with Escherichia coli (E. coli) concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Honey Creek at Wauwatosa, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 5 99

2.5 3.0 3.5 4.0 4.5 5.0

4.54.03.53.02.52.0

Measured log10 (Escherichia coli)

) Escherichia coli( 10 Predicted log

A

2 5 10 20 50 100 200

Turbidity, in nephelometric turbidity units

 5000 2000 1000

 500 200

 50000 20000 10000

200000100000

, in most probable Escherichia coli

number per 100 milliliters

B

Water temperature, in degrees Celsius

0 5 10 15 20

 500 200

 50000 20000 10000

 5000 2000 1000

200000100000

, in most probable Escherichia coli

number per 100 milliliters

C

Discharge, in cubic feet per second

1 5 10 50 500

 5000 2000 1000

 500 200

200000100000

 50000 20000 10000

, in most probable Escherichia coli

number per 100 milliliters

D

2.0 2.5 3.0 3.5 4.0 4.5

−0.5−1.0

1.00.50.0

Predicted log10 (Escherichia coli)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Escherichia coli at Honey Creek at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 5-6. U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (Escherichia coli 

(E. coli) concentration). B, Relation between turbidity and E. coli concentration in log10 space. C, Relation 

between water temperature and E. coli concentration in log10 space. D, Relation between discharge 

and E. coli concentration in log10 space. E, Relation between predicted log10 (E. coli concentration) and 

regression residuals. F, Relation between time and E. coli regression residuals. G, Probability plot of E. coli

regression residuals. 
100 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Escherichia coli (E. coli) bacteria at Menomonee River at Wauwatosa, WI 

(04087120)

Samples collected on 4/21/2009, 6/08/2009 – 6/09/2009, 08/07/2009 - 8/8/2009 at 09:45, 8/09/2009, 

and 9/22/2009 at 13:40 were not used in the regression analysis because of extreme fouling or because 

the MMSD laboratory qualified the results.

MODEL SUMMARY—Summary of final regression results for estimating E. coli concentrations at 

Menomonee River at Wauwatosa, WI.

Log10 (E. coli) = 1.28 + 0.063 (WT) + 0.884 log10 (Turb),

Where:

E. coli = Most Probable Number of E. coli per 100 ml (MPN/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 81,

Root-mean-squared error (RMSE) = 0.528

Model standard percentage error (MPSE) = +237 and -70 percent

90-percent prediction intervals (based on units in MPN/100ml) = +/- 807 percent 

Adjusted coefficient of determination (Adj R2

) = 0.66

Sum of squared error = 21.74

PRESS = 23.37

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.28 0.191 6.68 <0.0001

WT 0.063 0.007 9.07 <0.0001

Log 10 (Turb) 0.884 0.109 8.14 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.303 -0.878

WT -0.303 1 -0.071

Log10 (Turb) -0.878 -0.071 1 

Duan’s bias correction factor = 2.18
Appendix 5 101

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

11/20/2008 10:30 74 1.9 2.2

12/17/2008 12:30 500 6.8 0.0

12/27/2008 10:15 1,700 89.0 0.0

12/28/2008 7:45 1,200 36.0 0.0

1/20/2009 12:10 86 1.5 0.0

2/7/2009 11:25 3,400 72.3 0.0

2/7/2009 13:25 1,800 105.0 0.0

2/7/2009 13:40 2,400 110.0 0.0

2/7/2009 19:40 1,200 46.3 0.0

2/8/2009 13:40 340 26.0 0.0

2/9/2009 1:40 430 12.0 0.0

2/9/2009 19:40 320 64.0 0.0

2/9/2009 22:00 1,500 140.0 0.0

2/9/2009 23:15 2,100 140.0 0.1

2/10/2009 7:20 760 45.7 0.0

2/10/2009 11:00 880 100.0 0.1

2/10/2009 17:05 750 70.7 0.5

2/10/2009 23:25 570 41.3 0.2

2/16/2009 12:45 60 4.8 0.3

2/26/2009 14:35 120 66.0 0.4

2/26/2009 19:00 320 140.0 0.7

2/26/2009 19:45 1,900 170.0 0.7

2/26/2009 22:50 1,700 130.0 0.6

2/27/2009 4:50 1,100 70.0 0.0

3/2/2009 7:20 220 7.3 0.0

3/10/2009 0:15 290 34.0 2.3

3/10/2009 5:50 200 38.0 2.1

3/10/2009 11:45 370 38.0 1.9

3/10/2009 14:50 240 41.0 1.9

3/11/2008 1:10 150 45.5 2.2

3/24/2009 11:55 62 1.1 4.9

3/25/2009 1:30 2,200 38.0 6.2

3/31/2009 17:00 2,000 14.0 5.1

3/31/2009 17:35 1,900 33.0 5.2

4/1/2009 5:35 610 20.0 4.3

4/19/2009 19:10 1,300 17.0 11.4

4/20/2009 5:05 1,400 24.0 9.1

4/23/2009 11:00 85 1.4 8.2

4/25/2009 11:15 1,100 22.0 14.2

4/25/2009 12:40 3,700 160.0 13.8

4/25/2009 21:35 1,200 77.0 11.1

4/26/2009 2:35 2,200 68.0 9.6

4/26/2009 14:35 850 36.0 8.9

4/26/2009 16:00 1,300 150.0 10.0

4/26/2009 17:10 1,800 190.0 10.5

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

4/27/2009 0:30 1,600 76.0 10.2

5/9/2009 0:30 700 37.0 16.6

5/9/2009 9:30 990 17.0 14.6

5/9/2009 15:50 510 15.0 14.7

5/13/2009 20:40 2,400 68.0 15.2

5/13/2009 21:05 8,700 150.0 15.6

5/13/2009 22:00 5,500 140.0 15.9

5/14/2009 3:15 2,800 86.0 15.4

5/20/2009 11:15 73 4.8 17.4

6/16/2009 11:50 130 9.6 18.8

6/19/2009 9:15 9,600 84.0 19.6

6/19/2009 18:15 12,000 52.0 20.4

6/19/2009 21:20 9,300 150.0 20.5

6/20/2009 3:10 9,300 45.0 19.7

7/16/2009 11:45 2,600 3.5 21.8

8/8/2009 19:50 24,000 48.0 21.8

8/10/2009 2:00 24,000 110.0 22.3

8/10/2009 4:20 17,000 99.0 21.4

8/19/2009 12:20 320 2.7 21.9

8/25/2009 20:50 87,000 68.0 22.3

8/25/2009 21:25 32,000 110.0 22.4

8/25/2009 21:30 20,000 96.0 21.9

8/26/2009 3:30 34,000 47.0 21.5

8/27/2009 3:35 3,500 18.0 20.0

9/15/2009 11:00 130 2.8 20.0

9/20/2009 21:40 92,000 69.0 18.0

9/21/2009 3:40 200,000 51.0 17.8

9/22/2009 13:30 200,000 56.0 18.3

9/22/2009 21:50 200,000 56.0 19.5

9/22/2009 23:10 49,000 53.0 19.0

9/27/2009 20:35 46,000 100.0 17.8

9/27/2009 21:05 37,000 150.0 18.0

9/27/2009 21:20 69,000 180.0 18.1

9/28/209 0:05 55,000 70.0 17.1

9/28/2009 2:35 22,000 62.0 16.4

9/28/2009 20:35 8,000 25.0 14.8

MINIMUM 60 1.1 0.0

MAXIMUM 200,000 190.0 22.4

MEAN 16,476 63.7 10.1

MEDIAN 1,700 52.0 10.2

STANDARD 

DEVIATION

40,762 49.6 8.5

Table 5-4. Model-calibration dataset for Menomonee River at Wauwatosa, Wisconsin.

[MPN/100 mL, most probable number per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
102 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 5-7. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with Escherichia coli (E. coli) concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Menomonee River at Wauwatosa, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 5 103

2.0 2.5 3.0 3.5 4.0 4.5 5.0

4.54.03.53.02.52.01.5

Measured log10 (Escherichia coli)

) Escherichia coli( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

1 2 5 10 20 50 100 200

 50

 5000 1000

 500 100

 50000 10000

100000

, in most probable Escherichia coli

number per 100 milliliters

B

Water temperature, in degrees Celsius

0 5 10 15 20

 50

 500 100

 50000 10000

 5000 1000

100000

, in most probable Escherichia coli

number per 100 milliliters

C

Discharge, in cubic feet per second

5 10 20 50 100 500 2000 5000

 50

 5000 1000

 500 100

100000

 50000 10000

, in most probable Escherichia coli

number per 100 milliliters

D

1.5 2.0 2.5 3.0 3.5 4.0 4.5

−0.5−1.0

1.00.50.0

Predicted log10 (Escherichia coli)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Escherichia coli at Menomonee River at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 5-8. U.S. Geological Survey streamgage on Menomonee River at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (Escherichia coli 

(E. coli) concentration). B, Relation between turbidity and E. coli concentration in log10 space. C, Relation 

between water temperature and E. coli concentration in log10 space. D, Relation between discharge 

and E. coli concentration in log10 space. E, Relation between predicted log10 (E. coli concentration) and 

regression residuals. F, Relation between time and E. coli regression residuals. G, Probability plot of E. coli

regression residuals. 
104 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Escherichia coli (E. coli) bacteria at Menomonee River at 16th Street at 

Milwaukee, WI (04087142)

MODEL SUMMARY—Summary of final regression results for estimating E. coli concentrations at 

Menomonee River at 16th Street at Milwaukee, WI.

Log10 (E. coli) = 1.29 + 0.059 (WT) + 0.886 log10 (Turb),

Where:

E. coli = Most Probable Number of E. coli per 100 ml (MPN/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 76,

Root-mean-squared error (RMSE) = 0.542

Model standard percentage error (MPSE) = +248 and -71 percent

90-percent prediction intervals (based on units in MPN/100ml) = +/- 926 percent 

Adjusted coefficient of determination (Adj R2

) = 0.54

Sum of squared error = 21.45

PRESS = 24.05

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.29 0.222 5.82 <0.0001

WT 0.059 0.008 7.78 <0.0001

Log 10 (Turb) 0.886 0.122 7.26 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.513 -0.895

WT -0.513 1 0.191

Log10 (Turb) -0.895 0.191 1 

Duan’s bias correction factor = 2.34
Appendix 5 105

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

11/20/2008 11:45 160 3.1 9.7

12/17/2008 14:15 440 7.3 0.0

12/27/2008 12:35 1,500 52.3 0.3

12/28/2008 0:35 2,400 58.7 1.5

12/28/2008 6:35 930 44.0 0.5

1/20/2009 12:40 63 5.4 8.2

2/7/2009 11:40 52 3.6 5.7

2/7/2009 20:40 1,500 78.7 0.0

2/8/2009 5:40 1,100 34.7 0.0

2/8/2009 14:40 730 28.3 0.8

2/8/2009 23:40 1,100 28.0 0.0

2/9/2009 17:40 780 12.7 0.1

2/10/2009 5:40 1,100 98.0 0.0

2/11/2009 17:40 1,100 69.3 1.5

2/16/2009 13:40 70 8.1 0.1

2/26/2009 16:00 610 8.2 8.9

2/26/2009 19:00 3,300 200.0 0.2

2/26/2009 22:00 1,500 130.0 0.7

2/27/2009 4:00 1,400 85.0 0.6

2/27/2009 12:00 210 51.0 0.1

2/28/2009 12:00 990 19.0 0.0

3/7/2009 11:10 460 19.0 2.9

3/7/2009 14:10 1,200 89.0 2.9

3/7/2009 23:10 360 54.0 2.6

3/8/2009 12:10 430 35.0 1.2

3/8/2009 18:10 1,000 90.0 1.6

3/9/2009 0:10 570 61.0 0.9

3/10/2009 8:15 380 47.0 2.3

3/10/2009 12:55 280 41.0 2.1

3/10/2009 13:00 400 42.0 2.1

3/10/2009 20:30 160 41.0 2.2

3/11/2009 4:30 170 29.0 2.0

3/24/2009 12:25 63 4.0 12.0

4/1/2009 1:40 1,900 34.0 5.1

4/20/2009 3:05 520 12.0 10.9

4/20/2009 4:50 1,700 14.0 9.6

4/23/2009 11:15 110 5.7 12.5

4/25/2009 13:20 2,000 30.0 14.2

4/25/2009 20:00 2,400 61.0 11.8

4/26/2009 8:00 1,600 48.0 8.8

4/26/2009 14:00 980 39.0 8.8

Date Time

Escherichia 

coli

(MPN/100 mL)

Turbidity 

(NTU)

Water 

temperature

(°C)

4/26/2009 16:25 11,000 82.0 9.6

4/26/2009 17:10 16,000 210.0 10.3

4/26/2009 19:30 3,700 210.0 10.9

4/26/2009 19:35 3,200 190.0 10.9

5/13/2009 22:05 3,300 35.0 15.2

5/14/2009 0:35 5,200 67.0 16.4

5/14/2009 1:45 3,100 93.0 16.4

5/14/2009 3:35 4,100 70.0 16.0

5/20/2009 11:45 120 5.0 18.4

6/8/2009 12:40 3,600 42.0 13.1

6/8/2009 15:30 3,100 50.0 13.6

6/9/2009 2:35 5,200 32.7 14.3

6/9/2009 5:00 7,100 31.3 14.3

6/16/2009 13:00 60 5.3 22.7

6/19/2009 0:55 27,000 530.0 20.1

6/19/2009 1:10 16,000 400.0 20.0

6/19/2009 1:45 26,000 340.0 20.1

6/19/2009 9:35 18,000 95.0 19.6

6/19/2040 20:45 24,000 160.0 21.1

6/20/2009 2:25 20,000 84.0 19.8

7/16/2009 12:30 11,000 4.9 24.4

8/8/2009 22:30 17,000 24.0 21.6

8/9/2009 10:30 8,700 17.0 22.1

8/19/2009 13:30 240 4.7 22.1

8/26/2009 7:05 98,000 15.0 21.6

8/26/2009 17:00 16,000 13.0 22.0

8/26/2009 23:45 7,500 14.0 21.8

9/15/2009 11:30 41 2.9 26.3

9/23/2009 7:10 140,000 7.1 24.3

9/24/2009 7:00 18,000 9.2 23.7

9/28/2009 12:05 17,000 28.0 16.3

09/28/209 18:05 12,000 30.0 15.6

9/29/2009 0:05 7,000 30.0 15.1

9/29/2009 3:05 6,200 17.0 16.8

9/29/2009 5:00 7,000 16.0 17.2

MINIMUM 41 2.9 0.0

MAXIMUM 140,000 530.0 26.3

MEAN 7,937 63.0 10.4

MEDIAN 1,550 34.8 10.6

STANDARD 

DEVIATION

19,897 89.4 8.4

Table 5-5. Model-calibration dataset for Menomonee River at 16th Street at Milwaukee, Wisconsin.

[MPN/100 mL, most probable number per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
106 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 5-9. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with Escherichia coli (E. coli) concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 5 107

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

5.04.54.03.53.02.52.0

Measured log10 (Escherichia coli)

) Escherichia coli( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

5 10 20 50 100 200 500

 50

 5000 1000

 500 100

 50000 10000

100000

, in most probable Escherichia coli

number per 100 milliliters

B

Water temperature, in degrees Celsius

0 5 10 15 20 25

 50

 500 100

 50000 10000

 5000 1000

100000

, in most probable Escherichia coli

number per 100 milliliters

C

Discharge, in cubic feet per second

5 10 50 500 5000

 50

 5000 1000

 500 100

100000

 50000 10000

, in most probable Escherichia coli

number per 100 milliliters

D

2.0 2.5 3.0 3.5 4.0 4.5 5.0

−0.5−1.0−1.5

1.51.00.50.0

Predicted log10 (Escherichia coli)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0−1.5

1.51.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0−1.5

1.51.00.50.0

Theoretical quantiles

Residuals quantiles

G

Escherichia coli at Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008−September 2009

Figure 5-10. U.S. Geological Survey streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (Escherichia coli (E. coli) concentration). B, Relation between turbidity and E. coli concentration in log10

space. C, Relation between water temperature and E. coli concentration in log10 space. D, Relation 

between discharge and E. coli concentration in log10 space. E, Relation between predicted log10 (E. coli

concentration) and regression residuals. F, Relation between time and E. coli regression residuals. 

G, Probability plot of E. coli regression residuals. 

Appendix 6 109

Appendix 6. Regression analysis results for estimating fecal coliform bacteria 

concentration 

All data were collected using U.S. Geological Survey 

(USGS) protocols and are stored in the USGS National Water 

Information System (NWIS) database (http://waterdata.usgs.

gov/nwis). The regression models are based on measurements 

of turbidity and water temperature and concurrent fecal coliform bacteria samples collected from November 2008 to September 2009. Continuous water-quality data were collected at 

5-minute intervals using a YSI model 6920 V2 multiparameter 

water-quality monitor with a 6560 specific conductance and 

water temperature sensor, and a 6136 optical turbidity sensor. 

Turbidity and water temperature values are instantaneous unit 

values temporally corresponding to the collection of the fecal 

coliform bacteria samples. Samples were collected throughout the range of continuously observed hydrologic conditions. Summary statistics and the complete model-calibration 

dataset are provided. A comparison of cross-section mean and 

corresponding time-series monitor readings is archived at the 

Wisconsin Water Science Center and is available by request to 

Austin Baldwin (akbaldwi@usgs.gov).
110 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Fecal coliform bacteria at Little Menomonee River near Freistadt, WI (04087050)

Sample data on 2/16/2009 was not used in the regression development because there was a program 

change and the sonde data was lost. 

MODEL SUMMARY—Summary of final regression results for estimating fecal coliform concentrations at 

Little Menomonee River near Freistadt, WI.

Log10 (fecal coliform) = 1.49 + 0.035 (WT) + 0.777 log10 (Turb),

Where:

fecal coliform = colony forming units of fecal coliform per 100 ml (CFU/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 32,

Root-mean-squared error (RMSE) = 0.51

Model standard percentage error (MPSE) = +221 and -69 percent

90-percent prediction intervals (based on units in CFU/100ml) = +/- 639 percent 

Adjusted coefficient of determination (Adj R2

) = 0.58

Sum of squared error = 7.45

PRESS = 8.97

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.49 0.231 6.46 <0.0001

WT 0.035 0.014 2.48 0.019

Log10 (Turb) 0.777 0.130 5.97 <0.0001

Correlation matrix of coefficients:

Intercept WT Log10(Turb) 

Intercept 1 -0.348 -0.808

WT -0.348 1 -0.114

Log10 (Turb) -0.808 -0.114 1 

Duan’s bias correction factor = 1.79
Appendix 6 111

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

11/20/2008 9:45 16 1.6 1.2

1/20/2009 10:55 10 0.1 0.7

2/7/2009 18:50 590 0.0 19.7

2/9/2009 22:40 720 0.2 11.3

2/10/2009 10:45 760 0.3 38.0

2/10/2009 14:40 570 0.5 113.3

2/10/2009 20:40 950 0.3 46.0

2/11/2009 2:40 4,000 0.2 21.3

3/7/2009 12:55 71 1.8 130.0

3/7/2009 18:05 1,400 1.3 220.0

3/8/2009 7:05 2,800 1.0 62.0

3/9/2009 0:30 1,200 0.3 140.0

3/10/2009 3:20 330 1.9 68.0

3/10/2009 20:15 580 2.2 51.0

3/24/2009 10:40 95 4.0 2.8

4/23/2009 9:45 320 6.4 2.1

4/25/2009 15:10 370 10.7 100.0

4/26/2009 5:30 5,200 7.1 180.0

4/26/2009 19:30 4,000 9.7 200.0

4/27/2009 1:30 1,700 9.6 80.0

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

5/9/2009 7:25 4,600 11.7 81.0

5/9/2009 13:30 6,800 11.6 54.0

5/9/2009 19:30 1,800 12.0 15.0

5/14/2009 2:30 8,600 13.8 270.0

5/20/2009 9:00 100 14.0 4.5

6/8/2009 5:20 5,600 11.5 120.0

6/16/2009 8:45 240 14.0 12.0

6/19/2009 2:50 8,200 17.4 290.0

6/19/2009 8:50 30,000 17.4 89.0

7/16/2009 10:05 690 16.2 19.0

8/19/2009 10:00 300 16.0 8.8

9/15/2009 9:30 580 16.5 10.0

MINIMUM 10 0.0 0.7

MAXIMUM 30,000 17.4 290.0

MEAN 2,912 7.2 76.9

MEDIAN 740 6.8 52.5

STANDARD 

DEVIATION

5,534 6.4 80.9

Table 6-1. Model-calibration dataset for Little Menomonee River near Freistadt, Wisconsin.

[CFU/100 mL, colony forming units per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
112 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 6-1. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with fecal coliform bacteria concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Little Menomonee River near Freistadt, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 6 113

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

4.03.53.02.52.01.5

Measured log10(fecal coliform)

) fecal coliform( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Fecal Coliform, in colony forming

units per 100 milliliters

1 2 5 10 20 50 100 200

 500 100

 50 10

10000

 5000 1000

B

Water temperature, in degrees Celsius

Fecal Coliform, in colony forming

units per 100 milliliters

0 5 10 15

 500 100

 50 10

 5000 1000

10000

C

Discharge, in cubic feet per second

Fecal Coliform, in colony forming

units per 100 milliliters

0.2 0.5 1.0 2.0 5.0 20.0 50.0 200.0

 500 100

 50 10

10000

 5000 1000

D

1.5 2.0 2.5 3.0 3.5 4.0

−0.5−1.0

1.00.50.0

Predicted log10(fecal coliform)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Fecal Coliform Bacteria at Little Menomonee River near Freistadt, Wisconsin, November 2008−September 2009

Figure 6-2. U.S. Geological Survey streamgage on Little Menomonee River near Freistadt, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (fecal coliform 

bacteria concentration). B, Relation between turbidity and fecal coliform bacteria concentration in log10

space. C, Relation between water temperature and fecal coliform bacteria concentration in log10 space. 

D, Relation between discharge and fecal coliform bacteria concentration in log10 space. E, Relation 

between predicted log10 (fecal coliform bacteria concentration) and regression residuals. F, Relation 

between time and fecal coliform bacteria regression residuals. G, Probability plot of fecal coliform bacteria regression residuals. 
114 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Fecal coliform bacteria at Menomonee River at Menomonee Falls, WI 

(04087030)

MODEL SUMMARY—Summary of final regression results for estimating fecal coliform concentrations at 

Menomonee River at Menomonee Falls, WI.

Log10 (fecal coliform) = 1.07 + 0.063 (WT) + 0.834 log10 (Turb),

Where:

fecal coliform = colony forming units of fecal coliform per 100 ml (CFU/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

 

Model Information (in log units unless otherwise specified): 

Number of measurements = 49,

Root-mean-squared error (RMSE) = 0.540

Model standard percentage error (MPSE) = +246 and -71 percent

90-percent prediction intervals (based on units in CFU/100ml) = +/- 716 percent 

Adjusted coefficient of determination (Adj R2

) = 0.68

Sum of squared error = 13.39

PRESS = 14.99

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.07 0.222 4.81 <0.0001

WT 0.063 0.010 6.26 <0.0001

Log 10 (Turb) 0.834 0.144 5.79 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.296 -0.764

WT -0.296 1 0.293

log10 (Turb) -0.764 0.293 1 

Duan’s bias correction factor = 1.80
Appendix 6 115

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

11/20/2008 9:15 87 1.1 3.6

12/17/2008 12:00 190 0.0 2.7

12/27/2008 14:20 520 0.1 100.7

1/20/2009 9:55 10 2.0 2.5

2/16/2009 11:00 32 0.2 3.1

2/26/2009 15:05 320 0.1 86.0

2/26/2009 18:15 550 0.2 81.0

2/27/2009 0:15 210 0.0 30.0

3/7/2009 9:30 170 1.9 31.0

3/7/2009 15:30 130 2.0 29.0

3/8/2009 14:00 540 0.8 69.0

3/9/2009 2:00 270 0.0 34.0

3/24/2009 10:00 170 4.1 4.1

3/25/2009 5:25 100 5.1 16.0

4/19/2009 23:00 720 10.5 23.0

4/20/2009 23:15 250 8.3 11.0

4/23/2009 9:15 210 7.3 3.8

4/25/2009 10:50 570 14.6 71.0

4/26/2009 16:00 1,000 9.8 34.0

5/9/2009 1:05 150 16.9 83.0

5/9/2009 1:15 1,200 16.7 110.0

5/9/2009 10:25 810 14.0 12.0

5/9/2009 22:25 380 13.5 14.0

5/10/2009 10:25 280 11.9 8.2

5/13/2009 23:00 2,800 15.8 81.0

05/20/2009 9:30 87 16.5 6.3

6/8/2009 3:15 4,300 14.0 91.0

6/8/2009 3:25 10,000 13.5 220.0

6/8/2009 9:35 4,600 13.4 28.0

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

6/16/2009 10:15 100 19.1 13.0

6/19/2009 0:10 6,200 21.2 160.0

6/19/2009 0:50 16,000 21.1 110.0

6/19/2009 2:00 23,000 20.9 66.0

6/20/2009 2:00 4,200 20.1 21.0

7/16/2009 9:30 210 20.4 5.0

8/7/2009 19:35 20,000 20.2 46.0

8/8/2009 9:05 10,000 20.5 80.0

8/19/2009 9:00 270 20.1 3.2

8/25/2009 18:20 7,600 23.1 210.0

8/25/2009 18:45 46,000 23.1 85.0

8/26/2009 1:30 28,000 22.3 30.0

8/26/2009 1:55 44,000 22.4 48.0

9/15/2009 9:30 160 18.8 2.8

9/22/2009 13:15 20,000 18.9 62.0

9/22/2009 14:05 43,000 19.3 130.0

9/22/2009 15:20 19,000 18.4 21.0

9/27/2009 19:25 9,400 18.0 81.0

9/27/2008 21:30 9,200 17.1 51.0

9/28/2009 5:55 4,800 15.2 12.0

MINIMUM 10 0.0 2.5

MAXIMUM 46,000 23.1 220.0

MEAN 6,975 12.5 51.5

MEDIAN 570 14.6 31.0

STANDARD 

DEVIATION

11,911 8.1 51.9

Table 6-2. Model-calibration dataset for Menomonee River at Menomonee Falls, Wisconsin.

[CFU/100 mL, colony forming units per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
116 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 6-3. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with fecal coliform bacteria concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Menomonee River at Menomonee Falls, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 6 117

1 2 3 4

4.54.03.53.02.52.01.5

Measured log10(fecal coliform)

) fecal coliform( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Fecal Coliform, in colony forming

units per 100 milliliters

5 10 20 50 100 200

 500 100

 50 10

5000010000

 5000 1000

B

Water temperature, in degrees Celsius

Fecal Coliform, in colony forming

units per 100 milliliters

0 5 10 15 20

 500 100

 50 10

5000010000

 5000 1000

C

Discharge, in cubic feet per second

Fecal Coliform, in colony forming

units per 100 milliliters

2 5 10 20 50 100 200

 50 10

 5000 1000

 500 100

5000010000

D

1.5 2.0 2.5 3.0 3.5 4.0 4.5

−0.5−1.0−1.5

1.00.50.0

Predicted log10(fecal coliform)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0−1.5

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0−1.5

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Fecal Coliform Bacteria at Menomonee River at Menomonee Falls, Wisconsin, November 2008−September 2009

Figure 6-4. U.S. Geological Survey streamgage on Menomonee River at Menomonee Falls, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (fecal coliform 

bacteria concentration). B, Relation between turbidity and fecal coliform bacteria concentration in log10

space. C, Relation between water temperature and fecal coliform bacteria concentration in log10 space. 

D, Relation between discharge and fecal coliform bacteria concentration in log10 space. E, Relation 

between predicted log10 (fecal coliform bacteria concentration) and regression residuals. F, Relation 

between time and fecal coliform bacteria regression residuals. G, Probability plot of fecal coliform bacteria regression residuals. 
118 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Fecal coliform bacteria at Honey Creek at Wauwatosa, WI (04087119)

Sample data from 4/25/2009 at 12:40 through 4/26/2009, and sample data from 6/8/2009 were not 

used in the regression development because of excessive fouling of the data sonde. Sample data on 

6/19/2009 were not used because of damage to the sonde and sampler line during an extreme flood 

event.

MODEL SUMMARY—Summary of final regression results for estimating fecal coliform concentrations at 

Honey Creek at Wauwatosa, WI.

Log10 (fecal coliform) = 1.46 + 0.089 (WT) + 0.648 log10 (Turb),

Where:

fecal coliform = colony forming units of fecal coliform per 100 ml (CFU/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

Model Information (in log units unless otherwise specified): 

Number of measurements = 65,

Root-mean-squared error (RMSE) = 0.504

Model standard percentage error (MPSE) = +219 and -69 percent

90-percent prediction intervals (based on units in CFU/100ml) = +/- 687 percent 

Adjusted coefficient of determination (Adj R2

) = 0.74

Sum of squared error = 15.77

PRESS = 17.81

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.46 0.187 7.79 <0.0001

WT 0.089 0.008 10.88 <0.0001

Log 10 (Turb) 0.648 0.097 6.66 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.368 -0.815

WT -0.368 1 -0.123

Log10 (Turb) -0.815 -0.123 1 

Duan’s bias correction factor = 2.02
Appendix 6 119

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

12/17/2008 13:45 570 0.2 1.8

1/20/2009 11:55 400 0.0 1.7

2/10/2009 10:10 1,300 1.7 46.0

2/10/2009 13:25 760 2.5 123.3

2/10/2009 19:25 410 1.2 82.0

2/11/2009 1:25 1,500 1.9 41.3

2/11/2009 11:25 530 2.7 21.3

2/11/2009 12:00 840 2.9 97.0

2/11/2009 15:30 1,300 3.3 210.0

2/12/2009 2:25 610 2.3 32.7

2/16/2009 12:20 130 0.0 53.3

3/7/2009 9:25 210 3.2 74.0

3/7/2009 10:25 210 2.9 210.0

3/7/2009 12:10 720 3.0 140.0

3/7/2009 16:05 420 3.7 71.0

3/7/2009 22:05 400 3.0 46.0

3/8/2009 14:25 680 2.0 140.0

3/9/2009 1:00 480 2.0 32.0

3/10/2009 0:50 500 3.3 40.0

3/10/2009 5:30 180 2.6 50.0

3/10/2009 9:30 420 2.8 55.0

3/10/2009 12:10 1,600 3.1 33.0

3/10/2009 12:15 1,200 3.1 31.0

3/24/2009 11:40 190 4.6 1.8

3/25/2009 1:20 4,000 7.1 280.0

3/25/2009 3:45 22,000 7.1 183.3

3/31/2009 16:15 1,700 5.0 61.0

3/31/2009 17:05 1,600 5.0 390.0

4/1/2009 3:00 340 4.1 27.0

4/19/2009 17:10 2,300 9.1 17.0

4/19/2009 18:15 2,900 8.8 117.5

4/20/2009 17:20 880 8.5 18.5

4/23/2009 10:45 95 7.6 1.6

4/25/2009 10:50 840 12.3 21.0

5/13/2009 20:30 2,900 14.0 54.0

5/13/2009 20:50 16,000 16.6 280.0

5/13/2009 21:10 11,000 16.9 260.0

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

5/14/2009 0:55 6,200 16.2 130.0

5/14/2009 2:40 9,800 15.2 120.0

5/20/2009 11:00 120 14.6 2.7

6/16/2009 11:00 440 15.4 2.7

7/16/2009 11:00 400 18.6 4.0

8/7/2009 17:10 140,000 18.3 27.0

8/7/2009 20:20 27,000 19.6 170.0

8/7/2009 23:05 56,000 19.5 28.0

8/8/2009 9:10 93,000 20.4 240.0

8/8/2009 9:30 120,000 20.7 300.0

8/8/2009 19:55 35,000 21.4 59.0

8/10/2009 1:50 20,000 21.9 210.0

8/10/2009 4:10 67,000 21.5 100.0

8/19/2009 12:40 500 18.9 1.3

8/25/2009 20:55 12,000 21.0 63.0

8/28/2009 22:05 46,000 21.9 206.7

8/26/2009 4:05 28,000 21.5 34.0

9/15/2009 10:45 380 19.0 1.6

9/20/2009 20:20 7,600 17.8 44.0

9/20/2009 21:55 170,000 17.8 190.0

9/21/2009 3:55 160,000 18.2 34.0

9/22/2009 13:25 67,000 17.0 84.0

9/22/2009 14:05 140,000 19.7 210.0

9/22/2009 22:40 45,000 19.4 44.0

9/27/2009 20:20 120,000 18.0 110.0

9/27/2009 21:00 120,000 17.4 272.5

9/27/2009 23:35 38,000 17.1 99.0

9/28/2009 2:30 21,000 16.4 88.0

MINIMUM 95 0.0 1.3

MAXIMUM 170,000 21.9 390.0

MEAN 25,116 10.8 95.7

MEDIAN 1,600 9.1 59.0

STANDARD 

DEVIATION

44,561 7.7 91.7

Table 6-3. Model-calibration dataset for Honey Creek at Wauwatosa, Wisconsin.

[CFU/100 mL, colony forming units per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
120 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 6-5. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with fecal coliform bacteria concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Honey Creek at Wauwatosa, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 6 121

2.0 2.5 3.0 3.5 4.0 4.5 5.0

5.04.54.03.53.02.52.01.5

Measured log10(fecal coliform)

) fecal coliform( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Fecal Coliform, in colony forming

units per 100 milliliters

2 5 10 20 50 100 200

 5000 1000

 500 100

 50000 10000

100000 B

Water temperature, in degrees Celsius

Fecal Coliform, in colony forming

units per 100 milliliters

0 5 10 15 20

 500 100

 50000 10000

 5000 1000

100000 C

Discharge, in cubic feet per second

Fecal Coliform, in colony forming

units per 100 milliliters

1 5 10 50 500

 5000 1000

 500 100

100000

 50000 10000

D

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

−0.5−1.0

1.00.50.0

Predicted log10(fecal coliform)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Fecal Coliform Bacteria at Honey Creek at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 6-6. U.S. Geological Survey streamgage on Honey Creek at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (fecal coliform 

bacteria concentration). B, Relation between turbidity and fecal coliform bacteria concentration in log10

space. C, Relation between water temperature and fecal coliform bacteria concentration in log10 space. 

D, Relation between discharge and fecal coliform bacteria concentration in log10 space. E, Relation 

between predicted log10 (fecal coliform bacteria concentration) and regression residuals. F, Relation 

between time and fecal coliform bacteria regression residuals. G, Probability plot of fecal coliform bacteria regression residuals. 
122 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Fecal coliform bacteria at Menomonee River at Wauwatosa, WI (04087120)

Samples collected on 6/08/2009 – 6/09/2009, and 8/09/2009, were not used in the regression analysis 

because of extreme fouling or because the MMSD laboratory qualified the results.

MODEL SUMMARY—Summary of final regression results for estimating fecal coliform concentrations at 

Menomonee River at Wauwatosa, WI.

Log10 (fecal coliform) = 1.38 + 0.078 (WT) + 0.79 log10 (Turb),

Where:

fecal coliform = colony forming units of fecal coliform per 100 ml (CFU/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

 

Model Information (in log units unless otherwise specified): 

Number of measurements = 68,

Root-mean-squared error (RMSE) = 0.492

Model standard percentage error (MPSE) = +211 and -68 percent

90-percent prediction intervals (based on units in CFU/100ml) = +/- 553 percent 

Adjusted coefficient of determination (Adj R2

) = 0.74

Sum of squared error = 15.75

PRESS = 17.10

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.38 0.203 6.81 <0.0001

WT 0.078 0.007 10.90 <0.0001

Log 10 (Turb) 0.79 0.114 6.95 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.277 -0.861

WT -0.276 1 -0.155

log10 (Turb) -0.861 -0.155 1 

Duan’s bias correction factor = 1.70
Appendix 6 123

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

11/20/2008 10:30 110 2.2 1.9

12/27/2008 10:15 1,000 0.0 89.0

1/20/2009 12:10 64 0.0 1.5

2/7/2009 11:25 2,100 0.0 72.3

2/7/2009 13:25 2,400 0.0 105.0

2/7/2009 13:40 2,400 0.0 110.0

2/7/2009 19:40 840 0.0 46.3

2/8/2009 13:40 300 0.0 26.0

2/9/2009 22:00 910 0.0 140.0

2/9/2009 23:15 1,300 0.1 140.0

2/10/2009 11:00 1,300 0.1 100.0

2/10/2009 17:05 800 0.5 70.7

2/26/2009 14:35 140 0.4 66.0

2/26/2009 19:00 260 0.7 140.0

2/26/2009 19:45 2,000 0.7 170.0

2/26/2009 22:50 1,200 0.6 130.0

2/27/2009 4:50 720 0.0 70.0

3/2/2009 7:20 270 0.0 7.3

3/10/2009 0:15 340 2.3 34.0

3/24/2009 11:55 71 4.9 1.1

3/25/2009 1:30 2,100 6.2 38.0

3/31/2009 17:00 1,700 5.1 14.0

3/31/2009 17:35 1,000 5.2 33.0

4/1/2009 5:35 480 4.3 20.0

4/19/2009 19:10 1,200 11.4 17.0

4/21/2009 5:05 380 7.7 7.1

4/23/2009 11:00 48 8.2 1.4

4/25/2009 11:15 800 14.2 22.0

4/25/2009 12:40 3,300 13.8 160.0

4/26/2009 14:35 2,400 8.9 36.0

4/26/2009 17:10 3,300 10.5 190.0

5/9/2009 0:30 500 16.6 37.0

5/9/2009 9:30 730 14.6 17.0

5/13/2009 20:40 1,900 15.2 68.0

5/13/2009 21:05 3,500 15.6 150.0

5/13/2009 22:00 5,600 15.9 140.0

5/14/2009 3:15 4,600 15.4 86.0

5/20/2009 11:15 56 17.4 4.8

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

6/19/2009 9:15 9,000 19.6 84.0

6/19/2009 18:15 19,000 20.4 52.0

6/19/2009 21:20 18,000 20.5 150.0

6/20/2009 3:10 42,000 19.7 45.0

7/16/2009 11:45 4,200 21.8 3.5

8/7/2009 18:00 29,000 19.6 32.0

8/7/2009 20:40 38,000 19.8 60.0

8/8/2009 0:55 60,000 19.3 37.0

8/8/2009 8:50 47,000 19.8 74.0

8/8/2009 9:45 70,000 20.1 210.0

8/8/2009 19:50 41,000 21.8 48.0

8/10/2009 2:00 27,000 22.3 110.0

8/10/2009 4:20 25,000 21.4 99.0

8/25/2009 20:50 83,000 22.3 68.0

8/25/2009 21:25 46,000 22.4 110.0

8/25/2009 21:30 35,000 21.9 96.0

8/26/2009 3:30 41,000 21.5 47.0

8/27/2009 3:35 5,400 20.0 18.0

9/20/2009 21:40 90,000 18.0 69.0

9/21/2009 3:40 180,000 17.8 51.0

9/22/2009 13:30 130,000 18.3 56.0

9/22/2009 13:40 140,000 18.4 71.0

9/22/2009 21:50 93,000 19.5 56.0

9/22/2009 23:10 42,000 19.0 53.0

9/27/2009 20:35 32,000 17.8 100.0

9/27/2009 21:05 43,000 18.0 150.0

9/27/2009 21:20 46,000 18.1 180.0

09/28/209 0:05 42,000 17.1 70.0

9/28/2009 2:35 23,000 16.4 62.0

9/28/2009 20:35 8,300 14.8 25.0

MINIMUM 48 0.0 1.1

MAXIMUM 180,000 22.4 210.0

MEAN 22,956 11.9 71.3

MEDIAN 3,300 15.3 64.0

STANDARD 

DEVIATION

36,566 8.5 52.5

Table 6-4. Model-calibration dataset for Menomonee River at Wauwatosa, Wisconsin.

[CFU/100 mL, colony forming units per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
124 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 6-7. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with fecal coliform bacteria concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Menomonee River at Wauwatosa, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 6 125

2.0 2.5 3.0 3.5 4.0 4.5 5.0

4.54.03.53.02.52.01.5

Measured log10(fecal coliform)

) fecal coliform( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Fecal Coliform, in colony forming

units per 100 milliliters

1 2 5 10 20 50 100 200

 50

 5000 1000

 500 100

 50000 10000

100000 B

Water temperature, in degrees Celsius

Fecal Coliform, in colony forming

units per 100 milliliters

0 5 10 15 20

 50

 500 100

 50000 10000

 5000 1000

100000 C

Discharge, in cubic feet per second

Fecal Coliform, in colony forming

units per 100 milliliters

50 100 200 500 1000 5000

 50

 5000 1000

 500 100

100000

 50000 10000

D

1.5 2.0 2.5 3.0 3.5 4.0 4.5

−0.5−1.0−1.5

1.00.50.0

Predicted log10(fecal coliform)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−0.5−1.0−1.5

1.00.50.0

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−0.5−1.0−1.5

1.00.50.0

Theoretical quantiles

Residuals quantiles

G

Fecal Coliform Bacteria at Menomonee River at Wauwatosa, Wisconsin, November 2008−September 2009

Figure 6-8. U.S. Geological Survey streamgage on Menomonee River at Wauwatosa, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (fecal coliform 

bacteria concentration). B, Relation between turbidity and fecal coliform bacteria concentration in log10

space. C, Relation between water temperature and fecal coliform bacteria concentration in log10 space. 

D, Relation between discharge and fecal coliform bacteria concentration in log10 space. E, Relation 

between predicted log10 (fecal coliform bacteria concentration) and regression residuals. F, Relation 

between time and fecal coliform bacteria regression residuals. G, Probability plot of fecal coliform bacteria regression residuals. 
126 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Fecal coliform bacteria at Menomonee River at 16th Street at Milwaukee, WI 

(04087142)

MODEL SUMMARY—Summary of final regression results for estimating fecal coliform concentrations at 

Menomonee River at 16th Street at Milwaukee, WI.

Log10 (fecal coliform) = 1.07 + 0.062 (WT) + 1.00 log10 (Turb),

Where:

fecal coliform = colony forming units of fecal coliform per 100 ml (CFU/100ml)

WT = Water Temperature in o

C 

Turb = Turbidity (YSI 6136), in NTU

 

Model Information (in log units unless otherwise specified): 

Number of measurements = 56,

Root-mean-squared error (RMSE) = 0.652

Model standard percentage error (MPSE) = +348 and -77 percent

90-percent prediction intervals (based on units in CFU/100ml) = +/- 1585 percent 

Adjusted coefficient of determination (Adj R2

) = 0.54

Sum of squared error = 22.50

PRESS = 25.56

Coefficients: 

Coefficient Standard t p-value

error statistic 

Intercept 1.07 0.296 3.62 0.0007

WT 0.062 0.011 5.71 <0.0001

Log 10 (Turb) 1.001 0.159 6.31 <0.0001

Correlation matrix of coefficients:

Intercept WT log10 (Turb) 

Intercept 1 -0.522 -0.852

WT -0.522 1 0.108

log10 (Turb) -0.852 0.108 1 

Duan’s bias correction factor = 2.60
Appendix 6 127

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

11/20/2008 11:45 110 9.7 3.1

12/27/2008 12:35 840 0.3 52.3

12/28/2008 0:35 2,100 1.5 58.7

1/20/2009 12:40 24 8.2 5.4

2/7/2009 11:40 71 5.7 3.6

2/7/2009 20:40 1,800 0.0 78.7

2/8/2009 5:40 900 0.0 34.7

2/8/2009 14:40 870 0.8 28.3

2/8/2009 23:40 400 0.0 28.0

2/9/2009 17:40 1,000 0.1 12.7

2/16/2009 13:40 48 0.1 8.1

2/26/2009 16:00 32 8.9 8.2

2/26/2009 19:00 1,100 0.2 200.0

2/26/2009 22:00 1,700 0.7 130.0

2/27/2009 4:00 1,300 0.6 85.0

3/7/2009 11:10 270 2.9 19.0

3/7/2009 14:10 800 2.9 89.0

3/9/2009 0:10 720 0.9 61.0

3/10/2009 20:30 280 2.2 41.0

3/24/2009 12:25 71 12.0 4.0

4/1/2009 1:40 1,500 5.1 34.0

4/20/2009 3:05 1,700 10.9 12.0

4/23/2009 11:15 56 12.5 5.7

4/25/2009 13:20 2,200 14.2 30.0

4/26/2009 8:00 2,400 8.8 48.0

4/26/2009 14:00 2,700 8.8 39.0

4/26/2009 16:25 12,000 9.6 82.0

4/26/2009 17:10 17,000 10.3 210.0

4/26/2009 19:30 2,400 10.9 210.0

5/13/2009 22:05 2,000 15.2 35.0

5/14/2009 0:35 4,000 16.4 67.0

5/14/2009 1:45 5,800 16.4 93.0

5/14/2009 3:35 3,500 16.0 70.0

5/20/2009 11:45 130 18.4 5.0

Date Time

Fecal 

coliform 

bacteria 

(CFU/100 mL)

Water 

temperature 

(°C)

Turbidity 

(NTU)

6/8/2009 15:30 5,800 13.6 50.0

6/9/2009 2:35 9,200 14.3 32.7

6/9/2009 5:00 6,200 14.3 31.3

6/16/2009 13:00 340 22.7 5.3

6/19/2009 0:55 50,000 20.1 530.0

6/19/2009 1:10 36,000 20.0 400.0

6/19/2009 1:45 37,000 20.1 340.0

6/19/2009 9:35 110 19.6 95.0

6/19/2040 20:45 63,000 21.1 160.0

6/20/2009 2:25 60,000 19.8 84.0

7/16/2009 12:30 41,000 24.4 4.9

8/8/2009 22:30 97,000 21.6 24.0

8/9/2009 10:30 4,600 22.1 17.0

8/26/2009 7:05 110,000 21.6 15.0

8/26/2009 17:00 34,000 22.0 13.0

8/26/2009 23:45 6,000 21.8 14.0

9/15/2009 11:30 71 26.3 2.9

9/28/2009 12:05 19,000 16.3 28.0

09/28/209 18:05 9,600 15.6 30.0

9/29/2009 0:05 6,400 15.1 30.0

9/29/2009 3:05 5,600 16.8 17.0

9/29/2009 5:00 6,400 17.2 16.0

MINIMUM 24 0.0 2.9

MAXIMUM 110,000 26.3 530.0

MEAN 12,128 11.7 68.4

MEDIAN 2,150 13.1 32.0

STANDARD 

DEVIATION

23,421 8.1 100.8

Table 6-5. Model-calibration dataset for Menomonee River at 16th Street at Milwaukee, Wisconsin.

[CFU/100 mL, colony forming units per 100 milliliters; NTU, Nephelometric turbidity units; °C, degrees Celsius]
128 Use of Real-Time Monitoring to Predict Concentrations of Select Constituents, Menomonee River, Wisconsin, 2008–9

Figure 6-9. Duration curves for turbidity and water temperature (November 2008–September 2010) and corresponding values 

associated with fecal coliform bacteria concentration samples collected November 2008 to September 2009 at U.S. Geological Survey 

streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin.

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Turbidity, in nephelometric turbidity units 

Frequency of exceedance, in percent 

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60 70 80 90 100

Water temperature, in degrees Celsius 

Frequency of exceedance, in percent 
Appendix 6 129

2 3 4 5

5.04.54.03.53.02.52.0

Measured log10(fecal coliform)

) fecal coliform( 10 Predicted log

A

Turbidity, in nephelometric turbidity units

Fecal Coliform, in colony forming

units per 100 milliliters

5 10 20 50 100 200 500

 50

 5000 1000

 500 100

 50000 10000

100000 B

Water temperature, in degrees Celsius

Fecal Coliform, in colony forming

units per 100 milliliters

0 5 10 15 20 25

 50

 500 100

 50000 10000

 5000 1000

100000 C

Discharge, in cubic feet per second

Fecal Coliform, in colony forming

units per 100 milliliters

5 10 50 500 5000

 50

 5000 1000

 500 100

100000

 50000 10000

D

2.0 2.5 3.0 3.5 4.0 4.5 5.0

−1−2

10

Predicted log10(fecal coliform)

Residuals

E

2009.0 2009.2 2009.4 2009.6

−1−2

10

Time, in decimal year

Residuals

F

−2 −1 0 1 2

−1−2

10

Theoretical quantiles

Residuals quantiles

G

Fecal Coliform Bacteria at Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008−September 2009

Figure 6-10. U.S. Geological Survey streamgage on Menomonee River at 16th Street at Milwaukee, Wisconsin, November 2008 to September 2009. A, Relation between measured and predicted log10 (fecal 

coliform bacteria concentration). B, Relation between turbidity and fecal coliform bacteria concentration in log10 space. C, Relation between water temperature and fecal coliform bacteria concentration in log10

space. D, Relation between discharge and fecal coliform bacteria concentration in log10 space. E, Relation 

between predicted log10 (fecal coliform bacteria concentration) and regression residuals. F, Relation 

between time and fecal coliform bacteria regression residuals. G, Probability plot of fecal coliform bacteria regression residuals. 


Baldwin and others—Real-Time Monitoring of Select Constituents, Menomonee River, Wisconsin, 2008–9—Scientific Investigations Report 2012–5064