Prepared in cooperation with the U.S. Environmental Protection Agency

Simulation of Discharge, Water-Surface Elevations, 

and Water Temperatures for the St. Louis River Estuary, 

Minnesota-Wisconsin, 2016–17

Scientific Investigations Report 2020–5028

U.S. Department of the Interior

U.S. Geological Survey
Full cover. Photograph showing the St. Louis River and St. Louis Bay, Duluth, Minnesota, taken June 6, 2015. 

Photograph courtesy of James St. John, licensed under the Creative Commons Attribution 2.0 Generic license.

Back cover. Photograph looking upstream towards the Oliver Bridge at the U.S. Geological Survey acoustic Doppler 

velocity meter installation, St. Louis River, Minnesota-Wisconsin. Photograph taken July 30, 2015, by hydrologist 

Joel Groten, U.S. Geological Survey.
Simulation of Discharge, Water-Surface 

Elevations, and Water Temperatures 

for the St. Louis River Estuary, 

Minnesota-Wisconsin, 2016–17

By Erik A. Smith, Richard L. Kiesling, and Earl J. Hayter

Prepared in cooperation with the U.S. Environmental Protection Agency

Scientific Investigations Report 2020–5028

U.S. Department of the Interior

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

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment—visit https://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, visit 

https://store.usgs.gov/.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Smith, E.A., Kiesling, R.L., and Hayter, E.J., 2020, Simulation of discharge, water-surface elevations, and water 

temperatures for the St. Louis River estuary, Minnesota-Wisconsin, 2016–17: U.S. Geological Survey Scientific 

Investigations Report 2020–5028, 31 p., https://doi.org/10.3133/sir20205028.

Associated data for this publication:

Smith, E.A., 2020, St. Louis River Estuary (Minnesota-Wisconsin) EFDC hydrodynamic model for discharge and 

temperature simulations, 2016–17: U.S. Geological Survey data release, https://doi.org/10.5066/P990OUS6.

U.S. Geological Survey, 2020, USGS water data for the Nation: U.S. Geological Survey National Water Information 

System database, https://doi.org/10.5066/F7P55KJN.

ISSN 2328-0328 (online)
iii

Acknowledgments

Funding for this study was provided by the Great Lakes Restoration Initiative program through 

a joint partnership between the U.S. Geological Survey and the U.S. Environmental Protection 

Agency. This report presents a compilation of information supplied by several agencies and 

individuals, mainly the Minnesota Department of Natural Resources, Minnesota Pollution 

Control Agency, U.S. Geological Survey, and U.S. Army Corps of Engineers.

Christopher Warren of the U.S. Army Corps of Engineers—Detroit District is greatly 

acknowledged for a technical review of the report.

Samuel Rendon of the U.S. Geological Survey is also greatly acknowledged for a technical 

review of the report, in addition to a comprehensive review of the Environmental Fluid Dynamics 

Code model.

v

Contents

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

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

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................3

Study Area..............................................................................................................................................3

Previous Studies ...................................................................................................................................3

Methods...........................................................................................................................................................3

Bathymetric Data and Computational Grid .......................................................................................6

Model Data and Development ............................................................................................................6

Discharge and Flow Velocity .....................................................................................................6

Water Balance ..................................................................................................................10

Water-Surface Elevations ........................................................................................................10

Thermal Boundary Conditions .................................................................................................11

Meteorological Data .................................................................................................................12

Model Parameterization ....................................................................................................................12

Model Calibration and Results ..................................................................................................................14

Water-Surface Elevations .................................................................................................................14

Discharge.............................................................................................................................................16

Temperature .........................................................................................................................................20

Flow Velocity........................................................................................................................................22

Model Limitations.........................................................................................................................................23

Summary........................................................................................................................................................27

References Cited..........................................................................................................................................28

Figures

1. Map showing the St. Louis River drainage basin above the St. Louis River at 

Scanlon, Minnesota, streamgage, including the main stem of the St. Louis 

River, the Whiteface River, and the Cloquet River, major cities/towns, and 

other administrative boundaries ................................................................................................4

2. Map showing the St. Louis River estuary with bays, tributaries, and continuous 

measurement locations, Minnesota and Wisconsin ..............................................................5

3. Map showing the St. Louis River estuary Environmental Fluid Dynamics Code 

model domain, starting at the Fond du Lac Dam and extending into 

Lake Superior about 7.5 kilometers ...........................................................................................8

4. Charts showing the St. Louis River estuary water balance for 

the 2016 water year ....................................................................................................................11

5. Graphs showing hourly and daily mean water-surface elevation for 

St. Louis River estuary locations, Minnesota-Wisconsin, 2016 ..........................................15

6. Graphs showing hourly and daily mean water-surface elevation for 

St. Louis River estuary locations, Minnesota-Wisconsin, 2017 ..........................................16

7. Graph showing hourly water-surface elevation for the Superior Bay Duluth 

Ship Canal at Duluth, Minnesota, for July 18–25, 2016, demonstrating 

the subdaily water-level fluctuation cycle .............................................................................18
vi

8. Graphs showing hourly and daily mean discharge for St. Louis River estuary 

locations, Minnesota-Wisconsin, 2016 ...................................................................................21

9. Graphs showing hourly and daily mean discharge for St. Louis River estuary 

locations, Minnesota-Wisconsin, 2017 ...................................................................................22

10. Graph showing hourly water-surface discharge for the Superior Bay Duluth 

Ship Canal at Duluth, Minnesota, for July 19–22, 2016, demonstrating 

the subdaily discharge fluctuation cycle ................................................................................23

11. Graphs showing hourly and daily mean temperature for St. Louis River 

estuary locations, Minnesota-Wisconsin, 2016 .....................................................................25

12. Graphs showing hourly and daily mean temperature for St. Louis River 

estuary locations, Minnesota-Wisconsin, 2017 .....................................................................25

13. Graphs showing daily mean flow velocity for St. Louis River estuary locations, 

Minnesota-Wisconsin, 2016 ......................................................................................................27

Tables

1. Continuous measurements used in the St. Louis River estuary model 

development or evaluation of the model performance ..........................................................7

2. Model input flow series for the St. Louis River estuary model, 2016–17, 

including the gaged drainage basin area, associated ungaged drainage basin 

area, and the applied scalar factor between gaged and ungaged 

drainage basin area .....................................................................................................................9

3. Major parameters important for calibration in the St. Louis River estuary model, 

including the parameter description, final parameter value, and 

the variation range .....................................................................................................................13

4. Performance evaluation statistics for water-surface elevations of the St. Louis 

River estuary model, 2016–17, including mean error, mean absolute error, 

root mean square error, and Nash-Sutcliffe efficiency coefficient ...................................17

5. Measurement and simulation ranges for discharge, including the minimum, 

maximum, and average, of the following locations for 2016–17: St. Louis River 

at Oliver, Wisconsin; Superior Bay Entry Channel at Superior, Wisc.; Superior 

Bay Duluth Ship Canal at Duluth, Minnesota; and Superior Bay Entry Channel at 

Superior, Wisc., plus Superior Bay Duluth Ship Canal at Duluth, Minn ............................19

6. Water balance ratios, in percentages, for the measurement and simulation 

average discharges for 2016 and 2017 ....................................................................................20

7. Performance evaluation statistics for discharge of the St. Louis River 

estuary model, 2016–17, including mean error, mean absolute error, 

root mean square error, and Nash-Sutcliffe efficiency coefficient ...................................24

8. Performance evaluation statistics for water temperature of the St. Louis River 

estuary model, 2016–17, including mean error, mean absolute error, 

root mean square error, and Nash-Sutcliffe efficiency coefficient ...................................24

9. Performance evaluation statistics for flow velocity of the St. Louis River 

estuary model, 2016–17, including mean error, mean absolute error, 

root mean square error, and Nash-Sutcliffe efficiency coefficient ...................................26
vii

Conversion Factors

International System of Units to U.S. customary units

Multiply By To obtain

Length

meter (m) 3.281 foot (ft)

meter (m) 39.37 inches (in.)

kilometer (km) 0.6215 mile (mi)

Area

square kilometer (km2) 0.3861 square mile (mi2)

square meter (m2) 10.76 square foot (ft2)

hectare (ha) 2.47 acre (ac)

Flow rate

meter per second (m/s) 3.281 foot per second (ft/s)

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

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

°F = (1.8 × °C) + 32.

Datum

Vertical coordinate information is referenced to the International Great Lakes Datum of 1985 

(IGLD 1985), unless otherwise indicated.

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the vertical datum.

Supplemental Information

A water year is the period from October 1 to September 30 and is designated by the year in 

which it ends; for example, water year 2016 was from October 1, 2015, to September 30, 2016.
viii

Abbreviations

AOC Area of Concern

EFDC Environmental Fluid Dynamics Code

EPA U.S. Environmental Protection Agency

GLRI Great Lakes Restoration Initiative

MAE mean absolute error

ME mean error

MN DNR Minnesota Department of Natural Resources

MPCA Minnesota Pollution Control Agency

NDBC National Data Buoy Center

NSEC Nash-Sutcliffe efficiency coefficient

RMSE root mean square error

USAF U.S. Air Force

USGS U.S. Geological Survey
Simulation of Discharge, Water-Surface Elevations, 

and Water Temperatures for the St. Louis River Estuary, 

Minnesota-Wisconsin, 2016–17

By Erik A. Smith,1 Richard L. Kiesling,1 and Earl J. Hayter2

Abstract

The St. Louis River estuary is a large freshwater estuary, 

next to Duluth, Minnesota, that encompasses the headwaters of Lake Superior. The St. Louis River estuary is one of 

the most complex and compromised near-shore systems in 

the upper Great Lakes with a long history of environmental 

contamination caused by logging, mining, paper mills, and 

other heavy industrial activities. Presently (2020), a widely 

available, science-based assessment tool capable of evaluating ecosystem-level responses to remediation and restoration 

projects has not existed for the estuary. To address this need, 

the U.S. Geological Survey (USGS) built a predictive, mechanistic, three-dimensional hydrodynamic model for the estuary 

using the Environmental Fluid Dynamics Code framework. 

In the current version, the model can simulate continuous discharge, water-surface elevations, water temperature, and flow 

velocity, although the modular framework allows for future 

additions of water-quality modeling.

The model was calibrated using data collected from 

April 2016 through November 2016 and validated with 

data collected from April 2017 through November 2017. 

The four types of data used to evaluate model performance 

were water-surface elevations, discharge, water temperature, 

and flow velocities. Streamflow and temperature boundary 

condition data included a mixture of USGS streamgage data, 

Minnesota Department of Natural Resources gage data, and 

estimates derived from the gage data.

The model was able to simulate the water-surface elevations with generally good agreement between the simulated 

and measured values for both years at the daily time step. 

Specifically, the model was able to demonstrate excellent

agreement with the measured data with Nash-Sutcliffe efficiency coefficients greater than 0.8 for all three locations; 

however, the model was unable to produce hourly watersurface elevations with such accuracy for 2016–17.

Discharge was more dynamic than the water-surface elevations, both for the measured and simulated data. Generally, 

most of the discharge ranged from −650 to 1,200 cubic meters 

per second, but the constantly changing flux exiting the estuary 

into Lake Superior (positive flows) and entering the estuary 

from Lake Superior (negative flows) occurred throughout 

the year. Even upstream at the St. Louis River at Oliver, 

Wisconsin, gage (USGS station 0402403250), the effect of 

flows into the estuary from Lake Superior did occur, demonstrating the strong effect of the Lake Superior seiche on flows 

for the estuary.

From a performance standpoint, the model was able to 

simulate discharge with generally good agreement in both 

years, although the 2017 validation was better than the 2016 

calibration period. For the daily Nash-Sutcliffe efficiency 

coefficients, the simulated values were 0.98, 0.62, 0.49, and 

0.71 for the Oliver gage; the Superior Bay entry channel 

at Superior, Wisc., (USGS station 464226092005600); the 

Superior Bay Duluth Ship Canal at Duluth, Minn., (USGS station 464646092052900); and total entries (combination of the 

Superior entry and Duluth entry), respectively. For the hourly 

evaluation criteria, the model performed poorly, with NashSutcliffe efficiency coefficients less than 0 for the two entries 

into Lake Superior; therefore, as a predictor of discharge at 

the hourly scale, the model performed worse than using the 

measured data average. Similar to discharge, the model was a 

good predictor of flow velocity at the daily time scale but had 

difficulty matching the measured data at the hourly scale. For 

discharge and flow velocity, matching at subdaily time steps 

for a system as complicated as the St. Louis River estuary 

is considered difficult because the match is highly sensitive 

to coordinating the exact measurement location to the simulated value.

The final calibration target was water temperature, 

calibrated for the Oliver gage and the Duluth entry. For calibration purposes, the Duluth entry was the more important 

water temperature target because the Oliver gage was more of 

an internal check on the model. The Nash-Sutcliffe efficiency 

coefficients for the Duluth entry were high; hourly NashSutcliffe efficiency coefficients at the Duluth entry were either 

at or greater than 0.7 for both years, and daily values were 

0.84 and 0.82 for 2016 and 2017, respectively.

1U.S. Geological Survey.

2U.S. Army Corps of Engineers.
2 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

Introduction

The St. Louis River is the largest U.S. tributary to 

Lake Superior, flowing 323 kilometers (km) before discharging into Lake Superior between Duluth, Minnesota, and 

Superior, Wisconsin (Christensen and others, 2012). The 

last 38 km of the St. Louis River is a freshwater estuary that 

encloses several shallow bays, an 8-meter (m) dredged shipping channel, and an active shipping port. Also known as 

the St. Louis River estuary, the freshwater estuary is about 

4,850 hectares in area and encompasses the headwaters of 

Lake Superior (St. Louis River Estuary, 2019).

The St. Louis River estuary also is one of the most 

complex and compromised near-shore systems in the upper 

Great Lakes with a long history of environmental contamination caused by logging, mining, paper mills, and other heavy 

industrial activities. For the past 200 years, the St. Louis River 

estuary has been an economic hub for northeast Minnesota and 

northwest Wisconsin (Christensen and others, 2012). All these 

economic activities have deposited large loads of suspended 

solids and nutrients directly into the estuary. The International 

Joint Commission designated the estuary as a Great Lakes 

Area of Concern (AOC) in 1989 (Christensen and others, 

2012) because of severely degraded water quality.

In 2010, the Great Lakes Restoration Initiative (GLRI) 

was launched as a multiyear commitment to implement solutions to beneficial use impairments around the Great Lakes 

through monitoring, remediation, and restoration (Great Lakes 

Interagency Task Force, 2014). These monitoring and restoration efforts have moved forward on many fronts, often at 

the same time, with the stated objective of approaching or 

reaching previously established delisting targets for individual 

impairments. The estuary has been the recipient of multiple 

projects through the GLRI because there has been coordinated 

action by multiple partners in Minnesota and Wisconsin to 

delist the St. Louis River AOC (Anderson and others, 2013); 

however, one of the difficulties in delisting any AOC is how 

individual projects that have been implemented will produce 

a sustainable solution to the stressor gradients. This is particularly difficult for near-shore areas of the Great Lakes such 

as the St. Louis River, which itself is one of the largest and 

most complex tributary systems in the upper Great Lakes. 

For example, sediment and nutrient loading from this system 

dominates the near-shore nutrient economy of western 

Lake Superior (Robertson and Saad, 2011), so its effect on 

Lake Superior is substantial.

Presently (2020), a widely available science-based assessment tool capable of evaluating ecosystem-level responses 

to remediation and restoration projects that can consider the 

complex hydrodynamics of the St. Louis River estuary does 

not exist. A previous hydrodynamics model was completed in 

2013 on behalf of the U.S. Environmental Protection Agency 

(EPA) to address the mercury total maximum daily load for the 

estuary. The modeling framework combined Environmental 

Fluid Dynamics Code (EFDC) and the Water Quality Analysis 

Simulation Program, but the model calibration period was for 

less than 1 month and only included the Nemadji River and 

the St. Louis River main branch (RTI International, 2013). A 

second model, also built with EFDC, was completed to understand sediment transport caused by dredging activities within a 

section of Saint Louis Bay around 21st Avenue West (Mausolf, 

2014). However, this project was largely focused on a small 

area, so to help understand the cumulative effect of multiple, 

simultaneous aquatic restoration actions across the estuary, a 

new systems-level evaluation tool is required.

A first step in designing a new evaluation tool or modeling framework for the St. Louis River estuary is to incorporate 

all the hydrodynamics, including continuous discharge from 

the following sources: the main St. Louis River channel, 

Nemadji River, Pokegama River, Duluth-area (Minnesota) 

tributaries, northwest Wisconsin tributaries such as the 

Red River and Little Pokegama (not shown), and water 

treatment effluent. The new evaluation tools would need 

to also consider the effect of Lake Superior water-surface 

elevations because the lake causes frequent back flow into 

the estuary through storm surges and periodic seiche events 

(Mausolf, 2014; City of Superior, 2019). By incorporating 

all flow sources and Lake Superior water-surface elevations 

into the new model, the estuary water balance can be properly accounted for so that additional modeling of sediment, 

nutrients, and submerged aquatic vegetation can eventually be 

merged into this single modeling framework.

Starting in 2015, the U.S. Geological Survey (USGS) 

received GLRI funds from the EPA to collect new streamflow, stage, and water temperature datasets across the 

St. Louis River estuary, including the initiation of a new 

gaging and water-quality station near Oliver, Wisc. Funds also 

were provided to establish continuous velocity and discharge 

stations for the Superior and Duluth entries from the estuary 

into Lake Superior. These new datasets provided the necessary 

information for developing a three-dimensional hydrodynamic 

model of the St. Louis River estuary. Building on other data 

collected by multiple agencies across the estuary, including 

the Minnesota Department of Natural Resources (MN DNR); 

University of Minnesota-Duluth, Natural Resources Research 

Institute; and Minnesota Pollution Control Agency (MPCA), 

the USGS, in collaboration with the U.S. Army Corps of 

Engineers, Engineer Research and Development Center, 

and in cooperation with the EPA, developed a predictive, 

mechanistic, three-dimensional hydrodynamic model for the 

St. Louis River estuary, Minnesota-Wisconsin. This model was 

developed with EFDC, a grid-based, surface-water modeling 

package for simulating three-dimensional circulation, mass 

transport, sediments, and biogeochemical processes (Hamrick, 

1992, 2007). The new model simulates continuous discharge, 

water-surface elevations, water temperature, and flow velocities across the estuary. Furthermore, this model can be used as 

a framework for simulating other biogeochemical processes 

once the appropriate datasets have been collected and processed. The long-term goal for the model is to serve as an 
Methods 3

integrated, science-based assessment tool capable of evaluating ecosystem-level responses to remediation and restoration 

projects for the St. Louis River estuary.

Purpose and Scope

The purpose of this report is to describe the initial 

development of the hydrodynamic component of a new model 

to simulate discharge, water-surface elevations, water temperature, and flow velocity for the St. Louis River Estuary, in 

Minnesota and Wisconsin. The model was calibrated using 

data collected from April 2016 through November 2016 

and validated with data collected from April 2017 through 

November 2017. The report summarizes the development and 

calibration of the new model.

Study Area

The St. Louis River is the largest tributary to Lake Superior 

(fig. 1; Smith and others, 2017), flowing for 323 kilometers

(km) (201 mi) towards Lake Superior before discharging into 

Lake Superior at Duluth, Minn. (fig. 1). The St. Louis River 

drainage basin is one of the largest in northern Minnesota. The 

drainage basin above the St. Louis River at Scanlon, Minn. 

(USGS station 04024000), streamgage (hereafter referred to 

as “gage”) is 8,884 square kilometers (km2) (Smith and others, 2017). The drainage basin includes the main stem of the 

St. Louis River, in addition to the Whiteface River and the 

Cloquet River. The St. Louis River drainage basin is in a heavily 

forested region of northeastern Minnesota; most of the drainage basin is within the Northern Lakes and Forests ecoregion 

(Anderson and others, 2013). The climate in the basin is hemiboreal, a warm summer continental climate, and is characterized 

by long winters, moderate to heavy snow cover, and short summers. Precipitation in the area averages between 0.7 and 0.8 m

per year (Lindholm and others, 1979; National Climatic Data 

Center, 2018).

The last 24 km (15 mi) of the St. Louis River is considered a freshwater estuary that forms part of the border between 

Minnesota and Wisconsin (fig. 2). The St. Louis River estuary 

includes several shallow bays, including Saint Louis Bay, 

Superior Bay, and Allouez Bay, as well as Spirit Lake and the 

lower Nemadji River (fig. 2). Additionally, the Nemadji River 

flows into the estuary, and the system is sometimes referred to 

as the St. Louis River/Nemadji River estuary. The estuary has 

been affected by heavy industry since the late 1800s, although 

water quality has steadily improved since the Western Lake 

Superior Sanitary District began treating industrial and domestic effluent in 1979 (Lindgren and others, 2006). The estuary 

still contains several potential sources of contaminants, including two Superfund sites (Blazer and others, 2014) and several 

impairments related to altered hydrology and total suspended 

solids, although these are all being addressed by multiple 

Federal, State, and local partners.

Previous Studies

A preliminary water budget was included as part of a 

characterization of the St. Louis River surface-water and 

groundwater resources by Lindholm and others (1979). 

Separately, the Fond du Lac Indian Reservation water 

resources were characterized by Ruhl (1989). The physical 

characteristics and comprehensive water-quality synopses 

for the St. Louis River were summarized by Lindgren and 

others (2006). In 2010, chemicals of emerging concern were 

sampled at selected sites in Saint Louis and Superior Bays 

(Christensen and others, 2012). After the severe flooding of 

the St. Louis River in 2012, Czuba and others (2012) characterized the high-water marks for several communities in and 

around the St. Louis River, also creating flood-peak inundation maps and water-surface profiles for several of the most 

affected communities.

Other studies have included the numerical modeling and 

sediment transport analysis to identify optimal dredged placement sites within the estuary around the 21st Avenue West 

site in Saint Louis Bay (Mausolf, 2014). Across the drainage basin, multiple partners led by the MPCA contributed to 

the St. Louis River Watershed Monitoring and Assessment 

report, a summary of load and discrete sampling across the 

St. Louis River drainage basin (Anderson and others, 2013), 

and the more recent Watershed Restoration and Protection 

Strategy Report (MPCA, 2018). Tetra Tech, in cooperation 

with the State of Minnesota, completed a series of Hydrologic 

Simulation Program-Fortran models for subwatersheds across 

the St. Louis River drainage basin, including the Duluth-area 

tributaries (Tetra Tech, 2016). Finally, the USGS characterized 

the relative and cumulative streamflow distributions for the 

St. Louis River drainage basin (Smith and others, 2017).

Methods

The St. Louis River estuary model was constructed 

using EFDC, a grid-based surface-water modeling package 

developed in the 1990s for estuarine and coastal applications 

(Hamrick, 1992, 2007). EFDC solves the vertically hydrostatic, free-surface, turbulent-averaged equations of motions 

for a variable-density fluid. Dynamically coupled transport 

equations for kinematic energy, turbulent length scale, salinity, 

and temperature also are solved. EFDC is a widely used 

modeling framework that has been applied in a variety of 

surface-water studies (Ji and others, 2004; Elçi and others, 

2007; Dynamic Solutions, LLC, 2013; Ji, 2017). The new 

model discussed in this report simulates discharge, watersurface elevations. water temperature, and flow velocity.

The EFDC model structure used in this study required 

bathymetric data, bottom roughness coefficients, and tributary inflow locations. For all aspects of running the enhanced 

model, EFDC Explorer version 8.4 (compiled July 28, 2018), 
4 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

mad20-2006_fig01

Base map modified from U.S. Geological Survey, 

Minnesota Department of Natural Resources, 

and other digital data, various scales 

Universal Transverse Mercator projection, zone 15 N.

North American Datum of 1983

Duluth

04024000

ST. LOUIS

COUNTY

LAKE

COUNTY

ITASCA

COUNTY

CARLTON

COUNTY

AITKIN

COUNTY

93°00' 92°30' 92°00' 91°30'

47°30'

47°00'

EXPLANATION

04024000 U.S. Geological Survey 

streamgage and identifier

St. Louis drainage basin

Study area

0 10 20 5 KILOMETERS

0 5 10 MILES

WISCONSIN

WISCONSIN

CANADA

SOUTH 

DAKOTA

NORTH 

DAKOTA

St. Louis River

LAKE SUPERIOR

MINNESOTA

MINNESOTA

St. Louis River

St. Louis River

Whiteface River

Cloquet River

Figure 1. The St. Louis River drainage basin above the St. Louis River at Scanlon, Minnesota, streamgage (U.S. Geological Survey 

station 04024000), including the main stem of the St. Louis River, the Whiteface River, and the Cloquet River, major cities/towns, 

and other administrative boundaries.
mad20-2006_fig02

04024067

04024430

0402403250

464646092052900

St. Louis River St. Louis River

Po

kegama

Riv

e

r

Nemadji River

Pokegama Bay 

Spirit 

Lake

Saint Louis Bay

FOND DU LAC DAM

Superior Bay

92°20' 92°18' 92°16' 92°14' 92°12' 92°10' 92°08' 92°06' 92°04' 92°02' 

46°46'46°44'46°42'46°40'46°38'

Base map modified from U.S. Geological Survey and other digital data, various scales Universal Transverse Mercator projection, zone 15 N.North American Datum of 1983 0 

0 

MINNESOTA

LAKE SUP

WISCONSIN

EXPLANATION

U.S. Geological Survey streamgage and identifierGeneral outline of St. Louis River estuary

0402403250

Figure 2. The St. Louis River estuary with bays, tributaries, and continuous measurement locations, Minnesota and Wisconsin.
6 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

which is a pre- and postprocessor for EFDC models (Craig, 

2017), was selected. EFDC Explorer was used to enter the 

required input data into the model, control model parameters, 

manipulate run-time configurations, begin model runs, and 

complete postrun statistical comparisons. As previously noted, 

the model was calibrated for the period April–November 2016 

and validated using the period April–November 2017. Four 

primary statistics, including mean error (ME), mean absolute 

error (MAE), root mean square error (RMSE), and the NashSutcliffe efficiency coefficient (NSEC), were used to evaluate 

the degree of fit for the EFDC model.

The EFDC model was developed in several phases. First, 

data were collected and compiled to determine the hydrological and thermal boundary conditions. To prepare for running 

the model, these multiple datasets had to then be specially 

formatted for the EFDC model. A summary of the continuous datasets used for this study is shown in table 1. Next, the 

model grid was augmented, based on a previous EFDC model 

set-up (Mausolf, 2014). The final phase, which constitutes 

most of the second half of this report, was the calibration and 

validation of the model.

Bathymetric Data and Computational Grid

A curvilinear computational grid was developed based 

on a previous model set-up for the St. Louis River estuary, 

available from the U.S. Army Corps of Engineers (Mausolf, 

2014). The grid was augmented to cover the domain of the 

new model using CVLGrid, a preprocessing software package 

for creating and editing EFDC model grids (Craig, 2017). To 

add areas that were missing from the previous model, information from an available 2014 bathymetric survey was used 

(EPA, 2014). The missing grid information was assigned using 

the bathymetry assignment option within EFDC Explorer. 

Because the previous model set-up and 2014 survey were 

in the 1985 International Great Lakes Datum, the new grid 

datum was preserved in the same datum. Areas missing in the 

original grid included more detailed bathymetry information 

for the Pokegama River arm of the model domain and the 

St. Louis River main channel close to the Fond du Lac Dam.

The final model grid consisted of 11,326 grid cells, ranging in depth from less than 0.1 to 29.6 m (fig. 3). The model 

started at the Fond du Lac Dam and ran out into Lake Superior 

about 7.5 km. The deepest cells of the model were in the 

Lake Superior part of the model domain, which was included 

to give the model enough stability to transition from the relatively shallow depths of the estuary to the deeper depths in the 

open lake. The average grid size for non-Lake Superior cells 

was 5,200 square meters (m2), with an average side length of 

about 70 m. The deepest grid cells within the St. Louis River 

estuary were 16.3 m, and the average depth across the estuary part of the model was 4.0 m. Four vertical layers were 

included with each grid cell, divided equally across the given 

depth of an individual cell. This approach is the standard 

approach that has been available for EFDC since the model 

was created. A newer grid type, known as Sigma Zed layering 

(Craig, 2017), was attempted but did not improve the model 

calibration for water-surface elevations or discharge and added 

an extra 1–2 hours to the model run time.

Model Data and Development

Several continuous discharge stations were used to calculate the initial and boundary conditions for the St. Louis River

estuary model and to provide a calibration dataset. Data characterizing the hydrologic conditions and contributing areas, 

including water-surface elevations, flow velocities, and water 

temperatures, were compiled for this effort. Other compiled 

data included discharge from a subset of gaged inflow locations.

Discharge and Flow Velocity

The primary inflow to the estuary, provided as hourly 

data from the dam operator Minnesota Power and available as 

part of the ScienceBase model archive (Smith, 2020), was from 

Fond du Lac Dam. The Fond du Lac Dam is the upstream 

boundary condition for the EFDC model. Streamflow also 

was continuously measured for two major tributaries to 

the St. Louis River estuary (table 2): the Pokegama River 

at Logan Avenue at South Superior, Wisc. (USGS station 04024067), and the Nemadji River near South Superior, 

Wisc. (USGS station 04024430). Both sites were measured 

by the USGS. The finalized continuous streamflow record 

for the Nemadji River is available from the USGS National 

Water Information System database (USGS, 2020), and the 

Pokegama River is part of the model archive (Smith, 2020).

Additionally, the USGS collected continuous discharge 

for three gages established for this study: St. Louis River at 

Oliver, Wisc. (USGS station 0402403250; hereafter referred to 

as the “Oliver gage”); Superior Bay Entry Channel at Superior, 

Wisc. (USGS station 464226092005600; hereafter referred to 

as the “Superior entry”); and Superior Bay Duluth Ship Canal 

at Duluth, Minn. (USGS station 464646092052900; hereafter 

referred to as the “Duluth entry”). These locations were used 

for calibration and validation data. All three stations were 

satellite telemetered and transmitted data at subhourly resolution throughout 2016–17. For these three locations, the USGS 

deployed SonTek SideLookers (SonTek-SL) to measure water 

velocity and water-surface elevation (SonTek, 2019). The 

Oliver gage was bridge mounted, whereas the entry locations 

were mounted to the seawalls going into Lake Superior. The 

velocity was recorded in discrete bins that spanned the subsection, and then a data logger averaged those measurements 

from those discrete bins to calculate an average velocity every 

5 minutes (Levesque and Oberg, 2012).

As part of the continuous streamflow record development, instantaneous discharge and stage measurements were 

periodically completed at all USGS gage locations to verify 

and modify the stage-discharge relation (Rantz and others, 

1982a, b; Mueller and others, 2008). In addition to USGS 
Table 1. Continuous measurements used in the St. Louis River estuary model development or evaluation of the model performance (calibration/validtypes included discharge, water-surface elevation, flow velocity, and water temperature. Water temperature was not available for all inflows used for substitution was used as shown in the water temperature assignment column. Further information about the discharge (flow series) is shown in table [USGS, U.S. Geological Survey; MN DNR, Minnesota Department of Natural Resources; --, no station number or no data; X, data measured; nr, near; mi, mile; us, upstream; AWLSSD, Western Lake Superior Sanitary District; S, South; W, West; R, River; Wisc., Wisconsin; Minn., Minnesota]

USGS station 

number

MN DNR 

(or alternative) 

station number

Full station 

name

Short name

Model 

development

Model 

performance

Discharge

Water-surface 

elevation

Velocity

Water 

temperature

Water 

-- -- Fond du Lac Station Fond du Lac Dam X -- X -- -- -- 

-- 03010003 Mission Creek nr Fond du Lac, 

1 mi us of MN23

Mission Creek X -- X -- -- -- 

-- 03163011 Merritt Creek at Duluth, 

Grand Ave

Merritt Creek X -- X -- -- -- 

-- -- Western Lake Superior 

Sanitary District

WLSSD X -- X -- -- X WLSSD.

-- 03163012 Miller Creek at Duluth, 

S 24th Ave W

Miller Creek X -- X -- -- X Kingsbury Creek; Keene 

Superior City ungagedMiller Creek.

104024067 -- Pokegama R at Logan Ave. 

at S. Superior, Wisc.

Pokegama River X -- X -- -- X Red River; Little Pokega

Superior City ungaged

104024430 -- Nemadji River near 

South Superior, Wisc.

Nemadji River X -- X -- -- -- 

-- -- 2Lake Superior ADCIRC Lake Superior 

ADCIRC

X -- -- X -- -- 

-- 345028 Station 45028—Western 

Lake Superior

Lake Superior X -- -- X -- X Lake Superior ADCIRC

-- 4S004–364 Tischer Creek at Wallace Ave 

“Mt. Royal,” Duluth

Tischer Creek X -- -- -- -- X Mission Creek; Sargent 

Stewart Creek.

10402403250 -- St. Louis River at Oliver, Wisc. Oliver gage X X X X X X Fond du Lac Dam.1464646092052900 -- Superior Bay Duluth Ship 

Canal at Duluth, Minn.

Duluth entry -- X X X X X 

1464226092005600 -- Superior Bay Entry Channel at 

Superior, Wisc.

Superior entry -- X X X X -- 

1USGS National Water Information System database (USGS, 2020).2Nearshore Lake Superior water-surface elevations were provided from the Lake Superior ADCIRC model (Hayter and others, 2015).3National Data Buoy Center station identification, available at https://www.ndbc.noaa.gov/station_page.php?station=45028.4Minnesota Pollution Control Agency station identification.
mad20-2006_fig03

Fond du Lac Dam

WLSSD

Red River

Keene Creek

Miller Creek

Nemadji River

Merritt Creek

Stewart Creek

Sargent 

Creek

Mission Creek

Pokegama River

Kingsbury Creek

Little Pokegama

U.S. Steel Creek

Superior City ungaged,Pokegama River

Superior City ungaged,

Miller/Mission Creek

92°18' 92°16' 92°14' 92°12' 92°10' 92°08' 92°06' 92°04' 92°02' 92°00' 91°58' 91°

46°48'46°46'46°44'46°42'46°40'46°38'

Base map modified from U.S. Geological Survey and other digital data, various scales Universal Transverse Mercator projection, zone 15 N.North American Datum of 1983 0 1 

0 1 2 

464226092005600(Superior entry)

464646092052900

(Duluth entry)

0402403250(Oliver gage)

EXPLANATION

Flow seriesSt. Louis River EFDC grid

Depth, in meters

−29.6 to −25>−25 to −20>−20 to −15>−15 to −10>−10 to −5>−5 to 0

0402403250 U.S. Geological Survey 

streamgage and identifier

[WLSSD, Western Lake Superior Sanitary District; EFDC, Environmental Fluid Dynamics Code]

Figure 3. St. Louis River estuary Environmental Fluid Dynamics Code model domain, starting at the Fond du Lac Dam and extending into Lake Superi
Table 2. Model input flow series for the St. Louis River estuary model, 2016–17, including the gaged drainage basin area, associated ungaged drainathe applied scalar factor (K) between gaged and ungaged drainage basin area. For drainage basins either without a streamgage or missing streamgaappropriate gaged record was applied, with a separate scaling factor: Mission Creek scalar (Kmiss), Miller Creek scalar (Kmil), or Pokegama River scal[USGS, U.S. Geological Survey; MN DNR, Minnesota Department of Natural Resources; --, no station number or no data; nr, near; mi, mile; us, upstream; Ave, Avenue; S, SouWLSSD, Western Lake Superior Sanitary District; R, River; Wisc., Wisconsin]

USGS 

station 

number

MN DNR 

station 

number1

Full station name Flow time series (short name) Gaged drainage basin area Ungaged drainage basin area Scalar factor (K) Mission Creek scalar (Kmiss) M

(square kilometers)

Minnesota

-- -- Fond du Lac Station Fond du Lac Dam -- -- -- -- 

-- 03010003 Mission Creek nr Fond du 

Lac, 1 mi us of MN23

Mission Creek 28.33 2.482 1.088 -- 

-- -- -- Sargent Creek -- 10.558 -- 0.373 

-- -- -- U.S. Steel Creek -- 14.420 -- 0.509 

-- -- -- Stewart Creek -- 4.871 -- 0.172 

-- -- -- Kingsbury Creek -- 40.035 -- 1.413 

-- -- -- Keene Creek -- 12.846 -- 0.453 

-- 03163011 Merritt Creek at Duluth, 

Grand Ave

Merritt Creek 5.646 7.132 2.263 0.451 

-- 03163012 Miller Creek at Duluth, S 

24th Ave W

Miller Creek 25.825 15.525 1.601 1.459 

-- -- Western Lake Superior 

Sanitary District

WLSSD -- -- -- -- 

Wisconsin

-- -- -- Red River -- 42.923 -- -- 

-- -- -- Little Pokegama -- 29.131 -- -- 

04024067 -- Pokegama R at Logan Ave. 

at S. Superior, Wisc.

Pokegama River 82.530 -- -- -- 

-- -- -- Superior City ungaged, 

Pokegama River

-- 13.422 -- -- 

-- -- -- Superior City ungaged, 

Miller/Mission Creek

-- 38.316 -- 1.352 

04024430 -- Nemadji River near South 

Superior, Wisc.

Nemadji River 1,094.128 42.192 1.039 -- 

1For MN DNR sites, the full record can be accessed by looking up the site number at https://www.dnr.state.mn.us/waters/csg/index.html.
10 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

gages, additional streamflow data were available from three 

MN DNR gages (table 2): Mission Creek near Fond du Lac 

(MN DNR station 03010003; MN DNR, 2019a); Merritt Creek 

at Duluth, Grand Avenue (MN DNR station 03163011; 

MN DNR, 2019b); and Miller Creek at Duluth, South 24th 

Avenue West (MN DNR station 03001012; MN DNR, 2019c). 

The MN DNR followed standard gaging procedures similar to 

the USGS for establishing the continuous discharge and watersurface elevation records (MN DNR, 2019d).

Several tributary records were not available for the 

modeling period, particularly the Duluth-area tributaries, so a 

substitution method had to be used. To calculate how to assign 

discharge for these tributaries, drainage basin areas were delineated in ArcGIS 10.5 (Esri, 2019) using watershed boundary 

datasets available from the USGS (USGS, 2013) and watershed polygon grids available online (Lake Superior Streams, 

2019) for all the tributaries to the St. Louis River estuary. For 

tributaries (flow series) without available discharge, an arearatio method similar to methods described by Chow and others 

(1988) and applied by Rendon and Lee (2015) for another 

EFDC model was used. The ratio between the ungaged 

tributary drainage basin area and the closest appropriate gaged 

tributary drainage basin area was calculated using equation 1:

R A

A utw

utw

gtw

= (1)

where

Rutw is the ratio of the ungaged tributary drainage 

basin area (flow series) to the gaged 

tributary drainage basin area for a given 

drainage basin (unitless),

Autw is the ungaged tributary drainage basin area in 

square kilometers,

Agtw is the closest appropriate gaged tributary 

drainage basin area in square kilometers.

All records with the Miller Creek scalar for 2016 used the 

Mission Creek scalar for 2017 because the Miller Creek record 

was unavailable. Also, three of the Wisconsin tributaries 

applied the Pokegama River relation because these drainage 

basins were closer in slope and land-use characteristics.

There were several other Duluth-area tributaries not 

included in the model domain. Instead, these ungaged 

areas were allocated to one of the inflow series in table 2, 

accounting for the remainder of the ungaged area around the 

St. Louis River estuary. The same equation also was applied 

to the ungaged area for gaged drainage basins, except the ratio 

was the ungaged tributary area (in square kilometers) to the 

gaged tributary drainage basin area (in square kilometers) for 

the same drainage basin.

The ratio calculated using equation 1 was used to create 

a scalar factor to apply to the available streamflow data. The 

scalar factor (K) is computed using equation 2:

K=(1+Rutw) (2)

The scalar factors and the substituted gage records for all 

the tributaries (flow series) with substitutions are included in 

table 2, in addition to calculated gaged and ungaged drainage basin areas. The scalar factors used for this substitution 

included Mission Creek (Kmiss), Miller Creek (Kmil), and the 

Pokegama River (Kpok).

For the EFDC model, the major flow series included 

the following (table 2) datasets, all available as part of 

the model archive (Smith, 2020): Fond du Lac Dam into 

the main St. Louis River channel, Pokegama River, and 

Nemadji River. The following minor Minnesota tributaries were included as additional flow series: Mission Creek, 

Sargent Creek, U.S. Steel Creek, Stewart Creek, Kingsbury 

Creek, Keene Creek, Merritt Creek, and Miller Creek (table 1; 

not shown). For the Wisconsin side, the following minor 

tributaries were included: Red River and the Little Pokegama. 

In addition to these tributaries, areas of Superior, Wisc., were 

included as an approximation of runoff areas into the estuary (table 2): Superior City ungaged, Pokegama River, and 

Superior City ungaged, Miller/Mission Creek. A final discharge dataset for the effluent flow from the Western Lake 

Superior Sanitary District (fig. 3; table 1) was included.

Water Balance

As mentioned in the previous section, dozens of minor 

tributaries flow directly into the estuary in addition to the 

larger tributaries, the Pokegama and Nemadji Rivers (figs. 1–3; 

tables 1–2). The estuary water balance is controlled by a 

spring snowmelt in late March or early April, followed by 

periodic, large rainstorms in the summer. Primary inflow is 

from upstream at the Fond du Lac Dam. A water balance for 

the 2016 water year (from October 1, 2015, to September 30, 

2016) for the estuary indicated 83 percent of water originated 

upstream from the Oliver gage, 12 percent upstream from the 

Nemadji River gage, and 5 percent from all other tributary 

sources (fig. 4). To close the water balance, all other tributary 

sources (fig. 4) were set to 41 percent of the Nemadji River 

gage daily discharge. As mentioned in the previous section, 

outflow for the water balance occurred through two exit points 

into Lake Superior: the Superior entry and the Duluth entry. 

Between the two entries, about 70 percent of the water leaves 

the estuary through the Superior entry and about 30 percent 

leaves through the Duluth entry, based on the 2015–16 analysis (fig. 4).

Water-Surface Elevations

Water-surface elevations were collected for three locations as calibration datasets for the St. Louis River estuary 

model. The three locations included the Oliver gage, the 

Superior entry, and the Duluth entry (table 1), all included as 

part of the model archive (Smith, 2020). The datum for all 

three stations, for the purposes of this report, was the 1985 

International Great Lakes Datum. In addition to the three stations, continuous, water-surface elevations were simulated in 
Methods 11

2016 and 2017 for the Lake Superior nearshore to define the 

north open boundary of the EFDC model. The Lake Superior 

water-surface elevations were provided from an available 

Advanced Circulation (ADCIRC) model (Hayter and others, 2015). The EFDC model simulated the flow in and out of 

the St. Louis River estuary, through the two entry channels, 

by equilibrating to the simulated water-surface elevations as 

defined by the ADCIRC model along the north open boundary. 

With a north open boundary, water can flow both in and out of 

the model domain.

Thermal Boundary Conditions

Water temperature for the St. Louis River estuary had 

a predictable seasonal pattern, with frozen conditions from 

mid-November through March. Weather patterns were 

superimposed on the annual climate cycle, affecting water 

temperature on shorter timescales of several days to weeks. 

The diurnal cycle imposed daily variations in water temperature, producing variations of a few degrees Celsius, with the 

largest variations occurring in the summer when solar energy 

fluxes were strongest.

Each tributary or inflow (table 2) required a temperature 

assignment in the EFDC model. Because each tributary or 

inflow did not have a continuous temperature record available, a substitution from another location was required based 

on the closest or most appropriate available record (table 1). 

The following continuous water temperature records were 

available and included in the model archive (Smith, 2020), 

either for the open-water period (April–November) or the 

year: the Oliver gage, Pokegama River at Logan Avenue at 

South Superior, Wisc. (USGS station 04024067; hereafter 

referred to as the “Pokegama River” gage); Tischer Creek at 

Wallace Avenue, Duluth, Minn. (MPCA station S004–364); 

Miller Creek at Duluth, S. 24th Ave W (MN DNR station 03001012), Western Lake Superior (National Data Buoy 

Center [NDBC] Station 45028) (NDBC, 2019), and the 

Western Lake Superior Sanitary District effluent outflow. The 

assignment of each temperature record is shown in table 1; all 

temperature records are available as part of the model archive 

(Smith, 2020).

At the two USGS gages used for temperature input (the 

Oliver gage and the Pokegama River site), and a third location 

used for model calibration (Duluth entry), water temperature 

A. St. Louis River estuary inflow sources for the 2016 water year

St. Louis River at Oliver, Wisconsin—U.S. Geological Survey 

station 0402403250

Nemadji River near South Superior, Wisconsin—U.S. Geological Survey 

station 04024430

All other tributaries, combined 

B. St. Louis River estuary outflow sources for the 2016 water year

Superior Bay Duluth Ship Canal at Duluth, Minnesota— 

U.S. Geological Survey station 464646092052900

Superior Bay Entry Channel at Superior, Wisconsin—

U.S. Geological Survey station 464226092005600

83 percent 30 percent 70 percent 12 percent

5 percent

EXPLANATION EXPLANATION

Figure 4. St. Louis River estuary water balance for the 2016 water year (October 1, 2015, to September 30, 2016). A, inflow sources; 

B, outflow sources. Water balance based on daily mean discharge, in cubic feet per second. For the outflow sources, the category 

“all other tributaries, combined” was a percentage of the daily mean Nemadji River at South Superior, Wisconsin 

(U.S. Geological Survey station 04024430), discharge.
12 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

was sampled from the SonTek-SL. For the SonTek-SL, the 

temperature resolution was plus or minus 0.01 degree Celsius 

(°C) and the temperature accuracy was plus or minus 0.2 °C. 

All USGS temperature data were processed as outlined in 

Wagner and others (2006). For the data provided by either 

MPCA or MN DNR, a water temperature was collected using 

a multiparameter sonde with regular maintenance, including 

cleaning and calibrating; however, no information about the 

sonde model or the depth of the measurements was available. 

Water temperature at the Western Lake Superior location, a 

buoy owned and operated by the University of MinnesotaDuluth, was measured 1 m below the water line. Finally, the 

Western Lake Superior Sanitary District temperature was 

measured at the same location as the treatment plant effluent 

flow measurement.

Meteorological Data

Meteorological data are required as input to the EFDC 

model because of the importance of surface boundary conditions to the overall behavior of the model, specifically surface 

heat exchange, solar radiation absorption, wind stress, and 

gas exchange. Required meteorological data include air 

temperature, atmospheric pressure, relative humidity, total 

precipitation, wind speed, wind direction, and cloud cover. All 

unit conversions from the meteorological data to the required 

units for the model were straightforward with the exception of 

cloud cover. The qualitative sky cover parameter (that is, clear, 

scattered, broken, and overcast) was converted to a value 

ranging from 0 to 1: clear was 0, scattered (1/8 to 1/2 cloud 

coverage) was 0.3125, broken (5/8 to 7/8 cloud coverage) was 

0.75, and overcast was 1, with mixed sky cover conditions 

(for example, scattered and broken) averaged together.

All required data were available at least at hourly 

intervals for two locations: Richard I. Bong Airport (U.S. Air 

Force [USAF] station identification number [ID] 726427; 

not shown), in Superior, Wisc., within the model domain, 

and the Cloquet Carlton County Airport (USAF ID 726558; 

not shown), located closer to the Fond du Lac Dam (fig. 2). 

A third location, Sky Harbor International Airport (USAF 

ID 727456; not shown) in Duluth, Minn., was included only 

for wind speed and wind direction. All datasets were downloaded from the Climate Data Online portal (National Climatic 

Data Center, 2018). Based on the latitude and longitude of the 

estuary and the required meteorological inputs, evapotranspiration was included in the water balance as an internal EFDC 

calculation. Because multiple locations were used for the 

wind and meteorological series in the model, EFDC Explorer 

automatically calculated a weighting map for each series 

based on distance away from the station to every part of the 

model domain.

Model Parameterization

Most parameters that control the EFDC model were left 

as the default, as provided within the EFDC Explorer framework (Craig, 2017); however, certain parameters were varied 

to get an improved calibration fit (table 3), with emphasis 

on parameters that control the grid type, model run timing 

settings, hydrodynamics, and heat exchange. Many of these 

parameters were the same or similar to another published 

EFDC model, the Lake Houston EFDC model (Rendon and 

Lee, 2015). During the calibration process, all parameters 

were varied by trial and error through a series of calibration model runs to improve the overall fit of the model. Each 

calibration run had controlled variations in parameter settings 

across the ranges in table 3, with typically only one parameter 

changed for each calibration run to characterize the effect on 

the calibration metrics for water-surface elevations, discharge, 

and temperature. Major parameters important for calibration, 

including the parameter description, final parameter value, and 

the variation range, are shown in table 3. A truncated description of what each of these parameters control also is provided 

in table 3; for full parameter descriptions, consult the EFDC 

Explorer manual (Craig, 2017) or the original EFDC documentation (Hamrick, 1992, 2007).

A full sensitivity analysis was not completed for this 

study, although variation of these parameters did confirm the 

parameter sensitivity. Each parameter in table 3 was rated as 

either sensitive, neutral, insensitive, or important for model 

run stabilization. For a particular parameter to be considered 

sensitive, at least one of the calibration metrics needed to have 

a substantial change. Although this method was qualitative, 

the general practice for a parameter to be deemed sensitive 

was a change of at least 2 percent for the NSEC, discussed 

in the next section. For the model run stabilization criteria, 

these parameters did not necessarily change the evaluation 

criteria, but either made the run time more efficient or prevented the model from crashing. Although all the evaporation 

options available within EFDC Explorer were attempted, the 

EFDC original (default option) had the best calibration fit. 

Also, the minimum fraction of solar radiation in the top layer 

(FSWRATF) and the background light extinction (WQKEB) 

were highly sensitive, although the final values were close 

to the EFDC Explorer default. Alternatively, the parameters 

in table 3 that control hydrodynamics, including AVO, ABO, 

AVMX, and ABMX, were all neutral to insensitive in their 

effects on any of the primary calibration targets: water-surface 

elevation, discharge, water temperature, and flow velocity.

The selected grid type was the standard sigma vertical grid. Although the new grid type available with EFDC 

Explorer, sigma-zed layering, was attempted, it caused the 

water-surface elevation and discharge to drift far away from 
Table 3. Major parameters important for calibration in the St. Louis River estuary model, including the parameter description, final parameter value, Each parameter was either sensitive, neutral, insensitive, or instead was important for model run stabilization.[--, no data or not applicable; m2/s, square meter per second; EFDC, Environmental Fluid Dynamics Code; m−1, per meter]

Parameter Description Final parameter value Variation range 

IGRIDV Selection of grid type: standard sigma versus 

sigma-zed layering

Standard sigma vertical grid Attempted both grid types 

DTSSFAC Dynamic time stepping (in seconds) 0.2 0.2 to 0.4 DTSSDHDT Dynamic time stepping rate of depth change 

(change in height to change in time)

0.3 0.1 to 0.5 

NUPSTEP Minimum number of iterations for each time step 2 2 to 4 DTMAX Maximum time step for dynamic stepping (in seconds) 100 25 to 125 HDRY Depth at which cell or flow face become dry 0.1 -- HWET Depth at which withdrawals from cell are turned off 0.15 0.1 to 0.2 AVO Background, constant or eddy (kinematic) viscosity (m2/s) 1.0×10−6 1.0×10−5 to 1.0×10−7 ABO Background, constant or molecular diffusivity (m2/s) 1.0×10−6 1.0×10−5 to 1.0×10−9 AVMX Maximum kinematic eddy viscosity (m2/s) 1.1×10−5 1.0×10−5 to 1.0×10−6 ABMX Maximum eddy diffusivity (m2/s) 1.0×10−6 1.0×10−5 to 1.0×10−7 Z0 Bottom roughness 0.1 to 4.0×10−3 0.1 to 5.0×10−5 IEVAP Evaporation option for water flux (heat exchange) 2 (EFDC original) Attempted all combinations of heat 

exchange available (11 options)

FSWRATF Minimum fraction of solar radiation adsorbed 

in the top layer

0.3 0.25 to 0.6 

WQKEB Background light extinction (m−1) 1.6 1.2 to 2.5 
14 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

the calibration targets. The other four parameters in table 3

that were altered, DTSSFAC, DTSSDHDT, NUPSTEP, and 

DTMAX, dealt with model run timing and controlled the 

model run stability.

Finally, the final bottom roughness values for the grid 

were varied from 0.1 to 0.004, depending on location. Close 

to the Fond du Lac Dam, the bottom roughness was set to 0.1 

and most of the rest of the model was set to 0.004. Bottom 

roughness values help control the channel friction applied to 

the flow. The only other variation for bottom roughness was 

around the Duluth entry into Lake Superior, set to 0.05. Earlier 

attempts brought the bottom roughness values across the grid 

as low as 5×10−5.

Model Calibration and Results

The St. Louis River estuary EFDC model was calibrated 

for 2016 and validated for 2017. Specifically, the model 

parameters were varied to find the best fit for 2016, with the 

model only run once for 2017 as a validation check. Model 

results at three locations in the model grid were compared to 

measured data collected from the three gages (figs. 2 and 3). 

The four types of data used to verify model performance were 

discharge, water-surface elevations, water temperature, and 

flow velocities. Except for water temperature, which did not 

have a continuous record available for the Superior entry, 

subhourly comparisons were done for all four records at all 

three locations. For all the Oliver gage records, the continuous data collection was discontinued on October 24, 2017, so 

the Oliver comparisons stopped earlier for the 2017 validation. Additionally, a sum of total discharge from both entries 

was used to better understand the full water balance from the 

estuary. The general magnitude and seasonal patterns between 

simulated output and measured data should correspond, 

although an exact match was not expected. Measurements 

were made at a point, or at least averaged across a discrete bin 

in the case of velocities, whereas the model output represents 

simulated conditions across cells that were often greater than 

20 m per side, or 400 m2.

Four statistics were used to evaluate model performance: 

ME, MAE, RMSE, and the NSEC (Nash and Sutcliffe, 1970). 

The ME is the mean difference between the simulated (model) 

value and the measured values, whereas the MAE, computed 

by equation 3 (for example, see usage in Smith and others, 

2018), is the absolute mean difference between the simulated 

(model) value and the measured values:

MAE = 1_

n

∑i=1 n |simulated value − measured value

where

n is the number of observations.

The ME is a goodness-of-fit statistic to help identify 

possible bias in the simulated values (Wilks, 1995). A positive 

ME indicates that the model is simulating values that are on 

average higher than the measured values, whereas a negative ME indicates the simulation values are biased low. The 

MAE averages the absolute differences between simulated and 

measured values where all individual differences have equal 

weight, with lower values being superior.

The RMSE, as computed by equation 4, is a relative term 

that gives a measure of the variability between the simulated 

and measured value:

RMSE = √

___________________________________

1 _

n

∑i=1n  (simulated value − measured value2  

The RMSE has the same units of measure as the quantity 

being simulated, so it represents the error associated with 

individual simulated values (Hyndman and Koehler, 2006) 

and the RMSE can range from 0 to infinity.

The last goodness-of-fit statistic, the NSEC, has been 

classically used to evaluate hydrological model performance 

(Legates and McCabe, 1999). The NSEC ranges from minus 

infinity to positive 1.0: any value greater than 0 indicates 

that the model is a better predictor of the measured data than 

the mean of the measured data, with 1.0 indicating a perfect 

match. NSEC values less than 0.0 indicate the model is worse 

than the mean of the measured data. For the exact NSEC 

formula, also termed the coefficient of efficiency, consult Nash 

and Sutcliffe (1970) or Legates and McCabe (1999).

Water-Surface Elevations

The St. Louis River estuary water-surface elevations 

varied within a narrow range in 2016–17 (figs. 5 and 6), less 

than about 1 m (3.3 ft), for all three locations used as calibration datasets: the Oliver gage, Superior entry, and Duluth 

entry. Furthermore, the relative difference among the locations 

was relatively flat, given the low gradient of the estuary and 

the lack of any extreme events. In contrast, the extreme flow 

during the June 2012 Duluth flood event (Czuba and others, 

2012) caused water levels to rise several meters in sections of 

the river close to the Fond du Lac Dam.

The water-surface elevations of the St. Louis River 

estuary were calibrated for April 1–November 16, 2016, and 

validated April 1–November 16, 2017, by comparing measured 

water-surface elevations at three locations: the Oliver gage, 

the Duluth entry, and the Superior entry. The model was able 

to simulate the water-surface elevations with generally good 

agreement between the simulated and measured values for 

both years (figs. 5 and 6), although the degree of fit varied 

with the time resolution. At the daily time step in 2016, the 

model was able to demonstrate excellent agreement with the 

measured data with NSEC values at the Oliver gage, Superior 

entry, and Duluth entry of 0.81, 0.91, and 0.89, respectively 
Model Calibration and Results 15

(table 4). At the hourly time scale in 2016, the model did an 

adequate job for both entries but performed poorly for the 

Oliver gage. The hourly NSEC values at the Oliver gage, 

Superior entry, and Duluth entry were 0.21, 0.40, and 0.52, 

respectively. For all three locations, the hourly MAE and 

RMSE varied less than 0.1 m, with the daily values at or 

below 0.04 m. The ME for all three locations was at or below 

0.02 m, with only a small negative bias for the Duluth gage.

For 2017, the NSEC values were even better, with daily 

values for the Oliver gage, Superior entry, and Duluth entry 

of 0.92, 0.91, and 0.93, respectively. The hourly NSEC values 

also were improved over the 2016 values. NSEC values that 

are comparable or improved for a validation period versus a 

calibration period are generally considered a positive indication for a model calibration, given that no changes to the 

model framework were made for the validation period. For the 

MAE and RMSE, the calibration and validations periods were 

at or less than 0.08 m for the hourly evaluation criteria. For the 

same two statistics, the daily values were from 0.02 to 0.04 m 

for both years.

The general amplitude of water-surface elevations during 

an individual day was captured with the model, although the 

simulated results were generally out of sync from the measured data by at least a couple of hours (fig. 7). As shown in 

mad20-2006_fig05abc Water-surface elevation, in meters above the International Great Lakes Datum of 1985

2016

183.3

183.4

183.5

183.6

183.7

183.8

183.9

184.0

184.1

184.2

184.3

A. St. Louis River at Oliver, Wisconsin

U.S. Geological Survey station 0402403250 

183.3

183.4

183.5

183.6

183.7

183.8

183.9

184.0

184.1

184.2

184.3

B. Superior Bay Entry Channel at Superior, Wisconsin 

U.S. Geological Survey station 464226092005600 

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

183.3

183.4

183.5

183.6

183.7

183.8

183.9

184.0

184.1

184.2

184.3

C. Superior Bay Duluth Ship Canal at Duluth, Minnesota

U.S. Geological Survey station 464646092052900 

2016

Simulated, hourly

Measured, hourly

Simulated, daily

Measured, daily

EXPLANATION

Figure 5. Hourly and daily mean water-surface elevation for St. Louis River estuary locations, Minnesota-Wisconsin, 2016. 

Measured and modeled data are plotted at the same locations. A, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey [USGS] 

station 0402403250); B, Superior Bay Entry Channel at Superior, Wisconsin (USGS station 464226092005600); C, Superior Bay Duluth Ship 

Canal at Duluth, Minnesota (USGS station 464646092052900).
16 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

the Duluth entry example from July 2016, the daily amplitude during this period fluctuated from 0.1 to 0.2 m per day. 

This could be due, in part, to several factors including the 

varying resolution of inflow discharges, the usage of simulated Lake Superior water-surface elevations to calibrate 

the model, or the discrepancy between simulated flow and 

actual discharges. However, the most likely cause was the 

Lake Superior seiche cycle, a well-documented event triggered 

by the tidal cycle in the Great Lakes (Sorensen and others, 

2004; Trebitz, 2006).

Discharge

Like the water-surface elevations, the discharge across 

the model domain was calibrated for April 1–November 16, 

2016, and validated April 6–November 12, 2017, by comparing measured discharge at three locations (table 5): the 

Oliver gage, Superior entry, and Duluth entry. A fourth 

comparison was the combined flow from the Duluth entry 

and the Superior entry (table 5). The measurement and simulation ranges for discharge, in cubic meters per second, are 

mad20-2006_fig06abc Water-surface elevation, in meters above the International Great Lakes Datum of 1985

A. St. Louis River at Oliver, Wisconsin 

U.S. Geological Survey station 0402403250 

183.3

183.4

183.5

183.6

183.7

183.8

183.9

184.0

184.1

184.2

184.3

B. Superior Bay Entry Channel at Superior, Wisconsin 

U.S. Geological Survey station 464226092005600 

183.3

183.4

183.5

183.6

183.7

183.8

183.9

184.0

184.1

184.2

184.3

2017

2017

C. Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900 

183.3

183.4

183.5

183.6

183.7

183.8

183.9

184.0

184.1

184.2

184.3

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

Simulated, hourly

Measured, hourly

Simulated, daily

Measured, daily

EXPLANATION

Figure 6. Hourly and daily mean water-surface elevation for St. Louis River estuary locations, Minnesota-Wisconsin, 2017. 

Measured and modeled data are plotted at the same locations. A, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey [USGS] 

station 0402403250); B, Superior Bay Entry Channel at Superior, Wisconsin (USGS station 464226092005600); C, Superior Bay Duluth Ship 

Canal at Duluth, Minnesota (USGS station 464646092052900).
Table 4. Performance evaluation statistics for water-surface elevations of the St. Louis River estuary model, 2016–17, including mean error, mean abroot mean square error, and Nash-Sutcliffe efficiency coefficient.[USGS, U.S. Geological Survey; ME, mean error; MAE, mean absolute error; RMSE, root mean square error; NSEC, Nash-Sutcliffe efficiency coefficient; Wisc., Wisconsin; M

USGS station number USGS station name Short name

Hourly evaluation criteria Daily ev

ME MAE RMSE NSEC ME MAE 

(meters) (dimensionless) (meters) 

2016

0402403250 St. Louis River at Oliver, Wisc. Oliver gage 0.00 0.06 0.08 0.21 0.00 0.03 464226092005600 Superior Bay Entry Channel 

at Superior, Wisc. Superior entry 0.01 0.06 0.09 0.40 −0.02 0.02 

464646092052900 Superior Bay Duluth Ship 

Canal at Duluth, Minn. Duluth entry −0.02 0.05 0.07 0.52 −0.02 0.02 

2017

0402403250 St. Louis River at Oliver, Wisc. Oliver gage 0.02 0.08 0.10 0.42 0.02 0.03 464226092005600 Superior Bay Entry Channel 

at Superior, Wisc. Superior entry 0.02 0.07 0.10 0.56 0.02 0.03 

464646092052900 Superior Bay Duluth Ship 

Canal at Duluth, Minn. Duluth entry −0.01 0.06 0.08 0.70 −0.01 0.03 
18 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

summarized in table 5 for the three locations plus the combined entries, including the minimum, the maximum, and 

the average.

St. Louis River estuary discharge was largely controlled 

by dam outflow from the Fond du Lac Dam. Based on the 

water balance (fig. 4), about 83 percent of water flow was 

upstream from the Oliver gage for water year 2016 (October 1, 

2015, to September 30, 2016), of which most of the water was 

from the Fond du Lac Dam. Based on the overall measurement 

average for 2016–17, about 74 and 84 percent of the flow 

originated at or upstream from the Oliver gage for 2016 and 

2017, respectively (table 6). The simulations were closer to the 

assumed water balance ranges, falling in a narrower average 

range of 82 and 86 percent for 2016 and 2017, respectively, 

for the Oliver gage. For outflow, about 78 and 71 percent of 

the discharge flowed out through the Superior entry for 2016 

and 2017, respectively, with the assumed discharge to be close 

to about 70 percent in a given year (fig. 4). The simulated discharge through the Superior entry was close to the measured 

average for both years.

Discharge was more dynamic than the water-surface 

elevations, both for the measured data and simulated values, 

although the measurement range was wider for all three locations (table 5). For example, the 2016 measurement range for 

the Superior entry was −1,644 to 2,276 cubic meters per second (m3/s), almost double the range for the simulation values, 

although most of the range fell into a slightly narrower range 

from −600 to 1,200 m3/s. Generally, the constantly changing 

flux exiting the estuary into Lake Superior (positive flows) 

and entering the estuary from Lake Superior (negative flows) 

occurred throughout the year (fig. 8). The wider range also 

was apparent for the 2017 Superior entry discharge, with 

similar ranges, although the simulated range was slightly 

wider (fig. 9). The Duluth entry also had a dynamic range 

(figs. 8 and 9), given the effect from Lake Superior; however, 

upstream at the Oliver gage (figs. 8 and 9), the Lake Superior 

effect was subdued but negative flows did occur. This effect 

illustrated the strong effect of the Lake Superior seiche 

on flows for the estuary. This dynamic flow, even as far 

upstream as the Oliver gage, strengthened the importance of 

a hydrodynamic model for contaminant transport and confirmed the seiche effect (Trebitz, 2006).

A period of 3 days from July 2016 (July 19–22) is shown 

in figure 10 for the Duluth entry. Within 3 days, the measured 

discharge fluctuated from less than −650 to 1,200 m3/s. These 

changes from negative to positive flows also occurred within 

hours, once again illustrating the competing effects of constant 

discharge from upstream, particularly flow from Fond du Lac 

Dam, and the potential inflows coming into the estuary from 

Lake Superior seiche activity.

From a performance standpoint, the model was able to 

simulate discharge with generally good agreement in both 

years, although similar to the water-surface elevations, the 

2017 validation was better than the 2016 calibration period. 

For the daily NSEC values in 2016, the NSEC values were 

0.98, 0.62, 0.49, and 0.71 for the Oliver gage, Superior entry, 

Duluth entry, and total entries, respectively. The high NSEC 

value for the Oliver gage was expected, given its proximity 

mad20-2006_fig07

July 18 July 19 July 20 July 21 July 22 July 23 July 24 July 25

183.5

183.6

183.7

183.8

183.9

184.0

Water-surface elevation, in meters above 

the International Great Lakes Datum of 1985

Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900 

2016

Simulated, hourly

Measured, hourly

EXPLANATION

Figure 7. Hourly water-surface elevation for the Superior Bay Duluth Ship Canal at Duluth, Minnesota (U.S. Geological Survey 

station 464646092052900), for July 18–25, 2016, demonstrating the subdaily water-level fluctuation cycle.
Table 5. Measurement and simulation ranges for discharge (in cubic meters per second), including the minimum, maximum, and average, of the follofor 2016–17: St. Louis River at Oliver, Wisconsin; Superior Bay Entry Channel at Superior, Wisc.; Superior Bay Duluth Ship Canal at Duluth, Minnesota; Entry Channel at Superior, Wisc., plus Superior Bay Duluth Ship Canal at Duluth, Minn.[USGS, U.S. Geological Survey; Wisc., Wisconsin; Minn., Minnesota; --, no station number]

USGS station 

number USGS station name Short name

Measurement range (hourly) Sim

Minimum Maximum Average Minimum 

(cubic meters per seco

2016

0402403250 St. Louis River at Oliver, Wisc. Oliver gage −277.5 473.0 88.39 −113.3 464226092005600 Superior Bay Entry Channel at Superior, Wisc. Superior entry −1,644 2,276 93.54 −949.5 464646092052900 Superior Bay Duluth Ship Canal at Duluth, Minn. Duluth entry −1,510 1,737 26.27 −721.8 

--

Superior Bay Entry Channel at Superior, Wisc., and 

Superior Bay Duluth Ship Canal at Duluth, Minn. Total entries −3,154 4,013 120.1 −1,621 

2017

0402403250 St. Louis River at Oliver, Wisc. Oliver gage −350.4 524.0 139.6 −133.3 464226092005600 Superior Bay Entry Channel at Superior, Wisc.t Superior entry −1,586 1,770 118.7 −1,147 464646092052900 Superior Bay Duluth Ship Canal at Duluth, Minn. Duluth entry −1,482 1,445 47.93 −784.0 

--

Superior Bay Entry Channel at Superior, Wisc., and 

Superior Bay Duluth Ship Canal at Duluth, Minn. Total entries −2,801 3,043 167.1 −1,905 
20 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

to Fond du Lac Dam. The discharge for the total entries was 

better than the discharge for the two individual entries because 

the model was unable to completely distribute the flow according to the measured data but, collectively, was a reasonable 

simulation; however, based on the average discharge and 

NSEC at or greater than 0.49 for the daily values, the model 

was a fair approximation (table 7).

On the other hand, for the hourly evaluation criteria, 

the model performed poorly, with values less than 0 for the 

outflow locations. As a predictor, the model performed worse 

than using the measured data average, by the definition of 

the NSEC; however, when the data were aggregated to daily 

values, the seiche effect on discharge in and out of the estuary 

was suppressed. For the MAE and RMSE, the hourly MAE 

and RMSE were generally an order of magnitude higher for 

all four discharge evaluation targets than the daily MAE and 

RMSE, including the Oliver gage. Finally, the ME did not 

show a significant trend either positive or negative, except 

the Duluth gage in 2016 did show a negative bias but then the 

Duluth gage had a positive bias in 2017.

Temperature

Temperature calibration was important because temperature affects water density and the vertical exchange of 

constituents; furthermore, annual freezing cycles also are 

important to capture for general hydrodynamics. Finally, temperature affects all biogeochemical processes within the water 

column, so if the EFDC model is eventually expanded for 

water-quality modeling, the temperature calibration is considered a critical step in the model development.

Several boundary conditions affect the water temperature, including the initial water temperature and the sediment 

temperature exchange; however, the two most important 

boundary conditions are the availability of the inflow temperature records for at least a subset of the flow series (table 1) 

and high-resolution meteorological records from close to the 

model domain. A total of 6 records were available for at least 

part of the 2 simulation years for the inflow series, with all 

the inflow temperatures assigned a water temperature series 

(table 1). For meteorological records, 2 complete atmospheric 

records and 3 wind series were available. Because solar 

radiation was not directly available for any of the nearby 

meteorological records, an internal calculation within the 

model was made based on the amount of cloud cover and the 

latitude/longitude.

Like the water-surface elevations and discharge, water 

temperature was calibrated for April 1–November 16, 2016, 

and validated April 6–November 12, 2017, by comparing 

measured water temperature at two locations (table 8): the 

Oliver gage (truncated in 2017) and the Duluth entry. For 

calibration purposes, the Oliver gage was more of an internal check on the model. The Duluth entry was the only other 

independent temperature record available for model calibration, so this record was important as a model calibration 

check on the model’s heat budget. In both cases, the measured 

temperatures were compared to the simulated temperature 1 m 

below the water surface. The applied temperature for the Fond 

du Lac flow series, one of the most important flow series in the 

model domain, was the Oliver gage record, so the high NSEC 

and low MAE/RMSE were expected; however, the NSEC 

values for the Duluth entry also were favorable. The hourly 

NSEC values for the Duluth entry were at or greater than 0.70 

for both years, with daily NSEC values of 0.84 and 0.82 for 

2016 and 2017, respectively (table 8).

The water temperature amplitude during an individual 

day was generally small. For the Oliver gage temperature 

record, amplitude varied within a narrow range of less than 

1 °C (figs. 11A and 12A). Even for the Duluth entry record 

(figs. 11B and 12B), the measured and simulated fluctuations 

for hourly measurements had amplitudes of less than 2 °C. 

For the calibration (2016) and validation (2017) periods, 

the simulated temperatures were slightly higher by about 

1 °C for the Oliver gage (table 8; fig. 11A; fig. 12A) with 

MAE/RMSE values less than 1 °C (table 8). On the other 

hand, the Duluth entry had a higher drift for the simulated 

values, with MAE and RMSE values as high as 3 °C. The 

drift between measured and simulated values was most 

apparent during the summer months (figs. 11B and 12B). This 

drift is also highlighted with the ME values, as the simulated 

Table 6. Water balance ratios, in percentages, for the measurement and simulation average discharges for 2016 and 2017. 

The inflow ratio was based on all discharge measured at the 

Oliver gage, whereas the outflow ratio split the overall discharge 

between the Superior and Duluth entries, as shown in table 5.

[Oliver gage, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey 

[USGS] station 0402403250); Superior entry, Superior Bay Entry Channel 

at Superior, Wisc. (USGS station 464226092005600); Duluth entry, 

Superior Bay Duluth Ship Canal at Duluth, Minnesota (USGS station 

464226092005600)]

Short name Measurement Simulation

2016 inflow

Oliver gage 74 82

2016 outflow

Superior entry 78 77

Duluth entry 22 23

2017 inflow

Oliver gage 84 86

2017 outflow

Superior entry 71 72

Duluth entry 29 27
Model Calibration and Results 21

values were biased high for both locations, up to 1.8 °C for 

the Duluth gage. Although different evaporation options were 

attempted, as discussed in the “Model Parameterization” 

section, the best calibration fit was the EFDC original model 

despite the offset in the summer months.

The temperature offset for the calibration and validation periods could be explained by a couple of factors. 

Measurement location for the temperature calibration and validation data is important. With only single measurement locations available for each location, rather than several depths, 

the offset in temperature could be related to a data limitation. 

The measured temperature records might not be capturing 

the full temperature spectrum, so a proper match between the 

simulated and measured data can be challenging. Also, the 

continuous temperature records available for model construction were limited to a small set of locations, which had to be 

applied across multiple locations. In particular, the boundary 

condition for Lake Superior was based on a single observed 

temperature record from a buoy record, Western Lake Superior 

(NDBC Station 45028), about 12 mi offshore in Lake Superior 

from Duluth, Minn. However, it is known that Lake Superior 

is stratified, so a single water temperature measurement from 

1 m below the water surface would not represent the profile. 

Finally, the lack of a spin-up period for the model to reach 

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

2016

2016

Discharge, in cubic meters per second

−600

−500

−400

−300

−200

−100

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

−200

−100

0

100

200

300

400

500

600

−600

−500

−400

−300

−200

−100

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

mad20-2006_fig08abc

A. St. Louis River at Oliver, Wisconsin 

U.S. Geological Survey station 0402403250 

B. Superior Bay Entry Channel at Superior, Wisconsin 

U.S. Geological Survey station 464226092005600 

C. Superior Bay Duluth Ship Canal at Duluth, Minnesota

U.S. Geological Survey station 464646092052900 

Simulated, hourly

Measured, hourly

Simulated, daily

Measured, daily

EXPLANATION

Figure 8. Hourly and daily mean discharge for St. Louis River estuary locations, Minnesota-Wisconsin, 2016. Measured and simulated 

data are plotted at the same locations. A, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey [USGS] station 0402403250); 

B, Superior Bay Entry Channel at Superior, Wisc. (USGS station 464226092005600); C, Superior Bay Duluth Ship Canal at Duluth, 

Minnesota (USGS station 464646092052900).
22 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

equilibrium could have been an issue with calibration, leading 

to an offset in the summer heat budget between the model 

simulation and the measured data.

Flow Velocity

Because the discharge measurements and simulations are 

partially a product of the flow velocity, the similarity in the 

predictive success of the model was expected. The model was 

able to capture the complex dynamics of flow velocity in and 

out of the estuary into Lake Superior, although the amplitude 

for the simulated flow velocity was smaller than the measured 

flow velocity. For comparison purposes, all three gaging locations (the Oliver gage, Superior entry, and Duluth entry) were 

used as calibration datasets. To extract the results from the 

EFDC model, two outputs were used—the XYZ magnitude 

and the direction component—to calculate positive versus 

negative flow velocity. For the daily NSEC values in 2016, the 

NSEC values were 0.97, 0.69, and 0.43, for the Oliver gage, 

Superior entry, and Duluth entry, respectively. At the hourly 

time step, only the Oliver gage had a positive NSEC value. 

For all three locations in 2017, the daily NSEC values were 

higher (table 9).

Flow velocity for model calibration is generally considered a difficult calibration target; however, when the data 

are available, it is still considered an important check for the 

simulated flow velocities to see if the magnitudes are generally similar to the measured flow velocities. As an example, 

2017

2017

Discharge, in cubic meters per second

−600

−500

−400

−300

−200

−100

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

−200

−100

0

100

200

300

400

500

600

−600

−500

−400

−300

−200

−100

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

mad20-2006_fig09abc

A. St. Louis River at Oliver, Wisconsin 

U.S. Geological Survey station 0402403250 

B. Superior Bay Entry Channel at Superior, Wisconsin 

U.S. Geological Survey station 464226092005600 

C. Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900 

Simulated, hourly

Measured, hourly

Simulated, daily

Measured, daily

EXPLANATION

Figure 9. Hourly and daily mean discharge for St. Louis River estuary locations, Minnesota-Wisconsin, 2017. Measured and simulated 

data are plotted at the same locations. A, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey [USGS] station 0402403250); 

B, Superior Bay Entry Channel at Superior, Wisc. (USGS station 464226092005600); C, Superior Bay Duluth Ship Canal at Duluth, 

Minnesota (USGS station 464646092052900).
Model Limitations 23

the 2016 daily flow velocities (in meters per second) for the 

Duluth and Superior entries are shown in figure 13. Overall, 

the model was able to capture the general trajectory and timing 

of the water velocity at the daily scale, in addition to the seasonal trends in flow velocity. Attempts were made to further 

improve the simulated water velocities to the measured data 

by adjusting the bottom roughness values to increase the water 

velocities, but these adjustments did not appreciably alter flow 

velocity for either of the entry locations.

It is important to note that the velocity data are highly 

dependent on the SonTek SideLooker location and the part 

of the channel for which the velocity measurements were 

averaged. The model output was depth averaged, whereas the 

data measurement was set to specific locations and depths 

within the channel. With these considerations, the comparison 

between the simulated and measured velocities can be difficult 

and often is not presented.

Model Limitations

A full understanding of model limitations and data 

assumptions is necessary to better evaluate the performance 

of any hydrodynamic model. Because it is not possible to 

collect continuous data for every tributary, the extrapolation 

to ungaged tributaries was necessary to meet the boundary 

conditions for the model; for example, temperature records 

from other sites were applied, and discharge for many of the 

smaller tributaries was estimated through an area-ratio method 

rather than direct measurements. For the model simulation, 

the overall water balance was a good approximation of the 

measured data, but the estimated data could have been a factor 

in the poor approximation of the evaluation targets (discharge, 

water-surface elevations, water temperature) at the hourly 

time scale.

The time frame for the model calibration and validation 

was limited; however, funding for the USGS gages that provided the model calibration and validation data was limited to 

the 2 years used for this study. Other examples of EFDC models with a 1-year calibration period exist (Dynamic Solutions, 

LLC, 2013; Rendon and Lee, 2015), although in these cases, 

the calibration was a full year and these models also were in 

warmer climates without an ice season. Ideally, the calibration 

period would have run for a full year with a minimum of a 

short spin-up period of 2–3 months. The shorter period for this 

study could partially explain the temperature calibration offset 

in particular, making it more difficult for the model to properly simulate the proper heat budget. Also, the most important 

component of the calibration period for any hydrologic model 

such as EFDC is selecting a period with a range of hydrologic 

events (Yapo and others, 1996; Juston and others, 2009).

mad20-2006_fig10

Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900 

July 19, 0:00July 19, 6:00

July 19, 12:00July 19, 18:00

July 20, 0:00July 20, 6:00

July 20, 12:00

July 20, 18:00

July 21, 0:00July 21, 6:00

July 21, 12:00July 21, 18:00

July 22, 0:00July 22, 6:00

Discharge, in cubic meters per second

−600

−500

−400

−300

−200

−100

0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

2016

EXPLANATION

Simulated, hourly

Measured, hourly

Figure 10. Hourly water-surface discharge for the Superior Bay Duluth Ship Canal at Duluth, Minnesota (U.S. Geological Survey 

station 464646092052900), for July 19–22, 2016, demonstrating the subdaily discharge fluctuation cycle.
Table 7. Performance evaluation statistics for discharge of the St. Louis River estuary model, 2016–17, including mean error, mean absolute error, roand Nash-Sutcliffe efficiency coefficient. [USGS, U.S. Geological Survey; ME, mean error; MAE, mean absolute error; RMSE, root mean square error; NSEC, Nash-Sutcliffe efficiency coefficient; Wisc., Wisconsin; Minn., 

USGS station number USGS station name Short name Hourly evaluation criteria Daily eva

ME MAE RMSE NSEC ME MAE 

(cubic meters per second) (dimensionless) (cubic meters per s

2016 0402403250 464226092005600 464646092052900 -- St. Louis River at Oliver, Wisc. Superior Bay Entry Channel at Superior, Wisc. Superior Bay Duluth Ship Canal at Duluth, Minn. Superior Bay Entry Channel at Superior, Wisc., and Superior Bay Duluth Ship Canal at Duluth, Minn. Oliver gage Superior entry Duluth entry Total entries 0.28 −0.93 −10.41 −11.642017 70.94 335.7 306.3 615.0 90.29 428.8 385.8 781.2 0.27 −0.62 −0.43 −0.54 0.43 −1.78 −8.57 −11.70 6.052 29.65 29.44 42.44 

0402403250 464226092005600 464646092052900 -- St. Louis River at Oliver, Wisc. Superior Bay Entry Channel at Superior, Wisc. Superior Bay Duluth Ship Canal at Duluth, Minn. Superior Bay Entry Channel at Superior, Wisc., and Superior Bay Duluth Ship Canal at Duluth, Minn. Oliver gage Superior entry Duluth entry Total entries 3.92 −2.80 1.45 −0.92 75.16 404.5 341.6 721.0 95.96 513.0 429.3 910.3 0.38 −1.44 −0.71 −1.06 3.80 −2.54 0.62 −0.68 7.741 26.04 29.32 45.04 

Table 8. Performance evaluation statistics for water temperature of the St. Louis River estuary model, 2016–17, including mean error, mean absolute root mean square error, and Nash-Sutcliffe efficiency coefficient. [USGS, U.S. Geological Survey; ME, mean error; MAE, mean absolute error; RMSE, root mean square error; NSEC, Nash-Sutcliffe efficiency coefficient; Wisc., Wisconsin; Minn

Hourly evaluation criteria Daily eva

USGS station USGS station name Short name ME MAE RMSE NSEC ME MAE 

number (degrees Celsius) (dimensionless) (degrees Celsiu

2016 0402403250 St. Louis River at Oliver, Wisc. Oliver gage 0.4 0.6 0.9 0.98 0.4 0.6 

464646092052900 Superior Bay Duluth Ship Canal Duluth entry 1.5 2.3 3.0 0.73 1.5 1.9 

at Duluth, Minn.

2017

0402403250 St. Louis River at Oliver, Wisc. Oliver gage 1.8 0.7 0.9 0.97 1.8 0.6 464646092052900 Superior Bay Duluth Ship Canal at Duluth entry 1.5 2.2 2.9 0.70 0.6 1.8 

Duluth, Minn. w
Model Limitations 25

0

5

10

15

20

25

30

Water temperature, in degrees Celsius

0

5

10

15

20

25

30

2016 2016

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1 Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

mad20-2006_fig11ab

A. St. Louis River at Oliver, Wisconsin 

U.S. Geological Survey station 0402403250 

B. Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900

Simulated, hourly

Measured, hourly

Simulated, daily

Measured, daily

EXPLANATION

Figure 11. Hourly and daily mean temperature for St. Louis River estuary locations, Minnesota-Wisconsin, 2016. Measured 

and modeled data are plotted at the same locations. A, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey [USGS] 

station 0402403250); B, Superior Bay Duluth Ship Canal at Duluth, Minnesota (USGS station 464646092052900).

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1 Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

0

5

10

15

20

25

30

Water temperature, in degrees Celsius

0

5

10

15

20

25

30

2017 2017

A. St. Louis River at Oliver, Wisconsin 

U.S. Geological Survey station 0402403250 

B. Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900 

Simulated, hourly

Measured, hourly

Simulated, daily

Measured, daily

EXPLANATION

Figure 12. Hourly and daily mean temperature for St. Louis River estuary locations, Minnesota-Wisconsin, 2017. Measured 

and modeled data are plotted at the same locations. A, St. Louis River at Oliver, Wisconsin (U.S. Geological Survey [USGS] 

station 0402403250); B, Superior Bay Duluth Ship Canal at Duluth, Minnesota (USGS station 464646092052900).
Table 9. Performance evaluation statistics for flow velocity of the St. Louis River estuary model, 2016–17, including mean error, mean absolute error, and Nash-Sutcliffe efficiency coefficient. [USGS, U.S. Geological Survey; ME, mean error; MAE, mean absolute error; RMSE, root mean square error; NSEC, Nash-Sutcliffe efficiency coefficient; Wisc., Wisconsin; M

USGS station number USGS station name Short name Hourly evaluation criteria Daily eva

ME MAE RMSE NSEC ME MAE 

(meters per second) (dimensionless) (meters per seco

2016 0402403250 St. Louis River at Oliver, Wisc. Oliver gage 0.00 0.09 0.12 0.28 0.00 0.01 

464226092005600 Superior Bay Entry Channel at Superior, Wisc. Superior entry −0.01 0.16 0.21 −0.29 −0.01 0.02 

464646092052900 Superior Bay Duluth Ship Canal at Duluth, Minn. Duluth entry −0.01 0.31 0.39 −0.50 −0.01 0.03 

2017 0402403250 St. Louis River at Oliver, Wisc. Oliver gage 0.00 0.09 0.12 0.39 0.00 0.01 

464226092005600 Superior Bay Entry Channel at Superior, Wisc. Superior entry 0.00 0.18 0.23 −0.72 0.00 0.01 

464646092052900 Superior Bay Duluth Ship Canal at Duluth, Minn. Duluth entry −0.01 0.35 0.44 −0.80 −0.01 0.03 
Summary 27

Not only do data limitations exist, but structural selections such as segment geometry, the number of vertical layers, 

and the numerical transport scheme can potentially impose 

a bias in the outcome of the model. The grid is an approximation based on the available bathymetry, and the grid cell 

size can impose a bias in the final simulation. In the model 

construction, the final grid geometry was a balance between 

simulating the real conditions while preserving reasonable 

model run times. 

Summary

The St. Louis River estuary is a large freshwater estuary, next to Duluth, Minnesota, that encompasses the 

Lake Superior headwaters. The St. Louis River estuary also is 

one of the most complex and compromised near-shore systems 

in the upper Great Lakes with a long history of environmental contamination caused by logging, mining, paper mills, 

and other heavy industrial activities. Despite its designation 

as a Great Lakes Area of Concern and multiple remediation 

and restoration projects throughout the past several decades, 

a widely available assessment tool capable of evaluating 

ecosystem-level responses to these projects has not existed for 

the estuary.

To address the needs of multiple partners working to 

improve water quality for the estuary, the U.S. Geological 

Survey (USGS) in collaboration with the U.S. Army Corps of 

Engineers, Engineer Research and Development Center, and in 

cooperation with the U.S. Environmental Protection Agency, 

built a predictive, mechanistic, three-dimensional hydrodynamic model for the estuary using the Environmental Fluid 

Dynamics Code (EFDC) framework. The EFDC model solves 

the vertically hydrostatic, free-surface, turbulent-averaged 

equations of motions for a variable-density fluid. EFDC is a 

widely used modeling framework that has been applied in a 

variety of surface-water studies. In the current version, the 

model is capable of simulating continuous discharge, watersurface elevations, water temperature, and flow velocity, 

although the flow velocities were only used as a check rather 

than a model performance target. Also, the modular EFDC 

framework allows for future adaptations to simulate other 

water-quality modeling, such as sediment and nutrients, once 

the appropriate datasets have been collected and processed.

The St. Louis River estuary model was calibrated and 

validated for 2016 and 2017, respectively. Model results 

were compared to measured data collected from three gaging 

stations. The four types of data used to verify model performance were continuous discharge, water-surface elevations, 

water temperature, and flow velocities. Flow and temperature 

Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1 Apr. 1 May 1 June 1 July 1 Aug. 1 Sept. 1 Oct. 1 Nov. 1

−0.20

−0.15

−0.10

−0.05

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Water velocity, in meters per second

−0.05

0

0.05

0.10

0.15

0.20

0.25

2016 2016

B. Superior Bay Entry Channel at Superior, Wisconsin

U.S. Geological Survey station 464226092005600 

EXPLANATION

mad20-2006_fig13ab

A. Superior Bay Duluth Ship Canal at Duluth, Minnesota 

U.S. Geological Survey station 464646092052900 

Simulated, daily

Measured, daily

Figure 13. Daily mean flow velocity for St. Louis River estuary locations, Minnesota-Wisconsin, 2016. Measured and modeled 

data are plotted at the same locations. A, Superior Bay Duluth Ship Canal at Duluth, Minnesota (U.S. Geological Survey [USGS] 

station 464646092052900); B, Superior Bay Entry Channel at Superior, Wisconsin (USGS station 464226092005600).
28 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

boundary condition data included a mixture of USGS 

streamgage data, Minnesota Department of Natural Resources 

gage data, and estimates derived from the gage data.

The model was able to simulate the water-surface elevations with generally good agreement between the simulated 

and measured values for both years at the daily time step but 

only performed an adequate simulation at the hourly time 

step. At the daily time step, the model was able to demonstrate 

excellent agreement with the measured data based on NashSutcliffe efficiency coefficients greater than 0.8 for all three 

gaging station locations. For the mean absolute error and 

root mean square error, the calibration and validation periods 

were at or less than 0.1 meter for the hourly evaluation criteria. For the same two statistics, the daily values were from less 

than 0.04 meter for both years.

Discharge was more dynamic than the water-surface 

elevations, both for the measured and simulated data, although 

the measurement range was wider for all three locations. 

Generally, most of the discharge fell into a range from −650 

to 1,200 cubic meters per second, but the constantly changing 

flux exiting the estuary into Lake Superior (positive flows) 

and entering the estuary from Lake Superior (negative flows) 

occurred throughout the year. Even upstream at the St. Louis 

River at Oliver, Wisconsin, gage (USGS station 0402403250), 

the effect of flows into the estuary from Lake Superior did 

occur, although the effect was subdued. Despite the smaller 

reverse flows at the Oliver gage, these reversals did demonstrate the strong effect of the Lake Superior seiche on flows for 

the estuary.

From a performance standpoint, the model was able to 

simulate discharge with generally good agreement in both 

years, although the 2017 validation was better than the 2016 

calibration period. For the daily Nash-Sutcliffe efficiency 

coefficients, the simulated values were 0.98, 0.62, 0.49, and 

0.71 for the Oliver gage; the Superior Bay entry channel 

at Superior, Wisc. (USGS station 464226092005600); the 

Superior Bay Duluth Ship Canal at Duluth, Minn. (USGS station 464646092052900); and total entries (combination of the 

Superior entry and Duluth entry), respectively. The discharge 

for the total entries was better than the discharge for the two 

individual entries because the model was unable to completely 

distribute the flow according to the measured data. For the 

hourly evaluation criteria, the model performed poorly, with 

Nash-Sutcliffe efficiency coefficients less than 0 for the entries 

into Lake Superior, so as a predictor of discharge at the hourly 

scale, the model performed worse than using the measured 

data average. Similar to discharge, the model was a good predictor of flow velocity at the daily time scale but had difficulty 

matching the measured data at the hourly scale. For discharge 

and flow velocity, matching at subdaily time steps for a system 

as complicated as the St. Louis River estuary is considered difficult because the match is highly sensitive to coordinating the 

exact measurement location to the simulated value.

The final calibration target was water temperature, 

calibrated for the Oliver gage and the Duluth entry. For calibration purposes, the Duluth entry was the more important 

target because the Oliver gage was more of an internal check 

on the model. The Nash-Sutcliffe efficiency coefficient values 

for the Duluth entry were high; hourly Nash-Sutcliffe efficiency coefficients for the Duluth entry were at or greater than 

0.7 for both years, and daily values were 0.84 and 0.82 for 

2016 and 2017, respectively.

References Cited

Anderson, C.R., Niemala, S., Anderson, J., Grayson, S., 

Monson, B., Christopherson, D., Lundeen, B., Jasperson, 

J., Kennedy, M., Parson, K., and Kelly, M., 2013, St. Louis 

River watershed monitoring and assessment report: 

Saint Paul, Minnesota Pollution Control Agency document no. wq–ws3–04010201b, 200 p. [Also available at 

https://www.pca.state.mn.us/sites/default/files/wq-ws3-

04010201b.pdf.]

Blazer, V.S., Hoffman, J., Walsh, H.L., Braham, R.P., Hahn, 

C., Collins, P., Jorgenson, Z., and Ledder, T., 2014, Health 

of white sucker within the St. Louis River area of concern 

associated with habitat usage as assessed using stable 

isotopes: Ecotoxicology (London, England), v. 23, no. 2, 

p. 236–251. [Also available at https://doi.org/10.1007/

s10646-013-1167-5.]

Chow, V.T., Maidment, D.R., and Mays, L.W., 1988, Applied 

hydrology: New York, McGraw-Hill Book Co., 572 p.

Christensen, V.G., Lee, K.E., Kieta, K.A., and Elliott, S.M., 

2012, Presence of selected chemicals of emerging concern 

in water and bottom sediment from the St. Louis River, 

St. Louis Bay, and Superior Bay, Minnesota and Wisconsin, 

2010: U.S. Geological Survey Scientific Investigations 

Report 2012–5184, 23 p. with app. [Also available at 

https://doi.org/10.3133/sir20125184.]

City of Superior, 2019, Section 5—Coastal hazards: Superior, 

Wisc., City of Superior, 20 p., accessed November 4, 2019, 

at https://www.ci.superior.wi.us/DocumentCenter/View/

9005/Section-5-Coastal-Hazard-2015?bidId=.

Craig, P.M., 2017, User’s manual for EFDC_Explorer 8.3—A 

pre/post processor for the Environmental Fluid Dynamics 

Code—DSI, LLC: Washington, Edmonds, 454 p.
References Cited 29

Czuba, C.R., Fallon, J.D., and Kessler, E.W., 2012, Floods 

of June 2012 in northeastern Minnesota: U.S. Geological 

Survey Scientific Investigations Report 2012–5283, 42 p. 

with 3 app. [Also available at https://doi.org/10.3133/

sir20125283.]

Dynamic Solutions, LLC, 2013, Lake Thunderbird report 

for nutrient, turbidity, and dissolved oxygen TMDLs: 

Oklahoma City, Okla., Oklahoma Department of 

Environmental Quality, 306 p. [Also available at 

https://www.epa.gov/sites/production/files/2015-10/

documents/lakethunderbird_ok.pdf.]

Elçi, S., Work, P.A., and Hayter, E.J., 2007, Influence of stratification and shoreline erosion on reservoir sedimentation 

patterns: Journal of Hydraulic Engineering, v. 133, no. 3, 

p. 255–266. [Also available at https://doi.org/10.1061/

(ASCE)0733-9429(2007)133:3(255).]

Esri, 2019, ArcGIS 10.5 software: Esri web page, accessed 

November 4, 2019, at https://www.esri.com/en-us/home.

Great Lakes Interagency Task Force, 2014, Great Lakes 

Restoration Initiative Action Plan II: Great Lakes 

Restoration Initiative,30 p., accessed November 4, 2019, at 

https://www.glri.us/sites/default/files/glri-action-plan-2.pdf.

Hamrick, J.H., 1992, A three-dimensional Environmental 

Fluid Dynamics Computer Code—Theoretical and computational aspects: The College of William and Mary, Virginia 

Institute of Marine Science, Special Report 317, 63 p.

Hamrick, J.H., 2007, The Environmental Fluid Dynamics 

Code user manual, EPA version 1.0: Fairfax, Va., Tetra 

Tech, Inc., 231 p., accessed September 15, 2015, at 

https://www.epa.gov/sites/production/files/2016-01/

documents/efdc_user_manual_epa_ver-101.pdf.

Hayter, E.J., Chapman, R., Luong, P., Lin, L., and Mausolf, 

G., 2015, Focused feasibility study report for 40th Avenue 

project area in the St. Louis River area of concern: Engineer 

Research and Development Center (ERDC) Letter Report 

to the U.S. Army Corps of Engineers—Detroit District, 

42 p., accessed February 3, 2020, at https://www.fws.gov/

midwest/TwinCities/ec/pdf/40th%20Avenue%20West%20

FFS%20Appendix%20N%20-%20Sediment%20

Transport%20Modeling.pdf.

Hyndman, R.J., and Koehler, A.B., 2006, Another look at 

measures of forecast accuracy: International Journal of 

Forecasting, v. 22, no. 4, p. 679–688. [Also available at 

https://doi.org/10.1016/j.ijforecast.2006.03.001.]

Ji, Z.-G., 2017, Hydrodynamics and water quality—

Modeling rivers, lakes, and estuaries 2nd ed.: Hoboken, 

N.J., John Wiley and Sons, 617 p.

Ji, Z.-G., Morton, M.R., and Hamrick, J.H., 2004, Modeling 

hydrodynamic and water quality processes in a reservoir, in

Spaulding, M.L., ed., Proceedings of the 8th International 

Conference: Monterey, Calif., Estuarine and Coastal 

Modeling, p. 608–627. [Also available at https://doi.org/

10.1061/40734(145)38.]

Juston, J., Seibert, J., and Johansson, P.O., 2009, Temporal 

sampling strategies and uncertainty in calibrating a conceptual hydrological model for a small boreal catchment: 

Hydrological Processes, v. 23, no. 21, p. 3093–3109. [Also 

available at https://doi.org/10.1002/hyp.7421.]

Lake Superior Streams, 2019, Lake Superior Duluth streams: 

Lake Superior Streams web page, accessed November 4, 

2019, at https://www.lakesuperiorstreams.org/.

Legates, D.R., and McCabe, G.J., Jr., 1999, Evaluating the use 

of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation: Water Resources Research, v. 35, 

no. 1, p. 233–241. [Also available at https://doi.org/10.1029/

1998WR900018.]

Levesque, V.A., and Oberg, K.A., 2012, Computing discharge 

using the index velocity method: U.S. Geological Survey 

Techniques and Methods, book 3, chap. A23, 148 p. [Also 

available at https://doi.org/10.3133/tm3A23.]

Lindgren, J., Schuldt, N., Borkholder, B., Howes, T., Levar, 

A., Olson, C., Tillma, J., and Vogt, D., 2006, A study of 

the St. Louis River: Minnesota Department of Natural 

Resources, Section of Fisheries Completion Report 

F–29–R(P)–25, 153 p.

Lindholm, G.F., Ericson, D.W., Broussard, W.L., and 

Hult, M.F., 1979, Water resources of the St. Louis River 

watershed, northeastern Minnesota: U.S. Geological 

Survey Hydrologic Atlas 586, 3 pls. [Also available at 

https://doi.org/10.3133/ha586.]

Mausolf, G.M., 2014, Numerical modeling and sediment 

transport analysis for 21st Ave West Section 204 study in 

St. Louis Bay off Lake Superior in Duluth, WI: U.S. Army 

Corps of Engineers Hydraulic and Hydrology Technical 

Memorandum, 38 p.

Minnesota Department of Natural Resources [MN DNR], 

2019a, Site report—Mission Creek nr Fond du Lac, 1mi 

us of MN23 (03010003): MN DNR web page, accessed 

November 9, 2019, at https://www.dnr.state.mn.us/waters/

csg/site_report.html?mode=get_site_report&site=03010003.

Minnesota Department of Natural Resources [MN DNR], 

2019b, Site report—Merritt Creek at Duluth, Grand Ave 

(03163011): MN DNR web page, accessed November 9, 

2019, at https://www.dnr.state.mn.us/waters/csg/site_

report.html?mode=get_site_report&site=03163011.
30 Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary

Minnesota Department of Natural Resources [MN DNR], 

2019c, Site report—Miller Creek at Duluth, S 24th Ave W 

(03001012): MN DNR web page, accessed November 9, 

2019, at https://www.dnr.state.mn.us/waters/csg/site_

report.html?mode=get_site_report&site=03001012.

Minnesota Department of Natural Resources [MN DNR], 

2019d, Measuring hydrology—Measuring stream flow: 

MN DNR web page, accessed December 5, 2019, at 

https://www.dnr.state.mn.us/whaf/about/5-component/

hydro_measure.html.

Minnesota Pollution Control Agency [MPCA], 2018, 

St. Louis River Watershed Restoration and Protection 

Strategy Report: Minnesota Pollution Control Agency 

WQ–WS4–46A, St. Paul, Minn., 205 p. [Also available 

at https://www.pca.state.mn.us/sites/default/files/wq-ws4-

46a.pdf.]

Mueller, D.S., Wagner, C.R., Rehmel, M.S., Oberg, K.A., 

and Francois, R., 2008, Measuring discharge with acoustic Doppler current profilers from a moving boat (ver. 2.0, 

December 2013): U.S. Geological Survey Techniques 

and Methods, book 3, chap. A22, 86 p. [Also available at 

https://doi.org/10.3133/tm3A22.]

Nash, J.E., and Sutcliffe, I.V., 1970, River flow forecasting 

through conceptual models, Part 1—A discussion of principles: Journal of Hydrology (Amsterdam), v. 10, no. 3, 

p. 282–290. [Also available at https://doi.org/10.1016/0022-

1694(70)90255-6.]

National Climatic Data Center, 2018, Climate data online: 

National Oceanic and Atmospheric Administration web 

page, accessed April 14, 2018, at https://www.ncdc.noaa.

gov/cdo-web/.

National Data Buoy Center [NDBC], 2019, Station 45028—

Western Lake Superior: accessed December 5, 2019, at 

https://www.ndbc.noaa.gov/station_page.php?station=

45028.

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

of streamflow—Volume 1. Measurement of stage and discharge: U.S. Geological Survey Water-Supply Paper 2175, 

v. 1, 313 p. [Also available at https://pubs.usgs.gov/wsp/

wsp2175/.]

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

of streamflow—Volume 2. Computation of discharge: U.S. 

Geological Survey Water-Supply Paper 2175, v. 2, 373 p. 

[Also available at https://pubs.usgs.gov/wsp/wsp2175/.]

Rendon, S.H., and Lee, M.T., 2015, Simulation of the

effects of different inflows on hydrologic conditions in 

Lake Houston with a three-dimensional hydrodynamic 

model, Houston, Texas, 2009–10: U.S. Geological 

Survey Scientific Investigations Report 2015–5153, 42 p., 

accessed October 18, 2018, at https://doi.org/10.3133/

sir20155153.

Robertson, D.M., and Saad, D.A., 2011, Nutrient inputs 

to the Laurentian Great Lakes by source and watershed 

estimated using SPARROW watershed models: Journal of 

the American Water Resources Association, v. 47, no. 5, 

p. 1011–1033. [Also available at https://doi.org/10.1111/

j.1752-1688.2011.00574.x.]

R.T.I. International, 2013, St. Louis River estuary TMDL 

project—Preliminary EFDC-WASP modeling report: 

RTI International, Research Triangle Park, NC, 49 p.

Ruhl, J.F., 1989, Water resources of the Fond du Lac Indian 

Reservation, east-central Minnesota: U.S. Geological 

Survey Water-Resources Investigations Report 88–4114, 

42 p. [Also available at https://doi.org/10.3133/wri884114.]

Smith, E.A., 2020, St. Louis River Estuary (MinnesotaWisconsin) EFDC hydrodynamic model for discharge and 

temperature simulations, 2016–17: U.S. Geological Survey 

data release, https://doi.org/10.5066/P990OUS6.

Smith, E.A., Sanocki, C.A., Lorenz, D.L., and Jacobsen, K.E., 

2017, Streamflow distribution maps for the Cannon River 

drainage basin, southeast Minnesota, and the St. Louis 

River drainage basin, northeast Minnesota: U.S. Geological 

Survey Scientific Investigations Map 3390, pamphlet 16 p., 

2 sheets, accessed September 25, 2019, at https://doi.org/

10.3133/sim3390.

Smith, E.A., Kiesling, R.L., Ziegeweid, J.R., Elliott, S.M., and 

Magdalene, S., 2018, Simulation of hydrodynamics, water 

quality, and lake sturgeon habitat volumes in Lake St. Croix, 

Wisconsin and Minnesota, 2013: U.S. Geological Survey 

Scientific Investigations Report 2017–5157, 60 p., accessed 

September 25, 2019, at https://doi.org/10.3133/sir20175157.

SonTek, 2019, SonTek-SL series: SonTek web page, accessed 

December 5, 2019, at https://www.sontek.com/sonteksl-series.

Sorensen, J., Sydor, M., Huls, H., and Costello, M., 2004, 

Analyses of Lake Superior seiche activity for estimating 

effects on pollution transport in the St. Louis River estuary 

under extreme conditions: Journal of Great Lakes Research, 

v. 30, no. 2, p. 293–300. [Also available at https://doi.org/

10.1016/S0380-1330(04)70347-0.]
References Cited 31

St. Louis River Estuary, 2019, St. Louis River Estuary—

The stories and the science: St. Louis River Estuary 

web page, accessed November 4, 2019, at 

http://stlouisriverestuary.org/.

Tetra Tech, 2016, St. Louis, Cloquet, and Nemadji River basin 

models–volume 1—Hydrology and sediment model calibration: Minnesota Pollution Control Agency Final Report 

(February 4, 2016), 256 p.

Trebitz, A.S., 2006, Characterizing seiche and tide-driven 

daily water level fluctuations affecting coastal ecosystems 

of the Great Lakes: Journal of Great Lakes Research, v. 32, 

no. 1, p. 102–116. [Also available at https://doi.org/10.3394/

0380-1330(2006)32[102:CSATDW]2.0.CO;2.]

U.S. Environmental Protection Agency [EPA], 2014, 

Bathymetry interpolation for the St. Louis River estuary work order RSGISMED046: Duluth, Minn., U.S. 

Environmental Protection Agency Office of Research and 

Development, 9 p.

U.S. Geological Survey [USGS], 2013, Federal Standards and 

Procedures for the National Watershed Boundary Dataset 

(WBD) (4th ed.): Techniques and Methods, book 11, 

chap. A3, 63 p., accessed September 25, 2019, at 

https://doi.org/10.3133/tm11A34.

U.S. Geological Survey, [USGS], 2020, USGS surface-water 

data for Minnesota in USGS water data for the Nation: 

U.S. Geological Survey National Water Information System 

database, accessed February 3, 2020, at https://doi.org/

10.5066/F7P55KJN. [Site information directly accessible at https://waterdata.usgs.gov/mn/nwis/uv/?referred_

module=sw.]

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, book 1, chap. D3, 51 p., 

8 attachments. [Also available at https://doi.org/10.3133/

tm1D3.]

Wilks, D.S., 1995, Statistical methods in the atmospheric 

sciences—An introduction: San Diego, Calif., Academic 

Press, 467 p.

Yapo, P.O., Gupta, H.V., and Sorooshian, S., 1996, Automatic 

calibration of conceptual rainfall-runoff models—

Sensitivity to calibration data: Journal of Hydrology 

(Amsterdam), v. 181, no. 1–4, p. 23–48. [Also available at 

https://doi.org/10.1016/0022-1694(95)02918-4.]

For more information about this publication, contact:

Director, Upper Midwest Water Science Center

U.S. Geological Survey

2280 Woodale Drive

Mounds View, MN 55112

763–783–3100

For additional information, visit: 

https://www.usgs.gov/centers/umid-water

Publishing support provided by the Rolla and Madison 

Publishing Service Centers
Smith and others—Simulation of Discharge, Water-Surface Elevations, and Water Temperatures for the St. Louis River Estuary, 2016–17—SIR 2020–5028

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20205028