Prepared in Cooperation with the Great Lakes Commission

Uncertainty in the Great Lakes Water Balance

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2004-5100
Cover Photograph. Lake Michigan beach near Petoskey, Michigan. 

(Photograph courtesy of Travel Michigan.)
Uncertainty in the Great Lakes Water 

Balance

By Brian P. Neff and J.R. Nicholas

Prepared in cooperation with the Great Lakes Commission

Scientific Investigations Report 2004-5100

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

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reproduce any copyrighted materials contained within this report.

Suggested citation: 

Neff, Brian P. , and Nicholas, J.R., 2005, Uncertainty in the Great Lakes Water Balance: 

U.S. Geological Survey Scientific Investigations Report 2004-5100, 42 p.
Contents

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

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

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

Geographic and Hydrologic Setting ............................................................................................................................... 2

Components of the Great Lakes Water Balance ................................................................................................................. 4

Inflows............................................................................................................................................................................. 4

Over-Lake Precipitation.............................................................................................................................................. 6

Runoff ......................................................................................................................................................................... 6

Ground-Water Discharge ............................................................................................................................................ 6

Diversions................................................................................................................................................................... 6

Outflows.......................................................................................................................................................................... 6

Connecting-Channel Flow .......................................................................................................................................... 6

Lake Superior Outflow............................................................................................................................................ 6

Lakes Michigan-Huron Outflow............................................................................................................................. 7

Lake Erie Outflow................................................................................................................................................. 11

Lake Ontario Outflow ........................................................................................................................................... 11

Evaporation............................................................................................................................................................... 12

Diversions................................................................................................................................................................. 17

Consumptive Use ...................................................................................................................................................... 19

Change in Storage......................................................................................................................................................... 19

Methods for Quantifying Components and Potential Uncertainties................................................................................. 19

Inflows........................................................................................................................................................................... 21

Over-Lake Precipitation............................................................................................................................................ 21

Runoff ....................................................................................................................................................................... 23

Gaged Areas.......................................................................................................................................................... 23

Ungaged Areas...................................................................................................................................................... 25

Uncertainty In Total-Runoff Calculations ............................................................................................................ 25

Ground-Water Discharge .......................................................................................................................................... 25

Diversions................................................................................................................................................................. 26

Outflows........................................................................................................................................................................ 26

Connecting-Channel Flow ........................................................................................................................................ 26

Lake Superior Outflow.......................................................................................................................................... 26

Lakes Michigan-Huron Outflow........................................................................................................................... 27

Lake Erie Outflow................................................................................................................................................. 28

Lake Ontario Outflow ........................................................................................................................................... 30

Evaporation............................................................................................................................................................... 30

Diversions................................................................................................................................................................. 31

Change in storage.......................................................................................................................................................... 32

Current Approaches to Deriving Net Basin Supply.......................................................................................................... 34

Component NBS....................................................................................................................................................... 35

Residual NBS............................................................................................................................................................ 35

Relative Magnitude of Uncertainties in NBS Estimates........................................................................................... 35

Summary and Conclusions ............................................................................................................................................... 39

Acknowledgments......................................................................................................................................................... 39

References Cited ............................................................................................................................................................... 40

iii
Figures

1-2. Maps showing:

1. The Great Lakes and connecting channels ......................................................................................................3

2. Isostatic rebound in the Great Lakes Basin .....................................................................................................5

3. Graph showing:

3. Components of Great Lakes inflows and outflows ..........................................................................................7

4-12. Maps showing:

4. Ogoki diversion near Thunder Bay, Ontario ....................................................................................................8

5. Long Lac diversion near Terrace Bay, Ontario ................................................................................................9

6. St. Marys River near the twin cities of Sault Ste. Marie, Ontario, and Michigan .........................................10

7. Soo Navigation Locks at Sault Ste. Marie, Ontario, and Michigan ..............................................................11

8. Straits of Mackinac, Michigan ......................................................................................................................12

9. St. Clair River near St. Clair, Michigan .........................................................................................................13

10. Detroit River near Detroit, Michigan .............................................................................................................14

11. Welland Canal diversion, Ontario ..................................................................................................................15

12. The New York State Barge Canal near Buffalo, New York ...........................................................................16

13. Diagram showing:

13. Flow pattern from Lake Erie to Lake Ontario ...............................................................................................17

14. Map showing:

14. St. Lawrence River downstream from Kingston, Ontario, to Lake St. Francis .............................................18

15. Graph showing:

15. Monthly evaporation rates of Lake Superior .................................................................................................19

16-19. Maps showing:

16. Chicago diversion near Chicago, Illinois ......................................................................................................20

17. Weather stations in the Great Lakes Basin ....................................................................................................22

18. Stream-gage locations in the Great Lakes Basin ...........................................................................................24

19. Locations of lake level gages in the Great Lakes Basin... ............................................................................33

20-21. Graphs showing:

20. Total uncertainty in monthly net basin supply estimates for each method and each 

Great Lake, expressed as flow rate ................................................................................................................38

21. Potential range of percentage uncertainty in monthly net basin supply estimates for

 each method and each Great Lake ................................................................................................................38

iv
Tables

1. State of Illinois annual diversion flows. ..........................................................................................................21

2. Percentage of Great Lakes Basin area that is ungaged....................................................................................25

3. Summary of monthly component and net basin supply (NBS) uncertainty for Lake Superior.......................36 

4. Summary of monthly component and net basin supply (NBS) uncertainty for Lakes Michigan-Huron........36

5. Summary of monthly component and net basin supply (NBS) uncertainty for Lake Erie..............................37

6. Summary of monthly component and net basin supply (NBS) uncertainty for Lake Ontario. .......................37

7a. Summary of net basin supply (NBS) uncertainty, expressed as a percent of long term average 

monthly NBS...................................................................................................................................................38

7b. Summary of net basin supply (NBS) uncertainty, expressed in cubic feet per second ...................................38

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

foot (ft) 304.8 millimeter (mm)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic mile (mi3) 4.168 cubic kilometer (km3) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Temperature in degrees Celsius (

Temperature in degrees Fahrenheit (

v

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

°C=(°F-32)/1.8

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

°F=(1.8×°C)+32

.
Abbreviations and Acronyms

ADCP – Acoustic Doppler Current Profiler

AVM – Acoustic Velocity Meter

BOM – Beginning-of-Month 

Coordinating Committee – Coordinating Committee for Great Lakes Basic Hydraulic and Hydrologic Data 

(CCGLBHHD)

CSSC – Chicago Sanitary and Ship Canal

IJC – International Joint Commission

MEDS – Marine Environmental Data Service

MRCC – Midwestern Regional Climate Center

MSC – Meteorological Survey of Canada (formerly known as the Water Survey of Canada)

NBS – Net Basin Supply

NOAA – National Oceanic and Atmospheric Administration

NOS – U.S. National Ocean Service (a division of NOAA)

NWS – U.S. National Weather Service

NYPA – New York Power Authority

OPG – Ontario Power Generation 

TSC2 – Technical Subcommittee 2 

WRMDSS – Water Resources Management Decision Support System 

vi
Abstract

This report describes the Great Lakes hydrologic system 

and methods used to quantify individual components of the 

water balance. Potential sources of uncertainty are identified 

and, where appropriate, alternate or additional data, models, 

and estimation methods suitable for reducing uncertainties are 

discussed. Finally, approximate uncertainties of all components are identified, compared, and assessed within the context 

of net basin supply. Results indicate that average uncertainties 

in monthly estimates of individual water-balance components 

may range from 1.5 percent to 45 percent. These uncertainties 

may cause uncertainties in monthly net basin supply estimates 

of approximately 2,600 ft3/s to 33,500 ft3/s for individual Great 

Lakes. 

Introduction 

The Great Lakes are a profound element of the North 

American continent. Resources within and around these lakes 

are important to the cultural heritage of the continent, are 

esthetically pleasing, and support thriving economies based 

largely on recreation and manufacturing. Additionally, the 

Great Lakes and their connecting channels are essential watersupply and power-generating resources that support extensive 

economic and urban development throughout the region. 

The Great Lakes are an immense hydrologic system. To 

gain some perspective of their size, consider that the water 

contained in the Great Lakes could cover the continents of 

North America, South America, and Africa to a depth of more 

than 1 ft. Additionally, the bottom of Lake Superior is 731 ft 

below sea level. Water entering Lake Superior will take an 

estimated 191 years to travel to Lake Huron (Government of 

Canada and U.S. Environmental Protection Agency, 1995, 

p. 3). The surface of the Great Lakes spans approximately 

7.5 degrees of latitude, or nearly 575 mi. This is roughly equal 

to the same latitudinal change between the cities of Cleveland, 

Ohio, and Atlanta, Georgia. Longitudinally, the Great Lakes 

extend 16 degrees, or approximately 900 mi. The volume and 

surface size of the lakes have significant implications with 

regard to variability in the hydrologic system throughout the 

Great Lakes region.

Coping with fluctuating lake levels is an unavoidable 

facet of living and working on or near the Great Lakes. Rising 

and falling lake levels affect shipping, recreational boating, 

and water supply, and damage coastline through flooding and 

erosion. To minimize the damage resulting from fluctuating 

lake levels, decision makers must understand the processes 

that cause these fluctuations and manage activities accordingly. One way to evaluate these processes is to study the 

water balance of the Great Lakes.

A water balance is an accounting of all water entering and leaving a given body of water, for a given period of 

time. Mathematically, this can be expressed as “inflow equals 

outflow plus change in storage”. A water balance is quantified through the evaluation and accounting of these three 

components. Researchers have quantified water balances for 

many decades, and hundreds of water-balance studies have 

been done. However, uncertainties vary dramatically in water 

balances and are not addressed in most studies. For a review of 

recent literature on the subject, the reader is directed to Xu and 

Singh (1998).

One useful application of the water-balance approach is 

to quantify net basin supply (NBS) – the net amount of water 

entering each Great Lake, not counting the supply of water 

from upstream Great Lakes. One feature of NBS is that it 

can be computed two ways, by the component method or the 

residual method (Croley and others, 2001; Lee, 1992). Each 

method allows the researcher some freedom to evaluate select 

hydrologic parameters to derive NBS, an important feature for 

assessing uncertainty in current Great Lakes NBS estimates.

Flows into and out of the Great Lakes and the levels 

of the lakes are measured or calculated at hundreds of locations throughout the basin. Although lake levels are measured 

directly, most flows are based on estimates or measurements 

of other parameters and are computed using simple equations. 

Many agencies maintain a current understanding of the Great 

Lakes-St. Lawrence System through continuous and long-term 

monitoring. Funding sources for monitoring are diverse, ranging from federal governments to state, provincial, and municipal agencies and the private sector.

In this study, the term “uncertainty” is used qualitatively 

to describe errors and biases associated with measurements, 

calculations, and estimates. All measurements and calculations 

have uncertainty associated with them. Uncertainty does not 

necessarily indicate errors or flaws in monitoring. In some 

cases, uncertainty in a measurement or calculation may be 

present despite state-of-the-art instrumentation or estimation 

Uncertainty in the Great Lakes Water Balance

By Brian P. Neff and J. R. Nicholas
2 Uncertainty in the Great Lakes Water Balance

methods. In other cases, uncertainty may be reduced by additional monitoring or by application of more advanced instrumentation and estimation methods. The degree of uncertainty 

can vary as a function of the magnitude of physical process 

being measured, calculated, or estimated.

In June 2001, eight U.S. state governors and two Canadian province premiers signed an Annex to the 1985 Great 

Lakes Charter. Annex 2001 calls for, among other things, 

hydrologic data and information to support a new decision 

standard regarding proposals to withdraw water from the Great 

Lakes Basin. Uncertainty in calculations of flows and levels is 

closely linked to Great Lakes Charter Annex issues. If part of 

the system is poorly understood—has high uncertainty—then 

predicting the effects of a proposed withdrawal on flows, levels, and the ecosystem will be difficult. Conversely, if part of 

the system is well understood, then effects of a withdrawal on 

levels or flows can be predicted and used to evaluate ecological impacts. Current (2004) monitoring networks were not 

designed for the specific purpose of providing such decision 

support. The U.S. Geological Survey, in cooperation with the 

Great Lakes Commission, conducted a study to assess uncertainty in the Great Lakes water balance and address important 

questions regarding the status of existing hydrologic monitoring networks. Information from the study can help managers 

determine the usefulness of existing monitoring networks to 

Annex 2001 issues. 

Purpose and Scope

The purpose of this report is to describe uncertainty in the 

Great Lakes water balance. Specifically, this report

• describes the Great Lakes hydrologic system,

• describes how water-balance components are 

quantified,

• identifies potential sources of uncertainty in these 

estimates,

• determines the approximate uncertainty in estimates of individual components,

• compares uncertainties of each component, and

• evaluates how these uncertainties affect the reliability of NBS estimates.

There are no published uncertainty calculations associated with most of the flows and levels of the Great Lakes. 

Therefore, TSC2 used its best professional judgment to 

estimate ranges of uncertainty for flows and levels. These 

ranges are presented for the purpose of illustrating how well 

the hydrology of the Great Lakes-St. Lawrence System is 

understood.

Throughout this report, uncertainties are discussed within 

the context of monthly data and monthly NBS estimates. This 

context is used because the Great Lakes water balance is most 

commonly described on a monthly time scale, to calculate NBS. 

It is not known if monthly data, or if the concept of NBS, is well 

suited to the information needs of Annex 2001.

This report is a product of Technical Subcommittee 2 

(TSC2) of the Water Resources Management Decision Support 

System (WRMDSS) project supported by the Great Lakes Protection Fund. TSC2 was charged with providing a status assessment 

of water-resources information and availability. Most of the work 

of TSC2 was designed to evaluate the quantity and quality of 

water-resources data and information on a lakewide or systemwide scale. Specifically, the work and other publications resulting 

from TSC2 focused on flows and levels in the context of net basin 

supplies to each Great Lake. Additional information is available 

from two other project reports: “The Great Lakes Water Balance: Data Availability and Annotated Bibliography of Selected 

References” (Neff and Killian, 2003) and “Great Lakes Monthly 

Hydrologic Data” (Croley and others, 2001).

Geographic and Hydrologic Setting

The Great Lakes-St. Lawrence System comprises (1) Lakes 

Superior, Michigan, Huron, Erie, and Ontario, (2) their connecting channels, St. Marys River, St. Clair River, Lake St. Clair, 

Detroit River, and Niagara River, and (3) the St. Lawrence River, 

which carries the waters of the Great Lakes to the Atlantic Ocean 

(fig. 1). The system also includes several constructed canals and 

control structures that either interconnect Great Lakes or connect 

the Great Lakes to other river systems. The Great Lakes Basin, 

including the international section of the St. Lawrence River 

upstream from Cornwall, Ontario/Massena, New York, covers 

about 295,000 mi2. The basin includes parts of eight U.S. states 

and one Canadian province: Minnesota, Wisconsin, Illinois, 

Indiana, Michigan, Ohio, Pennsylvania, New York, and Ontario. 

Fifty-nine percent of the basin is in the United States; 41 percent 

is in Canada. The basin is about 700 mi long measured north to 

south and about 900 mi long measured west to east, at the outlet 

of Lake Ontario at Cornwall, Ontario/Massena, New York. The 

St. Lawrence River downstream from Cornwall, Ontario/Massena, New York, is about 540 mi long and flows through the state 

of New York and provinces of Ontario and Quebec.

In 1990, the population of the Great Lakes Basin was about 

33 million, not including Chicago. About 52 percent of the basin 

is forested; 35 percent is in agricultural uses; 7 percent is urban/

suburban; and 6 percent is in other uses. Major commerce and 

industries in the Great Lakes Basin are manufacturing, tourism, 

and agriculture, at about $308 billion, $82 billion, and $48 billion 

U.S. per year, respectively (Great Lakes Commission, 2003, 

p. 28).

Dredging, control structures, locks, dams, hydroelectric 

facilities, canals, and diversions have altered the hydrology of the 

Great Lakes-St. Lawrence System. Dredging and control structures have had the largest impacts. For instance, the dredging of 

the St. Clair River from 1880 to 1965 permanently lowered Lake 

Michigan and Lake Huron by 15.8 in (International Joint Commission, 1999). Control structures at the outlets of Lake 
 3

O N T A R I O

90 80

45

50

0 0

0

0

Base from ESRI, 2001; U.S. Army Corps of Engineers,1998; and Environment Canada,1995.

Q U E B E C

LAKE

HURON

LAKE

ERIE

LAKE

ONTARIO

LAKE SUPERIOR

LA

KE

MICHIGAN

ILLINOIS

INDIANA OHIO

PENNSYLVANIA

NEW

YORK

W I S C O N S I N

0 50 100 150 200 KILOMETERS

0 50 100 150 200 MILES

JAMES

BAY 

CANADA

U. S. A.

CANADA

U. S. A.

M I C H I

G

A

N

St. Lawrence River

St. Marys 

River

St. Clair 

 River

Detroit 

River

Niagra River

Straits of Mackinac

Figure 1. The Great Lakes and connecting channels.

GREAT LAKES BASIN

EXPLANATION

Lake

St. Clair

 Introduction
4 Uncertainty in the Great Lakes Water Balance

Superior and Lake Ontario keep the levels of these lakes regulated within a range that is smaller than the range of levels that 

would occur under natural outflow conditions.

The Great Lakes and their connecting channels cover 

approximately 32 percent of the entire Great Lakes-St. Lawrence River Basin upstream from Cornwall/Massena. The 

volume of each Great Lake and the land and water area of 

their individual basins are varied. For example, total area of 

the Lake Superior Basin is 81,000 mi2. Surface area of Lake 

Superior is 31,700 mi2, or 39 percent of its entire basin area. 

In contrast, surface area of Lake Ontario, 7,340 mi2, is only 23 

percent of the Lake Ontario Basin (Coordinating Committee on 

Great Lakes Basic Hydraulic and Hydrologic Data,1 1977). The 

proportion of a lake’s basin that consists of lake surface directly 

affects the amount and timing of over-lake precipitation and 

runoff from the basin’s tributary streams, as well as the amount 

of water lost from the lake surface through evaporation.

The climate of the Great Lakes Basin varies widely according to its long north-south extent and the effects of the Great 

Lakes on nearshore temperatures and precipitation. Precipitation is distributed relatively uniformly throughout the year, but 

it is variable from west to east across the basin. Mean annual 

snowfall is much more variable because of temperature differences from north to south and in snowbelt areas near the east 

side of the Great Lakes. Also, wind is an important component 

of the Great Lakes climate. During all seasons, the predominant 

wind direction has a westerly component. In fall and winter, 

very strong winds are common in nearshore areas, driven in part 

by temperature difference between the lakes and the air moving 

over them.

Fluctuations in Great Lakes water levels result from several 

natural factors and human influences. Levels of the Great Lakes 

depend on their storage capacity, outflow characteristics of the 

outlet channels, operating procedures of the regulatory structures, and the amount of water supply received by each lake. 

The primary natural factors affecting lake levels are over-lake 

precipitation, runoff from the drainage basin, evaporation from 

the lake surface, inflow from upstream lakes, and outflow to 

downstream lakes. Human factors include diversions into or out 

of the basin, consumption of water, dredging of outlet channels, 

and regulation of outflows.

There are three types of water-level fluctuations on the 

Great Lakes. First are long-term fluctuations, occurring on a 

time scale of many years, which result from persistent low or 

high water supplies. Second are seasonal fluctuations of the 

Great Lakes levels, occurring on a sub-annual time scale, which 

reflect variation in the annual hydrologic cycle. Seasonal waterlevel fluctuations are characterized by higher NBS during spring 

and early summer and lower NBS during the remainder of the 

year. Third are short-term fluctuations in water-level (lasting 

from a less than an hour to several days) that happen as water 

levels rise (set-up), fall (set-down), or oscillate (seiche) due to 

effects of wind and differences in barometric pressure over the lake 

surface. 

Short-term changes in outflows can result from storm surge or 

seiches. Storm surge, or wind set-up, is the phenomenon of a local 

rise in water level caused by winds pushing water to the downwind 

side of a lake. Seiche is a distinct phenomenon resulting when 

water levels of the lake oscillate as water rushes back and forth 

across the lake in response to sudden weather changes, such as in 

wind direction and barometric pressure (Manninen and Gauthier, 

1999; Government of Canada and U.S. Environmental Protection 

Agency, 1995). If water levels increase at the outlet end of the lake, 

outflows can temporarily increase. In contrast, if levels decline at 

the outlet end of the lake, outflows can be reduced. 

Ice formation and ice jams slow streamflow in outlet rivers 

of the lakes during winter. These conditions are not predictable for 

any specific winter, either as to severity or exact timing of their 

occurrence. Aquatic plant growth in the rivers during summer also 

slows outflow. This process varies from river to river.

Over time, water levels throughout the Great Lakes also are 

affected by isostatic rebound. Isostatic rebound is a gradual rising 

of the Earth’s crust caused by the removal of relatively heavy glaciers that once covered the Great Lakes-St. Lawrence River region. 

Rates of isostatic rebound are not uniform; generally, rates of 

rebound around Lakes Superior and Ontario are greater than those 

around Lakes Michigan-Huron and Erie. Water levels are affected 

as lake basins tilt by a gradual rising of their northeastern rims. 

As time progresses, water levels along shores south and west of a 

lake’s outlet are rising with respect to overall average lake level, 

whereas water levels along shores north and east of the outlet are 

receding with respect to land (fig. 2).

Components of the Great Lakes Water 

Balance 

Before beginning a detailed discussion on quantification 

of water-balance components and their potential uncertainties, a 

thorough qualitative description of each component of the water 

balance is in order. 

Inflows

In this report, the term “inflows” refers to water entering each 

Great Lake. Inflows include (1) over-lake precipitation, (2) runoff, 

(3) ground-water seepage into the Great Lakes, (4) diversion of 

water into the Great Lakes, and (5) flow from the connecting channels. As expressed mathematically, 

Inflows = P + R + GWin + Din + CCin, (1)

where P is precipitation falling directly on the lake, R is runoff, 

GWin is ground-water inflow (net discharge), Din is diversions into 

the Great Lakes, and CCin is connecting-channel inflow. Connecting-channel inflow is discussed in the outflows section. 1

The Coordinating Committee for Great Lakes Basic Hydraulic and 

Hydrologic Data (CCGLBHHD) will be referred to hereafter as simply the 

“Coordinating Committee.”
 5

Figure 2. Isostatic rebound in the Great Lakes Basin. (Adapted from Clark and Persoage, 

1970, Larsen, 1987.)

O N T A R I O

90 80

45

50

0 0

0

0

Base from ESRI, 2001; U.S. Army Corps of Engineers,1998; and Environment Canada,1995.

Q U E B E C

LAKE

HURON

LAKE

ERIE

LAKE

ONTARIO

LA

KE

MICHIGAN

ILLINOIS

INDIANA OHIO

PENNSYLVANIA

NEW

YORK

W I S C O N S I N

0 50 100 150 200 KILOMETERS

0 50 100 150 200 MILES

JAMES

BAY 

GREAT LAKES BASIN

EXPLANATION

CANADA

U. S. A.

CANADA

U. S. A.

M I C

H I

G

A

N

Chicago

Duluth

Toronto

Buffalo

Detroit

Sault Ste. Marie

Michipicoten

1.25

1.50

0.75

0.5

0.25

0

1.75

Cleveland

Thunder

Bay

ISOSTATIC REBOUND, IN FEET

PER CENTURY. Contour interval

0.25 foot, dashed where approximately

located

1.00

LAKE SUPERIOR

Lake

St. Clair

Components of the Great Lakes Water Balance 
6 Uncertainty in the Great Lakes Water Balance

Over-Lake Precipitation

In many water-balance studies, precipitation falling 

directly on the surface of a water body is a negligible component of the hydrologic cycle. However, the Great Lakes cover 

an area of approximately 94,250 mi2, about one-third of the 

total area of the Great Lakes Basin (Coordinating Committee, 1977). According to data presented by Croley and others 

(2001), the amount of water that falls directly on the surface of 

the Great Lakes is greater than all of the water that enters the 

lakes through runoff (fig. 3). 

Runoff 

Much of the precipitation that falls in the Great Lakes 

Basin drains into streams that discharge into the lakes. Thousands of streams drain approximately 200,000 mi2

 of land area 

and feed directly into the Great Lakes. Direct overland flow 

to the Great Lakes also is a component of runoff. According 

to data presented by Croley and others (2001), the amount of 

water that enters the Great Lakes as runoff is slightly less than 

the amount of water that enters the lakes through over-lake 

precipitation (fig. 3).

Ground-Water Discharge

Some of the precipitation that falls on the Great Lakes 

Basin land area infiltrates the soil and becomes ground water. 

Most ground water flows to and discharges into the many tributary streams to the Great Lakes. Some of this ground water, 

however, discharges directly into the Great Lakes through the 

lakebed. A few estimates of ground-water discharge into the 

Great Lakes have been made, and these are summarized by 

Grannemann and Weaver (1999).

Diversions 

Two large diversions of water into the Great Lakes 

constitute a significant part of the water balance. The Ogoki 

and Long Lac diversions redirect water that would normally 

flow into Hudson Bay by way of the Albany River to the Lake 

Superior Basin (figs. 4 and 5). The Ogoki diversion moves 

water through the Little Jackfish River, Lake Nipigon, and 

the Nipigon River into Lake Superior at a point 60 mi east 

of Thunder Bay. Three hydroelectric plants on the Nipigon 

River use this diverted water to generate power. The Long Lac 

diversion redirects water through Long Lake and the Aguasabon River into Lake Superior near Terrace Bay. The Long Lac 

diversion provides water for a hydroelectric plant near Terrace 

Bay and for pulpwood-log conveyance down the river. The 

Ogoki diversion redirects a drainage basin more than 3 times 

larger than that of the Long Lac diversion. Together, the Long 

Lac and Ogoki diversions increase water supply to the Lake 

Superior Basin by about 5,580 ft3/s. These two diversions into 

the Great Lakes Basin are more than 60 percent greater than 

all current diversions out of the Great Lakes Basin (International 

Joint Commission, 1999, p. 10). Other diversions of water into the 

Great Lakes Basin are relatively small and not discussed herein 

(International Joint Commission, 1999, p. 10). 

Outflows

In this report, “outflows” refers to water leaving each Great 

Lake by way of (1) evaporation, (2) flow through connecting 

channels, (3) diversion of water away from the Great Lakes, and 

(4) consumptive use of Great Lakes water. Consumptive use is 

water withdrawn or withheld from the Great Lakes Basin and not 

returned. As expressed mathematically, 

 Outflows = CCout + E + Dout +Cuse (2)

Where CCout is connecting-channel outflow, E is evaporation from the lake surface, Dout is diversions away from the Great 

Lakes, and Cuse is consumptive use of Great Lakes water.

Connecting-Channel Flow

Connecting channels are large, short rivers that flow from 

lake to lake, and to the Atlantic Ocean. Flow through each connecting channel increases as the water level rises in the upstream 

lake, but the size and position of each connecting channel restricts 

flow out of a lake as its water level rises. This constraint limits the 

outflow from the Great Lakes, allowing the lakes to store large 

amounts of water in times of above-average water supply and then 

release that water much later when supplies are likely to be lower. 

This results in a hydrologic system that is naturally resistant to 

large variation in river flows. The maximum St. Lawrence River 

flow (at Massena) of 356,700 ft3/s is only 2.3 times the all-time 

minimum flow of 154,000 ft3/s. In contrast, the historical peak 

flow of the Mississippi River at Arkansas City, Arkansas, is 

approximately 25 times the all-time minimum flow of 88,200 ft3/s.

As a component of the water balance, connecting-channel 

flows vary in magnitude from lake to lake (fig. 3). According to 

data reported by Croley and others (2001), connecting-channel 

flow represented 59 percent of all water outflows (and 0 percent 

of all water inflows) from Lake Superior for 1948-98. In contrast, 

connecting-channel flow represented 95 percent of all water outflows (and 77 percent of all water inflows) from Lake Ontario for 

the same period.

The influence of evaporation and runoff on connecting-channel flow is quite small in comparison to total volume of flow. For 

this reason, flows are commonly defined at one point on each 

connecting channel and not distinguished between outflow of one 

lake and inflow of the next lake.

Lake Superior Outflow

Water flows out of Lake Superior and into Lake Huron 

through the St. Marys River (fig. 6). Lake Superior outflows are 

regulated at the twin cities of Sault Ste. Marie, Ontario and Michi-
 7

gan, by the International Joint Commission (IJC) International 

Lake Superior Board of Control. Actual outflow is a combination of flows through three hydropowerplants, the Soo Navigation Locks, the international dam known as the Compensating 

Works, and minor amounts of water used for wildlife, domestic, 

and commercial use (fig. 7; Neff and Killian, 2003). The Board 

of Control sets Lake Superior outflow each month according to 

IJC Regulation Plan 1977A. This plan takes into consideration 

water levels of Lake Superior and Lakes Michigan-Huron. The 

objective in adjusting flows is to help maintain lake levels near 

their long-term seasonal averages. Since records have been kept, 

monthly Lake Superior outflows have averaged 75,000 ft3/s. 

Average monthly flows have been as high as 132,000 ft3/s and as 

low as 41,000 ft3/s (according to data presented by Croley and 

others, 2001).

Lakes Michigan-Huron Outflow

Lakes Michigan and Huron are connected hydraulically by 

the wide and deep Straits of Mackinac (fig. 8). The water level 

of both lakes is virtually identical because of this connection. As 

yet, few data describe direct measurements of flow through the 

Straits of Mackinac, and the three-dimensional pattern of flow 

through this connection between the lakes is possibly complex. 

Evaluation of the water balances of the two lakes shows that net 

flow direction is from Lake Michigan to Lake Huron in most 

years. For 1948-99, average flow from Lake Michigan to Lake 

Huron was approximately 49,000 ft3/s, based on water-balance data reported by Croley and others (2001). Typically, flow 

through the St. Clair River is considered to be outflow of both 

Lake Michigan and Lake Huron.

Water flows out of Lakes Michigan-Huron through the St. 

Clair-Detroit River waterway (figs. 9 and 10). Flows through the 

two rivers are determined primarily by size and dimensions of 

their channels and by levels of Lakes Michigan-Huron, St. Clair, 

and Erie. The St. Clair and Detroit River channels are wide and 

deep enough to permit shipping in their upper reaches, but they 

have been dredged to a depth of 27 ft in their lower reaches to 

improve navigation through the Great Lakes waterway. Lake St. 

Clair has an average depth of 11 ft and a maximum depth of 

21 ft, except for a 27-ft-deep channel that has been dredged 

across this body of water (Coordinating Committee, 1988, p. 9). 

 250

 200

 150

 100

 50

 0

 -50

-100

-150

-200

-250

-300

LAKE 

SUPERIOR

LAKE

MICHIGAN/

LAKE HURON

LAKE 

ERIE

LAKE

ONTARIO

FLOW, IN THOUSANDS OF CUBIC FEET PER SECOND

Upstream inflow

Streamflow

Precipitation

Diversions - in

Evaporation

Downstream outflow

Diversions - out

Figure 3. Components of Great Lakes inflows and outflows. 

(Modified from Great Lakes Commission, 2003.) Positive 

values denote inflows, and negative values denote outflows 

for each lake. 

Components of the Great Lakes Water Balance 
8 Uncertainty in the Great Lakes Water Balance

LAKE SUPERIOR

Diverted Ogoki

Drainage Basin

Area 5390 sq. mi.

Summit 

Control Dam

Nipigon

Nipigon River

Little 

Jackfish 

River

Thunder

Bay

Waboose

Dam

Albany

River

Ogoki

R

vi er

0

0

50 MILES

40 KILOMETERS

Lake

Nipigon

EXPLANATION

GREAT LAKES DRAINAGE BOUNDARY

Study area

Hydroelectric 

Power 

Plants

Figure 4. Ogoki diversion near Thunder Bay, Ontario.

Base from the International Joint Commission, 1985.

N
Components of the Great Lakes Water Balance 9

Base from the International Joint Commission, 1985.

Long Lake Control Dam

Diversion Channel

Great Lakes

Drainage Basin

Boundary

Diverted

Long Lake

Draingage

basin area

1690 square miles

Kenogami

Control 

Dam

Geraldton

Terrace 

Bay

LAKE SUPERIOR

Longlac

Aguasabon Generating Station

Long

Lake

Kenoga mi River

Schreiber

Rive r

Aguasabon

0

0 20 KILOMETERS

5 10 15 MILES

Figure 5. Long Lac diversion near Terrace Bay, Ontario.

Study area

EXPLANATION

GREAT LAKES DRAINAGE BOUNDARY

N
10 Uncertainty in the Great Lakes Water Balance

Two hydrologic phenomena can significantly affect Lakes 

Michigan-Huron outflow for short periods. First, the presence 

of ice affects St. Clair and Detroit River flows directly by 

slowing flow of water. Ice floes also can accumulate and form 

an ice jam, which retards river flow for a few hours or days 

to as much as several weeks or more. Ice jams are especially 

common to the St. Clair River delta and can reduce flows by 

as much as 65 percent (Derecki and Quinn, 1986). Compared 

to the pre-1930 flow regime, ice retardation of river flows has 

been reduced significantly by dredging (Coordinating Committee, 1988, p. 8). 

Second, wind set-up and seiche on Lake Erie significantly affect the timing of Detroit River flows. Wind set up on 

Lake Erie causing water levels 3-4 ft higher than normal at one 

end is not uncommon. The Detroit River descends only about 

3 ft in the 32 mi it flows from Lake St. Clair to Lake Erie. 

This makes Detroit River flows particularly sensitive to wind 

set-up and seiche on Lake Erie. When wind set-up occurs in 

conjunction with ice jams on the St. Clair River, flow of the 

Detroit River can, and actually does, reverse direction (Quinn, 

1988; Quinn and Derecki, 1990). Since records have been 

kept, monthly St. Clair and Detroit River flows have averaged 188,000 ft3

/s. Average monthly flows have been as high 

as 272,000 ft3/s and 250,000 ft3/s and as low as 106,000 ft3/s 

and 112,000 ft3/s, respectively (according to data reported by 

Croley and others, 2001).

Base from Coordinating Committee on Great Lakes Basic 

Hydraulic and Hydrologic Data, 1994.

Base from Coordinating Committee on Great Lakes Basic 

Hydraulic and Hydrologic Data, 1994.

ONTARIO

LAKE 

HURON

LAKE

SUPERIOR

MICHIGAN

Lake George

 Flats

Round

Island

Raber

Village

De Tour 

Village

Lime Island De Tour

Passage

Sugar

Island

Sault Ste

Marie

St. Marys 

Rapids Point 

aux Pins

N

Lake Munuscong

Lake Ni colet Neebish

Island

St. Joseph Island

Drummond 

Island

Lake

George

Whitefish

 Bay

Study area

Figure 6. St. Marys River near the twin cities of Sault Ste. Marie, Ontario, and Michigan.

0 5 MILES

0 5 KILOMETERS

Brush 

Point

Sault

Ste Marie

St. Marys River 
 11

Lake Erie Outflow

Water flows north out of Lake Erie and into Lake Ontario 

through the Niagara River and the Welland Canal (fig. 11). 

The Niagara River is about 36 mi long and drops 326 ft 

between Lakes Erie and Ontario, including the 167-ft drop 

at Niagara Falls (Coordinating Committee, 1976, p. 5). The 

Welland Canal flows roughly parallel to the Niagara River and 

permits shipping to bypass the Niagara River. 

Several phenomena affect Lake Erie outflow. Wind set-up 

and seiche on Lake Erie, ice floes and jams, frazil ice (also 

frequently called anchor ice), and summertime aquatic plant 

growth in the Niagara River channel all affect Lake Erie outflow. Installation of the Lake Erie Ice Boom has reduced ice 

floes and has eliminated almost all of the once-common ice 

jams (International Niagara Working Committee, 2001). 

There are many diversions of flow from and between the 

Niagara River and Welland Canal, including flows through 

the New York State Barge Canal and numerous hydropower 

related diversions. The complexity of this system is shown in 

figures 11, 12, and 13. Since records have been kept, monthly 

Lake Erie outflow has averaged approximately 210,000 

ft3/s. Maximum monthly average flows have been as high as 

268,000 ft3/s and as low as 118,000 ft3/s (according to data 

reported by Croley and others, 2001).

Lake Ontario Outflow

The St. Lawrence River flows northeast out of Lake 

Ontario at Kingston, Ontario. Several control structures that 

make up the St. Lawrence-Franklin D. Roosevelt Power 

Project (fig. 14) have been constructed for safety, to regulate 

Lake Ontario water levels and outflow, and to permit shipping.

Base from Coordinating Committee on Great Lakes Basic 

Hydraulic and Hydrologic Data, 1994.

St. Marys River

LAKE 

SUPERIOR

South Canal

Ashmum

Bay

North Canal

Sault Ste. Marie

 ONTARIO

Sault Ste. Marie

 MICHIGAN

U.S.

CANADA

Edison Sault

Electric Co.

 Plant

Great Lakes Power Limited Plant

Edison Sault 

Electric Co.

Canal

St. Marys 

Rapids

Power Canal

U.S. Power

Plant

Sabin Lock

Whitefish

 Island International 

Bridge

Davis Lock

Poe Lock

MacArthur Lock

Canadian 

 Lock

0 1000 2000 FEET

Study area

Figure 7. Soo Navigation Locks at Sault Ste. Marie, Ontario, and Michigan.

N

International 

Railroad 

Bridge

Compensating

Works

0 500 METERS

Components of the Great Lakes Water Balance 
12 Uncertainty in the Great Lakes Water Balance

Lake Ontario outflow is measured at the Moses-Saunders 

power dam, near the cities of Cornwall, Ontario, and Massena, 

New York. This dam is 112 mi downstream from where the St. 

Lawrence River leaves Lake Ontario at Kingston. 

The Moses-Saunders power dam is generally considered 

the downstream terminus of the Great Lakes and Lake Ontario 

Basins. Since records have been kept, monthly Lake Ontario

outflows have averaged 246,000 ft3/s. Average monthly flows 

have been as high as 357,000 ft3/s and as low as 154,000 ft3/s

(based on data reported by Croley and others, 2001).

Evaporation 

The Great Lakes are the single largest source of fresh 

surface water on Earth and cover a vast area. Large amounts of 

water evaporate from this surface: consider that water lost to 

evaporation exceeds the total amount of runoff into the Great 

Lakes (fig. 3; based on data presented by Croley and others, 

2001). 

Evaporation is a highly seasonal phenomenon on the 

Great Lakes. The general pattern consists of very high evaporation rates in fall and winter and very low evaporation rates 

in spring and summer (fig. 15). During winter, cold air moves 

over the relatively warm lakes. As the air warms, it is able 

St. Ignace

Mackinaw

City

Bois Blanc Island

Mackinac 

Island

Round 

Island

St. Helena 

Island

Mackinac 

Bridge

Base from U.S. Geological Survey 1:24,000 quadrangles.

0 5 MILES

0 5 KILOMETERS

Study area

Figure 8. Straits of Mackinac, Michigan.

N

STRAITS OF MACKINAC

LAKE

MICHIGAN

LAKE

HURON

STRAITS OF MACKINAC

MICHIGAN

MICHIGAN
 13

Base from Coordinating Committee on Great Lakes Basic 

Hydraulic and Hydrologic Data, 1994.

LAKE HURON

St. Clair River

MICHIGAN

ONTARIO

Lake 

St. Clair

Anchor Bay

Pine River

Belle 

River

Stag Island

St. Clair

Sarnia

International 

Blue Water Bridge

Port Huron

Fawn Island

Harsens 

Island 

Black River

Study area

Dickinson 

Island 

Seaway 

Island

Figure 9. St. Clair River near St. Clair, Michigan.

0 5 MILES

0 5 KILOMETERS

N

Walpole 

Island

Components of the Great Lakes Water Balance 
14 Uncertainty in the Great Lakes Water Balance

Base from Coordinating Committee on Great Lakes Basic 

Hydraulic and Hydrologic Data, 1994.

LAKE ERIE

MICHIGAN

ONTARIO

Lake 

St. Clair

Bois Blanc Island

Windsor

Detroit

Ambassador Bridge

DETROIT RIVER

Sugar Island

Zug 

Island

Peche 

Island

Ecorse River

Rouge River

River

Rouge

Belle Isle Bridge

Stony Island

Lower Bridge

Celeron Island

Grosse

 Ile

Upper Bridge

Fighting Island

Belle Isle

Study area

Figure 10. Detroit River near Detroit, Michigan.

0 5 MILES

0 5 KILOMETERS

N
Base from the International Joint Commission, 1985.

Fort Erie

Squaw 

Island

Black

Rock

Canal

Buffalo

New York State

 Barge Canal Allanburg

Grand 

Island

Niagara 

 Falls

Port

Colborne

Syphon 

Culverts

Youngstown

ONTARIO

NEW YORK

Niagara

on the

Lake

Port 

Weller

DeCew Falls

Power Plants

Tonawanda

Supply

Weir

Welland Canal Welland River

Port

Dalhousie

LAKE ONTARIO

LAKE ERIE 0 5 MILES

0 5 KILOMETERS

Study area

Figure 11. Welland Canal diversion, Ontario.

N

Lewiston

Queenston

Intake 

Structures

Sir Adam 

Beck Plants 

I and II

Maid of 

the Mist 

pool

Conduits

Lewiston Pump 

Generating Plant

Niagara 

Falls

Robert Moses 

Niagra Power Plant

Flow

Flow

Chippawa-Grass 

Island Pool

Ashland Ave. 

streamflow-gaging 

station

Pumping 

station

Chippawa Power Canal

Chippawa Channel

Tonawanda Channel

Niagara River

Control

Structure

Niagara River
16 Uncertainty in the Great Lakes Water Balance

Base from the International Joint Commission, 1985.

LAKE ONTARIO

LAKE 

ERIE

Niagara 

River

Great Lakes

Drainage Basin

Boundary

NEW YORK

Lockport

Buffalo

Grand Island Syracuse

Oswe go River

Lake

Champlain

Champla ni Canal

Albany

H

UDSON R VI ER

0 20 40 MILES

0 50 KILOMETERS

Whitehall

Atlantic Ocean

Long Is. Sound

SENECA LAKE

CAYUGA LAKE

NEW

JERSEY Long Island

VERMONT

MASS

CONN.

ONTARIO

PENNSYLVANIA

Study area

Figure 12. The New York State Barge Canal diversion near Buffalo, New York.

EXPLANATION

GREAT LAKES DRAINAGE BOUNDARY

Ithaca

Utica

New York State Barge Canal

N

Mohawk River

Oneida

Lake

Genesee River
 17

to absorb more moisture, causing evaporation to increase. 

Evaporation rates lessen as ice covers parts of the Great Lakes 

in winter (Eichenlaub 1979, p. 141-173). 

Ice formation on the Great Lakes varies greatly from 

lake to lake and from year to year. Lake Erie is the shallowest lake and has 90 percent ice cover in an average year. In 

contrast, deeper Lake Ontario has only 24 percent ice cover 

in an average year. Complete freezing of the Great Lakes is a 

rare occurrence; 1979 is the only year on record when all of 

the lakes froze over nearly completely (Assel and others, 1983, 

table 6-1). 

Diversions 

The first of three major diversions out of the Great 

Lakes (from west to east) is the Chicago diversion (fig. 16). 

The canal system intakes at Chicago draw water from Lake 

Michigan for municipal water supply, navigation, and dilution 

of effluent from several water reclamation plants near the city. 

The water is diverted into the Des Plaines and Calumet Rivers 

in the upper Mississippi River Basin. 

Total authorized annual diversion of Lake Michigan water 

by the State of Illinois has varied historically, though it has 

been set at an annual average of 3,200 ft3/s since 1967. Actual 

annual flows have at times exceeded this amount, although 

diverted flows have been reduced below this threshold since 

1994 in an effort to maintain a long-term average of 3,200 ft3/s 

or less (table 1). The quantity of water diverted at Chicago is 

relatively small when considered in the context of the Great 

Lakes water balance: it is approximately equal to 4 percent 

of the amount of water that evaporates from Lakes MichiganHuron, less than 2 percent of the outflow from Lakes Michigan-Huron, and slightly more than 1 percent of Lake Ontario 

outflow (based on data reported by Croley and others, 2001). 

However, the water withdrawn from the Chicago diversion has 

lowered the water level of Lakes Michigan-Huron by 2.5 in. 

and of Lake Erie by 1.7 in. (International Joint Commission, 

1985, p. 15). 

Two other diversions, the New York State Barge Canal 

(NYSBC, fig. 12), and the Welland Canal (fig. 11), divert 

major amounts of water into Lake Ontario from Lake Erie 

and the Niagara River, respectively. One important difference 

between these two canals and the Chicago diversion is that the 

Chicago diversion is an interbasin diversion, transferring water 

from the Great Lakes Basin to a non-Great Lakes Basin. Water 

is diverted from the Niagara River to supply the NYSBC. All 

the water passing through the NYSBC flows to Lake Ontario, 

except for small, non-quantifiable amounts lost to evaporation and seepage. The long-term Great Lakes water balance is 

not affected by the NYSBC, nor does the NYSBC have any 

hydraulic effect on any Great Lake. 

The Welland Canal is used for hydropower production 

and permits shipping to bypass the Niagara River and Falls 

and move between Lakes Erie and Ontario. Water enters the 

canal from Lake Erie at Port Colborne, Ontario, about 15 mi 

west of the head of the Niagara River, and flows north. Most 

of the water is diverted from the canal for power production 

at the OPG DeCew plants in St. Catharines, Ontario, and then 

enters Lake Ontario at Port Dalhousie, Ontario, about 9 mi 

Components of the Great Lakes Water Balance 

Welland 

Canal

Welland

River

Chippawa-Grass

Island Pool

Pumped Storage

Sir Adam Beck

Power Plants

Maid-of-the-Mist Pool

Robert Moses Niagara

Power Plant

Pumped Storage

Niagara River

at Queenston

Lake Ontario

Lake Erie

New York State Canals

Niagara River

at Buffalo

Figure 13. Flow pattern from Lake Erie to Lake Ontario. (Modified from Coordinating

Committee on Great Lakes Basic Hydraulic and Hydrologic Data, 1994.)

Chippawa

Power

Canal
18 Uncertainty in the Great Lakes Water Balance

west of the mouth of the Niagara River (fig. 11). The Welland 

Canal discharges into Lake Ontario at Port Weller, Ontario, a 

location about 7 mi west of the mouth of the Niagara River. 

Some of the water entering the Welland Canal is diverted 

into the Welland River at Welland, Ontario, where it flows 

eastward until it joins westbound Welland River flow. At this 

point, combined flow is routed into a canal and flows north 

to Sir Adam Beck powerplants I and II and is discharged into 

the Niagara River at Queenston, Ontario. Water entering the 

Welland Canal during 1973 through 2001 has averaged 

8,400 ft3/s, more than 2.5 times the flow through the Chicago 

diversion. This increase in Lake Erie outflow capacity has 

drawn down Lake Erie by approximately 5.3 in. Because the 

level of Lake Erie naturally affects the level of Lakes Michigan-Huron, the Welland Canal diversion has lowered those 

lakes by 2.2 in. By regulation agreements, this has resulted in 

lowering Lake Superior by 0.7 in (International Joint Commission, 1985, p. 18). All the water passing through the Welland 

Canal returns to Lake Ontario, except for small, non-quantifiable amounts lost to evaporation and seepage. The Welland 

Canal does not affect the long-term water balance of the Great 

Lakes. A schematic of Lake Erie outflow is shown in figure 

13. Other diversions of water out of the Great Lakes exist 

(International Joint Commission, 1999, p. 10), but are relatively small and not considered in this report.

Kingston

Howe Island

Wolfe Island

ONTARIO

NEW YORK

LAKE 

ONTARIO

St. Lawrence River

Study area

Iroquois 

Control Dam

Lake St. Lawrence Moses-Saunders 

Power Dam

Cornwall

Massena

Barnhart 

Island

Long Sault 

Dam

Wiley-Dondero 

Ship Canal

Eisenhower Lock

Snell Lock

Iroquois Lock ONTARIO

NEW YORK

QUEBEC

Lake St. Francis

International Rapids Section

0 5 KILOMETERS

N

0 5 MILES

Figure 14. St. Lawrence River downstream from Kingston, Ontario, to Lake St. Francis.

Lake St. Lawrence

St. Lawrence River

Base from Coordinating Committee on Great Lakes Basic 

Hydraulic and Hydrologic Data, 1994.
 19

Consumptive Use

Water withdrawn or withheld from the Great Lakes Basin 

and assumed to be lost or otherwise not returned to the Great 

Lakes Basin because of evapotranspiration, incorporation into 

products, or other processes is termed consumptive use. Consumptive use is a very small component of the water balance 

and is not considered in this report. A comprehensive discussion 

of consumptive use is included in chapter 3 of the GLC report, 

“Toward a Water Resources Management Decision Support System for the Great Lakes–St. Lawrence River Basin” (2003).

Change in Storage

Once inflow and outflow of each lake have been assessed, 

calculation of change in storage of the Great Lakes renders a 

complete water balance. Change-in-storage calculations are 

based on a net change in lake stage and the surface area of each 

Great Lake. As stated in the introduction, the Great Lakes have 

a very large capacity to store water. A relatively small change in 

lake stage can represent a vast amount of water that is being held 

by or released from the lake. 

The effect of changes in lake levels on surface area of the 

Great Lakes is assumed to be negligible. As water levels drop, 

the lakes cover less area. However, the large surface area of the 

Great Lakes mitigates any effect changing water levels have on 

total surface area. A change in lake level resulting in an average loss or gain of approximately 500 ft of shorefront would 

be needed to change the area of the lakes by 1 percent. For this 

reason, change in the surface area of the Great Lakes caused by 

changing water levels is not considered when quantifying change 

in storage or any other component in the Great Lakes water balance. 

The magnitude of change in storage is highly variable. At 

times, levels of the Great Lakes may be stable, and the change 

in storage term can be close to zero. At other times, however, 

the change in storage term can be positive or negative and 

greater than any other component of the water balance. Between 

1900 and 2000, Lake Superior monthly net change in storage 

ranged from –184,000 ft3/s in October 1952 to +303,100 ft3/s in 

May 1950 (based on data reported in Croley and others, 2001).

Methods for Quantifying Components 

and Potential Uncertainties

The Great Lakes water balance is a compilation of literally thousands of daily measurements of many hydrologic and 

atmospheric parameters. Additionally, numerous approaches to 

assess each component are available, and each approach introduces a different amount of potential uncertainty to the water 

balance. Types of uncertainties discussed in this section include 

measurement uncertainties, model uncertainties, and monitoring 

gaps.

Currently (2004), the uncertainty of most water-balance 

components is impossible to assess. For example, the overall 

uncertainty in runoff estimates cannot be calculated. In gaged 

areas, both the magnitude of streamflow and the uncertainties 

in estimates for individual stream gages constantly fluctuate in 

response to ever-changing hydrologic conditions. These fluctuations are also unique to each gage. In ungaged areas, little is 

known about the reliability of current estimates. 

JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

12,000

10,000

 8,000

 6,000

 4,000

 2,000

 0

 -2,000

EVAPORATION, IN CUBIC FEET  PER SECOND

Figure 15. Monthly evaporation rates of Lake Superior.

(From Great Lakes Commission, 2003.)

Methods of Quantifying Components and Potential Uncertainties
20 Uncertainty in the Great Lakes Water Balance

Base from the International Joint Commission, 1985.

Brandon Road

Lock and Dam

Lockport

Lock and Dam

Wilmette Inlet

Wilmette Pumping

Station 

LAKE

MICHIGAN

Grand Calumet

River

Chicago Chicago Lock

River

Calumet River Indiana

Harbor

Little 

Calumet

River

Cal- Sag Channel

Indiana Harbor Canal

Salt Creek

North Branch Chicago River

Des Plaines River

CS and SC

Thomas J. O'Brien 

 Lock and Dam

EXPLANATION

GREAT LAKES BASIN BOUNDARY

DIVERTED PORTION OF GREAT LAKES

WATERSHED

Study area

Figure 16. Chicago diversion near Chicago, Illinois.

N

0 5 MILES

0 5 KILOMETERS

Chicago Sanitary and

Ship

Canal Main

Channel

Chicago River

Controlling Works

Wilson Ave.

Intake Crib

Denver/Harrison

Intake Crib

68th Street Intake Crib

Romeoville 

streamflow-gaging 

station

N. Shore Channel

ILLINOIS INDIANA

Great Lakes basin boundary

Diverted portion of 

Great Lakes watershed
 21

Table 1. State of Illinois annual diversion flows, certified by 

the U.S. Army Corps of Engineers, Chicago District 

[ft3/s, cubic feet per second].

Accounting 

year

Certified Flow 

(ft3/s)

Accounting 

year

Certified Flow 

(ft3/s)

1981 3,106 1991 3,555

1982 3,087 1992 3,409

1983 3,613 1993 3,841

1984 3,432 1994 3,064

1985 3,472 1995 3,197

1986 3,751 1996 3,108

1987 3,774 1997 3,114

1988 3,376 1998 3,060

1989 3,378 1999 2,909

1990 3,531

This underscores the difficulty of this study. Runoff is a tangible 

component of the water balance. Other parts of the water balance, such as evaporation, are diffuse and invisible. It is intuitive 

that runoff should be the easiest component to understand, yet it 

is not even clear how accurately it is measured.

In such cases where estimating a single uncertainty for a 

water-balance component is impossible, a range of reasonable 

monthly estimate uncertainty is stated. This range is based on the 

professional judgment of members of the Status Assessment of 

Water Resources Technical Subcommittee 2, assembled in support of the GLC report “Toward a water resources management 

decision support system for the Great Lakes–St. Lawrence River 

Basin” (2003). The term “reasonable” is used to signify a 90-

percent confidence that the true magnitude of the quantity being 

estimated lies within a given percentage of the estimated value.

Inflows

Uncertainty of estimates of inflow to the Great Lakes 

depends on the methods used to quantify each component and on 

the nature and magnitude of each inflow component. Only two 

diversions of water into the Great Lakes Basin will be considered 

in this section–the Long Lac and Ogoki diversions. The methods 

used for quantifying connecting-channel flow and its potential 

uncertainty will be described in the outflows section.

Over-Lake Precipitation

Over-lake precipitation is a very large component of the 

Great Lakes water balance, larger than either runoff or evaporation. Yet, opportunities to verify current estimates of over-lake 

precipitation with direct observations of over-lake precipitation have been few. Understanding the uncertainty of over-lake 

precipitation estimates is perhaps the single largest obstacle to 

determining the uncertainty of the Great Lakes water balance. 

Improving over-lake precipitation estimates also may represent 

the single largest opportunity to improve estimates of the overall 

water balance. 

Uncertainty of over-lake precipitation estimates has two 

main sources, instrumentation uncertainty and inaccuracies in 

modeling. Precipitation measurement remains an inexact science. Precipitation gages are not perfect. Gages tend to underestimate precipitation largely because of wind-induced turbulence 

near the opening of the gage and adhesion of moisture to the 

internal walls of the gage. Bias can range from 5 percent to 

40 percent for monthly precipitation estimates (Groisman and 

Legates, 1994). Generally, accuracy is in inverse proportion to 

temperature and wind velocities; rain is more accurately gaged 

than snowfall, and wind exacerbates gaging problems. Legates 

and DeLiberty (1993) estimate that biases in monthly gagemeasured precipitation in the U.S. part of the Great Lakes Basin 

vary from 10 to 14 percent; the authors also point out that the 

uncertainty in gaging is not constant from year to year. Overall, 

uncertainty in gaged precipitation is highly dependent on wind 

conditions and amount of snowfall recorded in each specific 

year.

Modeling the amount and timing of precipitation over a 

system as highly variable as Great Lakes is no easy task. Currently (2004), estimates of over-lake precipitation are based on 

numerous nearshore precipitation measurements and the Thiessen weighting method (Croley and Hartmann, 1985). In effect, 

the precipitation falling over the lakes is assumed to be equal to 

the amount of precipitation recorded at the nearest land-based 

gaging station. The weather stations used to define the Thiessen 

polygons in current precipitation estimates are all on land, near 

the shoreline of each lake (fig. 17; Croley, 1998, p. 49). Stations 

on peninsulas or on islands should represent over-lake conditions better than stations on the mainland, but these are few in 

comparison to the number of mainland stations. Because of the 

lack of direct observations of over-lake precipitation, it is not 

possible to accurately assess the magnitude of uncertainty in 

current studies that report over-lake precipitation.

The lack of direct measurements of over-lake precipitation 

is potentially very significant. Weather in the Great Lakes Basin 

is highly variable, and much of the variability of precipitation 

takes place where the lakes meet the land. An excellent example 

of this variability is lake-effect snow. In fall and winter, cold 

air masses frequently move across the Great Lakes from the 

north and west. As these air masses move over a Great Lake, 

the relatively warm lake heats the air, permitting more evaporation from the lake surface. When the air mass moves inland, the 

cooler land surface cools the air mass and causes the additional 

moisture to precipitate as lake-effect snow. The net effect is for 

precipitation to be dramatically different over the lakes than it 

is on the land areas nearby. In this example, conditions on the 

upwind side of a Great Lake would be similar to over-lake conditions (dry). However, if a land-based gage on the downwind 

side of the lake were to catch lake-effect snow, the result could 

be substantial overestimation of over-lake precipitation. Another 

example of this kind of variability is caused by convective thunderstorms. In summer, the relatively cool lakes tend not

Methods of Quantifying Components and Potential Uncertainties
22 Uncertainty in the Great Lakes Water Balance

CANADA

CANADA

U. S. A.

U. S. A.

O N T A R I 

JAMES

 BAY 

O

Q U E B E C

900 0

0

0 

80

45

50

0 50 100 150 200 KILOMETERS

100 150 200 MILES

M I

H I G

A

N

GREAT LAKES BASIN 

WEATHER STATION--Canada

WEATHER STATION--United States

EXPLANATION

Figure 17. Weather stations in the Great Lakes Basin. (Canadian data from Ontario 

Climate Center, 2002; U.S. data from National Climatic Data Center, 2002.)

ILLINOIS INDIANA OHIO

PENNSYLVANIA

NEW

YORK

W I S C O N S I N

LAKE

HURON

LAKE

ERIE

LAKE

ONTARIO

LAKE SUPERIOR

LA

KE

MICHIGAN

0 50 Base from ESRI, 2001; Army Corps of Engineers,1998; and Environment Canada,1995.

C
 23

to generate or sustain convective thunderstorms; however, 

these storms can form and persist over land. If a land-based 

precipitation gage captures rainfall from convective storms 

that dissipate a short distance offshore, then the result would 

be overestimation of over-lake precipitation. A thorough 

discussion of these and other meteorological phenomena are 

given in Eichenlaub (1979).

Two potential tools for assessing precipitation over the 

Great Lakes are Doppler radar and weather buoys. Doppler 

radar, which has emerged in recent years as a useful tool in 

weather monitoring and forecasting, permits direct estimation 

of precipitation over the surface of the lake. The U.S. National 

Weather Service (NWS) currently maintains a network of 

Doppler radar stations in the Great Lakes Basin that could be 

used to estimate over-lake precipitation. Environment Canada 

(EC) is currently installing Doppler radar stations or retrofitting existing radar stations with a Doppler capacity. The entire 

over-lake area of the Great Lakes could be monitored by 

means of these networks. Radar-based precipitation estimates 

would not be without problems. Like traditional gage measurements, warm-weather precipitation is more reliably measured 

than cold-weather precipitation. Currently (2004), no datasets 

of Doppler-based Great Lakes precipitation are readily available. Despite these problems, use of Doppler radar technology to estimate over-lake precipitation could help researchers 

assess the variability in precipitation over the lakes.

The U.S. National Oceanic and Atmospheric Administration (NOAA) and EC operate a network of buoys throughout 

the Great Lakes that could potentially be outfitted with equipment to monitor precipitation. The accuracy of precipitation 

gages on buoys is affected by wave action, and therefore is 

likely to be highly variable. Buoy-based precipitation measurements could be worse than land-based gages, particularly 

in the fall and winter; but under ideal conditions, buoy-based 

precipitation measurements could possibly be used to help verify or corroborate current models. Because buoys are removed 

from the lakes each winter, year-round over-lake precipitation 

monitoring would not be possible with buoys.

Given the general uncertainty of monthly precipitation 

estimates from land-based gaging networks and possible differences in over-lake and over-land precipitation, the uncertainty is likely to be more than 15 percent and could be as high 

as 45 percent during some winters. Three steps would need to 

be taken to permit a better assessment of precipitation uncertainty. First, uncertainty and bias inherent to the binational 

Great Lakes gaging network would need to be quantified. Second, reliability of the Thiessen polygon approach would need 

to be evaluated with reference to accurate over-lake precipitation estimates. Third, possibilities of using Doppler radar and 

buoy-based precipitation measurements to verify the accuracy 

of current techniques would need to be explored.

Runoff 

Runoff includes streamflow and direct overland flow to 

the Great Lakes. Streamflow is calculated for gaged areas and 

ungaged areas. Official data, published by EC and the USGS, 

describe streamflow in gaged basins. All active stream gages 

in the Great Lakes Basin are shown in figure 18. These agencies do not publish basinwide data for ungaged areas. Some 

researchers generate estimates of runoff in ungaged areas to 

calculate total runoff to the Great Lakes.

Gaged Areas

Streamflow is generally not continuously measured; 

instead, a stage-discharge or velocity-discharge relation is 

established to estimate streamflow on a continuous basis. 

In these methods, streamflow is measured directly at many 

stream stages or velocities. These data are used to develop a 

regression relation that mathematically relates the stage or 

velocity of a stream and its discharge. Continuous records 

of stage or velocity can be used to determine streamflow on 

an ongoing basis. Some degree of uncertainty exists in these 

stage-discharge and velocity-discharge relations. Uncertainty 

may result from improperly measuring streamflow or from 

not recording the stage or velocity of the stream accurately. 

The USGS and the Meteorological Survey of Canada (MSC, 

formerly known as the Water Survey of Canada) take measures 

to minimize inaccuracy in these measurements.

Specialized gaging procedures and quality-assurance 

procedures followed by reporting agencies attempt to prevent biases and inaccuracies in calculated stage-discharge 

and velocity-discharge relations. Over time, the flow characteristics of a stream–and, consequently, the stage-discharge 

and velocity-discharge relation–tend to change. When field 

measurements of stage and discharge or velocity and discharge consistently fall outside the tolerances of the measuring 

agency for the existing stage-discharge or velocity-discharge 

regression, that agency will develop a new regression relation. 

If short-term or seasonal factors such as vegetation growth, ice 

cover, or debris in the river are influencing streamflow, correction factors are applied to the stage or velocity measurements 

using the shifting control method (Rantz and others, 1982). 

Streamflow is then based on these adjusted stage measurements. 

Special hydrologic conditions can affect the uncertainty 

of streamflow estimation. For example, floods present a special problem to estimating discharge. If a stream overflows its 

banks, the accuracy with which streamflow can be estimated 

decreases significantly. Compounding the problem is the fact 

that flood streamflows may be many times greater than the 

normal streamflow of the stream. So, the inaccuracies during a 

relatively short flood event (hours to weeks) may amplify the 

total uncertainty in longer-term runoff estimates significantly 

(days to years). 

Records of streamflow are often temporally incomplete. When temporal data gaps occur, they must be replaced 

somehow by estimated streamflows. Many estimation methods 

exist, but all introduce additional uncertainty to the streamflow 

record. Once a best estimate of streamflow at gaging stations 

is determined, streamflow data are published by the USGS 

(Blumer and others, 1999, p. 8) and the MSC.

Methods of Quantifying Components and Potential Uncertainties
24 Uncertainty in the Great Lakes Water Balance

Base from ESRI; 2001, Army Corps of Engineers,1998; and Environment Canada,1995.

LAK E

E RI E

LAKE

MICHIGAN

LAK E

ONTAR IO

LAK E

HUR ON

CANADA

CANADA

U. S. A.

U. S. A.

LAKE SUPERIOR

O N T A R I O

Q U E B E C

90 80

45

50

 

 

M

I

C

H I G

A

N

100 150 200 MILES

JAMES

 BAY

GREAT LAKES BASIN

STREAM GAGE--Canada,

STREAM GAGE--United States

EXPLANATION

0

Figure 18. Stream gage locations in the Great Lakes Basin.

(Canadian data from Meteorological Service of Canada, 2002.)

ILLINOIS

INDIANA OHIO

PENNSYLVANIA

NEW

YORK

W I S C O N S I N

0 50

0 50 100 150 200 KILOMETERS

0

0

0
 25

Statistical statements exist to describe uncertainty in 

streamflow estimates at individual stream gages, but no estimates of the total uncertainty in the Great Lakes stream gaging 

network are available. The USGS provides a statement of 

accuracy of its published data for individual stream gages. The 

streamflow estimates are rated as “excellent,” “good,” or “fair.” 

These terms signify confidence that 95 percent of the reported 

daily streamflows are within 5 percent, 10 percent, or 15 

percent of their true values, respectively. Sometimes a “poor” 

rating is given, indicating that 95 percent of the reported daily 

streamflows are believed to be more than 15 percent from their 

true values (Blumer and others, 1999, p. 10). Even with these 

statements of uncertainty, there is considerable difficulty in 

calculating the total uncertainty in streamflow estimates across 

the entire Great Lakes Basin. Many hundreds, or thousands, 

of gages need to be considered, and the uncertainty associated 

with each gage changes over time and is frequently independent of uncertainty observed at other gages. Additionally, the 

magnitude of streamflow at each stream gage is not uniform, 

or constant, and also must be considered in estimates of total 

uncertainty of streamflow in gaged areas of the Great Lakes 

Basin.

Ungaged Areas

Records of streamflow in the Great Lakes Basin are 

spatially incomplete for two reasons. First, gaging stations 

are usually several miles inland, rather than at stream mouths, 

leaving spatial gaps in data to describe streamflow in areas 

near the lakes. The inland locations of stream gages are due 

mainly to fluctuating water levels in the Great Lakes, which 

adversely affect the stage-discharge and velocity-discharge 

relation if stream gages are close to the mouth of the stream. 

Wind set-up and seiche exacerbate this problem. Factors 

dictating proper placement of stream gages are outlined more 

thoroughly in Rantz and others (1982, p. 5-8). Second, not 

every tributary to the Great Lakes is gaged. Neither the USGS 

nor the MSC reports values for runoff in ungaged areas. 

Rather, ungaged runoff is calculated in individual studies (for 

example, Croley and others, 2001; Quinn and Kelly, 1983). 

Table 2 gives the percentages of each Great Lake Basin that is 

gaged (modified from Lee, 1992, table 2.0). 

Table 2. Percentage of Great Lakes Basin area that is 

ungaged, 1992 [%, percent].

Lake 

Superior

Lake 

Michigan

Lake 

Huron

Lake St. 

Clair

Lake 

Erie

Lake 

Ontario

34% 24% 43% 50% 22% 25%

Runoff from ungaged areas, including direct overland 

flow to the Great Lakes, is usually estimated by means of the 

runoff-to-area ratio observed in other parts of the basin. In 

individual basins that are partially gaged, a multiplier is commonly applied to streamflows at a particular gage within the 

basin to compensate for any difference in runoff between the 

gaging station and the stream mouth (Lee, 1992). In completely ungaged basins, the area-to-runoff ratio for gaged areas 

of nearby basins is used. Currently, no standard approach is 

officially recognized by either MSC or USGS for estimating 

streamflow in ungaged areas. 

Uncertainty In Total-Runoff Calculations

Estimating the uncertainty in total-runoff calculations 

is currently difficult or impossible; however, steps could be 

taken to permit an estimate of this uncertainty. First would 

be to develop a statistical statement of the total uncertainty 

of streamflow estimates for all stream gages in a given Great 

Lake Basin. Due to the highly variable nature of streamflow 

estimation uncertainty over space and time, this would need 

to be calculated annually, if not monthly. Second would be to 

thoroughly examine the reliability of current methods used to 

estimate runoff in ungaged areas and develop a statement of 

uncertainty for these estimates. Lacking these kinds of information and procedures, it is currently possible to state only 

a reasonable range of uncertainty in current monthly runoff 

estimates, which is likely to be 15 percent to 35 percent. 

Ground-Water Discharge

Most water-balance studies of the Great Lakes ignore 

ground-water discharge to the Great Lakes or treat it as part 

of the residual in calculations. Though many studies have 

attempted to estimate direct ground-water discharge, to date 

(2004) no large-scale attempt to actually measure groundwater seepage throughout the Great Lakes has been done. A 

major reason for not studying ground-water discharge is the 

massive effort required to actually measure seepage along the 

estimated 6,820 mi of mainland Great Lake and connectingchannel shoreline (Coordinating Committee, 1977). Moreover, 

preliminary estimates show that ground-water inputs to the 

Great Lakes are not likely to be a large component of the 

water balance. 

According to Grannemann and Weaver (1999), past 

estimates of total ground-water inputs to Lake Michigan range 

from about 800 ft3/s to about 6,700 ft3/s. On the basis of all 

available data and information, these researchers estimated 

total direct seepage into Lake Michigan to be 2,700 ft3/s, 

approximately equivalent to 2 ft3/s per mile of shoreline. 

Grannemann and Weaver also advised that data are insufficient for estimates of ground-water seepage to the other Great 

Lakes, although estimated seepage rates from other studies 

are much smaller than those for Lake Michigan. Direct net 

ground-water seepage into the other Great Lakes could likely 

range from 0.5 ft3/s to 2.0 ft3/s per mile of shoreline. This 

amount is much smaller than that for other water-balance 

components, such as evaporation and direct precipitation, but 

Methods of Quantifying Components and Potential Uncertainties
26 Uncertainty in the Great Lakes Water Balance

it would be approximately the same magnitude of the Chicago 

diversion for each Great Lake. Ground-water inputs to the 

Great Lakes water balance remain an unmonitored component 

in the water balance. 

Diversions 

The flow through the Long Lac diversion is calculated 

as it passes through Long Lake Control Dam. This dam is a 

two-sluiceway structure with stop locks. Accounting of these 

flows is well established, is based on a stable rating curve, and 

is assumed to be very accurate. Water diverted from the Ogoki 

River flows through the Summit Control Dam. Flows through 

the Summit Dam are calculated on the basis of stage measurements made immediately downstream from the structure. The 

stream channel is stable in this section of the stream and has 

not changed much since the dam was built in the 1940s. Data 

for flows through Summit Control Dam are considered to be 

very accurate.

Uncertainty in diversion flows results from evaporative 

loss and the time lag as diverted water is in transit to Lake 

Superior. Data for diversion flows are generated at the point 

of diversion, and are representative of water diverted into the 

Lake Superior Basin but not necessarily the amount of water 

actually diverted into Lake Superior. Some quantity of the 

diverted water must evaporate between the points of diversion 

and Lake Superior, but this amount is unknown and could be 

negligible. 

Possibly of greater significance is the use of same-month 

diversion data to represent the amount of water diverted into 

Lake Superior. Flow through the Long Lac and Ogoki diversions varies seasonally, with average June diversion flows 

being approximately 2.2 and 3.2 times greater than April 

diversion flows, respectively (according to data presented in 

Croley and others, 2001). There is considerable lag time from 

when diverted flows are measured and when they actually 

reach Lake Superior. In this time the component of streamflow 

attributable to the diversion will likely be moderated in relation to the timing of diversion flows at the point of diversion. 

Using same-month diversion data from the points of diversion may not properly represent the timing of water diversion 

to Lake Superior from the Long Lac and Ogoki diversions. 

Ogoki-diversion flows have an especially long journey to Lake 

Superior. The water diverted from the Ogoki River is channeled into the Little Jackfish River, which flows through Lake 

Nipigon. Lake Nipigon is a particularly large lake, covering 

more than 1,741 mi2 (Environment Canada, 2003), with a 

maximum depth of greater than 400 ft. After leaving Lake 

Nipigon, water flows to Lake Superior. The total travel time is 

likely a matter of years.

Understanding of the Long Lac and Ogoki diversions 

is currently insufficient to permit an exact estimation of 

uncertainty. The largest issue to resolve is the effect of using 

same-month, point-of-diversion data to represent the amount 

of water diverted into Lake Superior. Additionally, any evaporative loss of diversion water not accounted for by the current 

accounting system will add to the uncertainty in diversion flow 

data. A reasonable range of uncertainty in monthly Long Lac 

and Ogoki diversion flows is 10-30 percent, without consideration of time-lag uncertainty.

Outflows

Uncertainty in estimates of outflows from the Great 

Lakes is dependent on the methods used to quantify each 

component and on the nature and magnitude of each outflow 

component. Only one diversion draws enough water to necessitate consideration in the Great Lakes water balance–the 

Chicago diversion. 

Connecting-Channel Flow

The accurate measurement of connecting-channel flow is 

critical for reliable water-balance and NBS calculations by use 

of the residual method. Past study by Quinn (1979) indicates 

that the standard error in connecting-channel-flow measurements may be as low as 3-5 percent. However, many sources 

of uncertainty in calculating Great Lake outflow and inflow 

are unaccounted for in error analyses of flow measurements. 

This report takes a more detailed look at each individual connecting channel. The uncertainty in calculated flows for each 

connecting channel is dealt with on a river-by-river basis, 

because each channel has a unique set of properties and challenges regarding accurate calculation of flow.

Lake Superior Outflow

Lake Superior outflow through the St. Marys River is calculated as the sum of flows through several control structures 

at the twin cities of Sault Ste. Marie, Ontario and Michigan. 

Careful examination of figure 7 is helpful in understanding the 

accounting of flow in the St. Marys River. The components 

of outflow are (1) three hydropower plants, (2) the U.S. and 

Canadian Soo Navigation Locks, (3) the international dam 

known as the Compensating Works, including flow for fisheries habitat, and minor amount of water used for (4) municipal, 

and (5) industrial uses.

Historically, flows have been calculated at these structures primarily for the purpose of partitioning water allotments 

rather than for water-balance accounting. Calculating flow 

through so many structures undoubtedly adds to the technical 

complexity of accounting for net outflow from Lake Superior. 

Nevertheless, this accounting system has been used to estimate 

net outflow from Lake Superior for two main reasons. First, 

considerable resources are already being devoted to measuring 

flows here, and the current accounting system is considered 

adequate for regulatory needs. Second, calculating flow here 

dramatically lessens the difficulty of determining flow during 

winter. At any other point on the St. Marys River, wintertime 

ice prevents accurate measurement of flows. 
 27

The largest component of flow through the St. Marys 

River at Sault Ste. Marie is the water flowing through the 

three hydropower plants. Two of these plants, the Edison-Sault 

and U.S. Government hydropower plants, are on the U.S. 

side of the river; the third, the Great Lakes Power Limited 

hydropower plant, is on the Canadian side. Accurate measurement of the powerplant flows is especially important to Lake 

Superior outflow estimates. Each plant calculates its diverted 

flow independently. In 2000, it was discovered that the 

reported flow through the U.S. Power and Edison Sault Electric Company power plants did not agree with flow measurements conducted by the Corps of Engineers and Environment 

Canada. The flows at the U.S. Government plant were being 

under-reported by about 9 percent (International Lake Superior 

Board of Control, 2001). The under-reporting at the Edison 

Sault Electric Company plant varied with the flow; smaller 

errors occurred at higher flows. This problem was detected as 

a result of an existing measurement program to verify flows, 

flow records have been corrected, and measures are being 

taken to prevent such miscalculations in the future (International Lake Superior Board of Control, 2002, 2003). Reported 

flows at the Great Lakes Power Limited plant were found to be 

within 7 percent of the independently measured values, with a 

mean error near zero, and are considered relatively accurate. 

Pending the successful implementation of new flow estimation 

practices at the U.S. Government hydropower plant, measurement of flows through the three powerplants will be relatively 

accurate, likely within 5 percent.

The next largest flow of St. Marys River water is through 

the Compensating Works. This dam is used to maintain water 

levels on Lakes Superior and Michigan-Huron close to historical levels and to prevent dramatic water-level fluctuations. The 

structure consists of 16 gates that can be opened and closed 

according to regulatory needs. A minimum of one-half gate 

(2,830 ft3/s) is kept open at all times to ensure sufficient water 

flow for fish spawning in the St. Marys Rapids. In practice, 

flow is regulated primarily by adjusting flow through the 

powerplants. Only when the powerplants are running at capacity is the flow increased by opening additional gates on the 

Compensating Works. The gates on the Compensating Works 

require regular maintenance, and leakage through the gates 

is inevitable. The U.S. Army Corps of Engineers (USACE) 

considers leakage to be 25 ft3/s per gate and incorporates this 

flow in Lake Superior outflow calculations. 

Significant amounts of water also flow through the Soo 

Navigation Locks. Of the four U.S. locks, only two are still 

in use: the Poe Lock and the MacArthur Lock. The Poe and 

MacArthur Lock chambers transfer a total of 2,825,000 ft3 and 

1,413,000 ft3 per lockage, respectively, less the water displaced 

by the ship in the lock. The one Canadian lock is much smaller 

than the U.S. locks and is primarily used for recreational 

boating. Flows through the locks are entered into the overall 

flow accounting for Lake Superior outflow. There has been no 

official statement of how accurate this system is. The seals on 

the lock doors also are prone to leakage, although to a lesser 

degree than the doors on the Compensating Works. Because of 

the relatively small amount of leakage, this quantity of water is 

not considered in Lake Superior outflow calculations. Uncertainty may result from not considering leakage from the locks. 

The remaining components of flow through the St. Marys 

River are small diversions for municipal and industrial use. 

These quantities also are measured and incorporated into the 

total estimated St. Marys River flow. The accuracy of these 

measurements is likely to be adequate. These flows are so 

small that allocating significant resources to improve their 

measurement is impractical, especially when uncertainties 

regarding leakage through the locks and Compensating Works 

remain unquantified.

One approach to quantify the total uncertainty in Lake 

Superior outflow estimates is to assess the uncertainty in each 

component and sum the uncertainties. At this time, such an 

estimate is problematic. The largest impediment to making an 

accurate uncertainty determination is the unquantified leakage 

through the locks and Compensating Works. Until this flow 

is quantified, an accurate statement of uncertainty is difficult. 

However, the uncertainty in calculated monthly St. Marys 

River flow is likely to be greater than 5 percent and less than 

15 percent.

An alternative to the current method of calculating Lake 

Superior outflow is to measure the river at another location. 

If accurately measured, researchers could assess and monitor 

long-term shifts in the uncertainty of the current accounting 

system. This method is not likely to be useful during winter 

because of ice-affected flows through the St. Marys River. 

However, a comparison of summertime flow estimates at the 

Soo structures with observations at an alternative location 

would be useful to verify the accuracy of current accounting 

methods during ideal conditions. One potential location to 

measure flows for the purpose of comparison is at the narrow section of the St. Marys River between Pointe aux Pins, 

Ontario, and Brush Point, Michigan (fig. 6).

Lakes Michigan-Huron Outflow 

Water flows from Lakes Michigan-Huron to Lake Erie 

through the St. Clair River-Detroit River waterway (fig. 9). 

Unlike Lake Superior outflow, there are no control structures 

in this system, and flow must be measured in the existing river 

channel. Ice jams can severely complicate flow accounting in 

this river system and present major potential for uncertainty in 

calculated flows.

Three agencies currently estimate monthly flows through 

the St. Clair River-Lake St. Clair-Detroit River system; 

NOAA, USACE, and EC. Each of these three agencies has 

slightly differing methods of estimating these flows. Also, 

these agencies estimate river flow at many locations along the 

rivers. The uncertainty in all three agency estimates is largely 

due to the nature of stage-fall-discharge estimates. Most 

notably, ice floes and ice jams affect this relation and increase 

the uncertainty of flow calculations in the winter. Periodically, the three agencies meet and decide on which estimate is 

most accurate for each month. The agreed-upon value is then 

Methods of Quantifying Components and Potential Uncertainties
28 Uncertainty in the Great Lakes Water Balance

considered official. Generally, the values are in relatively close 

agreement during non-ice periods. The average range of MayNovember monthly values of flow from the three agencies is 

between 3.5 and 4 percent. 

Estimating wintertime flows through this system can be 

considered the weak link in the chain of Lake Huron outflow 

accounting. The usual stage-fall-discharge equations used for 

the rivers cannot be applied to ice-affected flows, so alternative equations have been developed by each agency. The accuracy of these estimates remains unknown, although uncertainty 

is clearly higher than during periods of non-ice-affected flows. 

Official data for ice-affected flows are agreed upon in the 

same manner as non-ice-affected months, but the accuracy of 

these data is uncertain. 

Measuring wintertime flow on the St. Clair River near 

Fort Gratiot using an Acoustic Doppler Current Profiler 

(ADCP) could be the best method to measure Lake Huron outflow during winter. Use of ADCP would allow the river to be 

gaged at one specific, ideal location. The St. Clair River near 

the gage at Fort Gratiot is relatively narrow, drops quickly, and 

flows swiftly, which prevents ice from forming and affecting 

flow. Flow velocities also are highly variable here, in response 

to changing flow volumes in the river. 

Recent advances in instrumentation, including the use 

of ADCP technology by USACE and the renovation of many 

gaging stations on the St. Clair River by NOAA, may improve 

uncertainty in flow estimates. The function of ADCP measurements is to supply more reliable data on streamflow when 

developing stage-fall-discharge equations. The function of 

improving gaging stations at many locations on the river is to 

supply a wide range of reliable stage data when developing 

stage-fall-discharge equations. It is not yet clear if the placement of the ADCP is suitable to allow improved measurement 

of St. Clair River flow. Similarly, it is unclear which of the 

renovated gaging stations will supply the most useful data for 

stage-fall-discharge equations. 

Useful flow estimates of lower St. Clair and Detroit 

Rivers could be generated using a computer model recently 

developed at the USGS (Holtschlag and Koschik, 2001). 

This model is capable of accurately estimating water levels 

and the distribution of flows throughout the St. Clair-Detroit 

River system, given accurate measurements of flow at model 

boundaries. The most important boundary in the USGS model 

is flow through the St. Clair River near the gaging station at 

Fort Gratiot, near the headwaters of the river. Additional flow 

boundaries include numerous tributary streams to the St. ClairDetroit River waterway, net atmospheric and ground-water 

inflow to Lake St. Clair, and water level at the mouth of the 

Detroit River near Bar Point, Ontario.

The USGS model could be used to estimate flows 

throughout the St. Clair-Detroit River waterway without 

investing a great deal of additional resources. Many of the 

inputs to this model, namely river stage measurements and 

tributary streamflows, are already being monitored and represent no additional allocation of resources. The current ADCP 

operated by the USACE also may be able to provide information necessary to estimate flow through the St. Clair River near 

the Fort Gratiot gaging station. However, the current ADCP 

is mounted vertically in the river channel. Because the USGS 

model is a horizontal 2-D model, a horizontally mounted 

ADCP would provide more relevant data. Also, the location of 

the ADCP is several miles downstream from the Fort Gratiot 

gaging station. It is unclear if river flows measured at this 

location will be adequate for use with the USGS model. 

Estimating the uncertainty in Lakes Michigan-Huron 

outflow estimates is difficult or impossible. The close agreement in monthly non-ice-affected-flow estimates between 

USACE, NOAA, and EC (within 3.5-4.0 percent) indicates 

that relatively little uncertainty exists in these estimates. However, monthly estimates of ice-affected flows have much more 

uncertainty. At worst, uncertainty in monthly estimates of iceaffected flows could be many times the magnitude of non-iceaffected flows. It is not clear how much this affects average 

monthly estimates of Lakes Huron-Michigan outflow, because 

the existence and severity of ice on these rivers is highly variable over space and time. Also, it is not yet certain to what 

degree estimates have been improved by recent improvements 

in instrumentation. Without this information, only a reasonable 

range of uncertainty in current monthly runoff estimates can 

be stated, which is likely to be in the range of 5 percent to 

15 percent.

Lake Erie Outflow

Lake Erie outflow is calculated by adding Niagara River 

flow at Buffalo to the flow entering the Welland Canal as 

it leaves Lake Erie (figs. 11 and 13). The Niagara River at 

Buffalo is not an ideal place to measure flows accurately, so 

flows at Buffalo are estimated based on several measurements 

made downstream. Periodic discharge measurements are made 

immediately upstream from the generating stations at Queenston, Ontario, and Lewiston, New York. Niagara River stage 

is measured at the Ashland Avenue gage near the downstream 

end of the Maid-of-the-Mist Pool below Niagara Falls 

(fig. 11). These stage data are used together with the periodic 

discharge measurements to determine flow at the Maid-ofthe-Mist pool based on a stage-discharge relation. Flow at the 

Maid-of-the-Mist pool is combined with the outflow from the 

Sir Adam Beck 1 and 2 and the Robert Moses Niagara powerplants. The sum of these flows provides total Niagara River 

flow near Queenston. To calculate Niagara River flow at Buffalo, local inflow (between Buffalo and the Maid-of-the-Mist 

pool) and the amount of water diverted into the Niagara River 

from the Welland Canal are subtracted from the Queenston 

flows; then, the amount of water diverted into the NYSBC is 

added. 

The amount of water entering the Welland Canal is based 

on a stage-discharge rating for flow through the Welland Canal 

Supply Weir combined with calculated flow through Lock 8, 

both in Port Colborne. The calculated Welland Canal flow 

at this point is considered to be the actual amount of diverted 

water. 
 29

Eight distinct flows are calculated or estimated and then 

combined to determine Lake Erie outflow (nine different flows 

if the Sir Adam Beck powerplants 1 and 2 are considered separately). All components of this accounting system are labeled 

in the schematic in figure 13 and represented in equations 3-5.

EO = NBuf + WE (3)

NBuf = NMoM + PB 1 and 2 + PRM – R – Wd + Bc (4)

WE = Ww + WL8 (5)

Substitution of equations 4 and 5 into equation 3 yields 

equation 6:

EO = NMoM + PB 1and2 + PRM – R – Wd + Bc + Ww + WL8 (6)

where EO is Lake Erie outflow,

NBuf is Niagara River flow at Buffalo,

NMoM is Niagara River Maid-of-the-Mist pool outflow,

WE is Welland Canal flow at Lake Erie,

Ww is Welland Canal flow through the supply weir 

structure,

WL8 is Welland Canal Lock 8 flow,

Wd is Water diverted from the Welland Canal into the 

Welland River,

PB 1 and 2 is flow through Sir Adam Beck 1 and 2 

powerplants,

PRM is flow through Robert Moses powerplant,

R is local inflow, and

Bc is New York State Barge Canal flow.

This accounting system likely reduces the total uncertainty in Lake Erie outflow estimates but complicates assessment of total uncertainty. One interesting feature of these flow 

components is that only one of these flows is subject to ice and 

weed retardation, the Niagara River flow at the Maid-of-theMist pool.

Niagara River flows below the Maid-of-the-Mist pool 

(NMoM) are computed with stage measurements that are compared to an accepted stage-discharge relation curve. The types 

of uncertainty associated with this method of computing flow 

are basically the same as with other computations based on 

stage-discharge relations. Uncertainty in these measurements 

is currently unknown but is likely to average between 

5 percent and 15 percent, depending on the degree to which 

ice and weeds affect the system. Maid-of-the-Mist pool 

outflow is the largest component of the Lake Erie outflow 

computation, constituting slightly less than 60 percent of the 

total Lake Erie outflow.

The outflow from the Sir Adam Beck 1 and 2 powerplants (PB 1and2) and the Robert Moses Niagara powerplant 

(PRM) is based on power/output efficiency calculations. Ontario 

Power Generation (OPG) and New York Power Authority 

(NYPA) determine plant discharges using rating tables for 

generators. Detailed uncertainty analysis of flow through Sir 

Adam Beck 2 performed by OPG estimates uncertainty to be 

2.33 percent (Ontario Power Generation, written communication, 2003). Uncertainty in Sir Adam Beck 1 and Robert 

Moses Niagara flow estimates is presumably similar. The sum 

flow through the three powerplants accounts for about 

40 percent of the calculated Lake Erie outflow.

For accounting purposes, the amount of water diverted 

into the NYSBC (Bc) has traditionally been assumed to be 

1,100 ft3/s during the navigation season. A lack of knowledge 

about how representative this value is of actual withdrawals 

for the NYSBC constitutes a significant data gap.

The amount of water diverted from the Welland Canal 

to the Niagara River (Wd) is subtracted in equations 4 and 6 

to avoid double counting this water as it flows through the 

Sir Adam Beck powerplants farther downstream. This flow is 

normally assumed to be 700 ft3/s. As a result of a recent test 

program by the City of Welland and the local conservation 

authority, however, the assumption was reduced to 460 ft3/s. 

When this change became known, flow records were revised 

to the beginning of 2002. An improved method of determining 

this diversion from the Welland Canal has been implemented 

(Len Falkiner, Environment Canada, written communication, 

2004). 

Local inflow (R) into the Niagara River between Lake 

Erie and Queenston is taken into account by assigning a 

monthly value for runoff to each month rather than estimating 

local runoff each month on an ongoing basis. The reason for 

this practice is that streamflow records in the Niagara River 

Basin are inadequate to determine local inflow directly. The 

Coordinating Committee decided to assign an average monthly 

runoff value to each month of the year. The values assigned to 

each month are based on runoff records from the Grand River 

in Ontario and the Genesee River in New York during 

1913-60. This procedure is described by the Coordinating 

Committee (1976, p. 14-15). Direct runoff to the Niagara 

River represents less than one half of 1 percent of the total 

calculated Lake Erie outflow. Because local runoff data are 

unavailable, there is currently no way of judging how well this 

system estimates local runoff.

Flow from Lake Erie to the Welland Canal is calculated 

by means of a stage-discharge relation based on measurement 

programs at the Welland Canal Supply Weir (Ww) and calculated flow through Lock 8 (WL8). Flow through the 10 valves 

at the weir has been calibrated by the USACE and EC and is 

reviewed every few years. Rating equations have been developed that take into account the valve openings, the head differential from above and below the weir, and the elevation of 

Lake Erie. Flow through Lock 8 is computed as the number of 

lock cycles times the capacity of the lock relative to the head 

differential. Hydraulic assists to shipping also are added and 

Methods of Quantifying Components and Potential Uncertainties
30 Uncertainty in the Great Lakes Water Balance

taken into consideration in the lock flow accounting. Official 

Welland Canal data reports do not show whether this system 

considers the amount of water that each ship displaces in the 

lock. If water displacement is not taken into consideration, 

Welland Canal flow will be overreported. The uncertainty in 

Welland Canal component of Lake Erie outflow is currently 

unknown but is likely to be in the range of 10 percent to 

20 percent. The uncertainty in Welland Canal flow data could 

potentially be reduced by use of acoustic velocity metering 

(AVM) technology. The value of reducing the uncertainty in 

Welland Canal flow estimates to improving Lake Erie outflow 

estimates is questionable, however, because the total flow 

through the Welland Canal accounts for less than 5 percent of 

Lake Erie outflow.

Overall, the uncertainty of the Lake Erie outflow calculation is dominated by the uncertainty in the calculated Maidof-the-Mist outflow and discharges from the powerplants. 

Taking this into consideration, the total uncertainty in Lake 

Erie outflow is likely to be between 4 to 10 percent. Use of 

ADCP technology to measure the Niagara River could possibly reduce the uncertainty to some extent. The accuracy of 

estimates of the smaller components has the potential to be 

improved substantially; the practicality of this is questionable, 

however, because improvement of total uncertainty of Lake 

Erie outflow would likely be negligible. 

Lake Ontario Outflow

Water flows from Lake Ontario to the Atlantic Ocean 

through the St. Lawrence River. Flow through the river is 

measured at the Moses-Saunders powerplant. Detailed uncertainty analysis of flow through the Moses-Saunders facility 

performed by OPG estimates uncertainty to be 1.24 percent 

(Ontario Power Generation, written communication, 2003). 

This degree of accuracy is possible because nearly 100 percent 

of the river flows through the 32 turbines of the power dam, 

and the turbine hydraulics are very well known. The flows are 

not subject to change due to ice floes, weed effects, or changes 

in the river channel. 

Estimated flow at the Moses-Saunders powerplant is 

generally taken as Lake Ontario outflow even though this 

site is 112 mi downstream from the outlet of Lake Ontario at 

Kingston, Ontario. No attempt is made to compensate for local 

runoff between Kingston and Cornwall; from a management 

perspective, it may be convenient or even desirable to treat the 

Moses-Saunders hydropower plant as the downstream terminus of the Lake Ontario Basin. Overall, uncertainty in Lake 

Ontario outflow estimates at Moses-Saunders is less than 

2 percent.

Evaporation 

Evaporation from the Great Lakes is perhaps the single 

most difficult process in the Great Lakes hydrologic cycle to 

understand. Added to this difficulty is the size of the Great 

Lakes. Quantifying evaporation over parts of the lakes that 

may be tens of miles away from land is a difficult task. Considering that evaporation is greater in magnitude than runoff, 

assessing the current understanding of evaporation from the 

Great Lakes is of great importance.

Evaporation from the Great Lakes is not directly 

measured, but it is estimated by means of the Great Lakes 

Evaporation Model, which was developed at the Great Lakes 

Environmental Research Laboratory (GLERL) (Croley, 1989a, 

b; 1992; Croley and Assel, 1994). This model incorporates 

observations on many atmospheric and hydrologic parameters 

and generates an estimate for evaporation from the surface of 

each lake, plus Georgian Bay. Most of the data used for the 

model are collected at weather stations near the shoreline of 

the Great Lakes; however, the model also uses remotely sensed 

data in the form of satellite-based surface-water temperatures. 

The model is a “lumped” model of heat storage, meaning that 

it estimates average evaporation rates for an entire body of 

water. Unlike a distributed model of a water body, the Great 

Lakes Evaporation Model does not estimate evaporation at 

specific points on the Great Lakes.

Uncertainty has been estimated for many of the input 

variables of the Great Lakes Evaporation Model, but no 

official statement of the accuracy of evaporation estimates 

is currently available. Any attempt to verify the model using 

discrete (point) evaporation estimates made over a Great Lake 

must attempt to identify an average evaporation rate for the 

entire Lake. In a system as large as the Great Lakes, this can 

be a daunting challenge technically, logistically, and financially. Such a jump from discrete data to an average evaporation rate for the entire lake also would introduce considerable 

uncertainty to the estimate being used to verify the model. 

Consequently, verifying the Great Lakes Evaporation Model is 

not a straightforward task. 

One facet of the model that could be verified is the 

validity of using shore-based meteorological measurements 

to represent over-lake conditions. It is conceivable that the 

evaporation model could be run two times a month for verification purposes; first, using the current system of shore-based 

measurements and second, using measurements made over the 

lake using buoys or other research platforms. Comparing the 

resulting evaporation estimates would reveal biases resulting 

from variations in the input data. Such a comparison would be 

useful to assess the adequacy of current methods of generating 

input data for the evaporation model.

An accurate estimate of uncertainty in the Great Lakes 

Evaporation Model is difficult to make at this time. However, 

for the purpose of considering evaporation estimate uncertainty in NBS estimates, an uncertainty range of 10 percent to 

35 percent is assumed. 

If it is deemed necessary to improve current evaporation 

estimates, there are at least two basic approaches: improving 

input data for the current model and improving or replacing 

the current model. The clearest way to improve the current 

evaporation model is to improve the quality of the input data. 

Greater use of over-lake or remotely sensed measurements on 

a year-round basis deserves some consideration. 
 31

The second approach to improving evaporation estimates 

is to use an improved evaporation model. Many distinct methods for estimating evaporation have been developed, and the 

accuracies differ considerably (Winter and others, 1995). The 

more reliable methods tend to require a greater variety of input 

data and more extensive instrumentation; therefore, if more 

resources were devoted to monitoring the physical hydrology 

of the Great Lakes, a more reliable model could possibly be 

developed. 

Diversions

Of the numerous diversions of water from the Great 

Lakes, only two are large enough to significantly affect the 

water balance: the Chicago diversion, which transports water 

out of the Great Lakes Basin; and the Welland Canal, which 

transports water from Lake Erie to Lake Ontario. The Welland 

Canal is treated as part of Lake Erie outflow in the water 

balance. For this reason, uncertainties in measuring Welland 

Canal flows are discussed at length in the “Connecting-Channel Flow” section of this report. Only the Chicago diversion 

will be discussed in this section. 

Currently, accounting for water diverted from Lake 

Michigan at Chicago considers (1) pumpage from Lake Michigan that is used for domestic purposes and routed out of the 

basin, (2) runoff that is redirected to flow out of the basin, and 

(3) direct diversions through three lakefront control structures. 

Domestic wastewater is treated and routed into the Chicago 

Sanitary and Ship Canal (CSSC) system. Construction of the 

Chicago diversion has rerouted the runoff from 673 mi2 of 

Great Lakes Basin to flow out of the basin. Water is diverted 

directly from Lake Michigan at three locations, the Chicago 

River Controlling Works, the Thomas J. O’Brien Lock and 

Dam, and the Wilmette pumping station (U.S. Army Corps of 

Engineers, 2001, p. 7). 

The accounting system for the Chicago diversion is 

summarized in equation 7. This system is the product of a 

considerable history of litigation and is intended to satisfy a 

U.S. Supreme Court decree that limits diversion flows attributable to the State of Illinois. Figure 16 illustrates the points of 

withdrawal, and the points of measurement of the Chicago 

diversion. 

Dc = QR + Dm – RDP – QGW – IGW (7)

where Dc is total discharge from the Chicago diversion, 

 QR is measured streamflow at Romeoville, 

Dm is municipal and miscellaneous discharge of 

diversion water not measured at the Romeoville gaging station, 

RDP is runoff from the Des Plaines River that discharges into the CSSC upstream from 

Romeoville gaging station, 

QGW is the portion of the flow at Romeoville that 

originated as ground water that was pumped 

for Illinois municipal use and discharged 

to the CSSC or attributed to ground-water 

seepage into the canal, and 

I

GW is Indiana water discharge to the CSSC from the 

Calumet River system and the Calumet Sag 

Channel.

More than 90 percent of all flows diverted at Chicago 

pass the gaging station at Romeoville and are measured by 

AVM. Diverted flows not captured in this channel include 

treated wastewater discharged from communities that do not 

release their wastewater into the canal. Domestic and miscellaneous discharge of diversion water is estimated and added to 

the streamflow at Romeoville (U.S. Army Corps of Engineers, 

2001, p. 7).

Flow measured at the Romeoville gaging station also 

captures non-Great Lakes Basin water from three sources 

(U.S. Army Corps of Engineers, 2001, p. 8). Before Chicago 

diversion accounting can be complete, these three sources 

must be discounted from the Romeoville flows. First, stormwater discharge from the Des Plaines River Basin is captured 

in the Chicago stormwater system, treated, and discharged to 

the CSSC upstream from the gaging station at Romeoville. 

The routing of this water is not apparent on the map in figure 

16, but this stormwater must still be subtracted from Romeoville flows. The second source of non-Great Lakes water 

in Romeoville gaged flows is ground water. Ground-watersupply effluent from Illinois and ground-water seepage into 

tunnels that flow to the CSSC are considered to be “non-Great 

Lakes Basin water” under the U.S. Supreme Court decree that 

regulates Chicago diversion accounting. Third, Indiana water 

supply that is discharged to the CSSC from the Calumet River 

system and the Calumet Sag Channel is discounted. This also 

is an accounting detail attributable to the U.S. Supreme Court 

decree that dictates the legal accounting of the diversion. 

There are four primary categories of uncertainty in the 

official Chicago diversion accounting. First is the uncertainty 

associated with the measurement of CSSC flows at Romeoville. These flows are measured directly with an AVM. Such 

measurements are commonly believed to be reliable within 

5 percent. The second category of uncertainty is in the estimates of discharge from several water-treatment plants in 

the system. Flows through the treatment plants are closely 

monitored by means of water balances and then usually compared to recorded flows to ensure accuracy (U.S. Army Corps 

of Engineers, 2001, p. 8). This system is generally accepted 

as being effective, and the uncertainty is likely to be in the 

range of 5 percent-10 percent, although the actual uncertainty has not been officially established. The third category 

of uncertainty in the Chicago diversion accounting system is 

the estimation of the ground-water component of Romeoville 

streamflow. Most of this component is measured as ground 

water pumped for Chicago water supplies, and some of it is 

calculated as seepage into the system (U.S. Army Corps of 

Engineers, 2001). The quantity of water in this category is 

comparatively small, so the uncertainty in its estimation is of 

minor importance to the total uncertainty of the accounting 

Methods of Quantifying Components and Potential Uncertainties
32 Uncertainty in the Great Lakes Water Balance

method. The fourth and final category of uncertainty is the 

estimation of water supplies from Indiana. These flows are 

not gaged; they fluctuate as the elevation of Lake Michigan 

changes, and they are probably the least understood flows in 

the Chicago diversion system. 

The official Chicago diversion accounting dictated by 

the U.S. Supreme Court applies directly to Illinois and does 

not count diversion flows arising from three specific sources. 

The first source is pumpage of Lake Michigan waters by U.S. 

Federal facilities. The second source is diverted flow from 

Indiana. Finally, ground water pumped from inside the Great 

Lakes Basin that is ultimately diverted outside the Great Lakes 

Basin (U.S. Army Corps of Engineers, 2001, Appendix B, p. 

21-23). According to data reported by USACE (2001, p. 21), 

the sum of these three flows in water year 1995 totaled 4 percent of the total diversion flow accountable to Illinois. Therefore, certified flow statistics systematically underestimated the 

total flow of water diverted at and near Chicago by 4 percent 

for water year 1995. The magnitude of this bias is believed to 

be similar in other years of reporting.

There also are two small over deductions in certified 

diversion flow statistics. Mathematically, diversion amounts 

should be deducted by the quantity of consumptive use within 

the basin; that is, water consumed inside the basin should not 

count toward water diverted out of the basin. Currently (2004), 

engineers are unable to calculate consumptive use well enough 

to estimate a fair and reliable deduction; therefore, this amount 

is not deducted in certified Chicago diversion flows (U.S. 

Army Corps of Engineers, 2001, p. 23-24). This unknown but 

small amount should not contribute significantly to the total 

uncertainty in the Chicago diversion. The second over deduction happens when runoff to the Chicago diversion is counted 

100 percent as diverted water; despite the belief that evapotranspiration would diminish the amount of runoff that would 

naturally reach Lake Michigan. The degree to which these 

over deductions are significant is a matter of debate. For example, Croley and others (2001) consider the current accounting 

of diverted runoff to cause a significant overstatement in the 

amount of water removed from Lake Michigan. For a more 

in-depth discussion of the Chicago diversion computation 

procedures, the reader is directed to the latest Chicago District 

USACE publication titled, “Lake Michigan diversion accounting, water year [YEAR] annual report” (for example, U.S. 

Army Corps of Engineers, 2001). 

For the purpose of illustrating the importance of Chicago 

diversion accounting uncertainty in NBS estimates, a reasonable range of uncertainty in the official Chicago diversion 

accounting method is assumed to be in the range of 5 percent 

to 10 percent. There is also a 4 percent under-reporting bias 

related to water diverted away from Lake Michigan through 

Indiana.

Change in storage

Net change in storage is calculated as the product of the 

measured change in lake stage and surface area of each lake. 

Therefore, the uncertainty in change-in-storage calculations 

depends on the accurate measurement of these two parameters. 

Estimates of the surface area of the Great Lakes exist in Coordinating Committee (1977, table 1). Some amount of uncertainty is 

present in these data, but these measurements are generally taken 

as adequate to calculate change in storage on the Great Lakes. 

Uncertainty in lake-stage measurements is responsible for some 

uncertainty in change-in-storage estimates. Thermal expansion 

and contraction of water also contributes to uncertainty in estimates of change in storage. 

Computation of lake-stage data is complicated primarily by 

two processes–isostatic rebound and wind set-up and seiche. The 

USACE adjusts its computation of average lake stage for isostatic 

rebound, so this factor is not believed to contribute a significant 

amount of uncertainty to change-in-storage estimates. The previously described phenomena of wind set-up and seiche can cause 

great variability in lake stage at different parts of a lake. The 

method used to correct for these factors is to measure lake stage 

at selected locations and average the values in a weighted fashion 

to determine an average lake stage (Croley, 1987a, 1987b). The 

locations of all active lake gages are shown in figure 19. The 

Marine Environmental Data Service (MEDS) and the National 

Ocean Service (NOS, a division of NOAA) report Great Lakes 

stage measurements at individual gages throughout the basin. The 

uncertainties of these agencies’ stage data are 10 mm (0.39 in) 

and 5 mm (0.20 in) at individual gages, respectively. However, it 

is a weighted average of many gages around a given Great Lake 

that yields the “true” lake stage that is used in change-in-storage 

calculations. 

The USACE reports “normalized daily mean” water levels of 

the Great Lakes. These average daily values, which are generated 

from a coordination of the measurements of selected U.S. (NOS) 

and Canadian (MEDS) gages, consider the heterogeneous effect 

of isostatic rebound on the gage network. Beginning-of-month 

(BOM) lake stage is based on these USACE data and is determined by averaging the first day of the month with the last day of 

the previous month (Lee, 1992). The resulting BOM values are 

used to calculate monthly change in storage. The USACE does 

not publish an official statement of uncertainty in these data (Neff 

and Killian, 2003). However, statistically speaking, the uncertainty in these average stage data should be substantially smaller 

than the uncertainty of any one gage measurement. The uncertainty in the normalized daily mean lake-stage data is likely to be 

in the range of 2.0 mm (0.079 in). Croley (1987a, 1987b) points 

out that uncertainty from wind set-up is greatest in the fall and 

winter, when wind is more common than in spring or summer. 

Uncertainty is likely to be greater in individual months with nonideal weather and hydrologic conditions.

Whatever the uncertainty of the BOM mean stage, it must 

be remembered that change in storage is based on two separate 

BOM stage measurements (beginning and end of month measurements) and that both uncertainties must be summed statistically. 
Methods of Quantifying Components and Potential Uncertainties 33

CANADA

CANADA

U. S. A.

U. S. A.

O N 

JAMES

BAY 

T A R I O

Q U E B E C

ILLINOIS INDIANA OHIO

PENNSYLVANIA

NEW

YORK

900

800

450

500

 

M

I

H I G

A

N

Figure 19. Locations of lake level gages in the Great Lakes basin. 

(Canadian data from Marine Environmental Data Service, 2002; U.S. data from 

National Ocean Service, 2002.)

GREAT LAKES BASIN 

LAKE LEVEL GAGE--Canada

LAKE LEVEL GAGE--United States

EXPLANATION

W I S C O N S I N LAKE

HURON

LAKE

ERIE

LAKE SUPERIOR

LA

KE

MICHIGAN

LAKE

ONTARIO

0 50 100 150 200 KILOMETERS

Base from ESRI, 2001; Army Corps of Engineers,1998; and Environment Canada,1995. 0 50 100 150 200 MILES
34 Uncertainty in the Great Lakes Water Balance

Specifically, the uncertainty of the change-in-storage calculation 

increases beyond the uncertainty of one stage measurement. The 

statistical sum of the uncertainties related to lake-stage measurement data is likely to be within the range of ±3 mm (0.118 in).

One fundamental assumption in the change-in-storage 

calculation is that the thermal expansion or contraction of water 

is negligible. Water physically expands and contracts slightly 

in response to changes in temperature. Some researchers have 

shown that this fluctuation can become significant during some 

months of the year. Meredith (1975) and Quinn and Guerra 

(1986) used water-column temperature data to calculate monthly 

rates of thermal expansion of water in Lake Erie. Their results 

show that change in storage caused by thermal expansion and 

contraction can be as high as 106 m3/s (3,743 ft3/s; Meredith, 

1975) and 131 m3/s (4,626 ft3/s; Quinn and Guerra, 1986) for 

some months. Based on the area of Lake Erie presented in 

Coordinating Committee (1977), these rates are equivalent to a 

change in lake stage of approximately 10 mm (0.39 in) in one 

month. Lee (1992, p. 9 and 11) notes that significant error in 

change-in-storage estimates can result if thermal expansion of 

water is not considered and recommends that it be considered in 

NBS calculations.

Incorporating thermal expansion and contraction of the 

Great Lakes into change-in-storage calculations could be done 

two ways. The first and most simple method would be to use 

the estimated water-column data generated by the Great Lakes 

Evaporation Model, described previously, to calculate the thermal expansion or contraction of each Great Lake. The second 

way would require extensive monitoring of water-column temperatures. On the basis of published estimates of rates of thermal 

expansion of water in Lake Erie, it is possible that this process is 

insignificant during most months, but could cause an uncertainty 

of 10 mm (0.39 in) in monthly change-in-storage calculations in 

a worst-case scenario. 

Changes in salinity of water and depth also affect water 

density and are therefore of theoretical concern. However, these 

factors affect the Great Lakes system either very little or on time 

scales that are long term. For these reasons, changes in water 

density due to these factors are not considered here.

The two largest impediments to the development of an accurate uncertainty estimate are (1) the lack of an official statement 

of uncertainty in USACE-generated normalized daily mean stage 

data and (2) the need for additional information on the thermal 

expansion and contraction of the Great Lakes. In the absence of 

this information, it is apparent that for most months the uncertainty in monthly change-in-storage calculations could be as low 

as 3 mm (0.12 in), but for some months the uncertainty could be 

as high as 12 mm (0.47 in).

Current Approaches to Deriving Net 

Basin Supply

NBS can be thought of qualitatively as the net amount of 

water entering a Great Lake. This section describes the two 

methods of calculating NBS and considers how the uncertainties in the water-balance equation affect each method. A tabular 

comparison of the uncertainties also is given.

Two distinct approaches, the residual method and the 

component method, can be used to determine NBS. The methods 

differ in the water-balance components used to determine NBS. 

Each approach is better suited for certain situations than the 

other. Understanding the difference between the two methods is 

a key to maximizing the accuracy of NBS estimates. Mathematical expressions of the complete accounting of NBS for each 

method are given in equations 8 and 10. Simplified, commonly 

used expressions, in which terms considered to be negligible 

are omitted, are given in equations 9 and 11. Omission of these 

terms has substantial implications for the uncertainty of NBS 

estimates. The reader should be aware that both methods consider several components of the water balance, and that “components of the water balance” should not be confused with “the 

component method.” Readers also are directed to Lee (1992) for 

additional information on the two methods.

Component NBS calculation – full 

NBS = P + R – E + G (8)

Component NBS calculation – commonly used 

NBS = P + R – E (9)

Where P is over-lake precipitation, 

R is runoff to a Great Lake,

E is evaporation from the lake surface, and

G is ground-water flux into a Great Lake (net).

Residual NBS calculation – full 

NBS = O – I +∆ S – ∆ St + Do – Di (10)

Residual NBS calculation – commonly used 

NBS = O – I +∆ S + Do – Di (11)

Where O is outflow from a given Great Lake,

I is inflow from an upstream Great Lake (the water balance for Lake Superior does not have an I term),

∆S is change in water storage of a Great Lake,

∆St is change in water storage caused by thermal expansion or contraction of the water body,

Do is diversion of water out of a basin, and

Di is diversion of water into a basin.

Note the similarity between the residual method equations 

(10 and 11) and the traditional water-balance equation (Inflow = 

Outflow + ∆ Storage). In fact, these equations are conceptually 

the same. Also, note that the residual method NBS is equal to the 

component method NBS; subtracting one from the other should 

yield zero.

Consumptive use requires mention with regard to these 

equations. Consumptive use represents water that is supplied to a 

basin but is frequently removed before it can be accounted for by 
 35

other terms of the water balance. In many instances, but not all, 

it should be added to both the residual and the component NBS 

equations. For example, if water is removed from the headwaters 

of a river and consumed, it should be added to residual and component NBS estimates. However, if water is removed directly 

from a Great Lake and consumed, the quantity of water should 

be added to the residual NBS, but not to the component NBS, 

because the component method has already accounted for this 

water as runoff or precipitation. This point is somewhat moot 

and perhaps is best ignored in practice; no estimates of NBS 

attempt to account for consumptive use, and the magnitude of 

consumptive use is relatively small.

Component NBS

The component method calculates NBS by considering 

the actual inputs and outputs of each lake, without regard to 

connecting-channel flow or change in storage. Usually, the 

component NBS is calculated simply as NBS = P + R – E. The 

disadvantage to this method is that runoff, direct precipitation, 

and evaporation tend to be the elements of the water balance 

prone to the greatest percentage of uncertainty. The advantage 

to this method is that it avoids the need to measure flow through 

the connecting channels and change in storage. Even though the 

uncertainty in connecting-channel flow can be a relatively small 

percentage, the amount of flow being measured is relatively 

large, which can result in large total uncertainties. 

Although it is theoretically not necessary to consider diversion flow when using the component method, existing datasets 

of runoff and diversion flows necessitate their consideration. 

Streamflow entering Lake Superior from the Nipigon and Aquasabon Rivers include water diverted from the Ogoki and Long 

Lac diversions, respectively (figs. 4 and 5). There is no way to 

accurately measure runoff from these rivers without inadvertently measuring Ogoki and Long Lac diversion flows. However, 

it is possible to subtract Ogoki and Long Lac diversion flows 

from the total runoff to Lake Superior. This method yields the 

true Great Lakes Basin runoff from the Nipigon River with the 

least possible uncertainty. 

Flows through the Chicago diversion are dealt with differently than flows through the Ogoki and Long Lac diversions 

in component method NBS calculations. The simplest way to 

account for the Chicago diversion is to calculate runoff for all 

areas within the Lake Michigan Basin, including areas that are 

now diverted to the Mississippi River Basin at Chicago. Runoff 

from the Chicago area can be calculated using data provided 

in the latest Chicago District USACE publication titled, “Lake 

Michigan diversion accounting, water year [YEAR] annual 

report” (for example, U.S. Army Corps of Engineers, 2001). 

These runoff data can then be used to calculate NBS using the 

component method (eq. 9). A different way to account for Chicago diversion flows when calculating NBS using the component method is used by some authors (Croley and others, 2001, 

p. 7-8). 

Because the Welland Canal diversion is an interbasin diversion between Lake Erie and Lake Ontario, it is not treated as a 

diversion in either method of NBS estimation. In residual NBS 

estimates, it is lumped together with Niagara River flows to generate total Lake Erie outflow. The component method does not 

consider Welland Canal flows in any way.

Ground-water discharge to the Great Lakes and consumptive 

use within the Great Lakes Basin comprise part of NBS, but are 

generally assumed to be negligible. These components are not 

considered in any existing NBS calculations. As shown elsewhere 

in this report, these assumptions may introduce some uncertainty 

to NBS estimates. 

GLERL computes NBS on the basis of the component 

method and publishes the results periodically. The most recent 

published NBS data are in Croley and others (2001). The 

Midwestern Regional Climate Center (MRCC) also publishes a 

forecast of Great Lakes NBS based on the component method on 

their Web site (http://mcc.sws.uiuc.edu); this Web site is briefly 

described in Neff and Killian (2003, p. 21, 27).

Residual NBS

The residual method of calculating NBS considers connecting-channel inflow and outflow and the change in storage 

of each lake. For a complete accounting of NBS, adjustments 

need to be made to account for the change in storage caused by 

thermal expansion, diversions into and out of the Great Lakes, 

and consumptive use. Usually, however, thermal expansion and 

consumptive use are considered to be negligible and are treated as 

zero (equations 10-11). 

The advantage to calculating NBS with the residual method 

is that only water levels on the Great Lakes and flows in the 

connecting channels need to be measured to generate an estimate 

of NBS. This is both convenient and a relatively straightforward 

way to calculate NBS. The main problem with this method is 

that connecting-channel flows and change in storage in the Great 

Lakes system are very large in relation to NBS estimates. This 

issue is amplified in the lower reaches of the Great Lakes system. 

Therefore, even a small degree of uncertainty in the connectingchannel flow and change-in-storage estimates can cause a large 

degree of uncertainty in the calculated NBS. Quinn and Guerra 

(1986) showed that a 5-percent error in Lake Erie connectingchannel flow can result in a disproportionately large error in NBS 

calculation. 

 The way diversions are accounted for is the second problem 

with residual-method NBS estimates. Ideally, only the part of the 

diversion that actually affects a lake would be counted in equations 10 and 11. However, this is not always possible, and agencies reporting residual-method NBS estimates simply consider 

diversion flow data as is, without making adjustments in their 

calculations. This practice adds uncertainty to the NBS estimates.

Relative Magnitude of Uncertainties in NBS 

Estimates

Tables 3–7 and figures 20–21 summarize the findings of this 

report and illustrate how uncertainty in estimates of individual 

Current Approaches to Deriving Net Basin Supply
36 Uncertainty in the Great Lakes Water Balance

Table 3. Summary of monthly component and net basin supply (NBS) uncertainty for Lake Superior 

[ft3/s, cubic feet per second; in, inches; mm, millimeters; %, percent; N/A, not applicable].

Lake Superior

 Average 

 magnitude

Average monthly 

estimate uncertainty

Component of water balance ft3

/s Low High Low (ft3/s) High (ft3/s)

Connecting-channel inflow N/A N/A N/A N/A N/A

Connecting-channel outflow 79,118 5% 15% 3,956 11,868

Change in storage N/A 0.12 in (3 mm) 0.47 in (12 mm) 3,356 13,422

Over-lake precipitation 73,047 15% 45% 10,957 32,871

Runoff 55,619 15% 35% 8,343 19,467

Evaporation 54,233 10% 35% 5,423 18,982

Long Lac diversion 1,412 10% 30% 141 424

Ogoki diversion 4,035 10% 30% 404 1,211

Ground water Unknown 100% of 850 ft3

/s 100% of 3,500 ft3/s 850 3,500

Component NBS 70,398 11% 31% 7,567 21,848

Residual NBS 73,671 4% 12% 2,656 9,164

Table 4. Summary of monthly component and net basin supply (NBS) uncertainty for Lakes Michigan-Huron 

[ft3/s, cubic feet per second; in, inches; mm, millimeters; %, percent; N/A, not applicable].

Lakes Michigan-Huron

 Average 

 magnitude

Average monthly 

estimate uncertainty

Component of water balance ft3

/s Low High Low (ft3/s) High (ft3/s)

Connecting-channel inflow 75,430 5% 15% 3,772 11,315

Connecting-channel outflow 183,810 5% 15% 9,191 27,572

Change in storage N/A 0.12 in (3 mm) 0.47 in (12 mm) 4,796 19,182

Over-lake precipitation 106,610 15% 45% 15,992 47,975

Runoff 95,170 15% 35% 14,275 33,310

Evaporation 83,410 10% 35% 8,341 29,194

Chicago diversion 3,200 5% 10% 160 320

Ground water 

Unknown 100% of 1,625 

ft3/s

100% of 6,500 ft3/s 1,625 6,500

Component NBS 118,370 10% 28% 11,765 33,478

Residual NBS 111,580 5% 16% 5,629 18,084
 37

Table 6. Summary of monthly component and net basin supply (NBS) uncertainty for Lake Ontario [ft3/s, cubic feet 

per second; in, inches; mm, millimeters; %, percent; N/A, not applicable]

Table 5. Summary of monthly component and net basin supply (NBS) uncertainty for Lake Erie [ft3/s, cubic feet per 

second; m3/s, cubic meters per second; in. inches; mm, millimeters; %, percent; N/A, not applicable].

Lake Erie

Average 

magnitude

Average monthly 

estimate uncertainty

Component of water balance

 

 ft3/s

Low High Low 

 (ft3/s)

High 

(ft3/s)

Connecting-channel inflow 188,333 5% 15% 9,417 28,250

Connecting-channeloutflow 206,202 4% 10% 8,248 20,620

Change in storage N/A 0.12 in (3 mm) 0.47 in (12 mm) 1,049 4,197

Over-lake precipitation 25,497 15% 45% 3,825 11,474

Runoff 21,189 15% 35% 3,178 7,416

Evaporation 26,027 10% 35% 2,603 9,109

Ground water Unknown 100% of 400 ft3

/s 100% of 1,600 ft3/s 400 1,600

Component NBS 20,659 14% 41% 2,871 8,417

Residual NBS 17,869 36% 101% 6,412 17,991

Current Approaches to Deriving Net Basin Supply

Lake Ontario

Average 

magnitude

Average monthly 

estimate uncertainty

Component of water balance ft3

/s Low High Low (ft3/s) High (ft3/s)

Connecting-channel inflow 206,202 4% 10% 8,248 20,620

Connecting-channel outflow 246,461 1.5% 2% 3,697 4,929

Change in storage N/A 0.12 in (3 mm) 0.47 in (12 mm) 777 3,108

Over-lake precipitation 18,081 15% 45% 2,712 8,136

Runoff 37,539 15% 35% 5,631 13,139

Evaporation 14,091 15% 45% 2,114 6,341

Ground water Unknown 100% of 300 ft3

/s 100% of 1,250 ft3/s 300 1,250

Component NBS 41,530 8% 21% 3,370 8,546

Residual NBS 40,259 12% 27% 4,631 10,951
38 Uncertainty in the Great Lakes Water Balance

water-balance components affects uncertainty in monthly NBS 

estimates. Each table presents estimates of the reasonable range 

of percent uncertainty of each component as determined elsewhere in this report. The total uncertainty of each component is 

calculated by multiplying percent uncertainty by the long-term 

average magnitude of each component as determined from data 

reported by Croley and others (2001). In the case of ground 

water, the total uncertainty is 100 percent of net seepage. The 

range of total seepage for each lake is based on reasonable rates 

of seepage per mile of shoreline (0.5 ft3/s – 2.0 ft3/s) and the 

lengths of shoreline of each lake as reported by the Coordinating 

Committee (1977). Uncertainties related to consumptive use are 

not reflected here. Data given for total uncertainty in NBS estimates is the statistical sum of the uncertainties of each component, according to the methods explained in Hill (1998, 

p. 46-47). Total uncertainty in NBS estimates is presented 

both as an amount of flow and as a percent of the long-term 

average monthly NBS. Percent uncertainty in NBS is given 

for comparative purposes and should be interpreted with 

caution. During months with small NBS, the percent uncertainty could be greater than these tables indicate. Likewise, 

during months with large NBS, the percent uncertainty could 

be less than these tables indicate. 

As these results indicate, each of the two methods used 

to calculate NBS is better suited to particular situations. 

The residual method produces NBS estimates with the least 

amount of uncertainty for Lakes Superior and MichiganHuron. In contrast, the component method of calculating 

NBS provides the least amount of uncertainty for Lakes Erie 

and Ontario. There also is a large range in uncertainty for 

NBS estimates calculated with the two methods. The component method yields NBS estimates for Lake Superior with 

about 21⁄2 times greater uncertainty than the residual method 

does. However, for Lake Erie, the component method yields 

NBS estimates with less than half the uncertainty of residual 

NBS estimates.

Table 7a. Summary of net basin supply (NBS) 

uncertainty, expressed as a percent of long term 

average monthly NBS.

Component 

Method Residual Method

Lake Low High Low High

Superior 11 31 4 12

Michigan-Huron 10 28 5 16

Erie 14 41 36 101

Ontario 8 21 12 27

Table 7b. Summary of net basin supply (NBS) 

uncertainty, expressed in cubic feet per second.

Component 

Method Residual Method

Lake Low High Low High

Superior 7,567 21,848 2,656 9,164

Michigan-Huron 11,766 33,479 5,630 18,084

Erie 2,871 8,417 6,412 17,991

Ontario 3,370 8,546 4,631 10,951

0

20

40

60

80

100

120

LAKE SUPERIOR LAKE MICHIGAN/ LAKE ERIE LAKE ONTARIO

LAKE HURON 

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

LAKE SUPERIOR LAKE MICHIGAN/ LAKE ERIE LAKE ONTARIO

LAKE HURON 

TOTAL UNCERTAINTY IN MONTHLY NET BASIN SUPPLY  ESTIMATES, IN CUBIC FEET PER SECOND

Compoment 

method

PERCENTAGE UNCERTAINTY IN MONTHLY  NET BASIN SUPPLY ESTIMATE

Figure 20. Total uncertainty in monthly net

basin supply estimates for each method and 

each Great Lake, expressed as flow rate. 

Figure 21. Percentage uncertainty in monthly

net basin supply estimates for each method

and each Great Lake.

Residual

method

Compoment 

method

Residual

method
 39

Summary and Conclusions

In June 2001, eight U.S. state governors and two Canadian province premiers signed an Annex to the 1985 Great 

Lakes Charter. The Annex calls for, among other things, 

hydrologic data and information to support a new decision 

standard regarding proposals to withdraw water from the Great 

Lakes Basin. None of the existing Great Lakes hydrologic 

monitoring networks were designed to support such a system. 

An understanding of the limitations of the many monitoring 

networks in the context of Annex 2001 is both unknown and 

fundamental to the design and implementation of a successful 

decision-making standard. This report was written in response 

to this need, addresses several important questions regarding 

the status of existing hydrologic monitoring networks, and 

assesses uncertainty in the Great Lakes water balance.

This report is a product of Technical Subcommittee 2 

(TSC2) of the Water Resources Management Decision Support 

System (WRMDSS) project supported by the Great Lakes Protection Fund, prepared by the U.S. Geological Survey in cooperation with the Great Lakes Commission. TSC2 was charged 

with providing a status assessment of water-resources information and availability. Most of the work of TSC2 was designed 

to evaluate the quantity and quality of water-resources data 

and information on a lakewide or systemwide scale. Specifically, the work and other publications resulting from TSC2 

focused on flows and levels in the context of net basin supplies 

(NBS) to each Great Lake. Additional information is available from two other project reports: “The Great Lakes Water 

Balance: Data Availability and Annotated Bibliography of 

Selected References” (Neff and Killian, 2003) and “Great 

Lakes Monthly Hydrologic Data” (Croley and others, 2001).

This report describes the Great Lakes hydrologic system, 

and methods used to quantify individual components of the 

water balance. Specific water-balance components discussed 

include connecting channel flow, runoff, over-lake precipitation, evaporation, groundwater inputs, change in storage, and 

diversions in and out of the Great Lakes. Potential sources of 

uncertainty are identified and, where appropriate, alternate 

or additional data, models, and estimation methods suitable 

for reducing uncertainties are discussed. Finally, approximate uncertainties in monthly estimates of all water-balance 

components are identified and compared within the context of 

monthly NBS estimates. 

Throughout this report, the term “uncertainty” is used 

qualitatively to describe errors and biases associated with 

measurements, calculations, and estimates. All measurements and calculations have uncertainty associated with them. 

Uncertainty does not necessarily indicate errors or flaws in 

monitoring. In some cases, uncertainty in a measurement or 

calculation may be present despite state-of-the-art instrumentation or estimation methods. Also, this report discusses 

uncertainties within the context of monthly data and monthly 

NBS estimates. This context is used because the Great Lakes 

water balance is most commonly described on a monthly time 

scale, and is frequently used to calculate NBS. It is not known 

if monthly data, or if the concept of NBS, is well suited to the 

information needs of Annex 2001. 

Results indicate that average uncertainties in monthly 

estimates of individual water-balance components may range 

from 1.5 percent to 45 percent. This may result in monthly 

net basin supply uncertainties of approximately 2,600 ft3/s to 

33,500 ft3/s for individual Great Lakes. These results reflect 

estimates of uncertainty, rather than an absolute determination of uncertainty. It is not possible to conclusively determine 

uncertainties in the Great Lakes water balance for two reasons. 

First, the Great Lakes hydrologic system is highly variable 

and uncertainty of water-balance estimates is in a constant 

state of flux. Second, for several reasons it is not possible to 

conclusively determine uncertainty in estimates of individual 

components. In some instances, such as evaporation estimates, 

methods used to estimate a water-balance component preclude 

an effective assessment of uncertainty. In other cases, such 

as over-lake precipitation, there is a substantial data gap that 

prevents effective assessment of uncertainty. A lack of external 

review among agencies responsible for reporting hydrologic 

data in the Great Lakes Basin also complicates the determination of uncertainty in water-balance component estimates. 

Therefore, TSC2 used its best professional judgment to 

estimate ranges of uncertainty for monthly estimates of levels 

and flows.

This report identifies several data gaps and information needs that prevent a more conclusive determination of 

water-balance components. The greatest data gap is a lack 

of over-lake weather monitoring. Improvements to weather 

monitoring over the surface of the lakes could help researchers better assess over-lake rainfall and evaporation. A second 

need is for improvement in wintertime connecting-channelflow estimates, particularly on the St. Clair and Detroit Rivers. 

Third, improvements in estimates of ungaged basin runoff 

could reduce the uncertainty of runoff estimates. Fourth, 

current accounting of interbasin diversions may not properly 

describe each diversion’s impact on the water balance. As data 

gaps are filled, information needs are met, and external review 

of hydrologic data increases, uncertainty in estimates of waterbalance components will diminish.

Acknowledgments

This report is a result of cooperative efforts of members 

of Technical Subcommittee 2 of the Water Resources Management Decision Support System (WRMDSS) project, who 

defined the scope of work reported herein, provided substantive data and information, and reviewed all drafts of the report. 

In addition, members of the Project Management Team and 

Stakeholder Advisory Committee of the WRMDSS project 

reviewed and provided comment on drafts of the report. All 

these people and their agencies contributed significant staff 

time and other resources to this effort and they are named in 

the final report of the WRMDSS project, “Toward a Water 

Summary and Conclusions
40 Uncertainty in the Great Lakes Water Balance

Resources Management Decision Support System for the 

Great Lakes-St. Lawrence River Basin” (Great Lakes Commission, 2003).

This report has benefited from significant input and 

collaboration from Dick Bartz (Ohio Department of Natural 

Resources), Jim Bredin (Michigan Department of Environmental Quality), Andy Buschbaum (National Wildlife Federation), Ian Cameron (Ontario Ministry of Natural Resources), 

Len Falkiner (Environment Canada), Roger Gauthier (U.S. 

Army Corps of Engineers), Reg Gilbert (Great Lakes United), 

James Hebenstreit (Indiana Department of Natural Resources), 

Dan Injerd (Illinois Department of Natural Resources), Jim 

Japs (Minnesota Department of Natural Resources), George 

Kuper (Council of Great Lakes Industries), David Ladd (formerly of Michigan Department of Environmental Quality), 

Wendy Larson (Limno-Tech), Bob Metcalfe (Ontario Power 

Generation), Sarah Miller (Canadian Environmental Law 

Association), Nanette Noorbakhsh (U.S. Army Corps of Engineers), and Chuck Southam (Environment Canada). The assistance and advice of the Great Lakes Commission staff—Dan 

Blake, Tom Crane, Mike Donahue, and Becky Lameka—has 

been invaluable. Finally, the authors appreciate the thoughtful 

technical reviews of Tom Croley (National Oceanic and Atmospheric Administration) and Daniel Feinstein (U.S. Geological 

Survey), the careful editorial reviews of Mike Eberle and Leah 

Hout (U.S. Geological Survey), and the illustration and layout 

work of Sharon Baltusis (U.S. Geological Survey).

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Brian P. Neff and J.R. Nicholas—Uncertainty in the Great Lakes Water Balance—Scientific Investigations Report 2004-5100

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