UNITED STATES 

DEPARTMENT OF COMMERCE 

Carlos M. Gutierrez

Secretary 

NATIONAL OCEANIC AND 

ATMOSPHERIC ADMINISTRATION 

Conrad C. Lautenbacher, Jr. 

Administrator 

MODIFIED GREAT LAKES HYDROLOGY MODELING SYSTEM 

FOR CONSIDERING SIMPLE EXTREME CLIMATES 

Thomas E. Croley II 

NOAA, Great Lakes Environmental Research Laboratory, Ann Arbor, MI 48105 

Great Lakes Environmental Research Laboratory 

Ann Arbor, Michigan 

April 2006 

NOAA Technical Memorandum GLERL-137
ii

NOTICE 

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

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

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

authorized. This is GLERL Contribution No. 1386.

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

web site: www.glerl.noaa.gov. Hard copies can be requested from GLERL, Information services, 2205 Commonwealth Blvd., Ann Arbor, MI 48105. 

pubs@glerl.noaa.gov. 
iii

TABLE OF CONTENTS 

ABSTRACT.....................................................................................................................................1 

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

 1.1 Background and Purpose....................................................................................................1 

 1.2 Study Area ..........................................................................................................................2 

 1.3 Approach ............................................................................................................................3 

2. Changed-Climate Methodology ................................................................................................4

 2.1 Past Studies.........................................................................................................................4 

 2.2 Present Study ......................................................................................................................4 

3. Hydrology Models.....................................................................................................................6 

 3.1 Runoff.................................................................................................................................7 

 3.2 Evaporation.........................................................................................................................7 

 3.3 Lake Area Adjustment........................................................................................................7 

 3.4 Outflow Relations...............................................................................................................8 

 3.5 Hypsometric Relations .....................................................................................................12 

 3.6 Water Balance...................................................................................................................12 

4. Validation................................................................................................................................16 

5. Changed Climates ...................................................................................................................16 

 5.1 Steady-State Simulation ...................................................................................................19 

 5.2 Upper Great Lakes............................................................................................................19 

 5.3 Lower Great Lakes ...........................................................................................................20 

6. Sensitivities .............................................................................................................................21 

7. Summary .................................................................................................................................25 

8. References ...............................................................................................................................26 

LIST OF TABLES 

Table 1. Great Lake Outflow Ice and Weed Retardation (Southam 1989)..................................9 

Table 2. Selected Location Datum Elevation Differences, IGLD’85 – IGLD’55, m 

CCGLBHHD 1995).......................................................................................................9 

Table 3. Coordinated Values of Great Lake Parameters (CCGLBHHD 1977).........................11 

Table 4. Summary of Average Great Lakes Diversion Impacts (IJC 1985)..............................18 

LIST OF FIGURES 

Figure 1. Laurentian Great Lakes location map............................................................................2 
iv

Figure 2. Great Lakes meteorological station network .................................................................5 

Figure 3. Humidity adjustments....................................................................................................6 

Figure 4. Great Lakes hypsometric relationships........................................................................13 

Figure 5. Arrangement schematic of Great Lakes, connecting channels, and all water flows ...14 

Figure 6. Net basin supply comparison for 1950-1999 of observed (historical) and simulated 

(modeled) supplies.......................................................................................................17 

Figure 7. Great Lake levels comparison for 1950-1999 of observed (historical) and simulated 

(modeled) levels...........................................................................................................18 

Figure 8. Matching the Lake Michigan-Huron historical water balance ....................................20 

Figure 9. Steady-state upper Great Lakes water level scenarios for non-terminal lake 

 climates........................................................................................................................21 

Figure 10. Steady-state upper Great Lakes water level scenarios for all climates considered .....22 

Figure 11. Steady-state upper Great Lakes average water levels as a function of temperature rise 

and precipitation drop relative to the present base climate..........................................22 

Figure 12. Steady state lower Great Lakes average water levels as a function of temperature rise 

and precipitation drop relative to the present base climate..........................................23 

Figure 13. Steady state upper Great Lakes climate ranges for lake levels, areas, and volumes ...24 
1

Modified Great Lakes Hydrology Modeling System 

for Considering Simple Extreme Climates 

Thomas E. Croley II 

ABSTRACT. We (the Great Lakes Environmental Research Laboratory) want to 

simulate Great Lakes hydrology for simple hypothetical climate scenarios to understand the extremes necessary to cause closed (terminal) lakes, suspected to have occurred about 7,900 radiocarbon years ago. We use our Advanced Hydrologic Prediction System with some conditions estimated for this period. We use dynamic 

lake areas (which vary with lake depth) to correct modeled over-lake precipitation, 

runoff, and lake evaporation, and neglect existing diversions and consumptions. 

We use simple shifts in precipitation, air temperature, and humidity, relative to the 

present base climate, with 52 years of daily historical meteorology. For steady-state 

analysis of the interconnected Great Lakes, we employ lake outflow-depth rating 

curves (using estimated sill elevations) reasonable for a natural system and combine 

with a water balance for all the lakes connected by their channels. We consider the 

upper and lower Great Lakes separately with no river connection, as in the early 

Holocene basin configuration. We identify candidate climates that result in closed 

lakes by looking at lake outflows and levels, demonstrating that climate may have 

been the mechanism creating terminal lake status in the past. The lakes would close 

in the order: Erie, Superior, Michigan-Huron, and Ontario for increasingly drier and 

warmer climates. For a temperature rise of T oC and a precipitation drop of P % 

relative to the present base climate, conditions for complete lake closure range from 

4.7 51 T P + > for Erie to 3.5 71 T P + > for Ontario. 

1. INTRODUCTION 

1.1 Background and Purpose 

Geologic evidence exists suggesting that several of the Great Lakes were once terminal lakes 

(hydrologically closed with no outflow) about 7,900 to 7,000 radiocarbon (14C) years ago [8830 

to 7740 calendar years before present (BP)]. (At this time, glacial melt water was bypassing the 

Great Lakes, and their watersheds were receiving local inflows only from precipitation and runoff, as at present.) Since this evidence allowed for lake basin tilting, we are left with the possibility that past climate may have been responsible for the lower levels. To take a preliminary 

look at this possibility, the Great Lakes Environmental Research Laboratory (GLERL) adapted 

their Great Lakes hydrology modeling system [Advanced Hydrologic Prediction System (Croley, 

2005)] to consider simple changes to the present climate and the resultant effects on Great Lakes 

hydrology. 

The purpose of this report is to develop tools and methodology to demonstrate that if a climate is 

extreme enough, levels on some Great Lakes would drop sufficiently to cut off outflow, thereby 

making those lakes terminal. We look at excursions in temperature and precipitation from the 

present climate to disclose those values that would drive the Great Lakes hydrology to produce 

terminal lakes. This is not an attempt to simulate past hydrology exactly, but to explore the pos-
2

sible magnitude of changed climates that might have produced terminal lakes about 7,900 14C 

years ago in accordance with recently acquired glacial-isostatic rebound evidence that Huron and 

Michigan basin lake levels had descended below their overflow outlets. 

1.2 Study Area 

The Great Lakes basin area is 770,000 km2

 (300,000 mi2), about one-third of which is water surface. See Figure 1. The basin extends 3,200 km (2,000 mi) from the western edge of Lake Superior to the St. Lawrence Power Project, Cornwall, Ontario on the St. Lawrence River. The water surface drops in a cascade over this distance some 180 m (600 ft) to sea level. Lake Superior 

is largest and deepest and has two diversions into it: the Long Lac and Ogoki. Lake Superior 

flows through the lock and compensating works at Sault Ste. Marie and down the St. Mary’s 

River into Lake Huron where it is joined by water flowing from Lake Michigan. Lake Superior 

outflows and levels are regulated to balance Lakes Superior, Michigan, and Huron water levels, 

according to Regulation Plan 1977, under the auspices of the International Joint Commission. 

Figure 1. Laurentian Great Lakes location map.
3

Lakes Michigan and Huron are considered to be one lake hydraulically because of their connection through the deep Straits of Mackinac. A relatively small flow of Lake Michigan water is 

diverted into the Mississippi River basin at Chicago. The water flows from Lake Huron through 

the St. Clair River, Lake St. Clair, and Detroit River system into Lake Erie. The drop in water 

surface between Lakes Michigan-Huron and Lake Erie is only about 2 m (8 ft). This results in a 

large backwater effect between Lakes Erie, St. Clair, and Michigan-Huron; changes in Lakes St. 

Clair and Erie levels are transmitted upstream to Lake Michigan-Huron. 

From Lake Erie, the flow is through the Niagara River and Welland Diversion (used for navigation and hydropower) into Lake Ontario. There is also a small diversion into the New York State 

Barge Canal System which is ultimately discharged into Lake Ontario. Lake Ontario outflows 

and levels are regulated in accordance with Regulation Plan 1958D to balance interests upstream 

on Lake Ontario with those downstream on the St. Lawrence Seaway. The outflows are controlled by the Moses-Saunders Power Dam between Massena, New York and Cornwall, Ontario. 

From Lake Ontario, the water flows through the St. Lawrence River to the Gulf of St. Lawrence 

and to the Atlantic Ocean. Lakes Superior, Michigan, Huron, and Ontario are very deep (229—

405 m) while Lakes Erie and St. Clair are very shallow (6—64 m). 

1.3 Approach 

We use GLERL’s Advanced Hydrologic Prediction System (AHPS), a system of hydrology, 

thermodynamic, and hydraulic models for the Great Lakes (Croley 2005). GLERL uses these 

models to make probabilistic outlooks of Great Lakes hydrology and water levels (see 

http://www.glerl.noaa.gov/wr/ahps/curfcst/curfcst.html), and to assess climate change impacts in 

the Great Lakes (Croley and Luukkonen 2003; Croley 2003; Lofgren et al. 2002; Quinn and 

Croley 1999; Croley et al. 1998). We use them here with lake outflow rating curves, selected to 

represent “natural” or “pre-project” conditions by removing the influences of channel control 

works and regulation plans. We use them with water balances on all lakes. Today, lake area 

variations do not appreciably affect precipitation, evaporation, or runoff; however, we ensure 

these variations are considered in the simulations, as lake areas much smaller than today may be 

present. We test present-day modern diversions and consumptions for significance as they are 

used in simulations but were not present in the past. We found they are relatively insignificant 

for our purpose. However we do not use the (unknown) past hydrology conditions since we are 

only attempting to demonstrate the possibility that changed climates could produce terminal 

lakes. 

First we consider all lakes as interdependent (as they are now, but with “natural” outlet and connecting channel flows) to see if simulations with historical meteorology (1948-1999) produce 

hydrology and lake levels comparable with historical records. This allows us to assess the reasonableness of the modified models. Then, we model two systems of Great Lakes independently: 1) Lakes Superior, Michigan, and Huron (the upper Great Lakes), and 2) Lakes St. Clair, 

Erie, and Ontario (the lower Great Lakes) with no inflow from the upper Great Lakes as they 

were during the early Holocene, i.e. no outflow from the Huron basin to the St. Clair-Erie basin. 

Next, we consider closed lakes at steady state (as far as the climate is concerned) by repeating 

simulations under specified climates. 
4

2. CHANGED-CLIMATE METHODOLOGY 

2.1 Past Studies 

Great Lakes have tremendous water and heat storage capacities. The lakes respond slowly to 

changed meteorological inputs. This “memory” damps short-term meteorological fluctuations 

and allows response to longer-period fluctuations characteristic of climate change. The Great 

Lakes are ideal for studying regional effects of climate changes. Early Great Lakes climate 

change impact studies used simple constant changes in air temperature or precipitation in water 

balances. General circulation models (GCMs) of the atmosphere were used to simulate current 

and 2×CO2 conditions for both steady-state and transient increases of greenhouse gases. They 

evolved from 8o latitude-longitude grids down to 3o grids and they used internally consistent 

daily meteorology. The US Environmental Protection Agency (EPA) used hydrology components of GCMs to assess water availability for large regions and linked regional hydrology models to GCMs (USEPA 1984). 

Recent Great Lakes climate change impact studies use similar methodology. GLERL worked for 

the EPA to study 2×CO2 impacts in the Great Lakes (Croley 1990; Hartmann 1990). They simulated 30 yr of “present” hydrology (a “base case”) with historical data by using arbitrary initial 

conditions but repeated simulations (using end conditions in each simulation as initial conditions 

in the next) until they were unchanging (“steady-state”). They used GCM simulations for “present” and 2×CO2 steady-state from three different GCMs by extracting monthly ratios or differences of “present” to 2×CO2 for each meteorological variable and applying them to daily historical data to estimate 2×CO2 meteorological scenarios. They simulated 30 yr of steady-state 

2×CO2 hydrology and lake levels with the altered meteorological scenarios and interpreted differences between the 2×CO2 and base cases as climate change impacts. GLERL also transposed 

climate impacts from the South and Southwest to the Great Lakes (Croley et al. 1998) and reassessed Great Lakes climate change several more times by using more GCM climate scenarios as 

they became available (Croley 1992b; Lofgren et al. 2002; Croley 2003). 

2.2 Present Study 

The hydrology models here use daily meteorological data from 1948—1999, compiled from 

about 1,800 stations for overland meteorology (precipitation and air temperature) and about 40 

stations for overlake meteorology (air temperature, humidity, wind speed, and cloud cover); see 

Figure 2. These data, compiled for previous studies (Croley 1990; Hartmann 1990; Croley 

1992b; Croley et al. 1998; Lofgren et al. 2002; Croley 2003), provide daily meteorological time 

series over each of the 121 riverine watersheds that drain into the Great Lakes and the 7 Great 

Lake water surfaces. We used these historical meteorological data with our hydrology models 

(discussed subsequently) to compute the “present” or “base case” scenario. We then apply selected precipitation ratios and air temperature differences to the historical meteorological data 

and use these modified meteorological time series with our hydrology models to construct 

changed climate scenarios. 

All precipitation is adjusted by multiplying the actual precipitation by a single precipitation ratio 

and all air temperatures are adjusted by adding a single temperature difference to the actual temperatures. In addition, humidity is adjusted; see Figure 3. For precipitation ratios below unity, 
5

which are all that are considered here, the absolute humidity is multiplied by the ratio. Thus, if 

precipitation is halved, then so is humidity. (For precipitation ratios above unity, the difference 

between the adjusted saturation vapor pressure and the actual vapor pressure could be divided by 

the precipitation ratio and subtracted from the adjusted saturation vapor pressure. As the ratio 

a) Station locations for daily min. and max. air temperatures and precipitation.

b) Station locations for daily air temperature, humidity, wind speed, and cloud cover.

Figure 2. Great Lakes meteorological station networks. 
6

goes to unity, the adjusted would go to the actual and as the ratio goes to infinity, the adjusted 

would approach the saturation limit (Figure 3); thus, if twice as wet, then half as dry. This would 

insure that the adjusted vapor pressure is continuous with precipitation ratios across 1.0). Note 

that this adjustment works well intuitively for the case where we are adjusting air temperatures 

higher, which is all that is considered here; the adjusted saturation vapor pressure is always 

higher than the adjusted vapor pressure (no saturation). (If simulating lower air temperatures, 

this adjustment could result in saturation where additional adjustment would be necessary.) 

We use both the historical and modified meteorological time series with our models to simulate 

base case and climate change scenarios, respectively. We estimate “steady-state” conditions by 

repeating the 52-yr simulations (1948—1999) with initial conditions equal to end values, until 

they are unchanging. 

3. HYDROLOGY MODELS 

GLERL’s AHPS consists of daily runoff models for each of the 121 watersheds, lake thermodynamic models for each of the seven water bodies, hydraulic models for the four connecting channels and five water body outflow points with operating plans encoded for Lakes Superior and 

Ontario, and simultaneous water balances on all the lakes. It is described in detailed overviews 

elsewhere (Croley 2003, 2005). 

1.0

Precipitation Ratio, R

Adjusted Vapor Pressure, V’, @ T’

d

actual vapor pressure, V, @ Td

adjusted saturation, V’s, @ T’a

V‘ = V * R

adjust humidity deficit

adjust actual humidity

“if half as wet, then half as wet” “if twice as wet, then half as dry”

V‘ = V’s - (V’s - V) / R

Ta = air temperature

Td = dew point temperature

T’a = new air temperature

T’d = new dew point temperature

Figure 3. Humidity adjustments.
7

3.1 Runoff 

GLERL’s Large Basin Runoff Model (LBRM) consists of moisture storages arranged as a serial 

and parallel cascade of “tanks” coinciding with the upper and lower soil zones, a groundwater 

zone, and the surface channel system (Croley 2002). Water enters the snow pack, which supplies 

the basin surface (degree-day snowmelt). Infiltration is proportional to this supply and to saturation of the upper soil zone (partial-area infiltration). Water percolates from the upper to the 

lower soil zone tank and from the lower to the groundwater zone tank (deep percolation). Water 

also flows from the upper, lower, and groundwater zone tanks into the surface channel system, as 

surface runoff, interflow, and groundwater flow respectively. Flows from all tanks are proportional to their amounts (linear-reservoir flows). Evapotranspiration is proportional to available 

water and to sensible heat (a complementary concept in that evapotranspiration reduces available 

sensible heat). Mass conservation applies for the snow pack and tanks; energy conservation applies to evapotranspiration. Complete analytical solutions exist. The model has been calibrated 

to each of the 121 watersheds contributing to the Great Lakes by minimizing root mean square 

error between daily model outflows and adjusted outflow observations. Each calibration determined parameters for infiltration, snow melt, surface runoff, percolation, interflow, deep percolation, groundwater flow, surface storage, and evapotranspiration from all moisture storages by 

systematically searching the parameter space (with a gradient-search technique). The model 

agrees quite well with weekly and monthly observations (Croley 2002, 2003). These parameters 

represent present-day hydrology and are not changed in the simulations. All 121 model applications are used in the simulations. 

3.2 Evaporation 

GLERL’s Lake Thermodynamic Model adjusts over-land data (original or adjusted as a changedclimate scenario) from the 40 over-land stations that are used to estimate over water meteorology 

for over-water or over-ice conditions based on empirical relationships between the two (Croley 

1989, 1992a; Croley and Assel 1994). Surface flux processes are represented for reflection and 

short-wave radiation, net long-wave radiation, and advection. Aerodynamic equation bulk transfer coefficients for sensible and latent heat are formulated with atmospheric stability effects. Energy conservation accounts for heat storage; superposition of heat additions or losses determines 

temperature-depth profiles. Each addition is parameterized by age and mixes throughout the volume. Mass and energy conservation account for ice formation and decay. The model has been 

calibrated to each of the seven lake surfaces by minimizing root mean square error between daily 

model surface temperatures and observations. The model enables one-dimensional modeling 

throughout of spatially averaged water temperatures over the lake depth and can be used to follow thermal development and turnovers in the lake. 

3.3 Lake Area Adjustment 

For each lake, precipitation p is provided as a scenario-dependent boundary condition and runoff 

r and evaporation e are estimated with the runoff and evaporation models. They are expressed as 

depths over the lake surface, in m, for a given time interval (day), and are based on the lake area 

C as coordinated between the US and Canada (CCGLBHHD 1977). That is, no variation of 

lake area is actually considered in their determination in the runoff and evaporation models. 
8

However, we adjust to actual lake area A by converting these depth rates into volumetric flow 

rates, 

pA P = ∆ (1) 

C BA R r

B C

− = − ∆ (2) 

eA E = ∆ (3) 

where P = volumetric precipitation rate in m3

s

-1, R = volumetric runoff rate in m3

s

-1, E = 

volumetric evaporation rate in m3

s

-1, B = basin area (including the lake), and ∆ = number of 

seconds in the time interval. Note, B and C are constants for a lake while p, r, e, and A vary 

with time. Precipitation and evaporation are directly converted by simply multiplying the overlake rates by actual lake area. Runoff is first multiplied by the coordinated lake area (over which 

it was expressed) to calculate the modeled runoff volume, then divided by the coordinated land 

area (to express it as the equivalent yield per unit of land area), and then multiplied by the actual 

land area to calculate the adjusted runoff volume. Thus “R” gets bigger as “A” gets smaller. Of 

course, there is some error involved with this procedure since p , r , and e actually depend on 

actual lake area too and should have been computed from models considering actual lake area 

and volume changes. Also, exposed land areas would not have the same properties as the original basin. Consideration of the uncertainty associated with these errors is beyond the scope of 

this exploratory study. 

3.4 Outflow Relations 

Unmanaged lake outflow depends on lake level and outflow sill elevation for lakes not affected 

by backwater (such as Superior, Erie, and Ontario) or on these variables as well as downstream 

lake level for lakes affected by backwater (such as Michigan-Huron and St. Clair). In a study 

designed to assess the cumulative impact of all of Society’s developments on Great Lakes water 

levels, Southam (1989) described a quantitative empirical relationship between water elevation 

and outflow for each lake that represents “natural” conditions, prior to the introduction of societal developments. For the Laurentian Great Lakes watershed, these developments include regulation of outflows of Lakes Superior and Ontario, modification of connecting channels through 

dredging or shoreline changes, use of ice control measures, and diversion of water into and out of 

the lakes. Any impacts caused by land use modification, consumptive uses, and regulation of 

tributary rivers are viewed as reflected by changes in water supplies to the lakes and not by 

changes in elevation—outflow relationships, and were not considered in that study. We convert 

Southam’s relationships from their original English units and IGLD’55 water level datum to metric units and IGLD’85 water level datum. We also transform his Lake Erie adjustment for channel project removals to one compatible with basic weir formulae and express Ontario outflows in 

terms of the 1985 sill elevation. 
9

For Lake Superior, 

( )1.5 4901 593.99 QZ H SS S ′′ ′ =− − (4) 

where QS

′ = Lake Superior outflow in ft3

s

-1, ZS

′ = Lake Superior water elevation (at Point Iroquois) with respect to the IGLD’55 water level datum (CCGLBHHD 1979) in ft, and HS

′ = ice 

retardation, in ft3

s

-1, as given in Table 1. Converting units (1 ft = 0.3048 m), 

( ) ( ) ()

( )

1.5 3

1.5

1.5

4901 181.048 0.3048

0.3048

824.721 181.048

S SS

S S

Q ZH

Z H

⎡ ⎤

= −− ⎢ ⎥ ′′ ′

⎣ ⎦

= −− ′′

 (5) 

where QS = outflow in m3

s

-1, ZS

′′ = IGLD’55 elevation in m, and HS = ice retardation, in m3

s

-1, 

in Table 1. Lake levels relative to Point Iroquois in 1985 are equivalent to lake levels relative to 

Point Iroquois in 1955 plus 0.377 m, as shown in Table 2, because of upward crustal movement 

caused by isostatic rebound since the retreat of the glaciers. Converting to the current IGLD’85 

Table 1. Great Lake Outflow Ice and Weed Retardationa (Southam 1989). 

 Superior Michigan-Huron St. Clair Erie 

Month 103ft3s

-1 m3

s

-1 103

ft3s

-1 m3

s

-1 103

ft3s

-1 m3

s

-1 103

ft3s

-1 m3

s

-1

(1) (2) (3) (4) (5) (6) (7) (8) (9) 

January 4 113 36 1020 15 425 4 113 

February 4 113 48 136 15 425 5 142 

March 4 113 23 651 8 227 3 85 

April 4 113 6 170 2 57 5 142 

May 

June 2 57 

July 5 142 

August 4 113 

September 3 85 

October 2 57 

November 

December 4 113 5 142 

a

No values for Ontario are given in the reference. 

Table 2. Selected Location Datum Elevation Differences, IGLD’85 – 

IGLD’55, m (CCGLBHHD 1995). 

Pt. Iroquois Harbor Beach Gross Pointe Cleveland, 

Buffalo Oswego 

(1) (2) (3) (4) (5) 

0.377 0.214 0.200a 0.180a 0.158 a

Lake-wide average of all water level gages is used.
10

datum (CCGLBHHD 1995) by using this adjustment, 

( )1.5 824.721 181.425 , 181.425 QZ H Z SS S S = −− ≥ (6) 

where ZS = IGLD’85 elevation in m and QS = 0 when elevation is below the “sill” elevation of 

181.425 m; the sill is the lowest elevation for which flow from the lake is still possible. 

Southam (1989) gave relations for the other lakes as: 

( )

2 1

2

1 1 84.1168 545.74

2 2 Q Z Z ZZ H T T C TC T

⎛ ⎞ ′ ′ ′ ′′ ′ = +− −− ⎜ ⎟ ⎝ ⎠ (7) 

( )( )

1 2

128.0849 543.81 2 Q Z ZZ H C C CE C ′ ′ ′′ ′ = − −− (8) 

( )1.5 4058 556.95 5600 QZ H EE E ′′ ′ = − −+ (9) 

( ) ( ) 1.5 3430 0.0055 1903 227.45 QZ Y H OO O ′′ ′ = − −− − (10) 

where QT

′ , QC′ , QE′ , and QO′ = outflows from Lakes Michigan-Huron, St. Clair, Erie, and Ontario, respectively, in ft3

s

-1, ZT

′ , ZC′ , ZE′ , and ZO′ = water elevations with respect to the IGLD’55 

water level datum on Lakes Michigan-Huron (at Harbor Beach), St. Clair (at Grosse Pte.), Erie 

(at Cleveland or Buffalo, regarded here as the same), and Ontario (at Oswego), respectively, in 

ft, Y = year, and HT

′ , HC′ , HE′ , HO

′ , = ice retardations for Lakes Michigan-Huron, St. Clair, 

Erie, and Ontario, respectively, in ft3

s

-1; ice retardation values are given in Table 1. The 5,600 

ft3

s

-1 in (9) was added to adjust for channel project removals (Southam 1989). Here, it is presumed that the added 5,600 ft3

s

-1 represents an average flow adjustment for average flow conditions and should be zero for zero flow. Taking the average flow as 208,000 ft3

s

-1 [from the study 

outlined by Southam (1989)], using an average Erie ice retardation from Table 1 (2,750 ft3

s

-1), 

and solving (9) gives a corresponding water level elevation of 570.62 ft. Solving for an alternate 

formula, like (9) but without the flow adjustment, that gives the same values, 

( )1.5 4168.77 556.95 QZ H EE E ′′ ′ = −− (11) 

Converting (7), (8), (10), and (11) to metric units and to the current IGLD’85 datum (datum differences are given in Table 2) and using the 1985 version of (10), 

( )

( )

2 1

2

2 1

2

1 1 46.440 166.549 , 166.549 2 2

1 1 46.440 166.549 166.549 , 166.549 2 2

T T C TC T T C

T T TT C

Q Z Z ZZ H ZZ

Z Z HZ Z

⎛ ⎞ = + − − − ≥≥ ⎜ ⎟ ⎝ ⎠

⎛ ⎞ = − − − ≥> ⎜ ⎟ ⎝ ⎠

 (12) 
11

( )( )

( )( )

1 2

2

1 2

2

70.714 165.953 , 165.953

70.714 165.953 165.953 , 165.953

C C CE C C E

C C CC E

Q Z ZZ H ZZ

Z Z HZ Z

= − − − ≥≥

= − − − ≥>

 (13) 

( )1.5 701.504 169.938 , 169.938 QZ H Z EE E E = −− ≥ (14) 

( )1.5 577.187 69.622 , 69.622 QZ H Z OO O O = −− ≥ (15) 

where QT , QC , QE , and QO = outflows from Lakes Michigan-Huron, St. Clair, Erie, and Ontario, respectively, in m3

s

-1, ZT , ZC , ZE , and ZO = respective water elevations with respect to 

the IGLD’85 water level datum in m, and HT , HC , HE , HO , = respective ice retardations in 

m3

s

-1. We ignore the small elevation differences, introduced by the datum change, between 

Michigan-Huron and St. Clair levels and between St. Clair and Erie levels to keep the equations 

physically meaningful; i.e., when Lakes Michigan-Huron and St. Clair are at the same level ( ZT

= ZC ) or Lakes St. Clair and Erie are at the same level ( ZC = ZE ), there should be no flow between the respective pair of lakes (QT = 0 or QC = 0). However, backflow is possible from 

Lake Erie to Lake St. Clair and from Lake St. Clair to Lake Michigan-Huron. This backflow is 

not described by these equations (but is addressed subsequently). 

Note that when St. Clair water level is below the Michigan-Huron sill, the sill elevation is controlling in (12); likewise when Erie water level is below the St. Clair sill, the sill elevation is controlling in (13). These are reasonable extensions, made here to allow flow computations as lake 

levels drop below those historically experienced. Note that QT = 0 when the Michigan-Huron 

water level is below the sill of 166.549 m, QC = 0 when St. Clair is below the sill of 165.953 m, 

QE = 0 when Erie is below the sill of 169.938 m, and QO = 0 when Ontario is below the sill of 

69.622 m. 

Since (6) and (12)—(15) were derived from semi-empirical stage-fall-discharge or rating curves 

that were fit to a range of flows and elevations not necessarily close to the sill, the sill elevations 

estimated here are in error. Sill heights on all lakes but St. Clair are well above the bottom of the 

lake. On Lake St. Clair, the bottom of the lake is 168.4 m (subtract maximum coordinated depth 

from chart datum in column 6 of Table 3); this is above the Michigan-Huron and St. Clair sills. 

This corresponds to a channel running along the bottom of Lake St. Clair; i. e., the lake bottom is 

Table 3. Coordinated Values of Great Lake Parameters (CCGLBHHD 1977). 

 SUP MIC HUR GEO STC ERI ONT 

(1) (2) (3) (4) (5) (6) (7) (8) 

chart datum, m 183.2 176.0 176.0 176.0 174.4 173.5 74.2

maximum depth, m 405 281 229 164 6 64 244 

coordinated area, km2 82100 57800 40640 18960 1114 25700 18960 

coordinated volume, km3 12100 4920 2761 779 3.4 484 1640 
12

at the top of this channel and we can have flow from the Lake St. Clair basin without lake storage. Since the lake bottom is below the Erie sill of 169.938 m, we see that St. Clair will never be 

empty as long as Lake Erie is not terminal (water line above its sill). Lake outflows in (6) and 

(12)—(15) are set to zero when negative values would be computed (ice retardation would drop 

to equal flow rate). 

3.5 Hypsometric Relations 

The Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data 

(CCGLBHHD, 1977) provided graphical relations, for each lake, between depth and volume; 

inspection reveals that simple power relations are a very good fit, 

( )

( ) 1

b

b

V aM D

d A V ab M D

dD

−

= −

=− = − (16) 

where A = area of horizontal surface at depth D below a reference elevation, M = maximum 

depth, V = lake volume beneath horizontal surface at depth D , and a and b are empirical parameters. By requiring that the coordinated values of area, C , and volume, S , (CCGLBHHD, 

1977) exist at the reference elevation (chart datum), where D = 0, for each lake, as in Table 3, 

the parameters are 

a

C a M

S

S b

M

=

=

 (17) 

Writing (16) in terms of elevation instead of depth, 

( )

( ) 1

b

B

b

B

V aZ Z

A ab Z Z −

= −

= −

 (18) 

where Z = elevation at depth D , in m, and ZB = elevation of lake bottom, in m, given from Table 3 by subtracting maximum depth from chart datum. Figure 4 shows (18) for all lakes; note 

Michigan, Huron, and Georgian Bay are separate in (18). 

3.6 Water Balance 

The adjusted over-lake precipitation, runoff to the lake, and lake evaporation are used in a water 

balance, based on the arrangement of the Great Lakes and their connection channels, depicted in 

Figure 5. 

dV I QPRE dt

=− + + − (19) 
13

where t = time, I = volumetric water body inflow rate (outflow from the upstream lake) , and 

Q = volumetric water body outflow rate. Equations (1)—(3) and (19) are applied over time interval ∆ to each water body based on the lakes and connecting channels arrangement, 

( ) ( ) S

S S S SS S S S SS

S S

C V I Q pA R B A eA B C

∆ ≅ − ∆+ + − − − (20) 

( )( ) ( )

( )

( )

M

M H G T T MM M M M MM

M M

H

HH H H H HH

H H

G

GG G G G GG

G G

C V V V I Q pA R B A eA B C

C pA R B A eA B C

C pA R B A eA B C

∆ + + ≅ − ∆+ + − − −

+ + −− −

+ + −− −

 (21) 

( ) ( ) C

C C C CC C C C CC

C C

C V I Q pA R B A eA B C

∆ ≅ − ∆+ + − − − (22) 

( ) ( ) E

E E E EE E E E EE

E E

C V I Q pA R B A eA B C

∆ ≅ − ∆+ + − − − (23) 

( ) ( ) O

O O O OO O O O OO

O O

C V I Q pA R B A eA B C

∆ ≅ − ∆+ + − − − (24) 

Figure 4. Great Lakes hypsometric relationships.
14

where ∆V = change in volume and the subscripts refer to individual Great Lakes or extended 

water bodies: Superior (S), Michigan (M), Huron (H), Georgian Bay (G), Michigan-Huron (T), 

St. Clair (C), Erie (E), and Ontario (O). Equation (21) considers Lakes Michigan and Huron, 

including Georgian Bay, as one water body. Boundary conditions are 

 0 S I = (25) 

T S I = Q (26) 

Figure 5. Arrangement schematic of Great Lakes, connecting channels, and all water flows.
15

, for upper Great Lakes flowing into lower

0, for upper Great Lakes flowing into the Mattawa and Ottawa basins

C T I Q=

= (27) 

E C I = Q (28) 

O E I = Q (29) 

For each water body, it is necessary to compute the inflow as outflow from the upstream lake, 

the lake(s) area, and the adjusted net basin supplies as part of the solution. This requires calculating lake levels as part of the water balance. We solve (6), (12)—(15), (18) for each lake, (20)

—(24), and (25)—(29) simultaneously at each time step. Our numerical procedure at each time 

step is: i) given p , r , e , and Z0 (water elevation at beginning of time step) for all lakes, ii) calculate A0 (lake area at beginning of time step) and V0 (lake volume at beginning of time step) 

for all lakes from (18) and Q0 (outflow rate at beginning of time step) for all water bodies from 

(6) and (12)—(15), iii) approximate Z1 (end-of-time-step water elevation) as Z0 for all lakes, iv) 

calculate A1 (end-of-time-step lake area) for all lakes from (18) and Q1 (end-of-time-step water 

body outflow rate) for all water bodies from (6) and (12)—(15), v) approximate outflow rates 

and lake areas over the time increment as linear, Q QQ = + ( 0 1 ) 2 and ( ) 0 1 A AA = + 2 , vi) calculate the changes in storage for all water bodies over the time interval by using these approximate 

outflow rates and lake areas in (20)—(24) and (25)—(29), and vii) calculate VV V 1 0 = +∆ for 

each lake and then find Z1 by using V1 with (18) for each water body (for Lake Michigan-Huron, 

interpolate for Z1 by using V1 with (18) applied to Lakes Michigan, Huron, and Georgian Bay 

and summed). Repeat steps iv—vii until successive values of Z1 for all lakes change negligibly. 

Repeat steps i—vii for the next time step, and so forth. 

When solving (6), (12)—(15), (18), (20)—(24), and (25)—(29), we check and correct for backflow between lakes. This could occur if water levels on Lake Erie are above those on St. Clair 

(and above the St. Clair sill) or those on St. Clair are above those on Lake Michigan-Huron (and 

above the Michigan-Huron sill). For those times when backflow would occur between two 

lakes, we simply balance the lakes involved so that water levels on both are equal and the flow 

between them is zero. Furthermore, we consider sill heights in this adjustment and do not let 

backflow reduce a lake’s level below the upstream sill. Note that backflow does not occur when 

simulating the existing system with the existing climate. It also does not occur when simulating 

the upper lake system (Superior, Michigan, and Huron) with any climate since (12) is replaced 

with a relation that is a function of Michigan-Huron levels only (discussed subsequently). Backflow corrections are only required when simulating the existing system or the lower lake system 

(St. Clair, Erie, and Ontario) with warmer or dryer climates. The equations solution converges 

to an insignificant difference within 2-15 iterations (the difference between water elevations in 

successive iterations, summed over all lakes, is less than one thousandth of a millimeter). 
16

4. VALIDATION 

To check the models and water balance approximations, we simulated the entire interconnected 

Great Lakes for the historical meteorological record. First, we compared simulated net basin 

supplies (precipitation + runoff – lake evaporation) resulting from the model, applied to the historical meteorological record with actual initial conditions, directly to historical net basin supplies (computed as a water balance residual from historical lake levels and flows). Figure 6 

compares our estimates with historical NBS and shows good agreement, as expected since historical meteorology data are used in the simulation. Differences can be ascribed to water balance 

errors in the computation of residual NBS and to modeling errors in the computation of the NBS 

components. The biggest differences occur on Lake Ontario, suggesting they arise from water 

balance errors in computing the historical residual NBS. 

Next, we compared simulated lake levels resulting from the model, applied to the historical meteorological record with actual initial conditions, directly to historical levels. For this comparison, we included all diversions but used the natural outflow and channel relationships. Figure 7 

is a plot of daily simulated levels and monthly historical levels; it shows fair agreement, but has 

expected deviations. On Superior, levels match well with historical data after about 1965 but 

differ before; this could be due to sparse water level station networks prior to 1965 (hard to 

evaluate), poorer meteorological estimates prior to 1965 (when station densities are lowest on 

Superior and areal estimates are often underestimated), and differences in the outflow and channel relationships (water was released on Superior in 1965 to alleviate low water levels downstream; there were also changes in the Superior regulation plan between 1970-77; the model 

simulation uses an unchanging outflow and channel relationship). On Michigan-Huron, it appears that the historical water levels are lower than the simulated; this lowering probably results 

from the historical changes in Lake Superior operations and in the St. Clair River channel which 

has been dredged over time. It also may be related to variation in crustal rebound occurring after 

retreat of the last ice sheet; crustal rebound results in relative tilting of Lake Michigan-Huron 

towards its outlet suggesting higher outflows and lower levels in the historical record than simulated (Quinn and Sellinger 1990). Lakes St. Clair and Erie are very similar to the simulation but 

Ontario shows lower water levels historically, probably as a result of the difference between 

regulated Niagara flows and the natural outflow and channel conditions. The model appears to 

simulate the system reasonably well when all sources of differences between the simulations and 

historical flows are considered. Connecting channel flow differences (not shown here) also 

match well. 

5. CHANGED CLIMATES 

Before applying the simulations to changed climates (i.e. changed temperature and precipitation), 

we ascertained that the present-day diversions in the hydrology models were on the order of a 

few centimeters; see Table 4 (IJC 1985). [Note that these diversions affect lakes upstream as 

well as downstream. The Chicago diversion affects Superior because resultant lower MichiganHuron levels are used in regulation of Superior. The Welland diversion lowers Lake Erie and, 

because of connecting channel hydraulics (upstream and downstream lake levels determine channel flow), lower Erie levels lower Michigan-Huron and lower Michigan-Huron levels lower Superior as just discussed.] Thus, they are negligible compared to the changes in net basin supplies 
17

0

500

1000

1500

0

500

1000

1500

0

500

1000

1500

1000

1500

2000

2500

3000

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Superior

Michigan-Huron

Erie

Ontario

Net Basin Supplies (mm over lake surface)

Historical

Modeled

Figure 6. Net basin supply comparison for 1950-1999 of observed (historical) 

and simulated (modeled) supplies.
18

Figure 7. Great Lake levels comparison for 1950-1999 of observed (historical) and simulated 

(modeled) levels. 

Table 4. Summary of Average Great Lakes Diversion Impacts (IJC 1985). 

 Great Lake 

Diversion Amount Superior Mich.-Huron Erie Ontario 

 (m3s

-1) (cm) (cm) (cm) (cm) 

(1) (2) (3) (4) (5) (6) 

Ogoki-Long Lac 160 +6 +11 +8 +7 

Chicago 90 -2 -6 -4 -3 

Welland 270 -2 -5 -13 0 

COMBINED - +2 -1 -10 +2 
19

or drops in water levels to be simulated with changed climates. Therefore, we ignore them; no 

effort was made to remove these diversions from the existing models. 

5.1 Steady-State Simulation 

We use both the historical and modified meteorological time series with our models to simulate 

base case and climate change hydrology scenarios, respectively. We estimate steady state hydrology by modeling with arbitrary initial conditions (snow pack, water storages in the basins, 

thermal structure of the lakes, lake levels, and so forth) over an extended period constructed by 

repeating the adjusted meteorological record until consecutive 52-year simulations are identical. 

(The models always converge no matter where started). The number of iterations required to 

reach this state depends largely on the arbitrary lake level assumed at the beginning and the final 

lake levels; it sometimes represents a longer time than might be expected for the climate change 

itself. (The effect of the initial conditions other than lake levels is much shorter, usually on the 

order of a couple of years.) However, since lake levels are unknown prior to the changing climate and since we want to avoid representing climate change as abrupt, we use this “steadystate” behavior to assess the effects of climate change. 

5.2 Upper Great Lakes 

Separating upper lakes (Superior, Michigan, Huron) from lower lakes (St. Clair, Erie, Ontario), 

for purposes of simulating the system about 7,900 14C years BP, is accomplished by changing 

Lake Michigan-Huron outflow to a function only of the water level in Lake Michigan-Huron 

(and not of St. Clair) and then by modeling only these upper lakes. The outflow function ideally 

should represent conditions of 7,900 14C years ago but those are as yet unknown. As a proxy, the 

spillway equation of (6), (14), or (15) was arbitrarily used along with the present-day sill elevation taken from (12). We determined the leading coefficient by trial and error to match a longterm water balance with historical levels (see Figure 8), 

( )1.5 185 166.549 , 166.549 QZ H Z TT T T =− − ≥ (30) 

Note again, outflow in (30) is set to zero for negative values or for elevations below 166.549 m. 

When lake levels are always below the sill elevation, then the lake is terminal. We looked at 36 

climate scenarios, each defined in terms of the precipitation drop from the base case (0—50% in 

steps of 10%) and the temperature rise above the base case (0—5o

C in steps of 1oC). Figure 9 

shows 50 years of simulated steady-state water levels for the upper Great Lakes for all of the climate scenario experiments which did not produce a terminal lake. (Note that a 10% drop in precipitation corresponds closely to a 2 oC rise in air temperature.) The water levels drop with successively dryer and or warmer climates, approaching in both cases, the sill elevation for the lake. 

Figure 10 shows the 50-year time series for all 36 climate scenarios; while the highest levels are 

unlabeled since they are so close to each other, the bottom few are labeled as to which scenario 

they are and represent simulations in which the lake was terminal (closed). We calculated the 

steady-state average water level resulting from each and plotted it with precipitation drop and 

temperature rise as shown in Figure 11 for Lakes Superior and Michigan-Huron. Note three regions in each graph of Figure 11: the region where all water levels are above the sill elevation in 

the lower left of the graphs, the region where all water levels are below the sill elevation in the 
20

upper right of the graphs, and the intermediate region where water levels are both above and below the sill elevation. We determined the boundaries of these regions by looking at maximum 

and minimum water levels in each simulation and comparing them to the sill elevations. Since 

behavior of steady-state average water levels is fundamentally different in each of these regions, 

we restricted linear interpolation in each region to only values therein. 

By using linear approximations, note that the climate isolines for a terminal Lake Superior in 

Figure 11 drop about 1o

C for every 4.7% change in precipitation. Figure 11 suggests that Lake 

Superior should be a terminal lake for climates with a temperature rise T (o

C) and a precipitation 

drop P (%) such that 4.7T + P > 60. Likewise, the isolines in Figure 11 for a terminal Lake 

Michigan-Huron drop about 1o

C for every 4.5% change in precipitation; Lake Michigan-Huron 

should be terminal for climates with a temperature rise T (o

C) and a precipitation drop P (%) 

such that 4.5T + P > 63. 

5.3 Lower Great Lakes 

For the lower Great Lakes, we looked at Lakes St. Clair, Erie, and Ontario, with no inflow to 

Lake St. Clair as was the case prior to and after the low stand 7,900 years ago when MichiganHuron flowed into the Mattawa and Ottawa watersheds; see (27). Since the St. Clair lake bottom 

is above its sill elevation, there can be flow into Erie even when Lake St. Clair is empty. Thus, 

St. Clair can never be terminal (with water still in it); it can only dry up. We have to consider 

Lakes St. Clair and Erie as one water body to investigate Lake Erie becoming terminal. We 

Figure 8. Matching the Lake Michigan-Huron historical water balance. 
21

looked again at the 36 climate scenarios, previously defined, and calculated the steady-state water levels resulting from each. We found that Lake Erie became terminal in this range of climate 

variations but Lake Ontario did not. Therefore, we considered a larger range of climate variations by taking nine precipitation ratios (0—80% in steps of 10%) and eleven temperature rises 

(0—10o

C in steps of 1oC) and plotted the average steady-state water level resulting from each in 

Figure 12 for Lakes Erie and Ontario. 

Note that we again define three regions in each graph of Figure 12 for water levels above the sill, 

below the sill, and both above and below the sill, by looking at maximum and minimum water 

levels and sill elevations. We again restrict linear interpolation in each region to only values in 

that region. Note that the isolines for a terminal Lake Erie in Figure 12 drop about 1o

C for every 

4.7% change in precipitation. Figure 12 suggests that Lake Erie should be a terminal lake for 

climates with a temperature rise T (o

C) and a precipitation drop P (%) such that 4.7T + P > 51. 

Likewise, the isolines in Figure 12 for a terminal Lake Ontario drop about 1o

C for every 3.5% 

change in precipitation; Lake Ontario should be terminal for climates with a temperature rise T

(

o

C) and a precipitation drop P (%) such that 3.5T + P > 71. 

6. SENSITIVITIES 

Each climate considered herein is specified over the entire upper Great Lakes basin or over the 

entire lower Great Lakes basin in their respective analyses. That is, the same changes made to 

Figure 9. Steady-state upper Great Lakes water level scenarios for non-terminal lake climates.
22

historical data, to construct a hypothetical climate, were used across all water bodies and their 

basins in each analysis. For example, the 1o

C increase applied to Lake Ontario meteorological 

data was applied at the same time to the Lake Erie meteorological data in the analyses. Thus, no 

consideration is made of more complex changed climates (such as a 1oC change in Lake Erie air 

temperatures with a 2o

C change in Lake Ontario air temperatures). Given this limitation, the order of the lakes going terminal as climate gets warmer and drier is approximately: Erie, Superior, 

Figure 10. Steady-state upper Great Lakes water level scenarios for all climates considered. 

Figure 11. Steady-state upper Great Lakes average water levels as a function of temperature rise 

and precipitation drop relative to the present base climate. 
23

Michigan-Huron, and Ontario. (The order varies a little depending on the path of the changes 

from the present climate taken in Figures 11 and 12.) For both Great Lake subsystems (upper 

and lower), the uppermost lake goes terminal before the lowermost lake; this is not strictly necessary. There may be climates (where meteorological conditions are different over the uppermost lake and the lowermost lake) that would yield the lowermost lake terminal while the uppermost lake was not terminal. However, those changed climates were not investigated herein. 

As more is learned about past climates from paleoclimatic considerations, we can fine tune the 

observations made herein. 

Likewise, the climate changes considered herein were simplified. We multiplied all historical 

daily precipitation amounts, without regard to season of the year, by a constant ratio and we 

added to all historical daily air temperatures, again without regard to season of the year, a constant value. Undoubtedly, we could consider more reasonable changes by considering the season 

of the year, and even location. Again, as more is learned about past climates from paleoclimatic 

considerations, we can make these additional considerations. However, we think these results 

are generally indicative of how climate effects would influence Great Lakes terminal lake status 

Indeed, Lofgren et al. (2002) summarized many of the past Great Lake climate studies that used 

general circulation model experiments for 2×CO2 studies; those climates that were warmer and 

drier showed good agreement with Figure 11. 

Since we used only the available 52 years of daily meteorological data, continuously repeated, to 

represent steady-state, we biased our results somewhat; only the storm events on record are repFigure 12. Steady state lower Great Lakes average water levels as a function of temperature rise 

and precipitation drop relative to the present base climate.
24

resented. The “transitional zone” in both Figures 11 and 12 might be wider if a longer period 

were used since more marginal storm events would be included that allowed some small outflow 

at water levels close to sill elevations. 

There are also many errors of approximation in this study; our calculations used overlake precipitation, overlake evaporation, and runoff to the lake from models that assumed fixed values 

(coordinated between the U.S. and Canada) for lake areas and volumes, and then adjusted them 

for the actual lake and basin areas obtained in a comprehensive water balance. Better consideration would modify the runoff and lake evaporation models directly to consider the actual lake 

areas and volumes in an integrated water balance that employs these models directly. Also, exposed land areas would not have the same properties as the original basin. Likewise, the hypsometric relations and outflow relations (both rating coefficients and sill elevations) could be improved. Different sill elevations would shift the “terminal” lines in Figures 11 and 12. 

The errors, introduced by using runoff and evaporation models that do not consider changes in 

lake or basin area with water level and so were corrected through (1)—(3), are expected to 

worsen as average water levels depart from current values. Figure 13 presents the ranges of lake 

water levels, lake areas, and lake volumes actually simulated in the 50 years for the upper Great 

Lakes for all climate scenario experiments. While the Superior water level range is about 20% 

[(climate range of thick line segment in Figure 13) / (maximum apparent range of thin line segment in Figure 13) or 80 m / 400 m] lower than current values, the lake area range is only about 

33% lower (30 km2

 / 90 km2 or only down to 67% of its total range); while the Michigan-Huron 

water level range is about 13% lower (35 m / 275 m) then current values, the lake area range is 

about 25% lower (40 km2

 / 160 km2 or only down to 75% of its total range). We view these 

ranges as small enough that the errors associated with correcting precipitation, evaporation, and 

runoff with (1)—(3) are acceptable for a study of this type. 

Finally, the results do not exactly represent past hydrology (for example, paleo-lake areas have 

not been incorporated) so that results should be interpreted as exploration on the question of 

Figure 13. Steady state upper Great Lakes climate ranges for lake levels, areas, and volumes. 
25

what could be reasonably envisioned as the effect of various climate scenarios on the hydrology 

of the pre-development Great Lakes. This is an attempt to study the question of “What magnitude of drying and warming of the present climate might produce terminal lakes as a guide to 

possible climate that apparently produced hydrologic closure of at least some of the Great Lakes 

about 7,900 14C years BP?” 

7. SUMMARY 

A new empirical model of glacial rebound and comparison of past lake level indicators with outlet elevations showed that lake levels in the Huron and Michigan basins had fallen below their 

outlets about 7,900 14C years BP. As glacial-isostatic depression of outlets was accounted for, 

the only alternate known process that could close the lakes is enhanced evaporation, reduced 

precipitation, or both, in a dry climate. These findings motivated us to explore temperature and 

precipitation excursions of the present climate that might close the Laurentian Great Lakes as a 

guide to understanding possible conditions at 7,900 14C years BP. We demonstrate the possibility that changed climates could produce terminal Great Lakes by using present hydrology with 

natural (pre-development) channel and outflow conditions. We first integrated existing comprehensive models for present-day large basin runoff applied to each of the 121 watersheds draining 

into the Great Lakes, models of present-day large-lake thermodynamics applied to the seven water bodies of the Great Lakes, water balances of the lakes and their connecting channels, lake 

area adjustments relating supplies (lake precipitation, runoff, and evaporation) to the water balance, models of natural outflows and channel flows, present-day hypsometric relations, and a 

water balance of all lakes and connecting channels. We tested the integrated model with historical meteorological data (1948-1999) and found it to be a reasonable model of Great Lakes water 

levels. We built alternate climates from the historical meteorological record by reducing precipitation by fixed ratios and increasing temperature by fixed increments. We applied the integrated 

hydrology model to these alternate climates, producing associated alternate lake level time series. 

The applications were made separately in the upper and lower Great Lakes basins as overflows 

from the upper lakes prior to and after 7,900 14C years BP were routed via the Ottawa and St. 

Lawrence rivers, bypassing the Erie and Ontario basins completely. 

The changed climate scenarios used in this study were simple: spatially and temporally constant 

adjustments were applied to historical meteorology for each watershed and lake surface to estimate changed-climate meteorology for each watershed and lake surface. More complex climate 

change considerations in our study of terminal Great Lakes wait on improved paleoclimatic reconstructions. Our results are biased by the length of the historical meteorology record we used. 

Errors of approximation include linear adjustment of supplies for lake area, power equation hypsometric relations, and approximation of natural flow conditions and sill elevations for each 

Great Lake. 

We modeled each alternate climate by repeating our 52 years of adjusted meteorology until there 

were no changes, in an effort to simulate steady-state conditions. It appears that Lake Superior 

would be a terminal lake if precipitation dropped 60% or more from the present or if air temperature increased 60/4.7 = 13o

C or more above the present or some linear combination of the two, 

4.7T + P > 60 where T and P are temperature rise (o

C) and precipitation drop (%), respectively. Likewise, it appears Michigan-Huron would be a terminal lake for P > 63% or T > 
26

14o

C or 4.5T + P > 63. Erie would be a terminal lake for P > 51% or T > 11oC or 4.7T + P

> 51. Ontario would be a terminal lake for P > 71% or T > 20o

C or 3.5T + P > 71. 

Our study addresses only the question of climate change necessary to close the pre-development 

Great Lakes and does not represent past or present hydrology. We endeavored not to exactly 

model the hydrology of the lakes around 7,900 14C years BP, but to explore the potential magnitude of excursions in temperature and precipitation that could cause the lakes to drop so low as to 

become “terminal” lakes (with no outflow). 

8. REFERENCES 

Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data (CCGLBHHD) 

1977. Coordinated Great Lakes physical data. Physical Data Subcommittee, Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data, US Army Corps of Engineers, Detroit 

District, Detroit, Michigan. 

Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data (CCGLBHHD) 

1979. Establishment of international Great Lakes datum (1955), 2nd Edition. Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data, US Army Corps of Engineers, Detroit 

District, Detroit, Michigan. 

Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data (CCGLBHHD) 

1995. Establishment of international Great Lakes datum (1985). Appendix A - Tabulation of primary bench mark elevations at gauge sites. Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data, US Army Corps of Engineers, Detroit District, Detroit, Michigan. 

Croley, T.E., II 1989. Verifiable evaporation modeling on the Laurentian Great Lakes. Water Resources Research 25(5):781-792. 

Croley, T.E., II 1990. Laurentian Great Lakes double-CO2 climate change hydrological impacts. 

Climatic Change 17:27-47. 

Croley, T.E., II 1992a. Long-term heat storage in the Great Lakes. Water Resources Research

28(1):69-81. 

Croley, T.E., II 1992b. Climate change impacts on Great Lakes water supplies. In Proceedings of 

the Symposium on Managing Water Resources During Global Change, pp. 241-250, American Water Resources Association. 

Croley, T.E., II 2002. Large basin runoff model. In Mathematical Models in Watershed Hydrology 

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Croley, T.E., II 2003. Great Lakes Climate Change Hydrological Impact Assessment, IJC Lake Ontario—St. Lawrence River Regulation Study. Great Lakes Environmental Research Laboratory, 

Ann Arbor, Michigan, NOAA Tech. Memo. GLERL-126. 
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Croley, T.E., II 2005. Using Climate Predictions in Great Lakes Hydrologic Forecasts. In Climatic 

Variability, Climate Change, and Water Resources Management, eds. J. Garbrecht and T. Piechota, 

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Croley, T.E., II, and Assel, R.A. 1994. One-dimensional ice model for the Laurentian Great Lakes, 

Water Resources Research 30(3):625-639. 

Croley, T.E., II, and Luukkonen, C.L. 2003. Potential climate change impacts on Lansing, Michigan ground water. Journal of the American Water Resources Association 39(1):149-163. 

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transposed climates, Climatic Change 38:405-433. 

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GCMs. Journal of Great Lakes Research 28(4):537-554. 

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Quinn, F.H., and Sellinger, C.E. 1990. Lake Michigan record levels of 1838, a present perspective. 

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Southam, C. 1989. Procedure for developing the Great Lakes level and flow regime for pre-project 

conditions. Functional Group 1, Hydrology, Hydraulics, and Climate, IJC Great Lakes Water Levels Reference Study, Environment Canada, Burlington, Ontario. 

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of Policy, Planning, and Evaluation, Washington, D.C.