# Presentation: 248971

## Outline

- 		Work Statement *
- 		Relevance
- 		Study Area
- Methodology:	Past Studies
- 		Data Preparation *?
- 		Actual Data Adjustments *
- 		Modeling Procedure *?
- Models:		Hydrology Model
- 		Lake Thermodynamic Model
- 		Water Balance and Routing *
- 		Hypsometric Relations and Outflow Equations *
- Validation:		***Interdependent*** Lakes: Base Case vs. Historical *
- 		NBS, Levels, & Channel Flows for whole system * * *
- Terminal Lakes:	Split System & Replace St. Clair Equation *
- 		Consider removal of present-day diversions
- 		Look @ ***independent*** lakes NBS only (upstream lakes terminal) *
- 		NBS climate summary *
- 		Look @ ***interdependent*** lakes: Outflow climate summary *
- 		Lake Level summary * *

*Outline*

## Background

- 	Great Lakes in terminal state about 9000 years ago
- 	Hypothesize climate caused this
- 	Understand extremes of climate closing Great Lakes
- 	NSF proposal with 13 others funded late last year

**Notes:**
Background.  Geologic evidence exists suggesting that several of the Great Lakes were once terminal lakes (no outflow occurs) and a group of researchers were interested in why.  (Researchers at Geological Survey of Canada, Environment Canada, & Universities: Rhode Island, Michigan, Arizona, Kent State, Waterloo, Toronto, Queens, and Brock.)  They hypothesized that past climate may have been responsible and are looking for evidence.  They invited me to participate by demonstrating that if a climate is extreme enough, then lake levels on some Great Lakes could drop sufficiently to cut off lake outflow, thereby becoming terminal.
	I will look at climate scenarios to identify some that would drive present Great Lakes hydrology to produce terminal lakes.  This is not an attempt to simulate past hydrology but to demonstrate the possibility that changed climates could produce terminal lakes.  Others will look at paleoclimate characteristics and we’ll compare notes.

## Background

- 	Great Lakes in terminal state about 9000 years ago
- 	Hypothesize climate caused this
- 	Understand extremes of climate closing Great Lakes
- 	NSF proposal with 13 others funded late last year
*Work -- *Simulate Great Lakes hydrology under various climates
- 	Use GLERL’s AHPS
- 		includes basin hydrology, overlake precipitation, lake thermodynamics, channel routing
- 		used in climate change impact studies for EPA, IJC, NOAA, & IJC
- 	Adjust lake & connecting channel conditions
- 		outlets with “natural” outflow-elevation relationships and connecting channels
- 		remove French River watershed
- 		use dynamic areas in evaporation
- 		remove existing diversions & consumptions
- 	Use similar methodology here
- 		propose climate characteristics compatible with geologic evidence or GCM simulations
- 		modify meteorological record to reflect proposed climate changes
- 		simulate resulting hydrology & compare to base case
- 	Build WWW interface of project results for other researchers & public

**Notes:**
Work.  Will use AHPS, which is a system of models for the Great Lakes and which we’ve used before to assess climate change impacts in the Great Lakes.  We’ll use natural/pre-project rating curves and channel hydraulics (prepared in the 1989 IJC Great Lakes Water Levels Reference Study to estimate the extent Society has changed the water level regime).  We’ll remove the French River watershed as its flow was reversed 9000 years ago (into the Hudson Bay watershed).  Today, lake area variations do not appreciably affect evaporation; we’ll ensure these variations are considered in simulations.  We’ll remove modern diversions and consumptions but not use (unknown) hydrology conditions of the past.  We’ll use methodology similar to that used in our other climate change impact studies.  We’ll also build a web interface to share our results with other researchers and the public; it will be dynamic enough to allow us to add to it as we complete work items.

## Work (continued)

- 	Model entire interdependent system (Georgian Bay draining into St. Clair)
- 	Model two systems independently
- 		Lakes Superior, Michigan, Huron, and Georgian Bay (used to drain to Hudson Bay)		Lakes St. Clair, Erie, and Ontario (no inflow from above)
- 	Look at steady-state closed lake
- 		Steady-state (repeat adjusted meteorological record with initial conditions = ending)
- 		Sufficient to use zero outflow and look at climates giving levels below sill
- 			a) Superior terminal?
- 			b) Michigan-Huron-Georgian Bay terminal, given Superior terminal?
- 			c) Erie terminal?
- 			d) Ontario terminal, given Erie terminal?
- 		Relax constraint of upstream terminal lakes.

**Notes:**
Work. First, consider all lakes as interdependent (like they are now, but with “natural” outlet and connecting channel flows) and compare with historical record to see if we’re “in the ballpark.”

Then, model two systems independently:  1) Lakes Superior, Michigan, Huron, and Georgian Bay (the upper Great Lakes), and 2) Lakes St. Clair, Erie, and Ontario (the lower Great Lakes) with no inflow from the upper Great Lakes since they drained to the Hudson Bay watershed through the reversed French River 9000 years ago.

Next, consider a closed lake at steady state (as far as the climate is concerned) by repeating the simulation with initial conditions equal to ending conditions until there is no change.  Exit channels are unimportant after water gets below the lake’s sill elevation.  We can therefore use zero outflow for such channels (& no routing) to identify candidate climates that result in water levels below the sill.  Initially, we will consider steady state closed systems with a look at Lake Superior (by itself) being a terminal lake (zero St. Mary’s flow) and with a look at Huron-Michigan-Georgian Bay being terminal lakes given that Lake Superior is terminal.  We will also look at Erie (by itself) being a terminal lake (zero Niagara flow) and look at Ontario being a terminal lake given that Lake Erie is terminal.  Then we will relax the constraint of zero upstream inflows (upstream terminal lakes) and consider each lake as part of its parent system (upper or lower system).

## Relevance

- 	Increase understanding of Great Lakes sensitivity to climate change
- 		Previously, lake changes attributed to isostatic rebound & shifts in outlet elevation
- 		New findings suggest climate shifts
- 	Understand climate change impacts today

**Notes:**
Relevance.  This project helps us understand Great Lakes' sensitivity to climate change by looking at paleontology.  Previous reconstructions of late glacial and post-glacial lake phases in the Great Lakes attributed major changes in lake levels to non-climatic processes (e.g. isostatic rebound and shifts in outlet elevation).  New findings of early-middle Holocene lake closure events suggest an abrupt severe dry climate as they represent level changes much greater than recorded within the last two centuries.  Knowledge of past occurrences of high-amplitude rapid hydrological change is relevant as some scenarios of future climate driven by global warming suggest lake-level reductions below presently-known variability may be possible in the Great Lakes.

## Study Area

**Notes:**
The Great Lakes basin area is 770,000 sq. km. (300,000 sq. mi.), about one-third of which is water surface.  The basin extends 3,200 km. (2,000 mi.) from the western edge of Lake Superior to the Moses-Saunders Power Dam 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. Marys River into Lake Huron where it is joined by water flowing from Lake Michigan.  Lake Superior is completely regulated, to balance Lakes Superior, Michigan, and Huron water levels, according to Regulation Plan 1977, under the auspices of the International Joint Commission.
Lakes Michigan and Huron are considered to be one lake hydraulically because of their connection through the deep Straits of Mackinaw. A diversion takes place from Lake Michigan at Chicago where water is diverted into the Mississippi River Basin. 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 Lakes Michigan and 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 is completely regulated in accordance with Regulation Plan 1958D to balance damages upstream on Lake Ontario with those downstream on the St. Lawrence Seaway [estimated to have lowered Lake Ontario 0.75 m (2.5 ft) during the record high water levels of 1986]. 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 ocean.  Lakes Superior, Michigan, Huron, and Ontario are very deep, while Lakes Erie and St. Clair are very shallow.

## Past Studies

- Early Great Lakes Climate Change Impact Studies

-      used simple constant changes in air temperature or precipitation in water balances

-      GCMs simulate current & 2xCO2 conditions

-      GCMs used for transient increases of greenhouse gases

-      EPA in 1984 used hydrology components of GCMs to assess water availability

- Recent Similar Great Lakes Climate Change Impact Studies

-      GLERL-EPA 2xCO2 impacts (1989)

-      GLERL-IJC 2xCO2 impacts (1992)

-      US National Assessment in Great Lakes (1999)

-      Transposed Climate impacts (1998)

*Past Studies*

-      IJC LOSLR Regulation study (2004)

**Notes:**
Great Lakes have tremendous water & heat storage capacities
	respond slowly to changed meteorological inputs
	memory damps short-term meteorological fluctuations
	allows response to longer-period fluctuations characteristic of climate change
	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
	GCMs simulate current and 2xCO2 conditions
	GCMs used for transient increases of greenhouse gases
		evolved from 8o—3o grids
		internally consistent daily meteorology
	EPA in 1984 used hydrology components of GCMs to assess water availability
		only for large regions
		regional hydrology models linked to GCMs
Recent Similar Great Lakes Climate Change Impact Studies
	GLERL-EPA 2xCO2 Impacts (1989)
		simulated 30 yr of “present” hydrology with historical data & present conditions
		used arbitrary initial conditions but simulated until unchanging (“steady-state”)
		GCM simulations for “present” & 2xCO2 steady-state from GISS, GFDL, & OSU
		extracted monthly ratios/differences of “present” to 2xCO2 for each met. variable
		applied to daily historical data to estimate 2xCO2 meteorological scenarios
		simulated 30 yr of 2xCO2 hydrology
		interpreted differences between 2xCO2 & base case as climate change impacts
	GLERL-IJC 2xCO2 Impacts (1992)
		IJC reassessed climate change impacts with similar methods
		considered 2xCO2 GCM scenarios from Canadian Climate Centre
	Transposed Climate Impacts (1997)
		refill.................
	US National Assessment of Climate Change in the Great Lakes (1999)
		part of study on Potential Consequences of Climate Variability & Change
		part of US Global Change Research Program
		used Canadian model, v1, & United Kingdom model, v2 (current then)
		prescribed increasing greenhouse gases; enabled looks at chosen ranges
		full coupling between atmospheric & oceanic components
		used parameterizations of direct radiative effect of sulfate aerosols
		used similar methods to transfer climate changes to hydrology impacts
	IJC Lake Ontario-St. Lawrence River Regulation Study (2004)
		part conducted by Hydrology & Hydraulics TWG to create regulation scenarios to test management plans	
		repeated earlier methodology with latest GCM scenarios selected by H&H TWG
		used Canadian model, v2, & United Kingdom model, v3
		results presented last year at IAGLR conference

## Data Preparation

- Climate Data

-      models use daily data 1948—1999

-           ~1800 stations for overland meteorology

-           ~40 stations for overlake meteorology

-      Thiessen-averaged over 121 subbasins & 7 lakes

- Changed Climate

-      “base case” scenario

-      apply ratios & differences to historical data

*Data Preparation*

-      use with models to calculate climate change scenario

**Notes:**
Climate Data
	models use daily data 1948—1999
		about 1,800 stations for overland meteorology (precipitation & air temperature)
		about 40 stations for overlake meteorological (air temperature, humidity, wind speed, & cloud cover)
	Thiessen-averaged each day to find meteorological time series over each of the 121 sub-basins & 7 lakes
Changed Climate
	historical meteorological data represents “present” hydrology: models give “base case” scenario
	apply precipitation ratios and air temperature differences to historical data to construct changed climate meteorology
	use with models to calculate climate change scenario

## Actual Data Adjustments

- P’ = P * R
- T’ = T + D

**Notes:**
All precipitation is adjusted by multiplying the actual precipitation by the precipitation ratio and all air temperatures are adjusted by adding the temperature difference to the actual temperatures.  In addition, humidity is adjusted as shown above.  For precipitation ratios below unity, the absolute humidity is multiplied by the ratio (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 is divided by the precipitation ratio and subtracted from the adjusted saturation vapor pressure.  As the ratio goes to unity, the adjusted goes to the actual and as the ratio goes to infinity, the adjusted approaches the saturation limit (if twice as wet, then half as dry).  This insures 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; the adjusted saturation vapor pressure is always higher than the adjusted vapor pressure as shown (no saturation).  For the case where we are simulating lower air temperatures, this adjustment could result in saturation where additional adjustment would be necessary.

## Modeling Procedure

- Estimate “steady-state” conditions
- 	repeat 52-yr simulation with initial conditions equal to end values, until unchanging
- Simulate with models on adjusted data sets for all scenarios (including base case)
- 121 watersheds and 7 lakes
- Interpret differences between scenarios & base case as hydrology impacts

*Modeling Procedure*

## Slide 11

**Notes:**
Hydrology Model.  GLERL’s Large Basin Runoff Model (LBRM) consists of moisture storages arranged as a serial and parallel cascade of “tanks” to coincide with the perceived basin storage structure.  Water enters the snowpack, 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).  Excess supply is surface runoff.  Flows from all tanks are proportional to their amounts (linear-reservoir flows).  Evapotranspiration is proportional to available water and to sensible heat complementary concept).  Mass conservation applies for the snowpack and tanks; energy conservation applies to evapotranspiration.  Complete analytical solutions exist.

Applied to 121 river watersheds flowing into the Great Lakes; just now begun recalibrating with updated data sets.  It is a daily model that 

agrees quite well with weekly 

and monthly observations (these are “typical” comparisons: neither best nor worst).  Have complete documentation, including GUIs, for calibrating and using the model.

## Slide 12

**Notes:**
Lake Thermodynamic Model.  GLERL’s Lake Thermodynamic Model empirically adjusts over-land data for over-water or over-ice conditions.  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.

Enables 1D modeling throughout the lake depth (spatial averaged) and can be used to follow thermal development and turnovers in the lake

Plots like this can be created as estimates for all years of record (1948-2000) to aid in other studies.  Just begun recalibrating and preparing simulated water temperature data sets for use in alewife over-winter studies.

## NBS Adjustment

**Notes:**
Precipitation on each lake, runoff to each lake, and evaporation from each lake are estimated for a given climate with the runoff models and lake evaporation models.  They are expressed as daily depths over the lake surface and were determined using coordinated lake areas and volumes (i.e., no variation of lake area was actually considered in their determination).  We adjust to actual lake areas by converting these depth rates into volumetric flow rates.  Precipitation and evaporation are directly converted by simply multiplying the overlake rates by the lake area of the simulation, A.  Runoff is first multiplied by the coordinated lake area, AL (over which it was expressed), to calculate the original volumetric runoff rate, then divided by the coordinated land area, AB - AL (to express it as the equivalent unit rate over land), and then multiplied by the land area of the simulation, AB - A.

## Hypsometric Relations

**Notes:**
I built hypsometric curves (plots of Volume and Area with Elevation) for each of the lakes, based on the 1977 report on “Coordinated Great Lakes Physical Data” by the Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data.  I translated channel equations, of lake outflow vs. lake elevation for each lake, for “natural/pre-project” conditions  to the IGLD 1985 water datum from the 1989 report to the IJC Great Lakes Water Levels Reference Study on “Procedure for Developing the Great Lakes Level and Flow Regime for Pre-Project Conditions.”  This at least avoids the regulation and channel changes of the recent past.  I further adjusted the equations to make physical sense (e.g., for the same water elevations on two connected lakes, there should be no flow).

## Integrated System

*Integrated System*

- St. Mary’s River

- St. Clair River

- Detroit River

- Niagara River

- St. Lawrence River

**Notes:**
The adjusted NBS are used in a water balance based on the above arrangement of lakes and their connecting channels.  It is necessary to compute the outflows from all lakes as inflows to downstream lakes as part of the simulation.  This requires knowing outflow and connecting channel relationships and calculating lake levels as part of the simulation.  Further, the calculation of lake levels allows tracking of lake volume and area to further refine NBS component estimation.

NEED MORE FOR A PAPER, describing simultaneous solution of 7 water balances and 5 (make it 7?) channel rating equations, through iterative solution.

## NBS

*NBS*

**Notes:**
First, I compared the “base case” net basin supplies (precipitation + runoff – lake evaporation), resulting from the steady-state run (where simulation is repeated with initial conditions = final conditions until no change), with historical net basin supplies (computed as a water balance residual from historical lake levels and flows).  This plot of annual NBS actually shows pretty good agreement, as expected since historical meteorology is 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.  Differences due to comparing steady-state conditions (runoff based on initial “steady-state” moisture storages, evaporation based on initial “steady-state” heat storage) with the actual historical transient should be small since basin moisture and lake heat storages quickly become insensitive to initial conditions.  The biggest differences occur on Lake Ontario, suggesting they arise from water balance errors in computing the historical residual NBS.

## Slide 17

**Notes:**
Next, I compared the “base case” lake levels, resulting from the steady-state run, with historical levels.  For this comparison, I included all diversions but used the “natural/pre-project” outflow/channel relationships.  This plot of daily simulated levels and monthly historical levels 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 Thiessen-weighted estimates often underestimate at low station densities), and differences in the outflow/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 steady-state simulation uses an unchanging outflow/channel relationship).
On Michigan-Huron-Georgian Bay, it appears that the historical water levels are lower than the simulated steady-state; this lowering probably results from the historical changes in Lake Superior operations and the St. Clair river channel.  But it also may be related to the continental uplift occurring after the retreat of the glaciers.
Lakes St. Clair and Erie are very similar to the steady-state simulation but Ontario shows lower water levels historically, probably as a result of the difference between regulated Niagara flows and the natural/pre-project outflow/channel conditions
The model appears to simulate the system reasonably when all sources of differences between the simulations and historical flows are considered.

## Slide 18

**Notes:**
The connecting channel flow differences match well with the lake level differences.

## Matching MHG Historical Water Balance 

*Matching MHG Historical Water Balance *

- For Superior:  		QS = 824.721 (ES – 181.425)1.5
- For Mic-Hur-Geo:	QMHG = 185 (EMHG – 166.549)1.5

**Notes:**
I then separated the upper lakes from the lower lakes by making the outflow from Lake Michigan-Huron-Georgian Bay independent of Lake St. Clair, since MHG used to drain into the Hudson Bay watershed.  I used a weir equation for MHG outflow, as suggested by the natural/pre-project equation for Lake Superior outflow through the St. Mary’s river, but with a sill elevation taken from the natural/pre-project equation for Lake Michigan-Huron-Georgian Bay flow through the St. Clair River into Lake St. Clair; I then experimented with the coefficient until the water balance roughly matched simulated base-case MHG levels with historical, as shown above.

Note that the elevation inside of the parentheses is called the “sill” elevation and represents the elevation below which there is no outflow.

## Negligible Diversions 

|  |  | Great Lake |  |  |  |
| --- | --- | --- | --- | --- | --- |
| Diversion | Amount | Superior | Mich-Hur | 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 |

**Notes:**
Then, I ascertained that the present-day diversions in the hydrology models were actually negligible (on the order of a few centimeters)  compared to the changes in net basin supplies or drops in water levels to be simulated with changed climates.  Therefore, they are safely ignored; no effort was made to remove these diversions.

International Great Lakes Diversions and Consumptive Uses Study Board (1985)  Great Lakes Diversions and Consumptive Uses.  International Joint Commission, Washington.

## S2 – S1 = Inflow + NBS – Outflow

*NBS*

**Notes:**
NBS can be used to evaluate whether a lake will become terminal or not.  (A lake with no outflow is called “terminal.”)  For a terminal lake (outflow = zero) the water balance is determined by just the inflow and NBS.  If inflow plus NBS are positive, the lake rises, and if negative, the lake falls.  Conversely, at steady-state (long-term change in storage = 0), a lake with zero long-term inflow plus NBS must not have any outflow.  (See above.)  That is, a lake at steady-state with zero long-term inflow plus NBS must be a terminal lake.  By looking at the long-term average inflow plus NBS for a lake, associated with each changed climate scenario, we can identify those climates that will result in a terminal lake.  If we assume no inflow from an upstream lake, so that we are considering each lake independently, then we need only look at long-term average NBS.

## Steady-State NBS As a Function of Climate

*Steady-State NBS As a Function of Climate*

**Notes:**
I looked at 36 climate scenarios, each defined in terms of the precipitation drop (%) from the base case (0, 10, 20, 30, 40, 50) and the temperature rise (oC) above the base case (0, 1, 2, 3, 4, 5).  I calculated the steady-state average NBS resulting from each and plotted it with precipitation drop and temperature rise as  shown above for Lakes Superior and Michigan-Huron-Georgian Bay.  The “zero” isoline was interpolated from the non-zero values since the values at the orange points were all zero.

Note that NBS components (precipitation, runoff, and evaporation) vary with lake area (precipitation and evaporation increase with lake area and runoff decreases).  This means that, for a terminal lake, there should be some non-zero lake size for steady-state NBS equal to zero (where precipitation and runoff is balanced by evaporation).  (For zero terminal lake area, NBS consists solely of runoff, indicating the lake will rise.)  Thus, in the calculations that produced the above figure, long-term average NBS remain at zero, after they are reached, for all climates dryer and warmer.  That’s why the “zero” isoline was interpolated from the non-zero values.

The figure shows that Lake Superior should be a terminal lake for the four climates shown by the orange points: (40%, 5oC), (50%, 3oC), (50%, 4oC), and (50%, 5oC).  Lake Michigan-Huron-Georgian Bay should be a terminal lake for the three climates depicted: (50%, 3oC), (50%, 4oC), and (50%, 5oC).  Recall, that this reasoning assumes zero inflow, which is OK for Superior, but requires Superior to be a terminal lake for the Michigan-Huron-Georgian Bay analysis, which in this case it is.

## Steady-State Outflow As a Function of Climate

*Steady-State Outflow As a Function of Climate*

**Notes:**
To avoid having to consider that inflows from an upstream lake are zero (i.e., that the upstream lake is itself terminal) in our analysis of whether a lake is terminal under a given climate, we can look at outflows from the lake directly.  When the outflows from a lake are zero at steady-state, then the lake is terminal.  This figure shows much the same results as the previous NBS summary.  The graph on the left (for Superior) is identical for both NBS and outflow since Superior has no inflows and at, steady-state, average NBS = outflow.  The graph on the right (for Michigan-Huron-Georgian Bay) shows trends for outflow variation with climate change similar to the NBS trends.  However, the numbers are much higher because the steady-state average outflow = NBS + upstream inflow.  We see that, indeed, terminal lakes occur for the same experimental climates identified in the NBS summary.

Note that the MHG “zero” isoline (demarcation between terminal & non-terminal lakes), given by consideration of the outflow summary, is not quite the same as given by the NBS summary (the NBS zero isoline is shown here in light cyan).  The implication would be that there are some climates (zone between the two zero isolines), producing a terminal lake MHG, which have positive steady-state average NBS but zero outflow.  Since this is clearly impossible, the discrepancy should be regarded as due to interpolation errors on both summaries (linear interpolation was used); the area between the two zero isolines could serve as a measure of some of the uncertainty associated with this analysis.

Finally, these results suggest that:
	Lake Superior will be terminal for climates about 4.0oC or more warmer AND 41% or more dryer than present.
	Lake Michigan-Huron-Georgian Bay will be terminal for climates about 4.1oC or more warmer AND 43% dryer than present.

## Steady-State Water Levels As a Function of Climate

**Notes:**
We looked at 36 climate scenarios, each defined in terms of the precipitation drop (%) from the base case (0, 10, 20, 30, 40, 50) and the temperature rise (oC) above the base case (0, 1, 2, 3, 4, 5).  We calculated the steady-state average water level resulting from each lake and plotted it with precipitation drop and temperature rise as shown above for Lakes Superior and Michigan-Huron-Georgian Bay.

Three regions are identified for each lake’s graph: where levels are all above the sill, where levels are all below the sill, and where they are both above and below (an intermediate region). We found these regions by looking at maximum and minimum levels and comparing them to the sill elevations.  Of course, the lakes are terminal where all levels are below the sill.

## Steady-State Water Levels As a Function of Climate

- Terminal Lake Climates:
- 	Superior, 4.7 T + P > 60;		Michigan-Huron, 4.5 T + P > 63

**Notes:**
As the climate gets dryer or warmer, the average steady-state water level drops.  It appears that, for Lake Superior, a 1oC rise in temperatures is roughly equivalent to a 4.7% drop in precipitation and, for Lake Michigan-Huron, a 1oC rise in temperatures is roughly equivalent to a 4.5% drop in precipitation; climates to the right of the red lines produce terminal lakes (equations are given below the graphs).

## Steady-State Outflows As a Function of Climate

**Notes:**
Repeating lake response to climate in terms of steady state outflows from two slides ago.  Recall, when outflows from a lake are zero, then the lake is terminal.  These plots only show averages; so they are just a preliminary guide.  We superimposed the intermediate areas from the lake levels graphs here to indicate where interpolation of outflows is suspect.

## Steady-State NBS As a Function of Climate

*Steady-State NBS As a Function of Climate*

**Notes:**
Shown here are 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 degree C rise in air temperature.)  The water levels drop with successively dryer and or warmer climates, approaching in both cases the sill elevations shown in the preceding outflow equations.

## Steady-State NBS As a Function of Climate

*Steady-State NBS As a Function of Climate*

**Notes:**
Shown here are 50 years of simulated steady-state water levels for the upper Great Lakes for ALL climate scenario experiments, including those  which DID produce a terminal lake.  The water level drops for the terminal lake scenarios are impressive.

## Steady-State Climate Range

**Notes:**
Shown here are 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.

## Lower Great Lakes Without Upstream Inflows

- For St. Clair:
-   	QC	= 70.714 (EC – 165.953)2(EC – EE)0.5,	EC > EE > 165.953
- 		= 70.714 (EC – 165.953)2(EC – 165.953)0.5,	EC > 165.953 > EE
- For Erie:
- 	QE = 701.504 (EE – 169.938)1.5,	EE > 169.938
- For Ontario:
- 	QO = 577.187 (EO – 69.622)1.5,	EO > 69.622

**Notes:**
For the lower lakes, we took inflow to Lake St. Clair as zero since Lake Michigan-Huron drains to the Hudson Bay watershed.  Lake St. Clair’s bottom elevation is above its sill elevation, meaning that St. Clair can be empty but still have flow into Lake Erie.  Thus, St. Clair is never a terminal lake but simply part of the Lake Erie watershed as Lake Erie water levels drop.

## Steady-State Water Levels As a Function of Climate

*Steady-State Water Levels As a Function of Climate*
- Terminal Lake Climates:
- 	Erie, 4.7 T + P > 51;		Ontario, 3.5 T + P > 71

**Notes:**
We looked again at the 36 climate scenarios considered for the upper lakes and found that while Erie became terminal, Ontario did not.  So we looked at 99 climate scenarios, each defined in terms of the precipitation drop (%) from the base case (0, 10, 20, 30, 40, 50, 60, 70, 80) and the temperature rise (oC) above the base case (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10).  We calculated the steady-state average water level resulting from each lake and plotted it with precipitation drop and temperature rise as shown above for Lakes Erie and Ontario.

Three regions are again identified for each lake’s graph: all levels above the sill, all levels below the sill, and levels both above and below.  For Lake Erie, a 1oC rise in temperatures is roughly equivalent to a 4.7% drop in precipitation and, for Lake Ontario, a 1oC rise in temperatures is roughly equivalent to a 3.5% drop in precipitation; climates to the right of the red lines produce terminal lakes (equations are given below the graphs).

## Steady-State Outflows As a Function of Climate

**Notes:**
We can also consider lake response to climate in terms of steady state outflows.  When outflows from a lake are zero, then the lake is terminal.  These plots only show averages; so they are just a preliminary guide.  We superimposed the intermediate areas from the lake levels graphs here to indicate where interpolation of outflows is suspect.