Developing Multi-Lake Regulation Plans for the Great Lakes through Multi-Scenario OptimizationSaman Razavi, Bryan A. Tolson, and Masoud AsadzadehDept. of Civil & Environmental Engineering, University of Waterloo

PURPOSE AND SCOPE Water levels across Great Lakes – St. Lawrence River system are critically

important to the Canadian and US economies. The two existing control structures on St. Marys and St. Lawrence Rivers

may not prevent future excessively high and low levels across the system. This study aims to evaluate the system performance when enabled with

new control structures on St. Clair and Niagara Rivers under future extreme climate scenarios at an exploratory level.

1

1

1

s3

1

s1

s4

s2

d2 d1

ExcessShortage

Note: s3 ≥ s1

Upstream Storage Indicator at point i

Component 1

Note: s4 ≥ s2

USI(i) 1

Component 2

1

ExcessShortage

s5

s6

Downstream Storage Indicator between points i and i+1

DSI1(i) 1

Component 3

1

ExcessShortage

s7=p.s5

s8

s7

s8=p.s6

Downstream Storage Indicator between

points i+1 and i+2DSI2(i)

Target Release(i , t) = Component 1(i , t) + Component 2(i , t) + Component 3(i , t) + Baseline Flow(i) i = 1, …, 4 for control points at the outlet of Lakes Superior, MH, Erie, and Ontario, respectively t: time on a quarter-monthly basis – for Lake Superior only on a monthly basis

IF the lakes between control points i and i+1 and the lakes between control points i+1 and i+2 have not the same storage condition (both in shortage or both in excess)THEN Component 3 = 0

METHOD Base Case, system performance when regulated with

current regulation strategies, was deemed as baseline. Risk-based objective function aimed to improve the

system performance over the Base Case. Cost objective function aimed to reduce the cost of the

potential control structures. Pareto archived dynamically dimensioned search

(Asadzadeh & Tolson, 2011) enabled with “model preemption” strategy (Razavi et al., 2010) was used to solve the bi-objective optimization problem.

Three Regulation Plans were developed: - 4pt plan (four control points), controls on the outlets of Lakes Superior, MH, Erie, and Ontario

DESIRED PERFORMANCE OF THE SYSTEM Most of Great Lakes interests are able to cope with water levels within the

historical extremes range , but tend to suffer when levels exceed this range

PROPOSED RULE CURVE FORM

FUTURE HYDROLOGIC CONDITIONEight different 70-year NBS scenarios were chosen from the 50,000-year stochastic NBS dataset produced for the Lake Ontario-St. Lawrence River Study (Fagherazzi et al., 2005). These scenarios represent a diverse range of possible future severe climate conditions.

The desired water level range across the system is obtained by the system simulation over the historical 1900-2008 NBS data with the current control structures and regulation plans.

Water levels at seven evaluation points on Lakes Superior (Sup), Michigan-Huron (MH), St. Clair (SC), Erie (Er), and Ontario (On) as well as upper St. Lawrence River and lower St. Lawrence River are deemed representatives of all interests.

Evaluation of the direct impacts of the new control structures with multi-lake regulation plans on the different stakeholders is currently beyond the available data and tools.

KEY CONCLUSIONS Four-point and Niagara three-point plans could reduce the

frequency of extreme water levels across the eight extreme NBS scenarios at all evaluation points but lower St. Lawrence.

None of the multi-lake regulation plans could entirely eliminate the future extremes water levels.

Additional structures would be required to mitigate impacts of extreme levels at lower St. Lawrence River at Montreal.

Despite the excessive high cost, St. Clair 3pt plan cannot considerably improve the system performance.

ReferencesAsadzadeh, M., and B. A. Tolson (2009), A new multi-objective algorithm, Pareto Archived DDS, In Proceedings of

the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers (GECCO '09), 8-12 July 2009, Montreal, QC, Canada. ACM, New York, NY, USA. pp. 1963-1966.

Fagherazzi L., Guay R., Sparks D., Salas J., Sveinsson O., (2005)- Stochastic modeling and simulation of the Great Lakes – St Lawrence River system – Report submitted to the International Lake Ontario-St. Lawrence Study.

Levels Reference Study Board (1993). Levels Reference Study, Great Lakes-St. Lawrence River Basin, Final Report to the International Joint Commission, 144 pp.

Razavi, S., B. A. Tolson, L. S. Matott, N. R. Thomson, A. MacLean, and F. R. Seglenieks (2010), Reducing the computational cost of automatic calibration through model preemption, Water Resour. Res., 46, W11523.

Tolson B. A., S. Razavi, and M. Asadzadeh (2011), Formulation and evaluation of new control structures in the Great Lakes system, Technical Report produced for IUGLS International Joint Commission (IJC) Study. May, 9, 2011, 50 pages, (Project, principal investigator: Tolson).

ONTARIO

MICHIGAN

INDIANA OHIO

ILLINOIS

NEW YORK

PENNSYLVANIA

WISCONSIN

QUEBECMICHIGAN

LAKE SUPERIOR

LAKE ERIE

LAKE ONTARIO

LAKE HURON

LAKE

MIC

HIGA

N

LAKE ST. CLAIR

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

0%

4%

8%

12%

16%

20%

24%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

4%

8%

12%

16%

20%

24%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

0%

2%

4%

6%

8%

10%

12%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

2%

4%

6%

8%

10%

12%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

Driest Wettest

1

23 4

5

6

7

0%2%4%6%8%

10%12%14%16%18%20%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

0%2%4%6%8%

10%12%14%16%18%20%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

Driest Wettest

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

2

Superior Weir (Existing Structure)

Moses Saunders Dam(Existing Structure)

Hypothetical Structures(St. Clair and Niagara Rivers)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest WettestDriest Wettest

LOWER

ST.

LAWREN

CE

UPPER ST.

LAWRENCE

0

5

10

15

20

25

30

-25 -20 -15 -10 -5 0 5 10

Plan

Cos

t (bi

llion

$US

)

Risk-based Objective Function

4pt plans (without Lower St. Lawrence)

Niagara 3pt plans

$30 billion 4pt Plan

$6 billion 4pt Plan$2 billion

Niagara 3pt Plan

RISK-BASED OBJECTIVE FUNCTIONn: number of evaluation points (i.e., Lake Superior, Lake MH, …)m: number of NBS scenariosb = {bj,k | j = 1, 2, …, n & k = 1, 2, …, m}bj,k : base case performance on evaluation point j in scenario ky = {yj,k| j = 1, 2, …, n & k = 1, 2, …, m}yj,k : new regulation plan performance on evaluation point j in scenario k

Risk of Failure at evaluation point j in scenario k:Riskj,k = yj,k /T where T is the total number of time steps in simulation.

COST OBJECTIVE FUNCTION Excavation costs to increase the conveyance capacity of the St. Clair and

Niagara Rivers were functions of the maximum required increase in the regulated flow over the natural channel flow at the same condition.

Control structures costs on St. Clair and Niagara Rivers were assumed $513.1 and $533.2 million, constant for all degrees of flow regulation (updated from the Levels Reference Study, 1993)

- Niagara 3pt plan, controls on the outlets of Lakes Superior, Erie, and Ontario - St. Clair 3pt plan, controls on the outlets of Lakes Superior, MH, and Ontario

Estimated Tradeoffs between Risk-based and Regulation Cost Objective Functions

PLAN VALIDATIONS Validation experiments were performed by simulating

the plans with the full 50,000-year stochastic NBS sequence.

levels are exceeded when compared to the base case. Performance of the plans were also tested in terms of

vulnerability (i.e., magnitude of violating extreme levels).

Validation results that the $30 and $6 billion 4pt plans and $2 billion Niagara 3pt plan would reduce the risk that historical extreme water

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

Lake Superior

Lake M-H

Lake St. Clair

Lake Erie

Lake O

ntario

Upper St. Law

rence

Overall

Average

Risk

of F

ailu

re

Base Case $6 billion 4-pt plan

OPTIMIZATION RESULTS Bi-objective Trade-offs. St. Clair

3pt plan is not reported due to its considerably less benefit/cost

Risk of failure in Base Case and new plans at each evaluation point under each scenario

Average risks of failure in Base Case and new plans at each evaluation point under all scenarios

0%

5%

10%

15%

20%

25%

Lake Superior

Lake M-H

Lake St. Clair

Lake Erie

Lake O

ntario

Upper St. Law

rence

Overall

Average

Risk

of F

ailu

re

Base Case $30 billion 4pt plan$6 billion 4-pt plan $2 billion Niagara 3pt plan

ACKNOWLEDGEMENTThis poster partially presents a study funded by the International Upper Great Lakes

Study (IUGLS), International Joint Commission. Full details of the original study is available in Tolson et al. (2011).

0

100200

300

400

500600

700

800

900

1000

0<-0

.05

0.05

-0.1

0.1-

0.15

0.15

-0.2

0.2-

0.25

0.25

-0.3

0.3-

0.35

0.35

-0.4

0.4-

0.45

0.45

-0.5

0.5-

0.55

0.55

-0.6

0.6-

0.65

0.65

-0.7

0.7-

0.75

0.75

-0.8

0.8-

0.85

0.85

-0.9

0.9-

0.95

0.95

-1

Num

ber o

f Tim

es

in e

ach

Viol

ation

Bin

Bins (Exceedance Magnitude, m)

Lake MH - Violating Upper Extreme

Base Case$30 billion 4pt plan

0

500

1000

1500

2000

2500

3000

3500

0<-0

.05

0.05

-0.1

0.1-

0.15

0.15

-0.2

0.2-

0.25

0.25

-0.3

0.3-

0.35

0.35

-0.4

0.4-

0.45

0.45

-0.5

0.5-

0.55

0.55

-0.6

0.6-

0.65

0.65

-0.7

0.7-

0.75

0.75

-0.8

0.8-

0.85

0.85

-0.9

0.9-

0.95

0.95

-1

Num

ber o

f Tim

esin

eac

h Vi

olati

on B

in

Bins (Exceedance Magnitude, m)

Lake MH - Violating Lower Extreme

Base Case$30 billion 4pt plan

Developing Multi-Lake Regulation Plans for the Great Lakes through Multi-Scenario OptimizationSaman Razavi, Bryan A. Tolson, and Masoud AsadzadehDept. of Civil & Environmental Engineering, University of Waterloo AGU Fall Meeting, Dec 6, 2011. Paper Number: ????

PURPOSE AND SCOPE Water levels across Great Lakes – St. Lawrence River system are critically

important to the Canadian and US economies. The two existing control structures on St. Marys and St. Lawrence Rivers

may not prevent future excessively high and low levels across the system. This study aims to evaluate the system performance when enabled with

new control structures on St. Clair and Niagara Rivers under possible future climate scenarios at an exploratory level.

1

1

1

s3

1

s1

s4

s2

d2 d1

ExcessShortage

Note: s3 ≥ s1

Upstream Storage Indicator at point i

Component 1

Note: s4 ≥ s2

USI(1) = (ASup (ZSup – avgZSup)) / nSup

USI(2) = ((RVSup – avgRVSup) + AMH (ZMH - avgZMH)) / nMH

USI(3) = ((RVMH – avgRVMH) + ASC (ZSC – avgZSC) + AEr (ZEr – avgZEr)) / nErUSI(4) = ((RVEr – avgRVEr) + AON (ZON – avgZON)) / nON

DSI1(1) = (AMH (ZMH - avgZMH)) / ndMH

DSI1(2) = (ASC (ZSC – avgZSC) + AEr (ZEr – avgZEr)) / ndErDSI1(3) = (AON (ZON – avgZON)) / ndONDSI1(4) = (ZJetty1 – avgZJetty1) / ndJetty1

DSI2(1) = (ASC (ZSC – avgZSC) + AEr (ZEr – avgZEr))/ndMH

DSI2(2) = ((AON (ZON – avgZOn)) /ndEr

DSI2(3) = (ZJetty1 – avgZJetty1) /ndONUSI(i) 1

Component 2

1

ExcessShortage

s5

s6

Downstream Storage Indicator between points i and i+1

DSI1(i) 1

Component 3

1

ExcessShortage

s7=p.s5

s8

s7

s8=p.s6

Downstream Storage Indicator between

points i+1 and i+2DSI2(i)

Target Release(i , t) = Component 1(i , t) + Component 2(i , t) + Component 3(i , t) + Baseline Flow(i)i = 1, …, 4 for control points at the outlet of Lakes Superior, MH, Erie, and Ontario, respectivelyt: time on a quarter-monthly basis – for Lake Superior only on a monthly basis

IF the lakes between control points i and i+1 and the lakes between control points i+1 and i+2 have not the same storage condition (both in shortage or both in excess)THEN Component 3 = 0

RISK-BASED OBJECTIVE FUNCTIONn: number of evaluation points (i.e., Lake Superior, Lake MH, …)m: number of NBS scenariosb = {bj,k | j = 1, 2, …, n & k = 1, 2, …, m}bj,k : base case performance on evaluation point j in scenario ky = {yj,k| j = 1, 2, …, n & k = 1, 2, …, m}yj,k : new regulation plan performance on evaluation point j in scenario k

Single-scenario formulation (k=1)

zj = 0 if yj < bj (performance in point j better than baseline) zj = 1 if yj ≥ bj (performance in point j worse than baseline)

Risk of Failure at evaluation point j :

Riskj = yj /T where T is the total number of time steps in simulation.

METHOD Base Case, system performance when regulated with current

regulation strategies, was deemed as baseline of improvement.

Risk-based objective function aimed to improve the system performance over the Base Case.

Cost objective function aimed to reduce the cost of the potential control structures.

Pareto archived dynamically dimensioned search enabled with “model preemption” strategy was used to solve the bi-objective optimization problem.

DESIRED PERFORMANCE OF THE SYSTEM Most of Great Lakes interests are able to cope with water levels within the

range of historical extremes, but tend to suffer when levels exceed this range

PROPOSED RULE CURVE FORM

FUTURE HYDROLOGIC CONDITIONEight different 70-year NBS scenarios were chosen from the 50,000-year stochastic NBS dataset produced for the Lake Ontario-St. Lawrence River Study (Fagherazzi et al., 2005). These scenarios represent a diverse range of possible future severe climate conditions.

The desired water level range across the system is obtained by the system simulation over the historical 1900-2008 NBS data with the current control structures and regulation plans.

Water levels at seven evaluation points on Lakes Superior (Sup), Michigan-Huron (MH), St. Clair (SC), Erie (Er), and Ontario (On) as well as upper St. Lawrence River and lower St. Lawrence River are deemed representatives of all interests.

Evaluation of the direct impacts of the new control structures with multi-lake regulation plans on the different stakeholders is currently beyond the available data and tools.

ONTARIO

MICHIGAN

INDIANA OHIO

ILLINOIS

NEW YORK

PENNSYLVANIA

WISCONSIN

QUEBECMICHIGAN

LAKE SUPERIOR

LAKE ERIE

LAKE ONTARIO

LAKE HURON

LAKE

MIC

HIG

AN

LAKE ST. CLAIR

UPPER ST. LAWRENCE LOWER ST. LAWRENCEIroquois H. W. Saunders H.W.

Pointe-ClaireJetty 1

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

Three Regulation Plans and two Regulation Seasons were considered.4pt Plan: the outlets of Lakes Superior, MH, Erie, and Ontario are controlled. 39 rule curve parameters for each season, a total of 78 parameters

Niagara 3pt Plan: the outlets of Lakes Superior, Erie, and Ontario are controlled.St. Clair 3pt Plan: the outlets of Lakes Superior, MH, and Ontario are controlled. 29 rule curve parameters for each season, a total of 58 parameters

where Z : water level at the beginning of a regulation period avgZ : historical average monthly levels RV : release volume planned for the current regulation period avgRV : the historical average monthly flow volume n and nd : normalizing constants

Component 1

Component 2

Component 3

Multi-scenario formulation

COST OBJECTIVE FUNCTION Excavation costs to increase the conveyance capacity of the St.

Clair and Niagara Rivers were functions of the maximum required increase in the regulated flow over the natural channel flow at the same condition.

Control structures costs on St. Clair and Niagara Rivers were assumed $513.1 and $533.2 million, constant for all degrees of flow regulation (updated from the Levels Reference Study, 1993)

KEY CONCLUSIONSFour-point and Niagara three-point plans could reduce the frequency of extreme water levels across the eight extreme NBS scenarios at all evaluation points but lower St. Lawrence.

None of the multi-lake regulation plans could entirely eliminate the future extremes water levels.

Additional structures would be required to mitigate impacts of extreme levels at lower St. Lawrence River at Montreal.

Despite the excessive high cost, St. Clair 3pt plan cannot considerably improve the system performance.

The estimated cost o

ReferencesAsadzadeh, M., and B. A. Tolson (2009), A new multi-objective algorithm,

Pareto Archived DDS, In Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers (GECCO '09), 8-12 July 2009, Montreal, QC, Canada. ACM, New York, NY, USA. pp. 1963-1966.

Fagherazzi L., Guay R., Sparks D., Salas J., Sveinsson O., (2005)- Stochastic modeling and simulation of the Great Lakes – St Lawrence River system – Report submitted to the International Lake Ontario-St. Lawrence Study.

Levels Reference Study Board (1993). Levels Reference Study, Great Lakes-St. Lawrence River Basin, Final Report to the International Joint Commission, 144 pp.

Tolson B. A., S. Razavi, and M. Asadzadeh (2011), Formulation and evaluation of new control structures in the Great Lakes system, Technical Report produced for IUGLS International Joint Commission (IJC) Study. May, 9, 2011, 50 pages, (Project, principal investigator: Tolson).

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

0%

4%

8%

12%

16%

20%

24%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

4%

8%

12%

16%

20%

24%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

0%

2%

4%

6%

8%

10%

12%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

2%

4%

6%

8%

10%

12%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

His

toric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

Driest Wettest

1

23

4

5

67

0%2%4%6%8%

10%12%14%16%18%20%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

oric

al S

imul

ated

Ext

rem

es

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

0%2%4%6%8%

10%12%14%16%18%20%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

Driest Wettest

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest

2

0%

5%

10%

15%

20%

25%

30%

35%

Lake Superior

Lake M-H

Lake St. Clair

Lake Erie

Lake O

ntario

Upper St. Law

rence

Lower St.

Lawrence

Risk

of g

oing

bey

ond

Hist

oric

al Si

mul

ated

Extr

emes

Scenario 1 - Driest Condition .

Base CaseNew Regulation Plan

0%2%4%6%8%

10%12%14%16%18%20%

Lake Superior

Lake M-H

Lake St. Clair

Lake Erie

Lake O

ntario

Upper St. Law

rence

Lower St.

Lawrence

Risk

of g

oing

bey

ond

Hist

oric

al Si

mul

ated

Extr

emes

Scenario 8 - Wettest Condtion .

Base CaseNew Regulation Plan

0%

5%

10%

15%

20%

25%

30%

35%

Lake Superior

Lake M-H

Lake St. Clair

Lake Erie

Lake O

ntario

Upper St. Law

rence

Lower St.

Lawrence

Risk

of g

oing

bey

ond

Hist

oric

al Si

mul

ated

Extr

emes

Scenario 3 - Most Severe Condition .

Base CaseNew Regulation Plan

Single-scenario Optimization Results

Superior Weir (Existing Structure)

Moses Saunders Dam(Existing Structure)

Hypothetical Structures(St. Clair and Niagara Rivers)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Risk

of g

oing

bey

ond

Hist

orica

l Sim

ulat

ed E

xtre

mes

Scenario Number

Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan

Driest Wettest