Developing Multi-Lake Regulation Plans for the Great Lakes through Multi-Scenario Optimization Saman Razavi, Bryan A. Tolson, and Masoud Asadzadeh Dept. 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 s 3 1 s 1 s 4 s 2 d 2 d 1 Excess Shortage Note: s 3 ≥ s 1 Upstream Storage Indicator at point i Component 1 Note: s 4 ≥ s 2 USI(i) 1 Component 2 1 Excess Shortage s 5 s 6 Downstream Storage Indicator between points i and i+1 DSI1(i) 1 Component 3 1 Excess Shortage s 7 =p.s 5 s 8 s 7 s 8 =p.s 6 Downstream Storage Indicator between points i+1 and i+2 DSI2(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 CONDITION Eight 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. References Asadzadeh, 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 ONTARIO MICHIGAN INDIANA OHIO ILLINOIS NEW YORK PENNSYLVANIA WISCONSIN QUEBEC MICHIGAN LAKE SUPERIOR LAKE ERIE LAKE ONTARIO LAKE H U RON L A KE MI C HI GAN LAKE ST. CLAIR 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt. Law rence 4ptw ithout Low erSt.Lawrence ($30 B) 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt. Law rence 4ptw ithout Low erSt.Law rence ($30 B) 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case $2 billion Niagara 3pt plan $6billion4-ptplan Driest Wettest 0% 4% 8% 12% 16% 20% 24% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt. Law rence 4ptw ithout Low erSt.Law rence ($30 B) 0% 4% 8% 12% 16% 20% 24% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case $2billionNiagara3pt plan $6billion4-ptplan Driest Wettest 0% 2% 4% 6% 8% 10% 12% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt. Law rence 4ptw ithout Low erSt.Law rence ($30 B) 0% 2% 4% 6% 8% 10% 12% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case $2billionNiagara3pt plan $6billion4-ptplan Driest Wettest Driest Wettest 1 2 3 4 5 6 7 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case $2 billionNiagara3pt plan $6 billion4-ptplan 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt.Law rence 4ptw ithoutLow erSt.Law rence ($30 B) Driest Wettest 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt. Law rence 4ptw ithout LowerSt.Law rence ($30 B) 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case $2billionNiagara3pt plan $6billion4-ptplan 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 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case 4ptw ith Low erSt.Law rence 4ptw ithout Low erSt.Law rence ($30 B) 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 Riskofgoing beyond Historical Sim ulated Extrem es Scenario Num ber Base Case $2billionNiagara3pt plan $6billion4-ptplan Driest Wettest Driest Wettest LOWER ST. LAWRENCE UPPER ST . LAWREN CE 0 5 10 15 20 25 30 -25 -20 -15 -10 -5 0 5 10 Plan Cost(billion $US) Risk-based O bjectiveFunction 4ptplans(w ithoutLow erSt. Law rence) Niagara3ptplans $30 billion 4ptPlan $6 billion 4ptPlan $2billion N iagara 3ptPlan RISK-BASED OBJECTIVE FUNCTION n: number of evaluation points (i.e., Lake Superior, Lake MH, …) m: number of NBS scenarios b = {b j,k | j = 1, 2, …, n & k = 1, 2, …, m} b j,k : base case performance on evaluation point j in scenario k y = {y j,k | j = 1, 2, …, n & k = 1, 2, …, m} y j,k : new regulation plan performance on evaluation point j in scenario k Risk of Failure at evaluation point j in scenario k: 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 - 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 LakeM -H Lake St. Clair Lake Erie Lake O ntario UpperSt. Law rence O verall Average Risk ofFailure BaseCase $6 billion4-ptplan 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 LakeM -H Lake St. Clair Lake Erie Lake O ntario UpperSt. Law rence O verall Average Riskof Failure BaseCase $30 billion 4pt plan $6 billion 4-pt plan $2 billion Niagara3pt plan ACKNOWLEDGEMENT This 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). 0 100 200 300 400 500 600 700 800 900 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 berofTim es in each Violation Bin Bins(Exceedance M agnitude, m ) LakeM H -V iolatingU pperExtrem e BaseCase $30 billion 4ptplan 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 berofTim es in each Violation Bin Bins(Exceedance M agnitude, m ) LakeM H -V iolatingLow erExtrem e BaseCase $30 billion 4ptplan
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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
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
INDIANAOHIO
ILLINOIS
NEW YORK
PENNSYLVANIA
WISCONSIN
QUEBECMICHIGAN
LAKE SUPERIOR
LAKE ERIE
LAKE ONTARIO
LAKE H
URO
N
LA
KE M
ICH
IGA
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
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
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%
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
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
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
His
toric
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
His
toric
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
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
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
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
His
toric
al S
imul
ated
Ext
rem
es
Scenario Number
Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan
Driest WettestDriest Wettest
LOW
ER S
T.
LAW
RENCE
UPPER ST.
LAW
RENCE
0
5
10
15
20
25
30
-25 -20 -15 -10 -5 0 5 10
Plan
Cos
t (bi
llion
$U
S)
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.
Lawrence
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.
Lawrence
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
100
200
300
400
500
600
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.
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
INDIANAOHIO
ILLINOIS
NEW YORK
PENNSYLVANIA
WISCONSIN
QUEBECMICHIGAN
LAKE SUPERIOR
LAKE ERIE
LAKE ONTARIO
LAKE H
URO
N
LA
KE M
ICH
IGA
N
LAKE ST. CLAIR
UPPER ST. LAWRENCELOWER ST. LAWRENCE
Iroquois 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%
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Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)
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Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan
Driest Wettest
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Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)
0%
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8%
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Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan
Driest Wettest
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Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)
0%
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6%
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Scenario Number
Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan
Driest Wettest
Driest Wettest
1
2
3
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5
67
0%2%4%6%8%
10%12%14%16%18%20%
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Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan
0%2%4%6%8%
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1 2 3 4 5 6 7 8
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Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)
Driest Wettest
0%
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40%
1 2 3 4 5 6 7 8
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Scenario Number
Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)
0%
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Scenario Number
Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan
Driest Wettest
2
0%
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Lake Superior
Lake M-H
Lake St. Clair
Lake Erie
Lake O
ntario
Upper St.
Lawrence
Lower St.
Lawrence
Risk
of g
oing
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ated
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Scenario 1 - Driest Condition .
Base Case
New 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
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Lawrence
Lower St.
Lawrence
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Scenario 8 - Wettest Condtion .
Base Case
New Regulation Plan
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Lake Superior
Lake M-H
Lake St. Clair
Lake Erie
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Lower St.
Lawrence
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oing
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ated
Ext
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Scenario 3 - Most Severe Condition .
Base Case
New Regulation Plan
Single-scenario Optimization Results
Superior Weir (Existing Structure)
Moses Saunders Dam(Existing Structure)
Hypothetical Structures(St. Clair and Niagara Rivers)
0%
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Risk
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Base Case4pt with Lower St. Lawrence4pt without Lower St. Lawrence ($30 B)
0%
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1 2 3 4 5 6 7 8
Risk
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Scenario Number
Base Case$2 billion Niagara 3pt plan$6 billion 4-pt plan