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 s3s3 1 s1s1 s4s4 s2s2 d2d2 d1d1 ExcessShortage Note: s 3 ≥ s 1 Upstream Storage Indicator at point i Component 1 Note: s 4 ≥ s 2 USI( i ) 1 Component 2 1 ExcessShortage s5s5 s6s6 Downstream Storage Indicator between points i and i +1 DSI1( i ) 1 Component 3 1 ExcessShortage s 7 = p.s 5 s8s8 s7s7 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 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 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, W 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 QUEBEC MICHIGAN Driest Wettest Superior Weir (Existing Structure) Moses Saunders Dam (Existing Structure) Hypothetical Structures (St. Clair and Niagara Rivers) Driest Wettest 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: Risk j,k = y j,k /T where T is the total number of time steps in simulation. Single-scenario Optimization Results 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 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 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).

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 AGU Fall Meeting, Dec 6, 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 s3s3 1 s1s1 s4s4 s2s2 d2d2 d1d1 ExcessShortage Note: s 3 ≥ s 1 Upstream Storage Indicator at point i Component 1 Note: s 4 ≥ s 2 USI(1) = ( A Sup (Z Sup – avg Z Sup ) ) / n Sup USI(2) = ( (RV Sup – avg RV Sup ) + A MH (Z MH - avg Z MH ) ) / n MH USI(3) = ( (RV MH – avg RV MH ) + A SC (Z SC – avg Z SC ) + A Er (Z Er – avg Z Er ) ) / n Er USI(4) = ( (RV Er – avg RV Er ) + A ON (Z ON – avg Z ON ) ) / n ON DSI1(1) = ( A MH (Z MH - avg Z MH ) ) / nd MH DSI1(2) = ( A SC (Z SC – avg Z SC ) + A Er (Z Er – avg Z Er ) ) / nd Er DSI1(3) = ( A ON (Z ON – avg Z ON ) ) / nd ON DSI1(4) = (Z Jetty1 – avg Z Jetty1 ) / nd Jetty1 DSI2(1) = ( A SC (Z SC – avg Z SC ) + A Er (Z Er – avg Z Er ) ) /nd MH DSI2(2) = ( (A ON (Z ON – avg Z On ) ) /nd Er DSI2(3) = ( Z Jetty1 – avg Z Jetty1 ) /nd ON USI( i ) 1 Component 2 1 ExcessShortage s5s5 s6s6 Downstream Storage Indicator between points i and i +1 DSI1( i ) 1 Component 3 1 ExcessShortage s 7 = p.s 5 s8s8 s7s7 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 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 Single-scenario formulation (k=1) z j = 0 if y j < b j (performance in point j better than baseline) z j = 1 if y j ≥ b j (performance in point j worse than baseline) Risk of Failure at evaluation point j : Risk j = y j /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 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 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 QUEBEC MICHIGAN Iroquois H. W. Saunders H.W. Pointe-Claire Jetty 1 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 avg Z : historical average monthly levels RV : release volume planned for the current regulation period avg RV : 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 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. The estimated cost o 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 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). Driest Wettest Single-scenario Optimization Results Superior Weir (Existing Structure) Moses Saunders Dam (Existing Structure) Hypothetical Structures (St. Clair and Niagara Rivers) Driest Wettest