Masoud Asadzadeh 1, Masoud Asadzadeh 1, Saman Razavi 1, Bryan Tolson 1 David Fay 2, William Werick 3, Yin Fan 2 2- Great Lakes - St. Lawrence Regulation Office, Meteorologial Service of Canada, Environment Canada 1- Department of Civil and Environmental Engineering, University of Waterloo 3- Werick Creative Solutions

Outline Introduction Methodology  Rule Curve Form  System Simulation/Evaluation  Optimization Algorithm Results and Discussions Conclusions 2

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4 Objectives Develop a rule curve for Lake Superior Outflow  Preforms better than the current plan (Plan 1977A)  Respect the structural outflow constraints  Consider the storage conditions upstream and downstream  Parameterize the Lake Superior outflow Optimize the system performance by automatically calibrating the rule curve parameters  Utilize the most accurate simulation of the system  Consider multiple future climate conditions in the form of NBS

5 Beginning of Period Lake Superior Surface Elevation (m) a 1 b d c ef ExcessShortage a ≥ b d ≥ c 1 1 g h Beginning of Period Level MH Surface Elevation (m) Excess Shortage 22 2 (seasons) x 11 (a, b, …, j, Baseline Flow) = i j Beginning of Period Level ER Surface Elevation (m) Excess Shortage

6 System Simulation/Evaluation CGLRRM, Co-ordinated Great Lakes Regulation and Routing Model (Fortran executable) SP, Shoreline Protection (Microsoft Excel) SVM, Shared Vision Model (Microsoft Excel)  Commercial Navigation, Hydropower Generation, and Shoreline Protection benefits/costs relative to Plan 1977A  Criteria satisfaction/violations checks

7 Criteria (IUGLS) Lake Superior Levels  Highest level: m  Lowest level: m Lake Michigan-Huron Levels  Highest level: 77A  Lowest level: 77A  Average 2% high levels: 77A  Average 2% low levels: 77A

8 Selected NBS Scenarios (from stochastic NBS) The 109-year period Stationary HI Historical From Historical recorded NBS, adjusted to current demands and diversions. This sequence has as many as 7 consecutive years above, and 7 consecutive years below average NBS. Uncertain Change HM highest Michigan-Huron levels Based on current climate, but highest Michigan-Huron levels, with a great range between wettest and driest years. LM lowest Michigan-Huron levels Based on current climate, but creates the lowest Michigan-Huron levels while still producing a maximum level greater than historical. Includes 14 consecutive years of below average NBS. Change to Drier Period LS lowest Lake Superior level Based on current climate, but produces the lowest Lake Superior level in entire stochastic simulation. Change to Wetter Period HS highest Lake Superior level Current climate, average NBS close to historical NBS, but with the highest Lake Superior level. Its wettest portion comes early in the simulation, as would be expected if recent dry NBS forecast a reversal to wet conditions.

9 Modified Criteria Lake Superior Levels  Highest level: max( m, 77A)  Lowest level: min( m, 77A) Lake Michigan-Huron Levels  Highest level: 77A  Lowest level: 77A  Average 2% high levels: 77A  Average 2% low levels: 77A

10 Problem Formulation Optimize Criteria-Based Objective

11 Problem Formulation Optimize Benefit-Based Objective  Navigation, Hydropower, Shoreline Protection Sectors

Expected Solution F G 12 F F: Being Maximized Positive value: Benefits for Commercial Navigation, Hydropower Generation and Shoreline Protection across all 5 NBS scenarios G G: Being Maximized Positive value: No criteria Violation in any of the 6 criteria across all 5 NBS scenarios

Optimization Algorithm: PA-DDS Perturb current ND solution Update ND solutions Continue? STOP New solution is ND? Pick the New solution Pick a ND solution Initialize starting solutions Y N Create ND-solution set Y N 13

Simulation-Optimization Components 14 MATLAB: Solution Generation, preliminary Lake Superior Outflow Simulation Runtime < 1 sec/solution CGLRRM: Upper Great Lake Simulation by MATLAB results Runtime ~= 10 sec/solution MS Excel: Shared Vision Model Runtime ~= 20 sec/solution MS Excel: Shoreline Protection Runtime > 200 sec/solution 64-bit Intel ® Core i7™ 2.80 GHz with 12 GB of Ram

Model Pre-emption 15 F G 0 Scenario1 simulation Scenario2 simulation Scenario3 simulation Scenario4 simulation Scenario5 simulation Objective Function Calculation

Pareto Approximate Front Pareto Approximate Front (20,000 solutions eval.) 16 Benefit Selected Solution for further evaluations Raw sum of benefits and costs

Selected Solution Selected Solution (Validation) 17 Uncertain ChangeStationary Change to Drier Period WS AT LRDSAVT1T2TR Max SUP 77A UW Min SUP 77A < UW Max MH 77A UW Min MH 77A UW Avg 2% High MH 77A UW Avg 2% Low MH 77A UW

Selected Solution Selected Solution (Benefits in detail) 18 Annual Average ($M)CNHPSPTotal HI HS LS HM LM WS DS LR AT AV T T Average

19 A single solution (rule curve) cannot satisfy all the criteria across all future climate scenarios In comparison with Plan 1977A, the selected rule curve:  has a mixture of advantages and disadvantages in managing the water level at SUP and MH depending on the future climate scenario.  can handle extremely dry future scenarios better  is economically more beneficial almost regardless of the future climate scenario Model pre-emption saved almost 80% of the computational budget More explicit definition of good/bad solutions is required to formulate more reasonable objectives/criteria for possible future optimization based Great Lakes regulation studies

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Selection Metrics HyperVolume Contribution (HVC), HyperVolume Contribution (HVC), Knowles et al. (2003) 21 F G

Selected Solution Selected Solution (criteria in detail) 22 5 Scenarios (in the optimization) HIHSLSHMLM Max SUP 77A UW Min SUP 77A UW Max MH 77A UW Min MH 77A UW Avg 2% High MH 77A UW Avg 2% Low MH 77A UW

23 Selected Solution Compared to nat64S in New SVM

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