中文賽題：大湖水問題

背景

美國和加拿大的五大湖是世界上最大的淡水湖群。這些湖泊及其連接的水道構成了一個(ge) 龐大的排水盆地，包含了這兩(liang) 個(ge) 國家許多大型城市區域，氣候多樣，局部天氣條件各異。

湖水被用於(yu) 許多目的（漁業(ye) 、娛樂(le) 、發電、飲用水、航運、動植物棲息地、建築、灌溉等）。因此，眾(zhong) 多利益相關(guan) 者對流入和流出湖泊的水的管理抱有極大的興(xing) 趣。特別是，如果從(cong) 湖泊排放或蒸發的水太少，則可能發生洪水，沿岸的家庭和企業(ye) 會(hui) 受到影響；如果排放的水太多，則大型船隻無法通過水道運送物資，支持當地經濟。主要問題是調節水位，使所有利益相關(guan) 者都能受益。

每個(ge) 湖泊的水位由流入和流出湖泊的水量決(jue) 定。這些水位是溫度、風、潮汐、降水、蒸發、湖底地形（湖底的形狀）、河流流量和徑流、水庫政策、季節循環和長期氣候變化之間複雜相互作用的結果。在大湖水係統的水流中，有兩(liang) 個(ge) 主要的控製機製 - 蘇錫聖瑪麗(li) 的補償(chang) 工程（三座水電站、五個(ge) 航道閘和一個(ge) 大壩位於(yu) 急流的源頭）和康沃爾的摩西-桑德斯大壩，如附錄中所示。

雖然兩(liang) 座控製大壩、許多渠道和運河以及排水盆地水庫可能由人類控製，但降雨、蒸發、侵蝕、冰堵和其他水流現象的速率超出了人類的操縱能力。地方管轄區的政策可能會(hui) 產(chan) 生與(yu) 預期不同的效果，季節性和環境變化在水盆地中的變化也是如此。這些變化反過來影響該地區的生態係統，這對湖泊周圍發現的動植物的健康以及生活在水盆地中的居民產(chan) 生影響。盡管五大湖似乎有規律的年度模式，但水位正常變化兩(liang) 到三英尺可以顯著影響某些利益相關(guan) 者。

這個(ge) 動態網絡流問題是“棘手的” - 由於(yu) 相互依賴性、複雜的需求和固有的不確定性，這個(ge) 問題極其難以解決(jue) 。對於(yu) 湖泊的問題，我們(men) 有不斷變化的動態和利益相關(guan) 者的衝(chong) 突利益。

有關(guan) 更多信息，請查看問題D附錄。

要求

國際聯合委員會(hui) （IJC）請求貴公司，國際網絡控製模型師 - ICM，協助管理和模型控製機製（兩(liang) 座大壩 - 補償(chang) 工程和摩西-桑德斯大壩，如附錄中所示），這些機製直接影響大湖流域水位。你的ICM主管已經讓你的團隊負責開發模型和實施模型的管理計劃。你的主管指出有幾個(ge) 考慮因素可能有助於(yu) 實現這一目標，從(cong) 建立大湖和連接河流從(cong) 蘇必利爾湖到大西洋的網絡模型開始。你的主管提到的一些其他可選考慮因素或問題包括：

• 確定五大湖在一年中任何時間的最佳水位，考慮到各個(ge) 利益相關(guan) 者的願望（每個(ge) 利益相關(guan) 者的成本和收益可能不同）。

• 建立算法，根據湖泊的流入和流出數據維持五大湖的最佳水位。

• 了解你的控製算法對兩(liang) 座控製大壩的流出量的敏感性。給定2017年的數據，你的新控製是否會(hui) 導致對各個(ge) 利益相關(guan) 者來說滿意或比實際記錄的水位更好的結果？

• 你的算法對環境條件變化（例如，降水、冬季雪蓋、冰堵）的敏感性如何？

• 將你的廣泛分析僅(jin) 聚焦於(yu) 安大略湖的利益相關(guan) 者和影響因素，因為(wei) 最近對這個(ge) 湖的水位管理更為(wei) 關(guan) 注。

IJC還對你使用的曆史數據以及你建立參數的方法感興(xing) 趣，他們(men) 好奇你的管理和控製策略與(yu) 以往模型的比較結果。提供一份給IJC領導的一頁備忘錄，溝通你模型的關(guan) 鍵特點，以說服他們(men) 選擇你的模型。

你的PDF解決(jue) 方案不得超過總共25頁，應包括：

• 一份一頁的摘要，清楚描述你解決問題的方法和從你的分析中得出的最重要結論。目錄。
• 你的完整解決方案。
• 一頁備忘錄。
• 參考文獻列表。
• AI使用報告（如果使用）

注意：對於(yu) 完整的MCM提交沒有具體(ti) 要求的最小頁數。你可以使用最多25頁來展示你的解決(jue) 方案工作和任何你想包含的額外信息（例如：繪圖、圖表、計算、表格）。接受部分解決(jue) 方案。我們(men) 允許謹慎使用AI，如ChatGPT，盡管不必須通過AI創建解決(jue) 方案。如果你選擇使用生成式AI，你必須遵循COMAP的AI使用政策。這將導致你必須在PDF解決(jue) 方案文件的末尾添加一個(ge) 額外的AI使用報告，且不計入你的解決(jue) 方案的總頁數25頁限製內(nei) 。

提供的文件：

• Problem D Addendum - 額外的背景信息。

• Data Examples - 這些可能是數據來源。其中一些用於(yu) 填充Problem_D_Great_Lakes.xlsx 數據集。這些示例可以在問題D附錄的第4頁找到。注意：這些示例不是成功製定解決(jue) 方案所必需的。

• Problem_D_Great_Lakes.xlsx - 湖泊的流入、流出和水位數據。

參考資料（除了包括的背景數據文件）：

[1] Explanation of the IJC’s Efforts to Manage the Great Lakes Basin: National Research Council; The Royal Society of Canada. (2006). Review of Lake Ontario-St. Lawrence River Studies. Washington D.C.: National Research Council of the National Academies. Retrieved from https://nap.nationalacademies.org/catalog/11481/review-of-the-lake-ontario-st-lawrence-river-studies

[2] Description of the Great Lakes Navigation Systems: Great Lakes Seaway Navigation System. (2023). Retrieved from American Great Lakes Ports Association: https://www.greatlakesports.org/industry-overview/the-great-lakes-seaway-navigation-system/#:%7E:text=Lake%20Erie%20drains%20into%20Lake,in%20elevation%20approximately%20600%20feet

Problem D: Great Lakes Water Problem

Background

The Great Lakes of the United States and Canada are the largest group of freshwater lakes in the world. The five lakes and connecting waterways constitute a massive drainage basin that contains many large urban areas in these two countries, with varied climate and localized weather conditions.

The lakes’ water is used for many purposes (fishing, recreation, power generation, drinking, shipping, animal and fish habitat, construction, irrigation, etc.). Consequently, a vast variety of stakeholders have an interest in the management of the water that flows into and out of the lakes. In particular, if too little water is drained or evaporates from the lakes, then flooding may occur and homes and businesses along the shore suffer; if too much water is drained, then large ships cannot travel through the waterways to bring supplies and support the local economy. The main problem is regulating the water levels such that all stakeholders can benefit.

The water level in each lake is determined by how much water enters and leaves the lake. These levels are the result of complex interactions among temperature, wind, tides, precipitation, evaporation, bathymetry (the shape of the lake bottom), river flows and runoff, reservoir policies, seasonal cycles, and long-term climate changes. There are two primary control mechanisms within the flow of water in the Great Lakes system – Compensating Works of the Soo Locks at Sault Ste. Marie (three hydropower plants, five navigation locks, and a gated dam at the head of the rapids) and the Moses-Saunders Dam at Cornwall as indicated in the Addendum.

While the two control dams, many channels and canals, and the drainage basin reservoirs may be controlled by humans, the rates of rain, evaporation, erosion, ice jams, and other water-flow phenomena are beyond human manipulation. The policies of local jurisdictions may have different effects than expected, as can seasonal and environmental changes in the water basin. These changes in turn affect the ecosystem of the area, which impacts the health of the flora and fauna found in and around the lakes and the residents that live in the water basin. Even though the Great Lakes seem to have a regular annual pattern, a variance from normal of two to three feet of water level can dramatically affect some of the stakeholders.

This dynamic network flow problem is “wicked” – exceptionally challenging to solve because of interdependencies, complicated requirements, and inherent uncertainties. For the lake’s problems, we have ever-changing dynamics and the conflicting interests of stakeholders.

See Problem D Addendum for Additional Information.

Requirement

The International Joint Commission (IJC) requests support from your company, International network Control Modelers – ICM, to assist with management and models for the control mechanisms (the two dams – Compensating Works and Moses-Saunders Dam as indicated in the Addendum) that directly influence water levels in the Great Lakes flow network. Your ICM supervisor has given your team the lead in developing the model and a management plan to implement the model. Your supervisor indicates there are several considerations that may help to achieve this goal starting with the building of a network model for the Great Lakes and connecting river flows from Lake Superior to the Atlantic Ocean. Some other optional considerations or issues your supervisor mentioned were:

• Determination of the optimal water levels of the five Great Lakes at any time of the year, taking into account the various stakeholders’ desires (the costs and benefits could be different for each stakeholder).

• Establishment of algorithms to maintain optimal water levels in the five lakes from inflow and outflow data for the lakes.

• Understanding of the sensitivity of your control algorithms for the outflow of the two control dams. Given the data for 2017, would your new controls result in satisfactory or better than the actual recorded water levels for the various stakeholders for that year?

• How sensitive is your algorithm to changes in environmental conditions (e.g., precipitation, winter snowpack, ice jams)?

• Focus your extensive analysis of ONLY the stakeholders and factors influencing Lake Ontario as there is more recent concern for the management of the water level for this lake.

The IJC is also interested in what historical data you use to inform your models and establish parameters, as they are curious to compare how your management and control strategies compare to previous models. Provide a one-page memo to IJC leadership communicating the key features of your model to convince them to select your model.

Your PDF solution of no more than 25 total pages should include:

• One-page summary sheet that clearly describes your approach to the problem and your most important conclusions from your analysis in the context of the problem.
• Table of Contents.
• Your complete solution.
• One-page memo.
• References list.
• AI Use Report (if used)

Note: There is no specific required minimum page length for a complete MCM submission. You may use up to 25 total pages for all your solution work and any additional information you want to include (for example: drawings, diagrams, calculations, tables). Partial solutions are accepted. We permit the careful use of AI such as ChatGPT, although it is not necessary to create a solution to this problem. If you choose to utilize a generative AI, you must follow the COMAP AI use policy. This will result in an additional AI use report that you must add to the end of your PDF solution file and does not count toward the 25 total page limit for your solution.

Files provided:

• Problem D Addendum – Additional background information.

• Data Examples – These are possible sources for data. Some of which were used to populate the Problem_D_Great_Lakes.xlsx data set. These examples can be found on page 4 of the Problem D Addendum. Note: These examples are not required to successfully formulate a solution.

• Problem_D_Great_Lakes.xlsx – Data for the inflows, outflows, and water levels for the lakes.

References (in addition to the included background data file):

[1] Explanation of the IJC’s Efforts to Manage the Great Lakes Basin: National Research Council; The Royal Society of Canada. (2006). Review of Lake Ontario-St. Lawrence River Studies. Washington D.C.: National Research Council of the National Academies. Retrieved from https://nap.nationalacademies.org/catalog/11481/review-of-the-lake-ontario-st-lawrence-river-studies

[2] Description of the Great Lakes Navigation Systems: Great Lakes Seaway Navigation System. (2023). Retrieved from American Great Lakes Ports Association: https://www.greatlakesports.org/industry-overview/the-great-lakes-seaway-navigation-system/#:%7E:text=Lake%20Erie%20drains%20into%20Lake,in%20elevation%20approximately%20600%20feet