台灣帆船活動日漸發達，對於活動場址之風況掌握的需求更顯得急迫。風速和風向這兩個氣象因子不只是帆船活動的關鍵因素，對於成功的帆船賽事管理更是具有同等重要性，因此有必要對這兩個氣象特性有清楚的認識。澎湖自1999年開始有帆船競賽的發展，而且其規模逐步由國內層級擴展為國際層級。本研究發展了一個最小橢圓計算法，並以2011年澎湖海氣象浮標於澎湖海面觀測的逐時風力與風向為例，將每日24小時的逐時風力與風向資料摘要成為一個僅剩5個參數的最小橢圓。最小橢圓法的應用價值可由本文的三個分析案例來說明，分別是：(1)檢視颱風期間的風況隨颱風軌跡之變化、(2)提供一個篩選海陸風盛行日的簡單方法、及(3)針對帆船賽事規劃所做的全年風況分布圖。
透過最小橢圓的計算結果，我們可以進一步計算全年日風況的相似性矩陣，接著採用本研究引入的「幾何資料雲」群集分析法的計算，可將全年的逐日風況分類組織成一個階層式群集。幾何資料雲群集分析法提供多尺度的群集分析，比標準的階層式群集分析有更佳的量化表現，本研究透過實際資料所進行的全年風況群集分析再次驗證了幾何資料雲的優異特性。資料機制是本研究引入的另一個重要方法，其目的是將日風況的群集架構延伸至資料浮標所觀測的其他海氣象共變量資料。藉由資料機制的連結，我們得以計算內含風況架構的共變量距離矩陣，進而獲得共變量間的幾何資料雲群集。利用此資料雲群集，我們得以再次利用資料機制來計算含有風況資訊的逐日海氣象共變量之距離矩陣，並依此計算逐日共變量之幾何資料雲群集，該群集在未提供日期資訊的情況下，其群集架構仍能精確捕捉海氣象的季節性變化特質。
本研究的最後工作是將海氣象共變量群集架構與風況群集架構耦合，以檢視其相關性，透過heatmap檢視其耦合的色塊非常明顯，這代表風況與其它氣象因子明顯相關。若以風況為應變數，其它氣象因子為因變數，進行近來頗為盛行的決策樹分析，將決策樹之結果與風況群集偶合，可同樣透過heatmap檢視其關連性。我們發現以幾何資料雲所建立的耦合結構與決策樹有同等的預測效力，但其整體架構比決策樹更具一致性，且避免了決策樹經常為人詬病的過度配適問題。

As interest in sailing has increased in Taiwan, it has become essential to understand wind patterns in order to better organize sailing events. Penghu began to organize sail regatta in 1999 and extended the scale of their regatta from the national level to the international level. Knowledge of both wind speed and wind direction is equally critical to successful regatta management. In this dissertation, wind speed and wind direction observed in 2011 from the Penghu data buoy are used as an example. A simple computational method was developed to summarize 24 hours of observation into a minimum ellipse with only five parameters. This summarized daily ellipse reduces the dimensions of the problem efficiently but still retains hourly information. We demonstrate herein that this minimum ellipse computational method can be applied in at least three ways: (1) tracking the wind pattern trajectory of a typhoon, (2) providing a simple method to distinguish land-and-sea breeze days, and (3) visually exhibiting the global wind pattern for the planning of sailing events.
Based on the results of the minimum ellipse, daily wind patterns can be summarized, and cluster analysis on a daily basis can be performed. An important clustering technique, called a data cloud geometry-tree (DCG-tree) is introduced in this dissertation. The DCG-tree clustering method provides better quantification of the multi-scale geometric structures of the data under consideration than the standard Hierarchical Clustering method. This property was verified from real data by clustering daily wind patterns in Penghu.
The data mechanics method is another important concept which provides a tree structure-embedded linkage between the daily wind clusters and other meteorological covariates which were also observed from the data buoy in Penghu. The DCG-tree was used again to build the hierarchical structure of the relationships within the covariates which retain the information from daily wind pattern clusters. With the tree structure of these covariates, data mechanics was used to define the pairwise daily similarity from the point of view of the covariates. We then coupled the daily wind cluster with the daily covariate clusters. The coupling results indicated significant associations between these two types of meteorological characteristics. Taking into consideration predictions from the covariates to the wind patterns, the relationship built by the DCG-tree and data mechanics exhibited the same performance as that of the recently popular decision tree method. However, it provided more insight into the system dynamics and avoided the usual overfitting criticism lodged toward decision trees.

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