臺灣博碩士論文加值系統

本研究使用最大協變異數分析法(Maximum Covariance Analysis, MCA)探討1987年至2004年之侵台颱風個案，分析颱風侵台時期的測站風場和降雨觀測對應特徵。採用17個測站的小時風場觀測和21個測站的時雨量觀測紀錄資料，其中，增加選用4個位於雪山山脈山區的雨量測站，藉由測站數量的配置方式，突顯此區域降雨變異量的比重，使得風雨MCA的分析結果可反映北部山區降雨特徵。最大協變異數分析得到的前三個主要MCA風雨分量，共可解釋98.2%的風雨分量的交叉協變異數平方(squared cross-covariance)，分別為70%、20.6% 和7.6%，且風雨分量相關係數分別為0.59、0.48和0.49。其餘的MCA 風雨分量僅有1.8%的交叉協變異平方解釋能力，且相關性較低。
第一主要分量是反映雪山山脈降雨的整體變化型態；風向為垂直於山脈走向之西北風，降雨型態則以北部山區、雪山山脈區域及阿里山站的降雨為主。第二分量之風向為西南風，所對應之強降雨區域則是以阿里山站為中心，並且往北延伸至雪山山脈南端，主要是颱風中心位於台灣北部/西北部時，因為颱風環流逆旋或引進西南氣流所引起。第三分量主要在台灣東北部/東部有正對地形的東風，因此降雨發生地點是以東部/東北部為主。以上主要風雨型態特徵，皆呈現風向與山脈方向近似垂直，且降雨以山脈長軸為界線的相反相位型態；代表強降雨的正相位與迎風面區域吻合、雨量小的負相位則出現在背風面。
藉由MCA的風場特徵向量，以及群集分析法(Cluster Analysis)的邏輯，計算測站小時風場觀測與MCA風場奇異向量的距離相似性，並分析距離門檻值對於風雨分量相關性的影響，決定適當的風場群落分類的距離門檻值，將歷史颱風個案依照風場型態分類。其中，群落分類的距離門檻值越小，表示選取的風場資料群組，與MCA風場奇異向量的型態越相似，故風雨分量相關性將會隨著分類距離門檻值的縮小而遞增。
由風場群集分類的結果顯示，前三種主要風場型態分別由25%、9%和19%的颱風案例小時數所組成，且風雨分量相關性分別由原本的0.59、0.48、0.49，提升為0.69、0.66和0.58。不屬於以上三種類型的個案則歸類為第四型，約佔47%的個案小時數。第一型颱風個案多位於台灣東方/東北方，平均中心位置約位於(124.3E, 24.5N)；第二型個案多位於台灣西北方，平均中心位置約位於(120.5E, 25.1N)；第三型個案多位於北緯24度以南的區域，平均中心位置約位於(121.3E, 21.5N)。然而，由分類結果可知，颱風中心類似之颱風個案，風場型態並不一定會相同，中心位置類似的區域可能會有多種類型的風場型態，因此僅藉由颱風中心所在位置並不易準確判別台灣的風場型態。此外，第一、三和四型的颱風個案都是在9月份的發生次數為最多；第二型則是多發生於7、8月， 9月份發生台灣西部為西南風的第二型風場型態的機會則大幅減小。
透過前三個主要風場型態所對應的測站氣溫、相對溼度和氣壓觀測的差異分析，顯示迎風面有相對溼度增高、氣壓增強和氣溫降低的情形；背風面則由於過山下沉氣流的因素，導致氣溫升高、氣壓和相對溼度降低。其中，由於中央山脈之長軸主要為南北向，且長短軸比例差異大，因此地形對於第二型西南風的阻擋效應並不如第一型和第三型顯著，故氣溫、相對溼度、氣壓的差異稍小。
以第一型個案為例，討論「非阻擋流型」和「阻擋流型」的颱風個案差異。分析結果顯示，若位於背風面的成功、台東和大武站其中任一站發生焚風，西部迎風面山區的降雨將會更加顯著。此外，相較於背風面測站沒有發生焚風的「阻擋流型」個案，屬於「非阻擋流型」的颱風個案由於氣流過山，使得背風面測站的平均風速較強。而不容易產生強降雨的「沿山流型」，其風向平行於地形走勢，發生於第一~三型的局部區域:(1) 第一型:台灣西南部地區；(2)第二型: 台灣東部和西北部地區；(3)第三型: 台灣西北部和東南部地區。此外，因為第四型的颱風個案已經沒有包含第一~三型等三種較容易產生強降雨的主要風雨型態，故平均降雨量較小，且風場平均方向和主要變異方向皆屬於「沿山流型」，顯示第四型個案的風場主要型態，多為沿山方向的風速大小變化。
本研究提出的颱風風雨對應關係的分析和分類過程，可有效的從大量歷史資料抽離出主要的颱風風雨對應特徵，對於颱風侵台時期的地面測站風雨聯性，提供了詳細的定量分析結果，且特徵場皆為空間資訊，不僅是單一測站的單點資訊，研究人員可藉此進行較為全面性的物理機制解釋與探討。
本研究求得之風雨對應特徵，是經過增加雪山山脈降雨測站數量，表現雪山山脈地形雨所得到的結果。若要將本研究方法推展至全台，方法論可使用本文所提出的分析方法，再配合地面觀測資料分析風雨的對應關係；唯需增加能表現其他地區地形降雨的降雨強度觀測資料，分析結果才會較具有代表性。

The multivariate relationships between hourly surface wind and rainfall observations during typhoons affecting Taiwan are investigated by Maximum Covariance Analysis (MCA). Historical surface observations from 1987-2004 are used when typhoon centers were located inside the domain of 117-127E, 19-28N. In this study, 17 surface weather stations with hourly rainfall, wind speed, wind direction, air temperature, relative humidity records, and 4 automatic rainfall stations over the Snow Mountain Range (SMR) with hourly precipitation records were chosen. The three leading modes explain 70%, 20.6% and 7.6% of the Squared Covariance Fraction (SCF), and the correlation coefficients are 0.59, 0.48 and 0.49 respectively. Wind directions of the three leading modes are: (1) north-westerly and perpendicular to the SMR; (2) south-westerly with flow convergent at Alishan as well as at the junction of Central Mountain Range (CMR) and the southern SMR; (3) easterly toward the northeastern SMR and the northern CMR. The rainfall patterns of the three principal modes are all bipolar, with the positives (or negatives) occuring on the windward sides and the negatives (or positives) on the leeward sides of the mountain ranges.
Based on the MCA singular vectors and cluster analysis, historical typhoon surface wind patterns are classified into major types. The results show that the three major wind types consist of 53% of the data, which are 25%, 9%, and 19% respectively. The cases of Type 1 are generally located around northeast of Taiwan with the centroid coordinate of (124.3E, 24.5N). Type 2 cases are on the northwest, and the centroid coordinate is (120.5E, 25.1N). The centroid coordinate of type 3 cases is (121.3E, 21.5N). These cases are generally south of Taiwan. Furthermore, the analysis of corresponding surface air temperature, relative humidity, and air pressure also reveal the contrasting patterns between windward and leeward sides.
Take type 1 cases as examples to analyze the differences between “unblocked flow regime” and the “blocked flow regime.” To analyze the foehn phenomenon, the relative humidity and dew point temperature observations at leeward surface stations are used. It is observed that heavy rainfall appears on the windward side, and wind directions are more perpendicular to the SMR if the foehn can be seen on the leeward side. Furthermore, the analysis of wind speed averages on leeward side show that leeward wind speed is higher when flow is over the mountain (i.e. unblocked flow regime). The flow feature of “parallel flow regime” is parallel to the mountains, and the rainfall is relatively small. For type 1 to 3, the parallel flows can be seen over southwestern, eastern, and northwestern Taiwan respectively. The averages of wind and rainfall patterns for type 4 also show the parallel flow and include light rainfall. The wind pattern variations of type 4 cases are examined further, and the RVPCA (Real-Vector Principal Component Analysis) method is applied. The results again confirm that the parallel flow regime can easily happen when the typhoon enters into the NE, SE, and SW sub-domains. The major portions of the type 4 wind pattern variations inside these sub-domains are mainly along the mountains, thus the rainfall amounts are generally small.
The proposed analysis procedures would be useful for diagnosing the rainfall anomalies caused by wind patterns variations. Lastly, correctly categorizing the wind and rainfall data can help to clarify the interaction mechanism among typhoon wind, rainfall and topography. This is an important step to further improve the skill of typhoon rainfall inferences.

ㄧ、前言 1
1.1研究動機 1
1.2研究目標與研究方法 5
1.3論文架構 6
二、研究方法 8
2.1最大協變異數分析法 8
2.2 PCA法、CCA法概述及和MCA法異同 11
三、資料與分析項目 14
3.1地面氣象觀測與颱風路徑資料 14
3.2分析指標 18
3.3分析項目 19
四、颱風風雨MCA分析結果 20
4.1 風場-降雨量MCA主要分量特徵 20
4.2風雨MCA主要分量與颱風中心之對應關係 25
五、颱風風場群落分析 28
5.1 颱風風雨MCA監督式群集分析 28
5.2距離門檻值的選擇 31
5.3 分類結果討論 35
六、謝信良等人(1996)定義之流型的對應與分析 51
6.1颱風氣流流型 51
6.2 氣流流型的對應 53
七、類似中心位置之颱風個案分析 62
7.1東部外海區域(121.5~122.0E、23.5~24.0N) 62
7.2西北方區域(120.5~121.5E、26.0~27.0N) 78
7.3結果討論 82
八、結論與建議 83
8.1 結論 83
8.2 建議 86
參考文獻 87
Appendix A 颱風中心位置和風場型態差異分析 91
Appendix B 水氣含量的影響評估分析 95
Appendix C 雪山山脈區域測站之風雨MCA分析 102
Appendix D 風雨MCA分析—限定颱風個案選取區域 107

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