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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/63418


    Title: 資料時空前置處理對主成份分析法的影響: 一個基於AO和NAO訊號之研究;The influence of different spatial and temporal filters on principal component analysis: A study based on AO and NAO signal
    Authors: 許家華;Hsu,Chia-Hua
    Contributors: 大氣物理研究所
    Keywords: 主成份分析法;北極震盪;北大西洋震盪;型態穩定度分析;Arctic Oscillation;North Atlantic Oscillation;Principal component analysis;Pattern stability analysis
    Date: 2014-02-26
    Issue Date: 2014-04-02 14:50:34 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 主成分分析法(PCA)或稱經驗正交函數(EOF)為近年來被廣泛使用的統計方法。其目的為資料壓縮和尋找具有物理意義之特徵模。前人研究中利用主成份分析法對北半球和大西洋區域海平面氣壓場進行分析,發現北極震盪(Arctic Oscillation,AO)和北大西洋震盪(North Atlantic Oscillation,NAO)為主要之氣候特徵型態。但AO和NAO兩者在空間型態上相當類似,因此引起許多學者探討AO是否真實存在。另一方面,為了不受年週期訊號干擾,大多數研究會選擇在資料前置處理中濾除年週期訊號。但是卻很少研究探討不同資料前置處理對於主成份分析法結果之可能影響。考量目前氣候變遷正在加速的情境,資料的平均狀態 和年週期可能都會隨著時間有所改變,本研究重新思考這種濾除年週期資料前置處理之合理性,探討不同的時間和空間資料前置處理對於主成份分析的可能影響。我們比較三種不同資料前置處理(原始資料、移除算術平均資料,移除年週期資料)對於主成分分析所得的北大西洋震盪和北極震盪訊號是否有所影響。另一方面,為緩和傳統主成份分析法要求的時空同時正交的嚴格限制,本研究也進一步使用旋轉經驗正交函數(R-EOF)來對資料進行分析,並利用型態穩定度分析法來提出適當的旋轉特徵模數量之挑選方法。
    結果發現AO和NAO在三種資料前置處理的EOF分析中皆出現且相似度高。AO訊號受不同資料前置處理影響也較NAO來的小。高度場迴歸分析部分發現兩者最大差異是在極區,AO在極區能完整呈現出極區渦旋訊號,NAO則無法。比較原始資料和移除年週期資料的AO和NAO迴歸結果發現在各變數場上迴歸訊號上有很大差異,代表年週期在AO和NAO訊號中扮演一定角色,但以原始資料之平均緯向風和溫度場迴歸分析結果中較能反映出動力結構。合成分析部份AO和NAO兩者結果類似。正負相位氣象場變化主要出現在大西洋區,正相位時大西洋區域槽線系統較強,噴流強勁,而負相位時大西洋區有阻塞現象產生。
    利用型態穩定度分析發現全月份三種資料NAO都較穩定,而AO則在移除年週期資料中較不穩定。使用冬季資料進行分析發現三種資料之AO和NAO不穩定度增加,也會使得整體特徵模穩定度下降。在AO和NAO空間型態穩定度分析中,AO的空間型態穩定度較NAO來的佳,若要針對小區域進行主成份分析則時空前置處理要配合。
    在R-EOF部分,不同資料型態所反應出之最佳選取數量並不相同。在北半球全月份三種資料由AO模開始進行R-EOF結果中,若使用OEOF和RGEOF資料,則旋轉10個特徵模為較好選擇。在RAEOF部分以選轉4個特徵模較佳。在由AO後一特徵模開始進行R-EOF結果中,使用OEOF和RGEOF資料以旋轉9個特徵模為較好。在RAEOF部分以選轉4個特徵模較佳。在全月份大西洋區域三種資料之R-EOF,其整體穩定度都較北半球資料R-EOF結果來的高。不管是由NAO或由NAO下一特徵模開始進行R-EOF分析,三種資料皆以旋轉4個特徵模較好。在大西洋區域分析方面,選轉過多特徵模反而會使得REOF空間型態變得難以解釋。
    在探討不同資料範圍對特徵模影響部分,發現AO屬於較大尺度的特徵模,而NAO則屬於區域性特徵模,但兩者皆對大西洋子區域主成份分析結果有較高相關性,對太平洋子區域相關性較低。年週期模則為全球性訊號,其和各子區域相關性皆高。
    統合本篇研究內容,結果顯示AO穩定度較NAO高。因此在分析應用上,使用AO會比NAO來好。而在資料前置處理選擇上,使用全月份資料會讓特徵模較穩定。在進行R-EOF時,使用型態穩定度分析能夠提供分析者一適當方式來選擇旋轉特徵模數量。考量資料前置處理議題時,由於資料中有無年週期會影響到AO(NAO)的差異,且原始資料迴歸分析結果較能反映動力結構,本研究建議使用原始資料進行主成份分析,可以得到更多的資訊,並能把年週期模納入考量。; Principal component analysis (PCA) or empirical orthogonal function (EOF) is a very popular statistical method widely used in climate analyses for data reduction and mode extraction purposes. The PCA of northern hemisphere extratropical SLP field reveals that AO (Arctic Oscillation) and NAO (North Atlantic Oscillation) are dominant modes. However, the close resemblance of AO and NAO in Atlantic region leads to debates as whether AO is indeed an independent identity or is a fake signal due to PCA. Previous studies had shown that PCA contain problems such as domain shape dependence, sampling error, and orthogonality constraint. Nevertheless, none had focused on examining how spatial and temporal pre-procesing affect results of the PCA. In this study the influence of three different kinds of temporal data preprocessing (original data, remove grand mean data, remove annual cycle data) on PCA extracted AO and NAO signals are examined. Furthermore, analyses are applied to these resultant EOFs and Rotated EOFs to examine their pattern stability and to provide suggestions on the issue of modes selection in EOF and REOF analyses.
    Results showed that both AO and NAO appear in all temporal preprocessing data and have good similarity among them. However, AO seems to be less sensitive to different temporal preprocessing. Regression maps of various field variables revealed notable differences in polar region between AO and NAO. Furthermore, they suggest that annual cycle signal is an essential ingredient of AO and NAO signals.
    Pattern stability analyses demonstrated that both AO and NAO are very stable to temporal sampling variability. These analyses also showed that EOF modes after AO or NAO modes are vulnerable to temporal sampling variability. Therefore REOF analyses were applied to these less stable EOF modes. Pattern stability analyses of these REOF modes suggested that pattern stability can provide an objective way to select how many EOF modes should be involved in a REOF analysis. Generally speaking, retaining 15 or less EOF modes is adequate to extract most of stable REOF modes in the data. .
    In summary, our analysis indicates that using large domain and original data in PCA is better than small domain and most used remove grand mean or remove annual cycle temporal filter data.
    Appears in Collections:[大氣物理研究所 ] 博碩士論文

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