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研究生:劉浙仁
研究生(外文):Che-Jen Liu
論文名稱:應用圓柱座標MANDOP分析法反演颱風風場
指導教授:李天浩李天浩引用關係
指導教授(外文):Tim-Hau Lee
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:114
中文關鍵詞:反演颱風風場圓柱座標
外文關鍵詞:MANDOP
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在多雷達觀測區域中進行風場反演,可以獲得多個都卜勒風限制式,但無法取得所有點的三維正交風速分量觀測值。為了彌補觀測資訊的不足,可以使用連續方程式或其他限制條件結合多個都卜勒風限制式一起聯立求解;或是假設風場具有某種特性下,採用回歸方程式表現風的三維分量,以減少未知數的數量。Scialom 和 Lemaitre(1990)提出三維解析風場的概念,將其代入泛函求極小值的問題中,使原本的變分問題轉換為待定係數問題,利用最小誤差平方和法即可求解風場(MANDOP 分析),本研究將其延伸應用到求解颱風風場,希望藉由依環流特性所選擇的圓柱座標系統來提升風場反演的準確度。
選擇颱風風場函數時,採用以颱風中心為中心軸的圓柱座標系統,並假設風場解析函數為三個多項式函數的乘積,在徑向方向使用冪次(Power)多項式展開,切向方向使用傅利業(Fourier)多項式展開,而垂向方向則使用勒尖德(Lengendre)多項式展開。在限制條件方面,除了使用都卜勒風限制式與連續方程式限制條件外,還包括近地面、近對流層頂和颱風中心等三處垂直風為零的邊界條件。
在模擬實際應用時,除了使用均勻流與渦旋流進行測試外,並採用洪景山博士以MM5模式模擬賀伯颱風的三維風場輸出資料,作為真實颱風的風場。在探討風場反演的效果時,假設有二到三個雷達,分別設在不同位置,模擬各雷達的都卜勒風速觀測資料,接著利用研擬的方法反演風場,比較反演風場與真實風場在不同條件下,評估風場反演的效果與權重因子的影響。
Many Doppler wind constrains can be obtained in multiple radars observation area, but the three orthogonal wind components can not be acquired in full domain. In order to compensate the lost information of observation, continuity equation or other constrains combined with many Doppler wind constrains are used. Besides, under the assumption of certain characters of the wind field, regression equations can be applied for representing the wind components to reduce the unknown numbers. Scialom and Lemaitre (1990) addressed the concept of a three dimensional analytical wind field and brought it into the cost function, and thus converted the variational problem into the regression problem which can be solved by the least square error method. The present research is devoted to the application of MANDOP analysis in retrieving the typhoon wind field and introducing the cylinder coordinates to improve the accuracy of the result.
The present paper adopts the cylinder coordinates in which the center axis is typhoon center and assumes that the analytical wind components, with respect to each coordinate, may be written as a product of three functions of each coordinate. The base functions are power series in radial, Fourier series in tangential and Lengendre series in vertical direction. In the respect of constrains, except for using Doppler wind and continuity constrains, the boundary condition at ground, top of troposphere and typhoon center are included.
Besides using uniform flow and vortex for testing, the simulated typhoon Herb data, produced from MM5 model, are used as the real typhoon wind field. Doppler wind observations are simulated from two to three radars which are at different places. The wind retrieval method above is used to evaluate the results and the affects by comparing the retrieval wind with the true wind under different conditions.
誌謝 一
摘要 二
Abstract 三
目錄 四
圖目錄 七
表目錄 一三
第 1 章 緒  論 1
1.1 研究背景 1
1.2 研究目的 2
1.3 文獻回顧 2
1.4 研究方法與內容簡述 4
第 2 章 圓柱座標MANDOP分析 5
2.1 圓柱座標系統 5
2.2 座標系統轉換與空間尺度轉換 6
2.3 都卜勒風限制條件 7
2.4 連續方程式限制條件 11
2.5 邊界限制條件 17
2.6 限制條件範圍 20
2.7 最佳化分析 22
第 3 章 均勻流和渦旋流測試 27
3.1 均勻流與渦旋流風場 27
3.2 誤差評估統計量 31
3.3 權重之影響 33
3.3.1 均勻流 34
3.3.2 渦旋流 39
3.4 展開項數之影響 43
3.4.1 均勻流 43
3.4.2 渦旋流 44
3.5 應用於均勻流的問題 49
3.6 渦旋流中心定位誤差之影響 66
第 4 章 應用於模式颱風風場 73
4.1 模式風場 73
4.2 展開項數之影響 81
4.3 反演模式颱風風場實例 88
4.4 雷達位置之影響 91
第 5 章 結論與建議 95
5.1 結論 95
5.2 建議事項 97
參考資料 99
附錄A 各項展開函數 101
附錄B 連續方程限制式之各項積分 103
附錄C 各維風分量之空間分佈 109
1.Caillault, K., Lemaitre, Y. 1999: Retrieval of Three-Dimensional Wind Fields Corrected for the Time-Induced Advection Problem. Journal of Atmospheric and Oceanic Technology: Vol. 16, No. 6, pp. 708–722.
2.Dinku, Tufa, Anagnostou, Emmanouil N., Borga, Marco. 2002: Improving Radar-Based Estimation of Rainfall over Complex Terrain. Journal of Applied Meteorology: Vol. 41, No. 12, pp. 1163–1178.
3.Gal-Chen, Tzvi. 1982: Errors in Fixed and Moving Frame of References: Applications for Conventional and Doppler Radar Analysis. Journal of the Atmospheric Sciences: Vol. 39, No. 10, pp. 2279–2300.
4.Lee, Wen-Chau, Marks, Frank D. 2000: Tropical Cyclone Kinematic Structure Retrieved from Single-Doppler Radar Observations. Part II: The GBVTD-Simplex Center Finding Algorithm. Monthly Weather Review: Vol. 128, No. 6, pp. 1925–1936.
5.Liou, Yu-Chieng. 1999: Single Radar Recovery of Cross-Beam Wind Components Using a Modified Moving Frame of Reference Technique. Journal of Atmospheric and Oceanic Technology: Vol. 16, No. 8, pp. 1003–1016.
6.M. Ishihara, Z. Yanagisawa, H. Sakakibara, K. Matsuura and J. Aoyagi: Structure of Typhoon Rainband Observed by Two Doppler Radar. Journal of the Meteorological Society of Japan: Vol. 64, No. 6, pp. 923–938.
7.Montmerle, Thibaut, Lemaître, Yvon. 1998: Three-Dimensional Variational Data Analysis to Retrieve Thermodynamical and Dynamical Fields from Various Nested Wind Measurements. Journal of Atmospheric and Oceanic Technology: Vol. 15, No. 2, pp. 360–379.
8.Scialom, G., and Y. Lemaître, 1990: A new analysis for the retrieval of three-dimensional mesoscale wind fields from multiple Doppler radar. J. Atmos. Oceanic Technol., 7, 640–665.
9.Tabary, Pierre, Scialom, Georges. 2001: MANDOP Analysis over Complex Orography in the Context of the MAP Experiment. Journal of Atmospheric and Oceanic Technology: Vol. 18, No. 8, pp. 1293–1314.
10.Zhang, Jian, Gal-Chen, Tzvi. 1996: Single-Doppler Wind Retrieval in the Moving Frame of Reference. Journal of the Atmospheric Sciences: Vol. 53, No. 18, pp. 2609–2623.
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