應用圓柱座標MANDOP分析法反演颱風風場

劉浙仁(Che-Jen Liu)

指導教授 ： 李天浩

國立臺灣大學/工學院/土木工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00565

摘要

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。

關鍵字

反演颱風風場 ； 圓柱座標

並列摘要

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.

並列關鍵字

MANDOP

參考文獻

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