利用多雷達都卜勒觀測反演颱風風場

Abstract

在許多反演風場的方法中，GBVTD (Ground-Based Velocity Track Display)是單雷達針對颱風最常使用的方法。然而，受限於單一雷達資訊不足，以及颱風中心到雷達的距離影響到反演的範圍，再加上GBVTD本身演算法無法求得方位角(azimuthal)方向的平均風，及環流的徑向風只能求得傅立葉零階係數的問題，要使用GBVTD法將反演出來的風場應用到現今颱風降雨預報模式，仍有一些可改進的空間。而MANDOP (Multiple ANalytical DOPpler)分析法，則能用多雷達資料，再加上物理限制式和邊界條件等回歸出三維風場。此外也有專為颱風環流設計的圓柱座標系統的MANDOP分析法。唯獨MANDOP本身演算法在每次迭代修正都必須重解風場，相當費時，若要用於即時颱風降雨預報模式也需稍做簡化。本研究欲採用GBVTD和MANDOP兩者部分的概念，使用多雷達的都卜勒風觀測盡可能反演出風速的各個分量，以加入颱風降雨預報模式計算。 在表現颱風風場方面，由於欲將多雷達資料整合計算，故統一採用以颱風中心為原點的極座標系統。而各觀測點依照該點到中心的距離，分為不同的環區間做計算，各環的水平風場以颱風中心的切向方向和軸向方向分成兩個正交分量，將一環上的兩分量分別用傅立葉函數來擬合，再利用係數間的關係解出解析風場的各個係數。如此設計可使用較少的待定係數提供較高的反演準確度，且比GBVTD法或傳統雙雷達反演風場更具有自由的反演空間，能將雷達網所提供的資料發揮最大效益。 在模擬實際應用時，用已知的二到三維風場進行觀測系統模擬實驗(Observing System Simulation Experiments, OSSE)，將模擬的颱風渦旋中心設置在雷達網區域內不同的關鍵位置，比較各種不同中心位置得到的有效反演範圍和範圍內各處的結果。

The GBVTD(Ground-Based Velocity Track Display) technique is the most popular algorithm of single-Doppler retrieval in view of the typhoon. However, it is restricted in a certain part of single-Doppler observation area. Moreover, the algorithm cannot obtain the azimuthal mean-flow and some asymmetric structure wind, so that the analytical wind field is simplified. To estimate tropical cyclone rainfall, there are still some problem with the GBVTD technique and can be improved. On the other hand, the MANDOP (Multiple ANalytical DOPpler) analysis uses multi-Doppler radars to retrieve 3-dimensional wind field. Besides, there is a specific MANDOP analysis with cylindrical coordinate, designed for typhoon circulation system, but it takes too long time to calculate the completed analysis. In order to do real-time forecasting, we have to take some simplification to the MANDOP analysis. This research combines the GBVTD and the MANDOP method, and takes some advantages of both to retrieve horizontal wind field, and make the result can be applied to real-time rainfall forecast model. In the performance of typhoon wind field, a common polar coordinated system is used, and multi-Doppler radar data is sorted by the distance to cyclone center and calculating ring by ring. The horizontal wind is divided into two orthogonal components by tangent and radial direction, then expanded by Fourier series. Finally, by solving Fourier coefficient of tangent and radial wind, we can obtain the analytical wind field.