系集卡曼濾波器（EnKF）（Ensemble Kalman Filter）是一種資料同化方法。本研究是利用EnKF技術以及觀測系統模擬實驗（OSSE）（Observation System Simulation Experiments）來測試EnKF同化都卜勒雷達資料的表現。本研究使用的模式為ARPS（Advanced Regional Prediction System），此模式是ㄧ個包含多種微物理參數的非靜力可壓縮模式。模擬個案為1977年5月20日發生在美國中部的Del City Storm。本研究在無地形及有地形情況下，設計多組實驗，如「同化系集數目」、「同化時間間隔」、「同化次數」與「同化區域」等若干實驗，探討其對模式各氣象場預報誤差的影響，並且著重在定量降水預報度的改善。結果顯示，以40個系集樣本，每5分鐘同化一次，可得到足夠準確的結果。配合雷達觀測，盡量多次同化，可有助於誤差的降低，並避免誤差擴大而無法修正回來。在有地形時，只要在過山之前就同化初期暴風發展的資訊，便能快速地掌握住暴風的位置與型態，使後續的預報更加準確。同化一個小時雷達資料以後，此系集模式的降水預報能力約可維持至少一小時的準確度。使用EnKF同化雷達資料的確對降低預報誤差具有顯著的改進。

Ensemble Kalman filter (EnKF) is a method for data assimilation. In this study, we apply the Observation System Simulation Experiments (OSSE) type of experimental designs to explore the performance of assimilating Doppler radar data using EnKF. A general purpose non-hydrostatic compressible model, the ARPS (Advanced Regional Prediction System), with complex multi-class microphysics, is employed for conducting all the experiments. Artificial data sets are from a simulated classic storm case that occurred on 20 May 1977 in Del City, Oklahoma. With and without terrain, we investigate the impact of several factors on the model forecasts, with the emphasis on the issue of quantitative precipitation forecast (QPF). These factors consider the number of ensembles, the time interval and frequency of data injection, the area of data availability, and so on. The major results show that using 40 members, and assimilating the radar data once every 5 minutes, can effectively produce the forecasts with sufficient accuracy. Assimilating as many data sets as possible can help to reduce the errors, and prevent the errors from growing to an uncontrollable scale. When the terrain is present and becomes a potential blockage to the radar beams, and if one can assimilate into the model the information of the initial storm development before the storm reaches the lee side of the mountain, then it is still possible to catch the location and pattern of the storm. Such a measure makes the following model forecast maintain its accuracy, even after the storm passes the mountain, and arrives at a region where the radar beams are completely blocked. Finally, to obtain an accurate one-hour QPF also requires an one-hour of radar data assimilation. Overall speaking, the assimilation of Doppler radar data does reveal significant improvements on reducing the forecast errors.

摘要……………………………………………………………………i
致謝……………………………………………………………………iii
目錄……………………………………………………………………iv
圖表說明………………………………………………………………vi

第一章 序論
1.1 前言………………………………………………………1
1.2 文獻回顧…………………………………………………2
1.3 研究動機與方向…………………………………………3

第二章 研究方法
2.1 資料同化方法介紹………………………………………5
2.1.1 標準卡曼濾波器………………………………7
2.1.2 系集卡曼濾波器………………………………9
2.1.3 系集平方根濾波器……………………………10
2.2 觀測系統模擬實驗設計…………………………………12
2.2.1 預報模式與真實模擬…………………………12
2.2.2 模擬雷達觀測資料……………………………13
2.2.3 系集卡曼濾波器資料同化程序………………16
2.3 定量降水檢驗方法………………………………………18
2.3.1 GS得分…………………………………………18
2.3.2 相關係數………………………………………19

第三章 無地形的觀測系統模擬實驗
3.1 測試實驗…………………………………………………20
3.1.1 實驗一：「系集數」測試………………………20
3.1.2 實驗二：「掃瞄時間」測試……………………21
3.1.3 實驗三：「是否同化徑向風與回波」測試……22
3.2 實驗四：同化後並作長時間系集預報
──「同化次數」測試………………………25

第四章 有地形的觀測系統模擬實驗
4.1 加入鐘型山脈── 實驗五：「同化次數」測試………29
4.2 加入長條型山脈…………………………………………34
4.2.1 實驗六：「同化區域」測試……………………34
4.2.2 實驗七：同化後並作長時間系集預報………38

第五章 結論與未來展望
5.1 結論………………………………………………………40
5.2 未來展望…………………………………………………42

參考文獻………………………………………………………………44
附表……………………………………………………………………47
附圖……………………………………………………………………50
略語表…………………………………………………………………91
主要符號表……………………………………………………………92

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