都卜勒氣象雷達能提供對流演變高時空解度之觀測資訊，除降水物與風場觀測外，結合風場資訊實施的熱動力反演更能得到溫度、壓力擾動的三維分布，並以其對複雜尺度天氣系統演變過程有更深入的理解。
傳統熱力反演法僅以風場推導之水平壓力擾動梯度力作為強勢約束條件並以二維變分求解一與壓力擾動相關之波桑方程式(Poisson equation)，有著難以於多山地區實行、反演產品為扣除水平平均之偏差量，直接以之分析垂直熱力結構將有誤判發生等缺點。搭配反演範圍中額外垂直觀測，如探空和飛機觀測，能得絕對擾動量，並解決垂直分析的問題，卻將因此受到額外觀測的時、空限制。
為克服上述缺陷，本研究擬開發一結合三維動量、熱動力方程式作為三維變分之弱勢約束條件的新熱動力反演法，能直接獲得絕對擾動量，消除垂直結構誤判之情形。利用弱勢約束條件能調整各點權重之特性，僅極小化地形外之流域點，更能在保有無人為邊界條件下，使其運用於複雜地形上。
實行一系列Obervation System Simulation Experiment(OSSE)檢測新反演法的表現，將模擬之大氣變數分布視為真值，在無資料缺漏且各變數滿足控制方程式情況下，檢驗方法、程式的正確性與方法之敏感度。主要實施兩組相異實驗，一為乾山嶽波；二為濕對流，後者由於微物理過程的納入使反演方法面臨更嚴峻的挑戰。
並將新反演運用於實際個案分析，為2008年西南氣流實驗6月14日IOP#8 1500 UTC之線狀對流個案。在無額外探空觀測下，分析海上對流系統以及山區局部強回波區的熱力結構。並與地面、探空觀測和傳統方法之反演結果交叉比對驗證。
透過OSSE與實例之佐證顯示，新方法加入熱力方程式並由弱勢約束條件求解，利用弱勢約束條件可調整任一格點之約束強度大小的特性，僅極小化非地形內部、邊界的流域點，能成功反演地形上的熱動力結構，除有助研究者理解地形效應與對流演變之關係外，保有同雷達資料之高時空解析度特性的熱力資訊亦有放入資料同化(data assimilation)系統改善降水預報之潛力，更可依其計算相關之氣象預報因子，強化對流風暴強度增強、削弱之預報，進一步改善對流發展預報之技巧。

RADAR can provide observations of distributions of hydrometers and winds with high resolutions in both time and space. With multiple-Doppler-RADAR synthesized winds, thermodynamic parameters (i.e., pressure and temperature) can be retrieved.
Solving a Poisson equation for the pressure over each horizontal plane with strong constraints of variational analysis results in the ambiguity of the vertical structure due to the existence of unknown constants at each horizontal layers and forces user avoid terrain when utilizing traditional thermodynamic retrieval method..
In this study, a new method retrieving the thermodynamic fields over terrain has been developed. The unknown constants can be eliminated which means the three-dimensional thermodynamic structures can be accurately reconstructed. The aforementioned goals are accomplished by using three momentum equations and a simplified thermodynamic equation.as strong constraints. Via adjustable weighting at each grid points of feature of weak constraints, the minimization is handled differently at points in the flow regime and terrain.
A series of Observation System Simulation Experiment (OSSE) tests are conducted to examine the correctness of the method, and the sensitivity of the retrieved fields with respect to the input data and weighting of constraints. Besides, a real case study from 2008 Taiwan SoWMEX field experiment is carried out to assess the performance of new scheme in recovering the pressure and temperature fields over mountainous area under a realistic scenario.
Overall, the new retrieval algorithm can provide researchers a more comprehensive understanding of the convection evolution particularly over complex topography and be used in data assimilation system to enhance performance of weather prediction potentially.

摘要 i
ABSTRACT iii
致謝 iv
目錄 v
表目錄 viii
圖目錄 viii
第一章　前言 1
1.1　文獻回顧 1
1.2　研究動機與目的 2
1.3　論文架構 3
第二章　資料來源與研究方法 4
2.1　資料來源 4
2.1.1　七股雷達(RCCG) 4
2.1.2　SOPL雷達(SPOL) 4
2.1.3　墾丁雷達(RCKT) 5
2.1.4　剖風儀(NCU ISS) 5
2.2　多都卜勒雷達風場合成 5
2.2.1　徑向風方程式 6
2.2.2　非彈性連續方程式 7
2.2.3　渦度方程式 8
2.2.4　價值函數與地形邊界條件設定 8
2.3　熱動力反演 11
2.3.1　非彈性動量方程式 11
2.3.2　熱動力方程式 13
2.3.3　價值函數與複雜地形之處理 13
第三章　觀測系統模擬實驗 18
3.1　數值模式與模擬 18
3.2　反演表現之檢視 19
3.2.1　近似理想實驗 19
3.2.2　時步敏感度實驗 21
3.2.3　熱動力方程式係數敏感度實驗 21
3.2.4　亂流項誤差引入敏感度實驗 22
第四章　個案介紹與資料處理 23
4.1　2008 SoWMEX IOP#8 1500 UTC 線狀對流個案 23
4.2　雷達資料品質管理 25
4.3　風場合成背景場製作 25
第五章　驗證、分析反演結果 27
5.1　直接驗證 27
5.2　分析與討論 28
5.2.1　三維風場結構 28
5.2.2　三維熱動力場結構 30
5.3　間接驗證 32
5.3.1　風場驗證剖風儀 32
5.3.2　熱動力驗證探空觀測 33
5.3.3　熱動力驗證地面測站 34
5.3.4　熱動力驗證新、舊熱動力反演比較 34
第六章　結論與未來展望 36
6.1　結語 36
6.2　未來展望 37
參考文獻 39
附表與附圖 42
 

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