衛星遙測垂直大氣溫度剖面－研究“受約束之線性反演法”

Satellite Remote Sounding of Atmospheric Temperature Profile-The Study of the Constrained Linear Inversion Method

柳中明(C. M. Liu) ； 譚允中(Yeun-Chung Tan)

《大氣科學》 14卷1期 (1986/09) Pp. 77-90

摘要

本文採四階段研究“受約束之線性反演法”內參考波數、任意函數、展開項數、參考常數、先驗剖面等因子，對衛星遙測垂直大氣溫度剖面影響之敏感性與相關性問題，並研究應用此反演法於實際作業中之可能性。結果指出，若修正反演法為計算偏離先驗剖面之差值剖面時，將能至少改進反演誤差一倍以上。其次，反演結果受所選擇之任意函數影響至鉅，因此，若取具代表性之函數－譬如Wark and Fleming（1966）所建議之經驗正交函數，或將能降低反演誤差。此外，當取參考常數小於1時，將無法獲取穩定且誤差低之解；但參考常數大於1，再配以低函數展開項數，將能獲取穩定且誤差低之解。再者，修正後之反演法被應用於反演75年2月22日台北之溫度剖面，所得解在100 mb以下溫度之均方根差為2.3°C，已非常接近一般反演系統之結果2°C，更較原始之反演法降低誤差近10倍。綜結所得，修正反演法為反演偏離先驗剖面之偏差值的觀念，為Fritz et al（1972）所建議，並用於其他許多反演方法。修正後之形式，再配以參考常數與展開項數之選擇研究，已克服過去認為此反演法太受參考常數影響，而難用於實際作業中之困難。

並列摘要

The sensitivity and the interrelativity of the factors such as the referenced wave number, any function, series expansion terms, referenced constant, a priori profile, etc. referred in the constrained linear inversion method for the satellite sounding vetrieval, are carefully examined through a designed four-step research process. Further, the method is analyzed for the possibility of being used in an operational retrieval system.The results indicate that the retrieval method can be modified to calculate the deviation of the temperature profile from a priori profile, which substantially reduces the retrieval error to one-half. Also, the retrieval result is controlled significantly by the any function chosen to represent the planck function. Hence, the selection of a statistically meaningful function-e.g, the EOF suggested by Wark and Fleming (1966), may lead to the reduction of retrieval error. Besides, when the referenced constant is set to be smaller than 1, no stable with low estimation error solution can be achieved. However, when the referenced constant is set to be greater than 1, and the series expansion terms are minimized, stable with low error solution is easily obtained. Finally, the motified method is used on retrieving the temperature profile on Feb. 22, 1986 over Taipei. The result has an error root mean square value of temperature at levels below 100 mb to be 2.3°C, which is very close to the general retrieval error of 2°C obtained by many operational retrieval system, and is about one-tenth of the error obtained from the original method.In conclusion, the idea of modifying the retrieval method to retrieve the deviation of the temperature profile from a priori profile is originally suggested by Fritz et al (1972), and has been employed to modify many other retrieval method. The modified version along with the proper selection of the referenced constants and the series expansion terms, has overcome the difficulty recognized in the past of the uncontrollable effect of the referenced constant on influencing the retrieval error, and leads to a possible development of an operational retrieval system.