線性平衡之有限元素變分佳化分析

Objective Analysis based on Finite Element Method-Using the Linear Balance Equation as a Dynamic Strong Constraint

王金慶(Chin-Ching Wang)

《大氣科學》 8卷1期 (1981/05) Pp. 27-41

摘要

本研究應用有限元素法，以線性平衡方程式為強勢動力約束條件，進行大氣定壓層的高度場與風場的變分佳化分析，以測站為三角形元素的節點，直接佳化每一測站的氣象變數值，以供爾後數值天氣預報之用。本研究不需要傳統客觀分析的步驟，可避免因採用傳統客觀分析法可能引進的誤差。個案研究的結果顯示，佳化後高度塲、風塲以及渦度塲，其型態及強度與主觀分析的結果大致相同。雖在測站稀少地區與主觀分析的結果稍有出入，但佳化所得之渦度塲及高度塲，與衛星雲圖及降水報告，頗為脗合。

並列摘要

An objective analysis in an inequally spaced grid system is developed using variational approach. The scheme is performed to minimize the differences between the observational and the optimized height and wind fields subject to some constraints. In this study, the linear balance equation is employed as a dynamic strong constraint. The observational stations are chosen a grid points and the triangular element system is constructed on them for the finite element analysis. The real data during Mei-Yu season in East Asia are utilized to investigate the applicability of the scheme.The computational results show that the magnitudes and the general patterns of height, velocity and vorticity fields are in good agreement with the synoptic weather system and the NOAA-4 satellite pictures. Also, the comparison with the subjective and Cressman objective analysis is performed and discussed.The finite element scheme is quite general. It may be applied to various weather systems with various constraints. Several progressive and possible extensions are also dicussed.