半拉格朗日法雲模式在中小尺度模擬的應用

Application of Semi-Lagrangian Cloud Model to Meso and Small Scale Modelling

張博雄(Po-Hsiung Chang) ； 曾忠一(Chung-Yi Tseng)

《大氣科學》 28卷3期 (2000/09) Pp. 161-175

摘要

半拉格朗日法允許較大時步的優點十多年來一直受到很大的注目，例如歐洲中期天氣預報中心的全球波譜模式最近已採用半拉格朗日法進行預報。基於未來中小尺度模式的整合，半拉格朗日法正逐步朝向中小尺度非靜力模式進展。中小尺度模擬需考慮複雜的氣象場，而這些時空變化很大的物理量常常引起數值計算上的雜波，這些雜波往往使得正值的物理量變爲負值，而且透過非線性作用也會破壞數値解，不正確的處理方法會導致數值格式失去守恆性質，特別是在中小尺度的模式中。
在從事中小尺度的模擬時，如果要提高解析度，模式的時步往往受限於穩定度。本文透過對流實驗來探討半隱式半拉格朗日法應用在中小尺度模擬時出現的問題。在高解析度的平流實驗中我們發現，半拉格朗日法與單調格式在適當的Courant數，在節省積分時間的情況下，可以有更好的守恆性質。另一方面，熱胞對流實驗的研究結果顯示，在熱對流胞邊緣的強梯度處採用單調格式的半拉格朗日法，可以增加形狀的保存性和模式的穩定性。

關鍵字

半拉格朗日法 ； 單調格式 ； 雲模式

並列摘要

The advantage of semi-Lagrangian advection scheme that permits larger time step is attractive for along time. For example, ECMWF has used the semi-Lagrangian scheme in their global spectral model. Recently the semi-Lagrangian method is gradually extended to meso and small scale nonhydrostatic models. The variations in meso and small scale meteorological fields are very complicated and often induce spurious noises in the integration process. The noises make the solutions negative that must be positive physically. They also contaminate the solution through nonlinear interactions and make the advected quantities non-conservative, especially in meso and small scale cloud models.
The time step is constrained by stability condition when increased resolution is used in cloud models. We probe the application of semi-Lagrangian advection scheme in meso and small scale modeling by two convection problems. In a high resolution experiment, the monotone semi-Lagrangian method can conserve physical quantities with appropriate Courant number and save the computing time. In the thermal bubble experiment with strong gradient in thermal bubble boundary, the monotone semi-Lagrangian method achieves better shape-preserving and stability.

並列關鍵字

Semi-Lagrangian method ； Monotone scheme ； Cloud model