• 作者： 簡來成；江群從
• 作者服務機構： 中央研究院物理研究所
• 中文摘要： 高效率的數?積分法-交錯法，應用於四層斜壓準地轉模式，以探討東亞地區梅雨季節24小時之數?天氣預報。渦旋 度方程式與能量方程式的積分?時間階段計算兩次，第一次將i+J (i是行數，j是列數）?奇數諸點，以諸鄰點現時間階 段值計算；第二次計算i+j?偶數諸點，以鄰點新時間階段之?用explicit法求之。第一次計算是完全explicit法，第二 次計算是implicit法，但不用解代數聯立方程式。這方法相當於Peaceman-Rachford法，有無條件穩定之特性，積分的時 間增量可放大。計算速度比後者快3至4倍。本文以相同的起始條件，比較explicit法與本方法3至4倍的時間增量，預 報24小時的高度場，三位有效數字二者完全一致。
• 英文摘要： An efficient computational process, hopscotch method, has been applied to four-level baroclinic quasi-geostrophic diabatic model for 24-hour forecasting in Mei-Yu season over the East Asia. Numerical integrations of vorticity equation and energy equation are carried out by making use of this scheme. The method uses explicit and implicit finite difference schemes at alternate mesh points to solve the partial differential equations. Each time step is calculated in two sweeps of the mesh. In the first and subsequent odd-numbered time steps, the grid points with i+j odd (i is the row number, j the column number) are calculated based on current values of the neighboring points. For the second sweep at the same time level, the computation is excuted at points with i+j even, using the known advanced values of neighboring points calculated in the first sweep. The first sweep is explicit, the second is fully implicit with no simultaneous algebraic solution. The method, equivalent to Peacemen-Rachford procedure with coefficient matrix split in a novel way, is unconditionally stable and allowing arbitrarily large time step and is 3 to 4 time faster. This algorithm is very efficient with regard to storage requirement and ease of programming. For comparison, computations were made for the same initial and boundary conditions by applying both explicit method and the present method with triple and quadruple time increment. The results show that 24-hour predicted Z-field ageres excellently to 3 significant figures in both methods.
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