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Bates为了积分浅水方程而发展的有效的半拉格朗日交替方向隐式(SLADI)法被推广到多层原始方程模式。假定基本状态是等温的,线性分析表明这种模式对平流是无条件稳定的,对重力惯性波有与浅水情况相同的稳定性判据。使用实际大气资料进行的积分表明,与爱尔兰气象局业务上使用的显式半拉格朗日模式(Bates和Medonala,1982年)相比,该模式允许使用长的时间步长,并产生了相当大的效益。把这个模式写在C网格上(Arakawa C网格),在垂直方向上使用σ—坐标,(σ=P/P_s),使用图 1中给出的变量垂直分布。离散控制方程组如下:
Bates’s effective semi-Lagrangian alternating direction implicit (SLADI) method developed for the integral shallow water equation is extended to the multi-layer primitive equation model. Assuming that the basic state is isothermal, the linear analysis shows that this model is unconditionally stable to advection and has the same stability criterion for gravity inertial waves as for shallow water. The points using actual atmospheric data show that this model allows the use of long time steps and produces a considerable amount of power compared to the explicit Semi-Lagrange modes used by Irbets operations (Bates and Medonala, 1982) Benefit. Write this pattern on a C grid (Arakawa C grid) using σ-coordinates in the vertical direction (σ = P / P_s), using the variables shown in Figure 1 for vertical distribution. Discrete control equations are as follows: