Application of the semi-Lagrangian method to a multilevel spectral primitive-equations model
Application of the semi-Lagrangian method to a multilevel spectral primitive-equations model
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DOI：
10.1002/qj.49711749705
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发表时间：
1991
影响因子：
8.9
通讯作者：
H. Ritchie
中科院分区：
文献类型：
--
作者：
H. Ritchie
先前已经表明，半拉格朗日格式可以应用于使用大时间步长的浅水方程的谱模型（例如，参见里奇（1988）。本研究认为，这项工作的扩展到一个多层次的光谱连续方程模型。作为第一步，欧拉涡度发散谱模式转换为欧拉模式的基础上的矢量动量形式的运动方程。从后者出发，准备了几个半拉格朗日模型：一种是用水平方向对流的插值半拉格朗日处理（称为2DISL），同时保留欧拉平流在垂直，另一个使用三维插值半拉格朗日公式（称为3DISL），另一种是在水平方向上采用2DISL格式，在垂直方向上采用非插值半拉格朗日处理（简称NISLV）。中程相互比较实验使用的模型，包括简单的物理参数化。结果表明，半拉格朗日半隐式的方法可以准确和稳定地应用于产生中期（5天）的预测，使用的时间步长是远远大于所允许的柯朗-弗里德里希-路易（CFL）的稳定性标准相应的欧拉模型。NISLV版本比3DISL版本更准确，3DISL版本在对流层顶附近明显具有过度阻尼，所有模型场在垂直方向上都发生突然变化。
It has previously been shown that semi-Lagrangian schemes can be applied to spectral models of the shallow-water equations using large time-steps (e.g., see Ritchie 1988). The present study considers the extension of this work to a multilevel spectral primitive-equations model. As a first step, an Eulerian vorticity-divergence spectral model is converted to an Eulerian model based on a vector momentum form of the equation of motion. From the latter, several semi-Lagrangian models are prepared: one using an interpolating semi-Lagrangian treatment of advection in the horizontal (referred to as 2DISL) while retaining Eulerian advection in the vertical, another using a 3-dimensional interpolating semi-Lagrangian formulation (referred to as 3DISL), and another which combines the 2DISL scheme in the horizontal and a non-interpolating semi-Lagrangian treatment in the vertical (referred to as NISLV). Medium-range intercomparison experiments are performed using models that include simple physical parametrizations. It is shown that the semi-Lagrangian semi-implicit approach can be applied accurately and stably to produce medium-range (5-day) forecasts using time-steps that are far larger than those permitted by the Courant-Friedrichs-Lewy (CFL) stability criterion for the corresponding Eulerian model. The NISLV version is found to be more accurate than the 3DISL one which apparently has excessive damping in the vicinity of the tropopause, where all the model fields change abruptly in the vertical.