大气数值模式空间分辨率的确定方法

Determination of the Spatial Resolution Required by the Atmospheric Numerical Model

集中讨论了如何决定大气数值模式空间分辨率的问题。首先,给出模式分辨率的定义和模式各方程都应满足的不等式,并在此基础上,用尺度分析和单波的方法推出模式水平和垂直分辨率的预估公式。还给出针对一般模式,以预估公式作基础,选择一系列分辨率,用比较试验,结合大气结构特点,最终确定模式分辨率的方法。并用浅水模式进行了水平分辨率的试验。

Up to the present, with exception to the sensitivity test, no method has been published for determining the spatial resolution required by the atmospheric numerical model. For this reason a method is suggested to tackle the problem. At first the spatial resolution is defined as such a resolution with which every discrete term of each equation in the model except the tendency term, eould not remarkably be impacted by the corresponding truncation error and would possess appropriate accuracy and the accuracy of the tendency term would also be appropriate. Then based upon the definition two inequalities for use in spatial discretization are presented. Subject to the inequalities and on the basis of the scale analysis of the atmospheric motion two formulas for pre-estimating the horizontal and vertical resolutions are derived. With them an algorithm for determining the resolutions in the free atmosphere is suggested, which consists of the following steps： （1） Selecting several resolutions centered about the pre-estimated ones. （2） Performing time integration and computing the norm of each term and that of the truncation error of the largest term in magnitude in each equation of the model equation set. （3） Discriminating the resolutions which satisfy the inequalities from the other ones. Two numerical tests are implemented by using the shallow-water equation model. According to the scale analysis and the formula for pre-estimating horizontal resolution, the resolution is found to be 80 km. So in the first test the resolutions are taken as 400, 200, 80 and 50 km. And resolutions 200, 80 and 40 km are adopted in the second test, and the speed of the basic current and the amplitude of disturbance given at the initial instant are taken as half of those in the first test. The results show that resolutions 50 and 40 km satisfy the first inequality in the first and second tests respectively. Finally, two preliminary conclusions are drawn as follows. （1） From the two inequalities the resolutions suitable to the model could be discriminated from the ones unsuitable to the model. （2） The two formulas for determining the pre-estimated resolution not only take account of the scale of the atmospheric motion, but also involve the magnitude difference between the largest term and the least term in each equation of the model equation set, which is closely related to the features of the model.