非静力AREM模式设计及其数值模拟I:非静力框架设计

AREM（Advanced Regional Eta-coordinate Model）对中国暴雨、台风等中尺度天气系统的模拟、预报能力突出。但是伴随模式分辨率的提高，制约该模式发展的一个问题日渐突出，即"静力平衡近似"的约束。本文通过对原静力平衡系统进行修正，引入高阶订正参数定义第三运动方程来构建该模式的非静力动力框架。我们基于Euler原始方程组，有效结合原静力平衡模式的标准层结扣除及IAP（Institute of Atmospheric Physics）变换方法，推导出了球面余纬坐标下的非静力框架，并在E网格和η坐标下进行了时空离散。采用时间两部分离技术进行积分运算以提高计算效率，并通过"追赶法"结合迭代法计算声波。此框架可方便地继承静力平衡框架的特点，最大限度地保留静力平衡框架的优势。理论推导和数值试验表明，当非静力框架退化为静力平衡框架后，方程形式及其模拟结果一致。在文章第二部分将通过理想和实例试验检验非静力模式性能。

Design of Non-hydrostatic AREM Model and Its Numerical Simulation Part I: Design of Non-hydrostatic Dynamic Core

The Advanced Regional Eta-coordinate Model (AREM) is featured as a useful tool to simulate and forecast meso-scale systems such as torrential rainfall and typhoons in China. However, the hydrostatic approximation has curbed its further development, which is more and more noticeable with the increasingly high model resolution. In this paper, the authors present a non-hydrostatic extension to AREM through the consideration of higher-order correctness due to the vertical acceleration. The AREM non-hydrostatic dynamics employs a primitive Euler equation system of motion and effectively uses the deduction of standard stratification and IAP (Institute of Atmospheric Physics) transformation of the current hydrostatic model. Also, the non-hydrostatic version of AREM is formulated in the spherical colatitude-longitude mesh and discretized in the Arakawa-E grid and a vertical η coordinate system. The prognostic equations are split into two parts, that is, the quasi-hydrostatic system and non-hydrostatic system, which facilitates efficient integration of the dynamic core. The sound wave associated with the non-hydrostatic system is calculated through the Thomas algorithm and iteration method. This approach to non-hydrostatic modeling is favorable for the preservation of advantages of hydrostatic AREM. The non-hydrostatic and hydrostatic frames agree well with each other in terms of governing equations and modeling results when the non-hydrostatic core is degraded to the hydrostatic one. In part Ⅱ of this paper, the non-hydrostatic AREM will be verified through idealized and real-data numerical experiments.