非静力AREM模式设计及其数值模拟Ⅰ:非静力框架设计

程锐; 宇如聪; 徐幼平; 王斌

doi:10.3878/j.issn.1006-9895.1712.17200

非静力AREM模式设计及其数值模拟Ⅰ:非静力框架设计

doi: 10.3878/j.issn.1006-9895.1712.17200

程锐^{1, 2,},
宇如聪¹,
徐幼平¹,
王斌¹

1.
中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室(LASG), 北京 100029
2.
地理信息工程国家重点实验室, 西安 710054

基金项目:

国家重点研发计划项目 2017YFB1002702

国家自然科学基金项目 91637211

国家自然科学基金项目 61572058

详细信息

作者简介:
程锐：程税, 男, 1975年出生, 高工, 主要从事数值模式数值预报应用。E-mail:c4rui@mail.iap.ac.cn

中图分类号: P456
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出版历程
- 收稿日期: 2017-07-25
- 网络出版日期: 2018-02-02
- 刊出日期: 2018-11-15

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

Rui CHENG^{1, 2
,},
Rucong YU¹,
Youping XU¹,
Bin WANG¹

1.
State Key Laboratory of Numerial Modeling for Atmospheric Sciences and Geophysical Fluid Dynemics(LASG) Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
2.
State Key Laboratory of Geo-Information Engineering, Xi'an 710054

Funds:

National Key Research and Development Plan 2017YFB1002702

National Natural Science Foundation of China 91637211

National Natural Science Foundation of China 61572058

摘要

摘要: 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。
- AREM模式 /
- 非静力动力框架 /
- E网格 /
- ETA坐标 /
- IAP变换
Abstract: 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.
- AREM model /
- Non-hydrostatic dynamic core /
- E-grid /
- ETA coordinate /
- IAP transformation

HTML全文

图 1 模式变量分布形式。点号表示水平速度点，叉号表示质量点

Figure 1. The distribution of model variables. The dots denote horizontal velocity points, the cross denotes mass point

下载: 全尺寸图片幻灯片

图 2 模式积分24 h的500 hPa风场矢量对比：（a）非静力退化为静力平衡框架（黑色箭头）、原静力平衡框架（彩色箭头）；（b）非静力框架（彩色箭头）

Figure 2. Comparison of 24-hour simulations of 500-hPa wind vectors: (a) The hydrostatic core degraded from the non-hydrostatic one (black vectors), the original hydrostatic core (colored vectors), (b) the non-hydrostatic core (colored vectors)

下载: 全尺寸图片幻灯片

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