冯业荣,薛纪善,陈德辉,吴凯昕. 2020. GRAPES区域扰动预报模式动力框架的科学设计及检验[J]. 气象学报, (0):-, doi:10.11676/qxxb2020.048
GRAPES区域扰动预报模式动力框架的科学设计及检验
Scientific Design of Dynamical Core for Regional Perturbation Forecast Model of GRAPES and Its Verification
投稿时间:2019-05-05  修订日期:2020-03-12
DOI:10.11676/qxxb2020.048
中文关键词:  扰动预报模式,GRAPES非线性模式,4D-Var四维变分同化,半隐式半拉格朗日方案,赫姆霍兹方程
英文关键词:Perturbation forecast model, GRAPES nonlinear model, Four dimension variational data assimilation(4D-Var), Semi-implicit Semi-Lagrangian scheme, Helmholtz equation
基金项目:国家自然科学基金联合基金项目(U1811464)和国家重点研发计划重点专项项目(2018YFC1506900)资助。
作者单位E-mail
冯业荣 中国气象局广州热带海洋气象研究所/广东省区域数值天气预报重点实验室 yerong_feng@yahoo.com 
薛纪善 中国气象局广州热带海洋气象研究所/广东省区域数值天气预报重点实验室 jsxue@cma.cn 
陈德辉 国家气象中心 chendh@cma.cn 
吴凯昕 中国气象局广州热带海洋气象研究所/广东省区域数值天气预报重点实验室 Wukx@gd121.cn 
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中文摘要:
      文章设计建立了适用于4D-Var四维变分同化系统的扰动预报模式GRAPES_PF,即在地形追随坐标非静力原始方程组基础上,采用小扰动分离方法推导了微分形式的线性扰动预报方程组,并利用与GRAPES非线性模式相似的数值求解方案求解线性扰动微分方程组。在设计扰动预报模式时,采用两个时间层半隐式半拉格朗日方案对动量方程、热力学方程、水汽方程和连续方程进行时间差分,空间差分方案的变量分布水平方向采用Arakawa C跳点网格,垂直方向采用Charney/Phillips跳层。利用代数消元法进一步推导得到只包含未来时刻扰动气压Π''的Helmholtz方程,进而通过广义共轭余差法(GCR)求解,在此基础上得到未来时刻扰动量的预报值。基于所开发的扰动模式开展了数值试验,首先在非线性模式中施加一个初始扰动高压,得到初始扰动在非线性模式中的后续演变,然后将相同的初始扰动作为扰动模式的初值进行时间积分,将扰动模式预报的结果与非线性模式的结果进行对比。检验结果表明,本文开发的扰动模式GRAPES_PF较好地模拟了惯性重力内波的传播过程,与非线性模式得到的结果非常接近;初始高压扰动激发了一个迅速向外传播的惯性重力内波,在气压场向风场适应的过程中,水平风场、垂直运动、位温和湿度等变量均出现了扰动增量。线性扰动预报模式GRAPES_PF为将要建立的基于GRAPES区域模式的4D-Var同化系统奠定了重要科学基础。
英文摘要:
      In this paper, the perturbation forecast model GRAPES_PF has been developed so as to construct a four dimensional data assimilation (4D-Var) system to be implemented with the regional numerical weather prediction model GRAPES. GRAPES_PF involves a set of linear perturbation forecast equations including momentum, thermodynamic, moisture and continuity which are derived from the non-hydrostatic primitive equations of GRAPES on a terrain-following vertical coordinate framework. A semi-Lagrangian and semi-implicit two time-level integration scheme is applied to the linear equations. Spatial discretizations are performed on the Arakawa staggered C-grid in the horizontal and the Charney-Phillips grid in the vertical. We obtain the Helmholtz equation with respect to perturbation variable at future time step of integration by eliminating other variables in the linear perturbation equations. Similar to the nonlinear model, the generalized conjugate residual (GCR) method is used to solve the perturbation Helmholtz equation. A numerical experiment has been designed to evaluate the GRAPES_PF model by applying an initial perturbation of high pressure centered at model space and predicting its evolution with time. The same initial perturbation of high pressure is also added to nonlinear model so that the evolution of perturbation can be traced as truth in the verification. We then verify the perturbation predicted by linear GRAPES_PF model against nonlinear GRAPES model. Results show that the initial pressure perturbation induces a fast-moving-outbound internal inertial gravity wave through the well-known geostrophic adjustment process. The linear GRAPES_PF model produces almost the same result as nonlinear GRAPES model with a high degree of accuracy. The initial pressure perturbation induces subsequently the increments in the fields such as horizontal wind, vertical velocity, potential temperature and water vapor, which are highly identical with nonlinear model. The main conclusion is that the GRAPES-PF offers a good scientific base for the 4D-Var data assimilation system to be developed based on GRAPES model.
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