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设计及检验[J]. 气象学报, 78(5):805-815, doi:10.11676/qxxb2020.048
GRAPES区域扰动预报模式动力框架设计及检验
The dynamical core for GRAPES regional perturbation forecast model and verification
投稿时间:2019-05-15  修订日期:2020-04-09
DOI:10.11676/qxxb2020.048
中文关键词:  扰动预报模式  GRAPES非线性模式  四维变分同化  半隐式半拉格朗日方案  亥姆霍兹方程
英文关键词:Perturbation forecast model  GRAPES nonlinear model  Four dimensional 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)
作者单位
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广州510641 
薛纪善 中国气象科学研究院北京100081 
陈德辉 国家气象中心北京100081 
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广州510641 
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中文摘要:
      设计了适用于四维变分同化系统的扰动预报模式GRAPES_PF。根据GRAPES的地形追随坐标非静力原始方程组,采用小扰动分离方法推导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了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Exner气压的亥姆霍兹方程,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中尺度初始扰动高压,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做了对比。结果表明,所开发的扰动模式GRAPES_PF较好地模拟了惯性重力内波的传播过程: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,与非线性模式得到的结果相当接近。GRAPES_PF作为GRAPES非线性模式的合理线性模式为建立基于线性扰动预报的区域四维变分同化系统奠定了科学基础。
英文摘要:
      In this study, the perturbation forecast model GRAPES_PF appropriate for the implementation of four dimensional variational data assimilation (4D-Var) system has been developed based on 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 used in GRAPES on a terrain-following vertical coordinate framework. A semi-implicit, semi-Lagrangian and two time-level integration scheme is applied to the linear equations. Spatial discretization is performed on the Arakawa staggered C-grid in the horizontal and the Charney-Phillips grid in the vertical. The Helmholtz equation that only contains perturbation Exner pressure at future time step of integration is obtained 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 mesoscale high pressure centered at model domain and predicting its evolution with time. The same initial perturbation of high pressure is also added to nonlinear model so that the evolution of the perturbation can be traced as truth for verification. We then verify the perturbations predicted by the linear GRAPES_PF model against those of the nonlinear GRAPES model. Results show that the initial pressure perturbation induces a fast-moving-outbound internal inertial gravity wave through the well-known geostrophic adaptation process. The linear GRAPES_PF model produces results similar to that of nonlinear GRAPES model with high accuracy: the initial pressure perturbation subsequently induces increments in the fields such as horizontal winds, vertical velocity, potential temperature and water vapor, which are almost identical to those of the nonlinear model. The main conclusion is that the perturbation forecast model GRAPES-PF, as a reasonable linear version of the nonlinear GRAPES model, can offer a good scientific base for the 4D-Var data assimilation system to be developed in the future.
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