基于扰动模式的四维变分资料同化系统框架的设计完善和数值试验

The framework of the 4DVar data assimilation system based on perturbation forecast model：Development and numerical experiment

中文关键词:  四维变分资料同化（4DVar）  扰动预报模式  GRAPES区域模式

英文关键词:Four-dimensional variational data assimilation (4DVar)  Perturbation forecast model  Regional GRAPES model

中文摘要:

      为了建立一个应用于区域数值预报的四维变分资料同化（4DVar）系统，在近期开发的扰动预报模式GRAPES_PF基础上，开发完善增量四维变分同化系统框架。该框架中暂不包含物理过程（长短波辐射、边界层过程、对流参数化和云微物理等）。对比业务使用的GRAPES 3DVar系统，增加了温度控制变量。将无量纲Exner气压与流函数的线性风压平衡方程直接在地形追随垂直坐标面上求解，且通过广义共轭余差法（GCR）求解扰动亥姆霍兹（Helmholtz）伴随方程。利用人造“探空”资料对2015年10月台风“彩虹”进行了理想数值试验。试验结果表明，所开发的扰动四维变分同化框架得到了预期的结果，即同化更多资料并反复受到模式约束的四维变分同化系统能有效改善初值质量，进而改善区域数值预报。建立的区域四维变分同化框架合理可行，为进一步发展包含完整物理过程的区域四维变分同化系统奠定了研究基础。

英文摘要:

      In order to develop the four-dimensional variational data assimilation (4DVar) system that can be used in regional numerical weather prediction, the framework of the incremental 4DVar is developed in this study on the basis of the recently developed perturbation forecast model GRAPES_PF. At the current stage, this 4DVar framework does not include physical schemes such as short-wave and long-wave radiation, planetary boundary layer, cumulus convection, cloud microphysics, etc. Compared to the operational GRAPES 3DVar system, air temperature is chosen as an extra analysis control variable in the new framework. The linear balance equation, which relates the balanced Exner pressure with stream function, is deduced and solved numerically on the terrain-following vertical coordinate. The adjoint of perturbation Helmholtz equation is solved using the iterative generalized conjugate residual (GCR) approach. To evaluate the validity of this framework, a suite of idealized numerical experiments using pseudo radiosonde data have been carried out to simulate typhoon Mujigae, which occurred over South China Sea in October 2015. The experiments reveal that the 4DVar framework offers results in line with theoretical expectations, i.e., by ingesting more observations in time and through the constraint of perturbation forecast model, the 4DVar leads to more obvious improvements than the 3DVar in both analysis and forecast. This study provides a reasonable framework of four-dimensional variational data assimilation, which can be further implemented with full linear physical package soon.