The framework of the 4DVar data assimilation system based on perturbation forecast model:Development and numerical experiment
-
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。
-
关键词:
- 四维变分资料同化(4DVar) /
- 扰动预报模式 /
- GRAPES区域模式
Abstract: 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. -
图 1 台风“彩虹”的观测和预报路径:实况 (虚线)、业务模式 (点线) 和干模式 (实线),干模式台风初始位置 (A)位于台风实际位置 (O) 偏西32.6 km
Figure 1. The observed and forecasted tracks of typhoon Mujigae:best track (dashed),simulations of operational model (dotted) and dry model (solid),symbol A indicates Mujigae's initial position in the dry model,which is 32.6 km west of the observed position (O)
图 3 2015年10月2日12 (a、b) 和18 (c、d) 时850 hPa位势高度场 (黑色线条,单位:dagpm)、风矢量和风速 (色阶,单位:m/s)(a、c. “真实”大气,b、d. 人为改变的背景场)
Figure 3. Initial fields of 12:00 (a,b) and 18:00 (c,d) UTC 2 October 2015 at 850 hPa geopotential heights (black contour,unit:dagpm), wind vectors and wind speed (shaded,unit:m/s)(a,c. idealized "truth" fields;b,d. artificially changed fields)
图 4 四个试验850 hPa分析增量:风矢量 (箭头)、风速 (色阶) 和位势高度 (等值线,单位:gpm)(a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2;台风记号黑色为“实况”位置,蓝色为背景场位置,紫色为分析场位置)
Figure 4. Analysis increments at 850 hPa of four experments:wind vectors (arrow),wind speed (shaded) and geopotential height (contour,unit:gpm)(a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2;the typhoon symbols in black,blue and purple mark the positions of typhoon center for the "truth",the background and the analysis,respectively)
图 7 850 hPa风矢、风速 (色阶,单位:m/s) 和位势高度 (等值线,单位:dagpm) 的分析结果 (a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2;台风记号同图4)
Figure 7. Analyses of wind voctor,wind speed (shaded,unit:m/s) and geopotential height (contour,unit:dagpm) at 850 hPa (a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2;the symbols of typhoon are the same as Fig. 4)
图 8 850 hPa 风矢 (箭头)、风速 (色阶) 和位势高度 (等值线,单位:gpm) 分析场与“真值”之差(分析−观测)(a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2;台风记号同图4)
Figure 8. Analysis minus "truth" (A−O) for wind vector (arrow),wind speed (shaded) and geopotential height (contour,unit:gpm) at 850 hPa (a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2;the symbols of typhoon are same as Fig. 4)
图 12 基于不同初始场预报的2015年10月3日18时850 hPa“彩虹”台风的风场 (风矢和色阶) 和位势高度场 (等值线,单位:dagpm)(a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2,e. CTL,f. truth)
Figure 12. Model forecasts of wind (arrow and shaded) and geopotential height (contour,unit:dagpm) at 850 hPa at 18:00 UTC 3 October 2015 for typhoon Mujigae (a. 3DVar_1,b. 3DVar_2,c. 4DVar_1,d. 4DVar_2,e. CTL,f. truth)
表 1 不同同化试验目标函数的变化
Table 1. Variations of cost function value during minimization in different data assimilation experiments
同化试验 目标函数J 初始w 资料组数 资料时刻 分析时刻 初始Js 结束Je 减少率%((Je −Js)/Js×100) 3DVar_1 375.73 95.56 −74.57 取0 1 12时 12时 3DVar_2 417.54 160.00 −61.68 取0 1 18时 18时 4DVar_1 281.87 86.18 −69.43 取3DVar_1分析值 2 12、15时 12时 4DVar_2 538.66 158.38 −70.60 取3DVar_1分析值 3 12、15、18时 12时 表 2 不同同化试验方案的台风“彩虹”路径预报误差
Table 2. Absolute forecast errors of the path of typhoon Mujigae in different data assimilation experiments
预报时效(h) 位置偏差(km) 3DVar_1 3DVar_2 4DVar_1 4DVar_2 CTL 0 115.1 73.9 30.8 54.0 230.8 6 92.5 95.4 21.1 21.1 218.1 12 74.5 39.4 24.7 11.2 196.1 18 73.4 15.3 33.4 33.4 168.1 24 84.3 53.2 35.0 30.5 142.4 30 103.6 56.3 15.2 10.4 99.9 36 83.4 45.4 15.2 20.7 75.7 -
[1] 冯业荣,薛纪善,陈德辉等. 2020. GRAPES区域扰动预报模式动力框架设计及检验. 气象学报,78(5):805-815Feng Y R,Xue J S,Chen D H,et al. 2020. The dynamical core for GRAPES regional perturbation forecast model and verification. Acta Meteor Sinica,78(5):805-815 (in Chinese) [2] 薛纪善,陈德辉. 2008. 数值预报系统GRAPES的科学设计与应用. 北京:科学出版社,65-136Xue J S,Chen D H. 2008. Scientific Design of the GRAPES Numerical Weather Prediction Model and Its Application. Beijing:Science Press,65-136 (in Chinese) [3] Bauer P,Geer A J,Lopez P,et al. 2010. Direct 4D-Var assimilation of all-sky radiances. Part Ⅰ: Implementation. Quart J Roy Meteor Soc,136(652):1868-1885 doi: 10.1002/qj.659 [4] Bauer P,Thorpe A,Brunet G. 2015. The quiet revolution of numerical weather prediction. Nature,525(7567):47-55 doi: 10.1038/nature14956 [5] Bloom S C,Takacs L L,da Silva A M,et al. 1996. Data assimilation using incremental analysis updates. Mon Wea Rev,124(6):1256-1271 doi: 10.1175/1520-0493(1996)124<1256:DAUIAU>2.0.CO;2 [6] Courtier P,Thépaut J N,Hollingsworth A. 1994. A strategy for operational implementation of 4D-Var,using an incremental approach. Quart J Roy Meteor Soc,120(519):1367-1387 doi: 10.1002/qj.49712051912 [7] Courtier P,Andersson E,Heckley W,et al. 1998. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Ⅰ: Formulation. Quart J Roy Meteor Soc,124(550):1783-1807 [8] Dixon M,Li Z H,Lean H,et al. 2009. Impact of data assimilation on forecasting convection over the United Kingdom using a high-resolution version of the Met Office unified model. Mon Wea Rev,137(5):1562-1584 doi: 10.1175/2008MWR2561.1 [9] Fiorino M,Elsberry R L. 1989. Some aspects of vortex structure related to tropical cyclone motion. J Atmos Sci,46(7):975-990 doi: 10.1175/1520-0469(1989)046<0975:SAOVSR>2.0.CO;2 [10] Gauthier P,Tanguay M,Laroche S,et al. 2007. Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the meteorological service of Canada. Mon Wea Rev,135(6):2339-2354 doi: 10.1175/MWR3394.1 [11] Holland G J. 1983. Tropical cyclone motion:Environmental interaction plus a beta effect. J Atmos Sci,40(2):328-342 doi: 10.1175/1520-0469(1983)040<0328:TCMEIP>2.0.CO;2 [12] Jones C D,Macpherson B. 1997. A latent heat nudging scheme for the assimilation of precipitation data into an operational mesoscale model. Meteor Appl,4(3):269-277 doi: 10.1017/S1350482797000522 [13] Kurihara Y,Bender M A,Ross R J. 1993. An initialization scheme of hurricane models by vortex specification. Mon Wea Rev,121(7):2030-2045 doi: 10.1175/1520-0493(1993)121<2030:AISOHM>2.0.CO;2 [14] Liu D C,Nocedal J. 1989. On the limited memory BFGS method for large scale optimization. Math Program,45(1-3):503-528 doi: 10.1007/BF01589116 [15] Lorenc A C. 2003. Modelling of error covariances by 4D-Var data assimilation. Quart J Roy Meteor Soc,129(595):3167-3182 doi: 10.1256/qj.02.131 [16] Lorenc A C,Rawlins F. 2005. Why does 4D-Var beat 3D-Var?. Quart J Roy Meteor Soc,131(613):3247-3257 doi: 10.1256/qj.05.85 [17] Mathur M B. 1991. The national meteorological center's quasi-Lagrangian model for hurricane prediction. Mon Wea Rev,119(6):1419-1447 doi: 10.1175/1520-0493(1991)119<1419:TNMCQL>2.0.CO;2 [18] McNally A P,Watts P D,Smith J A,et al. 2006. The assimilation of AIRS radiance data at ECMWF. Quart J Roy Meteor Soc,132(616):935-957 doi: 10.1256/qj.04.171 [19] Rabier F,Järvinen H,Klinker E,et al. 2000. The ECMWF operational implementation of four-dimensional variational assimilation. Ⅰ: Experimental results with simplified physics. Quart J Roy Meteor Soc,126(564):1143-1170 doi: 10.1002/qj.49712656415 [20] Rawlins F,Ballard S P,Bovis K J,et al. 2007. The Met Office global four-dimensional variational data assimilation scheme. Quart J Roy Meteor Soc,133(623):347-362 doi: 10.1002/qj.32 [21] Zhang L,Liu Y Z,Liu Y,et al. 2019. The operational global four-dimensional variational data assimilation system at the China Meteorological Administration. Quart J Roy Meteor Soc,145(722):1882-1896 doi: 10.1002/qj.3533 -