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An Improvement of the Linearized Planetary Boundary Layer Parameterization Scheme for CMA-GFS 4DVar
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摘要: 持续发展和优化切线性模式的线性化物理过程，保持与非线性模式一致是改善四维变分同化（4DVar）分析和预报效果的有效方法之一。目前业务系统的CMA-GFS模式采用基于Charney-Phillips（C-P）跳点的边界层参数化方案，而CMA-GFS 4DVar系统中采用基于Lorenz跳点的边界层线性化方案。为改善CMA-GFS 4DVar系统的边界层分析和预报效果，基于C-P跳点的边界层参数化方案研发了新边界层线性化方案，并通过对方案中地表热量通量和水汽通量扰动、自由大气的理查逊系数扰动、边界层的热量和动量交换系数扰动等进行更加精细地规约化约束，在确保CMA-GFS切线性和伴随模式稳定运行的情况下，减少线性化过程对切线性模式预报精度的影响。切线性近似试验检验表明：相较于原方案，新边界层线性化方案可以减少边界层位温和比湿的相对误差，最大可减少10%。批量4DVar循环同化试验表明：新边界层线性化方案可以有效改善切线性模式对低层位温、风场和比湿扰动的预报精度，减少4DVar内外循环目标泛函的相对差异，并提高700 hPa位势高度的可预报时效。Abstract: By continuously developing and optimizing the linearized physical process of the tangent linear model and keeping it consistent with the nonlinear model, the analysis and forecasting performance of four-dimensional variational data assimilation (4DVar) of China Meteorological Administration Global Forecast System (CMA-GFS) can be effectively improved. Currently, the planetary boundary layer (PBL) parameterization scheme adopted by CMA-GFS model is based on Charney-Phillips (C-P) grid, while the linearization PBL parameterization scheme used in CMA-GFS 4DVar is on the basis of Lorenz grid. The zigzag noise of the temperature and moisture in the boundary layer is removed and the correspondent profiles appear to be smooth with C-P PBL parameterization scheme, and the forecast errors of CMA-GFS model are effectively reduced. To improve the analysis and prediction effects of 4DVar on the boundary layer, a new linearized PBL parameterization scheme based on the C-P grid (TL_NMRF_CP) is developed. By making more refined regularization constraints on the disturbances of the surface heat flux, the surface water vapor flux, Richardson coefficient of the free atmosphere, the heat and momentum exchange coefficient of the boundary layer, the influence of the linearization process on the accuracy of the tangent linear approximation is reduced while ensuring stable operation of the tangent linear and adjoint models. Two tests are designed, one is TL_MRF test based on the original TL_MRF scheme and the other is TL_NMRF_CP test based on the TL_NMRF_CP scheme. The tangent linear approximation tests show that, compared with the original scheme, the TL_NMRF_CP scheme can improve the tangent linear model forecast accuracy on the boundary layer, reduce the relative error of the potential temperature of the boundary layer by up to 10%, reduce the relative error of the specific humidity by 5% at the most, and reduce the relative error of zonal wind by up to 12%. In the minimization process of CMA-GFS 4DVar, the TL_NMRF_CP scheme can reduce the relative difference of the cost functions caused by different resolutions between inner and outer loops of the 4DVar system, and improve the convergence efficiency of 4DVar. The batch cycle assimilation forecast experiments of CMA-GFS 4DVar further verify that the TL_NMRF_CP scheme can provide better analysis and prediction results. The TL_NMRF_CP scheme has also been applied to CMA-GFS 4DVar operation system.
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图 1 CMA-GFS切线性模式全球平均位温扰动相对误差垂直分布
Fig. 1 Vertical distribution of global mean relative error of potential temperature perturbation in CMA-GFS tangent linear model
图 2 TL_MRF试验的位温扰动纬向平均绝对误差
Fig. 2 Zonal mean absolute errors of potential temperature perturbation for TL_MRF test
图 3 TL_NMRF_CP试验位温扰动相对于TL_MRF试验的改善
Fig. 3 Improvements in potential temperature perturbation of TL_NMRF_CP test relative to TL_MRF test
图 4 CMA-GFS切线性模式全球平均比湿扰动相对误差垂直分布
Fig. 4 Vertical distribution of global mean relative error of specific humidity perturbation in CMA-GFS tangent linear model
图 5 TL_MRF试验的比湿扰动纬向平均绝对误差
Fig. 5 Zonal mean absolute errors of specific humidity perturbation for TL_MRF test
图 6 TL_NMRF_CP试验比湿扰动相对于TL_MRF试验的改善
Fig. 6 Improvements in specific humidity perturbation of TL_NMRF_CP test relative to TL_MRF test
图 7 CMA-GFS切线性模式全球平均纬向风扰动相对误差垂直分布
Fig. 7 Vertical distribution of global mean relative error of zonal wind perturbation in CMA-GFS tangent linear model
图 8 TL_MRF试验的纬向风扰动纬向平均绝对误差
Fig. 8 Mean absolute errors of zonal wind perturbation for TL_MRF test
图 9 TL_NMRF_CP试验纬向风扰动相对于TL_MRF试验的改善
Fig. 9 Improvements in zonal wind perturbation of TL_NMRF_CP test relative to TL_MRF test
图 10 CMA-GFS 4DVar目标泛函的收敛
Fig. 10 Convergence of the cost function under CMA-GFS 4DVar
图 11 北半球和南半球700 hPa位势高度的相关系数
Fig. 11 Anomaly correlations of 700 hPa geopotential height for the Northern Hemisphere and the Southern Hemisphere
表 1 CMA-GFS 4DVar试验设置
Table 1 Setting of CMA-GFS 4DVar test
设置 详细配置 水平分辨率 外循环为1.0°×1.0°，内循环为1.0°×1.0° 模式积分步长 外循环为450 s，内循环为900 s 垂直层数 87层 同化时间窗长度 6 h 观测剖分间隔 30 m 线性化物理过程 垂直扩散、地形阻塞流拖曳、对流参数化、大尺度凝结 极小化算法 有预调节的Lanczos-CG算法 重力波控制 数字滤波弱约束 最大极小化迭代次数 50次 
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