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GRAPES模式切线性垂直扩散方案的误差分析和改进
Estimation of Linearized Vertical Diffusion Scheme in GRAPES Model
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摘要: 针对GRAPES四维变分同化系统的升级, 研究了GRAPES模式垂直扩散方案线性化问题。通过2005年8月7—27日21个个例的批量试验, 发现在GRAPES模式垂直扩散方案源代码的基础上逐句线性化得到的切线性垂直扩散方案即使能通过正确性测试试验, 在少数情况下也会存在很大误差。切线性模式计算的扰动气压场和扰动风场可能出现明显异常, 这种异常与垂直扩散方案中地表动量通量的强非线性有关。如果在切线性垂直扩散方案中忽略地表动量通量扰动, 既可以避免异常的出现, 又不影响其他正常时刻的计算精度。修改后的切线性垂直扩散方案能够在所有变量上一致地提高切线性模式的计算精度。Abstract: Four-dimensional variational data assimilation (4DVAR) is an optimal method to obtain a best estimate of the initial conditions for a forecast model. A cost function is defined that involves a model trajectory as compared with three-dimensional variational data assimilation. The minimization requires an adjoint model in order to solve the problem at a reasonable computing cost. A four-dimensional variational data assimilation system (GRAPES 4DVAR) based on regional GRAPES model is developed by Chinese Academy of Meteorological Sciences. There are only several 4DVAR systems based on the non-hydrostatic model as GRAPES worldwide. GRAPES 4DVAR also has the ability to assimilate the observations, including the new non-conventional satellite and radar data. For the operational implementation in the future, GRAPES 4DVAR system is designed in the incremental formulation. The tangent-linear and adjoint model are both required to calculate the cost function and its gradient in the inner-loop. As the starting point, an adiabatic version of the linerized model is developed in 2005. Recently, much more effort is spent in the development of the linerized physical parameterization scheme for the application in GRAPES 4DVAR system. The linearization of vertical diffusion scheme used in GRAPES model is discussed.MRF nonlocal boundary layer scheme is used by GRAPES model to describe the vertical diffusion within and above the mixed boundary layer. The vertical diffusion scheme for the free atmosphere is linearized. After the straightforw ard linearization of vertical diffusion scheme, the standard tests are carried out to check the correctness of the tangent-linear model with vertical diffusion. It is well known that all physical processes are characterized by discontinuities and nonlinearities by which the departures of their linearied schemes can be significantly increased. To evaluate the validity of tangent-linear approximation for vertical diffusion scheme, twentyone cases during August 7—27, 2005 are run to calculate the mean departure between the tangent-linear model and the nonlinear model. It is found that the discontinuity resulted from the "on-off" switch has little influence on the mean departure between the tangent-linear model and the nonlinear model. Indeed, significant departures caused by the nonlinearity of vertical diffusion scheme may be lead to by a straightforward linearization of vertical diffusion scheme. This is a clear demonstration of the possible detrimental impact on the perturbed pressure and wind fields. The problem is solved by neglecting the perturbation of the surface flux for momentum. After the simplification, a better agreement between the tangent-linear model and the nonlinear GRAPES model with full physics for all variables is resulted in by the inclusion of the linearized vertical diffusion scheme. In conclusion, the results are encouraging, and the linearized vertical diffusion scheme is applicable in GRAPES 4DVAR systems. More linearized physics parameterization schemes will also be developed in the near future.
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Key words:
- vertical diffusion scheme;
- linearization;
- GRAPES
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图 1 切线性模式与只有动力框架和垂直扩散方案非线性模式平均偏差 (虚线:切线性模式只有动力框架; 实线:切线性模式包括动力框架和垂直扩散方案) (a) 无量纲气压, (b) u风场, (c) v风场, (d) 比湿q
Fig. 1 Mean departure between the tangent-linear model and the nonlinear model including vertical diffusion (dashed line denotes the results are obtained with a dry tangent-linear model; solid line denotes a tangent-linear model including vertical diffusion) (a) non-dimensional pressure, (b) u-wind, (c) v-wind, (d) specific humidity
图 2 修改切线性垂直扩散方案前异常单格点上最低层扰动变量随时间演变 (a) 地表动量通量, (b) u风场
Fig. 2 Temporal evolution of perturbed variable at an abnormal grid from the original linearied vertical diffusion scheme (a) momentum flux at the surface, (b) u-wind
图 3 修改切线性垂直扩散方案后单格点最低层扰动u风场与非线性扰动u风场随时间演变
(实线:切线性模式的结果; 虚线:非线性模式的结果; 格点位置同图 2)
Fig. 3 Temporal evolution of perturbed u-wind at the same location as Fig.2 after the modification of linearied vertical diffusion scheme
(solid line denotes the results from the tangent-linear model, dashed line denotes those from the nonlinear model)
图 4 切线性模式和非线性模式的平均偏差 (a) 无量纲气压, (b) u风场
(均只有动力框架和垂直扩散方案; 虚线:切线垂直扩散方案修改前; 实线:切线垂直扩散方案修改后)
Fig. 4 Mean departure between the tangent-linear model and the nonlinear model including vertical diffusion (a) non-dimensional pressure, (b) u-wind
(dashed line denotes tangent-linear results are obtained with the original linearied vertical diffusion scheme, solid line denotes the modified scheme)
表 1 只包括动力框架的切线性模式的正确性测试结果
Table 1 Test results of tangent-linear model without physics
表 2 包括动力框架和垂直扩散方案的切线性模式的正确性测试结果
Table 2 Test results of tangent-linear model with vertical diffusion
表 3 切线性模式扰动无量纲气压场与包括全物理过程非线性模式扰动场平均偏差 (单位:10-4)
Table 3 Mean departure of the evolution of perturbed non-dimensional pressure between the tangent-linear model and the nonlinear model with full physics (unit:10-4)
表 4 切线性模式扰动u风场与包括全物理过程非线性模式扰动场平均偏差 (单位:m/s)
Table 4 Mean departure of the evolution of perturbed u-wind between the tangent-linear model and the nonlinear model with full physics (unit:m/s)
表 5 切线性模式扰动v风场与包括全物理过程非线性模式扰动场平均偏差 (单位:m/s)
Table 5 Mean departure of the evolution of perturbed v-wind between the tangent-linear model and the nonlinear model with full physics (unit:m/s)
表 6 切线性模式扰动比湿场与包括全物理过程非线性模式扰动场平均偏差 (单位:10-4kg/kg)
Table 6 Mean departure of the evolution of perturbed specific humidity between the tangent-linear model and the nonlinear model with full physics (unit:10-4kg/kg)
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