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Application of the Correction Algorithm to Mass Conservation in GRAPES_GFS
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摘要: 如何在长时间积分的过程中保证模式大气的质量守恒是数值模式动力框架面临的基本问题之一，对于半拉格朗日动力框架来说, 在理论上要满足质量守恒面临着诸多的困难，质量订正方案不失为一种简单可行的选择。中国气象局数值预报中心的GRAPES_GFS (Global-Regional Assimilation and PrEdiction System, Global Forecast System) 在长时间积分过程中质量损失问题较为明显，该研究工作借鉴C-CAM (Climate-Community Atmosphere Model) 中对地面气压进行订正控制模式质量守恒的思路，在GRAPES_GFS中开发了一种对每个网格内的质量按照不同权重系数进行调整、控制模式大气总质量守恒的算法。经过一系列的试验，验证了该方法在GRAPES_GFS中的可行性，在保证模式质量守恒的情况下可有效减小高度场的预报偏差，缓解模式预报结果中天气系统偏弱的问题，在实际业务预报中有一定应用价值。
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关键词:
- GRAPES_GFS;
- 质量守恒;
- 半拉格朗日
Abstract: The conservation of mass is very important for the dynamic core of numerical model, especially for climate simulation or medium and long term prediction. For the traditional semi-Lagrangian dynamic core, it is difficult to satisfy the mass conservation theoretically, the finite volume method can be used in the semi-Lagrangian continuous equation to satisfy the mass conservation in theory, but the practical application is more complex, and no operational center adopt the method at this time. On the other hand, the traditional semi-Lagrangian method combined with a simple and easy mass correction algorithm is also a good choice.The GRAPES_GFS (Global-Regional Assimilation and PrEdiction System, Global Forecast System) of Numerical Prediction Center of CMA (China Meteorological Administration) faces a problem that the mass loss is obviously in the process of long term integration. The global mean sea level pressure drops about 1 hPa in 10-day run, due to the choice of the continuity equation and the calculation accuracy of the dynamical core. In the early times of development, there is a very simple mass correction algorithm in GRAPES_GFS, however, in the process of batch testing of the system in 2013, it is found that this algorithm will lead to the increase of the height bias at the top level of the model, so the algorithm is closed.Ideas of C-CAM (Climate-Community Atmosphere Model) model are drawn on, to achieve mass conservation through the correction of surface pressure. A method is developed adjusting mass in each grid box according to different weight coefficient, with the basic idea of modifying more in the grid boxes which have larger changes in mass while less in those with smaller changes. The feasibility of this method is verified by a series of experiments, including ideal test, real case prediction and a batch of cycle prediction, illustrating that the method can effectively reduce the bias of height field under the premise of ensuring the mass conservation, and alleviate the problem of underestimating weather systems. It shows that this method has a certain application value in actual operational forecast, and be further studied in calculating the weight coefficient of each point. It can reduce the bias of the height field at the top level of the model, as well as the high latitude in the Southern Hemisphere.-
Key words:
- GRAPES_GFS;
- mass conservation;
- semi-Lagrangian
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图 1 积分180 d过程中模式总质量相对于初始时刻的变化
Fig. 1 The change of total mass during the 180-day integration
图 3 Sen_phyon试验积分1 h时刻单步调整的Exner气压 (填色)
(a) 模式面第15层 (箭头为水平风场, 单位：m·s-1), (b) 纬向平均的垂直剖面 (线条为垂直速度场, 单位：m·s-1)
Fig. 3 The magnitude of the adjusted Exner function for the Sen_phyon test after 1-hour integration (the shaded)
(a) the fifteenth model layer (arrow is the horizontal wind field, unit：m·s-1), (b) vertical profiles of zonal mean (contour is the vertical velocity field, unit:m·s-1)
图 4 积分72 h后试验Ctr_phyon和Sen_phyon差异的纬向平均垂直剖面
(a) 高度场，(b) 温度场
Fig. 4 The vertical profile of zonal mean of the difference between Ctr_phyon and Sen_phyon after 72-hour integration
(a) height field, (b) temperature field
图 5 北半球高度场均方根误差平均值随时间演变 (单位: gpm)
(a) Ctr2, (b) Sen2相对于Ctr2的差异
Fig. 5 The evolution of the height field mean square error in the Northern Hemisphere with the time (unit:gpm)
(a) Ctr2, (b) difference of Sen2 with respect to Ctr2
图 6 高度场第5天的预报相对于FNL分析场偏差的纬向平均垂直剖面 (单位: gpm)
(a) Ctr2, (b) Sen2
Fig. 6 The zonal mean vertical profile of the height bias for the fifth day with respect to the FNL analysis (unit:gpm)
(a) Ctr2, (b) Sen2
图 7 高度场第5天预报相对于FNL分析场偏差的500 hPa平面图 (a) Ctr2, (b) Sen2
Fig. 7 500 hPa height bias for the fifth day with respect to the FNL analysis (a) Ctr2, (b) Sen2
图 8 高度场的预报相对于分析场的距平相关系数
(a) 北半球, (b) 南半球
Fig. 8 The hight anomaly correlation coefficient for the cycle test
(a) the North Hemisphere, (b) the South Hemisphere
图 9 平均的5 d预报的500 hPa高度场 (单位: dagpm)
Fig. 9 Averaged 5-day forecast of 500 hPa height field (unit:dagpm)
表 1 3组试验的说明
Table 1 Instructions for the three groups of tests
试验分类 试验名称 积分时长/d 试验说明 理想试验 Ctr1 180 Rossby_Haurwitz波 Sen1 180 Ctr1及质量订正 实际个例预报试验 Ctr_phyoff 30 实际个例，关闭物理过程 Ctr_phyon 30 实际个例，打开物理过程 Sen_phyoff 30 Ctr_phyoff及质量订正 Sen_phyon 30 Ctr_phyon及质量订正 批量循环预报试验 Ctr2 8 批量循环预报试验 Sen2 8 Ctr2及质量订正 
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