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Boundary Layer Coupling to Charney-Phillips Vertical Grid in GRAPES Model
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摘要: 基于K廓线闭合方案，通过考虑不稳定边界层和稳定边界层中热量交换系数在半层上求取及下边界条件的设置，将温湿倾向在整层上直接计算，设计了Charney-Phillips跳点（简称C-P跳点）的边界层方案，使之与GRAPES全球模式的C-P跳点相协调，解决了Lorenz跳点物理过程与C-P跳点动力框架耦合时插值造成的不协调问题，同时避免了耦合时反复插值造成的误差，提高了边界层物理过程参数化方案及其反馈的准确性和合理性。试验表明：C-P跳点边界层方案因为避免了温度和湿度在垂直方向上的插值，消除了温湿变量在垂直方向上的锯齿状抖动，使温湿廓线分布更合理，减小了模式预报误差，形势场的预报效果也得到一定改善。C-P边界层方案的应用提升了GRAPES全球模式的总体预报性能。Abstract: It is an important challenge in numerical weather and climate prediction to obtain accurate coupling between physical parameterization and high resolution dynamic framework. Increased resolution in models and the use of large time-steps in semi-Langrangian advection stress the need for an equally accurate computation in time of the corresponding physical parameterizations and the physics-dynamics coupling on the temporal aspects. Physics-dynamics coupling on spatial aspects also plays a very important role on the accuracy of model predictions, for there is a choice for how to vertically arrange the predicted variables, namely, the Lorenz and Charney-Phillips grids.The physics-dynamics coupling on spatial aspects in GRAPES model is studied. As the Charney-Philips grid is used, the horizontal velocity is staggered relative to potential temperature, which means potential temperature and water substances are calculated at full levels, while horizontal velocity is calculated at half levels. In Lorenz physics scheme, all variables are set at half levels and the correspondent tendencies are estimated at half levels. The interpolation has to be used between full and half levels in physics-dynamics coupling before and after physics scheme package is called. The interpolation error is unavoidable and an unexpected zigzag noise appears because of the second-order difference in PBL (planetary boundary layer) scheme.In C-P PBL scheme, the momentum diffusivity KM is required at full levels and the heat diffusivity KH is required at half levels. It is easy to compute KM and KH in unstable PBL because KM and KH depend on the PBL height and surface variables. For local scheme in stable PBL and free convective atmosphere, diffusivities are functions of local Richardson number which has relation with both potential temperature and horizontal velocity. Here potential temperature gradient is averaged so that Richardson number is calculated at full levels. KM can be calculated at the full level and KH can be averaged at the half level. The boundary condition is given by the surface flux according to the constant flux layer. C-P PBL parameterization is developed to assure the accurate coupling of PBL physics and vertical Charney-Phillips grid.Improvements are detected using C-P PBL parameterization spatial physics-dynamics coupling in GRAPES_GFS model. The zigzag noise of temperature and moisture in PBL is removed and the correspondent profiles appear to be smooth with C-P PBL parameterization. The accuracy of PBL and dynamics coupling is improved, and an overall enhancement is found in the forecast of height and temperature.
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Key words:
- GRAPES model;
- planetary boundary layer;
- Charney-Phillips grid;
- Lorenz grid
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图 1 预报6 h的全球平均边界层过程瞬时位温和湿度倾向廓线(a)位温倾向廓线，(b)湿度倾向廓线
Fig. 1 Global averaged instantaneous potential temperature and moisture tendency profiles for planetary boundary layer (PBL) at 6 h forecast (a) potential temperature tendeny, (b) moisture tendency
图 2 预报6 h的边界层过程瞬时湿度倾向纬向平均(单位：10-4 g·kg-1·s-1) (a)控制试验，(b) C-P边界层方案
Fig. 2 Zonal mean instantaneous moisture tendency for PBL at 6 h forecast (unit:10-4 g·kg-1·s-1) (a) CTRL experiment, (b) C-P PBL scheme
图 3 预报6 h的全球平均温度和湿度廓线(a)位温廓线，(b)湿度廓线
Fig. 3 Global averaged potential temperature and moisture profiles at 6 h forecast (a) potential temperature, (b) moisture
图 4 预报6 h的30°S，60°E点的位温和湿度廓线(a)位温廓线，(b)湿度廓线
Fig. 4 Potential temperature and moisture profiles at 6 h forecast at 30°S, 60°E (a) potential temperature, (b) moisture
图 5 北半球850 hPa温度场的均方根误差检验(a)均方根误差，(b)显著性水平
Fig. 5 The root mean square error of 850 hPa temperature in the North Hemisphere during 1-15 May 2013 (a) root mean square error, (b) significance level
图 6 东亚地区500 hPa温度场距平相关系数对比检验(a)距平相关系数，(b)显著性水平
Fig. 6 The anomaly correlation coefficient of 500 hPa temperature in the North Hemisphere during 1-15 May 2013 (a) anomaly correlation coefficient, (b) significance level
图 7 不同方案积分2 h后的结果(a)整层上的瞬时温度倾向，(b)温度
Fig. 7 Forecast results at 2 h integration (a) temperature tendeny at the full level, (b) temperature
表 1 边界层方案变量在C-P和Lorenz垂直格点上的分布
Table 1 C-P and Lorenz configurations of variables in PBL scheme
垂直层次 C-P Lorenz n=N(上边界) θ, q n=N-0.5 u, v, KH θ, q, u, v ┋ ┋ ┋ n=1.5 u, v, KH θ, q, u, v n=1 θ, q，KM KH, KM n=0.5 u, v, (w′θ′)sKH θ, q, u, v n=0(地表) θ, q, u* w′θ′s, u* 
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