AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

作     者：辜旭赞 张兵 王明欢 

作者机构：Hubei Key Laboratory for Heavy Rain Monitoring and Warning Research Institute of Heavy Rain China Meteorological Administration 

出 版 物：《Journal of Tropical Meteorology》 (热带气象学报（英文版）)

年 卷 期：2013年第19卷第4期

页      面：388-396页

核心收录：

学科分类：07[理学] 070601[理学-气象学] 0706[理学-大气科学] 

基　　金：National Natural Science Fund(41275106) 

主　　题：numerical forecast and numerical simulation 2nd-order space-time differential remainder numerical model cubic spline functions Navier-Stokes primitive equations quasi-Lagrangian time-split integration scheme global simulation case 

摘      要：In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series *** we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm offitting cubic spline—time step integration—fitting cubic spline—……is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline *** the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical *** is pointed out that the Spline Model has mathematical laws ofconvergenceof the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order ***optimalityof the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original *** addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable ***,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic *** the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,***,a global simulation case of adiabatic,non-frictional andincompressiblemodel atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-calledshallow atmosphereNavier-