三次样条函数(格式)准拉格朗日积分方案Ⅰ——准均匀经纬网格样条格式准拉格朗日平流方案与理想场试验  

A quasi- Lagrangian integration scheme with unify finite-difference scheme of cubic spline function transformation, partⅠ: quasi- Lagrangian advection with spline scheme on quasi-uniform latitude-longitude grid and its exact tests

作　　者：辜旭赞[1] 赵军[2] 唐永兰[1] GU Xuzan;ZHAO Jun;TANG Yonglan(Hubei Key Laboratory for Heavy Rain Monitoring and Warning Research, Institute of Heavy Rain, China Meteorological Administration,Wuhan 430074;Institute of Ocean Science and Engineering, National University of Defence Technology, Changsha 410073)

机构地区：[1]中国气象局武汉暴雨研究所暴雨监测预警湖北省重点实验室,武汉430074 [2]中国人民解放军国防科学技术大学海洋科学与工程研究院,长沙410073

出　　处：《暴雨灾害》2016年第6期554-565,共12页Torrential Rain and Disasters

基　　金：国家自然科学基金项目"全球三次样条格式数值模式动力框架与理想场试验研究"(41275106)

摘　　要：研究经纬网格三次样条函数(样条格式)变换准拉格朗日平流方案,推导给出样条格式准拉格朗日预报方程通式,设计一种准均匀经纬网格,对气压、气温、风及广义牛顿力(加速度)场做"经纬网格-准均匀经纬网格"双三次曲面拟合,实现各个变量场在球面上的二阶可导,从而显式迭代插值求得上游点路径与预报变量值,上游点气块被限定在具备样条格式的斜率、曲率和挠率之变量场上运动。为验证样条格式求经纬网格上游点的可行性,采用了国际上通行、有效的一套理想场试验方案:平衡流试验、过极地气流试验和Rossby-Haurwitz波试验,用以检验经纬网格样条格式准拉格朗日平流方案的可行性、一致性、精确性及程序正确性。理想场试验表明,样条格式求上游点预报误差来源于三次样条函数"2阶空间余差"数学误差和上游点路径达不到精确轨迹的截断误差,其累积(积分)误差使得波动振幅变平,而波动位相传播无误差,且误差具有收敛性、球面对称性和单调有界性,同时证明,三次样条函数变换能够解决极区经纬网格点过密和极点奇异的经典问题。In this study, with transformation of cubic spline function (spline scheme) on latitude-longitude grid mapping a quasi-uniform latitude-longitude one, a new explicit quasi-Lagrangian integration scheme is introduced. Adopting the original atmospheric equations of motion,which includes atmospheres in the North Pole and the Sorth Pole, a general forecast equation of spline scheme of space-time second-order differential remainder is derived, that can be used for forecast variables of pressure, temperature, humidity, wind and acceleration (general Newtonian force acting to unit air mass on the rotating Earth). Their bicubic surfaces are fitted on latitude-longitude grid, and every“bicubic surface”field is second-order differentiable. So, the track of a Lagrangian air parcel and its interpolated values can be produced by an explic?it, iterative process, but it goes along a“spline scheme”path with fitted slopes, curvatures and torsions of the variable fields. In order to inspectits feasibility of the dynamic core of spline scheme on latitude-longitude grid, a full set of international current exact tests, i.e. balance flow, cross-polar flow and Rossby-Haurwitz wave flow, are experimented to try its different dynamical formulation and program correctness,and to verify accuracy of the spline scheme and uniformity to other scheme. The test of the balance flow verifies that“cubic motion”compatible with“linear motion”(no Gibbs wave) and the Coriolis force in the atmospheric equation of motion (or in quasi-geostrophic wind field) does no work. The test of the cross-polar flow shows that the geostrophic wind passes correctly polar area, including the South Pole and the North Pole, with transformation of fitting bicubic surfaces to those scalar and vector variables on the spherical quasi-uniform latitude-longitude grid. The test of Rossby-Haurwitz wave flow demonstrates that the measured wind-pressure field could keep shape and phase propagation correct in integration but that the disturbed pressure’s amplitu

关 键 词：三次样条函数 准均匀经纬网格 二阶时空离散预报方程 准拉格朗日平流 理想场试验 

分 类 号：P435[天文地球—大气科学及气象学]