初论双三次数值模式  

Introduction to Bicubic Numerical Model

作　　者：辜旭赞[1] 张兵[1] 

机构地区：[1]中国气象局武汉暴雨研究所,武汉430074

出　　处：《气象科技》2006年第4期353-357,共5页Meteorological Science and Technology

摘　　要：讨论在数学Rn空间里,存在孔斯双三次曲面拟合的可能数值模式(以下称双三次数值模式)。双三次数值模式特点是,在诊断上对天气系统中的由各个物理定律表述的(离散点)大气物理量场,可通过数学三次样条函数做双三次曲面拟合,则模式大气(包括天气系统)的各个物理量场均达到二阶可导,即是大气运动方程中的各个物理量场都存在各自的一、二阶空间微商,从而可以对模式大气与天气系统做时间积分。与有限差分模式和谱模式存在所谓的空间截断误差和波数截断误差相比较,双三次数值模式存在所谓的空间拟合误差,恰是现行有限差分模式空间截断误差的高阶小量。而双三次数值模式具有谱模式准确计算空间微商的优点,且双三次数值模式的数学构架能够较好地适应大气运动动力框架,是可与有限差分模式和谱模式相比较的另一数值分析新算法的气象数值模式。A conceivable Blcubic Numerical Model （BINM） is studied, which is used to fit the cubic curve function （spline） and the Coons Bicubic Surface. It is like fitting the three-dimension curved surface with a set of bicubic surface patches at the horizontal and vertical directions, on which many atmospheric physical quantity fields are all cubic continuous. So BINM is a new numerical model used to fit n bicubic surfaces in the mathematic R^n-space and the n squares of atmospheric quantity fields in the atmosphere, getting their all cubic continuous fields with their derivative, square derivative quotients. One of BINM＇s main mathematical characteristics is that the special differential quotients of the basic system of equations have their analytical solutions for the atmospheric kinematics, if the synoptic systems can be embodied by the ＂bicubic surface＂ of mathematics. Different from the finite-difference （linear） model and the truncated spectral model, which have their special and wave-number truncation error correspondingly, BINM has its special fitting error only. A computing case is given with a linear advection equation on the spherical coordinates, which is an air pressure field at sea level in a limited area, and got successfully its 6 hour forecast field with a time step of 12 seconds （1800 steps）. So, it is concluded that BINM＇s mathematical truss can adapt to the physical packages of the atmosphere; BINM may be the third kind of meteorological numerical forecast model and may be superior to our linear model and spectral model.

关 键 词：三次样条函数 双三次曲面拟合 双三次数值模式 

分 类 号：O241.82[理学—计算数学] U412.34[理学—数学]