摘要
基于半拉格朗日(semi-Lagrangian)方案的数值天气预报模式,求解半拉格朗日轨迹上游点变量,通常采用传统直线逐点拉格朗日多项式插值,由已知模式格点(欧拉网格点)的数值插值获得。对于三维空间上游点的插值,N阶精度需要O(N3)运算量。N增大,运算量将大幅增加,特别耗费计算机机时,而采用Cascade插值法(降阶插值法)则只需要O(N)运算量。它的显著特点是:用曲线代替直线,通过一系列中间过渡网格点,在曲线上用一维拉格朗日插值,使得相邻拉格朗日格点或中间过渡点的插值不再是孤立的,而且可以重复使用某些中间结果,达到减少运算量的目的。将这种方法合理应用于GRAPES模式,并根据模式的特点,对Cascade插值过程中独立变量的距离分段计算,从而有利于实现并行计算。计算结果表明Cascade插值法与传统直线逐点插值法相比,计算效率平均提高约30%,同时不降低精度。
For the numerical weather predicting model （NWM） based on semi-Lagrange scheme, it is not eco- nomical to apply the conventional point by point approach based on Cartesian product of one-dimensional Lagrange interpolation polynomials to evaluate up-stream variables at each integration time step. It takes O（Na） operations to calculate each point. The bigger the N value is, the more accurate the calculation may Become. However, it involves too much calculation. When the method of a Cascade of one-dimensional in- terpolation of the entire data is employed, it requires only O（N） operations. The so-called Cascade method is a highly efficient means of carrying out the grid-to-grid interpolations required by a high-order semi-La- grangian model. It goes like follows： The intersection points between the regular Eularian and curvilinear Lagrangian meshes form hybrid coordinate lines, and some variables of the intermediate points and the tar- get point of the Lagrangian mesh can be interpolated by using one-dimensional curvilinear Lagrange inter- polation method. First, the values of all intermediate points are interpolated. Then, the values of the tar- get points are interpolated from the evaluated intermediate values step by step. The interpolation of the target points is not isolated because the adjoining target point uses shared some intermediate points. Some intermediate results can be repeatedly utilized so that it reduces the amount of computation in interpolation process. GRAPES （Global/Regional Assimilation and Prediction System） is a new generation of numerical weather prediction system of China developed by Research Center for Numerical Meteorological Prediction of CAMS （Chinese Academy of Meteorological Sciences） of CMA （China Meteorological Administration）. It is designed based on the scheme using two time level semi-Implicit time integration and semi-Lagrangian backward trajectories. It is also a fully compressible, non-hydrostatic grid model using latitude and longi- tude, as well
出处
《应用气象学报》
CSCD
北大核心
2009年第2期164-170,共7页
Journal of Applied Meteorological Science
基金
国家自然科学基金项目(40675063
40745033
40675062)
"十一五"国家科技支撑项目"灾害天气精细数值预报及短期气候集合预测研究"共同资助
