向量场的经验正交展开及其应用
THE EMPIRICAL ORTHOGONAL EXPANSION FOR A VECTOR FIELD AND ITS APPLICATION TO METEOROLOGY
-
摘要: 本文提出了一种向量场经验正交展开的方法。我们对N×T个离散点上的向量所构成的一个N×T维矩阵,设法寻找一组称为经验正交函数的向量,使其中每一个分量都在均方意义下最接近矩阵的每一列。这组向量可以从特征方程确定。对于有N列元素的矩阵(注意每一个元素都是一个向量),有不少于N个经验正交函数分量。用这些分量所作向量场的正交展开级数收敛很快。给出的展开实际例子说明:向量场经验正交展开,可以比一般标量场经验正交展开,取得更好的效果。Abstract: In this paper, a method of empirical orthogonal expansion for a vector field is proposed. The vector values at N×T points form a N×T matrix. We can find the vector empirical orthogonal functions which approximate each column of the matrix more accurately in the Iight of root mean square error. This can be done by solving a complex eigen-value problem. There are N empirical orthogonal functions for a matrix of N columns. The meteorological vector field may be expanded into its empirical orthogonal functions. Examples of such vector expansion are given in this paper. It has been clearly shown that better results can be obtained by vector expanison as compared with ordinary scalar expansion.
-
-
郑庆林,杜行远,使用多时刻观测资料的数值顶报新模式,数值预报和数理统计预报会议论文集,科学出版社,1974. 章基嘉、孙照渤、陈松军,对自然正交函数稳定性条件的讨论,气象学报,39, No.1, 82-89 1981. 许乃欲、张家诚、赵潦,北太平洋海表温度距乎场变化因子与大气环流关系的初步研究,海洋学报2, No.1,17-32, 1980. Flattery, T., Spectral models for global analysis and forecasting. Proc. Sixth AWS Technical Exchange Conf., U. S. Naval Academy, 1970, Air Weather Serviee Technical Report 242, 92-54,1971.
Holmostrom, L, On empirical orthogonal functions and variational methods, Workshop on the use of e. o. f. in Meteorology, ECMWF, 21-26, 1977.
Karhila, V. and J., Rinne, Determination of empirical orthogonal functions from a large sample, Workshop on the use of e. o. f. in Meteorology, ECMWF, 84-96, 1977.
Harnett, T. P., The principal time and space scales of the Pacific trade wind fields, J. Atmos.Sci., 34, 221-235, 1977.
中央气象局研究所二室,二维数在天气预报中的应用(油印本)1973. 中央气象局研究所二室,副热带高压主体的长期预报(油印本),1973. 中央气象局研究所二室,台风登陆地点、时间和源地的年度预报(油印本),1973. Hardy, D. M, and J. J. Walton, Principal components analysis of vector wind measurements,J. Appl. Meteor., 17, 1153-1162, 1978.
Hardy, D. M., Empirical eigenvector analysis of vector observations, Geophs. Res. Lelt., 4,319-320, 1977.
Eberlein, P, J., Solution to the coraplex eigenproblem by a norm reducing jacobi type method,Numer, Math., 14, 232-245, 1970.
亚历山大洛夫等,数学—它的内容、方法和意义—第三卷,科学出版社,1962.
计量
- 文章访问数: 1847
- HTML全文浏览量: 5
- PDF下载量: 2507
下载:
