用解析的垂直正规模展开对大气数值模式进行垂直积分

Vertical Integrations of Numerical Models of the Atmosphere by Expansion of Analytic Vertical Normal Modes

本文提出了一个用大气自由振荡解析的垂直正规模为正交函数系构成一个完备的Hilbert空间,利用广义Fourier展开的概念,在垂直方向进行广义Fourier展开,对大气数值模式进行垂直积分.我们利用两组垂直正规模为正交函数系.第一组是等温大气的垂直正规模;第二组是多元大气的垂直正规模,并用变系数的一维平流方程进行试验积分,将积分结果与差分法、有限元法、Legendre多项式展开的结果进行比较.比较的标准是它们与解析解的均方根误差和相关系数.

This paper develops a technique of vertical integrations of numerical models of the atmosphere using generalized Fourier expansion in which orthogonal functions are analytic vertical normal modes, that construct a complete Hilbert space, two systems of vertical normal modes are used. One is in the isothermal atmosphere and the other is in the polytropic atmosphere. One dimension advection equation with variable advection velocity is integrated in vertical direction. Results of analytic vertical normal mode expansion are compared with that of the finite-difference, finite - element methods and Legendre polynomial expansion in root mean square error and correlation from analytic solution.