Vertical Integrations of Numerica! Models of the Atmospnere by Expansion of Analytic Vertical Normal Modes
用解析的垂直正规模展开对大气数值模式进行垂直积分

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.