ON THE VERTICAL DISCRETIZATION OF ATMOSPHERIC MODELS—PART Ⅱ:VERTICAL DISCRETIZATION

Two schemes for vertical discretization of the model are proposed,one with equal △lnσ andthe other in terms of Tschebyscheff polynomials.It is proved that in adiabatic and inviscid cases ifthe meteorological elements and related physical quantities are continuous in time and in thehorizontal,the total energy and total mass are conserved within a high approximation respectively,and there is a correct conversion between total kinetic and total potential energy.Numericalcomputations show that the schemes both have high accuracy.For example,in integrating thehydrostatic equation the computational errors of geopotential height resulting from the schemes aremuch less than those resulting from EC79 in a-coordinate.