A Mathematic Model of Climate Dynamics Suitable for Modern Mathematical Analysis
一个可供现代数学分析研究的气候动力学模型

With elimination of some approximations or assumptions which exist in the past mathematic models of weather and climate dynamics for mathematical analyses, a new mathematic model for modern mathematical analyses is developed in this paper. This model is closer to those which are applied to the practical predictions of weather and climate. (a) Its top is selected at p (pressure)=0 rather than p>0; (b) the model includes an explicit prediction of surface pressure with horizontal smoothing operator (representing the turbulent diffusion of density), and eliminates the approximation of verticially integrated nondivergence; and (c) the heating is caused by internal sources depending on the atmospheric motion rather than by an external one, and the internal heating function due to the phase change of water vapor is approximated by some properly analytical functions suitable for mathematical analyses. The corespondent boundary and initial conditions are also proposed. This paper is to prove the existence of solution to the problem (equations plus boundary and initial conditions). The general structure and long-term behaviors of the model are to be investigated in the next step.