Self-memorization Equation in Atmospheric Motion

Abstract

In view of the fact that the atmospheric motion isan irreversible process, a memory function which can recall observational data in the past is suggested. In terms of defining an inner product in Hilbert space, a new concept of self-memorization in the atmospheric motion is proposed, thus the traditional atmospheric motion equation is generalized to a self-memorization equation in inclusion of multi-time observations. Self-memorization equations of a barotropic nondivergent model and a barotropic primitive equation model are exemplified. It is proved that some existing difference schemes can be derived from the self-memorization equation by giving particular values to memory function. However, it demonstrates that multi-time numerical prediction models can be unified into a framework of self-memorization equation. If a stochastic method in solving the memory function is taken, the selfmemorization equation will be transformed to a sort of dynamic-stochastic prediction model.