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基于大气运动是一种不可逆过程的观点,引进了忆及过去时次资料的记忆函数。通过定义Hilbert空间中的内积,导出了大气运动的自忆性概念,从而把通常的大气运动方程推广为包含多时次观测的自忆性方程。作为示例,文中给出了正压无辐散模式和正压原始方程模式的自忆性方程。 文中证明了现存的若干差分格式可以通过给记忆函数以特殊值而从自忆性方程中导出,论证了现有的多时次数值预报模式可以统一在自忆性方程的框架中。在求记忆函数时若采用随机型方法,就可使自忆性方程变为一种动力-统计预报模型。
Based on the notion that atmospheric motion is an irreversible process, memory functions that recall past-time data have been introduced. By defining the inner product in Hilbert space, the concept of self-recall of atmospheric motion is derived, which generalizes the ordinary atmospheric motion equation to a self-remembering equation with multiple time-history observations. As an example, self-remembering equations for positive pressure non-divergence mode and positive pressure original equation mode are given. The paper proves that some existing differential schemes can be derived from self-recall equations by giving special values to memory functions. It is demonstrated that the existing multi-times numerical prediction models can be unified in the framework of self-recalling equations. When using random method to find memory function, self-remembering equation can be changed into a dynamic-statistical forecasting model.