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The prediction theories for complex systems with a hierarchical structure and their applications to the climate process are a significant and forward-looking field of research. However, up to the present, they are yet not known and understood very well. This paper presents a preliminary theoretical frame for them. As a normal example, the basic behaviors and the dynamic structure of the climate system arc discussed in detail. The conclusions indicate that the climate system may be considered as a cascade of several subsystems located in different hierarchies. Such a dynamic structure is just the cause resulting in the nonstationarity.The conclusions also indicate that the main barrier of the climate prediction in theory derives from the contrary between the stationarity hypothesis for the current prediction theory and the nonstationary behavior of the real climate process. In addition, some work is discussed for detecting the nonstationarity in climate and other geophysical data and predicting the nonstationary process developed in recent years. These works may construct a preliminary base for applying to the climate predictions.