Abstract: The concept of message approximate system for the long time evolution of dissipative system has been first proposed.The method of macro-descriptiop for the horizontal structure of long-range weather anomaly evolution given in this paper is used to study northern hemisphere 500hPa monthly mean anomaly data.The results show that the 500 hPa monthly mean anomaly field can be expressed by message approximate anomaly field which consists of a few points.The message approximate system not only slicked out the main information of anomaly evolution of long-range weather,but also filtered the "climate noise".It is believed that the concept and method will be helpful to establish effective long-range numerical forecast model.