The system boundary which plays a role in:Ι defending the existence of the system; and Ⅱ exchanging between the system and its environment is defined as a shell (Jieke).Some basic concepts in Jieke theory are described.Some applications of the theory are presented too, in particular,considering switch function of the gate in system, a new discrete logistical model is established.Mapping calculation for the model was conducted.Then nonlinear features of the model with parameter variation were analyzed and irrational numbers and cyclic small numbers are obtained.

The effects of stochastic forcing on air-sea interaction, energy baiance ciimate modei is considered.The noniinear source is dynamicai heat transport.The roie to coupiing different temporai and spatiai scaies of the atmosphere is examined.A stochastic dynamicai modei of air-sea interaction is derived via the Fokker-Pianck eguation (FPE).The FPE from statisticai mechanics is used to obtain a time evoiution of the probabiiity density function and the ciimatic potentiai function.The matrix-continued fraction method (MCFM) is appiied to get the soiution with which effect of greenhouse gases was caicuiated.As a resuit, sea surface temperature rises by 1.2 K,meanwhiie the basic period is about 3~4 years and becomes ionger on doubiing CO₂.

By virtue of non adiabatic thermodynamic and the moisture balance equations of the atmosphere, a mathematical model is presented for the short range climate, which is composed of difference-integration equations with variables: surface temperature, precipitation and height at 500 hPa, on the basis of the self-memorization principle of the atmosphere. The memorial coefficients in the model are estimated by utilizing the meteorological data in summer (June, July, August)in 1951 to 1985. This model was used to give the hindcasts of the temperature and precipitation in summer for the lead time 1986 to 1992.

The TKE (Turbulent Kinetic Energy) closure scheme with 1(1)/(2) order precision and the method of reducing vertical layers are used to decrease computing amount. Modelling results agree well with observations. Compared with results of 3 order closure schemes, there is no obvious reduction of precision. This scheme provides the possibility of inducting and improving the precision of PBL parameterization in three dimensional atmospheric models.

As weather forecasting is summed up as a problem of evolution of meteorological field, a forceasting model is derived by using a statistic discretization for the time differential term in a partial differnetial equation. Medium-range and month weather forecasting experiments are made with dynamic-stochastic difference schemes of barotropic model and two-layer baroclinic model respectively, forecast accuracy of models is comparable to a mumerical model.