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.

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.