Abstract: After the A_mk forecast equation being derived and physical significance of theeach term being discussed in detail,the author point that the A_mk forecast epuation may be substitute entierly for vorticity equation used to study and forecast the generation, development and motion of synoptic system in different latitude zone. It's superniority is following:1. We may hold that advection dynamic condition causeed generation and development of weather system is special example that all terms are equale zero,which are the production term, the release term, the velocity term of vapour condensation and the change term of efficiency factor in the A_mk forecast equation.2. It is favored research relation between them to combine the process of dynamic and thermodynamic macrocosmic physical with process of micro physical of velocity of which cloud precipitation is condeensated.3. The paper have given the criterion condition of generation and development such weather system as typhoon etc.4. When we integrate the moist air dynamic equation system which is composed of the A_mk forecast equation and the motion equation, it may be expected to increase accurace of forecasting generation, development and migration of weather system in lower latitude zone, and to provided a new model of nunerical forecast for lower latitude and heavy-rain.