Abstract: An accurate form of the moist potential vorticity (MPV) equation was deduced from a complete set of primitive equations system.It was shown that motion in a saturated atmosphere without diabatic heating and frictional dissipation conserves moist potential vorticity. This property was then used to investigate the development of vertical vorticity in moist baroclinic Processes.Results show that in the frame work of moist isentroPic coordinate,vorticity development can result from reduction of convective stability,or convergence,or latent heat release in isentropic surfaces.However,the application of the usual analysis of moist isentropic potential vorticity 15 limitted due to the declination of moist isentropic surfaces,and atheory of slantwise vorticity development based on Z-coordinate and P-coordinate was then proposed. According to this theory,whether the atmosphere 15 moist symetrically stable or unstable,or convectively stable or unstable,50 long as the moist insentropic surface 15 slantwise the reduction of convective stability,the increase of the vertical shear of horizontal wind or moist baroclinity can result in the increase of vertical vorticity.The larger the declination of the moist isentropes,the more vigorous the deveolopment of vertical vorticity.Ina region with a monsoonal front to the north and warm and moist air to the south,or bye the north of front the moist isentropes are very stiff.This 15 the region most favorable for the develoPment of vorticities and formation of torrential rain. For a case of Persistent torrential rain occuriny in the middle and lower reaches of the Yangtze and Huai River in June 12-15,1991,moist potential vorticity analysis,especially the isobaric analysis of its vertical and horizontal compoments,i e.MPVI and MPVZ respectively,is effective for inaentifying synoptic systems not only in middle and high latitudes,but also in the low latitudes and in the lower troposphere.It can serve as a powerful tool for the diagnosis and Prediction of torrential rain.