A rainfall that occurred during 0200-1400 Beijing Standard Time (BST) 25 August 2008 shows the rapid development of a convective system,a short life span,and a record rate of 117.5 mm h-1 for Xujiahui station since 1872.To study this torrential rainfall process,the partitioning method of Q vector is developed,in which a moist Q vector is first separated into a dry ageostrophic Q vector (QD) and a diabatic-heating component.The dry ageostrophic Q vector is further partitioned along isothermal lines in the natural coordinate to identify different scale forcing in adiabatic atmosphere,and the large-scale and convective condensational heating in non-uniform saturated atmosphere,convective condensational heating,and Laplace of diabatic heating that includes radiative heating and other heating and cooling processes,are calculated to study the forcing from diabatic heating.The effects of the environmental conditions on the development of the rainfall processes are diagnosed by performing the partitioning of Q vector based on 6-hourly NCEP/NCAR Final Analysis (FNL) data with the horizontal resolution of 1° × 1°.The results include the following:(1) a low-pressure inverted trough associated with the landfall of Typhoon Nuri (2008),a strong southwesterly jet along the western side of the subtropical high,and an eastward-propagating westerly low-pressure trough provide favorable synoptic conditions for the development of torrential rainfall; (2) the analysis of QD vector showed that the upward motions forced by the convergence of QD vector in the lower troposphere (1000-600 hPa) favor the development of torrential rainfall.When QD vector converges in the upper troposphere (500-100 hPa),upward motions in the whole air column intensify significantly to accelerate the development of torrential rainfall; (3) the partitioning analysis of QD vector reveals that large-scale forcing persistently favors the development oftorrential rainfall whereas the mesoscale forcing speeds up the torrential rainfall; (4) the calculations of large-scale condensational heating in non-uniform saturated atmosphere,convective condensational heating,and Laplace of diabatic heating showed that the forcing related to diabatic heating has the positive feedback on the convective development,and such positive feedback decays and dissipates when the convective system propagates eastward and weakens.