对于复杂地形下暴雨这一普遍性难题，由于采用等压坐标存在对流层低层等压面与地面相交的问题，从而不能准确分析和预报山地暴雨强度和移动。为了提高复杂地形条件下的暴雨预报技巧，有必要发展一套地形追随坐标系下的暴雨预报方法，既能够将地形影响直接体现在物理量中，又能够避免局地等压坐标中因地形导致的不同区域动力分析的差异性。本文以集合动力因子暴雨预报方法中的二阶湿位涡为例，对地形追随坐标系下的动力暴雨预报进行了研究和尝试，推导了二阶湿位涡在地形追随坐标系下的数学形式，再通过个例分析及与等压坐标下二阶湿位涡的对比，探讨了地形追随坐标系下的二阶湿位涡所包含的物理信息及其改进降水预报的可能性；进一步，引入相似法，对在地形追随坐标系下利用二阶湿位涡定量预报降水进行了预报检验，检验结果表明：在连续两年夏季降水预报的评估中，以地形二阶湿位涡为基础的降水订正预报评分高于模式原始预报降水评分。

For the general problem of rainstorm under complex terrain，the use of isobaric coordinates can not accurately analyze and predict the intensity and movement of mountain rainstorm due to the intersection of the lower troposphere isobaric surface and the ground. In order to improve the rainstorm prediction level under complex terrain conditions，it is necessary to develop a set of rainstorm prediction methods under the terrain following coordinate system，which can not only directly reflect the terrain impact in physical quantities，but also avoid the differences in dynamic analysis of different regions caused by terrain in local rectangular coordinates or isobaric coordinates. Taking the second-order moist potential vorticity in the ensemble dynamic factor heavy rainfall forecasting method as an example，this paper studies and attempts dynamic heavy rainfall forecasting under the terrain-following coordinate system. It derives the mathematical form of the second-order moist potential vorticity in the terrain following coordinate system，and then explores the physical information contained in the secondorder moist potential vorticity in the terrain following coordinate system and the possibility of improving the precipitation forecast through case analysis and comparison with the second-order moist potential vorticity in the iso‐ baric coordinate system. Furthermore，the analog method is introduced to conduct forecast verification on quantitative precipitation forecasting using the second-order moist potential vorticity in the terrain-following coordinate system. The verification results show that in the ETS score of summer precipitation forecast in 2016 and 2017， The score of precipitation similarity correction method based on topographic second-order moist potential vorticity is higher than that of original forecast precipitation of GFS model.