For large-scale weather systems, Ertel potential vorticity (PV) is a very useful quantity because of its properties of material conservation and invertibility for an adiabatic frictionless flow. However, for meso-or small-scale systems, applications of PV are limited because the baroclinic solenoid term, which characterizes baroclinicity of the atmosphere, is removed in PV. An alternative invariant is the generalized Ertel-Rossby invariant (GERI), which is derived from generalized velocity. GERI not only keeps the property of conservation but also includes helicity and the baroclinic solenoidal term, making it more suitable for analyzing evolutions of meso-and small-scale weather systems. In this study, the authors apply GERI to analyze an extreme heavy rainfall case that occurred in Beijing on 21 Jul 2012. It is showed that GERI exhibits large anomalies, having nearly the same phase as the appearance of the heavy precipitation region. It is concluded that GERI makes it possible to characterize fast mode properties during heavy rainfall because of the important physical information it contains, i.e., helicity, PV, and the effect of the solenoidal term. Therefore, GERI can be used to analyze and reveal the dynamical structure of the lower vortex that induces heavy rainfall, and provides a new dynamical quantity for diagnosing and forecasting regions of heavy precipitation.%在绝热无摩擦大气中，具有守恒性及可反演性的Ertel位涡（PV）在大尺度天气系统分析中有广泛应用。由于忽略了力管项的作用， PV 用于分析中小尺度天气系统演变时受到局限。从广义速度推导得到的广义Ertel-Rossby 不变量（GERI）除了包含有 PV 的守恒性，还包含了螺旋度效应及力管项的作用，对于分析研究快变流型的中小尺度系统演变有一定优势。用GERI分析2012年7月21日北京地区的特大暴雨过程，表明GERI在暴雨区有明显的异常出现，其异常基本与暴雨出现时间同位相，表明GERI的定义涵盖了螺旋度和PV，也包含了暴雨发生时的旋转斜压大气的力管项效应，确实能体现暴雨过程中的流型快变的特点，可以作为独立的变量来分析和揭示造成暴雨的低涡系统的动力结构，为诊断和预报暴雨落区提供新的动力物理量。
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