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.