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Moist Potential Vorticity Anomaly with Heat and Mass Forcings in Torrential Rain Systems

The moist potential vorticity (MPV) equation is derived from complete atmospheric dynamic equations with both heat and mass forcings, with which the impermeability theorem of the ``MPV substance'' is proven. It is clarified that both heat and mass forcings induced by the intensive precipitation in torrential rain systems can lead to the MPV anomaly. The MPV substance anomaly is a dynamical tracer for tracking a torrential rain system.