Abstract: Using empirical orthogonal function (EOF) expansion, this paper analyzes the Weather Research and Forecasting (WRF) simulative data of the torrential rain occurring on August 25 of 2008 to explore the possibility of EOF expansion for diagnosing a meso-βscale torrential rain system. The conclusions show that when sufficiently fine data are consistent with real data, it is possible to diagnose mesoscale systems with EOF expansion. The preceding three modes of EOF expansion reflect the evolvement characteristics of various-scale weather systems and correspond to various wave trains with various wavelengths and oscillation frequencies: ambient mode, torrential rain system mode, and rain clusters mode. The various waves are attributed to quasi-geostrophic Rossby, quasi-equilibrium eddy, and non-equilibrium gravity inertia waves, respectively. The physical essence of EOF expansion for a weather system is that a transformative weather system with locomotion can be separated to several mutually unattached modes, or wave trains, that differ in physical characteristics, which contributes to a better understanding of the weather system. Scale separation for weather systems is an advantage of EOF expansion because separate weather systems are unattached and have particular physical characteristics. When the space-time indices of different wave trains are in phase lock, a strongly convective precipitation will occur in the appropriate weather condition.