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Tropical waves are important tropical and global weather/climate systems as well as carriers for redistributing global energy. For decades, a multitude of tropical wave theories that attempt to explain the origins and maintenance mechanisms of tropical waves and the interactions between them and other tropical systems have been put forth by scientists. Partly due to the lack of effective analysis tools, observational studies of tropical waves have not been comprehensive enough, leaving many of the proposed theories unverified. For example, Fourier spectrum analysis based methods can hardly be used to obtain the accurate climatology of tropical waves because of the impacts of locality. This study serves two purposes: (1) To introduce and develop novel dynamics-based effective methods and to tailor them for isolating spatiotemporally local tropical waves of different spatiotemporal scales; and (2) To shed new insights into the climatological features of tropical waves, such as life cycles, their interactions with other tropical phenomena, and their dynamical implications. To accomplish the first goal, we introduce the multi-dimensional ensemble mode decomposition (MEEMD) method to decompose different meteorological variables. This method is combined with our newly developed optimization methods based on tropical wave theory in this study to form a dynamics based tropical wave diagnosis package. The capability of the new package is validated using both synthetic data and observational data. It is demonstrated that our package has high capability of separating tropical waves of different spatiotemporal scales as well as of different types. With the readiness of the above package, we systematically analyzed characteristic of tropical waves of different types, with emphases being placed on the spatiotemporal structures and their life cycle. It is revealed that all types of tropical waves have significantly different climatological characteristics, from wavenumbers and wave frequencies to their propagating properties. It is revealed that that upper and lower tropospheric tropical waves have distinguishable dynamic characteristics, too different for researchers to adopt a first baroclinic mode structure in the vertical to understand the origin and destiny of various tropical waves. We also quantify the modulation characteristics of high frequency tropical waves by intraseasonal oscillations.