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Tropical atmospheric waves play a major role in the variability and change of weather and climate in the tropics as well as in the globe. They also interact with other tropical systems such as tropical cyclones (TCs) and El Niño-Southern Oscillation (ENSO). The improved understanding of the tropical waves, such as their origins, their spatiotemporal structures, and their life cycles, can lead to better prediction of weather and climate change in the tropics as well as over many other areas of the globe. Most of the previous diagnoses of observed tropical waves came from two categories: (1) case studies in which individual waves of particular types are examined, leading to scattered information of the spatiotemporal characteristics of these waves; and (2) climatological studies using wavenumber-frequency domain analysis which is not able to identify spatiotemporal inhomogeneity of tropical waves. To fill the gap between these two approaches, we use a recently developed spatiotemporally local analysis method, the multi-dimensional ensemble empirical mode decomposition (MEEMD) method, and known spatial wind structures of different types of waves to systematically extract the evolution information of tropical waves over large temporal and spatial domains. Through further analysis of the extracted wave events, the spatiotemporal inhomogeneity of tropical waves is characterized. In this study, as the very first step toward a comprehensive study, our focus is placed on mixed Rossby-gravity (MRG) waves. The propagation characteristics, period, and horizontal (zonal and meridional) scale of MRG events detected in this study can match with both the theoretical results and observational studies. There are 23 MRG events detected from the 3rd MEEMD component in the year 2002, among which most events occurred over the western Pacific Ocean and fewest MRG events over the Indian Ocean. The phase velocity and meridional scale are largest over the Atlantic Ocean while smallest in the Indian Ocean. The locations and propagation characteristics of MRG events show great spatiotemporal inhomogeneity. After the evolution of MRG events are obtained, they can be connected with TCs. A new hypothesis, which better matches the observation, is proposed that the swelling and westward propagation of MRG wave pattern help the TCs moving westward and toward higher latitudes, which is necessary for TCs to develop at early stage.