|Tropical waves have relatively large amplitudes in and near convective systems, attenuating as they propagate away from the area where they are generated due to the dissipative nature of the atmosphere. Traditionally, nonlocal analysis methods, such as those based on the Fourier transform, are applied to identify tropical waves. However, these methods have the potential to lead to the misidentification of local wavenumbers and spatial locations of local wave activities. To address this problem, we propose a new method for analyzing tropical waves, with particular focus placed on equatorial mixed Rossby-gravity (MRG) waves. The new tropical wave analysis method is based on the multi-dimensional ensemble empirical mode decomposition and a novel spectral representation based on spatiotemporally local wavenumber, frequency, and amplitude of waves. We first apply this new method to synthetic data to demonstrate the advantages of the method in revealing characteristics of MRG waves. We further apply the method to reanalysis data (1) to identify and isolate the spatiotemporally heterogeneous MRG waves event by event, and (2) to quantify the spatial inhomogeneity of these waves in a wavenumber-frequency-energy diagram. In this way, we reveal the climatology of spatiotemporal inhomogeneity of MRG waves and summarize it in wavenumber-frequency domain: The Indian Ocean is dominated by MRG waves in the period range of 8–12 days; the western Pacific Ocean consists of almost equal energy distribution of MRG waves in the period ranges of 3–6 and 8–12 days, respectively; and the eastern tropical Pacific Ocean and the tropical Atlantic Ocean are dominated by MRG waves in the period range of 3–6 days. The zonal wavenumbers mostly fall within the band of 4–15, with Indian Ocean has larger portion of higher wavenumber (smaller wavelength components) MRG waves.