The multiscale tropical deep convective variability in the tropics is examined with 4-month high-resolution deep convection index (I_TBB) during TOGA COARE over the western Pacific and 23 years of global daily outgoing long-wave radiation (OLR). With a systemic view, we attempt to describe the complex phenomenon with succinct parameters known as generalized dimensions associated to the correlation structures embedded in the observed time series, with higher-order dimensions emphasizing extreme convective events. Through the I_TBB, it is found that, over the western Pacific, convective activities of lifetime ranging from ~1 hour to ~21 days may have interdependence across scales that can be described by a series of power laws, hence a spectrum of generalized dimensions. This means, the deep convective variability over the western Pacific has multifractal characteristics. The spatio-temporal features of I_TBB time series is preliminarily examined by changing the spatial domain for averaging. The multifractal features are weakened with increasing strength of spatial averaging but can not be eliminated. The scaling region is further confirmed by the OLR. Furthermore, the OLR time series suggests that a second scaling region beyond the 20-day scaling break exists. Similar scaling behaviors are found in other locations in the tropics such as the Indian Ocean and south America. However, the scaling break varies from one location to another, being shorter than 20 days over the Indian Ocean and longer further east; similarly, the extend of the time-scale within the second scaling region also increases. These may reflect the fact that the perturbations associated with an MJO system are better-defined locally over the Indian Ocean while gradually disperse as the system propagates eastward. However, none of the scaling regions in the geographical locations examined in this work extend to 1 year, setting large-scale tropical climate systems such as the inter-annual variability apart from the sometimes random processes-looking phenomena with time scales shorter than 1 year.