Evidence for widespread nonuniform vertical mixing of dust in Mars's tropical atmosphere (in the form of features called "detached dust layers" or DDLs) is a challenge for atmospheric modeling. We characterize the seasonal, diurnal, and geographic variability of DDL activity in retrievals from observations by the Mars Climate Sounder onboard Mars Reconnaissance Orbiter. We find that dust injection above the boundary layer, which forms DDLs, is a spatially ubiquitous phenomenon in the tropics during the daytime, implying that it has a significant nontopographic component. DDL formation is more intense in northern spring and summer than in southern spring and summer but is still common when the zonal average dust distribution appears uniformly mixed. DDLs do not appear to follow the upwelling associated with Mars's Hadley circulation or the extant climatology of local dust storm activity in the tropics. Geographic variability in the nightside vertical dust distribution does not always correlate with the dayside vertical dust distribution, implying that there is spatial and seasonal variability in the efficiency of dust deposition/removal processes. Nighttime dust removal is especially efficient over the Tharsis Montes during northern spring and summer, which suggests some association between water ice clouds and removal. Intense injection combined with efficient removal results in a high amplitude of diurnal variability in the dust distribution at 15-30 km above the surface of the tropics during much of the Martian year.