Soil aeolian erodibility is the efficiency with which soil produces dust for a given meteorological forcing. Quantifying soil erodibility is crucial for forecasting dust events and the climatological distribution and forcing of dust. We use long-term station observations and satellite indices of mineral dust to ascertain the role of regional topography, geomorphology, and hydrology in controlling sediment availability and erodibility. Our null hypothesis is that soil erodibility is globally uniform, so that emissions are determined by instantaneous local meteorology, vegetation, and soil moisture. We describe and quantify three competing hypotheses on regional processes which may affect local soil erodibility: (1) Erodibility is characterized by the relative elevation of source regions in surrounding basins. (2) Erodibility is characterized by the upstream area from which sediments may have accumulated locally through all climate regimes. (3) Erodibility is characterized by the local present-day surface runoff. These hypotheses are tested in 3-year simulations of the global Dust Entrainment and Deposition (DEAD) model. All three spatially varying erodibility hypotheses produce significantly better agreement with station and satellite data than the null (Uniform) hypothesis. The Uniform hypothesis explains none of the spatial structure of emissions in Australia. Heterogeneous erodibility may explain up to 15--20%, 15--20%, and 50% more of the spatial structure of dust emissions than Uniform erodibility in the Sahara+Arabian Peninsula, East Asia, and Australia, respectively. The Geomorphic erodibility hypothesis performs best overall, but results vary by region and by metric. These results support the hypothesis that dust emission hot spots exist in regions where alluvial sediments have accumulated and may be disturbed. Our physically based erodibility hypotheses help explain dust observations in some regions, particularly East Asia, and can be used to help discriminate between natural and anthropogenic soil emissions.