We interpret the distribution of tropical tropospheric ozone columns (TTOCs) from the Total Ozone Mapping Spectrometer (TOMS) by using a global 3-D model of tropospheric chemistry (GEOS-CHEM) and additional information from in-situ observations. The GEOS-CHEM TTOCs capture 44% of the variance of monthly mean TOMS TTOCs from the convective cloud differential method (CCD) with no global bias. Major discrepancies are found over northern Africa and South Asia where the TOMS TTOCs do not capture the seasonal enhancements from biomass burning found in the model and in aircraft observations. A characteristic feature of these northern tropical enhancements, in contrast to southern tropical enhancements, is that they are driven by the lower troposphere where the sensitivity of TOMS is poor due to Rayleigh scattering. We develop an efficiency correction to the TOMS retrieval algorithm that accounts for the variability of ozone in the lower troposphere. This efficiency correction increases TTOCs over biomass burning regions by 3-5 Dobson Units (DU) and decreases them by 2-5 DU over oceanic regions, improving the agreement between CCD TTOCs and in-situ observations. Applying the correction to CCD TTOCs reduces by ~5 DU the magnitude of the "tropical Atlantic paradox" [Thompson et al., 2000], i.e. the presence of a TTOC enhancement over the southern tropical Atlantic during the northern African biomass burning season in December-February. We reproduce the remainder of the paradox in the model and explain it by the combination of upper tropospheric ozone production from lightning NOx, persistent subsidence over the southern tropical Atlantic as part of the Walker circulation, and cross-equatorial transport of upper tropospheric ozone from northern mid-latitudes in the African "westerly duct". These processes in the model can also account for the observed 13-17 DU persistent wave-1 pattern in TTOCs with a maximum over the tropical Atlantic and a minimum over the tropical Pacific during all seasons. The photochemical effects of mineral dust have only a minor role on the modeled distribution of TTOCs, including over northern Africa, due to multiple competing effects. The photochemical effects of mineral dust globally decrease annual mean OH concentrations by 9%. A global lightning NOx source of 6 Tg N yr-1 in the model produces a simulation that is most consistent with TOMS and in-situ observations.