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Shortwave direct aerosol radiative forcing (DARF) is derived at the top of the atmosphere (TOA) and at the surface under clear-sky, cloudy-sky, and all-sky conditions using data of space-borne CALIOP lidar and MODIS sensor. We investigate four scenarios for evaluating the DARF: clear-sky, the case that aerosols exist above clouds, the case that aerosols exist below high-level clouds, and the case that aerosols are not detected by CALIOP in cloudy-sky condition. The cloudy-sky DARF is estimated by the latter three scenarios. The all-sky DARF is the combination of clear-sky and cloudy-sky DARF weighted by the cloud occurrence. They are then compared with DARF calculated by a global aerosol model, SPRINTARS. The results show that the TOA forcing over desert regions caused by dust with single scattering albedo (SSA) of 0.92 is positive regardless of cloud existence, due to high solar surface albedo. Off southern Africa, smoke aerosols with SSA of 0.84 above low-level clouds are observed and simulated and the annual mean TOA cloudy-sky DARF is estimated at more than +3 Wm-2, consistent with past studies. Aerosols with SSA of 0.96 within optically thin clouds cause a TOA negative forcing, while that within optically thick clouds cause a TOA positive forcing. This indicates that aerosols within optically thick clouds cause positive forcing in our radiative transfer calculation, regardless of SSA. Annual zonal averages of DARF from 60 degrees S to 60 degrees N under clear-sky, cloudy-sky, and all-sky are -2.97, +0.07, and -0.61 Wm-2 from CALIOP and -2.78, +1.07, and -0.58 Wm-2 from SPRINTARS.