This paper presents decadal simulations of stratospheric and tropospheric aerosol and its radiative effects by the chemistry general circulation model EMAC constrained with satellite observations in the framework of the ESA Aerosol CCI project such as GOMOS (Global Ozone Monitoring by Occultation of Stars) and (A)ATSR ((Advanced) Along Track Scanning Radiometer) on the ENVISAT (European Environmental Satellite), IASI (Infrared Atmospheric Sounding Interferometer) on MetOp (Meteorological Operational Satellite), and, additionally, OSIRIS (Optical Spectrograph and InfraRed Imaging System). In contrast to most other studies, the extinctions and optical depths from the model are compared to the observations at the original wavelengths of the satellite instruments covering the range from the UV (ultraviolet) to terrestrial IR (infrared). This avoids conversion artifacts and provides additional constraints for model aerosol and interpretation of the observations. MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) SO2 limb measurements are used to identify plumes of more than 200 volcanic eruptions. These three-dimensional SO2 plumes are added to the model SO2 at the eruption times. The interannual variability in aerosol extinction in the lower stratosphere, and of stratospheric aerosol radiative forcing at the tropopause, is dominated by the volcanoes. To explain the seasonal cycle of the GOMOS and OSIRIS observations, desert dust simulated by a new approach and transported to the lowermost stratosphere by the Asian summer monsoon and tropical convection turns out to be essential. This also applies to the radiative heating by aerosol in the lowermost stratosphere. The existence of wet dust aerosol in the lowermost stratosphere is indicated by the patterns of the wavelength dependence of extinction in observations and simulations. Additional comparison with (A)ATSR total aerosol optical depth at different wavelengths and IASI dust optical depth demonstrates that the model is able to represent stratospheric as well as tropospheric aerosol consistently.