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The effect of changing cloud cover on climate, based on cloud-aerosol interactions, is one of the major unknowns for climate forcing and climate sensitivity. It has two components: (1) the impact of aerosols on clouds and climate due to in situ interactions (i.e., rapid response) and (2) the effect of aerosols on the cloud feedback that arises as climate changesclimate feedback response. We examine both effects utilizing the NASA Goddard Institute for Space Studies ModelE2 to assess the indirect effect, with both mass-based and microphysical aerosol schemes, in transient twentieth century simulations. We separate the rapid response and climate feedback effects by making simulations with a coupled version of the model as well as one with no sea surface temperature or sea ice response (atmosphere-only simulations). We show that the indirect effect of aerosols on temperature is altered by the climate feedbacks following the ocean response, and this change differs depending upon which aerosol model is employed. Overall, the effective radiative forcing (ERF) for the direct effect of aerosol-radiation interaction (ERFari) ranges between -0.2 and -0.6Wm(-2) for atmosphere-only experiments, while the total effective radiative forcing, including the indirect effect (ERFari+aci) varies between about -0.4 and -1.1Wm(-2) for atmosphere-only simulations; both ranges are in agreement with those given in Intergovernmental Panel on Climate Change (2013). Including the full feedback of the climate system lowers these ranges to -0.2 to -0.5Wm(-2) for ERFari and -0.3 to -0.74Wm(-2) for ERFari+aci. With both aerosol schemes, the climate change feedbacks have reduced the global average indirect radiative effect of atmospheric aerosols relative to what the emission changes would have produced, at least partially due to its effect on tropical upper tropospheric clouds.