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A conceptual bulk model for a dry, convective boundary layer with prescribed horizontally homogeneous and heterogeneous low-level radiative cooling rates is developed. For horizontally homogeneous radiative cooling, the response of the system to varying its prescribed parameters is explored and formulated in terms of nondimensional parameters. Large-eddy simulations with prescribed radiative cooling rates match the results of the bulk model well. It is found that, depending on the strength of the surface coupling, the height of the boundary layer (BL) either increases or decreases in response to increasing radiative BL cooling. Another property of the system is that, for increasing surface temperature, the BL temperature decreases if the prescribed radiative BL cooling rates are strong. This counterintuitive behavior is caused by the formulation of the entrainment rate at the inversion. Heterogeneous radiative BL cooling is found to cause a circulation induced by pressure deviations between the area of weak radiative BL cooling and the area of strong radiative BL cooling. Including the feedback of the induced circulation on the BL in a two-column model leads to a modified equilibrium state, in which a weakened horizontal BL flow of about 1ms 21 is maintained for differences in radiative BL cooling rates larger than 1Kday 21. Such a circulation strength is comparable to a shallow circulation caused by surface temperature differences of a few kelvins. Spatial differences in radiative BL cooling should therefore be considered as a first-order effect for the formation of shallow circulations.