Radiation calculations in global numerical weather prediction (NWP) and climate models are usually conducted in 3‐hourly time interval in order to reduce the computational cost. This treatment can lead to an incorrect solar radiation at the Earth's surface which could be one of the error sources in modeled convection and precipitation. In order to improve the simulation of the diurnal cycle of solar radiation a fast scheme has been developed based on detailed radiative transfer calculations for a wide range of atmospheric conditions and can be used to determine the surface solar radiation at each model integration time step with affordable costs. This scheme is divided into components for clear‐sky and cloudy‐sky conditions. The clear‐sky component has been described in a companion paper. The cloudy‐sky component is introduced in this paper. The input variables required by this scheme are all available in NWP and climate models or can be obtained from satellite observations. Therefore, the scheme can be used in a global model to determine the surface GHI. It can also be used as an offline scheme to calculate the surface GHI using data from satellite measurements. SUNFLUX scheme has been tested using observations obtained from three Atmospheric Radiation Measurements (ARM) stations established by the U. S. Department of Energy. The results show that a half hourly mean relative error of GHI under all‐sky conditions is less than 7%. An important application of the scheme is in global climate models. The radiation sampling error due to infrequent radiation calculations is investigated using the SUNFLUX and ARM observations. It is found that errors in the surface net solar irradiance are very large, exceeding 800 W m−2at many non‐radiation time steps due to ignoring the effects of clouds. Use of the SUNFLUX scheme can reduce these errors to less than 50 W m−2.