A fast scheme for estimation of the instantaneous direct solar irradiance (DSI) at the Earth's surface is developed based on detailed radiative transfer calculations for the full range of atmospheric conditions. The parameterisation is divided into the components for clear sky and overcast conditions. For the clear sky condition, the effects of absorption due to water vapour, carbon dioxide and ozone on the DSI are explicitly treated. The effects of Rayleigh scattering, aerosols are also treated on a physical basis. Based on the clear sky results, the transmittances due to effects of clouds are determined for both liquid and ice clouds. The results are parameterised in terms of cloud visible optical depth. The input variables required for determination of DSI include precipitable water, column ozone amount, CO2 mixing ratio, aerosol optical depth, cloud visible optical depth, surface pressure and solar zenith angle. These variables are all available in numerical weather prediction (NWP) forecast models or can be obtained from satellite observations. Therefore, the scheme can be used to determine the DSI using NWP model products or satellite data. The scheme has been tested using the observations obtained at three stations of the US Department of Energy Atmospheric Radiation Measurements (ARM) program. The relative mean bias differences under clear-sky and all-sky conditions are better than 3.2% and 5.1%, respectively. The correlation coefficients between modelled results and observations are all greater than 0.99. The sampling errors of DSI due to the use of 3-hourly or 1-hourly low frequency in radiation calculations in NWP models are evaluated using the fast scheme and ARM observational data. It is found that these errors can be greater than 800 W m(-2) for many cases where sky condition changes from clear to overcast. Application of the current scheme can reduce these errors to less than 100 W m(-2). (C) 2012 Elsevier Ltd. All rights reserved.