Calculations of the spectral transmittance of the atmospheric aerosol, using Mie theory, for wavelengths between 0 and 40 mu m is presented. The chemical composition of the aerosol particles has been modelled in order to correspond to the atmospheric conditions of medium and large coastal or near coastal cities with important industrial and other anthropogenic emission sources. Individual size distributions and optical properties for each aerosol constituent have been considered. Based on the detailed aerosol model, and using parameterization techniques, analytical broadband aerosol transmission functions for the absorption and total attenuation are obtained. The accuracy of the proposed expressions are verified with various tests, using data from the National Observatory of Athens (NOA). The proposed broadband aerosol transmission functions can be incorporated directly into solar radiation models to predict accurately the beam, diffuse and global solar radiation at a given place.