Instruments that measure UV/visible scattered light from the Earth's limb are emerging as an important class of sensors capable of providing high-quality profiles of aerosols and trace gases from the upper troposphere to the mesosphere. Critical to the inversion of limb scatter observations is the forward radiative transfer model. A fast and accurate radiative transfer model, VECTOR (Vector Orders-of-scattering Radiative transfer model), is presented that is able to account for the diurnal variation of species such as NO2 and BrO along the observing line of sight and the incoming solar beam. VECTOR has been used to quantify for the first time diurnal effect errors in NO2 and BrO with application to OSIRIS (Optical Spectrograph and Infra-Red Imager System) and SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography), two limb viewing satellite instruments. For a solar zenith angle near 90¿ at the tangent point, errors can exceed 50% for NO2 and 100% for BrO in the lower stratosphere, with the largest errors generally occurring when viewing across, and at large angles to, the terminator. These results applied to OSIRIS NO2 and SCIAMACHY BrO reveal that diurnal effect errors are generally small (<10%). Yet 1 out of every 6 OSIRIS NO2 profiles experiences large (10--35%) errors and 1 out of every 11 SCIAMACHY BrO profiles experiences large (10--100%, or larger) errors in the lower stratosphere.