Improving the precision of ground-based astronomical observations is an objective of both current (e.g. PanSTARRS1) and future (e.g. Dark Energy Survey and the Large Synoptic Survey Telescope) sky surveys. An important element of this effort is to determine the optical attenuation imposed by the atmosphere. We have obtained atmospheric extinction observations from narrowband photometry (typically 10 nm bandwidth) at central wavelengths of 380 nm, 488 nm, 500 nm, 585 nm, 656 nm, 675 nm and 840 nm. The passbands were selected to measure the continuum component (predominantly from Rayleigh and aerosol scattering) of atmospheric attenuation, and to avoid molecular absorption features in the atmosphere. We compare these atmospheric extinction observations with predictions from MODTRAN5, a commonly used computer model of atmospheric optical transmission. The MODTRAN5 calculations were informed by a satellite-based determination of atmospheric ozone on the night of observations. We also adjusted the MODTRAN5 predictions of Rayleigh scattering to account for the difference between the default pressure and that measured at the observatory on the night of observations. We find excellent agreement across all passbands between the pressureadjusted MODTRAN5 extinction model and the observations, within our typical extinction uncertainty of 0.013 mag/airmass, but only if we exclude any aerosol scattering component in the MODTRAN5 model. Even though this is a very limited test, with observations of a single star for a single night, the fact that we obtain excellent agreement between extinction measurements and the MODTRAN5 model, with no adjustable fit parameters, bodes well for exploiting MODTRAN5 to increase the precision of ground-based flux measurements.