A detailed analysis of measurements and model calculations of clear-sky shortwave irradiances at the surface is presented for a set of 18 cases collected during 3 cloudless days in the Netherlands in 2000. The analysis is focused on the influence of the optical and physical properties of aerosols on simulations of direct and diffuse downward solar irradiance at the surface. The properties of aerosols in the boundary layer are derived from surface measurements, under the assumption that all aerosol is confined to a well-mixed atmospheric boundary layer. The simulations of the irradiances are performed with the radiative transfer model MODTRAN 4, version 1.1. The analysis reveals no discernable differences between model and measurement for the direct irradiance, but several significant differences for the diffuse irradiance. The model always overestimates the diffuse irradiance measurements by 7 to 44 Wm-2 (average: 25 Wm-2). On the basis of an estimated uncertainty in the differences of 18 Wm-2, it appears that for 13 out of 18 cases the model significantly overestimates the measurements. This number decreases if instrumental errors (e.g., pyranometer zero-offset) and assumptions on the model input (e.g., wavelength-independent surface albedo) are considered. Nevertheless, the analysis presented here points to a persistent and significant positive model-measurement difference for the diffuse irradiance, which typically amounts to 1--4% of the top-of-atmosphere irradiance, and does not depend on the solar zenith angle. The reason for the discrepancy may be found in the presence of ultrafine absorbing aerosol particles that were not detected by the surface instrument for measuring aerosol absorption. It is also possible that these particles are not present near the surface, due to dry deposition, but do contribute to the total extinction if they are situated higher up in the boundary layer.