Diffuse downward shortwave irradiance at the surface arises from the scattering of radiation by molecules and aerosol particles. Recently, we reported that pyranometer-measured diffuse solar irradiance in cloud-free atmospheres is overestimated by radiative transfer models at two low-altitude sites by an amount that exceeds modeling and measurement uncertainties but is correctly estimated within these uncertainties at two high-altitude sites <Halthore et al., 1998>. Here we explore this phenomenon in detail, with more cases and improved uncertainty analysis, confirming that the excess in modeled diffuse irradiance cannot be explained by uncertainties in measurements or aerosol-scattering properties that are input into the radiative transfer models or by errors in multiple-scattering schemes. The phenomenon is observed for all comparisons with data obtained intermittently over a 5-year period at the low-altitude sites. Model computations also exceed radiometer-measured sky radiance along the solar almucantar. Despite the inconsistencies between measured and modeled diffuse irradiance, atmospheric transmittance models correctly compute direct normal solar irradiance at all sites. These results indicate that at low altitudes a continuum atmospheric absorption process accounting for 0.022¿0.01 in vertical optical thickness at 550 nm, corresponding to 4¿2% absorptance, may need to be included in radiative transfer models and in models that retrieve aerosol optical thickness from extinction measurements. This is a substantial excess absorption with major implications for climate modeling and weather forecasting. In remote sensing studies, neglect of this excess absorption would lead to substantial errors in satellite sensor calibration and satellite inferred top-of-atmosphere flux. An agent or process for this absorption has not yet been identified. ¿ 2000 American Geophysical Union