Motivated by recent studies suggesting that the clear-sky atmosphere absorbs more shortwave (solar) radiation than the theoretical models, we have performed two consistency tests on the data used in several of these studies. These data consist of broadband measurements of shortwave irradiance to the surface (total, direct, and diffuse) taken in Oklahoma. In the absence of aerosols, Rayleigh scattering is the sole source of diffuse radiation and thus without any unknown source of atmospheric SW absorption, the measured diffuse irradiance should not be less than that produced by a model incorporating both Rayleigh scattering and conventional atmospheric absorption. The measurements of broadband diffuse irradiance, however, exhibit considerable sub-Rayleigh behavior. On the other hand, measurements of the diffuse irradiance in narrow spectral bands, centered at 415, 500, and 608 nm, indicate no sub-Rayleigh behavior, suggesting that exhibited by the broadband measurements is probably unrealistic. Related to this is the finding that the total surface SW irradiance, when evaluated as the sum of the direct-beam irradiance (pyrheliometer) and the diffuse irradiance (shaded pyranometer), differs considerably and diurnally from the single measurement of the total irradiance by the unshaded pyranometer under conditions in which possible cosine response errors of the unshaded pyranometer have been minimized. This indicates that the pyranometer daytime offsets differ from each other, suggesting their daytime offsets likewise differ from their nighttime offsets, which are nearly identical. We emphasize that these conclusions apply solely to the data for Oklahoma, and they are focused upon obtaining a better understanding of the clear-sky absorption problem that analyses of these data have raised. ¿ 2000 American Geophysical Union