The data set from ARESE II, sponsored by the Atmospheric Radiation Measurement Program, provides a unique opportunity to understand solar absorption in the atmosphere because of the combination of three broadband solar radiometers mounted on the Twin Otter aircraft and the ground based instruments at the ARM Southern Great Plains facility. We have analyzed the measurements taken on two clear sky days and three cloudy days and modeled the solar radiative transfer in each case with two different models. On the two clear days, the calculated and measured column absorptions agree to better than 10 Wm-2, which is about 10% of the total column absorption. Because both the model fluxes and the individual radiometer measurements are accurate to no better than 10 Wm-2, we conclude that the models and measurements are essentially in agreement. For the three cloudy days, the model calculations agree very well with each other and on two of the three days agree with the measurements to 20 Wm-2 or less out of a total column absorption of more than 200 Wm-2, which is again agreement at better than 10%. On the third day, the model and measurements agree to either 8% or 14% depending on how the value of surface albedo is computed. Differences exceeding 10% represent a significant absorption difference between model and observations. In addition to the uncertainty in absorption due to surface albedo, we show that including aerosol with an optical depth similar to that found on clear days can reduce the difference between model and measurement by 5% or more. Thus, we conclude that the ARESE II results are incompatible with previous studies reporting extreme anomalous absorption and can be modeled with our current understanding of radiative transfer.