As a follow-on to the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment (ARESE) I, which provided atmospheric shortwave measurements from collocated aircraft, ARESE II performed similar measurements with a single aircraft flying at an altitude of 7 km over an instrumented surface site. ARESE I and ARESE II absorptance measurements are found to agree with each other and, when converted to top of the atmosphere (TOA) instantaneous column absorption, are also consistent with GOES 8 and Scanner for Radiation Budget (ScaRaB) satellite observations. Measurements are compared to calculations performed with five different radiative transfer models. It is found that the calculated absorption differs systematically from the observations in cloudy conditions, with models underpredicting the absorption. In particular, all the models tested here underpredict the measured instantaneous cloudy column absorption by amounts ranging from 17 to 61 W m-2, depending on the models and cases studied. The various models, using identical input, differ among themselves; for example, for the same cloudy case, absorptance estimates range from 0.22 to 0.27 for the atmospheric column from the surface to the TOA. It is also found that model-calculated absorptances appear not as well correlated to cloud optical depth variations as the measured absorptances appear to be. Measured and calculated clear-sky absorptances agree well within the uncertainties. Cloudy-sky absorptances in the visible spectral region (300 to 700 nm) reach values of as much as 0.02 during ARESE II while the equivalent measurements for ARESE I range around 0.06. This visible absorptance may be related to aerosols and their day-to-day and seasonal variability.