The Department of Energy's Atmospheric Radiation Measurement (ARM) program sponsored a large aerosol intensive observation period (AIOP) to study aerosol during the month of May 2003 around the Southern Great Plains (SGP) Climate Research Facility (CRF) in north central Oklahoma. Redundant measurements of aerosol optical properties were made using different techniques at the surface as well as in vertical profile with sensors aboard two aircraft. One of the principal motivations for this experiment was to resolve the disagreement between models and measurements of diffuse horizontal broadband shortwave irradiance at the surface, especially for modest aerosol loading. This paper focuses on using the redundant aerosol and radiation measurements during this AIOP to compare direct beam and diffuse horizontal broadband shortwave irradiance measurements and models at the surface for a wide range of aerosol cases that occurred during 30 clear-sky periods on 13 days of May 2003. Models and measurements are compared over a large range of solar-zenith angles. Six different models are used to assess the relative agreement among them and the measurements. Better agreement than previously achieved appears to be the result of better specification of input parameters and better measurements of irradiances than in prior studies. Biases between modeled and measured direct irradiances are in the worst case 1%, and biases between modeled and measured diffuse irradiances are less than 1.9%.