Data from the near-wall-turbulent region of the high-Reynolds-number atmospheric surface layer are used to analyse the attached-eddy model of wall turbulence. All data were acquired during near-neutral conditions at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located in the western Utah Great Salt Lake Desert. Instantaneous streamwise and wall-normal components of velocity were collected with a wall-normal array of two-component hot wires within the first 2 m above the surface of the salt flats. Streamwise and wall-normal turbulence intensities and spectra are directly compared to corresponding laboratory data and similarity formulations hypothesized from the attached-eddy model of wall turbulence. This affords the opportunity to compare results with Reynolds numbers varying over three orders of magnitude. The wall-normal turbulence-intensity similarity formulation is extended. The results show good support for the similarity arguments forwarded by the attached-eddy model as well as Townsend's (1956) Reynolds-number similarity hypothesis and lack of the ‘inactive’ motion influence on the wall-normal velocity component. The effects of wall roughness and the spread in the convection velocity due to this roughness are also discussed.