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The structure df atmospheric surface layer turbulence low wavenumbers was analyzed using 56 Hz triaxial velocity and temperature measurements above a uniform dry lake bed, A key feature of this experiment was the, small roughness length of the surface that resulted in a small roughness Reynolds number. Under near-neutral atmospheric stability conditions, a -1 power law was observed in both measured velocity and temperature spectra which is consistent with previously proposed dimensional analysis for rough and smooth turbulent boundary layer flows. The wavenumber at which the -1 power law terminates and the -5/3 power law commences was derived as a function of the Kolmgorov and von Karman constants, Good agreement between the predicted and the measured transition. wavenumber from -1 to -5/3, was holed for fully rough-flow conditions. However, this was ndt the case fdr other roughness conditions. The similarity theory constants for the neutral case were determined and they compared favorably with other laboratory and field studies. For unstable atmospheric conditions, directional dimensional analysis was used to predict the slopes of the power spectra of temperature and velocity. It was demonstrated that for moderately unstable conditions, the temperature and vertical velocity power spectra exhibited a -1 power law, but the longitudinal velocity exhibited a -2 power law. The agreement between predicted and measured power laws was within experimental errors. Some differences between the constants determined from this experiment and other experiments are also discussed.