One year of Coherent Doppler Lidar (CDL) data collected at the U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) site in Oklahoma was analyzed to provide profiles of vertical velocity variance, skewness, and kurtosis for cases of cloud-free convective boundary layers. The variance was normalized by the Deardorff convective velocity scale, which was successful when the boundary-layer depth was stationary but failed in situations when the layer was changing rapidly. In this study the data are sorted according to time of day, season, wind direction, surface shear stress, degree of instability, and wind shear across the boundary-layer top. The normalized variance was found to have its peak value near a normalized height of 0.25. The magnitude of the variance changes with season, shear stress, degree of instability, and wind shear across the boundary-layer top. The skewness was largest in the top half of the boundary layer (with the exception of wintertime conditions). The skewness was also found to be a function of the season, shear stress, and wind shear across the boundary-layer top. Like skewness, the vertical profile of kurtosis followed a consistent pattern, with peak values near the boundary-layer top. The normalized altitude of the peak values of kurtosis was found to be higher when there was a large amount of wind shear at the boundary-layer top.