Free-surface turbulence in a fully developed, open-channel flow was measured for Reynolds numbers of 8,500-45,000. An analysis method of the 2-D divergence on the free surface has been developed to extract Hanratty's β values, or the velocity gradient into the free surface, from these measurements. Hanratty's β is the parameter that relates most directly to the turbulence effect on the liquid-film coefficient. Its measurement is a direct measurement of surface renewal. The spatial scales of β were 3 to 5 times smaller than those of the large upwelling events (boils) normally identified as surface renewal. The hypothesis is that the large upwelling events do not have the high-vorticity gradients associated with large β values. Instead, the locations of high-vorticity gradients on the free surface will also create the divergence required for high β values, occurring at the edges of a large upwelling event. Because the β frequency spectrum has properties to characterize the liquid-film coefficient, it was normalized to be determined from its maximum value, the wave number of this maximum value, and a shape factor used to scale the frequency. Measurements of the liquid-film coefficient from prior studies were also used to characterize the liquid-film coefficient by measured β values for this nonsheared surface. The larger β scales predominantly influence the liquid-film coefficient, in contrast to a previous study of a shear-free surface published by McCready et al. in 1986, where all β frequencies were equally important. Generally, higher frequency turbulence is more significant at a sheared water surface than at a water surface with minimal shear stress.