Many processes that affect ocean surface gravity waves in sea ice give rise to attenuation rates that vary with both wave frequency and amplitude. Here we particularly test the possible effects of basal friction, scattering by ice floes, and dissipation in the ice layer due to dislocations, and ice breakup by the waves. The possible influence of these processes is evaluated in the marginal ice zone of the Beaufort Sea, where extensive wave measurements were performed. The wave data includes in situ measurements and the first kilometer-scale map of wave heights provided by Sentinel-1 SAR imagery on 12 October 2015, up to 400 km into the ice. We find that viscous friction at the base of an ice layer gives a dissipation rate that may be too large near the ice edge, where ice is mostly in the form of pancakes. Further into the ice, where larger floes are present, basal friction is not sufficient to account for the observed attenuation. In both regions, the observed narrow directional wave spectra are consistent with a parameterization that gives a weak effect of wave scattering by ice floes. For this particular event, with a dominant wave period around 10 s, we propose that wave attenuation is caused by ice flexure combined with basal friction that is reduced when the ice layer is not continuous. This combination gives realistic wave heights, associated with a 100-200 km wide region over which the ice is broken by waves, as observed in SAR imagery.