Field observations of wave setup

Wave setup is assumed to be a balance between the cross‐shore convergence of the onshore flux of momentum (wave radiation stress S xx ) in the surfzone and a cross‐shore pressure gradient. Oceanic observations between the 2‐ and 8‐m isobaths near Duck, North Carolina, provide a test of the wave setup balance without assuming that wave height in the surfzone is proportional to water depth. Analysis of data from a cross‐shore array of 11 pressure gauges and 10 sonar altimeters deployed during the fall of 1994 indicates the wave setup balance holds to at least the accuracy of the pressure measurements (a few centimeters). The correlation between the two terms in the setup balance is 0.93, and the linear regression slope is 1.05±0.19. Accurate estimates of the cross‐shore pressure gradient require density measurements to adjust pressure measurements taken at different depths to the same level. The assumption that pressure and bathymetry are linear between the 2‐ and 8‐m isobaths (or the more common assumption that the height of normally incident, shallow water waves is proportional to the water depth) introduces errors of up to 6 cm for the conditions considered here. Given this assumption, 3.5 years of data from pressure gauges in 2 and 8 m of water indicate that the wave setup balance is valid for a wide range of conditions (correlation 0.71 and regression slope 0.98±0.08).