Free infragravity waves on the inner shelf: Observations and Parameterizations at two Southern California beaches

Co-located pressure and velocity observations in 10-15m depth are used to estimate the relative contribution of bound and free infragravity (IG) wave energy to the IG wave field. Shoreward and seaward going IG waves are analyzed separately. At the Southern California sites, shoreward propagating IG waves are dominated by free waves, with the bound wave energy fraction <30% for moderate energy incident sea-swell and <10% for low energy incident sea-swell. Only the 5% of records with energetic long swell show primarily bound waves. Consistent with bound IG wave theory, the energy scales as the square (frequency integrated) sea-swell energy, with a higher correlation with swell than sea energy. Seaward and shoreward free IG energy is strongly tidally modulated. The ratio of free seaward to shoreward propagating IG energy suggests between 50-100% of the energy radiated offshore is trapped on the shelf seaward of 10-15m and redirected shoreward. Remote sources of IG energy are small. The observed linear dependency of free seaward and shoreward IG energy on local sea-swell wave energy and tide are parameterized with good skill (R2 ~ 0.90). Free (random phase) and bound (phase-coupled) IG waves are included in numerically simulated timeseries for shoreward IG waves that are used to initialize (~ 10m depth) the numerical nonlinear wave transformation SWASH. On the low slope study beach, wave runup is only weakly influenced by free shoreward propagating waves observed at the offshore boundary (foreshore slope = 0.02).