Robert T. Guza

Infragravity (IG) waves (periods nominally 25–250 s) are generated in shallow water by nonlinear difference‐frequency interactions between shorter period (nominally 4–25 s) incident sea‐swell waves. Previous studies show strong IG reflection from the beach face and detectable IG energy in alongshore‐propagating edge waves. Here, a linear wave model is developed to invert observed pressure (P) and velocity (cross‐shore and alongshore, U, V) cross‐spectra (including sensors separated in both the alongshore and cross‐shore directions) into cross‐shore standing and alongshore progressive linear shallow‐water modes. This inversion uses the Bayesian maximum a posteriori method (MAP). Infragravity edge waves on a moderately sloped ocean beach are characterized using 60 days of observations with low‐to‐moderate energy incident waves. Colocated P and UV sensors were deployed from the shoreline to 30 m depth, with an eight‐element PUV array in 7 m depth spanning 1.5 km alongshore. MAP estimates qualitatively agree with previous results obtained using the maximum likelihood estimator and smaller arrays. Edge waves average (28%, 14%, 43%) of the IG (P, U, V) variances in 7 m depth. Edge waves are most energetic at high tide when the shoreline slope is largest, possibly because the steep beach supports the multiple constructively interfering shoreline reflections required to form edge waves. The numerical wave model SWASH 1D assumes normally incident waves and neglects edge waves, but reproduces approximately the energy and cross‐shore structure of P and U.

Shoreline position (e.g., beach width) is a critical component of flooding and overtopping forecasts but difficult to predict accurately. We model beach width changes with a supervised machine learning (ML) approach informed by equilibrium principles. The time history of wave energy anomalies that force equilibrium models is used as an ML input feature. The sweeping simplifying equilibrium model assumptions relating beach width change to anomalies are replaced with data‐based ML results. Supervised learning regression methods including linear, support vector, decision trees, and ensemble regressors are tested. Observations for model training and testing includes weekly to quarterly beach elevation surveys spanning approximately 500 m alongshore and 8 years at two beaches, each supplemented with several months of ∼100 sub‐weekly surveys. These beaches, with different sediment types (sand vs. sand‐cobble mix), both widen in summer in response to the seasonal wave climate, in agreement with a generic equilibrium model. Differences in backshore erodability contribute to differing beach responses in the stormiest (El Niño) year that are reproduced by a simple extra trees regression model but not by the equilibrium model. With sufficiently extensive training data, the ML model outperforms equilibrium by providing flexibility and complexity in the response to wave forcing. The present ML and equilibrium models both fail to simulate a uniquely stunted beach recovery unlike other recoveries in the training data.

Numerical predictions of nearshore waves and shoreline runup are usually initialized on the inner shelf, seaward of the surfzone, with sea‐swell (SS) waves from local wave buoys or regional wave models. Lower frequency infragravity (IG) waves are not reliably measured by buoys or included in regional models. Here, co‐located pressure and velocity observations are used to characterize IG waves in 10–15 m depth in southern California. Shoreward propagating IG waves are often dominated by free waves, with the boundwave energy fraction R² = 0.71). Including the tide level as a proxy for beach slope and modifying the SS frequency dependency increases R² to 0.91. The ratio of free seaward to shoreward propagating IG energy suggests between 50 and 100% of the energy radiated seaward in depths of 10–15 m is trapped offshore and redirected shoreward. Free (random phase) and bound (phase‐coupled) IG waves are combined to initialize the SWASH numerical model. SWASH predicted runup is only weakly influenced by waves at the offshore boundary. Nonlinear IG generation and dissipation in the shoaling and surfzone overwhelm the effects of shoreward propagating waves observed at the offshore boundary.

Understanding and predicting changes in shoreline location are critical for coastal planners. In situ monitoring is accurate but not widely available. Satellite observations of shorelines have global coverage, but their accuracy and predictive capacity have not been fully explored. Abundant beach surveys and extensive wave observations in Southern California provide a unique ground truth for the interpretation of satellite‐derived recently wetted waterlines. We combine 23 years of waterline position estimates from satellite imagery with nearshore wave hindcasts and tides to train and test a deep neural network (DNN). The trained DNN uses only tides and waves as predictors at transects with satellite coverage and wave estimates to predict beach width and, for the first time, seasonal average beach slopes. Beach width changes hindcast using DNN have at least fair skill (>0.3) for 50% of transects, where the skill was calculated relative to the mean of extensive new in situ survey data from in San Diego County. The DNN also predicted shoreline changes to within 10 m (the nominal uncertainty in satellite‐derived shorelines) for 64% of transects lacking ground truth. DNN and survey estimates of seasonal beach slope changes also agree qualitatively.

Weekly to quarterly beach elevation surveys spanning 700-800 m alongshore and 8 years at two beaches were each supplemented with several months of ∼100 sub-weekly surveys. These beaches, which have different sediment types (sand vs. sand-cobble mix), both widen in summer in response to the seasonal wave climate, in agreement with a generic equilibrium model. Results suggest differences in backshore erodability contribute to differing beach responses in the stormiest (El Niño) year. At both sites, the time dependence of the equilibrium modeled shoreline resembles the first mode of an EOF decomposition of the observations. With sufficient training, an equilibrium-informed Extra Tree Regression model, that includes features motivated by equilibrium modelling, can significantly outperform a generic equilibrium model.

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).

An empirically based sediment budget model is developed for Cardiff State Beach CA to assess management strategies to maintain beach width subject to mean sea level rise (MSLR) and potentially more frequent El Niño storms. Two decades (2000-2019) of surveys support the hypothesis that the rocky reefs bounding this beach retain sand added to the nearshore zone, except during strong El Niño years with more severe storm waves. The subaerial beach has widened by ~60 m during the last 20 years owing to nourishment (~17K m3/yr) of imported sand, and sand bypassed annually by dredging a lagoon inlet at the beach’s updrift end. The observed widening yields 1 m/yr of mean beach width increase for each 6 m3/m-shoreline of added sand. A strong El Niño year is modeled with a permanent volume loss coupled with a shoreline retreat that recovers partially as the beach profile adjusts between El Niño years. Calibrated with observations from Cardiff and South Torrey Pines (a control beach), the model is used to project beach change through 2050. All modeled scenarios suggest that no bypassing or nourishment (no “management”) will result in tens of meters of beach width loss. However, continued bypassing would partially mitigate MSLR and El Niño beach width losses. An artificially built (living shoreline) dune that backs the beach, if completely undermined during strong El Niño storm waves, stores enough sand to balance one-third of the expected volume loss that year, and may make the beach more resilient and speed subsequent beach recovery.

Frequent surveys using modern remote sensing technology enable observations of subaerial beach morphology and surface sediment type (sand vs. gravel/cobble) with unprecedented spatial and temporal resolution. Here we show weekly terrestrial mobile light detection and ranging (LiDAR) observations of cusps on a mixed sediment beach, consisting of sand and gravel/cobble, spanning ∼2 km alongshore. Surface gravel/cobble coverage varied from almost complete to none (e.g., all sand), over times ranging from weekly to seasonal, and with location. Cusp morphologies also varied in space and time. Cusps with 11–20 m alongshore wavelengths (L) primarily developed in winter and were composite with gravel‐cobble horns and sandy bays. Cusps with L between 21 and 40 m developed throughout the year and were either composite or entirely sandy. Previously not reported, composite mega cusps (L between 200 and 400 m) occurred in winter. Composite cusps, with L between 11 and 40 m, were clustered in gravel/cobble‐rich mega cusp bays and absent on the sandier mega cusp horns.

Widespread erosion associated with energetic waves of the strong 2015–2016 El Niño on the U.S. West Coast has been reported widely. However, Southern California was often sheltered from the northerly approach direction of the offshore waves. The few large swells that reached Southern California were not synchronous with the highest tides. Although west coast‐wide tidal anomalies were relatively large in 2015–2016, in Southern California, total water levels (sum of tides, anomalies, and wave superelevation) were lower than during the 1997–1998 Niño, and comparable to the 2009–2010 Niño. Airborne lidar surveys spanning 300 km of Southern California coast show the beach response varied from considerable erosion to accretion. On average, the shoreline moved landward 10 m, similar to the 2009–2010 El Niño. Some San Diego county beaches were narrower in the 1997–1998 El Niño than in 2015–2016, consistent with the higher erosion potential in 1997–1998. Beach retreat exceeded 80 m at a few locations. However, 27% of the shoreline accreted, often in pocket beaches, or near jetties. While adjacent beaches eroded, estuary mouths accreted slightly, and several estuaries remained or became closed during the study period. Only 12% of cliffs eroded (mostly at the base), and the average cliff face retreat was markedly less than historical values. Only two cliff‐top areas retreated significantly. Although some areas experienced significant change, the potential for coastal erosion and damage in Southern California was reduced compared to the 1997–1998 El Niño, because of low rainfall, a northerly swell approach, and relatively limited total high‐water levels.

Previous field observations indicate that the directional spread of swell-frequency (nominally 0.1 Hz) surface gravity waves increases during shoreward propagation across the surf zone. This directional broadening contrasts with the narrowing observed seaward of the surf zone and predicted by Snell’s law for bathymetric refraction. Field-observed broadening was predicted by a new model for refraction of swell by lower-frequency (nominally 0.01 Hz) current and elevation fluctuations. The observations and the model suggest that refraction by the cross-shore currents of energetic shear waves contributed substantially to the observed broadening.