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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. Plain Language Summary: Beach elevation surveys are compared at two beaches in San Diego County. Both beaches narrow during winter as large wave events transport sand offshore and widen during summer as gentle waves move sand onshore. The seasonality of such beaches has been characterized by simple models that primarily rely on wave energy relative to an average state to predict beach width changes, known as equilibrium models. Here, we highlight some of the limitations of equilibrium models, such as a tendency to over predict winter erosion at a beach backed by non‐erodible infrastructure. We demonstrate that machine learning models, when trained with sufficient observations, can predict beach width changes more accurately than equilibrium models. Key Points: The Equilibrium‐informed extra tree (ET) regression machine learning model uses input features of only wave history, inspired by equilibrium conceptsWith sufficient training, ET outperforms a widely used equilibrium model [ABSTRACT FROM AUTHOR]

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 <30% for moderate and low energy incident SS waves. Only 5% of records, with energetic long swell, show primarily bound waves. The shoreline slope of concave beaches increases by ∼3 between spring high and low tides, and free seaward and shoreward IG energy in 10–15 m vary tidally. The observed linear dependency of free IG energy on SS energy and period is consistent with Ardhuin et al. (2014, https://doi.org/10.1016/j.ocemod.2014.02.006)'s parameterization (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. Plain Language Summary: Infragravity (IG) waves are long‐period (25 s–2.5 min) waves that contribute to coastal flooding and beach erosion. IG waves, generated near the shoreline by short‐period sea‐swell (SS) wave groups (known by surfers as "sets"), have long wavelengths (100s of m) and do not typically curl and break like ordinary sea and swell waves. Instead, they can be reflected off the beach face and propagate seaward. Our study concerns IG waves on the inner shelf (10–15 m depth, ∼500–700 m offshore), seaward of the main region of IG generation. Similar to previous observations in Hawai'i and North Carolina, we find most of the reflected, seaward‐going IG energy cannot reach deep water and is trapped on the continental shelf. We develop an observation‐based estimate of IG wave energy on the inner shelf as a function of SS wave energy and tide level. Finally, we show with a numerical model that IG wave runup at the shoreline is influenced only weakly by IG waves on the inner shelf. Key Points: Infragravity (IG) waves on the inner shelf (10–15 m depth) in San Diego, USA are often dominated by refractively trapped free wavesFree IG energies are parameterized as a function of local sea‐swell conditions and tide levelNumerically modeled wave runup is only weakly influenced by the shoreward propagating IG waves observed at the offshore boundary [ABSTRACT FROM AUTHOR]

A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the nonlinear shallow water equations to study the nearshore dynamics of infragravity (IG) waves. Based on simulations of waves on a relatively moderate and mild beach slope with a non-hydrostatic wave-flow model (SWASH), the new theory shows that spatial gradients in IG energy flux are nearly completely balanced by the combined effect of bottom stresses and predominantly nonlinear triad interactions. The new balance confirms many features of existing weakly nonlinear theories, and yields an improved description in the inner surfzone where waves become highly nonlinear. A gain of IG energy flux throughout the shoaling and outer surfzones is driven by triad interactions between IG waves and pairs of sea-swell (SS) waves. The IG energy flux decreased in the inner surfzone, primarily through an energy cascade to the swell-band and superharmonic frequencies where wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. The IG wave breaking, characterized by triads between three IG or two IG waves and one SS wave, was significant only deep inside the surfzone of the mild slope. Even though IG waves broke on the mild slope, nonlinear interactions between IG waves and pairs of SS waves were responsible for at least half of the net IG flux loss. [ABSTRACT FROM AUTHOR]