This review focuses on recent advances in process-based numerical models of the impact of extreme storms on sandy coasts. Driven by larger-scale models of meteorology and hydrodynamics, these models simulate morphodynamics across the Sallenger storm-impact scale, including swash,collision, overwash, and inundation. Models are becoming both wider (as more processes are added) and deeper (as detailed physics replaces earlier parameterizations). Algorithms for wave-induced flows and sediment transport under shoaling waves are among the recent developments. Community and open-source models have become the norm. Observations of initial conditions (topography, land cover, and sediment characteristics) have become more detailed, and improvements in tropical cyclone and wave models provide forcing (winds, waves, surge, and upland flow) that is better resolved and more accurate, yielding commensurate improvements in model skill. We foresee that future storm-impact models will increasingly resolve individual waves, apply data assimilation, and be used in ensemble modeling modes to predict uncertainties.

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Infragravity (hereafter IG) waves are surface ocean waves with frequencies below those of wind-generated “short waves” (typically below 0.04 Hz). Here we focus on the most common type of IG waves, those induced by the presence of groups in incident short waves. Three related mechanisms explain their generation: (1) the development, shoaling and release of waves bound to the short-wave group envelopes (2) the modulation by these envelopes of the location where short waves break, and (3) the merging of bores (breaking wave front, resembling to a hydraulic jump) inside the surfzone. When reaching shallow water (O(1–10 m)), IG waves can transfer part of their energy back to higher frequencies, a process which is highly dependent on beach slope. On gently sloping beaches, IG waves can dissipate a substantial amount of energy through depth-limited breaking. When the bottom is very rough, such as in coral reef environments, a substantial amount of energy can be dissipated through bottom friction. IG wave energy that is not dissipated is reflected seaward, predominantly for the lowest IG frequencies and on steep bottom slopes. This reflection of the lowest IG frequencies can result in the development of standing (also known as stationary) waves. Reflected IG waves can be refractively trapped so that quasi-periodic along-shore patterns, also referred to as edge waves, can develop. IG waves have a large range of implications in the hydro-sedimentary dynamics of coastal zones. For example, they can modulate current velocities in rip channels and strongly influence cross-shore and longshore mixing. On sandy beaches, IG waves can strongly impact the water table and associated groundwater flows. On gently sloping beaches and especially under storm conditions, IG waves can dominate cross-shore sediment transport, generally promoting offshore transport inside the surfzone. Under storm conditions, IG waves can also induce overwash and eventually promote dune erosion and barrier breaching. In tidal inlets, IG waves can propagate into the back-barrier lagoon during the flood phase and induce large modulations of currents and sediment transport. Their effect appears to be smaller during the ebb phase, due to blocking by countercurrents, particularly in shallow systems. On coral and rocky reefs, IG waves can dominate over short-waves and control the hydro-sedimentary dynamics over the reef flat and in the lagoon. In harbors and semi-enclosed basins, free IG waves can be amplified by resonance and induce large seiches (resonant oscillations). Lastly, free IG waves that are generated in the nearshore can cross oceans and they can also explain the development of the Earth's “hum” (background free oscillations of the solid earth).

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Morphodynamic equilibrium is a widely adopted yet elusive concept in the field of geomorphology of coasts, rivers and estuaries. Based on the Exner equation, an expression of mass conservation of sediment, we distinguish three types of equilibrium defined as static and dynamic, of which two different types exist. Other expressions such as statistical and quasi-equilibrium which do not strictly satisfy the Exner conditions are also acknowledged for their practical use. The choice of a temporal scale is imperative to analyse the type of equilibrium. We discuss the difference between morphodynamic equilibrium in the "real world" (nature) and the "virtual world" (model). Modelling studies rely on simplifications of the real world and lead to understanding of process interactions. A variety of factors affect the use of virtual-world predictions in the real world (e.g., variability in environmental drivers and variability in the setting) so that the concept of morphodynamic equilibrium should be mathematically unequivocal in the virtual world and interpreted over the appropriate spatial and temporal scale in the real world. We draw examples from estuarine settings which are subject to various governing factors which broadly include hydrodynamics, sedimentology and landscape setting. Following the traditional "tide-wave-river" ternary diagram, we summarize studies todate that explore the "virtual world", discuss the type of equilibrium reached and how it relates to the real world.@en

Many tidal basins are connected to the open sea by multiple inlets. An example is the Guana-Tolomato-Matanzas (GTM) estuary (see Fig. 1), a 60 km long back-barrier estuarine system extending from Palm Valley to Palm Coast, Florida, US. A large area of this estuary ( 300 km2) is part of the GTM–National Estuarine Research Reserve with a great bio–diversity. This estuary is connected to the open sea by two inlets, the northern inlet is St. Augustine Inlet, located in St. Augustine, and the southern one, Matanzas inlet, is located 25 km southward. Hydrodynamics at the GTM estuary are primarily driven by the tidal propagation, although density driven flows might be relevant after major rainfall events (e.g. Sheng et al., 2008). Using parame- Figure 1. Guana–Tolomato–Matanzas estuary. ters characteristic for the GTM–estuary, the existence of morphodynamic equilibria of two–inlet systems is investigated using a width–averaged idealized morphodynamic model, and their sensitivity to parameters is assessed. @en