Storm surge has a significant impact on morphology in locations that are sheltered from waves and tides (e.g., near the heads of estuaries and landward sides of barrier islands), as well as low energy regions, especially when surge levels exceed tidal ranges. Surge allows wave processes to operate on the upper foreshore of beaches, which are typically only affected by aeolian processes [ Jackson et al ., 2002 ]. Storm inundation processes are nonlinear; inundation is gradual until a threshold is reached, followed by rapid inundation due to local topography [ Zhang , 2011 ]. Barrier islands are especially susceptible to impacts from storms, depending not only on the magnitude of the storm, but also characteristics such as surge, waves, wave runup, and the geometry of the island. Barrier island impact from tropical and extra‐tropical storms are typically characterized by the following four regimes: (1) the swash regime, (2) the collision regime, (3) the overwash regime, and (4) the inundation regime. In the swash regime, runup is confined to the foreshore, which typically erodes during the storm but recovers post storm; therefore, there is no net change. The collision regime occurs when wave runup exceeds the base of the foredune ridge and impacts the dune with net erosion. In the overwash regime, wave runup overtops the berm or foredune ridge. This causes net landward transport which contributes to the net migration of the barrier island landward. In the inundation regime, storm surge completely and continuously submerges the island, which initiates net landward sediment transport [ Sallenger , 2000 ]. However, these regimes do not consider the influence of storm surge ebb flows, which can transport sediment seaward across the shoreface, resulting in net losses. Although this phenomenon has been studied less, it has been well documented as a dominant erosive force during hurricanes including Hugo (1989) [ Hall et al ., 1990 ], Andrew (1992) [ Davis , 1995 ], and Ike (2008) [ Goff et al ., 2010 ] along the U.S. coasts. Although storms have the ability to reshape beach profiles from equilibrium conditions over a relatively short period of time [ Walton and Dean , 2007 ], shorelines and nearshore bathymetry tend to recover to the pre‐storm equilibrium conditions [ Leadon , 1999 ; Wang et al ., 2006 ].

Coastal environments can be generally characterized as wave dominated, tide dominated, or mixed (a balance between wave and tide forces), depending on the predominate force for sediment transport. Microtidal coasts are often wave dominant. Low‐mesotidal coasts have mixed wave and tidal energy but are more wave dominant. High‐mesotidal coasts also have mixed wave and tidal energy, but are more tide dominant. Low macrotidal and macrotidal coasts are tidal dominant [ Hayes , 1979 ]. Coastal morphology is often influenced by tidal range, except along coastlines with high wave energy and high tidal range (e.g., the Bay of Fundy), as well as low wave energy and low tidal range (e.g., the Gulf of Mexico). In high energy regions, high wave energy controls coastal morphology rather than tidal range. In low energy regions, there is a delicate balance between wave and tidal processes that allow tide‐dominant, wave‐dominant, or mixed energy morphology to develop with little variation in wave and tidal parameters; a low energy region may transition from wave‐dominant to mixed energy or tide dominant with a small increase in tidal range [ Davis and Hayes , 1984 ]. Additionally, because morphological response times in low energy regions are long, morphology is often dominated by high energy processes such as storms [ Masselink et al ., 2011 ].

Coasts are dynamic systems that are continuously transforming over different temporal and spatial scales as a result of geomorphological and oceanographical changes [ Cowell et al ., 2003a , 2003b ]. Shorelines assume a specific maintained state that can often be distinguished by a characteristic morphology. The state is sustained by negative feedbacks, but may be altered as a result of short‐term perturbations, the system exceeding an inherent threshold, or a change in boundary conditions (e.g., sea level). Shorelines can adopt different types of equilibrium. If the processes are balanced, the shoreline will remain constant in a static equilibrium. If the boundary conditions do not change and the average state of the shoreline is unchanged over time, a steady‐state equilibrium occurs. If the boundary conditions change and the landscape continuously evolves to adjust to the new conditions, a dynamic equilibrium occurs [ Woodroffe , 2003 , 2007 ].

Under some circumstances, changes in wave climates may cause shoreline recession to be an order of magnitude greater than recession due to SLR alone [ Cowell and Thom , 1994 ]. Changes in littoral transport budgets as well as changes in storm intensity and recurrence intervals will influence wave climates and alter episodic erosion and nearshore recovery [ Cowell and Kench , 2001 ]. For example, shifts in hurricane‐generated wave climates since the 1970s have already begun to reshape large‐scale, coastal cuspate features in North Carolina, U.S., by making them more asymmetrical [ Moore et al ., 2013 ]. SLR will likely contribute to changes in wave directions as a result of changes in water depths influencing nearshore wave refraction patterns [ Cowell and Kench , 2001 ].

Shoreline changes under SLR are not limited to beaches; SLR can be a major factor in estuarine shoreline changes resulting in the loss of intertidal areas, erosion of shorelines and increased flooding of low‐lying areas [ Rossington , 2008 ]. Estuarine shorelines are often comprised of both sandy and marsh shorelines that interact with physical processes including waves, winds, tides, and currents, which dictate erosion, transport, and deposition processes [ Riggs and Ames , 2003 ]. Estuarine shoreline response to SLR depends upon the amount of energy acting on the shoreline [ Stevens , 2010 ]; if the energy is high enough, the shoreline will erode, whereas if the energy is low, the shoreline will be inundated [ Department of Environmental and Heritage Protection , 2013 ]. The eroded material becomes part of the estuary's sediment budget and is deposited along other shorelines within the basin [ Stevens , 2010 ]. Inundated marsh shorelines in estuaries experience an increase in wave energy, which may erode the marsh platform and accelerate marsh loss [ Fitzgerald et al ., 2008 ].

Barrier islands are often considered to be either transgressive (consistently migrating landward) or regressive (consistently building seaward), depending on the rate of SLR and sand supply along a particular coast [ Curray , 1964 ]. A low sand supply and/or high SLR rate will cause barriers to migrate landward. Likewise, a high sand supply and/or low SLR rate will allow for seaward migration. Tidal prisms control the cross‐sectional area of inlets and ebb‐tidal delta volumes. Increases in bay tidal prisms as a result of SLR can increase the dimensions of tidal inlets. This allows for sand to be transferred from the adjacent barriers, which increases the volume of sand contained in the ebb‐tidal deltas. Ultimately, this may cause barrier segmentation and landward migration [ Hayes and Fitzgerald , 2013 ]. Barriers may experience one of three responses to high rates of SLR: erosion, translation, or overstepping. Barrier erosion occurs when the shoreface geometry is maintained but decreases over time as the entire profile migrates landward with SLR. Barrier translation or “roll over” entails the entire barrier migrating landward without loss of material as a result of erosion from the shoreface being deposited behind the barrier as washover fans. Overstepping occurs when SLR is too high and the barrier cannot respond, resulting in drowning. Determining the response of barriers to SLR depends on the SLR rate, the gradient of the underlying substrate, longshore transport, and sedimentation in back‐bays [ Masselink et al ., 2011 ].

The most simplistic approach to assess the physical response of shorelines to SLR is to consider inundation under a static rise (or fall) in sea level, often referred to as the “drowned valley concept” [ Leatherman , 1990 ]. Under this approach, the shoreline migrates landward according to the slope of the coast as the SLRs. The shore becomes submerged, but otherwise unaltered [ Leatherman , 1990 ]. Areas with mild slopes will experience more inundation for a given rise in sea level than areas with steep slopes [ Zhang et al ., 2004 ]. This concept is suitable for regions with rocky or armored shorelines, or even where the wave climate is subdued [ Leatherman , 1990 ]. Along sandy shorelines and coastal marshes, shoreline retreat has a more dynamic effect than just inundation, including permanent or long‐term erosion of sand from beaches as a result of complex, feedback‐dependent processes that occur within the littoral zone, as well as migration and loss of marshes [ Fitzgerald et al ., 2008 ] (Figures 1 and 2 ). Unlike inundation, erosion is a physical process in which sand is removed from the shoreface and deposited elsewhere, typically offshore. Long‐term, gradual shoreline recession is believed to be mainly a result of low energy processes such as SLR, as well as variations in sediment supplies [ Zhang et al ., 2002 ]. The relatively moderate era of SLR that shorelines have experienced in the recent past has concluded, and shorelines are beginning to adjust to new boundary conditions [ Woodruff et al ., 2013 ]. As SLR continues to accelerate, long‐term erosion rates are also expected to increase [ Zhang et al ., 2004 ], which may have significant consequences for barrier islands and coastal embayments.

3.3 Coastal Morphologic Modeling of SLR

Sampath et al., 2011 Fitzgerald et al., 2008 Bruun, 1954 Bruun, 1962 R) under a rise in mean sea level, given as (1) S is the rise in mean sea level, b is the elevation of the berm, h* is the depth of closure, and L* is the width of the active beach profile [Bruun, 1962 Fitzgerald et al., 2008 DECCW, 2010 Thieler et al., 2000 Cooper and Pilkey, 2004], and numerous studies that have applied the Bruun Rule have come to conflicting conclusions about its validity [Schwartz, 1967 1987 Rosen, 1978 Hands, 1983 List et al., 1997 Leatherman et al., 2000 Zhang et al., 2004 Hanson, 1989 Dean, 1991 Patterson, 2009 Ranasinghe et al., 2012 Dean and Maurmeyer, 1983 Rosati et al., 2013 Davidson‐Arnott, 2005 Ranasinghe et al., 2012 Projecting long‐term morphology is difficult due to the stochastic nature of the processes as well as a lack of understanding in the dynamic interactions and feedback that cause changes [.,]. As a result, coastal scientists do not have a reliable universal model to accurately predict the impacts of SLR along a variety of coastlines [.,]. Observations of beach profiles led to the characterization of the equilibrium beach profile concept, which assumes that the beach profile maintains an average, constant shape (aside from periods of storm‐induced changes) as the profile moves parallel to itself seasonally []. Assuming conditions, other than sea level, remain unchanged, the active beach profile extending from the shoreline to a seaward boundary denoted as the depth of closure will translate upward and landward to keep pace with rising seas, while maintaining shape (equilibrium) []. This concept, known as the Bruun Rule, can be used to predict shoreline recession () under a rise in mean sea level, given aswhereis the rise in mean sea level,is the elevation of the berm,* is the depth of closure, and* is the width of the active beach profile []. The depth of closure delineates the nearshore (landward of the closure depth to the shoreline) from the offshore (seaward of the closure depth) and represents the threshold where bed sediments are no longer significantly transported by waves. Therefore, it is assumed that all sediment erosion, transportation, and deposition occurs landward of the closure depth [.,]. The Bruun Rule is considered a coarse, first‐approximation approach, as it is a theoretical model and does not take into account the effects of longshore transport, coastal inlets or structures, or aeolian transport []. The legitimacy of the assumptions behind the Bruun Rule such as the existence of an equilibrium profile, and/or uniform alongshore transport have been questioned [.,, 2004], and numerous studies that have applied the Bruun Rule have come to conflicting conclusions about its validity [.,.,.,]. However, the underlying concept remains a central assumption in many coastal response models [.,]. In addition, various models have modified the Bruun Rule to incorporate factors such as barrier translation [], landward transport [.,], the dune sediment budget [], and variations in rainfall/runoff [.,].

Statistical methods such as extrapolation of historical trends have also been applied to predict future shoreline positions [Fenster et al., 1993; Crowell et al., 1997; Crowell and Leatherman, 1999; Galgano and Douglas, 2000]. This involves determining the location of new shorelines based on trends established from historical shoreline positions. Various methods have been used to compute shoreline change rates including linear regression, end point, and minimum description length criterion [Crowell et al., 1997]. The advantage of using historical trend analysis is that it takes into account the variability in shoreline response based on local coastal processes, sedimentary environments and coastline exposures, under the assumption that shorelines in the future will respond in a similar way as in the past (with a secondary assumption that SLR is the prominent function and all other parameters remain relatively constant) [Leatherman, 1990]. Passeri et al. [2014] compared erosion rates predicted by the Bruun Rule with historic shoreline erosion rates provided by the USGS Coastal Vulnerability Index (CVI) [Thieler and Hammar‐Klose, 1999, 2000] and the USGS National Assessment of Shoreline Change [Morton et al., 2004; Morton and Miller, 2005] along the U.S. South Atlantic Bight and Northern Gulf of Mexico coasts. The authors found that erosion rates predicted by the Bruun Rule matched long‐term erosion rates in parts of northeast Florida (e.g., Melbourne) and concluded the Bruun Rule could be used at these locations to predict future recession, under the assumption that historic erosion is completely attributed to the forces related to SLR. The CVI shoreline change rates were typically much larger than those provided by the National Assessment of Shoreline Change; therefore, the authors advise that care should be taken when extrapolating historical shoreline change rates to predict future shoreline positions [Passeri et al., 2014].

More recently, researchers have implemented probabilistic approaches to manage uncertainty associated with long‐term shoreline predictions [Cowell and Zeng, 2003; Cowell et al., 2006]. Statistical approaches using Bayesian networks have been applied to project long‐term shoreline changes under SLR [Hapke and Plant, 2010; Gutierrez et al., 2011; Yates and Le Cozannet, 2012]. The Bayesian network, based on the application of Bayes' theorem, is used to define relationships between driving forces, geological constraints, and coastal responses to make probabilistic predictions of shoreline changes under future SLR scenarios [Gutierrez et al., 2011]. Considering observations of local rates of relative sea level rise (RSLR), wave height, tidal range, geomorphic classification, coastal slope, and shoreline change rates, Gutierrez et al. [2011] developed a Bayesian network to predict long‐term shoreline changes. The Bayesian network was used to make probabilistic predictions of shoreline changes along the U.S. Atlantic coast under different SLR scenarios. Results indicated the probability of shoreline retreat increased with higher SLR rates. The accuracy of the model was assessed with a hindcast evaluation, in which the network correctly predicted 71% of the cases [Gutierrez et al., 2011]. Following this methodology, Yates and Le Cozannet [2012] created a Bayesian network to make statistical predictions of shoreline evolution along European coastlines. The output was compared with historic shoreline evolution trends and was found to accurately reproduce more than 65% of the trends. The authors concluded that the development of Bayesian networks is a useful tool for estimating future coastal evolution under changes in wave regimes or SLR [Yates and Le Cozannet, 2012]. Bayesian networks have also been applied to project retreat along coastal cliffs, which are typically more complex due to the need to model both sandy beaches in conjunction with the coastal cliff system. Hindcast evaluation accurately predicted 70%–90% of the modeled transects, indicating that the approach could be used to predict cliff erosion on time scales ranging from days (storm events) to centuries (SLR) [Hapke and Plant, 2010].

As changes in coastal morphology occur at time scales that are an order to two orders of magnitude greater than hydrodynamic time scales [Stive et al., 1990], conventional morphodynamic simulations using numerical models have been inefficient and lengthy [Dissanayake et al., 2012]. However, in more recent years, progress in process‐based models has allowed the simulation of multiscale hydrodynamics and morphology to be feasible. These simulations can be accomplished using numerical modeling in which the wave field, current field, and bathymetric changes are computed sequentially under the specified boundary conditions and sea level changes. The following are practical numerical models for simulating hydrodynamic and morphodynamic processes in coasts and estuaries: (1) 1D longshore coastline models that describe longshore sediment transport and shoreline evolution using the sand budget approach (2) 2D cross‐shore profile models that predict variations in coastal profiles but do not consider longshore transport (3) 2D horizontal coastal/estuarine/oceanic process models that simulate hydrologic and morphologic variations with a wide range of spatial scales but no considerations of variations in waves and currents (4) 3D models that take into account vertical and horizontal variations in waves and currents, but are generally restricted to predicting changes on small scales and in short durations [Ding, 2012].

Behavior‐oriented models based on empirical rules and analysis can be more effective for simulating long‐term shoreline evolution in comparison with numerical models, which are unable to account for variability in wave and current conditions on longer timescales. In the 1990s, large‐scale morphological‐behavior models were developed to simulate future changes in coastal morphology under SLR and variations in sediment supply. Many of these models are centered on the equilibrium profile translation principle, but incorporate additional drivers to predict shoreline evolution. However, validation of these models is difficult and can only be accomplished through inverse modeling, in which the model is calibrated with stratigraphic data and sea level history for specific areas and shoreline translation is recreated on geological time scales.

Early behavior‐oriented models include The Shoreface‐Translation Model [Cowell et al., 1995], and those of Stive and De Vriend [1995] and Niedoroda et al. [1995]. The coast‐basin interaction model ASMITA (Aggregated Scale Morphological Interaction between a Tidal basin and the Adjacent coast) was developed to describe the morphological interactions between tidal basins and the adjacent coast at various spatial and temporal scales in response to external forcing factors. This behavior‐oriented model is based on the assumption that a tidal basin can reach an equilibrium volume relative to mean sea level, at which point the accommodation space is equal to zero. A morphological equilibrium can be obtained for each element in the tidal system (e.g., ebb‐tidal delta, intertidal flats, etc.) depending on its hydrodynamic and morphometric conditions [Stive et al., 1998]. Van Goor et al. [2003] employed this model to examine whether the geomorphology of tidal inlets in the Dutch Wadden Sea could maintain equilibrium under rising sea levels. The authors found that if the rate of sediment import matched the rate of SLR, a new state of dynamic equilibrium was achieved, whereas if the import rate was less than SLR, the morphological state would deviate from equilibrium and the system would eventually drown. GEOMBEST (Geomorphic Model of Barrier, Estuarine, and Shoreface Translations) was developed to simulate the evolution of coastal morphology under changes in sea level and variations in sediment volume. The model is able to simulate the effects of geological framework on shoreline migration by defining the substrate with stratigraphic units characterized by erodibility and sediment composition. Unlike the Bruun Rule, changes in morphology are controlled by disequilibrium stress caused by changes in sea level, which vertically displace the equilibrium profile. This may result in net loss or gain of sediment volume as the profile tries to attain equilibrium. Applying GEOMBEST to simulate coastal stratigraphy in Washington, U.S. and North Carolina, U.S. indicated that the model could be used as a quantitative tool for coastal evolution assessments on geological time scales [Stolper et al., 2005]. Following the approach of Storms et al. [2002], Barrier Island Translation was developed to simulate the evolution of a sand barrier using simplified equations and taking into consideration the effects of various processes such as wind waves, storm surge, and sea level oscillations. The model is based on the assumptions of conservation of mass and conservation of the equilibrium profile. It is capable of simulating the processes of sediment redistribution by waves in the shoreface, sediment diffusion by waves in the inner shelf, overwash during storms, and lagoonal deposition in the back‐barrier. The model used to simulate the dynamics and evolution of a barrier island in Sand Key, Florida U.S. during the last 8000 years. Results indicated that the rate of overwash and lagoonal deposition was crucial for the survival for the barrier island under the historic sea level changes [Masetti et al., 2008]. Sampath et al. [2011] used a simplified behavior‐oriented model to predict long‐term morphological evolution in the Guadiana estuary, Portugal in response to SLR based on historic sedimentation rates and tidal inundation frequency. The model calculated the increased tidal inundation frequency under SLR using an empirical formula based on tidal range, determined from historic tide gauge data. However, the model did not take into account potential changes to tidal ranges or inundation areas under SLR. Ranasinghe et al. [2012] developed a physically based, scale‐aggregate model to estimate changes in coastlines due to SLR and variations in rainfall‐runoff in Vietnam. Results indicated changes can be very significant along shorelines adjacent to small inlet‐basin systems; these areas cannot be neglected in coastal management and planning decisions.