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Annual Review of Marine Science
Modeling the Morphodynamics
of Coastal Responses to
Extreme Events: What Shape
AreWeIn?
Christopher R. Sherwood,1Ap van Dongeren,2,3
James Doyle,4Christie A. Hegermiller,1Tian-Jian Hsu,5
Tarandeep S. Kalra,6Maitane Olabarrieta,7
Allison M. Penko,8Yashar Rafati,5Dano Roelvink,2,3,9
Marlies van der Lugt,2,9 Jay Veeramony,8
and John C. Warner1
1Woods Hole Coastal and Marine Science Center, US Geological Survey, Woods Hole,
Massachusetts 02543, USA; email: csherwood@usgs.gov
2Marine and Coastal Systems, Deltares, 2629 HV Delft, The Netherlands
3Coastal and Urban Risk and Resilience, IHE Delft Institute for Water Education, 2611 AX
Delft, The Netherlands
4US Naval Research Laboratory, Monterey, California 93943, USA
5Center for Applied Coastal Research, Department of Civil and Environmental Engineering,
University of Delaware, Newark, Delaware 19716, USA
6Integrated Statistics (contracted to the US Geological Survey), Woods Hole,
Massachusetts 02543, USA
7Department of Civil and Coastal Engineering, University of Florida, Gainesville,
Florida 32611, USA
8US Naval Research Laboratory, Stennis Space Center, Mississippi 39529, USA
9Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CD Delft,
The Netherlands
Annu. Rev. Mar. Sci. 2021. 14:5.1–5.36
The Annual Review of Marine Science is online at
marine.annualreviews.org
https://doi.org/10.1146/annurev-marine-032221-
090215
This is a work of the US government and not subject
to copyright protection in the United States
Keywords
coastal morphodynamics, extreme storms, coastal modeling, sandy coasts,
waves, sediment transport
Abstract
This review focuses on recent advances in process-based numerical mod-
els 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,
.
MA14CH05_Sherwood ARjats.cls July 19, 2021 10:22
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 ows 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 improve-
ments in tropical cyclone and wave models provide forcing (winds, waves, surge,and upland ow)
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.
1. INTRODUCTION
This review discusses advances in modeling coastal morphology changes caused by extreme storms
such as tropical cyclones and extratropical storms, with an emphasis on the morphological change
of sandy beaches and barrier islands. We focus on process-based models that are quantitative repre-
sentations of our understanding of coastal hydrodynamics, sediment transport, and morphological
change and that are intended to hindcast and/or forecast processes on the temporal and spatial
scales of extreme storms. These events produce the fastest and most severe natural morpholog-
ical changes that shape the coastal landscape, dene habitats, and present risks to humans and
infrastructure.
Our review draws on experience gained during the Increasing the Fidelity of Morphological
Storm Impact Predictions (IFMSIP) project, funded by the US Ofce of Naval Research and ex-
ecuted by a consortium of scientists from the US Geological Survey,US Naval Research Labora-
tory, University of Florida, University of Delaware, and IHE Delft Institute for Water Education,
coordinated by Deltares in the Netherlands. The aim of the project was to utilize advances in
process knowledge, data-acquisition techniques, and computing power to (a) better understand
the accuracy of morphodynamic numerical model results compared with observational data when
applied to extreme storms, (b) improve the accuracy of event-driven morphological predictions,
(c) improve predictions by improving parameter estimates and identifying key processes and sen-
sitivities to inputs, and (d) improve condence in model applications in new environments.
The extent of morphological change during a coastal storm, including dune/beach erosion,
overwash, and breach/inlet formation, has been related to a storm-impact scale proposed by
Sallenger (2000). Sallenger’s four impact regimes depend on the maximum total water level rela-
tive to the dune morphology.This simple scale provides an initial estimate of the impact severity
but masks the complexity of the hydrodynamic and sediment-transport processes and feedbacks
that drive the changes. Models must be capable of representing change across all stages of the
Sallenger scale, so our discussion of modeled processes takes this perspective.
Recent reviews related to morphodynamic modeling (de Swart & Zimmerman 2009, Coco
et al. 2013) focused on the evolution of coastal and uvial systems at temporal scales longer than
those corresponding to individual storms. No recent reviews have directly addressed the coastal
response to extreme storms, where changes are a short-term (∼hours–days) response to intense
forcing, rather than a long-term evolution of a self-organized system.
A 2016 review of the modeling of river morphodynamics (Siviglia & Crosato 2016) revealed
four recent trends: (a) the adoption of open-source and often community-developed codes; (b)the
tendency for simulations to be performed on ever-larger domains, often with mixed grain sizes;
(c) the expansion of morphological evolution beyond bathymetry, to include subaerial morpho-
logical changes such as bank erosion, braiding, and vegetation effects; and (d) the development of
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new numerical schemes. The authors also concluded that the many complicating factors (such as
roughness and sediment-transport formulae and forecasting of future hydrographs) lead to large
uncertainties and that the interpretation of model results depends strongly on the experience and
expertise of the modelers. Similar trends are recognized in coastal modeling, as detailed below.
Our review focuses on process-based modeling of the response of the coastal morphology to
extreme storms. Although our examples are drawn mostly from tropical storms, the processes dis-
cussed apply to most storms accompanied by large waves and elevated water levels. We limit our
review to open sandy coasts, including barrier islands, which constitute 31% of the world’s coasts
(Luijendijk et al. 2018). We discuss the hydrodynamic impacts of water levels and waves on the
coastal zone. To properly represent the far-eld hydrodynamics that ultimately force local change,
numerical models with domains of hundreds of kilometers and resolutions of hundreds of meters
are required. These elds of driving forces are nested down to compute the morphodynamic im-
pact at local scales with O(1)-m resolution, which (with current computational resources) limits
the extent of the morphological domain to O(10) km. We assess the state of our understanding of
essential processes, highlight particularly important developments, and touch on ongoing trends
in modeling.
In Section 2, we introduce the types of models used to simulate coastal morphodynamic change
and relate the processes included in these models to the Sallenger scale. Section 3 describes mod-
eling approaches to key coastal processes, and Section 4 discusses model skill. Finally, in Section 5,
we evaluate progress on particularly problematic processes and identify trends in coastal modeling.
2. PROCESS-BASED MODELS OF COASTAL STORM
MORPHODYNAMICS
We describe in this section the types of process-based models that are suitable for simulating mor-
phological impacts classied using the Sallenger (2000) scale. We describe the dominant forcing
and response in each regime and implications for modeling.
2.1. Types of Models
Roelvink & Reniers (2012) divided coastal morphology models into three types, based primarily on
dimensionality: (a) one-dimensional (1D) cross-shore prole models (Bruun 1954, 1962; Roelvink
& Brøker 1993; Schoonees & Theron 1995), including equilibrium shoreline models (Miller &
Dean 2004; Yates et al. 2009, 2011); (b) 1D alongshore coastline models (Pelnard-Considère 1957;
Dean 1991; Larson et al. 1997; Ashton et al. 2001; Buijsman et al. 2001; Ashton & Murray 2006;
Davidson et al. 2010, 2013; Splinter et al. 2014; Vitousek et al. 2017); and (c) two-dimensional
(2D) and three-dimensional (3D) models (de Vriend et al. 1993, Nicholson et al. 1997). Vitousek
et al. (2017) distinguished between physics-based and process-based models. In their vernacular,
physics-based models solve conservation equations for the mass and momentum of water and sed-
iment and attempt to treat all the processes important to coastal evolution, whereas process-based
models focus on a single dominant phenomenon. In this review, we equate physics-based mod-
els with Vitousek et al.’s (2017) denition of process-based models and note that all models rely
on empiricism at some scale. Examples of models describing phenomena include those by Bruun
(1962), Yates et al. (2009), and Long & Plant (2012). These models typically parameterize unre-
solved physics and use observations to optimize the model parameters with techniques ranging
from a simple least squares t to Kalman ltering. Hence, these models may apply only to specic
locations but have proved useful for the study of seasonal and long-term morphological changes.
Examples of (2D and 3D) process-based models include Delft3D (Roelvink & van Banning 1995,
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Lesser et al. 2004), XBeach (Roelvink et al. 2009), MIKE 21 (Warren & Bach 1992, Kaergaard &
Fredsoe 2013), NearCoM-TVD (Chen et al. 2014),FVCOM (Chen et al. 2003, Lai et al. 2010, Wu
et al. 2011), TELEMAC-MASCARET (http://www.opentelemac.org) (Hervouet 2007, Davies
& Robins 2017, Kaveh et al. 2019) and the accompanying sediment and morphology module
SISYPHE (Tassi & Villaret 2014), TK-2D software (Li et al. 2020), BASEMENT (Vetsch et al.
2014), ECOMSED (Han & Huang 2018), and COAWST (Warner et al. 2008b, 2010). These
models represent processes through equations that conserve mass and momentum but often pa-
rameterize small-scale processes. Many of these models were described and compared by Amoudry
& Souza (2011).
Murray (2003) suggested that models can be arranged in three ways: (a) simulation versus ex-
ploration,(b) bottom up versus top down (scale), and (c) equation based versus rules based. Process-
based models are what Murray (2003) would call “explicit numerical reductionism” (p. 152),in that
they attempt to start bottom up by representing processes at the smallest and fastest scales feasible
and then integrate those results temporally and spatially to produce results at useful scales (Coco
et al. 2013). As model integrations are upscaled, uncertainties and biases accumulate, possibly ren-
dering the results so uncertain as to be meaningless. This is especially a concern for long-term
(years or more) simulations of self-organized systems but may be less of a concern for event-scale
simulations, especially if these models are well calibrated against laboratory and eld data of past
events. The alternatives are top-down exploratory models that simplify the models by abstraction,
including only the most important factors relevant to the process at hand (Murray 2003, 2007;
Coco et al. 2013). These types of models have proven useful in isolating and demonstrating the
dominance of key processes in certain environments, such as the effect of wave angle on the devel-
opment of alongshore features (Ashton & Murray 2006), the role of roughness in the formation
of rippled scour depressions (Murray & Thieler 2004), and the importance of fetch and vegeta-
tion in dune formation (Durán & Moore 2013). However, because top-down models lack a full
suite of fundamental physics, they are restricted to special cases. Therefore, despite the poten-
tial drawbacks outlined above, bottom-up, process-based models are the most applicable types for
computing coastal morphological change in complex environments and are therefore the focus of
this review.
2.2. Sallenger Regimes
The Sallenger (2000) scale (Figure 1) provides a framework for discussing the most important
physical processes and their morphodynamic agency across the shoreface, beach, and backshore
during morphologically signicant storm events. Process-based models should include physics or
parameterizations to simulate processes across all Sallenger regimes, but not all physical processes
are dominant in every regime.
In the swash regime, incident-band (2–25-s periods) and infragravity (25–250-s periods) waves
run up the beach but do not reach the dune toe. Morphological changes are relatively minor and
conned to the subaqueous nearshore and the upper shoreface, despite strong motions and trans-
ports. Dominant morphodynamic processes in the swash regime include swash-induced transport
modulated by infragravity motions, longshore transport by wave-driven currents, and cross-shore
transport driven by wave asymmetry and undertow.
Beach proles can either erode or accrete during swash conditions, and surf-zone bars can
migrate onshore or offshore, depending on the balance of onshore sediment transport driven
by asymmetry in wave-orbital velocity or acceleration and offshore transport by undertow or
rip currents (e.g., Gallagher et al. 1998, Hoefel & Elgar 2003, Hsu et al. 2006, Fernández-Mora
et al. 2015). Whether berms accrete and the shoreline advances may depend on the value of the
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Barrier foot
Barrier crest
Fair-weather water level
Barrier foot
Barrier crest
Fair-weather water level
Setup + runup
Setup + runup
• Impact restricted to beachface and nearshore
• Erosion or deposition
• Onshore or oshore transport
• Large impacts on beach and barrier front
• Erosional scarp in the dune cli
• Intense oshore sediment transport
• Waves locally overtop the
barrier crest in its lower parts
• Washover deposition
• Occasional breaching and salt-water
intrusion in the back-barrier domain
Inundation regime
• General overtopping of the barrier
and attening of the barrier topography
• Massive landward sediment transport
and deposition
• Likely ecological impacts due to massive
salt-water input in the back-barrier domain
Barrier throat
Lagoon/pond
Washovers
Washovers
Fair-weather water level
Barrier crest
Barrier foot
Barrier foot
Setup + runup
Barrier crest
Fair-weather water level
Setup + runup
Swash regime
Collision regime
Overwash regime
Rhigh < Dlow
Rhigh > Dhigh
Rlow > Dhigh
Dlow < Rhigh << Dhigh
Figure 1
The Sallenger (2000) storm-impact scale. Dhigh denotes the height of the barrier crest, Dlow denotes the height of the barrier foot, Rhigh
denotes the highest action of the waves (tide +surge +setup +runup), and Rlow denotes the lowest action of the waves (tide +surge +
setup). Figure adapted with permission from Goslin & Clemmensen (2017); copyright 2017 Elsevier.
dimensionless fall velocity (Gorlay 1968) relative to some long-term equilibrium value, which is
the basis of some shoreline models (e.g., Miller & Dean 2004, Davidson et al. 2013, Splinter et al.
2014, Montaño et al. 2020).
Models of the swash zone should include the physics of wave refraction and transformation,
including wave breaking, wave-driven undertow and longshore currents, and wave- and current-
driven bedload and suspended sediment transport. While many models have incorporated these
processes, some struggle to correctly represent swash behavior on the upper shoreface, creating
scarps where this should not happen (e.g., Vousdoukas et al. 2012), especially when the beach
slope is relatively steep. The reason is that transport across the instantaneous water line is not
well resolved, and heuristic approaches to controlling the morphology of the foreshore beach
slope (as in Roelvink & Costas 2019 and Roelvink et al. 2019) are required to prevent unrealistic
behavior that eventually affects the whole prole.
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In the collision regime, swash consisting of incident and infragravity waves strike the dune face
(van Thiel de Vries et al.2008), releasing volumes of sand onto the beach, where it is within reach
of ows that can transport the sand alongshore or offshore. Models must represent incident and
infragravity waves, as the former are modulated by the latter, with a signicant effect on the dune
erosion process (e.g., van Thiel de Vries et al. 2008). Models must also incorporate the slumping
of sand from the dune face. Key transport processes in the collision regime are the same as those
for the swash regime, plus dune erosion and dune slumping.
In the overwash regime, waves occasionally reach and overtop the dune or berm, as their height
and runup are modulated by infragravity waves with amplitudes of a half meter or more (see
summaries in Bertin et al. 2018 and Billson et al. 2019). A subtle interplay of runup and backwash
processes may determine whether they lead to increased or decreased berm elevations. On longer
timescales, sediment transported offshore during collision can be returned during recovery of the
beach and dune, but overwash processes are less reversible and lead to barrier transgression. All
the processes listed above continue to be relevant in the overwash regime.
The inundation regime occurs when steady wave setup and surge exceed the dune or berm
elevation and water ows over the crest. Sallenger (2000) assigned this regime the highest po-
tential for morphological change. Inundation is associated with signicant onshore transport and
causes erosion and breaching. Cross-shore transport during inundation can occur as open-channel
ow and can be affected by ow impedance from vegetation and structures. Wave processes are
less dominant in this case, as the morphological development is dominated by current-induced
sediment transport and the slumping of sand into the newly formed breach (Visser 1994).
One common process that Sallenger (2000) did not include is seaward-directed ow,or outwash
(Over et al. 2021; see gure 7 in Harter & Figlus 2017), which can occur when back-barrier water
levels exceed those on the ocean side. Storm surge can inundate marshes or ood back-barrier
lagoons. As forcing relaxes, this water returns seaward (Lennon 1991, Goff et al. 2010, Harter
& Figlus 2017, Goff et al. 2019, Over et al. 2021) and can scour new breaches or deepen exist-
ing channels. Alternatively, winds blowing across back-barrier sounds can generate surge along
the backside of barrier islands. This can result in signicant seaward transport of sand and aid
in the establishment of new inlets. Although the ultimate stability of new inlets may depend on
the general setting of the barrier, back bay, and other inlets (e.g., van Ormondt et al. 2020), the
initial channel deepening by ebb-return scouring may be a decisive process in inlet formation. For
models to resolve this seaward-ow regime, they must include the dynamics of back-barrier water
levels.
3. METEOROLOGICAL FORCING, HYDRODYNAMIC,
AND MORPHODYNAMIC PROCESSES
3.1. Meteorology
The demand for more accurate forecasts of the tracks of tropical cyclones, as well as their intensity
and wind distribution (or structure), with greater lead times is higher than ever due to the large
economic and societal impacts of these storms. A noteworthy example occurred during October
2012, when Hurricane Sandy threatened many communities along the US East Coast. The path
and intensity of Sandy had profound implications for the surge and inundation that would ulti-
mately impact the millions of people and billions of dollars of vulnerable assets in its path. With an
estimated total damage amount of US$70 billion or more, Sandy was one of the costliest storms
in US history and the deadliest to hit the northeast United States in four decades (Blake et al.
2013).
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One of the challenges with the prediction of tropical cyclones is that the important processes
are inherently multiscale in nature. The tracks of tropical cyclones depend primarily on the steer-
ing ow arising from the larger-scale environment (e.g., Marks & Shay 1998),such as synoptic- and
mesoscale tropical and extratropical troughs and ridges, closed lows, tropical upper-tropospheric
troughs, monsoon troughs, and gyres. The processes governing the intensity and size of tropical
cyclones depend on both the inner-core dynamics and the larger-scale environment (e.g., Braun
et al. 2006, Rogers et al. 2006), as well as on air–sea interaction processes (e.g., Black et al. 2007,
Fairall et al. 2009, D’Asaro et al. 2011). This motivates the requirement for accurate represen-
tation in models of the key physical and dynamical processes within the storm itself and in the
larger-scale environment.
Key processes governing tropical cyclone structure (pressure and wind elds) and intensica-
tion include diabatic heating associated with atmospheric convection, particularly in the eye-wall
region, as well as boundary-layer processes, including air–sea interaction. High-resolution models
have been increasingly applied to capture these processes and resolve the critically important inner
part of the storm, which includes the eye, eye wall, and spiral rainbands (e.g., Davis et al. 2008).
The Coupled Boundary Layers Air–Sea Transfer (CBLAST) eld program (Black et al. 2007) pro-
vided important air–sea interaction observations in hurricanes and motivated new approaches to
the parameterization of these processes in tropical cyclone models. Coupled air–ocean and air–
ocean–wave tropical cyclone modeling systems represent these key air–sea interaction processes
in closer agreement with observations than noncoupled models (e.g., Bao et al. 2000, Chen et al.
2010, Olabarrieta et al. 2012, Zambon et al. 2014).
3.2. Improvement of Meteorological Forcing
The remarkable improvement of tropical cyclone track prediction (e.g., Goerss 2007, Hamill et al.
2011) (Figure 2a) has been fueled in part by more skillful global prediction models (Bauer et al.
2015). Improvements can be attributed to more sophisticated data-assimilation systems that take
advantage of many more satellite-based observations and more realistic representations of physical
processes or physical parameterizations of the boundary layer, clouds, radiative forcing, precipita-
tion, land surface, and ocean–atmosphere interactions (Bauer et al. 2015). A three-day hurricane
track forecast today is as skillful as a one-day forecast was 30 years ago. The costs of evacuating
coastal areas before a hurricane are substantial—broadly estimated to be US$1.4 million (adjusted)
for every mile of coastline evacuated (e.g., Whitehead 2003). The improved track forecasts have
steadily reduced the sizes of evacuation areas and mitigated costs. However, there has been less
emphasis on evaluating the skill of accurately predicting tropical cyclone translation speeds, which
is important for hydro- and morphodynamic models.
The prediction of tropical cyclone intensity and structure remains a challenge, and considerable
progress has been made in the last decade, but not as quickly as the track forecast improvements
(e.g., DeMaria et al. 2005, Rogers et al. 2006) (Figure 2b). The slower improvement in fore-
casts of tropical cyclone intensity and structure can be attributed to a lack of critical observations
in the tropical cyclone inner core and the surrounding environment and inaccurate representa-
tions of physical processes in numerical weather prediction models. It has been hypothesized that
track-prediction skill depends more on large-scale processes (e.g., Marks & Shay 1998), while
intensity-prediction skill depends on both the inner-core dynamics and their relationship to the
environment (e.g., Braun et al. 2006, Rogers et al. 2006), as well as air–sea interaction processes
(e.g., Black et al. 2007, Fairall et al. 2009, D’Asaro et al. 2011). Tropical cyclone intensity for strong
tropical cyclones is correlated with translation speed, which is associated with upper-ocean effects
(e.g., Mei et al. 2012).
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0
50
100
150
200
250
300
350
400
Forecast error (nautical miles)
a Track error trend
24 h
48 h
72 h
96 h
120 h
1990 1994 1998 2002 2006 2010 2014 2018
Year
0
5
10
15
20
25
30
Forecast error (knots)
b Intensity error trend
Figure 2
Time series of (a) hurricane track error and (b) hurricane intensity error in the Atlantic basin, showing the
error trends decreasing with time. Figure adapted from Natl. Hurric. Cent. (2020).
It remains a challenge for current operational models to predict tropical cyclone tracks and
intensities with enough delity and accuracy to provide forcing for real-time surge and inunda-
tion models. The averaged track errors from ve-day forecasts are ∼200 nautical miles, and the
averaged intensity (maximum wind speed) errors are ∼15–20 knots. To evaluate the state-of-the-
science hydro- and morphodynamic models, reanalysis-quality data sets of tropical cyclone track,
intensity,and wind elds are needed that have very small errors in the meteorological forcing. As
an example, a methodology has been developed to produce very accurate tropical cyclone elds
(intensity, track, and wind elds) using the US Navy’s Coupled Ocean–Atmosphere Mesoscale
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Prediction System for Tropical Cyclones (COAMPS-TC) (Doyle et al. 2012, 2014), which has
been utilized by hydro- and morphodynamic models (e.g., Hegermiller et al. 2019).
3.3. Water Levels and Currents
Nearshore and coastal conditions are affected by water levels and currents driven by large-scale
processes, including tides, winds,barometric pressure, and thermohaline circulation. Most of these
processes are well understood and can be adequately modeled, but some details can become im-
portant during extreme events, as changes in water levels may cause a change in the Sallenger
regime. Water elevation due to the inverse barometer effect can become the dominant compo-
nent of storm surge on steep coasts with no shelves (Ponte 1992). Olabarrieta et al. (2017) and
Shi et al. (2020) have shown that signicant (∼1 m) variations in total water levels with timescales
of minutes and spatial scales of hundreds of meters can be generated by meteotsunamis triggered
by spiral rainbands associated with tropical cyclones. The resulting small-amplitude (a few cen-
timeters), very-low-frequency water-level uctuations that can modulate infragravity waves and
runup were observed on the Texas coast during Hurricane Harvey (2017) by Anarde et al. (2020).
Forerunner (Ekman) surge forced by alongshore winds and the Coriolis effect can elevate water
levels well before storms arrive (e.g., Kennedy et al. 2011), causing back-barrier lagoons to ood
more easily, which leads to outwash (Goff et al. 2010, Sherman et al. 2013, Harter & Figlus 2017,
Over et al. 2021). Other contributors to unusual water levels include baroclinic gradients (Pringle
et al. 2019) and barotropic waves generated by moving fronts (e.g., Mercer et al.2002).
Large-scale ocean currents, such as the Gulf Stream, Kuroshio, and Agulhas currents, inuence
wave propagation (e.g., Holthuijsen & Tolman 1991, Wandres et al. 2017,Rapizo et al. 2018) and,
in the case of the Gulf Stream, have been linked to short-term but signicant anomalies in coastal
water levels (e.g., Ezer et al. 2017). Along the US East Coast, the Gulf Stream modulated coastal
water levels by nearly 20 cm and modied incident-wave directions by 15° during Hurricane
Matthew (2016) (Hegermiller et al. 2019). Furthermore, mesoscale circulation features, which are
often unresolved in ocean-scale models, have been increasingly identied as important for modi-
fying wave dynamics (e.g., Ardhuin et al. 2017, Romero et al. 2020). It is important to accurately
model the timing of storm-induced water-level anomalies relative to astronomical tidal phase, as
the arrival of surge at high tide may result in morphological changes associated with the overwash
or inundation regimes, whereas the arrival of surge at low tide may result in changes within the
swash or collision regimes.
Many of the processes affecting coastal water levels are well understood and can be accurately
modeled if the forcing and boundary conditions are well constrained. The leading causes of poor
model skill here are inaccurate bathymetry (especially dune-crest elevations, which determine, in
part, the Sallenger regime) and insufcient model resolution. In the coastal ocean, bed friction
can also exert strong control on hydrodynamics, though it is often unknown and used as a tuning
parameter in hydrodynamic models (Fringer et al. 2019). As model resolution has increased with
nesting and computational power,understanding of the importance of smaller-scale ocean features
in coastal processes has expanded (Ganju et al. 2011). At the regional and local scales, additional
factors may inuence nearshore and coastal water levels and currents, such as the discharges from
river mouths, estuaries, or tidal inlets.
Extreme wind speeds, such as those during hurricanes, push the limits of surface wind stress
formulations (Bryant & Akbar 2016, Curcic & Haus 2020), affecting the accuracy of modeled surge
and wave elds (e.g., Moon et al. 2009, Olabarrieta et al. 2012). In particular, it has proved difcult
to close the energy budget at the atmosphere–ocean boundary due to the inability to measure
each component in the eld and the challenges associated with deploying instrumentation under
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extreme conditions. Surface stresses are dependent on the ocean surface drag coefcient, which
is poorly understood for extreme conditions and has been parameterized to vary with the wind
speed, wave conditions, and even rainfall (Bryant & Akbar 2016 and references therein).
3.4. Waves and Wave-Driven Flows
Waves are ubiquitous in the coastal zone and—together with wind- and tide-driven currents—
provide much of the energy that ultimately drives morphodynamic change across all of the Sal-
lenger regimes. This section describes aspects of waves that are key to morphodynamic modeling.
3.4.1. Incident waves (seas and swell). Winds over the ocean exert a stress on the sea sur-
face that generates short-period waves (seas), which, through nonlinear interactions, develop into
longer-period waves (swell). Together, these waves form a spectrum in the incident band (2–25 s;
Holthuijsen 2007). As waves propagate over the deep ocean, they can break due to steepening
(whitecapping), redistribute energy over wave frequencies through wave–wave interactions, and
interact with currents. As seas and swell approach shallower water, they increase in height (shoal),
become more asymmetric (with higher peaks than troughs), change direction (refract) toward the
shoreline, and ultimately break due to depth limitations. As they shoal and break,waves impart mo-
mentum to the water column that drives currents, generates wave-induced turbulence, and exerts
shear stress on the bottom that can resuspend sediment, generate gradients in sediment transport,
and ultimately cause morphodynamic change (Roelvink & Reniers 2012, Davidson-Arnott et al.
2019).
Numerical modeling of coastal hydrodynamics requires the ability to simulate dominant wave
processes over a range of spatial scales and across hydrodynamic regimes and to parameterize
other processes that are less important, not well understood (such as depth-limited breaking), or
computationally too expensive to model (such as triad and quadruplet wave–wave interactions).
As the dominant physics change from deep water to intermediate and shallow water,including the
surf zone, coupling different models or different model modes becomes necessary to accurately
simulate the waves that drive coastal morphological change. Because wave-driven processes con-
tribute signicantly to the total water level (e.g., Stockdon et al. 2006), they determine in large
part the Sallenger regime and the timing of changes between regimes.
On the ocean scale, uncertainty in hydrodynamic forcing stems from parameterization of the
source, sink, and redistribution formulations for wave energy over the spectrum. Source, sink,
and redistribution terms for wave energy are sufcient to resolve bulk wave characteristics with
predictive skill but poorly capture wave spectral characteristics. There have not been recent major
advances in the development of these formulations (see Cavaleri et al. 2018, 2020, and references
therein). However, due to increased computational power, there have been large advances in the
size and resolution of the areas that can be modeled and the processes that can be simulated directly
(gure 2.4.1 in Cavaleri et al. 2018).
3.4.2. Shoaling-wave transformations. Shoaling transforms waves into nonlinear shapes that
generate skewed and asymmetric orbital velocities that can drive sediment transport. Wave shape
is not resolved in wave-averaged models, such as SWAN and WAVEWATCH III, so methods
have been devised to estimate skewness and asymmetry from local wave properties (Rienecker &
Fenton 1981, Isobe & Horikawa 1982, Doering & Bowen 1995, Doering et al. 2000, Ruessink
et al. 2012). Doering & Bowen (1995) rst parameterized wave skewness and asymmetry using
the local Ursell number Ur, and Ruessink et al. (2012) extended that parameterization using a
large data set from barred beaches with signicant wave heights ranging from 0.05 to 3.99 m
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(0.04 <Ur<24.8). However, there is a lot of scatter in the observations, which Rocha et al.
(2017) attributed to wave-propagation history. Using wave-ume measurements and numerical
simulations from the SERR1D model (Cienfuegos et al. 2006, 2007), Rocha et al. (2017) found
a correlation between the wave nonlinearity parameters and the offshore wave steepness, beach
slope, and spectral bandwidth, conrming earlier studies by Elgar & Guza (1985) and Norheim
et al. (1998). The parameterization of Rocha et al. (2017) extends that of Ruessink et al. (2012) by
incorporating nonlocal wave parameters and beach slope.
3.4.3. Infragravity waves. Incident waves with varying frequencies and directions can form
wave groups—sequences of waves with higher and then lower amplitudes (Figure 3). As these
waves exert a stress on the water column (the radiation stress; Longuet-Higgins & Stewart 1962),
the mean surface is depressed under the high waves and elevated under the low waves. This undula-
tion constitutes a wave with a period of ∼25–250 s that travels with the wave groups and is called
a bound infragravity wave (Munk 1949, Tucker 1950) (see the sidebar titled Infragravity Wave
Motions). Bound infragravity waves gain energy through the shoaling mechanism as wave groups
move into shallower water (List 1992, Masselink 1995, Janssen et al. 2003, Battjes et al. 2004).
Ultimately, they are released from the group as the incident waves dissipate and form free infra-
gravity waves that may reect from the shore to propagate seaward. Energy at infragravity-wave
frequencies can also be generated in the nearshore by modulations in wave breaking at the wave-
group scale, known as the breakpoint mechanism (Symonds et al. 1982). In the surf zone itself,
infragravity waves gain energy by radiation stress forcing (Foda & Mei 1981, Schäffer & Svend-
sen 1988) but may also lose energy through bottom-friction dissipation (Henderson & Bowen
2002) and infragravity-wave breaking (van Dongeren et al. 2007).
As a result of these processes, infragravity waves can have considerable wave heights (∼1m)
during storm conditions (see references summarized in Billson et al. 2019); modulate water levels,
short-wave characteristics (e.g., Tissier et al.2015), and surf-zone velocities; and exert fundamental
control on wave runup (e.g., van Gent 2001, Stockdon et al. 2006). Whereas Bertin et al. (2019,
gure 11) suggest that infragravity waves do not contribute signicantly to morphological change
in Sallenger’s swash and inundation regimes, their potential relevance for beach cusps and sand-
bar formation has been studied since the 1980s, and they have been linked to bar migration (e.g.,
Roelvink & Stive 1989). They are clearly important in the collision and overwash regimes, where
they contribute to dune erosion (e.g., van Thiel de Vries et al. 2008, Roelvink et al. 2009), inlet
closure (Bertin et al. 2019), and the formation of washover deposits (Baumann et al. 2017). (For
recent reviews of infragravity-wave dynamics and their inuence on morphology,see Bertin et al.
2018, Billson et al. 2019, and references therein.)
The inclusion of infragravity waves in models such as XBeach (Roelvink et al. 2009) and the In-
Wave component of COAWST (M. Olabarrieta, C.A. Hegermiller & J.C. Warner, manuscript in
review) may be the most important advance in coastal morphodynamic models in the last 15 years.
In these models, wave groups are statistically generated from short-wave spectra, assuming ran-
dom phases. The resulting infragravity wave is solved via an analytical solution (Herbers et al.
1994, van Dongeren et al. 2003) and imposed as water-level variations on the offshore boundary
of the model domain. Infragravity-wave energy generated by breakpoint forcing is resolved in the
models either by radiation stress or vortex force formulations. The inclusion of infragravity waves
and associated sediment transport in nearshore models requires high spatial resolution and short
time steps, which presently constrains the spatial and temporal scope of model simulations.
3.4.4. Wave-driven ows. Wave-generated ows are uniquely important in coastal models. As
waves shoal and break, kinetic energy is dissipated into foam, turbulence,and heat and converted
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Equilibrium bound wave
(Longuet-Higgins & Stewart 1962, 1964)
Surf zone
Breakpoint
Bound-wave shoaling
(List 1992, Masselink 1995)
Breakpoint generation
(Symonds et al. 1982)
Surf-zone generation (Foda & Mei 1981)
Bottom-friction dissipation (Henderson & Bowen 2002)
Infragravity-wave breaking (van Dongeren et al. 2007)
Reection
Reection
Leaky infragravity waves
Edge
wave
Land Foreshore
b
Side view
a
Top view
Shoreline
Runup overwash
Breakpoint
generation
Bound-wave
shoaling
Surf-zone
generation,
bottom-friction
dissipation,
and breaking
Bound wave
Incident-wave
groups
Incident-wave
groups
Breakpoint
Surf-zone generation
and dissipation
Figure 3
Schematic of infragravity waves, illustrating their formation from incident waves and breakpoint generation,
followed by shoaling, refraction, reection, breaking, and dissipation.
into the forward and rotational momentum of rollers, which are turbulent water masses that
slide down the faces of broken waves and contribute to the energy and momentum budgets of
the surf zone. The net effect of breaking waves on average momentum is called the radiation
stress (Longuet-Higgins & Stewart 1964). The alongshore component of radiation stress drives
alongshore ows. The cross-shore component is balanced on a closed coast by a pressure
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gradient, producing an increase of the mean water level toward the shoreline, called the wave-
induced setup. Radiation stress is formulated for depth-average ows. Alternate approaches are
required to resolve the forcing for 3D ow and include the formulations based on the generalized
Lagrangian mean and vortex force (Lane et al. 2007). The generalized Lagrangian mean was
introduced by Andrews & McIntyre (1978), with the approach of averaging over disturbance
positions of the uid particle, which is valid over the complete water column. Ardhuinet al. (2008)
developed a practical set of equations based on the work of Dingemans (1997), which have been
applied in several studies. A recent variation of the generalized Lagrangian mean approach has
been implemented in Delft3D (Nguyen et al. 2021). The vortex force approach was developed
by Craik & Leibovich (1976) and splits the wave-averaged effects into gradients of a Bernoulli
head pressure adjustment to accommodate incompressibility (Lane et al. 2007) and a vortex
force, which, after wave averaging, is a function of wave-induced Stokes drift and ow vorticity.
This approach allows for these conservative terms to be split from other, nonconservative
wave-dissipation-induced acceleration contributions and has been implemented in COAWST
(Kumar et al. 2012, following McWilliams et al. 2004 and Uchiyama et al. 2010).
The volume of water in the rollers is carried toward the shore and returned in rip currents or
below the troughs of the waves as an undertow current. The generation of rollers is modeled as a
function of a percentage of wave breaking and roller dissipation following one of several semiem-
pirical formulations (Walstra et al. 1996, Roelvink et al. 2009). Considerable effort has gone into
modeling the vertical distribution of the cross-shore and longshore wave-driven current, with
key ingredients being the near-surface stress associated with rollers, the vertical distribution of
turbulence and near-bed streaming, and bottom friction (e.g., Kumar et al. 2012). Given along-
shore variations in bathymetry or wave forcing, the return ow may concentrate into rip currents
(MacMahan et al. 2006). Gradients in the alongshore component of the radiation stress drive a
nearshore longshore current that can be O(1 m/s) in magnitude.
3.5. Sediment Transport
Sediment transport in nearshore environments is driven mainly by short waves (seas and swell),
infragravity motions, and wave-induced currents. The short timescales of seas and swell are a
computational challenge for models that must integrate their effects over storm-event timescales,
so most morphodynamic models consider time-averaged waves and resolve more slowly varying
currents. From a sediment-transport perspective, infragravity waves act on a timescale that blurs
INFRAGRAVITY WAVE MOTIONS
Infragravity waves, also known as surf beat, are long-period waves (periods of ∼25–250 s) generated by the in-
teraction of short waves to form wave groups. Since their discovery in the late 1940s, they have been thought to
cause a range of phenomena, some of which are now attributed to other processes. But what has remained a well-
established mechanism is the role of infragravity runup in elevating water levels at the coast, particularly during
storms. In addition, the elevated water surfaces generate the undertow responsible for offshore transport, and the
modulation of short waves drives cross-shore transport in both directions. Most importantly, the increased water
levels can push storm conditions into a higher Sallenger regime, elevating swash conditions to collision or collision
to overwash. The incorporation of infragravity motions into coastal sediment-transport models like XBeach and
COAWST may be the most signicant advance in coastal model physics in the last two decades and has led to
substantial improvements in our ability to model extreme events (e.g., gure 11 in Bertin et al. 2018).
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the distinction between wave motions and mean currents, which is one reason that resolving them
has improved model skill.
Sediment-transport formulations can represent the total load or split it among bedload and
suspended-load models. Both modes of transport are important for morphological evolution (e.g.,
Reniers et al. 2013). Bedload transport occurs with high sediment concentrations very close to the
seabed, so bedload ux is parameterized by local near-bed ows in the form of mean currents,
wave-orbital motions, and boundary-layer streaming acting on sediment properties. By contrast,
suspended-sediment transport, which is dominant during storm events, is the product of current
velocities and relatively small sediment concentrations over the entire water column. Models of
suspended-load ux explicitly account for the spatial variabilities of waves, turbulence, currents,
and bathymetry by solving the advection–diffusion–settling equation for the conservation of sedi-
ment mass, either in a depth-averaged formulation (Galappatti & Vreugdenhil 1985) for 2D mod-
els such as XBeach (Roelvink et al. 2009) or in a depth-resolving formulation in 3D models such
as COAWST (Warner et al. 2008b). Suspended-sediment formulations include a mechanism for
depositional uxes to the seaoor (based on the product of near-bed concentration and settling
velocity) and resuspension from the seaoor, represented by an erosional ux or via changes in
a near-bed reference concentration. Both approaches usually rely on the wave-stirring concept
(e.g., Soulsby 1997; van Rijn 2007a,b), which is driven by bottom shear stress generated by the
combined inuence of waves and currents (Smith 1977, Grant & Madsen 1979). In shallow wa-
ter, turbulence produced by breaking waves that penetrates to the seabed can further enhance
resuspension (Roelvink & Stive 1989).
Bedload transport under shoaling waves is inuenced by a wave skewness that generates asym-
metry in velocity and acceleration over the wave cycle (Nielsen 1992) (Figure 4), horizontal pres-
sure gradients (Drake & Calantoni 2001, Hsu & Hanes 2004, Foster et al. 2006), and bedload
streaming (Longuet-Higgins 2005; Nielsen 2006; Kranenburg et al. 2012, 2013; Fuhrman et al.
2013). The classic quasi-steady energetics approach to wave-induced bedload transport of Bailard
& Inman (1981) captures only velocity asymmetry. Kim et al. (2018, 2019) showed that progres-
sive wave streaming contributes an additional 60–300% of the total load onshore transport rate,
depending on wave-orbital velocity skewness and asymmetry. Wave models that simulate wave-
averaged action density, such as SWAN and WAVEWATCH III, cannot represent the shoaling
transformations that generate skewness and asymmetry,but parameterizations of wave asymmetry
based on local conditions (water depth and wave height and period; van Thiel de Vries et al.2008,
Ruessink et al. 2012) have been used to determine wave-orbital velocities over all portions of the
wave period (Figure 4). These velocities can then be used in bedload transport formulae like the
SANTOSS equation (Ribberink et al. 2010, van der A et al. 2013). Despite the detailed physics
represented in these equations, modelers have found it necessary to modify the results with leading
coefcients: In XBeach, the facua calibration coefcient adjusts the effect of wave shape on cross-
shore transport, and in COAWST, separate coefcients modify the wave- and current-induced
transport rates. Some studies have found that the same value of the XBeach facua parameter per-
formed well in simulations at different sites (van der Lugt et al. 2019), but others have found
that different values were needed to successfully model onshore versus offshore transport rates
depending on the energy of the incoming waves (Rafati et al. 2021). The need for model-tuning
parameters that vary with wave conditions indicates that not all the physics are being captured in
these parameterizations and reinforces the argument that nonlocal conditions, wave-propagation
history, and sediment response are important factors in determining wave-shape-induced
transport.
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Shoreward ow (Stokes + rollers)
Seaward ow (undertow)
Bedload transport
Velocity (m/s)
Distance oshore (m)
Elevation (m)
60 m 135 m 210 m
2
0
–2
–4
–6
–8
–100 0 100 200 300 400 500 600 700
0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0
t/T
0.10
Onshore
0.08
0.06
0.04
0.02
0
–0.02
–0.04
–0.06
–0.08
–0.10
Oshore
Ur (m/s)
1.2
0.8
0.4
0
–0.4
–0.8
Figure 4
Schematic of wave shoaling and vertical circulation in the nearshore, showing the bed prole along a cross-shore transect measured in
the DUCK94 experiment on October 12, 1994, and the simulated ow eld (Kalra et al. 2019). Cross-shore velocities are shown with
shading and arrows. The inset graphs illustrate intrawave near-bed velocities over wave period Tat three cross-shore locations,
calculated from the Ursell number Urof waves in the SWAN model according to Abreu et al. (2010) and Ruessink et al. (2012).
Supplemental Video 1 shows the development of the nearshore circulation and evolution of the nearshore and beach bathymetry and
topography at Matanzas, Florida, during Hurricane Matthew.
3.6. Vegetation and Hydraulic Roughness
Coastal vegetation (submerged aquatic vegetation, marsh vegetation, dune grasses, and woody
vegetation) inuences morphological evolution during storms in multiple ways: Vegetation im-
pedes ow,damps wave motions, reduces sediment resuspension, affects near-bed turbulence, and
stabilizes the seabed (Hemminga & Duarte 2000, Wamsley et al. 2010, Carr et al.2012). On longer
timescales, vegetation reduces coastline erosion and aids dune growth. Two general approaches
have been proposed to account for the effect of vegetation on uid dynamics and thus morpho-
logical change: (a) parameterize the effect of vegetation as enhanced hydraulic roughness, and
(b) resolve the effects of vegetation using explicit formulae to model hydrodynamics in the vege-
tation canopy.
The rst approach aims to translate land-cover information on vegetation type, usually de-
rived from remote sensing, to hydraulic roughness (Schambach et al. 2018, de Vet et al. 2015).
Roughness values are typically parameterized by a bed-friction coefcient (e.g., Manning’s nor
the Chezy coefcient). Conversion from land cover to roughness is done through conversion ta-
bles (e.g., Arcemet & Schneider 1989, Mattocks & Forbes 2008). This allows the initial bed fric-
tion to vary spatially and, in some models, change as land cover evolves with the erosion or burial
(van der Lugt et al. 2019). Semisupervised machine learning techniques such as the conditional
random eld method (Buscombe & Ritchie 2018) can help map land cover from imagery, but
the initialization and evolution of roughness values remain subjective. The overall impact of the
bottom roughness on the simulated hydrodynamics (and therefore morphodynamics) varies de-
pending on the source of the land-cover data, the method for converting it to roughness, and the
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geographic distribution of roughness in the affected area (Ferreira et al. 2014, Machineni et al.
2019). Supplemental Video 2 shows an example of the effect of varying the bottom-roughness
parameterization in a coupled hydro- and morphodynamic model simulation of the passage of
Hurricane Ike over Bolivar Peninsula in Galveston, Texas (from the simulation described in
Figure 7 below; see Section 5.2.4).
The second approach aims to explicitly resolve stem shape and density and use these in momen-
tum equations to model drag and turbulence (e.g., van Rooijen et al. 2016,Beudin et al. 2017). Veg-
etation affects wave-induced streaming (Luhar et al. 2010, Luhar & Nepf 2011) and the vertically
varying production and dissipation of turbulence (Uittenbogaard 2003). The effect of vegetation
on wave damping was derived parametrically by Dalrymple et al. (1984) and Mendez & Losada
(2004) and has been implemented in spectral wave models such as SWAN (Suzuki et al. 2012).
Vegetation effects on infragravity waves are implicitly accounted for by bottom drag, which is
considered appropriate because the wave-orbital excursion of infragravity waves is generally much
larger than the spacing between vegetation (Svendsen 2006). Although most of these explicit ap-
proaches have been developed for submerged aquatic vegetation (see Nepf 2012), modelers (e.g.,
C.A. Hegermiller, J.C. Warner, M. Olabarrieta, C.R. Sherwood & T.S. Kalra, manuscript in re-
view, using the model described in Beudin et al. 2017) are adjusting the physical parameters to
adapt them to emergent vegetation such as dune grasses and mangroves. Both the empirical and
physics-based approaches have been shown to improve model skill, as discussed below.
3.7. Wetting and Drying
A robust wetting and drying procedure is required for simulating the uprush and backwash during
swash and collision regimes, the overtopping during the overwash regime, and the inundation of
marshes and tidal ats by tides and surge. The procedure must be able to handle both subcritical
and supercritical ows without numerical oscillations. In XBeach, this has been achieved by adopt-
ing explicit upwind schemes with automatic time steps (similar to Stelling & Duinmeijer 2003),
which is especially suitable for drying and ooding and which allows a combination of sub- and
supercritical ows. This scheme guarantees positive water depths if the Courant–Friedrichs–Lewy
criterion is observed and removes the need for special ooding procedures. The original imple-
mentation applied rst-order discretizations and momentum conservation; later implementations
include second-order advective terms and a switch (as in Stelling & Duinmeijer 2003) between
momentum conservation and conservation of energy head. Validation of the implemented scheme
was provided for runup cases by Roelvink et al. (2009) and for a range of inundation and dam-
break problems by Hartanto et al. (2011). A slightly different approach is required for COAWST
because of its staggered grid, but an effective numerical scheme has been implemented and tested
by Warner et al. (2013).
3.8. Morphological Change
In this section, we describe how sediment transport is coupled with morphodynamic change and
discuss techniques to speed up computational time.
3.8.1. The Exner equation. Morphological change is governed by the Exner equation (Exner
1920, 1925), a simplied version of the generalized sediment mass-balance equation (Paola &
Voller 2005), which states that porosity-corrected bed elevation changes are caused by horizon-
tal divergence in sediment ux. The main challenge in solving the Exner equation is modeling
sediment ux, which includes both bedload and suspended-sediment transport (Paola & Voller
2005, Mendoza et al. 2017), based on at least partly empirical formulae (Kaveh et al. 2019) that
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require calibration (Mendoza et al. 2017, Baar et al. 2019). Even with accurate transport for-
mulae, attention to the numerical discretization used to solve the Exner equation is required;
poorly formulated methods can lead to excess dispersion and bed elevation oscillations ( Johnson &
Zyserman 2002, Callaghan et al. 2006, Chiang et al. 2011).
3.8.2. Morphological acceleration. Numerical simulations of long-term morphological
change can be computationally demanding if done by brute force (e.g., Safak et al. 2017),so meth-
ods have been developed to speed up morphodynamical models (Lesser et al. 2004, Roelvink 2006,
Ranasinghe et al. 2011, Roelvink & Reniers 2012, Luijendijk et al. 2019, Morgan et al. 2020) us-
ing a combination of two approaches: input reduction (or input schematization; e.g., Walstra et al.
2013, Luijendijk et al. 2019) and morphological acceleration (Lesser et al. 2004, Roelvink 2006,
Ranasinghe et al. 2011). Input reduction seeks to force the model using representative conditions
(e.g., the average wave height) or only the conditions that effect morphodynamic change (e.g.,
waves greater than some threshold). The morphological acceleration factor assumes a linear re-
lationship between the divergence in horizontal sediment ux and the change in bed elevation
over some effective time and multiplies the bed changes by a morphological acceleration factor
(Mf) to simulate change over a longer time period. For example, simulations made over a tidal
cycle with representative tidal conditions (from input reduction) with an Mfof 4 are intended
to represent morphological change for two days. The key assumption is that bed changes, even
after being multiplied by Mf, do not signicantly change the sediment-transport rate—or, more
specically, the divergence in sediment transport. One method used in storm simulations is to
divide the time series of wave spectra into hours and, for each hour, to simulate waves for only
1/Mfhours. The time axis of the other forcing conditions (water level, wind speed and direction,
etc.) is shrunk by the same Mf. Experience in many actual cases has shown that an Mfof 5–10
yields very small deviations relative to brute-force simulations. Although Mfvalues of up to 100
have been used successfully in long-term simulations (e.g., Lesser et al. 2004, van der Wegen &
Roelvink 2008), extreme events have strongly time-varying forcing conditions that preclude the
use of a high Mf, and the events are often short enough that simulating the entire forcing time
series is computationally affordable.
4. MODEL SKILL AND UNCERTAINTY
The greatest challenge in assessing the skill of morphological models is often the lack of accurate
and timely data for comparison. But even when good data are available, assessing morphological
model skill and uncertainty is tricky. Whereas hydrodynamic model output can be compared ob-
jectively to observed integral parameters (wave heights, wave periods, etc.) or time series, it is dif-
cult to assess morphological model skill because the output concerns changes in shape (Sutherland
et al. 2004). Point-by-point metrics based on the mean-squared difference between modeled and
observed elevation maps, such as the Brier skill score (van Rijn et al. 2003, Stow et al. 2009), tend
to favor model results that underestimate the variance of changes (Bosboom et al. 2014). One ap-
proach from meteorology is to assess the magnitude of displacement required to minimize the dif-
ference between the model and observations, which can produce multiple metrics over a range of
spatial scales (Bosboom & Reniers 2014). For the case of storm-driven morphodynamic elevation
change, volume changes and the locations and elevations of dune features can be considered. Cate-
gorical approaches can help with broad-scale comparison between models and observations (C.A.
Hegermiller, J.C. Warner, M. Olabarrieta, C.R. Sherwood & T.S. Kalra, manuscript in review)
(Figure 5). Unfortunately, because different metrics are often selected, it is difcult to compare
skill across model applications.
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a Observed prestorm topography
and bathymetry b Observed change c Modeled change d Modeled change with
vegetation
e Assessment of panel c
skill f Assessment of panel d
skill
Cross-shore
distance (m)
0
400
800
1,200
Cross-shore
distance (m)
0
400
800
1,200
0 1,000 2,000
Alongshore distance
0 1,000 2,000
Alongshore distance
0 1,000 2,000 0 1,000 2,000
0 1,000 2,000 0 1,000 2,000
(m)
5
0
–5
Hit
False Alarm
Correct Reject
Miss
Figure 5
(a) Observed topography and bathymetry of the Wilderness Breach on Fire Island, New York, before Hurricane Sandy (2012).
(b) Observed change due to Hurricane Sandy,where red indicates erosion and blue indicates deposition. Note that the apparent
back-barrier deposition is likely an artifact. (c) Modeled change from COAWST simulations that did not account for effects of
land-cover variation. (d) Modeled change from COAWST simulations with the vegetation module activated. (e) Assessment of the skill
of the modeling shown in panel c, where Hit indicates that the model correctly predicted observed erosion or deposition, False Alarm
indicates that the model predicted erosion or deposition that was not observed, Correct Reject indicates that the model correctly
predicted no change, and Miss indicates that the model did not predict observed erosion or deposition. Note that accounting for
vegetation effects on hydrodynamics and sediment transport minimizes the False Alarm areas associated with overwash. (f) Assessment
of the skill of the modeling shown in panel d.
Accurate pre- and poststorm measurements are required to initialize models and assess changes.
Nearshore bathymetry is measured by various methods (lidar,occupied and autonomous oating
vessels with sonar,bottom-crawling vehicles, and inference from wave motions). All of these have
trade-offs in terms of expense, areal coverage, resolution, accuracy, and timeliness, and none are
currently able to provide bathymetric updates at the peak of extreme storms. Poststorm obser-
vations must be made immediately (within days) after the event, before natural or human pro-
cesses of recovery can change the landscape (Lazarus & Goldstein 2019). The recent increase
in rapid-response ights like the NOAA National Geodetic Survey emergency-response ights
(https://storms.ngs.noaa.gov) and the ability to process those images using modern multiview
photogrammetry (also known as structure from motion) can provide timely information about
subaerial conditions, but sometimes that is not fast enough, as repair efforts can start the day after
an event (Sherwood et al. 2018). New breaches tend to evolve rapidly: The Wilderness Breach
on Fire Island changed remarkably in the days, weeks, and months after Hurricane Sandy (Hapke
et al. 2017), and the data available for model validation (summarized in van Ormondt et al.2020)
were collected at various points during the inlet evolution. Determination of the extent of storm-
induced scour in channels is difcult because scour can continue after the storm passes, and chan-
nel depths cannot be monitored with subaerial techniques. Model parameterizations governing
scouring are therefore calibrated on specically designed controlled experiments, such as those
described by Visser (1994) for a ow-dominated breach and Schweiger et al. (2020) for a wave-
dominated breach through a dune.
Uncertainty in initial conditions, forcing, or model formulations combine to compound
model errors. We often lack spatially resolved hydrodynamic observations in the study area: Wave
buoys and water-level measurements are sparse, and there are often few current measurements
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MA14CH05_Sherwood ARjats.cls July 19, 2021 10:22
0
2
4
6
Poststorm
maximum
crest level (m)
–4
–2
0
Crest level change
during storm (m)
–400
–300
–200
–100
0
Eroded volume
(m3/m)
Observations
Computations
Wave angle
Wave magnitude
Surge
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Alongshore distance (km)
0
50
100
150
200
Deposited volume
(m3/m)
Figure 6
Sensitivity of XBeach-computed dune shape change to uncertainty in offshore forcing during Hurricane Sandy (2012) at the
Wilderness Breach on Fire Island, New York: (a) poststorm maximum crest level (meters above NAVD 88), (b) crest level change
throughout the storm, (c) total eroded volume in the dune section, and (d) total deposited volume in the dune section. Observations are
shown in black, and base computations are shown in red. The shaded areas indicate the variability of the parameters as a result of
variations in hydrodynamic forcing: Wave angle (purple) shows a variation of ±5° in the offshore mean wave direction,wave magnitude
(blue)showsa±10% variation around the predicted offshore signicant wave height, and surge (green)showsa±10% variation of
predicted offshore water levels. The observed breaching extent is indicated in gray shading because no subaerial poststorm observations
are available there. Supplemental Video 3 shows the simulated hydro- and morphodynamics at the Wilderness Breach during the
event for best-estimate parameter settings. Figure adapted with permission from van der Lugt et al. (2019); copyright 2019 Elsevier.
to constrain the model outcome. Uncertainty in initial and forcing conditions propagates into
model results; for example, a study by van der Lugt et al. (2019) demonstrated the limitations of
single deterministic model runs in forecasting storm impact (Figure 6).
5. OUTLOOK AND TRENDS
5.1. Processes
Morphodynamic models have become both wider and deeper—wider as more processes are added
(like the effects of vegetation or even bulldozers; Lazarus & Goldstein 2019), and deeper as de-
tailed physics replace earlier parameterizations (e.g., vortex forcing and incident-wave runup) and
more information on initial and boundary conditions becomes available. We cite this as one of the
overall trends in coastal models in the Section 5.2. In this section, we discuss some additions and
improvements.
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5.1.1. Wave-resolving models. One solution to the difculty in parameterizing wave behav-
ior in shallow water is to resort to wave-resolving models such as MITgcm, TRIM, SUNTANS,
SWASH, CROCO, NHWAVE, FUNWAVE, Celeris, and XBeach-NH+(Marshall et al. 1997,
Casulli 1999, Fringer et al. 2006, Zijlema et al. 2011, Debreu et al. 2012, Ma et al. 2014, Malej et al.
2015, Tavakkol & Lynett 2017, and de Ridder et al. 2021, respectively), which are capable of skill-
fully simulating the shapes and orbital motions of nonlinear waves (e.g., Tissier et al. 2011, Smit
et al. 2014) and, critically, can resolve water-level variations associated with setup and swash. Al-
though most wave-resolving models lack sediment-transport formulations and are still too compu-
tationally expensive to simulate regional-scale nearshore morphodynamics, we anticipate that this
will change, and that wave-resolving models will be improved to incorporate breaking-induced
turbulence, be coupled with sediment-transport formulae (e.g., van der A et al. 2013, Fringer et al.
2019), and become more common components of coastal morphodynamic models.
5.1.2. Soil mechanics, groundwater, and dune vegetation. The mechanics of dune and fore-
shore erosion are represented by relatively simple parameterizations based on, for example, wave
impact (Overton & Fisher 1988), dry cell erosion, or critical slope (Roelvink et al. 2009). Although
the primary controls on dune scarping (relative water level, beach width, dune volume,and beach
slope; Palmsten & Holman 2011, Héquette et al. 2019, Davidson et al. 2020) are incorporated
in storm-event models (e.g., Cohn et al. 2019b), secondary factors (Davidson et al. 2020), such
as vegetation, root mass, the presence of wrack or woody debris, and compaction, are often not.
Although simple parameterizations have provided adequate results in terms of slumping rate and
postevent prole shape, more physically based modeling of dune and foreshore processes based
on soil-mechanics principles may be the key to improving models of dune stability and beach
trafcability. Recent progress in sensors to rapidly characterize key soil properties, such as sedi-
ment strength and its relationship to wave energy,friction angle, and moisture content (Stark et al.
2017, Albatal et al. 2019), may lead to improved modeling of soil mechanics in morphodynamic
models. However, with improved physical description of these processes will come a demand for
more data regarding soil moisture, geological framework, and sediment characteristics, for which
observations at the appropriate scale are often lacking.
5.1.3. Hydrologic coupling. Signicant rainfall on land and over water often accompanies
storms, with quantiable contributions to water levels in back-barrier lagoons or sounds by direct
precipitation (Rey et al. 2020), elevated groundwater tables, and potential for compound ood-
ing from runoff in large watersheds. Surface runoff and elevated groundwater can impact beach
stability and lead to barrier-island ooding (Housego et al. 2018, Huizer et al. 2018). Coupling
of hydrologic, groundwater, and ocean hydrodynamic models will provide improved boundary
conditions and increase our ability to predict total water levels for inundation and morphologi-
cal change models (Santiago-Collazo et al. 2019, Bakhtyar et al. 2020, Gori et al. 2020, Yin et al.
2020). Increased computational resources, improved nesting schemes, and use of input-reduced
and reduced-physics approaches will support the inclusion of hydrological processes in coastal
ocean modeling.
5.2. Trends
Here we summarize emergent trends in storm-impact models.
5.2.1. Community and open-source models. Early earth-science open-source models
were developed in the 1990s to address air-quality modeling, climate prediction, and weather
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forecasting (Voinov et al. 2010). Open-source ocean and nearshore models began to emerge
in the late 1990s and early 2000s with ROMS, POM, and COHERENS, and the Community
Sediment Transport Model project that would eventually become COAWST was launched
in 2000 (Sherwood et al. 2000, 2002). Codes for models that were previously proprietary,
such as Delft3D and TELEMAC, have been released, and since then, models have often been
open source from their conception (e.g., XBeach and COAWST). The use and maintenance
of models have become much easier with the advent of public source-code repositories like
SourceForge and GitHub and the development of niche earth-science and marine model
repositories, such as those hosted by the Community Surface Dynamics Modeling System
(https://csdms.colorado.edu/wiki/Model_download_portal) and the OpenEarth initiative at
Technische Universiteit Delft and Deltares (https://www.deltares.nl/en/software/openearth).
Most of the models used for coastal morphodynamics research are open source, and we anticipate
that this trend will continue.
5.2.2. Increased physical detail. The information presented above makes it clear that more
processes are being included in models (see next section) and more physics are being included in
the processes, replacing earlier parameterizations. Physics of infragravity waves, vortex forcing,
wave shape, rollers, boundary-layer streaming, ows in submerged and emergent vegetation, land
cover, and dynamic roughness have been incorporated in existing models, and we expect this trend
of increasingly detailed physical processes to continue.
5.2.3. Inclusion of more and more-detailed processes. More processes are being incorpo-
rated into coastal morphodynamic models. In addition to those listed above, four models are cap-
turing important features of aeolian dune formation and vegetation: the Coastal Dune Model
(Durán & Moore 2013), AEOLIS (Hoonhout & de Vries 2016), Duna (Roelvink & Costas 2019),
and Windsurf (Cohn et al. 2019a). Although aeolian transport plays a minor role relative to the
wave-driven processes in storms, even during the recovery phase (e.g., Kombiadou et al. 2021),
the inclusion of these processes will improve simulations on timescales of years to decades. The
effects of wave growth due to local winds can also be included. Although additional wind-driven
wave growth in the nearshore domain is negligible compared with transformation and dissipation
processes, changes in the air–sea drag coefcient occur as waves shoal and break (Ginis et al.2021).
In lagoons behind reefs or in bays behind sandy barriers, the situation may be quite different, and
both infragravity waves (not resolved by spectral wave models) and wind growth (not resolved in
time-domain models) may be relevant (e.g., Drost et al. 2019). The role of structures in morpho-
dynamic processes can also be included (e.g., Smallegan et al. 2016 for the case of a seawall in New
Jersey). These and other processes (e.g., biological effects on sediment mobility and groundwater
controls on dune and beach erosion) are being added to coastal morphodynamic models, making
them more general.
5.2.4. Improved initial, lateral, and bottom-boundary conditions. The accuracy of coastal
morphology models is highly dependent on the accuracy of the meteorological, wave, and
hydrodynamic models by which they are forced, as well as the prescription of the initial and
bottom boundary conditions. The hindcast and forecast skill of these models is increasing as
the availability of computational power allows for higher resolution and less parameterization of
physics in parent models, from which the lateral boundary conditions for the coastal morphology
model are extracted. Additionally, parent models have expanded grid exibility, allowing for
stepwise renement and making the nesting of high-resolution coastal morphology model
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Nearshore domain (2 km)
Coastal domain (0.5 km)
Coastal domain (0.5 km)
Galveston Bay domain (50 m)
NLCD class
number NLCD class name Manning’s n
0 No value 0.02
11 Open Water 0.02
21 Developed – Open Space 0.02
22 Developed – Low Intensity 0.05
23 Developed – Medium Intensity 0.1
24 Developed – High Intensity 0.15
31 Barren Land (Rock/Sand/Clay) 0.09
41 Deciduous Forest 0.1
42 Evergreen Forest 0.11
43 Mixed Forest 0.1
52 Shrub/Scrub 0
71 Grassland/Herbaceous 0.05
81 Pasture/Hay 0.033
82 Cultivated Crops 0.037
90 Woody Wetlands 0.1
95 Emergent Herbacious Wetlands 0.045
NOS tide guage
CMAN station
NOS tide guage
CMAN station
Gulf of Mexico domain (10 km)
Gulf of Mexico domain (10 km)
Latitude
Longitude
32°N
30°N
28°N
26°N
24°N
22°N
20°N
18°N
16°N 100°W 95°W 90°W 85°W 80°W
Latitude
Longitude
29°48'N
29°36'N
29°24'N
29°12'N
29°00'N
95°12'W 95°00'W 94°48'W 94°36'W 94°24'W
NLCD value
0
11
21
22
23
24
31
41
42
43
52
71
81
82
90
95
ab
cd
42007
42040 42039
42035
42019
42020
42002 42001
42055
42056
42036
Figure 7
(a) Example of a nested domain simulation, where each of the three domains passes boundary conditions to its child domain. (b)The
initial bathymetry of the innermost domain, as set by a high-resolution digital elevation model. (c) Manning’s nbottom-friction
coefcients assigned to NLCD values (Mattocks & Forbes 2008). (d) The NLCD values used to specify the initial bottom-roughness
formulation in the model. Abbreviations: CMAN, Coastal Marine Automated Network; NLCD, National Land Cover Database; NOS,
National Ocean Service. Supplemental Video 2 shows an example of the effect of varying the bottom-roughness parameterization in a
coupled hydro- and morphodynamic model simulation of the passage of Hurricane Ike over Bolivar Peninsula in Galveston, Texas.
domains more computationally feasible (Figure 7). The increasing availability of high-resolution
bathymetry and land cover from remotely sensed sources allows for more accurate depths and
hydraulic roughness in coastal regions. Databases can provide an estimate of the spatial variations
in the bottom-friction coefcient due to land-cover type and sediment grain size, both of which
play key roles in the fundamental processes of coastal morphology (Figure 7).
Grain size affects sediment mobility and bottom roughness, and therefore erosion and depo-
sition patterns, and it also affects the slope of dune faces and beach proles (Dean 1991). Many
models can treat a range of sediment classes (e.g., Warner et al. 2008a). However, in extreme con-
ditions, most noncohesive sediment particles will mobilize, so spatially resolved initial grain-size
variations are not widely used because any variations in the mobilization patterns that would be
due to grain-size differences are overshadowed by the hydrodynamics. Additionally, measurements
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MA14CH05_Sherwood ARjats.cls July 19, 2021 10:22
of grain size over entire model domains are rare, and therefore the initialization or validation of
morphodynamic models with grain size is atypical (one exception is Reniers et al. 2013). Finally,
differences in modeled morphology that might be associated with grain size may be obscured
because the calibration of morphological models relies on sensitivity testing and reduction of er-
ror through adjustments of unconstrained parameters, including those related to grain size (e.g.,
bed roughness, bedload transport rates, settling velocities, and critical shear stresses), for which
observations often are not available. We anticipate that more attention will be paid to the role
of variable sediment characteristics as new mapping methods are developed and computational
resources continue to become more available.
5.2.5. Data assimilation. Data assimilation is being increasingly incorporated into coastal mor-
phology models. Direct inference of bathymetry from observations of the sea surface has been used
since World War II (Williams 1947) and is now based on estimates of wave dissipation and/or
wave celerity,current velocity, and shoreline location derived from video imagery (e.g.,Stockdon
& Holman 2000; Alexander & Holman 2004; van Dongeren et al. 2008; Wilson et al.2010, 2014;
Birrien et al. 2013; Holman et al. 2013; Kurapov & Özkan-Haller 2013; Brodie et al. 2018, 2019;
Wilson & Berezhnoy 2018; Collins et al. 2020). So far, data assimilation has been coupled with
relatively simple morphological models: Plant & Holland (2011) used a Bayesian approach to as-
similate bathymetry, bar location, and wave breaking into a surf-zone wave-propagation model;
Vitousek et al. (2017) used an extended Kalman lter to assimilate historical shoreline data into
a model for predicting shoreline change; and Ghorbanidehno et al. (2019) demonstrated a fast
Kalman lter for assimilating wave data into a bathymetry model. Smith et al. (2009) used a 3D
variational assimilation to improve the parameterization of a 1D model of bedform propagation.
Scott & Mason (2007) demonstrated improvement in a 2D horizontal (2DH) model of a tidal
embayment using data assimilation but noted that both the model and the assimilation methods
could be improved.
5.2.6. Ensemble and probabilistic modeling. We predict that ensemble and probabilistic ap-
proaches, which are already used in shoreline models (e.g., Montaño et al. 2020), will become
more widely used to estimate uncertainties in storm-impact forecasts. Ensemble modeling is one
approach for estimating uncertainties. Morphodynamic ensemble modeling of coastal evolution
on the decadal scale, such as the MorMerge approach (Roelvink 2006), assumes that conditions
can be run in parallel, but this is not yet broadly feasible for the more computationally demand-
ing models applied on the storm-event scale. Instead, recent work has used reduced-complexity
hydrodynamic models with simplied physics to rapidly generate a range of input boundary con-
ditions, such as surge simulations with SFINCS (Leijnse et al. 2021).Reduced-complexity models
have found more widespread use for timescales of ∼10–100 years under sea-level rise (Ranasinghe
2020). Ensemble modeling can also be used to account for the variations in modeled oceano-
graphic forcing and morphodynamic response due to uncertainty in model parameters. By vary-
ing the parameters (sediment size, type, and depth; eddy viscosity; the breaker index; the critical
Shields parameter; etc.) over a realistic range within the ensemble members, one can output a
probabilistic representation of the morphological response for a given domain.
5.2.7. More observations. The greatest uncertainties in initializing, forcing, and validating
models of morphodynamic change arise from sparse, missing, or untimely data. While there are
an increasing number of remotely sensed coastal observations (e.g., from surf cameras, satellites,
and crowdsourced data), some sources of data have not kept pace. The number of long-term
coastal observation stations (water-level measurements and offshore buoys) has not increased
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MA14CH05_Sherwood ARjats.cls July 19, 2021 10:22
signicantly, nor has the frequency of topo-bathymetric lidar data acquisition. Although new
technology has been developed for measuring nearshore bathymetry (autonomous vessels, au-
tonomous bottom vehicles, bathymetric lidar on unmanned aircraft systems, and inversion from
wave information) and surf-zone conditions (visual and infrared imagery, radar,and lidar; Holman
& Haller 2013), these methods have not been widely deployed, are expensive, and may not be
robust enough to measure during storms. There is, however, a trend toward increased rapid-
response measurements, including various National Science Foundation–funded rapid-response
projects (Raubenheimer 2020; https://converge.colorado.edu/research-networks); expanded
emergency-response ights (https://storms.ngs.noaa.gov); a recently funded initiative by the US
Ofce of Naval Research (NOPP 2020); operational efforts by the US Federal Emergency Man-
agement Agency, US Geological Survey, and US Army Corps of Engineers; and crowdsourced
data like CoastSnap (Harley et al. 2019) and the Federal Crowdsourcing and Citizen Science
Catalog (https://www.citizenscience.gov/catalog). Despite the improvement in rapid-response
observations, the overall paucity of data remains the greatest challenge for improving models of
morphodynamic responses to extreme events.
DISCLOSURE STATEMENT
The authors are not aware of any afliations, memberships, funding, or nancial holdings that
might be perceived as affecting the objectivity of this review.
AUTHOR CONTRIBUTIONS
J.D.contributed to Sections 3.1 and 3.2 and Figure 2. C.A.H. contributed to Sections 2.2, 3.3, 3.4,
and 4; Figure 5;andtheSupplemental Material. T.-J.H. contributed parts of Sections 3.5 and
5.1. T.S.K. contributed to Sections 3.4–3.6 and created Figure 4. M.O.contributed to Sections 1
and 3.3 and edited the manuscript. A.M.P. contributed to Sections 3.6 and 5.2, Figure 3,andthe
Supplemental Material and created Figure 7. Y.R. contributed to Sections 2.2, 3.4,and 3.5 and
Figure 4. D.R. contributed to Sections 3.4, 3.5, 3.8, and 3.9. C.R.S. contributed to Sections 1, 2.1,
2.2, 3.4, 3.5, 3.8, 3.9, 4, and 5; modied Figure 1; assembled the Literature Cited; and edited the
manuscript. M.v.d.L. contributed to Sections 3.6, 3.8, 4, and 5.2; Figure 6;andtheSupplemental
Material. A.v.D.contributed to Sections 2.1, 2.2, 3.4,5.1, and 5.2 and the Supplemental Material
and edited the manuscript. J.V. contributed to Sections 1, 3.4, and 5 and Figure 7.
ACKNOWLEDGMENTS
All authors except D.R. were partially supported by the IFMSIP project, funded by US Of-
ce of Naval Research grant PE 0601153N under contracts N00014-17-1-2459 (Deltares),
N00014-18-1-2785 (University of Delaware), N0001419WX00733 (US Naval Research Labo-
ratory, Monterey), N0001418WX01447 (US Naval Research Laboratory, Stennis Space Center),
and N0001418IP00016 (US Geological Survey). C.R.S., C.A.H., T.S.K., and J.C.W. were sup-
ported by the US Geological Survey Coastal/Marine Hazards and Resources Program. A.v.D.
and M.v.d.L.were supported by the Deltares Strategic Research project Quantifying Flood Haz-
ards and Impacts. M.O. acknowledges support from National Science Foundation project OCE-
1554892. We thank Jim Duncan at Annual Reviews for handling this review and outstanding
copyediting, and Glenda Mahoney for editing the gures. Early drafts of this article were greatly
improved by comments and suggestions from Meg Palmsten and Sean Vitousek.
. Sherwood et al.
MA14CH05_Sherwood ARjats.cls July 19, 2021 10:22
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