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date: 30 September 2022

Climate, Coast, and Morphologyfree

Climate, Coast, and Morphologyfree

  • Wenyan ZhangWenyan ZhangInstitute of Coastal Systems, Helmholtz Center Geesthacht
  •  and Peter ArlinghausPeter ArlinghausHelmholtz-Zentrum Hereon

Summary

Coastal morphology refers to the morphology and morphological development of the coast in response to a combined influence of atmospheric, oceanic and anthropogenic forcing. Coastal morphology comprises a wide variety of landforms (exposed to air) and bedforms (submerged in water) manifested in a large spectrum of spatial scales (10−2–105 m scale) and shapes ranging from mildly sloping lower shoreface to steep cliffs, from small ripples to large river deltas.

Coastal zones are cradles for life. About 40% of the global human population and 50% of marine life are living in low-lying coastal zones with elevation less than 10 m above the mean sea level. Coasts contain the highest biodiversity in the surface earth system yet are highly vulnerable to environmental stressors associated with human activities and climate change. Climate impacts coastal morphology in multiple ways, including ice cover/melting, precipitation, temperature, and wind. In response to a changing climate, adaptation of coastal morphology can be categorized into three basic states: erosional, stable, and accretionary. Each state may persist or iterate at any given part of a coast, even in the context of a persistently warming or cooling climate. Anthropogenic protection has been globally implemented to ease erosion and protect human property. However, it remains largely unknown whether the existing measures would be able to counteract the effects of climate change in the upcoming decades.

Subjects

  • Climate and Coasts

Impacts of Climate on Coastal Morphology

The morphology of the world’s coast is made up of a wide variety of landforms and bedforms manifested in a large spectrum of sizes and shapes depending on the forces acting on the coast (e.g., tides, waves, wind, river runoff, biota, and humans), sediment supply and properties (e.g., grain size, lithology), and underlying geological constraints (Arlinghaus et al., 2021; Coco et al., 2013; Cooper et al., 2018; Galloway, 1975; Walsh et al., 2004; Zhang et al., 2012; Zhang & Eschenbach, 2020). Conventionally, based on the major phenomenological or morphological features, coasts can be classified as barrier islands, cliff coasts, coral reef coasts, deltas, sandy dune coasts, or vegetated coasts (mangroves/grass/marsh). The actual shape of these coastal morphological units is largely determined by the dominant forces acting on them and can be further clarified accordingly into, wave-dominated, tide-dominated, or river-dominated types (Galloway, 1975; Seybold et al., 2007).

Climate impacts coastal morphology in multiple ways, including ice cover/melting, precipitation, temperature, and wind. The impact of ice is profound in polar and temperate regions that are subject to periodic ice cover and melting either at short-term (e.g., at an annual cycle) or long-term (e.g., at a glacial-interglacial cycle) scales (Forbes et al., 1995; Lauzon et al., 2019). It affects coastal morphology both directly, such as by forming glacial deposits, and indirectly, such as by exposure to wave erosion due to ice melting (Overeem et al., 2011). In addition, the load and decay of ice sheets causes a response of the solid earth and the oceans known as glacial isostatic adjustment (GIA). The response of the solid earth to the melting of ice sheets since the Last Glacial Maximum (∼21,000 years ago) continues today at a remarkable rate in the Northern Hemisphere. For example, the present-day GIA uplift rate is larger than 10 mm/yr near the Hudson Bay, accompanied by a subsidence up to −2 mm/yr south of the Great Lakes (Sella et al., 2007). The GIA-induced uplift of the Baltic (Fennoscandian) Shield is also up to 10 mm/yr in the northern coasts of the Baltic Sea, which outcompetes the eustatic sea level rise (~1.2 mm/yr), causing a persistent marine regression (i.e., coastline progradation) in the northern Baltic Sea and its coast. Conversely, GIA-induced subsidence in the southern Baltic Sea amplifies the effect of eustatic sea level rise on the coast, causing a persistent marine transgression (i.e., coastline retreat) (Harff et al., 2017).

Wind affects coastal morphology in the form of wind-induced waves and aeolian transport. Coasts under the impact of long wind fetches and large waves, such as the southern North Sea barrier islands, are normally featured by a wider surfzone and beach than those coasts with shorter wind fetches and smaller wave impact, such as the Baltic Sea coasts (Zhang et al., 2011; Weisse et al., 2021). The angle at which the waves approach the coastline also controls sediment transport along the coast. Waves hitting the nearshore surfzone with a zero incidence angle (i.e., perpendicular to the shoreline) mainly influence cross-shore sediment transport and morphology but have little impact on the alongshore sediment transport, while waves with an increasing incidence angle increase alongshore sediment transport rate and amplify instabilities (e.g. megacusps, spits, bars) in the shoreline morphology, often leading to development of self-organized shoreline undulations (Ashton & Murray, 2006; Deng et al., 2019; Idier et al., 2011; Zhang et al., 2012, 2014). Long-lasting shoreward blowing winds at many parts of the world’s coastlines produce sand dunes where enough sediment is available and where there is a space large enough for sands to migrate and accumulate. Dune formation is a self-organized process of sand transport. Large dune fields that are actively migrating (e.g., at Skeleton Coast of Namibia, Leba of Poland, and Sylt of Germany), as well as smaller dune ridges that are fixed by vegetation (e.g., along the southern Baltic Sea coast, Cape San Blas of Florida, United States, and the Mahia Peninsula of New Zealand) exist at the coasts. The actual morphology of coastal dunes depends on many factors, including wind strength, wind direction, sediment supply rate, frequency and strength of storm surges, vegetation species, coverage, and growth rate (Hesp, 2002; Zhang et al., 2015) as well as sea level oscillations (Tamura, 2012; Zhang et al., 2017).

The effect of temperature on coastal morphology is multifold. Beyond the ice cover/melting cycles, temperature also controls: (a) physical weathering of sediments and rocks, which affects the sediment supply rate and lithology; (b) type of coastal vegetation; (c) sea level; and (d) the probability of occurrence, intensity, as well as tracks of extreme weather events. Mangroves are restricted in tropical and subtropical regions, while seagrass and saltmarshes are more tolerable to temperature gradient and are found from cold polar regions to the tropics (Pendleton et al., 2012). Furthermore, temperature is closely related to precipitation. The latter induces runoff, which produces and transports sediment to the coast. The rates of sediment supply as well as sediment type directly affect coastal morphology. In addition, precipitation contributes to erosion of coastal cliffs through sheet erosion and rilling in the upper part. It has been found that upper cliff erosion is mostly induced by precipitation, whilst lower cliff erosion is mainly by waves in some regions such as the Del Mar, California (Young et al., 2021).

In response to a changing climate, adaptation of coastal morphology can be categorized into three basic states: erosional, stable, and accretionary. Each state may persist or iterate at any given part of a coast, even in the context of a persistently warming or cooling climate. It is the net change of the sediment budget, namely the difference between the incoming mass (sources) and the outgoing mass (sinks) within the period of interest, determining the morphological state of a coast at the end of that period. An analysis based on satellite derived shoreline data for the period 1984–2016 revealed that 24% of the world’s sandy coasts are eroding at rates higher than 0.5 m/yr, 48% are stable, and 28% are accreting (Luijendijk et al., 2018). On the other hand, an earlier study by Bird (1985) suggested that 70% of the global sandy coasts had been under erosion up to the early 1980s. The ease of sandy coastal erosion since the 1980s on a global scale is largely attributed to anthropogenic protection, for example, by beach nourishments that have intensified in the past few decades (Hanson et al., 2002) and by hard protection structures such as groynes, dykes, seawalls, revetments, artificial headlands, and breakwaters (Meier et al., 2022; Weisse et al., 2021). However, it remains largely unknown whether the existing measures would be enough to counter the effects of accelerated sea-level rise and sediment deficit in the upcoming decades (Vousdoukas et al., 2020).

Equilibrium and Disequilibrium in Coastal Morphology

Historical Development of the Concept of Equilibrium

In the historical development of coastal morphological research, morphological equilibrium is very important. In geomorphology, equilibrium refers to a self-correcting balance of material and geometry in response to external forcing.

The concept of equilibrium and quasi-equilibrium has been widely accepted and applied in studies of fluvial systems such as river morphology. Natural fluvial systems always dynamically adjust their morphology in response to erosional and depositional processes that are triggered by change in river runoff, sediment supply, and sediment properties. However, despite the dynamics, the morphology of rivers (channel pattern and geometry) is believed to “strive” to attain a state of dynamic equilibrium between the imposed external forcing and internal configuration of river geometry and sediments (Blom et al., 2017; Lane, 1955; Mackin, 1948). Lane (1955) proposed a simple yet useful relationship elucidating such dynamic equilibrium: Qs×d50Qw×S, where Qs is the rate of sediment discharge, d50 is the median grain size, Qw is the rate of water discharge, and S is the bed slope of the river channel. This relationship indicates a balance between sediment transport (mass and grain size) and stream power (runoff and bed slope). It implies that a change in river morphology would occur if either sediment transport or stream power changes, so that a new balance between them would be attained. For example, if the stream power decreases due to reduction of runoff, some of the entrained sediment load is no longer able to be transported further downstream and then subsequently deposited. The aggradation process will transform the channel morphology and reduce sediment transport (mass and/or grain size). Similar channel adjustment would occur when the sediment supply increases or the grains become larger during unchanged flow conditions. By contrast, in case of a reduction of sediment transport (e.g., by river damming), stream power would be too high for the available sediment load, and the river will compensate for such a deficit by eroding the local bed and banks, leading to channel degradation downstream of the dam (Huang & Nanson, 2007).

The concept of equilibrium has also been widely applied in studying estuaries, deltas, and wave-dominated coastal systems such as barrier islands and dune coasts (Deng et al., 2014; FitzGerald et al., 2008; Wright & Coleman, 1972; Zhang, 2016). Zhou et al. (2017) classified two types of equilibrium in dynamic transport systems based on the Exner equation, which attributes the change of bed level to a joint result of sediment transport flux divergence (i.e., the difference between incoming and outgoing fluxes) and the impact of source/sink term (i.e., the subsidence and/or uplift of seabed/land). Bed level remains unchanged in an equilibrium morphology, implying a balance between the sediment deficit or excess caused by transport processes and the source/sink term, so that they counteract each other. Type I dynamic equilibrium refers to a consistent balance between the two terms over time, while Type II refers to a balance between these two terms integrated over a certain timescale (predefined period of interest), but allowing unbalance in shorter time scales (i.e., all unbalances are canceled out when integrated over the predefined period of interest). On a broader implication, morphological equilibrium also accounts for statistical and quasi-equilibrium which do not strictly satisfy the Exner equilibrium conditions but point to a convergence of the system toward a specific configuration (e.g., a constant ratio between subtidal and intertidal area in a tidal embayment). This broader-scale equilibrium is widely applied to understand shoreface morphology under the impact of waves (Anthony & Aagaard, 2020).

Coastal morphology and dominant wave regimes strive to attain mutual adjustment along the coastline (Wright & Coleman, 1972). The coastal shoreface geometry develops in such a way as to minimize or eliminate longshore gradients in wave forces. Under the impact of a statistically stable wind-wave climate, the resultant shoreface morphology tends to attain a quasi-equilibrium in response to such a statistically stable climate (Wright & Coleman, 1972). It is worth noting that a quasi-equilibrium does not refer to a static state. The upper shoreface, including the wave-breaking surfzone and the beach zone, is consistently changing in response to wind waves, currents, and storms (Zhang et al., 2013). On the other hand, the upper shoreface commonly exhibits an envelope of profile change (Anthony & Aagaard, 2020). In regions where seasonality in wind waves is distinct (such as North Atlantic coasts), the profile change is characterized by migration of one or a few bars directed onshore during mild seasons and offshore during stormy seasons (Deng et al., 2014; Larson & Kraus, 1995; Patterson & Nielsen, 2016; Zhang et al., 2015). The envelope of profile change diminishes down to the so-called “closure depth,” where seaward of it, no notable change in bed level occurs (Hallermeier, 1981). Clearly, for any specific site, its closure depth is not a fixed point but rather is timescale-dependent; for example, closure depth at a seasonal or annual time scale is shallower than at longer time scales (Deng et al., 2014). Despite active changes in the upper shoreface, the general shape of the shoreface profile derived from averaging over a significantly long period appears to follow an equilibrium shape. Theoretically, a profile with such an equilibrium shape is able to effectively dissipate incident wave energy so that net sediment transport is zero at any location of the profile (Bruun, 1954; Dean, 1991).

The equilibrium shoreface profile concept dates back to Cornaglia (1889/1997), who hypothesized that equilibrium is reached when onshore sediment transport by velocity-skewed incident waves is counteracted by gravity-induced offshore transport everywhere along the shoreface. This concept was further refined by Bruun (1954, 1962). Bruun (1954) proposed that the vertical shape of a cross-shore coastal profile can be approximated by the formulation h=Ayn, where h is water depth, A is a sediment scale parameter, n is an empirical parameter (= 2/3 as the best fit found by Dean [1977]), and y is the cross-shore distance from the shoreline. Based on this formulation, Bruun (1962) suggested a simple relationship to link the coastal retreat rate (R) with the sea-level rise rate (S):R=SL/(dc+B), where L is the cross-shore width of the active profile, dc is the closure depth, and B is the elevation of the beach or dune crest. This relationship assumes a balance between the sediment yield R(dc+B) from the horizontal retreat of the profile, and the sediment demand to fill the increased accommodation space SL from a vertical rise in the profile. The equilibrium shoreface profile formulation was later confirmed by more field data worldwide and has gained its popularity in coastal engineering applications over decades (e.g., Ashton et al., 2011; Davidson-Arnott, 2005; Dean, 1977, 1991; Deng et al., 2014; Wolinsky & Murray, 2009; Zhang et al., 2015).

Strictly, the formulation by Bruun (the so-called “Bruun rule”) describes an idealized coastal setting based on assumptions that sands are conserved in the system and that no gradients exist in the longshore or cross-shore transport of sands (Dean et al., 2002). Because of these restrictions, other researchers questioned its applicability to real coasts (e.g., Cooper & Pilkey, 2004; Cooper et al., 2018 ) based on the fact that the preconditions are rarely met in reality and a beach never attains an equilibrium due to always-changing hydrodynamic and boundary sediment supply conditions. Pilkey et al. (1993) pointed out that the equilibrium equation is oversimplified by considering the sediment grain size (expressed as A in the h=Ayn formulation) as the only variable influencing the shape of the profile, whilst hydrodynamic variables such as waves, currents, inherited morphology, and underlying geology are omitted. Furthermore, Thieler et al. (1995) noted that the heterogeneity in grain size distribution across the shoreface cannot be accounted for by a single parameter A. Zhang et al. (2015) demonstrated that A is not constant even within a small (1 km in length) sandy coastal section with almost homogeneous sands, despite that the shoreface profile can still be approximated by an equilibrium shape function. In particular, at places where the shoreface is affected by geological constraints such as rocky outcrop and sub-crop, the validity of the Bruun rule is seriously restricted (Browder & McNinch, 2006; Cooper et al., 2018).

Despite the apparent flaws in the formulation, the concept of equilibrium shoreface profile has not lost attention. Various modifications of the Bruun rule have been made to increase its applicability to real coasts by including the impacts of additional sources, sinks, and fluxes of sediment associated with hydrodynamic forcing (e.g., Deng et al., 2014; Karunarathna et al., 2018; Vousdoukas et al., 2020).

Disequilibrium in Coastal Morphology

The concept of equilibrium is useful in understanding morphology and morphological evolution in coastal systems in response to (statistically) stable external forcing. To reconcile the debates on whether equilibrium exists in real coastal environments, it is vitally important to understand what determines an equilibrium in morphology and how much time a coastal system needs to achieve an equilibrium under stable (statistically) external forcing. It is also important to understand the sensitivity of equilibrium to the chronological sequence of forcing within the statistically stable spectrum (of forcing) and altered boundary sediment supply. With such understanding, the concept of disequilibrium may be useful to describe (a) the development phase toward an equilibrium, and (b) the transition of one equilibrium to another due to changes in forcing and/or boundary sediment supply.

In an open sandy coastal system with free exchange of water and sediment at its boundaries, a quasi-equilibrium morphology is expected to develop under (statistically) stable conditions of flow and sediment supply (Figure 1), despite actively migrating bedforms. Transverse dunes or ripples will develop if sediment supply is sufficient (Figure 1a and b). The morphology of these bedforms (wave length and height, symmetry between upstream and downstream sides) depends on the stability of the flow (e.g., whether the flow is constant in speed and direction or varies within a certain frequency band). Larger bedforms (e.g., mega-ripples and dunes with a wave length of a few meters to a few tens of meters) are formed by low-frequency and large-scale forcing (e.g., tides), while smaller bedforms (e.g., ripples with wave length of a few centimeters to a few tens of centimeters) are mainly driven by low-frequency and small-scale forcing (e.g., wind waves). In real coastal systems, small bedforms are often superimposed to large bedforms as a result of compound impact of various forcing acting on different scales. Bedforms would reorganize and transform when change in forcing and/or sediment supply occurs. Barchanoid and barchan dunes or ridges would develop along with a decrease of sediment supply (Figure 1c and d). Larger bedforms develop and migrate at a slower rate than smaller bedforms. For example, it takes about a few years to a few decades for an established foredune to fully develop from embryo dunes along the North Sea and the Baltic Sea coasts (Lindhorst et al., 2010; Ludwig et al., 2017; Zhang et al., 2015), and during the development, storm surges may partly or completely destroy the embryo dunes (Bateman et al., 2018; Zhang et al., 2017). In this sense, the morphology of coastal foredunes can be described as an equilibrium on a decadal time scale but disequilibrium on a shorter time scale.

Figure 1. Simulated quasi-equilibrium dune patterns driven by different flow directions and sediment supply rates. The arrows indicate the flow directions. (a) Meandering seif dunes developed due to the alternate action of obliquely incident winds onto both flanks of the dunes. (b) Transverse dunes developed by unidirectional wind. (c) Barchan dunes developed in bidirectional winds with a prevailing component. (d) Barchan dunes developed by unidirectional wind.

In any given period of interest, the driving force for morphological change (e.g., as reflected in flow speed or water level) can be decomposed into a series of periodical forces. Given a statistical stable distribution of forcing, the bandwidth of frequency in the forcing may influence the time that a coastal system needs to achieve a quasi-equilibrium. To test this hypothesis, a series of numerical experiments based on an idealized configuration of coastal morphology were carried out. This configuration mimics a typical tidal embayment that is partly connected to the open sea through a narrow inlet/outlet. The initial morphology of the seabed is characterized by a seaward gradual deepening from 2 m above to 8 m below the mean sea level (Figure 2). The seabed is assumed to be erodible so that morphological change occurs due to sediment resuspension and deposition caused by tidal currents. Sediment grain size is assumed to be uniform and represents very fine sands.

Figure 2. Initial morphological configuration of a coastal embayment. The color indicates the seabed elevation with negative value for subaqueous area and positive value for subaerial area. The southern boundary (8 m water depth) refers to the offshore boundary where driving forces are implemented.

Periodic tidal forcing was imposed at the offshore boundary to drive morphological change of the embayment. To test the sensitivity of morphological equilibrium to the bandwidth of frequency in the forcing, four experiments were designed (Figure 3). Exp_1 includes a single signal with 12-hour period to mimic semi-diurnal tide; Exp_2 superimposes a 30-day neap-spring cycle to the 12-hour period signal; Exp_3 superimposes a 24-hour diurnal signal to the 12-hour period signal; and Exp_4 is a combination of three different frequencies (30-day neap-spring signal, 24-hour diurnal signal and 12-hour signal).

Figure 3. Scenarios of tidal forcing in the simulations: (a) single signal with 12-hour period; (b) a 30-day neap-spring signal superimposed on the 12-hour period signal; (c) a 24-hour diurnal variation superimposed on the 12-hour period signal; (d) a combination of 30-day neap-spring signal, 24-hour diurnal signal, and 12-hour signal.

Simulation results suggest that a complex tidal channel network develops in all experiments (Figure 4). On the other hand, a remarkable difference is also seen between these results. The most important results from these experiments are as follows:

1.

Morphological development of a coastal system is scale-dependent. Small-scale units (e.g., a single channel or shoal) may approach quasi-equilibrium in a few years to a few decades (Figure 4, middle column), whilst a tidal embayment or basin would need a few centuries to attain a quasi-equilibrium under stable forcing (Figure 4, right column). This result is in line with existing knowledge (Wang et al., 2018).

2.

The wider the bandwidth of the forcing (i.e., more frequencies in the forcing), the more time that is needed for coastal morphology to achieve quasi-equilibrium. This applies to both small- (single channel) and large-scale (embayment) morphological units.

3.

The vertical dimension of morphological units (e.g., channel depth, elevation of shoals and flats) increases along with a wider bandwidth of the forcing. This seems to be attributed to a compound impact of various forcing when they approach a similar phase, so that the combined force reaches a maximum. A similar trend was also observed on real coasts. Benninghoff and Winter (2019) reported that the Wadden Sea tidal basins experienced a general deepening in its channels and a shallowing in its intertidal flats, along with a sea level rise (which amplifies the tides and waves), from 1996 to 2016.

Figure 4. Simulated morphological change in the four experiments with varying frequencies in forcing. Note that river channels are indicated by the dark curves in the morphological maps (left column), and a darker color refers to a larger depth of the channel. Temporal development of maximum channel length and total channel length in each experiment is shown in the middle and right columns, respectively.

Not only the external forcing, but also sediment properties in the coastal system influence the morphology and morphological equilibrium. To derive insights into this, another set of experiments was designed. Sediment grain size and corresponding settling velocity were set to decrease along with the number of the experiments from Exp_S1 to Exp_S4. Sediment was coarsest (very fine sands) in Exp_S1, with largest settling velocity (0.75 mm/s); and finest (fine silts) in Exp_S4, with smallest settling velocity (0.1 mm/s). Other environmental parameters, including the forcing, remain the same in these experiments. Simulation results indicate that:

1.

The complexity of the channel network increases along with a decrease in sediment grain size and settling velocity (Figure 5, left column). More channels, especially secondary channels, develop where sediment is finer, along with an increase in channel length (Figure 5, middle column).

2.

Sediment grain size also influences the time needed for coastal morphology to achieve quasi-equilibrium. The finer the sediment grain size, the shorter the time needed for achieving a quasi-equilibrium (Figure 5, right column).

Figure 5. Simulated morphological change in the four experiments with varying sediment grain size. River channels are indicated by the dark curves in the morphological maps (left column), and a darker color refers to a larger depth of the channel. Temporal development of maximum channel length and total channel length in each experiment is shown in the middle and right columns, respectively.

Particularly noteworthy is that the location of primary and secondary channels varies among the simulations (Figures 4 and 5). This result suggests that a change in either external forcing (e.g., inclusion of stochastic events such as storms or shift of regional circulation pattern) or sediment properties could lead to migration or relocation of channels. Once disrupted, it may take from a few years to a few decades for a channel to readapt and attain a new quasi-equilibrium, and much longer for a tidal embayment or basin.

Conclusion

Coasts are constantly changing their morphology through erosion and deposition. The morphological change in turn influences the overlying medium, including air, water, and biota. As a result, such dynamic interactions lead to permanent transformations of coastal morphology and its functioning on physical, biological, and geochemical levels. Climate impacts coastal morphology in multiple ways, including ice cover/melting, precipitation, temperature, and wind. Each of the elements may individually or jointly affect coastal morphological development.

In the historical development of coastal morphological research, a very important concept is equilibrium. In geomorphology, equilibrium refers to a self-correcting balance of material and geometry in response to external forcing. The concept of equilibrium has been widely adopted and applied in studying coastal systems, including rivers, estuaries, deltas, and wave-dominated coastal systems such as barrier islands and dune coasts, despite the representation of equilibrium differing among these systems. On the other hand, extensive debates have persisted since the 1990s on whether equilibrium exists in real coastal systems. The argument to oppose this concept is that natural coasts never attain an equilibrium due to always-changing hydrodynamic and boundary sediment supply conditions. To reconcile such debates, it is vitally important to understand what determines an equilibrium in coastal morphology and how long it takes a coastal system to achieve an equilibrium under statistically stable external forcing. Furthermore, it is important to understand the sensitivity of morphological equilibrium to chronological sequence of forcing within the statistically stable distribution and altered boundary sediment supply. With such understanding, the concept of disequilibrium may be useful to describe (a) the development phase toward an equilibrium, and (b) the transition of an equilibrium to another due to changes in forcing and/or boundary sediment supply.

Based on a literature review and own investigations, the following conclusions can be drawn:

1.

Morphological development of a coastal system is scale-dependent. Under the condition of stable forcing, small-scale morphological units (e.g., tidal channel, shoal, or sand ridge) may approach quasi-equilibrium in a relatively short period (at the time scale of years to decades), whilst large-scale morphological units (e.g., tidal embayment or basin, river delta) would need much longer (at the time scale of centuries to millennia) to attain a quasi-equilibrium.

2.

The greater the variability in the forcing (e.g., wider bandwidth in the frequency distribution of the forces), the more time that is needed for coastal morphology to achieve quasi-equilibrium. This applies to both small- and large-scale morphological units.

3.

The vertical dimension of the morphological units increases along with the bandwidth of the forcing.

4.

Morphological complexity (e.g., number of channels, channel length) increases along with a decrease in sediment grain size and settling velocity.

5.

A change in either external forcing (e.g., inclusion of stochastic events such as storms or shifts in regional circulation pattern) or sediment properties could lead to migration or relocation of morphological units (such as channels or shoals). Once disrupted, it may take a few years to a few decades for small-scale units (e.g., channels) to readapt and attain a new quasi-equilibrium, and much longer (centuries to millennium) for a large-scale coastal system (e.g., tidal embayment/basin, barrier islands, river delta) to achieve a new quasi-equilibrium.

6.

Last but not least, climate change would inevitably lead to change of coastal morphology across local, regional, and global scales. On the other hand, morphological change is both site- and scale-dependent. The understanding of equilibrium–disequilibrium cycles may provide a useful means to improve predictability of coastal morphological development in response to climate change.

Acknowledgments

This study is a contribution to the I2B project “Unravelling the Linkages between Benthic Biological Functioning, Biogeochemistry and Coastal Morphodynamics—From Big Data to Mechanistic Modelling” funded by Helmholtz-Zentrum Hereon as part of the PoF program “The Changing Earth—Sustaining our Future” on its Topic 4, “Coastal Zones at a Time of Global Change.

Further Reading

References