The white chalk cliffs on the south coast of England are one of the most iconic coastlines in the world. Rock coasts located in a weak lithology, such as chalk, are likely to be most vulnerable to climate-change-triggered accelerations in cliff retreat rates. In order to make future forecasts of cliff retreat rates as a response to climate change, we need to look beyond individual erosion events to quantify the long-term trends in cliff retreat rates. Exposure dating of shore platforms using cosmogenic radionuclide analysis and numerical modelling allows us to study past cliff retreat rates across the Late Holocene for these chalk coastlines. Here, we conduct a multi-objective optimisation of a coastal evolution model to both high-precision topographic data and 10Be concentrations at four
chalk rock coast sites to reveal a link between cliff retreat rates and the
rate of sea-level rise. Furthermore, our results strengthen evidence for a
recent acceleration in cliff retreat rates at the chalk cliffs on the south
coast of England. Our optimised model results suggest that the relatively
rapid historical cliff retreat rates observed at these sites spanning the
last 150 years last occurred between 5300 and 6800 years ago when the rate
of relative sea-level rise was a factor of 5–9 times more rapid than during the recent observable record. However, results for these chalk sites also indicate that current process-based models of rock coast development are overlooking key processes that were not previously identified at sandstone rock coast sites. Interpretation of results suggest that beaches, cliff debris and heterogenous lithology play an important but poorly understood role in the long-term evolution of these chalk rock coast sites. Despite these limitations, our results reveal significant differences in intertidal weathering rates between sandstone and chalk rock coast sites, which helps to inform the long-standing debate of “wave versus weathering” as the primary control on shore platform development. At the sandstone sites, subaerial weathering has been negligible during the Holocene. In contrast, for the chalk sites, intertidal weathering plays an active role in the long-term development of the shore platform and cliff system. Overall, our results demonstrate how an abstract, process-based model, when optimised with a rigorous optimisation routine, can not only capture long-term trends in transient cliff retreat rates but also distinguish key erosion processes active in millennial-scale rock coast evolution at real-world sites with contrasting rock types.
Natural Environment Research CouncilScience and Solutions for a Changing Planet DTPIntroduction
Rock coasts are dynamic, erosional landscapes that form as a result of
landward retreat of bedrock at the coastline (Kennedy et
al., 2014) and are often identified by features such as a sea cliff and
shore platform. Climate change threatens the stability of rock coasts and is
expected to increase rock coast erosion through accelerations in relative
sea-level (RSL) rise and increased storminess
(Trenhaile, 2011; Oppenheimer et al., 2019).
However, the quantification of sea cliff response to climate change is
challenging because both marine and terrestrial factors at variable temporal
and spatial scales influence rock coast evolution. Improving forecasts of
future cliff retreat rates is necessary because of the socioeconomic
importance of rock coasts and associated hazards, which are further
threatened by climate change and increased urbanisation
(Hurst et al., 2016). Understanding the
long-term, antecedent trajectory of rock coast evolution is central to the
development of predictive models of cliff retreat that account for a
changing climate (Hurst et
al., 2016; Trenhaile, 2018).
In order to understand the trajectory of long-term rock coast evolution, the
interactions between cliff and shore platform dynamics and their combined
impact on cliff retreat need to be considered. Cliff retreat is foremost
driven by assailing wave force at the cliff base, and the cliff-platform
junction corresponds to the elevation of maximum horizontal marine erosion
(Trenhaile, 2018). The shore platform fronting the
sea cliff plays an important role in mediating the wave energy available to
erode the cliff. It is, therefore, vital to understand wave and weathering
processes working concurrently to result in lowering of the shore platform
and landward retreat of the cliff (Sunamura, 1992).
The relative importance of “waves versus weathering” as the primary control
on shore platform development has been debated (Stephenson and Kirk, 1998; Trenhaile and Kanyaya, 2007; Kennedy et al., 2011; Retallack and Roering, 2012; Matsumoto et al., 2018). Whereas weathering relates to the weakening of the rock material through a combination of physical, chemical and biological processes, wave erosion relates to the physical removal of (weakened) rock material from the shore platform surface and cliff by means of wave action. The dominance of either wave or weathering processes in rock coast evolution still remains uncertain, but it is recognised to vary in importance in different marine, lithological (i.e. rock type) and climatic settings (Dickson, 2006). In general, weathering processes often dominate in low wave energy, micro-mesotidal, weak lithology and warmer climate rock coast sites, whereas wave processes often dominate in high wave energy, meso- or megatidal, more resistant lithology and temperate climate rock coast sites (Stephenson and Kirk, 2000; Dickson, 2006; Trenhaile and Porter, 2007; Kennedy et al., 2011; Retallack and Roering, 2012).
The erosion of rock coasts is highly contingent on the type and structure of
the bedrock present at the coast
(Rosser
et al., 2013; Sunamura, 2015; Buchanan et al., 2020). In fact, a global
database identified rock resistance, rather than climate or marine forcings,
as the strongest factor controlling rock coast erosion rates
(Prémaillon et al.,
2018). Rock coasts located in a weak lithology, such as chalk
(Hoek and Brown, 1997), are therefore likely to be most
vulnerable to climate change-triggered accelerations in cliff retreat rates.
Correspondingly, Trenhaile (2011) conducted a
theoretical investigation into the prediction of rock coast response to
climate change using a numerical model and compared results from different
rock resistances. He concluded that, although absolute cliff retreat rates
will be greatest in weaker rock types, the proportional increase in cliff
retreat rates will be greater at rock coasts with more resistant material
and historically slower cliff retreat rates
(Trenhaile, 2011). Further work is needed to
understand the sensitivity of long-term rock coast evolution in real-world
settings in different lithologies to external changes in climate.
A methodology that has facilitated the study of site-specific,
millennial-scale rock coast evolution is the application of cosmogenic
radionuclide (CRN) analysis on shore platforms. Concentrations of CRNs
across a shore platform are proportional to the time of surface exposure to
cosmic rays and rate of erosion, and long-term cliff retreat rates can be
quantified when coupled with a coastal evolution model
(Regard et al.,
2012; Hurst et al., 2017). Relatively few studies of CRN applications at
chalk rock coast sites have been conducted to date. However, previous
applications of CRN analysis at rock coasts across a range of rock types
were able to date shore platform surfaces (Choi et al., 2012)
and quantify long-term cliff retreat rates
(Regard
et al., 2012; Rogers et al., 2012; Hurst et al., 2016; Swirad et al., 2020;
Duguet et al., 2021; Shadrick et al., 2021). By quantifying past long-term
cliff retreat rates, comparisons can be made to observed historical cliff
retreat rates. Using these techniques, both Hurst et al.
(2016) and Duguet et al.
(2021) identified modern accelerations
in cliff retreat rates for chalk cliffs on the south coast of England and
Normandy coast in France, respectively.
Previous CRN analyses at chalk rock coasts have given novel insights into
the long-term cliff retreat, yet these studies have always assumed a
simplistic, steady-state geometric model of coastal evolution (Regard et
al., 2012; Hurst et al., 2016). The validity of cliff retreat rates derived
from CRN concentrations is dependent on the coastal evolution models that
are used to interpret the measured CRN concentration data
(Trenhaile, 2018). It is important, therefore, to
ensure the coastal evolution model that is applied faithfully approximates
cliff and shore platform weathering and erosion processes as accurately as
possible across the millennial timescales over which CRNs accumulate.
Furthermore, a rigorous optimisation routine is required to optimise a
process-based coastal evolution model to high-precision 10Be CRN
concentrations and topographic data
(Shadrick et al., 2021).
Long-term cliff retreat rates for the past 7000 years, and, in turn,
projections of future cliff retreat rates to the year 2100 have been made
for two sandstone rock coast sites in the UK by combining the best
available rock coast morphodynamic model with simulated CRN accumulation and
optimising the model to high-precision CRN concentration measurements and
topographic survey data (Shadrick et al.,
2022). Application of a
process-based, transient coastal evolution model to interpret 10Be
concentrations has revealed a linear positive relationship between cliff
retreat rates and the rate of relative sea-level rise
(Shadrick et al., 2021). These results
indicated that negligible subaerial weathering occurred at these sandstone
sites, which was required for the model to match the measured topography and
concentrations at the two sandstone sites
(Shadrick et al., 2021).
Until now, a process-based model has not been used to quantify long-term
cliff retreat rates for chalk rock coast sites. Here, we apply a
process-based model at contrasting lithological settings, including both
chalk and sandstone rock coasts, to provide further insights into the
dominant coastal erosion processes acting across millennial timescales at
sites with varied rock types, which helps to inform the “wave versus
weathering” debate
(e.g.
Stephenson and Kirk, 1998; Trenhaile and Kanyaya, 2007; Kennedy et al.,
2011; Retallack and Roering, 2012; Matsumoto et al., 2018). This study
expands on the application of CRN exposure analysis of shore platforms in
the UK by investigating the long-term rate and nature of cliff retreat using
our coastal evolution model and multi-objective optimisation approach
(Shadrick et al., 2021; see Sect. 3.1) for two new UK, chalk rock coast
sites: Seven Sisters and St Margaret's. As well as modelling the new
datasets, we revisit data from two previously studied UK chalk rock coast
sites: Hope Gap and Beachy Head (Hurst et
al., 2016). Revisiting previous studies provides a unique opportunity to
compare long-term cliff retreat results from dissimilar coastal evolution
models. Here, we compare results between different models and discuss the
influence of, for example, beach material and cliff debris, as well as cliff
retreat rates derived from historical records, which helps to advance our
understanding of how rock coasts evolved both in the long-term past and more
recently.
Background on south coast chalk cliffs
The white chalk cliffs found on the south coast of England are iconic and
recognisable landforms in the UK and worldwide. Their towering heights of up
to ∼165 m at Beachy Head
(Robinson, 2020) and white chalk lithology are
both visually striking and extremely hazardous. As a result, the chalk
cliffs on the south coast of England are some of the most well-studied rock
coast settings in the world (Moses and Robinson,
2011). A range of previous studies located at the south coast chalk cliffs
have, for example, quantified the following: (1) millennial-scale cliff retreat rates using
CRN analysis (Hurst et al., 2016); (2) modern
cliff retreat rates using historical maps
(Dornbusch et al., 2008); (3) modern cliff
failure using UAV photogrammetry
(Barlow et
al., 2017; Gilham et al., 2019); (4) hazard classification and risk
assessment
(Mortimore et al., 2004a; Stavrou et al., 2011); and (5) platform downwear rates using
micro-erosion meters (MEMs) (Foote et al., 2006).
The retreat of chalk cliffs is primarily a function of episodic cliff
collapses, where the type, volume and frequency of collapse are controlled
primarily by the chalk type and structure and cliff height
(Mortimore et al., 2004a; Dornbusch et al., 2008; Robinson, 2020). The porosity of
chalk means that groundwater saturation, rainfall and storms also play an
important role in cliff collapse occurrence at these vulnerable coastlines
(Duperret
et al., 2004, 2005; Mortimore et al., 2004a). One of the largest recent
cliff collapses occurred near Beachy Head in 1999 with a total chalk volume
loss of up to 150 000 m3, which produced a debris apron that extended
up to 130 m across the shore platform
(Mortimore et al., 2004a; Moses and Robinson, 2011; Robinson, 2020). In contrast,
smaller collapses of volumes <1000m3 occur much more
frequently and often multiple times within a year
(Duperret
et al., 2004; Williams et al., 2004; Robinson, 2020). The removal rate of
fallen cliff debris is widely unquantified (Moses
and Robinson, 2011). Nevertheless, it is suggested that small-scale falls
(<1000m3) may be removed in a matter of days to weeks,
medium-scale falls (1000–10 000 m3) can be removed over a few months,
and large-scale falls (>10000m3) may take decades to
transport all the material
(Mortimore et al., 2004a; Moses and Robinson, 2011). As well as the total volume of
fallen cliff debris, the size of debris produced can also influence the rate
of removal, but this has not been fully explored
(Moses and Robinson, 2011).
The Cretaceous white chalk cliffs and shore platforms contain bands of
nodular and continuous sheets of flint parallel to bedding
(Robinson, 2020; Mortimore et al., 2001).
Because flints are composed of diagenetic silica and are, therefore, more
resistant to weathering (and, by proxy, erosion) than the carbonate chalk
itself, beach material is made up of flint gravels left behind after the
chalk is eroded as well as sediment from palaeo-gravel barriers
(Dornbusch et al., 2006a; Mellett and
Plater, 2018). These flint beaches, which have a harder material strength
relative to the chalk, are therefore effective abrasion tools that
contribute to the erosion of both the shore platform and cliff base
(Costa et al., 2006; Robinson, 2020).
Conversely, beach material can also act as protection from incoming wave
erosion (Trenhaile,
2016; Earlie et al., 2018). There is evidence of beach thinning across these
southern English coastlines across the Holocene due to diminishing supplies
of flints from cliff erosion
(Dornbusch et al., 2006a, 2008),
increased regional storminess and the introduction of coastal defences
(Hurst et al., 2016).
A review of datasets acquired from a range of techniques, including
MEM measurements, laser scanning and historical maps,
estimated average cliff retreat rates of 11–87 cmyr-1 and average
platform downwear rates of 0.8–7.2 mmyr-1 for the chalk cliffs and
platforms, respectively, at the south coast in England and north in France
(Moses and Robinson, 2011). In England, the
longest record of historical cliff retreat rates was quantified using
digitised cliff positions from historical Ordnance Survey maps for a time
period of 130 years, which calculated an average cliff retreat of 35 cmyr-1 for the chalk coastline between Brighton and Eastbourne between
1873 and 2001 (Dornbusch et al., 2008). As
well as platform downwearing, step backwearing is another erosional
mechanism active on chalk shore platforms. Irregular steps form across the
shore platform due to the chalk and flint bedding of variable resistances.
The seaward edge of the step erodes landward primarily by means of
mechanical wave processes and, although highly spatially variable, the rate
of step retreat is of similar magnitude to platform downwear at the same
sites
(Dornbusch
and Robinson, 2011; Moses and Robinson, 2011; Robinson, 2020).
We focus our study on two new chalk rock coast sites at Seven Sisters and St
Margaret's at Cliffe (St Margaret's hereafter) as well as two previously
studied chalk rock coast sites at Hope Gap and Beachy Head (Hurst et al.,
2016) (Fig. 1). The Seven Sisters site is located on the south coast in
Sussex between the two coastal towns of Seaford and Eastbourne (Fig. 1).
This rock coast site is located within the Seaford Chalk Formation within
the White Chalk Subgroup, which is composed of weak, fine-grained chalk with
extensive bands of nodular and tabular flints
(Mortimore et al., 2001) (Fig. 1). A series of
low-amplitude anticlinal and synclinal structures shape the sinuous cliff
forms found at Seven Sisters
(Mortimore et al., 2004b). As a
result, cliffs range from maximum heights of 60–165 m associated with the
termination of valley peaks to minimum heights of 12–14 m associated with
the termination of valley troughs (Robinson,
2020). At this field site, the shore platform extends ∼226 m
offshore from the cliff base with a beach of ∼50 m width
overlying the cliff-platform junction. Cliff height reaches ∼47 m above the shore platform where we collected samples for CRN analyses.
Mean spring tidal range is measured as 5.97 m at the Newhaven tide gauge
site (National Tidal and Sea Level Facility, 2021).
Locations and regional geology for the St Margaret's and Seven
Sisters sites. (a) Location of rock coast sites on the south coast of England and chalk bedrock shown. (b) Regional chalk geology for Kent coastline and St Margaret's site. (c) Regional chalk geology for Sussex coastline and location of new Seven Sisters site and previously studied
sites Hope Gap and Beachy Head. (d) Hillshade (lidar) draped with aerial imagery (Channel Coastal Observatory, 2021) and 10Be sample
locations at St Margaret's. (e) Hillshade (lidar) draped with aerial imagery (Channel Coastal Observatory, 2021) at high tide (platform is
submerged) and 10Be sample locations at Seven Sisters.
The St Margaret's site, on the south-east coast of Kent, is situated
∼5 km north along the coastline from Dover (Fig. 1). The rock
coast at St Margaret's is located within the Lewes Nodular Chalk formation
within the White Chalk Subgroup, which is composed of hard to very hard
nodular chalk interbedded with softer chalks and marls
(Mortimore, 1987; Mortimore et al., 2001)
(Fig. 1). Beach widths range from 15 to 73 m in the area with the shore
platform extending ∼195 m offshore from the cliff base along
the CRN sampling transect. Just east of the field site is St Margaret's Bay,
where substantial beach material and groyne coastal defences are present.
The cliff height is ∼60 m directly above the shore platform
where we sampled for CRN analysis, but cliff heights reach >90 m
∼1 km further west along the coastline. Mean spring tidal
range is measured as 5.82 m at the Dover tide gauge site (National
Tidal and Sea Level Facility, 2021).
RSL histories have been supplied from a glacial isostatic adjustment (GIA)
model (Bradley et al., 2011). The three
sites, including Seven Sisters, Hope Gap and Beachy Head, on the Sussex
coast have the same reference location for the GIA model (“Sussex”,
Bradley et al., 2011). The GIA reference
location for the St Margaret's site was “Kent”
(Bradley et al., 2011). All four chalk
sites show very comparable RSL histories and show that RSL was at an
elevation ∼15 m lower than present day 8000 years BP (Fig. 2). Results from the GIA model for the chalk sites also shows that the rate
of RSL rise reached a maximum of ∼7mmyr-1 at 8000 years BP; this quickly declined to ∼2.6mmyr-1 at 7000 years BP and continued to gradually decline to rates of ∼0.3mmyr-1 at present day (Fig. 2).
Relative sea-level (RSL) (m) and the rate of RSL rise (mmyr-1) calculated every 1000 years for the site St Margaret's (blue) and
the East Sussex sites, including Seven Sisters, Beachy Head, and Hope Gap
(pink). RSL histories were provided by the GIA model of Bradley et al.
(2011).
MethodsNumerical modelling and model optimisation
Methods associated with our coastal evolution model and multi-objective
optimisation approach are provided in detail by Shadrick et al.
(2021); however, a basic overview is provided
here.
The numerical model couples an exploratory rock coast evolution model (Matsumoto et al., 2016) and a dynamic model for shore platform evolution and 10Be production (Hurst et al., 2017) to simultaneously model rock coast erosion and 10Be production. The model applies a dynamic form of coastal evolution that allows for transient cliff retreat, rather than Holocene-averaged cliff retreat rates, in order to quantify a time series of cliff retreat across millennial timescales. Platform morphology is an emergent model element instead of being fixed through model simulation time
(e.g. Regard et al., 2012; Hurst et al., 2016; Swirad et al., 2020). Simulated wave erosion is highly simplified by expressing wave hydraulic and
mechanical properties as wave assailing force and follows established
conceptual rock coast evolution models (Sunamura, 1992; Trenhaile, 2008; Payo et al., 2015). Erosion of the shore platform and cliff is achieved once wave
assailing force exceeds a material resistance value assigned to the rock
material. Subaerial weathering is also simulated and works to lower the
resistance of the rock material value (Matsumoto et al., 2016). Free parameters chosen to vary within the Markov chain Monte Carlo (MCMC) simulation were wave erodibility by means of wave height decay rate (y), material resistance (FR) and maximum intertidal weathering rate (K). Free parameter selection was informed by previous investigations that found these variables had the greatest influence on whether rock coast evolution was dominated by either wave or weathering-driven erosion (Matsumoto et al., 2018). The defined parameter space was informed by modelling-based and field-based investigations (Sunamura, 1992; Ogawa et al., 2011; Matsumoto et al., 2018; Trenhaile, 2000; Porter et al., 2010a). Altering the value of wave height decay rate (y), with units m-1, varies the spatial distribution and magnitude of wave energy. A greater value for y means wave height will decay more quickly and wave erosion covers a shorter distance across the shore platform, whereas a lower value for y means wave height will decay more slowly and wave energy dissipates across a greater distance across the shore platform. The conceptual value for material resistance (FR), with units kgm-2yr-1, simplifies mechanical, geological and structural rock factors into a single
value (Matsumoto et al., 2016). Maximum weathering rate (K), with units kgm-2yr-1, occurs at the mean high water neap (MHWN) tidal level defined by a weathering efficacy function (Porter et al., 2010a). The range of K explored encompasses a parameter space where negligible intertidal weathering and where weathering rate equal to the material resistance (FR) can be replicated in the MCMC simulations. Maximum weathering rate (K) was varied as a function of the material resistance (FR) within the MCMC simulations. The 10Be concentration is calculated across the shore platform surface and as a function of depth for every annual time step. Both spallation-produced 10Be and muon-produced 10Be are calculated as a function of depth by summing the exponential functions specific to spallation and muon production (Braucher et al., 2013). Cliff retreat exposes new shore platform material to 10Be spallation production. Exposure to 10Be production is modulated through time by the rate of cliff retreat, platform lowering, water cover (including tidal variation and RSL) and topographic shielding (Choi et al., 2012; Regard et al., 2012; Rogers et al., 2012). These factors combine to result in the predicted “humped” 10Be concentration horizontal profile offshore. A full description of the 10Be production model can be found in Hurst et al. (2017).
For each site, the two model outputs, including a topographic profile and
10Be concentration profile, were optimised simultaneously using
multi-objective optimisation with the QUESO Bayesian calibration library
(Estacio-Hiroms et al., 2016) within Dakota
optimisation environment (Adams et al., 2019). Before
implementing the full optimisation routine, exploration of the parameter
space using random sampling was performed to (1) refine the parameter ranges
and (2) tailor the proposal distribution variance for optimal chain mixing
with acceptance values of ∼23 %
(Gelman et al., 1997). The proposal distribution is
used to select and move to new samples in the MCMC chain, which directly
impacts the acceptance rate. The scaling values, which were used before the
topographic and 10Be concentration residual scores were combined, also
impact the acceptance rates. These scaling values are needed to equalise the
magnitude ranges of the two single residual scores. The topographic profile
scaling value is equal to the standard error from a linear regression of the
topographic profile; the 10Be concentration scaling value is the
average measurement error of the 10Be concentrations
(Shadrick et al., 2021). Table 1 includes
inputs and ranges for values used for the optimisation routine implemented
using Dakota for all four chalk sites.
Ranges and proposal distributions (PDs) for the free parameters y
(wave height decay rate), FR (material resistance) and K (maximum
weathering rate) for the St Margaret's, Seven Sisters, Hope Gap and Beachy
Head sites. Maximum weathering rate is varied as a function of material
resistance following Matsumoto et al.
(2018) (maximum weathering rate =K×FR). Scaling values for the weighted multi-objective MCMC routine for
the topographic profile and 10Be concentration profile are also shown.
A 10 000-iteration Metropolis–Hastings MCMC
(Metropolis et al., 1953) simulation was used to target
a set of model input parameters that produce a model output that best matches
the measured data. Optimisation is achieved by minimising the negative
log-likelihood score from an equally weighted objective function that
combines both topographic profile residuals and 10Be concentration
residuals between modelled and measured results.
Shadrick et al. (2021) provide a full
explanation of how this objective function is formulated and applied within
the Dakota environment.
Long-term cliff retreat rates are measured from the model simulation with
the best set of input parameters from the MCMC simulation. Uncertainty on best-fit results was defined by the 16 % and 84 % confidence intervals of likelihood weighted posterior distributions of accepted sample positions. Time stamps of modelled cliff positions were back calculated and used to estimate at what time cliff positions occurred at different distances relative to the present-day cliff position.
GIS-based methods for topographic data acquisition
To quantify recent cliff retreat rates for the past ∼130 years, georectified historical Ordnance Survey maps were used to digitally
map past cliff positions, and then these past cliff positions were compared
to the most recent cliff positions taken from aerial photographs. Historical
cliff retreat rates were previously quantified between the years 1873 and
2001 across all chalk sites on the south coast (Dornbusch et al.,
2008). We have used these historical cliff
retreat rates as a comparison to the long-term cliff retreat rates produced
from the coastal evolution model. At St. Margaret's, we updated previous
historical cliff retreat calculations made by Dornbusch et al. (2008) to
include up to the year 2020. Here, we used a similar approach to Dornbusch et
al. (2008) and used the Digital Shoreline Analysis System (DSAS) 5.0
(Himmelstoss
et al., 2018) to quantify cliff retreat rates between the years 1898 and
2020. Historical cliff positions were digitised from OS maps
(Digimap, 2021), and present-day cliff positions were digitised
from recent aerial photographs and light detection and ranging (lidar)
imagery (Channel Coastal Observatory, 2021). Historical cliff
retreat rates were quantified for ∼5.5 km of the coastline
that included the site where rock samples for CRN analysis were collected.
Using DSAS, a total of 1081 transects were made perpendicular to the
shoreline at 5 m intervals to intersect the past and present-day digitised
cliff positions. The cliff retreat rate was calculated by dividing the
distance between the two cliff lines by the time interval (122 years). The
uncertainty is calculated by propagating the uncertainty of the historical
and present-day cliff positions in quadrature and dividing by the time
interval
(Jonah
et al., 2016; Himmelstoss et al., 2018).
A modern cross-shore topographic profile of the shore platform was required
for optimisation of the cross-shore profile generated by the rock coast
evolution model (described in Sect. 3.1). The model tries to match the
intertidal topography to the observed cross shore profile.
The Channel Coast Observatory (Channel
Coastal Observatory, 2021) provides high-quality coastal lidar and multibeam
bathymetry that were combined and from which an intertidal topographic
cross-section 10 m wide swath profile was extracted to a distance of 300 m
from the modern cliff. The location of the swath profile follows the same
transect as the 10Be rock sample collection.
10Be sample collection and processing
The second output of the coastal evolution model is a predicted 10Be concentration profile along the same transect as the topographic profile. Flint nodules, which are composed of amorphous SiO2, in the chalk have the required target elements needed for cosmogenic 10Be production (e.g. primarily O) (Gosse and Phillips, 2001). Flint samples were collected from the intertidal platforms at Seven Sisters in July 2013 and at St Margaret's in August 2018 (Fig. 3). Before sampling, field reconnaissance was conducted to locate a flint bed with sufficient number and size of flint nodules that followed roughly the same transect, which extended from the beach toe to the low tide level. We maximised the distance offshore because the offshore sampling distance is proportional to the duration of time to which we can calibrate our coastal evolution model. As exactly as possible, field studies were timed to sample the shore platform at the lowest annual tides to ensure sampling could extend to the furthest offshore and widest width of the shore platform. In situ, exposed flint nodules were then excavated from the chalk shore platform at ∼10 m intervals, which resulted in 9 samples at Seven Sisters and 16 samples at St. Margaret's. High-accuracy (1–3 cm) Global Navigation Satellite System (GNSS) coordinates and elevation data were taken at each sample point using a Trimble Geo 7X and external antenna. A laser range finder was used to measure ∼10 m intervals between sample points. As well as the shore platform samples, where possible, a sample from a sea cave (Fig. 3b) was also taken to correct for inherited, muogenic-produced 10Be; i.e. the 10Be concentration present in the rock before the intertidal platform was exposed by erosion during cliff retreat. We assume the concentration of the sea cave sample at each site is entirely muon-produced and use this as our inheritance correction concentration for the shore platform samples at that site. At Seven Sisters, 10Be concentrations were corrected for inheritance using the full concentration of sample (SS09), which is closest to the modern cliff, because there was not a sea cave (Table 2); this was the same approach taken by Hurst et al. (2016)
for the Beachy Head site where a sea cave was not present. The concentration
at SS09 is similar to that which would be expected directly beneath a 47 m
high cliff for a secular equilibrium between muon production at depth and
radioactive decay. However, some minor (300–400 atomsg-1) additional 10Be accumulation may have occurred since the cliff retreat from the site of SS09 over the last 100 years.
Photos taken in the field at the St. Margaret's site. (a) The
chalk coastal cliff and shore platform identified at the site showing
evidence of previous cliff fall. (b) Example of flint bands found in the
chalk cliffs and sea cave. (c) Photo of sample SM05, which was taken from
the sea cave in photo (b). Sample SM05 was used as the shielded sample to
correct shore platform samples for inherited 10Be concentrations.
10Be sample and concentration data for Seven Sisters.
a Normalised to the 07KNSTD3110 standard with an assumed ratio of
2.85×10-12. Values corrected for chemistry background
using average and standard deviation of two full chemistry blanks
CFG1416A and CFG1416B (Table S1) processed in each batch with errors in sample and blank propagated in quadrature. b All SS samples were corrected for inheritance with SS09, the sample closest to the cliff base, assuming little accumulation of 10Be concentrations. c Error propagated as σc=σa2+σb2, where σa is the error of the measured concentration, and σb is the error of the measured concentration used for the inheritance correction SS09.
The shore platform samples were prepared using mineral separation and
isotope dilution chemistry methods based on either standard procedures
(Kohl
and Nishiizumi, 1992; Corbett et al., 2016) or methods previously used for
flint samples (Hurst et al., 2016) at the CosmIC laboratory at Imperial
College London (St Margaret's) and the Scottish Universities Environmental
Research Centre (SUERC) (Seven Sisters), respectively. The
10Be/9Be analyses by accelerator mass spectrometry (AMS) of the St
Margaret's samples were conducted at the Centre for Acceleration Science at
the Australian Nuclear Science and Technology Organisation (ANSTO) using the
6 MV Sirius tandem accelerator (Wilcken
et al., 2017). For the Seven Sisters samples, 10Be/9Be analyses
were conducted at Lawrence Livermore National Laboratory (LLNL) (Rood et
al., 2010). For St Margaret's samples, measured 10Be concentrations
were normalised to the KN-5-3 standard with an assumed ratio of 6.320×10-12 (t1/2=1.36 Ma, Nishiizumi et
al., 2007). For Seven Sisters samples, measured 10Be concentrations
were normalised to the 07KNSTD3110 standard with an assumed ratio of 2.85×10-12. Measured ratios were then corrected for background and inherited
10Be concentrations using the process blank samples and “shielded”
cliff (St Margaret's) or shore platform (Seven Sisters) sample, with errors
propagated in quadrature, allowing for calculation of absolute 10Be
concentrations (Tables 2, 3, S1, and S2 in the Supplement). Chemistry background
blanks for St Margaret's contained 19 100–71 710 10Be atoms, equivalent
to 4 %–40 % of total atoms in shore platform samples. For Seven Sisters,
chemistry background blanks contained 34 794–35 599 10Be atoms,
equivalent to 10 %–20 % of total atoms in shore platform samples.
10Be sample and concentration data for St
Margaret's.
a Normalised to the KN-5-3 standard with an assumed ratio of 6.320×10-12 (t1/2=1.36 Ma, Nishiizumi et al., 2007). Values corrected for chemistry background using average and standard deviation of three full chemistry blanks BLK101218, BLK1090119 and BLK2090119 (Table S2) processed in each batch; except for SM05 was background corrected with batch-specific chemistry blank BLK101218, with errors in sample and blank propagated in quadrature. b All SM samples were corrected for inheritance with SM05, a fully shielded cave sample. c Error propagated as σc=σa2+σb2, where σa is the error of the measured concentration, and σb is the error of the measured concentration used for the inheritance correction SM05.
ResultsHistorical cliff retreat rates
At the St Margaret's site, historical cliff retreat rates that were
quantified using DSAS are on average 7 cmyr-1 with an uncertainty of ±4.3cmyr-1 across the ∼5.5 km of coastline (Fig. 4). The maximum cliff retreat rate was measured as 29 cmyr-1 at St Margaret's, which coincides with locations that have
evidence of cliff failure. The historical cliff retreat rates for all three
Sussex coast sites, including Seven Sisters, Hope Gap and Beachy Head, were
on average 31 cmyr-1, according to Dornbusch et al. (2008), and
are an order of magnitude greater than the historical retreat rate at St
Margaret's (Table 4).
Historical cliff retreat rates (change in cliff edge position)
over the period 1894–2020 calculated for ∼5.5 km coastline
including St Margaret's site using DSAS
(Himmelstoss
et al., 2018).
Measured historical cliff retreat rates for Seven Sisters, Hope Gap
and Beachy Head (Dornbusch
et al., 2008, 2006b). Also using DSAS
(Himmelstoss
et al., 2018) for St Margaret's. Uncertainty and variability across the
∼5.5 km Kent and East Sussex coastline are also shown.
Acceptance ratios of the MCMC chains were between 23 % and 31 %, which
ensures chain mixing and that the parameter space was explored within the
optimal range (Gelman et al., 1997). Best-fit results
of the three free parameters FR, K and y from the 50 %–50 %,
topographic 10Be concentration MCMC inversion are shown in Table 5.
For the best-fit results for wave height decay rate (y), the slowest wave
height decay (0.07 m-1) is found for the St Margaret's and Beachy Head
sites. The slowest wave height decay rates will result in greatest wave
erosion being distributed across the longest distance across the shore
platform. The faster wave height decay rate (i.e. rapid wave energy
dissipation), as fast as 0.01 m-1, is found for the Seven Sisters and
Hope Gap sites, which results in less wave erosion localised across a
shorter distance and closer to where wave breaking is initialised offshore
from the cliff, i.e. when wave height >0.8× water depth. For
the best-fit results for material resistance (FR), all sites generally
show large uncertainty; however, the exception is for the Seven Sisters
site, which shows material resistance must be low (16–127 kgm-2yr-1) to match the datasets. Results also show that subaerial
weathering (K) is active in the long-term evolution of all chalk rock coast
sites that were studied with the greatest weathering rates (0.73–4.00 kgm-2yr-1) calculated at Beachy Head.
Optimised model parameters from a 50 %–50 % weighted
topographic–10Be concentration MCMC inversion. Range of best-fit
results expressed as 16 %–84 % confidence intervals calculated from
likelihood-weighted accepted parameter posterior distributions.
Best-fit model results from a 50 %–50 % topographic–10Be concentration weighted MCMC inversion for chalk sites at St Margaret's, Hope Gap, Beachy Head and Seven Sisters. Dark lines show best-fit results, and shaded areas show the confidence interval uncertainty range. The 16 %–84 % confidence interval for each free parameter in the MCMC inversion (FR, K, and y) was simulated against the median results for the other parameters. The shaded uncertainty was constructed from the upper and lower limits of the model outputs. For both the topographic profile and 10Be concentrations, the width of the modern-day, 300 m intertidal shore platform is shown. The modern-day cliff position is at 0 m. The panels on the left side compare the modelled results (coloured) to the measured data (black line) of the topographic profile. The panels on the right side compare the modelled results (coloured) to the measured data (black scatter points) of the 10Be concentration profile. Measured 10Be concentrations plotted here have been corrected for inheritance as described in Sect. 3.3.
Comparisons between the modelled output and measured data are shown using the
best-fit results and uncertainty defined by the 50 %–50 % weighted
topographic–10Be concentration MCMC results (Fig. 5). These results
are shown for the present-day timestamp when time is equal to 0 kyr before
present (BP) and the present-day cliff position is at 0 m. The best-fit
topographic profiles at St Margaret's and Beachy Head best fit the measured
data furthest offshore from the cliff; however, the model output is at a
lower elevation than the measured topographic profile further inshore and
closer to the cliff base. This mismatch suggests that the gradient of the
modelled topographic profile is not as steep as the observed shore platform
profile. Most notably, the modelled topographic profiles at the Hope Gap and
Seven Sisters sites poorly match the section of the shore platform in the
upper-intertidal zone; the modelled elevation is considerably lower than the
measured topographic profile in this zone. While the model can replicate the
general slope of the platform, it has not been able to capture the
topographic step in the shore platform observed at the Hope Gap and Seven
Sisters sites. The measured nearshore platform extending from
∼0–200 m from the cliff base is at a higher elevation
relative to the general slope of the shore platform with a stepped increase
from the offshore platform of ∼5 m at Seven Sisters and
∼2 m at Hope Gap (Fig. 5). The model best-fit results (shown
by the solid lines) at these two sites are located at the upper elevation of
the model uncertainty. These best-fit results relative to the uncertainty
range suggests the model was unable to move into a parameter space in the
MCMC inversion to match these elevations while trying to simultaneously
match the 10Be concentrations (see Sect. 5.5.2 for discussion).
The best-fit model results for 10Be concentration profiles show the
general trends in the 10Be concentration distributions match the
measured data. The best match between modelled results and measured
10Be concentration data is for the Hope Gap site. In contrast, at the
Beachy Head site, although the modelled 10Be concentration profile
replicates the average magnitude in measured 10Be concentrations, the
model has not captured the peak in 10Be concentrations (Fig. 5). In
fact, the peak in modelled 10Be concentrations at Beachy Head is
∼4.5×103atomsg-1 lower than the measured
10Be concentration peak. The model also underestimates the peak in
10Be concentrations by ∼2.5×103atomsg-1 at
St Margaret's. Moreover, at St Margaret's, a localised drop in measured
10Be concentrations ∼120–150 m from the cliff base is
not captured in the modelled 10Be concentrations. Similar to the
topographic results, the 10Be concentrations closest to the cliff base
cannot be well matched, especially at the Beachy Head and Seven Sisters
sites. Specifically, the model is overestimating the 10Be
concentrations by at most ∼1×103atomsg-1 at
∼50–150 m offshore from the cliff, in the upper-intertidal
zone at both Beachy Head and Seven Sisters sites. Also similar to the
topographic results, the best-fit results are at the lowest limit of the
model uncertainty for 10Be concentrations. Best-fit results found at
the outer limits of the uncertainty range further suggest that optimisation
of the topography and 10Be concentrations occurred in contrasting areas
of the parameter space, and, therefore, the model was unable to
simultaneously optimise both datasets.
The long-term trend in these new cliff retreat rates calculated from the
optimised models across the past 7000 years reflect the trend in the rate of
RSL for all four chalk sites (Figs. 2 and 6). For all chalk sites, cliff
retreat rates are fastest at 7000 years BP and then decline most rapidly between 7000 and 6000 years BP and then continue to decline gradually to present day. Overall, the slowest cliff retreat rates are calculated for the St Margaret's site where cliff retreat rates decline from 15–35 cmyr-1 at 7000 years BP to 1–3 cmyr-1 at present day. The Hope Gap and Beachy Head sites show similar patterns of cliff retreat rates through time, which decline from 20–55 cmyr-1 at 7000 years BP to 1–5 cmyr-1 at present day. The fastest cliff retreat rates are calculated for the Seven Sisters site where cliff retreat rates of 60–110 cmyr-1 at 7000 years BP were up to approximately 7 times faster than the other chalk sites at 7000 years BP. The cliff retreat rates at Seven Sisters follow the same trend and decline to 4–12 cmyr-1 at present day. The greatest decline in cliff retreat rates is also seen at Seven Sisters where cliff retreat rates declined by as much as 27 times the cliff retreat rate from 7000 years BP to present day.
Time series of cliff retreat rates (myr-1) and uncertainty
shown by the solid line and shaded area from 7000 years BP to present day.
Cliff retreat rates are calculated from modelled cliff positions every 100 years. The time period between 8000 and 7000 years BP is excluded
as this corresponds to the burn-in period of the model. The cliff retreat
rates highlighted by the dashed-line box are shown at a larger scale on the
right and correspond to the distance across the shore platform over which
measured data were analysed (∼250 m).
Time stamps of cliff positions were back calculated to estimate the duration
of time required to erode the present-day, ∼250 m wide intertidal platform. According to these best-fit MCMC results, the slowest cliff retreat rates at St Margaret's eroded the present-day intertidal platform during the past ∼5300 years. Faster cliff retreat rates modelled at Hope Gap and Beachy Head eroded the present-day intertidal shore platform during the past ∼4100 and ∼4000 years, respectively. The fastest cliff retreat rates modelled at Seven Sisters eroded the present-day intertidal shore platform during the past ∼1800 years. Overall, the low 10Be
concentrations and long-term cliff retreat rates at all four of these chalk
sites confirm the observed shore platforms at these sites are Holocene
features and not reoccupied from a previous interglacial period.
Discussion
Our results show that long-term cliff retreat rates reflect the rate of RSL
rise across the Holocene for all four chalk sites. Comparisons between these
model results and historical observations further support previous findings
of a recent acceleration in cliff retreat rates at the south coast
(Hurst et al., 2016). Our results also reveal
contrasting results between chalk and previously studied sandstone sites
(Shadrick et al., 2022) regarding
the key erosional mechanisms controlling long-term evolution. However,
best-fit model results for the chalk sites have inconsistent, and, in some
cases, relatively poor fit to the measured data, which contrasts the
well-fit model to data comparisons at the sandstone sites
(Shadrick et al., 2021). Below, we make
comparisons between long-term cliff retreat trends at rock coast sites with
differing lithologies using our dynamic model, as well as comparisons
between different model results of cliff retreat rates at our same chalk
sites. We also discuss what factors are likely to contribute to the
contrasting success of the model when applied to different lithologies.
Nevertheless, despite these potential limitations, we are still able to use
results from our dynamic, process-based model to identify key distinctions
in erosion processes active across millennial timescales at coasts with
differing lithology.
Long-term trends in cliff retreat rates
Our model results for the chalk sites are consistent with previous results
for two sandstone sites (Bideford and Scalby) and suggest that long-term
trends in cliff retreat rate are reflective of the rate of RSL rise
(Shadrick et al., 2021). As a result, the
model suggests that the fastest rates of cliff retreat for the Late Holocene
are found when the rates of RSL are greatest. Due to similar RSL histories
for all chalk rock coast sites, the greatest rate of RSL rise during the
model simulation time is found at 7000 years BP (Fig. 5). We have excluded
the time period between 8000 and 7000 years BP because this interval occurred
during the model's burn-in period. For the two sandstone sites previously
studied, Bideford and Scalby, best-fit cliff retreat rates were
∼5.2 and ∼14.4 times faster, respectively, at
7000 years BP in comparison to historical rates of cliff retreat
(Shadrick et al., 2021). As for the chalk
sites, cliff retreat rates were ∼1.2 times faster at Hope
Gap, ∼1.4 times faster at Beachy Head, and ∼2.1 times faster at Seven Sisters 7000 years BP in comparison to historical
rates of cliff retreat. These results are generally consistent with
Trenhaile's (2011) findings, which concluded that a
greater proportional increase will be found at historically slower sites in
relation to increased rates of RSL rise. However, Trenhaile's
(2011) predictions are for future cliff retreat
response to projected accelerations in RSL rise and are entirely
theoretical with no calibration to measured data. In contrast, here, we have
used empirical data to reconstruct how cliff retreat responded in the past
when rates of RSL rise were comparable to these future projections.
Comparisons between historical cliff retreat rates and long-term
cliff retreat rates derived from both a dynamic model and a geometric model.
Note that the decline in long-term transient cliff retreat rates follows the
pattern of RSL rise rate, and the long-term steady-state cliff retreat rates
are a step change (see Fig. 7).
SiteHistorical cliff Long-term, dynamic Long-term, geometric retreat rates cliff retreat rates cliff retreat rates Time periodRateTime periodRateTime periodRate(years BP)(cmyr-1)(years BP)(cmyr-1)(years BP)(cmyr-1)St Margaret's1227±453007 to 3––Seven Sisters12839±4180018 to 13––Hope Gap12832±4410010 to 343156 to 1Beachy Head12822±4400010 to 461393 to 30Comparisons of long-term to historical cliff retreat rates
Contradictory to the long-term trends in modelled cliff retreat rates that
reflect the rate of RSL rise, the discrepancies between long-term modelled
and short-term, historically observed cliff retreat rates suggest that RSL
does not have the greatest control of cliff retreat rates at these chalk
sites. Comparisons between short-term, historically observed cliff retreat
rates, long-term retreat rates derived from the dynamic model, and, where
available, long-term retreat rates from a geometric model (Hurst et al., 2016) (see Sect. 5.3) are shown (Table 6). Using the steady-state model, previous work by Hurst et al. (2016) identified up to an order of magnitude
increase in recent cliff retreat rates compared to long-term, Holocene-average rates at Beachy Head and Hope Gap. This previous work is
consistent with our new results from the dynamic model, which suggests that
long-term rates of cliff retreat across the Late Holocene are an order of magnitude less than the historical rates quantified by Dornbusch et al. (2008). Furthermore, our antecedent cliff
retreat rates quantified using the dynamic model reveal that the historical
rates of 22 cmyr-1 at Beachy Head last occurred ∼6400 years BP and historical rates of 32 cmyr-1 at Hope Gap last occurred ∼6800 years BP. The rates of RSL rise during these times of accelerated cliff retreat were 2.2 mmyr-1 at Beachy Head and 2.6 mmyr-1 at Hope Gap, which are approximately 7.3 and 8.7 times faster than the rate of RSL rise experienced during the observational record, respectively. Similarly, observed rates of 39 cmyr-1 at Seven Sisters last occurred ∼6200 years ago when the rate of RSL was 2 mmyr-1, which is 7 times faster than the rate of RSL rise over the observable record. The acceleration in recently observed cliff retreat rates must, therefore, be caused by additional factors other than accelerations in RSL rise (see Sect. 5.5).
Although recent observations of cliff retreat rates at St Margaret's are not
as fast as those on the Sussex coast, by using the dynamic model, we
calculate these recent rates of cliff retreat (7 cmyr-1) were last
experienced at St Margaret's 5300 years BP. At this time, the rate of RSL
rise was ∼1.4mmyr-1, which is nearly 5 times the rate
of RSL rise experienced during the past 122 years (0.3 mmyr-1) over
which the historical cliff retreat rates were quantified. The slower
historical cliff retreat rates calculated at St Margaret's in comparison to
the Sussex coast sites could be a result of the harder Lewes Nodular
Chalk lithology at St Margaret's, in comparison to the soft, low-density,
more densely fractured and high-porosity Seaford Chalk Formation on the
Sussex coast (Mortimore et al., 2004b). Furthermore, Dornbusch et al. (2006b) suggest
that cliff retreat along the Kent coast is linked to larger-scale erosion
events with return periods longer than the observational record. Larger-scale erosion events with longer return periods can, therefore, result in
apparent slower retreat rates if a mass erosion event has not occurred
within the survey period. In contrast, episodic, large erosion events can
also result in apparent faster retreat rates if a mass erosion event has
occurred within the survey period relative to the long-term trend in cliff
retreat, which requires integration across multiple events to quantify.
Return periods that are longer than the observational record again
highlight the relatively large uncertainty in short records and the need
for cliff retreat rates quantified across millennial timescales
(Sunamura, 2015).
Geometric retreat versus dynamic retreat evolution
Long-term cliff retreat rates were previously quantified for the chalk
coasts at the Hope Gap and Beachy Head sites using a geometric coastal
evolution model (Hurst et al., 2016). This
geometric model was optimised to the same 10Be concentration datasets
used here. We next compared the best-fit cliff retreat rates derived for
both our new dynamic and the previous geometric model and discuss their key
similarities and differences (Fig. 7).
Comparisons between cliff retreat rates produced from a dynamic
coastal evolution model (Matsumoto et al., 2016), in purple; and a geometric coastal evolution model
(Hurst et al., 2016), in blue; for sites Hope Gap and
Beachy Head. Cliff retreat rates (myr-1) are shown for 7000 years BP
to present day. The darker shaded regions highlight the time frames that extend
beyond the measured data in the past.
At Hope Gap, both the geometric and dynamic models reveal that cliff retreat
rates declined during the Holocene, but the trend of decline differs between
each model (Fig. 7). The best-fit result from the geometric model finds a
step change in cliff retreat rates from 5.7 to 1.3 cmyr-1
at 308 years BP (Hurst et al., 2016). The
best-fit results from the dynamic model show a decrease in cliff retreat
rates from 10 cmyr-1 4100 years ago to 3 cmyr-1 at present day.
Although the geometric model cannot capture transient cliff retreat like the
dynamic model, both models show the 250 m intertidal platform at Hope Gap
was formed over comparable time frames: ∼4100 years using the
dynamic model and ∼4315 years using the geometric model (Fig. 7). Moreover, the present-day cliff retreat rates found by both models are
within uncertainty of each other: 1–2.4 cmyr-1 from the steady-state
model and 2–4 cmyr-1 using the dynamic model. These comparable
results found at Hope Gap validate both models' findings of declining rates
of cliff retreat across the Late Holocene. Nevertheless, neither model
captures the recent acceleration evidenced with historic observations (see
Sect. 5.2).
At Beachy Head, results for the two models do not agree as well. The
best-fit result from the geometric model finds a step change in cliff
retreat rates with a significant increase in cliff retreat rates from
2.6 to 30.4 cmyr-1 at 293 years ago
(Hurst et al., 2016). In contrast, the
best-fit results from the dynamic model shows a declining trend in cliff
retreat rates. The dynamic model reveals best-fit cliff retreat rates that
fall from 10 cmyr-1 at ∼4000 years ago to 4 cmyr-1 at present day. Observed cliff retreat rates for the past 130 years at Beachy Head were previously quantified as 22 cmyr-1
(Dornbusch et
al., 2008; Hurst et al., 2016), which agrees with the geometric model's
scenario of a step increase in cliff retreat rates to 30.4 cmyr-1 at
293 years ago. This step increase in cliff retreat rates had to be forced in
the geometric model to match the low 10Be concentrations <150 m from the cliff. We, however, cannot force changes in cliff retreat rates
in the dynamic model because cliff retreat rates are emergent from the
topographic evolution that is controlled by physical erosion processes.
Moreover, the best-fit 10Be concentration results found for the dynamic
model at Beachy Head could not match the inshore low concentrations (Fig. 5;
see Sect. 5.5.2 for discussion). This mismatch between measured and
modelled 10Be concentrations could support the finding that there was a
significant increase in cliff retreat rates in the recent past at Beachy
Head that could not be captured by the processes represented in the dynamic
model.
Comparisons between weathering rates and processes at chalk and sandstone rock coasts
Unlike the two previously studied sandstone rock coast sites (Bideford and
Scalby; Shadrick et al., 2021), all the chalk sites in this study (St
Margaret's, Hope Gap, Beachy Head and Seven Sisters) show well-defined
normal posterior distributions for weathering rates (Fig. 8). For all four
chalk sites over the 8000-year simulation time, we calculated that if the
magnitude of weathering rates fell below approximately 5-5× material
resistance (FR) (kgm-2yr-1) (shown by the dashed line in
Fig. 8), the material resistance of the rock cells could not be lowered
enough by intertidal weathering for waves to erode the rock cells. In other
words, when K<5-5 as a fraction of material resistance, intertidal
weathering has limited influence on reducing rock cell material resistance
and wave erosion is the dominant erosion process. In contrast, for the
previous sandstone site at Bideford, zero weathering (K<5-5)
had to occur to match both the topographic and 10Be concentration
dataset (Shadrick et al., 2021). The
10Be concentrations at the other previous sandstone site at Scalby
could be matched with active weathering, hence the spread of accepted K
samples above 5-5 (Fig. 8). However, like at Bideford, only with
negligible weathering could the 10Be concentrations and topographic
data be matched simultaneously at Scalby
(Shadrick et al., 2021). For both previous
sandstone sites, once weathering rates become negligible (K<5-5), there is no change to the model output, which results in broad,
near-uniform distributions in K to which the model is insensitive (Fig. 8).
For all chalk rock coast sites, however, the best-fit results contrast with
the sandstone sites and show that active subaerial weathering is needed to
match the topographic and 10Be concentration data.
Posterior histograms of likelihood-weighted, accepted MCMC
weathering efficacy rate (K) samples. Here weathering rate is calculated as
FR×K. Red and orange histograms show the results for the two
sandstone sites: Bideford and Scalby. Blue, purple and green histograms show
the results for the four chalk sites: St. Margaret's, Hope Gap, Beachy Head
and Seven Sisters. Above the dashed line (where K<5-5) is when
weathering is active across the shore platform. Below the dashed line (where
K<5-5) is when weathering processes are negligible.
Greater weathering rates at chalk rock coasts compared to sandstone rock
coast is supported by field measurements of platform downwear using
MEMs, laser scanning and structure from motion (SfM).
Although not as commonly studied as shore platform downwear rates at chalk
lithology coasts, downwear rates of harder lithologies tend to have lower
rates compared to softer chalk: for example, downwear rates of 0.25 mmyr-1 were recorded for a sandstone platform
(Yuan et al., 2020); 0.242 mmyr-1 for a mudstone and siltstone platform
(Porter et al., 2010b); 0.528 mmyr-1 for a mudstone, sandstone and shale platform; and 0.625 mmyr-1 for a greenschist platform (Mottershead,
1989). This is in contrast to overall higher rates of platform downwear
measured at chalk sites, for example, average chalk platform erosion rates
of 0.791–7.202 mmyr-1 measured across 18 sites (Moses and Robinson,
2011). However, these rates of downwear measured
in the field do not exclusively relate to intertidal weathering. In the
dynamic coastal evolution model used here, vertical downwear is accounted
for by (1) the vertical component of wave assailing force
(Stephenson
and Kirk, 2000; Trenhaile, 2000; Matsumoto et al., 2016) and (2) intertidal
weathering defined by a weathering efficacy function
(Porter et al., 2010a;
Matsumoto et al., 2016). The down-wearing component of wave erosion follows
Stephenson and Kirk (2000) and Trenhaile
(2000) and is proportional to the back-wearing
force at the still water level, with intensity declining exponentially with
water depth (Matsumoto et al., 2016). The
weathering efficacy function (Porter et al.,
2010a) dictates that maximum weathering occurs at the mean elevation of the
lowest high tide and efficacy decreased above and below this elevation
(Matsumoto et al., 2016). The implications of
the model's representation of subaerial weathering are further discussed in
Sect. 5.5.1.
Furthermore, the best-fit results for material resistance for the new chalk
sites show wide distributions (Table 5). This wide distribution of best-fit
material resistance was also the case for the previous sandstone sites
(Shadrick et al., 2021) and is caused by
correlation between the free parameters, especially between material
resistance and wave height decay rate
(Shadrick et al., 2021). Due to the dynamic
model's abstract representation of physical rock qualities and erosion
processes, these results show that material resistance alone is not
sufficient to make distinctions between different lithologies at rock coast
sites. Clear distinctions for the weathering rate shown here between the
sandstone and chalk sites show that weatherability of the shore platform at
the rock coast site is a more significant indicator than the material
resistance when assessing long-term platform downwear.
The representation of near-shore processes
The best-fit results derived from the dynamic model for the chalk sites,
particularly seen at sites Hope Gap, Beachy Head and Seven Sisters, have
been unable to simultaneously match both the topographic and 10Be
datasets. This is in contrast to highly comparable modelled and measured
results for the previously studied sandstone sites
(Shadrick et al., 2021). These results
suggest that additional processes not yet implemented within the model are
important in the long-term evolution of chalk rock coasts, which play a
comparatively minor role at the sandstone rock sites previously studied. At
the Beachy Head site, we suggest that the misfit between observed and
modelled 10Be concentrations close to the cliff base is caused by an
acceleration in recent cliff retreat rates that could not be captured by the
dynamic model (see Sect. 5.3). Similarly, at Seven Sisters, because the
dynamic model could also not match the low 10Be concentrations closest
to the cliff (Fig. 5), this mismatch could also suggest there was a recent
increase in cliff retreat rates at the Seven Sisters site as well. This
explanation, however, may not exclusively account for the over-predicted
nearshore 10Be concentrations calculated by the model and also may not
explain the mismatch in nearshore topography (Fig. 5). Below, we discuss the
representation of nearshore processes used in the model, as well as
processes overlooked by the model, that may explain the discrepancies
between the modelled results and measured data at the chalk sites.
Intertidal weathering and other contributions to platform erosion
Intertidal weathering can be an important precursor for erosion by weakening
the substrate so that less energy is required to mobilise rock mass. Tides
control the duration and frequency over which different elevations of the
shore platform are immersed and exposed by water. Tidally controlled
variations in water level mean that the efficacy of weathering in the form of
wetting and drying, as well as salt and frost weathering, i.e. processes controlled by
cycles of water exposure, varies with elevation across the shore platform
(Stephenson and Kirk, 2000;
Trenhaile, 2018). Weathering of the shore platform is exclusively considered
by the model as tidally controlled weathering processes, which are
represented as a weathering efficacy shape function that dictates maximum
weathering occurs at the lowest high tide level and decreases above and
below this elevation
(Porter
et al., 2010a; Matsumoto et al., 2016, 2018). This weathering function is
based on results from laboratory experiments of wetting and drying and salt
weathering (Porter et al., 2010a). However,
field results do not match this spatial pattern of weathering efficacy; for
example, corresponding MEM field measurements (Porter et al.,
2010a) and further comparisons of
field-measured downwear rates across various studies
(Trenhaile, 2003, 2018) found no
significant relationship between platform downwear and elevation in relation
to tides. In the field, platform downwear is also influenced by frost,
abrasion, bioerosion and rock surface swelling, which all have variable
efficacies in relation to elevation that may explain differences found
between the laboratory and field results
(Trenhaile, 2018; Porter
et al., 2010a). Studies on the south coast of the UK all found greatest
downwear on chalk platforms to be at the top of the platform in the zone of
beach-supplied abrasion (Ellis,
1986; Andrews, 2001; Foote et al., 2006). The influence of beach material on
shore platform erosion is discussed in the following section (see Sect. 5.5.2).
It is suggested that intertidal weathering mainly dictates platform downwear
where abrasive material and bioerosion are absent
(Trenhaile, 2018). This cannot be said for the chalk
shore platforms studied here because there is evidence of abrasive beach
material and biological activity. Both abrasion and bioerosion are not
included in the coastal evolution model used here. Abrasion of the shore
platform surface is especially efficient when beach material is harder than
the bedrock it is eroding (Costa et al.,
2006; Robinson, 2020). Because this relative hardness is the case between
flint gravel beaches and chalk shore platforms at our south coast sites,
abrasion from beach material is likely to contribute to considerable
platform downwear and is discussed in the following section (see Sect. 5.5.2). Offshore from the abrasion zone, it is thought that bioerosion,
e.g. changing pool chemistry, weakening fractures in rocks, and boring into
the platform surface (Naylor et
al., 2012; Trenhaile, 2018), may even dominate shore platform erosion
(Foote et al., 2006; Henaff et al.,
2006; Robinson, 2020). Because bioerosion is so spatially varied, however,
the overall contribution to platform downwear remains uncertain, especially
in non-tropical environments and in the subtidal/submarine zone
(Trenhaile, 2018). Future research into the
distribution of species in the intertidal zone on chalk platforms may help
to shed light on bioerosion-controlled downwear at these sites.
Our modelling results and relevant literature suggest that our dynamic
model's representation of platform downwear, which is controlled principally
by a single function describing intertidal weathering in the model, may not
be the most appropriate mechanism of platform downwear for these chalk coast
sites. Nevertheless, clear differences between best-fit modelled weathering
rates at chalk and sandstone sites (Fig. 8) reveal that long-term platform
downwear occurred at much faster rates at the chalk sites. More work is
needed to establish which specific processes are more dominant at the chalk
sites in order to result in greater platform downwear.
Beach material and cliff debris
Beach material and cliff debris have the potential to both enhance and limit
erosion of the shore platform and cliff base
(Sunamura, 1982; Limber and Murray, 2011).
Evidence of beaches that enhance erosion includes field studies that have
measured downwear with MEMs on chalk platforms; these field studies have
consistently found greatest downwear to occur at top of the platform where
abrasion from beach material occurs
(Ellis, 1986;
Andrews, 2001; Foote et al., 2006; Moses and Robinson, 2011). Furthermore, a
regional assessment of cliff retreat in California found that cliffs fronted
by beaches retreated nearly 50 % further than cliffs without beaches
(Young, 2018). In contrast, beaches and
fallen cliff debris can also act to dissipate wave energy that reduces
platform downwear and wave impact at the cliff base, which slows cliff
retreat (Sunamura, 1992; Walkden and Hall,
2005). These contrasting impacts on erosion as a result of beach material
make it difficult to understand their role in long-term rock coast
development.
The coastal evolution model used here
(Matsumoto et al., 2016) does not consider the
impact of beach material on cliff retreat rates. The combination of
across-shore and along-shore processes involved with transport of beach
material and limited data on long-term beach evolution has meant that the
role of beaches in the long-term evolution of rock coasts remains uncertain
and understudied (Naylor et al.,
2014; Hurst et al., 2016). As a result, only a select number of modelling
studies have investigated interactions between rock coast evolution and
beach dynamics. A beach profile was incorporated into the Soft Cliff And
Platform Erosion (SCAPE) model as exclusively a protective feature
(Walkden and Hall, 2005). Beach protection
of the upper intertidal platform, and resultant decreased cliff retreat, is
countered with the presence of beach material steepening the rock shore
platform, which makes the shore platform and cliff more vulnerable to
erosion (Walkden and Hall, 2005). Both the
abrasive and protective roles of beaches were incorporated into the Limber
and Murray (2011) model, in which cliff retreat increases with
active abrasion and cliff retreat decreases with either limited beach
sediment that prevents abrasion or too much sediment that prevents wave
erosion.
At our chalk sites, there is evidence of beach thinning across the Holocene
(Dornbusch et al., 2006a, 2008). It
has also been suggested that beach thinning has contributed to the recent
accelerations in cliff retreat rates due to diminished protection and
abrasive material
(Dornbusch et
al., 2008; Hurst et al., 2016). Thicker and wider beaches in the past are
likely to have played a protective role and dampened wave erosion and slowed
cliff retreat rates at these south coast chalk sites. Although widely
variable spatially and temporally, Dornbusch et al.
(2008) suggested that past average beach
widths of ∼37 m were unable to protect the cliff from erosion
and that average beach widths need to exceed ∼70 m to
entirely prevent wave erosion, including from storm waves, at the cliff.
With observed beach widths <37 and >70 m at
local scale, protection and abrasion must be varied spatially across the
south coast chalk cliffs. Due to our limited current knowledge, we are
unable to quantify at what time, on average, flint beaches along south coast
chalk cliffs crossed the threshold from a protective feature to an abrasive
one. Our work highlights the importance of beach material at rock coast
sites and that we need to better understand feedbacks between beach
dynamics, wave erosion and cliff failure.
Although not modelled here, incorporation of beach material into the rock
coast system will consistently lower the modelled 10Be concentrations.
The presence of beach material lowers 10Be concentrations by (1)
shielding the platform from cosmic rays, which prevents production in the
shore platform
(Regard et al.,
2012; Hurst et al., 2017) and (2) abrading and removing the surficial layers
of rock with the highest 10Be concentrations to expose rock with lower
concentrations beneath. Hurst et al. (2017) found that
beach widths must be >50 m to lower concentrations significantly
(by >15 %). Because beach cover has not been incorporated
within our dynamic model simulations, our model results may be
overestimating long-term cliff retreat rates because we model low
concentrations to indicate fast cliff retreat rates without the influence of
beaches
(Regard
et al., 2012; Hurst et al., 2016, 2017). However, accounting for the
influence of beaches would make long-term cliff retreat rates slower than
our estimations and, in turn, the recent acceleration seen in historical
cliff retreat rates even greater (Hurst et
al., 2016).
Furthermore, because beach presence lowers CRN concentrations, the low
10Be concentrations measured nearest the beach at Beachy Head and Seven
Sisters could be caused by beach cover, recent cliff retreat accelerations,
or a combination of the two. At Beachy Head, the nearshore concentrations
are ∼39 %–74 % lower than the best-fit model predictions
(Fig. 4). Similarly, at Seven Sisters, nearshore concentrations are
∼57 %–84 % lower than the best-fit model predictions.
According to Hurst et al. (2017), the beach width
would need to exceed ∼100 m for at least the past 600 years
for model predictions to align with the measured data at Beachy Head and
Seven Sisters. Observed beach widths are 15–73 m at these four south coast
sites; therefore, even with thicker and wider beaches in the past
(Dornbusch et al., 2006a, 2008), it
is unlikely for overestimations in nearshore concentrations to be
exclusively as a result of shielding from beach material or cliff debris.
Furthermore, even the most massive cliff falls (>100003)
can transport material away in a number of decades
(Mortimore et al., 2004a; Moses and Robinson, 2011). Observed beach widths and
transportation time of fallen cliff debris further support the scenario of
a recent acceleration in cliff retreat rates, which may be responsible for
the low 10Be concentrations that the dynamic model outputs are unable
to fit at Seven Sisters and Beachy Head. Nevertheless, beach thinning and
resultant increased abrasion has the potential to enhance cliff retreat rate
and contribute to such an acceleration that would account for the low
10Be concentrations (Limber and Murray, 2011).
Shore platform stepped topography
At Hope Gap (see Fig. 5), there is a notable step in the topography at a
distance of ∼180 m from the modern cliff. The next samples
offshore from this location (200–250 m from the cliff) were sampled from
lower elevations and have a lower concentration. These steps found at the
south coast chalk platforms are caused by heterogeneous beds of chalk and
flint that vary in thickness and material strength
(Moses and Robinson, 2011). However, the model's
implementation of lithology assumes homogenous material resistance across
the shore platform and cliff with no consideration of stratigraphic layers
(Matsumoto et al., 2016). Unlike at the
previously studied sandstone sites
(Shadrick et al., 2021), observed local
variations in lithology have greater control on the shore platform
meso-morphology at these chalk coasts sites, and this variation has not yet
been incorporated into our dynamic model optimisation. Such developments
might also help to better match the relatively high concentrations at St.
Margaret's and Beachy Head, which might reflect limited surface lowering
locally. Future work should aim to include heterogeneous material resistance
into the model to better replicate the topographic steps and associated
processes, such as step backwearing, at these chalk sites.
Conclusions
In this study, we have quantified transient, long-term cliff retreat rates
across the Late Holocene for four chalk rock coast sites in the south of
England. We have achieved this through multi-objective optimisation of a
process-based coastal evolution model to measured topographic and 10Be
CRN concentration data. An improved understanding of how cliff retreat rates
responded to past changes in RSL helps to inform models that forecast cliff
retreat rate response to climate-change-driven accelerations in RSL rise.
We have compared millennial-scale cliff retreat rates quantified by a
previous steady-state equilibrium coastal evolution model
(Hurst et al., 2016) to rates derived from
our new transient, process-based coastal evolution model
(Matsumoto et al., 2016) for two sites on the
Sussex coastline at Hope Gap and Beachy Head. Our results provide further
support for previous findings of a significant recent acceleration in cliff
retreat rates compared to the long-term rates quantified for the
Late Holocene at the Sussex coastline (Hurst et al., 2016). Measured historical rates of cliff
retreat during the past ∼130 years range from 22–40 cmyr-1 for the three Sussex coast sites
(Dornbusch et al., 2008). However, our
model results optimised to 10Be concentration and topographic data
suggest cliff retreat rates during the past ∼2000 years were
6–18 cmyr-1 across these three Sussex coast sites. This is consistent
with another recent study that has suggested recent acceleration in cliff
retreat rates based on 10Be concentrations measured on chalk shore
platforms (including sub-tidal measurements) on the French coast of the
English Channel at Mesnil-Val (Duguet et al., 2021). Long-term cliff retreat
rates for these sites also track the rate of RSL across the Holocene, which
is similar to results found for two previously studied sandstone sites in
the UK (Shadrick et al., 2022).
However, the recent acceleration in cliff retreat rates evidenced by
historical observations suggests that the rate of RSL rise is not necessarily
the greatest control on cliff retreat rates at our chalk rock coast sites.
Optimised results from the process-based model suggest the observed cliff
retreat rates quantified for the past ∼150 years at the south
coast chalk sites (Dornbusch et al., 2008)
were last experienced between 5300 and 6800 years ago when the rate of
relative sea-level rise was 5–8.7 times greater than the rate of RSL
experienced during the observational record. Model results suggest that
cliff retreat rates were as much as 110 cmyr-1 when the rate of RSL
rise was 2.6 mmyr-1 at the Seven Sisters site 7000 years BP. For other
chalk sites that we studied, including Hope Gap, Beachy Head and St
Margaret's, when the rate of RSL was 2.6 mmyr-1 7000 years BP, cliff
retreat rates ranged from 15 to 55 cmyr-1.
It is important to understand the long-term processes acting at shore
platforms because these landforms play a critical role in mediating cliff
erosion. The application of a process-based model used here has identified
contrasting results for relative intertidal weathering rates across shore
platforms between relatively strong sandstone and relatively weak chalk rock
types. The optimised model results suggest that the rate of intertidal
weathering was ∼2–3 orders of magnitude greater at the chalk
sites compared to the sandstone rock coast sites. However, at sandstone
sites, optimised results suggest that negligible subaerial weathering had to
occur to match the measured data, whereas, at all chalk sites that we
studied, active subaerial weathering was required to match the measured
topography and 10Be concentrations. Furthermore, our results found no
significant differences between best-fit material resistances for the
sandstone and chalk sites. This indicates that it is not only the material
strength of the lithology but also how weatherable the material is that is
important in the long-term evolution of rock coast sites.
Comparisons between modelled results and measured data also suggest
heterogeneous lithologic resistance and beach presence play an important
role in the control of shore platform morphology, resultant 10Be
concentrations and, as a result, the long-term evolution of chalk rock
coasts. These results particularly illustrate the importance for future work
to consider the role of beaches to ensure long-term cliff retreat rates are not
overestimated from 10Be concentrations.
Nevertheless, results provided here have advanced the understanding of the
long-term drivers of rock coasts in different lithological settings,
particularly intertidal weathering and beach material. Using a
process-based coastal evolution model to interpret 10Be concentrations
has allowed us to not only quantify long-term transient cliff retreat rates,
but also to help inform the “wave versus weathering” debate across
millennial timescales. This is one of the first applications of a
process-based model used to interpret 10Be CRN concentrations, which
has, in turn, identified contrasts in prevailing long-term erosional
mechanisms at coasts with different lithologies. Our findings highlight
strong potential in our methodology to quantify long-term drivers of rock
coast erosion at a variety of real-world sites. Quantifying cliff retreat
rates and key erosion mechanisms across millennial timescales is especially
important for rock coasts vulnerable to climate change, such as the UK chalk
south coast.
Code and data availability
Input datasets can be found in the Supplement. Input data files, plotting scripts, code and documentation can be found at 10.5281/zenodo.5645478 (Hurst et al., 2021).
The supplement related to this article is available online at: https://doi.org/10.5194/esurf-11-429-2023-supplement.
Author contributions
JRS, MDH, MDP and DHR designed the research and analysed the data; JRS, DHR, MDH and KMW collected measured datasets; DHR, JRS and AJS prepared samples in the laboratory; JRS developed the optimisation routine with support from MDH and MDP; KMW performed AMS measurements; JRS, MDH, DHR and MDP wrote the paper.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We thank Michael Ellis for general and ongoing support with the project and editorial assistance. We also thank Sarah Bradley for providing RSL history data, which is an essential component to this project. We would like to thank Emily Gusterson and Jay Ward for support with field data collection. Finally, we would like to thank the reviewers, whose comments have greatly strengthened this paper.
Financial support
This work was supported by a studentship from the Natural Environment Research Council (NERC) Science and Solutions for a Changing Planet Doctoral Training Partnership (DTP), with additional funding by the British Geological Survey (BGS) to Jennifer R. Shadrick. Dylan H. Rood received support of ANSTO Research Portal (grant no. 10955).
Review statement
This paper was edited by Veerle Vanacker and reviewed by Nathan Vandermaelen and Anne Duperret.
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