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281
Scour and Erosion – Harris, Whitehouse & Moxon (Eds)
© 2016 Taylor & Francis Group, London, ISBN 978-1-138-02979-8
Thermomechanical erosion modelling of Baydaratskaya Bay,
Russia with COSMOS
S.G. Pearson, R. Lubbad & T.M.H. Le
Sustainable Arctic Marine and Coastal Technology (SAMCoT), Centre for Research-based Innovation (CRI),
Norwegian University of Science and Technology (NTNU), Trondheim, Norway
R.B. Nairn
W.F. Baird & Associates Coastal Engineers Ltd., Oakville, ON, Canada
ABSTRACT: Rapid coastal erosion threatens Arctic coastal infrastructure, including communities and
industrial installations. Erosion of permafrost depends on numerous processes, including thermal and
mechanical behaviour of frozen and unfrozen soil, nearshore hydrodynamics, atmospheric forcing, and
the presence of sea ice. The quantification and numerical modelling of these processes is essential to
predicting Arctic coastal erosion. This paper presents a case study of Baydaratskaya Bay, Russia, using
the COSMOS numerical model to predict thermal-mechanical erosion. In particular, this study focuses
on thermoabrasional rather than thermodenudational processes. A field dataset of onshore thermal and
mechanical soil characteristics was supplemented by sources from the literature to serve as input for the
model. A detailed sensitivity analysis has been conducted to determine the influence of key parameters
on coastal erosion rates at the study site. This case study highlights the need for expanded data collection
on Arctic coastlines and provides direction for future investigations.
Approximately two thirds of the Arctic coastline
is composed of unlithified material vulnerable to
erosion (Lantuit et al., 2013). The average rate of
erosion in the Arctic is approximately 0.5 m/year,
and 90% of the coastline experiences between 0–2 m
of erosion annually (Lantuit et al., 2012). Local
geology and climate also influence rates of coastline
change, making its prediction a complex task.
Arctic coastal dynamics have increasing relevance
in the 21st century. Climate change is expected to
decrease Arctic sea ice coverage, cause widespread
permafrost degradation, and increase coastal ero-
sion (Couture and Pollard, 2007, Barnhart et al.,
2014). The convergence of natural changes and
human development will threaten communities,
infra-structure, and industry in the Arctic, as well
as sites of cultural or historical significance.
Furthermore, the erosion of permafrost coast-
lines has also been linked to an increased flux
of organic carbon into the Arctic Ocean and
atmosphere (Lantuit et al., 2009). More accurate
predictions of coastal erosion rates could yield
better estimates of carbon flux for the purposes of
improving oceanographic and climate models.
This paper examines thermo-mechanical ero-
sion at Baydaratskaya Bay, Russia, using the
COSMOS numerical model. In particular, this
study focuses on thermoabrasional rather than
1 INTRODUCTION
1.1 Background
Climate change offers a daunting prospect for
Arctic coastlines in the 21st century. Longer open
ice seasons, warmer sea temperatures, increased
storminess and rising sea levels may compound
already rapid coastal erosion rates.
In order to understand existing coastal mor-
phodynamics in the Arctic and make predictions
of future change, numerical modelling techniques
may be employed. Application of existing tools
and techniques developed for use in temperate cli-
mates may be limited by the unique physical proc-
esses influencing high-latitude coasts. On Arctic
coasts, frozen sediment is subject to both thermal
and mechanical effects. The thawing of frozen sedi-
ment by sea-water and air makes it more vulnerable
to wave action and hastens its removal from shore.
Nairn et al. (1998) identify three key factors
which differentiate erosion of permafrost coast-
lines from those in temperate climates: (1) Melting
of exposed frozen sediment by seawater. (2) Eroded
material consisting of ice and fine sediment cannot
be reconstituted in the littoral zone and thus will
not contribute to the sediment balance. (3) Littoral
zone subsidence due to melting.
282
thermodenudational processes. A field dataset of
onshore thermal and mechanical soil characteris-
tics was collected for the site and supplemented by
sources from the literature to serve as input for the
model. A sensitivity analysis has been conducted
to determine the influence of key parameters on
coastal erosion rates at the study site. This case
study highlights the need for expanded data col-
lection on Arctic coastlines and offers direction for
future investigations.
1.2 Environmental forcing
Multiple processes drive the erosion of Arctic
coastlines, including sea ice, nearshore hydrody-
namics, sea level change, and atmospheric and
meteorological forcing. The many possible combi-
nations of different coastline geometries and cry-
olithology and paucity of observational data make
it extremely challenging to predict coastal erosion
in the Arctic.
1.2.1 Sea ice
Sea ice plays a complicated role in Arctic coastal
erosion processes. On one hand, sea ice covers the
sea surface for much of the year, preventing the
generation of wind waves and the resulting ero-
sion (Wegner et al., 2005). Sea ice typically forms
during the fall and remains until early summer. In
the ice-free season, the coastline becomes exposed
and is vulnerable to wave action. Hence, if recent
trends continue (Forbes, 2011) and the duration or
extent of open water is increased through climate
change, the coast remains unprotected for longer
and potential for erosion grows (Lantuit et al.,
2012; Overeem et al., 2011)).
Conversely, the presence of sea ice can also serve
as a mechanism of erosion and sediment transport
through processes like ice bulldozing or entrain-
ment by frazil ice (Are et al., 2008).
1.2.2 Nearshore hydrodynamics
Hydrodynamic processes act on several different
spatial and temporal scales, ranging from global
(sea level rise, oceanic circulation) to regional (tides,
storm surge) to local (waves, nearshore circulation).
Storm surge has a strong influence on coastal
erosion. By exposing a greater area of coastal
bluffs to wave attack and thermal degradation, it
greatly accelerates the thermoerosion process (Lan-
tuit et al., 2011; Overeem et al., 2011; Nairn et al.,
1998). Furthermore, water level setup against the
coastline can force strong offshore-directed cur-
rents that rapidly remove sediment from the near-
shore area (Leont’yev, 2003). Much of the coastal
permafrost erosion in the Arctic can be associated
with these large storm surge events (Lantuit et al.
2011; Nairn et al. 1998).
Wind waves in the Arctic Ocean are character-
ized by their seasonality, sea ice-limited fetch, and
the depth-limiting influence of the shallow seabed
found in many coastal regions. The largest storms
that influence coastal erosion tend to occur during
the fall when sea ice cover is still in the early stages
of growth (Overeem et al. 2011), since ice cover
inhibits wave generation during winter storms.
Leont’yev (2003) observes that the shallow, gently
sloping shelves offshore of many vulnerable Arc-
tic coasts have a dissipative influence on incoming
waves. Thus nearshore wave heights during extreme
events may be depth-limited, but higher water lev-
els due to storm surge could permit greater wave
energy to reach the coast.
1.2.3 Sea temperature & salinity
Sea temperature is a key controlling variable
for Arctic coastal erosion, since warm seawater
degrades submarine permafrost in quiescent peri-
ods and drives thermoabrasion in storms. Specifi-
cally, it is the difference in temperature between
seawater and melting point of the permafrost that
determines the rate of erosion (Nairn et al. 1998).
Lantuit et al (2012) find sea temperature to play a
more prominent role in governing erosion than air
temperature. Warm seawater enables thermoero-
sion to continue even during calm periods (Over-
duin et al., 2012).
Salinity plays a secondary role in Arctic coastal
erosion as it governs the freezing temperature of
seawater. Baird & Associates (1995) found that
typical seasonal variations in salinity did not have
a major impact on thermal erosion rates.
1.2.4 Sea level change
Sea level change is relevant to Arctic coastal ero-
sion in that rising water levels may increase vul-
nerability to coastal flooding, allow larger waves
close to shore, and increase accommodation space
for sediment. Global mean sea levels are projected
to continue rising over the next century (Church
et al., 2013), although the situation in the Arctic
is complicated by the area’s legacy of glaciation.
Isostatic uplift may in some cases lead to localized
sea level fall (Forbes, 2011). Conversely, relative sea
level rise may also result from subsidence of the
land. Wolfe et al (1998) found that thaw subsidence
(wherein massive ground ice formations melt and
cause lowering of the surface) was a major driver
of erosion in the community of Tuktoyaktuk,
Canada.
1.2.5 Atmospheric & meteorological
Atmospheric processes play a crucial role in the
behaviour of Arctic coastal environments, especially
in the response of permafrost to changes in thermal
forcing. Air temperature is relevant to permafrost
283
erosion in that convective heat transfer helps drive
the thermodenudation and permafrost degrada-
tion process. Solar radiation drives thermoerosion
through radiative heat transfer directly to the per-
mafrost, but also by warming the seawater.
Snow has an insulating effect on permafrost, pre-
venting freezing at greater depths but also delaying
thaw. Snow cover protects the shore in early spring
and summer, delaying the onset of thermodenu-
dation, but can thaw and erode frozen sediment
through nivation (Guégan & Christiansen, 2016).
Storms are typically weaker during the open ice
season than winter (Serreze et al., 1993), although
late summer storms like those observed in 2006
and 2012 (Simmonds & Drinkwater, 2007; Sim-
monds & Rudeva, 2012) have the potential to cause
significant erosion to Arctic coasts.
1.3 Geomorphology & cryology
1.3.1 Permafrost
The key factor differentiating Arctic coastal
dynamics from temperate locations is the pres-
ence of perennially frozen soil. The water normally
present in soil freezes, changing the structure and
properties of the soil with it.
Frozen soils are characterized by high strength
and low permeability, properties which signifi-
cantly influence their mechanical behaviour. Two
key processes occur as soil freezes: volume expan-
sion and segregation of ice lenses by cryosuction.
The changes to the physical properties of frozen soil
have implications for its strength and consequent
behaviour in terms of slope stability, settlement,
and erodibility. When frozen, the unconsolidated
sediments have much higher mechanical strength,
and must be thawed before they can erode (Are
et al. 2008). Conversely, permafrost degrades when
subject to warmer temperatures and solar radia-
tion. During the thawing process, soils become
more vulnerable to deformation and erosion. Fur-
thermore, frozen soil is relatively impermeable and
prevents drainage of melted water, thus increasing
excess porewater pressures and decreasing shear
strength of the soil (Yesuf et al., 2013).
Together, these Thermal, Hydraulic, and
Mechanical (THM) properties and processes drive
Arctic geomorphologic changes, including solif-
luction, thermokarst formation, frost heave, differ-
ential settlement, and slope instability (Nishimura
et al., 2009). Due to their influence on the strength
and composition of soil, the formation and deg-
radation of permafrost are essential processes in
determining the erosion of Arctic coastlines.
1.3.2 Ice & sediment composition
Sediment composition varies on Arctic coastlines
from coarser gravel and sand beaches to fine silt
and clay bluffs. The volume of coarse sediment in
a coastal profile determines beach erosion rates
(Kobayashi et al. 1999), since ice and fine mate-
rial cannot be reconstituted in their original form
and are effectively lost from the littoral sediment
budget. Only coarse sediment can form bars and
beaches to protect the shore. Hence, coastlines
with high ice content and fine content are corre-
lated with higher rates of erosion (Lantuit et al.,
2012; Are & Reimnitz, 2008). Variations in sedi-
ment and ice composition along the coastline will
subsequently lead to variations in erosion rates. In
general, ice content exerts a strong positive influ-
ence on erosion rates (Barnhart, Overeem, et al.,
2014; Kobayashi et al., 1999)
1.3.3 Submarine permafrost
The influence of permafrost also extends beyond
the land to the coastal seabed. Coastal erosion is
controlled by the shape, depth, slope, and sedi-
ment characteristics of the shoreface, so subma-
rine permafrost may also play a role in the unique
behaviour of Arctic coastlines. Nairn et al. (1998)
suggest that the main driver of thermoabrasional
erosion is underwater erosion of the shore profile
(seabed downcutting). Further compounding this
problem is thaw subsidence from melting sub-
merged permafrost (Are et al. 2008). Deepening of
the nearshore profile allows larger waves to reach
the bluff, increasing the potential for erosion. It is
thus important for Arctic coastal erosion studies to
characterize the properties of frozen soil not just
on land, but also in the nearshore zone.
1.4 Thermoerosional processes
In temperate climates, coastal erosion is linked to
the mechanical action of waves and currents, with
influence from mechanical, chemical, and biologi-
cal weathering. However in high latitudes, there is
also a thermal component to the erosion process.
The two main erosion processes for such coastlines
are called thermodenudation and thermoabrasion,
and are differentiated by the relative influence of
thermal and mechanical factors. While thermoden-
udation results from gradual thawing in quiet con-
ditions, thermoabrasion is driven by high-energy
storms.
1.4.1 Thermodenudation
A frozen bluff gradually thaws under the influence
of warmer air temperatures, solar radiation, and
snowmelt (Guégan & Christiansen, 2016), losing
its strength in the process. It gradually becomes
unstable and eventually fails, depositing scree at
the base of the slope. This thawed, unconsolidated
material is then available for removal by waves and
currents (Lantuit et al. 2011).
284
Thermodenudation is most common in coast-
lines with high ice and fine sediment content. It
tends to occur during calm conditions, which are
more typical in the early open water season when
there are fewer storms (Overeem et al. 2011). As
such, it is a thermally rather than mechanically-
dominated process, and the seawater has little to no
direct contact with permafrost (Lantuit et al. 2013;
Are et al. 2008). The failure debris can significantly
delay the direct wave attack of the bluff (Baird &
Associates 1995), and its removal is comparable to
erosion in temperate zones (Lantuit et al. 2013). As
such, it is possible that existing methods of pre-
dicting erosion can be used to model the removal
of the failed sediment.
1.4.2 Thermoabrasion
Whereas thermodenudation tends to dominate in
calm conditions, thawed sediment may be removed
faster than the frozen sediment can be melted
during storms. This exposes the frozen sediment
directly to the mechanical and thermal action
of seawater in a process known as thermoabra-
sion (Günther et al., 2012; Nairn et al., 1998; Are
et al., 2008). Without significant wave action, the
unfrozen sediment will insulate the frozen material
beneath, greatly limiting the severity of thermoa-
brasion (Kobayashi & Aktan, 1986; Kobayashi
et al., 1999).
With warmer, turbulent seawater in direct contact
with the frozen soil, it thaws quickly via convective
heat transfer, melting the interstitial ice matrix that
bonds sediment particles together (Wobus et al.,
2011; Lantuit et al., 2013; Overeem et al., 2011).
The temperature difference between the seawater
and sediment is a key factor in determining the rate
of cliff retreat (Kobayashi et al. 1999). Fine mate-
rial and melted ice are then moved offshore and
effectively removed from the littoral system (Nairn
et al. 1998; Kobayashi & Aktan 1986).
This rapid thawing and removal of sediment can
result in the formation of horizontal notches in the
frozen bluff face (Overeem et al. 2011). Eventu-
ally the mass of the overhanging bluff exceeds the
shear or bending strength of the soil, and the bluff
face collapses as a massive block (Hoque & Pollard
2009; Ravens et al. 2012; Wobus et al. 2011; Barn-
hart, Anderson, et al. 2014).
1.4.3 Relative influence of thermoerosion
Effective prediction of coastal retreat in the Arc-
tic will rely on a clear understanding of when
and where thermodenudation or thermoabrasion
dominates for a given site. Thermodenudation is
controlled by subaerial and underwater conductive
heat transfer through thawed sediment, whereas
thermoabrasion is governed by convective heat
transfer from warm, turbulent seawater directly to
exposed frozen sediment. Numerous factor may
influence the dominance of a given process, includ-
ing time of year, sea ice, snow, solar radiation and
air temperature, sea water temperature, waves, ice
content, and geology (Günther et al., 2012). Both
processes may act at the same site over different
time scales, with thermodenudation dominating
quiescent periods and thermoabrasion occurring
episodically during storms.
2 SITE DESCRIPTION
Baydaratskaya Bay is a shallow Russian gulf
located at the southwest margin of the Kara Sea
(Figure 1). The region is sparsely populated with
few roads or settlements, and the harsh climate
and re-mote location make access to the study site
challenging. The Nord-Stream gas pipeline was
constructed across Baydaratskaya Bay in 2011
(Ogorodov et al., 2013), making landfall along the
west coast, approximately 85 km southeast of Ust-
Kara (68°51’ N, 66°47’ E). The threat of coastal
erosion to the pipe-line landfall provides moti-
vation for understanding the processes at work
there.
Baydaratskaya Bay was formed as a glacial
depression during the Late Pleistocene and then
sub-merged in the Holocene (Levitan & Lavrushin,
2009). The coastal sediment largely consists of
consolidated silty clays with sand, gravel, and peat
lenses. Massive ground ice bodies up to 7 m thick
are also present along the coastline (Belova et al.,
1998). Seabed permafrost may extend to a depth of
at least 25 m (Osterkamp & Romanovsky, 1997).
The seabed slope is shallow, between 0.004–0.01 in
the nearshore (Kamalov et al., 2006; Bogorodskii
et al., 2010), and the maximum depth in the bay is
approximately 23 m (Ogorodov et al., 2013).
Figure 1. Map illustrating the location of the study site
on the western coast of Baydaratskaya Bay, Russia.
285
Sea ice typically forms on the bay in mid-late
October and reaches an annual maximum thickness
of 1.2 m at the west coast of the bay (Ogodorov
et al., 2013). The length of the ice-free season on
the West Kara Sea has extended by approximately
34 days be-tween 1979–2006 (Rodrigues, 2008).
Seabed gouging due to ice ridges and icebergs has
been observed even in the deepest portions of the
bay (23 m), and the nearshore zone is also subject
to mechanical action by landfast ice (Ogorodov
et al., 2013).
The oceanographic properties of Baydaratskaya
Bay are influenced by inflow through the Kara
Strait from the Barents Sea, which brings warmer,
saltier water into the bay. This inhibits thermoha-
line stratification and typically keeps the bay ice-
free until later in the autumn than other parts of
the Kara Sea (Harms & Karcher, 1999). Sea sur-
face temperatures reach their maximum in August
at approximately 6–7°C (Harms & Karcher, 1999).
The salinity of the bay depends mainly on inflow
from the Barents Sea, brine release due to ice for-
mation, and freshwater input from rivers or melting
ice. The bay typically has a salinity ranging from
20–25 ppt (Pivovarov et al., 2003). Baydaratskaya
Bay has a tidal range of 70 cm, leading to currents
in excess of 30 cm/s (Harms & Karcher, 1999).
The annual mean air temperature at Marre Sale
(located on the eastern side of Baydaratskaya Bay)
from 1961–1990 was −8.3°C, with mean January
and July air temperatures of −22.4°C and 7.1°C,
respectively (Goryainov & Kryjov, 2000). Annual
precipitation ranges from 300–500 mm/year, and
thick snowbanks typically accumulate at the toe
of coastal bluffs (Aleksyutina et al., 2013). Winds
during the ice-free season (June to September)
are typically weak, but strengthen in October to
December (Harms & Karcher, 1999), giving the
strongest potential for erosive wave and surge
conditions.
Leont’yev (2003) suggests that storm surges can
reach up to 2 m and that the average annual maxi-
mum root-mean-square wave height (Hrms) is 1.3–
1.8 m, with peak periods (Tp) between 5–6 seconds.
No long or short-term wave statistics are available
for the site.
Historical rates of recession at the site vary from
0.5–1.5 m/year (Leont’yev & Rachold, 2005), and
up to 5–10 m/year for locations with significant
ground ice deposits (Ogorodov et al., 2013). Both
thermodenudation and thermoabrasion processes
act on the site to varying degrees.
3 METHODOLOGY
In order to predict future erosion rates at the study
site, we applied a coastal profile model using meas-
ured geotechnical data and sources in the litera-
ture. Due to limited availability of metocean and
nearshore data, a sensitivity analysis approach was
chosen to characterize the dominant processes at
the site and inform future investigations.
3.1 Modelling approach
Numerical models are instrumental in understand-
ing the physical processes involved in Arctic coastal
erosion and can be used to quantify and predict
its effects. Most coastal engineering models devel-
oped for temperate climates are insufficient for
predicting Arctic coastal erosion since they do not
account for the thermal processes involved. How-
ever, they may still be useful as inputs for dedicated
thermoerosion models by simulating processes like
sediment transport, hydrodynamics, or ice cover-
age at larger scales.
Several studies have developed detailed models
of thermomechanical block erosion using observa-
tions from the Alaskan coast (Barnhart, Ander-
son, et al., 2014; Hoque & Pollard, 2009; Ravens
et al., 2012). Leont’yev (2003; 2004) developed a
morphodynamic profile model for decadal predic-
tions of erosion at several sites in the Russian Arc-
tic. However, the model did not directly account
for thermal processes, assuming the net shoreline
change to be controlled more by mechanical action
of waves.
To describe the complex interactions of soil, ice,
and unfrozen water, a Thermo-Hydro-Mechani-
cal (THM) model can be used (Nishimura et al.,
2009; Thomas et al., 2009). These models consider
elasto-plastic mechanical behaviour of frozen and
unfrozen soil and processes like cryosuction, two-
sided freezing, and the formation of ice lenses. This
enables the thaw-related mass wasting processes in
thermodenudation to be simulated.
3.2 COSMOS model
This study relies on the coastal profile model COS-
MOS for the prediction of thermoabrasion. It was
developed as a deterministic process-based hydro-
dynamic and sediment transport model by Nairn
& Southgate (1993a; 1993b). The hydrodynamic
component models waves, currents for 1D profiles
on alongshore uniform coastlines.
The sediment transport module represents both
alongshore and cross-shore transport processes.
COSMOS uses an adapted Energetics approach
to wave-induced sediment transport and the van
Rijn approach to tidal current transport. It has
been developed to model the erosion of cohesive
bluffs, and was validated using laboratory experi-
ments and data from the field (Nairn & Southgate,
1993). COSMOS describes downcutting of cohe-
286
sive shorelines due to bed shear stress from wave
orbital velocity, and energy dissipation due to wave
breaking.
In addition to hydrodynamic and sediment
transport processes, COSMOS is also capable of
simulating thermo-mechanical erosion of frozen
soils. This module was developed for use in the
Canadian Arctic (Nairn et al. 1998; Baird & Asso-
ciates 1995) using the method of Kobayashi &
Aktan (1986) for thermoabrasion. A full descrip-
tion of the thermo-mechanical module can be
found in (Nairn et al. 1998; Kobayashi et al. 1999;
Baird & Associates 1995).
COSMOS treats the soil as existing in two discrete
states: frozen and unfrozen. The fraction of coarse
sediment can be specified, which is important for
determining the amount of material that remains
in the littoral zone and the amount that is lost off-
shore (fine sediment and melted ice). The depth to
the frozen layer (corresponding to the thickness of
the active layer) is provided as input for the model,
and it is thawed by conduction through unfrozen
soil or directly through convective heat transfer by
warm, turbulent seawater (thermoabrasion).
The thermal erosion module of COSMOS was
developed and tested on sites on the Canadian
Beaufort Sea coast (Kobayashi et al. 1999; Nairn
et al. 1998; Baird & Associates 1995). The model
was able to successfully predict erosion of Arctic
coastal bluffs and a barrier spit due to storm events
(Nairn et al. 1998).
3.3 Sensitivity analysis
A field measurement campaign reported in Ale-
ksyutina et al (2013) focused mainly on ther-
modenudation processes, characterizing the
middle and upper portions of the bluff in Bay-
daratskaya. Boreholes yielded information on the
grain size characteristics and stratigraphy of the
bluffs, and in-situ thermistors were used to meas-
ure changes in soil temperature as a function of
depth and time. However, to model thermoabra-
sion, metocean conditions, subsea permafrost and
sediment characteristics, and nearshore bathym-
etry are all required. Furthermore, thermoabra-
sion is episodic, so immediate pre- and post-storm
surveys are essential to discerning the impact of a
particular event from other more gradual processes
like thermodenudation. In the absence of meas-
ured data for these input parameters, a sensitivity
analysis was undertaken to explore the applicabil-
ity of COSMOS to the study site.
An idealized one-dimensional coastal profile
was used as the basis for modelling (Figure 2). 239
different scenarios were simulated in COSMOS,
each altering a single parameter from a base case.
With the exception of wave height and period,
interactions between input variables are not con-
sidered. The combined influence of wave height
and period was examined by expressing the two
variables in terms of the Iribarren number (ξ = tan
α⁄(H0⁄L0)1/2), where tan α is the seabed slope, H0
is the offshore wave height, and L0 = gT2/2π is the
deep water wavelength. ξ is less than 0.5 for all
tested cases, placing the site firmly in a dissipative
regime with spilling breakers.
The parameter space was defined using typical
site characteristics from the field investigations
reported in (Aleksyutina et al., 2013) and the afore-
mentioned sources in the literature (Table 1).
There were no tidal currents or variations in
water level over the simulation period. A range of
water levels (∆η) from −0.50–3.00 m were consid-
ered, allowing for the combined effects of tides and
storm surge. Normally incident waves were selected
in the absence of measured directional wave data
for the site. COSMOS is a spectrally averaged
model with significant wave height and peak wave
period specified. Significant wave heights from 0.5
to 3.0 m were simulated in combination with peri-
ods from 5 to 12 s. Wave conditions were assumed
to be constant for the duration of the 24 hour sim-
ulation period.
The model domain extends 2000 m offshore to
a depth of 12 m, with grid spacing varying from
100 m at the offshore boundary up to 0.25 m in
the nearshore and at the bluff. In the absence of
nearshore bathymetric data, idealized profiles of
constant seabed and bluff slopes were developed
based on typical gradients for the region. Bluff
height was varied to represent the range of heights
observed in the study area.
The depth to frozen soil (active depth) was based
on thermistor temperature profiles measured in
boreholes along top of the bluff (Aleksyutina
et al., 2013). Active depth varies seasonally from a
maximum of 1.3 m in late summer to a minimum
of 0 m in winter. Since no measurements of sub-
Figure 2. Schematic of COSMOS model setup for sen-
sitivity analysis.
287
sea permafrost were available, active depth was
assumed to be constant across the profile.
Grain size characteristics were also obtained
from these boreholes. The sediment profiles indi-
cate predominantly fine materials interspersed
by layers of sand (80–90% fines). In COSMOS,
the fraction of coarse material is specified to
distinguish beach-forming sediment from fine
sediment and ground ice that will be lost from
the littoral system. A d50 of 100 µm was used to
represent coarse sediment material, and held con-
stant across the profile in the absence of measured
grain sizes for the beach or nearshore. Due to the
strong cohesion of sediment in the bluff, the proc-
ess of avalanching beyond a critical slope angle
was disabled.
The model is not able to simulate the long-term
subaerial thawing and slope failures central to the
thermodenudation process, and the direct morpho-
logical effects of sea ice were considered beyond
the scope of the present study. Unknown model
parameters and constants were defined based on
calibrated values for similar thermoabrasive sites in
the Canadian Arctic (Baird & Associates, 1995).
4 RESULTS
4.1 Base case
As an example, pre- and post-storm profiles for the
base case are provided in (Figure 3). COSMOS has
a 1D horizontal computational grid, and as such
cannot directly represent the lateral undercutting
process of notch formation. Nonetheless, a vertical
scour hole forms, which may be used as a proxy for
notch depth, given the equivalent energy dissipa-
tion at the toe of the bluff. (Baird & Associates,
1995). Thus scour hole depth (∆znotch) and lateral
retreat of the bluff (∆xtoe) are used as an indication
of the degree of thermoabrasion.
Notch depth (2.99 m) is given as the maximum
cumulative lowering of the frozen subsoil surface
across the profile, and toe retreat (4.8 m) indicates
the lateral migration of the bluff toe at 0 m eleva-
tion. A series of small bars form seaward of the
scour hole, and the seabed lowers by an average
of 0.04 m between 50–500 m offshore due to wave
energy dissipation by breaking.
4.2 Sensitivity analysis
To quantify model sensitivity, notch depth and
toe retreat were compared (Table 2). The relative
change from the base case across the tested param-
eter space, i.e. (∆xtoe (max/min) – ∆xtoe (base case))/∆xtoe (base case)
is used as an indication of model sensitivity, and
the linear correlation (R) is given.
The largest notch depth comes from higher
water levels, larger waves, and reduced coarse
fractions, which suggests that storm surge condi-
tions affecting ice-rich, fine sediment bluffs could
cause the most significant erosion rates. The larg-
Table 1. Parameter space for model sensitivity analysis
based on typical characteristics of Western Baydarat-
skaya Bay coastline.
Parameter Units
Lower
Bound
Base
Case
Upper
Bound
hbluff m 6.0 12.0 20.0
βbluff – 0.20 0.50 1.00
βseabed – 0.001 0.006 0.015
fvc – 0.00 0.10 0.60
D50 µm70 100 2000
dactive m 0.00 0.75 1.50
S ppt 0 35 35
T °C 0 5 10
∆η m –0.50 1.00 3.00
Hsm 0.50 1.50 3.00
Tps 5 6 12
Where hbluff = bluff height; βbluff = bluff slope; βseabed = sea-
bed slope; fvc = fraction of coarse sediment; D50 = median
grain size; dactive = active layer thickness; S = sea salinity;
T = sea temperature; ∆η = water level above the bluff toe;
Hs = significant wave height; and Tp = peak wave period.
Figure 3. COSMOS post-storm profile for base case of
sensitivity analysis.
288
est toe retreat comes from higher water levels,
gentler bluff slopes, higher bluffs, and steeper
seabed slopes. Whether due to storm surge, high
tide, steep seabed slopes, or profile downcutting,
deeper water at the bluff toe enables larger waves
to reach the bluff, increasing the modelled erosion
rates.
No retreat was observed for smaller waves, lower
water levels, and largest grain sizes. There is very
little retreat at low water levels because the major-
ity of wave energy is dissipated on the foreshore
and beach rather than on the bluff. As the frac-
tion of coarse sediment and grain size increase, a
larger beach builds out in front of the bluff, pro-
tecting it from further wave action. Steeper bluff
slopes decrease the rate of toe retreat but increase
the notching depth, likely as a result of wave
reflection.
Salinity and temperature exert a negligible influ-
ence on toe retreat rates. There is a minor increase
in notch depth with temperature, although salinity
has limited influence. Hence, coastal erosion may
be less sensitive to seasonal fluctuations in salinity
associated with the spring freshet.
Nearshore profile downcutting increases sig-
nificantly for scenarios with thin active layers,
suggesting that the characterization of subsea
permafrost may be important. The presence of a
thawed layer of sediment acts as an effective buffer
against rapid thermoabrasion processes. Seasonal
variations in active depth and storm conditions
may offset each other, since thawing is deeper in
the late summer and early fall when stronger forc-
ing occurs.
Notch depth tends to increase for decreases in
ξ, suggesting that more dissipative conditions may
lead to greater thermoabrasion.
5 DISCUSSION
This case should thus be viewed as a proof-of-
concept study, which demonstrates the use of
COSMOS as a thermoabrasional model in a data-
poor environment. It highlights the data needs for
meaningful predictions of Arctic coastal erosion,
and gives direction for future investigations.
The model suggests that thermoabrasion is
most sensitive to water level, which underscores
the threat posed by relative sea level rise. This cor-
roborates with findings in the literature that link
accelerated erosion to high storm surges (Koba-
yashi et al., 1999; Leont’yev, 2003; Barnhart, Over-
eem, et al., 2014). The more sensitive variables (i.e.
water level, wave characteristics, and profile geom-
etry) should be the highest priority for future data
collection efforts.
In particular, annual profile surveys extending out
to the lower shoreface will provide a valuable dataset
for understanding long-term Arctic coastal dynam-
ics. This field work could be supplemented by labora-
tory experiments to calibrate and validate numerical
models of permafrost erosion, similar to Skafel &
Bishop’s work on cohesive sediment (1994).
Given the limited availability of Arctic coastal
erosion data and challenges associated with data
collection in cold climates, innovative measure-
ment techniques could be used. For instance,
seismic monitoring of cliff motion, time-lapse
cameras, drone-based photography and LiDAR,
portable free-fall penetrometers, and geoelectric
measurements have all been used successfully to
obtain relevant coastal datasets. Combinations of
the above sources can be used with conventional
measurements to paint a more complete picture
upon which to base our understanding of Arctic
coastal dynamics.
Without observations of the hydrodynam-
ics and timing of erosion events, it is difficult to
accurately model erosion of frozen coastlines.
Over what timescale do observed erosion rates
occur? Separating the relative influence of episodic
storms (thermoabrasion) and gradual deteriora-
tion (thermodenudation) is key to understanding
the specific mechanisms of each process. Hence, to
satisfactorily predict erosion of Arctic coastlines,
modelling techniques must be able to account for
the full range of processes involved over multiple
spatial and temporal scales.
Existing hydrodynamic and thermo-hydro-me-
chanical models could also be coupled to capture
full range of thermoerosion processes (thermoa-
brasion and thermodenudation). Furthermore,
probabilistic approaches such as Monte Carlo
simulation or Bayesian network modelling could
be used to account for the uncertainty in the avail-
able and missing data.
Table 2. Model sensitivity to changes in each
parameter.
Toe Retreat (∆xtoe) Notch Depth (∆znotch)
−%+%R−%+%R
hbluff −27.1 25.0 0.937 −18.3 22.4 0.441
βbluff −47.9 87.5 −0.858 −99.5 27.5 0.716
βseabed −27.1 20.8 0.913 −13.1 24.3 0.926
fvc −100.0 0.0 −0.689 −57.5 0.0 −0.971
D50 −100.0 0.0 −0.654 −99.6 25.8 −0.642
dactive 0.0 0.0 0.000 −25.6 12.1 −0.686
S 0.0 0.0 0.000 −5.9 8.2 0.039
T 0.0 0.0 0.000 −16.8 14.6 0.901
∆η −100.0 145.8 0.985 −99.6 153.5 0.975
Hs−100.0 14.6 0.637 −99.4 46.9 0.882
Tp−1.000 0.146 −0.052 −0.994 0.469 −0.279
ξ −1.000 0.146 −0.628 −0.994 0.469 −0.833
289
Dissipative beaches like this study site are
dominated by infragravity energy (Wright et al.,
1982). Infragravity waves (characterized by peri-
ods in the range of 30–300 s) have been little
studied in the context of Arctic coastal erosion.
However, it may be possible to hypothesize their
role by drawing analogy to their behaviour in
temperate seas. Infragravity waves form by way
of nonlinear interactions between higher-fre-
quency waves, and may become freed or trapped
in the nearshore. These long waves are greatest
in height at the shoreline and can amplify short
wave height by effectively increasing local water
depth (Beetham & Kench, 2011). Higher levels of
wave energy can thus reach the shore and lead to
greater erosion.
Infragravity waves play a crucial role in dune
erosion, driving swash processes and inducing
dune face avalanching (Roelvink et al., 2009). The
onshore mass flux is countered by an offshore-
directed flow or rip current that results in rapid
offshore sediment transport. On cliffed coast-
lines, infragravity waves may result in long period
water level fluctuations at the cliff face, increased
depth for short waves crossing the platform, and
strong return flows transporting sediment away
from the cliff toe (Beetham & Kench, 2011). Ear-
lie et al (2015) found that the largest contribution
to clifftop motion during storm conditions is from
energy at infragravity frequencies, and linked the
timing of energetic cliff motion to collapse. Thus,
these combined mechanisms may contribute to
bluff erosion.
Sea and swell waves are typically blocked by the
presence of sea ice. However, Wadhams & Doble
(2009) find that long waves (>20–30 s) may sur-
vive up to 1000 km of ice cover without signifi-
cant attenuation. As a result, the wave energy at
ice-sheltered Arctic sites may be effectively filtered
to include only low-frequency components (Squire
et al., 2009).
Field measurements of nearshore wave energy
and clifftop motion should be carried out to deter-
mine whether these mechanisms are relevant to
erosion of frozen sediment bluffs in the Arctic.
6 CONCLUSIONS
Arctic coastal dynamics are becoming more rel-
evant as climate change progresses and human
development in the north increases. To better
understand the influence of changes in environ-
mental forcing and geomorphology on coastal
erosion rates at Baydaratskaya Bay, a sensitiv-
ity analysis was carried out using the COSMOS
numerical model.
Key findings of this study include:
− Thermoabrasional notch erosion increases with
higher water levels, larger waves, and high ice/
fine sediment content
− Rapid toe retreat rates result from higher water
levels, gentler bluff slopes, higher bluffs, and
steeper seabed slopes.
− Larger sediment sizes and thicker active layers
have a retarding effect on erosion, protecting the
frozen sediment from thermoabrasion.
− Seawater temperature and salinity have a negli-
gible influence on erosion rates when compared
to the other parameters.
This study is limited by the availability of
metocean and nearshore data. Without wave and
water level conditions, pre- and post-storm sur-
veys, or subsea permafrost and sediment charac-
teristics, it was not possible to calibrate the model.
Long-term, high resolution datasets on both the
land and water sides of the coastline are necessary.
Experimental laboratory data from physical mod-
elling and other tests could be used to calibrate and
validate numerical models of the thermal erosion
process. These data gaps are the biggest roadblock
to research and must be addressed prior to the fur-
ther development of models.
COSMOS does not account for the gradual sub-
aerial thawing and slope failure processes associ-
ated with thermodenudation, nor does it consider
the morphological influence of sea ice in the near-
shore. Nevertheless, the model’s potential for use
in determining relative rates of erosion for a given
coastline is valuable, and may be best utilized when
supplemented with additional field data.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the support
from the Research Council of Norway through the
Centre for Research-based Innovation SAMCoT
and the support from all SAMCoT partners. The
authors are also grateful to Baird & Associates for
making the COSMOS model available and pro-
viding support. We would like to thank Moscow
State University (MSU) for making their field data
available to us for this project. S.G.P. acknowledges
funding provided by the European Commission
Erasmus Mundus Program.
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