The Earth is currently 180 Myr into a supercontinent
cycle that began with the break-up of Pangaea and which will end around 200–250 Myr (million years) in the future, as the next supercontinent forms. As
the continents move around the planet they change the geometry of ocean
basins, and thereby modify their resonant properties. In doing so, oceans
move through tidal resonance, causing the global tides to be profoundly
affected. Here, we use a dedicated and established global tidal model to
simulate the evolution of tides during four future supercontinent scenarios.
We show that the number of tidal resonances on Earth varies between one and five in
a supercontinent cycle and that they last for no longer than 20 Myr. They
occur in opening basins after about 140–180 Myr, an age equivalent to the
present-day Atlantic Ocean, which is near resonance for the dominating
semi-diurnal tide. They also occur when an ocean basin is closing,
highlighting that within its lifetime, a large ocean basin – its history
described by the Wilson cycle – may go through two resonances: one when
opening and one when closing. The results further support the existence of a
super-tidal cycle associated with the supercontinent cycle and gives a
deep-time proxy for global tidal energetics.
Introduction
The continents have coalesced into supercontinents and then dispersed
several times in Earth's history in a process known as the supercontinent
cycle (Nance et al., 1988). While the cycle has an irregular period
(Bradley, 2011), the break-up and reformation typically occurs over 500–600 Myr (Nance et al., 2013; Davies et al., 2018; Yoshida and Santosh, 2017,
2018). Pangaea was the latest supercontinent to exist on Earth, forming
∼300 Ma ago, and breaking up around 180 Ma ago, thus
initiating the current supercontinent cycle (Scotese, 1991; Golonka, 2007).
Another supercontinent should therefore form within the next 200–300 Myr
(e.g. Scotese, 2003; Yoshida, 2016; Yoshida and Santosh, 2011, 2017;
Duarte et al., 2018; Davies et al., 2018).
The supercontinent cycle is believed to be an effect of plate tectonics and
mantle convection (Torsvik, 2010, 2016; Pastor-Galan, 2018), and the
break-up and accretion of supercontinents are a consequence of the opening
and closing of ocean basins (Wilson, 1966; Conrad and Lithgow-Bertelloni,
2002). The life cycle of each ocean basin is known as the Wilson cycle. A
supercontinent cycle may be comprised of more than one Wilson cycle, as several
oceans may open and close between the break-up and reformation of a
supercontinent (e.g. Hatton, 1997; Murphy and Nance, 2003; Burke, 2011;
Duarte et al., 2018; Davies et al., 2018). As ocean basins evolve during the
progression of the Wilson cycle (and associated supercontinent cycle), the
energetics of the tides within the basins also change (Kagan, 1997; Green et
al., 2017). Green et al. (2017, 2018) simulated the evolution of tides from
the break-up of Pangaea until the formation of a future supercontinent, thus
spanning a whole supercontinent cycle, and found a link between Wilson
cycles and tides. They also found that the unusually large present-day tides
in the Atlantic, generated because of the near-resonant state of the basin
(Platzman, 1975; Egbert et al., 2004; Green, 2010; Arbic and Garrett, 2010),
have only been present for the past 1 Myr. However, because the Atlantic is
still spreading apart, it will eventually become too wide to sustain
resonant tides in the near (geological) future. However, when exactly will this
happen, and is it possible that while the continents diverge and converge,
other basins will reach the right size to become resonant?
The initial simulation of deep-time future tides by Green et al. (2018) used
a scenario of the Earth's tectonic future presented by Duarte et al. (2018)
and strengthened the proof-of-concept for the existence of a super-tidal
cycle associated with the supercontinent cycle. Their simulations were done
using 50–100 Myr intervals between simulations. They acknowledged that this
was not long enough to resolve details of the future tidal maxima, including
their duration. In this work, we therefore revisit the future evolution of
Earth's tides by simulating the tide at 20 Myr intervals during the four
different tectonic modes of supercontinent formation summarized by Davies et al. (2018): Pangaea Ultima (based on Scotese, 2003), Novopangaea (Nield,
2007), Aurica (Duarte et al., 2018), and Amasia (based on Mitchell et al.,
2012). Pangaea Ultima is a scenario governed by the closing of the Atlantic
– an interior ocean – leading to the reformation of a distorted Pangaea
(Murphy and Nance 2003, 2008, call this “closure through introversion”).
Novopangaea, in contrast, is dominated by the closing of the Pacific Ocean –
an exterior ocean – and the formation of a new supercontinent at the
antipodes of Pangaea (this is closure through extroversion; Murphy and Nance,
2003). Aurica is a scenario in which the Atlantic and the Pacific close
simultaneously and a new ocean opens across Siberia, Mongolia, and India,
bisecting Asia (a combination scenario in which two oceans close, one by
introversion and another by extroversion; Murphy and Nance, 2005; Duarte et
al., 2018). Finally, in the Amasia scenario, the continents gather at the
North Pole, 90∘ from Pangaea (this is known as orthoversion;
Mitchell et al., 2012). Every scenario has the potential to develop
different tidal resonances in different ocean basins at different stages in
each ocean's evolution. We focus here on identifying the timing of the
occurrence of resonant basins, and on mapping the large-scale evolution of
tidal amplitudes and tidal energy dissipation rates in each of the
investigated scenarios. We were particularly interested in understanding how
common the resonant super-tidal states are, for how long they last, and
their relationship with the Wilson cycle.
MethodsTidal modelling
The future tide was simulated using the Oregon State University Tidal
Inversion Software, OTIS, which has been extensively used to simulate
global-scale tides of the past, present, and future (Egbert et al., 2004;
Green, 2010; Green and Huber, 2013; Wilmes and Green, 2014; Green et al.,
2017, 2018). OTIS was benchmarked against other software that simulate
global tides and was shown to perform well (Stammer et al., 2014). It
provides a solution to the linearized shallow water equations (Egbert et
al., 2004):
1∂U∂t+f×U=gh∇η-ηSAL-ηEQ-F,2∂η∂t-∇⋅U=0.
Here, U is the tidal volume transport vector defined as
uh, where u is the horizontal velocity vector and h the
water depth, f is the Coriolis parameter, g the acceleration due to gravity,
η the sea surface elevation, ηSAL the self-attraction and
loading elevation, ηEQ the elevation of the equilibrium
tide, and F the energy dissipation term. The latter is defined as
F=Fb+Fw, where Fb=Cdu|u| parameterizes energy due to bed
friction using a drag coefficient, Cd =0.003, and Fw=CU represents losses due to tidal conversion. The conversion
coefficient, C, is based on Zaron and Egbert (2006) and modified by Green
and Huber (2013), computed from
Cx,y=γNHN‾8πω(∇H)2.
In Eq. (3) γ=50 is a dimensionless scaling factor accounting for
unresolved bathymetric roughness, NH is the buoyancy frequency (N) at
seabed, N‾ is the vertically averaged buoyancy frequency, and ω is the frequency of the M2 tidal constituent, the only constituent
analysed here. The buoyancy frequency, N, is based on a statistical fit to
present-day climatology (Zaron and Egbert, 2006) and given by N(x,y)=0.00524exp(-z/1300), where z is the vertical coordinate counted positively
upwards from the sea floor. We did not change N throughout the simulations
because the stratification in the future oceans is yet to be quantified.
Each run simulated 14 d, of which 5 d were used for harmonic analysis
of the tide. The model output consists of amplitudes and phases of the sea
surface elevations and transports, which was used to compute tidal
dissipation rates, D, as the difference between the time average of the work
done by the tide generating force (W) and the divergence of the horizontal
energy flux (P; see Egbert and Ray, 2001, for details):
D=W-∇⋅P,
where W and P are given by
W=gρU⋅∇(ηEQ+ηSAL),P=gρUη.
The orbital configuration of the Earth–Moon system, and thereby the tidal
and lunar forcing was not changed during the future simulation. The
difference in tidal period (+0.11 h) and lunar forcing (-3 %) that
occurs after 250 Myr was applied to a sensitivity simulation, which found
that the altered parameters do not affect the results sufficiently to
warrant changing the values from present day.
Mapping of future tectonic scenarios
We coupled the kinematic tectonic maps produced by Davies et al. (2018) with
OTIS at incremental steps of 20 Myr by using the tectonic maps as boundary
conditions in the tidal model. The maps were produced using GPlates, a
software specifically designed for the visualization and manipulation of
tectonic plates and continents (e.g. Qin et al., 2012; Müller et al.,
2018). We used GPlates to digitize and animate a high-resolution
representation of present-day continental shelves and coastline (with no ice
cover), created from the NOAA ETOPO1 global relief model of the Earth (see Amante and Eakins, 2009 for details). For
simplification purposes, shelf extents are kept for the full duration of the
scenarios. The continental polygons do not deform, though some overlap is
allowed between their margins, to simulate rudimentary continental collision
and shortening. Intracontinental break-up and rifting were introduced in
three of the scenarios, allowing new ocean basins to form. No continental
shelves were extrapolated along the coastlines of these newly formed basins'
margins. For more details about the construction of the tectonic scenarios and
the respective maps, see Davies et al. (2018).
The resulting maps were then given an artificial land mask 2∘ wide
on both poles to allow for numerical convergence (simulations with
equilibrium tides near the poles in Green et al., 2017, 2018, did not change
the results there), and were constrained to a horizontal resolution of
0.25∘ in both latitude and longitude. They were
then assigned a simplified bathymetry; continental shelves were set a depth
of 150 m, and mid-ocean ridges were assigned a depth of 1600 m at the crest
point and deepening to the abyssal plains within a width of 5∘.
Subduction trenches were made 5800 m deep. The depth of the abyssal plains
in the maps changes dynamically to retain present-day ocean volume
throughout the scenarios. This allows the tidal results of future
simulations to be comparable to a present-day simulation, which was tested
against real-world tidal observations.
To test the accuracy of our results, we produced and used two present-day
bathymetries. The first – a present-day control – is based on version 13 of the
Smith and Sandwell bathymetry (Smith and Sandwell, 1997;
https://topex.ucsd.edu/marine_topo/, last access: 3 June 2019). A second map was then
produced – the present-day degenerate bathymetry – which included a
bathymetry created by using the depth values and the method described for
the future slices (see Fig. 1 and the corresponding description in Sect. 2.2).
(a) The PD bathymetry in m.
Panel (b) is the same as (a) but for the degenerate PD bathymetry (see text for details).
(c–d) The simulated M2 amplitudes (in m) for the control PD (c) and
degenerate PD (d) bathymetries. Note that the colour scale saturates at 2 m. Panels (e–f) are the same as (c)–(d) but show M2 dissipation rates in Wm-2.
Results
The tidal amplitude results for the present-day control simulation (Fig. 1c), when compared to the TPX09 satellite altimetry constrained tidal
solution (Egbert and Erofeeva, 2002; https://www.tpxo.net/global/tpxo9-atlas, last access: 28 May 2019), produced an rms error
of ±12 cm. Comparing the present-day degenerate simulation (Fig. 1d)
results to TPXO9 resulted in an rms error of 13 cm. This is consistent with
previous work (Green et al., 2017, 2018) and gives us a quantifiable error
of the model's performance when there is a lack of topographic detail (e.g.
as in our future simulations).
The present-day control simulation (Fig. 1e) has a dissipation rate of 3.3 TW with 0.6 TW dissipating in the deep ocean. This corresponds to 137 %
of the observed (real) global dissipation rate (2.4 TW for M2; see Egbert et
al., 2004) and 92 % of the measured deep ocean rates (0.7 TW). The
present-day degenerate bathymetry underestimates the globally integrated
dissipation by a factor of 0.9, and the deep ocean rates by a factor of
∼0.8 (Fig. 1f). Sensitivity tests for the present-day control
simulation with varying bed friction and buoyancy frequency did not produce
any significant difference in the result. The future tidal dissipation
results (Fig. 3) were therefore normalized against the degenerate
present-day value (2.2 TW) to account for the bias due to under-represented
bathymetry caused when using the simplified bathymetry in the future
simulations (see Green et al., 2017, for a discussion).
Global M2 amplitudes for six representative time slices of
the Pangaea Ultima scenario. The colour scale saturates at 2 m. For the full
set of time slices covering every 20 Myr, see the Supplement. Additionally,
note that the figures presented for each scenario display different time
slices to highlight periods with interesting tidal signals and that the
centre longitude varies between panels to ensure the supercontinent forms in
the middle of each figure (where possible).
Normalized (against PD degenerate) globally integrated dissipation
rates for the Pangaea Ultima (a), Novopangaea (b), Aurica (c), and Amasia (d)
scenarios. The lines refer to total (solid line), deep (dashed line), and
shelf (dotted–dashed line) integrated dissipation values. Each super-tidal peak
is marked where it reaches its peak. Pac stands for Pacific and Atl stands for Atlantic.
The resulting tidal amplitudes and associated integrated dissipation rates
are shown in Figs. 2, 4–6 (amplitudes), and 3 (dissipation). The latter
is split into the global total rate and rates in shallow (depths of
< 500 m) and deep water (depths of > 500 m; Egbert and
Ray, 2001) to highlight the mechanisms behind the energy loss. In the
following we define a super-tide as occurring when (i) tidal amplitudes in a
basin are on average meso-tidal or above, i.e. larger than 2 m, and (ii) the
globally integrated dissipation is equivalent to or larger than present-day
values.
Pangaea Ultima
In the Pangaea Ultima scenario, the Atlantic Ocean continues to open for
another 100 Myr, after which it starts closing, leading to the formation of
a slightly distorted new Pangaea in 250 Ma (Fig. 2 and Davies, 2019a). The continued opening of the Atlantic in the first
60 Myr moves the basin out of resonance, causing the M2 tidal amplitude
and dissipation to gradually decrease (Figs. 2 and 3a). During this period,
the total global dissipation drops to below 30 % of the PD (present-day)
rate (note that this is equivalent to 2.2 TW, as we compare it to the
degenerate bathymetry simulation), after which, at 80 Ma, it increases
rapidly to 120 % of PD (Figs. 3a and 2b). This peak at 80 Ma is due to a
resonance in the Pacific Ocean initiated by the shrinking width of the basin
(Fig. 2b). The dissipation then drops again until it recovers and peaks
around 120 Ma at 130 % above PD (Fig. 3a). This second peak is caused by
another resonance in the Pacific, combined with a local resonance in the
northwestern Atlantic (Fig. 2c). This period also marks the initiation of
closure of the trans-Antarctic ocean, a short-lived ocean, which began
opening at 40 Ma and was micro-tidal for its entire tenure (Fig. 2a–c). A
third peak then occurs at 160 Ma, the most energetic period of the
simulation, with the tides being 215 % more energetic than at present due
to both the Atlantic and the Pacific being resonant for M2 frequencies (Fig. 2d). After this large-scale double resonance, the
first described in detail in deep-time simulations and the most energetic
relative dissipation rate encountered, the tidal energy drops, with a small
recovery occurring at 220 Ma due to a further minor Pacific resonance (Fig. 2e). When Pangaea Ultima forms at 250 Ma (see Fig. 2f), the global energy
dissipation has decreased to 25 % of the PD value or 0.5 TW (Fig. 2f).
Novopangaea
In the Novopangaea scenario, the Atlantic Ocean continues to open for the
remainder of the supercontinent cycle. Consequently, the Pacific closes,
leading to the formation of a new supercontinent at the antipodes of Pangaea
in 200 Ma (Fig. 4 and Davies, 2019b). As a result,
within the next 20 Myr the global M2 dissipation rates decrease to half
of present-day values (see Figs. 3b and 4). The
energy then recovers to PD levels at 40 Ma as a result of the Pacific Ocean
becoming resonant. From 40 to 100 Myr, the dissipation rates drop,
reaching 15 % of the PD value at 100 Ma. There is a subsequent recovery
to values close to 50 % of PD, with a tidal maximum at 160 Ma due to
local resonance in the newly formed East African Ocean (Davies et al.,
2018). Even though the tidal amplitude in this new ocean reaches meso-tidal
levels (i.e. 2–4 m tidal range, Fig. 3b), the increased dissipation in this
ocean only increases the global total tidal dissipation to 50 % PD (Fig. 4e). Therefore, this ocean cannot be considered super-tidal. The tides then
remain at values close to half of present day, i.e. equal to the long-term
mean over the past 250 Myr in Green et al. (2017), until the formation of
Novopangaea at 200 Ma. After 100 Myr there is a regime shift in the location
of the dissipation rates, with a larger fraction dissipated in
the deep ocean than before (Fig. 3b).
The same as in Fig. 2 but for the Novopangaea scenario.
Aurica
Aurica is characterized by the simultaneous closing of both the Atlantic and
the Pacific Oceans and the emergence of the new pan-Asian Ocean. This
allows Aurica to form via combination in 250 Ma (Fig. 5 and Davies, 2019c). In this scenario, the tides remain close to
present-day values for the next 20 Myr (see Figs. 3c and 5 for the results),
after which they drop to 60 % of PD at 40 Ma, only to rise to 114 % of
PD values at 60 Ma, and then to 140 % of PD rates at 80 Ma. This period
hosts a relatively long super-tidal period, lasting at least 40 Myr, as the
Pacific and Atlantic go in and out of resonances at 60 and 80 Ma,
respectively. The dissipation then drops to 40 %–50 % of PD, with a local
peak of 70 % of the PD value at 180 Ma due to resonance in the pan-Asian
Ocean. This is the same age as the North Atlantic today, which strongly
suggests that oceans go through resonance around this age. By the time
Aurica forms, at 250 Ma, the dissipation is 15 % of PD, the lowest of all
simulations presented here.
The same as in Fig. 2 but for the Aurica scenario.
Amasia
In the Amasia scenario, all the continents except Antarctica move north,
closing the Arctic Ocean and forming a supercontinent around the North Pole
in 200 Ma (Fig. 6 and Davies, 2019d). The results
show that the M2 tidal dissipation drops to 60 % of PD rates within
the next 20 Myr (Figs. 3d and 6 for continued discussion). This minimum is
followed by a consistent increase, reaching 80 % of PD rates at 100 Ma,
and then, after another minimum of 40 % of PD rates at 120 Ma, tidal
dissipation increases until it reaches a maximum of 85 % at 160 Ma. These
two maxima are a consequence of several local resonances in the North
Atlantic, North Pacific, and along the coast of South America, and the
minimum at 120 Ma is a result of the loss of the dissipative Atlantic shelf
areas due to continental collision. A major difference between Amasia and
the scenarios previously described is that here we never encounter a full
basin-scale resonance. This is because the circumpolar equatorial ocean that
forms is too large to host tidal resonances and the closing Arctic Ocean is
too small to ever become resonant. However, the scenario is still rather
energetic, with dissipation rates averaging around 70 % of PD rates
because of several local areas of high tidal amplitudes and corresponding
high shelf dissipation rates (Fig. 3d).
The same as in Fig. 2 but for the Amasia scenario.
Summary of the number of super-tidal peaks for each scenario.
SupercontinentMode ofNumber ofResonant basin(s),Averagescenariosupercontinentsuper-tidal peaks,including PDnormalized*formationincl. PDdissipationPangaea UltimaIntroversion5Atlantic, Pacific, Pacific and Atlantic,0.877Pacific and Atlantic, PacificNovopangaeaExtroversion2Atlantic, Pacific0.520AuricaCombination4Atlantic, Pacific, Atlantic, pan-Asian0.647AmasiaOrthoversion1Atlantic0.723
* Against PD degenerate =2.2 TW.
Discussion
We investigated how the tides may evolve during four probable scenarios of
the formation of Earth's future supercontinent. The results show large
variations in tidal energetics between the scenarios (see Table 1 and Fig. 3), with the number of tidal maxima ranging from 1 (at present during the
Amasia scenario) to 5 (including today's in the Pangaea Ultima scenario);
see Table 1 for a summary. These maxima occur because of tidal resonances in
the ocean basins as they open and close. Furthermore, we have shown that an
ocean basin becomes resonant for the M2 tide when it is around 140–180 Myr old (as is the PD Atlantic). The reason for this is simple: assuming
the net divergence rate of two continents bordering each side of an ocean
basin is ∼3 cm yr-1 (which is close to the average drift
rates today), after 140 Myr it will be 4500 km wide. Tidal resonance occurs
when the basin width is half of the tidal wavelength (Arbic and Garrett,
2010):
L=cgT,
where the wave speed is given by
cg=(gh)0.5,
and T is the tidal period (12.42 h). For a 4000 m deep ocean, resonance
thus occurs when the ocean is 4429 km wide, i.e. at the age given above. The
depth of the simulated oceans changes between the scenarios to preserve
ocean volume at that of present day. These changes are too small to affect
the resonant scales in the different simulations, especially at the
resolution we are using here (0.25∘ in latitude and longitude). For
example, in the Novopangaea scenario, which has the shallowest average ocean
depth at 3860 m, the resonant basin scale is 4350 km, whereas in the Pangaea
Ultima scenario, in the present day the overall deepest at 4395 m, the basin
scale would be 4642 km. This again highlights the relationship between the
tidal and tectonic evolution of an ocean basin. It also reiterates that
ocean basins must open for at least 140 Myr to be resonant during their
opening at present-day drift speeds (e.g. the pan-Asian ocean). If an ocean
opens for less than 140 Myr, e.g. the trans-Antarctic (80 Myr of opening) or
Arctic ocean (60 Myr of opening; Miller et al., 2006), or if they drift
slower than 3 cm yr-1, they will not become resonant. After this 140 Myr and 4500 km age and width threshold has been reached, the ocean may then be
resonant again if it closes.
Therefore, if the geometry and mode of supercontinent formation permits
(i.e. multiple Wilson cycles are involved), several oceans may go through
multiple resonances – sometimes simultaneously – as they open and close during
a supercontinent cycle. For example, in the Pangaea Ultima scenario, the
Atlantic and Pacific are simultaneously resonant at 160 Ma (Table 1), and,
as Aurica forms, the Atlantic is resonant twice (at present and when
closing at 80 Ma), the Pacific is resonant once (closing), and the pan-Asian ocean is resonant once
(after 180 Ma, when opening; Table 1 and Sect. 3.3).
Summary of the total time each scenario was in a super-tidal state.
SupercontinentNumber ofTime span ofTotal timeT(future)scenariosuper-tidalsupercontinentspan of tidal(%)cyclescycle* (Myr)Pangaea Ultima573010013.7Novopangaea2680405.9Aurica47308011.0Amasia1680202.9
* From the formation of
maxima (Myr) Pangaea to the break-up
of the future supercontinent.
The simulations here expand on the work of Green et al. (2018) regarding
the tidal evolution of Aurica. They find a more energetic future compared to
the present Aurica simulations (e.g. our Fig. 3c): their average tidal
dissipation is 84 % of the PD value, with a final state at 40 % of PD,
whereas we find dissipation at 64 % of PD on average and 15 % of PD at
250 Myr. This discrepancy can be explained by two factors present in the
work of Green et al. (2018): a lack of temporal resolution and a systematic
northwards displacement in the configuration of the continents, meaning
their tidal maxima are exaggerated. Despite these differences, the results
are qualitatively similar, and we demonstrate here that under this future
scenario the tides will be even less energetic than suggested in Green et al. (2018). This, along with results from tidal modelling of the deep past
(Green et al., 2017, this paper, and unpublished results) lends further
support to the super-tidal cycle concept and again shows how strong the
current tidal state is.
All four scenarios presented have an average tidal dissipation lower than
the present day, and all scenarios, except Amasia, have a series of
super-tidal periods analogous to present day. The results presented here can
supplement the fragmented tidal record of the deep past (Kagan and
Sundermann, 1996; Green et al., 2017) and allow us to draw more detailed
conclusions about the evolution of the tide over geological time, and the
link between the tide, the supercontinent cycle, and the Wilson cycle.
We have estimated the number tidal maxima that have occurred in the Earth's
history (N) and the total time that the Earth was in a super-tidal state
(T) as follows:
N=Nsc⋅Nwc⋅Nt,
and
T=N⋅TtmTE.Nsc represents the number of supercontinent cycles that have occurred
on Earth, including the present one (we assume a minimum of five supercontinent
cycles; e.g. Davies et al., 2018, and references therein), Nwc is the
number of Wilson cycles per supercontinent cycle (we assume an average of
two), Nt is the number of tidal maxima per Wilson cycle (we assume an
average of two; this work). Ttm is a representative time duration for
each tidal maximum (20 Myr), and TE is the age of the Earth (4.5 Gyr; e.g.
Brent, 2001). This Fermi estimation suggests that there may have been
∼20 super-tidal periods on Earth (N) spanning over 400 Myr
(8.9 %) of the Earth's history. This value is corroborated by the results
in Table 2.
Data availability
The data generated and used in the current study are available in the OSF (Open Science Framework) repository and can be accessed at 10.17605/OSF.IO/8NEQ4 (Davies, 2020).
The data is freely available to use according to the CC0 1.0 license.
Video supplement
The figures available in the supplement have been made into four short videos illustrating the tidal evolution (in 20 Myr increments) of each scenario as they progress from the present day to the eventual formation of the next supercontinent. The Pangea Ultima scenario is illustrated in video S1 (Davies, 2019a, 10.5446/43738). The Novopangea scenario is illustrated in video S2 (Davies, 2019, 10.5446/43739). The Aurica scenario is illustrated in video S3 (Davies, 2019, 10.5446/43740). The Amasia scenario is illustrated in video S4 (Davies, 2019, 10.5446/43741).
The supplement related to this article is available online at: https://doi.org/10.5194/esd-11-291-2020-supplement.
Author contributions
HSD contributed to conceptualization, formal analysis, investigation,
methodology, software, validation, visualization, writing of the original draft, and the review and editing process.
JAMG contributed to conceptualization, data curation, funding acquisition,
methodology, project administration, resources, software, supervision,
validation, and the review and editing process.
JCD contributed to conceptualization, funding acquisition, project
administration, resources, supervision, and the review and editing process.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Hannah S. Davies acknowledges funding from FCT (ref. UIDB/50019/2020 – Instituto
Dom Luiz; FCT PhD grant ref. PD/BD/135068/2017). J. A. Mattias Green acknowledges
funding from NERC (MATCH, NE/S009566/1), an internal travel grant from the
School of Ocean Science, and a Santander travel bursary awarded through
Bangor University. Joao C. Duarte acknowledges an FCT Researcher contract, an
exploratory project grant (ref. IF/00702/2015), and the FCT project
UIDB/50019/2020 – Instituto Dom Luiz. Tidal modelling was carried out using HPCWales with
the support of Ade Fewings. We would like to thank Filipe Rosas, Pedro Miranda, Wouter Schellart, and Célia Lee for their insightful discussions and
for providing support related to several aspects of the work. We would also
like to thank Daniel Pastor-Galán, the anonymous reviewer, and the
editor Ira Didenkulova for their efforts in providing constructive comments
and moderation, which we believe have improved the paper.
Financial support
This research has been supported by the Fundação para a Ciência e a Tecnologia through grant
no. UIDB/50019/2020 – Instituto Dom Luiz, grant no. IF/00702/2015, and PhD grant no. PD/BD/135068/2017 and the Natural Environment Research Council (grant no. NE/S009566/1).
Review statement
This paper was edited by Ira Didenkulova and reviewed by Daniel Pastor-Galán and one anonymous referee.
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