Is the Earth currently in a Global tidal maximum? 500 Ma of coupled tectonic and tidal modelling

Resumen   Abstract   Índice   Conclusiones


Davies, Hannah Sophia

2023-A
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Resumen

Os continentes que observamos hoje na superfície da Terra são os fragmentos de um supercontinente
que existiu há cerca de 300-200 milhões de anos atrás, a Pangeia. A rutura deste
supercontinente marcou o início de um novo ciclo dos supercontinentes em que os continentes,
após um período de dormência, voltaram a separar-se. Estes ciclos ocorrem ao longo de períodos
de cerca de 500 milhões de anos. Tendo em conta que a separação da Pangea se iniciou
há cerca de 180 milhões de anos, prevê-se que o próximo supercontinente ir-se-á formar daqui
a cerca de 200-250 milhões de anos. O ciclo dos supercontinentes está intimamente ligado ao
ciclo de Wilson, que descreve o ciclo de vida dos oceanos. Sempre que os supercontinentes se
formam e se separam, terminam e iniciam-se novos ciclos de Wilson. Tanto o ciclo dos supercontinentes,
como o ciclo de Wilson, são controlados pelo afundamento da litosfera oceânica
no manto. À medida que as placas oceânicas envelhecem e arrefecem, tornam-se mais espessas
e densas, e acabam por afundar no manto subjacente. O afundamento ocorre ao longo de
zonas de subducção, arrastando consigo as placas e os continentes que nelas estão contidos.
Este processo leva a que as placas oceânicas sejam recicladas, que os oceanos fechem e que
os continentes acabem por voltar a colidir. O planeta atualmente não contém placas oceânicas
com idades superiores a 200 milhões de anos, e pensa-se que esta é a idade máxima que uma
placa oceânica pode atingir antes de começar a subductar.
Atualmente, o Oceano Pacífico é quase totalmente rodeado por zonas de subducção (o “Anel
de Fogo” do Pacífico), levando vários autores a prever que este irá ser o próximo grande oceano
a fechar, formando um novo supercontinente nos antípodas da Pangea chamado Novopangea.
Um cenário alternativo considera que será o Oceano Atlântico a fechar, isto porque as placas
oceânicas no Atlântico estão perto de atingir os 200 milhões de anos, e há evidências do início
de formação e propagação de novas zonas de subducção no seu interior (nos arcos da Nova
Escócia e das Pequenas Antilhas, e na Margem Sudoeste Ibérica). O alastramento destas zonas
de subducção a todo o oceano poderá levar ao seu fecho e à consequente formação de um
supercontinente a que se chamou Pangeia Ultima. Combinando a lógica dos cenários anteriores,
é possível que ambos os oceanos fechem simultaneamente, reciclando totalmente as placas
oceânicas do Atlântico e do Pacífico. Para tal é necessário que um novo grande oceano se
desenvolva eventualmente a partir do Oceano Índico e fraturando a Eurásia. O supercontinente
resultante deste cenário foi denominado Aurica. Embora a subducção das placas oceânicas seja
a principal causa para o movimento das placas tectónicas, pensa-se que as cicatrizes deixadas no manto pela Pangeia (e pelo oceano circundante Panthalassa) podem ter um efeito na forma
e local de formação do próximo supercontinente. Segundo este cenário, os supercontinentes
formam-se a 90  do supercontinente anterior, pelo que o próximo supercontinente se deverá
formar junto ao polo Norte. O supercontinente resultante deste cenário foi denominado de
Amásia.
O primeiro objetivo deste trabalho consistiu em reconstruir os quatro cenários, acima mencionados,
propostos para a formação do próximo supercontinente, utilizando o software GPlates,
de forma a obter uma melhor compreensão acerca da dinâmica do ciclo dos supercontinentes e
dos ciclos de Wilson associados. Estudar estes ciclos a partir de um ponto de partida comum e
conhecido (o Presente), permitiu-nos explorar de que forma estes ciclos funcionam e manipular
os diferentes cenários. Começámos por construir um conjunto de modelos da Terra futura que
fossem comparáveis e sobre os quais fosse possível modelar outras componentes do Sistema
Terra, como as marés, circulação oceânica e o clima. O segundo objetivo deste trabalho foi tentar compreender, no contexto dos ciclos dos supercontinentes
e ciclos de Wilson, o como e porquê do Oceano Atlântico estar em ressonância
com a maré M2. Esta ressonância leva a que as marés no Atlântico atinjam amplitudes superiores
a 4 metros, com taxas de dissipação na ordem dos 2,5 TW, as mais altas dos últimos 250
milhões de anos. A questão que se levantou foi: se a maré atualmente é a mais energética desde
a fractura da Pangeia, será que é a mais energética de todo o atual ciclo dos supercontinentes?
Para resolver esta questão, utilizaram-se os quatro cenários tectónicos acima referidos como
base para a modelação de marés utilizando o software OTIS (Oregon State University Tidal Inversion
Software). Os resultados mostraram que em todos os cenários, à medida que o Oceano
Atlântico continua a abrir, a energia dissipada pela maré irá diminuir (nos próximos 25 milhões
de anos). No entanto, a partir deste ponto os cenários começam a divergir, sendo que nalguns
cenários surgem novos períodos de ressonância. O cenário que leva à formação da Pangea Ultima
(com fecho do Oceano Atlântico) é o que possui maior número de períodos de ressonância,
com ambos os oceanos Atlântico e Pacífico a passarem por dois períodos de ressonância cada.
No cenário “Aurica” os oceanos passam por três períodos de ressonância, ao passo que no
cenário “Novopangea” apenas surge um. No cenário “Amasia” não ocorre nenhum período de
ressonância. O aumento da energia dissipada difere entre os vários cenários, sendo que os picos
podem variar entre 70 e 250% da energia dissipada no presente. Estes resultados demonstram
que existe um ciclo de “super” marés associado ao ciclo dos supercontinentes, caracterizado pelo aumento cíclico da energia dissipada pelas marés, devido às bacias oceânicas atingirem
dimensões nas quais as marés sofrem processos de ressonância. Estes ciclos não estão, no entanto,
perfeitamente sincronizados, sendo que cada ciclo dos supercontinentes pode conter, em
média, entre um a três ciclos de supermarés. Esta dessincronização deve-se à relação complexa
que existe entre os ciclos dos supercontinentes e os ciclos de Wilson.
Foram também desenvolvidos modelos de marés específicos para o Criogénico e o Arcaico.
No Criogénico o sinal da maré apresentou uma redução drástica generalizada, devido
às glaciações globais (“Terra Bola de Neve”) que ocorreram neste período. O enfraquecimento
das marés durante os períodos de glaciação podem ter reduzido a mistura de água sob o gelo,
permitindo a formação de uma camada de água doce e fria, isolando-o e prevenindo o degelo.
Este efeito, embora reduzido, poderá ter produzido um feedback positivo que contribuiu para
prolongar as glaciações. No Arcaico foram também identificados períodos de supermarés. O
estudo referente a este período mostrou que as marés eram, em geral, 1.5 vezes mais energéticas
que atualmente, em parte devido à Lua se encontrar mais próxima da Terra. Os resultados
também mostram que terá havido períodos de ressonância, sendo que nesta fase da história
do planeta, a tectónica de placas seria ainda muito primitiva e o ciclo dos supercontinentes
poderia ainda não existir. Estas marés energéticas poderão ter tido um papel importante no
aparecimento e evolução da vida.
Os resultados referentes à modelação de marés realizados no âmbito desta tese mostram que
a Terra, durante a sua evolução, poderá ter passado por vários períodos de supermarés (cerca
de 9% do total da sua idade). Estas supermarés podem estender-se por períodos de tempo
na ordem dos 25 milhões de anos, e têm um papel importante na variação da velocidade de
recessão da Lua, que aumenta sempre que a Terra passa por um período de supermarés.
Um outro objectivo desta tese foi tentar compreender o efeito do ciclo dos supercontinentes
e das supermarés noutras componentes do Sistema Terra, como, por exemplo, a sua influência
no clima. Neste âmbito, o clima dos supercontinentes Aurica e Amasia foi simulado com um
General CirculationModel (GCM), o ROCKE-3D. Os resultados mostraram que os dois potenciais
supercontinentes apresentam climas muito distintos. A Aurica seria um supercontinente
equatorial com um clima quente e árido, ao passo que a Amásia teria um clima mais frio que
o atual, com grandes áreas cobertas por gelo, devido à aglomeração dos continentes junto ao
polo Norte.
Todos estes modelos ajudam-nos a compreender como o Sistema Terra funciona em longas escalas de tempo e ao longo de períodos em que o planeta apresentava características significativamente
diferentes das atuais. Isto permite, por exemplo, testar os diferentes estados pelos
quais um planeta semelhante à Terra pode passar, o que nos pode ajudar a compreender os outros
planetas do sistema solar e até mesmo os exoplanetas que estamos a começar a descobrir e
observar.



Abstract

Earth’s continents in the present day are the dispersed fragments of the former supercontinent
Pangea which existed from 330 – 180 Ma. In around 200 – 250 Myr, following the
progression of the current supercontinent cycle, the Earth’s continents will reform into another
supercontinent. The supercontinent cycle is closely linked to the Wilson cycle which describes
the life cycle of oceans as they form, grow, shrink, and eventually close. As oceans grow and
shrink with theWilson cycle the tides within them are affected. The present day North Atlantic
ocean, which formed as a result of the breakup of Pangea, is resonant with the M2 tide, causing
macrotidal (>4m) tidal amplitudes and strengthening the global M2 tidal dissipation rate to 2.5
TW. Is this a unique occurrence in the present supercontinent cycle or is the tide periodically
buoyed by resonance in ocean basins because of geometry changes brought about by the progression
of the Wilson cycle? Here we will reconstruct predictions of the progression of the
current supercontinent cycle into the future (+250 Ma) with GPlates which we will then use
as a boundary condition for tidal modelling at 20 Myr intervals with OTIS (Oregon state Tidal
Inversion Software). We present four unique scenarios of the Earth’s future, each arguing a different
style of supercontinent formation. In all scenarios of the future, we find that the Atlantic
continues to widen over the next 25 Myrs, causing the tide within it to weaken as resonance is
lost. However, we find several other occurrences of tidal resonance during the future scenarios,
which causes tidal dissipation rates to increase to 70 – 250% of the present-day value. This
periodic increase in tidal amplitudes and dissipation affects the evolution of the Earth-Moon
system over geological time and has implications for ocean circulation, climate and the ocean’s
ability to host and support life in the past and future.



Índice

Contents
Abstract I
Resumo II
1 Introduction 1
1.1 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Background 4
2.1 Plate Tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 The origins of Plate Tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Continental drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Seafloor spreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Plate boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 The Wilson cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 The Supercontinent cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Modes of Supercontinent formation . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Earth’s interior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7.1 Half wavelength open ocean resonance . . . . . . . . . . . . . . . . . 18
2.7.2 Tidal energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7.3 Lunar recession and tidal friction . . . . . . . . . . . . . . . . . . . . 20
3 Methods 22
3.1 GPlates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Oregon State Tidal Inversion Software – OTIS . . . . . . . . . . . . . . . . . . 26
3.2.1 Using the GPlates kinematic model with OTIS . . . . . . . . . . . . . 28
3.3 ROCKE3-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 Using the GPlates kinematic model with ROCKE-3D . . . . . . . . . . 30
4 Back to the future: Testing different scenarios for the next supercontinent gathering 32
4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4 Main concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4.1 Supercontinent Cycles and Wilson Cycles (modes of aggregation) . . . 35
4.4.2 How do oceans start to close? The problem of subduction initiation . . 36
4.4.3 Plate tectonics and mantle convection . . . . . . . . . . . . . . . . . . 38
4.5 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6 Back to the future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.6.1 Introversion: Pangea Ultima . . . . . . . . . . . . . . . . . . . . . . . 43
4.6.2 Extroversion: Novopangea . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6.3 Combination: Aurica . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.6.4 Orthoversion: Amasia . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6.5 Ocean Divergence and convergence rates . . . . . . . . . . . . . . . . 52
4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Back to the future II: Tidal evolution of four supercontinent scenarios 56
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.4.1 Tidal Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.4.2 Mapping of the future tectonic scenarios . . . . . . . . . . . . . . . . . 61
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5.1 Pangea Ultima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.5.2 Novopangea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.5.3 Aurica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.5.4 Amasia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6 Analysing the tidal state of a pre-Plate tectonic Earth during the Archean Eon (3.9 Ga) 72
6.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3.1 Mapping of the Archean conceptual scenarios . . . . . . . . . . . . . . 73
6.3.2 Tidal modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7 Co-authored papers 81
7.1 Is there a tectonically driven supertidal cycle? . . . . . . . . . . . . . . . . . . 81
7.1.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.1.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.1.3 Results – Tidal Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . 84
7.1.4 Results – Tidal Dissipation . . . . . . . . . . . . . . . . . . . . . . . . 86
7.1.5 My contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2 Weak tides during Cryogenian glaciations . . . . . . . . . . . . . . . . . . . . 88
7.2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2.3 Results – Tidal Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2.4 Results – Tidal Dissipation . . . . . . . . . . . . . . . . . . . . . . . . 90
7.2.5 My contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Deep Future Climate on Earth: effects of tectonics, rotation rate, and insolation 93
7.3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.3.3 My contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95



Conclusiones

The primary research question of this work was «Is the Earth currently in a Global tidal
maximum?» Green et al. (2017) shows tides during the tenure of Pangea, and for the past 200
Ma are quiescent, being around half present day values. The tidal modelling of Green et al.
(2017) ends at the present day with a much more energetic tide showing that compared to the
last 200 Myr since the breakup of Pangea, the present day tides are anomalously energetic.
However, is this a unique phenomenon and how long will this period of more energetic tides
last for?
Green et al. (2018) show using preliminary tidal modelling on the Aurica scenario of the
future that the present day tides are also anomalously high when compared to the next 250 Myr.
They identify other periods of enhanced tidal dissipation and amplitudes in the future, where the
global tidal energetics are around twice the average for the scenario and around 80% of present
day values. Furthermore, they show that the present period of more energetic tides occurs
for approximately the next 20 Myrs and establish that because of the average drift velocity of
continental plates in the present day, half wavelength resonance will rarely last longer than 20
Ma (see section 5.6 for a full explanation).
Davies et al. (2018) presented four scenarios of the next supercontinent gathering allowing
us to further investigate tidal evolution into the geological future. In tidal modelling results
of these scenarios, Davies et al. (2020) shows in all future scenarios, global tidal energetics
decrease as the next supercontinent forms, regardless of which mode of ocean closing the supercontinent
formed under. Despite this, periods of enhanced tidal energetics do emerge in the
future (Fig. 5.3). All the periods of enhanced tidal dissipation or «super-tide» occur when the
supercontinent is coalescing and ocean basins are widening and/or narrowing. As we know
an ocean basin can only be resonant at a width equal to the half wavelength of the tidal wave,
meaning very large and very small oceans cannot support resonant tides. Therefore tidal resonance
should be most likely to occur in a supercontinent cycle when the supercontinent is
dispersing or converging and ocean basins are moving through this resonant width, which is
confirmed in Davies et al. (2020).
Compiling the results of Green et al. (2017, 2018); Davies et al. (2020) we can establish the
tidal evolution of Earth for 500 Myrs, equivalent to an entire supercontinent cycle, beginning at
the breakup of Pangea and ending in the formation of the next supercontinent. With this work
we can confidently say that the present day is in a global tidal maximum. Furthermore, it is
not a unique occurrence on geological timescales. Notwithstanding, while it is likely a supertidal
period or global tidal maximum will occur at least once during a supercontinent cycle,
the period of elevated tides (~20 Myr) is very short when compared to the whole period of the
supercontinent cycle (~500 Myr).
Looking at the tidal dissipation over a whole supercontinent cycle, the global average is
around half present day values for the majority of the supercontinent cycle, with periods of
super-tide when resonance occurs. Once a supercontinent has fully coalesced, tidal dissipation
decreases further, by as much as half again (25% of present day values). Illustrating the
change in tidal energetics over a supercontinent cycle – very quiescent tides during supercontinent
tenure and slightly elevated tides during the dispersed phase of the supercontinent cycle
permeated by periods of harmonically enhanced tidal energetics.
Further studies revealed the above to be true in deep time periods of Earth history also.
Based on the results detailed above in Green et al. (2020) of coupled tidal tectonic model
results from the Cryogenian, the present day tides are anomalously high when compared to
the geological average for the periods studied (Fig. 8.1). This is further corroborated by tidal
modelling carried out during the Cenozoic (Green et al., 2017), Devonian (Byrne et al., 2020)
and Phanerozoic (Hadley-Pryce & Green personal communication, June, 2020).
Figure 8.1: Relative tidal dissipation (Present-Day = 1) from 1500 Million years ago to 250 Million years in the future, dashed
black lines represent supercontinent tenures, and blue dots represent ice ages (Green personal communication, Feb, 2020).
The anomalously energetic present day tide is due to harmonic open ocean resonance in the
Atlantic (Green et al., 2017). We know the Atlantic has been opening for ~180 Myr and if the
average divergence rate of the bordering continents is ~3 cmyr-1, after 140 Myr the ocean will
be ~4500 km wide – which is near the harmonic width for an ocean 4 km deep (where 4 km is
the average global ocean depth) (see section 2.7.1 for a full explanation). Therefore, if an ocean
opens for at least 140 – 180 Myr, tidal resonance will likely develop within it. This is true for
oceans which form at the beginning of the supercontinent cycle (i.e., when the supercontinent
98
breaks up) e.g., the Atlantic, and for oceans which form later in the supercontinent cycle, e.g.,
the Pan-Asian ocean. This holds true for all of the periods of dispersed continent phase where
tidal modelling has been conducted, both in the past and the future (Green et al., 2020; Byrne
et al., 2020; Davies et al., 2020). The best example in the future is during the Aurica scenario,
the Pan-Asian ocean begins opening near the start of the Aurica scenario, and becomes harmonically
resonant with the tide at 140 Ma (Fig. 5.5). Despite the fact that the Pan-Asian
ocean is the second ocean to open sufficiently during the present cycle to be resonant, it still
shows proof that a minimum age is required for an ocean to be harmonically resonant.
This result of a minimum age of 140 – 180 Myr before resonance is possible in an ocean can
be seen in past supercycles also, the tidal modelling results of Byrne et al. (2020) show elevated
global tidal amplitudes consistent with present day values (average M2 amplitude 0.3 – 0.5 m)
around 400 – 380 Ma, which is around 160 – 180 Ma after the breakup of Gondwana/Pannotia
(Scotese, 2009; Merdith et al., 2017).
Looking at the tidal modelling results of the supercycle before Gondwana/Pannotia, beginning
with the breakup of Rodinia at 800 Ma (Merdith et al., 2017), Green et al. (2020) finds
enhanced tidal dissipation at 715, 680, and 630 Ma. The first two periods do not coincide
with the prediction, however Green et al. (2020) attributes the resonance at 715 Ma to ocean
basin shortening due to large scale eustatic sea level reduction as the Sturtian glaciation begins,
this resonance is forced more by ice formation than geodynamics. This can be likened to the
Atlantic resonance which occurred 21 Ka which was also due to ocean basin shortening as a
result of eustatic sea level reduction during an ice age (Green et al., 2017). Green et al. (2020)
attributes the enhanced tidal energetics at 680 to the emergence of land over the south pole,
this is also not within the timing of the prediction (being only 120 Ma from the breakup of Rodinia)
however, this period of enhanced tide is localised to the proto-tethys ocean and is more
likely related to the continents orthoverting to form Gondwana/Pannotia. A similar period of
enhanced tide is observed in the Amasia scenario at 100 Ma in Davies et al. (2020). The two
periods also have similar energetics (680 Ma = ~50% PD and +100 Ma = ~80% PD dissipation).
The third period of enhanced tidal dissipation during the Rodinia – Pannotia supercycle
is at 630 Ma is when Gondwana/Pannotia has already arguably assembled (Murphy and Nance,
2005). This resonance is more local as Green et al. (2020) mentions, it mostly occurs in the
Kipchak, Uralian, and Aegir seas, which surround the Proto-tethys ocean (Fig. 8.2).
The two snowball glaciations which occur during the Cryogenian period dampen any res-
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onance which may have occurred. Furthermore, the breakup of Rodinia and the formation of
Gondwana/Pannotia are only separated by around 150 Ma. This is a much shorter period of
dispersed continents than other supercontinent cycles and may have made resonance far less
likely.
Figure 8.2: 650 Ma ago as represented by (Scotese, 2017) illustrating the landmasses, oceans, and seas of the time.
With regards to any tidal resonances which occurred as a result of the breakup of the supercontinent
to precede Rodinia, the reconstructions begin to be too low resolution, both temporally
and spatially to confidently predict and model the tidal environment. Figure (8.1) shows
tidal results from this period conducted as a test of concept, and they do record a tidal peak
at 1300 Ma, however it is smaller than the two neighbouring peaks at 1450 Ma and 1100 Ma,
which occur just after the breakup of Columbia/Nuna, and during the formation of Rodinia respectively
(Dalziel et al., 2000; Rogers and Santosh, 2003; Murphy and Nance, 2003; Merdith
et al., 2017).
Going further back to the Archean, tidal modelling is only possible by using ensemble
bathymetries to establish a statistically significant picture of the Archean tide which is in general
far more energetic than the present day. In the context of open ocean resonance the Archean
does exhibit some, however in general the continental area is too small to allow for the large
scale open ocean resonance seen in the other periods modelled. The work presented in section
6 is preliminary however, meaning our conclusions here could change.
Including the results of Byrne et al. (2020); Green et al. (2017), and Hadley-Pryce (personal
Communication, June, 2020) with those presented in this work, we now have tidal modelling
results for over three supercontinent cycles and four supercontinents (Rodinia – Gondwana/
Pannotia – Pangea – Future). Several distinct periods of enhanced tidal energetics have
been identified, most due to open ocean resonance, and some due to regional resonances at
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coastlines. Tidal resonance appears to be not uncommon at geological timescales. As concluded
in 5.6 and presented in Table (5.1), each future scenario experiences a number of tidal
maxima or Super-tides. Open ocean resonance is also recorded in the tidal modelling results
of Green et al. (2017, 2018, 2020); Byrne et al. (2020), indicating that resonance may occur at
least once or twice during the dispersed continent phase of a supercontinent cycle.
Above we have discussed how tidal resonance might arise while a Supercontinent is dispersing
and new ocean(s) are being formed e.g. the Rheic, Tethys or Atlantic. We also established
a method of predicting these initial open ocean resonances with geodynamic constraints
(divergence rates and ocean depth). Predicting successive periods of tidal resonance in the
supercontinent cycle is more difficult. As Table (5.1) shows, the four scenarios each have a
different number of super-tidal peaks. This is because of the mode of formation each scenario
illustrates. Different modes of supercontinent formation allow for different ocean morphologies
and developments which can make harmonic resonance more or less likely. Based on the
results of Davies et al. (2020), one might assume that each mode of supercontinent formation
can be attributed to a generally more or less tidally active dispersed supercontinent phase
i.e., Introversion (assuming the ocean opening does not fail) scenarios always exhibit a more
tidally energetic dispersed continent phase than orthoversion scenarios. This appears to not be
possible however. Comparing the Introversion scenario from Davies et al. (2020) with Byrne
et al. (2020) and Hadley Pryce (personal communication, June, 2020) the tidal energetics for
the period between the breakup of Pannotia/Gondwana and the formation of Pangea – which
was an introversion event (Murphy and Nance, 2005), the results are not at all comparable.
Only one period of enhanced tidal dissipation appears in the Devonian (Byrne et al., 2020).
This is compared to the five of the Pangea Ultima introversion. Furthermore, when comparing
the Amasia scenario with the period between the breakup of Rodinia and the formation
of Pannotia/Gondwana – an orthoversion event (Murphy and Nance, 2005), Green et al. (2020)
finds three periods of enhanced tidal dissipation, where the Amasia scenario is tidally quiescent
throughout.
It must be noted that the deep-time periods highlighted cannot be faithfully compared with
the scenarios of the future. Reconstructions of the Devonian and the Phanerozoic as a whole
are not well resolved and fully agreed on. Not only are the continental geolocations debated
but the mode of formation of Pangea is also debated, as it may have formed by Introversion,
Orthoversion, or a combination of the both (see Davies et al. (2018) for a full explanation).
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With regards to the Cryogenian, the maps used in Green et al. (2020) are rough estimations of
the continental extent at the time and differences in the true continental extent could alter the results
completely for some periods, particularly where resonance occurs. Furthermore, the tidal
modelling conducted in Green et al. (2020) alters the tidal conversion and sea level to simulate
the glaciations where the Amasia scenario retains present day ocean volume (and therefore sea
level), and conversion throughout. That in mind, Way et al. (2019) finds significant ice sheet
growth in ROCKE-3D models of the Amasia scenario which would alter eustatic sea level. If
the Amasia scenario induced another «Snowball» glaciation, then the global sea level could be
reduced by a similar amount to that estimated for the Sturtian or Marinoan glaciations. This
would alter the effective shape of every ocean basin on Earth which could drastically alter the
tidal energetics. Even regular ice ages such as the last glacial maximum are capable of altering
ocean basin shape enough to alter the open ocean tidal energetics (Wilmes and Green, 2014).
Even a small scale glaciation of the Amasia supercontinent could alter the results presented in
Davies et al. (2020).
All of the periods of enhanced tidal energetics or Super-tides presented have two things in
common, the timing of their emergence during the Supercontinent cycle, and their duration. As
has been discussed above, around 140 – 180 Myr must pass for resonance to have a chance to
occur in an ocean forming from the breakup of a supercontinent. Glaciations can alter ocean
basin geometry significantly enough to expedite resonance in an ocean as seen in 715 Ma in
Green et al. (2020), however this appears rare. After this period of 140 – 180 Myr, it appears
resonance can develop at any time and any number of times during the dispersed phase of
the Supercontinent cycle (Table 5.1). As the Supercontinent begins to enter a terminal stage
of formation when its contingent parts are only separated by narrow seaways, resonance may
still occur, however it is in surrounding oceans, not the seaways, which often resemble the
Mediterranean sea in geology and tidal state. This is best illustrated at 220 Ma of the Pangea
Ultima scenario (Fig. 5.2e), and 630 Ma of the Cryogenian simulations of Green et al. (2020)
(Fig. 7.5). Pangea Ultima is only 30 Ma away from being fully assembled, the Atlantic now
separated into two narrow seaways by a partial collision of Africa and South America, however
the Pacific becomes resonant one last time before the Supercontinent fully forms. With the
Cryogenian resonance at 630 Ma, it is arguably a regional case of resonance, as does occur
once some supercontinents have assembled (e.g., Amasia, see Fig. 5.6f) however, it is still
worth noting here as it was highlighted as a period of enhanced tidal energetics by Green et al.
(2020).
Therefore, while there appears to be a time after a supercontinent opens when resonance is
not possible (or very unlikely) resonance can occur right up to the formation of a supercontinent.
After a Supercontinent has formed, it may have some regional resonances at the coast,
however these are localised and far weaker than when open ocean resonance occurs (Fig. 5.3).
None of the supercontinents that have been tidally modelled have sustained large tides Green
et al. (2017), Hadley-Pryce (personal communication June 2020), and Fig. (5.3). Geodynamically
this makes sense, the majority of the Earth’s water mass would be in a super ocean which
would behave in a similar way to a water world exhibiting only small tides (Rohling (2020), and
section 2.7). Furthermore, the supercontinent is fully assembled which means the Earth’s continents
are in a configuration with the smallest surface area. As coastlines (shelf seas) represent
a major area of tidal dissipation on Earth, dissipating 1.8 TW of the M2 tide in the Present Day
(Munk and Wunsch, 1998), reducing that surface area will reduce the amount of tidal energy
dissipated at the coast and thereby reduce global total ocean dissipation.
The Amasia scenario end member time slice (+200 Ma; Fig. 5.6f) represents the most
tidally energetic supercontinent at ~80% of PD values. This we believe is a product of how the
future supercontinents formed. Each scenario used present day coastlines with very detailed
morphology (<0.25°). As each supercontinent forms in the future scenarios the sum total surface
area of the continent(s) drops. Amasia however retains a much larger portion of coastline
than Pangea Ultima, Novopangea, or Aurica, and therefore has a much larger coastline surface
area where the M2 tide can dissipate. Where one or two large ocean basins (and their coastlines)
close, and the supercontinent forms made up of every continent in the Pangea Ultima,
Novopangea, and Aurica scenarios, the only ocean basin to close in the Amasia scenario is the
Arctic ocean, a much smaller basin than the Atlantic or Pacific. Furthermore, Amasia forms
with Antarctica remaining an independent separate continent. These both mean Amasia retains
a much larger coastline area. It is therefore not prudent to use Amasia as a standard of tidal
energetics during a supercontinent’s tenure. Perhaps an upper bound, although this is uncertain
as Davies et al. (2020) mentions, their tidal results may overestimate the true tidal energetics
meaning the tidal state of the end member of the Amasia scenario could be more quiescent.
After modelling the tidal environment of several periods in Earth history the aim of this
work was to quantify the relationship between tides and the supercontinent cycle. The tide
represents a regular and predictable force in the Earth system, however the supercontinent
cycle is far less predictable and somewhat chaotic in its motions. Past work has attempted
to predict the motions of the continents, i.e., a regular accordion like motion or introversion
and extroversion (Murphy and Nance, 2003), or a regular polar to equatorial alternation of
supercontinents (Mitchell et al., 2012). However, Davies et al. (2018) struggles to find this
correlation, mainly because there have been so few complete, and well mapped supercontinent
cycles on Earth.
It appears to be very difficult to objectively compare supercontinent cycles, either of the past
or future. When looking at the different supercontinent cycles of Earth history it is tempting
to try to find repetition and coincidences, however the motion of continents over geological
time scales appears random. One could argue repetition can be found in the Wilson cycle as
oceans close and re-open, however, the Rheic and Atlantic, while being similar oceans, are
not identical and have different suture zones marking their closure and opening respectively
(Burke et al., 1977). That in mind, as has been touched on above, the Wilson cycle dictates
the mode of formation of supercontinents and that allows classification, however the fact that
the mode of formation of Pannotia/gondwana and Pangea is still debated (Murphy and Nance,
2005; Mitchell et al., 2012) and that four completely different predictive scenarios of the Earth’s
future (among possibly more) exist and are debated, shows that understanding and predicting
the motions of the continents as they progress through the supercontinent cycle is very difficult.
It may not be impossible to predict what the next supercontinent will look like however,
and each academic will have their reasons for supporting one of the predictions in Davies et al.
(2018). We know the primary forcing of plate tectonics is slab pull from sinking oceanic plate.
We know that ocean plate is gravitationally unstable after 20 Ma (Condie, 1997), and will likely
not remain on the surface of Earth for much longer after 180 Ma (Müller et al., 2008). We also
know this sinking slab hydrates and disrupts the chemical equilibrium of the Mantle causing
upwelling (Torsvik et al., 2016) which also plays a role in plate tectonics in the form of hot
spots and LIPs argued to be the mechanism by which supercontinents break up (Pastor-Galán
et al., 2019). We do not know how subduction initiates (Duarte et al., 2013; Marques et al.,
2014; Stern and Gerya, 2018). If we are to assume the same as Davies et al. (2018) and simply
assume subduction must somehow initiate in the present day Atlantic because of the average
plate age at the boundaries of the ocean basin then it must be assumed the Atlantic will close.
However the Pacific is already surrounded by subduction zones and the prevailing present day
continental plate velocity suggests the Pacific is closing (Schellart et al., 2008). Here in lies the
problem, which Duarte et al. (2018) attempts to solve with the Aurica scenario.
Perhaps the question of «how a supercontinent forms» is not the correct one but instead
«are supercontinents forming and dispersing» is more pertinent. Condie (1997); Pastor-Galán
et al. (2019); Waltham (2019) and others emphasise that plate tectonics has impacted the Earth
more than any other component of the Earth system, and that plate tectonics is necessary for
a planet to have a long habitable period (~6 Ga). Regardless of how a supercontinent forms,
its formation, tenure, and eventual breakup will affect the Earth system. As this thesis has
shown, supercontinent formation is correlated with tidal quiescence which may in extreme
cases result in ocean anoxia due to reduced mixing (Wignall and Hallam, 1992), however this
link should be further investigated to confidently attribute anoxia to reduced tidal mixing during
supercontinent tenure.
There is certainly also a link between supercontinents and climate. Supercontinents have
fundamentally altered the climate in the past (Parrish, 1993; Santosh, 2010), and the formation
of the next supercontinent in 250 Ma will also alter the climate significantly from its present
day state (section 7.3). Way et al. (2019) shows that latitudinal concentration of landmasses significantly
affects climate. When compared, the climate of the end member Aurica and Amasia
scenario are very different (Fig. 7.8). Aurica being a mostly equatorial landmass experiences
very little snow and ice cover, where in contrast the Amasia end member is almost completely
covered >30°N in Northern hemisphere winter months. Where the Amasia end member is
much colder, the Aurica end member is potentially more arid, and has weaker ocean circulation.
The Aurica simulation has a weaker stream function meaning less moisture uptake to the
atmosphere. Way et al. (2019) finds interesting results from climate modelling of Aurica and
Amasia, however their study represents more of a test of concept than a complete investigation.
Further multi-disciplinary modelling is required to fully resolve the relationship between
climate the the supercontinent cycle over geological time.
This work has addressed the main question of if the present day has anomalously high
tides when compared to the geological average, however the full relationship between tides
and tectonics is very complex. This work has shown that the elevated tidal energetics of the
present day is not unique in the tidal record over geological time but a result of a confluence
of tectonics and tidal period. This has occurred several times in Earth history and will occur
in Earth’s future. This is not the only way tides affect Earth though, just as the supercontinent
cycle is not the only way tectonics affects Earth. Chapter 6 shows that the early Earth Moon
relationship and the tide that occurred because of that may have impacted the development of
life. It may not be necessary for a planet like ours to have a Moon to first cause life to develop,
however the tides may have helped by mixing the primordial oceans.