Earth-Science Reviews
Predicting shoreline depositional process regimes using insights from palaeotidal modelling --Manuscript Draft--
Manuscript Number: Article Type: Review Article Keywords: Numerical Modelling; Wave; Tide; Fluvial; Palaeotidal; Mixed process; Shoreline; Deltaic; Shelf; Sedimentary Preservation Corresponding Author: Daniel Collins Shell International Ltd London, London UNITED KINGDOM First Author: Daniel Collins Order of Authors: Daniel Collins Alexandros Avdis Martin H. Wells Andrew J. Mitchell Peter A. Allison Howard D. Johnson Gary J. Hampson Jon Hill Christopher D. Dean Matthew D. Piggott Abstract: Tides are a fundamental element of predictive depositional models of ancient shoreline process regimes. These models principally relate ancient tidal potential to shelf width (c. 10–100 km) and shoreline geometry (c. 1–10 km) but rarely consider larger-scale basin physiography (100–1000 km) or variability related to changing shoreline geometry. A refined predictive decision tree for ancient shoreline process regimes is developed based on a review of modern shoreline processes, supported by new insight from numerical palaeotidal modeling studies. Modern depositional shorelines are overwhelmingly wave dominated, suggesting a first-order control of wave fetch and wave-generating wind conditions on shoreline processes. Several numerical palaeotidal modeling studies highlight the following controls on tidal processes: (1) 100–1000 km-scale basin physiography on tidal inflow versus outflow; (2) 10–100 km- scale shelf physiography on shelf tidal resonance potential; (3) tidal amplification (funnelling and shoaling) versus frictional effects in shoreline embayments (1–10 km scale); and (4) palaeogeographic uncertainty, which affects prediction of these latter three controls. The predictive decision tree considers the effects of basin physiography, shelf width and shoreline morphology on wave, tide and fluvial processes separately. The two-tier classification of process regime in the decision tree (limited to primary and secondary processes) reflects uncertainty and ambiguity in applying three-tier process classification schemes to modern shorelines and, especially, to ancient shoreline deposits. This review demonstrates the benefit of numerical tidal modeling, calibrated by integrated comparison to the preserved stratigraphic record, and offers a refined classification and prediction of shoreline process regimes. Wider and consistent utilisation of these concepts, and numerical simulations of other depositional processes, will further improve process-based classifications and predictions of modern and ancient shoreline systems. Suggested Reviewers: Valentina Marzia Rossi [email protected] Mixed-process shoreline-shelf systems Shahin Dashtgard
Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Simon Fraser University - Surrey [email protected] Mixed-process shoreline-shelf systems Bruce Ainsworth Chevron Corp [email protected] Mixed-process shoreline-shelf systems Robert Dalrymple [email protected] Mixed-process shoreline systems with focus on tidal systems Chris Paola [email protected] Numerical modelling of sedimentary systems Opposed Reviewers:
Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Cover Letter
Daniel S. Collins Shell International Ltd Shell Centre, London SE1 7NA 14th July 2020 [email protected]
Dear Editor,
We are pleased to submit our manuscript entitled ‘Predicting shoreline depositional process regimes using insights from palaeotidal modelling’ for your consideration as an original research article.
The submitted manuscript is a timely review of three intersecting facets of recent shoreline– shelf sedimentological and stratigraphic research: 1. Classification and prediction of modern and ancient shorelines in terms of mixed process (fluvial, wave, tide) dynamics; 2. Calibration of numerical simulations of shoreline processes by process-based interpretations of the preserved facies and stratigraphic record; and 3. Understanding the sensitivity of tides to physiographic controls. Through a review of three palaeotidal modelling case studies, the overall aim is to demonstrate the benefit of numerical simulations of ancient shoreline processes, calibrated by integrated comparison to the preserved stratigraphic record, in improving and refining classification and prediction of process regimes of modern and ancient shoreline systems. The three case studies investigated ancient tides in strongly contrasting geological settings and on various spatial and temporal scales: (1) the Oligocene–Miocene South China Sea (SCS); (2) the Early Cretaceous Lower Greensand Seaway, NW Europe; and (3) the Late Cretaceous Bohemian Cretaceous Basin, Central Europe. The comparison between palaeotidal model results and sedimentological and stratigraphic data in the rock record establishes the strengths, limitations and potential biases of the numerical simulation approach. Last, the implications of palaeotidal model simulations provide an updated framework for classification and prediction of shoreline depositional process regime to test against future modelling approaches for assessing ancient tidal, wave and additional shoreline sedimentary processes.
The paper is widely applicable to understanding modern shoreline processes, especially tides, and interpreting ancient mixed-process shoreline systems. This has applied significance on multiple fronts, for example: understanding modern shoreline dynamics, with implications for shoreline stability during climate and sea level change; and petroleum exploration and production, where predicting and characterising ancient shoreline–shelf depositional processes is vital to reconstructing depositional models, including reservoir, seal and source rock facies distribution.
The authors have no conflict of interests to declare. We look forward to hearing the outcome of your assessment in due course. .
Yours sincerely,
Daniel S. Collins (corresponding author and on behalf of all co-authors)
Information on submission:
Number of words in main text and captions: 25,864 Number of figures: 31 Number of tables: 4 Number of Supplementary figures: 1 Highlights
HIGHLIGHTS
Rivers, waves and tides impact sediment dynamics along shorelines
Modern shoreline dynamics are overwhelmingly wave dominated
Tides are controlled by basin, shelf and shoreline physiography
Paleotidal models can be calibrated to preserved facies and stratigraphy
Numerical models refine classifications and prediction of shoreline process regimes Abstract
ABSTRACT
Tides are a fundamental element of predictive depositional models of ancient shoreline
process regimes. These models principally relate ancient tidal potential to shelf width (c. 10–
100 km) and shoreline geometry (c. 1–10 km) but rarely consider larger-scale basin
physiography (100–1000 km) or variability related to changing shoreline geometry. A refined
predictive decision tree for ancient shoreline process regimes is developed based on a review
of modern shoreline processes, supported by new insight from numerical palaeotidal
modelling studies. Modern depositional shorelines are overwhelmingly wave dominated,
suggesting a first-order control of wave fetch and wave-generating wind conditions on
shoreline processes. Several numerical palaeotidal modelling studies highlight the following
controls on tidal processes: (1) 100–1000 km-scale basin physiography on tidal inflow versus
outflow; (2) 10–100 km-scale shelf physiography on shelf tidal resonance potential; (3) tidal
amplification (funnelling and shoaling) versus frictional effects in shoreline embayments (1–
10 km scale); and (4) palaeogeographic uncertainty, which affects prediction of these latter
three controls. The predictive decision tree considers the effects of basin physiography, shelf
width and shoreline morphology on wave, tide and fluvial processes separately. The two-tier
classification of process regime in the decision tree (limited to primary and secondary
processes) reflects uncertainty and ambiguity in applying three-tier process classification
schemes to modern shorelines and, especially, to ancient shoreline deposits. This review
demonstrates the benefit of numerical tidal modelling, calibrated by integrated comparison to
the preserved stratigraphic record, and offers a refined classification and prediction of
shoreline process regimes. Wider and consistent utilisation of these concepts, and numerical
simulations of other depositional processes, will further improve process-based classifications
and predictions of modern and ancient shoreline systems.
Manuscript File Click here to view linked References
1 2 3 4 5 1 Predicting shoreline depositional process regimes using insights 6 7 8 2 9 from palaeotidal modelling 10 11 1,2 2 3 2 12 3 Daniel S. Collins , Alexandros Avdis , Martin H. Wells , Andrew J. Mitchell , Peter A. 13 14 4 Allison2, Howard D. Johnson2, Gary J. Hampson2, Jon Hill4, Christopher D. Dean5, and 15 16 5 Matthew D. Piggott2 17 18 19 6 1 Shell International Ltd, London, SE1 7NA, UK 20 21 7 2 Department of Earth Science and Engineering, Imperial College London, South Kensington 22 23 24 8 Campus, London, SW7 2AZ, UK 25 26 9 3 BP plc, Chertsey Road, Sunbury-on-Thames, Middlesex TW16 7LN, UK 27 28 4 29 10 Environment Department, University of York, Heslington, York, YO10 5DD, UK 30 31 11 5School of Geography, Earth & Environmental Sciences, University of Birmingham, 32 33 34 12 Birmingham, B15 2TT, UK 35 36 13 37 38 14 ABSTRACT 39 40 41 15 Tides are a fundamental element of predictive depositional models of ancient shoreline process 42 43 16 regimes. These models principally relate ancient tidal potential to shelf width (c. 10–100 km) and 44 45 46 17 shoreline geometry (c. 1–10 km) but rarely consider larger-scale basin physiography (100–1000 47 48 18 km) or variability related to changing shoreline geometry. A refined predictive decision tree for 49 50 51 19 ancient shoreline process regimes is developed based on a review of modern shoreline processes, 52 53 20 supported by new insight from numerical palaeotidal modelling studies. Modern depositional 54 55 21 shorelines are overwhelmingly wave dominated, suggesting a first-order control of wave fetch 56 57 58 22 and wave-generating wind conditions on shoreline processes. Several numerical palaeotidal 59 60 1 61 62 63 64 65 1 2 3 4 23 modelling studies highlight the following controls on tidal processes: (1) 100–1000 km-scale 5 6 7 24 basin physiography on tidal inflow versus outflow; (2) 10–100 km-scale shelf physiography on 8 9 25 shelf tidal resonance potential; (3) tidal amplification (funnelling and shoaling) versus frictional 10 11 12 26 effects in shoreline embayments (1–10 km scale); and (4) palaeogeographic uncertainty, which 13 14 27 affects prediction of these latter three controls. The predictive decision tree considers the effects 15 16 28 of basin physiography, shelf width and shoreline morphology on wave, tide and fluvial processes 17 18 19 29 separately. The two-tier classification of process regime in the decision tree (limited to primary 20 21 30 and secondary processes) reflects uncertainty and ambiguity in applying three-tier process 22 23 24 31 classification schemes to modern shorelines and, especially, to ancient shoreline deposits. This 25 26 32 review demonstrates the benefit of numerical tidal modelling, calibrated by integrated 27 28 29 33 comparison to the preserved stratigraphic record, and offers a refined classification and 30 31 34 prediction of shoreline process regimes. Wider and consistent utilisation of these concepts, and 32 33 34 35 numerical simulations of other depositional processes, will further improve process-based 35 36 36 classifications and predictions of modern and ancient shoreline systems. 37 38 37 39 40 41 38 Keywords: Numerical Modelling; Wave; Tide; Fluvial; Palaeotidal; Mixed process; Shoreline; 42 43 39 Deltaic; Shelf; Sedimentary Preservation 44 45 46 40 47 48 41 1 INTRODUCTION 49 50 51 42 Shorelines are amongst the most geologically variable, environmentally diverse and climatically 52 53 43 sensitive sedimentary environments, with important social and economic implications (Giosan 54 55 44 and Bhattacharya, 2005; Syvitski and Saito, 2007). Physical, biological and chemical exchange 56 57 58 45 between the continents and oceans across this interface is fundamentally impacted by the 59 60 2 61 62 63 64 65 1 2 3 4 46 interaction of hydrodynamic processes relating to fluvial, wave and tidal influence. Improved 5 6 7 47 understanding and recognition of process interactions along modern and ancient shorelines has 8 9 48 led to refined process-based classifications and predictive models of shoreline systems 10 11 12 49 (Ainsworth et al., 2008; Ainsworth et al., 2011; Vakarelov and Ainsworth, 2013; Nyberg and 13 14 50 Howell, 2016). An important component has been wider application of theoretical relationships 15 16 51 between the strength of wave or tide processes and shoreline–shelf physiography, derived from 17 18 19 52 palaeogeographic reconstructions, in order to support facies and stratigraphic interpretations of 20 21 53 ancient depositional processes, most notably the impact of shoreline geometry and on tidal 22 23 24 54 resonance or amplification (Godin, 1993; Yoshida et al., 2007; van Cappelle et al., 2018; 25 26 55 Zuchuat et al., 2019). Simple theoretical relationships are a quick method of estimating 27 28 29 56 shoreline–shelf wave and tidal potential, but without the ability to assess or understand spatio- 30 31 57 temporal variability and the sensitivity to, and interaction of, potential physiographic controls. 32 33 34 58 Instead, hydrodynamic numerical modelling enables deeper discussion of these factors, ranging 35 36 59 from multi-process morphodynamic simulations (Geleynse et al., 2011; Rossi et al., 2016) to 37 38 60 simulations of specific shorelines processes. In particular, numerical tidal simulations (e.g. 39 40 41 61 Slingerland, 1986; Ericksen and Slingerland, 1990; Martel et al., 1994; Wells et al., 2005a; 42 43 62 Mitchell et al., 2010; Collins et al., 2018a; Dean et al., 2019) have been extensively validated 44 45 46 63 against modern sedimentary environments and, through integration with sedimentological and 47 48 64 stratigraphic datasets, have provided unique information on the physiographic controls on tidal 49 50 51 65 processes and sedimentary preservation along ancient tide-influenced shorelines. However, the 52 53 66 implications of ancient tidal model simulations on the classification, prediction and interpretation 54 55 67 of shoreline–shelf depositional process regimes has not yet been fully explored. 56 57 58 68 59 60 3 61 62 63 64 65 1 2 3 4 69 The aims of this review article are threefold. First, the results of three palaeotidal modelling 5 6 7 70 studies are integrated to identify the dominant physiographic controls on shoreline tidal 8 9 71 processes. The three case studies investigated ancient tides in strongly contrasting geological 10 11 12 72 settings and on various spatial and temporal scales: (1) the Oligocene–Miocene South China Sea 13 14 73 (SCS); (2) the Early Cretaceous Lower Greensand Seaway, NW Europe; and (3) the Late 15 16 74 Cretaceous Bohemian Cretaceous Basin, Central Europe. Second, the comparison between 17 18 19 75 model results and sedimentological and stratigraphic data in the rock record establishes the 20 21 76 strengths, limitations and potential biases of the palaeotidal modelling approach. Third, the 22 23 24 77 implications of palaeotidal model simulations for classification and prediction of shoreline 25 26 78 depositional process regime are assessed. 27 28 29 79 30 31 80 2 BACKGROUND 32 33 34 81 2.1 Tidal theory and numerical modelling 35 36 82 2.1.1 Equilibrium tidal theory 37 38 83 The non-mathematical theory of Earth tides has been extensively reviewed (Defant, 1961; 39 40 41 84 MacMillan, 1966; Dalrymple, 1992; Allen, 1997; Open University Course Team, 1999; Willis, 42 43 85 2005; Kvale, 2006; Kvale, 2012; Longhitano et al., 2012). Astronomical tides are defined as ‘any 44 45 46 86 periodic fluctuation in the water level that is generated by the gravitational attraction of the 47 48 87 Moon and Sun’ (Dalrymple, 1992). The Moon, although smaller than the Sun, accounts for c. 49 50 51 88 70% of the tide-raising force due to its closer proximity. However, the tide-generating forces are 52 53 89 small. Significant tides, though typically <1 m in tidal range (the difference in sea level between 54 55 90 high and low tide), only develop in the open oceans. Smaller enclosed water bodies (seas, lakes) 56 57 58 91 and water on continental shelves do not develop appreciable in situ tides (Dalrymple, 1992). 59 60 4 61 62 63 64 65 1 2 3 4 92 5 6 7 93 Tides are most commonly understood in the context of equilibrium tidal theory, in which the 8 9 94 Earth is covered by water of uniform depth that responds instantaneously to changes in tractive 10 11 12 95 forces and the Moon rotates around the equator at a constant distance (e.g. MacMillan, 1966; 13 14 96 Dalrymple, 1992) The lunar tidal force, in combination with centrifugal forces associated with 15 16 97 the rotation of the earth-moon system about its common centre of mass, leads to the development 17 18 19 98 of two oceanic tidal bulges: one beneath the moon, one on the opposite side of the Earth. The 20 21 99 rotation of Earth every 24 hours, and the Moon around the Earth every 29 days (in the same 22 23 24 100 direction as the Earth rotates), means these bulges appear to move clockwise around the Earth. 25 26 101 This produces two high and two low (semi-diurnal) tides each day at a period of 12.42 hours, 27 28 29 102 with rising and falling tides termed ‘flood tide’ and ‘ebb tide’, respectively (Dalrymple, 1992). 30 31 103 Equilibrium model tides vary on many timescales due to changes in the magnitude of the tide- 32 33 34 104 generating forces produced by the Sun and Moon (Defant, 1961; MacMillan, 1966; Dalrymple, 35 36 105 1992; Kvale, 2006). For example, spring-neap tidal cycles (14.77 days) are caused by the relative 37 38 106 positioning of the Earth, Sun and Moon. Spring tides occur when the Earth, Moon and Sun are 39 40 41 107 aligned in a straight line at new or full Moon, resulting in greater than average tidal ranges. In 42 43 108 contrast, neap tides occur when the Sun and Moon are at right angles to the Earth at first- and 44 45 46 109 third-quarter phases of the Moon, resulting in smaller tidal ranges (Fig. 1A and B). The time 47 48 110 between successive new moons is called the ‘synodic month’, which has a modern period of 49 50 51 111 29.53 days and encompasses two spring-neap cycles. For semi-diurnal tides, each spring-neap 52 53 112 cycle (every 14.77 days) contains up to 28 tidal cycles (Dalrymple, 1992; Kvale, 2006). 54 55 113 Furthermore, due to the tilt of the Earth’s axis, the declination of the Moon varies by 28.5˚ north 56 57 58 114 and south of the equator monthly (Fig. 1C). Daily, the declination of the Moon can lead to one 59 60 5 61 62 63 64 65 1 2 3 4 115 semi-diurnal tide being higher (dominant) than the other (subordinate), which is termed ‘diurnal 5 6 7 116 inequality’ (Fig. 1D). Monthly, there is a ‘tropical’ spring–neap cyclicity with increased diurnal 8 9 117 inequality when the Moon is at its maximum declination (Fig. 1D) (e.g. Kvale, 2012). 10 11 12 118 13 14 119 While equilibrium tidal theory explains the astronomical forcing causing tides, real-world tides 15 16 120 are complicated by several factors. First, a mean ocean depth of c. 22 km is needed to account 17 18 19 121 for rotation of a tidal bulge around the circumference of the Earth in 24 hours, whereas the mean 20 21 122 measured ocean depth is c. 4 km (Wells et al., 2005a). Second, ocean basins are interrupted by 22 23 24 123 landmasses and the ocean water depth varies globally, which means two bulges either side of the 25 26 124 Earth cannot exist. Instead, oceanic tides rotate as waves around fixed (amphidromic) points with 27 28 29 125 negligible tidal amplitude (half the tidal range) (Fig. 2). Third, inertia and friction mean that the 30 31 126 ocean does not respond instantaneously to the tidal forcing. Last, equilibrium tidal theory does 32 33 34 127 not explain the occurrence of the following: (1) diurnal (one high tide and one low tide in a tidal 35 36 128 day) tides in low latitude positions, which are only predicted at high latitudes; (2) mid-latitude 37 38 129 semi-diurnal tides with minimal diurnal inequality; and (3) spring-neap cycles synchronized with 39 40 41 130 the 27.32 day (tropical month) lunar orbital cycle of the Moon (tropical month), rather than the 42 43 131 more common 29.53 day cycle of lunar phases (synodic month or ‘lunar month’). 44 45 46 132 47 48 49 50 51 52 53 54 55 56 57 58 59 60 6 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 133 34 35 134 Fig. 1. (A) Astronomical explanation of synodic spring-neap tidal cycles. Synodic spring tides 36 37 135 occur when the Sun and Moon are above the same line of Earth’s longitude (conjunction) or are 38 39 136 180° of longitude apart (opposition). Synodic neap tides occur when the Sun and Moon are 40 137 separated by 90° of Earth’s longitude. (B) Graph of equilibrium tidal amplitude over a 30-day 41 42 138 period displaying synodic spring-neap tidal cycles caused by the interaction of M2 and S2 tidal 43 44 139 constituents. (C) Monthly variation in the Moon’s declination between 28.5˚ north and south of 45 46 140 the Earth’s equatorial plane caused by the tilt of the Earth’s axis, which is accounted for by the 47 48 141 K1 and O1 tidal constituents (Table 1). (D) Graph of equilibrium tidal amplitude over a 27-day 49 50 142 period caused by the interaction of the M2 and K1 tidal constituents. Daily, one tide is larger than 51 143 the other (diurnal inequality). Monthly, there is a ‘tropical’ spring-neap cyclicity of more 52 53 144 pronounced diurnal inequality when the Moon is at its maximum declination north or south of 54 55 145 the equator. N—Moon north of the Equator; W—Moon west of the equator; S—Moon south of 56 57 146 the equator; E—Moon east of the equator. After Wells (2008). 58 59 60 7 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 147 8 61 62 63 64 65 1 2 3 4 148 Fig. 2. (A) Present day global tidal range based on the FES 2014 tidal model (Carrère et al., 5 6 149 2015), showing the locations (pink dots) of tide-dominated deltas (Goodbred and Saito, 2012): 7 8 150 A) Copper; B) Colorado; C) Amazon; D) Shatt-al-Arab; E) Indus; F) Ganges-Brahmaputra; G) 9 10 151 Irrawaddy; H) Red River; I) Yangtze; J) Mekong; K) Rajang; L) Mahakam; and M) Fly. Pink 11 12 152 boxes show approximate locations of the palaeotidal modelling case studies. (B, C) Global map 13 153 of M (B) and K tidal amplitude (C) from FES 2014. Contours join lines of equal phase in 30° 14 2 1 15 154 intervals and white arrows give the sense of rotation of the major ocean amphidromic systems. 16 17 155 (D) Maximum tidal bed shear stress, plotted as the equivalent grain size that could be entrained if 18 19 156 available, for FES2014, including the difference in sediment grain size class. Grain size 20 21 157 abbreviations: vf = very fine; f = fine; m = medium; c = coarse; vc = very coarse. 22 23 158 24 25 159 2.1.2 Dynamic tidal theory 26 27 160 Given the limitations of equilibrium tidal theory, real-world tides are more accurately explained 28 29 30 161 by dynamic tidal theory. In this model, the tidal forcing due to the movement and angular speed 31 32 162 of the Moon and Sun are modelled as the combined effects of a series of imaginary satellites 33 34 35 163 (Foreman and Henry, 1979; Pugh, 1987; Kvale, 2006; Kvale, 2012). Each modelled satellite 36 37 164 generates its own tidal wave of a given tidal amplitude, period and phase angle (response time) 38 39 40 165 moving around an amphidromic point (Pugh, 1987; Kvale, 2006; Kvale, 2012). Each tide is 41 42 166 referred to as a tidal constituent, each of which are represented by alphanumeric terms and can 43 44 167 be derived from the harmonic decomposition of tidal station water level measurements. From 45 46 47 168 over 100 possible tidal constituents, 11 account for c. 82% of the variability observed in 48 49 169 measured tides (Table 1) (e.g. Defant, 1961; Kantha and Clayson, 2000). The main tidal cycles 50 51 52 170 (i.e. synodic, tropical and anomalistic) are related to harmonic convergence and divergence of 53 54 171 major tidal constituents, most notably: (1) diurnal inequality exists because the O1 and M2 tidal 55 56 57 172 constituents are in phase only once a day; (2) synodic neap–spring cycles are generated when the 58 59 60 9 61 62 63 64 65 1 2 3 4 173 M2 and S2 constituents are in phase (every 14.77 days); and (3) tropical neap–spring cycles 5 6 7 174 reflect the convergence of the K1 and O1 constituents (every 13.66 days) (Kvale, 2006; Kvale, 8 9 175 2012). Amphidromic systems are primarily the result of the combined interaction of tidal 10 11 12 176 constituents, basin geometry and the Coriolis force. Table 2 provides a summary of key tide- 13 14 177 related terms. 15 16 178 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 179 47 180 Table 1. Origin, period (in solar hours, hr or days, d) and equilibrium amplitude of 11 important 48 49 181 tidal constituents (after Defant, 1961; Kantha and Clayson, 2000; Wells, 2008). 50 51 182 52 53 54 55 56 57 58 59 60 10 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 183 34 35 36 184 Table 2. Explanations of several tide-related terms used in this paper (modified from Wells et 37 185 al., 2010b). 38 39 186 40 41 42 187 2.1.3 Shoaling, funneling and resonance effects on tides 43 44 188 When oceanic tides encounter areas of shallower water and constricted physiography, they may 45 46 47 189 undergo amplification due to shoaling, funnelling and resonance (Table 2). 48 49 190 50 51 191 Shoaling effects involve a transformation of the tidal wave in order to conserve the energy flux. 52 53 54 192 This occurs by a reduction in the wave speed and wavelength and an associated increase in the 55 56 193 wave amplitude and the current velocity (Allen, 1997). Assuming a flat bed and ignoring 57 58 59 60 11 61 62 63 64 65 1 2 3 4 194 reflected energy and bottom drag, the relative change in amplitude is proportional to the 5 6 7 195 quadratic root of the relative change in water depth: 8 9 10 11 12 196 13 14 15 197 where, h1 and h2 are the deep and shallow water depths and A1 and A2 are the corresponding 16 17 198 amplitudes, respectively (Allen, 1997). The relative current velocity U (ms−1) increases by 18 19 20 21 22 23 199 24 25 200 where subscripts 1 and 2 denote the initial deep shallow water depths, respectively (Allen, 1997). 26 27 201 28 29 30 202 Funnelling of a tidal wave occurs when the flow is physically constricted by a physiographic 31 32 203 feature like a strait or embayment. For a landward-tapering and landward-shallowing 33 34 204 embayment, assuming that energy is conserved and ignoring bottom friction, the combined effect 35 36 37 205 of funnelling and shoaling (convergence effects) are estimated by 38 39 40 41 206 42 43 207 where A= tidal range (m), w = water body width (m), h = water body depth (m), subscript ‘o’ 44 45 46 208 denotes the open deeper water body and subscript ‘e’ the constricted shallower water body 47 48 209 (Slingerland, 1986; Allen, 1997). The comparison between theoretical convergence effects (Ae/ 49 50 51 210 Ao) on tides in ancient physiographic embayments calculated using this equation, and tidal 52 53 211 amplitude and convergence effects predicted by palaeotidal modelling, can illustrate the possible 54 55 56 212 effects of bottom friction and attenuation by physiographic features (e.g. shoals, islands, 57 58 213 headlands) (Wells et al., 2007a; Collins et al., 2018a). 59 60 12 61 62 63 64 65 1 2 3 4 214 5 6 7 215 Resonance occurs when the natural period of oscillation on the shelf, or within a shoreline 8 9 216 bathymetric constriction, is coincident with the tidal period (Slingerland, 1986; Allen, 1997). For 10 11 12 217 an idealized straight and laterally extensive continental shelf, tidal resonance reaches a maximum 13 14 218 when shelf width is one-quarter the tidal wavelength (and for widths 3/4, 5/4, etc.), assuming the 15 16 219 incident tide is perpendicular to the shelf, friction is inversely proportional to depth and no 17 18 19 220 Coriolis effect (Fig. 3A) (e.g. Proudman, 1953; Howarth, 1982). The resonance pattern is likely 20 21 221 to be similar if bathymetry and rotational effects are included (Howarth, 1982). However, the 22 23 24 222 wavelength of tides strongly depends on the dominant phase and water depth (Fig. 3B). At 25 26 223 typical continental shelf water depths (100 m), the wavelengths of the semi-diurnal M2 and 27 28 29 224 diurnal K1 tides are 1,400 km and 2,700 km, respectively (Fig. 3B) (Kowalik and Luick, 2013). 30 31 225 Therefore, resonance of M2 and K1 tides requires very different shelf widths of 350 km and 675 32 33 34 226 km, respectively. As the majority (c. 70%) of modern shelves are <75 km wide (Nyberg and 35 36 227 Howell, 2016), tides are closer to resonance as shelf width increases, hence tidal amplitude 37 38 228 increases with shelf width (Redfield, 1958; Off, 1963; de Vries Klein, 1977; Cram, 1979; 39 40 41 229 Ainsworth et al., 2011). High tidal ranges along embayed coasts occur partly as a consequence of 42 43 230 the effective widening of the shelf, with the tidal system closer to resonance (e.g. Willis, 2005). 44 45 46 231 For a closed or ‘blind’ embayment (gulf), the simplest period of resonance (T) is a quarter 47 48 232 wavelength 49 50 51 52 53 54 233 55 56 57 58 59 60 13 61 62 63 64 65 1 2 3 4 234 where l = embayment length (m), g = gravitational acceleration (ms-2), and h = embayment depth 5 6 7 235 (m) (e.g. Allen, 1997). In an ‘enclosed’ water body, the simplest period of resonance (T) is a half 8 9 236 wavelength 10 11 12 13 14 237 15 -2 16 238 where l = basin width (m), g = gravitational acceleration (ms ) and h = water depth (m) (e.g. 17 18 239 Allen, 1997). In these situations, resonance occurs when the tidal wave reflected off one 19 20 21 240 boundary of the embayment entrance reaches the opposite boundary (for a partly enclosed water 22 23 241 body) at the same time as another tidal wave begins to propagate, such that the waves 24 25 26 242 constructively interfere. 27 28 243 29 30 244 Tidal resonance in embayments is illustrated by using the tidal model Fluidity (Section 3.1) and 31 32 33 245 simple physiographic box models that were centred on the equator, ranged between 0 to 3000 km 34 35 246 wide and 0 to 300 m deep (192 experiments in total), and had a constant bottom drag coefficient 36 37 38 247 of 0.0025 and mesh resolution of c. 15 km (Fig. 4) (Wells, 2008). The model was forced with the 39 40 248 M2, S2, K1, and O1 tidal constituents such that the total boundary tide amplitude was 1 m, the 41 42 43 249 total amplitudes of semidiurnal (i.e. M2+S2) and diurnal (i.e. K1+O1) constituents were equal, and 44 45 250 the ratios of the M2 to S2 constituents and K1 to O1 constituents were equal to the ratio of their 46 47 48 251 equilibrium amplitudes (Table 1). The modelled tidal range at the head of the embayment was 49 50 252 plotted on a graph of basin width versus depth, which illustrates that even the shallowest basins 51 52 253 must be several hundred kilometres wide to attain resonance (Fig. 4). 53 54 55 254 The relative importance of diurnal (K1 and O1) to semidiurnal (M2 and S2) tides is quantified 56 57 255 using the ratio F, where 58 59 60 14 61 62 63 64 65 1 2 3 4 5 6 7 256 8 9 10 257 If F<0.25, the tide is semi-diurnal, 0.25
4 middle Seaway of finite element P1, K1, Mf, Mm and Ssa tidal mesotidal (2–4 m) along most of 5 Campanian, c. North America scheme; Navier constituents; Variable the eastern margin of the seaway; 6 75-77.5 Ma Stokes equations; bathymetry; Bottom drag increased tidal bed shear stress 7 8 (Dean et al., Coriolis parameter applied as surface-integral when seaway center and entrance 9 2019) included. based on quadratic friction to Gulf of Mexico are deeper. 10 law. 11 290 12 13 14 291 Table 3. Summary of previously published palaeotidal models from deep geologic time 15 16 292 (excluding the Quaternary). 17 18 293 19 20 21 294 2.2 Process-based sedimentological analysis 22 23 295 The study and interpretation of ancient physical processes from sedimentary rocks requires a 24 25 26 296 rigorous, multi-scale approach that has developed over the last 60–70 years (see reviews by 27 28 297 Walker and Plint, 1992; Reading, 1996). The approach is underpinned by rigorous facies 29 30 31 298 analysis, which relies on detailed, qualitative descriptions of distinctive combinations of 32 33 299 sedimentary and biological structures (e.g. Reading, 1978; Reading, 1996)}(De Raaf et al., 1965; 34 35 300 Walker, 1979; Anderton, 1985). However, small-scale (c. 1–100s cm) facies are typically based 36 37 38 301 on subtle differences that are non-unique in terms of depositional processes and environment 39 40 302 (Walker and James, 1992). Process and environment interpretation more readily occurs at the 41 42 43 303 facies association (typically several metres to 10s metre) and facies succession (10s-100s m) 44 45 304 levels but even at these scales process and environment interpretation may remain ambiguous 46 47 48 305 (Walker and James, 1992; Dalrymple, 2010; Colombera and Mountney, 2020b). Understanding 49 50 306 the relationship between process, sedimentation and resultant sedimentary structures and 51 52 307 stratigraphy ideally requires close comparison to the modern, where these aspects may be 53 54 55 308 observed and measured directly in different environments (Middleton, 1965; Allen, 1968; Allen, 56 57 309 1982b; Collinson and Mountney, 2019). 58 59 60 20 61 62 63 64 65 1 2 3 4 310 5 6 7 311 In shoreline systems, the process-based sedimentological approach centres upon determining the 8 9 312 relative influence of river, wave and tide processes, with the inherent understanding that these 10 11 12 313 are characterised by different groups of physical process types, principally unidirectional and 13 14 314 bidirectional traction currents and gravitational, oscillatory and suspension flow processes. The 15 16 315 application of a three-tier process classification depends on: (1) the availability and quality of the 17 18 19 316 rock data; and (2) the process implications of sedimentological and biological features. However, 20 21 317 both these considerations are subject to potential biases. For example, higher-quality exposure 22 23 24 318 may be sandstone dominated due to preferential weathering of finer-grained or thinner-bedded 25 26 319 facies, the identification and interpretation of which often requires exceptional outcrop or core 27 28 29 320 data quality. Furthermore, sediment texture, particularly grain size distribution, has a significant 30 31 321 control on the type of sedimentary structures and facies formed, and can vary significantly 32 33 34 322 between different sedimentary systems (Jopling and Walker, 1968; Allen, 1982b; Harms et al., 35 36 323 1982; Kvale et al., 1989; Orton and Reading, 1993; Yoshida et al., 2007). 37 38 324 39 40 41 325 A statistical method for classifying shoreline deposits involves assigning a percentage likelihood 42 43 326 that a bed or stratal unit was formed by wave, tide or fluvial processes (‘process percentage’) and 44 45 46 327 quantifying the relative proportion of each bed or stratal unit (Rossi et al., 2017; Peng et al., 47 48 328 2018). The ‘process percentage’ is determined based on the proportion of preserved sedimentary 49 50 51 329 structures, and also the proportion of wave-, tide- or fluvial-dominated interpretations of each 52 53 330 sedimentary structure in an extensive literature database (Rossi et al., 2017; Peng et al., 2018). 54 55 331 However, end-member process interpretations of various sedimentary structures are commonly 56 57 58 332 ambiguous, and it is difficult to assign percentage values to those formed by combined processes. 59 60 21 61 62 63 64 65 1 2 3 4 333 Whilst this statistical method provides a theoretical framework for more accurate estimation of 5 6 7 334 process variability, in reality interpretations may be subjective and biased, partly reflecting 8 9 335 uncertainties in original literature studies and revisions in process interpretations of different 10 11 12 336 sedimentary structures. Indeed, original literature interpretations may have skewed, and even 13 14 337 self-reinforced, the process interpretation of some key sedimentary structures and facies 15 16 338 (Colombera et al., 2012; Rossi et al., 2017). For example, it is now recognized that heterolithic 17 18 19 339 facies are not limited to tidal settings, as was originally emphasized (e.g. Reineck and 20 21 340 Wunderlich, 1968), but can form in a wider range of depositional environments (e.g. Ainsworth 22 23 24 341 et al., 2012). This effect is captured in the growing uncertainty regarding the process 25 26 342 classification of heterolithic deposits in terms of the balance of fluvial versus tidal processes, 27 28 29 343 especially: (1) those displaying unidirectional-dominated, current ripple cross-lamination (e.g. 30 31 344 Dalrymple et al., 2015; Gugliotta et al., 2016b; Kurcinka et al., 2018; Collins et al., 2020; Van 32 33 34 345 Yperen et al., 2020), including within inclined heterolithic strata (Thomas et al., 1987; Martinius 35 36 346 et al., 2015; Jablonski and Dalrymple, 2016); and (2) discriminating between tidal influence 37 38 347 (secondary process) versus tidal modulation (tertiary processes) in cross-stratification (Martinius 39 40 41 348 and Gowland, 2011; Gugliotta et al., 2016a) (Martinius et al., 2015). Similarly, hummocky and 42 43 349 swaley cross-stratification with mudstone drapes have been interpreted to record mixed storm 44 45 46 350 and tidal processes (Vakarelov et al., 2012; Wei et al., 2016), but the variability in flow and 47 48 351 sedimentation required for mud draping may occur inherently occur during storm flows (e.g. 49 50 51 352 Collins et al., 2017b). A further example is the process origin of hummocky and swaley cross- 52 53 353 stratification and related structures (e.g. combined-flow ripples and planar lamination), including 54 55 354 the balance of oscillatory to unidirectional flow and the influence of hyperpycnal flow (Dott and 56 57 58 355 Bourgeois, 1982; Arnott and Southard, 1990; Myrow and Southard, 1996; Myrow et al., 2002; 59 60 22 61 62 63 64 65 1 2 3 4 356 Dumas and Arnott, 2006; Lamb et al., 2008; Tinterri, 2011; Basilici et al., 2012; Perillo et al., 5 6 7 357 2014). Consequently, assigning the relative contribution of wave, tidal or fluvial processes to a 8 9 358 given sedimentary structure remains uncertain. 10 11 12 359 13 14 360 2.3 Classification and prediction of shoreline depositional process regime 15 16 361 2.3.1 Process classifications 17 18 19 362 Shoreline systems encompass a wide range of depositional settings, including deltas, 20 21 363 strandplains, estuaries, barrier islands and a host of sub-environments (e.g. lagoons, tidal flats, 22 23 24 364 distributary channels, mouth bars, etc.). Seminal models for clastic shoreline systems initially 25 26 365 focused on modern deltas, particularly the relationship between delta front morphology and the 27 28 29 366 relative influence of wave, tidal and fluvial process (Coleman and Wright, 1975; Galloway, 30 31 367 1975). This ternary classification scheme was widely adopted and modified to include a wider 32 33 34 368 range of depositional settings by Boyd et al. (1992), notably the bivariate wave versus tide 35 36 369 classification of clastic coasts (Hayes, 1975; Hayes, 1979) and variability in grain size (Orton 37 38 370 and Reading, 1993). Furthermore, Boyd et al. (1992) and Dalrymple et al. (1990) interpreted the 39 40 41 371 predictive evolutionary relationships between long-term equilibrium depositional environments 42 43 372 and the rates of sediment supply versus relative sea level change (shoreline transgression vs. 44 45 46 373 regression). The most recent manifestation of the ternary classification scheme has been a more 47 48 374 detailed descriptive process model of the spectrum of shoreline systems, including aspects of 49 50 51 375 their spatial and temporal variability (Ainsworth et al., 2011). 52 53 376 54 55 377 However, Ainsworth et al. (2011) also noted that these relatively long-term equilibrium models 56 57 58 378 are unable to predict more precise process variations in space at a given time (‘environmental 59 60 23 61 62 63 64 65 1 2 3 4 379 disequilibrium’; (Boyd et al., 1992). In addition, they cannot convolve the effects of dynamic 5 6 7 380 temporal changes (at varying timescales) in depositional processes caused by (1) changes in 8 9 381 shoreline physiography (morphology and bathymetry), (2) fluctuations in accommodation space 10 11 12 382 creation versus sediment supply rates, and (3) variations in regional basin physiography. 13 14 383 15 16 384 Within individual shoreline systems, complex arrangements of discrete depositional elements 17 18 19 385 attributed to different combinations of wave, tide and fluvial processes have been recognized in 20 21 386 analyses of: (1) modern delta geomorphology and sedimentological data, including the Danube 22 23 24 387 (e.g. Bhattacharya and Giosan, 2003), Ganges-Brahmaputra (e.g. Willis, 2005), Mahakam (e.g. 25 26 388 Allen and Chambers, 1998), Mekong (e.g. Nguyen et al., 2000; Ta et al., 2002b), Mitchell (e.g. 27 28 29 389 Nanson et al., 2013) and Changjiang (Yangtze) (e.g. Hori et al., 2002) deltas; and (2) 30 31 390 approximately contemporaneous ancient stratigraphic units, including the Permian Kookfontein 32 33 34 391 and Waterford formations in the Karoo Basin (Gomis-Cartesio et al., 2016), Cretaceous Ferron 35 36 392 Sandstone, Western Interior Seaway (e.g. Gardner et al., 2004; Bhattacharya and MacEachern, 37 38 393 2009; Li et al., 2011; Li et al., 2015), Cretaceous Sego Sandstone, Western Interior Seaway 39 40 41 394 (Willis and Gabel, 2001; Legler et al., 2014; van Cappelle et al., 2016), Cretaceous Horseshoe 42 43 395 Canyon Formation, Western Interior Seaway (Willis and Gabel, 2001; Legler et al., 2014; 44 45 46 396 Ainsworth et al., 2015; Ainsworth et al., 2016; van Cappelle et al., 2016) and Miocene Belait 47 48 397 Formation, NW Borneo (Lambiase et al., 2003; Collins et al., 2017b; Collins et al., 2018b). 49 50 51 398 Consequently, these and many other depositional systems indicate frequent mixed-process 52 53 399 regimes, with variable wave, tide and fluvial interactions in both space (e.g. along and/or 54 55 400 perpendicular to depositional strike) and time (on various timescales e.g. daily, seasonal, annual 56 57 58 401 or longer). These mixed-energy systems cannot be fully resolved in the early process 59 60 24 61 62 63 64 65 1 2 3 4 402 classification models (Coleman and Wright, 1975; Galloway, 1975; Boyd et al., 1992). 5 6 7 403 Therefore, Ainsworth et al. (2011) developed a new semi-quantitative, process-based 8 9 404 classification scheme based on the relative importance of primary, secondary and tertiary 10 11 12 405 processes (generating ‘dominated’, ‘influenced’ or ‘affected’ descriptors, respectively). This 13 14 406 higher-resolution process-based approach enables a more rigorous comparison of modern and 15 16 407 ancient shoreline deposits (Fig. 5A). However, a quantitative process analysis of modern 17 18 19 408 shorelines by Nyberg and Howell (2016) suggests the thresholds separating primary, secondary 20 21 409 and tertiary processes are ambiguous, resulting in these authors favouring a two-tier 22 23 24 410 classification (Fig. 5B). Furthermore, the additional ambiguity in the process interpretation of 25 26 411 several common sedimentary structures means that most studies of ancient, mixed-process 27 28 29 412 shoreline deposits have adopted a two-tier process classification (e.g. Bhattacharya and Giosan, 30 31 413 2003; Lambiase et al., 2003; Coates and MacEachern, 2007; Gani and Bhattacharya, 2007; 32 33 34 414 Hansen et al., 2007; Buatois et al., 2012; Vakarelov et al., 2012; Amir Hassan et al., 2013; Legler 35 36 415 et al., 2013; Chen et al., 2014; Legler et al., 2014; Ainsworth et al., 2015; Gugliotta et al., 2015; 37 38 416 Li et al., 2015; Ainsworth et al., 2016; Amir Hassan et al., 2016; Gomis-Cartesio et al., 2016; 39 40 41 417 Gugliotta et al., 2016a; Rossi and Steel, 2016; Vaucher et al., 2016; Collins et al., 2017b; Collins 42 43 418 et al., 2018b). 44 45 46 419 47 48 49 50 51 52 53 54 55 56 57 58 59 60 25 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 420 24 25 421 Fig. 5. Two contrasting ternary process classifications for shoreline depositional systems. (A) 26 27 422 The three-tier classification of Ainsworth et al. (2011) utilizes primary, secondary, and tertiary 28 29 423 processes, which are referenced as ‘dominated’ (capitalized and bold), ‘influenced’ (lower case 30 31 424 and bold) and ‘affected’ (lower case italics and not bold), respectively. For example, wave 32 425 dominated, tide influenced and fluvial affected is written Wtf. (B) The two-tier classification of 33 34 426 Nyberg and Howell (2016) recognizes the primary and secondary processes, and is favored in 35 36 427 this study (see text for discussion). 37 38 428 39 40 429 2.3.2 Process classification of present-day global shorelines 41 42 43 430 Nyberg and Howell (2016) developed the first, systematic, semi-automated classification of 44 45 431 global shoreline process regime (Fig. 6) by combining several datasets and methodologies: (1) 46 47 48 432 proxies for wave, tide and fluvial processes, including wave height, tidal amplitude and river 49 50 433 discharge; (2) depositional versus erosional shorelines, determined by combining global 51 52 434 lithology maps and digital elevation models; and (3) algorithms for determining the ‘tidal 53 54 55 435 coefficient’ for modifying tidal amplitude using shoreline rugosity or ‘roughness index’. This 56 57 436 integrated approach predicts shoreline classification with an 85% success rate compared to 58 59 60 26 61 62 63 64 65 1 2 3 4 437 manual interpretation based principally on shoreline morphology (e.g. Ainsworth et al., 2011), 5 6 7 438 and is consistent with earlier comparisons of shoreline morphology with quantitative metrics of 8 9 439 wave, tide and river power along large, but non-global, stretches of siliciclastic coastlines (e.g. 10 11 12 440 Harris et al., 2002). By subdividing the global shoreline into 5 km segments, this methodology 13 14 441 classifies 28% of global shorelines as depositional, of which 62% are wave-dominated, 35% 15 16 442 tide-dominated and 3% fluvial-dominated (Fig. 6A) (Nyberg and Howell, 2016). On a global 17 18 19 443 scale, over 90% of shorelines on narrow shelves (≤25 km) are wave-dominated and <5% tide- 20 21 444 dominated, whereas over 30% of shorelines on wide shelves (>75 km) are tide-dominated (Fig. 22 23 24 445 6B). Along depositional shorelines, tide dominance increases from <20% on narrow shelves to 25 26 446 >50% on wide shelves (Fig. 6C). Fluvial systems along shorelines are more wave modified on 27 28 29 447 narrow shelves and more tide modified on wide shelves (Fig. 6B and C). 30 31 448 32 33 34 449 Tide-dominated deltas are widely distributed (Figs 2A and 6A), including: (1) at low and high 35 36 450 latitudes; (2) along open-ocean shorelines and in partly enclosed oceans and seas; and (3) along 37 38 451 straight and highly embayed shorelines. Their locations encompass a range of tectonic settings, 39 40 41 452 including strike-slip transtensional rift (e.g. Colorado delta), forearc (e.g. Cooper delta), foreland 42 43 453 (e.g. Mahakam and Fly deltas) and passive margin settings (Ganges Brahmaputra delta) (Nyberg 44 45 46 454 and Howell, 2016). Whilst tide-dominated deltas preferentially occur along macrotidal shorelines 47 48 455 (Fig. 2A), they also occur along mesotidal shorelines (e.g. Mekong and Mahakam deltas). 49 50 51 456 However, tide-dominated deltas exclusively occur along shorelines with elevated tidal bed shear 52 53 457 stresses, where tidal currents at their maximum strength are capable of transporting at least 54 55 458 coarse sand (Fig. 2D). 56 57 58 459 59 60 27 61 62 63 64 65 1 2 3 4 460 Although the Nyberg and Howell (2015) classification provides a consistent, reproducible 5 6 7 461 approach for identifying process distribution along global shorelines, it has significant 8 9 462 limitations. There are inherent biases between shoreline morphology and process dominance: i.e. 10 11 12 463 more rugose and funnel-shaped shorelines are inherently biased towards tide dominance and 13 14 464 smoother shorelines towards wave-dominance. None of the tidal coefficients consider theoretical 15 16 465 and quantifiable relationships between shoreline physiography and the tidal prism. Lastly, wave 17 18 19 466 height and tidal range are inadequate proxies for differentiating wave- and tide-dominance in 20 21 467 mixed-energy systems (e.g. Anthony and Orford, 2002; Mulhern et al., 2017) because these 22 23 24 468 parameters are not directly related to sediment entrainment (unlike bed shear stress). 25 26 469 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 28 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 470 39 40 471 Fig. 6. Quantification of modern global shoreline process regimes (from Nyberg and Howell, 41 42 472 2016). (A) Two-tier ternary process classification of modern shorelines (see Fig. 5B) showing 43 44 473 the locations (pink dots) of tide-dominated deltas (Goodbred and Saito, 2012): A) Copper; B) 45 46 474 Colorado; C) Amazon; D) Shatt-al-Arab; E) Indus; F) Ganges-Brahmaputra; G) Irrawaddy; H) 47 48 475 Red River; I) Yangtze; J) Mekong; K) Rajang; L) Mahakam; and M) Fly. Figures 2A and D 49 50 476 show the same delta locations on a global map of tidal range and tidal bed shear stress, 51 477 respectively. (B) Proportion of the two-tier process classifications along depositional shorelines. 52 53 478 (C) Relationship between binned shelf width and proportion of the two-tier process classification 54 55 479 along depositional shorelines. The miscellaneous class is for shallow seas and seaways (e.g. 56 57 480 Baltic and Red seas). 58 59 60 29 61 62 63 64 65 1 2 3 4 481 5 6 7 482 2.3.3 Prediction of ancient shoreline process regime 8 9 483 Ainsworth et al. (2011) extended previous process-based models of shoreline systems by 10 11 12 484 introducing other critical aspects to the palaeoenvironmental diagnosis, most notably: (1) basin 13 14 485 physiography (100–1000 km scale), (2) shelf width (10–100 km scale), (3) fluvial versus wave 15 16 486 effectiveness, (4) accommodation versus sediment supply (A/S ratio), and (5) shoreline 17 18 19 487 morphology (1–10 km scale). These were incorporated into a predictive decision tree (Fig. 7A) 20 21 488 and matrices (Fig. 7B and C) for shoreline depositional process regime. 22 23 24 489 25 26 490 Basin physiography and shelf width are combined to determine the ‘tidal resonance potential of 27 28 29 491 the basin’, which is the first query on the decision tree (Fig. 7A) and distinguishes two predictive 30 31 492 matrices (Fig. 7B and C). Tidal resonance occurs when the natural period of oscillation on the 32 33 34 493 shelf, or within a shoreline embayment, is coincident with the tidal period (Slingerland, 1986; 35 36 494 Allen, 1997; Collins et al., 2018b). In the predictive model, the interpretation of tidal resonance 37 38 495 potential is calibrated empirically to shelf width (cf. Howarth, 1982). Since analysis of present- 39 40 41 496 day shorelines suggests that they are more likely to be tide-dominated adjacent to shelves greater 42 43 497 than 75 km in width (Heap et al., 2004; Ainsworth et al., 2011), a shelf width of 75 km is an 44 45 46 498 approximate empirical cut-off between modern and ancient shorelines with lower (<75 km shelf 47 48 499 width) and higher tidal potential (>75 km shelf width), respectively. 49 50 51 500 52 53 501 The effect of basin physiography is complicated by (1) the influence of tidal inflow versus 54 55 502 outflow to partly enclosed water bodies, and (2) the funnelling, shoaling and resonance effects on 56 57 58 503 continental shelves and within shoreline embayments, which occur on a range of scales (c. 1– 59 60 30 61 62 63 64 65 1 2 3 4 504 1000s km width and 1–100s m depth) (Mitchell et al., 2010; Wells et al., 2010b; Collins et al., 5 6 7 505 2018b). However, despite this complexity, basin physiography does not constitute a separate 8 9 506 query in the predictive model (Fig. 7) and is treated as a modifying factor to shelf tidal resonance 10 11 12 507 potential (Ainsworth et al., 2011). Open oceans are sufficiently large to allow generation of 13 14 508 relatively high in-situ tides (Dalrymple, 1992). Therefore, basins that have restricted access to 15 16 509 the open oceans generally have a lower potential for producing amplified tidal currents by 17 18 19 510 resonance effects, whereas basins with less restricted access to open oceans have a higher tidal 20 21 511 resonance potential. An exception is that certain restrictive basin physiographies, typically on a 22 23 24 512 smaller-scale (1–10s km), may cause significant amplification of tides by funnelling, shoaling 25 26 513 and/or resonance effects (Piper et al., 1990; Martel et al., 1994) (Mitchell et al., 2010; Ainsworth 27 28 29 514 et al., 2011; Mitchell et al., 2011) (Androsov et al., 2002; Leckie and Rumpel, 2003). 30 31 515 Consequently, the generalized treatment of basin physiography in the existing predictive model 32 33 34 516 (Ainsworth et al., 2011) combines two very different effects on tides relating to: (1) basin 35 36 517 geography (100–1000 km width scale) and bathymetry (100–1000 m depth scale), which has a 37 38 518 first order control on the balance of tidal inflow versus outflow; and (2) second-order funnelling 39 40 41 519 and resonance effects relating to basin physiography (10–100s km width scale and 1–100s m 42 43 520 depth scale) (Wells et al., 2005a; Wells et al., 2007a; Mitchell et al., 2010; Wells et al., 2010b; 44 45 46 521 Collins et al., 2018a). Distinguishing between these two controls of basin physiography is 47 48 522 achieved most rigorously through numerical tidal modelling (Slingerland, 1986; Martel et al., 49 50 51 523 1994; Wells et al., 2007a; Collins et al., 2018a). 52 53 524 54 55 525 Fluvial versus wave effectiveness is related to ancient shoreline palaeogeography. Hence, 56 57 58 526 shorelines facing large open water bodies are likely to be strongly influenced by wind-driven 59 60 31 61 62 63 64 65 1 2 3 4 527 waves, with a large fetch resulting in a relatively high wave effectiveness. In contrast, shorelines 5 6 7 528 that are more sheltered from direct oceanic waves and/or face smaller water bodies experience 8 9 529 lower wave effectiveness. Fluvial effectiveness is controlled by a range of continental processes, 10 11 12 530 including climate, weathering, river hydrology, drainage basin area, slope of the alluvial plain, 13 14 531 and hinterland relief and gradient. Predictions of higher fluvial effectiveness must be supported 15 16 532 by palaeogeographic, palaeodrainage and palaeohydrological reconstructions, especially where 17 18 19 533 these indicate proximity to large fluvial drainage areas. Consequently, wave and fluvial 20 21 534 effectiveness are determined by very different factors. Hence, determining the nature of wave 22 23 24 535 and fluvial interactions, including predictions of their relative effectiveness, must rely on facies 25 26 536 analysis of preserved stratigraphy. 27 28 29 537 30 31 538 The rate of accommodation space creation versus sediment supply (A/S ratio) is a useful 32 33 34 539 theoretical concept (Muto and Steel, 1997) but difficult to apply practically, even for extensive 35 36 540 datasets (Ainsworth et al., 2008; Ainsworth et al., 2011), and for predictions based on 37 38 541 parasequence characteristics (Colombera and Mountney, 2020a). The A/S ratio does not directly 39 40 41 542 affect shoreline depositional processes but may modify their relative interaction through changes 42 43 543 in physiography. For embayed shorelines, which favour tidal amplification, the degree of wave 44 45 46 544 protection will be: (1) reduced under low A/S conditions because higher progradation rates cause 47 48 545 shorelines to straighten more quickly; and (2) increased under high A/S conditions, when 49 50 51 546 accommodation exceeds sediment supply, because the embayed shoreline geometry will more 52 53 547 likely persist (Fig. 7) (Ainsworth et al., 2011). 54 55 548 56 57 58 59 60 32 61 62 63 64 65 1 2 3 4 549 Shoreline morphology (c. 1–10 km scale) can have a significant impact on the relative balance of 5 6 7 550 tide, wave and fluvial processes (Fig. 2) (Boyd et al., 1992; Dalrymple et al., 1992; Ainsworth et 8 9 551 al., 2008; Ainsworth et al., 2011). Highly-embayed, more rugose, shoreline morphologies may 10 11 12 552 promote: (1) amplification of the tidal wave by funnelling and/or resonance effects (Slingerland, 13 14 553 1986; Allen, 1997); and (2) protection from direct wave approach from the open ocean or sea. 15 16 554 Therefore, Ainsworth et al. (2011) use shoreline rugosity as a direct proxy for tidal influence: 17 18 19 555 increasing rugosity corresponds to increased potential for tidal influence (Fig. 7). Their model 20 21 556 predicts that all interpreted highly embayed shorelines, and half of interpreted moderately 22 23 24 557 embayed shorelines, are tide-dominated, whereas only a quarter of interpreted straight to lobate 25 26 558 shorelines are tide-dominated (Fig. 7A). However, this simplified differentiation is inconsistent 27 28 29 559 with observations of Holocene to present-day embayed shorelines, most notably estuaries (e.g. 30 31 560 Dalrymple, 1992; Roy et al., 2001; Boyd et al., 2006; Dalrymple, 2006), which may be wave- 32 33 34 561 dominated (e.g. Roy et al., 1980; Honig and Boyd, 1992; Cooper, 2001; Anthony et al., 2002), 35 36 562 tide-dominated (e.g. Hori et al., 2001; Dalrymple et al., 2012), river-dominated (e.g. Cooper, 37 38 563 1993; Sondi et al., 1995), and mixed process (d'Anglejan and Brisebois, 1978; Jouanneau and 39 40 41 564 Latouche, 1981; Clifton, 1983; Allen and Posamentier, 1993; Roy et al., 2001). Furthermore, 42 43 565 amplifying of tides due to funnelling and resonance effects in embayments may be counteracted 44 45 46 566 by frictional effects (e.g. Dalrymple et al., 1992; Allen, 1997; Mitchell et al., 2010; Collins et al., 47 48 567 2018a). Consequently, the variability in predicted processes for ancient embayed shorelines may 49 50 51 568 be higher than that proposed by Ainsworth et al. (2011) (Fig. 7). 52 53 569 54 55 570 For prediction of ancient shoreline processes, it is important that the data used to interpret the 56 57 58 571 impact of the different controls on shoreline processes have: (1) reliable chronostratigraphic 59 60 33 61 62 63 64 65 1 2 3 4 572 information with an appropriate resolution; and (2) overlapping age ranges (‘temporal 5 6 7 573 resolution’). The temporal resolution of data and interpretations relating to the inferred controls 8 9 574 varies significantly. For example, the temporal resolution of interpreted system tracts relating to 10 11 th 12 575 3rd-order (c. 0.5–3.0 Myr) or 4 -order (few 10s ka to c. 0.5 Myr) sea-level cycles (Haq, 2014; 13 14 576 Sames et al., 2016) will likely fall within the temporal resolution of regional-scale 15 16 577 palaeogeographic maps, which are typically driven by plate tectonics and used for interpreting 17 18 19 578 basin physiography and fluvial versus wave effectiveness (Markwick and Valdes, 2004). In 20 21 579 contrast, the physiography of shoreline embayments and the continental shelf may be driven by 22 23 24 580 relative sea level changes or local tectonics, which vary on much smaller timescales (e.g. Collins 25 26 581 et al., 2018a). 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 34 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 582 54 55 56 583 Fig. 7. Predictive model for shoreline process regime (modified from Ainsworth et al. (2011). 57 584 (A) Decision tree with four main queries predicting shoreline process regime. (B) Predictive 58 59 60 35 61 62 63 64 65 1 2 3 4 585 matrix for settings with a low tidal potential. (C) Predictive matrix for settings with a high tidal 5 6 586 potential. Abbreviations and color coding are shown in the inset (opposite B). 7 8 587 9 10 588 3 METHODS 11 12 13 589 3.1 Numerical tidal modelling 14 15 590 3.1.1 Mesh generation 16 17 18 591 Fluidity (http://fluidityproject.github.io/), formerly the Imperial College Ocean Model (ICOM), 19 20 592 is a hydrodynamic, finite element ocean model that solves the Navier-Stokes equations and uses 21 22 23 593 unstructured, multi-scale, three-dimensional, tetrahedral meshes that (1) smoothly and accurately 24 25 594 conform to coastline and bathymetry, (2) have focused resolution in areas of complex 26 27 595 bathymetry (e.g. straits and embayments), along coastlines and/or in areas of interest, and (3) 28 29 30 596 maximize computational accuracy and efficiency (Pain et al., 2005; Wells et al., 2005a; Gorman 31 32 597 et al., 2007; Gorman et al., 2008; Piggott et al., 2008; Geuzaine and Remacle, 2009; Avdis et al., 33 34 35 598 2018). Meshes used in Fluidity palaeotidal simulations may be global or regional and have been 36 37 599 constructed using Terreno (Gorman et al., 2007; Gorman et al., 2008) or qmsh (Avdis et al., 38 39 40 600 2018). By working directly on an arbitrary geodetic in Cartesian space, Fluidity eliminates the 41 42 601 ‘pole problem’ by which lines of constant longitude converge at the poles producing very small 43 44 602 elements (Madec and Imbard, 1996; Comblen et al., 2009; Wells et al., 2010a). A minimum 45 46 47 603 depth of 10 m along the shoreline prevents the free surface from intersecting the bottom surface 48 49 604 as it propagates but the increased water depth impacts shallow water current velocities and 50 51 52 605 possibly tidal amplification effects (e.g. Wells et al., 2010a). 53 54 606 55 56 57 607 3.1.2 Hydrodynamic modelling of astronomical and forced boundary tides 58 59 60 36 61 62 63 64 65 1 2 3 4 608 Fluidity can simulate both astronomical and co-oscillating boundary tides (Table 2). The 5 6 7 609 astronomical tide results directly from the tide-generating force on the water in an open ocean or 8 9 610 seaway due to the gravitational and rotational effects of the Moon and Sun. Astronomical tidal 10 11 12 611 potential is calculated at each mesh node for each time step using the multi-constituent 13 14 612 equilibrium theory of tides: 15 16 17 18 19 20 21 22 23 24 613 25 26 614 where ηeq = equilibrium tidal potential (m), λ = east longitude (radians), θ = colatitude (π/2 – 27 28 -1 29 615 latitude, radians), χ = astronomical argument (radians), σ = frequency of tidal constituent (s ), t 30 31 616 = universal standard time (s) and K = equilibrium amplitude of tidal constituent (m). Subscripts i, 32 33 617 j and k represents the semidiurnal, diurnal and long-period tidal constituents, respectively, which 34 35 36 618 allows constituents to be modelled individually or in combination (Schwiderski, 1980; Kantha 37 38 619 and Clayson, 2000; Wells et al., 2007a; Mitchell et al., 2010). The overall forcing is applied as 39 40 41 620 the product of the equilibrium tidal potential gradient and the gravitational acceleration (g) 42 43 621 (Mellor, 1996; Kantha and Clayson, 2000). 44 45 46 622 47 48 623 The co-oscillating or boundary tide results from propagation of the astronomical tidal wave into 49 50 51 624 a connected water body. This is especially important for simulations of tides in partly-enclosed 52 53 625 seas and shallow seaways (straits), which typically have limited potential for internally generated 54 55 626 astronomical tides because of their smaller water masses (Tsimplis et al., 1995; Wells et al., 56 57 58 627 2005a). Co-oscillating tides along designated open boundaries are forced as either one fixed 59 60 37 61 62 63 64 65 1 2 3 4 628 cosine wave of constant amplitude and phase applied across the entire boundary length or 5 6 7 629 interpolated as many cosine waves of different amplitudes and phases at a series of points along 8 9 630 the boundary. Ideally, the amplitude and phase values for each tidal constituent would be derived 10 11 12 631 from a larger-scale model of the adjacent water body. 13 14 632 15 16 633 The bottom drag is applied as a surface integral boundary condition based on a quadratic friction 17 18 19 634 law of the form -CD ū |ū| where C = drag coefficient and depth averaged current velocity |ū| = 20 21 2 2 2 22 635 √푢 + 푣 + 푤 , where u, v and w represent the velocities in the x, y, and z dimensions, 23 24 636 respectively (ms-1) (Wells et al., 2007a; Mitchell et al., 2010). The drag coefficient is set as 25 26 637 0.0025, a generic value used in most ocean models (Pietrzak et al., 2002), but the drag 27 28 -2 -3 29 638 coefficient may vary between 10 –10 as a function of bathymetry and sediment grain size, 30 31 639 shape and sorting (Safak, 2016). 32 33 34 640 35 36 641 A spin-up period of at least 120 hours (five days) simulation time is sufficient to remove spin-up 37 38 39 642 effects and reach steady state (Wells et al., 2007a; Wells et al., 2007b), after which all fields are 40 41 643 set to zero. 42 43 644 44 45 46 645 The equations of motion describing the movement of the tidal bulge include the Coriolis 47 48 646 acceleration (f), which is simplified to f = 2Ωsin φ (Cushman-Roisin, 1994; Cushman-Roisin and 49 50 -1 51 647 Beckers, 2011), where Ω is the rotation rate of the Earth (7.27×10−5 rad s ) and φ is the latitude. 52 53 648 Model outputs are the amplitude of tidal components, tidal range, average and maximum tidal 54 55 56 649 current velocity, the magnitude and direction of average and maximum tidal bed shear stress, and 57 58 650 the tidal phase. Tidal range is calculated as the difference between the maximum and minimum 59 60 38 61 62 63 64 65 1 2 3 4 651 free surface heights over the post spin-up simulation period, which approximately equals the 5 6 7 652 maximum spring tidal range. The amplitude and phase of the four major tidal constituents (M2, 8 9 653 S2, K1 and O1) are determined using tidal harmonic analysis of the modelled time series of free 10 11 12 654 surface heights (Foreman, 1979). Tidal bed shear stress (τ) is the frictional force exerted by tides 13 14 655 on the sediment surface and is calculated using τ = ρ CD ū |ū| where ρ = the density of water 15 16 656 (1023 kg m–3) (Pingree and Griffiths, 1979; Wells et al., 2007a; Mitchell et al., 2010). Bed shear 17 18 19 657 stress magnitudes can be converted to the equivalent grain size that could be entrained by the 20 21 658 tidal flow based on the modelled and calculated critical bed shear stress values for sediment 22 23 24 659 transport (Miller et al., 1977; Soulsby et al., 1993; Julien and Raslan, 1998). 25 26 660 27 28 29 661 3.1.3 Validation of tidal model results 30 31 662 Tidal modelling using Fluidity has been extensively validated against real-world modern tidal 32 33 34 663 amplitude (Wells et al., 2005a; Wells et al., 2005b; Wells et al., 2007a; Wells, 2008; Wells et al., 35 36 664 2010a; Wells et al., 2010b; Collins et al., 2017a; Collins et al., 2018a) and tidal bed shear 37 38 665 stress(Mitchell et al., 2010; Mitchell et al., 2011; Collins et al., 2017a; Collins et al., 2018a). This 39 40 41 666 includes global (Wells et al., 2010a; Collins et al., 2018a) and regional comparisons in the 42 43 667 Mediterranean Sea (Wells et al., 2005a), North Sea (Wells et al., 2007a; Mitchell et al., 2010), 44 45 46 668 Baltic Sea (Wells, 2008) and South China Sea (Collins et al., 2017a; Collins et al., 2018a). 47 48 669 49 50 51 670 On a global-scale, comparison of the modeled amplitude of the M2, S2, K1 and O1 tidal 52 53 671 constituents using Fluidity, which utilises the GEBCO (General Bathymetric Chart of the 54 55 672 Oceans) 2014 bathymetric data and an unstructured mesh with maximum resolution of 10 km, to 56 57 58 673 tidal guage data and the FES 2014 tidal model, clearly illustrates that Fluidity accurately predicts 59 60 39 61 62 63 64 65 1 2 3 4 674 tidal range without the need for data assimilation (Fig. 8). Tidal constituent amplitudes at 423 5 6 7 675 stations were calculated using tidal harmonic analysis of sea surface elevation data (Caldwell et 8 9 676 al., 2015) (Fig. 8A–F) and the calculated mean root-mean-squared (RMS) error includes absolute 10 11 12 677 values of both tidal amplitude and phase (Cummins and Thupaki, 2018). Fluidity very slightly 13 14 678 underpredicts tidal amplitude compared to tidal gauge data, with the relative error varying 15 16 679 between -0.01% (S tide) to -0.23% (O tide) and the root-mean-squared (RMS) amplitude 17 2 1 18 19 680 varying between 0.10 m (K1 and O1 tide) to 0.37 m (M2 tide) (Fig. 8B–F). However, these errors 20 21 681 are comparable to those between the FES 2014 tidal model and tidal gauge data for 162 stations 22 23 24 682 (Fig. 8B, G–J), despite the FES2014 model using tidal data from satellite altimetry and gauges, 25 26 683 highly-accurate global and regional bathymetries, an unstructured mesh with up to c. 7 km 27 28 29 684 (1/16°) resolution, and corrections for internal and load tides (Carrère et al., 2015). Local-scale 30 31 685 differences between the Fluidity model and the FES 2014 model and tidal gauge data are likely 32 33 34 686 caused by (1) mesh resolution limitations that simplify bathymetry (e.g. between islands) and 35 36 687 affect modelled tidal flow and frictional effects, (2) the lack of correction for internal drag and 37 38 688 load tides, and (3) frictional drag parameterisation (Egbert et al., 2004; Wells et al., 2010a). 39 40 41 689 Overall, tidal modelling using Fluidity accurately predicts present-day global tidal amplitude 42 43 690 without the need for data assimilation and to a degree of accuracy that is sedimentologically 44 45 46 691 useful, most notably predicting the following: (1) tidal amplitude and range to a decimetre-scale 47 48 692 accuracy; (2) microtidal (<2 m), mesotidal (2–4 m) and macrotidal (>4 m) regimes, which is 49 50 51 693 within the limit of ancient tidal range estimates e.g. (Wells et al., 2005a); (3) the position of 52 53 694 amphidromic systems; (4) predominance of semidiurnal versus diurnal tides; and (5) areas of 54 55 695 tidal amplification due to shoaling, funnelling and/or resonance effects. 56 57 58 696 59 60 40 61 62 63 64 65 1 2 3 4 697 On a global scale, the maximum bed shear stress and potential sediment grain size transport 5 6 7 698 modeled by Fluidity (Fig. 2B) have been compared to those modeled using FES 2014 (Fig. 9), 8 9 699 which were calculated based on the modeled tidal current velocity vectors (Equation 1) 10 11 12 700 (Supplementary Fig. 1). Overall, the patterns of potential sediment mobility are similar for the 13 14 701 two models, with elevated bed shear stress (and equivalent grain size) in areas of shallower 15 16 702 bathymetry and/or physiographic constriction (Fig. 9A and B). However, the potential sediment 17 18 19 703 grain size mobility in shelf areas modeled using Fluidity tends to be one or two grain size classes 20 21 704 above or below that modeled by FES 2014 (Fig. 10A and B). Overprediction most likely reflects 22 23 24 705 insufficient frictional damping of modeled tidal energy due to locally coarser mesh and 25 26 706 bathymetry resolution and lack of internal drag in the Fluidity model. Underprediction is 27 28 29 707 especially common in relatively large, shallow areas that are partially restricted from the open 30 31 708 ocean due to complex physiography. For example, results from the high-latitude seas of North 32 33 34 709 America probably reflect reduced penetration of the ocean tidal wave through the constricted 35 36 710 physiography due to coarse mesh and bathymetry resolution. Despite these differences, modeled 37 38 711 bed shear stress using Fluidity and FES2014 are closely matched in many areas, notably the Gulf 39 40 41 712 of Saint Lawrence, Meditarranean Sea, North Sea and South China Sea. These results illustrate 42 43 713 that Fluidity is capable of reproducing the first-order variability in modeled tidal bed shear stress 44 45 46 714 related to physiography in modern domains and is capable of modelling the same in ancient 47 48 715 domains, provided that palaeobathymetric and palaeogeographic uncertainties are adequately 49 50 51 716 defined. 52 53 717 54 55 56 57 58 59 60 41 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 718 40 41 719 Fig. 8. Validation of modeled tidal amplitude using Fluidity and FES2014 (Carrère et al., 2015). 42 43 720 (A) Number (n) and position of a global set of tidal stations used for the comparisons to 44 45 721 FES2014 (white circles, n = 162) and Fluidity (red circles, n = 423) model data. (B) Summary of 46 47 722 root-mean-squared (RMS) and relative percentage errors between the model and tidal gauge data 48 723 of tidal constituent amplitude. Tidal gauge amplitude data was derived by tidal harmonic analysis 49 50 724 of sea surface elevation data. (C–J) Plots of tidal gauge versus modeled tidal amplitude for the 51 52 725 K1 (C, G), M2 (D, H), O1 (E, I) and S2 (F, J) tidal constituents using Fluidity (C–F) and FES2014 53 54 726 (G–J). 55 56 727 57 58 59 60 42 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 728 40 41 729 Fig. 9. (A) Maximum tidal bed shear stress modeled using Fluidity, plotted as the equivalent 42 43 730 grain size that could be entrained if available. (B) Difference in sediment grain size class 44 45 731 between maximum tidal bed shear stress for Fluidity (A) and FES2014 (Fig. 2D) (Carrère et al., 46 47 732 2015). Grain size abbreviations: vf = very fine; f = fine; m = medium; c = coarse; vc = very 48 733 coarse. Pink dots show location of tide-dominated deltas (Goodbred and Saito, 2012): A) 49 50 734 Copper; B) Colorado; C) Amazon; D) Shatt-al-Arab; E) Indus; F) Ganges-Brahmaputra; G) 51 52 735 Irrawaddy; H) Red River; I) Yangtze; J) Mekong; K) Rajang; L) Mahakam; and M) Fly. 53 54 736 55 56 737 3.2 Comparison of tidal model results with the rock record 57 58 59 60 43 61 62 63 64 65 1 2 3 4 738 For each case study, tidal model results have been compared to available ‘rock-record’ data, 5 6 7 739 notably palaeogeographic, stratigraphic, sedimentological and micropaleontological information 8 9 740 and interpretations. The majority of referenced datasets invariably include both (1) well- 10 11 12 741 documented sedimentological and/or micropaleontological data, and (2) interpretations of 13 14 742 depositional processes and environments that are supported by the available data. Comparison of 15 16 743 tidal model results with rock-record data from the equivalent stratigraphic interval relies on 17 18 19 744 several steps at different scales but is fundamentally underpinned by detailed facies analysis. 20 21 745 22 23 24 746 3.2.1 Tidal facies analysis 25 26 747 Validation of tidal model results using sedimentological data relies on recognising sedimentary 27 28 29 748 characteristics at the bedform-scale (c. mm–10s m-scale) that are indicative of tidal processes. 30 31 749 These have been widely documented from several different shallow-water depositional 32 33 34 750 environments, most notably deltas, estuaries, barrier inlets, embayments, straits and open shelves 35 36 751 (e.g. De Raaf and Boersma, 1971; Ginsburg, 1975; De Raaf and Boersma, 1977; Reineck and 37 38 752 Singh, 1980; Terwindt, 1981; De Boer et al., 1988; Nio and Yang, 1991; Smith et al., 1991; 39 40 41 753 Shanley et al., 1992; Flemming and Barthloma, 1995; Willis, 2005; van den Berg et al., 2007; 42 43 754 MacEachern and Bann, 2008; Martinius and van den Berg, 2011; Davis, 2012; Shanmugam, 44 45 46 755 2013). The most significant features are those related to tidal flow reversals, flood–ebb tide 47 48 756 versus slack water dynamics, tide-related periodicity and/or physico-chemical stress, particularly 49 50 51 757 the following: (1) bidirectional cross-bedding and cross-lamination (cm–dm-scale), including the 52 53 758 relatively rare variant of ‘herringbone’ patterns (e.g. Van Straaten, 1953; Reineck, 1963; 54 55 759 Boersma, 1969; Klein, 1970a; Klein, 1970b; Klein, 1971; Hayes, 1980; Boersma and Terwindt, 56 57 58 760 1981; Yoshida et al., 2004); (2) larger-scale (10s m-scale) bidirectionality, such as between 59 60 44 61 62 63 64 65 1 2 3 4 761 separate but closely spaced sand bodies with oppositely-dipping cross-bedding, which have been 5 6 7 762 interpreted to reflect mutually evasive ebb- and flood-tidal channels and bars (Robinson, 1966; 8 9 763 Johnson, 1975; Johnson and Levell, 1995; Sixsmith et al., 2008; Legler et al., 2013; Levell et al., 10 11 12 764 2020); (3) sigmoidal ‘shovel-shaped’ cross-bed sets, with extended mud-rich toesets, sometimes 13 14 765 with oppositely-dipping current ripples (e.g. Boersma and Terwindt, 1981; Mutti et al., 1984; 15 16 766 Mutti et al., 1985; Kreisa and Moila, 1986; Dalrymple and Rhodes, 1995; van den Berg et al., 17 18 19 767 2007; Tinterri, 2011); (4) multiple reactivation surfaces with an apparent cyclicity or predictable 20 21 768 and repeated pattern (e.g. Boersma, 1969; McCabe and Jones, 1977; Reineck and Singh, 1980; 22 23 24 769 Boersma and Terwindt, 1981; Allen, 1982a; Allen and Homewood, 1984); (5) ‘paired drapes’ or 25 26 770 ‘double drapes’ comprising sandy foresets and associated mudstone and/or carbonaceous 27 28 29 771 (typically finely comminuted ‘coffee ground’ type) drapes (mm–cm-scale), which are interpreted 30 31 772 to form by semi-diurnal to diurnal tidal inequality (e.g. Reineck and Singh, 1980; Visser, 1980; 32 33 34 773 Smith, 1988; De Boer et al., 1989; Nio and Yang, 1991); (6) ‘tidal bundles’ in the form of lateral 35 36 774 and vertical thickness variations of sandy foresets and associated mudstone/carbonaceous drapes 37 38 775 (dm–m-scale) , which have been related to spring–neap semi-lunar cycles (e.g.Visser, 1980; 39 40 41 776 Allen, 1981b; Boersma and Terwindt, 1981; Allen and Homewood, 1984; Kreisa and Moila, 42 43 777 1986; Nio and Yang, 1991) (cf. Martinius and Gowland, 2011); (7) heterolithic bedding (cm–m- 44 45 46 778 scale) with apparent, or preferably measured and statistically analysed, cyclicity in the thickness 47 48 779 of sandstone–mudstone layers, which are referred to as ‘couplets’ if other evidence of tidal 49 50 51 780 deposition (e.g. bidirectional current ripples etc.) are observed (Reineck and Wunderlich, 1968; 52 53 781 Terwindt, 1971; Terwindt and Breusers, 1972; Reineck and Singh, 1980; Kvale et al., 1989; 54 55 782 Archer et al., 1991; Archer, 1995; Greb and Archer, 1995; Kvale, 2006; Kvale, 2012); (8) 56 57 58 783 inclined heterolithic strata (dm–10s m-scale) (Thomas et al., 1987; Smith, 1988; Dalrymple et 59 60 45 61 62 63 64 65 1 2 3 4 784 al., 2003; Choi et al., 2004; Dalrymple and Choi, 2007); (cf. Sisulak and Dashtgard, 2012; 5 6 7 785 Jablonski and Dalrymple, 2016); and (9) ichnofabrics which, in general, show reduced but 8 9 786 variable and sporadic bioturbation intensities and predominance of facies-crossing ichnofauna 10 11 12 787 (MacEachern et al., 2005; McIlroy, 2006; McIlroy, 2007; MacEachern and Bann, 2008; 13 14 788 Longhitano et al., 2010; Gingras and MacEachern, 2012; Gingras et al., 2012). 15 16 789 17 18 19 790 Definitive recognition of tide-influenced sedimentation relies on observing combinations of the 20 21 791 features described above because, in isolation, some of these features can form by other 22 23 24 792 processes (e.g. wave, storm and/or fluvial) operating by themselves or, especially, in 25 26 793 combination with tides (Frey and Howard, 1986; Thomas et al., 1987; Shanley et al., 1992; 27 28 29 794 Hovikoski et al., 2008; MacEachern and Bann, 2008; Ichaso and Dalrymple, 2009; Martinius and 30 31 795 Gowland, 2011; Tinterri, 2011; Sisulak and Dashtgard, 2012; Vakarelov et al., 2012; Johnson 32 33 34 796 and Dashtgard, 2014; Dalrymple et al., 2015; Gugliotta et al., 2016a; Gugliotta et al., 2016b; 35 36 797 Jablonski and Dalrymple, 2016; Kurcinka et al., 2018). Mixed-process settings, especially those 37 38 798 where fluvial and tidal currents coexist, can exacerbate differences in the strength and sediment 39 40 41 799 transport capacity of ebb- and flood-tidal currents. Strongly skewed palaeocurrent patterns, with 42 43 800 one dominant offshore-directed mode, and a weaker oppositely-directed secondary mode, may 44 45 46 801 occur when fluvial and ebb-tidal processes are combined, such as in deltaic and estuarine settings 47 48 802 (Legler et al., 2013; van Cappelle et al., 2016; Collins et al., 2020; Levell et al., 2020). For 49 50 51 803 example, in the modern microtidal Po Delta, preserved tidal signals in open-water prodelta facies 52 53 804 are correlatable to cyclical variation in water-surface steepness and consequent changes in river 54 55 805 discharge velocity and sediment transport capacity in distributary channels (Maselli et al., 2020). 56 57 58 806 In modern open-marine shelf settings, storm-induced currents can also contribute to tidal current 59 60 46 61 62 63 64 65 1 2 3 4 807 sediment transport asymmetry (Stride, 1973; Belderson et al., 1982; Stride, 1982). Similarly, 5 6 7 808 storm-enhanced tidal transport systems have been inferred to explain unidirectional 8 9 809 palaeocurrent patterns in ancient shallow-marine deposits (Banks, 1973; Johnson, 1975; 10 11 12 810 Anderton, 1976; Levell, 1980). Autogenic tidal processes responsible mutually evasive ebb and 13 14 811 flood tidal channels can also create skewed palaeocurrent patterns in the stratigraphic record, 15 16 812 particularly where: (1) channel preservation is unequal, (2) ebb and flood tidal channels are so 17 18 19 813 effectively shielded from each other that evidence of the secondary reversing tide is absent, 20 21 814 and/or (3) incomplete outcrop or subsurface dataset (Sixsmith et al., 2008; Legler et al., 2014). 22 23 24 815 25 26 816 Confident identification of tidal influence and its relative importance with respect to other 27 28 29 817 processes (e.g. wave, storm and/or fluvial) requires reconstruction of shoreline palaeo- 30 31 818 geomorphology at the scale of the depositional system (c. 1–100s km), based on detailed facies 32 33 34 819 analysis in the context of high-resolution stratigraphic and regional palaeogeographic 35 36 820 relationships. Such confidence in interpretation requires data of high quality and density, such as 37 38 821 provided by extensive outcrop data (e.g. Willis and Gabel, 2001; Legler et al., 2013; Legler et 39 40 41 822 al., 2014; Ainsworth et al., 2016; Rossi et al., 2016; van Cappelle et al., 2016; Kurcinka et al., 42 43 823 2018; Van Yperen et al., 2020) or subsurface datasets containing 3D seismic data, densely 44 45 46 824 spaced wells and/or extensive cores (e.g. Hubbard et al., 2011; Willis and Fitris, 2012; Holgate et 47 48 825 al., 2013). In practice, such datasets and confident interpretations are rare. It is therefore 49 50 51 826 appropriate to focus comparison of ‘rock-record’ data with tidal model predictions at bedform 52 53 827 scale (c. mm–10s m), at which interpretations of bed shear stress as a proxy for tidal current 54 55 828 velocity (section 3.2.3) can be readily made. Other tidal model outputs, including tidal range 56 57 58 59 60 47 61 62 63 64 65 1 2 3 4 829 (section 3.2.2) and tidal phase, are typically less straightforward to interpret from available 5 6 7 830 ‘rock-record’ data (e.g. Wells et al., 2005a; (Mitchell et al., 2010)). 8 9 831 10 11 12 832 3.2.2 Palaeotidal range analysis 13 14 833 Analysis of palaeotidal range from the rock record requires observations and interpretation at a 15 16 834 range of scales: depositional system morphology (c. 1–100s km), depositional environments (c. 17 18 19 835 0.1–1 km) and depositional elements and facies (<1 to 10s m) may all preserve an imprint of 20 21 836 tidal sedimentary processes, but do not offer more detailed constraints on tidal range beyond 22 23 24 837 inferring microtidal, mesotidal and macrotidal regimes (Table 4) (Wells et al., 2005a). 25 26 838 Alternative methods used to estimate palaeotidal range are: (1) interpretations of water depth 27 28 29 839 from stratigraphic position within interpreted fining-upward channel-fill units (Nio et al., 1983) 30 31 840 (Yang and Nio, 1985); (2) stratigraphic thickness estimates of interpreted intertidal deposits in 32 33 34 841 tidal flat units (Klein, 1970a; Klein, 1971), although these units are very similar to interpreted 35 36 842 channel-fill units within the fluvial-to-marine transition zone (e.g. Olson, 1972; Dalrymple and 37 38 843 Choi, 2007; Amir Hassan et al., 2013; Gugliotta et al., 2016a; Collins et al., 2018b; Collins et al., 39 40 41 844 2020); and (3) average calculations of characteristic mudstone drape spacings based on groups of 42 43 845 sandstone–mudstone couplets from interpreted spring and neap conditions, and various 44 45 46 846 assumptions regarding dune height and speed, dry bulk sediment density, and current velocity for 47 48 847 sediment entrainment (Allen, 1981b). Depositional systems subject to higher tidal ranges are 49 50 51 848 more likely to be tide-dominated, but this relationship is inconsistent, especially for mixed- 52 53 849 process systems (e.g. Davis and Hayes, 1984). Furthermore, higher tidal ranges may not always 54 55 850 correspond to stronger tidal currents (Mitchell et al., 2011). 56 57 58 851 59 60 48 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Indicator Size Description Tidal range 21 Delta morphology 10s - 100s km Tide-dominated deltas display wide, landward-tapering river mouths, Mesotidal to macrotidal 22 23 elongate shore-normal mouth bars, sinuous tidal creeks, tidal flats, 24 saltmarsh and/or mangroves, and smaller-scale tidal indicators (e.g. 25 Ganges-Brahmaputra, Irrawaddy, Fly deltas) 26 27 28 29 30 Fluvial-dominated deltas display digitate (‘birds-foot’) to lobate Microtidal to mesotidal 31 morphologies and rapid progradation due to higher relative stream 32 power compared to wave/tide reworking (e.g. Mississippi delta). 33 34 35 36 Wave-dominated deltas display cuspate geometries with intermediate Microtidal to mesotidal 37 progradation rates due to wave action ('littoral energy fence') (e.g. 38 39 Baram) 40 41 42 Open shelf tidal sand-sheets 10s - 100s km Tabular sandbodies with planar tops and bases formed by open-shelf Mesotidal to macrotidal 43 tidal currents. Super-imposed sedimentary structures including scour 44 hollows, longitudinal furrows, obstacle marks, sand ribbons, sand 45 waves, rippled sand sheets and longitudinal sand patches. 46 47 48 49 Furrows and gravel waves L < 150 km; W < Mostly erosional features with small (ca 1 m high, 10 m wavelength) Macrotidal 50 50 km gravel-rich subaqueous dunes, formed due to low sediment supply and 51 52 strong tidal currents (e.g. Bristol Channel) 53 54 55 56 57 58 59 60 49 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Offshore tidal sand ridges L ca 50 km; W 1–3 Linear bedforms with long axes orientated up to 20 obliquely to tidal Mesotidal 21 km; T 10–50 m currents. Distinguished from Aeolian dunes by the presence of 2 main to 22 23 current directions at 180, shelly debris, mud drapes, reactivation macrotidal 24 surfaces, low angle (3–6) cross-stratification and marine trace fossils 25 (e.g. Norfolk Ridges, southern North Sea). 26 27 28 29 Estuarine/incised valley-fill W < 30 km; T ca 1 Outer estuary characterized by elongate sand ridges and tidal channels Microtidal to macrotidal 30 tidal sandbodies m with super-imposed, smaller-scale tidal indicators. Middle and inner 31 32 estuary characterized by heterolithic strata with isolated sandbodies 33 (e.g. Thames estuary, southern North Sea) 34 35 36 37 Sand ribbons L < 15 km; W < Ribbons or strips of sand elongated parallel to tidal currents consisting Mesotidal to Macrotidal 38 200 m; T ca 1 m of sandwaves trains (e.g. western English Channel). 39 40 41 Saltmarsh L 10 km; W < 5 Gently sloping coastal wetland which extends landwards to the high- Mesotidal to macrotidal 42 km; T < 10 m tide mark. Evaporating pools of saline water form localized ‘salt-pans’ 43 and fauna and flora adapted to highly fluctuating salinities dominate. 44 45 46 47 Mangroves L <200 km; W <60 Densely vegetated forests occupying the lower intertidal zone (ca mean Mesotidal to macrotidal 48 km; T <10 m sea level to low-tide mark) of tide-dominated, typically mud-rich deltaic 49 shorelines. Flora sub-zonations related to topography and often diverse 50 51 fauna adapted to salinity variations (e.g. Mekong, Ganges-Brahmaputra 52 deltas). 53 54 55 56 Tidal creeks W < 100 m; T 10 Shore-normal creeks which do not pass into a fluvial system landwards, Microtidal to macrotidal 57 m often mud-rich. 58 59 60 50 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 852 Table 4. Larger-scale tidal indicators, ranging from depositional environments to systems, and their generalized implication for tidal- 21 22 853 range prediction in the geological rock record (modified after Wells et al., 2005a). 23 24 854 25 855 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 61 62 63 64 65 1 2 3 4 856 3.2.3 Ancient bed shear stress analysis 5 6 7 857 Analysis of ancient bed shear stress is possible based on preserved grain size distribution and 8 9 858 sedimentary structures (Fig. 10). Tidal currents that exceed the critical bed shear stress threshold 10 11 12 859 for sediment entrainment will impact sedimentary processes (Mitchell et al., 2011; Collins et al., 13 14 860 2018a). However, the type of sedimentary structures formed by currents of varying flow velocity 15 16 861 is also strongly dependent on the available grain size and water depth during deposition (Fig. 17 18 19 862 10), which can only be estimated in the context of facies successions, permitted by the 20 21 863 availability of appropriate rock record data. Less reliable predictions of available grain size range 22 23 24 864 may be possible based on catchment area geology, interpreted palaeo-drainage systems and other 25 26 865 indirect data sources (e.g. seismic geometries of clinoforms, seismic amplitudes, well logs and 27 28 29 866 other borehole data). For a given water depth, if tidal bed shear stress was insufficient to rework 30 31 867 the minimum grain size available, tides will not have influenced sediment transport. In contrast, 32 33 34 868 the size, type and texture of sedimentary structures may vary depending on tidal current strength 35 36 869 and the frequency with which the critical bed shear stress for entrainment of the available grain 37 38 870 size range was exceeded. 39 40 41 871 42 43 872 Comparison of tidal model results to micropaleontological information strongly depends on the 44 45 46 873 availability of suitable data. The most important potential indicator of tidal processes are 47 48 874 palynomorph acmes of coastal biomes whose distribution, abundance and productivity within a 49 50 51 875 depositional system is strongly related to tidal processes, most notably those associated with 52 53 876 deposition in mangrove, seagrass and salt marsh settings (e.g. Grindrod, 1988; Wolanski et al., 54 55 877 1992; Woodroffe et al., 2016). 56 57 58 878 59 60 52 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 879 18 19 880 Fig. 10. (A) Bedform stability diagram, including bed shear stress, for unidirectional flow at 20 21 881 approximately 20 cm water depth (flume tank) (Harms et al., 1982; Mitchell et al., 2010). (B) 22 23 882 Bedform stability diagram, including bed shear stress, for unidirectional flow at approximately 2 24 883 m water depth (Rubin and McCulloch, 1980). 25 26 884 27 28 29 885 4 RESULTS 30 31 886 4.1 Oligocene–Miocene South China Sea, Southeast Asia 32 33 34 887 4.1.1 Overview 35 36 888 The Oligocene–Miocene SCS provides a compelling case study for investigating the impact of 37 38 889 regional-scale (100–1000s km) physiographic changes on shoreline tidal processes and 39 40 41 890 stratigraphic preservation for several reasons. Firstly, the region underwent significant, 42 43 891 geologically-rapid, tectonically-driven (plate-related) palaeogeographic changes during a c. 25 44 45 46 892 Myr time period in the Oligo–Miocene, which would have impacted large-scale oceanic flow 47 48 893 patterns (e.g. Kuhnt et al., 2004; Hall, 2009; Hall, 2011). Second, several circum-SCS 49 50 51 894 Oligocene–Miocene basins with high tectonic subsidence and sediment supply rates preserve 52 53 895 stratigraphic archives of sedimentary environment and process changes (e.g. Doust and Sumner, 54 55 56 896 2007). During this period, there was considerable variability in the physiographic configuration 57 58 897 of the SCS, which resulted in the formation of several shoreline embayments that were 59 60 53 61 62 63 64 65 1 2 3 4 898 influenced by local-scale (10–100s km) tidal processes (Collins et al., 2017a; Collins et al., 5 6 7 899 2018a). 8 9 900 10 11 12 901 4.1.2 Geological Setting 13 14 902 During the Oligo–Miocene, the SCS and wider Southeast Asia region experienced extensive 15 16 903 tectonic reorganization of several microplates and sub-plates in response to major movements of 17 18 19 904 the Indo-Australian, Eurasian, Pacific and Philippine Sea plates (Fig. 11) (Lee and Lawver, 20 21 905 1995; Hall, 1996; Hall, 2002). Extensional rifting preceding oceanic spreading in the SCS 22 23 24 906 occurred from the latest Cretaceous (e.g. Hinz and Schlüter, 1985; Ru and Pigott, 1986). Active 25 26 907 spreading of the SCS initiated in the Early Oligocene at c. 32 Ma (Briais et al., 1993; 27 28 29 908 Barckhausen et al., 2014) or 31 Ma (Barckhausen and Roeser, 2004) due to the combination of 30 31 909 (1) slab-pull effect due to subduction of the proto-SCS beneath north-west Borneo, which caused 32 33 34 910 rifting along southern China (Fig. 3) (Holloway, 1982; Taylor and Hayes, 1983; Huchon et al., 35 36 911 1994; Hall, 1996), and (2) extrusion of Indochina along the sinistral Ailao Shan-Red River Fault 37 38 912 Zone, and other faults, during collision of the India-Australia plate with Eurasia (e.g. Tapponnier 39 40 41 913 et al., 1982; Tapponnier et al., 1986; Peltzer and Tapponnier, 1988; Replumaz and Tapponnier, 42 43 914 2003). Spreading ceased at around 20.5 Ma (Barckhausen and Roeser, 2004) or 15 Ma (Briais et 44 45 46 915 al., 1993); tectonic flow lines of the c. 32–15 Ma spreading model (Briais et al., 1993) are 47 48 916 consistent with the trend of ocean floor fracture zones, unlike the c. 31–20.5 Ma model 49 50 51 917 (Barckhausen and Roeser, 2004), but the c. 32–20.5 Ma spreading model (Barckhausen et al. 52 53 918 (2014) has not yet been tested (Mazur et al., 2012). Cessation of spreading was approximately 54 55 919 simultaneous with final closure of the proto-SCS and subsequent collision between Borneo and 56 57 58 920 extended continental crust from the rifted South China margin (Taylor and Hayes, 1983; Hall, 59 60 54 61 62 63 64 65 1 2 3 4 921 2002; Hutchison, 2010), as evidenced by the 17–15 Ma Deep Regional Unconformity (in Sabah) 5 6 7 922 and its broadly equivalent Base Middle Miocene Unconformity (in Sarawak) throughout the 8 9 923 Neogene basins of NW Borneo (Levell, 1987; Hazebroek and Tan, 1993; Hutchison, 1996; 10 11 12 924 Hutchison et al., 2000). Post-collision uplift resulted in formation of a foredeep trough along NW 13 14 925 Borneo by the Late Miocene (Fig. 11) (Hinz et al., 1989; Hall, 2002; Ingram et al., 2004; Franke 15 16 926 et al., 2008; Hutchison, 2010). 17 18 19 927 20 21 928 During the Oligocene–Miocene, clockwise rotation and northward translation of the Philippine 22 23 24 929 Sea Plate, and the Izu-Bonin-Mariana (IBM) arc along its eastern margin, was associated with 25 26 930 (1) complex assembly of the present-day Philippine islands by the Middle–Late Miocene, (2) 27 28 29 931 narrowing of the oceanic connections into the SCS (Luzon Strait) and to the Pacific Ocean (north 30 31 932 of the IBM arc), and (3) back-arc rifting in the IBM arc (Taylor, 1992; Hall et al., 1995; Hall, 32 33 34 933 2002; Gaina and Müller, 2007), which is modelled as emergent in some palaeogeographic 35 36 934 interpretations due to physiographic uncertainty (Fig. 11) (Collins et al., 2017a; Collins et al., 37 38 935 2018a). Emergence of the Sunda Shelf created a ‘blind gulf'-type basin morphology throughout 39 40 41 936 the Oligocene–Miocene (Fig. 11) (van Hattum et al., 2006; Hall, 2013; Shoup et al., 2013). In 42 43 937 contrast, the Sunda Shelf is presently submerged, which facilitates ocean outflow from the SCS, 44 45 46 938 with connections via the Malacca Straits, among others, into the Indian Ocean (e.g. Gordon et 47 48 939 al., 2012; Hu et al., 2015). The western SCS margin experienced spatially- and temporally- 49 50 51 940 variable extension and compression, combined with frequent variations in eustatic sea level and 52 53 941 sediment supply. This resulted in the rapid subsidence and infill of several shelf basins, including 54 55 942 the Gulf of Thailand and, further south, the Malay, Penyu and West Natuna basins (Doust and 56 57 58 943 Sumner, 2007; Miller et al., 2011; Shoup et al., 2013; Morley, 2016; Collins et al., 2018a). 59 60 55 61 62 63 64 65 1 2 3 4 944 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 945 44 45 946 Fig. 11. Gross depositional environmental reconstructions for the Late Oligocene–Late Miocene 46 47 947 in Southeast Asia based on sea-level highstand for eight time-slices: (A) 26 Ma (Chattian); (B) 48 49 948 21 Ma (Aquitanian); (C) 18 Ma (Burdigalian); (D) 15 Ma (Langhian); (E) 12 Ma (Serravallian); 50 51 949 (F) 11 Ma (Tortonian); (G) 6 Ma (Messinian). Alternative gross depositional environmental 52 53 950 reconstructions include a submerged Palawan: (H) 26 Ma (Chattian); (I) 21 Ma (Aquitanian); (J) 54 951 18 Ma (Burdigalian). After Collins et al. (2018a). 55 56 952 57 58 59 60 56 61 62 63 64 65 1 2 3 4 953 4.1.3 Model Setup and Outputs 5 6 7 954 Global simulations using Fluidity represent full astronomical tidal forcing with a spin-up period 8 9 955 of period of 120 hours and no open boundary tidal forcing or data assimilation. Global 10 11 12 956 computational meshes produced using qmsh (Avdis et al., 2018) were three-dimensional and 13 14 957 multi-scale, with the highest mesh resolution of ca 10 km in areas of complex bathymetry. 15 16 958 Model outputs included herein are maximum spring tidal range and the magnitude and direction 17 18 19 959 of maximum tidal bed shear stress, plotted as the equivalent grain size capable of being 20 21 960 transported (see Section 3.1.3). ‘Base case’ model simulations use the preferred 22 23 24 961 palaeogeographic interpretations at sea level highstand for three timeslices in the Early, Middle 25 26 962 and Late Miocene (Fig. 12). Sensitivity tests of the base-case models include (1) tidal models for 27 28 29 963 50 m sea level lowstand palaeogeographic interpretations for Late Oligocene–Late Miocene 30 31 964 timeslices, and (2) a Late Miocene (6 Ma; Messinian) tidal model for a palaeogeographic 32 33 34 965 reconstruction with a submerged (10 m) IBM arc. A wider range of model outputs, timeslices 35 36 966 and sensitivity analyses have also been evaluated (Collins et al., 2017a; Collins et al., 2018a). 37 38 967 39 40 41 968 4.1.4 Model Results 42 43 969 On a regional-scale, the base-case palaeotidal model suggests an overall decrease in prevailing 44 45 46 970 maximum tidal range and bed shear stress through the Miocene in the SCS (Fig. 12). Tidal range 47 48 971 in the central part of the SCS decreased from macrotidal (>4 m) in the Early Miocene (Fig. 12A) 49 50 51 972 to mesotidal (>2 to 4 m) in the Middle–Late Miocene (Figs 12C, E). This was contemporaneous 52 53 973 with a decrease in the incoming boundary tide from the Pacific Ocean, from high microtidal– 54 55 974 mesotidal in the Early Miocene to microtidal in the Middle–Late Miocene. Along shorelines in 56 57 58 975 the central SCS, maximum strength tidal currents in base-case simulations could generally 59 60 57 61 62 63 64 65 1 2 3 4 976 transport up to coarse sand to gravel in the Early Miocene (Fig. 12B), fine to coarse sand in the 5 6 7 977 Middle Miocene (Fig. 12D), and fine sand to silt in the Late Miocene (Fig. 12F). These regional- 8 9 978 scale changes in modelled tidal processes were coincident with (1) narrowing of the Luzon Strait 10 11 12 979 from c. 1500 km to 350 km and the Pacific Ocean connection between the IBM arc and Eurasia 13 14 980 from c. 1600 km to 370 km through the Miocene (Fig. 11), and (2) obstruction of a major 15 16 981 outflow from the SCS at its southwestern end due to the emergent Sunda Shelf. 17 18 19 982 20 21 983 Sensitivity analyses also emphasize the potential impact of regional-scale physiographic changes 22 23 24 984 on shoreline tides. Tidal models for sea-level lowstand during the Miocene suggest that 25 26 985 shutdown of throughflow into the Sea of Japan increased tidal inflow into the SCS. This causes 27 28 29 986 an increase in modelled maximum tidal range and bed shear stress along SCS shorelines (Fig. 30 31 987 13A–B) compared to equivalent highstand models (Fig. 12E–F). A Late Miocene tidal model 32 33 34 988 with a submerged IBM arc (to only 10 m water depth) causes a substantial increase in maximum 35 36 989 tidal range and bed shear stress in all areas of the SCS (Fig. 13C–D) compared to the base-case 37 38 990 model (Fig. 12 E–F). 39 40 41 991 42 43 992 On a local-scale, temporal variation in the magnitude of modelled tidal processes generally 44 45 46 993 reflects the fundamental control of regional-scale tectonophysiographic changes. However, 47 48 994 whereas on a regional-scale tidal range decreased through the Miocene, tidal range in the Gulf of 49 50 51 995 Thailand (western SCS) generally increased from microtidal to low mesotidal (cf. Figs. 12C, E): 52 53 996 widening and deepening of the submerged region permitted greater tidal inflow and larger tidal 54 55 997 prism, potentially enhanced by resonance effects (Collins et al., 2018a). Furthermore, the 56 57 58 998 disconnection between calculated and modelled funnelling potential in the Miocene Gulf of 59 60 58 61 62 63 64 65 1 2 3 4 999 Thailand illustrates the strong modifying effect of embayment physiography relative to incoming 5 6 7 1000 tidal potential: the narrow and shallow entrance in the Early–Middle Miocene initially prevented 8 9 1001 tidal inflow into the restricted embayment despite the higher-magnitude regional tides. 10 11 12 1002 Nonetheless, tidal range and bed shear stress maxima in the Oligo–Miocene SCS invariably 13 14 1003 occurred within embayed shoreline areas, particularly those with (1) relatively wide and deep 15 16 1004 entrances open to the incoming tide, and (2) high resonance and theoretical funnelling potential 17 18 19 1005 (Collins et al., 2018a). 20 21 1006 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 59 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 1007 44 45 1008 Fig. 12. Palaeotidal model results in the Oligo–Miocene South China Sea for tidal range (A, C, 46 47 1009 E) and maximum tidal bed shear stress plotted as the maximum sediment calibre entrained (B, D, 48 49 1010 F), for three ‘base case’ palaeogeographic reconstructions: (A, B) Early Miocene at 21 Ma; (C, 50 51 1011 D) Middle Miocene at 15 Ma; and (E, F) Late Miocene at 6 Ma (see Fig. 11). The thicker black 52 53 1012 line (A–F) is the reconstructed present-day coastline. The thinner black lines in the bed shear 54 55 1013 stress plots indicate the orientation of maximum tidal bed shear stress. The pink lines (A–F) 56 1014 indicate the interpreted 200 m palaeobathymetric contour and approximate palaeo-shelf edge. 57 58 1015 See Collins et al. (2018a) for all model results and sensitivity analyses. Map abbreviations: IBM 59 60 60 61 62 63 64 65 1 2 3 4 1016 – Izu-Bonin-Mariana Arc; LS – Luzon strait; PS – Philippine Sea; SCS – South China Sea; SS – 5 6 1017 Sunda Shelf. Grain size abbreviations: vfs = very fine sand; fs = fine sand; ms = medium sand; cs 7 8 1018 = coarse sand; vcs = very coarse sand; fg = fine gravel; cg = coarse gravel. 9 10 1019 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 1020 39 40 1021 Fig. 13. Sensitivity analyses of the base-case for the Late Miocene (6 Ma) base case 41 1022 palaeogeographic reconstruction (cf. Fig. 12E, F) showing modeled tidal range (A, C) and 42 43 1023 maximum tidal bed shear stress, plotted as the maximum sediment caliber entrained (B, D), for a 44 45 1024 50 m sea-level lowstand reconstruction (A, B) and submerged Izu-Bonin-Mariana (IBM) arc (C, 46 47 1025 D). Refer to Fig. 12 for abbreviations. 48 49 1026 50 51 1027 4.1.5 Comparison with the rock record 52 53 54 1028 Maximum tidal range and bed shear stress model results have been compared with Miocene 55 56 1029 sedimentological and micropaleontological data for several circum-SCS basins (Collins et al., 57 58 59 1030 2017a; Collins et al., 2018a). 60 61 61 62 63 64 65 1 2 3 4 1031 5 6 7 1032 Model results are broadly corroborated by sedimentological and micropaleontological data (Fig. 8 9 1033 14) and are consistent with previous Miocene paleoenvironmental stratigraphic interpretations 10 11 12 1034 (e.g. Doust and Sumner, 2007), including the distribution of interpreted mangrove-related facies 13 14 1035 in the western SCS (Morley et al., 2011; Shoup et al., 2013). Modelled highs in regional-scale 15 16 1036 tidal range and bed shear stress compare favourably with Late Oligocene to Middle Miocene 17 18 19 1037 sedimentological and mangrove palynomorph data in several basins (Fig. 14), including the 20 21 1038 following open shoreline systems: (1) mangrove palynomorph acmes in the approximately Late 22 23 24 1039 Oligocene, late Early Miocene and Middle Miocene Bach Ho and Con Son Formations in the 25 26 1040 Cuu Long Basin (basin 2—Fig. 14) (Morley et al., 2011; Chung et al., 2015); (2) the Late 27 28 29 1041 Oligocene–Early Miocene Dua Formation in the Nam Con Son Basin, southern Vietnam (basin 30 31 1042 3—Fig. 14), which contains paralic coals and mudstones with abundant mangrove pollen 32 33 34 1043 (Morley et al., 2011) and tide-influenced fine- to medium-grained sandstones (Tin and Ty, 35 36 1044 1995); (3) very fine- to fine-grained tidal cross-bedded sandstones and heterolithic facies, and 37 38 1045 interstratified carbonaceous mudstone and coals, with abundant mangrove material and pollen, in 39 40 41 1046 the Early Miocene Nyalau Formation, Sarawak Basin (Wan Hasiah, 2003; Amir Hassan et al., 42 43 1047 2013; Togunwa et al., 2015; Amir Hassan et al., 2016; Murtaza et al., 2018); and (4) mixed 44 45 46 1048 fluvial- and tide-influenced, very fine- to fine-grained cross-bedded sandstones and heterolithic 47 48 1049 facies, and mangrove-bearing carbonaceous mudstones in mixed-process deltaic units in the 49 50 51 1050 early Middle Miocene Lambir Formation, Baram-Balabac Basin (basin 8—Fig. 14) (Collins et 52 53 1051 al., 2020). Evidence of tidal influence is also preserved from the Late Oligocene–Early Miocene 54 55 1052 embayed Gulf of Thailand, most notably: (1) medium-grained tidal sandstones and abundant 56 57 58 1053 mangrove pollen in carbonaceous mudstones and coals in the Early Miocene Pattani Basin (basin 59 60 62 61 62 63 64 65 1 2 3 4 1054 4–Fig. 14) (Jardine, 1997; Lockhart et al., 1997; Charusiri and Pum-Im, 2009; Ridd et al., 2011); 5 6 7 1055 and (2) paralic mudstones and coals with abundant mangrove and freshwater flora pollen in the 8 9 1056 Late Oligocene–Early Miocene Malay Basin (basin 5—Fig. 6) (Todd et al., 1997; Morley et al., 10 11 12 1057 2011; Shoup et al., 2013). However, sedimentary evidence for preservation of wave-dominated 13 14 1058 processes (e.g. swaley and hummock cross-stratification) and environments in regions of 15 16 1059 modelled tidal range and bed shear stress include: (1) interpreted barred, wave- and storm- 17 18 19 1060 dominated, shoreface–shelf system in the Early Miocene, southern Malay Basin (Ramli, 1986); 20 21 1061 and (2) wave- and storm-dominated environments in locations relatively distal and/or lateral to 22 23 24 1062 tidally-influenced coastal–delta environments in the Early Miocene Nyalau Formation (Amir 25 26 1063 Hassan et al., 2013; Amir Hassan et al., 2016; Murtaza et al., 2018) and early Middle Miocene 27 28 29 1064 Miri Formation (Abieda et al., 2005; Siddiqui et al., 2016; Collins et al., 2020) in the Sarawak 30 31 1065 and Baram-Balabac basins, NW Borneo, respectively. 32 33 34 1066 35 36 1067 Tidal signals are less widespread in Middle–Late Miocene strata (Fig. 14) but preferentially 37 38 1068 occurred in the embayed shoreline settings, including: (1) medium-grained sandstones with 39 40 41 1069 mangrove-bearing mudstones and coals in the Middle–Late Miocene Pattani Basin, Gulf of 42 43 1070 Thailand (Jardine, 1997; Lockhart et al., 1997; Charusiri and Pum-Im, 2009; Ridd et al., 2011); 44 45 46 1071 (2) medium-grained sandstones and mangrove-bearing mudstones and coals deposited under 47 48 1072 tidally-influenced conditions in the Middle Miocene Malay Basin (Todd et al., 1997; Morley et 49 50 51 1073 al., 2011; Shoup et al., 2013); and (3) tide-influenced deltaic units (e.g. channels) comprising 52 53 1074 very fine- to fine-grained sandstone and mangrove-bearing mudstones in embayed areas in the 54 55 1075 Baram-Balabac Basin, NW Borneo (Hadley et al., 2006; Ainsworth et al., 2011; Collins et al., 56 57 58 1076 2018b). This distribution is consistent with the preferential occurrence of tidal shoreline 59 60 63 61 62 63 64 65 1 2 3 4 1077 environments and mangroves within present-day embayed areas, such as the NE shoreline of the 5 6 7 1078 Gulf of Thailand and, in NW Borneo. The latter includes the Lupar embayment, which hosts the 8 9 1079 tide-dominated Rajang delta (Staub and Gastaldo, 2000), and Brunei Bay (e.g. Staub and Esterle, 10 11 12 1080 1994; Nyberg and Howell, 2016; Collins et al., 2018b; Twilley et al., 2018). However, open- 13 14 1081 coastline systems in the Middle–Late Miocene overwhelmingly preserve evidence for reduced 15 16 1082 tidal influence, most notably: (1) a pronounced decrease in abundance of mangrove pollen and 17 18 19 1083 increase in freshwater pollen in shallow-marine strata after the Middle Miocene in the Cuu Long 20 21 1084 Basin (Chung et al., 2015); (2) a sharp reduction in terrestrial and mangrove-derived pollen and 22 23 24 1085 transition from tidally-influenced deltaic to shoreface–shelf deposition through the Middle 25 26 1086 Miocene in the Nam Con Son Basin, mostly due to increased sea level in the Middle Miocene 27 28 29 1087 thermal maximum (Morley et al., 2011); (3) overall decrease in abundance of mangrove pollen 30 31 1088 and extent of interpreted mangrove-bearing environments in the Middle–Late Miocene Gulf of 32 33 34 1089 Thailand (Shoup et al., 2013); and (4) storm-dominated, fluvial-influenced and tide-affected 35 36 1090 deposition in open coastline areas of the Middle–Late Miocene Baram-Balabac Basin (Lambiase 37 38 1091 et al., 2003; Hadley et al., 2006; Ainsworth et al., 2011; Collins et al., 2018b) (Collins et al., 39 40 41 1092 2017b). In open-coastline settings of the Middle–Late Miocene, as well as lower modelled tidal 42 43 1093 potential, a large fetch and possible increased influence of typhoons (Collins et al., 2017b) would 44 45 46 1094 have increased the potential for wave and storm overprinting of higher frequency, lower 47 48 1095 magnitude tidal processes (e.g. Dott, 1983; Dott, 1996; Miall, 2015; Collins et al., 2018a; Collins 49 50 51 1096 et al., 2018b). Nonetheless, mixed wave- and tide-influenced, mangrove-bearing, open-coastline 52 53 1097 and deltaic strata are preserved in the Middle Miocene Cuu Long Basin, which are similar to the 54 55 1098 present day, mixed wave- and tide-influenced, mangrove-bearing Mekong delta, southern 56 57 58 1099 Vietnam (e.g. Ta et al., 2002a). 59 60 64 61 62 63 64 65 1 2 3 4 1100 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1101 35 36 1102 Fig. 14. Evidence of tide-influenced deposition based on sedimentological and 37 38 1103 micropaleontological data, mainly from petroleum exploration wells, and comparison to base 39 40 1104 case tidal model results (Fig. 12) in South China Sea shelf basins. Rock-record data include grain 41 42 1105 size, cross lamination (ripples) and/or cross bedding interpreted to preserve evidence of tidal 43 1106 process (e.g. bidirectional palaeocurrents, scoop-shaped foresets, mudstone drapes), mangrove 44 45 1107 pollen acmes and the occurrence of paralic, mangrove-bearing coals and source rocks. Studied 46 47 1108 formations and key references for each basin are: (1) Upper Zhuhai (Zh) Formation, Pearl River 48 49 1109 Mouth Basin (Zheng and Deng, 2012); (2) Bach Ho (BH) and Con Son (CS) formations, Cuu 50 51 1110 Long Basin (Morley et al., 2011); (3) Dua (Du), Thong (Th) and Mang Cau (MC) formations, 52 1111 Nam Con Son Basin (Tin and Ty, 1995; Morley et al., 2011); (4) Sequences II–IV, Pattani Basin 53 54 1112 (Jardine, 1997; Lockhart et al., 1997); (5) Groups L–J and E, Malay Basin (Morley et al., 2011); 55 56 1113 (6) Arang (Ar) Formation, West Natuna Basin (Morley et al., 2011); (7) Nyalau (Ny) Formation, 57 58 1114 Balingian Province, Sarawak Basin (Amir Hassan et al., 2013; Amir Hassan et al., 2016); (8) 59 60 65 61 62 63 64 65 1 2 3 4 1115 Lambir (L) and Belait (B) formations, Baram Delta Province, Baram-Balabac Basin (Lambiase 5 6 1116 et al., 2003; Collins et al.). 7 8 1117 9 10 1118 4.2 Early Cretaceous (Aptian–Albian) Lower Greensand Seaway, north-west Europe 11 12 13 1119 4.2.1 Overview 14 15 1120 The Early Cretaceous Lower Greensand Group in Southeast England is well known for its tidal 16 17 18 1121 sandstone deposits (Allen, 1982a; Bridges, 1982; Johnson and Levell, 1995; Wonham and 19 20 1122 Elliott, 1996; Yoshida et al., 2004). The study area is very different to our previous (SCS) 21 22 23 1123 example: it covers a much smaller area, it was part of a larger epicontinental sea and it was 24 25 1124 entirely shallow water, far removed from coeval oceanic basins. The larger-scale (10–100s km) 26 27 1125 basin physiography was determined by a series of precursor, west-east-trending, rift basins (c. 28 29 30 1126 50–100 km long and 10–30 km wide; e.g. Weald , Wessex and Channel basins) that were 31 32 1127 initiated during the Early Cretaceous (e.g. Ziegler, 1990; Hawkes et al., 1998). These basins were 33 34 35 1128 initially (Berriasian–Barremian) filled by thick (100s m; up to ca 1 km) alluvial plain successions 36 37 1129 (Wealden Group). These successions were succeeded by Aptian-Albian deposits that comprise 38 39 40 1130 shallow-marine sandstones (Lower Greensand Group) with exemplary evidence of tidal 41 42 1131 sedimentation (e.g. De Raaf and Boersma, 1977) overlain by offshore marine mudstones (Gault 43 44 1132 Clay Formation). Hence, the Aptian-Albian succession reflects overall marine transgression, 45 46 47 1133 which was accompanied by an overall increase in basin width, length, bathymetry and 48 49 1134 connectivity. Consequently, predicting tidal circulation in this setting is complicated by several 50 51 52 1135 uncertainties, most notably (1) variability in palaeobathymetry caused by the drowning of 53 54 1136 previously separate rift basins with differing initial water depths, (2) complex marine flooding of 55 56 57 1137 these basins, with competing marine incursions entering the Weald Basin through connections to 58 59 60 66 61 62 63 64 65 1 2 3 4 1138 three major marine water bodies during drowning: the Boreal Sea (to the north), proto-Atlantic 5 6 7 1139 Ocean (to the south-west), and Neotethys Ocean (to the south-east) (Fig. 15A–B). Palaeotidal 8 9 1140 modelling and comparison to the stratigraphic record, with emphasis on the Lower Greensand 10 11 12 1141 Group, has been used to understand these uncertainties across a range of different age, 13 14 1142 palaeobathymetric and palaeogeographic scenarios (Wells et al., 2010b). 15 16 1143 17 18 19 1144 4.2.2 Geological Setting 20 21 1145 During the Early Cretaceous, an increase in eustatic sea level, and a waning of rift-related 22 23 24 1146 subsidence, resulted in the marine flooding and connection of several previously isolated 25 26 1147 continental rift basins (Fig. 15A–C). Many of these basins became connected as marine 27 28 29 1148 transgression flooded several relatively narrow (c. 10s km wide) seaways, which exploited pre- 30 31 1149 existing structural lineaments, including basement-linked syn-rift faults (Hawkes et al., 1998). 32 33 34 1150 Thus, the Weald and Paris basins were connected via a northwest-southeast-trending seaway 35 36 1151 along the major Pays de Bray Fault, while the Weald and Southern North Sea basins were 37 38 1152 connected across the London-Brabant Massif via the northeast–southwest-trending ‘Bedfordshire 39 40 41 1153 Strait’ (Ziegler, 1990). Transgression of the Wessex Basin exploited the major basin-bounding 42 43 1154 Purbeck-Isle of Wight Fault Zone (Gupta and Johnson, 2002). 44 45 46 1155 47 48 1156 The various sedimentary basins were infilled with highly diachronous, but broadly Aptian– 49 50 51 1157 Albian age, glauconite-rich shallow-marine sandstones, informally referred to ‘greensands’. The 52 53 1158 first of these shallow-marine sandstone units, the Lower Greensand Group (LGG), is the primary 54 55 1159 focus of this review. The term ‘Lower Greensand Seaway’ is used here to refer to an 56 57 58 1160 interconnected network of three main seaways of latest Aptian-Albian age, each one connecting 59 60 67 61 62 63 64 65 1 2 3 4 1161 with larger marine water bodies (i.e. Boreal, proto-Atlantic and Neothys; Fig. 15A–B). The LGG 5 6 7 1162 stratigraphy and palaeogeography is supported by a robust ammonite biostratigraphic framework 8 9 1163 and contains unconformities of local-to-regional extent (Fig. 15D) (Bridges, 1982). Two 10 11 12 1164 stratigraphic intervals and associated phases of basin-fill deposition are considered below. The 13 14 1165 first phase of deposition (labelled ‘FH’ in Fig. 15D) is represented by the upper part of the 15 16 1166 fissicostatus–martinioides Zone, which comprises the Ferruginous Sands Formation (Isle of 17 18 19 1167 Wight, Wessex and Channel basins) (Ruffell, 1992) and the Hythe Formation (Weald Basin) 20 21 1168 (Bridges, 1982; Ruffell, 1992; Rawson, 2006). These deposits display negligible evidence of 22 23 24 1169 tidal currents, suggesting low tidal range (microtidal–low mesotidal) (Ruffell and Wach, 1991; 25 26 1170 Wells et al., 2010b). The second phase of deposition (labelled ‘FSW’ in Fig. 15E) is represented 27 28 29 1171 by the mid-to-upper part of the upper martinioides– lower tardefurcata Zone, and comprises 30 31 1172 several high-energy, shallow-marine sandstone units, most notably (1) the Woburn Sands 32 33 34 1173 Formation (in Leighton Buzzard) (Johnson and Levell, 1995; Wonham and Elliott, 1996; 35 36 1174 Yoshida et al., 2004); (2) the Folkestone Sands Formation (Weald Basin) (Allen, 1981a; Allen, 37 38 1175 1981b; Allen, 1982a; Bridges, 1982); and (3) the Sandrock Formation (Isle of Wight, Wessex 39 40 41 1176 and Channel basins) (Ruffell and Wach, 1991; Insole et al., 1998; Rawson, 2006) (Fig. 15D). 42 43 1177 These deposits all display compelling evidence of deposition by strong tidal currents within an 44 45 46 1178 inferred macro-tidal setting (Allen, 1982a; Johnson and Levell, 1995). Mud drape spacing in the 47 48 1179 Folkestone Sands has been interpreted to form spring–neap tidal bundles that were deposited in 49 50 51 1180 an ebb-dominated diurnal, or mixed, predominantly diurnal tidal regime (Allen, 1982a). The 52 53 1181 LGG succession is capped everywhere by offshore marine mudstones of the Gault Clay 54 55 1182 Formation, which transgressively onlaps the underlying tidal sandstones (Johnson and Levell, 56 57 58 59 60 68 61 62 63 64 65 1 2 3 4 1183 1995). Palaeotidal modelling has focused on the two stratigraphic intervals outlined above (‘FH’ 5 6 7 1184 and ‘FSW’ in Fig. 15D) (Wells et al., 2010b), as summarised below. 8 9 1185 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 1186 49 50 1187 Fig. 15. Geological and stratigraphic framework of the Early Cretaceous ‘Lower Greensand 51 52 53 1188 Seaway’, NW Europe. (A) Global Aptian palaeogeographic framework. (B) Aptian 54 55 1189 palaeogeographic framework of northwest Eurasia. In A and B, darker grey are significant 56 57 58 1190 uplifted highs and lighter grey shallow-water seas (< 200 m depth). (C) Aptian palaeogeographic 59 60 69 61 62 63 64 65 1 2 3 4 1191 map of southern UK and northern France with significant uplifted highs in dark grey and basins 5 6 7 1192 in light brown. Basin abbreviations: BCB – Bristol Channel Basin; BS – Bedfordshire Strait; 8 9 1193 CCB – Central Channel Basin; PB – Pewsey Basin; PWB – Purbeck-Wright Basin; SCSB – 10 11 12 1194 South Celtic Sea Basin; WAT – Western Approaches Trough; WB – Weald Basin. High 13 14 1195 abbreviations: AM – Armorcian Massif; CM – Cornubian Massif; LBM – London-Brabant 15 16 1196 Massif; MM – Midlands Massif. (D) Aptian palaeogeographic map illustrating key locations for 17 18 19 1197 the chronostratigraphic and lithostratigraphic framework of the Lower Greensand Group (section 20 21 1198 X–Y in E). Location abbreviations in addition to those labelled in C: LB – Leighton Buzzard. (E) 22 23 24 1199 Illustrative chronostratigraphic and lithostratigraphic section of the Lower Greensand Group in 25 26 1200 southern England. Two ‘‘base case’’ palaeogeographies are considered (Fig. 16): ‘FH’ 27 28 29 1201 represents the upper part of the fissicostatus–martinioides Zone depositional sequence, 30 31 1202 corresponding to the Ferruginous Sands Formation on the Isle of Wight and the Hythe Formation 32 33 34 1203 in the Weald; ‘FSW’ represents the mid to upper part of the upper martinioides–lower 35 36 1204 tardefurcata Zone depositional sequence, corresponding to the Folkestone Sands Formation in 37 38 1205 the Weald, the Sandrock Formation on the Isle of Wight, and the Woburn Sands Formation 39 40 41 1206 around Leighton Buzzard. After Wells et al. (2010b), Yoshida et al. (2004) and references 42 43 1207 therein. 44 45 46 1208 4.2.3 Model Setup 47 48 1209 Regional-scale tidal simulations were forced with both astronomical and boundary tides for the 49 50 51 1210 four most significant tidal constituents (M2, S2, K1, and O1) (Kantha and Clayson, 2000); each 52 53 1211 constituent was run independently for an 8-day period (simulated time), with a time step of 5 54 55 1212 minutes, in order to reach a steady-state solution. Tidal amplitude and phase were calculated 56 57 58 59 60 70 61 62 63 64 65 1 2 3 4 1213 using harmonic analysis on the last 30 hours of the simulated free-surface height; tidal range is 5 6 7 1214 twice the total tidal amplitude values. 8 9 1215 10 11 12 1216 Tidal open boundary conditions for regional-scale tidal simulations were generated using a 13 14 1217 global-scale Lower Cretaceous (Aptian) palaeotidal model (Wells et al., 2010a) along the 15 16 1218 southern (Neo-Tethys) and western (proto-Atlantic) margins, and positioned oceanward of the 17 18 19 1219 shelf edge, in order to better resolve the propagation of the oceanic tidal wave onto the 20 21 1220 continental shelf and minimised boundary effects within the Lower Greensand Seaway. The 22 23 24 1221 plate-tectonic and palaeocoastline reconstructions were based on the Palaeogeographic Atlas 25 26 1222 Project (Paul Markwick, personal communication 2007), underpinned by ocean-floor ages 27 28 29 1223 (Müller et al., 1997) and further literature review (Wells et al., 2010a). Palaeobathymetry was 30 31 1224 estimated by reference to modern analogues (Wells et al., 2010a). The Aptian global palaeotidal 32 33 34 1225 model predicts low microtidal ranges in the proto-Atlantic (<1 m) and Boreal (<0.5 m) oceans, 35 36 1226 and higher diurnal-dominated microtidal (c. 1.5–2 m) ranges in the Neotethys (Wells et al., 37 38 1227 2010a). 39 40 41 1228 42 43 1229 Modified versions of the published Lower Greensand Seaway palaeocoastline (Tyson and 44 45 46 1230 Funnell, 1987; Ziegler, 1990; Hancock and Rawson, 1992) were used in regional-scale tidal 47 48 1231 simulations of the Lower Greensand Seaway (Wells, 2008; Wells et al., 2010b). Maximum 49 50 51 1232 modelled water depths in the seaway are typically 25 m and do not exceed 75 m by analogy to 52 53 1233 sand-wave deposits in the present-day English Channel and Southern North Sea (Allen, 1982a; 54 55 1234 Stride, 1982). Numerous sensitivity tests were performed on two ‘base-case’ palaeogeographies 56 57 58 1235 for (1) the upper part of the fissicostatus–martinioides Zone depositional sequence (the ‘FH’ 59 60 71 61 62 63 64 65 1 2 3 4 1236 series, Fig. 15E), referred to as FH1 (Fig. 16A–B), and (2) mid to upper part of the upper 5 6 7 1237 martinioides–lower tardefurcata Zone depositional sequence (the ‘FSW’ series, Fig. 15E), 8 9 1238 referred to as FSW1 (Fig. 16C–D). A key difference between the ‘base case’ scenarios for these 10 11 12 1239 two timeslices is widening of the oceanic connections, especially through the Paris Basin, in the 13 14 1240 upper martinioides–lower tardefurcata Zone due to transgression in the nutfieldensis Zone 15 16 1241 (Casey, 1961; Wells et al., 2010b). 17 18 19 1242 20 21 1243 Eight sensitivity analyses were performed for each ‘base-case’ palaeogeography (Wells et al., 22 23 24 1244 2010b), of which four are discussed herein (Scenarios 2, 4, 6 and 8, using the numbering system 25 26 1245 of Wells et al. (2010b)): (1) closure of the Paris Basin connection to the Neotethys Ocean 27 28 29 1246 (Scenario 2: cases FH2 and FSW2; Fig. 17A, B); (2) connection through the Pewsey Basin to the 30 31 1247 proto-Atlantic Ocean (Scenario 4; FH4 and FSW4; Fig. 17C, D); (3) opening of all oceanic 32 33 34 1248 connections (Scenario 6; FH6 and FSW6; Fig. 17E, F); and (4) doubling the water depth between 35 36 1249 0 and 200 m, whilst maintain the same palaeoshoreline (Scenario 8; FH8 and FSW8; Fig. 17G, 37 38 1250 H). 39 40 41 1251 42 43 1252 4.2.4 Model Results 44 45 46 1253 Base-case simulations for both timeslices suggest propagation of two progressive tidal waves 47 48 1254 into the Lower Greensand Seaway: (1) a generally dominant tide from the Neotethys Ocean to 49 50 51 1255 the south-east, via the Paris Basin, and (2) a generally subordinate tide from the proto-Atlantic 52 53 1256 Ocean to the west and south-west, via Western Approaches Trough (Fig. 16). A connection to 54 55 1257 the Boreal Ocean to the north, via the ‘Bedfordshire Strait’ and North Sea (Fig. 15C, D), had not 56 57 58 1258 yet been established in either base-case simulation (Fig. 16). In the base-case simulation of the 59 60 72 61 62 63 64 65 1 2 3 4 1259 older timeslice (scenario FH1; Fig. 16A), a microtidal (c. 1–2 m) diurnal-dominated tidal regime 5 6 7 1260 in the Lower Greensand Seaway is predicted. The restricted connection between the seaway and 8 9 1261 Paris Basin is associated with funnelling, shoaling and amplification of tides in the northern Paris 10 11 12 1262 Basin, and decreased tidal inflow into the Weald Basin (e.g. Guillocheau et al., 2000). In the 13 14 1263 ‘base-case’ simulation of the younger timeslice (scenario FSW1; Fig. 16B), tides in the Lower 15 16 1264 Greensand Seaway are diurnal-dominated but higher than in scenario FH1: high mesotidal to low 17 18 19 1265 macrotidal in the western Weald and Leighton Buzzard –Bedfordshire Strait area, and mesotidal 20 21 1266 in the rest of the seaway. The simulation shows the northward-propagating tidal wave from the 22 23 24 1267 Neotethys Ocean being significantly amplified by funnelling and shoaling effects as the seaway 25 26 1268 narrows and shallows towards the northwest (Fig. 16B). Furthermore, Coriolis deflection to right 27 28 29 1269 steers the tidal wave into the funnel shaped ‘Leighton Buzzard Trough’, causing further 30 31 1270 amplification and formation of macrotidal conditions here (Fig. 16B). 32 33 34 1271 35 36 1272 Compared to the base-case simulations (Fig. 16), four sensitivity analyses (Scenarios 2, 4, 6 and 37 38 1273 8) indicate the following effects on tides in the Lower Greensand Seaway: 39 40 41 1274 (1) Scenarios FH2 and FSW2 represents closure of the Paris Basin connection to the 42 43 1275 Neotethys Ocean, and therefore loss of the dominant tidal inflow into the seaway. This 44 45 46 1276 substantially decreases modelled tidal range within the seaway in both timeslices, 47 48 1277 decreasing tidal range by up to c. 75% to microtidal in scenario FSW2 (Fig. 17A–B), and 49 50 51 1278 causing local increases in semi-diurnal tides (Fig. 18). 52 53 1279 (2) Scenarios FH4 and FSW4 includes an additional connection to the proto-Atlantic Ocean 54 55 1280 through the Pewsey Basin, which decreases modelled tidal range within the seaway in 56 57 58 1281 both time-slices (Fig. 17C–D). Tidal range is decreased due to destructive interference of 59 60 73 61 62 63 64 65 1 2 3 4 1282 out-of-phase tidal waves, which enter from the Weald Basin from the Pewsey Basin and 5 6 7 1283 the Paris Basin in scenario FH4, and from the English Channel Basin and the Paris Basin 8 9 1284 in scenario FSW4 (Fig. 17C–D). Additionally, some tidal energy may outflow through 10 11 12 1285 the Pewsey Basin in both scenarios. 13 14 1286 (3) Scenarios FH6 and FSW6 reflects opening of an additional oceanic connection through 15 16 1287 the Bedfordshire Strait (Fig. 15D) and first communication with the Boreal Sea, to the 17 18 19 1288 north. This results in decreased modelled tidal range across much of the LGS because the 20 21 1289 various tidal waves are not in phase, leading to destructive interference (Fig. 17E–F). 22 23 24 1290 Additionally, rather than being trapped, funnelled, and amplified within the seaway, the 25 26 1291 dominant incoming tide from the southeast may outflow via the additional connections. 27 28 29 1292 Tides in the seaway become more semi-diurnal influenced in scenario FH6 but remain 30 31 1293 diurnal dominated in scenario FSW6 (Fig. 18). 32 33 34 1294 (4) Scenarios FH8 and FSW8 comprises a doubling the water depth between 0 and 200 m, 35 36 1295 whilst maintaining the same palaeoshoreline. This significantly increases modelled tidal 37 38 1296 range in both timeslices, to high microtidal-mesotidal (c. 1.8–3 m) in scenario FH8 and 39 40 41 1297 macrotidal (c. 5–7 m) in scenario FSW8. This is partially due to enhanced inflow of tidal 42 43 1298 energy and shoaling caused by the larger change in water depth across the shelf. 44 45 46 1299 However, the ratio of diurnal to semi-diurnal tides changes in both time-slices, which 47 48 1300 suggests that regional physiography also had an important effect on tidal resonance (Fig. 49 50 51 1301 18). 52 53 1302 54 55 1303 These scenarios illustrate that the regional-scale (100s km) balance between tidal inflow and 56 57 58 1304 outflow has a first-order control on tides in smaller-scale (10s km) areas and can supersede 59 60 74 61 62 63 64 65 1 2 3 4 1305 funnelling effects within physiographic constrictions, such as in straits and embayments. 5 6 7 1306 Predicted tidal ranges in simulations of the upper martinioides–lower tardefurcata Zone (‘FSW’; 8 9 1307 Figs. 16B, D, 17B, D, F, H) are consistently higher in the Lower Greensand Seaway than 10 11 12 1308 equivalent base-case and sensitivity simulations of the fissicostatus–martinioides Zone (‘FH’; 13 14 1309 Figs. 16 A, C, 17A, C, E, G). The larger tidal ranges in the FSW simulations result from 15 16 1310 increased inflow of tidal energy due to the greater width of the seaway and its ocean connections. 17 18 19 1311 This is especially the case for the Paris Basin, because the maximum depth is similar in 20 21 1312 equivalent FH simulations and the same open tidal boundary conditions are used in FSW and FH 22 23 24 1313 simulations. In addition, in all scenarios for each timeslice, tidal range is higher along the eastern 25 26 1314 margins of the seaway and the Paris Basin, due to Coriolis deflection of the northward 27 28 29 1315 propagating tidal wave from the Neotethys Ocean. 30 31 1316 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 1317 58 59 60 75 61 62 63 64 65 1 2 3 4 1318 Fig. 16. Base case palaeotidal model results in the Early Cretaceous Lower Greensand Seaway 5 6 7 1319 for the fissicostatus–martinioides Zone (A, C) and upper martinioides–lower tardefurcata Zone 8 9 1320 (B, D) timeslices (respectively ‘FH’ and ‘FSW’ in Fig. 15D) showing modelled tidal range (0–4 10 11 12 1321 m) for the four principal tidal constituents (M2 + S2 + K1 + O1), with 20 cm contours and bold, 13 14 1322 annotated contours every 100 cm (A–B), and the ‘F-ratio’ between the amplitudes of diurnal and 15 16 1323 semidiurnal tidal constituents (C–D). After Wells et al. (2010b). Pink labelled dots show 17 18 19 1324 positions of ‘virtual tidal gauges’ in the East Weald Basin (EW), Isle of Wight (IW), Leighton 20 21 1325 Buzzard (LB) and West Weald Basin (WW). Basin abbreviations: CCB – Central Channel Basin; 22 23 24 1326 BCB – Bristol Channel Basin; BS – Bedfordshire Strait; CCB – Central Channel Basin; PB – 25 26 1327 Pewsey Basin; WAT – Western Approaches Trough. Modified from Wells et al. (2010b). 27 28 29 1328 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 76 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 1329 57 58 59 60 77 61 62 63 64 65 1 2 3 4 1330 Fig. 17. Modelled tidal range for the four principal tidal constituents (M2 + S2 + K1 + O1) in 5 6 7 1331 sensitivity analyses of base-case reconstructions for the fissicostatus–martinioides Zone (A, C, E, 8 9 1332 G) and upper martinioides–lower tardefurcata Zone (B, D, F, H) timeslices in the Early 10 11 12 1333 Cretaceous Lower Greensand Seaway (respectively ‘FH’ and ‘FSW’ in Fig. 15D); tidal range 13 14 1334 contours are drawn for 20 cm intervals and bold, annotated contours every 100 cm. Pink labelled 15 16 1335 dots show positions of ‘virtual tidal gauges’ in the East Weald Basin (EW), Isle of Wight (IW), 17 18 19 1336 Leighton Buzzard (LB) and West Weald Basin (WW).Basin abbreviations: CCB – Central 20 21 1337 Channel Basin; BCB – Bristol Channel Basin; BS – Bedfordshire Strait; CCB – Central Channel 22 23 24 1338 Basin; PB – Pewsey Basin; WAT – Western Approaches Trough. Modified from Wells et al. 25 26 1339 (2010b). 27 28 29 1340 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 78 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 1341 40 41 1342 Fig. 18. Bar graphs of modelled tidal range at ‘virtual tide gauge’ locations (see Fig. 16 & 17) 42 43 44 1343 for base-case (Fig. 16) and sensitivity simulations (Fig. 17) for the fissicostatus– martinioides 45 46 1344 Zone (A) and upper martinioides–lower tardefurcata Zone (B) timeslices (respectively ‘FH’ and 47 48 1345 ‘FSW’ in Fig. 15D). Modified from Wells et al. (2010b). 49 50 51 1346 52 53 1347 4.2.5 Comparison with the Rock Record 54 55 56 1348 Modelled tides for the fissicostatus–martinioides Zone (‘FH’ in Fig. 15D) predict microtidal 57 58 1349 conditions across most models (FH2, FH4 and FH6 scenarios; Fig. 17A, C, E) and low mesotidal 59 60 79 61 62 63 64 65 1 2 3 4 1350 in scenario FH8 (Fig. 17G). These results are broadly consistent with the time-equivalent 5 6 7 1351 sedimentary record, which contains little evidence of tidal influence on deposition (see review in 8 9 1352 Wells et al. (2010b)). In the western Weald Basin, putative tidal deposits in the uppermost part of 10 11 12 1353 this interval (Hythe Formation) are of limited areal extent and contain no published evidence of 13 14 1354 bidirectional currents or mud drapes (Casey, 1961; Narayan, 1971; Bridges, 1982; Ruffell and 15 16 1355 Wach, 1991; Rawson, 2006). This comparison supports modest tidal amplification and high 17 18 19 1356 microtidal–low mesotidal tides in the western Weald Basin (Figs. 16A and 17). The comparison 20 21 1357 also suggests that the connection between the Lower Greensand Seaway and Paris Basin may 22 23 24 1358 have been wider, which decreases amplification within the strait and increases tidal inflow into 25 26 1359 the seaway (see scenario FH7 in Wells et al. (2010b)). 27 28 29 1360 30 31 1361 Modelled tides for the upper martinioides–lower tardefurcata Zone (‘FSW’ in Fig. 15D) 32 33 34 1362 consistently predict high mesotidal to low macrotidal conditions across all model scenarios (Figs 35 36 1363 16B, 17D, F, H, 18B), except when the Paris Basin is not connected (Fig. 17B). Closure of the 37 38 1364 Paris Basin connection may have occurred for a short time during a global eustatic sea level fall 39 40 41 1365 in the jacobi Zone, as indicated by a minor non-depositional or erosional hiatus (Fig. 15D) 42 43 1366 (Casey, 1961). Tidal deposits are widespread throughout the seaway at this time, including the 44 45 46 1367 following: (1) mudstone draped cross-bedding and brackish ichnofauna in the Sandrock 47 48 1368 Formation (Isle of Wight, English Channel Basin) (Ruffell and Wach, 1991; Insole et al., 1998; 49 50 51 1369 Rawson, 2006); (2) various combinations of large cross-sets (up to 15 m thick) with mudstone 52 53 1370 drapes (some double mudstone drapes), reactivation surfaces and bidirectional palaeocurrent 54 55 1371 directions, wavy-, flaser- and lenticular-bedded heterolithic toesets, and a shallow-marine 56 57 58 1372 ichnofauna in the Woburn Sands Formation (‘Leigh Buzzard Trough’) (Bridges, 1982; Johnson 59 60 80 61 62 63 64 65 1 2 3 4 1373 and Levell, 1995; Wonham and Elliott, 1996; Yoshida et al., 2004; Wells et al., 2010b), which 5 6 7 1374 are interpreted to preserve large migrating bedforms in tide-dominated estuaries and marine 8 9 1375 embayments (e.g. Yoshida et al., 2004); and (3) compound cross-bedded sandstones with 10 11 12 1376 abundant mud drapes, reactivation surfaces, spring–neap tidal bundles, heterolithics and a 13 14 1377 shallow-marine ichnofauna in the Folkestone Sands Formation (Weald Basin), which are 15 16 1378 interpreted to preserve tidal sand waves formed in a shallow sea (Allen, 1982a; Bridges, 1982). 17 18 19 1379 These deposits record deposition under strong tidal currents, with probable mesotidal to 20 21 1380 macrotidal ranges (Allen, 1981b), which is supported by palaeotidal model results (Fig. 17B and 22 23 24 1381 18). Furthermore, the predicted diurnal-dominated tidal regime in the LGS in all modelled 25 26 1382 scenarios (Fig. 18) matches the interpretation of diurnal-dominated spring–neap tidal bundles in 27 28 29 1383 the Folkestone Sands Formation (Allen, 1981a; Allen, 1982a). 30 31 1384 32 33 34 1385 4.3 Late Cretaceous (Turonian-Cenomanian), Bohemian Cretaceous Basin, Central 35 36 1386 Europe 37 38 1387 4.3.1 Overview 39 40 41 1388 The Bohemian Cretaceous Basin (BCB) contains prominent tide-influenced shallow-marine 42 43 1389 sandstones of Turonian-to-early-Coniacian age (e.g. Jerzykiewicz and Wojewoda, 1986; Uličný, 44 45 46 1390 2001; Uličný et al., 2009; Mitchell et al., 2010). The BCB was a slowly subsiding, transtensional 47 48 1391 basin that together with other, linked basins formed a large and shallow epicontinental sea across 49 50 51 1392 much of Europe (e.g. Ziegler, 1990; Mitchell et al., 2010). As with the LGS example presented 52 53 1393 above, the BCB was far removed from coeval oceanic basins; over a thousand kilometres from 54 55 1394 the Neotethys Ocean to the southeast and the Proto-Atlantic Ocean to the west (Fig. 19) (e.g. 56 57 58 1395 Ziegler, 1990; Mitchell et al., 2010). Several emergent landmasses lay in between these oceans 59 60 81 61 62 63 64 65 1 2 3 4 1396 and the BCB (Fig. 19), such that boundary tides are likely to have been significantly blocked and 5 6 7 1397 damped by seabed friction (Mitchell et al., 2010). However, funnelling and shoaling effects may 8 9 1398 have been important in local-scale straits (c. 10s km wide) within the basin (Fig. 20). In this 10 11 12 1399 context, two depositional models have been proposed for Turonian-to-early-Coniacian shallow- 13 14 1400 marine sandstones in the BCB. Early models interpreted the sandstones as the deposits of large 15 16 1401 offshore bedforms sculpted by storms and tides (cf. tidal sand banks or ridges) and accumulated 17 18 19 1402 in fault-bounded bathymetric depressions (e.g. Jerzykiewicz and Wojewoda, 1986). More 20 21 1403 recently, the sandstones were re-interpreted as the deposits of localised, top-truncated, coarse- 22 23 24 1404 grained deltaic shorelines that were reworked by tidal currents in the basin (Uličný, 2001; Uličný 25 26 1405 et al., 2009). Palaeotidal modelling has been used with two aims (Mitchell et al., 2010): (1) to 27 28 29 1406 understand how boundary tides from the Neotethys and Proto-Atlantic oceans were expressed as 30 31 1407 tidal circulation in the BCB, by considering regional-scale (10–100s km) basin physiography 32 33 34 1408 (Fig. 19); and (2) to assess whether modelled tidal bed shear stress was capable of generating the 35 36 1409 grain-size distributions, bedform types and palaeocurrent orientations observed at local-scale 37 38 1410 (1s–10s km) in the Turonian-to-early-Coniacian shallow-marine sandstones (Fig. 20). 39 40 41 1411 42 43 1412 4.3.2 Geological Setting 44 45 46 1413 Turonian-to-early-Coniacian strata in the BCB were deposited shortly after peak eustatic 47 48 1414 flooding at the Cenomanian–Turonian boundary and the maximum extent of the Cretaceous 49 50 51 1415 shallow epicontinental sea in Europe (Fig. 19) (Hancock and Kauffman, 1979; Ziegler, 1990; 52 53 1416 Miller et al., 2003). These strata record drowning of Cenomanian fluvio-estuarine deposits 54 55 1417 around the basin margin (Uličný and Špičáková, 1996), and the onset of open marine conditions 56 57 58 1418 throughout the BCB. Turonian and early Coniacian strata contain eight basinward-thinning 59 60 82 61 62 63 64 65 1 2 3 4 1419 sandstone wedges (‘TUR1-7’ and ‘CON1’ genetic sequences of Uličný et al. (2009)), some of 5 6 7 1420 which terminate against or show abrupt thickness changes across syn-depositional faults 8 9 1421 (Jerzykiewicz and Wojewoda, 1986; Uličný et al., 2009). Each wedge consists of several 10 11 12 1422 tongues, and the basinward-lying part of each tongue contains a single, basinward-dipping set of 13 14 1423 thick (up to 80 m), steeply dipping (up to 30˚) foresets. Each tongue is interpreted to record the 15 16 1424 progradation of a coarse-grained, Gilbert-type delta from the basin margin, with delta topsets 17 18 19 1425 having been removed by later transgressive erosion (Uličný, 2001; Uličný et al., 2009). Tidal 20 21 1426 influence was pervasive, as indicated by: (1) cross-bedded, coarse-grained sandstones with 22 23 24 1427 bidirectional palaeocurrents oriented parallel to the basin axis, commonly perpendicular to the 25 26 1428 delta-front foresets that contain the cross-beds; (2) reactivation surfaces in cross-bed sets; and (3) 27 28 29 1429 mudstone, siltstone and silty sandstone drapes, which are sometimes paired, along the foresets of 30 31 1430 cross-beds (e.g. Jerzykiewicz and Wojewoda, 1986; Uličný, 2001; Uličný et al., 2009; Mitchell 32 33 34 1431 et al., 2010). A dataset combining outcrops and densely spaced boreholes provides good 35 36 1432 constraint on the basin-fill thickness and syn-depositional physiography of the BCB (Uličný et 37 38 1433 al., 2009), which contained islands with intervening, fault-bounded, local-scale (c. 10s km) 39 40 41 1434 straits (e.g. ‘Elbe Strait’ of Mitchell et al. (2010); Fig. 20). However, the physiography of many 42 43 1435 areas in the wider European epicontinental sea is poorly constrained (Ziegler, 1990). 44 45 46 1436 Consequently, modelled palaeobathymetric scenarios are similar for the BCB, but differ by up to 47 48 1437 100 m water depth in other basin centres in the epicontinental European seaway (Fig. 19B–C). 49 50 51 1438 52 53 1439 Palaeotidal modelling work on the BCB has focussed on Early to Middle Turonian deltaic to 54 55 1440 shallow-marine strata, which form the intermediate part of the ‘TUR 2’ genetic sequence of 56 57 58 1441 Uličný et al. (2009), and occur in three tectonically controlled depocenters: (1) the Lužice-Jizera 59 60 83 61 62 63 64 65 1 2 3 4 1442 Sub-basin in the eastern Elbe Strait, fed by sediment sourced from the Western Sudetic Island; 5 6 7 1443 (2) the Ohře Ramp on the western flank of the Elbe Strait, fed by sediment sourced from the 8 9 1444 Most-Teplice Palaeohigh; and (3) Orlice-Žďár Sub-basin, fed by sediment sourced from an 10 11 12 1445 unnamed palaeohigh at the south-eastern edge of the Central European Island (Fig. 20A). The 13 14 1446 Lužice-Jizera Sub-basin records a major regressive episode in the TUR 2 genetic sequence, 15 16 1447 comprising a 20-35 m-thick delta-front clinoform set, which prograded into the up to ca. 40-m- 17 18 19 1448 deep Elbe Strait (Fig. 20B) (Uličný, 2001; Uličný et al., 2009; Mitchell et al., 2010). 20 21 1449 Palaeocurrent data from deposits representing early-to-intermediate regression of the TUR 2 22 23 24 1450 deltas (i.e. the modelled interval) in the Elbe Strait and north-western Lužice-Jizera Sub-basin 25 26 1451 indicate dominant palaeoflow towards the northwest (Fig. 20A; Uličný et al., 2009; Mitchell et 27 28 29 1452 al., 2010), while palaeocurrent data for late TUR 2 deltaic regression in the central Lužice-Jizera 30 31 1453 Sub-basin indicate dominant palaeoflow towards the southeast (Uličný, 2001; Uličný et al., 32 33 34 1454 2009). In the Ohře Ramp depocenter, TUR 2 clinoforms are mud-dominated with a large-scale 35 36 1455 sigmoidal geometry (Uličný et al., 2009; Mitchell et al., 2010). In the Orlice-Žďár Sub-basin, the 37 38 1456 correlative unit to the TUR 2 sequence in the Elbe Strait comprises erosively-based, channelised 39 40 41 1457 sandstones interpreted as tidal shoals deposited during a relative sea-level lowstand (Čech and 42 43 1458 Uličný, 1996). 44 45 46 1459 47 48 49 50 51 52 53 54 55 56 57 58 59 60 84 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 1460 50 51 1461 52 53 1462 Fig. 19. (A) Stratigraphic chart showing the chronostratigraphy (modified after Ogg et al. 54 55 1463 (2004)), main lithofacies in the Lužice-Jizera Sub-basin (see Fig. 20A), genetic sequences 56 57 1464 recognized in this paper, and phases of basin evolution (after Uličný et al., 2009). (B) Regional 58 59 60 85 61 62 63 64 65 1 2 3 4 1465 palaeogeography for the Mid-Cretaceous European Epicontinental Sea (Ziegler, 1990; Dercourt 5 6 1466 et al., 2000; Golonka, 2004; Gil et al., 2006; Golonka et al., 2006; Golonka, 2007; Mitchell et al., 7 8 1467 2010). The approximate outline of the Bohemian Cretaceous Basin (BCB) is shown in red. (c) 9 10 1468 Gross depositional environmental map of central-western mainland Europe for the Cenomanian– 11 12 1469 Turonian (from Ziegler, 1990). (D–E Regional palaeobathymetries for palaeotidal modelling of 13 1470 the Mid-Cretaceous European Epicontinental Sea (MCEES), showing major contours for (D) 14 15 1471 minimum and (E) maximum depth scenarios (after Mitchell et al., 2010). Red box shows the 16 17 1472 position of the BCB. Abbreviations: AM = Amorican Massif; BCB = Bohemian Cretaceous 18 19 1473 Basin; BM = Bohemian Massif; C = Cracow Swell; CM = Cornubian Massif; CCM = Central 20 21 1474 Carpathian Massif; CSH = Corso-Sardinian High; EH = Ebro High; FH = Faeroe High; GH = 22 23 1475 Grampian High; HB = Hatton Bank; HP = Hebrides Platform; IbM = Iberian Massif; IM = Irish 24 1476 Massif; M = Moesia; MC = Massif Central; SP = Shetland Platform; R = Rodopes; RB = Rockall 25 26 1477 Bank; RM = Rhenish Massif. 27 28 1478 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 1479 47 1480 Fig. 20. Local scale palaeogeography (A) and palaeobathymetric (B) for the early Middle 48 49 1481 Turonian Bohemian Cretaceous Basin (onset of Collignoniceras woollgarii Zone). The extent of 50 51 1482 deltaic depocenters correspond to intermediate regression of the ‘TUR 2’ siliciclastic wedge (see 52 53 1483 Fi. 19A). Circled numbers (1) to (3) indicate the three main depocenters: (1) the Lužice-Jizera 54 55 1484 Sub-basin; (2) the Ohře Ramp; and (3) the Orlice-Žďár Sub-basin. MTP – Most-Teplice 56 57 1485 Palaeohigh; LuFZ – Lužice (Lausitz) Fault Zone; LZHFZ – Labe-Železné Hory Fault Zone. 58 1486 Modified after (Uličný et al., 2009). (B) Palaeobathymetric interpretation based on facies 59 60 86 61 62 63 64 65 1 2 3 4 1487 analysis of preserved outcrop and subsurface data (Uličný, 2001; Uličný et al., 2009). The 5 6 1488 heights of delta-front clinoforms suggests minimum depths of c. 35 m in the Elbe Strait, whereas 7 8 1489 a maximum depth of c. 50 m is estimated for the basin interior as inferred from trace fossil 9 10 1490 assemblages. After Mitchell et al. (2010). 11 12 1491 13 1492 4.3.3 Model Setup 14 15 16 1493 Palaeotidal model simulations in the Mid-Cretaceous European Epicontinental Sea (MCEES) 17 18 1494 and BCB were forced with both astronomical and co-oscillating boundary tides with the four 19 20 21 1495 main tidal constituents (M2, S2, K1 and O1). To reduce the impact of uncertain co-oscillating 22 23 1496 boundary tides in the BCB, the regional-scale modelled domain covers much of the surrounding 24 25 26 1497 MCEES (Fig. 19). Open boundaries occur adjacent to the deep, expansive Proto-Atlantic and 27 28 1498 Neotethys oceans, whereas the boundaries adjacent to the extensive shallow seas of Arctic region 29 30 1499 and Russian Platform are unforced, because they are deemed unlikely to have had a significant 31 32 33 1500 tidal range (Fig. 19) (Wells et al., 2007a; Mitchell et al., 2010). The co-oscillating boundary tide 34 35 1501 is set in phase with the natural resonance at each respective boundary to give the maximum tidal 36 37 38 1502 potential in the seaway. This is determined by running a model with astronomical forcing, 39 40 1503 undertaking harmonic analysis of tidal amplitude time series collected at various points along the 41 42 43 1504 forced boundary, and interpolating the phase values at each point along the boundary so that the 44 45 1505 spacing between them matches the resolution of the mesh (Section 3.1.2) (Wells et al., 2007a; 46 47 48 1506 Mitchell et al., 2010). 49 50 1507 51 52 1508 Two sensitivity cases of tides in the MCEES were considered: (1) palaeobathymetric uncertainty 53 54 55 1509 was tested using two scenarios (Fig. 19D, E), and (2) resonance of different tidal constituents 56 57 1510 was tested by imposing different boundary tides weighted towards semi-diurnal (M2, S2; F-ratio 58 59 60 87 61 62 63 64 65 1 2 3 4 1511 of 0.1) and diurnal components (K1, O1; F-ratio of 10). All simulations included a spin-up period 5 6 7 1512 of five days and were run for a single spring–neap cycle lasting 14.8 days with a time step of 5 8 9 1513 min. These regional-scale tidal simulations were subsequently investigated on a more local scale 10 11 12 1514 in the BCB. 13 14 1515 15 16 1516 4.3.4 Model Results 17 18 19 1517 On a regional scale, modelled tidal range in the interior of the MCEES is consistently microtidal 20 21 1518 to mesotidal (Fig. 21), which supports attenuation of the tidal wave by seabed friction and 22 23 24 1519 emergent landmasses as it propagated across the continental shelf (Shaw, 1964; Hallam, 1981; 25 26 1520 Wells et al., 2005a; Mitchell et al., 2010). Tidal amplification forming macrotidal conditions is 27 28 29 1521 limited to embayments and straits. For example, macrotidal conditions are predicted on the 30 31 1522 southern margin of the Fenno-Scandian High (Fig. 21), but this only occurs with specific 32 33 34 1523 boundary and bathymetric conditions, consistent with the influence of tidal resonance (Fig. 7) 35 36 1524 (Wells et al., 2007a). 37 38 1525 39 40 41 1526 On a local scale within the BCB, modelled tidal range also varies from microtidal to mesotidal, 42 43 1527 with elevated tidal ranges mainly restricted to the embayed western and southern margins (Fig. 44 45 46 1528 21). Modelled values of maximum tidal bed shear stress are consistently elevated locally in 47 48 1529 palaeogeographic constrictions between islands, including the Elbe Strait (Fig. 22). Maximum 49 50 51 1530 bed shear stress values are slightly higher for the diurnal regime compared to the semidiurnal 52 53 1531 regime (Fig. 22B, D), and increase with increasing boundary tide magnitude (Fig. 22A–B). 54 55 1532 Water depth in the regional seaway also influences the predicted maximum bed shear stresses 56 57 58 1533 locally in the BCB: modelled values are higher in the minimum depth scenario for the semi- 59 60 88 61 62 63 64 65 1 2 3 4 1534 diurnal regime, but higher in the maximum depth scenario for the diurnal tidal regime (Fig. 22C, 5 6 7 1535 D). This result suggests variations in resonance potential between boundary tide and 8 9 1536 palaeobathymetry scenarios. However, this inference is not shown in the modelled tidal range 10 11 12 1537 (Fig. 21) or explained by simple models of tidal resonance (e.g. Fig. 7), which indicate that 13 14 1538 slower and shorter-wave semi-diurnal tides are typically closer to resonance in deeper domains 15 16 1539 (Wells, 2008; Mitchell et al., 2010). Instead, these modelled bed shear stress patterns probably 17 18 19 1540 result from relatively complex, constructive interaction between the different co-oscillating 20 21 1541 boundary tides and the relative depths of the otherwise unchanged domains (Mitchell et al., 22 23 24 1542 2010). 25 26 1543 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 1544 49 50 51 1545 Fig. 21. Modelled tidal range in the Mid-Cretaceous European Epicontinental Sea (MCEES) for 52 1546 eight sensitivity tests for co-oscillating diurnal (A–D) versus semi-diurnal (E–H) boundary tide 53 54 1547 regimes, 0.5 m (A, B, E, F) versus 1.5 m (C, D, G, H) boundary tidal range, and minimum (min.) 55 56 1548 (A, C, E, G) and maximum (max.) (B, D, F, H) regional palaeobathymetry in the MCEES. 57 58 1549 Fluidity consistently predicts a microtidal to mesotidal range in the interior of the seaway, 59 60 89 61 62 63 64 65 1 2 3 4 1550 suggesting attenuation of the boundary tidal waves across the continental shelf by bed friction 5 6 1551 and blocking by emergent landmasses. After Mitchell et al. (2010). 7 8 1552 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1553 35 -2 36 1554 Fig. 22. Modeled maximum bed shear stress in the Bohemian Cretaceous Basin. The 0.5 Nm 37 38 1555 contours show the approximate minimum bed shear stress required for the formation of dunes in 39 1556 coarse sand (Fig. 10) (Harms et al., 1982), whereas 1.0 Nm-2 is the approximate minimum bed 40 41 1557 shear stress required to form the observed scale of 3D dunes in coarse-grained sand in the Elbe 42 43 1558 Strait. Results for a 0.5 m (A) and 1.5 m (B) semi-diurnal boundary tide regime in the minimum 44 45 1559 (min.) depth regional palaeobathymetric domain (Fig. 19D) indicate that the modeled maximum 46 47 1560 bed shear stress is strongly dependent on the amplitude of the co-oscillating boundary tide. 48 49 1561 Results for the 1.5 m diurnal boundary tide regime in (C) minimum and (D) maximum (max.) 50 1562 regional paleobathymetries indicate that the modeled maximum bed shear stress is strongly 51 52 1563 dependent on regional palaeobathymetry (Fig. 19D, E). After Mitchell et al. (2010). 53 54 1564 55 56 1565 4.3.5 Comparison with the Rock Record 57 58 59 60 90 61 62 63 64 65 1 2 3 4 1566 At the regional scale, palaeotidal modelling demonstrates that it is plausible for boundary tides 5 6 7 1567 from the Neotethys and Proto-Atlantic oceans to have propagated into the BCB and influenced 8 9 1568 water circulation here during the late Cretaceous, even allowing for uncertainty in the 10 11 12 1569 physiography and boundary tides of the European Mid-Cretaceous European Epicontinental Sea 13 14 1570 (Fig. 21). Modelled tidal range in the BCB is microtidal to mesotidal, due to attenuation and 15 16 1571 blocking of the boundary tidal waves as they propagated from the open ocean. These results are 17 18 19 1572 inconsistent with early interpretations of Turonian-to-early-Coniacian sandstones as large tidal 20 21 1573 bedforms (Jerzykiewicz and Wojewoda, 1986), which implies a macro-tidal regime (Stride, 22 23 24 1574 1973; Stride, 1982). Modelled bed shear stress in the BCB is only sufficiently high to transport 25 26 1575 coarse sand where the shoreline is constricted along straits and embayments. These results 27 28 29 1576 support recent interpretations of a tide-influenced deltaic origin for the Turonian-to-early- 30 31 1577 Coniacian sandstones (Uličný, 2001; Uličný et al., 2009; Mitchell et al., 2010), in which fluvio- 32 33 34 1578 deltaic sediment supplied laterally from the basin margins was reworked along the basin axis by 35 36 1579 strong, locally constricted tidal currents. 37 38 1580 39 40 41 1581 Within the Elbe Strait and northwestern Lužice-Jizera Sub-basin (Figs 20 & 22), the early-to- 42 43 1582 intermediate regressive part of the TUR 2 genetic sequence comprises an upward-coarsening, 20- 44 45 46 1583 35 m-thick delta-front clinoform set that is dominated by coarse-grained sandstone. The 47 48 1584 dominant cross-bedding, including in gravelly sandstones to granule conglomerates, displays the 49 50 51 1585 following characteristics: (1) cross-sets 10 cm thick in the lower parts of the clinoform set and up 52 53 1586 to 30–40 cm thick in its upper parts; (2) tabular sets with abundant reactivation surfaces in the 54 55 1587 middle parts of the clinoform set; (3) silty, fine-grained to very fine-grained sandstone drapes 56 57 58 1588 occur locally on foresets; and (4) consistent WNW-directed palaeoflow in the lower to middle 59 60 91 61 62 63 64 65 1 2 3 4 1589 part and bi-directional trough cross-sets in the upper part of the clinoform set (Fig. 23) (Mitchell 5 6 7 1590 et al., 2010). These features indicate extensive reworking of the seabed by tidal currents with 8 9 1591 velocities in excess of 0.6 to 0.8 ms-1, equivalent to bed shear stresses in excess of c. 1.0 Nm-2 10 11 12 1592 (Fig. 10) (Harms et al., 1982; Southard and Boguchwal, 1990). All modelled scenarios with 13 14 1593 forced boundary conditions generated maximum bed shear stresses in excess of c. 2.0 Nm-2 in 15 16 1594 the Elbe Strait (Fig. 22), which is capable of forming 3D dunes in coarse sand in up to c. 20 m 17 18 19 1595 water depths. Instantaneous bed shear stress vectors in all models show clear northwest- and 20 21 1596 southeast-directed bi-polarity in the Elbe Strait, in accordance with the flood and ebb of the tide, 22 23 24 1597 and consistent with recorded palaeocurrent directions (Mitchell et al., 2010). In contrast, 25 26 1598 maximum and mean bed shear stress vectors, which are time-averaged over each model run, lack 27 28 29 1599 a consistent pattern across the range of palaeogeographic sensitivity tests, and are instead highly 30 31 1600 sensitive to subtle changes in local palaeogeography (Mitchell et al., 2010). The range and 32 33 34 1601 variability of maximum and mean bed shear stress vectors in palaeogeographic sensitivity tests 35 36 1602 encompasses the dominant WNW-directed palaeocurrents from early-to-intermediate regression 37 38 1603 of the TUR 2 deltas in the Elbe Strait and northwestern Lužice-Jizera Sub-basin (Fig. 23; Uličný 39 40 41 1604 et al., 2009; Mitchell et al., 2010) and also the dominant southeast-directed palaeocurrents from 42 43 1605 late regression of the TUR 2 deltas in the central Lužice-Jizera Sub-basin (Uličný, 2001; Uličný 44 45 46 1606 et al., 2009), but there are insufficient data to constrain detailed local palaeogeography such that 47 48 1607 a dominant tidal palaeoflow direction can be confidently predicted from model output (Mitchell 49 50 51 1608 et al., 2010). This result demonstrates the limitation of paleotidal modelling for prediction at a 52 53 1609 higher resolution than available geological data can support. In addition, the outcrop-scale detail 54 55 1610 of the extensive current modification of delta-front clinoforms recorded by the sedimentary 56 57 58 1611 structures represents the time-integrated record of local tidal reworking during specific 59 60 92 61 62 63 64 65 1 2 3 4 1612 increments of delta progradation at specific locations, at higher spatial resolutions and potentially 5 6 7 1613 lower temporal resolutions than palaeotidal model runs. 8 9 1614 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1615 31 32 1616 Fig. 23. Close-up view of the Elbe Strait area within the BCB (Fig. 20), showing the 33 34 1617 progradation extent and direction of sandy clinoforms (Voigt and Tröger, 1996; Uličný et al., 35 36 1618 2009), and typical palaeocurrent rose diagrams for small-scale cross-sets in clinoforms recording 37 38 1619 intermediate regression of TUR 2 deltas. Circled numbers indicate (1) the Lužice-Jizera Sub- 39 40 1620 basin; (2) the Ohře Ramp. 41 42 1621 43 44 1622 5 DISCUSSION 45 46 1623 5.1 Comparing Tidal Model and Rock Record Data 47 48 49 1624 The comparison of palaeotidal model to rock-record data involves the evaluation of different 50 51 1625 data types with contrasting dimensions and spatial-temporal scales (Fig. 24). This review has 52 53 54 1626 highlighted favourable comparisons between (1) palaeotidal model predictions of tidal range 55 56 1627 (Wells et al., 2005a; Wells et al., 2007a; Wells et al., 2010a; Wells et al., 2010b; Collins et al., 57 58 59 60 93 61 62 63 64 65 1 2 3 4 1628 2017a; Collins et al., 2018a; Dean et al., 2019) and tidal bed shear stress (Mitchell et al., 2010; 5 6 7 1629 Collins et al., 2017a; Collins et al., 2018a; Dean et al., 2019), with (2) the occurrence of tidally- 8 9 1630 influenced strata in the spatial and temporal domains of the modelled areas. However, the 10 11 12 1631 comparison of palaeotidal model results and the time-equivalent rock record is limited by several 13 14 1632 factors, in particular: (1) the spatial and temporal resolutions of the palaeogeographic data and 15 16 1633 related interpretations underpinning palaeotidal simulations (e.g. basin morphology, 17 18 19 1634 palaeobathymetry, gross depositional environments); and (2) the relationship between model 20 21 1635 outputs (e.g. palaeotidal range and bed shear stress) and interpretations of shoreline depositional 22 23 24 1636 processes and geomorphology based on rock-record observations. These issues are discussed 25 26 1637 below. 27 28 29 1638 30 31 1639 5.1.1 Spatial and temporal resolution 32 33 34 1640 Palaeogeographic reconstructions underpinning palaeotidal simulations involve combining, 35 36 1641 simplifying and averaging multiple geological data types (e.g. sedimentological, biostratigraphic, 37 38 1642 seismic). Each data type contains uncertainties, especially the quality of age dating and 39 40 41 1643 geological interpretations (Markwick and Valdes, 2004). The resolution of geologic data used to 42 43 1644 underpin palaeogeographic maps is user defined and may vary depending on many factors, 44 45 46 1645 including available data and project aims. With increasing spatial extent, the minimum temporal 47 48 1646 resolution of the geologic data underpinning palaeogeographic maps generally coarsens, 49 50 51 1647 becomes more variable and forms a composite ‘time-slice’ rather than a single ‘time plane’ (Fig. 52 53 1648 24A). 54 55 1649 56 57 58 59 60 94 61 62 63 64 65 1 2 3 4 1650 Palaeotidal modelling provides areal (2D) and temporal data on three main parameters: (1) tidal 5 6 7 1651 amplitude, (2) tidal range and (3) tidal bed shear stress (magnitude and direction of 8 9 1652 instantaneous, mean and maximum values). In existing palaeotidal simulations, the maximum 10 11 12 1653 spatial resolution of computational meshes is on the order of 10 km and the temporal resolution 13 14 1654 is typically c. 2–5 Ma (Fig. 24B and C). However, the resolutions of model timeslices are often 15 16 1655 much broader and vary significantly on a case-by-case basis (Table 3). Rock record data is 17 18 19 1656 typically one-dimensional (e.g. stratigraphic logs, core and well data), occasionally two- 20 21 1657 dimensional (e.g. outcrop panels, well-log correlation panels, seismic cross-sections and maps) 22 23 24 1658 and rarely three-dimensional (e.g. curvilinear and/or multiple outcrop panels, multiple and 25 26 1659 closely-spaced cores and wells, 3D seismic volumes) (Fig. 24B). Such data may lie at spatial 27 28 29 1660 resolutions much smaller than those of palaeotidal model meshes and model timeslices (e.g. 30 31 1661 individual stratigraphic logs, cores, wells and outcrop panels). It is possible to address the 32 33 34 1662 discrepancy in spatial scales between rock record data and palaeotidal models by combining rock 35 36 1663 record data from multiple locations, although such amalgamation of data should be carried out 37 38 1664 carefully so as not to obscure important local patterns (e.g. within the context of facies analysis 39 40 41 1665 carried out in the hierarchical stratigraphic framework of Vakarelov and Ainsworth (2013), as 42 43 1666 outlined below). For example, in paleotidal models of the Bohemian Cretaceous Basin (section 44 45 46 1667 4.3), instantaneous bed shear stress provides a more reliable model output for comparison with 47 48 1668 rock-record paleocurrent data than values of mean and maximum bed shear stress collated over 49 50 51 1669 multiple tidal cycles (Mitchell et al., 2010). 52 53 1670 54 55 1671 Facies modelling aimed at deciphering the relative influence of tide, wave and fluvial processes 56 57 58 1672 involves analysis at a wide range of scales, from facies (mm–m) to systems tracts (10–100s km) 59 60 95 61 62 63 64 65 1 2 3 4 1673 (Van Wagoner et al., 1990; Walker and James, 1992; Posamentier and Walker, 2006; Hampson 5 6 7 1674 et al., 2008). Vakarelov and Ainsworth (2013) have formalized this range for shoreline 8 9 1675 depositional systems into five stratigraphic hierarchical levels, each with different spatial 10 11 12 1676 resolutions and dimensions (Fig. 25): (1) facies (element), a component of a depositional 13 14 1677 element; (2) facies association (element set), a depositional environment; (3) parasequence 15 16 1678 (element complex assemblage), a facies model for part of a depositional system; (4) 17 18 19 1679 parasequence or parasequence set (element complex assemblage set), a depositional system 20 21 1680 model; and (5) a transgressive-regressive sequence or sequences, a depositional system evolution 22 23 24 1681 model. Comparing tidal model and rock-record data most often occurs at the facies, facies- 25 26 1682 association and parasequence levels, and possibly the parasequence-set level. This is due in part 27 28 29 1683 to data availability, but also because the variability in process dominance and preservation 30 31 1684 typically increases up the stratigraphic levels. For example, mixed energy depositional systems 32 33 34 1685 (parasequence set level and above) often comprise several depositional sub-environments 35 36 1686 (parasequence level) with varying degrees of tide, wave and/or fluvial influence (e.g. Ainsworth 37 38 1687 et al., 2011; Vakarelov and Ainsworth, 2013). 39 40 41 1688 42 43 1689 Deciphering the degree and extent of tidal influence is further complicated by incomplete 44 45 46 1690 stratigraphic preservation, including preservational bias. Tidal deposits may be preferentially 47 48 1691 preserved in a wide range of depositional environments and with variable significance. For 49 50 51 1692 example, such deposits are often widespread in coastal embayments, but geographically 52 53 1693 restricted elsewhere, such as in tidal inlets within larger barrier-lagoon systems. However, the 54 55 1694 maximum resolution of computational meshes used in palaeotidal modelling, especially for 56 57 58 1695 regional-scale studies, is significantly larger than the typical spatial dimensions of facies (mm– 59 60 96 61 62 63 64 65 1 2 3 4 1696 m) and facies associations (1–100s m) (Fig. 24B). Consequently, the comparison of model to 5 6 7 1697 rock-record data may be biased by the preservation of tide-influenced deposits related to smaller- 8 9 1698 scale spatial and temporal changes in tidal processes, especially for depositional systems with 10 11 12 1699 limited rock-record data and where data are selectively compared to model results. Hence, it is 13 14 1700 important to consider the potential for any preservational bias in the rock record regarding 15 16 1701 depositional processes. This could be highlighted by apparently unfavourable comparisons 17 18 19 1702 between model outputs and rock-record data. 20 21 1703 22 23 24 1704 For one- and two-dimensional stratigraphic data, interpretation of areal depositional morphology 25 26 1705 and up-scaling to the depositional system scale is typically guided by comparison to process- 27 28 29 1706 based interpretations of modern shoreline environments (Fig. 25B). Process-based classifications 30 31 1707 of modern shoreline systems are principally based on 2D areal morphology, ideally supported by 32 33 34 1708 data on hydrodynamics and sediment type (e.g. Coleman and Wright, 1975; Galloway, 1975; 35 36 1709 Hayes, 1979; Boyd et al., 1992; Hori and Saito, 2007; Ainsworth et al., 2011; Nyberg and 37 38 1710 Howell, 2016) and sedimentary facies characteristics (e.g. Ta et al., 2002a; Lambiase et al., 39 40 41 1711 2003; Salahuddin and Lambiase, 2013; Fanget et al., 2014; Gugliotta et al., 2018). Hence, the 2D 42 43 1712 morphologies of end-member tide-, wave- and fluvial-dominated shorelines are embedded in 44 45 46 1713 ternary-process models of shoreline depositional systems (Ainsworth et al., 2011; Vakarelov and 47 48 1714 Ainsworth, 2013; Nyberg and Howell, 2016). 49 50 51 1715 52 53 1716 The morphological characteristics of tide-dominated shorelines typically display (1) complex and 54 55 1717 intricately branching networks of funnel-shaped (seaward-flaring) tidal channels, (2) elongate 56 57 58 1718 tidal bars (mainly subtidal but often with subaerial tops), which partly infill tidal channels and 59 60 97 61 62 63 64 65 1 2 3 4 1719 often extend seaward from channel mouths, and (3) more extensive (‘land-fringing’) intertidal 5 6 7 1720 and supratidal areas with, depending principally on latitude, salt marsh or mangrove colonization 8 9 1721 (e.g. Ainsworth et al., 2011; Nyberg and Howell, 2016). Tide-dominated shorelines are more 10 11 12 1722 likely to be rugose to funnel shaped, and vice versa, whereas straighter shorelines are more likely 13 14 1723 to be wave-dominated, and vice versa (e.g. Fig. 2) (e.g. Ainsworth et al., 2011; Nyberg and 15 16 1724 Howell, 2016). These generalized relationships are useful but oversimplified, especially when 17 18 19 1725 they are an intrinsic component of algorithms for classifying modern shoreline process regime 20 21 1726 (Nyberg and Howell, 2016). For example, this relationship does not include quantifiable 22 23 24 1727 variations in tidal range, tidal prism and/or tidal bed shear with shoreline rugosity, or complex 25 26 1728 related feedbacks (e.g. D'Alpaos et al., 2010). A more rigorous, albeit ambitious, approach for 27 28 29 1729 determining the process regime along shorelines would be to compare measured values of tidal 30 31 1730 strength (bed shear stress), tidal range, wave strength, wave height and fluvial discharge (Harris 32 33 34 1731 et al., 2002) with those from numerical models, preferably including data assimilation. 35 36 1732 37 38 1733 The temporal resolution of rock-record data is highly dependent on the methodology of absolute 39 40 41 1734 dating and the degree of interpolation between control ages (Fig. 24C). For example, in the 42 43 1735 Cretaceous of the Western Interior Basin of North America, an estimated temporal resolution of 44 45 46 1736 c. 200 ka has been achieved because high-resolution ammonite biozones have been calibrated to 47 48 1737 radiometric age dates (Obradovich, 1993) (Krystinik and DeJarnett, 1995). In contrast, a paucity 49 50 51 1738 of absolute age dates in the Miocene–Pliocene Baram Delta Province, and the vast majority of 52 53 1739 similar Tertiary delta provinces around the world, means biostratigraphic zones have a temporal 54 55 1740 resolution of >1 Ma, based partly on correlation to adjacent basins with absolute ages (Sandal, 56 57 58 1741 1996). 59 60 98 61 62 63 64 65 1 2 3 4 1742 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 1743 47 48 49 1744 Fig. 24. Variable resolution of palaeogeographic, tidal modelling and rock record data. (A) 50 1745 Illustration of the minimum temporal resolution of geologic data underpinning a 51 52 1746 palaeogeographic ‘timeslice’ (after (after Markwick and Valdes, 2004). Each data point is 53 54 1747 assumed to represent a single observation of equivalent area, but the temporal resolution of each 55 56 1748 point is generally variable (red cylinders), due in part to imprecise or uncertain dating and 57 58 1749 correlation. Defining a timeslice instead of a time-plane maximizes data density. (B) 59 60 99 61 62 63 64 65 1 2 3 4 1750 Thickness/spatial resolution of rock and model data. Rock data are differentiated by general 5 6 1751 versus exceptional dataset quality: in this context, exceptional being, for example, extensive and 7 8 1752 continuous outcrops or several tens of correlated cores and well logs. Numbers 1-5 represent the 9 10 1753 five hierarchical levels of rock data (or levels; e.g. Vakarelov and Ainsworth, 2013), showing 11 12 1754 varying areal and thickness scales (see full text and legend in the bottom panel). Tidal model 13 1755 data is area based. (C) Temporal resolution of rock and model data. The inset (bottom panel) 14 15 1756 shows (i) the five hierarchical levels of rock data (Vakarelov and Ainsworth, 2013); (ii) the most 16 17 1757 common methods of absolute rock dating include geomagnetic, isotopic, biostratigraphy 18 19 1758 (calibrated to absolute dates), and interpolation between dates; and (iii) data quality types. 20 21 1759 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 100 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 1760 45 46 1761 Fig. 25. Scale and methodology of process classification and depositional model reconstruction 47 48 1762 (after Vakarelov and Ainsworth, 2013). (A) Five hierarchical levels of process-based 49 1763 architectural classification based on one-dimensional thickness and two-dimensional cross- 50 51 1764 section and plan-view data. (B) Simplified workflow for determining process depositional model 52 53 1765 from one-dimensional rock-record data. Refer to Figure 7 and Tables 2 and 3 in Vakarelov and 54 55 1766 Ainsworth (2013) for further information. 56 57 1767 58 59 60 101 61 62 63 64 65 1 2 3 4 1768 5.1.2 Palaeotidal range and bed shear stress as proxies for depositional process regime 5 6 7 1769 It is common for sedimentological and stratigraphic analysis of tidal range in the rock record to 8 9 1770 be limited to differentiating microtidal, mesotidal and macrotidal regimes (Wells et al., 2005a). 10 11 12 1771 Methods proposed for more detailed interpretation of palaeotidal range suffer from several 13 14 1772 assumptions and limitations (Section 3.2). In the present-day, long-term tidal shoreline 15 16 1773 morphologies are related to the net exchange of water and sediment across the fluvial-to-marine 17 18 19 1774 transition zone, which is controlled by tidal range through its effect on the tidal prism (D'Alpaos 20 21 1775 et al., 2010). Furthermore, changes in tidal range and tidal prism impact the degree and 22 23 24 1776 physiography of tidal channelization, and vice versa (D'Alpaos et al., 2010). In mixed tide-wave 25 26 1777 systems, tidal range versus wave height is an approximate proxy for coastal energy regime and 27 28 29 1778 coastal morphology, especially for barrier islands (Hayes, 1979; FitzGerald, 1982; Davis and 30 31 1779 Hayes, 1984; Davis, 1994; FitzGerald et al., 1994; Anthony and Orford, 2002; McBride et al., 32 33 34 1780 2013; Mulhern et al., 2017). However, coastal barrier morphologies in mixed tide-wave regimes 35 36 1781 are statistically indistinct from one another (Mulhern et al., 2017). Consequently, in ancient 37 38 1782 domains without quantitative information on both wave and tide processes, modelled palaeotidal 39 40 41 1783 range only indicates ‘tidal potential’. Hence, coastlines with relatively high tidal ranges (i.e. high 42 43 1784 mesotidal to macrotidal) tend towards a ‘higher potential’ for tide dominance compared to 44 45 46 1785 coastlines with relatively low tidal ranges (microtidal to low mesotidal) and a ‘lower tidal 47 48 1786 potential’ (Wells et al., 2010a; Collins et al., 2018a). The precision of ‘tidal potential’ estimation 49 50 51 1787 is limited by the difficulties of quantifying tidal range from the rock record, and the complex 52 53 1788 relationships between tidal range, tidal dominance and shoreline morphology in the present-day. 54 55 1789 56 57 58 59 60 102 61 62 63 64 65 1 2 3 4 1790 Tidal bed shear stress controls subaqueous sediment transport pathways and bedform distribution 5 6 7 1791 (e.g. Stride, 1973; Pingree and Griffiths, 1979; Howarth, 1982; Hulscher et al., 1993; Ward et al., 8 9 1792 2015), but very few studies have compared tidal bed shear stress patterns to shoreline 10 11 12 1793 morphology (e.g. Friedrichs, 1995; Coco et al., 2013). In models relating the tidal prism to 13 14 1794 equilibrium tidal channel physiography, the maximum bottom tidal shear stress equates to the 15 16 1795 critical threshold for incipient motion of sediment (D'Alpaos et al., 2010). At higher bed shear 17 18 19 1796 stresses, resultant bedform stability depends on the full range of flow conditions during transport 20 21 1797 and deposition (e.g. Baas et al., 2016). Consequently, modelled maximum palaeotidal bed shear 22 23 24 1798 stress, plotted as the equivalent transportable grain size based on critical bed shear stress 25 26 1799 thresholds, can be used as a proxy for tidal influence on sediment transport, bedform formation 27 28 29 1800 and shoreline morphology. This approximation is supported by favourable comparisons between 30 31 1801 model results and preserved sedimentary strata in earlier palaeotidal modelling case studies 32 33 34 1802 (Mitchell et al., 2010; Collins et al., 2017a; Collins et al., 2018a). 35 36 1803 37 38 1804 Bedform phase diagrams are predominantly based on laboratory experiments that use depth- 39 40 41 1805 averaged flow velocity or bed shear stress; narrow depth and grain size ranges; and the 42 43 1806 assumption that bedforms are in equilibrium with flow conditions (Figs. 10, 26A–B ) (Allen, 44 45 46 1807 1968; Rubin and McCulloch, 1980; Allen, 1982b; Harms et al., 1982; Southard and Boguchwal, 47 48 1808 1990; Baas et al., 2016). Bedform stability varies significantly with grain size and water depth, 49 50 51 1809 which has fundamental implications for comparison of modelled tidal bed shear stress and rock 52 53 1810 record data, and prediction of rock-record characteristics based on modelled tidal bed shear 54 55 1811 stress. For a given water depth, if the minimum available grain size during deposition (‘rock 56 57 58 1812 grain size’) is finer than the potential grain size transportable by maximum strength modelled 59 60 103 61 62 63 64 65 1 2 3 4 1813 tides (‘model grain size’), the resultant bedform will be different from the equilibrium bedform 5 6 7 1814 (e.g. points V, X and Z; Fig. 26). For example, the resultant bedform may be in a different field 8 9 1815 (e.g. point V) or larger (e.g. point Z) (Fig. 26). If the minimum grain size available during 10 11 12 1816 deposition cannot be entrained by the modelled tides (Fig. 26C), tides will not influence bedform 13 14 1817 formation and sedimentary preservation (e.g. point Y; Fig. 26). The ‘rock grain size’ depends on 15 16 1818 the grain size available at the time of deposition, which is controlled by the geological and 17 18 19 1819 hydrological characteristics of the ancient source-to-sink system. The grain size range of 20 21 1820 available sediment is difficult to predict. 22 23 24 1821 25 26 1822 Bedform formation or type also varies significantly with water depth (Fig. 26A, B). For example, 27 28 29 1823 an increase in water depth from c. 20 cm to c. 20 m at point Z results increases the size of dune- 30 31 1824 scale cross bedding from decimetre- to meter-scale, but a similar increase in water depth at 32 33 34 1825 points U and W causes cessation of bedform formation (Fig. 26A, B). Comparing the preserved 35 36 1826 rock grain size and sedimentary structure to the model grain size can potentially be used to 37 38 1827 estimate water depth. For example, preservation of metre-scale tidal cross-stratification in coarse 39 40 41 1828 to very coarse sandstone in an area with sufficiently strong modelled tides would suggest a 42 43 1829 palaeowater depth of c. 20 m (e.g. point Z; Fig. 26). Alternative independent estimates of ancient 44 45 46 1830 water depth are extremely uncertain (e.g. Immenhauser, 2009). 47 48 1831 49 50 51 52 53 54 55 56 57 58 59 60 104 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 1832 30 31 1833 Fig. 26. The influence of current velocity, bed shear stress and sediment grain size on sediment 32 33 1834 traction, bedform stability and comparison of tidal model and rock-record data. (A) Bedform 34 1835 stability diagram, including bed shear stress, for unidirectional flow at c. 20 cm water depth (i.e. 35 36 1836 flume tank) (Harms et al., 1982; Mitchell et al., 2010). (B) Bedform stability diagram, including 37 38 1837 bed shear stress, for unidirectional flow at c. 20 m water depth (Rubin and McCulloch, 1980). 39 40 1838 (C) Simplified Hjulström diagram constructed by plotting sediment grain size to threshold bed 41 42 1839 shear stress for sediment entrainment (Berenbrock and Tranmer, 2008) (Hjulström, 1939). (D) 43 1840 Simplified table of various plotted positions (U–Z) on the bedform stability and simplified 44 45 1841 Hjulström diagrams (A–C) comparing the rock record grain size to modeled grain size and the 46 47 1842 depth dependence of potential bedform formation (or non-formation). 48 49 1843 50 51 1844 5.2 Controls on Tidal Processes and Sedimentation 52 53 54 1845 5.2.1 Basin Physiography 55 56 57 58 59 60 105 61 62 63 64 65 1 2 3 4 1846 The influence of regional-scale (100–1000s km) basin physiography on shoreline tides depends 5 6 7 1847 on the overall physiographic setting and regional-scale physiography of the basin, and the 8 9 1848 influence of shelf width on tidal resonance. 10 11 12 1849 13 14 1850 Shoreline systems can be broadly subdivided into two physiographic categories. First, open- 15 16 1851 ocean systems directly face a typically large-scale (1000s km) open ocean (e.g. modern Niger 17 18 19 1852 delta shelf facing the southern Atlantic Ocean). Second, partly enclosed systems face seas or 20 21 1853 oceans that are partly landlocked, have variable connectivity to an open ocean (s), and display a 22 23 24 1854 large variation in size (100s to 1000s km) (e.g. present-day North Sea). The case studies 25 26 1855 presented earlier (Section 4) are all partly enclosed systems. 27 28 29 1856 For present-day open-ocean systems, there is no obvious systematic, qualitative relationship 30 31 1857 between tidal amplitude and latitude (e.g. Fig. 2). This is due to strong modification of tidal 32 33 34 1858 circulation by rotational, funnelling, shoaling and resonance effects, especially in shallower 35 36 1859 bathymetric areas and shoreline constrictions (Allen, 1997; Wells, 2008; Dalrymple and Padman, 37 38 1860 2015). These effects are complicated and difficult to predict. However, numerical tidal 39 40 41 1861 modelling, such as shown here with Fluidity, integrates these effects and provides more rigorous 42 43 1862 and quantitative predictions of tidal potential in modern and ancient, open-ocean systems. 44 45 46 1863 47 48 1864 For partly enclosed systems, the foremost control on shoreline tides is the balance between the 49 50 51 1865 amount of tidal energy entering and exiting the basin (Fig. 27). Tidal potential is highest when 52 53 1866 tidal inflow exceeds outflow. Tidal inflow is mainly controlled by the angle between the basin 54 55 1867 entrance and tidal flow in the adjacent open ocean, which principally depends on latitude and 56 57 58 1868 Coriolis rotation (Leeder, 2011), and the physiography of the basin entrance (Fig. 27A). Tidal 59 60 106 61 62 63 64 65 1 2 3 4 1869 inflow will be relatively high where open-ocean tides flow directly towards the basin entrance, 5 6 7 1870 minimizing loss of tidal energy to frictional damping, and/or the entrance is relatively wide, deep 8 9 1871 and unobstructed (Fig. 27A). Tidal outflow depends on the number, size, configuration and 10 11 12 1872 physiography of outflow connections (Fig. 27B). Tidal outflow is highest if there are several, 13 14 1873 wide, deep and unobstructed outflow connections (Fig. 27B). The tidal energy distribution within 15 16 1874 partly enclosed systems depends on the relative positioning of inflow positions versus outflow 17 18 19 1875 positions and embayments, and the tidal flow dynamics within the basin. This point is clearly 20 21 1876 illustrated in palaeotidal modelling sensitivity tests of the Lower Greensand Seaway (section 22 23 24 1877 4.2), in which the number and location of tidal inflow and outflow positions is varied (Fig. 17). 25 26 1878 27 28 29 1879 Partly enclosed systems may also include relatively shallow (up to a few hundreds of metres) but 30 31 1880 wide (up to several 100s km) basins, for example, the present-day Baltic Sea and ancient 32 33 34 1881 epicontinental seaways. The physiography of these systems may also result in tidal resonance of 35 36 1882 the incoming boundary tide due to the tidal periodicity matching a natural oscillation frequency 37 38 1883 of water within the basin. Tidal resonance potential has been approximated for simple, 39 40 41 1884 rectangular-shaped, open-ended water bodies (Section 2.3; Fig. 4) but for more complex ancient 42 43 1885 basin physiographies, palaeotidal modelling can provide quantitative information on integrated 44 45 46 1886 resonance potential for all tidal constituents. 47 48 1887 49 50 51 52 53 54 55 56 57 58 59 60 107 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1888 35 36 37 1889 Fig. 27. Regional-scale (100–1000s km) basin physiographic controls on tidal energy potential in 38 1890 partly-enclosed basins, related to the balance of tidal inflow versus outflow. (A) The control of 39 40 1891 inflow physiography on tidal inflow includes the width, depth and degree of obstruction of the 41 42 1892 main tidal inflow position to the basin. Larger, thicker arrows indicate higher inflow. (B) The 43 44 1893 control of outflow physiography on tidal outflow includes the number, width, depth and degree 45 46 1894 of obstruction of main tidal outflow positions and their configuration with respect to the main 47 48 1895 tidal inflow positions and boundary tide pathway. 49 1896 50 51 52 1897 5.2.2 Tidal resonance on continental shelves 53 54 1898 Funnelling, shoaling and resonance effects across continental shelves are important secondary 55 56 57 1899 controls on tides. Analysis of modern tides suggests that the relative importance of tides 58 59 60 108 61 62 63 64 65 1 2 3 4 1900 increases with shelf width perpendicular to the coastline (e.g. Redfield, 1958; Cram, 1979; 5 6 7 1901 Howarth, 1982; Ainsworth et al., 2011). For example, analysis of 110 shoreline profiles 8 9 1902 surrounding Australia and 9 other global systems indicates that most wave-dominated systems 10 11 12 1903 have shelf widths perpendicular to the coastline of <75 km, whereas most tide-dominated 13 14 1904 systems have shelf widths >75 km (Heap et al., 2004; Ainsworth et al., 2011). This is principally 15 16 1905 due to an increase in tidal resonance (Howarth, 1982; Ainsworth et al., 2011) and shoaling 17 18 19 1906 effects, assuming sea-bed friction is ignored (Allen, 1997). Consequently, a 75 km shelf width is 20 21 1907 an approximate cut-off for high tidal resonance potential (>75 km) in predictive shoreline 22 23 24 1908 process models (Fig. 7). 25 26 1909 27 28 29 1910 However, it is important to consider potential variability in this relationship for ancient domains 30 31 1911 related to resonance theory, shelf width and regional controls. Simple resonance theory for 32 33 34 1912 straight, laterally extensive shelves with a boundary tide perpendicular to the shelf (Section 2.3) 35 36 1913 indicates that maximum tidal resonance occurs when shelf width is one-quarter the tidal 37 38 1914 wavelength (and for widths 3/4, 5/4, etc.) (Fig. 3A and 28A–B). This is equivalent to several 39 40 41 1915 hundred kilometres for the dominant M2 and diurnal K1 tides (Fig. 3B) (e.g. Proudman, 1953; 42 43 1916 Howarth, 1982). In general, an increase in resonance potential with shelf width below one- 44 45 46 1917 quarter tidal wavelength is partly offset by an increase in frictional drag (Fig. 28A–B). However, 47 48 1918 the relationship between shelf width, tidal range and tidal dominance (Nyberg and Howell, 2016) 49 50 51 1919 varies globally due to changes in the following controls (Fig. 28C): (1) the relative amplitude of 52 53 1920 semi-diurnal to diurnal tidal constituents, which have significantly different wavelengths (e.g. 54 55 1921 Kowalik and Luick, 2013); (2) the geometry of continental shelves; (3) the incidence angle of 56 57 58 1922 tides and tidal flow patterns, which partly relates to latitude and Coriolis rotation; and (4) 59 60 109 61 62 63 64 65 1 2 3 4 1923 frictional effects, which may exceed tidal amplification across wide shelves and seaways. 5 6 7 1924 Continental shelf width may change significantly on short geological timescales due to relative 8 9 1925 sea level changes related to global eustasy, isostatic adjustment, and tectonic subsidence and 10 11 12 1926 uplift (e.g. Miller et al., 2005; Haq, 2014; Sames et al., 2016). Furthermore, within short-term 13 14 1927 eustatic sea level changes (10–100s ka), shelf width may change due to shoreline progradation, 15 16 1928 which is likely to be pronounced adjacent to major delta systems (e.g. Burgess and Hovius, 1998; 17 18 19 1929 Hori et al., 2001; Ta et al., 2002a; Chamberlain et al., 2018). In addition, changes to regional- 20 21 1930 scale tidal flow can supersede the effect of shelf width changes on shelf tidal resonance. For 22 23 24 1931 example, despite a decrease in shelf width during 50 m sea-level lowstands, tidal range along 25 26 1932 northern SCS coastlines was higher during the Late Oligocene–Late Miocene because the 27 28 29 1933 boundary tide had a higher tidal range (section 4.1; Figs. 12, 13). 30 31 1934 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 1935 58 59 60 110 61 62 63 64 65 1 2 3 4 1936 Fig. 28. Local-scale (10–100s km) controls on continental shelf tidal resonance. (A–B) Simple 5 6 1937 resonance scenario for a straight shelf, perpendicular boundary tide and uniform shelf width (w), 7 8 1938 where maximum tidal resonance occurs when shelf width is one-quarter the tidal wavelength (λ) 9 10 1939 (cf. Fig. 3) (after Howarth, 1982). (C) A more realistic resonance scenario for a curvilinear shelf, 11 12 1940 variable angle (θ) and dominant tidal constituent of the boundary tide, Coriolis rotation and 13 1941 variable shelf width (w versus w ) compared to one-quarter the tidal wavelength. NH = 14 1 2 15 1942 Northern Hemisphere. SH = Southern Hemisphere. 16 17 1943 18 19 20 1944 5.2.3 Shoreline Geometry 21 22 1945 Funnelling, shoaling and resonance effects in shoreline embayments are tertiary controls on tides 23 24 1946 (e.g. Slingerland, 1986; Dalrymple, 1992; Wells et al., 2007a; Ainsworth et al., 2011). Protection 25 26 27 1947 from wave processes along embayed shorelines also increases the relative strength of tide and 28 29 1948 fluvial processes (e.g. Ainsworth et al., 2008; Ainsworth et al., 2011; Plink-Björklund, 2012). 30 31 32 1949 Consequently, increased shoreline rugosity is used as a proxy for increased tidal influence and 33 34 1950 decreased wave influence in predictive shoreline process models (Fig. 2) (Ainsworth et al., 2008; 35 36 37 1951 Ainsworth et al., 2011). However, as outlined below, modern tides and palaeotidal modelling 38 39 1952 suggest that tidal amplification in coastal embayments is variable and depends on the balance 40 41 1953 between tidal amplification, due to funnelling, shoaling and/or resonance effects, and frictional 42 43 44 1954 damping. 45 46 1955 47 48 49 1956 Modern river-linked embayments (e.g. estuaries and interdistributary bays) are typically 50 51 1957 classified as either hyposynchronous, where tidal range decreases landward because frictional 52 53 54 1958 damping exceeds tidal amplification, or hypersynchronous, where tidal range initially increases 55 56 1959 landward due tidal amplification exceeding frictional damping, before decreasing to the tidal 57 58 1960 limit (e.g. Godin, 1999; Dalrymple and Choi, 2007). The degree of tidal amplification versus 59 60 111 61 62 63 64 65 1 2 3 4 1961 frictional damping can vary between adjacent embayments and show complex patterns within 5 6 7 1962 embayments, as seen along eastern North America and western India (Fig. 29). Differentiating 8 9 1963 between ancient hypersynchronous and hyposynchronous embayments is difficult and requires 10 11 12 1964 interpretation of the process balance and extent of turbidity maximum zone in the fluvial-to- 13 14 1965 marine transition zone (e.g. Gugliotta et al., 2016a). However, palaeotidal modelling can reveal 15 16 1966 spatial and temporal variations in tidal processes within ancient embayments. For example, as 17 18 19 1967 the entrance to the palaeo-Gulf of Thailand became wider and deeper during the Miocene, 20 21 1968 greater tidal inflow and reduced frictional damping shifted the tidal maxima landward (Fig. 12). 22 23 24 1969 25 26 1970 The relative strength of tidal amplification versus frictional damping depends on several factors: 27 28 29 1971 (1) The geometry and bathymetry of the embayment, especially its sinuosity (e.g. 30 31 1972 Slingerland, 1986; Allen, 1997). Frictional effects will be higher in more sinuous and 32 33 34 1973 rapidly shallowing embayments compared to straighter, gently shallowing embayments 35 36 1974 (Fig. 29, 30A). 37 38 1975 (2) The geometry and bathymetry of the embayment entrance impacts inflow and outflow of 39 40 41 1976 tidal energy. A narrower, shallower and obstructed entrance increases dissipation and 42 43 1977 reflection of tidal energy (e.g. Chesapeake Bay), whereas a wider, deeper and 44 45 46 1978 unobstructed entrance permits greater tidal inflow (e.g. Bay of Fundy) (Figs. 29, 30C). 47 48 1979 (3) The angle between the embayment axis and incoming tide influences tidal inflow. Tidal 49 50 51 1980 inflow increases and frictional effects decrease when the incoming tide is more parallel to 52 53 1981 the embayment axis (Fig. 30B). 54 55 1982 (4) Embayment physiography and the dominant tidal constituent control the resonance 56 57 58 1983 potential of embayment tides (Section 2.3). 59 60 112 61 62 63 64 65 1 2 3 4 1984 5 6 7 8 1985 Hyposynchronous embayments are more likely if the tidal inflow and resonance potential are 9 10 1986 low and frictional drag potential is high (Fig. 29A). Hypersynchronous embayments are more 11 12 1987 likely if tidal inflow and resonance potential are high and frictional drag potential is low (Fig. 13 14 15 1988 29B). However, even if tidal amplification exceeds frictional effects, embayments may be 16 17 1989 dominated by fluvial or wave processes (Dalrymple, 1992). 18 19 20 1990 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 1991 57 58 59 60 113 61 62 63 64 65 1 2 3 4 1992 Fig. 29. Tides in shoreline embayments. (A) A hyposynchronous system in which frictional 5 6 1993 damping exceeds amplification of tides due to funneling, shoaling and resonance effect, resulting 7 8 1994 in a seaward to landward decrease in tidal range and tidal current speed. (B) A hypersynchronous 9 10 1995 system in which tidal amplification exceeds friction, causing a seaward-to-landward increase in 11 12 1996 tidal range and current speed, before friction causes tidal range and current speed to decrease to 13 1997 zero at the tidal limit (after Dalrymple and Choi, 2007). (C, D) Modeled tidal range from FES 14 15 1998 2012 for north-east America (C) and north-west India (D) illustrating the varying relationship 16 17 1999 between tidal range and position within adjacent embayments: (1) hyposynchronous Chesapeake 18 19 2000 Bay; (2) moderately hypersynchronous Long Island Sound; (3) strongly hypersynchronous Bay 20 21 2001 of Fundy; (4) strongly hypersynchronous St. Lawrence River mouth; (5) strongly 22 23 2002 hyposynchronous Gulf of Khambhat; and (6) complex hyposynchronous and hypersynchronous 24 2003 Gulf of Kutch. 25 26 2004 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 2005 50 51 2006 Fig. 30. Physiographic controls on tides in shoreline embayments. A schematic matrix includes 52 53 2007 the influence of (A) shoreline geometry, for example, sinuosity and rugosity, (B) the relative 54 2008 orientation of the embayment axis and incoming tide, and (C) the physiography of the 55 56 2009 embayment entrance, on (1) high versus (2) low tidal energy potential within the embayment. 57 58 2010 Note this matrix excludes the influence of wave or fluvial processes. 59 60 114 61 62 63 64 65 1 2 3 4 2011 5 6 7 2012 5.3 Modified decision tree for prediction of shoreline processes 8 9 2013 The original process-based, decision tree hierarchy for predicting shoreline-shelf systems uses a 10 11 12 2014 sequential procedure (Ainsworth et al., 2011) (Fig. 7A) of assessing tidal resonance potential, 13 14 2015 wave versus fluvial effectiveness, low versus high A/S, shoreline morphology (relative degree of 15 16 2016 rugosity), and coastal process dominance. Our evaluation proposes replacing this procedure with 17 18 19 2017 one that uses two decision trees, reflecting low and high wave energy potential, respectively. The 20 21 2018 procedure for using each decision tree comprises the following hierarchy (compare Figs. 7A and 22 23 24 2019 31): (1) wave energy potential, (2) tidal energy potential, (3) shelf tidal resonance potential, (4) 25 26 2020 fluvial potential, and (5) shoreline geometry. The justification for this revision is outlined below, 27 28 29 2021 based on the preceding review of tidal theory, the physiographic influence on modern tides and 30 31 2022 present-day shoreline process regimes (e.g. Nyberg and Howell, 2016), and the physiographic 32 33 34 2023 controls on tides highlighted by palaeotidal modelling studies and the corresponding 35 36 2024 stratigraphic record with preserved tidal influence. 37 38 2025 39 40 41 2026 The dominance of wave-dominated process regimes along present-day depositional shorelines 42 43 2027 (Fig. 6) (Nyberg and Howell, 2016) supports this being the first-order control on shoreline 44 45 46 2028 process regime (hierarchical query #1 in Fig. 31). In modern systems, the height and strength of 47 48 2029 wind-generated surface waves are primarily controlled by the speed, duration and fetch of the 49 50 51 2030 wind (e.g. Allen, 1997). Wave dominance also depends on the frequency of larger-magnitude 52 53 2031 storms. In ancient domains, determining the speed and duration of wind, and the effect on wave 54 55 2032 processes, would ideally require sophisticated analyses integrating palaeogeographic 56 57 58 2033 reconstructions and numerical climate and wave modelling. More generally, predicting wave 59 60 115 61 62 63 64 65 1 2 3 4 2034 energy potential along ancient shorelines relies on larger scale palaeogeographic reconstructions. 5 6 7 2035 If a system is open to a large water body or ocean, wave fetch and consequently wave potential 8 9 2036 would be relatively high. Any protection that restricts access to oceanic waves will lower wave 10 11 12 2037 potential (e.g. Ainsworth et al., 2011). Protection from ocean waves may be tectonic (e.g. 13 14 2038 emergent fault blocks, tectonically controlled seaways) or depositional (e.g. rugose coastal 15 16 2039 morphology, depositional headland, barrier islands, asymmetric deltas). 17 18 19 2040 20 21 2041 The tidal energy potential of a basin (hierarchical query #2 in Fig. 31) is dependent on whether 22 23 24 2042 the basin is adjacent to an open ocean or partly enclosed. For open-ocean basins, tidal energy 25 26 2043 potential is assumed to be relatively high, given the relative lack of dissipation effects compared 27 28 29 2044 to partly enclosed systems. However, the absolute amount and distribution of tidal energy in an 30 31 2045 open ocean basin is related to its size, geometry and latitudinal distribution. For partly-enclosed 32 33 34 2046 systems, the tidal energy potential depends on the balance of tidal inflow versus outflow, which 35 36 2047 is controlled by: (1) the relative orientation of the partly enclosed basin and incoming tide; (2) 37 38 2048 the physiography of the basin entrance; and (3) the number, position and physiography of 39 40 41 2049 outflow positions (Fig. 27). Tidal resonance may also be important in partly enclosed systems of 42 43 2050 certain depth and geometry (Fig. 4). 44 45 46 2051 47 48 2052 Shelf resonance potential (hierarchical query #3 in Fig. 31) is related to shelf width and the 49 50 51 2053 dominant tidal constituent of the incoming tide (Figs. 3, 28). Analysis of modern shoreline 52 53 2054 processes suggest a cut-off of c. 75 km between mainly tide-dominated (>75 km) and wave- 54 55 2055 dominated (<75 km) systems (Ainsworth et al., 2011). However, tides only dominate on c. 50% 56 57 58 2056 of depositional shorelines associated with shelf widths of >75 km, with 47% being wave 59 60 116 61 62 63 64 65 1 2 3 4 2057 dominated (Fig. 6) (Nyberg and Howell, 2016). This suggests that a more representative shelf 5 6 7 2058 width threshold may be even higher, which would be closer to the theoretical shelf width for 8 9 2059 resonance of the typically dominant semi-diurnal M2 or diurnal K1 tidal components (Figs. 3, 10 11 12 2060 28). However, without a more accurate and globally applicable cut-off value, the 75 km cut-off is 13 14 2061 retained in the proposed process prediction decision tree (Fig. 31). Nevertheless, this should be 15 16 2062 critically assessed on a case-by-case basis, considering other local geological factors. 17 18 19 2063 20 21 2064 Assessing fluvial potential (hierarchical query #4 in Fig. 31) relies on (1) measured or inferred 22 23 24 2065 drainage area, hinterland relief and rock types (e.g. Milliman and Syvitski, 1992; Syvitski and 25 26 2066 Milliman, 2007{Sømme, 2009 #1471); (2) paleoclimate and its effects on water and sediment 27 28 29 2067 discharge (Hovius, 1998; Syvitski et al., 2003; Milliman and Farnsworth, 2011), and/or (3) 30 31 2068 observational evidence of fluvial influence in the rock record (Bhattacharya and Walker, 1992; 32 33 34 2069 MacEachern and Bann, 2008; Ainsworth et al., 2016). In general, large drainage basins would 35 36 2070 have higher fluvial potential than smaller drainage basins. However, an exception may be river 37 38 2071 systems with short, steep drainage basins subject to high rainfall storms, which often preserve 39 40 41 2072 river-influenced shoreline deposits (e.g. Bhattacharya and MacEachern, 2009; Collins et al., 42 43 2073 2017b). The overwhelming dominance of wave- and tide-dominated shoreline morphologies 44 45 46 2074 along present-day coastlines indicates effective reworking of riverine sediment by marine 47 48 2075 processes (Fig. 6). However, sedimentary dynamics and deposition may still be dominated by 49 50 51 2076 river floods, even in deltas with lobate-to-cuspate geometries typical of wave dominance 52 53 2077 (Rodriguez et al., 2000; Fielding et al., 2005; Gani and Bhattacharya, 2007). Consequently, for 54 55 2078 ancient shoreline systems, any information suggesting a closely adjacent river system may 56 57 58 59 60 117 61 62 63 64 65 1 2 3 4 2079 suggest relatively high potential for river-influenced sedimentary dynamics and deposition (Fig. 5 6 7 2080 31). 8 9 2081 10 11 12 2082 Shoreline geometry (hierarchical query #5 in Fig. 31) mainly relates to the degree of rugosity, 13 14 2083 recognizing that tides are commonly amplified in many present-day embayments and along 15 16 2084 embayed shorelines. However, embayments along present-day shorelines and those in 17 18 19 2085 palaeotidal simulations are not exclusively tide dominated (e.g. Figs. 6, 9, 31; cf. Fig. 2). The 20 21 2086 balance of tidal amplification and frictional damping depends on the physiography and 22 23 24 2087 orientation of the embayment (Fig. 30). Tides may also undergo excess frictional damping 25 26 2088 compared to amplification, due to funnelling, shoaling and/or resonance). Embayed shorelines 27 28 29 2089 are also inevitably more protected from direct wave processes. However, wave processes may 30 31 2090 still be dominant along the back of moderately embayed shorelines, especially adjacent to 32 33 34 2091 embayment mouths with access to open ocean waves (Fig. 31). In fluvially linked embayments, 35 36 2092 river processes may dominate over tides and waves (e.g. Dalrymple and Choi, 2007). Therefore, 37 38 2093 shoreline geometry can have a variable potential influence on depositional processes. 39 40 41 2094 42 43 2095 The A/S ratio of a shoreline–self system is a widely-used theoretical concept that links tectonics, 44 45 46 2096 eustatic sea-level change and sediment supply (Muto and Steel, 1997), and features prominently 47 48 2097 in the original process-based decision tree of Ainsworth et al. (2011) (hierarchical query #3 in 49 50 51 2098 Fig. 7A). A/S ratio has been removed from our revised predictive decision tree (Fig. 30) due to 52 53 2099 limitations with the concept. For example, identifying relatively ‘high’ and ‘low’ A/S ratio relies 54 55 2100 on generalized relationships between A/S ratio and sequence stratigraphic systems tracts, which 56 57 58 2101 in turn relies on extensive datasets for sequence stratigraphic and/or shoreline trajectory analysis 59 60 118 61 62 63 64 65 1 2 3 4 2102 (Ainsworth et al., 2008). Quantification of ‘high’ versus ‘low’ A/S ratios also relies upon 5 6 7 2103 sufficient well log, core and/or outcrop data to calculate the thickness of a sedimentary unit to 8 9 2104 approximate accommodation and the sand-to-shale ratio and approximate coarse sediment supply 10 11 12 2105 rate (Ainsworth, 2003; Ainsworth, 2005; Ainsworth et al., 2008). However, even if sufficient 13 14 2106 data are available, the exact ratios for ‘high’ and ‘low’ A/S regimes are yet to be determined. The 15 16 2107 reliance on available data and interpretations seriously limits the applicability of the A/S ratio for 17 18 19 2108 predicting shoreline processes in ancient systems with limited data. Furthermore, the A/S ratio is 20 21 2109 a subordinate control on tides compared to the tidal energy potential of a basin, shelf tidal 22 23 24 2110 resonance potential and shoreline geometry. Process changes relating to A/S ratio only apply for 25 26 2111 moderately- to highly-embayed shorelines and relate to inferred changes to shoreline geometry 27 28 29 2112 (Section 1.2) (Ainsworth et al., 2011). 30 31 2113 32 33 34 2114 In contrast to the three-tier process prediction scheme used in the original process-based decision 35 36 2115 tree of {Ainsworth, 2011 #345@@author-year} (Figs. 5A, 7A), we propose a two-tier process 37 38 2116 prediction scheme that is limited to the primary and secondary processes (Figs. 5B, 31). Analysis 39 40 41 2117 of modern shorelines suggests the thresholds for process classification in a three-tier scheme are 42 43 2118 ambiguous (e.g. Fig. 6) (Nyberg and Howell, 2016). While a three-tier scheme has the superficial 44 45 46 2119 appearance of greater precision (Figs. 5A, 7) (Ainsworth et al., 2011), it requires definitive 47 48 2120 process classification and quantitative analysis of sedimentary structures that is rarely, if ever, 49 50 51 2121 available. At present, the range of mixed process sedimentary structures and variability between 52 53 2122 different modern and ancient depositional systems are not yet fully documented or understood, 54 55 2123 leading to ambiguities in the process interpretations of several sedimentary structures (Section 56 57 58 2124 2.2) (e.g. Ainsworth et al., 2011; Dashtgard et al., 2012; Legler et al., 2014; Gugliotta et al., 59 60 119 61 62 63 64 65 1 2 3 4 2125 2016a; Gugliotta et al., 2016b; Jablonski and Dalrymple, 2016; Rossi and Steel, 2016). A more 5 6 7 2126 holistic framework for interpreting mixed process deposition and preservation would also 8 9 2127 include the effect of grain size availability on sedimentary facies characteristics and preservation, 10 11 12 2128 plus integration with a range of observational techniques from both modern and ancient systems. 13 14 2129 However, the application of this understanding to the ancient record is still limited by several 15 16 2130 factors, including preservation bias in the rock record, dataset quality, and time available for data 17 18 19 2131 collection and process analysis. 20 21 2132 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 120 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 2133 50 51 52 2134 Fig. 31. Proposed revision to decision trees for predicting shoreline process dominance (cf. 53 2135 Error! Reference source not found.7A) (after Ainsworth et al., 2011) for systems with (A) low 54 55 2136 wave energy potential, and (B) high wave energy. The two decision trees each include five 56 57 2137 hierarchical queries: (1) wave energy potential of the basin; (2) tidal energy potential of the 58 59 60 121 61 62 63 64 65 1 2 3 4 2138 basin; (3) shelf tidal resonance potential; (4) fluvial potential; and (5) shoreline geometry. Key to 5 6 2139 color coding is shown in the inset. Shoreline geometry abbreviations: SL-straight/lobate; ME- 7 8 2140 moderately embayed; HE-highly embayed 9 10 2141 11 12 2142 6 CONCLUSIONS 13 14 2143 Palaeotidal modelling investigations, integrating comparisons to the equivalent stratigraphic 15 16 2144 record, indicate that numerical tidal modelling can demonstrate the potential sensitivity of tides 17 18 19 2145 to physiographic uncertainty and potential influence of tidal processes along ancient shorelines. 20 21 2146 Present-day global tidal measurements, and the spatio-temporal sensitivity of modelled ancient 22 23 24 2147 tides, indicate the following physiographic controls on tidal processes: (1) regional physiography 25 26 2148 (100–1000 km-scale) controls tidal inflow versus outflow in partly-enclosed oceans and seas; (2) 27 28 29 2149 shelf physiography (10–100 km-scale), latitude, and the boundary tide orientation and dominant 30 31 2150 tidal constituent control shelf tidal resonance; and (3) embayment physiography (1–10 km-scale), 32 33 34 2151 especially at the entrance, and the relative orientation of the incoming tide, control tidal 35 36 2152 amplification (funnelling and shoaling) versus frictional effects in shoreline embayments. 37 38 2153 However, validation of palaeotidal simulations using the rock record is limited by the difficulty 39 40 41 2154 in determining ancient tidal range from stratigraphic data and variability in the relationship 42 43 2155 between bed shear stress, grain size and bedforms (and primary sedimentary structures). 44 45 46 2156 47 48 2157 The overwhelming dominance of waves along modern shorelines indicates existing predictive 49 50 51 2158 models for shoreline process regime overstate the role of tides relative to waves. This supports 52 53 2159 the proposed revised model for classifying and predicting modern and ancient shoreline process 54 55 2160 regimes, capturing the relative influence of fluvial, tide and wave processes. Our revised model 56 57 58 2161 includes the first-order control of wave fetch and associated meteorological conditions, and 59 60 122 61 62 63 64 65 1 2 3 4 2162 improved understanding of physiographic controls on tides from numerical tidal modelling. 5 6 7 2163 However, determining process regime from ancient shoreline successions is limited by several 8 9 2164 factors that are undergoing renewed investigation, including: (1) the quality and availability of 10 11 12 2165 rock-record data; (2) uncertainty and biases in the process classification of common sedimentary 13 14 2166 structures; (3) grain size controls on formation and preservation of sedimentary structures; and 15 16 2167 (4) skewed preservation of certain depositional processes in different environments and on 17 18 19 2168 different timescales. These uncertainties and limitations, combined with those in classifying 20 21 2169 mixed-process modern shorelines, lead us to advocate a two-tier approach to process 22 23 24 2170 classification of shoreline systems (identifying only primary and secondary processes), but wider 25 26 2171 and consistent utilisation of these concepts is required to demonstrate their applicability. 27 28 29 2172 30 31 2173 ACKNOWLEDGEMENTS 32 33 34 2174 The authors acknowledge financial support from Natural Environment Research Council 35 36 2175 (NERC), Leverhulme Trust, Shell International Exploration and Production, and the Academy of 37 38 2176 Sciences of the Czech Republic. We also acknowledge support of Getech and Imperial College’s 39 40 41 2177 Grantham Institute and High Performance Computing Service. D.M. Hodgson, B.K. Levell, R.B. 42 43 2178 Ainsworth and B.K. Vakarelov are thanked for valuable comments and discussion. 44 45 46 2179 47 48 2180 SUPPLEMENTARY MATERIAL 49 50 51 52 53 54 55 56 57 58 59 60 123 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 2181 47 48 2182 Supplementary Fig. 1. Global map of modern tidal bed shear stress calculated from (A) tidal 49 50 51 2183 modelling using Fluidity and (B) tidal velocity magnitude from FES2014. C) Difference in 52 53 2184 maximum tidal bed shear stress between (A) Fluidity and (B) FES2014; Blue indicates FES2014 54 55 56 2185 has a higher maximum tidal bed shear stress. 57 58 2186 59 60 124 61 62 63 64 65 1 2 3 4 2187 REFERENCES CITED 5 6 7 2188 8 9 2189 Abieda, H.S., Harith, Z.Z.T. and Rahman, A.H.A., 2005. Depositional controls on petrophysical 10 2190 properties and reservoir characteristics of Middle Miocene Miri Formation sandstones, 11 12 2191 Sarawak. 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Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: