Controls on submarine canyon connection to the shoreline : a numerical modelling approach 1

Submarine canyons with heads located close to shorelines, known as shore-connected canyons, provide a focussed pathway for basinward sediment transport. Placing greater constraints on the key parameters that control the formation of shore-connected canyons can help us predict the efficiency of sediment export to deep-water under different environmental conditions and through time. Using a numerical model incorporating geomorphic principles, we show that shore-connected canyons are most active when fluvial discharge is high, the continental shelf is steep and narrow, and the magnitude of relative sea-level change is high. The numerical model reproduces observed bathymetric distributions of shore-connected submarine canyons, indicating that the empirical relationships underlying these numerical models are accurate descriptions of shore-connected canyon formation in nature. Our study provides constraints on the key quantifiable parameters controlling shore-connected submarine canyon formation and maintenance, such as fluvial discharge and basin physiography, allowing for more accurate predictions of the efficiency and timing of sediment transfer to the deep sea under different conditions. The model results suggest that; 1) submarine canyons may form frequently on the slope due to submarine processes, but subaerial processes control which submarine canyons are most likely to connect to the shoreline, 2) margin physiography and sediment supply are more influential in driving submarine canyon incision across the shelf and sediment transfer than the exact nature of the gravity flow triggering mechanism, and 3) the stratigraphic records of shore-connected submarine canyons and fans are more influenced by onshore climate and tectonics than eustasy.

triggering mechanism, and 3) the stratigraphic records of shore-connected submarine canyons and fans are more 23 influenced by onshore climate and tectonics than eustasy.

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The distance between the canyon head and the shoreline plays a critical role in determining the calibre of sediment 36 transported through the canyon, with analysis of Quaternary canyons revealing that the canyon head must come within 37 5 km of the shoreline in order to transfer sand-grade sediment to deeper water (Sweet and Blum, 2018). The prevalence 38 of shore-connected canyons along continental margins is therefore a fundamental control on the transport efficacy of 39 terrigenous sediment, organic matter, and pollutants, to submarine environments. Shore-connected canyons can form  Three key factors have been suggested to increase the prevalence of shore-connected canyons; 1) narrow shelves, 2) 45 high supply of coarse-grained sediment, and 3) high magnitude relative sea-level change (Harris and Whiteway, 2011; 46 Sweet and Blum, 2018;Smith et al., 2017;2018). This is supported by analysis of present-day canyons, with canyons 47 formed on narrow shelves, steep shelves, and subject to high subaerial discharge from relatively unerodible bedrock 48 hinterlands more likely to remain connected to the shoreline (Bernhardt and Schwanghart, 2021), which is also reflected 49 in the prevalence of river-associated canyons on active margins characterised by these factors (Fig. 1B) (Harris and 50 Whiteway, 2011). The observed correlation between slope, discharge and submarine canyon erosion implies that 51 submarine canyon formation may be described through heuristic geomorphic principles commonly applied to rivers, 52 such as the stream power law (e.g. Whipple and Tucker, 1999; Braun and Willet, 2013). The stream power law describes 53 5 vertical incision of river channels into bedrock as a function of channel slope and discharge, and has been used 54 extensively in numerical modelling of landscape and stratigraphic evolution (e.g. Ding et al, 2019; Zhang et al. 2020).

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Modifications of the stream-power law for the purpose of modelling submarine canyon erosion has been applied 56 previously by Petit et al. (2015), who reconstructed canyon evolution in the NW Mediterranean, and by Thran et al.

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(2020), who showed how carbonate mounds control submarine erosion and canyonisation in the Great Barrier Reef.

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In order to assess whether these geomorphic principles can replicate the observed distributions of shore-connected 60 submarine canyons, we aim to generalise these more targeted case-studies within a synthetic continental margin. If 61 replicable, then these principles may be more confidently applied to 1) model periods of geological time where canyon 62 distribution cannot be directly measured, thus providing insights into the efficacy of sediment transport to deeper-water 63 during past and future tectonic and climatic conditions, and 2) predict the rate at which present-day canyons may incise   (2)

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where rs is the sediment density and rw is the water density. Submarine erosion and entrainment by turbidity currents 78 is initiated when the sediment-water mixture within the hyperpycnal flow network reaches a pre-defined critical density 79 (1000.04 kg/m 3 ). The critical density is required to be low as the model is unable to episodically trigger turbidity 80 currents, therefore erosion by turbidity currents is modeled over longer timescales (Thran et al., 2020). Deposition (dprop) 81 from turbidity currents occurs as a function of the local slope and a dimensionless scaling parameter (a) (Lowe, 1976):

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This numerical description of turbidity current erosion and deposition has been used successfully to recreate the    submarine margin is 300 km in length (Y-direction, or depositional strike), with the source area, and transfer zone held 8 at constant planform width of 50 km (X-direction, or depositional dip). In order to maintain a 300 x 300 km grid, the 108 slope width varies from 150 to 200 km as the shelf width is varied ( Fig. 2A).

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Three groups of models were designed based on this initial configuration, with two of these groups varying a different 111 shelf property six times (Fig. 2B). The first group tested the effect of shelf width on canyon connection (0 -50 km in varied for a 30 km wide shelf and 0.1° dipping shelf, and each group of models ran for a period of 500 kyr, 119 approximating five 100 kyr (eccentricity) cycles, at a time-step of 10 kyr. Reconstructed sea-level curves, such as those 120 from the Quaternary, were not used in order to more fully control and isolate the influence of sea-level change.

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Results are presented as: 1) maps of positive (deposition) and negative (erosion) elevation at model end, and 2) shore 122 erosion through time in both the high supply and low supply segments of the margin (Fig. 3, 4, 5). The shore is defined 123 as the median sea-level position plus a horizontal distance of 5 km, assuming that canyons that do not intersect this 124 zone are much less able to transport sand-grade sediment down-slope (Sweet and Blum, 2018). In order to calculate

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In all models, uplift of the source area results in subaerial erosion and marine deposition (Fig. 3, 4, 5). Once sediment 141 reaches the marine environment it is either: 1) deposited and stored on the shelf, 2) deposited on the shelf and 142 remobilised along-or down-slope by mass-movements or wave currents, or 3) bypassed across the shelf entirely and 143 deposited beyond the shelf-break by turbidity currents. Deposition below the shelf-break is concentrated where slope 144 angle drops below ~0.5° (Fig. 3, 4, 5). Submarine erosion occurs in all the models to varying degrees, with increased  is inhibited by the canyon confinement, so back-filling tends to occur quickly once the canyon-mouth is choked.

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When the shelf width is varied, slope canyon prevalence and shore erosion increase with decreasing shelf width. Coastal 153 erosion is greatest on the high supply side of the model and during the fastest rate of sea-level fall in all cases. When 154 no shelf is present, shore erosion continues to increase as sediment supply increases, resulting in canyons remaining 155 connected to shoreline irrespective of the sea-level change. With the addition of a shelf, shore erosion drops to almost 156 zero during highstand, but the drop occurs from a higher erosion rate when the shelf is narrower. Canyon connection 157 therefore only occurs during lowstands, and at increasingly short durations of the lowstand as the shelf width increases.

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When shelf angle is varied, canyons generally become more numerous and incise deeper into the slope as the shelf 160 steepens. An exception to this trend occurs when the shelf is almost horizontal, and numerous canyons form on the 161 slope. These canyons do not extend far down the slope, however. Shore erosion shows a more complicated pattern, 162 11 with erosion being greatest when the shelf is shallowest and when the shelf is steepest, and little erosion occurs between 163 these end-member points. Shore erosion is therefore somewhat decoupled from slope canyon prevalence, i.e., when 164 the shelf is steep, coastal erosion is more similar to the models with wide shelves, even though slope canyons are much 165 more prevalent when the shelf is steep. Shore erosion and canyon prevalence is again reduced on the low-supply side 166 of the model, although the trend of erosion through time is similar. Interestingly, shore erosion reaches a maximum 167 when sea-levels are highest as the shelf angle increases.

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When the magnitude and rate of sea-level change is varied, both slope canyon prevalence and shore erosion increases 170 with increasing sea-level change., with the fastest rates of shore erosion associated with the fastest rates of sea-level fall.  supply and basin physiography are more important controls on submarine connection to the shoreline than the exact 12 triggering mechanism, e.g., hyperpycnal flows or delta-front failure, over millennial timescales. In other words, the 187 frequency of gravity flow generation and the slope over which these flows travel are the dominant controls on 188 submarine canyon incision, and both of these are best predicted by sediment supply and basin physiography. This also 189 implies that while submarine canyons may form frequently on the slope through submarine processes, the conditions 190 required for certain canyons to incise across the shelf are dictated by onshore processes.

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Narrow shelves increase shore-connected canyon prevalence by increasing the likelihood of gravity flows bypassing the 193 shelf and reaching the higher gradient slope before they dissipate by deposition and dilution, forming mouth bars (e.g.  (Fig. 7). Similarly, steep shelves increase the prevalence of submarine canyons 196 by increasing the erosive potential of gravity flows. This is mediated by the increased accommodation associated with 197 higher shelf angles, however, which allows for sediment to accumulate between adjacent rivers and between rivers and 198 the shelf-break, thus shallowing the shelf gradient (Fig. 7).

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High magnitude sea-level falls influence coastal erosion by increasing the duration of fluvial erosion on the shelf, 201 forming incised valleys that are later exploited by submarine flows, forming deeper submarine canyons in a feedback 202 loop (Fig. 7). Sea-level fall also increases shore-connected canyon prevalence by perching river mouths on the steep 203 continental slope during lowstand, thus increasing the erosive potential of the hyperpycnal flows they produce (Fig. 7), 204 and the erosive potential of flows derived from failure of accumulated sediment. If the shelf is wide these canyons are 205 then mostly abandoned when the sea-level rises (Fig. 6).

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All of these canyon-forming processes are enhanced when discharge is high enough to generate frequent hyperpycnal

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Therefore, on passive margins, low gradient rivers tend to produce wide shelves as rivers have to travel a further distance 227 to reach the shelf margin. Conversely, high-gradient rivers typically produce narrow shelves, as rivers have to travel less 228 distance to reach the shelf margin (Sweet and Blum, 2018). During periods of high-magnitude sea-level change, when 229 shore-connected submarine canyons are expected to be prevalent, shelves tend to be wider, which reduces the

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The Congo example also indicates that shore-connected canyons can be maintained well after the environmental 247 conditions that led to their inception, as long as the location of the fluvial system feeding the canyon is maintained.

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In the case where sediment supplies are consistently high, such as during sustained hinterland uplift, slope erosion and 250 submarine fan deposition will also be high (Fig. 3, 4, 5). This study suggests that this will result in rapid back-filling of 251 the submarine canyon, as increasing submarine fan relief on the basin floor and increased erosional confinement on 252 the slope prevent avulsion. Submarine canyons consistently connected to shorelines may therefore aggrade more 253 quickly than canyons periodically disconnected from shorelines. During greenhouse periods of earth history, characterised by lower-magnitude sea-level changes, shelf widths are 256 naturally narrowed by higher sea-levels (Sweet and Blum, 2018). Submarine canyon incision is therefore balanced by 257 the positive influence of narrow-shelves and the negative influence of lower-magnitude sea-level changes. On active 258 margins with elevated river gradients, the relative impact of narrowed shelves will therefore be reduced when compared 259 to icehouse climates, as the magnitudes of sea-level change are reduced. This indicates that shore-connected submarine 260 canyons will be most prevalent on active margins during periods of high-magnitude sea-level change, such as during 261 icehouse climates or periods of tectonically-induced relative-sea-level change, which is supported by the observed 262 prevalence of river-associated canyons on active margins in the present ( Fig. 1; Harris and Whiteway, 2011).

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We therefore speculate that the inception and maintenance of shore-connected submarine canyons on active margins

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Shore-connected submarine canyons greatly enhance the potential for sediment bypass from shallow-to deep-water.

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Numerical modelling has revealed that shore-connected canyons are most likely to form when fluvial discharge is high, 273 21 the shelf is narrow and steep, and the magnitude of sea-level change is great, in agreement with modern observations.

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This indicates that shore-connected canyon formation is fundamentally linked to quantifiable climatic and tectonic 275 factors, such as precipitation, tectonic uplift and sea-level fall. Periods of Earth history when sediment bypass to deep-276 water was most efficient can therefore be estimated, with active margins during icehouse climates expected to be the 277 most efficient configurations for sediment export from shallow-to deep-water. Tectonism and enhanced subaerial 278 erosion may therefore have a much more pronounced impact on climate change during icehouse periods than 279 greenhouse periods. This will also be reflected in the stratigraphy of deep-marine successions, with eustasy having a 280 more muted influence than onshore climate and tectonics on active margins characterised by narrow and steep shelves.