Comparing Aggradation, Superelevation, and Avulsion Frequency of Submarine and Fluvial Channels

Constraining the avulsion dynamics of rivers and submarine channels is essential for predicting the distribution of sediment, organic matter, and pollutants in alluvial, deltaic, and submarine settings. We create a geometric channel-belt framework relating channel, levee, and floodplain stratigraphy that allows comparative analysis of avulsion dynamics for rivers and submarine channels. We utilize 52 channel-overbank cross-sections within this framework to provide avulsion criteria for submarine channels, and how they differ from rivers. Superelevation and a new channel-floodplain coupling metric are two key parameters that control channel-belt thickness in both rivers and submarine channels. While rivers only superelevate 1 channel depth above the floodplain prior to avulsion, submarine channels are more stable during aggradation, with superelevation values commonly > 3 channel depths. Additionally, channel-floodplain coupling in rivers is often weak, with floodplain aggradation negligible compared to channel aggradation, making rivers avulsion-prone. However, floodplain aggradation is more significant for submarine channels, resulting in stronger channel-floodplain coupling and thus a decreased potential for avulsion. The combination of enhanced superelevation and strong channel-floodplain coupling results in submarine channel-belts that can be as thick as ∼10 channel depths, while fluvial channel belts are limited to 2 channel depths. Submarine channels are more stable because turbidity currents have ∼50x lower density contrast between flow and ambient fluid as compared to rivers. This density contrast creates far less potential energy for avulsion, despite the much greater relief of submarine levees compared to fluvial levees. The modern Amazon submarine channel showcases this stability, with a channel belt that is ∼5 channel-depths thick for more than 400 streamwise km, which is more than twice the superelevation that a river is capable of. We interpret that enhanced floodplain aggradation and levee aggradation (and thus superelevation) in submarine channel belts are promoted by unique submarine flow characteristics, including turbidity current overspill, flow-stripping, and hemipelagic processes. We emphasize that rivers and submarine channels display very different avulsion dynamics and frequencies, profoundly affecting the stratigraphic architecture of channel-belt and downstream distributary deposits.


INTRODUCTION
Rivers and submarine channels carry and distribute sediment, organic matter, pollutants around the world (Hodgson et al., 2018;Kane and Clare, 2019), and it is of paramount importance to understand the dynamics controlling sediment distribution in these channelized depositional systems. Rivers and submarine channels have similar planform morphologies (Flood and Damuth, 1987;Pirmez and Imran, 2003;Kolla et al., 2007) but with markedly different preserved stratigraphic architecture due primarily to differences in channel aggradation during channelbelt evolution (Imran et al., 1998(Imran et al., , 1999Peakall et al., 2000;Jobe et al., 2016). A channel belt is typically defined as the genetic deposits of one avulsion cycle (Leeder, 1978;Bridge and Leeder, 1979). In this study, the channel belt encompasses all channelrelated sediment in one avulsion cycle (thalweg, bar, splay, internal and external levee, and floodplain deposits; Figures 1, 2). Aggradation of the channel above the floodplain results in storage of potential energy in the flow to cause an avulsion (Imran et al., 1998;Mohrig et al., 2000). For rivers, this potential energy is high because of the large excess density between the flow (water) and the ambient fluid (air; Imran et al., 1998), resulting in rivers that can only reach 1 channel depth above the floodplain before avulsion (Mohrig et al., 2000). In submarine channels sculpted by turbidity currents, however, the potential energy is much lower due to the relatively small excess density between a turbidity current and the ambient seawater, leading to taller external levees and less frequent avulsion (Imran et al., 1998). However, the amount of pre-avulsion aggradation possible in submarine channel-belts has never been quantified.
In both rivers and submarine channels, avulsion is an important process for the construction of fluvial (Heller and Paola, 1996;Ganti et al., 2016) and submarine stratigraphic architecture (Flood et al., 1991;Torres et al., 1997;Schwenk et al., 2003). Avulsion is defined as the process by which flow is diverted out of an established channel belt into a new flow pathway on the adjacent floodplain (Mohrig et al., 2000;Slingerland and Smith, 2004). For avulsion to occur, the channel belt must aggrade above the adjacent floodplain to create a favorable potential energy gradient (i.e., the 'setup'; Bridge and Leeder, 1979;Bryant et al., 1995;Heller and Paola, 1996;Mohrig et al., 2000) and there must be a trigger/initiation event (Jones and Schumm, 1999). Sometimes, these criteria are met but the channel does not avulse, generating crevasse-splay deposits that further help to aggrade the channel-belt (Burns et al., 2017;Nienhuis et al., 2018;van Toorenenburg et al., 2018).
River avulsions are well-studied, and numerous avulsions have been observed during historic times (e.g., Smith et al., 1989). Avulsion setup criteria for rivers are well-constrained (Mohrig et al., 2000;Ganti et al., 2016) and documented triggers are commonly levee breaches during floods (e.g., Smith, 1998, 2004). Although a specific event (e.g., a levee failure) can trigger avulsion, normal overspill from a bankfull flow may be enough to generate channel avulsions (Edmonds et al., 2009), particularly when avulsion criteria have been reached.
In submarine channel settings, no historical avulsions have been observed or documented, and both the setup and triggering mechanisms are poorly constrained. Most work has focused not on the setup, but instead on interpreting triggers, which include flow-overspill and flow-stripping (Piper and Normark, 1983;Fildani et al., 2006), channel-floor aggradation (Kolla, 2007;Armitage et al., 2012), levee failure by mass-wasting (Flood et al., 1991;Brunt et al., 2013), mass-transport deposition/erosion (Ortiz-Karpf et al., 2015), and climate cyclicity (Picot et al., 2019). Avulsion triggers are difficult to predict due to their dependence on local factors and their opportunistic nature (Slingerland and Smith, 2004); however, the setup can easily be measured and constrained using the abundant seafloor, seismic reflection, and core data that documents Quaternary submarine channel avulsions (e.g., Pirmez and Flood, 1995;Manson, 2009 for the Amazon, Torres et al., 1997 for the Rhone). In this study, we document aggradation metrics and develop avulsion setup criteria for leveed, aggradational submarine channels. We also develop a theory for coupling between channels and their associated floodplains and explore differences between fluvial and submarine channel-floodplain coupling and the implications for channel-belt stability and avulsion frequency.

GOVERNING EQUATIONS Superelevation
The relative superelevation (S E ) is defined as the relief between the levee crest (L R ) and the adjacent floodplain, normalized by the channel depth (H; Eq. 1) (Bryant et al., 1995;Mohrig et al., 2000). Superelevation (S E ) of the channel should not be confused with superelevation of the water/flow surface at the apex of a meander bend due to centrifugal acceleration (Dietrich and Whiting, 1989 for riverine flow ;Hay, 1987 for turbidity currents).
Equation 1, avulsion criterion for rivers using relative superelevation: A superelevation S E = 1 indicates that the channel thalweg is at the same elevation as the floodplain (i.e., the elevation of the levee crest is 1 channel depth above the floodplain); data from modern and ancient fluvial systems (Mohrig et al., 2000;Jerolmack, 2009) suggest this value is a practical maximum for rivers. In other words, the avulsion setup is complete when the channel is superelevated one channel depth above the surrounding floodplain and only a trigger event is required to cause an avulsion. The rationale for this maximum value of S E is that by the time the channel thalweg reaches the elevation of the adjacent floodplain (S E ∼ 1), there is sufficient potential energy for avulsion to take place (Imran et al., 1998;Mohrig et al., 2000).
Tall and thick external levees and a channel perched high above the submarine floodplain have long been recognized in submarine settings (Buffington, 1952;Hübscher et al., 1997) and explained by the flow properties of turbidity currents (Imran et al., 1998(Imran et al., , 1999. We use the term floodplain to describe the far-field overbank areas of submarine  channel-belts for simplicity and consistency when comparing to rivers. Levee relief above the floodplain has also been documented for many submarine channels (e.g., Pirmez and Imran, 2003;Babonneau et al., 2010;compilation of Nakajima and Kneller, 2012) and shown to be larger than that of rivers; however, superelevation and how it evolves through channel-belt evolution has never before been compiled for submarine settings, nor has a maximum S E value been proposed as an avulsion criteria for submarine channels.

Channel-Floodplain Coupling
Superelevation theory (Eq. 1; Mohrig et al., 2000) is useful for characterizing modern geomorphological parameters for rivers. However, we are interested in the preserved record of channel-belt evolution and the potential coupling between the channel and its floodplain. Hence, we use parameters that can be measured from the preserved stratigraphic record to define a geometric equation that governs the amount of coupling between the channel and its floodplain in both fluvial and submarine settings (Figure 1): , Channel-floodplain coupling (fluvial and submarine): This geometric coupling equation relates the aggradation of the levee and floodplain to the channel aggradation, where L R is levee relief, A C is channel aggradation, A F is floodplain aggradation, and A L is levee aggradation (Figure 1). The necessary conditions to form this geometric relationship are: (1) channel depth H must be constant during channel evolution for A C and A L to be equal, (2) L R = 0 at channel initiation (Figure 1), and (3) channels are net aggradational. We acknowledge that H is spatially and temporally variable in both fluvial (Nittrouer et al., 2011) and submarine (Shumaker et al., 2018) channels, but this assumption is made for simplicity. We also acknowledge that many fluvial and submarine channels evolve through an incisional phase (e.g., Strong and Paola, 2008;Sylvester et al., 2011;Jobe et al., 2016), but this study is focused on aggradational channels that have well-defined external levees (sensu Kane and Hodgson, 2011) and lack a significant incisional phase (e.g., the Amazon submarine channel, Pirmez and Flood, 1995).

Channel-Floodplain Coupling in Rivers
In rivers, A F is here considered negligible because channel-belt deposition (A C , A L ) will be much more rapid than far-field, distal floodplain aggradation (Figure 1; Wolman and Leopold, 1957;Leeder, 1978;Bridge and Leeder, 1979;Brizga and Finlayson, 1990;Jerolmack and Paola, 2007;Hajek and Edmonds, 2014). We acknowledge that A F = 0 is an assumption that may not be valid for all rivers, but available data from modern rivers validate this assumption: numerous aggradation rate measurements from modern floodplains demonstrate that A C is 10-55 times greater than A F (Bridge and Leeder, 1979;Pizzuto, 1987;Törnqvist and Bridge, 2002;Jerolmack and Paola, 2007;Aalto et al., 2008). This indicates very weak coupling between the aggradation of the channel and its floodplain for rivers.
If A F = 0, Eq. 2 can be re-written as: We assume a simplified (i.e., flat) floodplain, while acknowledging that floodplain topography/dynamics can be complex (Lewin and Ashworth, 2014;Nienhuis et al., 2018;Johnston et al., 2019), affecting crevasse/avulsion location (Jerolmack and Paola, 2007) and crevasse/avulsion style (Hajek and Edmonds, 2014;Burns et al., 2017). The theory in Eq. 3 is also restricted to normal-flow fluvial reaches upstream of the backwater limit (the location where the mean elevation of the riverbed drops below sea-level or lake-level; Nittrouer et al., 2011). In the backwater zone, the sediment-transport regime is modified by spatial and temporal flow non-uniformity (Nittrouer et al., 2011), which affects channel-floor aggradation and scouring (Nittrouer et al., 2011(Nittrouer et al., , 2012, reduces levee growth and relief (Ganti et al., 2016), and changes channel belt dynamics and dimensions (Fernandes et al., 2016;Martin et al., 2018). Due to these complex hydro-and morpho-dynamics, this study will not further discuss coastal/backwater river systems, instead focusing on the differences between submarine channels and alluvial river reaches upstream of the backwater limit.

Channel-Floodplain Coupling in Submarine Channels
Floodplain aggradation A F in submarine channel settings must be considered a non-zero value, as it often attains a thickness that is comparable to other channel-belt thickness metrics (e.g., A L , A C , H; Figure 1). We use the term 'floodplain' to describe the far-field overbank areas of submarine channel-belts for simplicity and consistency when comparing to rivers; other terms like 'overbank wedge' (Normark et al., 1993), 'distal external levee' (Kane and Hodgson, 2011;Morris et al., 2014Morris et al., , 2016, 'farfield overbank, ' 'open slope, ' and 'basin plain' are commonly used for this submarine geomorphic area (depending on the documented/inferred slope position of the channel-belt) and are synonymous to floodplain in this study.
Enhanced floodplain aggradation in submarine channel settings is influenced by turbidity current overspill and flow stripping (Piper and Normark, 1983;Hiscott et al., 1997;, overbanking dilute, sheet-like turbidity currents (Stow and Piper, 1984;Jobe et al., 2011;Shumaker et al., 2017), and hemipelagic deposition (Stow et al., 2001). Unfortunately, datasets with paired channel and floodplain aggradation rate data do not exist, but several examples contain paired channel and levee-crest aggradation rates, demonstrating the importance of floodplain deposition in submarine channel belts. In the Bengal submarine channel, floodplain aggradation rates are ∼50 cm/ky (core 120KL) when levee-crest aggradation rates are ∼100 cm/ky (core 118KL, Weber et al., 1997). In the Amazon submarine channel, leveecrest aggradation rates are 360-517 cm/ky (sites 936, 946) while floodplain aggradation rates are 50-125 cm/ky (sites 930, 932, 935) (Mikkelsen et al., 1997). These two examples indicate that A C is only 2-10 times greater than A F , and thus A F cannot be neglected in submarine settings (Figure 1), and Eq. 2 is modified accordingly: This suggests that for a given channel dimension, submarine channel-belts will be systematically thicker than a fluvial channelbelt due to a positive A F (Figure 1) and greater levee relief (Buffington, 1952;. While Dorrell et al. (2015) demonstrate that aggrading submarine channels eventually become unstable and avulse due to geometric constraints, we suggest that submarine channel-floodplain Frontiers in Earth Science | www.frontiersin.org coupling is stronger than that in rivers, and as a result submarine channels are more stable than rivers under aggradational conditions (i.e., with S E > 1, see Figure 1). A compilation of data from rivers and submarine channel belts (Jobe et al., 2016) supports this hypothesis.
Channel-Belt Thickness: Combining Superelevation and Coupling Parameters Figure 1 shows the geometric relationships between the various measurable channel-belt parameters, and these can be arranged to define the thickness of the channel belt (H CB ) by relating the channel depth H and the aggradation of the channel A C : , Channel-belt thickness for fluvial and submarine channels Because H tends to be quite variable between (and sometimes within) systems (Shumaker et al., 2018), normalized channel-belt thickness (Eq. 5B also see Jobe et al., 2016) is preferred when comparing systems, and we will subsequently use this form. By expanding the A C /H term in Eq. 5B to include L R , we obtain a more general form that defines channel-belt thickness using a dimensionless superelevation term and a dimensionless coupling term:

Equation 6. Channel belt thickness
We can further modify the A C /L R term in Eq. 6 by utilizing the relationship in Eq. 2 to derive; Equation 7. Channel-floodplain coupling parameter The parameter χ describes channel-floodplain coupling without using L R or H, which define the superelevation parameter S E (Eq. 1). Substituting χ and S E into Eq. 6, we can rewrite the final form of the channel-belt thickness equation as: Equation 8, Channel-belt thickness with superelevation and channel-floodplain coupling terms: Using Eq. 8 and our understanding of channel-belt evolution and avulsion, we can estimate H CB when avulsion occurs for both fluvial and submarine settings.

Fluvial Conditions for Avulsion
Rivers have well-documented avulsions and the avulsion setup is well-constrained (Bridge and Leeder, 1979;Smith et al., 1989). In particular, Mohrig et al. (2000) established a superelevation criteria for river crevasse development and avulsion, with S E ∼ 1 at avulsion. Under the condition where H remains constant through channel-belt construction, fluvial channels become unstable and are prone to avulse when H = L R = A C = A L (Figure 1; Eq. 1). Assuming A F = 0 for rivers (see section "Discussion" above, Eq. 3), the avulsion criteria for rivers can therefore be summarized as: Solving Eq. 8 using these values, the normalized channelbelt thickness for a river at avulsion is 2 (i.e., H CB /H = 2; also see Figure 1). This is consistent with superelevation theory (Mohrig et al., 2000) as well as channel-floodplain coupling discussed above.

Submarine Conditions for Avulsion
For submarine channel belts, very little data has been collected on measurable parameters as compared to rivers. However, levee relief values are extremely large compared to channel depth in active channels Hübscher et al., 1997), suggesting that submarine channels are more stable at higher S E values than rivers (cf. Dorrell et al., 2015). Floodplain aggradation is significant (Mikkelsen et al., 1997;Weber et al., 1997) and cannot be ignored. Thus, we can summarize the avulsion criteria for submarine channels as: Hence, if we solve Eq. 8 using these values, H CB /H > 2 and potentially > > 2 (Figure 1). It is the aim of this paper to determine these values more precisely for submarine channel belts and quantify exactly how much more aggradational submarine channels are than rivers prior to avulsion.

DATA COLLECTION METHODOLOGY
We restricted our study to submarine channel-belts that have external levees and a relatively simple evolutionary history, excluding those channels that are purely incisional (i.e., canyons, Normark et al., 1993), had a complex incisional phase prior to aggrading (e.g., Kolla et al., 2012), or complex internal-levee architecture (Kane and Hodgson, 2011). Since we are interested in the aggradation of the channel-belt through time, bathymetric profiles do not provide enough information; rather, seismicreflection profiles are needed to constrain the base of the channel belt. The five submarine channel-belts that met these criteria and had high-quality seismic-reflection data are the Amazon, Zaire, Danube, Rhone, Magdalena, and Mississippi (Table 1). Submarine channel-belt cross-sections in our compilation were selected to (1) include extant channels on the seafloor (i.e., not necessarily active but not buried or compacted), (2) not be affected by large faults or other allogenic factors, and (3) be approximately perpendicular to the channel (see Table 1) so that measurements of channel and channel-belt dimensions are accurate (i.e., no artificially wide channels due to oblique crosssections). In planform view, the 52 cross-sections are, on average, within 19 • of perpendicular to the local downstream direction of the channel ( Table 1). If a cross-section displayed two-way travel time as the vertical unit, we converted to meters using a seawater velocity of 1500 m/s (i.e., 100 ms TWT = 75 m). While the shallow subsurface often has velocities 1400-2000 m/s (e.g., Flood et al., 1997), and we acknowledge that using 1500 m/s may slightly underestimate subsurface thickness, this value most accurately represents the seafloor surface, which is important for our calculations of L R and H. Coupling between the channel and the floodplain for any channelized setting can be described by measuring four channelbelt parameters: the channel depth H, levee relief above the floodplain L R , the aggradation of the channel A C , and the aggradation of the floodplain A F (Figure 1). In order to measure these variables, we collected the following data from the scaled cross-sections (examples in Figure 2): • A line trace of the seafloor (upper black line in Figures 1,  2); • A line trace of the base of the channel belt (lower black line in Figures 1, 2); • 2 points marking the external levee crests (red dots in Figures 1, 2); • 2 points marking the floodplain elevation (blue dots in Figures 1, 2); • 1 point marking the initial/deepest location of the channelbase (green dot in Figures 1, 2).
Where available, we utilized previous authors' interpretation of the lines and points (e.g., Pirmez and Flood, 1995). Our methods for defining (1) the locations of the levee crest, channel thalweg, floodplain, and channel-belt base elevations; and (2) the derivation of channel belt metrics (e.g., H, A C , A F , H CB ) are described here and graphically depicted in Figure 1. The levee crest and channel thalweg are straightforward to define by using the highest and lowest point, respectively, on a crosssectional profile of the seafloor (Figure 1; Shumaker et al., 2018). The channel-belt base can be defined as the deepest/lowest location that the channel occupied, which in most cases is the initial channel location at the beginning of channel-belt deposition. The channel-belt base is typically straightforward to locate in simple aggradational channel belts by using the geometries and cross-cutting relationships of the channel-belt deposits (Figure 2). Where the channel-belt base location was uncertain, we selected the deepest/lowest point of the interpreted channel belt (Figures 1, 2). The most subjective and interpretive FIGURE 2 | Seismic-reflection profiles and associated measurements of the Amazon channel (A) and Danube channel (B). Both profiles displayed at 10x vertical exaggeration but are not scaled to each other. Note the significant aggradation of the channel above the floodplain in both channels. Note also the difference in superelevation between the Danube abandoned channel (left) and the modern channel (right). Image in (A) from Pirmez and Flood (1995); image in (B) from Popescu et al. (2001). data to collect is the floodplain elevation (i.e., the base of the levee). The location of this point can be difficult to define, given that levee relief decreases asymptotically toward the floodplain in rivers (Pizzuto, 1987;Ferguson and Brierley, 1999) and submarine channels (Normark et al., 1993;Skene et al., 2002;Nakajima and Kneller, 2012). We tested various methods to define the floodplain elevation, including (1) picking where the levee-slope derivative stabilizes, (2) where the levee-slope becomes asymptotic with respect to a horizontal line, and (3) fitting of power law and/or exponential equations to the levee slope. However, these methods can generate spurious results due to variations in data quality, cross-section orientation, and local factors that affect the levee such as sediment waves, gullies, faults, and older/younger channel belts on the levee (Nakajima and Kneller, 2012; Figure 2). Hence, we select the floodplain elevation qualitatively (i.e., via 'ocular inspection'), constraining this location according to two criteria: (1) where the levee slope becomes asymptotic to the regional floodplain -this point defines the base of the levee; and (2) where the channel-belt thickness stabilizes wth increasing distance from the channel -this defines the point where floodplain aggradation is the chief process rather than levee deposition (Figures 1, 2). Generally, these two criteria are spatially correlated, but we recognize this qualitative method has inherent uncertainty. For example, selecting the floodplain elevation (i.e., base of the levee) in Figure 2B is more subjective than in Figure 2A because of data quality and complexity of antecedent topography. However, it does not appear to be possible to define the floodplain elevation in a more rigorous, quantitative manner (see discussion in Normark et al., 1993).
With the afore-mentioned points selected on a particular cross-section, two values of L R are calculated (as shown in Figure 1) as the vertical distance between each levee crest points and the floodplain elevation; those two values are averaged into the final value of L R . Two values of A F are also calculated as the vertical distance between the floodplain elevation and the line defining the channel-belt base (Figure 1); again, those two values are averaged into the final value of A F . We average the two values of L R and A F rather than take a maximum or minimum value because of local variations in levee morphology and variations in data quality (Figure 2). For example, the cross-section in Figure 2A is not exactly perpendicular to the flow direction of the channel, causing a slight elevation difference between the two floodplains, and an average of the two measurements alleviates this issue. The channel aggradation A C is calculated as the vertical distance between the point marking the initial location of the channel and the channel thalweg (defined as the minimum y value of the line trace of the seafloor between the levee crests; Figure 1). Examples of typical seismic-reflection profiles are shown in Figure 2.
As a proxy for sediment volume encompassed in the channel belt, we calculated the area of each channel-belt cross-section (Figure 4). These values are normalized by channel crosssectional area, and the P 10 -P 50 -P 90 distribution of channel-belt area is 11-84-249 channel areas. This suggests that a typical submarine channel-belt (gray area in Figure 3A) contains 80-100 times more sediment than the cross-sectional area of the channel (Figure 4). Values of fluvial channel belt area (or volume) are not available for comparison, but the channel belt data from Jobe et al. (2016) suggests that while rivers are much less aggradational, they build much wider channel belts than submarine channels; thus, both environments may have similar channel belt area values.
To enable comparison between channel-belt parameters, we compiled available data from the literature. Jobe et al. (2016) provide values of normalized channel belt thickness (H cb /H) from submarine and fluvial settings, and Mohrig et al. (2000) provide values of superelevation (S E ) for rivers ( Figure 5). Submarine channel-belts are ∼10 times thicker than fluvial channel-belts (Figure 5), supporting the theory developed above as well as qualitative (e.g., Peakall et al., 2000;Kolla et al., 2007) and quantitative (Jobe et al., 2016)  The magnitude of levee relief L R for submarine channel-belts (P 50 of 64 m) is 10 to 70 times larger than fluvial channelbelt L R (P 50 of 1 m from Mohrig et al., 2000). Some larger rivers can have taller levees; for example, the Mississippi river has 6 m high levees (Shen et al., 2015) and the Rhine-Meuse river has 3-5 m high levees (Törnqvist, 1994). However, we cannot find an example of a fluvial levee > 10 m high, so an average submarine levee is still an order of magnitude taller than an average fluvial levee. This comparison is not normalized, and it is well-documented that submarine channels are larger than rivers (Konsoer et al., 2013). Normalizing levee relief by channel depth (Eq. 1; Mohrig et al., 2000) produces superelevation (S E ), which is shown in Figure 5. We find that submarine channel S E values have a P 10−50−90 distribution of 0.8/1.9/4.5, while fluvial S E values are consistently lower, with a distribution of 0.4/0.7/1.3 (Figure 5). From these distributions, submarine S E values are 1.2 to 3.5 times larger than fluvial S E values (Figure 5), suggesting that submarine channels can be stable when superelevated up to 3.5 channel depths above the floodplain, while rivers nearly always avulse before reaching 1 channel depth of superelevation.

Danube_F1_Popescu2001a
Amazon_F4-11_Manson2009f Amazon_F4-11_Manson2009b Amazon_F4-15A_Manson2009m Amazon_F23-13_Flood1991 Amazon_F4-15B_Manson2009c Amazon_F4-11_Manson2009d  Figure 3A, and normalized by the cross-sectional area of the channel in Figure 3B. This data suggests that a typical submarine channel-belt contains ∼ 100 times more sediment than the channel that created it.
No published values of paired A F and A C values from rivers were available to compute χ to compare to submarine values ( Figure 5). However, ratios of floodplain-aggradation to channel-aggradation rates range from 0.02 to 0.25 for rivers (Figure 6; Allison et al., 1998;Makaske et al., 2002;Törnqvist and Bridge, 2002;Aalto et al., 2008). While aggradation-rate data from submarine channel-belts would be best for comparison, no reliable data exist. Hence, we simply compare the submarine A F /A C ratio (from thickness data) to the fluvial A F /A C ratio (from rate data), with the assumption that the larger values should most closely align with avulsion conditions (Figure 6). The submarine P 90 and fluvial P 10 values of A F /A C do not overlap (Figure 6), supporting the avulsion criteria discussed above, specifically: (1) A F in fluvial channel-belts is insignificant compared to A C and thus can be ignored when considering avulsion criteria for rivers (see Eq. 3; Figure 1); and (2) A F cannot be ignored in submarine channel belts and thus must be included in the avulsion criteria (see Eq. 4; Figure 1). We caution that while these A F /A C results are intuitive and consistent with theory and available data, they should be considered preliminary until A F /A C rate data can be collected from submarine channel belts.

Why Are Submarine Channel Belts So Thick and Superelevated?
The results of this study clearly demonstrate that submarine channels commonly attain S E and χ > 1 (Figure 5), values much higher than observed in rivers. We interpret that the unique turbidity current flow properties in submarine channels are responsible for the significant superelevation and aggradation of submarine channel-belts. Flows in submarine channels have ∼50 times lower density contrast between the flow and ambient fluid than rivers (Imran et al., 1998). This promotes higher sediment concentration in the upper portion of the flow, leading to levee and floodplain aggradation caused by enhanced overspill and flow stripping, particularly around channel bends (Piper and Normark, 1983;Hiscott et al., 1997). In addition, turbidity currents are strongly vertically stratified and the velocity maximum is located much closer to the bed than in a riverine flow (Sequeiros et al., 2010;Dorrell et al., 2014;Azpiroz-Zabala et al., 2017). This vertical stratification limits the potential for avulsion because: (1) the dense, energetic, coarse-grained portion of the flow remains near the channel thalweg rather than near the levee crest (Hansen et al., 2015;Jobe et al., 2017), and (2) the top of the flow has very low sediment concentration and density contrast with the ambient fluid (Imran et al., 1998) and thus little to no driving force for erosion as compared to rivers (Konsoer et al., 2013), suggesting there is diminished ability for turbidity currents to erode the external levee and trigger an avulsion. Collectively, these factors cause flows in submarine channels to have lower potential energy as compared to rivers (Imran et al., 1998;Mohrig et al., 2000). Therefore, submarine channels commonly attain larger values of levee relief, superelevation, and channel belt thickness prior to autogenic avulsion.

Criteria for Submarine Channel Avulsion
The theory and results demonstrated above allow us to develop avulsion criteria for submarine channels. Using Eq. 8, these criteria should consist of a maximum value of S E and χ that creates a maximum H CB /H. For rivers, the avulsion criteria are S E = 1, χ = 1, and H CB /H = 2 (see section "Fluvial Conditions for Avulsion"). We know that since the majority of H CB /H values for submarine channel-belts are greater than 2 (Figure 5), avulsion values of S E and χ must be > > 1. Using the distribution of fluvial S E values shown in Figure 5, S Efluvial = 1 occurs at the P 80 position of the distribution; Mohrig et al. (2000) suggest that while 1 is the practical avulsion threshold, some rivers can attain a slightly higher superelevation before avulsing. Using this reasoning, we can use the P 80 as a proxy for what the S E value should be at avulsion in a submarine channel-belt; again using

Fluvial
(n=5) (compiled from Alison et al. 1998, Makaske et al. 2002, Tornquist and Bridge 2002, Aalto et al. 2008 A F A C (floodplain aggradation) (channel aggradation) FIGURE 6 | Ratio between channel aggradation and floodplain aggradation in fluvial and submarine channel-belts. This relationship suggests that the relative contribution of floodplain aggradation is much more important in submarine channel belt growth, supporting the formulation of Eqs. 3 and 4. Figure 5, the P 80 S Esubmarine = 3.4. Using the same reasoning for χ , the P 80 submarine χ value is 2.5 ( Figure 5). Revisiting Eq. 8, we can compute the value of H CB /H for submarine channel-belts at avulsion: → H CB H = 9.5 at avulsion These avulsion thresholds are derived from our worldwide compiled dataset (n = 52), but it is important to note that these values (particularly H CB /H) likely vary from system to system based on slope position, the average excess density of flows, Froude number and vertical position of the velocity maximum (Sequeiros et al., 2010), and other factors not discussed here. For example, a system with higher excess density flows may build channel belts with lower S E and χ values, leading to an earlier avulsion (i.e., prior to attaining H CB /H ∼ 9.5). Other systems may build channels without significant levees (e.g., Picot et al., 2019) and thus promote more rapid avulsions before levee relief can develop.
To test the validity of these avulsion criteria, we construct a simple model of Eq. 8 that calculates H CB /H from any value of S E and χ (colored lines in Figure 7A). The independently measured H CB /H values from this study (black dots and red numbers in Figure 7A) agree very well with the modeled H CB /H values derived using Eq. 8. To quantify this agreement, Figure 7B cross plots the measured H CB /H values (method defined in Figures 1,  2) to the H CB /H values calculated using Eq. 8. Although there is variability, Eq. 8 accurately predicts the observed values, with a coefficient of determination (R 2 ) of 0.40.

Comparison to Modern Seafloor Data
This study has focused on seismic-reflection data, where the base of the channel-belt can be confidently mapped (e.g., Figure 2). However, there is a wealth of publicly available bathymetry data where the concepts presented here can be observed. Three passive-margin and four active-margin channels with easily accessible bathymetry data were chosen: Amazon (Pirmez and Imran, 2003), Bengal (Schwenk et al., 2003;Kolla et al., 2012), Joshua (Posamentier, 2003), and New Zealand (Hikurangi, Bounty, Haast, and Hokitika channels; Mountjoy et al., 2009). While the Amazon and New Zealand channels have bathymetry coverage over most of their lengths, only the middle portion of the Joshua channel and the distal portion of the Bengal channel are imaged (Shumaker et al., 2018). Figure 8A displays bathymetry-based cross-sections of the Joshua, Amazon, Bengal, and Hikurangi submarine channels, and Figure 8B quantifies S E values for all seven mapped channels. Passive-margin channels (Amazon, Joshua, Bengal) show larger values of S E and simpler seafloor topography, while activemargin channels are entrenched, with low values of S E , and more complex seafloor topography ( Figure 8A). The Amazon channel shows high levee relief (L R ) that decreases downstream, consistent with previous observations (e.g., Pirmez and Imran, 2003;Shumaker et al., 2018) and our compiled data (see next section and Figures 9, 10). The Amazon and Joshua channels have very large values of S E , up to almost 6 ( Figure 8B), consistent with their aggradational, avulsive nature Posamentier, 2003) and slope position. Since only the distal portion and channel mouth of the studied Bengal channel has bathymetry coverage (Shumaker et al., 2018), values of S E are small ( Figure 8B), but more proximal data shows a more aggradational channel similar to the Joshua and Amazon Schwenk and Spieß, 2009). All four of the active-margin channels near New Zealand (Figure 8) have high-relief submarine topography near the channel and thus are variably incised/entrenched ( Figure 8A). Values of S E for the four active-margin channels are < < 1 and do not change predictably downslope (Figure 8). We interpret that this difference is caused chiefly by the tectonic setting and associated seafloor deformation. While the Joshua, Amazon, and Bengal channels can build an equilibrium profile and thus have strong channel-floodplain coupling, and can aggrade a channel belt to the avulsion thresholds, the abundant seafloor topography in the Hikurangi, Haast, Bounty, and Hokitika channels creates a disequilibrium slope that perturbs the channel-floodplain coupling (Figure 8). Hence, these active-margin channels are less likely to reach avulsion threshold values of S E and χ than passive-margin submarine channels.

Levee Slope as a Potential Predictor of Avulsion
There is wide variability in the lateral slope of the external levees in submarine channel belts (Figures 3, 8). Intuitively, one would think that a steep levee slope would lead to more rapid avulsion. Indeed, the lateral levee slope has been proposed as an alternative (to superelevation) control on channel avulsion in rivers (Mackey and Bridge, 1995). The reasoning is that a higher levee slope leads to more rapid avulsion due to the erosional power of water on that slope, given a levee breach (see discussion in Mohrig et al., 2000). It is also geometrically intuitive that superelevation and levee slope are correlated, with the levee slope becoming steeper as superelevation increases (Slingerland and Smith, 1998). The cursory analysis of Mohrig et al. (2000) indicates that superelevation is a more reliable predictor of avulsion than levee slope by comparing both metrics from five modern rivers. We do not specifically measure levee slope because most of our cross-sections are not perfectly perpendicular to the channel flow direction (Table 1). However, with the burgeoning amount of high-quality topography and bathymetry data now available, a valuable future study could rigorously compare levee slopes to superelevation for submarine and fluvial channel-belts. Of particular interest would be to consider how the differing flow characteristics (e.g., excess density differences between riverine flow and turbidity currents) may influence erosion of shallow and steep levee slopes and thus avulsion.

Downstream Changes in Channel-Belt Dimensions in the Amazon Submarine Fan
The Amazon submarine sediment routing system is a wellcharacterized locale for understanding submarine fan/channel dynamics (Damuth and Kumar, 1975;Flood and Damuth, 1987;Pirmez and Flood, 1995;Pirmez and Imran, 2003;Jegou et al., 2008;Manson, 2009  system Damuth et al., , 1988Flood et al., 1991;Pirmez and Flood, 1995;Piper and Normark, 2001;Manson, 2009;Maslin, 2009). Pirmez and Flood (1995) established a naming scheme for Quaternary channel avulsions on the Amazon Fan, and this study focuses on three of those named channels (Figure 9): 'Brown' (oldest), '1E, ' and ' Amazon' (youngest, and the modern, most recently active channel). While older channels (e.g., ' Aqua, ' 'Orange') and other channels/avulsions have been documented during the studied time period (e.g., 1A, 1B, 1C, 1D, 1F; see Pirmez and Flood, 1995), suitable seismic-reflection profiles are absent or insufficient for full characterization. Figure 9 shows a map of the Brown, 1E, and Amazon channels and their associated channel-belt crosssections. There are 16 cross-sections that intersect the Brown   channel from the canyon-channel transition to the last mapped Brown channel location (Figure 9). An avulsion to the northwest created the subsequent 1E channel, which is constrained by 21 cross-sections (Figure 9). Finally, the most recent avulsion (again to the northwest) created the Amazon channel, which is constrained by 21 cross-sections (Figure 9). It is important to note that all turbidity currents that built the Brown, 1E, and Amazon channels traversed through the 14 most upstream crosssections, denoted as vertically stacked color gradients in Figure 9 and stacked datapoints in Figure 10. We measured channelbelt dimensions at each cross-section location from the seafloor to the base of the oldest channel-belt genetically linked to that cross-section (Figure 9; e.g., base-Brown for the 14 cross-section furthest upstream, then base-1E for the next four cross-sections, etc.). This is the most accurate method available to measure true channel-belt dimensions, but it does not account for modification of the channel and channel-belt morphology that has likely occurred post-Brown and post-1E (i.e., during development of the modern Amazon channel; Figure 9). Since there presently is no way to reconstruct the channel dimensions for Brown and 1E time at each cross-section location, we utilize modern seafloor channel and levee dimensions (e.g., H, L R ) to compare all three channel belts (Brown, 1E, Amazon). Channel and channel-belt metrics generally show pronounced decreases downstream (Figure 10). Channel cross-sectional area in all three channel-belts (Brown, 1E, and Amazon) decreases by nearly 100x downstream ( Figure 10A). We also computed the area of the channel belt (gray area between the points defining the floodplain, Figure 3) as a proxy for total sediment volume contained within the channel belt (Figures 4,  10B). The channel belt area also shows a steady downstream decrease in each of the three channel belts, with nearly two orders of magnitude of total change ( Figure 10B). Channel belt parameters that record aggradation (H CB , A F , A C ) show consistent decreasing values downstream (Figures 10C-E), with total change from upstream to downstream approximately 10fold. Levee relief (L R ) also decreases consistently downstream, with upstream values near 200 m and downstream values of only 10 m ( Figure 10F). This downstream decrease in L R is well-documented for the Amazon channel (e.g., Figure 4 of Piper and Normark, 2001;Pirmez and Imran, 2003) and other large, leveed submarine channels (e.g., Babonneau et al., 2002Babonneau et al., , 2010. These downstream-thinning trends in channel-belt parameters are consistent with qualitative models of submarine fan growth (Mutti and Normark, 1987;Damuth et al., 1988). However, S E and χ show very different trends that are related to submarine channel avulsion dynamics. Upstream S E is relatively low (S E ∼ 1), but increases downstream to the Brown avulsion location, where S E values approach 6 ( Figure 10G). Downstream of the Brown avulsion, S E values for Brown significantly decrease, consistent with models of autogenic channel avulsion dynamics (Brizga and Finlayson, 1990;Mohrig et al., 2000). While we cannot rule out the possibility that L R and/or H were modified post-Brown and post-1E and these values of S E are not accurate, the close proximity of three independently-measured cross-sections with almost identical values of S E ∼ 6 (Figures 9, 10G) suggests that this value may be the avulsion 'setup' for the modern Amazon channel. For the 1E channel, the avulsion location is not marked by a large S E value (Figure 10G), suggesting that either (1) L R and H are not accurately measured or have been modified by the Amazon channel at this locale, or (2) that the 1E avulsion was caused by allogenic forcing (e.g., in-channel mass transport deposition, levee failure) rather than a large value of S E . While poor absolute age control prevents us from unequivocally demonstrating an allogenic trigger at 1E time, Maslin (2009) reports emplacement of a large mass transport deposit at approximately 1E time, supporting one potential allogenic mechanism. If these trends in downstream S E are correct, the next autogenic avulsion in the Amazon channel should occur near the Brown channel avulsion, as this remains the highest measured S E (Figures 9, 10G). Why the channel has remained stable at this location with S E ∼ 6 is not clear, but this behavior suggests that submarine channels are quite stable in highly aggradational settings (cf. Dorrell et al., 2015). Channelfloodplain coupling is consistent in the Amazon, with values of χ ∼ 2 for approximately 400 km ( Figure 10H). Interestingly, the Brown and 1E avulsions do not result in a change in χ, suggesting that strong channel-floodplain coupling may be inherent to submarine channels ( Figure 7A). Modification of χ from a value of ∼ 2 seems to be related to local factors; for example, very high values of χ exist in the canyon-channel transition zone, and the distalmost measurement has a very low χ value (Figure 10H).
Using Eq. 8, we would predict that with variable S E and consistent χ , the normalized channel-belt thickness (H CB /H) would mimic the trend of S E . Indeed, our measurements of H CB /H show the highest values just upstream of the Brown avulsion location, supporting our theory of channel-belt aggradation and avulsion. The very large H CB /H measurement at ∼ 420 km (cross-section F23-13, Flood et al., 1991) may have been caused by the improper selection of channel-belt base, resulting in a channel belt that is falsely thick; however, this was chosen by Flood et al. (1991) and we have no data to provide an alternate interpretation.

CONCLUSION
Avulsions are important drivers for creating channelized stratigraphy in both fluvial and submarine channels, and constraining the avulsion setup is critical for predicting the distribution of sediment, organic matter, and pollutants in these sediment routing systems. The relative aggradation of the channel, external levee, and floodplain are the dominant drivers for autogenic avulsion dynamics, and they can be related in a geometric form. This study establishes a geometric channel-belt framework for predicting avulsions for both rivers and submarine channels and provides the first reported avulsion criteria for submarine channels. Prior studies have focused on superelevation of the channel above the floodplain, an important predictor of avulsion for rivers. While rivers can only superelevate an amount equivalent to 1 channel depth above the floodplain prior to avulsion, submarine channels are more stable during aggradation, and we document new data demonstrating superelevation values > 3 channel depths.
These observations result in a normalized channel-belt thickness for submarine channels that can be as thick as ∼ 10 channel depths, while fluvial channel belts are limited to a belt thickness of 2 channel depths. This disparity is caused by the differences in superelevation, but also by differences in channel-floodplain coupling. Since floodplain aggradation values reported from fluvial channel belts are only 1-10% compared to channel aggradation, the floodplain contributes a negligible amount to channel-belt thickness and thus can be disregarded. In submarine channels, however, floodplain aggradation is significant (up to 50% the value of channel aggradation) due to levee overspill, flow stripping, and hemipelagic deposition. We summarize these observations with a coupling parameter chi (χ) that relates floodplain aggradation to channel aggradation A C /(A C -A F ). This coupling parameter is effectively 1 for rivers but ranges from 1 to 6 for submarine channels.
Submarine channel belts can be up to 10 times thicker than their fluvial counterparts at avulsion due to enhanced superelevation and channel-floodplain coupling, and we interpret that these enhancements are related to the unique flow properties of turbidity currents. External levee aggradation and thus superelevation is promoted by overspill from flows with 50x lower density contrast with the ambient fluid as compared to riverine flows. Submarine floodplains are aggradational as well, contributing significantly to channelbelt growth. When the channel is perched far above the floodplain (i.e., significantly superelevated), there is far less potential energy in the flow as compared to a river, leading to a stable, aggradational channel. We demonstrate this stability using downstream trends in the Amazon channel, where superelevation and the channel-floodplain coupling parameter χ remain at 2 or greater for more than 400 streamwise km, resulting in a channel belt that is ∼ 5 channel-depths thick, more than twice the aggradation that a river is capable of.

DATA AVAILABILITY STATEMENT
All datasets generated for this study are included in the article/supplementary material.

AUTHOR CONTRIBUTIONS
ZJ wrote the manuscript and prepared the figures. NH developed concepts and performed data analysis. KS developed concepts and co-wrote the manuscript. DC performed data collection. HD performed data analysis. LS performed data analysis. LP helped develop concepts and perform data analysis. FL helped develop concepts and perform data analysis.