Slope geomorphological modelling

Canyons in continental slopes of passive margins

In models for bedrock stream erosion in which erosion rate varies with the flow power or bed shear stress ("detachment limited flow power" models), channel bed erosion rates (E) depend on rainfall catchment area A and channel gradient S: E~A^mS^n (m and n are constant exponents). Mountain rivers are typically upwards concave and plots of their log(S) against log(A) often are nearly straight lines (an inverse power-law reflecting the concave shapes of streams). Although now controversial because of other factors, this "concavity" has previously been interpreted by saying that erosion rate E decreases slowly towards base-level or is spatially uniform, which lead to an inverse relationship between A and S with a power-law slope m/n.

For the submarine canyons, if erosion rate is assumed to be similarly controlled by flow power or bed shear stress (as erosion by turbidity currents is most likely similarly caused by abrading particles carried by the flow or flow-induced bed failure), the relationship between channel gradient and catchment area is a clue to the origin of the incision. The central USA Atlantic continental slope is known to have been aggrading for a long time by the accumulating hemipelagic sediments deposited from the water column (top figure, right). The accumulating sediments form unstable deposits around the walls of canyons, which occasionally fail, initiating sedimentary flows (debris flows and turbidity currents). The frequency and maximum size of sedimentary flows experienced by the canyon channel should relate to the up-slope canyon area. (E.g., lower figure right: the channel at 'A' experiences all five flow events whereas that at 'B' experiences only three.) If other factors were constant, this will cause a tendency for erosion rate to depend on hemipelagic catchment area. As the specific flow power and bed shear stress of a sedimentary flow both depend on the channel gradient, then erosion rate may also be expected to vary in a similar way to E~A^mS^n. The gradient-area curves can therefore be interpreted if the channels are approaching a form of erosional balance in which the erosion rate is spatially uniform or at least slowly varying spatially. The effect of frequency of flow events increasing down-canyon (with increasing A) is then balanced by shallower channel gradient, producing the inverse power law relationship that is observed also in submarine canyons.

In order to explore this idea, a database of hemipelagic catchment area and channel gradient was created for dendritic canyons in the upper continental slope using the USA east coast multibeam dataset. The figure left shows a series of hemipelagic catchment areas interpreted from the USA east coast bathymetry. The figure below shows an enlargement of a small amount of that interpretation (solid circles mark confluences). Channel gradient was measured for each channel immediately above the confluences, so the database consists of pairs of gradients and areas for each confluence.
The graphs on the right show the gradient-area data for canyons reaching the continental shelf break (A) and those isolated from the shelf break (B). It is commonly thought that canyons were fed by rivers or shelf sediments during sea-level lowstands such as during the Last Glacial Maximum ("spillover"), however here the two kinds of canyon have the same gradient-area relationships. If fed by shelf sediment directly, the canyons heading at the shelf break might be expected to have become more eroded and adopted a shallower gradient at their heads leading to different average gradients, but this is not the case. This is consistent with other observations that the slope sediments are predominently muddy and don't contain abundant shelf sands as might be expected if there had been extensive spillover. If there were enhanced low-stand erosion, it may have involved enhanced supply of hemipelagic sediment across the whole slope rather than just shelf-break-heading canyons.

At a river confluence, the long-term erosion rates of the two branches must be equal, otherwise we would observe a waterfall at the confluence and the tributary would drain a hanging valley. Their contrast in areas and gradients can reveal the ratio of exponents m/n and how well the drainage system follows the erosion law (Seidl and Dietrich, 1992). Such data for these submarine canyons (graphs to the left) show significant scatter, but they suggest on average E~A^mS^n with m/n=0.2-0.3. Gradient and area are also related by a power-law relationship (S~A^-0.3) that is consistent with the erosion law if the landscape is in a steady state.

Seidl, M., and Dietrich, W. E., 1992, The problem of channel erosion into bedrock: Catena Suppl., v. 23, p. 101-124.

Mitchell, NC, Interpreting long-profiles of canyons in the USA Atlantic continental slope, Marine Geology, 214, 75-99, 2005. (abstract.)

Mitchell, NC, Form of submarine erosion from confluences in Atlantic USA continental slope canyons, American Journal of Science, 304, 590-611, 2004. (full article (PDF).)



Canyons in slopes of active margins

Developing a physical model of the above slope canyons is difficult because many elements are poorly known: how the sedimentary flows are initiated, how they change behaviour down-canyon and how they erode their substrates. A different approach is therefore taken here. Sections of canyons are examined where the channel cuts through anticlines created by thrust faulting along accretionary prism slopes. The amount eroded from these sections is small compared with the amount of sediment that has passed through them so we can assume a uniform average solid flux . The channel shape then suggests how erosion or sediment transport have responded to the channel's gradient, an approach that has been taken with river knickpoints.

Detachment-limited erosion?

In detachment-limited erosion of river beds, loose material is easily removed and erosion is limited by how fast material can be plucked or abraded from the bed. In "flow power" erosion schemes, the erosion rate is typically related to the shear stress the flow imposes on its bed or the specific flow power. Either implies that, as a river speeds up, it should become more erosive. Progressive erosion then leads to steep reaches migrating upstream over time (if lithology, fractures, etc are uniform).

This image (right) shows channels cut through anticlines in the Gulf of Alaska. Whereas the range-front fault might be expected to lie along the southeast front of the southern-most ridge, the channel contains two steep reaches upstream from it and a further steep reach within a piggy back basin. Other steep sections can be found upstream of likely faults or of the SE edges of anticlines. These are evidence for upstream migration and "detachment-limited" styles of erosion.


Transport-limited erosion?

 Alternatively, material within the bed is easily detached but the transport flux of sediment is controlled by the strength of the stream. In "transport-limited" erosion rules, deposition occurs where the transport flux slows down (where the channel shallows) and erosion occurs where flux increases (where the channel steepens). In alluvial channels, these effects cause the channel to smooth out.

The graphs (left) show profiles through channels of the Barbados accretionary prism (data of Huyghe et al., Geology, 2004). Compared with the profiles taken from outside the channels (dotted lines), the channel bed is indeed smoother and rounded. Some channels therefore show "transport-limited" styles of erosion.

Mitchell, NC, The morphologies of knickpoints in submarine canyons, Geol. Soc. Am. Bull., 118, 589-605, 2006. (full article (PDF)*.)

Erosion by hyperpycnal flows

At river mouths, turbidity currents occur but it is often unclear if they form because outflowing river waters initiate hyperpycnal (negatively buoyant) flows directly or if they occur from failure of sediments rapidly deposited at the river mouth. The events occur during floods when rivers have the greatest sediment loads and consequently the processes are difficult to observe. In this dataset (right) collected by the USGS/NOAA, a series of fine gullies can be seen seaward of the river mouth and away from possible landslide sources, so this is evidence for hyperpycnal flow erosion. Mitchell, NC, Channelled erosion through a marine dump site of dredge spoils at the mouth of the Puyallup River, Washington State, Marine Geology, 220, 131-151, 2005. (abstract.)


Funding for this work was provided partly by a Research Fellowship from the Royal Society. Much of the data studied were provided by the NOAA and USGS.

*The Geological Society of America owns the copyright to this document. Further reproduction or electronic distribution of them is not permitted.


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