Autogenic terraces and non-linear incision rates under steady external forcing

Luca C Malatesta1, Jeffrey P Prancevic1, Jean-Philippe Avouac1,2 California Institute of Technology, University of Cambridge

ics Obser ton vato c ry Te

California Institute of Technology Common in incising alluvial : Abandonment of wide terraces followed by (accelerated) entrenchment

Commonly interpreted as an acceleration of tectonic or climatic forcing during incision discussed in Bull (1991); Molnar et al. (1994); Poisson & Avouac (2004); Pazzaglia (2012); Gong et al. (2014); Finnegan et al. (2014) among others Kuitun River, Tian Shan, China. Luca Malatesta Common in incising alluvial rivers: Abandonment of wide terraces followed by (accelerated) entrenchment

Can accelerated incision rates result from autogenic processes?

Commonly interpreted as an acceleration of tectonic or climatic forcing during incision discussed in Bull (1991); Molnar et al. (1994); Poisson & Avouac (2004); Pazzaglia (2012); Gong et al. (2014); Finnegan et al. (2014) among others Kuitun River, Tian Shan, China. Luca Malatesta Our understanding of incision in transport-limited rivers is rooted in 1D

1D MORPHODYNAMICS with applications to RIVERS AND TURBIDITY CURRENTS © Gary Parker November, 2004 TO A NEW MOBILE-BED EQUILIBRIUM

Bed evolution Bed evolution

90 90

80 0 yr 80 0 yr 0.2 yr 2 yr 70 70 0.4 yr 4 yr 60 0.6 yr 60 6 yr 0.8 yr 8 yr 50 50 1 yr 10 yr 40 Ultimate 40 Ultimate

30 30 Elevation in m in Elevation m in Elevation 20 20

10 10

0 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 Distance in m Distance in m

Bed evolution Bed evolution

90 90 80 80 0 yr 0 yr 20 yr 50 yr 70 70 40 yr 100 yr 60 60 yr 60 150 yr 80 yr 200 yr 50 50 100 yr 250 yr Ultimate 40 Ultimate 40

30 30 Elevation in m in Elevation Elevation in m in Elevation 20 20

10 10 0 0 33 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 Distance in m Distance in m

Gary Parker’s morphodynamics e-book available online We propose to test two autogenic processes that enhance vertical incision as entrenchment proceeds.

1. high banks reduce the channel 2. large cliff collapse cannot be lateral migration rate, vertical immediately removed by the river, creating incision happens over the same a talus that shields the bank from area and is enhanced while vertical incision continues.

mentioned in Hancock and Anderson, 2002; Nicholas and

Anji Hai River tributary, Tian Shan, China. Quine, 2007a,b; Clarke et al., 2010; Nicholas et al., 2009 Model for cross-section evolution of entrenchment

Erosivity of a food Bankfull lateral migration

Strength of bank COVARY

Anji Hai River tributary, Tian Shan, China. The geometric model is made of a series of independent cross-sections

Sediment fux in each cross-section depends on channel slope, width and water discharge Erosion is defned by the divergence of sediment fux between the profles (Exner) In each cross-section erosion is partitioned between bed erosion and lateral erosion Lateral migration is independently picked in each cross-section following a random walk 1

foodplain river elevation

0 0

distance along river 1 1 0 distance across the geometric model reflects the main processes: starting with a random migration to erode a set area

f(S,W) erosion capacity

lateral migration channel foodplain

total erosion capacity the geometric model reflects the main processes: migration and erosion within the floodplain

f(S,W) =

lateral migration channel pre-incision foodplain pre-incision channel post-incision foodplain post-incision total erosion capacity within-foodplain incision the geometric model reflects the main processes: migration against a short bank

lateral migration channel foodplain

total erosion capacity the geometric model reflects the main processes: results in floodplain and bank erosion

= + +

lateral migration channel pre-incision foodplain pre-incision channel post-incision foodplain post-incision total erosion capacity bank-abutting incision within-foodplain incision bank erosion the geometric model reflects the main processes: against a tall bank (cliff), excess material is

=

+

lateral migration channel pre-incision foodplain pre-incision channel post-incision foodplain post-incision total erosion capacity bank-abutting incision within-foodplain incision bank erosion the geometric model reflects the main processes: deposited as a talus and constrains the channel

channel pre-talus foodplain pre-talus channel post-talus foodplain post-talus talus area 180 runs to test parameters Erosion capacity captures variability of entrenchment dynamics best

High erosion capacity result in Low erosion capacity result in deep rectangular funnel-shaped canyons

foodplain foodplain channel channel

1 1

0 0 0 0

1 1

1 1 0 0

Limited terrace record Extensive terrace record Moderate channel narrowing Important channel narrowing 180 runs to test parameters Erosion capacity captures variability of entrenchment dynamics best

High erosion capacity result in Low erosion capacity result in deep rectangular canyons funnel-shaped canyons

foodplain foodplain channel channel

1 1

0 0 0 0

1 1

1 1 0 0

Limited terrace record Extensive terrace record Moderate channel narrowing Important channel narrowing High erosion capacity steady incision rate Low erosion capacity acceleration of incision rate River incision at high erosion capacity River incision at low erosion capacity

500 500 2D incision 1D incision

400 400 Elevation Elevation 2D incision 300 1D incision 300

200 200 0 2000 4000 6000 0 2000 4000 6000 Time Time Evolution of cross-section geometry Evolution of cross-section geometry

500 500

400 400 elevation elevation timesteps timesteps 0 0 375 1250 300 750 300 2500 1125 3750 1500 5000 4000 6000 8000 4000 6000 8000 distance across stream distance across stream Channel narrowing mitigates the Channel narrows while the channel remains slowdown of incision. steep, forcing acceleration of the incision Conclusions

Terrace record Autogenic effects have to be factored in to quantify the relationship between forcing and incision Accelerated incision does not require a change in external forcing. A combination of topography and ages is generally required to identify external forcing

Sediment routing system Lateral feedbacks cause channel narrowing, and rivers can erode (and remobilize) deeper and older strata.