River Incision into Bedrock Interaction of a suite of processes Plucking, Abrasion (bedload & suspended load), Cavitation (?), Weathering Vortices shed off macro-roughness drive processes Relation to mean bed shear stress? Critical stress for incision/flood frequency Adjustment of channel morphology / bed state How non-linear? Relation to Climate?

Orogen-Scale Erosion Rule: 3 Assumptions 1. Flint’s Law Describes Equilibrium Chns 2. Channel Steepness is a power function of Rock Uplift Rate (U = E), Climate and Rock Type set Prefactor (C’ ) 3. Concavity Index is Invariant with U and C’

Flint’s Law: Mixed Bedrock-Alluvial Stream (Appalachians, VA)

S = k s A -  k s is a more-general equivalent to the SL index: No dependence on basin shape colluvial reach ksks --

King Range: Concavity Invariant with Rock Uplift Rate Snyder et al, 2000, GSAB Directly Contradicts Earlier Finding of Merritts and Vincent, 1989, GSAB

Concavity invariant with U Steepness varies with U

Orogen-Scale Erosion Rule: 3 Assumptions 1. Flint’s Law Describes Equilibrium Chns 2. Channel Steepness is a power function of Rock Uplift Rate (U = E), Climate and Rock Type set Prefactor (C’ ) 3. Concavity Index is Invariant with U and C’

Channel Steepness Index – Spatial Information about Relative Rock Uplift Rate Siwalik Hills, Nepal San Gabriel Mountains, CA Nepal Himalaya (Wobus et al.) Olympic Mountains, WA (Gasparini and Brandon) Bolivian Andes (Safran et al) Santa Ynez Mtns, CA (Duvall et al) King Range, CA (Snyder et al) Eastern Margin, Tibetan Plateau (Ouimet et al)

Siwalik Hills, Nepal

Bakeya Transect Bagmati Transect Data from Lave and Avouac, 2000, JGR

Siwalik Hills Anticline Himalaya Foreland, Nepal Strike-Parallel: Uniform Uplift Along Stream

Strike-Parallel: Normal, uniform concavity Strike-Parallel: Steepness varies with U 14 mm/yr 7 mm/yr

Siwalik Hills, Nepal

Kirby and Whipple, 2001, Geology

Transverse: U(x) Reflected in Concavity

San Gabriel Mountains, CA N 50 km SGM San Jacinto Fault Zone San Andreas Fault LA SGM = San Gabriel Mountains SMFS = Sierra Madre Fault System LA = Los Angeles relative plate motion SMFS

DiBiase et al., 2010, Earth and Planetary Science Letters

Erosion and hillslope angle SoilBedrock DiBiase et al., 2010 EPSL Hillslope angle increases with erosion rate until ~200 m/Ma Above this rate, hillslopes fail to record information about E (maximum soil production rate)

DiBiase et al., 2010, EPSL Comparison with 1-D Theory (Roering)

Erosion and channel steepness index Data shown only for basins > 3km 2 Relationship rolls over at high E; channels become more efficient as they steepen DiBiase et al., 2010 EPSL Channel steepness increases beyond hillslope threshold SoilBedrock

Why is there a roll over? Possible factors controlling roll over Precipitation increase with relief Channels narrowing as they steepen Non-linear incision process (n>1) Debris Flows in Steeper Catchments Thresholds of motion and/or detachment E ksks Slope of curve depends on erosional efficiency (lower slope  more efficient) The shape of this relationship provides information about channel incision processes – and sets the strength of climate-tectonic feedbacks

Precipitation gradients? At the individual basin scale, concavity decreases with increasing relief (Roe et al., 2002) Not observed in DEM analysis At the range scale, precipitation gradient could lead to spatial variability in erosional efficiency. Limited range in MAP among basins PRISM climate group, Oregon State University Sample basins

Channel narrowing?

Why is there a roll over? Possible factors controlling roll over Precipitation increase with relief Channels narrowing as they steepen Non-linear incision process (n>1) Debris Flows in Steeper Catchments Thresholds of motion and/or detachment E ksks Slope of curve depends on erosional efficiency (lower slope  more efficient) The shape of this relationship provides information about channel incision processes – and sets the strength of climate-tectonic feedbacks

Non-linear incision process? Low E Moderate E High E Transient Mean bed exposure = 4.8% (n=1314, ~40 km of surveys) No more non-linear than sediment transport

Concavity invariant with U Steepness varies with U

Stochastic-threshold incision model Baldwin et al, 2003, JGR

Stochastic-threshold incision model

Exponential vs. Powerlaw Tail

Stochastic-threshold incision model (Tucker & Bras, 2000) E = K R K C K  c A m S n K R =K R (physical parameters, , g, k e, width, lithology) K C =K C (climate parameters, P, T r, T b ) K  c =K  c (R c /P  c /P, A, S; varies from 0 to 1) Key unknown parameters:  c, k e, and a (or n) –From the basic postulate, E=k e (  b a -  c a )

K  c at steady state

Channel steepness vs. E Threshold term is necessary in order to explain steep channels, but unsatisfying at low erosion rates DiBiase et al., 2010 EPSL

Exponential Stochastic Model Misfit DiBiase et al., unpublished analysis

Powerlaw Flood Distribution DiBiase et al., unpublished analysis

Distribution of Large Floods Critical at Low Slopes/Low Erosion Rates DiBiase et al., unpublished analysis

Powerlaw Stochastic/Threshold Model (Lague et al. 2005) DiBiase et al., unpublished analysis

Siwalik Hills, Nepal Wobus et al., 2006, Penrose Volume – Climate and Tectonics