Landscape form and millennial erosion rates in the San Gabriel Mountains, CA

Abstract It has been long hypothesized that topography, as well as climate and rock strength, exert first order controls on erosion rates. Here we use detrital cosmogenic 10 Be from 50 basins, ranging in size from 1 to 150 km 2 , to measure millennial erosion rates across the San Gabriel Mountains in southern California, where a strong E–W gradient in relief compared to weak variation in precipitation and lithology allow us to isolate the relationship between topographic form and erosion rate. Our erosion rates range from 35 to 1100 m/Ma, and generally agree with both decadal sediment fluxes and long term exhumation rates inferred from low temperature thermochronometry. Catchment-mean hillslope angle increases with erosion rate until ∼ 300 m/Ma, at which point slopes become invariant with erosion rate. Although this sort of relation has been offered as support for non-linear models of soil transport, we use 1-D analytical hillslope profiles derived from existing soil transport laws to show that a model with soil flux linear in slope, but including a slope stability threshold, is indistinguishable from a non-linear law within the scatter of our data. Catchment-mean normalized channel steepness index increases monotonically, though non-linearly, with erosion rate throughout the San Gabriel Mountains, even where catchment-mean hillslope angles have reached a threshold. This non-linearity can be mostly accounted for by a stochastic threshold incision model, though additional factors likely contribute to the observed relationship between channel steepness and erosion rate. These findings substantiate the claim that the normalized channel steepness index is an important topographic metric in active ranges.

[1]  P. Allen,et al.  Sediment flux from a mountain belt derived by landslide mapping , 1997 .

[2]  G. Tucker,et al.  Landscape response to tectonic forcing: Digital elevation model analysis of stream profiles in the Mendocino triple junction region, northern California , 2000 .

[3]  Dimitri Lague,et al.  Discharge, discharge variability, and the bedrock channel profile , 2005 .

[4]  Mark D. Petersen,et al.  Fault slip rates and earthquake histories for active faults in southern California , 1994 .

[5]  J. Pelletier,et al.  Nonlinear slope-dependent sediment transport in cinder cone evolution , 2007 .

[6]  Kelin X. Whipple,et al.  Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison , 2002 .

[7]  W. Dietrich,et al.  The illusion of diffusion: Field evidence for depth-dependent sediment transport , 2005 .

[8]  R. F. Yerkes,et al.  Preliminary Geologic Map of the Los Angeles 30´ x 60´ Quadrangle, Southern California , 1997 .

[9]  D. F. Ritter,et al.  Rates of regional denudation in the United States , 1964 .

[10]  J. Roering,et al.  Systematic variation of bedrock channel gradients in the central Oregon Coast Range: implications for rock uplift and shallow landsliding , 2004 .

[11]  Burbank,et al.  Structural and topographic evolution of the central Transverse Ranges, California, from apatite fission‐track, (U–Th)/He and digital elevation model analyses , 2000 .

[12]  M. Summerfield,et al.  Tectonic uplift, threshold hillslopes, and denudation rates in a developing mountain range , 2007 .

[13]  F. K. Miller,et al.  Geologic map of the San Bernardino and Santa Ana 30' x 60' quadrangles, California , 2006 .

[14]  Robert S. Anderson,et al.  Evolution of the Santa Cruz Mountains, California, through tectonic growth and geomorphic decay , 1994 .

[15]  S. Schumm.  The disparity between present rates of denudation and orogeny , 1963 .

[16]  James W. Kirchner,et al.  Spatially Averaged Long-Term Erosion Rates Measured from in Situ-Produced Cosmogenic Nuclides in Alluvial Sediment , 1996, The Journal of Geology.

[17]  W. Dietrich,et al.  The soil production function and landscape equilibrium , 1997, Nature.

[18]  N. Snyder,et al.  Tectonics from topography: Procedures, promise, and pitfalls , 2006 .

[19]  J. T. Hack.  Studies of longitudinal stream profiles in Virginia and Maryland , 1957 .

[20]  G. Tucker,et al.  Dynamics of the stream‐power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs , 1999 .

[21]  F. Blanckenburg.  The control mechanisms of erosion and weathering at basin scale from cosmogenic nuclides in river sediment , 2005 .

[22]  F. Ahnert.  Functional relationships between denudation, relief, and uplift in large, mid-latitude drainage basins , 1970 .

[23]  William E. Dietrich,et al.  Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology , 1999 .

[24]  W. Davis.  THE CONVEX PROFILE OF BAD-LAND DIVIDES. , 1892, Science.

[25]  K. Whipple,et al.  Geomorphic limits to climate-induced increases in topographic relief , 1999, Nature.

[26]  Kelin X. Whipple,et al.  Beyond threshold hillslopes: Channel adjustment to base-level fall in tectonically active mountain ranges , 2009 .

[27]  D. Montgomery,et al.  Limits to Relief , 1995, Science.

[28]  W. Dietrich,et al.  Hillslope evolution by nonlinear creep and landsliding: An experimental study , 2001 .

[29]  J. Flint.  Stream gradient as a function of order, magnitude, and discharge , 1974 .

[30]  D. Montgomery,et al.  Effects of orographic precipitation variations on the concavity of steady-state river profiles , 2002 .

[31]  G. Tucker.  Drainage basin sensitivity to tectonic and climatic forcing: implications of a stochastic model for the role of entrainment and erosion thresholds , 2004 .

[32]  Walther Penck,et al.  Morphological analysis of land forms : a contribution to physical geology , 1953, Geological Magazine.

[33]  N Strahler Arthur,et al.  Equilibrium theory of erosional slopes approached by frequency distribution analysis , 1973 .

[34]  J. Spotila,et al.  Controls on the Erosion and Geomorphic Evolution of the San Bernardino and San Gabriel Mountains, Southern California , 2002 .

[35]  K. Nishiizumi,et al.  Chemical isolation of quartz for measurement of in-situ-produced cosmogenic nuclides , 1992 .

[36]  Robert E. Wallace,et al.  Modification of wave-cut and faulting-controlled landforms , 1984 .

[37]  K. Whipple.  BEDROCK RIVERS AND THE GEOMORPHOLOGY OF ACTIVE OROGENS , 2004 .

[38]  Gregory E. Tucker,et al.  A stochastic approach to modeling the role of rainfall variability in drainage basin evolution , 2000 .

[39]  David R. Montgomery,et al.  Topographic controls on erosion rates in tectonically active mountain ranges , 2002 .

[40]  T. Dunne,et al.  Geomorphic Controls on Andean Denudation Rates , 2006, The Journal of Geology.

[41]  W. Dietrich,et al.  The role of sediment in controlling steady-state bedrock channel slope : Implications of the saltation-abrasion incision model , 2006 .

[42]  J. Matti,et al.  Chapter 2: Paleogeographic evolution of the San Andreas fault in southern California: A reconstruction based on a new cross-fault correlation , 1993 .

[43]  E. Gabet.  Sediment transport by dry ravel , 2003 .

[44]  Gregory E. Tucker,et al.  Hillslope processes, drainage density, and landscape morphology , 1998 .

[45]  K. Whipple,et al.  Quantifying differential rock-uplift rates via stream profile analysis , 2001 .

[46]  P. Bierman,et al.  ESTIMATING RATES OF DENUDATION USING COSMOGENIC ISOTOPE ABUNDANCES IN SEDIMENT , 1996 .

[47]  George E. Hilley,et al.  Geomorphic response to uplift along the Dragon's Back pressure ridge, Carrizo Plain, California , 2008 .

[48]  J. G. King,et al.  Mountain erosion over 10 yr, 10 k.y., and 10 m.y. time scales , 2001 .

[49]  R. Stallard,et al.  Denudation rates determined from the accumulation of in situ-produced 10Be in the luquillo experimental forest, Puerto Rico , 1995 .

[50]  V. Vanacker,et al.  Constraining landscape development of the Sri Lankan escarpment with cosmogenic nuclides in river sediment , 2007 .

[51]  William E. Dietrich,et al.  Valley incision by debris flows: Evidence of a topographic signature , 2003 .

[52]  M. Caffee,et al.  Temporally and spatially uniform rates of erosion in the southern Appalachian Great Smoky Mountains , 2003 .

[53]  E. Foufoula‐Georgiou,et al.  Channel network source representation using digital elevation models , 1993 .

[54]  A. Howard.  A detachment-limited model of drainage basin evolution , 1994 .

[55]  P. Bierman,et al.  ROCK TO SEDIMENT—SLOPE TO SEA WITH 10BE—RATES OF LANDSCAPE CHANGE , 2004 .

[56]  A. Heimsath,et al.  Effects of bedrock landslides on cosmogenically determined erosion rates , 2005 .

[57]  G. Tucker,et al.  Importance of a stochastic distribution of floods and erosion thresholds in the bedrock river incision problem , 2003 .

[58]  Rolf Aalto,et al.  Erosion rates driven by channel network incision in the Bolivian Andes , 2005 .

[59]  N. Hovius,et al.  Large-scale erosion rates from in situ-produced cosmogenic nuclides in European river sediments , 2001 .

[60]  S. Schumm,et al.  Yield of sediment in relation to mean annual precipitation , 1958 .

[61]  T. Dunai.  Scaling factors for production rates of in situ produced cosmogenic nuclides: a critical reevaluation , 2000 .

[62]  Arthur Newell Strahler,et al.  Equilibrium theory of erosional slopes approached by frequency distribution analysis; Part II , 1950 .

[63]  E. Kirby,et al.  Tectonic and lithologic controls on bedrock channel profiles and processes in coastal California , 2004 .

[64]  R. Anderson,et al.  Estimates of the rate of regolith production using and from an alpine hillslope , 1999 .

[65]  D. Burbank,et al.  Denudation processes and rates in the Transverse Ranges, southern California: Erosional response of a transitional landscape to external and anthropogenic forcing , 2004 .

[66]  Nicholas Brozovic,et al.  Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas , 1996, Nature.

[67]  G. Stock,et al.  Spatial and temporal variations in denudation of the Wasatch Mountains, Utah, USA , 2009 .

[68]  K. Norton,et al.  Relation between rock uplift and denudation from cosmogenic nuclides in river sediment in the Central Alps of Switzerland , 2007 .

[69]  D. Lague,et al.  Constraints on the long‐term colluvial erosion law by analyzing slope‐area relationships at various tectonic uplift rates in the Siwaliks Hills (Nepal) , 2003 .

[70]  W. Dietrich,et al.  A mechanistic model for river incision into bedrock by saltating bed load , 2004 .

[71]  Kelin X. Whipple,et al.  River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion and cavitation , 2000 .

[72]  D. Montgomery,et al.  Controls on the channel width of rivers: Implications for modeling fluvial incision of bedrock , 2005 .

[73]  G. Tucker,et al.  Numerical and analytical models of cosmogenic radionuclide dynamics in landslide-dominated drainage basins , 2009 .

[74]  K. Sieh,et al.  Uplift and erosion of the San Bernardino Mountains associated with transpression along the San Andreas fault, California, as constrained by radiogenic helium thermochronometry , 1998 .

[75]  J. Kirchner,et al.  Functional relationships between denudation and hillslope form and relief , 2007 .