Modelling sediment clasts transport during landscape evolution

Abstract. Over thousands to millions of years, the landscape evolution is predicted by models based on fluxes of eroded, transported and deposited material. The laws describing these fluxes, corresponding to averages over many years, are difficult to prove with the available data. On the other hand, sediment dynamics are often tackled by studying the distribution of certain grain properties in the field (e.g. heavy metals, detrital zircons, 10Be in gravel, magnetic tracers). There is a gap between landscape evolution models based on fluxes and these field data on individual clasts, which prevent the latter from being used to calibrate the former. Here we propose an algorithm coupling the landscape evolution with mobile clasts. Our landscape evolution model predicts local erosion, deposition and transfer fluxes resulting from hillslope and river processes. Clasts of any size are initially spread in the basement and are detached, moved and deposited according to probabilities using these fluxes. Several river and hillslope laws are studied. Although the resulting mean transport rate of the clasts does not depend on the time step or the model cell size, our approach is limited by the fact that their scattering rate is cell-size-dependent. Nevertheless, both their mean transport rate and the shape of the scattering-time curves fit the predictions. Different erosion–transport laws generate different clast movements. These differences show that studying the tracers in the field may provide a way to establish these laws on the hillslopes and in the rivers. Possible applications include the interpretation of cosmogenic nuclides in individual gravel deposits, provenance analyses, placers, sediment coarsening or fining, the relationship between magnetic tracers in rivers and the river planform, and the tracing of weathered sediment.

[1]  E. Foufoula‐Georgiou,et al.  A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems , 2013 .

[2]  David Jon Furbish,et al.  From divots to swales: Hillslope sediment transport across divers length scales , 2010 .

[3]  H. Kooi,et al.  Escarpment evolution on high‐elevation rifted margins: Insights derived from a surface processes model that combines diffusion, advection, and reaction , 1994 .

[4]  Marwan A. Hassan,et al.  Simulation of individual particle movement in a gravel streambed , 2002 .

[5]  B. Minasny,et al.  Resolving the integral connection between pedogenesis and landscape evolution , 2015 .

[6]  G. Tucker,et al.  Modelling landscape evolution , 2010 .

[7]  B. Niviére,et al.  Do river profiles record along‐stream variations of low uplift rate? , 2006 .

[8]  Frank J. Pazzaglia,et al.  Quantitative testing of bedrock incision models for the Clearwater River, NW Washington State , 2003 .

[9]  C. Paola,et al.  Grain Size Patchiness as a Cause of Selective Deposition and Downstream Fining , 1995 .

[10]  F. Charru Selection of the ripple length on a granular bed sheared by a liquid flow , 2006 .

[11]  G. Domokos,et al.  Quantifying the significance of abrasion and selective transport for downstream fluvial grain size evolution , 2014 .

[12]  J. Perron,et al.  Numerical methods for nonlinear hillslope transport laws , 2011 .

[13]  E. Lajeunesse,et al.  Tracer dispersion in bedload transport , 2013 .

[14]  Dimitri Lague,et al.  Fluvial erosion/transport equation of landscape evolution models revisited , 2009 .

[15]  B. Meade,et al.  Spatial Variability of Erosion Rates Inferred from the Frequency Distribution of Cosmogenic 3He in Olivines from Hawaiian River Sediments , 2008 .

[16]  S. Carretier,et al.  Is it possible to quantify pebble abrasion and velocity in rivers using terrestrial cosmogenic nuclides , 2011 .

[17]  D. Lague Reduction of long‐term bedrock incision efficiency by short‐term alluvial cover intermittency , 2010 .

[18]  J. Lavé,et al.  Changes of bedload characteristics along the Marsyandi River (central Nepal): Implications for understanding hillslope sediment supply, sediment load evolution along fluvial networks, and denudation in active orogenic belts , 2006 .

[19]  E. Gabet,et al.  Particle transport over rough hillslope surfaces by dry ravel: Experiments and simulations with implications for nonlocal sediment flux , 2012 .

[20]  T. Quine,et al.  Crossing the divide: Representation of channels and processes in reduced-complexity river models at reach and landscape scales , 2007 .

[21]  J. Roering,et al.  Sediment disentrainment and the concept of local versus nonlocal transport on hillslopes , 2013 .

[22]  I. Rodríguez‐Iturbe,et al.  Results from a new model of river basin evolution , 1991 .

[23]  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 .

[24]  Sunil Kumar Singh,et al.  Predominant floodplain over mountain weathering of Himalayan sediments (Ganga basin) , 2012 .

[25]  P. Parseval,et al.  Gold grain morphology and composition as an exploration tool: application to gold exploration in covered areas , 2003, Geochemistry: Exploration, Environment, Analysis.

[26]  S. P. Anderson,et al.  Landscape scale linkages in critical zone evolution , 2012 .

[27]  R. Anderson,et al.  Cosmogenic dating of fluvial terraces, Fremont River, Utah , 1997 .

[28]  T. Hoffmann Sediment residence time and connectivity in non-equilibrium and transient geomorphic systems , 2015 .

[29]  David R. Montgomery,et al.  Geologic constraints on bedrock river incision using the stream power law , 1999 .

[30]  S. Carretier,et al.  Theoretical cosmogenic nuclide concentration in river bed load clasts: Does it depend on clast size? , 2009 .

[31]  T. Reimer,et al.  Microbial Processes in Gold Migration and Deposition: Modern Analogues to Ancient Deposits , 1999 .

[32]  E. Lajeunesse,et al.  Bedload Transport in Laboratory Rivers: the Erosion-Deposition Model , 2015 .

[33]  C. Paola,et al.  Properties of a cellular braided‐stream model , 1997 .

[34]  A. Murray,et al.  Reducing model complexity for explanation and prediction , 2007 .

[35]  W. Dietrich,et al.  Implications of the saltation–abrasion bedrock incision model for steady‐state river longitudinal profile relief and concavity , 2008 .

[36]  M. Raymo,et al.  Tectonic forcing of late Cenozoic climate , 1992, Nature.

[37]  G. Hancock,et al.  The mARM spatially distributed soil evolution model: A computationally efficient modeling framework and analysis of hillslope soil surface organization , 2009 .

[38]  P. Davy,et al.  Mesoscale fluvial erosion parameters deduced from modeling the Mediterranean sea level drop during the Messinian (late Miocene) , 2006 .

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

[40]  D. N. Bradley,et al.  Fractional dispersion in a sand bed river , 2010 .

[41]  P. Wilcock,et al.  Downstream Fining by Selective Deposition in a Laboratory Flume , 1992, Science.

[42]  G. Tucker,et al.  Implications of sediment‐flux‐dependent river incision models for landscape evolution , 2002 .

[43]  F. Stuart,et al.  Single-grain cosmogenic 21Ne concentrations in fluvial sediments reveal spatially variable erosion rates , 2008 .

[44]  Philippe Fullsack,et al.  Erosional control of active compressional orogens , 1992 .

[45]  E. Lajeunesse,et al.  Cross-stream diffusion in bedload transport , 2014 .

[46]  Alan D. Howard,et al.  Channel changes in badlands , 1983 .

[47]  J. Ritz,et al.  Control of geomorphic processes on 10Be concentrations in individual clasts: Complexity of the exposure history in Gobi-Altay range (Mongolia) , 2011 .

[48]  B. Minasny,et al.  A quantitative model for integrating landscape evolution and soil formation , 2013 .

[49]  F. Bretherton,et al.  Stability and the conservation of mass in drainage basin evolution , 1972 .

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

[51]  T. Hanks The Age of Scarplike Landforms From Diffusion‐Equation Analysis , 2013 .

[52]  Paul Bishop,et al.  Cenozoic river profile development in the Upper Lachlan catchment (SE Australia) as a test of quantitative fluvial incision models , 2003 .

[53]  D. N. Bradley,et al.  Trouble with diffusion: Reassessing hillslope erosion laws with a particle-based model , 2010 .

[54]  A. Einstein Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.

[55]  S. Carretier,et al.  Mean bedrock-to-saprolite conversion and erosion rates during mountain growth and decline , 2014 .

[56]  E. Lajeunesse,et al.  Bed load transport in turbulent flow at the grain scale: Experiments and modeling , 2010 .

[57]  B. Andreotti,et al.  Measurements of the aeolian sand transport saturation length , 2008, 0806.3931.

[58]  J. Laird,et al.  Supergene gold transformation: Biogenic secondary and nano-particulate gold from arid Australia , 2012 .

[59]  Alan D. Howard,et al.  BADLAND MORPHOLOGY AND EVOLUTION: INTERPRETATION USING A SIMULATION MODEL , 1997 .

[60]  J. Richards,et al.  Gold , Platinum and Diamond Placer Deposits in Alluvial Gravels , Whitecourt , Alberta , 2007 .

[61]  Lubos Mitas,et al.  Path sampling method for modeling overland water flow, sediment transport, and short term terrain evolution in Open Source GIS , 2004 .

[62]  T. Hanks,et al.  Scarp degraded by linear diffusion: Inverse solution for age , 1985 .

[63]  W. Culling,et al.  Analytical Theory of Erosion , 1960, The Journal of Geology.

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

[65]  F. Chabaux,et al.  238U–234U–230Th disequilibria and timescale of sedimentary transfers in rivers: Clues from the Gangetic plain rivers , 2006 .

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

[67]  M. Reich,et al.  Geological and economic significance of supergene metal deposits , 2015 .

[68]  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 .

[69]  J. Wheaton,et al.  The relationship between particle travel distance and channel morphology: Results from physical models of braided rivers , 2015 .

[70]  J. Viers,et al.  Sediment provenances and drainage evolution of the Neogene Amazonian foreland basin , 2005 .

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

[72]  H. Kooi,et al.  Large‐scale geomorphology: Classical concepts reconciled and integrated with contemporary ideas via a surface processes model , 1996 .

[73]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[74]  S. Mudd,et al.  Reservoir theory for studying the geochemical evolution of soils , 2010 .

[75]  E. Foufoula‐Georgiou,et al.  A nonlocal theory of sediment transport on hillslopes , 2010 .

[76]  S. P. Anderson,et al.  Rock damage and regolith transport by frost: an example of climate modulation of the geomorphology of the critical zone , 2013 .

[77]  M. Kirkby,et al.  A cellular model of Holocene upland river basin and alluvial fan evolution , 2002 .

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

[79]  G. Tucker,et al.  Measuring gravel transport and dispersion in a mountain river using passive radio tracers , 2012 .

[80]  M. Church,et al.  Size and distance of travel of unconstrained clasts on a streambed , 1992 .

[81]  F. Petit,et al.  Long-term bedload mobility in gravel-bed rivers using iron slag as a tracer , 2011 .

[82]  M. Church,et al.  Distance of movement of coarse particles in gravel bed streams , 1991 .

[83]  Vikrant Jain,et al.  Conceptual assessment of (dis)connectivity and its application to the Ganga River dispersal system , 2010 .

[84]  R. Sillitoe Porphyry Copper Systems , 2010 .

[85]  S. Carretier,et al.  Erosion dynamics modelling in a coupled catchment–fan system with constant external forcing , 2010 .

[86]  W. Dietrich,et al.  Sediment and rock strength controls on river incision into bedrock , 2001 .

[87]  F. Herman,et al.  Provenance analysis using Raman spectroscopy of carbonaceous material: A case study in the Southern Alps of New Zealand , 2015 .

[88]  Hillslope evolution by nonlinear creep and landsliding: An experimental study: Comment and Reply , 2002 .

[89]  C. Paola,et al.  The large scale dynamics of grain-size variation in alluvial basins , 1992 .

[90]  C. Paola,et al.  Similarity solutions for fluvial sediment fining by selective deposition , 2007 .

[91]  P. Bierman,et al.  Millennial-scale record of landslides in the Andes consistent with earthquake trigger , 2014 .