@article{Abramowitz1988,
author = {Abramowitz, Milton and Stegun, Irene A and Romer, Robert H},
doi = {10.1119/1.15378},
number = {958},
title = {{Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables}},
url = {http://dx.doi.org/10.1119/1.15378},
volume = {56},
year = {1988}
}
@article{Ahnert1977,
author = {Ahnert, Frank},
doi = {10.1002/esp.3290020211},
issn = {03601269},
journal = {Earth Surface Processes},
keywords = {Denudation processes,Geomorphological process equations,Slope models,Weathering},
month = {apr},
number = {2-3},
pages = {191--201},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Some comments on the quantitative formulation of geomorphological processes in a theoretical model}},
url = {http://doi.wiley.com/10.1002/esp.3290020211},
volume = {2},
year = {1977}
}
@article{Ahnert1987,
abstract = {Ahnert, F., , Earth Surf. Processes Landforms, 12, 3-15, 1987a},
author = {Ahnert, Frank},
doi = {10.1002/esp.3290120103},
issn = {10969837},
journal = {Earth Surface Processes and Landforms},
keywords = {Dynamic equilibrium,Inselberg development,Relaxation time,Rock resistance,Slope development,Theoretical models,West,varying Germany},
month = {jan},
number = {1},
pages = {3--15},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Approaches to dynamic equilibrium in theoretical simulations of slope development}},
url = {http://doi.wiley.com/10.1002/esp.3290120103},
volume = {12},
year = {1987}
}
@article{Ahnert1976,
abstract = {Ahnert, F. "Brief description of a comprehensive three-dimensional process-response model of landform development." 25 (1976): 29-49.},
author = {Ahnert, Frank},
isbn = {3-443-21025-2},
journal = {Zeitschrift f{\"{u}}r Geomorphologie Supplemental},
pages = {29--49},
title = {{Brief description of a comprehensive three-dimensional process-response model of landform development}},
volume = {25},
year = {1976}
}
@article{Baartman2012,
author = {Baartman, Jantiene E. M. and Gorp, Wouter and Temme, Arnaud J. A. M. and Schoorl, Jeroen M.},
doi = {10.1002/esp.3208},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
month = {jul},
number = {9},
pages = {923--935},
title = {{Modelling sediment dynamics due to hillslope-river interactions: incorporating fluvial behaviour in landscape evolution model LAPSUS}},
url = {http://doi.wiley.com/10.1002/esp.3208},
volume = {37},
year = {2012}
}
@article{Baumgarten2018,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1807.07647},
  title = {A {{General Fluid}}-{{Sediment Mixture Model}} and {{Constitutive Theory}}},
  abstract = {We present a thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes, developed from the basic balance laws for two phase-mixtures. The model can represent various limiting cases, such as pure fluid and dry grains. It is formulated to capture a number of key behaviors such as: (i) viscous inertial rheology of submerged wet grains under steady shearing flows, (ii) the critical state behavior of grains, which causes granular Reynolds dilation/contraction due to shear, (iii) the viscous thickening of the fluid response due to the presence of suspended grains, and (iv) the Darcy-like drag interaction observed in both dense and dilute mixtures, which gives rise to complex fluid-grain interactions under dilation and flow. The full constitutive model is combined with the basic equations of motion for each mixture phase and implemented in the material point method (MPM) to accurately model the coupled dynamics of the mixed system. Qualitative results show the breadth of problems which this model can address. Quantitative results demonstrate the accuracy of this model as compared with analytical limits and experimental observations of fluid and grain behaviors in inhomogeneous geometries.},
  author = {Baumgarten, Aaron S. and Kamrin, Ken},
  month = jul,
  year = {2018},
  keywords = {Condensed Matter - Soft Condensed Matter},
  eprintclass = {cond-mat}
}

@article{Ancey2015,
  title = {Stochastic {{Interpretation}} of the {{Advection}}-{{Diffusion Equation}} and {{Its Relevance}} to {{Bed Load Transport}}},
  volume = {120},
  issn = {2169-9011},
  doi = {10.1002/2014JF003421},
  abstract = {The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.},
  language = {English},
  number = {12},
  journal = {Journal of Geophysical Research: Earth Surface},
  author = {Ancey, C. and Bohorquez, P. and Heyman, J.},
  month = dec,
  year = {2015},
  keywords = {sediment transport,advection diffusion equation,birth-death Markov processes,nonlocal effect,stochastic model},
  pages = {2529-2551}
}

@article{Banavar2001a,
abstract = {A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d = 1. Results of numerical simulations in d = 2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.},
author = {Banavar, Jayanth R. and Colaiori, Francesca and Flammini, Alessandro and Maritan, Amos and Rinaldo, Andrea},
doi = {10.1023/A:1010397325029},
issn = {00224715},
journal = {Journal of Statistical Physics},
keywords = {Landscape evolution,optimal transportation networks,rivers,scaling,landscape evolution,optimal transportation,rivers,scaling},
number = {1-2},
pages = {1--48},
title = {{Scaling, optimality, and landscape evolution}},
volume = {104},
year = {2001}
}
@article{Benaichouche2016,
abstract = {In landscapes dominated by fluvial erosion, the landscape morphology is closely related to the hydrographic network system. In this paper, we investigate the hydrographic network reorganization caused by a headward piracy mechanism between two drainage basins in France, the Meuse and the Moselle. Several piracies occurred in the Meuse basin during the past one million years, and the basin's current characteristics are favorable to new piracies by the Moselle river network. This study evaluates the consequences over the next several million years of a relative lowering of the Moselle River (and thus of its basin) with respect to the Meuse River. The problem is addressed with a numerical modeling approach (landscape evolution model, hereafter LEM) that requires empirical determinations of parameters and threshold values. Classically, fitting of the parameters is based on analysis of the relationship between the slope and the drainage area and is conducted under the hypothesis of equilibrium. Application of this conventional approach to the capture issue yields incomplete results that have been consolidated by a parametric sensitivity analysis. The LEM equations give a six-dimensional parameter space that was explored with over 15,000 simulations using the landscape evolution model GOLEM. The results demonstrate that stream piracies occur in only four locations in the studied reach near the city of Toul. The locations are mainly controlled by the local topography and are model-independent. Nevertheless, the chronology of the captures depends on two parameters: the river concavity (given by the fluvial advection equation) and the hillslope erosion factor. Thus, the simulations lead to three different scenarios that are explained by a phenomenon of exclusion or a string of events.},
author = {Bena{\"{i}}chouche, Abed and Stab, Olivier and Tessier, Bruno and Cojan, Isabelle},
doi = {10.1016/j.geomorph.2015.10.001},
issn = {0169555X},
journal = {Geomorphology},
keywords = {GOLEM,LEM,Landscape evolution model,Long-term erosion,Meuse and Moselle watersheds,Sensitivity analysis,Stream piracy},
month = {jan},
pages = {168--180},
title = {{Evaluation of a landscape evolution model to simulate stream piracies: Insights from multivariable numerical tests using the example of the Meuse basin, France}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0169555X15301665},
volume = {253},
year = {2016}
}
@article{Bennett2015,
author = {Bennett, Sean J. and Gordon, Lee M. and Neroni, Vera and Wells, Robert R.},
doi = {10.1007/s11069-015-1599-8},
issn = {0921-030X},
journal = {Natural Hazards},
keywords = {bennett,buffalo,department of geography,development {\'{a}} landscape degradation,gordon {\'{a}} v,j,m,neroni,ny 14261-0055,rill erosion {\'{a}} network,s,university at buffalo,usa,{\'{a}} l},
month = {nov},
number = {S1},
pages = {7--24},
title = {{Emergence, persistence, and organization of rill networks on a soil-mantled experimental landscape}},
url = {http://link.springer.com/10.1007/s11069-015-1599-8},
volume = {79},
year = {2015}
}
@article{Bennett2016,
author = {Bennett, Sean J. and Liu, Renjie},
doi = {10.1130/G37214.1},
issn = {0091-7613},
journal = {Geology},
month = {jan},
number = {1},
pages = {35--38},
publisher = {Geological Society of America},
title = {{Basin self-similarity, Hack's law, and the evolution of experimental rill networks}},
url = {http://geology.gsapubs.org/lookup/doi/10.1130/G37214.1},
volume = {44},
year = {2016}
}
@article{Berger2010,
author = {Berger, Catherine and Schulze, Marcel and Rieke-Zapp, Dirk and Schlunegger, Fritz},
doi = {10.1002/esp.1989},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {close range photogrammetry,digital elevation model,rainfall simulation,rill network,soil erosion},
month = {sep},
number = {12},
pages = {1456--1467},
title = {{Rill development and soil erosion: A laboratory study of slope and rainfall intensity}},
url = {http://doi.wiley.com/10.1002/esp.1989},
volume = {35},
year = {2010}
}

@article{Benson2013,
  series = {35th Year Anniversary Issue},
  title = {Fractional {{Calculus}} in {{Hydrologic Modeling}}: {{A Numerical Perspective}}},
  volume = {51},
  issn = {0309-1708},
  shorttitle = {Fractional {{Calculus}} in {{Hydrologic Modeling}}},
  doi = {10.1016/j.advwatres.2012.04.005},
  abstract = {Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable L\'evy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and L\'evy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.},
  journal = {Advances in Water Resources},
  author = {Benson, David A. and Meerschaert, Mark M. and Revielle, Jordan},
  month = jan,
  year = {2013},
  keywords = {Fractional Brownian motion,Fractional calculus,Mobile/immobile,Subordination},
  pages = {479-497},
  shortjournal = {Advances in Water Resources}
}

@article{Bigi2006,
abstract = {Hillslope stability depends strongly on local conditions, such as lithology and rock strength, degree of saturation, and critical slope angle. Common triggers for slope failure include severe storms, earthquakes, and removal of material from the toe of the hillslope. In this paper, we focus on the latter, in a model in which streams incise the toe and destabilize the hillslope. We investigate possible interactions between migrating knickpoints and hillslope failures in a small-scale, steadily eroding experimental landscape that experiences steady rainfall and base-level fall conditions. We monitored knickpoint propagation and hillslope failure activity with time lapse photography over a time period in which numerous knickpoints migrated through the drainage basin. We then investigated temporal and spatial relationships between hillslope failures and knickpoints and compared these results to Monte Carlo simulations of hillslope failure distributions. When focusing along a single channel, we found that, statistically (significant at the 98{\%} confidence level), a greater number of failures occur downstream from a migrating knickpoint. These results highlight both the organized and random nature of hillslope and knickpoint interactions.},
author = {Bigi, Alessandro and Hasbargen, Leslie E and Montanari, Alberto and Paola, Chris},
doi = {10.1130/2006.2398(18)},
issn = {0072-1077},
journal = {Geological Society of America Special Papers},
number = {March},
pages = {295--307},
title = {{Knickpoints and hillslope failures: Interactions in a steady-state experimental landscape}},
url = {http://specialpapers.gsapubs.org/content/398/295.abstract},
volume = {398},
year = {2006}
}
@article{Blackman1958,
author = {Blackman, R. B. and Tukey, J. W.},
doi = {10.1002/j.1538-7305.1958.tb03874.x},
issn = {00058580},
journal = {Bell System Technical Journal},
month = {jan},
number = {1},
pages = {185--282},
publisher = {Blackwell Publishing Ltd},
title = {{The measurement of power spectra from the point of view of communications engineering - Part I}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6768513},
volume = {37},
year = {1958}
}
@article{Bonetti2020,
author = {Sara Bonetti  and Milad Hooshyar  and Carlo Camporeale  and Amilcare Porporato },
title = {Channelization cascade in landscape evolution},
journal = {Proceedings of the National Academy of Sciences},
volume = {117},
number = {3},
pages = {1375-1382},
year = {2020},
doi = {10.1073/pnas.1911817117},
URL = {https://www.pnas.org/doi/abs/10.1073/pnas.1911817117},
eprint = {https://www.pnas.org/doi/pdf/10.1073/pnas.1911817117}
}
@article{Bonnet2009,
abstract = {Climate, and in particular the spatial pattern of precipitation, is thought to affect the topographic and tectonic evolution of mountain belts through erosion1–5. Numerical model simulations of landscape erosion controlled by horizontal tectonic motion6 or orographic precipitation7,8 result in the asymmetric topography that characterizes most natural mountain belts6, and in a continuous migration of the main drainage divide. The effects of such a migration have, however, been challenging to observe in natural settings6. Here I document the effects of a lateral precipitation gradient on a landscape undergoing constant uplift in a laboratory modelling experiment. In the experiment, the drainage divide migrates towards the drier, leeward side of the mountain range, causing the drainage basins on the leeward side to shrink and split into smaller basins. This mechanism results in a progressively increasing number of drainage basins on the leeward side of the mountain range as the divide migrates, such that the expected relationship between the spacing of drainage basins and the location of the main drainage divide9 is maintained. I propose that this mechanism could clarify the drainage divide migration and topographic asymmetry found in active orogenic mountain ranges, as exemplified by the Aconquija Range of Argentina10},
author = {Bonnet, Stephane},
doi = {10.1038/ngeo700},
isbn = {1752-0894},
issn = {1752-0894},
journal = {Nature Geoscience},
month = {nov},
number = {12},
pages = {897--897},
publisher = {Nature Publishing Group},
title = {{Shrinking and splitting of drainage basins in orogenic landscapes from the migration of the main drainage divide}},
url = {http://www.nature.com/doifinder/10.1038/ngeo666 http://dx.doi.org/10.1038/ngeo666},
volume = {2},
year = {2009}
}
@article{Bonnet2006,
abstract = {We review results from laboratory-scale modelling of erosion and relief dynamics under variable uplift and rainfall rates. Under constant values of these forcing parameters an experimental landscape typically evolves towards a steady-state between uplift and erosion, and we show how the geometry of the steady-state landscape adjusts to the rates of uplift and rainfall. The comparison between these laboratory-scale landscapes and the natural ones is not straightforward because contrary to analogue modelling in tectonics, natural conditions of relief evolution cannot be downscaled to the laboratory without any scale distortions. Laboratory-scale modelling in geomorphology is therefore only experimental, not analogue. Despite these limitations, experimental models may be used to provide physical tests for numerical models and they give insights into first-order behaviours and directions for future research. The},
author = {Bonnet, Stephane and Crave, Alain},
doi = {10.1144/GSL.SP.2006.253.01.17},
isbn = {1-86239-191-2},
issn = {0305-8719},
journal = {Geological Society, London, Special Publications},
number = {1},
pages = {327--339},
title = {{Macroscale dynamics of experimental landscapes}},
volume = {253},
year = {2006}
}
@article{Bonnet2003,
abstract = {We present the results of an experimental investigation of the concurrent action of tectonic uplift and climate variation on relief evolution. We designed an experimental apparatus that allows the study of erosion of laboratory-scale topographies that evolve under given uplift and rainfall rates. For constant uplift and rainfall rates, the experimental topography evolves toward a statistical steady state defined by a mean elevation constant with time. Starting from such a steady state and keeping the input uplift rate constant, a subsequent change in the rainfall rate yields a change in the mean elevation of the landscape to a new equilibrium elevation. An increase in precipitation yields a lower mean steady-state elevation, whereas for a decrease in precipitation the surface is uplifted. We define this phenomenon as a climatically induced surface uplift, as opposed to a tectonically induced surface uplift. The climatically and tectonically induced surface uplifts correspond to different dynamics of denudation so that it is theoretically possible to differentiate between the climatic or tectonic causes of surface uplift from records of output sediment fluxes.},
author = {Bonnet, St{\'{e}}phane and Crave, Alain},
doi = {10.1130/0091-7613(2003)031<0123:LRTCCI>2.0.CO},
isbn = {0091-7613},
issn = {00917613},
journal = {Geology},
keywords = {Climate change,Erosion,Geomorphology,Landscape evolution,Steady state,Uplift},
number = {2},
pages = {123--126},
publisher = {Geological Society of America},
title = {{Landscape response to climate change: Insights from experimental modeling and implications for tectonic versus climatic uplift of topography}},
url = {http://geology.gsapubs.org/cgi/doi/10.1130/0091-7613(2003)031{\%}3C0123:LRTCCI{\%}3E2.0.CO;2},
volume = {31},
year = {2003}
}

@article{Bonetti2017,
  title = {On the {{Dynamic Smoothing}} of {{Mountains}}},
  volume = {44},
  issn = {1944-8007},
  doi = {10.1002/2017GL073095},
  abstract = {After their formation, mountainous landscapes gradually evolve toward smoother geometries controlled by the interplay of erosion and sedimentation. The statistical mechanical properties of this process and the link between topography and geology have remained largely unexplored. We analyze the slope statistics of different mountains worldwide, showing that landscape age is fingerprinted in their distribution tails. Data reveal a universal relaxation process, through an algebraic decay progressively replaced by an exponential one, with exponents described by a global monotonic function. We then investigate the dominant components of this dynamic smoothing using a landscape evolution model, showing that the time evolution of slope statistics results from a delicate balance between diffusive soil creep, noise, and advective river incision, with the relaxation phase mainly dominated by diffusion. Results may suggest ways to formulate reduced order topographic evolution models for geomorphological and climatological applications, and to explore similarities in surface evolution in different contexts.},
  language = {English},
  number = {11},
  journal = {Geophysical Research Letters},
  author = {Bonetti, S. and Porporato, A.},
  month = jun,
  year = {2017},
  keywords = {landscape evolution,topography,mountain age,relaxation process,statistical mechanics,topographic slope},
  pages = {5531-5539}
}

@article{Bras2015,
author = {Bras, Rafael L.},
doi = {10.1002/2015WR016958},
issn = {00431397},
journal = {Water Resources Research},
keywords = {complexity,fluvial geomorphology,hydrology,land energy fluxes,land‐atmosphere interactions,maximum entropy},
month = {aug},
number = {8},
pages = {6532--6548},
title = {{Complexity and organization in hydrology: A personal view}},
url = {http://doi.wiley.com/10.1002/2015WR016958},
volume = {51},
year = {2015}
}
@article{Brasington2003,
abstract = {Despite the difficulties of establishing formal hydraulic and geometric similarity, small-scale models of drainage basins have often been used to investigate the evolution and dynamics of larger-scale landforms. Historically, this analysis has been restricted to planform basin characteristics and only in the last decade has the topographic similarity of experimental landscapes been explored through explicitly three-dimensional parameters such as the distributions of cumulative drainage area, area–slope and catchment elevation. The current emphasis on three-dimensional morphometry reflects a growing awareness of the descriptive paucity of planform data and the need for more robust analysis of spatial scaling relationships. This paradigm shift has been significantly facilitated by technological developments in topographic survey and digital elevationmodelling (DEM) which now present the opportunity to acquire and analyse high-resolution, distributed elevation data. Few studies have, however, attempted to use topographic modelling to provide information on the changing pattern and rate of sediment transport though an evolving landscape directly by using multitemporal DEM differencing techniques. This paper reports a laboratory study in which digital photogrammetry was employed to derive high-resolution DEMs of a simulated landscape in declining equilibrium at 15 minute frequency through a 240 minute simulation. Detailed evaluation of the DEMs revealed a vertical precision of 1Ð2 mm and threshold level of change detection between surfaces of {\v{s}}3 mm at the 95 per cent confidence level. This quality assurance set the limits for determining the volumetric change between surfaces, which was used to recover the sediment budget through the experiment and to examine local- and basin-scale rates of sediment transport. A comparison of directly observed and morphometric estimates of sediment yield at the basin outlet was used to quantify the closure of the sediment budget over the simulation, and revealed an encouragingly small 6Ð2 per cent error. The application of this dynamic morphological approach has the potential to offer new insights into the controls on landform development, as demonstrated here by an analysis of the changing pattern of the basin sediment delivery ratio during network growth.},
author = {Brasington, J. and Smart, R. M A},
doi = {10.1002/esp.480},
isbn = {1096-9837},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {DEMs,Digital photogrammetry,Drainage basin evolution,Sediment budgets},
number = {3},
pages = {231--247},
title = {{Close range digital photogrammetric analysis of experimental drainage basin evolution}},
volume = {28},
year = {2003}
}
@article{Braun1997,
author = {Braun, Jean and Sambridge, Malcolm},
doi = {10.1046/j.1365-2117.1997.00030.x},
issn = {0950-091X},
journal = {Basin Research},
month = {jan},
number = {1},
pages = {27--52},
title = {{Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization}},
url = {http://doi.wiley.com/10.1046/j.1365-2117.1997.00030.x},
volume = {9},
year = {1997}
}

@article{Brunton2000,
author = {Brunton, D. A. and Bryan, R. B.},
doi = {10.1002/1096-9837(200007)25:7<783::AID-ESP106>3.3.CO;2-N},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {hydraulics,network,rill,sediment budgets},
month = {jul},
number = {7},
pages = {783--800},
title = {{Rill network development and sediment budgets}},
url = {http://doi.wiley.com/10.1002/1096-9837{\%}28200007{\%}2925{\%}3A7{\%}3C783{\%}3A{\%}3AAID-ESP106{\%}3E3.3.CO{\%}3B2-N},
volume = {25},
year = {2000}
}
@article{Bryan1989,
abstract = {Experiments to test relationships between slope length, percolation, and runoff were carried out in a laboratory flume under simulated rainfall at intensities from 24.2-26 mm h -'. A composite soil subject to sealing was mixed from a clay and a sand and tested on 2.39 m, 7.18 m, and 17 m slopes for a minimum of 200 min. Runoff discharge is not a simple function of rainfall excess and slope length but shows a complex pattern dominated by surface sealing, rill development and headcut incision. Rill development by concentrated surface wash conformed to established threshold hydraulic conditions, but subsequent headcut incision was necessary to breach the seal and significantly affect percolation/runoff ratios. Headcut evolution is complex, apparently reflecting hydraulic instability and possibly different stages in seal development. Headcut and rill incision shows a cyclic pattern interspersed with broad areas of sheetwash and colluvial deposition where percolation rates are very low.},
author = {Bryan, R. B. and Poesen, J.},
doi = {10.1002/esp.3290140304},
isbn = {1096-9837},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {Cyclic rilling,Headcut migration,Percolation,Rill incision,Runoff,Slope length,Surface sealing},
month = {may},
number = {3},
pages = {211--231},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Laboratory experiments on the influence of slope length on runoff, percolation and rill development}},
url = {http://doi.wiley.com/10.1002/esp.3290140304},
volume = {14},
year = {1989}
}
@book{burger2016digital,
author = {Burger, Wilhelm and Burge, Mark J},
publisher = {Springer},
title = {{Digital image processing: an algorithmic introduction using Java}},
year = {2016}
}
@article{Caldarelli1997,
  title = {Randomly {{Pinned Landscape Evolution}}},
  volume = {55},
  doi = {10.1103/PhysRevE.55.R4865},
  abstract = {A simple scheme for the evolution of a fluvial landscape in heterogeneous environments is critically examined to capture the essential mechanism responsible for the recurrent scale-free landforms in the river basin. It is shown that, regardless of boundary and initial conditions, geomorphological constraints in the form of quenched randomly pinned regions play a key role in the robust emergence of aggregation patterns with a scaling behavior in agreement with that of real river basins.},
  number = {5},
  journal = {Physical Review E},
  author = {Caldarelli, Guido and Giacometti, Achille and Maritan, Amos and {Rodriguez-Iturbe}, Ignacio and Rinaldo, Andrea},
  month = may,
  year = {1997},
  pages = {R4865-R4868},
  shortjournal = {Phys. Rev. E}
}

@article{Calvert2018,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1801.02810},
  title = {Unifying {{Particle}}-{{Based}} and {{Continuum Models}} of {{Hillslope Evolution}} with a {{Probabilistic Scaling Technique}}},
  abstract = {Relationships between sediment flux and geomorphic processes are combined with statements of mass conservation, in order to create continuum models of hillslope evolution. These models have parameters which can be calibrated using available topographical data. This contrasts the use of particle-based models, which may be more difficult to calibrate, but are simpler, easier to implement, and have the potential to provide insight into the statistics of grain motion. The realms of individual particles and the continuum, while disparate in geomorphological modeling, can be connected using scaling techniques commonly employed in probability theory. Here, we motivate the choice of a particle-based model of hillslope evolution, whose stationary distributions we characterize. We then provide a heuristic scaling argument, which identifies a candidate for their continuum limit. By simulating instances of the particle model, we obtain equilibrium hillslope profiles and probe their response to perturbations. These results provide a proof-of-concept in the unification of microscopic and macroscopic descriptions of hillslope evolution through probabilistic techniques, and simplify the study of hillslope response to external influences.},
  author = {Calvert, Jacob and Bal\'azs, M\'arton and Michaelides, Katerina},
  month = jan,
  year = {2018},
  keywords = {Condensed Matter - Statistical Mechanics,Mathematics - Probability,Physics - Geophysics},
  file = {/home/mohsen/Zotero/storage/279D5UIG/Calvert et al. - 2018 - Unifying particle-based and continuum models of hi.pdf;/home/mohsen/Zotero/storage/9Q6CL4FW/Calvert et al. - 2018 - Unifying particle-based and continuum models of hi.pdf;/home/mohsen/Zotero/storage/BTP8ZRCX/1801.html;/home/mohsen/Zotero/storage/SGVKYY5T/1801.html},
  eprintclass = {cond-mat, physics:physics}
}

@article{Carson1972,
abstract = {Hillslopes occupy most the landscape. Studies of process mechanisms and rates have become sufficiently numerous to allow a systematic study of slopes. Only by making a synthesis of quantitative process studies and relating them to the development of slope forms can the shape of the landscape be understood and the separate effects of lithology and climate assessed. In the introductory part of this book, the choice of appropriate system and scale is discussed, and models for uplift and erosion evaluated. Attention is thus focused on the dynamic equilibrium of the slope profile and its erosional development over time. Part I then examines the forces encouraging hillslope movement and the resistances opposing movement. Part 2 considers processes of rock instability, soil instability, wash, solution and soil creep. Each is discussed in terms of its mechanism and rate of operation, and the slope provides it produces. Part 3 outlines how this systematic approach may be applied to areas of different climate and the extent to which there is an assemblage of processes characteristic of each area. In part 4, the process evidence and models are combined into theoretical sequences of slope profile development, and the effect of contour curvature in modifying these profiles on spurts and in hollows is examined.},
author = {Carson, M. A. and Kirkby, M. J.},
doi = {10.1126/science.178.4065.1083-a},
isbn = {9780521109116},
issn = {00137952},
journal = {Science},
number = {4065},
pages = {1083--1084},
pmid = {2209161},
title = {{Hillslope Form and Process}},
url = {http://www.sciencemag.org/cgi/doi/10.1126/science.178.4065.1083-a},
volume = {178},
year = {1972}
}
@article{Chen2014a,
author = {Chen, Alex and Darbon, Jerome and Buttazzo, Giuseppe and Santambrogio, Filippo and Morel, Jean Michel},
doi = {10.4171/IFB/315},
issn = {14639963},
journal = {Interfaces and Free Boundaries},
keywords = {Conservation laws,Partial differential equations,Physical model,River networks,Stream incision,Synthetic landscape evolution},
number = {1},
pages = {105--136},
title = {{On the equations of landscape formation}},
url = {http://www.ems-ph.org/doi/10.4171/IFB/315},
volume = {16},
year = {2014}
}
@article{Chen2014b,
abstract = {a b s t r a c t This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith–bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general phys-ically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs) illustrate the discussion and show results of landscape evolution with the proposed synthetic models.},
author = {Chen, Alex and Darbon, J{\'{e}}r{\^{o}}me and Morel, Jean-Michel},
doi = {10.1016/j.geomorph.2014.04.037},
isbn = {0169-555X},
issn = {0169555X},
journal = {Geomorphology},
keywords = {Conservation laws,Detachment-limited and transport-limited erosion,Landscape evolution model,Partial differential equations,River networks,Stream incision law},
month = {aug},
pages = {68--86},
publisher = {Elsevier B.V.},
title = {{Landscape evolution models: A review of their fundamental equations}},
url = {http://dx.doi.org/10.1016/j.geomorph.2014.04.037 http://dx.doi.org/10.1016/j.geomorph.2014.04.037{\%}5Cnhttp://linkinghub.elsevier.com/retrieve/pii/S0169555X14002402},
volume = {219},
year = {2014}
}
@article{Cheraghi2016,
author = {Cheraghi, Mohsen and Jomaa, Seifeddine and Sander, Graham C. and Barry, D. A.},
doi = {10.1002/2016WR019314},
issn = {1944-7973},
journal = {Water Resources Research},
keywords = {Hairsine‐Rose model,discharge‐concentration plot,flume experiment,particle swarm optimization,sediment transport},
number = {11},
pages = {8613--8629},
title = {{Hysteretic sediment fluxes in rainfall-driven soil erosion: Particle size effects}},
volume = {52},
year = {2016}
}

@article{Cheraghi2018,
author = {Cheraghi, Mohsen and Rinaldo, Andrea and Sander, Graham C. and Perona, Paolo and Barry, D. A.},
title = {Catchment Drainage Network Scaling Laws Found Experimentally in Overland Flow Morphologies},
journal = {Geophysical Research Letters},
volume = {45},
number = {18},
pages = {9614-9622},
doi = {10.1029/2018GL078351},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018GL078351},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018GL078351},
year = {2018}
}

@inproceedings{Christiansen1942,
address = {https://archive.org/stream/irrigationbyspri670chri/irrigationbyspri670chri{\_}djvu.txt},
author = {Christiansen, J. E.},
isbn = {University of California Agricultural Experiment Station Bulletin 670},
publisher = {California Agricultural Experiment Station Bulletin 670, Berkeley},
title = {{Irrigation by sprinkling}},
year = {1942}
}
@article{Clarke2010,
author = {Clarke, Brian A. and Burbank, Douglas W.},
doi = {10.1029/2009JF001279},
journal = {Journal of Geophysical Research: Earth Surface},
month = {jun},
number = {F2},
pages = {n/a--n/a},
title = {{Evaluating hillslope diffusion and terrace riser degradation in New Zealand and Idaho}},
url = {http://doi.wiley.com/10.1029/2009JF001279},
volume = {115},
year = {2010}
}
@article{Cohen2015a,
author = {Cohen, Sagy and Willgoose, Garry and Svoray, Tal and Hancock, Greg and Sela, Shai},
doi = {10.1002/2014JF003186},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {aeolian,evolution,pedogenesis,sediment transport,soil,weathering},
month = {feb},
number = {2},
pages = {260--274},
title = {{The effects of sediment transport, weathering, and aeolian mechanisms on soil evolution}},
url = {http://doi.wiley.com/10.1002/2014JF003186},
volume = {120},
year = {2015}
}
@article{Cohen2015,
abstract = {River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.},
author = {Cohen, Yossi and Devauchelle, Olivier and Seybold, Hansj{\"{o}}rg F and Yi, Robert S and Szymczak, Piotr and Rothman, Daniel H},
doi = {10.1073/pnas.1413883112},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
keywords = {1,Loewner equation,and daniel h,fracture mechanics,growth of rivers,h selection in the,hansj{\"{o}}rg f,harmonic growth,olivier devauchelle b,piotr szymczak c,principle of local symmetry,river channels,robert s,rothman a,seybold a,yi a,yossi cohen a},
month = {nov},
number = {46},
pages = {14132--14137},
pmid = {26578756},
publisher = {National Academy of Sciences},
title = {{Path selection in the growth of rivers}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/26578756 http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC4655524 http://www.pnas.org/lookup/doi/10.1073/pnas.1413883112},
volume = {112},
year = {2015}
}
@article{Cordier2006,
author = {Cordier, S. and Harmand, D. and Frechen, M. and Beiner, M.},
doi = {10.1016/j.quascirev.2005.11.007},
issn = {02773791},
journal = {Quaternary Science Reviews},
month = {jul},
number = {13-14},
pages = {1460--1474},
title = {{Fluvial system response to Middle and Upper Pleistocene climate change in the Meurthe and Moselle valleys (Eastern Paris Basin and Rhenish Massif)}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0277379105003203},
volume = {25},
year = {2006}
}
@article{Corenblit2015,
author = {Corenblit, Dov and Davies, Neil S. and Steiger, Johannes and Gibling, Martin R. and Bornette, Gudrun},
doi = {10.1002/esp.3643},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {ecosystem engineer,ecosystem resistance and resilience,fluvial biogeomorphic succession,functional effect and response traits,niche construction,riparian vegetation,scale‐dependant feedback,vegetation evolution},
month = {feb},
number = {2},
pages = {189--207},
title = {{Considering river structure and stability in the light of evolution: Feedbacks between riparian vegetation and hydrogeomorphology}},
url = {http://doi.wiley.com/10.1002/esp.3643},
volume = {40},
year = {2015}
}
@article{Costa-Cabral1994,
author = {Costa-Cabral, Mariza C. and Burges, Stephen J.},
doi = {10.1029/93WR03512},
issn = {00431397},
journal = {Water Resources Research},
month = {jun},
number = {6},
pages = {1681--1692},
title = {{Digital Elevation Model Networks (DEMON): A model of flow over hillslopes for computation of contributing and dispersal areas}},
url = {http://doi.wiley.com/10.1029/93WR03512},
volume = {30},
year = {1994}
}
@article{Coulthard2001,
author = {Coulthard, T. J.},
doi = {10.1002/hyp.426},
issn = {0885-6087},
journal = {Hydrological Processes},
month = {jan},
number = {1},
pages = {165--173},
publisher = {John Wiley {\&} Sons, Ltd.},
title = {{Landscape evolution models: a software review}},
url = {http://doi.wiley.com/10.1002/hyp.426},
volume = {15},
year = {2001}
}
@article{Crosby2007,
author = {Crosby, Benjamin T. and Whipple, Kelin X. and Gasparini, Nicole M. and Wobus, Cameron W.},
doi = {10.1029/2006JF000566},
issn = {0148-0227},
journal = {Journal of Geophysical Research},
keywords = {threshold,transient,tributary},
month = {aug},
number = {F3},
pages = {F03S10},
title = {{Formation of fluvial hanging valleys: Theory and simulation}},
url = {http://doi.wiley.com/10.1029/2006JF000566},
volume = {112},
year = {2007}
}
@article{Culling1960,
author = {Culling, WEH},
doi = {10.1086/626663},
journal = {The Journal of Geology},
keywords = {Culling1960},
number = {3},
pages = {336--344},
title = {{Analytical theory of erosion}},
url = {http://www.journals.uchicago.edu/doi/abs/10.1086/626663},
volume = {68},
year = {1960}
}
@article{Culling1965,
author = {Culling, WEH},
doi = {10.1086/627060},
journal = {The Journal of Geology},
keywords = {Culling1965},
number = {2},
pages = {230--254},
title = {{Theory of erosion on soil-covered slopes}},
url = {http://www.journals.uchicago.edu/doi/abs/10.1086/627060},
volume = {73},
year = {1965}
}
@article{Culling1963,
author = {Culling, WEH},
doi = {10.1086/626891},
journal = {The Journal of Geology},
keywords = {Culling1963},
number = {2},
pages = {127--161},
title = {{Soil creep and the development of hillside slopes}},
url = {http://www.journals.uchicago.edu/doi/abs/10.1086/626891},
volume = {71},
year = {1963}
}
@article{Davis1895,
author = {Davis, W. M.},
doi = {10.3406/geo.1895.5779},
issn = {0003-4010},
journal = {Annales de G{\'{e}}ographie},
number = {19},
pages = {25--49},
title = {{La Seine, la Meuse et la Moselle}},
url = {http://www.persee.fr/web/revues/home/prescript/article/geo{\_}0003-4010{\_}1895{\_}num{\_}4{\_}19{\_}5779},
volume = {4},
year = {1895}
}

@article{Davis1892,
abstract = {1. Science. 1892 Oct 28;20(508):245. THE CONVEX PROFILE OF BAD - LAND DIVIDES . Davis WM. PMID: 17812307 [PubMed].},
author = {Davis, W. M.},
doi = {10.1126/science.ns-20.508.245},
issn = {0036-8075},
journal = {Science},
number = {508},
pages = {245--245},
pmid = {17812307},
title = {{The Convex Profile of Bad-land Divides}},
url = {http://www.sciencemag.org/content/ns-20/508/245.1.citation?sid=0ecd2862-2fe5-4281-b382-cd6163050cad{\%}5Cnhttp://www.jstor.org/stable/1765582{\%}5Cnhttp://www.sciencemag.org/cgi/doi/10.1126/science.ns-20.508.245},
volume = {20},
year = {1892}
}
@article{DeLinares2007,
abstract = {A new model for the critical shear stress and the transport of graded$\backslash$nsediment is presented. The model is based on the size distribution$\backslash$nof the bed surface and can be used to compute sediment transport$\backslash$nrates in numerical simulations with an active layer model. This model$\backslash$nmakes a distinction between unimodal and bimodal sediments. It is$\backslash$nassumed that all size fractions of unimodal sediments have the same$\backslash$ncritical shear stress while there is selective transport for the$\backslash$ngravel fractions of bimodal sediments. A recently published laboratory$\backslash$ntransport data set is used to calibrate our model.},
author = {{De Linares}, Matthieu and Belleudy, Philippe},
doi = {10.1061/(ASCE)0733-9429(2007)133:5(555)},
issn = {0733-9429},
journal = {J. Hydr. Eng.},
number = {5},
pages = {555--559},
title = {{Critical Shear Stress of Bimodal Sediment in Sand-Gravel Rivers}},
volume = {133},
year = {2007}
}
@article{Demoulin2009,
author = {Demoulin, A. and Hallot, E.},
doi = {10.1016/j.tecto.2009.05.015},
issn = {00401951},
journal = {Tectonophysics},
month = {sep},
number = {3-4},
pages = {696--708},
title = {{Shape and amount of the Quaternary uplift of the western Rhenish shield and the Ardennes (western Europe)}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0040195109002959},
volume = {474},
year = {2009}
}

@article{Dorrell2018,
  title = {Particle {{Size Distribution Controls}} the {{Threshold}} between {{Net Sediment Erosion}} and {{Deposition}} in {{Suspended Load Dominated Flows}}},
  volume = {45},
  issn = {1944-8007},
  doi = {10.1002/2017GL076489},
  abstract = {The central problem of describing most environmental and industrial flows is predicting when material is entrained into, or deposited from, suspension. The threshold between erosional and depositional flow has previously been modeled in terms of the volumetric amount of material transported in suspension. Here a new model of the threshold is proposed, which incorporates (i) volumetric and particle size limits on a flow's ability to transport material in suspension, (ii) particle size distribution effects, and (iii) a new particle entrainment function, where erosion is defined in terms of the power used to lift mass from the bed. While current suspended load transport models commonly use a single characteristic particle size, the model developed herein demonstrates that particle size distribution is a critical control on the threshold between erosional and depositional flow. The new model offers an order of magnitude, or better, improvement in predicting the erosional-depositional threshold and significantly outperforms existing particle-laden flow models.},
  language = {English},
  number = {3},
  journal = {Geophysical Research Letters},
  author = {Dorrell, R. M. and Amy, L. A. and Peakall, J. and McCaffrey, W. D.},
  month = feb,
  year = {2018},
  keywords = {sediment transport,equilibrium flow,erosion-deposition},
  pages = {1443-1452}
}
@book{Abrahams1986,
abstract = {Hillslopes occupy most of the land surface of the earth. Consequently, they are a major focus of research in geomorphology. Their study is essential not only in order to understand the natural landscape better but also for many practical reasons, such as controlling soil erosion and sedimentation on agricultural lands and mitigating the hazards posed by landslides. Studies within geomorphology owe a considerable debt to and are often closely linked with other disciplines, which include hydrology, pedology, agricultrual engineering, civil engineering, and engineering geology. This volume encompasses contributions from many of these fields.},
address = {Boston, MA},
author = {Dunne, Thomas and Aubry, Brian F and Abrahams, A.},
booktitle = {Chapter 2 - Evaluation of Horton's theory of sheetwash and rill erosion on the basis of field experiments},
editor = {Abrahams, A. D.},
isbn = {9780045511020},
keywords = {-- geology {\&} hydrology-- (-1989),-- geophysics-- (-1989),agriculture,engineering geology,environmental sciences,erosion,geologic strata,geologic structures,geology,geomorphology,geophysics,geosciences,hydrology,inclined strata,industry,land resources,land use,landslides,management,research programs,resource management,sedimentation,soil mechanics},
pages = {No. of pages: 416},
publisher = {Allen and Unwin Inc.,Winchester, MA},
title = {{Hillslope processes}},
year = {1986}
}
@article{Dunne2016,
author = {Dunne, Thomas and Malmon, Daniel V. and Dunne, Kieran B. J.},
doi = {10.1002/2015JF003737},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {climatic effects,hillslope evolution,rain splash transport},
month = {mar},
number = {3},
pages = {609--622},
title = {{Limits on the morphogenetic role of rain splash transport in hillslope evolution}},
url = {http://doi.wiley.com/10.1002/2015JF003737},
volume = {121},
year = {2016}
}
@article{Dunne2010,
author = {Dunne, Thomas and Malmon, Daniel V. and Mudd, Simon M.},
doi = {10.1029/2009JF001302},
issn = {0148-0227},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {doi:10.102,erosion,hillslope geomorphology,http://dx.doi.org/10.1029/2009JF001302,sediment transport},
month = {jan},
number = {F1},
pages = {F01001},
title = {{A rain splash transport equation assimilating field and laboratory measurements}},
url = {http://doi.wiley.com/10.1029/2009JF001302},
volume = {115},
year = {2010}
}

@article{Edwards1982,
  title = {The {{Surface Statistics}} of a {{Granular Aggregate}}},
  volume = {381},
  issn = {0080-4630, 2053-9169},
  doi = {10.1098/rspa.1982.0056},
  abstract = {The problem of the surface fluctuations in a settled granular material is posed. A simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of Langevin equations for the Fourier modes of the surface are derived. These equations imply that the Fourier amplitudes behave like the velocities of a set of independent Brownian particles. We show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random, the divergence being removed by a more accurate description of the settling material, for example by having the granules fall through a sieve.},
  language = {English},
  number = {1780},
  journal = {Proc. R. Soc. Lond. A},
  author = {Edwards, Samuel Frederick and Wilkinson, D. R.},
  year = {1982},
  pages = {17-31},
  shortjournal = {Proc. R. Soc. Lond. A}
}

@article{Fatichi2016,
  title = {An {{Overview}} of {{Current Applications}}, {{Challenges}}, and {{Future Trends}} in {{Distributed Process}}-{{Based Models}} in {{Hydrology}}},
  volume = {537},
  issn = {0022-1694},
  doi = {10.1016/j.jhydrol.2016.03.026},
  abstract = {Summary Process-based hydrological models have a long history dating back to the 1960s. Criticized by some as over-parameterized, overly complex, and difficult to use, a more nuanced view is that these tools are necessary in many situations and, in a certain class of problems, they are the most appropriate type of hydrological model. This is especially the case in situations where knowledge of flow paths or distributed state variables and/or preservation of physical constraints is important. Examples of this include: spatiotemporal variability of soil moisture, groundwater flow and runoff generation, sediment and contaminant transport, or when feedbacks among various Earth's system processes or understanding the impacts of climate non-stationarity are of primary concern. These are situations where process-based models excel and other models are unverifiable. This article presents this pragmatic view in the context of existing literature to justify the approach where applicable and necessary. We review how improvements in data availability, computational resources and algorithms have made detailed hydrological simulations a reality. Avenues for the future of process-based hydrological models are presented suggesting their use as virtual laboratories, for design purposes, and with a powerful treatment of uncertainty.},
  journal = {Journal of Hydrology},
  author = {Fatichi, Simone and Vivoni, Enrique R. and Ogden, Fred L. and Ivanov, Valeriy Y. and Mirus, Benjamin and Gochis, David and Downer, Charles W. and Camporese, Matteo and Davison, Jason H. and Ebel, Brian and Jones, Norm and Kim, Jongho and Mascaro, Giuseppe and Niswonger, Richard and Restrepo, Pedro and Rigon, Riccardo and Shen, Chaopeng and Sulis, Mauro and Tarboton, David},
  month = jun,
  year = {2016},
  keywords = {Modeling,Change assessments,Interdisciplinary,Natural and built environment,Virtual experiments,Watershed processes},
  pages = {45-60}
}
@article{Ferdowsi2018,
  title = {Glassy {{Dynamics}} of {{Landscape Evolution}}},
  issn = {0027-8424, 1091-6490},
  doi = {10.1073/pnas.1715250115},
  abstract = {Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed-upon model that captures the full range of behavior. Here we examine the granular origins of hillslope soil transport by discrete element method simulations and reanalysis of measurements in natural landscapes. We find creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical gradient there is a continuous transition to a dense-granular flow rheology. Slow earthflows and landslides thus exhibit glassy dynamics characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales.},
  language = {English},
  journal = {Proceedings of the National Academy of Sciences},
  author = {Ferdowsi, Behrooz and Ortiz, Carlos P. and Jerolmack, Douglas J.},
  month = apr,
  year = {2018},
  keywords = {landscape evolution,granular flow,creep,dynamical phase transition},
  pages = {201715250},
  eprinttype = {pmid},
  eprint = {29686102},
  shortjournal = {PNAS}
}
@article{Fernandes1997,
abstract = {Diffusive processes such as creep, rain splash, and biogenic transport play a major role in controlling the development of convex hilltops on soil-mantled landscapes. Although many diffusion-based models have been proposed, little attention has been given to the effects of changing transport rates and boundary conditions. We use numerical and analytical solutions of the one-dimensional diffusion equation to explore whether hilltop convexities can be in equilibrium with contemporary climate and local channel incision rates. The results show that the timescale of such morphological adjustments varies substantially depending on whether the hillslope is tending to increase or decrease its convexity through time. By comparing the relaxation times estimated here with the frequency of the climatic oscillations observed in the last few million years, we argue that most of the convex hilltops observed in the field today are likely to be far from time-independent morphological features.},
author = {Fernandes, Nelson F. NF and Dietrich, WE William E.},
doi = {10.1029/97WR00534},
isbn = {0043-1397},
issn = {00431397},
journal = {Water Resources Research},
keywords = {doi:10.1029/9,http://dx.doi.org/10.1029/97WR00534},
number = {6},
pages = {1307--1318},
title = {{Hillslope evolution by diffusive processes: The timescale for equilibrium adjustments}},
url = {http://onlinelibrary.wiley.com/doi/10.1029/97WR00534/full{\%}5Cnhttp://doi.wiley.com/10.1029/97WR00534},
volume = {33},
year = {1997}
}
@article{Forte2016,
author = {Forte, Adam M. and Yanites, Brian J. and Whipple, Kelin X.},
doi = {10.1002/esp.3947},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {detrital mineral records,erodibility,landscape evolution,rock strength,steady state},
month = {sep},
number = {12},
pages = {1736--1757},
title = {{Complexities of landscape evolution during incision through layered stratigraphy with contrasts in rock strength}},
url = {http://doi.wiley.com/10.1002/esp.3947},
volume = {41},
year = {2016}
}
@article{Foufoula-Georgiou2010,
  title = {Introduction to {{Special Section}} on {{Stochastic Transport}} and {{Emergent Scaling}} on {{Earth}}'s {{Surface}}: {{Rethinking Geomorphic Transport}}\textemdash{{Stochastic Theories}}, {{Broad Scales}} of {{Motion}} and {{Nonlocality}}},
  volume = {115},
  issn = {0148-0227},
  doi = {10.1029/2010JF001661},
  abstract = {In many geomorphic transport systems, the time and length scales of motion vary widely: particles can be trapped for both short and long periods of time and they can travel large or small distances in very short intervals of time. To model such systems we need fresh conceptual and mathematical formalisms. The goal of this collection of papers is to challenge existing thinking in geomorphic transport by putting forward new ideas and theories for environmental fluxes, from particle transport in a single stream, to landslide debris mobilization, sediment and water transport on hillslopes, dynamic transport on river networks, and interpretation of sedimentary deposits over geologic time. Advanced stochastic theories of transport are proposed, the notion of nonlocal flux is introduced, and fractional advection-diffusion equations are explored as possible models of geomorphic transport.},
  number = {F2},
  journal = {Journal of Geophysical Research: Earth Surface},
  author = {{Foufoula-Georgiou}, Efi and Stark, Colin},
  year = {2010},
  keywords = {fractional advection-diffusion,geomorphic transport,stochastic theories},
  shortjournal = {Journal of Geophysical Research: Earth Surface}
}
@article{Francipane2015,
abstract = {t Hydrologic and geomorphic responses of watersheds to changes in climate are difficult to assess due to projection uncertainties and nonlinearity of the processes that are involved. Yet such assessments are increasingly needed and call for mechanistic approaches within a probabilistic framework. This study employs an integrated hydrology-geomorphology model, the Triangulated Irregular Network-based Real-time Integrated Basin Simulator (tRIBS)-Erosion, to analyze runoff and erosion sensitivity of seven semiarid headwater basins to projected climate conditions. The Advanced Weather Generator is used to produce two climate ensembles representative of the historic and future climate conditions for the Walnut Gulch Experimental Watershed located in the southwest U.S. The former ensemble incorporates the stochastic variability of the observed climate, while the latter includes the stochastic variability and the uncertainty of multimodel climate change projections. The ensembles are used as forcing for tRIBS-Erosion that simulates runoff and sediment basin responses leading to probabilistic inferences of future changes. The results show that annual precipitation for the area is generally expected to decrease in the future, with lower hourly intensities and similar daily rates. The smaller hourly rainfall generally results in lower mean annual runoff. However, a non-negligible probability of runoff increase in the future is identified, resulting from stochastic combinations of years with low and high runoff. On average, the magnitudes of mean and extreme events of sediment yield are expected to decrease with a very high probability. Importantly, the projected variability of annual sediment transport for the future conditions is comparable to that for the historic conditions, despite the fact that the former account for a much wider range of possible climate “alternatives.” This result demonstrates that the historic natural climate variability of sediment yield is already so high, that it is comparable to the variability for a projected and highly uncertain future. Additionally, changes in the scaling relationship between specific sediment yield/runoff and drainage basin area are detected.},
author = {Francipane, A. and Fatichi, S. and Ivanov, V. Y. and Noto, L. V.},
doi = {10.1002/2014JF003232},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {climate impacts,erosion,geomorphology,modeling},
month = {mar},
number = {3},
pages = {507--533},
title = {{Stochastic assessment of climate impacts on hydrology and geomorphology of semiarid headwater basins using a physically based model}},
url = {http://doi.wiley.com/10.1002/2014JF003232},
volume = {120},
year = {2015}
}
@article{Franke1980,
abstract = {Methods for solving the following data-fitting problems are discussed: given the data (xi, yi, fi),i = 1,,N construct a smooth bivariate function S with the property that S(xi, yi) = fii = 1,,N. Because the desire to fit this type of data is encountered frequently in many areas of scientific applications, an investigation of the available methods for solving this problem was undertaken. Several aspects, such as computational efficiency, fitting characteristics and ease of implementation, were analysed and compared. Within the context of a general-purpose method for large sets of data, two of these methods emerged as being generally superior to the others. It is the purpose of this paper to describe these two methods and present examples illustrating their use and application.},
author = {Franke, Richard and Nielson, Greg},
doi = {10.1002/nme.1620151110},
isbn = {1097-0207},
issn = {0029-5981},
journal = {International Journal for Numerical Methods in Engineering},
month = {nov},
number = {11},
pages = {1691--1704},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Smooth interpolation of large sets of scattered data}},
url = {http://doi.wiley.com/10.1002/nme.1620151110},
volume = {15},
year = {1980}
}
@article{Freeman1991,
abstract = {A new procedure is described for determining the catchment areas for all cells in a regular elevation grid, a problem of fundamental importance in analyzing drainage patterns, mineral deposition, erosion, and pollution in streams and groundwater. The new procedure allows for divergent flow, which arises in most natural terrain on hill slopes. Failure to allow for this can introduce serious artifacts in the calculations. The procedure is demonstrated on analytic surfaces that give poor results if divergent flow is ignored, and is applied to natural terrain. Also discussed is the problem of clearing sinks or pits in the elevation model and flat spots.},
author = {Freeman, T.Graham},
doi = {10.1016/0098-3004(91)90048-I},
issn = {00983004},
journal = {Computers {\&} Geosciences},
number = {3},
pages = {413--422},
publisher = {Pergamon},
title = {{Calculating catchment area with divergent flow based on a regular grid}},
volume = {17},
year = {1991}
}

@article{Furbish2007a,
abstract = {Rain splash transport of sediment on a sloping surface arises from a downslope drift of grains displaced ballistically by raindrop impacts. We use high-speed imaging of drop impacts on dry sand to describe the drop-to-grain momentum transfer as this varies with drop size and grain size and to clarify ingredients of downslope grain drift. The “splash” of many grains involves ejection of surface grains accelerated by grain-to-grain collisions ahead of the radially spreading front of a drop as it deforms into a saucer shape during impact. For a given sand size, splash distances are similar for different drop sizes, but the number of displaced grains increases with drop size in proportion to the momentum of the drop not infiltrated within the first millisecond of impact. We present a theoretical formulation for grain ejection which assumes that the proportion of ejected grains within any small azimuthal angular interval d$\theta$ about the center of impact is proportional to the momentum density of the spreading drop within d$\theta$ and that the momentum of ejected grains at angle $\theta$ is, on average, proportional to the momentum of the spreading drop at $\theta$. This formulation, consistent with observed splash distances, suggests that downslope grain transport involves an asymmetry in both quantity and distance: more grains move downslope than upslope with increasing surface slope, and, on average, grains move farther downslope. This latter effect is primarily due to the radial variation in the surface-parallel momentum of the spreading drop. Surface-parallel transport increases approximately linearly with slope.},
author = {Furbish, David Jon and Hammer, Katherine K and Schmeeckle, Mark and Borosund, Miriam N. and Mudd, Simon Marius and Hamner, Katherine K. and Schmeeckle, Mark and Borosund, Miriam N. and Mudd, Simon Marius},
doi = {10.1029/2006JF000498},
issn = {0148-0227},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {doi:10.102,doi:10.1029/2006JF000498,erosion,http://dx.doi.org/10.1029/2006JF000498,momentum,sediment},
month = {jan},
number = {F1},
pages = {F01001},
title = {{Rain splash of dry sand revealed by high-speed imaging and sticky paper splash targets}},
url = {http://doi.wiley.com/10.1029/2006JF000498},
volume = {112},
year = {2007}
}
@article{Furbish2013,
  title = {Sediment {{Disentrainment}} and the {{Concept}} of {{Local}} versus {{Nonlocal Transport}} on {{Hillslopes}}},
  volume = {118},
  issn = {2169-9011},
  doi = {10.1002/jgrf.20071},
  abstract = {A local formulation of the sediment flux on a hillslope describes the flux as a unique function of local hillslope conditions at any contour position x, whereas a nonlocal formulation must take into account nonlocal (upslope or downslope) conditions that influence the flux at x. Local formulations are reasonable when particle motions involve small length scales associated with localized bioturbation of the soil column or with proximal surface transport such as rain splash. Nonlocal formulations may be more appropriate in steeplands where patchy, intermittent motions involve large travel distances, mostly over the surface. Once sediment motions are initiated, the disentrainment process determines the distribution of particle travel distances, which, in turn, forms the basis of nonlocal formulations that involve a convolution of hillslope surface conditions, for example, the land-surface slope. The kernel in the convolution integral, which weights the effect of land-surface conditions (e.g., slope) at all positions upslope or downslope of x, derives from the formulation of the disentrainment rate and characterizes whether particle travel distances depend on conditions at the position where motions originate or vary as particles experience changing surface conditions during their downslope motions. If hillslope properties controlling transport (e.g., surface slope) are defined or measured at a specified resolution, then motions smaller than this resolution cannot be attributed to these properties resolved at a smaller scale. In essence, the relative importance of local and nonlocal transport depends on the scale of particle motions compared to the relevant scale of hillslope properties that drive transport.},
  language = {English},
  number = {2},
  journal = {Journal of Geophysical Research: Earth Surface},
  author = {Furbish, David Jon and Roering, Joshua J.},
  month = jun,
  year = {2013},
  keywords = {sediment transport,hillslope,nonlocal transport,local transport},
  pages = {937-952}
}
@article{Gabet2012,
  title = {Particle {{Transport}} over {{Rough Hillslope Surfaces}} by {{Dry Ravel}}: {{Experiments}} and {{Simulations}} with {{Implications}} for {{Nonlocal Sediment Flux}}},
  volume = {117},
  issn = {0148-0227},
  doi = {10.1029/2011JF002229},
  abstract = {Past studies of hillslope evolution have typically assumed that soil creep processes are governed by a linear relationship between local hillslope angle and transport distance. The assumption of ?linear diffusion? has fallen out of favor because, when coupled with an expression of mass continuity, it yields unrealistic hillslope profiles. As a consequence, a better understanding of the mechanics of sediment transport is needed. Here we report results from a series of flume experiments performed to investigate sediment transport by dry ravel, a common soil creep process in arid and semiarid environments. We find that, at gentle slopes, transport distances follow distributions characteristic of local transport. As gradients steepen, a fraction of the particles begins to exhibit nonlocal transport, and that fraction increases rapidly with slope. A stochastic discrete element model that couples an effective friction term with a shock term reproduces the results from the flume experiments, suggesting that it can be used to explore the nature of particle transport on rough surfaces. The model predicts that exponential distributions of transport distances on gentle slopes evolve into quasi-uniform distributions on steep slopes, and the transition occurs as slopes approach the angle of repose. Our results support previous findings that the angle of repose represents a threshold between friction and inertial regimes. In addition, we propose that the angle of repose represents a fuzzy boundary between local and nonlocal transport.},
  number = {F1},
  journal = {Journal of Geophysical Research: Earth Surface},
  author = {Gabet, Emmanuel J. and Mendoza, Morgan K.},
  year = {2012},
  keywords = {nonlocal transport,angle of repose,dry ravel,granular flow},
  shortjournal = {Journal of Geophysical Research: Earth Surface}
}


@article{Gasparini2014,
author = {Gasparini, Nicole M},
doi = {10.1038/513490a},
issn = {1476-4687},
journal = {Nature},
month = {sep},
number = {7519},
pages = {490--1},
pmid = {25254468},
publisher = {Nature Publishing Group},
title = {{Earth science: A fresh look at river flow.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/25254468},
volume = {513},
year = {2014}
}

@article{Giacometti1995,
  title = {Continuum {{Model}} for {{River Networks}}},
  volume = {75},
  doi = {10.1103/PhysRevLett.75.577},
  abstract = {The effects of erosion, avalanching, and random precipitation are captured in a simple stochastic partial differential equation for modeling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.},
  number = {3},
  journal = {Physical Review Letters},
  author = {Giacometti, Achille and Maritan, Amos and Banavar, Jayanth R.},
  month = jul,
  year = {1995},
  pages = {577-580},
  shortjournal = {Phys. Rev. Lett.}
}

@article{Gilbert1877a,
abstract = {If these pages fail to give a correct account of the structure of the Henry Mountains the fault is mine and I have no excuse. In all the earlier exploration of the Rocky Mountain Region, as well as in much of the more recent survey, the geologist has merely accompanied the geographer and has had no voice in the determination of either the route or the rate of travel. When the structure of a mountain was in doubt he was rarely able to visit the points which should resolve the doubt, but was compelled to turn regretfully away. Not so in the survey of the Henry Mountains. Geological exploration had shown that they were well disposed for examination, and that they promised to give the key to a type of structure which was at best obscurely known; and I was sent by Professor Powell to make a study of them, without restriction as to my order or method. I was limited only in time, the snow stopping my work two months after it was begun. Two months would be far too short a period in which to survey a thousand square miles in Pennsylvania or Illinois, but among the Colorado Plateaus it proved sufficient. A few comprehensive views from mountain tops gave the general distribution of the formations, and the remainder of the time was spent in the examination of the localities which best displayed the peculiar features of the structure. So thorough was the display and so satisfactory the examination, that in preparing my report I have felt less than ever before the desire to revisit the field and prove my conclusions by more extended observation.},
author = {Gilbert, G.K. K},
doi = {10.1038/022266c0},
issn = {0028-0836},
journal = {Monograph},
keywords = {eaes580},
pages = {i--160},
title = {{Land Sculptures - Geology of the Henry Mountains}},
url = {http://pubs.er.usgs.gov/publication/70038096},
year = {1877}
}
@article{Gilley1993,
abstract = {This study was conducted to identify critical shear stress and critical flow rates required initiate rilling on selected sites. The data used in this investigation were collected from soils located throughout the USA where crop residues had been removed, and moldboard plowing and disking had occurred. Runoff and soil loss measurements were made on sites where simulated rainfall was applied to preformed rills. Multiple regression analyses were used to relate critical shear stress values and critical flow rates to selected soil properties. The soil-based regression equations were found to provide reliable estimates. Information identified in this study will improve our ability to understand and properly model upland runoff and erosion processes. ?? 1993.},
author = {Gilley, J. E. and Elliot, W. J. and Laflen, J. M. and Simanton, J. R.},
doi = {10.1016/0022-1694(93)90013-Y},
issn = {00221694},
journal = {Journal of Hydrology},
month = {feb},
number = {1-4},
pages = {251--271},
title = {{Critical shear stress and critical flow rates for initiation of rilling}},
url = {http://linkinghub.elsevier.com/retrieve/pii/002216949390013Y},
volume = {142},
year = {1993}
}
@article{Godard2013,
author = {Godard, Vincent and Tucker, Gregory E. and {Burch Fisher}, G. and Burbank, Douglas W. and Bookhagen, Bodo},
doi = {10.1002/grl.50253},
issn = {00948276},
journal = {Geophysical Research Letters},
keywords = {climate change,continental denudation,landscape evolution,numerical modelling},
month = {mar},
number = {5},
pages = {859--863},
title = {{Frequency-dependent landscape response to climatic forcing}},
url = {http://doi.wiley.com/10.1002/grl.50253},
volume = {40},
year = {2013}
}
@article{Gomez1992,
author = {Gomez, Basil and Mullen, Victor T.},
doi = {10.1002/esp.3290170506},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {drainage network development sapping,sediment discharge},
number = {5},
pages = {465--476},
title = {{An experimental study of sapped drainage network development}},
url = {http://doi.wiley.com/10.1002/esp.3290170506},
volume = {17},
year = {1992}
}
@article{Gomez2003,
abstract = {[1] The evolution of drainage networks at large scales has been shown to follow a principle of minimization of the global rate of energy dissipation. This study was undertaken to evaluate whether a principle similar to that holds for rill networks at a much smaller scale. Simulated rainfall was applied to a 2 m by 4 m flume with varied initial slope (5{\{}{\%}{\}} and 20{\{}{\%}{\}}) and roughness (low, moderate, and great) conditions. The results indicated that assuming the validity of a local optimality principle, the rill networks evolved according to a global principal of energy optimization in situations where rilling was intense, 20{\{}{\%}{\}} slope, but not at 5{\{}{\%}{\}} slope where diffusive processes played a dominant role in the overall erosion process. These results suggest that the application of models similar to some used to explain the evolution of river networks may have a role in understanding the initiation and evolution of rill networks in situations of intensive rilling. Our results and analysis suggest that further experiments might be undertaken to study the spatial distribution of flow velocity within the rill networks at a given flow discharge and the local rate of energy dissipation at rill links. Despite the convergence toward similar values of some of the network characteristics, differences in the microrelief of the initial surfaces were translated into significant differences between the final rill networks.},
author = {G{\'{o}}mez, J A and Darboux, F and Nearing, M A},
doi = {10.1029/2002WR001437},
isbn = {1944-7973},
issn = {00431397},
journal = {Water Resources Research},
number = {6},
pages = {1148},
title = {{Development and evolution of rill networks under simulated rainfall}},
volume = {39},
year = {2003}
}
@article{Gordon2011,
author = {Gordon, Lee M and Bennett, Sean J and Wells, Robert R},
journal = {Landform Analysis},
keywords = {digital elevation models,headcuts,rill erosion,rill networks,simulated rainfall},
pages = {57--63},
title = {{Evolution of rill networks on soil-mantled experimental landscapes driven by rainfall and baselevel adjustments}},
volume = {17},
year = {2011}
}
@article{Gordon2012,
author = {Gordon, Lee M. and Bennett, Sean J. and Wells, Robert R.},
doi = {10.1029/2012WR012283},
issn = {00431397},
journal = {Water Resources Research},
keywords = {"headcuts,rill erosion,rill networks"},
number = {10},
pages = {1--15},
title = {{Response of a soil-mantled experimental landscape to exogenic forcing}},
volume = {48},
year = {2012}
}
@article{Goren2014a,
abstract = {The Earth's topography is shaped by surface processes that operate on various scales. In particular, river processes control landscape dynamics over large length scales, whereas hillslope processes control the dynamics over smaller length scales. This scale separation challenges numerical treatments of landscape evolution that use space discretization. Large grid spacing cannot account for the dynamics of water divides that control drainage area competition, and erosion rate and slope distribution. Small grid spacing that properly accounts for divide dynamics is computationally inefficient when studying large domains. Here we propose a new approach for landscape evolution modeling that couples irregular grid-based numerical solutions for the large-scale fluvial dynamics and continuum-based analytical solutions for the small-scale fluvial and hillslope dynamics. The new approach is implemented in the landscape evolution model DAC (divide and capture). The geometrical and topological characteristics of DAC's landscapes show compatibility with those of natural landscapes. A comparative study shows that, even with large grid spacing, DAC predictions fit well an analytical solution for divide migration in the presence of horizontal advection of topography. In addition, DAC is used to study some outstanding problems in landscape evolution. (i) The time to steady-state is investigated and simulations show that steady-state requires much more time to achieve than predicted by fixed area calculations, due to divides migration and persistent reorganization of low-order streams. (ii) Large-scale stream captures in a strike-slip environment are studied and show a distinct pattern of erosion rates that can be used to identify recent capture events. (iii) Three tectono-climatic mechanisms that can lead to asymmetric mountains are studied. Each of the mechanisms produces a distinct morphology and erosion rate distribution. Application to the Southern Alps of New Zealand suggests that tectonic advection, precipitation gradients and non-uniform tectonic uplift act together to shape the first-order topography of this mountain range. {\textcopyright} 2014 John Wiley {\&} Sons, Ltd.},
author = {Goren, Liran and Willett, Sean D. and Herman, Fr{\'{e}}d{\'{e}}ric and Braun, Jean},
doi = {10.1002/esp.3514},
isbn = {01979337 (ISSN)},
issn = {10969837},
journal = {Earth Surface Processes and Landforms},
keywords = {Fluvial geomorphology,Landscape evolution model,River capture,Tectonic geomorphology},
number = {4},
pages = {522--545},
title = {{Coupled numerical-analytical approach to landscape evolution modeling}},
volume = {39},
year = {2014}
}
@article{Graveleau2012,
author = {Graveleau, Fabien and Malavieille, Jacques and Dominguez, St{\'{e}}phane},
doi = {10.1016/j.tecto.2012.01.027},
issn = {00401951},
journal = {Tectonophysics},
pages = {1--66},
title = {{Experimental modelling of orogenic wedges: A review}},
volume = {538},
year = {2012}
}
@article{Grieve2016,
author = {Grieve, Stuart W.D. and Mudd, Simon M. and Hurst, Martin D.},
doi = {10.1002/esp.3884},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {hillslopes,length scales,sediment flux,topographic analysis},
month = {jun},
number = {8},
pages = {1039--1054},
title = {{How long is a hillslope?}},
url = {http://doi.wiley.com/10.1002/esp.3884},
volume = {41},
year = {2016}
}
@article{Hack1957,
author = {Hack, J.T.},
issn = {2330-7102},
journal = {Professional Paper},
pages = {45--97},
title = {{Studies of longitudinal stream profiles in Virginia and Maryland}},
volume = {294-B},
year = {1957}
}
@article{Hadka2013,

  author={Hadka, David and Reed, Patrick},

  journal={Evolutionary Computation}, 

  title={Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework}, 

  year={2013},

  volume={21},

  number={2},

  pages={231-259},

  doi={10.1162/EVCO-a-00075}
}

@article{Hairsine1992b,
abstract = {The model of soil erosion on a plane slope introduced by Hairsine and Rose (this issue) is further developed by considering rill flow.},
author = {Hairsine, P. B. and Rose, C. W.},
doi = {10.1029/91WR02381},
isbn = {1944-7973},
issn = {00431397},
journal = {Water Resources Research},
month = {jan},
number = {1},
pages = {245--250},
title = {{Modeling water erosion due to overland flow using physical principles: 2. Rill flow}},
url = {http://doi.wiley.com/10.1029/91WR02381},
volume = {28},
year = {1992}
}
@article{Hairsine1992a,
abstract = {A new model for erosion of plane soil surfaces by water is developed using physical principles. Raindrop impact and overland flow remove soil from the original cohesive soil. Once eroded soil enters overland flow, either as aggregates or primary particles, a significant proportion of it returns to the soil bed, forming a cohesionless deposited layer from which it can be removed again by the same erosion processes. The action of the eroding agents will be divided between eroding the unshielded original cohesive soil and reintroducing sediment from the deposited layer. The theory recognizes that the nature of the surface is modified by the erosion and deposition processes affecting it. Solutions of the governing differential equations describing sediment concentration are developed for two distinct equilibrium cases. The first case, when the deposited layer completely shields the original soil, appears to correspond with what has been previously called a “transport-limited” situation. The second case occurs when such shielding is incomplete, and sediment concentration is affected by the cohesive strength of the soil. The resulting equations for sediment concentration at equilibrium are compared with existing equations. Firstly, the equation for the case where the soil is lacking cohesion is shown to be similar to the semiempirical equation of Yang (1973). Secondly, when the soil is cohesive the slope length relationships are shown to be in good agreement with the universal soil loss equation over a wide range of slope steepness.},
author = {Hairsine, P. B. and Rose, C. W.},
doi = {10.1029/91WR02380},
isbn = {1944-7973},
issn = {00431397},
journal = {Water Resources Research},
month = {jan},
number = {1},
pages = {237--243},
title = {{Modeling water erosion due to overland flow using physical principles: 1. Sheet flow}},
url = {http://doi.wiley.com/10.1029/91WR02380 http://doi.wiley.com/10.1029/91WR02381},
volume = {28},
year = {1992}
}
@article{Hairsine1991,
abstract = {Erosion of soils in nonchannelized soil surfaces areas is generally driven by the agents of raindrop impact and overland flow. This study considers soil erosion in portions of the landscape where the combination of land slope and water flux is relatively low so that overland flow driven processes are absent and raindrop impact is the only erosion agent. A model of soil erosion was developed to describe situations where the soil surface is covered by a water layer, and where the only processes acting are rainfall detachment and deposition. The model uses physical principles and recognizes that once soil has been detached by the impact of raindrops, soil aggregates or particles return to the bed by deposition to form a deposited layer from which they can be subsequently redetached. Since sediment in the deposited layer can have quite different characteristics from the original soil, it was necessary to distinguish between rainfall detachment of the original bed and rainfall redetachment of the deposited layer. The principle of mass conservation was then applied both to water and to soil, considering the settling velocity characteristic of sediment. This yields equations describing sediment transport in gentle overland flow on a plane land surface where the thresholds of entrainment and reentrainment by flow have not been exceeded. These equations were solved for the equilibrium situation only, and these solutions discussed and limitations outlined. It was proposed that three distinct regimes exist for shallow flow low slope erosion, each with a different dependency on slope steepness, when: (i) the depth is less than or equal to a breakpoint depth and flow-driven processes are inactive, erosion is independent of slope; (ii) flow depth is greater than the breakpoint depth and flow-driven processes are inactive, erosion is slightly dependent on slope; and (iii) the combination of slope and discharge is such that flow-driven processes are active, then erosion is strongly dependent on slope.},
author = {Hairsine, P.B. B. and Rose, C.W. W.},
doi = {10.2136/sssaj1991.03615995005500020003x},
issn = {0361-5995},
journal = {Soil Science Society of America Journal},
number = {2},
pages = {320},
shorttitle = {Rainfall detachment and deposition},
title = {{Rainfall detachment and deposition: Sediment transport in the absence of flow-driven processes}},
url = {https://dl.sciencesocieties.org/publications/sssaj/abstracts/55/2/SS0550020320 https://www.soils.org/publications/sssaj/abstracts/55/2/SS0550020320},
volume = {55},
year = {1991}
}
@article{Han2015,
abstract = {We explore the imprint of spatial rainfall patterns on steady-state landscapes with uniform rock uplift rate. A two-dimensional (2D) orographic precipitation module is incorporated into the CHILD numerical landscape evolution model to provide a quantitative tool for exploring the co-evolution of rainfall patterns and fluvial topography. Our results suggest that network organization and planform morphology are strongly impacted by rainfall patterns. Rainfall gradients that are perpendicular to a mountain range front produce narrower watersheds because channels show a tendency to flow along the rainfall gradient, rather than across it. The change in watershed shape is evidenced by smaller values of the exponent on distance in Hack's law and a less peaked width function. Narrower watersheds also lead to an increase in the valley spacing ratio and constrain trunk channels to follow a more direct path to the mountain front. Rainfall gradients also influence the distribution of topography across a watershed. Channel profiles record rainfall patterns in both the channel concavity and the channel steepness index (ksn). Across short tributaries along which rainfall rate changes little, ksn decreases systematically with tributary-averaged rainfall rate. The hypsometric integral (HI), which increases with the amount of topography that is at relatively high elevations within a watershed, is negatively correlated with the profile concavity of the trunk channel. High rainfall rates at the ridge top lead to mainstem channels that have relatively low concavity, and watersheds with relatively higher HI in comparison with landscapes that have uniform rainfall. Finally, we contrast the impacts of rainfall patterns on landscape morphology with those resulting from a linear rock uplift gradient and uniform rainfall. Uplift patterns may have a similar impact on landscape morphology as rainfall gradients, making it challenging to decipher the relative roles of climate and tectonics on landscape evolution without a quantitative assessment of morphologic parameters. Copyright {\textcopyright} 2015 John Wiley {\&} Sons, Ltd.},
author = {Han, Jianwei and Gasparini, Nicole M. and Johnson, Joel P. L.},
doi = {10.1002/esp.3723},
issn = {10969837},
journal = {Earth Surface Processes and Landforms},
keywords = {Landscape evolution model,Orographic precipitation,Planform morphology,River profile},
month = {aug},
number = {10},
pages = {1334--1350},
title = {{Measuring the imprint of orographic rainfall gradients on the morphology of steady-state numerical fluvial landscapes}},
url = {http://doi.wiley.com/10.1002/esp.3723},
volume = {40},
year = {2015}
}
@article{Hancock2002,
abstract = {SIBERIA is a physically based model for the geomorphic evolution of landforms. It is essential that the SIBERIA model be tested or validated against controlled landform development. Previous studies have demonstrated that SIBERIA is able to simulate declining equilibrium landforms and in this paper we examine SIBERIA's ability to simulate landforms as they evolve to their declining equilibrium form. These landscapes are termed transient landforms. Landscapes generated by SIBERIA were compared to those produced by a physical model (experimental model landforms) at stages of evolution. Comparison of the experimental landscapes with the simulated landscapes using total mass, hypsometric curve, width function, cumulative area distribution and area-slope demonstrate that SIBERIA can simulate the experimental model landscape during development (i.e. transient landscapes). Copyright (C) 2002 John Wiley Sons, Ltd.},
author = {Hancock, G. R. and Willgoose, G. R.},
doi = {10.1002/esp.414},
isbn = {0197-9337},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {Digital elevation model,Geomorphology,Hydrology,Landscape simulation,SIBERIA},
number = {12},
pages = {1321--1334},
title = {{The use of a landscape simulator in the validation of the Siberia landscape evolution model: Transient landforms}},
volume = {27},
year = {2002}
}
@article{Hancock2017,
abstract = {Landscape Evolution Modelling (LEM) technologies provide a means by which it is possible to simulate the long-term geomorphic stability of a conceptual rehabilitated landform. However, simulations rarely consider the potential effects of anthropogenic climate change and consequently risk not accounting for the range of rainfall variability that might be expected in both the near and far future. One issue is that high resolution (both spatial and temporal) rainfall projections incorporating the potential effects of greenhouse forcing are required as input. However, projections of rainfall change are still highly uncertain for many regions, particularly at sub annual/seasonal scales. This is the case for northern Australia, where a decrease or an increase in rainfall post 2030 is considered equally likely based on climate model simulations. The aim of this study is therefore to investigate a spatial analogue approach to develop point scale hourly rainfall scenarios to be used as input to the CAESAR - Lisflood LEM to test the sensitivity of the geomorphic stability of a conceptual rehabilitated landform to potential changes in climate. Importantly, the scenarios incorporate the range of projected potential increase/decrease in rainfall for northern Australia and capture the expected envelope of erosion rates and erosion patterns (i.e. where erosion and deposition occurs) over a 100year modelled period. We show that all rainfall scenarios produce sediment output and gullying greater than that of the surrounding natural system, however a ‘wetter' future climate produces the highest output. Importantly, incorporating analogue rainfall scenarios into LEM has the capacity to both improve landform design and enhance the modelling software. Further, the method can be easily transferred to other sites (both nationally and internationally) where rainfall variability is significant and climate change impacts are uncertain.},
author = {Hancock, G.R. and Verdon-Kidd, D. and Lowry, J.B.C.},
doi = {10.1016/j.scitotenv.2017.04.038},
issn = {00489697},
journal = {Science of The Total Environment},
pages = {109--121},
title = {{Soil erosion predictions from a landscape evolution model – An assessment of a post-mining landform using spatial climate change analogues}},
url = {http://www.sciencedirect.com/science/article/pii/S0048969717308665},
volume = {601},
year = {2017}
}
@article{Hancock2010,
author = {Hancock, GR and Lowry, JBC and Coulthard, TJ and Evans, KG and Moliere, DR},
doi = {10.1002/esp.1863},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
month = {may},
number = {8},
pages = {863--875},
title = {{A catchment scale evaluation of the SIBERIA and CAESAR landscape evolution models}},
url = {http://doi.wiley.com/10.1002/esp.1863},
volume = {35},
year = {2010}
}
@article{Harmand2004,
author = {Harmand, Dominique and Lejeune, Olivier and Jaillet, St?phane and Allouc, Jacques and Occhietti, Serge and Brulhet, Jacques and Fauvel, Pierre Jean and Hamelin, Bruno and Laurain, Michel and {Le Roux}, Jacques and Marre, Alain and Pons-Branchu, Edwige and Quinif, Yves and Devos, Alain},
doi = {10.3406/quate.2004.1777},
issn = {1142-2904},
journal = {Quaternaire},
number = {4},
pages = {305--318},
title = {{Dynamique de l'?rosion dans le Barrois et le Perthois (Est du Bassin de Paris) : incision et karstification dans les bassins-versants de la Marne, de la Saulx et de l'Ornain. [Dynamics of erosion in the Barrois and the Perthois regions (East of the Paris }},
url = {http://www.persee.fr/web/revues/home/prescript/article/quate{\_}1142-2904{\_}2004{\_}num{\_}15{\_}4{\_}1777},
volume = {15},
year = {2004}
}
@article{Hasbargen2000a,
abstract = {Do drainage basins develop static river networks when subject to steady forcing? While cur- rent landscape evolution models differ in formulation and implementation, they have the com- mon characteristic that when run for long times at constant forcing, they evolve to a static steady- state configuration in which erosion everywhere balances uplift rate. This results in temporally stationary ridge and valley networks. We have constructed a physical model of a drainage basin in which we can impose constant rainfall and uplift conditions. The model landscapes never be- come static, and they are not sensitive to initial surface conditions. Ridges migrate laterally, change length, and undergo topographic inversion (streams occupy former ridge locations). Lat- eral stream migration can also produce strath terraces. This occurs without any change in exter- nal forcing, so the terraces must be considered autocyclic. The experimental drainage basin also exhibits autocyclic (internally generated) oscillations in erosion rate over a variety of time scales, despite constant forcing. The experimental landforms are clearly not perfect analogs of natural erosional networks, but the results raise the possibility that natural systems may be more dynamic than the current models would suggest, and that features like strath terraces that are generally interpreted in terms of external forcing may arise autocyclically as well.},
author = {Hasbargen, L. E. and Paola, C.},
doi = {10.1130/0091-7613(2000)28<1067:LIIAED>2.0.CO},
isbn = {0091-7613},
issn = {00917613},
journal = {Geology},
keywords = {Autocyclic,Landscape evolution,Strath,Topographic inversion},
number = {12},
pages = {1067--1070},
pmid = {2355021},
title = {{Landscape instability in an experimental drainage basin}},
volume = {28},
year = {2000}
}
@article{Hasbargen2003,
abstract = {The current suite of numerical landscape models suggest that, under steady forcing, erosional landscapes evolve to a static steady state in which erosion everywhere balances uplift. Among other things, this implies that the only limita- tion on our ability to predict the future configuration of a landscape is imperfect knowledge of initial conditions and stochastic forcing events (e.g. storms, earth- quakes). These are formidable obstacles to prediction, but they are apparently not the only ones. We have constructed a physical model of a drainage basin which erodes through several units of relief. We conducted several constantly forced rc runs at various base level fall and rainfall rates. The landscapes develop 3 * to 5 {\^{}} order stream networks, and erode by surface runoff, hillslope failures, and upstream migrating knickpoints. Within the constraints of an overall balance between uplift and erosion, interactions between streams and hillslopes result in spatially and temporally variable erosion rates. These results suggest that eroding drainage basins at steady forcing are intrinsically dynamic structures. Current numerical models do not exhibit the same level of erosional variability at steady forcing, suggesting that some feedback mechanisms may be missing from model formulations. The presence of inherent dynamism in eroding landscapes could seriously complicate predictions of local erosion rate, even if an average balance between uplift and erosion rate has been attained for a given drainage basin.},
author = {Hasbargen, Leslie E and Paola, Chris},
doi = {10.1029/135GM16},
isbn = {9781118668559},
journal = {Prediction in Geomorphology},
keywords = {Geomorphology{\&}{\#}8212,Geophysical Monograph,Geophysical Monograph Series,Mathematical models,Prediction in Geomorphology,doi:10.1029/135,doi:10.1029/135GM16,http://dx.doi.org/10.1029/135GM16,vol. 135},
pages = {231--240},
title = {{How predictable is local erosion rate in eroding landscapes?}},
year = {2003}
}
@article{Hancock2001,
abstract = {An experimental landscape simulator has been developed which uses a rainfall simulator to create overland flow and erosion. The simulator uses rainfall sprinklers that eliminate rainsplash and an artificial soil which has little cohesion. Experimental landscapes developed in the simulator evolved according to Howard's headward growth model. Elements of Glock's model could be identified during evolution (i.e. initiation and maximum extension), but other stages of this model were not observed (i.e. extension and integration). The Horton concept of cross-grading and micropiracy and stream piracy was not observed despite the dominance of overland flow, nor the groundwater headward growth mechanism proposed by Dunne, the latter due to experimental design, which eliminated any perched groundwater table. The experimental apparatus produced model landscapes that are scaled-down analogues of real world processes. Copyright {\{}{\textcopyright}{\}} 2001 John Wiley {\{}{\&}{\}} Sons, Ltd.},
author = {Hau{\ss}els, R. and Klenke, Th and Kropp, J. and Ebenh{\"{o}}h, W. and Hancock, Greg and Willgoose, Garry},
doi = {10.1002/hyp.143},
isbn = {1099-1085},
issn = {08856087},
journal = {Hydrological Processes},
keywords = {Evolution,Experiment lanscape,Geomorphology,Hydrology,Landscape simulator,Rainfall simulator,experimental landscape,geomorphology,hydrology,landscape evolution,landscape simulator,rainfall simulator},
month = {jan},
number = {1},
pages = {115--133},
publisher = {John Wiley {\&} Sons, Ltd.},
title = {{The interaction between hydrology and geomorphology in a landscape simulator experiment}},
url = {http://doi.wiley.com/10.1002/hyp.143},
volume = {15},
year = {2001}
}
@article{He2014,
author = {He, Jijun and Li, Xiaojuan and Jia, Lijuan and Gong, Huili and Cai, Qiangguo},
doi = {10.2136/sssaj2014.02.0063},
issn = {0361-5995},
journal = {Soil Science Society of America Journal},
number = {5},
pages = {1716},
title = {{Experimental study of rill evolution processes and relationships between runoff and erosion on clay loam and loess}},
url = {https://dl.sciencesocieties.org/publications/sssaj/abstracts/78/5/1716},
volume = {78},
year = {2014}
}

@article{Heng2009,
author = {Heng, B. C. Peter and Sander, Graham C. and Scott, Cecil F.},
title = {Modeling overland flow and soil erosion on nonuniform hillslopes: A finite volume scheme},
journal = {Water Resources Research},
volume = {45},
number = {5},
pages = {},
keywords = {soil erosion, multisize class, Saint-Venant equations, finite volume method, Hairsine-Rose},
doi = {https://doi.org/10.1029/2008WR007502},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2008WR007502},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008WR007502},
year = {2009}
}
@article{Hooshyar2019,
author = {Hooshyar, Milad and Singh, Arvind and Wang, Dingbao and Foufoula-Georgiou, Efi},
title = {Climatic Controls on Landscape Dissection and Network Structure in the Absence of Vegetation},
journal = {Geophysical Research Letters},
volume = {46},
number = {6},
pages = {3216-3224},
doi = {10.1029/2019GL082043},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019GL082043},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2019GL082043},
abstract = {Abstract Drainage networks emerge due to the movement of sediment driven by climatic and tectonic forcings. Previous observations revealed the dependence of drainage density (Dd) on climatic factors such as mean annual precipitation (MAP). Specifically, it has been observed in intermediate climate (~175 mm < MAP < 700 mm) that Dd decreases with increasing MAP. This declining trend has been argued to be attributed to biotic activity, that is, the dominance of vegetation growth over runoff erosive force. Using high-resolution topographic data from a physical experiment, we show that increasing rainfall may result in decreasing Dd even in the absence of biotic activity. Increasing rainfall rate results in narrower and less variable bifurcation angle and relatively longer links. The response of the evolving network in terms of bifurcation angle continues beyond the time when Dd has reached a new stable value, indicating that the network's topological response is relatively slower than the geomorphic response.},
year = {2019}
}

@article{Hooshyar2021,
author = {Hooshyar, Milad and Porporato, Amilcare},
title = {Mean Dynamics and Elevation-Contributing Area Covariance in Landscape Evolution Models},
journal = {Water Resources Research},
volume = {57},
number = {8},
pages = {e2021WR029727},
keywords = {channel instability, fluvial erosion, landscape evolution, turbulence, self-similarity, specific contributing area, Reynolds decomposition},
doi = {https://doi.org/10.1029/2021WR029727},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021WR029727},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021WR029727},
note = {e2021WR029727 2021WR029727},
year = {2021}
}


@article{Horton,
abstract = {The composition of the stream system of a drainage basin can be expressed quantitatively in terms of stream order, drainage density, bifurcation ratio, and stream-length ratio. Stream orders are so chosen that the fingertip or unbranched tributaries are of the 1st order; streams which receive 1st order tributaries, but these only, are of the 2d order; third order streams receive 2d or 1st and 2d order tributaries, and so on, until, finally, the main stream is of the highest order and characterizes the order of the drainage basin. Two fundamental laws connect the numbers and lengths of streams of different orders in a drainage basin: (1) The law of stream numbers. This expresses the relation between the number of streams of a given order and the stream order in terms of an inverse geometric series, of which the bifurcation ratio is the base. (2) The law of stream lengths expresses the average length of streams of a given order in terms of stream order, average length of streams of the 1st order, and the stream-length ratio. This law takes the form of a direct geometric series. These two laws extend Playfair's law and give it a quantitative meaning. The infiltration theory of surface runoff is based on two fundamental concepts: (1) There is a maximum or limiting rate at which the soil, when in a given condition, can absorb rain as it falls. This is the infiltration-capacity. It is a volume per unit of time. (2) When runoff takes place from any soil surface, there is a definite functional relation between the depth of surface detention {\^{I}}´, or the quantity of water accumulated on the soil surface, and the rate of surface runoff or channel inflow. For a given terrain there is a minimum length of overland flow required to produce sufficient runoff volume to initiate erosion. The critical length depends on surface slope, runoff intensity, infiltration-capacity, and resistivity of the soil to erosion. This is the most important single factor involved in erosion phenomena and, in particular, in connection with the development of stream systems and their drainage basins by aqueous erosion. The erosive force and the rate at which erosion can take place at a distance from the watershed line is directly proportional to the runoff intensity, in inches per hour, the distance , a function of the slope angle, and a proportionality factor , which represents the quantity of material which can be torn loose and eroded per unit of time and surface area, with unit runoff intensity, slope, and terrain. The rate of erosion is the quantity of material actually removed from the soil surface per unit of time and area, and this may be governed by either the transporting power of overland flow or the actual rate of erosion, whichever is smaller. If the quantity of material torn loose and carried in suspension in overland flow exceeds the quantity which can be transported, deposition or sedimentation on the soil surface will take place. On newly exposed terrain, resulting, for example, from the recession of a coast line, sheet erosion occurs first where the distance from the watershed line to the coast line first exceeds the critical length and sheet erosion spreads laterally as the width of the exposed terrain increases. Erosion of such a newly exposed plane surface initially develops a series of shallow, close-spaced, shoestring gullies or rill channels. The rills flow parallel with or are consequent on the original slope. As a result of various causes, the divides between adjacent rill channels are broken down locally, and the flow in the shallower rill channels more remote from the initial rill is diverted into deeper rills more closely adjacent thereto, and a new system of rill channels is developed having a direction of flow at an angle to the initial rill channels and producing a resultant slope toward the initial rill. This is called cross-grading. With progressive exposure of new terrain, streams develop first at points where the length of overland flow first exceeds the critical length , and streams starting at these points generally become the primary or highest-order streams of the ultimate drainage basins. The development of a rilled surface on each side of the main stream, followed by cross-grading, creates lateral slopes toward the main stream, and on these slopes tributary streams develop, usually one on either side, at points where the length of overland flow in the new resultant slope direction first exceeds the critical length . Cross-grading and recross-grading of a given portion of the area will continue, accompanied in each case by the development of a new order of tributary streams, until finally the length of overland flow within the remaining areas is everywhere less than the critical length . These processes fully account for the geometric-series laws of stream numbers and stream lengths. A belt of no erosion exists around the margin of each drainage basin and interior subarea while the development of the stream system is in progress, and this belt of no erosion finally covers the entire area when the stream development becomes complete. The development of interior divides between subordinate streams takes place as the result of competitive erosion, and such divides, as well as the exterior divide surrounding the drainage basin, are generally sinuous in plan and profile as a result of competitive erosion on the two sides of the divide, with the general result that isolated hills commonly occur along divides, particularly on cross divides, at their junctions with longitudinal divides. These interfluve hills are not uneroded areas, as their summits had been subjected to more or less repeated cross-grading previous to the development of the divide on which they are located. With increased exposure of terrain weaker streams may be absorbed by the stronger, larger streams by competitive erosion, and the drainage basin grows in width at the same time that it increases in length. There is, however, always a triangular area of direct drainage to the coast line intermediate between any two major streams, with the result that the final form of a drainage basin is usually ovoid or pear-shaped. The drainage basins of the first-order tributaries are the last developed on a given area, and such streams often have steep-sided, V-shaped, incised channels adjoined by belts of no erosion. The end point of stream development occurs when the tributary subareas have been so completely subdivided by successive orders of stream development that there nowhere remains a length of overland flow exceeding the critical length . Stream channels may, however, continue to develop to some extent through headward erosion, but stream channels do not, in general, extend to the watershed line. Valley and stream development occur together and are closely related. At a given cross section the valley cannot grade below the stream, and the valley supplies the runoff and sediment which together determine the valley and stream profiles. As a result of cross-grading antecedent to the development of new tributaries, the tributaries and their valleys are concordant with the parent stream and valley at the time the new streams are formed and remain concordant thereafter. Valley cross sections, when grading is complete, and except for first-order tributaries, are generally S-shaped on each side of the stream, with a point of contraflexure on the upper portion of the slope, and downslope from this point the final form is determined by a combination of factors, including erosion rate, transporting power, and the relative frequencies of occurrence of storms and runoff of different intensities. The longitudinal profile of a valley along the stream bank and the cross section of the valley are closely related, and both are related to the resultant slope at a given location. Many areas on which meager stream development has taken place, and which are commonly classified as youthful, are really mature, because the end point of stream development and erosion for existing conditions has already been reached. When the end point of stream and valley gradation has arrived in a given drainage basin, the remaining surface is usually concave upward, more or less remembling a segment of a parabaloid, ribbed by cross and longitudinal divides and containing interfluve hills and plateaus. This is called a {\^{a}}€{\oe}graded{\^{a}}€ surface, and it is suggested that the term {\^{a}}€{\oe}peneplain{\^{a}}€ is not appropriate, since this surface is neither a plane nor nearly a plane, nor does it approach a plane as an ultimate limiting form. The hydrophysical concepts applied to stream and valley development account for observed phenomena from the time of exposure of the terrain. Details of these phenomena of stream and valley development on a given area may be modified by geologic structures and subsequent geologic changes, as well as local variations of infiltration-capacity and resistance to erosion. In this paper stream development and drainage-basin topography are considered wholly from the viewpoint of the operation of hydrophysical processes. In connection with the Davis erosion cycle the same subject is treated largely with reference to the effects of antecedent geologic conditions and subsequent geologic changes. The two views bear much the same relation as two pictures of the same object taken in different lights, and one supplements the other. The Davis erosion cycle is, in effect, usually assumed to begin after the development of at least a partial stream system; the hydrophysical concept carries stream development back to the original newly exposed surface.},
archivePrefix = {arXiv},
arxivId = {10/25/2014},
author = {Horton, Robert E.},
eprint = {25/2014},
isbn = {0016-7606},
issn = {00167606},
journal = {Bulletin of the Geological Society of America},
number = {3},
pages = {275--370},
pmid = {224732},
primaryClass = {10},
title = {{No Title}},
url = {http://gsabulletin.gsapubs.org/cgi/doi/10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2},
volume = {56},
year = {1945}
}
@article{HORTON1945,
author = {HORTON, ROBERT E.},
doi = {10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2},
issn = {0016-7606},
journal = {Geological Society of America Bulletin},
number = {3},
pages = {275},
title = {{EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY}},
url = {http://gsabulletin.gsapubs.org/cgi/doi/10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2},
volume = {56},
year = {1945}
}

@article{Houssais2015,
  title = {Onset of {{Sediment Transport Is}} a {{Continuous Transition Driven}} by {{Fluid Shear}} and {{Granular Creep}}},
  volume = {6},
  issn = {2041-1723},
  doi = {10.1038/ncomms7527},
  abstract = {The onset of sediment transport is commonly believed to be an abrupt process, which influences our understanding of river erosion and landscape dynamics. Houssais et al. show instead a continuous transition from a creeping to a granular-flow regime by monitoring internal motion in a sediment bed.},
  language = {English},
  journal = {Nature Communications},
  author = {Houssais, Morgane and Ortiz, Carlos P. and Durian, Douglas J. and Jerolmack, Douglas J.},
  month = mar,
  year = {2015},
  pages = {6527}
}

@article{Houssais2016,
abstract = {Landscape evolution models typically parse the environment into different process domains, each with its own sediment transport law: e.g., soil creep, landslides and debris flows, and river bed-load and suspended-sediment transport. Sediment transport in all environments, however, contains many of the same physical ingredients, albeit in varying proportions: grain entrainment due to a shear force, that is a combination of fluid flow, particle-particle friction and gravity. We present a new take on the perspective originally advanced by Bagnold, that views the long profile of a hillsope-river-shelf system as a continuous gradient of decreasing granular friction dominance and increasing fluid drag dominance on transport capacity. Recent advances in understanding the behavior and regime transitions of dense granular systems suggest that the entire span of granular-to-fluid regimes may be accommodated by a single-phase rheology. This model predicts a material-flow effective friction (or viscosity) that changes with the degree of shear rate and confining pressure. We present experimental results confirming that fluid-driven sediment transport follows this same rheology, for bed and suspended load. Surprisingly, below the apparent threshold of motion we observe that sediment particles creep, in a manner characteristic of glassy systems. We argue that this mechanism is relevant for both hillslopes and rivers. We discuss the possibilities of unifying sediment transport across environments and disciplines, and the potential consequences for modeling landscape evolution.},
author = {Houssais, Morgane and Jerolmack, Douglas J},
doi = {10.1016/j.geomorph.2016.03.026},
issn = {0169555X},
journal = {Geomorphology},
keywords = {granular physics,landscape evolution,phase transitions},
title = {{Creepy landscapes : toward a unifying constitutive relation for sediment transport across environments ?}},
url = {http://dx.doi.org/10.1016/j.geomorph.2016.03.026},
year = {2016}
}
@book{Howard1987,
abstract = {Classification has log been b=practised by geomorphologists; the process of cclassifying landforms implies the existence of some theory or hypothesis for their formation, which may provide the basis for detailed work. Rivers have been classified frequently by different practitioners. Motivations have ranged from the desire to enhance understanding to the need to engineer or manage the river. It will be apparent that the characteristics of rivers empahsices in the varous classificatory approaches may vary widely, depending on the purpose of the classifier. The include the relationship of the river to its geologic envrionment, the characteristics of the sediment of which the channel is composed, the chenical composition of the water conveyed, and the species of fish and other life forms which inhabit the river},
address = {Blackwell, Oxford},
author = {Howard, AD Allan D.},
booktitle = {River channels: environment and process},
pages = {69--94},
title = {{Modelling fluvial systems: Rock-, Gravel-, and Sand-bed Channels}},
url = {http://erode.evsc.virginia.edu/papers/howard{\_}channel{\_}types.pdf},
year = {1987}
}
@article{Howard1994a,
author = {Howard, AD and Dietrich, WE},
journal = {Journal of Geophysical},
title = {{Modeling fluvial erosion on regional to continental scales}},
url = {http://onlinelibrary.wiley.com/doi/10.1029/94JB00744/full},
year = {1994}
}
@article{Howard1972,
author = {Howard, Alan D.},
doi = {10.1029/WR008i002p00532},
issn = {00431397},
journal = {Water Resources Research},
month = {apr},
number = {2},
pages = {532--532},
title = {{Correction [to ?Optimal angles of stream junction: Geometric, stability to capture, and minimum power criteria? by Alan D. Howard]}},
url = {http://doi.wiley.com/10.1029/WR008i002p00532},
volume = {8},
year = {1972}
}
@article{Howard1994,
abstract = {A drainage basin simulation model introduced here incorporates creep and threshold slumping and both detachment- and transport-limited fluvial processes. Fluvial erosion of natural slopes and headwater channels is argued to be dominantly detachment-limited. Such slopes undergo nearly parallel retreat and replacement with alluvial surfaces under fixed base level, in contrast with gradual slope decline for transport-limited conditions. The arrangement of divides and valleys is sensitive to intial conditions, although average morphology is insensitive.},
author = {Howard, Alan D.},
doi = {10.1029/94WR00757},
isbn = {0043-1397},
issn = {0043-1397},
journal = {Water Resources Research},
number = {7},
pages = {2261},
title = {{A detachment-limited model of drainage basin evolution}},
volume = {30},
year = {1994}
}
@article{HOWARD1983,
author = {HOWARD, ALAN D. and KERBY, GORDON},
doi = {10.1130/0016-7606(1983)94<739:CCIB>2.0.CO;2},
issn = {0016-7606},
journal = {Geological Society of America Bulletin},
number = {6},
pages = {739},
title = {{Channel changes in badlands}},
url = {http://gsabulletin.gsapubs.org/cgi/doi/10.1130/0016-7606(1983)94{\%}3C739:CCIB{\%}3E2.0.CO;2},
volume = {94},
year = {1983}
}

@article{Hu2021,
title = {Covariation of cross-divide differences in denudation rate and $\chi$: Implications for drainage basin reorganization in the Qilian Shan, northeast Tibet},
journal = {Earth and Planetary Science Letters},
volume = {562},
pages = {116812},
year = {2021},
issn = {0012-821X},
doi = {10.1016/j.epsl.2021.116812},
url = {https://www.sciencedirect.com/science/article/pii/S0012821X21000716},
author = {Kai Hu and Xiaomin Fang and Ken L. Ferrier and Darryl E. Granger and Zhijun Zhao and Gregory A. Ruetenik}
}
@article{Istanbulluoglu2005,
author = {Istanbulluoglu, Erkan and Bras, Rafael L.},
doi = {10.1029/2004JF000249},
isbn = {0148-0227},
issn = {21699011},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {channel initiation,drainage density,ecogeomorphology,landscape evolution,vegetation dynamics},
number = {2},
pages = {F02012},
title = {{Vegetation-modulated landscape evolution: Effects of vegetation on landscape processes, drainage density, and topography}},
url = {http://doi.wiley.com/10.1029/2004JF000249},
volume = {110},
year = {2005}
}
@article{Jeffery2014,
author = {Jeffery, M. Louise and Yanites, Brian J. and Poulsen, Christopher J. and Ehlers, Todd A.},
doi = {10.1002/2013JF002919},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {Central Andes,climate,hillslope,vegetation},
month = {jun},
number = {6},
pages = {1354--1375},
title = {{Vegetation-precipitation controls on Central Andean topography}},
url = {http://doi.wiley.com/10.1002/2013JF002919},
volume = {119},
year = {2014}
}
@article{Kennedy1995,
abstract = {A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described},
author = {Kennedy, J},
doi = {10.1109/ICNN.1995.488968},
isbn = {0-7803-2768-3},
issn = {1935-3812},
journal = {Encyclopedia of Machine Learning},
keywords = {learning method,particle swarm optimization,recurrent neural network,spiking neural network},
number = {11},
pages = {685--691},
pmid = {20371407},
title = {{Particle swarm optimization}},
url = {http://link.springer.com/content/pdf/10.1007/978-0-387-30164-8{\_}630.pdf},
volume = {46},
year = {2010}
}
@phdthesis{Kirby1971,
author = {Kirby, M. J.},
school = {http://www.geo.brown.edu/geocourses/geo292/papers.},
title = {{Hillslope process-response models based on the continuity equation}},
year = {1971}
}
@article{Kirby1985,
author = {Kirby, M. J.},
doi = {10.1111/j.1365-2389.1985.tb00316.x},
issn = {13652389},
journal = {Journal of Soil Science},
month = {mar},
number = {1},
pages = {97--121},
publisher = {Blackwell Publishing Ltd},
title = {{A basis for soil profile modelling in a geomorphic context}},
url = {http://doi.wiley.com/10.1111/j.1365-2389.1985.tb00316.x},
volume = {36},
year = {1985}
}
@article{Kirby1967,
abstract = {Reprint of 1967 paper; measurement over two years, rates, Scotland},
author = {Kirby, M.J.},
doi = {10.1086/627267},
issn = {0022-1376},
journal = {The Journal of Geology},
keywords = {1967,359-378,4,75,author,j,jul,kirkby,m,no,pp,published by,s,soil creep,source,surement and theory of,the journal of geology,university of chicago press,vol},
number = {4},
pages = {359--378},
title = {{Measurement and theory of soil creep}},
volume = {75},
year = {1967}
}
@book{Knighton2014,
abstract = {David Knighton's best-selling book looks at the wide range of forms developed by natural rivers and the processes responsible for that development. The book combines empirical and theoretical approaches, and provides a critical assessment of the many schools of thought which have emerged for dealing with adjustment in the fluvial system. It is fully illustrated throughout by a superb range of figures, photographs and tables.Starting with the network scale, the book examines the interaction of hillslopes, drainage networks and channels, and goes on to considerations of catchment hydrology and catchment denudation. Fluvial processes are analysed in detail, from the mechanics of flow to sediment transport and deposition. Detailing the major components of river channels, the book examines the nature of river adjustment, particularly with respect to equilibrium concepts, and concludes with a look at channel changes through time, affected by flood discharges, climatic change and human activities.},
author = {Knighton, David.},
isbn = {1134666616},
issn = {0004-0894},
pages = {400},
publisher = {Routledge},
title = {{Fluvial forms and processes: A new perspective}},
url = {https://books.google.com/books?id=evRRAwAAQBAJ{\&}pgis=1 https://books.google.com/books?hl=en{\&}lr={\&}id=vftQAwAAQBAJ{\&}pgis=1},
year = {2014}
}

@article{Kwang2021,
author = {Jeffrey S. Kwang  and Abigail L. Langston  and Gary Parker },
title = {The role of lateral erosion in the evolution of nondendritic drainage networks to dendricity and the persistence of dynamic networks},
journal = {Proceedings of the National Academy of Sciences},
volume = {118},
number = {16},
pages = {e2015770118},
year = {2021},
doi = {10.1073/pnas.2015770118},
URL = {https://www.pnas.org/doi/abs/10.1073/pnas.2015770118},
eprint = {https://www.pnas.org/doi/pdf/10.1073/pnas.2015770118}
}
@article{Lague2003,
abstract = {We present the results of an experimental study of topography dynamics under conditions of constant precipitation and uplift rate. The experiment is designed to develop a complete drainage network by the growth and propagation of erosion instabilities in response to tectonic perturbations. The quantitative analysis of topographic evolution is made possible by using telemetric lasers that perform elevation measurements at an excellent level of precision. We focus our study on the effect of initial surface organization and of uplift rate on both the transient dynamics and the steady state forms of topography. We show that the transient phase is strongly dependent on the initial internally drained area, which is found to decrease exponentially with time. The topography always reaches a steady state whose mean elevation depends linearly on uplift rate with a strictly positive value when uplift is zero. Steady state surfaces are characterized by a well-defined slope-area power law with a constant exponent of -0.12 and an amplitude that depends linearly on uplift rate with a strictly positive value when uplift is zero. These results are consistent with a stream power law erosion model that includes a nonnegligible threshold for particle detachment. Uncertainty regarding the sediment transport length is resolved by calibrating the transient dynamics with a surface process model. Reappraising published results on the linear dependency between mean elevation, or relief, and denudation rate, we suggest that an erosion threshold is worth considering for large-scale systems.},
author = {Lague, Dimitri and Crave, Alain and Davy, Philippe},
doi = {10.1029/2002JB001785},
isbn = {0148-0227},
issn = {01480227},
journal = {Journal of Geophysical Research: Solid Earth},
keywords = {Hydrology: Erosion and sedimentation,Hydrology: Geomorphology (1625),Tectonophysics: Continental tectonics-general (09,Tectonophysics: Instruments and techniques,experimental modeling,landscape evolution,numerical modeling,relief,tectonic geomorphology,topography},
month = {jan},
number = {B1},
pages = {ETG 3--1--ETG 3--20},
title = {{Laboratory experiments simulating the geomorphic response to tectonic uplift}},
url = {http://doi.wiley.com/10.1029/2002JB001785},
volume = {108},
year = {2003}
}
@misc{Lamb2015,
abstract = {River incision into bedrock drives the topographic evolution of mountainous terrain and may link climate, tectonics, and topography over geologic time scales. Despite its importance, the mechanics of bedrock erosion are not well understood because channel form, river hydraulics, sediment transport, and erosion mechanics coevolve over relatively long time scales that prevent direct observations, and because erosive events occur intermittently and are difficult and dangerous to measure. Herein we synthesize how flume experiments using erodible bedrock simulants are filling these knowledge gaps by effectively accelerating the pace of landscape evolution under reduced scale in the laboratory. We also build on this work by providing new theory for rock resistance to abrasion, thresholds for plucking by vertical entrainment, sliding and toppling, and by assessing bedrock-analog materials. Bedrock erosion experiments in the last 15. years reveal that the efficiency of rock abrasion scales inversely with the square of rock tensile strength, sediment supply has a dominant control over bed roughness and abrasion rates, suspended sediment is an efficient agent of erosion, and feedbacks with channel form and roughness strongly influence erosion rates. Erodibility comparisons across rock, concrete, ice, and foam indicate that, for a given tensile strength, abrasion rates are insensitive to elasticity. The few experiments that have been conducted on erosion by plucking highlight the importance of block protrusion height above the river bed, and the dominance of block sliding and toppling at knickpoints. These observations are consistent with new theory for the threshold Shields stress to initiate plucking, which also suggests that erosion rates in sliding- and toppling-dominated rivers are likely transport limited. Major knowledge gaps remain in the processes of erosion via plucking of bedrock blocks where joints are not river-bed parallel; waterfall erosion by toppling and plunge-pool erosion; feedbacks between weathering and physical erosion; erosional bedforms; and morphodynamic feedbacks between channel form and erosion rates. Despite scaling challenges, flume experiments continue to provide much needed tests of existing bedrock-erosion theory, force development of new theory, and yield insight into the mechanics of landscapes.},
author = {Lamb, Michael P. and Finnegan, Noah J. and Scheingross, Joel S. and Sklar, Leonard S.},
booktitle = {Geomorphology},
doi = {10.1016/j.geomorph.2015.03.003},
issn = {0169555X},
keywords = {Abrasion,Bedrock erosion,Flume experiments,Fluvial geomorphology,Plucking,River incision},
pages = {33--55},
title = {{New insights into the mechanics of fluvial bedrock erosion through flume experiments and theory}},
volume = {244},
year = {2015}
}
@article{Leopold1953,
abstract = {Quantitive measurement of some of the hydraulic factors that help to determine the shpae of natural stream channels: depth, width, belocity, and suspended load, and how they vary with discharg as simple power functions. Their interrelations are described by the term "hydraulic geometry".},
author = {Leopold, Luna B. and {Maddock Jnr}, Thomas. and Maddock, Thomas Jr.},
isbn = {978-0-607-69460-4},
issn = {2330-7102},
journal = {Geological Survey Professional Paper 252},
pages = {1--56},
pmid = {2094},
title = {{The Hydraulic Geomtry of Stream Channels and Some Physiographic Implications}},
year = {1953}
}
@article{LEROUX1998,
author = {LEROUX, J and HARMAND, D},
doi = {10.1016/S0985-3111(98)80001-6},
issn = {09853111},
journal = {Geodinamica Acta},
month = {aug},
number = {4},
pages = {149--162},
title = {{Contr?le morphostructural de l'histoire d'un r?seau hydrographique: le site de capture de la Moselle}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0985311198800016},
volume = {11},
year = {1998}
}
@article{Lisle2017,
author = {Lisle, I.G. and Sander, G.C. and Parlange, J.-Y. and Rose, C.W. and Hogarth, W.L. and Braddock, R.D. and Stagnitti, F. and Lockington, D.A. and Jomaa, S. and Cheraghi, M. and Barry, D.A.},
title = {Transport Time Scales in Soil Erosion Modeling},
journal = {Vadose Zone Journal},
volume = {16},
number = {12},
pages = {vzj2017.06.0121},
doi = {10.2136/vzj2017.06.0121},
url = {https://acsess.onlinelibrary.wiley.com/doi/abs/10.2136/vzj2017.06.0121},
eprint = {https://acsess.onlinelibrary.wiley.com/doi/pdf/10.2136/vzj2017.06.0121},
abstract = {Core Ideas Erosion timescales inherent in the Hairsine–Rose soil erosion are exposed. Both fast and slow timescales are isolated and can be estimated a priori. The maximum sediment settling rate controls the possible range of timescales. In practice, the full range of erosion timescales are not seen in flume experiments. Unlike sediment transport in rivers, erosion of agricultural soil must overcome its cohesive strength to move soil particles into suspension. Soil particle size variability also leads to fall velocities covering many orders of magnitude, and hence to different suspended travel distances in overland flow. Consequently, there is a large range of inherent timescales involved in transport of eroded soil. For conditions where there is a constant rainfall rate and detachment is the dominant erosion mechanism, we use the Hairsine–Rose (HR) model to analyze these timescales, to determine their magnitude (bounds) and to provide simple approximations for them. We show that each particle size produces both fast and slow timescales. The fast timescale controls the rapid adjustment away from experimental initial conditions—this happens so quickly that it cannot be measured in practice. The slow timescales control the subsequent transition to steady state and are so large that true steady state is rarely achieved in laboratory experiments. Both the fastest and slowest timescales are governed by the largest particle size class. Physically, these correspond to the rate of vertical movement between suspension and the soil bed and the time to achieve steady state, respectively. For typical distributions of size classes, we also find that there is often a single dominant timescale that governs the growth in the total mass of sediment in the non-cohesive deposited layer. This finding allows a considerable simplification of the HR model, leading to analytical expressions for the evolution of suspended and deposited layer concentrations.},
year = {2017}
}
@article{Leyland2009,
author = {Leyland, Julian and Darby, Stephen E},
doi = {10.1002/esp.1872},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
month = {nov},
number = {14},
pages = {1878--1893},
title = {{Effects of Holocene climate and sea-level changes on coastal gully evolution: insights from numerical modelling}},
url = {http://doi.wiley.com/10.1002/esp.1872},
volume = {34},
year = {2009}
}


@article{Mahmoodabadi2016,
abstract = {Soil erosion during rainfall is a complex phenomenon resulting from detachment by raindrop impact and overland flow. The objective of this study is to investigate the transportation rate of splash load (SL) and that of wash load (WL) and their relative contributions to the rain-induced erosion rate affected by rain intensity, slope gradient and particle size distribution. A total of 60 simulation runs were carried out using a detachment tray under simulated rainfall with no inflow. The experiments were done on two soil samples (aggregate sizes finer than 2 and 4.75mm) from an agricultural land use at different rain intensities (57 and 80mmh−1) and varying slope gradients (0.5{\%}, 2.5{\%}, 5{\%}, 10{\%}, and 20{\%}). Under unsteady state conditions, WL showed relatively high dependency on slope gradient, whereas approaching steady state conditions, nearly similar values of WL occurred at different slopes. SL and WL increased with increasing rain intensity and slope gradient, implying the importance of rain-induced erosion on bare agriculture lands especially at steeper slopes. The ratio of WL/SL decreased when slope gradient increased; however, WL increased more significantly than SL as soil aggregates became finer. The result indicates that at all the slope gradients, WL was much larger than SL, indicating that wash load significantly contributes to the rain-induced erosion in the agricultural soil. Furthermore, with increasing slope gradient, the contribution of wash load to rain-induced erosion decreased, while it was greater in the soil containing finer aggregates. Also, with increasing rain intensity at lower slope gradients ({\textless}10{\%}), further increase in splashed materials than that in washed materials occurred, whereas the reverse order was found at steeper slopes ({\textgreater}10{\%}). The finding of this study revealed that the rain-induced erosion was transport-limited at the gentler slopes, whereas at the steeper slopes, it shifted to detachment-limited conditions.},
author = {Mahmoodabadi, Majid and Sajjadi, Sara Arjmand},
doi = {10.1016/j.geomorph.2015.10.010},
issn = {0169555X},
journal = {Geomorphology},
pages = {159--167},
title = {{Effects of rain intensity, slope gradient and particle size distribution on the relative contributions of splash and wash loads to rain-induced erosion}},
volume = {253},
year = {2016}
}
@article{Maritan1996,
abstract = {Seemingly unrelated empirical hydrologic laws and several experimental facts related to the fractal geometry of the river basin are shown to hand a natural explanation into a simple finite-size scaling ansatz for the power laws exhibited by cumulative distributions of river basin areas. Our theoretical predictions suggest that the exponent of the power law is directly related to a suitable fractal dimension of the boundaries, to the elongation of the basin, and to the scaling exponent of mainstream lengths. Observational evidence from digital elevation maps of natural basins and numerical simulations for optimal channel networks are found to be in good agreement with the theoretical predictions. Analytical results for Scheidegger s trees are exactly reproduced. PACS number(s): 64.60.Ht, 68.70.+w, 92.40.Gc, 92.40.Fb I. INTR.ODUCTION Power laws, which are the signature of fractal behav-ior [1], have been experimentally observed over a huge range of scales in probability distributions describing river basin morphology [2 — 6]. As a part of the river basin, Quvial networks display a rich variety of fractal and multi{\&}actal structures [1,7] whose dynamic origin and geometrical description are of greatest importance both {\&}om the practical point of view and for a deeper understanding of how natural events occur. The starting point for this work is the seminal work of Hack [8]. He demonstrated the applicability and the far-reaching implications of a power function by relating the area of a drainage basin with the length of the principal river of the basin, for rivers of the Shenandoah Valley and adjacent mountains in Virginia. This empirical relation is widely accepted nowadays although its spatial range of validity [9 — ll] and the inference of the complex role},
archivePrefix = {arXiv},
arxivId = {arXiv:cond-mat/9808244v3},
author = {Maritan, Amos and Rinaldo, Andrea and Rigon, Riccardo and Giacometti, Achille and Rodriguez-Iturbe, Ignacio},
doi = {10.1103/PhysRevE.53.1510},
eprint = {9808244v3},
issn = {1063-651X},
journal = {Physical Review E},
number = {2},
pages = {1510--1515},
pmid = {9964414},
primaryClass = {arXiv:cond-mat},
title = {{Scaling laws for river networks}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.53.1510},
volume = {53},
year = {1996}
}
@article{Martin2000,
abstract = {Many recent models of landscape evolution have used a diffusion relation to simulate hillslope transport. In this study, a linear diffusion equation for slow, quasi-continuous mass movement (e.g., creep), which is based on a large data compilation, is adopted in the hillslope model. Transport relations for rapid, episodic mass movements are based on an extensive data set covering a 40-yr period from the Queen Charlotte Islands, British Columbia. A hyperbolic tangent relation, in which transport increases nonlinearly with gradient above some threshold gradient, provided the best fit to the data. Model runs were undertaken for typical hillslope profiles found in small drainage basins in the Queen Charlotte Islands. Results, based on linear diffusivity values defined in the present study, are compared to results based on diffusivities used in earlier studies. Linear diffusivities, adopted in several earlier studies, generally did not provide adequate approximations of hillslope evolution. The nonlinear transport relation was tested and found to provide acceptable simulations of hillslope evolution. Weathering is introduced into the final set of model runs. The incorporation of weathering into the model decreases the rate of hillslope change when theoretical rates of sediment transport exceed sediment supply. The incorporation of weathering into the model is essential to ensuring that transport rates at high gradients obtained in the model reasonably replicate conditions observed in real landscapes. An outline of landscape progression is proposed based on model results. Hillslope change initially occurs at a rapid rate following events that result in oversteepened gradients (e.g., tectonic forcing, glaciation, fluvial undercutting). Steep gradients are eventually eliminated and hillslope transport is reduced significantly. (C) 2000 Elsevier Science B.V. All rights reserved.},
author = {Martin, Yvonne},
doi = {10.1016/S0169-555X(99)00127-0},
isbn = {0169-555X},
issn = {0169555X},
journal = {Geomorphology},
keywords = {Creep,Erosion,Landform evolution,Landslides,Mass movements,Weathering},
number = {1-2},
pages = {1--21},
title = {{Modelling hillslope evolution: Linear and nonlinear transport relations}},
volume = {34},
year = {2000}
}
@article{Massong2000,
author = {Massong, T. M. and Montgomery, D. R.},
doi = {10.1130/0016-7606(2000)112<591:IOSSLA>2.0.CO;2},
issn = {0016-7606},
journal = {Geological Society of America Bulletin},
month = {apr},
number = {4},
pages = {591--599},
publisher = {Geological Society of America},
title = {{Influence of sediment supply, lithology, and wood debris on the distribution of bedrock and alluvial channels}},
url = {http://gsabulletin.gsapubs.org/cgi/doi/10.1130/0016-7606(2000)112{\%}3C591:IOSSLA{\%}3E2.0.CO;2},
volume = {112},
year = {2000}
}


@Article{Meena2019,
AUTHOR = {Meena, Sansar Raj and Gudiyangada Nachappa, Thimmaiah},
TITLE = {Impact of spatial resolution of digital elevation model on landslide susceptibility Mapping: A Case Study in Kullu Valley, Himalayas},
JOURNAL = {Geosciences},
VOLUME = {9},
YEAR = {2019},
NUMBER = {8},
ARTICLE-NUMBER = {360},
URL = {https://www.mdpi.com/2076-3263/9/8/360},
ISSN = {2076-3263},
DOI = {10.3390/geosciences9080360}
}


@article{McGuire2016,
author = {McGuire, Luke A. and Pelletier, Jon D.},
doi = {10.1002/esp.3837},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {base level,drainage network,numerical model,valley spacing},
month = {mar},
number = {4},
pages = {460--472},
title = {{Controls on valley spacing in landscapes subject to rapid base-level fall}},
url = {http://doi.wiley.com/10.1002/esp.3837},
volume = {41},
year = {2016}
}
@article{McGuire2013,
author = {McGuire, Luke A. and Pelletier, Jon D. and G{\'{o}}mez, Jos{\'{e}} A. and Nearing, Mark A.},
doi = {10.1002/jgrf.20028},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {drainage network,erosion,numerical model,rill},
month = {mar},
number = {1},
pages = {241--256},
title = {{Controls on the spacing and geometry of rill networks on hillslopes: Rain splash detachment, initial hillslope roughness, and the competition between fluvial and colluvial transport}},
url = {http://doi.wiley.com/10.1002/jgrf.20028},
volume = {118},
year = {2013}
}

@article{McMaster2002,
author = {McMaster, Kevin J.},
title = {Effects of digital elevation model resolution on derived stream network positions},
journal = {Water Resources Research},
volume = {38},
number = {4},
pages = {13-1-13-8},
keywords = {streamflow, terrain modeling, digital elevation model (DEM), resolution, hydrologic networks, hillslope length},
doi = {10.1029/2000WR000150},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000WR000150},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000WR000150},
abstract = {This study examines the effect of digital elevation model (DEM) resolution on the positional accuracy of derived hydrologic networks and quantitatively confirms that DEM resolution should be greater than the average hillslope length when used for hydrologic modeling. Seven hundred kilometers of mapped stream networks are compared to stream networks derived from 17 DEMs with resolutions ranging from 30 m to 3 km. Comparison between predicted and mapped streams reveals that accuracy of predicted stream locations decays quickly beyond a DEM resolution of 180 m. A new application of Gyasi-Agyei et al.'s [1995] DEM resolution suitability test based on average slope and vertical resolution indicates an average hillslope length of between 150 and 180 m. Tarboton et al.'s [1991] method of determining average hillslope length based on slope and accumulation areas reconfirms the length to be 150 m and verifies the link between network accuracy and hillslope scale. Two algorithms are used to derive stream networks: the D∞ algorithm [Tarboton, 1997], which allows for flow dispersion, and the D8 algorithm [O'Callaghan and Mark, 1984], which does not. A comparison between the D8 and D∞ algorithms shows that modeling flow dispersion is not necessary in steep terrain, as both algorithms performed equally well. However, the D∞ algorithm is found to be less susceptible to modeling erroneous hillside flow convergence, making it preferable to the D8 algorithm when used by Tarboton et al.'s [1991] method of determining the average hillslope lengths. Finally, field observation indicates that predicted first- and second-order streams tend to exist when predicted; however, mapped streams have a higher positional accuracy.},
year = {2002}
}





@misc{Meinhardt1982,
author = {Meinhardt, H},
doi = {10.1016/S0070-2153(07)81001-5},
isbn = {9780124886209},
issn = {0070-2153},
number = {March},
pages = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=},
pmid = {18023723},
title = {{Models of biological pattern formation}},
url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.388.7697{\&}rep=rep1{\&}type=pdf{\#}page=55 http://scholar.google.com/scholar?hl=en{\&}btnG=Search{\&}q=intitle:Models+of+Biological+Pattern+Formation{\#}0 https://www.researchgate.net/profile/Hans{\_}Meinhardt/publicat},
year = {1982}
}
@article{MEINHARDT1976,
abstract = {Complex linear appearing structures and networks (e.g. blood vessels, leaf veins, nerves) are formed reproducibly during the development of nearly every organism, but the molecular mechanism leading to such patterns is still unknown. A model is proposed in which a few simple coupled biochemical reactions are able to generate such structures. Among undifferentiated cells, a local peak of differentiation-inducing substance (activator) is formed by autocatalysis and lateral inhibition. The activator peak triggers the differentiation of the cell at that location. Due to changes in metabolism, the differentiated cell repels the activator peak and drives it to a neighbouring cell which then also differentiates. The repulsion between the activator peak and the already differentiated cells forces the activator peak to move ahead of the tip of the extending filament. Long filaments of differentiated cells may be formed, which can split, branch laterally, reconnect with each other and grow towards specific target cells. Partial differential equations describing the mutual interaction of the substances involved were presented and solved with a computer. The resulting patterns show self-regulating properties and other features found in the leaf vascular system, the pattern of tracheae in insect epidermis, and other biological networks.},
author = {Meinhardt, H.},
doi = {10.1111/j.1432-0436.1976.tb01478.x},
issn = {03014681},
journal = {Differentiation},
keywords = {Biological,Cell Differentiation,Cell Movement,Cells,Growth Substances,Mathematics,Models,Morphogenesis,Plants},
month = {oct},
number = {1-3},
pages = {117--123},
pmid = {1010155},
title = {{Models and hypotheses}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/1010155 http://linkinghub.elsevier.com/retrieve/pii/S0301468111610736},
volume = {6},
year = {1976}
}
@incollection{Meinhardt2008,
abstract = {An inroad into an understanding of the complex molecular interactions on which development is based can be achieved by uncovering the minimum requirements that describe elementary steps and their linkage. Organizing regions and other signaling centers can be generated by reactions that involve local self-enhancement coupled to antagonistic reactions of longer range. More complex patterns result from a chaining of such reactions in which one pattern generates the prerequisites for the next. Patterning along the single axis of radial symmetric animals including the small freshwater polyp hydra can be explained in this way. The body pattern of such ancestral organisms evolved into the brain of higher organisms, while trunk and midline formation are later evolutionary additions. The equivalent of the hydra organizer is the blastopore, for instance, the marginal zone in amphibians. It organizes the anteroposterior axis. The Spemann organizer, located on this primary organizer, initiates and elongates the midline, which is responsible for the dorsoventral pattern. In contrast, midline formation in insects is achieved by an inhibitory signal from a dorsal organizer that restricts the midline to the ventral side. Thus, different modes of midline formation are proposed to be the points of no return in the separation of phyla. The conversion of the transient patterns of morphogenetic signaling into patterns of stable gene activation can be achieved by genes whose gene products have a positive feedback on the activity of their own gene. If several such autoregulatory genes mutually exclude each other, a cell has to make an unequivocal decision to take a particular pathway. Under the influence of a gradient, sharply confined regions with particular determinations can emerge. Borders between regions of different gene activities, and the areas of intersection of two such borders, become the new signaling centers that initiate secondary embryonic fields. As required for leg and wing formation, these new fields emerge in pairs at defined positions, with defined orientation and left-right handedness. Recent molecular-genetic results provide strong support for theoretically predicted interactions. By computer simulations it is shown that the regulatory properties of these models correspond closely to experimental observations (animated simulations are available at www.eb.tuebingen.mpg.de/meinhardt). ?? 2008 Elsevier Inc. All rights reserved.},
author = {Meinhardt, Hans},
doi = {10.1016/S0070-2153(07)81001-5},
isbn = {0123742536},
issn = {00702153},
number = {March},
pages = {1--63},
pmid = {18023723},
title = {{Models of biological pattern formation: From elementary steps to the organization of embryonic axes}},
volume = {81},
year = {2008}
}
@article{Montgomery1992,
abstract = {Since the 1940s it has been proposed that landscape dissection into distinct valleys is limited by a threshold of channelization that sets a finite scale to the landscape. This threshold is equal to the hillslope length that is just shorter than that necessary to support a channel head. A field study supports this hypothesis by showing that an empirically defined topographic threshold associated with channel head locations also defines the border between essentially smooth, undissected hillslopes and the valley bottoms to which they drain. This finding contradicts assertions that landscapes are scale-independent and suggests that landscape response to changes in climate or land use depends on the corresponding changes in the threshold of channelization.},
author = {Montgomery, D R and Dietrich, W E},
doi = {10.1126/science.255.5046.826},
isbn = {0036-8075},
issn = {0036-8075},
journal = {Science (New York, N.Y.)},
month = {feb},
number = {5046},
pages = {826--830},
pmid = {17756428},
title = {{Channel initiation and the problem of landscape scale.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17756428},
volume = {255},
year = {1992}
}


@article{Muthusamy2021,
title = {Understanding the effects of Digital Elevation Model resolution in urban fluvial flood modelling},
journal = {Journal of Hydrology},
volume = {596},
pages = {126088},
year = {2021},
issn = {0022-1694},
doi = {10.1016/j.jhydrol.2021.126088},
url = {https://www.sciencedirect.com/science/article/pii/S0022169421001359},
author = {Manoranjan Muthusamy and Mónica Rivas Casado and David Butler and Paul Leinster},
keywords = {Digital Elevation Model, Resolution, Fluvial flood, Urban flood, Flood extent, Flood depth},
abstract = {With the extensive use of 2D flood models, the resolution and quality of Digital Elevation Models (DEMs) have come under greater focus especially in urban hydrology. One of the major research areas, in this regard, is the effect of DEM resolution on flood modelling. This study first investigates the root causes of the impact of DEM resolution on urban fluvial flood modelling outputs using DEMs with grid resolutions ranging from 1 m to 50 m. The study then investigates how DEM resolution affects the definition and characterisation of the river channel and the consequences of this for the modelled results. For this purpose, a separate set of merged DEMs was generated where the river channel as defined by the 1 m resolution DEM is merged with coarser resolution DEMs. Data obtained during the flood event caused by Storm Desmond (2015) in Cockermouth (Cumbria, UK) was used for this study. The HEC-RAS 2D model was used for all of the simulations. The benchmark model obtained with the 1 m resolution DEM was calibrated using measured water levels at two locations within the rivers. Results show that there is a 30% increase in flood extent from 58.9 ha to 79.0 ha and a 150% increase in mean flood depth from 1.74 m to 4.30 m when the resolution reduces from a 1 m grid to a 50 m grid. The main reason for this is the increasing lack of definition of the river channel with an associated reduction in the estimated depth of the river resulting in reduced river channel conveyance. This then leads to an increase in the flood extent and depth especially in the immediate vicinity of the river. This effect is amplified when the DEM grid size is greater than the river width. When the 1 m resolution DEM for the river channel is used in conjunction with coarser resolution DEMs for the surrounding areas (merged DEMs), there is a significant improvement in the agreement between the modelled and the reference case (obtained from the benchmark model) flood extents and depths. The use of merged DEMs reduces the error in mean flood depth from 90% to 4% and reduces the overall RMSE in flood depths from 2.6 m to 0.9 m at 30 m resolution. The use of merged DEMs, where a higher resolution DEM is used to characterise the river channel in conjunction with, for example, a 30 m resolution DEM (e.g., the freely available NASA Shuttle Radar Topography Mission DEMs) for the wider area could be a cost-effective solution for locations where higher resolution DEMs may not be available.}
}





@article{Dietrich1989,
abstract = {An analysis of channel head locations provides insight into controls on drainage density, the response of landscapes to climatic change, and the delineation of source areas for channel network simulations. Channel heads and colluvial deposits were mapped in a roughly 2 km2 area near San Francisco, California, and, although channel heads are located within colluvial deposits in hollows, many such deposits do not support channel heads. Channel heads were classified as either gradual or abrupt. For either type of channel head, the channel reach immediately downslope may be contiguous with the channel network or may consist of a series of short discontinuous channel segments. The local valley slope at the channel head is inversely related to both source area and source-basin length as well as to the contributing area per unit contour length at the channel head. In contrast, valley slope does not vary with drainage area upslope of channel heads. Field observations and a similarity between predicted and observed area-slope relations suggest that the location of channel heads on steep slopes may be controlled by subsurface flow-induced instability of the colluvial fill. Preliminary field observations also suggest that abrupt channel heads on gentle slopes are controlled by seepage erosion, whereas gradual channel head locations appear to be governed by saturation overland flow. Consideration of the geometric relationship between source areas and the first-order drainages that contain them results in an inverse relation between mean source-basin length and drainage density.},
address = {Chichester, UK},
author = {Montgomery, David R. and Dietrich, William E.},
doi = {10.1029/WR025i008p01907},
institution = {Massachusetts Institute of Technology},
isbn = {0043-1397},
issn = {19447973},
journal = {Water Resources Research},
keywords = {Abrasion,BEDLOAD,Bedrock erosion,Conservation laws,Detachment-limited and transport-limited erosion,ENTRAINMENT,Flume experiments,Fluvial geomorphology,GRAVEL-BED STREAMS,LOAD,Landscape evolution model,MIXED-SIZE SEDIMENT,MOTION,MOVEMENT,Partial differential equations,Physical model,Plucking,RIVERS,River incision,River networks,Shields stress,Stream incision,Stream incision law,Synthetic landscape evolution,THRESHOLD,TRANSPORT,bank evolution models,bed evolution,bedform models,channel,channel head advance,channels,critical shear stress,doi:10.102,entrainment,erosion,flow conservation laws,flows,fluvial hydraulics,granular physics,hillslope,http://dx.doi.org/10.1029/2002GL015144,incipient motion,landscape evolution,landscape evolution model,model,modeling flow,morphodynamics,movement,one‐dimensional model,phase transitions,probabilistic methods,probability,protrusion,pseudoplastic fluid,river basin evolution,rivers,sediment transport,shear stress,transport,two‐dimensional model},
month = {aug},
number = {8},
pages = {1907--1918},
pmid = {25254474},
publisher = {Elsevier B.V.},
title = {{Source areas, drainage density, and channel initiation}},
url = {http://doi.wiley.com/10.1029/WR025i008p01907 http://www.ems-ph.org/doi/10.4171/IFB/315 http://dx.doi.org/10.1016/j.geomorph.2014.04.037{\%}5Cnhttp://linkinghub.elsevier.com/retrieve/pii/S0169555X14002402 http://www.ncbi.nlm.nih.gov/pubmed/25254468 http://lin},
volume = {25},
year = {1989}
}

@article{Litwin2022,
author = {Litwin, David G. and Tucker, Gregory E. and Barnhart, Katherine R. and Harman, Ciaran J.},
title = {Groundwater Affects the Geomorphic and Hydrologic Properties of Coevolved Landscapes},
journal = {Journal of Geophysical Research: Earth Surface},
volume = {127},
number = {1},
pages = {e2021JF006239},
keywords = {landscape evolution, groundwater, hillslope, Dupuit, drainage density, transmissivity},
doi = {https://doi.org/10.1029/2021JF006239},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021JF006239},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021JF006239},
note = {e2021JF006239 2021JF006239},
year = {2022}
}
@article{Malmud2004,
author = {Malamud, Bruce D. and Turcotte, Donald L. and Guzzetti, Fausto and Reichenbach, Paola},
title = {Landslide inventories and their statistical properties},
journal = {Earth Surface Processes and Landforms},
volume = {29},
number = {6},
pages = {687-711},
keywords = {landslides, earthquakes, erosion, natural hazards, frequency-size statistics, intensity scale},
doi = {10.1002/esp.1064},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/esp.1064},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/esp.1064},
year = {2004}
}




@article{Montgomery1988a,
author = {Montgomery, David R. and Dietrich, William E.},
doi = {10.1038/336232a0},
issn = {0028-0836},
journal = {Nature},
month = {nov},
number = {6196},
pages = {232--234},
title = {{Where do channels begin?}},
url = {http://www.nature.com/doifinder/10.1038/336232a0},
volume = {336},
year = {1988}
}
@article{Montgomery1988,
abstract = {The closer channels begin to drainage divides, the greater will be the number of channels that occupy a unit area, and consequently the more finely dissected will be the landscape. Hence, a key component of channel network growth and landscape evolution theories1-7, as well as models for topographically controlled catch-ment runoff8, should be the prediction of where channels begin. Little field data exist, however, either on channel head locations9-14 or on what processes act to initiate and maintain a channel14-17. Here we report observations from several soil-mantled regions of Oregon and California, which show that the source area above the channel head decreases with increasing local valley gradient for slopes ranging from 5 to 45 degrees. Our results support a predicted relationship between source area and slope for steep humid landscapes where channel initiation is by landsliding, but they contradict theoretical predictions for channel initiation by overland flow in gentle valleys. Our data also suggest that, for the same gradient, drier regions tend to have larger source areas.},
author = {Montgomery, David R. and Dietrich, William E.},
doi = {10.1038/336232a0},
isbn = {0028-0836},
issn = {0028-0836},
journal = {Nature},
number = {6196},
pages = {232--234},
title = {{Where do channels begin?}},
volume = {336},
year = {1988}
}
@article{Mudd2016,
author = {Mudd, Simon M.},
doi = {10.1002/esp.3923},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {cosmogenic nuclides,landscape evolution,tectonic geomorphology,transience},
month = {jan},
number = {1},
pages = {24--41},
title = {{Detection of transience in eroding landscapes}},
url = {http://doi.wiley.com/10.1002/esp.3923},
volume = {42},
year = {2016}
}
@article{Mudd2004,
author = {Mudd, Simon Marius and Furbish, David Jon},
doi = {10.1029/2003JF000087},
issn = {01480227},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {hillslope geomorphology,steady state landscapes,weathering},
month = {jun},
number = {F2},
pages = {n/a--n/a},
title = {{Influence of chemical denudation on hillslope morphology}},
url = {http://doi.wiley.com/10.1029/2003JF000087},
volume = {109},
year = {2004}
}
@article{Murray2014,
abstract = {Many studies focus on the emergence and development of rhythmic landscape patterns. In this contribution we explore the different behaviors found as patterns evolve; the trajectories that patterns exhibit as they transit from infinitesimal-amplitude perturbation to a statistically steady state (or in some cases to continued statistical evolution). The variety of behaviors observed, either through field and laboratory experiments or numerical modeling, can be reduced to four classes: (a) simple stabilization where predictions based on the initial growth of small perturbations corresponds with the characteristics of patterns observed in nature; (b) significant pattern coarsening en route to saturated wavelength, where non-linear interactions between finite-amplitude pattern elements change the geometric properties of a pattern as it approaches steady-state; (c) perpetual coarsening where the wavelength associated with the emerging pattern continues to grow over time and is only limited by physical boundaries or external constrains; (d) slow evolution toward a different attractor, a novel behavior observed in numerical modeling that involves profound temporal changes in pattern characteristics. Within these classes we also observe generalizable non-linear behaviors: dependence on initial conditions, the emergence of pattern-scale variables such as pattern defects, and the presence of multiple stable states. Predicting the shape of patterns to come remains a challenge - one that we suggest requires a range of modeling approaches to address both initial instabilities and the emergent properties of evolving patterns, which involve disparate forms of non-linear interactions. Consideration of generic system behaviors at the pattern scale could enhance future pattern formation studies, facilitating appropriate pairings of analysis approaches and pattern-evolution modes. {\textcopyright} 2013 John Wiley {\&} Sons, Ltd.},
author = {Murray, A. Brad and Goldstein, Evan B. and Coco, Giovanni},
doi = {10.1002/esp.3487},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {Emergent phenomena,Non-linear dynamics,Pattern formation},
month = {jan},
number = {1},
pages = {62--70},
title = {{The shape of patterns to come: From initial formation to long-term evolution}},
url = {http://doi.wiley.com/10.1002/esp.3487},
volume = {39},
year = {2014}
}
@article{Nanson2016,
abstract = {Until recently no universal agreement as to a philosophical or scientific methodological framework has been proposed to guide the study of fluvial geomorphology. An understanding of river form and process requires an understanding of the principles that govern the behaviour and evolution of alluvial rivers at the most fundamental level. To date, the investigations of such principles have followed four approaches: develop qualitative unifying theories that are usually untested; collect and examine data visually and statistically to define semi-quantitative relationships among variables; apply Newtonian theoretical and empirical mechanics in a reductionist manner; resolve the primary flow equations theoretically by assuming maximum or minimum outputs. Here we recommend not a fifth but an overarching philosophy to embrace all four: clarifying and formalising an understanding of the evolution of river channels and iterative directional changes in the context of least action principle (LAP), the theoretical basis of variational mechanics. LAP is exemplified in rivers in the form of maximum flow efficiency (MFE). A sophisticated understanding of evolution in its broadest sense is essential to understand how rivers adjust towards an optimum state rather than towards some other. Because rivers, as dynamic contemporary systems, flow in valleys that are commonly historical landforms and often tectonically determined, we propose that most of the world's alluvial rivers are over-powered for the work they must do. To remain stable they commonly evolve to expend surplus energy via a variety of dynamic equilibrium forms that will further adjust, where possible, to maximise their stability as much less common MFE forms in stationary equilibrium. This paper: 1. Shows that the theory of evolution is derived from, and applicable to, both the physical and biological sciences; 2. Focusses the development of theory in geomorphology on the development of equilibrium theory; 3. Proposes that river channels, like organisms, evolve teleomatically (progression towards an end-state by following natural laws) and iteratively (one stage forming the basis for the next) towards an optimal end-state; 4. Describes LAP as the methodological basis for understanding the self-adjustment alluvial channels towards MFE. 5. Acknowledges that whereas river channels that form within their unmodified alluvium evolve into optimal minimum-energy systems, exogenic variables, such as riparian or aquatic vegetation, can cause significant variations in resultant river-styles. We specifically attempt to address Luna Leopold's lament in 1994 that no clearly expressed philosophy explains the remarkable self-adjustment of alluvial channels.},
author = {Nanson, Gerald C. and Huang, He Qing},
doi = {10.1016/j.geomorph.2016.07.024},
issn = {0169555X},
journal = {Geomorphology},
title = {{A philosophy of rivers: Equilibrium states, channel evolution, teleomatic change and least action principle}},
year = {2016}
}
@incollection{Nelson2016,
address = {Chichester, UK},
author = {Nelson, Jonathan M. and McDonald, Richard R. and Shimizu, Yasuyuki and Kimura, Ichiro and Nabi, Mohamed and Asahi, Kazutake},
booktitle = {Tools in Fluvial Geomorphology},
doi = {10.1002/9781118648551.ch18},
keywords = {bank evolution models,bed evolution,bedform models,flow conservation laws,modeling flow,morphodynamics,one‐dimensional model,sediment transport,two‐dimensional model},
month = {apr},
pages = {412--441},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Modelling flow, sediment transport and morphodynamics in rivers}},
url = {http://doi.wiley.com/10.1002/9781118648551.ch18},
year = {2016}
}
@article{OCallaghan1984,
abstract = {The extraction of drainage networks from digital elevation data is important for quantitative studies in geomorphology and hydrology. A method is presented for extracting drainage networks from gridded elevation data. The method handles artificial pits introduced by data collection systems and extracts only the major drainage paths. Its performance appears to be consistent with the visual interpretation of drainage patterns from elevation contours.},
author = {O'Callaghan, John F. and Mark, David M.},
doi = {10.1016/S0734-189X(84)80011-0},
isbn = {0734-189X},
issn = {0734189X},
journal = {Computer Vision, Graphics, and Image Processing},
month = {dec},
number = {3},
pages = {323--344},
publisher = {Academic Press},
title = {{The extraction of drainage networks from digital elevation data}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0734189X84800110},
volume = {28},
year = {1984}
}
@inproceedings{Oliveto2010,
address = {Braunschweig, Germany, http://vzb.baw.de/e-medien/river-flow-2010/PDF/B2/B2{\_}14.pdf},
author = {Oliveto, G and Palma, D and Domenico, A. Di},
booktitle = {Proceedings of the International Conference on Fluvial Hydraulics},
isbn = {9783939230007},
keywords = {drainage basins,laboratory tests,river systems},
title = {{Scaling properties of laboratory-generated river networks}},
year = {2010}
}
@article{Orlandini2011,
author = {Orlandini, Stefano and Tarolli, Paolo and Moretti, Giovanni and {Dalla Fontana}, Giancarlo},
doi = {10.1029/2010WR009648},
issn = {00431397},
journal = {Water Resources Research},
month = {feb},
number = {2},
title = {{On the prediction of channel heads in a complex alpine terrain using gridded elevation data}},
url = {http://doi.wiley.com/10.1029/2010WR009648},
volume = {47},
year = {2011}
}
@misc{Palmer2008,
abstract = {A s humans have adapted river systems to meet their needs, the natural variability characteristic of rivers has been greatly reduced. Most rivers are no longer free to course across the landscape unimpeded by infrastruc-ture (Surian and Rinaldi 2003; Pinter 2005), and most major rivers no longer exhibit their historic range of flow variability (Postel and Richter 2003; Poff et al. 2007). Yet, flow variability over time and space is a fundamental characteristic of natural rivers and a river's " flow regime " , in concert with sediment inputs, determines not only geomorphic adjustments, but biotic composition and rates of key ecosystem processes, such as primary produc-tion (Poff et al. 1997). These adjustments, which include the lateral migration of channels and dynamic interac-tions between the streambed, floodplain, and riparian zone, are part of a healthy river's response to changes in the surrounding landscape and changes in discharge. In fact, these adjustments allow rivers to absorb disturbances and buffer the ecosystem and surrounding land from the impacts of floods and anthropogenic effects. The ability of rivers and their biota to respond to altered flow regimes is not, however, unbounded. Changes brought on by urbanization, excessive water withdrawals, or climate shifts that occur rapidly and lead to flows outside the natural range of variability will have important consequences for river ecosystems and the people who depend on them (Lettenmaier et al. 1999; Poff et al. 2002; Palmer et al. 2007). Native riverine biodiversity and productivity may decline, water quality for human consumption may be compromised, and in some regions, the risk of flooding, with concomitant damage to property and people, may increase (Bunn and Arthington 2002; Allan et al. 2005; Naiman et al. 2005). While the effects of global change on water availability and sustainability of river ecosystem services have received attention (V{\"{o}}r{\"{o}}smarty et al. 2000; Alcamo et al. 2003a; Milly et al. 2005; Schr{\"{o}}ter et al. 2005), the over-lapping impacts of climate change and the impacts caused Major rivers worldwide have experienced dramatic changes in flow, reducing their natural ability to adjust to and absorb disturbances. Given expected changes in global climate and water needs, this may create serious problems, including loss of native biodiversity and risks to ecosystems and humans from increased flooding or water short-ages. Here, we project river discharge under different climate and water withdrawal scenarios and combine this with data on the impact of dams on large river basins to create global maps illustrating potential changes in dis-charge and water stress for dam-impacted and free-flowing basins. The projections indicate that every populated basin in the world will experience changes in river discharge and many will experience water stress. The magni-tude of these impacts is used to identify basins likely and almost certain to require proactive or reactive manage-ment intervention. Our analysis indicates that the area in need of management action to mitigate the impacts of climate change is much greater for basins impacted by dams than for basins with free-flowing rivers. Nearly one billion people live in areas likely to require action and approximately 365 million people live in basins almost cer-tain to require action. Proactive management efforts will minimize risks to ecosystems and people and may be less costly than reactive efforts taken only once problems have arisen. Front Ecol Environ 2008; 6(2): 81–89, doi:10.1890/060148},
author = {Palmer, Margaret A. and {Reidy Liermann}, Catherine A. and Nilsson, Christer and Fl{\"{o}}rke, Martina and Alcamo, Joseph and Lake, P. Sam and Bond, Nick},
booktitle = {Frontiers in Ecology and the Environment},
doi = {10.1890/060148},
isbn = {1540-9295},
issn = {15409295},
number = {2},
pages = {81--89},
title = {{Climate change and the world's river basins: Anticipating management options}},
volume = {6},
year = {2008}
}
@article
{randey2016,
abstract = {A plenty of models exist for study of the soil erosion and sediment yield processes. However, these models vary significantly in terms of their capability and complexity, input requirements, representation of processes, spatial and temporal scale accountability, practical applicability, and types of output they provide. The present study reviews 50 physically based soil erosion and sediment yield models with respect to these factors including shortcomings and strengths. The literature generally suggests the use of models like SWAT, WEPP, AGNPS, ANSWERS and SHETRAN for soil erosion and sediment studies. Most of the developed soil erosion and sediment yield models are capable of simulating soil detachment and sediment delivery processes at hillslope scale; a limited development was found in the field of reservoir siltation and channel erosion processes. The study proposes a guideline for selection of an appropriate model to the reader for a given application or case study. The future research suggested to improve the simulation and prediction capability of physically based soil erosion and sediment yield models, and should focus on incorporation of improved global web based weather database, inclusion of sediment associated water quality and gully erosion simulation module, and improvement in reservoir siltation and channel erosion simulation processes.},
author = {Pandey, Ashish and Himanshu, Sushil K. and Mishra, S.K. and Singh, Vijay P.},
doi = {10.1016/j.catena.2016.08.002},
issn = {03418162},
journal = {Catena},
pages = {595--620},
title = {{Physically based soil erosion and sediment yield models revisited}},
volume = {147},
year = {2016}
}
@article{Paola2011,
author = {Paola, Chris and Leeder, Mike},
doi = {10.1038/469038a},
issn = {0028-0836},
journal = {Nature},
month = {jan},
number = {7328},
pages = {38--39},
publisher = {Nature Research},
title = {{Environmental dynamics: Simplicity versus complexity}},
url = {http://www.nature.com/doifinder/10.1038/469038a},
volume = {469},
year = {2011}
}
@article{Paola2009,
abstract = {The growth of quantitative analysis and prediction in Earth-surface science has been accompanied by growth in experimental stratigraphy and geomorphology. Experimenters have grown increasingly bold in targeting landscape elements from channel reaches up to the entire erosional networks and depositional basins, often using very small facilities. The experiments produce spatial structure and kinematics that, although imperfect, compare well with natural systems despite differences of spatial scale, time scale, material properties, and number of active processes. Experiments have been particularly useful in studying a wide range of forms of self-organized (autogenic) complexity that occur in morphodynamic systems. Autogenic dynamics creates much of the spatial structure we see in the landscape and in preserved strata, and is strongly associated with sediment storage and release. The observed consistency between experimental and field systems despite large differences in governing dimensionless numbers is what we mean by “unreasonable effectiveness”. We suggest that unreasonable experimental effectiveness arises from natural scale independence. We generalize existing ideas to relate internal similarity, in which a small part of a system is similar to the larger system, to external similarity, in which a small copy of a system is similar to the larger system. We propose that internal similarity implies external similarity, though not the converse. The external similarity of landscape experiments to natural landscapes suggests that natural scale independence may be even more characteristic of morphodynamics than it is of better studied cases such as turbulence. We urge a shift in emphasis in experimental stratigraphy and geomorphology away from classical dynamical scaling and towards a quantitative understanding of the origins and limits of scale independence. Other research areas with strong growth potential in experimental surface dynamics include physical–biotic interactions, cohesive effects, stochastic processes, the interplay of structural and geomorphic self-organization, extraction of quantitative process information from landscape and stratigraphic records, and closer interaction between experimentation and theory.},
author = {Paola, Chris and Straub, Kyle and Mohrig, David and Reinhardt, Liam},
doi = {10.1016/j.earscirev.2009.05.003},
issn = {00128252},
journal = {Earth-Science Reviews},
number = {1},
pages = {1--43},
title = {{The “unreasonable effectiveness” of stratigraphic and geomorphic experiments}},
volume = {97},
year = {2009}
}
@article{Park2015,
author = {Park, Edward and Latrubesse, Edgardo M.},
doi = {10.1002/2014WR016757},
issn = {00431397},
journal = {Water Resources Research},
keywords = {Amazon,confluence,floodplain ecology,large rivers,sediment transport,surface water distribution},
month = {aug},
number = {8},
pages = {6197--6213},
title = {{Surface water types and sediment distribution patterns at the confluence of mega rivers: The Solim{\~{o}}es-Amazon and Negro Rivers junction}},
url = {http://doi.wiley.com/10.1002/2014WR016757},
volume = {51},
year = {2015}
}
@phdthesis{Parker1977,
author = {Parker, Randolph A},
keywords = {knickpoints,rivers,tectonic geomorphology},
number = {June},
pages = {Hydrology papers, Colorado State Uni. Fort Collin},
school = {Fort Collins, Colorado State University, http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2{\&}doc=GetTRDoc.pdf{\&}AD=ADA051839},
title = {{Experimental Study of Basin Evolution and its Hydrologic Implications}},
type = {PhD thesis},
year = {1977}
}

@article{Pastor-Satorras1998,
  title = {Stochastic {{Equation}} for the {{Erosion}} of {{Inclined Topography}}},
  volume = {80},
  doi = {10.1103/PhysRevLett.80.4349},
  abstract = {We present a stochastic equation to model the erosion of topography with fixed inclination. The inclination causes the erosion to be anisotropic. A zero-order consequence of the anisotropy is the dependence of the prefactor of the surface height-height correlations on direction. The lowest higher-order contribution from the anisotropy is studied by applying the dynamic renormalization group. In this case, assuming an inhomogenous distribution of soil material, we find a one-loop estimate of the roughness exponents. The predicted exponents are in good agreement with new measurements made from seafloor topography.},
  number = {19},
  journal = {Physical Review Letters},
  author = {{Pastor-Satorras}, Romualdo and Rothman, Daniel H.},
  month = may,
  year = {1998},
  pages = {4349-4352},
  shortjournal = {Phys. Rev. Lett.}
}
@article{Passalacqua2006,
  title = {Application of {{Dynamic Subgrid}}-{{Scale Concepts}} from {{Large}}-{{Eddy Simulation}} to {{Modeling Landscape Evolution}}},
  volume = {42},
  issn = {1944-7973},
  doi = {10.1029/2006WR004879},
  abstract = {Landscapes share important similarities with turbulence: both systems exhibit scale invariance (self-similarity) over a wide range of scales, and their behavior can be described using comparable dynamic equations. In particular, modified versions of the Kardar-Parisi-Zhang (KPZ) equation (a low-dimensional analog to the Navier-Stokes equations) have been shown to capture important features of landscape evolution. This suggests that modeling techniques developed for turbulence may also be adapted to landscape simulations. Using a ``toy'' landscape evolution model based on a modified 2-D KPZ equation, we find that the simulated landscape evolution shows a clear dependence on grid resolution. In particular, mean longitudinal profiles of elevation at steady state and bulk erosion rates both have an undesirable dependence on grid resolution because the erosion rate increases with resolution as increasingly small channels are resolved. We propose a new subgrid-scale parameterization to account for the scale dependence of the sediment fluxes. Our approach is inspired by the dynamic procedure used in large-eddy simulation of turbulent flows. The erosion coefficient, assumed exactly known at the finest resolution, is multiplied by a scale dependence coefficient, which is computed dynamically at different time steps on the basis of the dynamics of the resolved scales. This is achieved by taking advantage of the self-similarity that characterizes landscapes over a wide range of scales. The simulated landscapes obtained with the new model show very little dependence on grid resolution.},
  language = {English},
  number = {6},
  journal = {Water Resources Research},
  author = {Passalacqua, Paola and Port\'e-Agel, Fernando and Foufoula-Georgiou, Efi and Paola, Chris},
  month = jun,
  year = {2006},
  keywords = {turbulence,landscapes,large-eddy simulation,subgrid-scale modeling}
}
@misc{Passalacqua2015,
abstract = {The study of mass and energy transfer across landscapes has recently evolved to comprehensive considerations acknowledging the role of biota and humans as geomorphic agents, as well as the importance of small-scale landscape features. A contributing and supporting factor to this evolution is the emergence over the last two decades of technologies able to acquire high resolution topography (HRT) (meter and sub-meter resolution) data. Landscape features can now be captured at an appropriately fine spatial resolution at which surface processes operate; this has revolutionized the way we study Earth-surface processes. The wealth of information contained in HRT also presents considerable challenges. For example, selection of the most appropriate type of HRT data for a given application is not trivial. No definitive approach exists for identifying and filtering erroneous or unwanted data, yet inappropriate filtering can create artifacts or eliminate/distort critical features. Estimates of errors and uncertainty are often poorly defined and typically fail to represent the spatial heterogeneity of the dataset, which may introduce bias or error for many analyses. For ease of use, gridded products are typically preferred rather than the more information-rich point cloud representations. Thus many users take advantage of only a fraction of the available data, which has furthermore been subjected to a series of operations often not known or investigated by the user. Lastly, standard HRT analysis work-flows are yet to be established for many popular HRT operations, which has contributed to the limited use of point cloud data. In this review, we identify key research questions relevant to the Earth-surface processes community within the theme of mass and energy transfer across landscapes and offer guidance on how to identify the most appropriate topographic data type for the analysis of interest. We describe the operations commonly performed from raw data to raster products and we identify key considerations and suggest appropriate work-flows for each, pointing to useful resources and available tools. Future research directions should stimulate further development of tools that take advantage of the wealth of information contained in the HRT data and address the present and upcoming research needs such as the ability to filter out unwanted data, compute spatially variable estimates of uncertainty and perform multi-scale analyses. While we focus primarily on HRT applications for mass and energy transfer, we envision this review to be relevant beyond the Earth-surface processes community for a much broader range of applications involving the analysis of HRT.},
author = {Passalacqua, Paola and Belmont, Patrick and Staley, Dennis M. and Simley, Jeffrey D. and Arrowsmith, J. Ramon and Bode, Collin A. and Crosby, Christopher and DeLong, Stephen B. and Glenn, Nancy F. and Kelly, Sara A. and Lague, Dimitri and Sangireddy, Harish and Schaffrath, Keelin and Tarboton, David G. and Wasklewicz, Thad and Wheaton, Joseph M.},
booktitle = {Earth-Science Reviews},
doi = {10.1016/j.earscirev.2015.05.012},
issn = {00128252},
keywords = {Bathymetry,Change detection,Filtering,Geomorphic features,IfSAR,InSAR,Lidar,Point cloud,Structure from motion},
pages = {174--193},
title = {{Analyzing high resolution topography for advancing the understanding of mass and energy transfer through landscapes: A review}},
volume = {148},
year = {2015}
}
@article{Passalacqua2010,
author = {Passalacqua, Paola and Tarolli, Paolo and Foufoula-Georgiou, Efi},
doi = {10.1029/2009WR008812},
issn = {00431397},
journal = {Water Resources Research},
month = {nov},
number = {11},
title = {{Testing space-scale methodologies for automatic geomorphic feature extraction from lidar in a complex mountainous landscape}},
url = {http://doi.wiley.com/10.1029/2009WR008812},
volume = {46},
year = {2010}
}
@incollection{Pazzaglia2015,
author = {Pazzaglia, Frank J. and Carter, Mark and Berti, Claudio and Counts, Ron and Hancock, Greg and Harbor, David and Harrison, Richard and Heller, Matt and Mahan, Shannon and Malenda, Helen and McKeon, Ryan and Nelson, Michelle and Prince, Phillip and Rittenour, Tammy and Spotila, James and Whittecar, Rich},
booktitle = {Field Guides},
doi = {10.1130/2015.0040(06)},
issn = {2333-0937},
pages = {109--169},
publisher = {Geological Society of America},
title = {{Geomorphology, active tectonics and landscape evolution in the Mid-Atlantic region}},
url = {http://fieldguides.gsapubs.org/lookup/doi/10.1130/2015.0040(06)},
volume = {40},
year = {2015}
}
@article{Pedrazzini2016,
abstract = {The influence of gravitational slope deformation (GSD) on erosion rates and the shape of mountain belts has been identified worldwide, particularly in valleys affected by glacial retreat. However, due to a lack of understanding about the main predisposing factors influencing their spatial distribution, size and failure mechanisms, the effective impact of GSD on the evolution of the landscape remains difficult to quantify. This study presents the first detailed, regional-scale GSD inventory of the entire Upper Rhone catchment (western Switzerland). The detection and mapping of GSD are performed by combining different remote sensing approaches. Moreover, we propose a detailed characterisation of GSD, taking into account geometry, morphology and failure mechanisms. Based on these analyses, more than 300 GSD are identified, corresponding to 11 {\%} of the entire study area. Spatial and statistical analyses indicate that GSD are not uniformly distributed across the study area: six GSD clusters are highlighted, containing more than 80 {\%} of the GSD events detected. Our observations suggest that the distribution of GSDs is primarily related to coexisting active tectonic processes (including high uplift gradients and earthquake activity) and pre-existing regional-scale, tectonic weakness zones. The region's lithological and structural conditions, on the other hand, appear largely to influence the failure mechanisms and the sizes of the GSD detected.},
author = {Pedrazzini, Andrea and Humair, Florian and Jaboyedoff, Michel and Tonini, Marj},
doi = {10.1007/s10346-015-0562-9},
isbn = {1612-510X$\backslash$r1612-5118},
issn = {16125118},
journal = {Landslides},
keywords = {Inventory,Predisposing factors,Slope deformation,Spatial Cluster distribution,Swiss Alps},
month = {apr},
number = {2},
pages = {259--277},
publisher = {Springer Berlin Heidelberg},
title = {{Characterisation and spatial distribution of gravitational slope deformation in the Upper Rhone catchment (Western Swiss Alps)}},
url = {http://link.springer.com/10.1007/s10346-015-0562-9},
volume = {13},
year = {2016}
}
@article{Pelletier2003,
abstract = {Four experiments in alluvial drainage basin evolution were carried out in the Rainfall Erosion Facility (REF) at Colorado State University to investigate the dependence of basin evolution on initial topography. Basins were initially undissected. Each experiment began with a unique initial condition representing various end-members of relief and hypsometry. Drainage network development, hillslope processes, basin denudation, and basin response to base-level lowering all depended strongly on the initial topography. No classic model of drainage network evolution was found to be generally applicable. Initially, planar slopes first developed subparallel channels that extended headward dendritically during an early phase of extension. Channel incision occurred first in the interior of the basin where saturation overland flow was greatest, not at the basin outlet as assumed in most classic models of network development. Channels widened over time, initiating lateral migration and drainage capture in the downslope portion of the watershed before transferring lateral migration upslope. Planar basins of larger initial gradient grew headward more quickly and become more deeply entrenched, inhibiting late-stage lateral migration. An experiment with initial relief concentrated at a plateau edge evolved in several unique ways. A high ratio of subsurface-to-surface flow gave rise to mass movements at the plateau edge and outlet channels. Deep channels were quickly cut initially but did not extend far upslope because slope instability undermined channel head migration, leaving the plateau undissected and hence very slow to erode. These results suggest that the distribution of relief within a basin exerts an important control on drainage network pattern and basin denudation. In addition, erosional basins may evolve in several distinct modes characterized by particular combinations of hypsometry, hillslope processes, and mean denudation rate. ?? 2002 Elsevier Science B.V. All rights reserved.},
author = {Pelletier, Jon D.},
doi = {10.1016/S0169-555X(02)00353-7},
isbn = {0169-555X},
issn = {0169555X},
journal = {Geomorphology},
keywords = {Drainage network,Flume experiment,Landform evolution},
number = {1-2},
pages = {183--196},
title = {{Drainage basin evolution in the rainfall erosion facility: Dependence on initial conditions}},
volume = {53},
year = {2003}
}


@article{Pelletier2007,
  series = {38th Binghamton Geomorphology Symposium: Complexity in Geomorphology},
  title = {Fractal {{Behavior}} in {{Space}} and {{Time}} in a {{Simplified Model}} of {{Fluvial Landform Evolution}}},
  volume = {91},
  issn = {0169-555X},
  doi = {10.1016/j.geomorph.2007.04.015},
  abstract = {Two general approaches have been applied to understanding the fractal structure of fluvial topography: (1) deterministic, process-based models, and (2) stochastic partial differential equations (PDE). Deterministic models reproduce the fractal behavior of fluvial topography but have two limitations: they often underestimate the amount of lateral valley and ridge migration that occurs in nature, and the complexity has made it difficult to identify the precise origin of fractal behavior in fluvial landscapes. The simplicity of stochastic PDE models has made them useful for investigating fractal behavior, but they incorrectly suggest that fractal behavior is only possible with stochastic forcing. In this paper I investigate whether simplified, deterministic PDE models of landform evolution also exhibit fractal behavior and other features of complexity (i.e. deterministic chaos). These models are based on the KPZ equation, well known in the physics literature. This equation combines diffusion (i.e. hillslope processes) and nonlinear advection (i.e. bedrock or alluvial channel incision). Two models are considered: (1) a deterministic model with uniform erodibility and random initial topography, and (2) a deterministic model with random erodibility and uniform initial topography. Results illustrate that both of these deterministic models exhibit fractal behavior and deterministic chaos. In this context, chaotic behavior means that valley and ridge migration and nonlinear amplification of small perturbations in these models prevent an ideal steady state landscape from ever developing in the large-system limit. These results suggest that fractal structure and deterministic chaos are intrinsic features of the evolution of fluvial landforms, and that these features result from an inverse cascade of energy from small to large wavelengths in drainage basins. This inverse cascade differs from the direct cascade of three-dimensional turbulence in which energy flows from large to small wavelengths.},
  number = {3},
  journal = {Geomorphology},
  author = {Pelletier, Jon D.},
  month = nov,
  year = {2007},
  keywords = {Fractals,Drainage basin,Numerical model},
  pages = {291-301},
  shortjournal = {Geomorphology}
}
@article{Perron2017,
author = {Perron, J. Taylor},
title = {Climate and the Pace of Erosional Landscape Evolution},
journal = {Annual Review of Earth and Planetary Sciences},
volume = {45},
number = {1},
pages = {561-591},
year = {2017},
doi = {10.1146/annurev-earth-060614-105405},

URL = { 
        https://doi.org/10.1146/annurev-earth-060614-105405
    
},
eprint = { 
        https://doi.org/10.1146/annurev-earth-060614-105405
    
}

}
@article{Perron,
abstract = {Bedrock river profiles are often interpreted with the aid of slope–area analysis, but noisy topographic data make such interpretations challenging. We present an alternative approach based on an integration of the steady-state form of the stream power equation. The main component of this approach is a transformation of the horizontal coordinate that converts a steady-state river profile into a straight line with a slope that is simply related to the ratio of the uplift rate to the erodibility. The transformed profiles, called chi plots, have other useful properties, including co-linearity of steady-state tributaries with their main stem and the ease of identifying transient erosional signals. We illustrate these applications with analyses of river profiles extracted from digital topographic datasets.},
author = {Perron, J Taylor and Royden, Leigh},
doi = {10.1002/esp.3302},
keywords = {bedrock river,longitudinal profile,slope–area,stream power},
title = {{An integral approach to bedrock river profile analysis}}
}
@article{Perron2008a,
abstract = {Many landscapes are composed of ridges and valleys that are uniformly spaced, even where valley locations are not controlled by bedrock structure. Models of long-term landscape evolution have reproduced this phenomenon, yet the process by which uniformly spaced valleys develop is not well understood, and there is no quantitative framework for predicting valley spacing. Here we use a numerical landscape evolution model to investigate the development of uniform valley spacing. We find that evenly spaced valleys arise from a competition between adjacent drainage basins for drainage area (a proxy for water flux) and that the spacing becomes more uniform as the landscape approaches a topographic equilibrium. Valley spacing is most sensitive to the relative rates of advective erosion processes (such as stream incision) and diffusion-like mass transport (such as soil creep) and less sensitive to the magnitude of a threshold that limits the spatial extent of stream incision. Analysis of a large number of numerical solutions reveals that valley spacing scales with a ratio of characteristic diffusion and advection timescales that is analogous to a P?clet number. We use this result to derive expressions for equilibrium valley spacing and drainage basin relief as a function of the rates of advective and diffusive processes and the spatial extent of the landscape. The observed scaling relationships also provide insight into the cause of transitions from rill-like drainage networks to branching networks, the spatial scale of first-order drainage basins, the contributing area at which hillslopes transition into valleys, and the narrow range of width-to-length ratios of first-order basins.},
author = {Perron, J. Taylor and Dietrich, William E. and Kirchner, James W.},
doi = {10.1029/2007JF000977},
isbn = {0148-0227},
issn = {21699011},
journal = {Journal of Geophysical Research: Earth Surface},
number = {4},
pages = {1--21},
title = {{Controls on the spacing of first-order valleys}},
volume = {113},
year = {2008}
}
@article{Perron2009a,
abstract = {One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys1, 2, 3, 4, 5, 6. Despite the prevalence of uniform valley spacing, no theory has been shown to predict this fundamental topographic wavelength. Models of long-term landscape evolution can produce landforms that look realistic7, 8, 9, but few metrics exist to assess the similarity between models and natural landscapes. Here we show that the ridge–valley wavelength can be predicted from erosional mechanics. From equations of mass conservation and sediment transport, we derive a characteristic length scale at which the timescales for erosion by diffusive soil creep and advective stream incision are equal. This length scale is directly proportional to the valley spacing that emerges in a numerical model of landform evolution, and to the measured valley spacing at five field sites. Our results provide a quantitative explanation for one of the most widely observed characteristics of landscapes. The findings also imply that valley spacing is a fundamental topographic signature that records how material properties and climate regulate erosional processes.},
author = {Perron, J. Taylor and Kirchner, James W. and Dietrich, William E.},
doi = {10.1038/nature08174},
isbn = {0028-0836},
issn = {0028-0836},
journal = {Nature},
number = {7254},
pages = {502--505},
pmid = {6373},
title = {{Formation of evenly spaced ridges and valleys}},
url = {http://dx.doi.org/10.1038/nature08174},
volume = {460},
year = {2009}
}
@article{Perron2013a,
author = {Perron, J. Taylor and Royden, Leigh},
doi = {10.1002/esp.3302},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
month = {may},
number = {6},
pages = {570--576},
title = {{An integral approach to bedrock river profile analysis}},
url = {http://doi.wiley.com/10.1002/esp.3302},
volume = {38},
year = {2013}
}
@article{Perron2013,
author = {Perron, J. Taylor and Royden, Leigh},
doi = {10.1002/esp.3302},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {area,bedrock river,longitudinal profile,slope,stream power},
month = {may},
number = {6},
pages = {570--576},
title = {{An integral approach to bedrock river profile analysis}},
url = {http://doi.wiley.com/10.1002/esp.3302},
volume = {38},
year = {2013}
}
@article{Pissart1997,
author = {Pissart, Albert and Harmand, Dominique and Krook, Leendert},
doi = {10.7202/033127ar},
issn = {0705-7199},
journal = {G{\'{e}}ographie physique et Quaternaire},
number = {3},
pages = {267},
title = {{L'{\'{e}}volution de la Meuse de Toul {\`{a}} Maastricht depuis le Mioc{\`{e}}ne : corr{\'{e}}lations chronologiques et traces des captures de la Meuse lorraine d'apr{\`{e}}s les min{\'{e}}raux denses}},
url = {http://id.erudit.org/iderudit/033127ar},
volume = {51},
year = {1997}
}
@article{Planchon2002,
abstract = {The usual numerical methods for removing the depressions of a Digital Elevation Model (DEM) gradually fill the depressions and merge the embedded ones. These methods are complex to implement and need large computation time, particularly when the DEM contains a high proportion of random noise. A new method is presented here. It is innovative because, instead of gradually filling the depressions, it first inundates the surface with a thick layer of water and then removes the excess water. The algorithm is simple to understand and to implement, requiring only a few tens of code lines. It is much faster than usual algorithms. Moreover, this method is versatile: depressions can be replaced with a surface either strictly horizontal, or slightly sloping. The first option is used for the calculation of depression storage capacity and the second one for drainage network extraction. The method is fully detailed and a pseudo-code is provided. Its practical computation time, evaluated on generated fractal surfaces, is asymptotically proportional to N1.2 where N is the number of grid points. The theoretical computation time is asymptotically proportional to N1.5 in all cases, with the exception of some exotic ones with no practical interest. By contrast, existing methods have a computation time asymptotically proportional to N2. Applications are done for both generated and measured surfaces with 256 cells to 6.2 million cells. ?? 2002 Elsevier Science B.V. All rights reserved.},
author = {Planchon, Olivier and Darboux, Fr??d??ric},
doi = {10.1016/S0341-8162(01)00164-3},
isbn = {0341-8162},
issn = {03418162},
journal = {Catena},
keywords = {Depression-filling,Digital elevation model,Drainage network,Soil roughness,Storage capacity,Topography},
number = {2-3},
pages = {159--176},
title = {{A fast, simple and versatile algorithm to fill the depressions of digital elevation models}},
volume = {46},
year = {2002}
}
@article{Polyakov2003,
abstract = {The understanding of soil erosion processes and the development of accurate erosion prediction models require understanding of detachment, deposition, and sediment transport in rills. The objectives of this study were to determine whether sediment transport capacity is a unique value for given soil, flow rate, and slope, and to determine if equilibrium sediment concentration in the rill obtained by detachment was different from that observed under depositional conditions. Experiments on a Carmi loam (fine, mixed, mesic Typic Hapludalf) simulated rill erosion under net detachment and net deposition conditions. Two discharge rates of 6 and 9 1 min-1 and two sediment input regimes of 0 and excess of transport capacity were tested on soil beds with lengths of 2, 4, 6, 7, and 8 m at 7{\%} slope. Sediment load reached steady state conditions within the 8-m distance on the rill. At 9 1 min-1 discharge, 8 m length, and excess sediment added to the flow, sediment delivery was 71 g 1-1 versus 31 g 1-1 for the corresponding case with no sediment added. Overall, for the conditions tested, rill flow transported two times more sediment than it could detach. The flow did not reach its maximum potential transported load through detachment of soil due in part to changes in the sediment size distribution under deposition and possibly to the protective action of bedload particles moving along the rill bottom and/or changes in flow turbulence associated with sediment laden flow. ?? 2003 Elsevier Science B.V. All rights reserved.},
author = {Polyakov, V. O. and Nearing, M. A.},
doi = {10.1016/S0341-8162(02)00090-5},
isbn = {0341-8162},
issn = {03418162},
journal = {Catena},
keywords = {Erosion,Rill erosion,Runoff,Sediment,Sediment transport,Soil erosion},
month = {jan},
number = {1},
pages = {33--43},
title = {{Sediment transport in rill flow under deposition and detachment conditions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0341816202000905},
volume = {51},
year = {2003}
}
@book{Press1992,
abstract = {3rd ed. Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. New key features: 2 new chapters, 25 new sections, 25{\%} longer than Second Edition; Thorough upgrades throughout the text; Over 100 completely new routines and upgrades of many more; New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector Machines; New Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions; An expanded treatment of ODEs with completely new routines; Comprehensive coverage of: linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory, and more. - Publisher. Preliminaries -- Solution of linear algebraic equations -- Interpolation and extrapolation -- Integration of functions -- Evaluation of functions -- Special functions -- Random numbers -- Sorting and selection -- Root finding and nonlinear sets of equations -- Minimization or maximization of functions -- Eigensystems -- Fast Fourier transform -- Fourier and spectral applications -- Statistical description of data -- Modeling of data -- Classification and inference -- Integration of ordinary differential equations -- Two-point boundary value problems -- Integral equations and inverse theory -- Partial differential equations -- Computational geometry -- Less-numerical algorithms.},
address = {New York},
author = {Press, William H. and Teukolsky, Saul A. and Vettering, Willaim T and Flannery, Brian P},
isbn = {978-0-521-88068-8},
pages = {1235},
publisher = {Cambridge University Press},
title = {{Numerical recipes in C: The art of scientific computing}},
year = {1992}
}
@book{Press2007,
  address = {Cambridge, UK},
  title = {Numerical {{Recipes}}: {{The Art}} of {{Scientific Computing}}},
  isbn = {978-0-521-88068-8},
  abstract = {3rd ed. Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. New key features: 2 new chapters, 25 new sections, 25\% longer than Second Edition; Thorough upgrades throughout the text; Over 100 completely new routines and upgrades of many more; New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector Machines; New Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions; An expanded treatment of ODEs with completely new routines; Comprehensive coverage of: linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory, and more. - Publisher. Preliminaries -- Solution of linear algebraic equations -- Interpolation and extrapolation -- Integration of functions -- Evaluation of functions -- Special functions -- Random numbers -- Sorting and selection -- Root finding and nonlinear sets of equations -- Minimization or maximization of functions -- Eigensystems -- Fast Fourier transform -- Fourier and spectral applications -- Statistical description of data -- Modeling of data -- Classification and inference -- Integration of ordinary differential equations -- Two-point boundary value problems -- Integral equations and inverse theory -- Partial differential equations -- Computational geometry -- Less-numerical algorithms.},
  publisher = {{Cambridge University Press}},
  author = {Press, William H. and Teukolsky, Saul A. and Vettering, Willaim T and Flannery, Brian P},
  year = {2007}
}
@article{Quinn1991,
abstract = {The accuracy of the predictions of distributed hydrological models must depend in part on the proper specification of flow pathways. This paper examines some of the problems of deriving flow pathways from raster digital terrain data in the context of hydrological predictions using TOPMODEL. Distributed moisture status is predicted in TOPMODEL on the basis of spatial indices that depend on flow path definition. The sensitivity of this index to flow path algorithm and grid size is examined for the case where the surface topography is a good indicator of local hydraulic gradients. A strategy for the case where downslope subsurface flow pathways may deviate from those indicated by the surface topography is described with an example application.},
author = {Quinn, P. and Beven, K. and Chevallier, P. and Planchon, O.},
doi = {10.1002/hyp.3360050106},
isbn = {1099-1085},
issn = {08856087},
journal = {Hydrological Processes},
keywords = {digital terrain data flow,pathways distributed hydrological models},
month = {jan},
number = {1},
pages = {59--79},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models}},
url = {http://doi.wiley.com/10.1002/hyp.3360050106},
volume = {5},
year = {1991}
}
@article{Raei2015,
abstract = {Critical shear stress and threshold stream power are two important soil characteristics controlling detachment of soil particles by runoff and have been used in process-based erosion models such as WEPP, GUEST and EUROSEM. In this research, laboratory experiments were conducted in a 20. ??. 350. cm flume to study the effects of particle size and density on initial motion. Two contrasting soil samples, a well-aggregated forest soil and non-cohesive fluvial sand, were used to provide particles with different densities. Each sample was divided into six size classes. Flow bed in the flume was roughed according to testing area for each size class using a plate which sand particles from each size class were glued on it. The initial motion of the particles was determined by two methods. In the first method, slope was increased gradually for a given constant discharge until particles start to move from every point of the testing area. In the second method, flume slope was set to a given steepness and discharge was gradually increased until particles start to move. Three different discharges and three slopes were tested in the first and second methods, respectively. Each test replicated two times. Analysis of the data showed that the particle size and density and also their interaction significantly affect (P. {\textless}. 0.001) critical shear stress and threshold stream power. The critical shear stress and threshold stream power increased with increasing particle size and density, but the impact of particle density is higher on the coarser particles than the finer ones. Threshold values measured for the sand particles were about 2.3 times of those measured for soil particles in the three coarser classes, this difference decreased to about 65{\%} (1.65 times) in the three finer classes, and even the difference between the two types of particles was not significant for the finest class (0.125-0.053).},
author = {Raei, B. and Asadi, H. and Moussavi, A. and Ghadiri, H.},
doi = {10.1016/j.catena.2014.12.031},
issn = {03418162},
journal = {Catena},
keywords = {Critical shear stress,Modeling,Particle density,Soil erosion,Threshold stream power},
month = {apr},
pages = {279--286},
publisher = {Elsevier B.V.},
title = {{A study of initial motion of soil aggregates in comparison with sand particles of various sizes}},
url = {http://dx.doi.org/10.1016/j.catena.2014.12.031 http://linkinghub.elsevier.com/retrieve/pii/S0341816214003919},
volume = {127},
year = {2015}
}

@article{Ranjbar2020,
author = {Ranjbar, Sevil and Singh, Arvind and Wang, Dingbao},
title = {Controls of the Topological Connectivity on the Structural and Functional Complexity of River Networks},
journal = {Geophysical Research Letters},
volume = {47},
number = {22},
pages = {e2020GL087737},
keywords = {structural complexity, functional complexity, channel network, hillslopes, entropy},
doi = {10.1029/2020GL087737},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020GL087737},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2020GL087737},
note = {e2020GL087737 2020GL087737},
abstract = {Abstract Catchments are complex systems containing channel networks and hillslopes. Channel networks interact with hillslopes and are pathways for transporting water, sediment, and nutrients. Understanding the branching and flux transport patterns of channel networks is critical for predicting the response of catchments to external forcing such as climate and tectonics. However, factors creating complexities in catchments are not fully understood. Here, we propose a new framework based on multiscale entropy approach to evaluate complexity of catchments using two different representations of channel networks. First, we investigate the structural complexity using the width-function, which characterizes the spatial arrangement of channels. Second, we utilize the incremental area-function along the main channel to study the functional complexity that captures the patterns of transport of fluxes. Our analysis reveals stronger controls of topological connectivity on the functional complexity than on structural complexity, indicating unchannelized surface (hillslope) contribution to the increase of heterogeneity in transport processes.},
year = {2020}
}


@article{Raff2004,
abstract = {Rainfall simulator experiments were structured to develop erosion rill-channel networks for 9° and 5° slopes subject to constant rainfall. Quantitative measurements included measurements of rill-channel width, depth, and width-to-depth ratios aggregated over the slope, and measures of the scaling characteristics and space filling tendencies of the networks. Trends in fractal dimensions and width functions with time are presented and compared to previous qualitative descriptions of network evolution. Our results imply that the equilibrium scaling characteristics of rill-channel networks are similar to those of river networks. For a given slope, the fractal dimension increases with time toward an equilibrium value. This equilibrium value is hypothesized to be a function of the effective storm, the initial hillslope-scale slope, and the geologic properties of the substrate. Results also imply that the rate of increase of the fractal dimension of the developing erosion networks (i.e., the rate at which the erosion networks fill space) may increase with increasing hillslope-scale slope. In addition, the growing rill-channel networks possess width functions whose bifurcation characteristics, as described by the power contained in the high wave numbers of the Fourier series fit, remain constant throughout the evolution of the networks. {\textcopyright} 2004 Elsevier B.V. All rights reserved.},
author = {Raff, David A. and Ram{\'{i}}rez, Jorge A. and Smith, James L. and Ramı, Jorge A.},
doi = {10.1016/j.geomorph.2004.02.011},
isbn = {0169-555X},
issn = {0169555X},
journal = {Geomorphology},
keywords = {Erosion,Fractals,Geomorphology,Sedimentation,erosion,fractals,geomorphology,sedimentation},
number = {3-4},
pages = {169--180},
title = {{Hillslope drainage development with time: A physical experiment}},
volume = {62},
year = {2004}
}





@article{Reinhardt2015,
abstract = {We conducted a series of four physical modeling experiments of mountain growth at differing rates of uplift and three distinct climates ranging from relatively wet to relatively dry. The spatial and tem- poral pattern of landscape behavior is characterized by ?f21 scaling in sediment discharge and power law scaling in the magnitude and frequency of ridge movement in all four experiments. We find that internally generated self-organized critical (SOC) processes generate dynamically stable catchment geometries after ?1 relief depths of erosion: these regularly spaced catchments have an average outlet-spacing ratio of 2.16, well within the range of values reported in field studies. Once formed, large catchment bounding ridges oscillate about a critically balanced mean location, with occasional large-scale changes in catchment size. Ridge movement appears to be driven by the competition for discharge as landslides push ridges back and forth. These dynamics lead to the emergence of a complex twofold scaling in catchment dynamics that is fully established by 1.8 relief depths of erosion; at this stage, a clear threshold has emerged separating two distinct scaling regimes, where large ridge mobility is insensitive to relief and small ridge mobility is relief dependent. Overall, we demonstrate that the development of dynamically stable large-scale landforms is related to the emergence of a complex-system hierarchy in topographic dynamics. Once formed, these landscapes do not evolve; statistical properties such as average topography and discharge become station- ary while topography remains highly dynamic at smaller length scales.},
author = {Reinhardt, Liam and Ellis, Michael A.},
doi = {10.1002/2014WR016223},
isbn = {1858453410},
issn = {00431397},
journal = {Water Resources Research},
keywords = {SOC,analogue model,autogenic,complexity,landscape dynamics,mountain,physical model},
month = {jul},
number = {7},
pages = {4986--5003},
title = {{The emergence of topographic steady state in a perpetually dynamic self-organized critical landscape}},
url = {http://doi.wiley.com/10.1002/2014WR016223},
volume = {51},
year = {2015}
}
@article{Rengers2014,
author = {Rengers, Francis K. and Tucker, G. E.},
doi = {10.1002/2013JF002962},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
month = {may},
number = {5},
pages = {983--1003},
title = {{Analysis and modeling of gully headcut dynamics, North American high plains}},
url = {http://doi.wiley.com/10.1002/2013JF002962},
volume = {119},
year = {2014}
}
@article{Reusser2015,
author = {Reusser, L. and Bierman, P. and Rood, D.},
doi = {10.1130/G36272.1},
journal = {Geology},
month = {feb},
number = {2},
pages = {171--174},
publisher = {Geological Society of America},
title = {{Quantifying human impacts on rates of erosion and sediment transport at a landscape scale}},
url = {http://geology.gsapubs.org/cgi/doi/10.1130/G36272.1},
volume = {43},
year = {2015}
}
@article{Rieke-ZappD.H.Nearing2005,
abstract = {Data on soil erosion at the slope scale is essentially limited to experiments on uniform slopes. The objective of this research was to measure the rates and patterns of erosion on complex shaped slope elements under controlled laboratory conditions where surface morphology changes could be carefully quantified. Artificial rainfall was applied for 90 min to a silt loam soil in a 4 by 4 m box. Five slope shapes were formed: uniform, concave-linear, convex-linear, nose slope, and head slope. Digital elevations models (DEMs) of the surface were measured using photogrammetry after 0, 10, 20, 40, 60, and 90 min. Slope shape had a significant impact on rill patterns, sediment yield, and runoff production. The uniform, nose, and convex-linear slopes yielded more sediment than the concave-linear and head slopes, where sediment deposited on toeslopes. Soil topography led to flow convergence and divergence, resulting in a nonuniform distribution of rill spacing and efficiency. The degree of rill incision was related to slope steepness and length, and rill success was related to the contribution area of the rill. Drainage density approached a similar value for all networks during the experiments. Development of the drainage system was similar to the development of optimum channel networks, in that during the evolution of the rill network energy expenditure was reduced. This indicated that energy expenditure was a quantifiable measure of network development and self-organization. {\textcopyright} Soil Science Society of America.},
author = {Rieke-Zapp, D. H. and Nearing, M. A.},
doi = {10.2136/sssaj2005.0015},
isbn = {0361-5995},
issn = {1435-0661},
journal = {Soil Science Society of America Journal},
keywords = {[laboratory techniques,rill erosion,runoff,sediment deposition,sediment yield,silt loam soils,slope,slope shape,topography,water erosion]},
number = {5},
pages = {1463--1471},
title = {{Slope shape effects on erosion: A laboratory study}},
volume = {69},
year = {2005}
}
@article{Rigon1996,
abstract = {Hack's law is reviewed, emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics. The relation between Hack's law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hack's exponent, elongation, and some relevant fractal characters are closely related. The self-affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to Hack's law. An explanation for Hack's law is derived from scaling arguments. From the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of Hack's law.},
archivePrefix = {arXiv},
arxivId = {arXiv:1011.1669v3},
author = {Rigon, Riccardo and Rodriguez-iturbe, Ignacio and Maritan, Amos and Giacometti, Achille and Tarboton, David G. and Rinaldo, Andrea},
doi = {10.1029/96WR02397},
eprint = {arXiv:1011.1669v3},
isbn = {1944-7973},
issn = {0043-1397},
journal = {Water Resources Research},
month = {nov},
number = {11},
pages = {3367--3374},
pmid = {15991970},
title = {{On Hack's law}},
url = {http://doi.wiley.com/10.1029/96WR02397},
volume = {32},
year = {1996}
}
@article{Rinaldo1993,
abstract = {Optimal channel networks obtained by minimizing the local and global rates of energy expenditure evolve automatically from arbitrary inital conditions to network configurations exhibiting fractal and multi-fractal staticstics indistinguishable from those observed in nature. OCN's may be SOC and natural fracture structures like river networks may arise as a joint consequence of optimality and randomness.},
author = {Rinaldo, A. and Rodriguez-Iturbe, I. and Rigon, R. and Ijjasz-Vasquez, E. and Bras, R. L.},
doi = {10.1103/PhysRevLett.70.822},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {6},
pages = {822--825},
pmid = {10054212},
title = {{Self-organized fractal river networks}},
volume = {70},
year = {1993}
}
@article{Rinaldo2014,
abstract = {Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-invariant structure of optimal river patterns. Optimal channel networks (OCNs) are feasible optimal configurations of a spanning network mimicking landscape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless configurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics--every spanning tree is exactly a local minimum of total energy dissipation. It is remarkable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms that are nevertheless characterized by universal statistical features. Such universal features explain very well the statistics of, and the linkages among, the scaling features measured for fluvial landforms across a broad range of scales regardless of geology, exposed lithology, vegetation, or climate, and differ significantly from those of the ground state, known exactly. Results are provided on the emergence of criticality through adaptative evolution and on the yet-unexplored range of applications of the OCN concept.},
author = {Rinaldo, Andrea and Rigon, Riccardo and Banavar, Jayanth R and Maritan, Amos and Rodriguez-Iturbe, Ignacio},
doi = {10.1073/pnas.1322700111},
issn = {1091-6490},
journal = {Proceedings of the National Academy of Sciences},
keywords = {Environment,Geological Processes,Hydrodynamics,Models,Rivers,Theoretical,adaptive evolution,erosional mechanics,feasible optimality,river network patterns,trees and networks},
month = {feb},
number = {7},
pages = {2417--24},
pmid = {24550264},
publisher = {National Academy of Sciences},
title = {{Evolution and selection of river networks: Statics, dynamics, and complexity}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24550264 http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=PMC3932906 http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3932906{\&}tool=pmcentrez{\&}rendertype=abstract},
volume = {111},
year = {2014}
}
@article{Rinaldo1992a,
abstract = {This paper explores the similarities of digital elevation maps (DEMs) of natural river basins and optimal channel network (OCN) configurations obtained minimizing the total rate of energy expenditure in the system as a whole and in its parts. Striking similarities are observed for natural and optimal networks in their fractal aggregation structure and in certain multifractal structures found to be characteristic of river basins. Our results suggest, upon critical assessment of the reliability of the identification of the attractor of the underlying dynamics implied by our optimality concepts, that fractal structures are indeed possibly a product of least energy dissipation. Power laws emerging in the description of the distribution of aggregated quantities from both DEMs and OCNs suggest a link with the framework of self-organized criticality in the dynamics of natural channel network formation. Also, the geomorphological description of OCNs reveals surprising analogies with well-known empirical or experimental results, A comparison of Peano's basins with OCNs suggests that nature seems to reject the type of strict self-similarity exhibited by Peano's construct in favor of different shapes implying statistical self-similarity not only because of chance acting through random conditions but also because of necessity as reflected by least energy expenditure considerations.},
author = {Rinaldo, Andrea and Rodriguez-Iturbe, Ignacio and Rigon, Riccardo and Bras, Rafael L. and Ijjasz-Vasquez, Ede and Marani, Alessandro},
doi = {10.1029/92WR00801},
isbn = {0043-1397},
issn = {00431397},
journal = {Water Resources Research},
month = {sep},
number = {9},
pages = {2183--2195},
title = {{Minimum energy and fractal structures of drainage networks}},
url = {http://doi.wiley.com/10.1029/92WR00801},
volume = {28},
year = {1992}
}
@article{Rodrfguez-iturbe1992,
author = {Rodrfguez-iturbe, Ignacio and Rinaldo, Andrea and Bras, Rafael L and Sz-vxsquez, E D E I J J},
number = {4},
pages = {1095--1103},
title = {{Energy Dissipation , Runoff Production , and the Three-Dimensional Structure of River Basins}},
volume = {28},
year = {1992}
}
@book{Rodriguez-Iturbe1997,
abstract = {This book considers river basins and drainage networks in the light of their scaling and multi-scaling properties, and the dynamics responsible for their development. The hydrology of river basins, and prediction of their growth, demands knowledge of a range of temporal and spatial scales. The core of Fractal River Basins is the search for the hidden order of these temporal and spatial variabilities in river basins, despite variations in size, climate and geology. The commonality of branching networks to other natural phenomena will make this book applicable to a wide range of disciplines. Hydrologists and geomorphologists will find that this book opens up the important topic of the fractal structure of networks at an accessible level. Mathematicians and physicists will appreciate the application of the theory to this aspect of the earth sciences. Comprehensive, well illustrated and with many real-world examples Fractal River Basins will be useful to researchers and students alike.},
address = {Cambridge University Press, UK},
author = {Rodriguez-Iturbe, I and Rinaldo, A},
publisher = {Cambridge University Press},
isbn = {0521004055},
pmid = {1179449},
title = {{Fractal river basins: Chance and self-organization}},
year = {2001}
}
@article{Rodriguez-Iturbe1992,
abstract = {Natural drainage networks, like river basins, exhibit fractal and multifractal properties. This work shows that these properties evolve from arbitrary initial conditions by minimizing the local and global rates of energy expenditure in the system. This suggests that many fractal structures may arise as a natural consequence of least energy dissipation requirements.},
author = {Rodriguez-Iturbe, Ignacio and Rinaldo, Andrea and Rigon, Riccardo and Bras, Rafael L. and Ijjasz-Vasquez, Ede and Marani, Alessandro},
doi = {10.1029/92GL00938},
isbn = {0094-8276},
issn = {1944-8007},
journal = {Geophysical Research Letters},
number = {9},
pages = {889--892},
title = {{Fractal structures as least energy patterns: The case of river networks}},
url = {http://onlinelibrary.wiley.com/doi/10.1029/92GL00938/abstract{\%}5Cnhttp://onlinelibrary.wiley.com/store/10.1029/92GL00938/asset/grl6087.pdf?v=1{\&}t=hchlowx4{\&}s=80c9c770e75a4184ef5e3dc0543c17040538da84},
volume = {19},
year = {1992}
}
@article{Rodriguez-Lloveras2015,
abstract = {Modelling hydrology and sediment yield and its scale dependency has been limited by the quantity and quality of instrumental data. This paper aims to apply alternative methods to estimate runoff and sediment production rates at the event-scale and to characterize the hydro-sedimentary response of a highly torrential Mediterranean catchment to historical changes in land use and vegetation. A selection of well-dated and spatially-distributed check dams within the catchment were used to calibrate and validate a hydro-sedimentary distributed model (TETIS). Sediment volumes deposited by individual runoff events and trapped in check dams were estimated on the bases of detailed stratigraphic descriptions and subsequent GPS/TLS surveys. The model results showed a good agreement with the observed water flows and sediment volumes deposited behind several check dams. Management and land uses proved to be a decisive factor in the hydrological behaviour of the catchment, especially affecting erosion and sediment yield. It was observed that while the hydrological response of the catchment was sensitive to the percentage of each land use type, the sedimentary response was more dependent on the spatial distribution of land use. These differences between hydrology and sedimentary behaviour imply that the optimal soil use distribution for soil conservation may differ from the optimal soil use scenario oriented to attenuate flood peaks. This study suggest that soil use policies and erosion mitigation strategies should consider a holistic hydro-sedimentary approach, in order to become an adaptive option to reduce and mitigate the effects of erosion and flood peaks under global change.},
author = {Rodriguez-Lloveras, Xavier and Bussi, Gianbattista and Franc{\'{e}}s, F{\'{e}}lix and Rodriguez-Caballero, Emilio and Sol{\'{e}}-Benet, Albert and Calle, Mikel and Benito, Gerardo},
doi = {10.1016/j.jhydrol.2015.11.014},
issn = {00221694},
journal = {Journal of Hydrology},
keywords = {Check dams,Erosion,Extreme events,Land use,Scale factor,TETIS},
pages = {1054--1066},
title = {{Patterns of runoff and sediment production in response to land-use changes in an ungauged Mediterranean catchment}},
volume = {531},
year = {2015}
}
@article{Roering2008,
author = {Roering, J. J.},
doi = {10.1130/B26283.1},
issn = {0016-7606},
journal = {Geological Society of America Bulletin},
month = {sep},
number = {9-10},
pages = {1248--1262},
title = {{How well can hillslope evolution models "explain" topography? Simulating soil transport and production with high-resolution topographic data}},
url = {http://gsabulletin.gsapubs.org/cgi/doi/10.1130/B26283.1},
volume = {120},
year = {2008}
}
@article{Rohais2012,
abstract = {This article deals with the stratigraphic record of a climatic or tectonic perturbation of an experimental coupled catchment-fan system. Following Bonnet {\&} Crave's results (2003), which suggest that it is possible to differentiate between climatic or tectonic causes of surface uplift of an erosional topography from the record of sediment flux output, we design a new experimental device to test this proposition in the sedimentary signal. This device allows the study of a coupled erosionsedimentation system at the laboratory scale for given and changing uplift and rainfall rates. On the basis of experimental results, we propose a methodology to study alluvial fan architecture from large-scale geometries to stacking pattern and sequence analysis. In these experiments, the erosional perturbation resulting from climate or tectonic forcing induces a typical dynamic in terms of both sediment supply and the ratio between the sediment and water supply, which controls the transport capacity. The four possible forcings (rainfall rate and uplift rate increase or decrease, respectively) then result in unique dynamics of the combined parameters such as the fan slope, apex aggradation, mean sedimentation rate, grain size distribution, bed thickness and frequency and facies stacking. We first analyse large-scale geometries (onlap, toplap, downlap or truncation) and then fine-scale sedimentological features (fining, thinning, coarsening, thickening) in order to discriminate the nature of the forcing. This conceptual model could be adapted to real world alluvial fans in order to recognize and separate the driving mechanisms from each other.},
author = {Rohais, S{\'{e}}bastien and Bonnet, St{\'{e}}phane and Eschard, R{\'{e}}mi},
doi = {10.1111/j.1365-2117.2011.00520.x},
isbn = {0950-091X},
issn = {0950091X},
journal = {Basin Research},
keywords = {Rohais2012},
month = {apr},
number = {2},
pages = {198--212},
title = {{Sedimentary record of tectonic and climatic erosional perturbations in an experimental coupled catchment-fan system}},
url = {http://doi.wiley.com/10.1111/j.1365-2117.2011.00520.x},
volume = {24},
year = {2012}
}
@article{Romkens2001,
abstract = {Soil erosion is a complex phenomenon involving the detachment and transport of soil particles, storage and runoff of rainwater, and infiltration. The relative magnitude and importance of these processes depends on a host of factors, including climate, soil, topography, cropping and land management practices, control practices, the antecedent conditions, and the size of the area under consideration. In this study, the results of a series of experiments are reported, summarizing the soil loss and runoff response from a 0.6 × 3.75 m area to different rainstorm regimes, slope steepnesses, subsurface soil water pressures, and surface roughnesses under controlled laboratory conditions using a flume and rainfall simulator as water applicators, and a laser microreliefmeter and tensiometric system as soil response measuring devices. The soil chosen was a highly erodible Grenada loess (fine silty, mixed, thermic, Glossic Fragiudalf). The results showed: (1) a sequence of rainstorms of decreasing intensity on an initially air-dry smooth surface caused more soil loss than a sequence of similar storms of increasing intensity; (2) the surface roughness - sediment concentration relationship was not monotonic in nature; (3) subsurface soil water pressure substantially affected sediment concentration in runoff but only marginally impacted runoff amounts; (4) initially smooth, uniform surfaces may yield less soil loss than initially rough surfaces; (5) interrill runoff occurred as spatially varying flow in which flow patterns determine the locations of rills. Published by Elsevier Science B.V.},
author = {R{\"{o}}mkens, M. J M and Helming, K and Prasad, S N},
doi = {10.1016/S0341-8162(01)00161-8},
isbn = {0341-8162},
issn = {03418162},
journal = {Catena},
keywords = {Drainage networks,Erosion processes,Roughness,Sediment concentration,Seepage,Soil water pressure,Surface microrelief},
number = {2-3},
pages = {103--123},
title = {{Soil erosion under different rainfall intensities, surface roughness, and soil water regimes}},
volume = {46},
year = {2002}
}
@article{Rose1983,
author = {Rose, C. W. and Williams, J. R. and Sander, G. C. and Barry, D. A.},
doi = {10.2136/sssaj1983.03615995004700050030x},
issn = {0361-5995},
journal = {Soil Science Society of America Journal},
number = {5},
pages = {991},
publisher = {Soil Science Society of America},
title = {{A Mathematical Model of Soil Erosion and Deposition Processes: I. Theory for a Plane Land Element1}},
url = {https://www.soils.org/publications/sssaj/abstracts/47/5/SS0470050991},
volume = {47},
year = {1983}
}
@article{Rossi2015,
author = {Rossi, M. and Torri, D. and Santi, E.},
doi = {10.1007/s11069-015-1701-2},
issn = {0921-030X},
journal = {Natural Hazards},
month = {nov},
number = {S1},
pages = {51--69},
title = {{Bias in topographic thresholds for gully heads}},
url = {http://link.springer.com/10.1007/s11069-015-1701-2},
volume = {79},
year = {2015}
}
@article{Sadeghi2017,
abstract = {The particle size distribution (PSD) of the splashed sediment is expected to vary depending on rainfall intensity, slope steepness and slope position. This study therefore discusses the results of analysis of laboratorial experiments to compare PSDs of splashed materials in upward and downward directions of splash cup with original soil PSDs before runoff initiation from different parts of an erosion plot under different rainfall intensities at various slope gradients. To achieve the objectives, a set of laboratorial experiments were conducted using rainfall simulator at erosion plots scale. The rainfall intensities of 30, 60, and 90mmh−1 were applied at 5, 15 and 25{\%} plot slopes for a soil collected from Kojour rangeland watershed in the Alborz Mountains, northern Iran. Besides very oft-reported results of more splashed material in downward direction and positive effects of rainfall intensities (P{\textgreater}0.05) on rate of splashed materials, it was found that there were significant differences between clay, silt and sand contents of original soil and upward and downward splashed materials on slopes of 5 and 15{\%} in all study rainfall intensities. In general, comparison of D10, D50 and D90 of splashed materials in upward and downward splash cups were larger than those of original soil. Furthermore, the sorting of splashed materials in upward and downward of splash cups with respective amounts of 4.84–6.62$\mu$m and 5.13–6.54$\mu$m under different rainfall intensities and slopes were less than that of the original soil (8.12$\mu$m).},
author = {Sadeghi, Seyed Hamidreza and {Kiani Harchegani}, Mahboobeh and Asadi, Hossein},
doi = {10.1016/j.geoderma.2016.12.007},
issn = {00167061},
journal = {Geoderma},
pages = {100--106},
title = {{Variability of particle size distributions of upward/downward splashed materials in different rainfall intensities and slopes}},
volume = {290},
year = {2017}
}
@article{Sarmiento2006,
abstract = {The overall, spatially averaged, mean magnitude of local, spatially averaged (over a small area enclosing the particles' projected area), instantaneous, critical Shields shear-stress parameters required for incipient motion of uniform-sized sand grains, independent of the bed shear-velocity particle Reynolds number, equal to 0.16, is obtained from calibration of a theory for bed load sediment transport, by minimizing the sum of the squares of the deviations between theoretical and experimental bed load rates. Additionally, optimized expressions for a proposed probability density distribution of the bed shear stresses, for its standard deviation, for finite, maximum, and minimum bed shear stresses, and a bed load rate are obtained. In terms of the mean fluid shear stress, a dimensionless, critical, shear-stress parameter equal to 0.0513 is obtained. Investigation of the probability density distribution of the spatially varying, critical shear stresses would allow a more accurate formulation for the case of low transport rates.},
author = {Sarmiento, O A and Falcon, M A},
doi = {10.1061/(asce)0733-9429(2006)132:2(172)},
isbn = {0733-9429},
issn = {0733-9429},
journal = {Journal of Hydraulic Engineering-Asce},
keywords = {channels,entrainment,erosion,flows,fluvial hydraulics,incipient motion,movement,probabilistic methods,probability,protrusion,rivers,sediment transport,shear stress,transport},
number = {2},
pages = {172--179},
title = {{Critical bed shear stress for unisize sediment}},
volume = {132},
year = {2006}
}
@article{Schorghofer2002,
abstract = {For real landscapes, the local slope is related to the area of the$\backslash$ndrainage basin. Such relations do not always indicate a casual link$\backslash$nbetween drainage area and local slope. We provide a general and quantitative$\backslash$nassessment of this statistical effect. Slope-area relations in which$\backslash$nslopes decay slower than roughly the cube root of drainage area are$\backslash$ninsensitive to processes that have shaped the landscape. To illustrate$\backslash$nthis point, surfaces unrelated to erosion are compared to real landscapes.$\backslash$nThe fluctuations of slope for constant drainage area provide a means$\backslash$nof distinguishing between causal and random effects.},
author = {Schorghofer, Norbert},
doi = {10.1029/2002GL015144},
issn = {0094-8276},
journal = {Geophysical Research Letters},
keywords = {doi:10.102,http://dx.doi.org/10.1029/2002GL015144},
number = {13},
pages = {1633},
title = {{Acausal relations between topographic slope and drainage area}},
url = {http://www.ifa.hawaii.edu/{~}norb1/Papers/2002-slope.pdf{\%}5Cnhttp://segovia.mit.edu/publications/2002/slope.pdf{\%}5Cnhttp://www.agu.org/pubs/crossref/2002/2002GL015144.shtml{\%}5Cnhttp://doi.wiley.com/10.1029/2002GL015144},
volume = {29},
year = {2002}
}
@article{Seidl1992a,
abstract = {Although river incision into the bedrock of uplifted regions creates the dissected topography of landscapes, little is known about the process of channel erosion into bedrock. Here we present a testable framework for the study of fluvial incision into bedrock that combines theory with field observation. We quantify a simple erosion law by measuring drainage areas and slopes on both principal channels and tributaries. The data suggest that both a bedrock tributary and main stem will lower at the same rate at their confluence if the ratio of main stem to tributary drainage area equals the ratio of tributary to main stem channel slope at the junction. Erosion across several tributary junctions is therefore linearly related to stream power. Our results suggest three general mechanisms by which bedrock channels erode: 1) vertical wearing of the channel bed due to stream flow, by such processes as abrasion by transported particles and dissolution; 2) scour by periodic debris flows; and 3) knickpoint propagation. -from Authors},
author = {Seidl, Ma and Dietrich, We},
isbn = {3923381328},
issn = {0722-0723},
journal = {Catena Supplement},
pages = {101--124},
title = {{The problem of channel erosion into bedrock}},
url = {http://geography.uoregon.edu/amarcus/geog607w09/Readings/Seidl-Dietrich1992{\_}Catena{\_}Bedrock.pdf},
volume = {23},
year = {1992}
}

@Article{Shelef2021,
AUTHOR = {Shelef, E. and Goren, L.},
TITLE = {The rate and extent of wind-gap migration regulated by tributary confluences and avulsions},
JOURNAL = {Earth Surface Dynamics},
VOLUME = {9},
YEAR = {2021},
NUMBER = {4},
PAGES = {687--700},
URL = {https://esurf.copernicus.org/articles/9/687/2021/},
doi = {10.5194/esurf-9-687-2021}
}


@article{Shit2013,
author = {Shit, PK and Bhunia, GS and Maiti, Ramkrishna},
doi = {10.4236/jwarp.2013.52015},
journal = {Journal of Water Resource and Protection},
keywords = {rainfall simulation,rill network,sediment yield,slope gradient},
number = {2},
pages = {133--141},
title = {{Developments of rill networks: An experimental plot scale study}},
url = {http://www.scirp.org/journal/PaperInformation.aspx?paperID=27682},
volume = {5},
year = {2013}
}
@article{Shvidchenko2001,
abstract = {Results of an experimental study of the incipient motion of streambeds composed of sand/gravel sediment mixtures are reported and compared with the earlier findings for uniform sediments. The experiments were conducted in an 8 m long by 0.30 m wide glass-walled tilting flume and an 18 m long by 0.80–1.10 m wide trapezoidal concrete channel. A reference transport method is used to define the beginning of bed material movement. The experiments demonstrate that the incipient motion of individual size fractions within a mixture is controlled by their relative size with respect to median size (intergranular effects), mixture standard deviation (effect of the shape of grain-size distribution), absolute value of median size (absolute size effect), and bed slope (effect of relative depth on overall flow resistance). The shear stress at incipient motion of median-sized grains in mixtures is found to be the same as for uniform sediment of this size. The present findings are consistent with available flume and field data. A technique for calculating the critical shear stress of different grain sizes in coarse uniform sediments and unimodal/weakly bimodal sediment mixtures is proposed.},
author = {Shvidchenko, Andrey B. and Pender, Gareth and Hoey, Trevor B.},
doi = {10.1029/2000WR000036},
isbn = {0043-1397},
issn = {00431397},
journal = {Water Resources Research},
number = {8},
pages = {2273--2283},
title = {{Critical shear stress for incipient motion of sand/gravel streambeds}},
volume = {37},
year = {2001}
}
@article{Simpson2006,
abstract = {This paper presents a mathematical model coupling water flow and sediment transport dynamics that enables calculating the changing surface morphology through time and space. The model is based on the shallow water equations for flow, conservation of sediment concentration, and empirical functions for bed friction, substrate erosion and deposition. The sediment transport model is a non-capacity formulation whereby erosion and deposition are treated independently and influence the sediment flux by exchanging mass across the bottom boundary of the flow. The resulting hyperbolic system is solved using a finite volume, Godunov-type method with a first-order approximate Riemann solver. The model can be applied both to short time scales, where the flow, sediment transport and morphological evolution are strongly coupled and the rate of bed evolution is comparable to the rate of flow evolution, or to relatively long time scales, where the time scale of bed evolution associated with erosion and/or deposition is slow relative to the response of the flow to the changing surface and, therefore, the classical quasi-steady approximation can be invoked. The model is verified by comparing computed results with documented solutions. The developed model can be used to investigate a variety of problems involving coupled flow and sediment transport including channel initiation and drainage basin evolution associated with overland flow and morphological changes induced by extreme events such as tsunami.},
author = {Simpson, Guy and Castelltort, S{\'{e}}bastien},
doi = {10.1016/j.cageo.2006.02.020},
isbn = {0098-3004},
issn = {00983004},
journal = {Computers {\&} Geosciences},
keywords = {channel spacing,deposition,erosion,finite volume method,numerical modelling,riemann solver,shallow water equations},
number = {10},
pages = {1600--1614},
title = {{Coupled model of surface water flow, sediment transport and morphological evolution}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0098300406000458},
volume = {32},
year = {2006}
}
@article{Simpson2003,
author = {Simpson, Guy and Schlunegger, Fritz},
doi = {10.1029/2002JB002162},
keywords = {doi:10.102,http://dx.doi.org/10.1029/2002JB002162},
pages = {1--16},
title = {{Topographic evolution and morphology of surfaces evolving in response to coupled fluvial and hillslope sediment transport}},
journal = {Journal of Geophysical Research: Solid Earth},
volume = {108},
year = {2003}
}
@article{Sinclair2017a,
author = {Sinclair, Hugh},
doi = {10.1038/542041a},
issn = {0028-0836},
journal = {Nature},
month = {feb},
number = {7639},
pages = {36--41},
publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
title = {{Earth science: Making a mountain out of a plateau}},
url = {http://dx.doi.org/10.1038/542041a http://10.0.4.14/542041a http://www.nature.com/doifinder/10.1038/542041a},
volume = {542},
year = {2017}
}
@article{Singh2015,
author = {Singh, Arvind and Reinhardt, Liam and Foufoula-Georgiou, Efi},
doi = {10.1002/2015WR017161},
issn = {00431397},
journal = {Water Resources Research},
keywords = {climate change,landscape evolution,power spectral density,river network,slope‐area},
month = {jun},
number = {6},
pages = {4320--4337},
title = {{Landscape reorganization under changing climatic forcing: Results from an experimental landscape}},
url = {http://doi.wiley.com/10.1002/2015WR017161},
volume = {51},
year = {2015}
}
@article{Sklar2001,
abstract = {Recent theoretical investigations suggest that the rate of river incision into bedrock depends nonlinearly on sediment supply, challenging the common assumption that incision rate is simply proportional to stream power. Our measurements from laboratory abrasion mills support the hypothesis that sediment promotes erosion at low supply rates by pro-viding tools for abrasion, but inhibits erosion at high supply rates by burying underlying bedrock beneath transient deposits. Maximum erosion rates occur at a critical level of coarse-grained sediment supply where the bedrock is only partially exposed. Fine-grained sediments provide poor abrasive tools for lowering bedrock river beds because they tend to travel in suspension. Experiments also reveal that rock resistance to fluvial erosion scales with the square of rock tensile strength. Our results suggest that spatial and tem-poral variations in the extent of bedrock exposure provide incising rivers with a previously unrecognized degree of freedom in adjusting to changes in rock uplift rate and climate. Furthermore, we conclude that the grain size distribution of sediment supplied by hill-slopes to the channel network is a fundamental control on bedrock channel gradients and topographic relief. INTRODUCTION The topography of mountainous landscapes is created by the interaction of rock uplift and erosion. River incision into bedrock is the key erosional process that controls the rate of land-scape response to changes in rock uplift rate and climate (Howard et al., 1994). Numerical models of landscape evolution (e.g., Howard, 1994; Tucker and Slingerland, 1994; Willett, 1999) commonly assume that incision rate is proportional to stream power (Seidl and Die-trich, 1992), or equivalently shear stress (Howard and Kerby, 1983), and lump the in-fluence of rock strength, sediment supply, grain size, and other factors into a poorly de-fined ''rock erodibility'' coefficient. This sim-ple ''stream power'' bedrock-incision model has also been used in analysis of real land-scapes to infer patterns of crustal deformation (Kirby and Whipple, 2001) and the possible influence of climate change on late Cenozoic mountain uplift (Whipple et al., 1999). Studies of river longitudinal profiles suggest, however, that the stream power model may be too sim-ple to explain observed variations in incision rates (Stock and Montgomery, 1999) and pro-file shape (Sklar and Dietrich, 1998). In ad-dition, theoretical investigations (Sklar and Dietrich, 1998; Slingerland et al., 1997) sug-gest that the influences of sediment supply and grain size are too complex to fit into a linear coefficient and must be explicitly represented in models of bedrock incision. Our goal here is to pry open the conceptual black box of ''rock erodibility,'' and explore experimental-ly the role of sediment supply, grain size, and rock strength in controlling bedrock erosion rates. Gilbert (1877) was the first to propose that the quantity of sediment supplied to the river should influence bedrock-incision rates in two essential yet opposing ways: by providing tools for abrasion of exposed bedrock and by limiting the extent of exposure of bedrock on the channel bed. According to Gilbert's hy-pothesis, the maximum rate of incision should occur when the stream receives a moderate supply of sediment, relative to its sediment transport capacity. Incision rate is limited at lower supply rates by a shortage of abrasive tools (the ''tools effect'') and at higher supply rates by partial burial of the bedrock substrate beneath transient sediment deposits (the ''cov-erage effect''). The size distribution of sedi-ment grains supplied to the channel should also influence incision rates, because only the coarser fraction is capable of forming an al-luvial cover in actively incising river channels and because the finer fraction is carried in sus-pension and rarely collides with the bedrock bed. Various alternative incision models explic-itly include sediment supply through simple parameterization of the tools effect (Foley, 1980), the coverage effect (Beaumont et al., 1992), or both (Slingerland et al., 1997). We previously derived an incision rate law from the mechanics of saltating bedload (Sklar and Dietrich, 1998) that predicts a nonlinear de-pendence of incision rate on sediment supply,},
author = {Sklar, Leonard S. and Dietrich, William E.},
doi = {10.1130/0091-7613(2001)029<1087:SARSCO>2.0.CO;2},
isbn = {0091-7613},
issn = {0091-7613},
journal = {Geology},
keywords = {Erodibility,Erosion,Grain size,Landscape evolution,Rivers,Sediment supply,erodibility,erosion,grain size,landscape evolution,rivers,sediment supply},
number = {12},
pages = {1087},
publisher = {Geological Society of America},
title = {{Sediment and rock strength controls on river incision into bedrock}},
url = {http://geology.gsapubs.org/cgi/doi/10.1130/0091-7613(2001)029{\%}3C1087:SARSCO{\%}3E2.0.CO;2},
volume = {29},
year = {2001}
}
@article{Smith1972,
abstract = {Drainage basin evolution is modeled as the time development of an initial surface subject to conservation of sediment and water and a transport law qs = F(S, q) connecting the sediment flux qs with the local slope S and the discharge of surface water q. Two models are presented. The first is appropriate to a smooth surface on which no discrete channels have formed, and the second is appropriate to a family of V-shaped valleys, each containing a separate stream of negligible width. For the first model, some solutions are presented that describe the evolution of a long ridge for which the profile is independent of one spatial coordinate. The stability of such surfaces is then discussed. It is shown that, if F/q {\textless} ∂F/∂q, disturbances of small amplitude and small lateral scale will grow rapidly and presumably will lead to the formation of closely spaced channels directed down the slope, whereas, if F/q ≥ ∂F/∂q, such channels will tend to disappear. For a surface eroding without change of shape, convex portions are stable, and concave segments are unstable. The second model is less well developed, since conservation principles alone are insufficient to determine its evolution without some additional postulate describing the sideways migration of individual streams. It is shown how, if each stream moves so that the sediment fluxes entering from its two side slopes remain equal, a system of similar parallel valleys is unstable, and neighbors will tend to coalesce on a time scale comparable to that for erosion through a layer as thick as a valley is deep.},
author = {Smith, Terence R. and Bretherton, Francis P.},
doi = {10.1029/WR008i006p01506},
issn = {0043-1397},
journal = {Water Resources Research},
number = {6},
pages = {1506},
title = {{Stability and the conservation of mass in drainage basin evolution}},
volume = {8},
year = {1972}
}
@article{Stefanon2012,
abstract = {How do tidal networks respond to changes in relative mean sea level (RMSL)? The question on whether the morphological features of a tidal landscape retain signatures of past environmental forcings, or are in equilibrium with current ones, is critical to our prediction of the fate of residual tidal landforms. In the case of tidal networks, the issue is quite relevant owing to their fundamental role on landscape eco-morphodynamic evolution. Here we explore the response of tidal networks to cyclic variations in RMSL triggering tidal prism changes on the basis of laboratory experiments carried out in a synthetic lagoonal environment. A decrease in the tidal prism leads to network retreat and contraction of channel cross sections. Conversely, an increase in the tidal prism promotes network re-incision and re-expansion of channel cross sections: Network retreat and expansion tend to occur within the same planar blueprint. Our results show that the drainage density of tidal channels is linearly related to the landscape-forming prism, although this relation is speculated to hold with reasonable approximation as a statistical tendency rather than as a pointwise, instantaneous adaptation. Changes in tidal prism rapidly influence network efficiency in draining the intertidal platform and the related transport of water, sediments, nutrients and pollutants. This bears important consequences for quantitative predictions of the long-term ecomorphological adaptation of the tidal landscape to RMSL changes.},
author = {Stefanon, Luana and Carniello, Luca and D'Alpaos, Andrea and Rinaldo, Andrea},
doi = {10.1029/2012GL051953},
isbn = {0094-8276},
issn = {00948276},
journal = {Geophysical Research Letters},
keywords = {geomorphology,hydrology,tidal morphodynamics,tidal networks},
number = {12},
pages = {1--6},
title = {{Signatures of sea level changes on tidal geomorphology: Experiments on network incision and retreat}},
volume = {39},
year = {2012}
}
@article{Sweeney2015,
abstract = {University of Oregon geologists have seen ridges and valleys form in real time and—even though the work was a fast-forwarded operation done in a laboratory setting—they now have an idea of how climate change may impact landscapes.},
author = {Sweeney, Kristin E. and Roering, Joshua J. and Ellis, C.},
doi = {10.1126/science.aab0017},
isbn = {0036-8075},
issn = {0036-8075},
journal = {Science},
keywords = {r e p o,r t s,s ear ch},
number = {6243},
pages = {51--53},
title = {{Experimental evidence for hillslope control of landscape scale}},
url = {http://www.sciencemag.org/cgi/doi/10.1126/science.aab0017},
volume = {349},
year = {2015}
}
@article{Tamburrino2016,
author = {Tamburrino, Aldo and Carrillo, Daniela and Negrete, Felipe and Ihle, Christian},
doi = {10.1002/cjce.22498},
isbn = {9781634394444},
issn = {00084034},
journal = {The Canadian Journal of Chemical Engineering},
keywords = {Shields stress,critical shear stress,incipient motion,pseudoplastic fluid},
month = {jun},
number = {6},
pages = {n/a--n/a},
title = {{Critical shear stress for incipient motion of non-cohesive particles in open-channel flows of pseudoplastic fluids}},
url = {http://doi.wiley.com/10.1002/cjce.22498},
volume = {94},
year = {2016}
}
@article{Tarboton1997,
abstract = {A new procedure for the representation of flow directions and calculation of upslope areas using rectangular grid digital elevation models is presented. The procedure is based on representing flow direction as a single angle taken as the steepest downward slope on the eight triangular facets centered at each grid point. Upslope area is then calculated by proportioning flow between two downslope pixels according to how close this flow direction is to the direct angle to the downslope pixel. This procedure offers improvements over prior procedures that have restricted flow to eight possible directions (introducing grid bias) or proportioned flow according to slope (introducing unrealistic dispersion). The new procedure is more robust than prior procedures based on fitting local planes while retaining a simple grid based structure. Detailed algorithms are presented and results are demonstrated through test examples and application to digital elevation data sets.},
archivePrefix = {arXiv},
arxivId = {arXiv:1011.1669v3},
author = {Tarboton, David G.},
doi = {10.1029/96WR03137},
eprint = {arXiv:1011.1669v3},
isbn = {9788578110796},
issn = {00431397},
journal = {Water Resources Research},
keywords = {doi:10.1029/96WR03137,http://dx.doi.org/10.1029/96WR03137},
month = {feb},
number = {2},
pages = {309--319},
pmid = {25246403},
title = {{A new method for the determination of flow directions and upslope areas in grid digital elevation models}},
url = {http://doi.wiley.com/10.1029/96WR03137},
volume = {33},
year = {1997}
}
@article{Tatard2008,
abstract = {The study presented here is focussed on the question of the hydraulic nature of the threshold that allows a rill to start. A rainfall-simulation experiment was carried out to produce high-resolution flow-velocity data. The experiment employed a 10 m ?? 4 m experimental plot with a 1{\%} slope, which had been previously eroded and had a small rill formed in the middle. The experiment consisted of a 2 h 15???-long rainfall at a constant intensity of 69 mm h-1. Surface elevation was measured before rainfall at a horizontal resolution of 2.5 cm across, and 5 cm along the slope direction. During rainfall, flow-velocities were measured at 68 locations on the plot with the salt velocity gauge technology, an automated, miniaturized device based on the inverse modelling of the propagation of a salt plume. The experiment led to the collection of flow-velocity measurements which are novel in three ways: (i) the small size of the measured section, which was only 10-cm long and 1-cm wide, (ii) the wide range of measured flow-velocities, which ranged from 0.006 m s-1 to 0.27 m s-1 and, (iii) the large number of measured locations. The flow-velocity field was simulated with three models: PSEM{\_}2D solves the Saint-Venant equations in 2D, MAHLERAN uses a 1D kinematic wave in the slope direction coupled with a 2D flow-routing algorithm, and Rillgrow2, which involves an empirical runoff algorithm that is close in principle to the diffusion-wave equation in 2D. The Darcy-Weisbach friction factor (ff) and the infiltration parameters were calibrated in all cases to investigate the capabilities of the different models to reproduce flow hydraulics compatible with the onset of rilling. In a first set of numerical experiments, ff was set uniform, and calibration used only the hydrograph. The comparison of simulated and observed flow-velocity field showed that PSEM{\_}2D was the most satisfying model, at the cost of longer computational time. MAHLERAN gave surprisingly good results with regards to the simplicity of the model and its low computational needs. However, all models largely underestimated the highest velocity values, located in the rill. Furthermore, none of the models was able to simulate the Reynolds (Re) and Froude (Fr) numbers. The next numerical experiment was done with PSEM{\_}2D. Non-uniform ff values were calibrated by fitting the simulated flow-velocity field to the observed one. The latter simulation produced realistic simulations of Re and Fr. The hydraulic conditions at the transition from interrill flow to rill flow are discussed. The results support the theory that supercritical flows are a necessary condition for a rill to emerge from a smooth surface. ?? 2007 Elsevier B.V. All rights reserved.},
author = {Tatard, L and Planchon, O and Wainwright, J and Nord, G and Favis-Mortlock, D. and Silvera, N. and Ribolzi, O. and Esteves, M. and Huang, Chi Hua},
doi = {10.1016/j.jhydrol.2007.07.016},
issn = {00221694},
journal = {Journal of Hydrology},
keywords = {Erosion models,Interrill,Rainfall-simulation,Rill,Senegal,Water erosion},
number = {1-2},
pages = {1--12},
title = {{Measurement and modelling of high-resolution flow-velocity data under simulated rainfall on a low-slope sandy soil}},
volume = {348},
year = {2008}
}
@article{Temme2009,
author = {Temme, A. J. A. M. and Veldkamp, A.},
doi = {10.1002/esp.1758},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
month = {mar},
number = {4},
pages = {573--589},
title = {{Multi-process Late Quaternary landscape evolution modelling reveals lags in climate response over small spatial scales}},
url = {http://doi.wiley.com/10.1002/esp.1758},
volume = {34},
year = {2009}
}
@article{Tian2012,
author = {Tian, W. and Li, X. and Wang, X.-S. and Hu, B. X.},
doi = {10.5194/hessd-9-1163-2012},
issn = {1812-2116},
journal = {Hydrology and Earth System Sciences Discussions},
month = {jan},
number = {1},
pages = {1163--1205},
title = {{Coupling a groundwater model with a land surface model to improve water and energy cycle simulation}},
url = {http://www.hydrol-earth-syst-sci-discuss.net/9/1163/2012/},
volume = {9},
year = {2012}
}
@article{Torri2006,
abstract = {Research conducted during the first half of the last century has shown that a strong power relationship exists between channel width and total flow discharge in streams. Recent studies have shown that this power relationship can be theoretically derived for bankfull discharge in channels. The relationship has been extended empirically to rills and gullies, revealing that the discharge exponent for rills and gullies is significantly smaller than that for rivers. However, water flow in rills and gullies is only rarely bankfull, indicating that the theoretical explanation for the power relationship found for rivers does not apply to rills and gullies. In order to investigate the width−discharge relationships for rills and gullies, a new method is proposed based on field measurements of widths of concentrated-flow erosion channels both upstream and downstream of channel junctions. Although the method only allows the determination of the exponent of the power relationship, it is easy and inexpensive to apply. A total of 322 rill and gully channel junctions with various soils and land use types were investigated in Belgium, Italy and Spain. The obtained data confirmed the existence of the power relationship for rills and gullies, with the exponent varying from 0.43 for small rills (about 3 cm in width) to 0.5 for gullies (about 50 to 100 cm in width). The data did not allow deciding whether the exponent varies consistently with channel width or in a step-wise fashion. The exponent values obtained in this study are larger than those reported in previous studies, but this may result from differences in the definition of the discharge that eroded the channel to its current width.},
author = {Torri, D. and Poesen, J. and Borselli, L. and Knapen, A.},
doi = {10.1016/j.geomorph.2005.11.010},
issn = {0169555X},
journal = {Geomorphology},
number = {3},
pages = {273--279},
title = {{Channel width–flow discharge relationships for rills and gullies}},
volume = {76},
year = {2006}
}
@article{Torri2014,
abstract = {Gully head development represents a significant geomorphic process in a wide range of environments. Several studies investigated the critical topographic conditions, expressed by local slope gradient (s) and drainage area (A), controlling the development and position of gully heads in various landscapes. This review examines over 39 publications. After critically analysing the reported threshold data and after standardisation of the procedure to determine the critical topographic conditions for gully head development, i.e., sAb{\textgreater}k or s{\textgreater}kA−b some data sets were discarded because they were not compatible with the standard presentation of data as reported by the majority of studies. Hence, a detailed analysis was made of 63 reported s–A relationships for overland-flow induced gully-heads extracted from data sets collected in various parts of the world. A first examination of the behaviour of both the exponent b and the threshold coefficient k, which reflects the resistance of the site to gully head development, shows clear effects of land use on the value of k whereas the value of b does not seem to be affected. Further analyses are conducted of the recalculated threshold coefficients k, for two predefined constant values of the exponent b. The lowest k-values were observed for cropland followed by values for rangeland, pasture and forest. Effects of climate, rock fragment cover at the soil surface and water storage capacity of the gully catchment on k-values were also shown. The most interesting result is that for a given and constant b-value, the threshold coefficient k can be predicted using soil and vegetation characteristics, based on the NRCS Runoff Curve Number values and on surface rock fragment cover. Furthermore, the underlying physical processes explaining the value of the exponent b were analysed. Finally, a physically-based model, well anchored in the established theories, is proposed as a first step to predict gully head development in various landscapes and under changing environmental conditions. The results of this review clearly show that better and more reliable models can be built, including effects of land use, climate changes and natural disasters.},
author = {Torri, Dino and Poesen, Jean},
doi = {10.1016/j.earscirev.2013.12.006},
issn = {00128252},
journal = {Earth-Science Reviews},
pages = {73--85},
title = {{A review of topographic threshold conditions for gully head development in different environments}},
volume = {130},
year = {2014}
}
@article{Tucker2002,
author = {Tucker, G. E. and Whipple, K. X.},
doi = {10.1029/2001JB000162},
issn = {01480227},
journal = {Journal of Geophysical Research: Solid Earth},
month = {sep},
number = {B9},
pages = {ETG 1--1--ETG 1--16},
title = {{Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison}},
url = {http://doi.wiley.com/10.1029/2001JB000162},
volume = {107},
year = {2002}
}
@article{Tucker1994,
abstract = {Erosional escarpments are common features of high-elevation rifted$\backslash$ncontinents. Fission track data suggest that these escarpments form$\backslash$nby base level lowering and/or marginal uplift during rifting, followed$\backslash$nby lateral retreat of an erosion front across tens to hundreds of$\backslash$nkilometers. Previous modeling studies have shown that this characteristic$\backslash$npattern of denudation can have a profound impact upon marginal isostatic$\backslash$nuplift and the evolution of offshore sedimentary basins. Yet at present$\backslash$nthere is only a rudimentary understanding of the geomorphic mechanisms$\backslash$ncapable of driving such prolonged escarpment retreat. In this study$\backslash$nwe present a nonlinear, two-dimensional landscape evolution model$\backslash$nthat is used to assess the necessary and sufficient conditions for$\backslash$nlong-term retreat of a rift-generated escarpment. The model represents$\backslash$ntopography as a grid of cells, with drainage networks evolving as$\backslash$nwater flows across the grid in the direction of steepest descent.$\backslash$nThe model accounts for sediment production by weathering, fluvial$\backslash$nsediment transport, bedrock channel erosion, and hillslope sediment$\backslash$ntransport by diffusive mechanisms and by mass failure. Numerical$\backslash$nexperiments presented explore the effects of different combinations$\backslash$nof erosion processes and of dynamic coupling between denudation and$\backslash$nflexural isostatic uplift. Model results suggest that the necessary$\backslash$nand sufficient conditions for long-term escarpment retreat are (1)$\backslash$nincising bedrock channels in which the erosion rate increases with$\backslash$nincreasing drainage area, so that the channels steepen and propagate$\backslash$nheadward; (2) a low rate of sediment production relative to sediment$\backslash$ntransport efficiency, which promotes relief-generating processes$\backslash$nover diffusive ones; (3) high continental elevation, which allows$\backslash$ngreater freedom for fluvial dissection; and (4) any process, including$\backslash$nflexural isostatic uplift, that helps to maintain a drainage divide$\backslash$nnear an escarpment crest. Flexural isostatic uplift also facilitates$\backslash$nescarpment retreat by elevating topography in the vicinity of an$\backslash$neroding escarpment, thereby increasing channel gradients and accelerating$\backslash$nerosion which in turn generates additional isostatic uplift. Of all$\backslash$nthe above conditions, high continental elevation is common to most$\backslash$nrift margin escarpments and may ultimately be the most important$\backslash$nfactor.},
author = {Tucker, Gregory E and Slingerland, Rudy L},
doi = {10.1029/94JB00320},
isbn = {0148-0227},
issn = {01480227},
journal = {Journal of Geophysical Research: Solid Earth},
keywords = {DENUDATION,EVOLUTION,MAR,MOUNTAIN BELTS,UPLIFT},
number = {B6},
pages = {12229--12243},
title = {{Erosional dynamics, flexural isostasy, and long-lived escarpments: A numerical modeling study}},
url = {http://doi.wiley.com/10.1029/94JB00320},
volume = {99},
year = {1994}
}
@article{Tucker2010,
author = {Tucker, Gregory E. and Bradley, D. Nathan},
doi = {10.1029/2009JF001264},
issn = {0148-0227},
journal = {Journal of Geophysical Research},
keywords = {anomalous dispersion,hillslopes,nonlocality},
month = {mar},
number = {F1},
pages = {F00A10},
title = {{Trouble with diffusion: Reassessing hillslope erosion laws with a particle-based model}},
url = {http://doi.wiley.com/10.1029/2009JF001264},
volume = {115},
year = {2010}
}
@article{Tucker2010b,
author = {Tucker, Gregory E. and Hancock, Gregory R.},
doi = {10.1002/esp.1952},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {computer modelling,digital elevation model,geomorphology,hydrology,landscape evolution,numerical model},
month = {jan},
number = {1},
pages = {28--50},
publisher = {John Wiley {\&} Sons, Ltd.},
title = {{Modelling landscape evolution}},
url = {http://doi.wiley.com/10.1002/esp.1952},
volume = {35},
year = {2010}
}
@article{Tucker2010a,
author = {Tucker, Gregory E. and Hancock, Gregory R.},
doi = {10.1002/esp.1952},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
keywords = {computer modelling,digital elevation model,geomorphology,hydrology,landscape evolution,numerical model},
month = {jan},
number = {1},
pages = {28--50},
publisher = {John Wiley {\&} Sons, Ltd.},
title = {{Modelling landscape evolution}},
url = {http://doi.wiley.com/10.1002/esp.1952},
volume = {35},
year = {2010}
}
@article{Tucker2010c,
author = {Tucker, Gregory E. and Hancock, Gregory R.},
doi = {10.1002/esp.1952},
issn = {01979337},
journal = {Earth Surface Processes and Landforms},
month = {jan},
number = {1},
pages = {28--50},
title = {{Modelling landscape evolution}},
url = {http://doi.wiley.com/10.1002/esp.1952},
volume = {35},
year = {2010}
}
@article{Tucker1997,
author = {Tucker, Gregory E. and Slingerland, Rudy},
doi = {10.1029/97WR00409},
issn = {00431397},
journal = {Water Resources Research},
month = {aug},
number = {8},
pages = {2031--2047},
title = {{Drainage basin responses to climate change}},
url = {http://doi.wiley.com/10.1029/97WR00409},
volume = {33},
year = {1997}
}

@Article{vanderMeij2020,
AUTHOR = {van der Meij, W. M. and Temme, A. J. A. M. and Wallinga, J. and Sommer, M.},
TITLE = {Modeling soil and landscape evolution -- The effect of rainfall and land-use
change on soil and landscape patterns},
JOURNAL = {SOIL},
VOLUME = {6},
YEAR = {2020},
NUMBER = {2},
PAGES = {337--358},
URL = {https://soil.copernicus.org/articles/6/337/2020/},
DOI = {10.5194/soil-6-337-2020}
}
@article{VanderBeek2002,
author = {van der Beek, Peter and Champel, B{\'{e}}n{\'{e}}dicte and Mugnier, Jean-Louis},
doi = {10.1130/0091-7613(2002)030<0471:CODDOD>2.0.CO;2},
issn = {0091-7613},
journal = {Geology},
number = {5},
pages = {471},
publisher = {Geological Society of America},
title = {{Control of detachment dip on drainage development in regions of active fault-propagation folding}},
url = {http://geology.gsapubs.org/cgi/doi/10.1130/0091-7613(2002)030{\%}3C0471:CODDOD{\%}3E2.0.CO;2},
volume = {30},
year = {2002}
}
@article{Venditti2014,
abstract = {Bedrock erosion in rivers sets the pace of landscape evolution, influences the evolution of orogens and determines the size, shape and relief of mountains. A variety of models link fluid flow and sediment transport processes to bedrock incision in canyons. The model components that represent sediment transport processes are increasingly well developed. In contrast, the model components being used to represent fluid flow are largely untested because there are no observations of the flow structure in bedrock canyons. Here we present a 524-kilometre, continuous centreline, acoustic Doppler current profiler survey of the Fraser Canyon in western Canada, which includes 42 individual bedrock canyons. Our observations of three-dimensional flow structure reveal that, as water enters the canyons, a high-velocity core follows the bed surface, causing a velocity inversion (high velocities near the bed and low velocities at the surface). The plunging water then upwells along the canyon walls, resulting in counter-rotating, along-stream coherent flow structures that diverge near the bed. The resulting flow structure promotes deep scour in the bedrock channel floor and undercutting of the canyon walls. This provides a mechanism for channel widening and ensures that the base of the walls is swept clear of the debris that is often deposited there, keeping the walls nearly vertical. These observations reveal that the flow structure in bedrock canyons is more complex than assumed in the models presently used. Fluid flow models that capture the essence of the three-dimensional flow field, using simple phenomenological rules that are computationally tractable, are required to capture the dynamic coupling between flow, bedrock erosion and solid-Earth dynamics.},
author = {Venditti, Jeremy G. and Rennie, Colin D. and Bomhof, James and Bradley, Ryan W. and Little, Malcolm and Church, Michael},
doi = {10.1038/nature13779},
isbn = {0028-0836},
issn = {0028-0836},
journal = {Nature},
month = {sep},
number = {7519},
pages = {534--537},
pmid = {25254474},
title = {{Flow in bedrock canyons}},
url = {http://www.nature.com/doifinder/10.1038/nature13779 http://www.ncbi.nlm.nih.gov/pubmed/25254474},
volume = {513},
year = {2014}
}
@article{Viveen2014,
abstract = {A terrace formation model (TERRACE) combined with a longitudinal river profile model (FLUVER) was used to simulate fluvial terrace formation and preservation in the northwest Iberian lower Mi{\~{n}}o River basin under the influence of three tectonic conditions; namely regional vertical uplift, local basin subsidence, and localised differential uplift. The simulation results were compared against mapped terrace altitudes and deposit thicknesses. The best results were achieved by combining all three tectonic factors, indicating that specific terrace formation is a complex interplay of regional and local tectonics. The best fit regional uplift rate of 0.10mka−1 over the past 600ka is higher than the 0.08mka−1 previously estimated for a section farther to the west, which can be attributed to an increase in tectonic uplift from the NW Iberian Atlantic margin toward the east. Local relative subsidence causes sediment accumulation in the local basin and less sedimentation in the fluvial terraces on the surrounding uplifting blocks. Different uplift rates on both sides of the valley caused preservation of unpaired terraces, which are fill terraces on one side of the valley and strath terraces on the other side. Usually, the formation of fill or strath terraces is considered to be only climate-dependent. Our results indicate that local tectonics can be important in the terrace formation and preservation. This suggests that terrace correlations in other river systems, based on deposit thicknesses only, might be over-simplified.},
author = {Viveen, W. and Schoorl, J.M. and Veldkamp, A. and van Balen, R.T.},
doi = {10.1016/j.geomorph.2013.12.026},
issn = {0169555X},
journal = {Geomorphology},
pages = {119--135},
title = {{Modelling the impact of regional uplift and local tectonics on fluvial terrace preservation}},
volume = {210},
year = {2014}
}
@book{Wainwright2005,
abstract = {2nd ed.},
address = {Chichester, UK},
editor = {Wainwright, John and Mulligan, Mark},
isbn = {978-0-470-74911-1},
pages = {494},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Environmental modelling : Finding simplicity in complexity}},
year = {2005}
}
@article{Wang2014,
abstract = {Rainfall kinetic energy (KE) can break down aggregates in the soil surface. A better understanding of sediment sorting associated with various KEs is essential for the development and verification of soil erosion models. A clay loam soil was used in the experiments. Six KEs were obtained (76, 90, 105, 160, 270, and 518Jm-2h-1) by covering wire screens located above the soil surface with different apertures to change the size of raindrops falling on the soil surface, while maintaining the same rainfall intensity (90±3.5mmh-1). For each rainfall simulation, runoff and sediment were collected at 3-min intervals to investigate the temporal variation of the sediment particle size distribution (PSD). Comparison of the sediment effective PSD (undispersed) and ultimate PSD (dispersed) was used to investigate the detachment and transport mechanisms involved in sediment mobilization. The effective-ultimate ratios of clay-sized particles were less than 1, whereas that of sand-sized particles were greater than 1, suggesting that these particles were transported as aggregates. Under higher KE, the effective-ultimate ratios were much closer to 1, indicating that sediments were more likely transported as primary particles at higher KE owing to an increased severity of aggregate disaggregation for the clay loam soil. The percentage of clay-sized particles and the relative importance of suspension-saltation increased with increasing KE when KE was greater than 105Jm-2h-1, while decreased with increasing KE when KE was less than 105Jm-2h-1. A KE of 105Jm-2h-1 appeared to be a threshold level beyond which the disintegration of aggregates was severe and the influence of KE on erosion processes and sediment sorting may change. Results of this study demonstrate the need for considering KE-influenced sediment transport when predicting erosion. {\textcopyright} 2014 Elsevier B.V.},
author = {Wang, L. and Shi, Z.H. and Wang, J. and Fang, N.F. and Wu, G.L. and Zhang, H.Y.},
doi = {10.1016/j.jhydrol.2014.02.066},
isbn = {0022-1694},
issn = {00221694},
journal = {Journal of Hydrology},
keywords = {Rainfall kinetic energy,Sediment size,Transport mechanisms},
month = {may},
pages = {168--176},
title = {{Rainfall kinetic energy controlling erosion processes and sediment sorting on steep hillslopes: A case study of clay loam soil from the Loess Plateau, China}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022169414001772},
volume = {512},
year = {2014}
}
@article{Whipple2017a,
author = {Whipple, K. X. and Forte, A. M. and DiBiase, R. A. and Gasparini, N. M. and Ouimet, W. B.},
doi = {10.1002/2016JF003973},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {divide migration,landscape evolution,response time,river profiles},
month = {jan},
number = {1},
pages = {248--273},
title = {{Timescales of landscape response to divide migration and drainage capture: Implications for the role of divide mobility in landscape evolution}},
url = {http://doi.wiley.com/10.1002/2016JF003973},
volume = {122},
year = {2017}
}
@article{Whipple2016,
author = {Whipple, K. X. and Forte, A. M. and DiBiase, R. A. and Gasparini, N. M. and Ouimet, W. B.},
doi = {10.1002/2016JF003973},
issn = {21699003},
journal = {Journal of Geophysical Research: Earth Surface},
keywords = {Divide migration,Landscape evolution,Response time,River profiles,divide migration,landscape evolution,response time,river profiles},
title = {{Timescales of landscape response to divide migration and drainage capture: Implications for the role of divide mobility in landscape evolution}},
url = {http://doi.wiley.com/10.1002/2016JF003973},
year = {2016}
}
@article{Whipple2017,
author = {Whipple, Kelin X. and DiBiase, Roman A. and Ouimet, William B. and Forte, Adam M.},
doi = {10.1130/G38490.1},
issn = {0091-7613},
journal = {Geology},
month = {jan},
number = {1},
pages = {91--94},
publisher = {Geological Society of America},
title = {{Preservation or piracy: Diagnosing low-relief, high-elevation surface formation mechanisms}},
url = {http://geology.gsapubs.org/lookup/doi/10.1130/G38490.1},
volume = {45},
year = {2017}
}
@article{Whipple1999,
author = {Whipple, Kelin X. and Tucker, Gregory E.},
doi = {10.1029/1999JB900120},
issn = {01480227},
journal = {Journal of Geophysical Research: Solid Earth},
month = {aug},
number = {B8},
pages = {17661--17674},
title = {{Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs}},
url = {http://doi.wiley.com/10.1029/1999JB900120},
volume = {104},
year = {1999}
}
@article{Wiberg1987,
abstract = {An expression for the critical shear stress noncohesive sediment is derived from the balance of forces on individual particles at the surface of a bed. The resulting equation, for a given grain size and density, depends on the near-bed drag force, lift force to drag force ratio, and particle angle of repose. Calculated values of the critical shear stress for uniformly sized sediment correspond closely to those determined from Shields' diagram. The initial motion problem for mixed grain sizes additionally depends on the relative protrusion of the grains into the flow and the particle angle of repose. The latter decreases when the diameter of a moving grain, D, is larger than the length scale of the bed roughness, ks (D/ks {\textgreater} 1), and increases when D/ks {\textless} 1, producing a corresponding decrease or increase in critical shear stress. Using the Miller and Byrne experimental relationship between D/ks and particle angle of repose, which is consistent with Shields' definition of initial motion, we obtain results that are in good agreement with the available experimental critical shear stress data for heterogeneous beds.},
author = {Wiberg, Patricia L. and Smith, J. Dungan},
doi = {10.1029/WR023i008p01471},
isbn = {0043-1397},
issn = {19447973},
journal = {Water Resources Research},
month = {aug},
number = {8},
pages = {1471--1480},
title = {{Calculations of the critical shear stress for motion of uniform and heterogeneous sediments}},
url = {http://doi.wiley.com/10.1029/WR023i008p01471},
volume = {23},
year = {1987}
}

@article{Whipple2002,
author = {Whipple, Kelin X. and Tucker, Gregory E.},
title = {Implications of sediment-flux-dependent river incision models for landscape evolution},
journal = {Journal of Geophysical Research: Solid Earth},
volume = {107},
number = {B2},
pages = {ETG 3-1-ETG 3-20},
keywords = {Tectonic geomorphology, Erosion, Sediment-flux, Bedrock channels, Relief},
doi = {10.1029/2000JB000044},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000JB000044},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB000044},
abstract = {Developing a quantitative understanding of the factors that control the rate of river incision into bedrock is critical to studies of landscape evolution and the linkages between climate, erosion, and tectonics. Current models of long-term river network incision differ significantly in their treatment of the role of sediment flux. We analyze the implications of various sediment-flux-dependent incision models for large-scale topography, in an attempt (1) to identify quantifiable and diagnostic differences between models that could be detected from topographic data or from the transient responses of perturbed systems and (2) to explain the apparent ubiquity of mixed bedrock-alluvial channels in active orogens. Although certain forms of the various models can be discarded as inconsistent with morphological data, we find that the relative intrinsic concavity indices of detachment- and transport-limited systems (defined herein) largely dictate whether the various models can be tied to distinctive steady state morphologies. Preliminary data suggest that no such diagnostic differences may exist, and other methods must be developed to test models. Accordingly, we develop and explore differences in the scaling behavior of topographic relief and the extent of detachment- versus transport-limited channels as a function of rock uplift rate that may allow discrimination among various models. Further, we explore potentially diagnostic differences in the rates and patterns of transient channel response to changes in rock uplift rate. In addition to general differences between detachment- and transport-limited systems our analysis identifies an interesting hysteresis in landscape evolution: “hybrid” channels at the threshold between detachment- and transport-limited conditions are expected to act as detachment-limited systems in response to an increase in rock uplift rate (or base level fall) and as transport-limited systems in response to a decrease in rock uplift rate, especially during postorogenic topographic decline. The analyses presented set the stage for field studies designed to test quantitatively the various river incision models that have been proposed.},
year = {2002}
}
@article{Wilcock1993,
abstract = {The critical shear stress of individual fractions tau(ci) in unimodal and weakly bimodal sediments shows little variation with grain size and depends only on the mean grain size of the mixture. For strongly bimodal sediments, tau(ci) increases with grain size, an apparent result of a lateral segregation of the finer and coarser fractions on the bed surface that causes tau(ci) to deviate from size independence in the direction of unisize (Shields) values. A quantitative definition of mixture bimodality may be used to estimate the degree of mixture bimodality beyond which a substantial size dependence of tau(ci) is observed and to predict the variation of tau(ci) with grain size in bimodal sediments. Because properties of sediment grain-size distributions other than bimodality appear to have little influence on tau(ci) the trends presented here for 14 unimodal and bimodal sediments may be quite general.},
author = {Wilcock, Peter R},
doi = {10.1061/(ASCE)0733-9429(1993)119:4(491)},
isbn = {0733-9429},
issn = {0733-9429},
journal = {Journal of Hydraulic Engineering},
keywords = {BEDLOAD,ENTRAINMENT,GRAVEL-BED STREAMS,LOAD,MIXED-SIZE SEDIMENT,MOTION,MOVEMENT,RIVERS,THRESHOLD,TRANSPORT},
number = {4},
pages = {491--505},
title = {{Critical Shear Stress of Natural Sediments}},
volume = {119},
year = {1993}
}
@article{Willett2014,
abstract = {River networks evolve as migrating drainage divides reshape river basins and change network topology by capture of river channels. We demonstrate that a characteristic metric of river network geometry gauges the horizontal motion of drainage divides. Assessing this metric throughout a landscape maps the dynamic states of entire river networks, revealing diverse conditions: Drainage divides in the Loess Plateau of China appear stationary; the young topography of Taiwan has migrating divides driving adjustment of major basins; and rivers draining the ancient landscape of the southeastern United States are reorganizing in response to escarpment retreat and coastal advance. The ability to measure the dynamic reorganization of river basins presents opportunities to examine landscape-scale interactions among tectonics, erosion, and ecology.},
author = {Willett, S D and McCoy, S W and Perron, J T and Goren, L and Chen, C Y},
doi = {10.1126/science.1248765},
isbn = {1095-9203 (Electronic)$\backslash$r0036-8075 (Linking)},
issn = {1095-9203},
journal = {Science},
keywords = {*Rivers,*Water Movements,Climate,Geologic Sediments,Models, Theoretical,Soil,Taiwan,United States},
number = {6175},
pages = {1248765},
pmid = {24604204},
title = {{Dynamic reorganization of river basins}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24604204},
volume = {343},
year = {2014}
}
@article{Willett2014a,
author = {Willett, S. D. and McCoy, S. W. and Perron, J. T. and Goren, L. and Chen, C.-Y.},
doi = {10.1126/science.1248765},
issn = {0036-8075},
journal = {Science},
month = {mar},
number = {6175},
pages = {1248765--1248765},
title = {{Dynamic Reorganization of River Basins}},
url = {http://www.sciencemag.org/cgi/doi/10.1126/science.1248765},
volume = {343},
year = {2014}
}
@article{Willgoose2005,
abstract = {The mathematical modeling of landform evolution consists of two components: the processes represented (i.e., considered dominant) in the model and the (typically computer) model representation of these processes. This review discusses the current debates surrounding processes represented in landform evolution. The potential impact on both evolving landforms and computer model structure is discussed. Issues specifically discussed include (a) the fundamental nature of mass conservation and the role of detachment- and transport-limited processes in mass conservation equations, (b) the interaction between detachment- and transport-limitation in channels, (c) the role of hillslope erosion and soil properties and their interaction with channel processes, (d) the interactions with tectonics when applying these models at large scale, (e) depositional structures and implications for paleo-climatic interpretation, (f) engineering applications of these models, and (g) numerical issues in the computer implementations. This review is not a model comparison. However, many applications are at the boundaries of computer capabilities so a comparison of existing models is provided.},
author = {Willgoose, Garry},
doi = {10.1146/annurev.earth.33.092203.122610},
isbn = {0084-6597$\backslash$r1545-4495},
issn = {0084-6597},
journal = {Annual Review of Earth and Planetary Sciences},
keywords = {LEMs,erosion,landform evolution models,quantitative dynamic stratigraphy,sedimentology},
month = {may},
number = {1},
pages = {443--459},
publisher = {Annual Reviews},
title = {{Mathematical Modeling of Whole Landscape Evolution}},
url = {http://www.annualreviews.org/doi/10.1146/annurev.earth.33.092203.122610 http://www.annualreviews.org/doi/abs/10.1146/annurev.earth.33.092203.122610{\%}5Cnhttp://www.annualreviews.org/doi/pdf/10.1146/annurev.earth.33.092203.122610},
volume = {33},
year = {2005}
}
@phdthesis{Willgoose1989,
abstract = {Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1989.},
author = {Willgoose, Garry Raymond},
keywords = {Civil Engineering.},
pages = {TR 322},
publisher = {Massachusetts Institute of Technology},
school = {Massachusetts Institute of Technology, https://dspace.mit.edu/handle/1721.1/14316},
title = {{A Physically Based Channel Network and Catchment Evolution Model}},
url = {http://hdl.handle.net/1721.1/14316 http://dspace.mit.edu/handle/1721.1/14316},
year = {1989}
}
@article{Willgoose1991,
abstract = {This paper explores the scaling and similitude properties of the system of governing equations for a catchment evolution model that was presented in an accompanying paper (Willgoose et al., this issue). Similitude is an important concept that allows the quantification of the similarities of, and differences between, two catchments. Through the use of a small number of nondimensional numbers the governing physics of the channel network and surrounding hillslopes in a catchment may be summarized. These nondimensional numbers lead to similarity conditions that allow for the quantitative comparison of data between field catchments and between the field scale and the controlled experimental scale. Derived relationships are presented for the drainage density of the channel network and the rate at which the network grows, parameterized using the nondimensional numbers. Drainage density is shown to be mostly a function of the hillslope channel initiation number that relates the slopes and lengths of hillslopes in a very simple fashion. Finally, it is shown that the form of a channel network is very sensitive to initial conditions. Though the exact form of the network and the hillslopes may vary greatly, along with their topological statistics, physical statistics such as drainage density are only slightly affected.},
author = {Willgoose, Garry and Bras, Rafael L. and Rodriguez-Iturbe, Ignacio},
doi = {10.1029/91WR00936},
isbn = {0043-1397},
issn = {19447973},
journal = {Water Resources Research},
number = {7},
pages = {1685--1696},
title = {{A coupled channel network growth and hillslope evolution model: 2. Nondimensionalization and applications}},
volume = {27},
year = {1991}
}
@article{Willgoose1992,
abstract = {A recently proposed model of catchment evolution is used as the basis to study the relationships between catchment and hillslope properties. The results highlight the interaction of the large-scale and small-scale features of the landscape. Tectonic uplift influences the catchment gradient, in turn influencing the hillslope gradient and thus the drainage density. But equally the hillslope ad channel gradients are related by sediment transport continuity so that catchment gradient is influenced by hillslope gradient. Neither the hillslope nor the channel network can be studied independently of the other. Catchment gradients are explicitly related to regional climatic and geologic conditions. Hillslope gradient and lenght are related via runoff and soil erosional properties. If hillslope gradient is known, then hillslope lenght and drainage density can be determined. In turn, drainage density can also be related to catchment scale properties. Via drainage density, it is then possible to obtain an explicit relationship between hillslope length and catchment gradient and area, lingking the basin's small-and large-scale features. {\textcopyright} 1992.},
author = {Willgoose, Garry and Bras, Rafael L. and Rodriguez-Iturbe, Ignacio},
doi = {10.1016/0169-555X(92)90056-T},
isbn = {0169-555X},
issn = {0169555X},
journal = {Geomorphology},
number = {1-2},
pages = {21--37},
title = {{The relationship between catchment and hillslope properties: Implications of a catchment evolution model}},
volume = {5},
year = {1992}
}
@article{Willgoose1990,
abstract = {The new landscape evolution model has two main elements. First, the elevations within the catchment - both hillslope and channel - are simulated by a mass transport continuity equation applied over geologic time. The model explicitly differentiates between the processes that act on the hillslopes and in the channels. The model's second element is an equation that initiates the advance of the channel heads into the surrounding hillslopes. -from Authors},
author = {Willgoose, Garry and Bras, Rafael L. and Rodriguez-Iturbe, Ignacio},
doi = {10.1029/90EO00349},
isbn = {00963941 (ISSN)},
issn = {00963941},
journal = {Eos},
keywords = {channel,channel head advance,hillslope,landscape evolution model,model,river basin evolution},
number = {47},
pages = {1806--1807},
title = {{A model of river basin evolution}},
url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0025691075{\&}partnerID=40{\&}md5=549bfae8d9d46bbeeea802d4258ae7be},
volume = {71},
year = {1990}
}
@article{Wu2020,
author = {Wu, Songbai and Chen, Li},
title = {Modeling Soil Erosion With Evolving Rills on Hillslopes},
journal = {Water Resources Research},
volume = {56},
number = {10},
pages = {e2020WR027768},
keywords = {rill network, hillslope, soil erosion, geomorphic evolution, model, WEPP},
doi = {10.1029/2020WR027768},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020WR027768},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2020WR027768},
note = {e2020WR027768 2020WR027768},
abstract = {Abstract Whereas current erosion models are successful in quantitative estimates of soil erosion by water flow, modeling the coevolution of geomorphological features, particularly rill network properties and soil erosion on hillslopes, is still a major challenge. In this study, we propose a rill evolution modeling approach and combine it with a rainfall-runoff and soil erosion model to simulate the feedback loop of hillslope geomorphic development and soil erosion processes. Rill evolution is mainly characterized by three rill network attributes, rill density, orientation angle, and rill width, all modeled with physical equations. The entire rainfall-runoff-erosion and rill evolution model is tested against a set of rill network evolution and soil erosion data from an experimental hillslope subjected to successive rainfall events. The simulated spatial and temporal variations of rill network characteristics and soil erosion agree well with the measured data. The results demonstrate that the three rill network characteristics continually alter the partitioning of interrill and rill flows and affect the interrill and rill flow erosivity and soil erosion, which in turn modify the rill geometry and rill network planform. Comparatively, existing approaches such as Water Erosion Prediction Project (WEPP) that ignore the rill evolution processes largely underestimate the hillslope soil erosion when using time independent model parameters. Moreover, a sensitivity analysis indicates that both the rill evolution and soil erosion processes are sensitive to the rill evolution parameters, rainfall intensity, and slope angle. These results can inform the development of general geomorphic evolution and soil erosion models on evolving rilled hillslopes.},
year = {2020}
}
@article{Yang2015,
abstract = {Landscapes on Earth retain a record of the tectonic, environmental and climatic history under which they formed. Landscapes tend towards an equilibrium in which rivers attain a stable grade that balances the tectonic production of elevation and with hillslopes that attain a gradient steep enough to transport material to river channels. Equilibrium low-relief surfaces are typically found at low elevations, graded to sea level. However, there are many examples of high-elevation, low-relief surfaces, often referred to as relict landscapes, or as elevated peneplains. These do not grade to sea level and are typically interpreted as uplifted old landscapes, preserving former, more moderate tectonic conditions. Here we test this model of landscape evolution through digital topographic analysis of a set of purportedly relict landscapes on the southeastern margin of the Tibetan Plateau, one of the most geographically complex, climatically varied and biologically diverse regions of the world. We find that, in contrast to theory, the purported surfaces are not consistent with progressive establishment of a new, steeper, river grade, and therefore they cannot necessarily be interpreted as a remnant of an old, low relief surface. We propose an alternative model, supported by numerical experiments, in which tectonic deformation has disrupted the regional river network, leaving remnants of it isolated and starved of drainage area and thus unable to balance tectonic uplift. The implication is that the state of low relief with low erosion rate is developing in situ, rather than preserving past erosional conditions.},
author = {Yang, Rong and Willett, Sean D and Goren, Liran},
doi = {10.1038/nature14354},
isbn = {0028-0836},
issn = {1476-4687},
journal = {Nature},
number = {7548},
pages = {526--9},
pmid = {25903633},
title = {{In situ low-relief landscape formation as a result of river network disruption}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/25903633},
volume = {520},
year = {2015}
}
@article{Yao2008,
abstract = {Quantifying critical conditions of rill formation can be useful for$\backslash$na better understanding of soil erosion processes. Current studies$\backslash$nlack a consensus and related rationale on how to describe these conditions.$\backslash$nThis study was based on the concepts that (1) the shear stress available$\backslash$nfor erosion at any given point is a function of the runoff rate,$\backslash$nthe slope steepness, and hydraulic characteristics of the surface;$\backslash$n(2) rill incision begins when overland flow shear stress exceeds$\backslash$nsoil critical shear stress; and (3) the distance from the top of$\backslash$nthe slope to the point where rills form can be measured and analyzed$\backslash$nas length to rill initiation and decreases with increase in slope$\backslash$nand rainfall intensity. These concepts were tested with a representative$\backslash$nsilty-clay soil from the Loess Plateau in northwestern China on a$\backslash$nlarge sloping indoor plot (8 × 3 m), with five different slopes using$\backslash$nsimulated rainfall at three rainfall intensities. Values of several$\backslash$nhydraulic parameters at rill initiation were determined from the$\backslash$nexperimental data. The results showed relationships among slope steepness,$\backslash$nrainfall intensity, and location of rill initiation. It was found$\backslash$nthat slope was relatively more important than rainfall intensity$\backslash$nin determining the location of rill initiation. Soil critical shear$\backslash$nstress determined in this study ranged from 1.33 to 2.63 Pa, with$\backslash$nan average of 1.94 Pa. Soil critical shear stress was inversely related$\backslash$nto slope and was not influenced by rainfall intensity. The results$\backslash$nof this study were comparable with those of previous investigators.},
author = {Yao, C. and Lei, T. and Elliot, W. J. and McCool, D. K. and Zhao, J. and Chen, S.},
issn = {21510032},
journal = {Transactions Of The American Society of Agricultural and Biological Engineers},
keywords = {1947,a process of detachment,agents,and transportation of soil,as,critical condition,critical shear,elliot and,ellison and ellison,erosion,hillslope,material by erosive,oil erosion is defined,rill initiation},
number = {1},
pages = {107--114},
title = {{Critical conditions for rill initiation}},
volume = {51},
year = {2008},
doi= {10.13031/2013.24231}
}
@article{Yetemen2015,
author = {Yetemen, Omer and Istanbulluoglu, Erkan and Flores-Cervantes, J. Homero and Vivoni, Enrique R. and Bras, Rafael L.},
doi = {10.1002/2014WR016169},
issn = {00431397},
journal = {Water Resources Research},
keywords = {catchment evolution,ecohydrology,geomorphology,landscape evolution,solar radiation,vegetation dynamics},
month = {feb},
number = {2},
pages = {1127--1157},
title = {{Ecohydrologic role of solar radiation on landscape evolution}},
url = {http://doi.wiley.com/10.1002/2014WR016169},
volume = {51},
year = {2015}
}
@article{Zongping2021,
title = {Sand cover enhances rill formation under laboratory rainfall simulation},
journal = {Catena},
volume = {205},
pages = {105472},
year = {2021},
issn = {0341-8162},
doi = {10.1016/j.catena.2021.105472},
url = {https://www.sciencedirect.com/science/article/pii/S0341816221003301},
author = {Zongping Ren and Xing Zhang and Xun-chang {(John) Zhang} and Zhanbin Li and Peng Li and ZhuangZhuang Zhou},
keywords = {Rill formation and development, Sand cover, Soil loss, Runoff generation mechanism},
abstract = {Soil erosion was severe in the wind-water erosion crisscross region of the northern Loess Plateau of China, where aeolian sand cover may enhance water erosion. In order to evaluate the effects of sand cover on runoff, soil loss and rill information, a series of rainfall simulation experiments was conducted in two contrasting treatments. One is a bare loess soil slope serving as a control, and another is a sand-covered loess slope (namely sand cover treatment). Nine simulated rains, 60 min each, were applied to each treatment in duplicates. The results showed that the runoff generation mechanism changed from infiltration-excess runoff in the control to subsurface saturation-excess runoff in the sand cover treatment. The runoff initiation was delayed about three folds in the sand cover treatment as compared to the control. Total runoff volumes and total soil loss in the sand cover treatment in each event were 1.1–1.2 times and 1.9–9.3 times those in the control treatment. A paired t-test showed that the runoff rates were greater in sand cover than in control in all events except for the last run at P < 0.05. The soil loss rates were greater in sand cover than in control for all events except the first rain at P < 0.05. Measured total rill length, width, and degree of rill dissection in the sand cover treatment were much greater than those in the control. The rill erosion of sand cover slope was dominated by the shallow and wider rills, while loess slope was dominated by the narrow and deeper rills. The results clearly indicated that a sand layer overlying a less pervious loess soil facilitated return flow and thus accelerated rill formation and development. This finding is in line with the common understanding that return flow in layered soil can promote rill formation and cause severe rill erosion, which is also important to understand the effect of wind-blown sand cover on water erosion in the wind-water erosion crisscross region.}
}