Topographic evolution and morphology of surfaces evolving in response to coupled fluvial and hillslope sediment transport

Simpson, Guy; Schlunegger, Fritz

doi:10.1029/2002jb002162

Cited by 119 publications

(127 citation statements)

References 44 publications

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“…6 and 8) then the models are linear, and we can solve the equations both analytically and in 1-D and 2-D numerical schemes. For the stream power model we use an implicit finite-difference scheme (Braun and Willett, 2013) and for the transport model we use an explicit finite-element scheme with linear elements (Simpson and Schlunegger, 2003). If n = 1 and if γ = 1 the equations become non-linear.…”

Section: Linear and Non-linear Solutionsmentioning

confidence: 99%

“…We then solve for Eq. (11) using the numerical model Fastscape (Braun and Willett, 2013), with a resolution of 1000 by 1000 nodes for a 100 by 100 km domain, giving a spatial resolution of 100 m. Erosion by sediment transport in 2-D is solved following the MATLAB model of Simpson and Schlunegger (2003), which is available from Simpson (2017). We solve Eq.…”

Section: Generalizing To a Two-dimensional Systemmentioning

confidence: 99%

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Numerical modelling of landscape and sediment flux response to precipitation rate change

et al. 2018

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Abstract. Laboratory-scale experiments of erosion have demonstrated that landscapes have a natural (or intrinsic) response time to a change in precipitation rate. In the last few decades there has been growth in the development of numerical models that attempt to capture landscape evolution over long timescales. However, there is still an uncertainty regarding the validity of the basic assumptions of mass transport that are made in deriving these models. In this contribution we therefore return to a principal assumption of sediment transport within the mass balance for surface processes; we explore the sensitivity of the classic end-member landscape evolution models and the sediment fluxes they produce to a change in precipitation rates. One end-member model takes the mathematical form of a kinetic wave equation and is known as the stream power model, in which sediment is assumed to be transported immediately out of the model domain. The second end-member model is the transport model and it takes the form of a diffusion equation, assuming that the sediment flux is a function of the water flux and slope. We find that both of these end-member models have a response time that has a proportionality to the precipitation rate that follows a negative power law. However, for the stream power model the exponent on the water flux term must be less than one, and for the transport model the exponent must be greater than one, in order to match the observed concavity of natural systems. This difference in exponent means that the transport model generally responds more rapidly to an increase in precipitation rates, on the order of 10 5 years for post-perturbation sediment fluxes to return to within 50 % of their initial values, for theoretical landscapes with a scale of 100 × 100 km. Additionally from the same starting conditions, the amplitude of the sediment flux perturbation in the transport model is greater, with much larger sensitivity to catchment size. An important finding is that both models respond more quickly to a wetting event than a drying event, and we argue that this asymmetry in response time has significant implications for depositional stratigraphies. Finally, we evaluate the extent to which these constraints on response times and sediment fluxes from simple models help us understand the geological record of landscape response to rapid environmental changes in the past, such as the Paleocene-Eocene thermal maximum (PETM). In the Spanish Pyrenees, for instance, a relatively rapid (10 to 50 kyr) duration of the deposition of gravel is observed for a climatic shift that is thought to be towards increased precipitation rates. We suggest that the rapid response observed is more easily explained through a diffusive transport model because (1) the model has a faster response time, which is consistent with the documented stratigraphic data, (2) there is a high-amplitude spike in sediment flux, and (3) the assumption of instantaneous transport is difficult to justify for the transport of large grain sizes as an alluvi...

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Section: Linear and Non-linear Solutionsmentioning

confidence: 99%

Section: Generalizing To a Two-dimensional Systemmentioning

confidence: 99%

Numerical modelling of landscape and sediment flux response to precipitation rate change

et al. 2018

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show abstract

“…For the stream power model we use an implicit finite difference scheme (Braun and Willett, 2013) and for the transport model we use an explicit finite element scheme with linear elements (Simpson and Schlunegger, 2003). If n = 1 and if γ = 1 the equations become non-linear.…”

Section: Linear and Non-linear Solutionsmentioning

confidence: 99%

“…In our case, to explore how a model landscape responds to change in uplift and precipitation rate we will make the simplest assumption available; that water flows down the steepest slope. We then solve for equation 6 using the numerical model Fastscape 15 (Braun and Willett, 2013), with a resolution of 1000 by 1000 nodes for a 100 by 100 km domain, giving a spatial resolution of 100 m. Erosion by sediment transport is solved following the methods of Simpson and Schlunegger (2003). We solve Equation 11 on a triangular grid with a resolution of 316 by 316 nodes for a 100 by 100 km domain, giving a spatial resolution of the order of 300 m. The time step used for both models is 10 kyrs.…”

Section: Generalizing To a Two Dimensional Systemmentioning

confidence: 99%

Numerical modelling landscape and sediment flux response to precipitation rate change

Armitage¹,

Whittaker²,

Zakari³

et al. 2017

Preprint

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Abstract. Laboratory-scale experiments of erosion have demonstrated that landscapes have a natural (or intrinsic) response time to a change in precipitation rate. In the last few decades there has been a growth in the development of numerical models that attempt to capture landscape evolution over long time-scales. Recently, a sub-set of these numerical models have been used to invert river profiles for past tectonic conditions even during variable climatic conditions. However, there is still an 5 uncertainty over validity of the basic assumption of mass transport that are made in deriving these models. In this contribution we therefore return to a principle assumption of sediment transport within the mass balance for surface processes, and explore the sensitivity of the classic end-member landscape evolution models to change in precipitation rates. One end-member model takes the mathematical form of a kinetic wave equation and is known as the stream power model, where sediment is assumed to be transported immediately out of the model domain. The second end-member model takes the form of a diffusion equation, 10 and assumes that the sediment flux is a function of the water flux and slope. We find that both of these end-member models have a response time that has a proportionality to the precipitation rate that follows a negative power law. For the stream power model the exponent on the water flux term must be less than one, and for the sediment transport model the exponent must be greater than one in order to match the observed concavity of natural systems. This difference in exponent means that sediment transport model responds more rapidly to an increase in precipitation rates, on the order of 10 5 years for a landscape with 15 a scale of 10 5 m. In nature, landscape response times to a rapid environmental change have been estimated for events such as the Paleocene-Eocene thermal maximum (PETM). In the Spanish Pyrenees, a relatively rapid, 20 to 100 kyr, duration of deposition of gravel during the PETM is observed for a climatic shift that is thought to be towards increased precipitation rates. We suggest the rapid response observed is more easily explained through a diffusive sediment transport model, as (1) this model has a faster response time, consistent with the documented stratigraphic data, and (2) the assumption of instantaneous 20 transport is difficult to justify for the transport of large grain sizes as an alluvial bed-load.

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“…Following earlier workers (see Simpson and Schlunegger [2003] for a review), Perron et al (2009) developed a framework for assessing landscape dissection by quantifying how the relative magnitudes of hillslope and valley-forming processes control the spacing of hills and valleys in soilmantled terrain. Their model separates hillslope transport and valley incision processes into diffusive (D) and advective (K) components, respectively.…”

Section: Introductionmentioning

confidence: 99%

Shaping post-orogenic landscapes by climate and chemical weathering

Chadwick

Roering

Heimsath

et al. 2013

Geology

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The spacing of hills and valleys refl ects the competition between disturbance-driven (or diffusive) transport on hillslopes and concentrative (or advective) transport in valleys, although the underlying lithologic, tectonic, and climatic controls have not been untangled. Here, we measure geochemical and geomorphic properties of catchments in Kruger National Park, South Africa, where granitic lithology and erosion rates are invariant, enabling us to evaluate how varying mean annual precipitation (MAP = 470 mm, 550 mm, and 730 mm) impacts hill-valley spacing or landscape dissection. Catchment-averaged erosion rates, based on 10 Be concentrations in river sands, are low (3-6 m/m.y.) and vary minimally across the three sites. Our lidar-derived slope-area analyses reveal that hillslopes in the dry site are gentle (3%) and short, such that the terrain is low relief and appears highly dissected. With increasing rainfall, hillslopes lengthen and increase in gradient (6%-8%), resulting in less-dissected, higher-relief catchments. The chemical depletion fraction of hilltop regoliths increases with rainfall, from 0.3 to 0.7, refl ecting a climate-driven increase in chemical relative to physical erosion. Soil catenas also vary systematically with climate as we observe relatively uniform soil properties in the dry site that contrast with leached sandy crests and upper slopes coupled with downslope clay accumulation zones in the intermediate and wet sites. The geomorphic texture of this slow-eroding, granitic landscape appears to be set by climate-driven feedbacks among chemical weathering, regolith fabric differentiation, hydrological routing, and sediment transport that enhance the vigor of hillslope sediment transport relative to valley-forming processes for wetter climates.

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Topographic evolution and morphology of surfaces evolving in response to coupled fluvial and hillslope sediment transport

Cited by 119 publications

References 44 publications

Numerical modelling of landscape and sediment flux response to precipitation rate change

Numerical modelling of landscape and sediment flux response to precipitation rate change

Numerical modelling landscape and sediment flux response to precipitation rate change

Shaping post-orogenic landscapes by climate and chemical weathering

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