Modelling hillslope evolution: linear and nonlinear transport relations

Martin, Y. E.

doi:10.1016/s0169-555x(99)00127-0

Cited by 96 publications

(92 citation statements)

References 39 publications

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“…Constraints on k at other sites are lacking, but given the range in T and V, we expect D to vary over less than 1 order of magnitude (D % 0.08 -0.6). It should be noted, however, that this value of diffusivity is much larger than those estimated for soil creep and other diffusion-like processes that have been measured at the hillslope scale where k ranges from 10 À2 to 10 À4 m 2 a À1 [see Martin and Church, 1997;Martin, 2000]. Diffusivity calculated for hillslopes experiencing episodic landslides tends to be $10 À1 m 2 a À1 [Martin, 2000].…”

Section: Appendix A: Equations For Nondimensional Variables and Parammentioning

confidence: 87%

“…It should be noted, however, that this value of diffusivity is much larger than those estimated for soil creep and other diffusion-like processes that have been measured at the hillslope scale where k ranges from 10 À2 to 10 À4 m 2 a À1 [see Martin and Church, 1997;Martin, 2000]. Diffusivity calculated for hillslopes experiencing episodic landslides tends to be $10 À1 m 2 a À1 [Martin, 2000]. The much higher estimates for the Siwalik Hills, estimated at a much larger length-scale than a single hillslope, suggest that nondiffusive processes are being included.…”

Section: Appendix A: Equations For Nondimensional Variables and Parammentioning

confidence: 97%

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Characteristics of steady state fluvial topography above fault‐bend folds

2007

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[1] In steady state convergent orogens, erosion balances lateral as well as vertical bedrock motions. For simple geometrical reasons, the difference between the total steady state erosion flux and its vertical component is up to 30% for typical fluvial slopes and bedrock streamline inclinations, suggesting that lateral advection is also likely to be expressed topographically. In order to understand these geomorphologic consequences, we focus on steady state topography developed on active fault-bend folds. First, we derive an analytical solution for the slopes of detachment-limited streams that incorporates lateral advection. Next, we conduct experiments using a numerical two-dimensional landscape evolution model (Channel-Hillslope Integrated Landscape Development model (CHILD)) incorporating linear diffusion on hillslopes and detachment-limited stream channel incision above a fault-bend fold. The concavity and steepness indices of steady state long profiles are functions of bedrock velocity magnitude and direction, streamflow direction, and fluvial erosivity. Asymmetry of mountain range profiles varies as a function of fluvial erosivity or bedrock velocity only if we account for the lateral velocity component. This asymmetry is equally sensitive to this lateral component, fluvial incision, and hillslope diffusion. However, the effect of diffusion on drainage divide position is significant only at high diffusivities, short length scales, low bedrock advection rates, or relatively low fluvial erosivity. Thus in most mountain ranges and fault blocks, drainage divide migration is expected to be dictated by stream channel erosion. Model results are shown to be consistent with topography in the Siwalik Hills, Nepal, which overlie fault-bend folds produced above the frontal fault systems in the Himalayan foreland.

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Section: Appendix A: Equations For Nondimensional Variables and Parammentioning

confidence: 87%

Section: Appendix A: Equations For Nondimensional Variables and Parammentioning

confidence: 97%

Characteristics of steady state fluvial topography above fault‐bend folds

2007

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“…with values for K D , the diffusivity, derived from hillslope measurements [Martin, 2000], i.e., in the range 0.01 to 1 m 2 yr -1 , leads to a substantial reduction in total eroded volume but does not affect the scaling of erosion with wavelength of dynamic topography (see Figure 1c), unless very large and unreasonable values of the diffusivity are assumed (> 1 m 2 yr -1 ).…”

Section: Discussionmentioning

confidence: 99%

Eroding dynamic topography

Braun

Robert

Simon‐Labric

2013

Geophysical Research Letters

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[1] Geological observations of mantle flow-driven dynamic topography are numerous, especially in the stratigraphy of sedimentary basins; on the contrary, when it leads to subaerial exposure of rocks, dynamic topography must be substantially eroded to leave a noticeable trace in the geological record. Here, we demonstrate that despite its low amplitude and long wavelength and thus very low slopes, dynamic topography is efficiently eroded by fluvial erosion, providing that drainage is strongly perturbed by the mantle flow driven surface uplift. Using simple scaling arguments, as well as a very efficient surface processes model, we show that dynamic topography erodes in direct proportion to its wavelength. We demonstrate that the recent deep erosion experienced in the Colorado Plateau and in central Patagonia is likely to be related to the passage of a wave of dynamic topography generated by mantle upwelling.

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“…There is growing evidence that many diffusional processes do behave more non-linear than previously assumed (Roering et al, 1999;Martin, 2000). Corresponding models suggest a continuous transition between linear diffusion at small slope angles, towards landsliding-like strongly nonlinear transport at high slope angles.…”

Section: Hillslope Gradientmentioning

confidence: 93%

Curvature distribution within hillslopes and catchments and its effect on the hydrological response

Bogaart

Troch

2006

Hydrol. Earth Syst. Sci.

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Abstract. Topographic convergence and divergence are first order controls on the hillslope and catchment hydrological response, as evidenced by similarity parameter analyses. Hydrological models often do not take convergence as measured by contour curvature directly into account; instead they use comparable measures like the topographic index, or the hillslope width function. This paper focuses on the question how hillslope width functions and contour curvature are related within the Plynlimon catchments, Wales. It is shown that the total width function of all hillslopes combined suggest that the catchments are divergent in overall shape, which is in contrast to the perception that catchments should be overall convergent. This so-called convergence paradox is explained by the effect of skewed curvature distributions and extreme curvatures near the channel network. The hillslopestorage Bossiness (hsB) model is used to asses the effect of within-hillslope convergence variability on the hydrological response. It is concluded that this effect is small, even when the soil saturation threshold is exceeded. Also described in this paper is a novel algorithm to compute flow path lengths on hillslopes towards the drainage network, using the multidirectional flow redistribution method.

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Modelling hillslope evolution: linear and nonlinear transport relations

Cited by 96 publications

References 39 publications

Characteristics of steady state fluvial topography above fault‐bend folds

Characteristics of steady state fluvial topography above fault‐bend folds

Eroding dynamic topography

Curvature distribution within hillslopes and catchments and its effect on the hydrological response

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