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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
19 May 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).
Numerical modelling landscape and sediment flux response to precipitation rate change
John J. Armitage1, Alexander C. Whittaker2, Mustapha Zakari1, and Benjamin Campforts3 1Institut de Physique du Globe de Paris, Université Sorbonne Paris Cité, Paris, France
2Department of Earth Science and Engineering, Imperial College London, London, UK
3Division Geography, Department of Earth and Environmental Sciences, KU Leuven, Heverlee, Belgium
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 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, 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 105 years for a landscape with a scale of 105 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 transport is difficult to justify for the transport of large grain sizes as an alluvial bed-load.

Citation: Armitage, J. J., Whittaker, A. C., Zakari, M., and Campforts, B.: Numerical modelling landscape and sediment flux response to precipitation rate change, Earth Surf. Dynam. Discuss.,, in review, 2017.
John J. Armitage et al.
John J. Armitage et al.
John J. Armitage et al.


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Publications Copernicus
Short summary
We explore how two landscape evolution models respond to a change in climate. The two models are developed from a divergent assumption on the efficiency of sediment transport. Despite the different resulting mathematics, both numerical models display a similar functional response to change in precipitation. However, if we model sediment transport, rather than assume it is instantaneously removed, we find that the model responds more rapidly, with a response time similar to observed in Nature.
We explore how two landscape evolution models respond to a change in climate. The two models are...