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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Volume 6, issue 1 | Copyright
Earth Surf. Dynam., 6, 77-99, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 15 Feb 2018

Research article | 15 Feb 2018

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

John J. Armitage1, Alexander C. Whittaker2, Mustapha Zakari1, and Benjamin Campforts3 John J. Armitage et al.
  • 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 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 105 years for post-perturbation sediment fluxes to return to within 50% of their initial values, for theoretical landscapes with a scale of 100×100km. 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 50kyr) 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 alluvial bedload. Consequently, while these end-member models do not reproduce all the complexity of processes seen in real landscapes, we argue that variations in long-term erosional dynamics within source catchments can fundamentally control when, how, and where sedimentary archives can record past environmental change.

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 a change in precipitation. However, if we model sediment transport rather than assume it is instantaneously removed, the model responds more rapidly, with a response time similar to that observed in nature.
We explore how two landscape evolution models respond to a change in climate. The two models are...