Preprints
https://doi.org/10.5194/esurf-2021-76
https://doi.org/10.5194/esurf-2021-76

  03 Nov 2021

03 Nov 2021

Review status: this preprint is currently under review for the journal ESurf.

Comparing the transport-limited and ξ−q models for sediment transport

Jean Braun1,2 Jean Braun
  • 1Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Potsdam, Germany
  • 2Institute of Earth and Environmental Sciences, University of Potsdam, Potsdam, Germany

Abstract. We present a comparison between two of the most widely used reduced-complexity models for the representation of sediment transport and deposition processes, namely the transport limited (or TL) model and the under-capacity (or ξ−q) model more recently developed by Davy and Lague (2009). Using both models, we investigate the behavior of a sedimentary continental system fed by a fixed sedimentary flux from a nearby active orogen though which sediments transit to a fixed base level representing a large river, a lake or an ocean. Our comparison shows that the two models share the same steady-state solution, for which we derive a simple 1D analytical solution that reproduces the major features of such sedimentary systems: a steep fan that connects to a shallower alluvial plain. The resulting fan geometry obeys basic observational constraints on fan size and slope with respect to the upstream drainage area, A0. The solution is strongly dependent on the size of the system, L, in comparison to a distance L0 that is determined by the size of A0 and gives rise to two fundamentally different types of sedimentary systems: constrained system where L<L0 and open systems where L>L0. We derive simple expressions that show the dependence of the system response time on the system characteristics, such as its length, the size of the upstream catchment area, the amplitude of the incoming sedimentary flux and the respective rate parameters (diffusivity or erodibility) for each of the two models. We show that the ξ−q model predicts longer response times, which we relate to its greater efficiency at propagating signals through its entire length. We demonstrate that, although the manner in which signals propagates through the sedimentary system differs greatly between the two models, they both predict that perturbations that last longer than the response time of the system can be recorded in the stratigraphy of the sedimentary system and in particular of the fan. Interestingly, the ξ−q model predicts that all perturbations in incoming sedimentary flux will be transmitted through the system whereas the TL model predicts that rapid perturbations cannot. We finally discuss why and under which conditions these differences are important and propose observational ways to determine which of the two models is most appropriate to represent natural systems.

Jean Braun

Status: open (until 01 Jan 2022)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on esurf-2021-76', Sebastien Carretier, 06 Dec 2021 reply

Jean Braun

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Short summary
By comparing two models for the transport of sediment, we find that they share a similar steady-state solution that adequately predicts the shape of most depositional systems made of a fan and an alluvial plain. The length of the fan is controlled by the size of the mountain drainage area feeding the sedimentary system and its slope by the incoming sedimentary flux. We show that the models differ by their transient behavior to external forcing and are characterized by different response times.