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.

Highlights

  • 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 model and the under-capacity model more recently developed by Davy and Lague (2009)

  • 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

  • We have derived a new analytical solution for the shape of a sedimentary system comprising a fan/piedmont deposit and the adjacent alluvial plain. This analytical solution shows that both model formulations can reproduce these first-order features and that, in both models, the transition between fan and plain deposits corresponds to the point where the contribution to runoff from the sedimentary system equals that of the upstream orogenic area

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Summary

Introduction

Sedimentary basins contain the record of Earth’s past tectonic and climatic histories To untangle this record, scientists often rely on the use of numerical models that simulate the physical processes controlling sediment production, transport and deposition. Sediment transport has been represented using a non-linear diffusion equation assuming that the process is limited by the transport capacity of rivers (the main transport agents) that is assumed to be proportional to slope and discharge and to other factors, including grain size (Henderson, 1966). We will name this model the transport-limited or T L model. The model has been used to study sedimentary systems away from the orogenic area (Carretier et al, 2016; Shobe et al, 2017; Yuan et al, 2019) and this has led to attempts (Guerit et al, 2019) to quantify the value of the main model parameter, ξ, originally described as a characteristic distance for deposition that depends on discharge but later remapped into the inverse of a rate (Carretier et al, 2016) or a dimensionless number (the Θ parameter of Davy and Lague (2009) or the G parameter of Yuan et al (2019))

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