A stream-power law for glacial erosion and its implementation in
large-scale landform-evolution models

Hergarten, Stefan

doi:https://doi.org/10.5194/esurf-2021-1

Preprints

https://doi.org/10.5194/esurf-2021-1

Preprints

22 Jan 2021

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

A stream-power law for glacial erosion and its implementation in large-scale landform-evolution models

Stefan Hergarten Stefan Hergarten Stefan Hergarten

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Institut für Geo- und Umweltnaturwissenschaften, Albert-Ludwigs-Universität Freiburg, Albertstr. 23B, 79104 Freiburg, Germany

Received: 14 Jan 2021 – Accepted for review: 20 Jan 2021 – Discussion started: 22 Jan 2021

Abstract. Modeling glacial landform evolution is more challenging than modeling fluvial landform evolution. While several numerical models of large-scale fluvial erosion are available, there are only a few models of glacial erosion, and their application over long time spans requires a high numerical effort. In this paper, a simple formulation of glacial erosion which is similar to the fluvial stream-power model is presented. The model reproduces the occurrence of overdeepenings, hanging valleys, and steps at confluences at least qualitatively. Beyond this, it allows for a seamless coupling to fluvial erosion and sediment transport. The recently published direct numerical scheme for fluvial erosion and sediment transport can be applied to the entire domain, where the numerical effort is only moderately higher than for a purely fluvial system. Simulations over several million years on lattices of several million nodes can be performed on standard PCs. An open-source implementation is freely available as a part of the landform evolution model OpenLEM.

Stefan Hergarten

Status: open (until 06 Mar 2021)

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RC1:
'Comment on esurf-2021-1', Eric Deal, 17 Feb 2021 reply

The comment was uploaded in the form of a supplement: https://esurf.copernicus.org/preprints/esurf-2021-1/esurf-2021-1-RC1-supplement.pdf
Reply

Citation: https://doi.org/10.5194/esurf-2021-1-RC1
- AC1: 'Reply on RC1', Stefan Hergarten, 22 Feb 2021 reply
  
  Dear Eric Deal,
  thanks a lot for your thorough and even inspiring review! I must apologize that I was indeed not aware of your latest paper in GRL. The first part of the theory was developed in a slightly different way, but is in fact basically the same. And you were definitely earlier, although I spent a lot of time on the numerics before submitting my manuscript.
  There is only one point where I clearly disagree with your opinion. This is the way erosion models of the stream-power type are formulated for non-constant precipitation. Probably owing to the fundamental studies of Hack, erodibilities have been expressed in terms of catchment size instead of discharge until now. If we want to keep this convention, there is no way of avoiding the definition of a reference precipitation p0 and imagining that a given erodibility refers to p0 . Then we can replace the catchment size A by either q/p0 where q is the discharge or even by pA/p0 , but where p is the mean discharge over the upstream catchment. Both versions become
  
  increasingly cumbersome when proceeding to the shared stream-power model and also for the fluvio-glacial version. Beyond this, I do not really like the concept where a mean upstream precipitation occurs in the erosion model and a local precipitation in the climatic component. Therefore, I do not like the version used by the Tübingen/Potsdam groups for some years, which also applies to the version with the product IA in your 2012 paper. My version of defining the ratio q/p0 as the catchment-size equivalent of the actual discharge provides a clear definition that keeps the equations similar to the original stream-power model. I am convinced that reminding
  
  the reader of this definition at some occurrences of A is sufficient to avoid confusion. So there is no realistic chance to convince me here.
  There is another point where I am not sure at all. In your final comment, you suggest to consider the version where the thickness is parameterized in terms of flux and slope instead of flux alone. However, my results already show that such a parameterization leads to a weird scaling of thickness vs. width in a steady state. While width is proportional to q^0.3 then, thickness is proportional to q^0.7. As far as I can see, your recent approach including deformation softens this problem, but thickness still increases more rapidly with flux than width. I guess that the problem already comes in when parameterizing the width by the flux alone without taking into account the slope. If so, it already affects the 2020 EPSL paper by Günther Prasicek where both of us were coauthors, but unfortunately I did not think about this at that time. So it would also be interesting to look at thickness vs. width in your recent results. But for my concept, this mainly tells me that we must consider all approximations as a package and compare it, e.g., to simulations with iSOSIA.
  Best regards,
  
  Stefan
  
  Reply
  
  Citation: https://doi.org/10.5194/esurf-2021-1-AC1

Stefan Hergarten

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Short summary

This paper presents a new approach to modeling glacial erosion on large scales. The formalism is similar to large-scale models of fluvial erosion, so glacial and fluvial processes can be easily combined. The model is simpler and numerically less demanding than established models based on a more detailed description of the ice flux. The numerical implementation achieves almost the efficiency of purely fluvial models, so that simulations over millions of years can be performed on standard PCs.


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