Preprints
https://doi.org/10.5194/esurf-2020-45
https://doi.org/10.5194/esurf-2020-45

  18 Jun 2020

18 Jun 2020

Review status: a revised version of this preprint is currently under review for the journal ESurf.

Graphically interpreting how incision thresholds influence topographic and scaling properties of modeled landscapes

Nikos Theodoratos1 and James W. Kirchner1,2 Nikos Theodoratos and James W. Kirchner
  • 1Dept. of Environmental Systems Science, ETH Zurich, Zurich, 8092, Switzerland
  • 2Swiss Federal Research Institute WSL, Birmensdorf, 8903, Switzerland

Abstract. We examine the influence of incision thresholds on topographic and scaling properties of landscapes that follow a landscape evolution model (LEM) with terms for stream-power incision, linear diffusion, and uniform uplift. Our analysis uses three main tools. First, we examine the graphical behavior of theoretical relationships between curvature and the steepness index (which depends on drainage area and slope). These relationships plot as straight lines for the case of steady-state landscapes that follow the LEM. These lines have slopes and intercepts that provide estimates of landscape characteristic scales. Such lines can be viewed as counterparts of slope–area relationships, which follow power laws in detachment-limited landscapes, but not in landscapes with diffusion. We illustrate the response of these curvature–steepness-index lines to changes in the values of parameters. Second, we define a Péclet number that quantifies the competition between incision and diffusion, while taking the incision threshold into account. We examine how this Péclet number captures the influence of the incision threshold on the degree of landscape dissection. Third, we characterize the influence of the incision threshold using a ratio between it and the steepness index. This ratio is a dimensionless number in the case of the LEM that we use, and reflects the fraction by which the incision rate is reduced due to the incision threshold; in this way, it quantifies the relative influence of the incision threshold across a landscape. These three tools can be used together to graphically illustrate how topography and process competition respond to incision thresholds.

Nikos Theodoratos and James W. Kirchner

 
Status: final response (author comments only)
Status: final response (author comments only)
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

Nikos Theodoratos and James W. Kirchner

Nikos Theodoratos and James W. Kirchner

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Short summary
We examine stream-power incision and linear diffusion landscape evolution models, with and without incision thresholds. We present a steady-state relationship between curvature and the steepness index, which plots as a straight line. We view this line as a counterpart to the slope–area relationship for the case of landscapes with hillslope diffusion. We show that simple shifts and rotations of such lines express graphically the topographic response of landscapes to changes in model parameters.