Abstract
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.
Highlights
Processes that shape landscapes leave topographic signatures, which can often be visualized by plotting different topographic metrics against one another
In the case of the landscape evolution model (LEM) that we examine, the assumption of constant and uniform precipitation implies that any given combination of drainage area A and slope |∇z| would lead to the same value of stream power for any storm event, and this value of stream power would either be above or below the incision threshold
We present graphical methods that summarize topographic and scaling properties of landscapes following a simple stream-power incision and linear diffusion LEM (Eq 1) and that illustrate the effects of adding an incision threshold θ (Eq 2)
Summary
Processes that shape landscapes leave topographic signatures, which can often be visualized by plotting different topographic metrics against one another. The stream-power incision model predicts that if tectonics, climate, and rock properties are uniform, bedrock rivers should approach a steady state in which their gradient scales as a power law of drainage area (e.g., Tucker, 2004; Lague, 2014). Kirchner: Graphically interpreting landscape properties includes linear diffusion (along with stream-power incision and uplift) This relationship predicts that in steady state, curvature and the steepness index (which depends on drainage area and slope; e.g., Whipple, 2001) plot as a straight line against each other on linear (i.e., non-logarithmic) axes. The slope and intercept of this line depend on characteristic scales of length and height of the landscape, which in turn depend on the relative strengths of the processes that shape it This relationship predicts a link between topographic and scaling properties of landscapes that follow the LEM. The graphical explanatory power of these plots is further highlighted by comparing plots of LEMs with and without an incision threshold (Figs. 1 and 2)
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