Research ArticleGEOLOGY

Scale-dependent erosional patterns in steady-state and transient-state landscapes

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Science Advances  27 Sep 2017:
Vol. 3, no. 9, e1701683
DOI: 10.1126/sciadv.1701683
  • Fig. 1 Schematic representation of the XLE facility at St. Anthony Falls Laboratory, University of Minnesota.
  • Fig. 2 Characterization of statistical SS landscapes.

    (A) Slope-area curves of the landscape at SS computed for four different instances, separated by 5-min intervals. Note that the curves show averages over logarithmic area bins. (B) PDFs of the pixel-wise ED computed by differencing the topographic data of the SS landscape at consecutive (5 min apart) instances. The shape of the PDF confirms the statistical nature of the SS landscape (a frozen landscape would have a Dirac delta PDF centered at the uplift depth corresponding to 5 min). The question we pose is whether every pixel of the SS landscape has an equal likelihood to experience any value of this PDF (an equal chance of experiencing above or below the landscape median erosion), as commonly assumed. We show that this is not the case, and there is a preferential scale-dependent organization of erosional fluxes, as shown in Fig. 3.

  • Fig. 3 Scale-dependent SS landscape.

    (A) E50-area curves: The four curves (green, blue, red, and black) correspond to the fraction of pixels that erode more than the landscape median plotted against upstream contributing area, A, and are estimated using five consecutive (5 min apart) topographies at SS. The four curves overlap with each other, revealing a stationary statistical signature of the erosional processes acting on the landscape. The shape of E50-area curves for SS topographies differs from the straight line at 0.5 probability, which would be expected either for a strict topographic (frozen) SS landscape or for the case where the likelihood of experiencing any value of the PDF of ED is the same across the landscape. (B) Dynamic landforms at SS: The nonlinear shape of the E50-area curve shows the dynamic nature of the landforms. To illustrate the degree of their dynamic behavior, we identify the location of all the pixels on the landscape characterized by A < 0.5 mm2 (100%) at a given time (t0). For subsequent topographies acquired 5 min apart, we compute the percentage of these locations, which are still characterized by A in the same interval (A < 0.5 mm2). A similar analysis for different values of A is shown in fig. S1. (C) Random locations: For a sample consisting of 1% of the landscape extent chosen randomly across the spatial domain, we examine the fraction of pixels within the sample that erode more and less than the median of the landscape over subsequent topographies. This figure evidences how the pattern revealed by the E50-area curve can be easily dismissed when spatial erosional depth patterns are interrogated in a different manner (for example, random sampling).

  • Fig. 4 Spatial patterns of erosion in SS and TS landscapes.

    Locations (black) of the highly eroding pixels (with local ED above the landscape median) superimposed on the Digital Elevation Models (DEMs) for (A) SS and (B) TS. The distinct patterns of erosion corresponding to SS and TS are apparent by visual inspection. Note, for example, the lack of highly eroding pixels within the channel network at TS in comparison to SS.

  • Fig. 5 Scale-dependent reorganization of the landscape.

    (A) E50-area curves for both SS (blue) and TS (red). The slope-area curve for SS (black) is also shown, and the three geomorphic regimes of hillslopes (H), colluvial (C), and fluvial (F) are noted. After the onset of TS conditions, we observe increased erosion in response to increased precipitation, with this trend inverted within the colluvial regime where erosion systematically decelerates downstream. In the channels, a sediment flux–dependent incision behavior is observed, as depicted by the divergence of the E50-area curves in the fluvial part of the landscape. The vertical gray bars depict the transitions in the behavior of E50-area curves when SS and TS are compared. (B) DEM of a drainage basin from the experimental landscape with the river network superimposed as a reference. (C) Locations in the basin (red pixels) where the ED has shifted from a value below the landscape median at SS (LESS) to above the landscape median at TS (HETS), showing that increased erosion occurs predominantly on hillslopes. (D) Locations in the basin (blue pixels) where the ED has shifted from a value above the landscape median at SS (HESS) to below the landscape median at TS (LETS), showing that decreased erosion occurs predominantly within the fluvial regime.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/9/e1701683/DC1

    Scale-dependent erosional patterns in SS and TS landscapes

    fig. S1. Dynamic landforms at SS.

    fig. S2. Estimation of the probability of erosion larger than the landscape median at SS for different sample sizes.

    fig. S3. Comparison of the SS and TS landscapes in terms of the aggregate statistics of ED.

  • Supplementary Materials

    This PDF file includes:

    • Scale-dependent erosional patterns in SS and TS landscapes
    • fig. S1. Dynamic landforms at SS.
    • fig. S2. Estimation of the probability of erosion larger than the landscape median at SS for different sample sizes.
    • fig. S3. Comparison of the SS and TS landscapes in terms of the aggregate statistics of ED.

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