www.sciencemag.org/content/349/6243/51/suppl/DC1

Supplementary Materials for

Experimental evidence for hillslope control of landscape scale K. E. Sweeney,* J. J. Roering, C. Ellis

*Corresponding author. E-mail: kristin.e.sweeney@gmail.com

Published 3 July 2015, Science 349, 51 (2015) DOI: 10.1126/science.aab0017

This PDF file includes:

Materials and Methods Figs. S1 to S3 Table S1 References

Materials and Methods Steady state of experimental landscapes We defined flux steady state in our experiments as the point at which the spatially-averaged erosion rate was approximately equal to the imposed rate of baselevel fall (Table S1; Figure S1). To measure erosion rate, we divided the elevation change per pixel (obtained by differencing topographic scans) by the time between scans and then calculated the average value for the entire landscape. The knickpoints visible in the steady-state topography (Fig 3A-E) are related to local accelerated erosion from drop impacts and do not introduce significant transience in our experiments (Figure S2). Mapping the channel network and channel slope-area analysis To define the channel network, we must determine both the location of channel heads (e.g., 11) and how water travels across the landscape surface (35). At low drainage areas (hillslopes and colluvial hollows) multidirectional flow algorithms are more representative of natural flow paths (35), while at high drainage areas, steepest descent flow routing captures the behavior of flowing water in the channel network (e.g., 29). Hence, we defined the channel network using two different approaches: (1) GeoNet, a curvature-based multidirectional channel identification routine (31), to map low-order channels and set the spatial framework for quantifying hillslope metrics (Figure S3A-E) and (2) steepest descent routing to delineate higher order channels for the advective component (Figure S3F-J). GeoNet includes a Perona-Malik wavelet filter that removes topographic noise while preserving sharp edges common at the hillslope-valley transition (31); we used unfiltered topographic data for the steepest descent flow routing. Because the definition of channel heads in the steepest descent network requires the use of an arbitrary drainage area threshold, our analysis of slope-area scaling in the channel network only considers regions where drainage area is greater than values associated with channel initiation. To find the advective process parameters (see main text), we extracted slope and drainage area from the steepest descent network for each experiment and fit a power law to the data using the Matlab nonlinear curve-fitting toolbox. Mapping hilltops and extracting hillslope metrics On diffusive hillslopes, disturbance agents (e.g., trees) impart a characteristic scale on the topography that obscures the topographic form associated with long-term continuum sediment transport (7). For our experiments, the impacting raindrops dominate topography at the spatial scale of the drop diameter (~3 mm). Hence, before mapping the hilltops in our experiments, we smoothed topography in a moving window using a second-order polynomial fit (7,30), setting the diameter of the moving window to the 3 mm diameter of the raindrops. To locate hilltops, we identified areas of the topography with negative curvature, drainage area < 0.5 mm2, and slopes < 1.2 mm/mm (28). We used the hillslope tracing algorithm from ref. (30) to calculate average values of hillslope gradient and length for each experiment, using the GeoNet network (Fig S3A-E) to define the end of hillslope traces.

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Fig. S1. Spatially-averaged erosion rate (black) and mean relief of the main divide (grey) for each experiment. Spikes in mean erosion rate of 66% and 100% drip runs are due to priming the drip box; these spikes do not correlate with knickpoints generation and mean erosion rate rapidly returns to its previous value.

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Fig. S2 Average erosion rate calculated over 7.5 mm x 500 mm rectangular moving window oriented parallel to the main divide for all experiments. Large spikes are correlated with knickpoints; the lack of a clear difference in erosion rate between the landscape above and below knickpoints indicates that these features do not result in transient vertical erosion.

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Fig. S3 Hilltop and channel networks; width of topography is 475.5 mm. A-E Hillshades of steady-state experimental topography from A: 0% drip B: 18% drip C: 33% drip D: 66% drip E: 100% drip overlain with GeoNet channel (blue) and hilltop (red) networks. F-J: Hillshades of steady-state topography in (A-E)overlain with steepest descent networks (blue). Note that the initiation of steepest descent channels is defined solely by a drainage area threshold and should not be taken as an alternative to the curvature-derived GeoNet channel heads.

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Table S1. Experimental variables, topographic metrics, and transport coefficients for steady-state landscapes.

0% drip 18% drip 33% drip 66% drip 100% drip Uplift rate

(mm/hr)*

11.74 12.11 11.92 11.81 11.46

Rainfall rate

(mm/hr)†

38 35.5 33 28 23

Length of drip

periods (s/600s)

0 100 200 400 600

Steepness index‡

3.71 + 1.00 1.76 + 0.21 0.52 + 0.1 0.52 + 0.1 0.6 + 0.1

Stream power

exponent m‡

0.34 + .06 0.19 + .02 0.12 + .03 0.18 + 0.02 0.21 + 0.02

Stream power

constant K§,||

0.93 + 0.32 3.41 + 0.44 15.03 + 3.25 12.55 + 2.43 9.76 + 1.72

Mean hillslope length (mm)¶

7.36 13.49 17.73 19.39 22.41

Mean hillslope gradient

(mm/mm)¶

1.39 + 0.002 0.99 + 0.004 0.75 + 0.005 0.48 + 0.008 0.37 + 0.002

Hillslope diffusivity, D (mm2

hr -1)**

30.8 + 4.5 82 + 6 141 + 8 238 + 12.5 345 + 16

Pe||.†† 322.9 + 233.2 93.9 + 21.9 104.3 + 37.9 94.3 + 31.2 76.57 + 23.3 * Calculated by differencing initial and final position of sliding weirs and dividing by the total run time. † Calculated by multiplying the % drip and % mist for each experiment by the discharge from the drip box and mister (23 mm/hr and 38 mm/hr, respectively). For example, rainfall rate for the 18% drip case = 0.18*23 mm/hr + 0.82 *38 mm/hr. ‡ Parameters from power-law fit of channel slope-area plots. Parameter uncertainty is from nonlinear least squares fits. § Calculated using Eqn. 4 (main text) assuming n = 1. || Standard error from Gaussian error propagation. ¶ Measured using hillslope tracing algorithm. Uncertainty is +/- standard error.

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** Calculated from Eqn. 3 (main text) using iterative procedure, setting Sc to be large (9999). Uncertainty reflects upper and lower bounds of hillslope length and gradient measurements. †† Calculated from Eqn. 2 (main text).

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