Preservation or Piracy: Diagnosing low relief, high elevation surface formation mechanisms. Supplemental Methods: Additional methodological details.

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1 GSA Data Repository Preservation or Piracy: Diagnosing low relief, high elevation surface formation mechanisms Kelin X. Whipple 1, Roman A. DiBiase 2, William B. Ouimet 3, Adam M. Forte 1 Contents Supplemental Methods: Additional methodological details. Supplemental Figures and Movies: Figure DR1. Diagnostic characteristics of low relief, high elevation surface formation mechanisms, additional detail. Figure DR2. Diagnostic characteristics of low relief, high elevation surface formation mechanisms, from 2D landscape evolution simulations with CHILD. Figure DR3. Causes of expected variation of knickpoint elevations. Figure DR4. Regional map and topographic swath profiles. Figure DR5. Erosion rate, incision history, channel steepness, and chi maps of the SE Tibetan Plateau example. Figure DR6. transformed profiles of all major streams draining catchments F P (Fig. 2). Figure DR7. Example of stream capture during landscape incision. Movie DR1. Low relief, high elevation surface formation in response to an 8x increase in rock uplift rate relative to baselevel. Movie DR2. Low relief, high elevation surface formation in a tributary responding to the beheading of a mainstem river. References Cited

2 Supplemental Methods We use the well known detachment limited stream power river incision model to illustrate fundamental, diagnostic differences in landscape morphology resulting from an increase in rock uplift rate relative to baselevel (U) as opposed to drainage area loss by stream capture (Howard, 1994; Whipple and Tucker, 1999):, (1) where dz/dt is the rate of change of river bed elevation, K is the erosion coefficient (set by climate and rock properties), A is upstream drainage area (a proxy for water and sediment discharge), and S is local channel gradient (assumed positive). We assume K = 1e 5 yr 1, m/n = ½ and n = 1 in all simulations (both 1d and 2d). For 1d river profile simulations we use a simple forward time, forward space finite difference solution implemented in Matlab. For 2d landscape evolution simulations (using identical model parameters) we use CHILD (Tucker et al., 2001). We acknowledge the limitations of the detachment limited stream power model with n = 1. This simple model cannot hope to capture the rich dynamics of natural landscapes. Simulations are used as semiquantitative guidelines to frame conceptual understanding only. For analysis of topography in the natural landscape considered, we use current standard metrics of river profile form, evaluated from a 90 m resolution digital elevation model (Farr et al., 2007) ( using in house scripts based on TopoToolbox (Schwanghart and Scherler, 2014). We compute local relief as the elevation range within a 2.5 km radius at every pixel. Channel steepness (ksn) is determined based on Flint s law for a fixed reference concavity index, ref, of 0.45 (Flint, 1974; Hack, 1957; Wobus et al., 2006a):. (2) Note that at steady state, the stream power river incision model predicts ref = m/n and ksn = (U/K) 1/n. We further utilize the so called integral method (Harkins et al., 2007; Perron and Royden, 2012) to facilitate our analyses of river profiles. Integrating both sides of equation (2) upstream (in x) from the outlet (x = 0) and solving for elevation we can write:, (3a) where z is river bed elevation, zb is catchment outlet elevation, and:

3 , (3b) where Ao is a reference area (Perron and Royden, 2012), here set to unity such that the slope of transformed river profiles (plots of z vs. ) is equal to the channel steepness. Absent smooth spatial or temporal gradients in U or K (and thus ksn), transformed river profiles are predicted by the stream power model to be piece wise linear; abrupt transitions between quasi linear segments are termed slope break knickpoints (Kirby and Whipple, 2012; Whipple et al., 2013). Supplemental Figures

4 Figure DR1. Diagnostic characteristics of low relief, high elevation surface formation mechanisms, additional detail. (A D) River profile response to an 8x increase in rock uplift rate relative to baselevel. (E H) Response of a tributary to a beheaded river (confluence 160 km from outlet). In all plots, profiles are shown for initial steady state (blue), 4 intermediate (green) and the final timestep (magenta). Plots show river profiles (A and E), channel steepness (ksn) vs distance (B and F), transformed river profiles (D and G), a slope area plots (D and H). In panels (F), (G), and (H) red lines show channel profiles immediately after the loss of drainage area in the simulated beheading of the mainstem (beheading occurs at 160 km from the outlet at the confluence with the modeled tributary).

5 Figure DR2. Diagnostic characteristics of low relief, high elevation surface formation mechanisms, from 2D landscape evolution simulations with CHILD. All model parameters are identical to the 1D profile model simulations, solved here for a 35 km x 35 km catchment draining to a corner point. (A) Preservation mechanism: topographic (left) and slope (right) maps of a low relief upland formed 2.0 Myr after an 8x increase in rock uplift rate relative to baselevel. (B) Piracy mechanism: topographic (left) and slope (right) maps of a low relief upland formed 2.5 Myr after the modeled catchment begins to feel a rising baselevel equal to 7/8 th of the initial steady state uplift rate, mimicking tributary response to the loss of erosive power in a beheaded mainstem (history of baselevel rise at the tributary junction is identical to that in 1D simulation in Fig. 1a).

6 0 Figure DR3. Expected variability in knickpoint elevation formed in response to an increase in channel steepness (ksn). X axis variable,, is defined by equation in (A) (see DR text). Note with Ao = 1 as used here, the slope of z vs plots is ksn. (A) Idealized transformed transient river profile (heavy black) with knickpoint (black dot) at intersection of uplifted (thin dark grey) initial steady state profile (heavy dark grey) and final steady state (thin light grey) profile. (B) Variation in predicted knickpoint elevation (gray band) about the ideal case (as in A) for illustrative variation in initial erosion rate (Ei_min, Ei_max, thin solid lines, light grey filled dots), in initial channel steepness (ksn_i_min, ksn_i_max, dotted lines, dark grey filled dots), and in final channel steepness (ksn_f_min, ksn_f_max, dashed lines, white filled dots).

7 Figure DR4. Regional map and topographic swath profiles. (A) Regional map identical to Fig. 2, Inset, except also showing extent of Miocene lakes east of ~89 E (Wu et al., 2008). (B) Mean elevation (thin black line) and min max bounds (shaded grey) in a 10 km wide swath profile along W W shown in comparison to mean (heavy black line), min (heavy blue), and max (thin blue) elevations in a 160 km wide swath profile along W W. Intersection with mapped (Clark et al., 2006) low relief surface patches indicated. Heavy blue line captures the profile of the Yangtze River. Boundaries of internally drained plateau and the downstream limit of Miocene lakes are indicated. (C) Replica of Figure 2b, clearly highlighting the pattern of incision into a regional low relief surface.

8 A. Figure DR5a.

9 B. Figure DR5b

10 C. Figure DR5. Erosion rate, incision history, channel steepness, and chi maps of the SE Tibetan Plateau example. (A) Map as in Fig. 2a showing major faults (dark red), tributary and headwater catchments color coded by catchment mean erosion rate (Henck et al., 2011; Ouimet et al., 2009), and locations where the initiation of rapid exhumation has been constrained with thermochronometric data and models (1. Clark et al. (2005); 2. Ouimet et al. (2010); 3. Tian et al. (2015); 4. Tian et al. (2014)). (B) Map as in (A) but with coloring by elevation removed and the channel network colored by channel steepness (ksn (m 0.9 )) for ref = (C) Map as in (B) but with the channel network colored by.

11 Figure DR6. transformed profiles of all major streams draining two large low relief surface patches. (A) Catchments F J (Fig. 2) with Yangtze and Yalong profiles in blue. (B) Catchments K P (Fig. 2) with Yalong profile in blue. All profiles draining a given surface show similar form with a significant slope break knickpoint with elevations varying within about 500 m (grey bands, see Fig. DR3). Two outliers in (B) are the small, western most tributaries to the main gorge in catchment M and may be hanging valleys (Crosby et al., 2007; Wobus et al., 2006b).

12 Figure DR7. Example of stream capture during landscape incision. (A) Inset shows location of this map on Fig. 2a (black box). Map shows elevation shaded by local relief with hillshading (as in Fig. 2a) with major streams (blue), portions of catchments A, D, and E (outlined in white) and margins of a large low relief surface from Clark et al. (2006) (black lines), see Fig. 2a. Captured and beheaded stream segment are indicated. (B) Modification of Fig. 2c, with profiles of all major streams in catchments C E shown in light gray and the Yangtze River profile in blue. The beheaded and captured river profiles are shown in black and show that the capture is part of the regional incision response and not a driver of low relief surface formation the captured reach is typical of channel profiles on the surface, the capturing reach is over steepened by the recent addition of drainage area, and the beheaded reach is typical of profiles below slopebreak knickpoints, except in the vicinity of the wind gap, as expected (Willett et al., 2014).

13 Captions for Supplemental Movies Movie DR1. Low relief, high elevation surface formation in response to an 8x increase in rock uplift rate relative to baselevel. CHILD simulation of a 35 km x 35 km catchment draining to a corner point. Initial condition is steady state for uplift = 1e 4 m/yr. All model parameters are identical to the 1D profile model simulation in Fig. 1a. Topographic (left) and slope (right) maps shown for 3.5 Myr of simulation. Movie DR2. Low relief, high elevation surface formation in a tributary responding to the beheading of a mainstem river (not modeled). CHILD simulation of a 35 km x 35 km catchment draining to a corner point, taken to represent the confluence with a mainstem river beheaded at the start of the simulation. Initial condition is steady state for uplift = 8e 4 m/yr. All model parameters are identical to the 1D profile model simulation in Fig. 1b. Topographic (left) and slope (right) maps shown for 3.5 Myr of simulation after the modeled catchment begins to feel a rising baselevel equal to 7e 4 m/yr of the initial steady state uplift rate, mimicking tributary response to the loss of erosive power in a beheaded mainstem (history of baselevel rise at the tributary junction is identical to that in 1D simulation in Fig 1b). References Cited Clark, M.K., House, M.A., Royden, L.H., Whipple, K.X., Burchfiel, B.C., Zhang, X., and Tang, W., 2005, Late Cenozoic uplift of southeastern Tibet: Geology, v. 33, p Clark, M.K., Royden, L.H., Whipple, K.X., Burchfiel, B.C., Zhang, X., and Tang, W., 2006, Use of a regional, relict landscape to measure vertical deformation of the eastern Tibetan Plateau: Journal of Geophysical Research Earth Surface, v Crosby, B.T., Whipple, K.X., Gasparini, N.M., and Wobus, C.W., 2007, Formation of fluvial hanging valleys: Theory and simulation: Journal of Geophysical Research Earth Surface, v Farr, T.G., Rosen, P.A., Caro, E., Crippen, R., Duren, R., Hensley, S., Kobrick, M., Paller, M., Rodriguez, E., Roth, L., Seal, D., Shaffer, S., Shimada, J., Umland, J., Werner, M., Oskin, M., Burbank, D., and Alsdorf, D., 2007, The shuttle radar topography mission: Reviews of Geophysics, v. 45. Flint, J.J., 1974, Stream gradient as a function of order, magnitude, and discharge: Water Resources Research, v. 10, p Hack, J.T., 1957, Studies of longitudinal stream profiles in Virginia and Maryland: U.S. Geological Survey Professional Paper, v. 294 B, p. 97.

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15 Wobus, C., Whipple, K.X., Kirby, E., Snyder, N., Johnson, J., Spyropolou, K., Crosby, B., and Sheehan, D., 2006a, Tectonics from topography: Procedures, promise, and pitfalls: Geological Society of America Special Paper 398, p Wobus, C.W., Crosby, B.T., and Whipple, K.X., 2006b, Hanging valleys in fluvial systems: Controls on occurrence and implications for landscape evolution: Journal of Geophysical Research Earth Surface, v Wu, Z.H., Barosh, P.J., Hu, D.G., Xun, Z., and Ye, P.S., 2008, Vast early Miocene lakes of the central Tibetan Plateau: Geological Society of America Bulletin, v. 120, p