Rapid erosion increases the efficiency of hillslope sediment transport

The shape of soil-mantled hillslopes is typically attributed to erosion rate and the transport efficiency of the various processes that contribute to soil creep. While climate is generally hypothesized to have an important influence on soil creep rates, a lack of uniformity in the measurement of transport efficiency has been an obstacle to evaluating the controls on this important landscape parameter. We addressed this problem by compiling a data set in which the transport efficiency has been calculated using a single method, the analysis of hilltop curvatures using 1-m LiDAR data, and the erosion rates have also been determined via a single method, in-situ ¬cosmogenic 10Be concentrations. Moreover, to control for lithology, we chose sites that are only underlain by resistant bedrock. The sites span a range of erosion rates (6 – 922 mm/kyr), mean annual precipitation (39 – 320 cm/yr), and aridity index (0.08 – 1.38). Surprisingly, we find that hilltop curvature varies with the square root of erosion rate, whereas previous studies predict a linear relationship. In addition, we find that the inferred transport coefficient also varies with the square root of erosion rate but is insensitive to climate. We explore various mechanisms that might link the transport coefficient to the erosion rate and conclude that present theory regarding soil-mantled hillslopes is unable to explain our results and is, therefore, incomplete. Finally, we tentatively suggest that processes occurding in the bedrock (e.g., fracture generation) may play a role in the shape of hillslope profiles at our sites.

measurement of transport efficiency has been an obstacle to evaluating the controls on this 23 important landscape parameter. We addressed this problem by compiling a data set in which 24 the transport efficiency has been calculated using a single method, the analysis of hilltop 25 curvatures using 1-m LiDAR data, and the erosion rates have also been determined via a 26 single method, in-situ cosmogenic 10 Be concentrations. Moreover, to control for lithology, 27 we chose sites that are only underlain by resistant bedrock. The sites span a range of erosion 28 rates (6 -922 mm/kyr), mean annual precipitation (39 -320 cm/yr), and aridity index (0.08 -29 1.38). Surprisingly, we find that hilltop curvature varies with the square root of erosion rate, 4/6/2021 whereas previous studies predict a linear relationship. In addition, we find that the inferred 31 transport coefficient also varies with the square root of erosion rate but is insensitive to 32 climate. We explore various mechanisms that might link the transport coefficient to the 33 erosion rate and conclude that present theory regarding soil-mantled hillslopes is unable to 34 explain our results and is, therefore, incomplete. Finally, we tentatively suggest that 35 processes occurding in the bedrock (e.g., fracture generation) may play a role in the shape of 36 hillslope profiles at our sites. 37 Index Terms: 1826, 1819, 1862 38

Introduction 39
On soil-mantled surfaces too gentle for significant landsliding, particles are primarily 40 transported downslope by soil creep. Soil creep is a general term for the cumulative effect of 41 myriad individual processes that locally disturb soil, such as the freezing and thawing of pore 42 water [Anderson et al., 2013], shrink-swell cycles [Carson and Kirkby, 1972], dry ravel 43 [Anderson et al., 1959;Gabet, 2003], burrowing by animals [Gabet et al., 2003], and tree 44 throw [e.g., Denny and Goodlett, 1956]. Culling [1963] proposed that the rate of soil creep 45 (q s ; L 2 /T) is linearly proportional to hillslope gradient, S (L/L), such that 46 where D (L 2 /T) is a sediment transport coefficient. The sediment transport coefficient, D, is a 48 measure of the efficiency of the various soil creep processes, and its magnitude sets the pace 49 for hillslope evolution [e.g., Fernandes and Dietrich, 1997;Roering et al., 1999]. Although a 50 nonlinear relationship between gradient and flux is supported by topographic analysis 51 [Andrews and Bucknam, 1987 To ensure a consistent method for calculating erosion rates, they were determined 120 from 10 Be concentrations in detrital quartz grains (Table 1). For five of the study regions, 121 published 10 Be concentrations were used to calculate basin-scale erosion rates. For the Idaho 122 Plateau sites, 10 Be concentrations were measured from soil and fluvial sediment samples 123 collected for this study (see below). For all six study regions, erosion rates were calculated 124 from the 10 Be concentrations using a single algorithm [Mudd et al., 2016]. 125 A full description of the Idaho Plateau field area can be found in Wood [2013]. 126 Ridgetop and basin-scale denudation rates were determined by measuring cosmogenic 10 Be 127 concentrations in quartz [Brown et al., 1995;Granger et al., 1996]. The ridgetop rates were 128 determined from soil samples taken from the top 20 cm of the regolith at three sites. For the 129 basin-scale erosion rates, fluvial sediment was taken from three 1 st -order streams. Pure quartz 130 fractions from the crushed and sieved (250-710 µm) and magnetically separated samples 131 were obtained using published procedures [Kohl and Nishiizumi, 1992;Mifsud et al., 2013]. 132 ICP-OES analysis of purity was undertaken on splits of the etched quartz. Samples were 133 spiked with ~200 µg of a commercial Be carrier (Scharlab Berylium ICP standard solution) 134 and prepared as AMS targets at the University of Cologne using a standard sample 135 preparation method [2015]. The samples were prepared alongside a reagent blank; 10 Be 136 concentrations following blank subtraction are reported in Table 2 were converted to snow shielding values by assuming that snow reduces production solely by 148 spallation [Mudd et al., 2016]. Snow shielding is highly uncertain because of the difficulty of 149 estimating the average SWE over the timescales of 10 3 -10 4 years. We calculated 150 denudation rates with no snow shielding to assess the sensitivity of denudation rate to snow 151 thickness and found that, without accounting for snow, denudation rate estimates could be as 152 much as 15% higher (for sample S3) but, for most samples, the differences were less than 153 10%. Uncertainties from analytical error and from uncertainties in production scaling and 154 shielding are presented in Table 1  Ridge, nearly 95% of the area analyzed had slopes < 20°. Finally, an automated procedure 175 was used to detect the presence of bedrock outcrops along the ridgelines [Milodowski et al., 176 2015] to confirm that the sites were mantled with soil. One Yucaipa Ridge site had 75% soil-177 cover and the other had 90% soil-cover; the soil-cover at the other sites ranged from 97 to 178 100%. Observations of Google Earth TM imagery supported these estimates.  (Table 1). From this compilation, four sites met our 182 criteria: the ridgelines were symmetrical, transport coefficients were estimated by analyzing 183 ridgetop curvatures from 1-m LiDAR data, erosion rates were determined with cosmogenic 10 Be, and the soils were derived from resistant lithologies ( Table 1). The only difference is 185 that Richardson et al. used a 15-m window for their curvature analysis whereas our study 186 used a 14-m window; we consider this difference to be insignificant. With the combined 187 datasets, the sites represent a range of erosion rates from 6 to 922 mm/kyr, a range of mean 188 annual precipitation from 39 to 320 cm/yr, a range of mean annual temperature from 2 to 15° 189 C, and range of aridity index from 0.08 to 1.38 (Table 1). 190

Correcting for Grid Resolution 191
As erosion rates increase, ridgelines become sharper, which could potentially weaken 192 the ability to accurately measure curvature given a fixed grid resolution. In particular, this 193 grid-resolution effect could lead to an increasing underestimate of curvature as ridgelines 194 sharpen with increasing erosion rates, thereby artificially introducing a positive relationship 195 between D and E. To correct for this potential artefact, we performed an analysis in which we 196 compared the estimates of the transport efficiency with those from idealized one-dimensional 197 (1D) hillslopes. We assumed our ridges can be approximated as one-dimensional because 198 curvature perpendicular to ridgelines far exceeds curvature parallel to our ridgelines. 199 To begin, we solved for the elevation of an idealized 1D hillslope by assuming that a 200 nonlinear sediment flux law describes sediment transport on our hillslopes [e.g., Andrews 201 and Bucknam, 1987; Roering et al., 1999] 202 where q s is sediment flux (m 2 /yr), D is the sediment transport coefficient (m 2 /yr), z is the 204 surface elevation, x is a horizontal distance, and S c is a critical slope angle. As noted earlier, 205 4/6/2021 this equation reduces to Eqn. (1) at gentle slopes. Inserting Eqn. (4) into a statement of mass 206 conservation and solving it under steady-state conditions yields an expression for the 207 elevation of a hillslope [Roering et al., 2001a]: 208 where β is the ratio between rock and soil density multiplied by the erosion rate ((ρ r /ρ s )*E) 210 and c is a constant that sets the absolute elevation of the hillslope profile. At the divide (x = 0 211 m), the curvature is equal to: 212 As described earlier, curvature at each site was measured from gridded 1-m 214 topographic data. To mimic this procedure on the synthetic hillslope, we solved Eqn. (5) on a 215 grid of points with a spacing of 1 m. Random noise was then imposed on each gridded data 216 point from a uniform distribution ranging from -0.1 to 0.1 m, which is a conservative 217 estimate of vertical error in typical airborne LiDAR data. As with the real landscapes, a 2 nd -218 order polynomial equation was fitted across the ridgetop over a 14-m window and the 219 curvature was calculated at the center node. 220 However, in any gridded topography, the highest true elevation of the ridge may not 221 be located exactly on the grid sampling point. The exact location of the ridge may be offset 222 from the highest gridded pixel by up to half a pixel width. In Eqn. (5), the ridge is located at 223 x = 0 meters, but to account for the possibility that the ridgeline does not correspond to the 224 highest pixel, we allowed the gridded points to shift laterally by 0.5 m to produce an offset 225 between the center point in the gridded data and the ridgeline. 4/6/2021 For each study site (Table 1), the values of β and S c were calculated using the erosion 227 rate and measured curvature to produce idealized ridgetop profiles. Random noise was then 228 applied to the profile, the grid was shifted, and the 'synthetic' curvature was calculated from 229 the fitted 2 nd -order polynomial. This process was repeated with variations in D until the 230 synthetic curvature matched the curvature measured from the topographic data. We  processes [Rasmussen and Tabor, 2007].

Discussion 249
Our results indicate that, at the sites we examined, erosion rate appears to have a 250 where k is an empirically determined dimensionless constant that accounts for particle shape 281 and the relationship between mean free path length and the vertical displacement of particles, 282 R is particle radius (L), h is soil thickness (L), P is particle concentration (L 3 L -3 ), P m is the 283 maximum value of P, N a is the particle activation rate (T -1 ), θ is the hillslope angle (°) (equal 284 to zero at the ridgecrest), and the overbar signifies vertically averaged quantities. opposite of what we have found. With respect to particle activation rate, we are not aware of 292 any studies that have correlated this variable with erosion rate; however, because rapidly 293 eroding hillslopes tend to have thinner and more exposed soils [e.g., Gabet et al., 2015], the 294 particle activation rate in these landscapes could potentially be higher, which could lead to an 295 increase in D with E. For example, a decrease in vegetation biomass with increasing erosion 296 rate [Milodowski et al., 2014] could leave the soil surface more vulnerable to raindrop impact 297 [Dunne et al., 2010]. Nevertheless, as noted above, a reduction in biomass might also be 298 expected to damp bioturbation, thereby reducing the transport efficiency. suggest that coarser soils have a higher transport coefficient, laboratory experiments have 307 demonstrated that, for the same input of energy, coarse-grained soils will creep faster than 308 fine-grained soils [Supplement to Deshpande et al., 2020]. In addition, of the various factors 309 that could affect the rate of soil creep, particle size is the one with the most potential to vary 310 by multiple orders-of-magnitude between watersheds eroding at different rates [Marshall and 311 Sklar, 2012]. For example, while the data are limited, particle radius along a ridgeline 312 increases with erosion rate at the Feather River site (Figure 6). 313 While particle size is a potential candidate for explaining the relationship between 314 transport efficiency and erosion rate found here, this hypothesis raises some perplexing 315 issues. First, whereas the relationship between particle size and erosion rate is likely to be constant within a single region, one would expect them to vary between regions according to 317 climate and lithology (although we tried to control for rock strength, variations in texture, for 318 example, could affect particle size). However, despite the expected regional variations in 319 these factors, the sites fall along the same D vs. E trendline (Figure 3). Second, because the 320 more rapid weathering rates in wetter climates should lead to smaller soil particles [Marshall 321 and Sklar, 2012], the transport coefficient should decrease in wetter climates. However, we 322 find no relationship between mean annual precipitation and D ( Figure 5). 323 Another potential explanation may be that the transport efficiency is sensitive to slope. 324 Landscapes that are eroding quickly are generally steeper than those that are eroding more 325 slowly. For example, the slopes at the ridgecrests (S HT ) at our sites increase with the 326 approximate square root of erosion rate (Figure 7). Some property of the soil (e.g., its 327 resistance to disturbance) may be affected by the gradient such that its transport efficiency 328 increases on steeper slopes (P. Richardson Thus, the assumption that the transport coefficient increases linearly with slope implies a 344 linear relationship between the erosion rate and the product of curvature and slope. Indeed, a 345 power-law regression between the two yields an exponent of unity, offering support for the 346 hypothesis that the transport coefficient is slope-dependent ( Figure 8). However, because 347 slope and curvature are linearly related along a parabolic curve, Eqn. (13b) is functionally 348 , which is the original relationship presented in Figure 3. In 349 other words, the linear relationship between E and C HT S HT may simply be a mathematical  [Andrews and Bucknam, 1987;Gabet, 2003;353 Roering et al., 1999], particularly at lower slopes (Figure 9). 354 The lack of a clear and robust mechanistic link between D and E, as well as the square 355 root dependency of the hilltop curvature on erosion rate when Eqn. (2) predicts a linear 356 relationship, suggests that the present theory explaining the profile of soil-mantled hillslopes 357 is incomplete. We tentatively propose that, in resistant lithologies, hillslope curvature may be 358 partially, if not mostly, controlled by processes occuring within the bedrock, rather than the 359 soil. Indeed, in an eroding landscape, the soil on a hill is just a thin mantle covering a much 360 larger bedrock mass; the shape of the hill, therefore, should reflect the shape of the 4/6/2021 underlying bedrock and the processes acting within it [e.g., Rempe and Dietrich, 2014]. 362 However, the absence of any climatic influence in our results suggests that these bedrock 363 processes are not associated with the typical chemical and physical weathering processes; 364 instead, they are likely related to a more universal mechanism. Recent work has begun 365 investigating how, even in soil-mantled landscapes, the generation of fractures in bedrock by 366 topographic stresses may exert an important influence on landform shape [e.g., Clair et al., where the erosion rate is slower and the rejuvenation of the surface occurs less frequently, the 379 near-surface bedrock may have a higher fracture density as it accumulates damage over time. 380 The relationship found here between hilltop curvature and erosion rate, therefore, may be 381 related to the strength of the underlying rock mass in a way that is not yet understood. As a 382 preliminary test of this idea, we analyzed the data from four sites that met our criteria but 383 were underlain by presumably weak lithologies, sedimentary bedrock or highly sheared 4/6/2021 metamorphic bedrock [Perron et al., 2012;Richardson et al., 2019]. A comparison of the 385 hilltop curvatures between our original data-set consisting of resistant rocks and the data 386 from the weaker lithologies suggests that, for the same erosion rate, the weaker bedrock 387 forms hilltops with lower curvatures (Figure 10). While the data set from presumably weak 388 lithologies is limited, it supports our hypothesis that weaker bedrock is associated with lower 389 curvatures. Although one might argue that the lower curvatures seen in hillslopes underlain 390 by weaker lithologies could be a result of higher transport efficiencies, a clear mechanistic 391 link between bedrock strength and transport efficiency is lacking (see below), especially 392 considering that most soil creep processes (e.g., tree throw) do not appear to be limited by 393 soil texture. coefficients estimated from relief and hilltop curvature are generally 5 -10 times higher than 403 those estimated from the modeling of scarps for the same aridity index (a factor that was 404 determined to be a control on D) despite the fact that estimates based on scarp evolution were 405 often performed on slopes comprised of unconsolidated sediment, which might be expected 406 to have higher values of D. Therefore, the mismatch between the estimates of the transport coefficient based on topographic metrics and those based on other techniques suggests that 408 some other factor is influencing hillslope shape. 409

Conclusions 410
The square-root dependency of hilltop curvature on erosion rate challenges the 411 prevailing theory linking soil creep to the shape of soil-mantled hillslopes, which predicts a 412 linear relationship between the two. This dependency could be explained if the transport 413 coefficient also varies with the square root of erosion rate. However, we are unable to 414 propose a robust mechanism linking the transport coefficient to the erosion rate. Given the 415 difficulties in accounting for our results within the standard theory of hillslope evolution, we 416 tentatively propose that in landscapes underlain by resistant lithologies, hillslope curvature is 417 not related to soil creep but is, instead, controlled by processes in the underlying bedrock. at regular intervals along a ridge with a gradient in erosion rates. Because local topography 4/6/2021 along the ridgeline (i.e., saddles and knobs) was found to have a strong control on soil 666 properties at this site, we present here only the data from the knobs. Erosion rate calculated 667 from ridgetop curvatures using the relationship reported in the present study. 1σ for particle 668 size data averages 5.8 mm (error bars not shown for clarity).