and strength controls on incision into

Leonard S. Sklar William E. Dietrich Department of Earth and Planetary Science, University of California, 307 McCone Hall, Berkeley, California 94720-4767, USA

ABSTRACT Recent theoretical investigations suggest that the rate of into bedrock depends nonlinearly on sediment supply, challenging the common assumption that incision rate is simply proportional to power. Our measurements from laboratory mills support the hypothesis that sediment promotes at low supply rates by pro- viding tools for abrasion, but inhibits erosion at high supply rates by burying underlying bedrock beneath transient deposits. Maximum erosion rates occur at a critical level of coarse-grained sediment supply where the bedrock is only partially exposed. Fine-grained provide poor abrasive tools for lowering beds because they tend to travel in suspension. Experiments also reveal that rock resistance to ¯uvial erosion scales with the square of rock tensile strength. Our results suggest that spatial and tem- poral variations in the extent of bedrock exposure provide incising with a previously unrecognized degree of freedom in adjusting to changes in rock uplift rate and climate. Furthermore, we conclude that the grain size distribution of sediment supplied by hill- slopes to the network is a fundamental control on bedrock channel gradients and topographic relief.

Keywords: rivers, sediment supply, grain size, erodibility, landscape evolution, erosion.

INTRODUCTION ly the role of sediment supply, grain size, and similar to Gilbert's qualitative hypothesis. Our The topography of mountainous landscapes rock strength in controlling bedrock erosion model also predicts a nonlinear dependence of is created by the interaction of rock uplift and rates. incision rate on grain size due to the twin con- erosion. River incision into bedrock is the key Gilbert (1877) was the ®rst to propose that straints that for a grain to erode bedrock it erosional process that controls the rate of land- the quantity of sediment supplied to the river must be small enough to be in motion, yet scape response to changes in rock uplift rate should in¯uence bedrock-incision rates in two large enough to move as rather than and climate (Howard et al., 1994). Numerical essential yet opposing ways: by providing as ; thus, predicted incision models of landscape evolution (e.g., Howard, tools for abrasion of exposed bedrock and by rates are highest for intermediate grain sizes. 1994; Tucker and Slingerland, 1994; Willett, limiting the extent of exposure of bedrock on In every model we are aware of, bedrock re- 1999) commonly assume that incision rate is the channel bed. According to Gilbert's hy- sistance to erosion is treated as a free param- proportional to stream power (Seidl and Die- pothesis, the maximum rate of incision should eter unrelated to any objective measure of trich, 1992), or equivalently shear stress occur when the stream receives a moderate rock strength. (Howard and Kerby, 1983), and lump the in- supply of sediment, relative to its sediment ¯uence of rock strength, sediment supply, transport capacity. Incision rate is limited at ABRASION EXPERIMENTS grain size, and other factors into a poorly de- lower supply rates by a shortage of abrasive Because of the inherent dif®culty of mea- ®ned ``rock erodibility'' coef®cient. This sim- tools (the ``tools effect'') and at higher supply suring bedrock erosion and sediment supply ple ``stream power'' bedrock-incision model rates by partial burial of the bedrock substrate rates in the ®eld, we developed an experimen- has also been used in analysis of real land- beneath transient sediment deposits (the ``cov- tal bedrock abrasion mill designed to replicate scapes to infer patterns of crustal deformation erage effect''). The size distribution of sedi- the small-scale interaction of coarse bed load (Kirby and Whipple, 2001) and the possible ment grains supplied to the channel should with the rock ¯oor of an actively incising river in¯uence of climate change on late Cenozoic also in¯uence incision rates, because only the channel. We bolted 20-cm-diameter disks of mountain uplift (Whipple et al., 1999). Studies coarser fraction is capable of forming an al- rock to the bottom of a set of 10 vertical wa- of river longitudinal pro®les suggest, however, luvial cover in actively incising river channels ter-®lled cylinders, in which motor-driven pro- that the stream power model may be too sim- and because the ®ner fraction is carried in sus- pellers circulated water (Fig. 1). We added ple to explain observed variations in incision pension and rarely collides with the bedrock sediment of various amounts and sizes, which rates (Stock and Montgomery, 1999) and pro- bed. moved primarily as saltating bed load across ®le shape (Sklar and Dietrich, 1998). In ad- Various alternative incision models explic- the surface of the bedrock disks in response dition, theoretical investigations (Sklar and itly include sediment supply through simple to the tractive force of the rotating water. In Dietrich, 1998; Slingerland et al., 1997) sug- parameterization of the tools effect (Foley, all the experiments reported here, we held the gest that the in¯uences of sediment supply and 1980), the coverage effect (Beaumont et al., rotational velocity of the water constant. In a grain size are too complex to ®t into a linear 1992), or both (Slingerland et al., 1997). We river, this would be equivalent to holding coef®cient and must be explicitly represented previously derived an incision rate law from channel slope, cross-sectional area, and water in models of bedrock incision. Our goal here the mechanics of saltating bedload (Sklar and constant. The walls and base of one is to pry open the conceptual black box of Dietrich, 1998) that predicts a nonlinear de- abrasion mill were made of transparent ma- ``rock erodibility,'' and explore experimental- pendence of incision rate on sediment supply, terial to allow observation of sediment mo-

᭧ 2001 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. Geology; December 2001; v. 29; no. 12; p. 1087±1090; 5 ®gures. 1087 Figure 1. Schematic of bed- rock abrasion mill. tion. Bedrock abrasion occurred primarily due to impacts by saltating grains. We determined the erosion rate by weighing the rock disks before and after each run and dividing the Figure 2. Variation in measured erosion rate with rock tensile strength. Sediment loading mass lost by the run duration. Rock samples for this set of runs was 150 g of 6-mm-diameter gravel. Each data point represents mean were kept saturated and gently toweled off pri- of 12 to 20 measurements of tensile strength and two to six replicate erosion runs; error or to weighing to remove ponded water. Rep- bars are omitted because standard errors of these means are smaller than data symbols. licate weight measurements reduced typical Uncertainty in best-®t log-linear regression line is standard error. :cement ratios and curing conditions are listed for arti®cial rocks. standard error to below 0.2 g. Run duration ranged from 0.25 to 72 h. We eroded a suite of 22 lithologies, includ- strong rock type. Although disks of weaker we increased the mass of abrasive sediment ing highly resistant greenstone, quartzite, and bedrock abraded by the strong quartzite gravel (Fig. 4A). However, as we continued to in- granite, moderate strength basalt, limestone, eroded up to three times as fast as when abrad- crease sediment mass, erosion rates peaked and , and weakly cemented sand- ed by gravel made from the same weaker li- and then declined. The peak and subsequent stone and mudstone. Samples were collected thology (Fig. 3), the exponent in the power decline in wear rate corresponded to the for- from the beds and banks of actively incising law relationship between erosion rate and ten- mation and growth of a deposit of immobile bedrock channels, from in-channel boulders, sile strength did not change. sediment that protected parts of the underlying and from quarries. We also tested a set of six To measure the in¯uence of sediment sup- bedrock (Fig. 4B). The sediment deposit arti®cial , composed of various ply on incision rates, we varied the total mass formed initially around the center of the bed- mixtures of ®ne sand and portland cement, to of sediment placed in the abrasion mills, while rock disk where the concentration of mobile supplement the range of rock strengths. Be- holding constant the grain size and the lithol- sediment was greatest. As we supplied more cause rocks fail in tension when subjected to ogy of both bedrock and sediment. Because sediment, the deposit grew outward, bridged low-velocity particle impacts (Johnson, 1972), the motor speed and thus water velocity were to the walls and eventually covered the entire tensile strength is the mechanistically appro- held constant throughout, we were able to ef- surface of the disk. Erosion continued at a priate rock strength parameter for character- fectively vary the ratio of sediment supply to very slow rate even when the rock disks were izing rock resistance to ¯uvial abrasion. We capacity. At relatively low fully covered by a thin layer of sediment, pre- used the Brazilian tension splitting test (Vu- supply rates, erosion rates increased rapidly as sumably because of the force imparted by mo- tukuri et al., 1974) to determine the tensile strength of each rock type, because this test produces valid results over the widest possible range of rock strengths. To measure the in¯uence of rock tensile Figure 3. Variation in measured strength on bedrock erosion rates, we varied erosion rate with rock tensile bedrock lithology while holding constant the strength for rocks eroded by number, size, and lithology of abrasive gravel quartzite gravel (solid symbols, grains. Erosion rates increased rapidly with solid line) and rocks eroded by gravel composed of same rock decreasing tensile strength (Fig. 2). The data (open symbols, dashed line). are well ®t by a power-law relationship where Sediment loading for this set of erosion rate varies inversely with the square runs was a single 30-mm-diam- of tensile strength. To make sure that this re- eter 70 g grain. Note that quartz- sult was not an artifact of changing the rela- ite bedrock data symbols are superimposed because this tive strength difference between the mobile point is included in both gravel and stationary bedrock, we compared regressions. wear rates for rocks abraded by gravel com- posed of the same lithology with wear rates for rocks abraded by quartzite, a particularly

1088 GEOLOGY, December 2001 Figure 5. Variation in erosion rate with sed- iment grain size. Data are for limestone eroded by total gravel mass of 70 g. Trans- port mode was observed in clear-walled mill.

threshold of motion bracket the range of grain sizes capable of effectively lowering a bed- Figure 4. A: Variation in erosion rate with sediment loading. Data for three rock types are collapsed by multiplying erosion rate (g/h) by square of tensile strength (MPa). Sediment rock river bed. In our experiments, the largest -ux at erosion rate peak was ~0.01 kg ´ s؊1 ´m؊1. Additions of gravel mass did not increase grains tested (Ͼ35 mm) produced no measur¯ ¯ux much beyond this level but rather increased the mass of the stationary deposit. Grain able wear, because they moved infrequently or diameter for these runs was 6 mm. B: Photographs showing gradual alluviation with in- not at all. In rivers, the minimum channel creasing sediment loading, taken from below abrasion mill looking up through glass slope necessary for incision to occur is set by bottom. the threshold of motion for the coarsest grain sizes that, if supplied in suf®cient quantity, bile grains impacting stationary grains resting changes in channel slope, and thus sediment would accumulate and bury the bed in the ab- on the bedrock surface, and by occasional transport capacity (Montgomery et al., 1996). sence of regular transport and particle break- sliding of the alluvial bed. In our experiments, the coverage effect con- down (Sklar and Dietrich, 1998; Howard, We also measured the in¯uence of sediment trols erosion rates over a much larger range of 1998). grain size on incision rates by simultaneously sediment supply rates than does the tools ef- Our data show that rock resistance to ¯uvial varying the mean grain diameter and the num- fect (Fig. 4A). This may be analogous to many abrasion, de®ned here as the inverse of ero- ber of grains such that the total mass of sed- actively incising river networks where channel sion rate, scales with the square of rock tensile iment remained constant. For example, assem- beds are mostly mantled with a continuous al- strength, providing the ®rst determination of a bling a total sediment mass of 70 g required luvial cover. In these rivers, bedrock erosion quantitative relationship between rock resis- approximately 3000 grains of 0.7-mm-diame- may occur only during high-¯ow events when tance to ¯uvial erosion and an objective mea- ter sand, only 150 grains of 6-mm gravel, or the entire alluvial bed is put into motion or sure of rock strength (Fig. 2). In ®eld studies just a single grain of 35-mm gravel. We chose when temporary local scour exposes bedrock. of bedrock incision, quantitative comparisons this low level of sediment loading to avoid the We now have experimental evidence to sup- among rock types can now be made by testing confounding in¯uence of partial bed coverage. port our hypothesis (Sklar and Dietrich, 1998) the tensile strength of bedrock samples. Where Measured erosion rates peaked near the coarse that the grain size distribution of sediment nonuniform lithology presents a confounding end of the range of grain sizes tested and de- supplied to the channel is a key control on variable, erosion rate data can be collapsed by clined rapidly with decreasing grain size, be- river incision rates (Fig. 5). The majority of normalizing by tensile strength, as we have coming negligible for grain sizes smaller than sediment mass transported by mountain rivers done in Figure 3. In experimental studies of coarse sand (Fig. 5). Unlike gravel, which is typically in the sand-, -, and clay-size bedrock incision, where weak materials are moved as bed load, we observed sand (Ͻ2 fractions (e.g., Nordin, 1985), and it moves needed to accelerate rock erosion rates, tensile mm diameter) moving primarily in suspen- suspended in the water column. The rapid de- strength measurements can be used to scale sion, rarely interacting with the bedrock bed. cline in rock erosion rate with decreasing the relative resistance to wear. The inverse Grain sizes larger than 35-mm produced neg- grain size in our experiments suggests that ®n- square relationship between tensile strength ligible erosion because there was insuf®cient er sediments are inef®cient tools for abrading and erosion rate can be used as a diagnostic shear stress to keep them in motion. bedrock river beds, compared to coarser sed- test to ensure that simulated bedrock reliably iments that travel as bed load. The observed reproduces the wear-resistant properties of DISCUSSION low erosion rates of ®ne sediments may be natural rock, as our arti®cial sandstone does. Our experimental results provide the ®rst due to both the reduced frequency of contact These results should have wide applicabil- empirical con®rmation of Gilbert's hypothesis with the bed and the possible existence of a ity even though we eroded bedrock that was and are consistent with observations of sedi- threshold impact intensity that must be ex- not strongly jointed or fractured and thus did ment dynamics in mountain river channels. ceeded to detach a fragment of bedrock. Sus- not capture the mechanism of wear by clear Mixed bedrock-alluvial bedded channels are pended sediments may be most important in water plucking of loosely held rock fragments. common in actively incising terrain (Howard, abrading blocks of rock that protrude high into In our experience, massive bedrock in channel 1998). Temporal and spatial variations in the the ¯ow above the reach of bed load (Whipple beds is common. Moreover, the fracture spac- extent of bedrock exposure have been shown et al., 2000a) and in abrading the walls of nar- ing in jointed rock is often wide enough that to depend on ¯uctuations in sediment supply row bedrock channels (Whipple et al., 2000b). the rate of bed lowering is limited by the in- (Howard and Kerby, 1983) and on subtle Both the threshold of suspension and the tact strength of the intervening blocks. Fur-

GEOLOGY, December 2001 1089 thermore, the ef®ciency of all bedrock ero- produce large changes in the extent of bed ex- Howard, A.D., Dietrich, W.E., and Seidl, M.A., sional mechanisms, with the possible posure and consequently large changes in the 1994, Modeling ¯uvial erosion on regional to continental scales: Journal of Geophysical Re- exception of dissolution, should depend on the rate of incision into bedrock, we might expect search, v. 99, p. 13 971±13 986. size and supply rate of sediment carried by rivers ¯owing over more resistant rocks, or Johnson, W., 1972, Impact strength of materials: incising rivers. Bed coverage by alluvial de- subject to faster uplift rates, to have margin- New York, Edward Arnold, 361 p. posits insulates underlying bedrock not only ally steeper slopes but much greater extents of Kirby, E., and Whipple, K., 2001, Quantifying dif- ferential rock-uplift rates via stream pro®le from wear by abrasion, but also from wear by bedrock exposure. Moreover, because basin analysis: Geology, v. 29, p. 415±418. plucking and cavitation. Abrasion by coarse relief is simply the integral of local channel Montgomery, D.R., Abbe, T.B., Buf®ngton, J.M., bed load can create small-scale bed irregular- slopes along the length of the river, it follows Peterson, N.P., Schmidt, K.M., and Stock, ities that promote cavitation where local ¯ow that relief may be much less sensitive to dif- J.D., 1996, Distribution of bedrock and allu- separation occurs. Even in weak, ®nely jointed ferences in lithology or rates of rock uplift vial channels in forested mountain drainage basins: Nature, v. 381, p. 587±589. rock, where plucking is often inferred to be than previous studies using the stream power Nordin, C.F., 1985, The sediment loads of rivers, in the primary erosional mechanism, bed-load law (Whipple and Tucker, 1999) have sug- Rodda, J.C., ed., Facets of hydrology II: Chich- impacts may be responsible for weakening gested. Similarly, where landscapes are sub- ester, UK, John Wiley & Sons, Ltd., p. 183±204. and ultimately overcoming the forces holding jected to changes in the rate of rock uplift, or Seidl, M.A., and Dietrich, W.E., 1992, The problem of channel erosion into bedrock, in Schmidt, jointed blocks in place (Whipple et al., to long-term shifts in climate, river incision K.H., and de Ploey, J., eds., Functional geo- 2000a). rates may adjust through changes in the extent morphology: Catena, suppl. 23, p. 101±124. of bedrock exposure over a period of time that Sklar, L.S., and Dietrich, W.E., 1998, River longi- IMPLICATIONS is relatively short compared to the long time tudinal pro®les and bedrock incision models: required (Whipple and Tucker, 1999) for sig- Stream power and the in¯uence of sediment The complex role of sediment in in¯uenc- supply, in Tinkler, K., and Wohl, E.E., eds., ing bedrock incision rates has important im- ni®cant changes in relief to occur. Rivers over rock: in bedrock plications for understanding the controls on In summary, the experimental results re- channels: American Geophysical Union Geo- river slope and basin relief and the time scale ported here suggest that understanding and physical Monograph 107, p. 237±260. modeling the dynamic coupling of climate, Slingerland, R., Willett, S.D., and Hennessey, H.L., of landscape response to changes in rock up- 1997, A new ¯uvial bedrock incision model lift rate and climate. When subjected to pro- tectonics, and topography will require explic- based on the work-energy principle [abs.]: Eos longed steady rock uplift, river channel slopes itly accounting for the role of sediment supply (Transactions, American Geophysical Union), tend to adjust so that incision rate matches and grain size in controlling rates of river in- v. 78, p. F299. rock uplift rate. According to the stream pow- cision into bedrock. Stock, J.D., and Montgomery, D.R., 1999, Geologic constraints on bedrock river incision using the er view of river incision, slope is determined, stream power law: Journal of Geophysical Re- ACKNOWLEDGMENTS for a given drainage area, by rock resistance search, v. 104, p. 4983±4993. We are grateful to J. Potter, A. Geddes-Osborne, Tucker, G.E., and Slingerland, R.L., 1994, Erosional and uplift rate; slopes roughly twice as steep A. Foster, H. Brown, D. Straube, C. Freel, M. Trso, dynamics, ¯exural isostasy, and long-lived es- would be required for rock twice as resistant, T. Teague, and S. Tepperman-Gelfant for assistance carpments; a numerical modeling study: Jour- with the erosion experiments, to W. MacCracken or for uplift rates twice as rapid. nal of Geophysical Research, v. 99, and S. Glaser for help with the rock strength mea- Sediment supply and grain size effects, p. 12 229±12 243. surements, and to A. Heimsath and G. Day for help Vutukuri, V.S., Lama, R.D., and Saluja, S.S., however, may produce an entirely different in obtaining rock samples. We thank J. Kirchner, J. 1974, Handbook on mechanical properties dependence of channel slope on uplift rate and Roering, J. Stock, C. Riebe, A. Luers, E. Maurer, of rocks. Volume 1: Testing techniques and rock strength, because the minimum slope that K. Gale, and G. Hauer for discussions and/or critical results: Bay Village, Ohio, Trans Tech Pub- readings of the manuscript. J. Buf®ngton and R. allows a river to incise into bedrock is set pri- lishers, p. 105±115. Slingerland provided helpful reviews. This research marily by the threshold of motion of the Whipple, K.X., and Tucker, G.E., 1999, Dynamics was supported by National Science Foundation of the stream-power river incision model: Im- coarse fraction of the sediment load. Incre- grant EAR-9706082 and a Switzer Environmental plications for height limits of mountain ranges, ments in channel slope above the minimum Fellowship to Sklar. landscape response timescales, and research will depend on the total load of bed-load-size needs: Journal of Geophysical Research, REFERENCES CITED sediment, which controls the extent of bed- v. 104, p. 17 661±17 674. Beaumont, C., Fullsack, P., and Hamilton, J., 1992, Whipple, K.X., Kirby, E., and Brocklehurst, S.H., rock exposure in the channel bed. For steady- Erosional control of active compressional or- 1999, Geomorphic limits to climate-induced state landscapes, the total sediment load is ogens, in McClay, K.R., ed., Thrust tectonics: increases in topographic relief: Nature, v. 401, proportional to the rock uplift rate; however, New York, Chapman and Hall, p. 1±18. p. 39±43. 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At pre- Henry Mountains: Geographical and geologi- Bulletin, v. 112, p. 490±503. cal survey of the Rocky Mountain region: sent, little is known about how rock uplift rate Whipple, K.X., Snyder, N.P., and Dollenmayer, K., Washington, D.C., Government Printing Of- and rock strength in¯uence the grain size dis- 2000b, Rates and processes of bedrock inci- ®ce, 106 p. sion by the Upper Ukak River since the 1912 tribution of sediment entering the channel net- Howard, A.D., 1994, A detachment-limited model Novarupta ash ¯ow in the of Ten Thou- work. The initial grain size distribution is like- of evolution: Water Resources sand Smokes, Alaska: Geology, v. 28, Research, v. 30, p. 2261±2285. ly to depend on the bedrock lithology and its p. 835±838. Howard, A.D., 1998, Long pro®le development of tectonic history, the climatically in¯uenced Willett, S.D., 1999, Orogeny and orography: The bedrock channels: Interaction of , effects of erosion on the structure of mountain weathering rate and style, and hillslope sedi- mass wasting, bed erosion, and sediment ment transport processes. belts: Journal of Geophysical Research, transport, in Tinkler, K., and Wohl, E.E., eds., v. 104, p. 28 957±28 981. Partial bedrock exposure, controlled by the Rivers over rock: Fluvial processes in bedrock rate and size of sediment supplied to the chan- channels: American Geophysical Union Geo- Manuscript received April 5, 2001 physical Monograph 107, p. 297±319. nel, introduces a previously unrecognized de- Revised manuscript received July 11, 2001 Howard, A.D., and Kerby, G., 1983, Channel Manuscript accepted July 27, 2001 gree of freedom for channel adjustment. 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1090 GEOLOGY, December 2001