Experimental migration of knickpoints : influence of style of base-level fall and bed lithology

Knickpoints are fascinating and common geomorphic features whose dynamics influence the development of landscapes and source-to-sink systems – in particular the upstream propagation of erosion. Here, we study river profiles and associated knickpoints experimentally in a microflume filled with a cohesive substrate made of silica, water and kaolinite. We focus on the effect on knickpoint dynamics of varying the distribution of base-level fall (rate, increment, and period) and substrate strength, i.e., kaolinite content. Such simple cases are directly comparable to both bedrock and alluvial river systems. Under a constant rate of base-level fall, knickpoints of similar shape are periodically generated, highlighting self-organized dynamics in which steady forcing leads to multiple knickpoint events. Temporary shielding of the bed by alluvium controls the spacing between these unit knickpoints. Shielding is, however, not effective when base-level drops exceed alluvium thickness. While the base-level fall rate controls the overall slope of experiments, it is not instrumental in dictating the major characteristics of unit knickpoints. Instead the velocity, face slope and associated plunge pool depth of these knickpoints are all strongly influenced by lithology. The period between knickpoints is set by both alluvium thickness and base-level fall rate, allowing use of knickpoint spacing along rivers as an indicator of base-level fall rate.


2) RESPONSES TO INDIVIDUAL COMMENTS
In this section, we respond to individual comments made by referees. Comments/suggestions are in black and our responses are in blue.

Reviewer #1 (J. Turowski)
In the paper, the authors report on a number of experiments on knickpoint migration in an experimental flume. The results suggest new insights in knickpoint behavior and challenge some of the conceived notions of the field. I have no major problems with the paper. The following point could be clarified in the manuscript and picked up in discussion. Recent research has shown the important of bedload tools in bedrock erosion in field settings (e.g., the cited paper of Cook et al. 2013). From the statements made (page 4, line 24), it seems that clear water can erode the substrate, but it is unclear to me how much this process contributes to total erosion. This is an important point for the upscaling of the results and should also be picked up in the discussion. For example, do the authors see a change in knickpoint retreat speed during episodes when sediment is evacuated from the stream bed? In this context, the authors may also be interested in the publication by Jansen et al. (2011).
We agree that quantifying background erosion is a requirement for understanding processes within the flume as well as upscaling the results. The term 'clear water' refers to water that has a bedload flux of around ~ 3 g. min -1 . We postulated in the manuscript that this amount provides the tools for a minimum erosion rate; in the current version of the paper this has not been quantified. We thank the referee for giving us the opportunity to clarify this point. Looking at Fig. 4a, one can see the evolution in our experimental flume between 105 and 130 min. During this phase, no knickpoint is observed and the bedrock is eroded up to 10mm in the downstream part and about 5 mm in the upstream part. The erosion in this case is triggered by clear water and thus we can use these observations to estimate local incision rates between 0.4 and 0.2 mm.min -1 . Because downstream bedload is increased by remobilization of the alluvium in the flume, we suggest that the upstream 0.2 mm.min -1 is the most realistic assessment of this background erosion rate. In comparison, the erosion rate associated to knickpoint retreat, calculated after 10 minutes, is ~ 1.5 mm.min -1 , i.e. almost an order of magnitude higher than the 'background' rate. The corresponding bedload calculated over this 10 minute time period is ~ 30 g. min -1 . To first order, these results seem coherent, i.e. erosion rate increases by roughly the same factor as bedload. One has to keep in mind, however, that loads are local and that, after the plunge pool forms, most sediments cover the bedrock surface, preventing further erosion. Also, one key aspect for a correct upscaling is to quantify the bedload vs suspended load during knickpoint propagation. The difficulty here is that, at this point, it is still unclear how much of the sand is in suspension in the plunge pool. Finally, we did observe variation of knickpoint retreat rate, i.e. retreat rates increased in the first portion (~100 mm) of the flume, reached a maximum in the middle, and then, with further upstream movement, decreased or remained steady. We relate the former to the carving of the plunge pool (p. 784, line 28), and believe that the associated increase in sediment production (e.g. Bennett et al., 2000) is a consequence and not the cause of this deepening. In general, we found that the knickpoint retreat in the flume is responsible for bedload increase only at the plunge pool, as opposed to the studies of Jansen et al. (2011) and Cook et al. (2012), where additional bedload is transported from upstream. For this reason, it is not clear that knickpoint retreat speed has been affected by sediment evacuation from the bed during our experiments.

Reviewer #2
[…] I think this is a fantastic paper. I just have a few points that I would suggest that the authors expand on and/or clarify that I think will help contextualize the results better and hence increase the impact here. 1. Not all knickpoints are waterfalls, and not all waterfalls form from abrasion and necessarily have plunge pools. This is not to diminish the results here. Rather, I think the MS would be improved by noting the processes and morphologies that the results bear directly on. For example, knickpoints to many people simply mean a transition in slope area space from one normalized steepness to a different one. How this type of transition propagates into a river may occur due to different processes and different physics. Alternatively, when plucking is the primary mode of waterfall retreat, as is observed in many locations, again different physics are at play. Although some of the general results may hold, it would benefit this paper to perhaps delve a little more deeply into waterfall retreat mechanics and what has been written about them. For example, people will I think be surprised to find that Mike Lamb is cited nowhere in this paper despite many very insightful papers on waterfall processes. In addition, Seidl et al (1994) hypothesized long ago that alluvial cover played an important role in the dynamics of knickpoint retreat in that it inhibits bed erosion, thereby leading to propagation of knickpoints under the armor layer. This should also undoubtedly be referenced here.
2. The conclusion that only base-level drops that exceed the alluvial cover thickness can be directly recorded by a river is really important. That said, the corollary is also worth emphasizing. The alluvial cover thickness acts like a filter on the base-level fall such that we will never see base-level fall events smaller than the alluvial cover thickness. Except in exceptional places like Taiwan, or during exceptional events like glacial floods, this means that for most rivers impulsive base-level falls are not directly recorded. Or, put another way, the depth of alluvial cover provides a simple metric to use in order to determine whether a knickpoint is autogenic or might contain base-level fall information directly (though even here, figure 10 suggests we should be extremely cautious).
Our approach focuses on the variation of bedrock strength on knickpoint dynamics. Lithological variations such as the effect of bedrock jointing or weathering (Miller, 1990)  Assuming that abrasion increases with shear stress, we can compare the abrasion capacity along the flume using slopes. Shear stress is overall 0.9-1.9 Pa in the experiments (Table 1) and 2-5 Pa along the knickpoint faces (assuming flow depth is 1 mm), in accordance with erosion being maximal along the knickpoint face (i.e. higher than the 'background' erosion rate, see response to referee #1). A more accurate quantification of erosion through abrasion would require detailed tracking of sediment and flow dynamics than we were able to do. Our observations are limited by the size of the experiment but detailed study using advanced particle-and flowtracking techniques such as laser holography (Toloui and Hong, 2015) in a larger facility would be a logical next step in this line of research. Finally, undercutting and collapse of the knickpoint face are observed in the case of more resistant bedrock (2-5 % kaolinite), similarly to natural examples Lamb et al., 2007). In this case, we hypothesize that sediment-laden flows in the pool are able to erode backward compared to the overall flow sense due to vorticity in the pool and, potentially, the angle of incidence of the flow, which is set by the knickpoint slope. The conditions necessary for undercutting would be worth investigation in the future, for example combining physical experiments and high-resolution numerical simulations of flow and sediment transport.
All line edits suggested by the editor will be made in the manuscript, particularly the addition of curve fits in Fig. 7d. Finally we will further develop the discussion regarding the potential filtering of base level variation on scales smaller than the alluvium thickness (i.e. p. 783, lines 10-27).

17
Knickpoints are fascinating and common geomorphic features whose dynamics influence the 18 development of landscapes and source-to-sink systemsin particular the upstream propagation 19 of erosion. Here, we study river profiles and associated knickpoints experimentally in a micro 20 flume filled with a cohesive substrate made of silica, water and kaolinite. We focus on the effect 21 on knickpoint dynamics of varying the distribution of base-level fall (rate, increment, and period) 22 and substrate strength, i.e. kaolinite content. Such simple cases are directly comparable to both 23 bedrock and alluvial river systems. Under a constant rate of base-level fall, knickpoints of similar 24 shape are periodically generated, highlighting a self-organized dynamics in which steady forcing 25 leads to multiple knickpoint events. Temporary shielding of the bed by alluvium controls the 26 spacing between these unit knickpoints. Shielding is however not effective when base-level drops 27 exceed alluvium thickness. While the base-level fall rate controls the overall slope of 28 experiments, it is not instrumental in dictating the major characteristics of unit knickpoints.

29
Instead the velocity, face slope and associated plunge pool depth of these knickpoints are all 30 strongly influenced by lithology. The period between knickpoints is set by both alluvium 31 thickness and base-level fall rate, allowing use of knickpoint spacing along rivers as an indicator 32 of base-level fall rate.     We carried out several experimental sets. Experiment #1 is the base case to which other 97 experiments can be compared (rate of base-level fall, U = 2.5 cm h -1 ; incremental base-level 98 drops, ΔZ = 0.25 cm and kaolinite fraction fk = 1% by weight when dry; see Table 1). First, we 99 tested base-level fall scenarios. During experiments # 2, #3, #5 and #6, U was set to 5, 1.25, 0.5 100 and 50 cm h -1 , respectively, while ΔZ and fk were kept similar to experiment #1. In other words, 101 the base-level was dropped 0.25 cm every 30 minutes to get a 0.5 cm h -1 rate and every 3 102 minutes to get a 5 cm h -1 rate. During experiment #7, U and fk were similar to experiment #1 (2.5 103 cm h -1 and 1%) but ΔZ was changed to 2.5 cm (Table 1). To keep the same base-level fall rate, 104 the base level was then dropped 2.5 cm every 60 minutes. Similarly, the base-level was dropped 105 2.5 cm every 30 minutes in experiment #8 so that it could be compared to experiment #2. 106 Finally, different substrate lithologies were tested. The kaolinite fraction, fk, was changed to 0, 2 and 5 % during experiments #9, #10 and #11, respectively, while U and ΔZ were kept similar to 108 experiment #1 (Table 1).  (Table 1). Reynolds numbers fall between 1900 and 2700 while 120 Froude numbers are all above 1, indicating that the flow regime is respectively transitional to 121 turbulent and supercritical (Table 1).

122
On the extracted pictures, any vertical or horizontal position could not be accurately 123 measured below a two-pixel resolution, i.e. 1.33 mm. These vertical and horizontal errors were 124 combined in a simple propagation formula based on variance (Ku, 1966) to assess uncertainties 125 of the metrics used in this study. A test evaluation calculated for experiment #3 showed that 126 variance of the overall experiment's slope was around 0.0017 (i.e. ~ 5% equilibrium slope of 127 experiment #3) and knickpoint velocity variance was about 2 mm h -1 (i.e. ~ 3% of average 128 knickpoint velocity for experiment #3). Therefore, both overall slope and knickpoint velocity do   143 We observe threshold behavior in the total base-level drop needed to generate a 144 knickpoint. In the case of ΔZ = 0.25 cm, 2 to 8 drops are needed to generate the first knickpoint.  After the plunge pool reaches a depth of 1 -3 cm (Fig. 4), the knickpoint begins to retreat at 150 constant speed. In the case of ΔZ = 2.5 cm, a knickpoint is generated for each base-level drop and retreats uniformly (Fig. 4e). During knickpoint retreat, the sand-kaolinite substrate is eroded and 152 the kaolinite and sand separate. The kaolinite is transported out of the system in suspension while 153 the sand is deposited downstream of the knickpoint to form a layer (alluvium; Figs. 3, 4a and 4e).

154
Once a knickpoint reaches the upstream end of the flume, the alluvium remains along the profile 155 ( Figs. 4b and 4f). This layer is slowly removed as the river profile is smoothly lowered by 156 overall diffusion over both the alluvium and the bedrock substrate (Fig. 4b, 4c and 4f). This  The face of a new knickpoint is irregular, i.e. its slope changes at the transition between the 165 bedrock and the remaining bed sediments (Fig. 4g). In that case, the average period between 166 knickpoints corresponds to the time between each base-level drop (e.g. 60 min for experiment #7 167 and 30 min for experiment #8; Table 1). In the case of ΔZ = 0.25 cm, the alluvium has to be 168 removed before a new knickpoint can be generated and retreat (Figs. 4c and 4d). In this regime, 169 the average period between knickpoints is therefore a function of the alluvium thickness to be 170 eroded in the flume (Table 1)   fall rate similar to experiments #1 and #2, respectively, but a ΔZ ten times higher (e.g. 2.5 cm). shear stress calculated at the equilibrium slope for experiments #1, # 2, #3, #5 and #6 goes as the 213 base-level fall rate (Fig. 7d). A tentative exponential fit suggests that the shear stress for U = 0 214 cm h -1 (0.91 ± 0.5) would be above the shear stress of motion (i.e. ~ 0.13 Pa for d50 = 0.1 mm; 215 Julien, 1998) and that the evolution of these slopes is controlled by alluvium removal. The 216 comparison between Figs. 7a and 7c further suggests that the overall equilibrium slope varies 217 more strongly with base-level fall rate than lithology. When fk = 5 %, no equilibrium is attained 218 and the quasi-equilibrium state has a strong sinusoidal shape (Fig. 7c) (Fig. 8h), an increase from 0 to 5 233 % kaolinite is responsible for a knickpoint velocity decrease from 17 to 0.7 cm h -1 (Fig. 8g). The which in the experiments increases with kaolinite content (Fig. 8) rather than just one is generated. Together, these findings suggest that, similarly to drainage 291 basins that tend to be regularly spaced in mountain belts (Hovius, 1996), knickpoints tend toward 292 an optimal knickpoint shapea kind of 'unit knickpoint'. This unit knickpoint is a function of 293 water discharge and lithology (Eq. (2)), and presumably could be strongly influenced by, for under rapid base-level fall (Fig. 6e). However, while Parker described these features as self- watersheds, base-level history is controlled by the evolution of the level of Lake Superior during 379 glaciation / deglaciation cycles (Wright, 1973). The major difference between the two 380 watersheds is their bedrock lithology (Fig 11a; Fitzpatrick et al., 2006). While the stream flowing 381 above a loose sedimentary bedrock shows a small knickpoint located 10 km upstream (Fig. 11b), 382 the stream flowing over a resistant gabbroic bedrock displays a big knickpoint located closer to 383 the watershed outlet (4 km; Fig. 11c). These first-order observations are consistent with our 384 experimental results that the increasing rock strength is favorable to the creation of bigger 385 knickpoints whose upstream propagation is slower.   Table 1).    (Table 1).