Dear authors,
thanks for the revised manuscript. I read it with interest. The paper is somewhat improved and the methods are largely clear now. Nevertheless, I still find inaccuracies especially in the introduction, and the research gap and aims are not cleanly set up. The material presented in the introduction needs to be focused and stream-lined.
I appreciate that you picked up some of my previous suggestions in the discussion. Yet, I am a little surprised that some of the most obvious similarities are glanced over. As an example, in the Turowski and Hodge paper, we derive a cover equation with a logarithmic shape somewhat similar to what you fit to the experimental data (see eq. 27 and 31 in that paper). I wonder why this is not discussed.
There is also a mixture of discussion material in the results. Please look out for this and move / rewrite accordingly. I might have overlooked something, but it seems to me that some of the methodological points were answered in the rebuttal, but didn't make their way into the manuscript (e.g., properties of the cement, asked both by me and Christian Braudrick). Please review and amend this.
Finally, the 6 points in the conclusion do not directly pertain to the four points that are said to be addressed by the study at the end of the introduction. It would be good to rewrite this to have a direct relationship.
2.8 …Gilbert did not specifically use…
2.14 only the 2001 paper includes experimental work
2.15 The description here relates just to the cover effect. The tools effect is parameterized as a linear dependence on sediment supply in the saltation-abrasion model.
2.16 The saltation-abrasion model…
2.25 Lague’s model is not for bedrock incision, but for bedrock channel morphodynamics
2.26 Misleading: his cover model is equivalent as described, the context suggests that you mean the morphodynamics model.
2.28 and following: the paragraph features a string of loosely connected statement (jumping from a brief description of Zhang’s cover model, to Turowski’s 1D model of steady state channel morphology to Mishra’s experiments) and lacks a clear line of argument. The references are treated at different level of detail; a symmetry is lacking. The point of the introduction should not be to list all previous cover models and their applications, but provide an argument that leads to the research gap and question.
3.4-5 I somewhat disagree with this statement of the research gap, because in my mind it confounds two unconnected problems. Let me explain this briefly. When we think about cover, we have two problems to solve. Consider a particular control area on the bed (in a discrete model, this would be a pixel, in a continuous formulation an infinitesimal area element). 1) For a given amount of sediment mass or volume, we need to know how this is distributed to give a particular cover fraction. As a concrete example, if we have, say, 1/100 of a cubic meter of sediment deposited on an area of 1m2, we could have a complete cover of 1cm thickness of the entire area, or we could cover half of the area by a 2cm thick layer. Or there are an infinity of other possibilities to distribute this sediment. Therefore, we need a relationship between cover fraction and sediment mass (or volume). The point of the exponential cover function of Turowski et al. 2007 and Turowski 2009, and of the P function of Turowski and Hodge 2017 is to provide such a relationship. 2) We need to know how much sediment deposits in a given area element (the total mass or volume per area element of the bed). This is done by relating deposition and erosion to hydraulics. In general, this is done either using a framework based on the Exner equation (e.g. Zhang’s or Inoue’s work) or on the entrainment-deposition framework (e.g., Turowski and Hodge 2017, Shobe et al. 2017).
3.7 There is also earlier work by Nelson and Seminara (2011 and 2012).
3.8 Again, here is a confusion between morpho-dynamic models and models of bedrock incision. As an example, the saltation-abrasion model is a model of bedrock incision; it predicts erosion rate (that is volume removed per time and per bed area) as a function of hydraulics, and sediment properties and transport rate. It has been used in 0D/1D morphodynamics models for example by Sklar and Dietrich 2006, by Zhang et al., or by Turowski 2018. Similarly, the stream power / shear-stress model is a bedrock incision model, which has been used in a number of morphodynamics frameworks (e.g., Wobus et al. 2006, Stark, 2006).
3.9-11 What about the experiments by Friedl (chapter 7 of https://www.ethz.ch/content/dam/ethz/special-interest/baug/vaw/vaw-dam/documents/das-institut/mitteilungen/2010-2019/245.pdf, mentioned in one of my previous comments)?
3.10 I still think the formulation is misleading. The reply in the rebuttal does not convince me (it is not the assumption of the model that sediment can only be transport on covered parts of the bed). Maybe it would be good if you make the assumptions underlying your interpretation of the model explicit, and more clearly explain your line of thinking.
3.13 Maybe it would be helpful to define ‘throughput load’ here.
3.14 Again, this is inaccurate. Yes, some models, notably the linear cover model, are based on temporally representative values (essentially using long-term ‘effective’ values for hydraulics and sediment supply). Still, sediment supply and transport capacity could be written as functions of time. In that way, one can model temporally evolving cover. This approach neglects the response time of cover to changing conditions, i.e., cover is always adjusted to the boundary conditions and any lags are neglected. The mass/volume based formulations are more general, one could write mass/volume as a function of time. The crux is to couple these cover models to proper hydraulic and sediment transport models. And even this has been done in a handful of papers (most of which you cite earlier). Finally, in the Turowski and Hodge 2017, we devoted an entire section to response time scales, including analytical solutions and explicit formulations of response time scales, and a discussion of leads and lags, going far beyond the ‘loose definition’ that you claim to exist to date. Regarding the spatial time scale, there are papers that upscale from the grain scale (which I already pointed out in the last round of reviews). Again, here the problem is related to appropriate length scales of hydraulics, rather than cover.
3.17 I still think you need to supply a clear definition of what you mean by transient cover.
3.20-24 Again, I point to the Turowski and Hodge paper. The model provided therein for sediment transport is physically based and can deal with temporal cover fluctuations (see their figures 10, 11 for examples of temporal evolution of cover in generic situations and 14 for an example calculation for a real flood event). Another model (that I did not mention in my previous review) is the one of Johnson, JGR 2014. He deals with feedbacks between cover and bed roughness.
3.25 From an experimental point of view the question is fair. However, I suggest to state that there are models that predict a much wider range of behaviors. See for example the cellular automaton of Hodge and Hoey 2012 or the simulations of Aubert et al. (ESurf 2016). The P-function framework of Turowski and Hodge is sufficiently flexible to be able to describe all of these observations.
3.28 It has also been shown to not be an acceptable approximation in previous work (incidently, also in some of the cases described in the cited paper).
4.7 why ‘alternative’? The saltation-abrasion model evaluates to the same equation (2) once all the terms in (1) are evaluated.
4.13 I do not see this readily. If we view p_0 and p_c as a function of time and space, the equation is still valid. (And this is exactly what is done in the following paragraph.) See also my comment to 3.14.
4.14 Full stop instead of comma after sense.
4.15 grammar / sentence unclear (P_0 is this but instead that).
14.12 Slightly inaccurate; the assumption is of uniformity within the area of consideration. One could divide the bed in multiple cells where this assumption is (approximately) valid and in this way model cross-stream variations.
Although in my previous papers, I have dealt with a control area with homogenous conditions, it would be straight-forward to expand this to full 2D models, by placing a number of homogenous control areas in the long- and in the cross channel direction (building up a grid that represents the bed). Then, the only thing that needs to be added is the long- and cross-stream sediment mass balance as a function of hydraulics, i.e., we need to specify how much sediment moves from a given cell into the neighboring cells. This is straight-forward (though not necessarily easy) because the tools to do this are available (for example, the Nelson and Seminara papers, or other work that deals with 2D resolved sediment transport in alluvial rivers). The question again becomes of how large/small can the considered cells become. We want to make them as small as possible to properly resolve the hydraulic variations, but large enough so that numerical computations are feasible, and that we can treat sediment as a continuous mass and do not need to deal with granular effects.
4.19 It is not an arbitrary function. ‘Arbitrary’ means that it does not matter which function is chosen. Instead, there are some clear constraints on the function, both from fundamental logic / definitions (i.e., cover cannot be smaller than 0) and from observations.
4.20 What are your arguments to judge this as the ‘simplest realistic form’? What observations does your realism hang on? Not sure whether I would call a discontinuous function realistic…
4.27 The statement ‘…and channel geometry would not change over time’ does not follow from what has been said before. Clearly, channel morphology changes if, say, only the right side of the channel bed erodes and not the left side. I would even argue the other way round: as long as there is erosion somewhere (partially covered bed) persistent cover necessarily leads to an adjustment of channel geometry!
4.28 Again, this is not necessarily true. You may have patches of cover moving through and still adjust the channel (for example if wall erosion rates are much high than bed erosion rates). This is because erosion rate is not only dependent on the cover effect, but also on the tools effect (tools concentration may vary, as may the impact rate for a given concentration, or there may be a lateral sorting of grain sizes).
5.1 Better: may form – not all meander bends necessarily have point bars at all times. Also consider temporal variation of floods – we do not really know whether point bars persist throughout the largest floods.
5.2 …breaks down…
5.18 What point cloud?
5.31 The term macro-roughness appears here for the first time pertaining to the experiment. What do you mean by it?
9.20 Eq. (8) – compare to the results of Turowski and Hodge, e.g., eq. 27 and 31 in their paper. This gives a similar logarithmic function in the cover domain, where the exponential term is approximately zero.
Aubert et al. (ESurf 2016) also predict a similar function from their models.
9.31 I am still not convinced by the use of the logistic curve. For qs/qt=0, this gives finite cover, which is unphysical. It is not difficult to find an equation that honors that condition and otherwise has similar poperties.
11.30 this is an interpretation that should be placed into the discussion section
13.12-26 this is discussion material
13.31-14.3 discussion material
14.28 no comma after ‘above’
16.7 ...and Nelson and Seminara 2011
17.2 They showed that energy can transferred, not that erosion is possible. Erosion was not investigated in this study.
17.15 citation incorrect, should be Turowski and Hodge 2017 |