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| 26 Mar 2025
Improving a multi-grain size total sediment load model through a new standardized reference shear stress for incipient motion and an adjusted saltation height description
Abstract. Modelling sediment transport is important to understand how fluvial systems respond to climatic change or other transient conditions such as catastrophic sediment release. In natural rivers, heterogeneity of sediment properties and variability of flow regime result in different modes of transport that all contribute to the total sediment load. Le Minor et al. (2022) presented a sediment transport law for rivers that extends from bed load to suspended load while being relevant for a wide range of grain sizes but not specifically addressing the case of a distribution of grain sizes, which must also consider the interactions between grain classes that are mainly important during the sediment erosion phase. If these interactions are not properly considered, the model overestimates transport rates compared to measured ones. We present a new formalism for the reference shear stress of multiple-size sediments, a parameter governing the onset of transport. We show that using a reference shear stress standardized across datasets improves transport rate predictions made with the model of Le Minor et al. (2022). We show that considering the bed roughness length as a reference transport height for single- and multiple-size sediments significantly improves transport rate predictions. We also suggest that, for multiple-size sediments where the bed surface is not fully mobile, the entrainment coefficient should include a dependency on the fraction of mobile grain sizes at the bed surface, although data are insufficient to add this effect in a definite parameterization. Therefore, using a standardized reference shear stress and a transport length adjusted with a common reference height across all sizes appear to be two critical ingredients of a fully functional multi grain-size total sediment load model based on the disequilibrium length. This adjusted model offers the potential to quantify grain-size specific sediment fluxes when different modes of transport may be observed simultaneously, paving the way for more informed numerical modelling of fluvial morphodynamics and sediment transfers.
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Status: open (until 15 May 2025)
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RC1: 'Comment on egusphere-2025-1271', Maarten Kleinhans, 21 Apr 2025
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Review of: IMPROVING A MULTI-GRAIN SIZE TOTAL SEDIMENT LOAD MODEL THROUGH A NEW STANDARDIZED REFERENCE SHEAR STRESS FOR INCIPIENT MOTION AND AN ADJUSTED SALTATION HEIGHT DESCRIPTION
Authors: Marine Le Minor, Dimitri Lague, Jamie Howarth, Philippe Davy
Reviewer: Maarten G Kleinhans, d.d. 21 April 2025The manuscript provides an analysis that is long overdue: the combined Shvidchenko and Crowe datasets for mixed sediment motion and transport. It is technically well done and rather clearly written up with a comfortable information density and with, as far as I can judge, deep insight into the relevant sediment transport mechanisms. I also appreciate the extensive sensitivity analysis to various choices/hypotheses provided in Table S3. A few graphs are dearly needed in section 2 for a broader readership (like you do in Fig 1 in section 3). Furthermore I thank the authors for providing the data and code online.
MAJOR POINTS
* While technically correct, chapter 2 is in need of some figures showing example shapes of functions in units that are understandable to a larger readership, lest the paper and the online provided code might become a black box to some users.* Certain choices (e.g. logarithmic velocity profile, adjusting the saltation height while neglecting saltation roughness) may have an effect on the coefficients in the final set of equations, which is fine but need to be stated and briefly discussed. See detailed comments.
* Certain phenomena need better support by references while other references may perhaps be removed (see detailed points).
DETAILED POINTS (with reference to line and figure numbers)10,36 why is such catastrophic release relevant for this paper? I can guess, but it would be good to spend a sentence more on this, explaining the importance of armouring and such in the quasicyclic landscape processes described in Tunnicliffe. Adding another reference would nicely contextualize this, for example the review by de Haas et al. (2015) also points at the links between debris flow fans and fluvial fans, armouring and the river valley dynamics. The challenges of linking mountain slope to valley and fluvial plain go far beyond that of downstream fining and indeed require a very universal transport relation suitable for extremely wide grain size distributions.
43 I do not agree prima vista, because it all depends on what one calls continuous. One can argue that van Rijn 1984 is sufficiently continuous because it honours the physical difference in sediment motion modes (saltation vs suspension) but uses the bedload relation as a basis for the suspended load relation because the saltation layer is where the suspended sediment originates. In fact, Le Minor et al. 2022 use the saltation height (here too in eq. 11). So this points at a question: why should it be more continuous in the sense meant by the authors when the physical phenomena are in fact not more continuous? This needs a convincing argument, or a brief explanation why this concept is equally interesting as the one used by van Rijn and others.
65-85 the Parker approach for reference transport and his notion that it is the surface layer composition that matters, not the bulk, is missing from this otherwise insightful review. Parker (1982, 1993) argues, and presents some evidence, that the hiding-exposure phenomenon and the armouring (and as shown by Blom as cited and myself in 2005, bedforms) are linked intricately. In this sense the system is complex (with feedbacks) rather than complicated.
98 at this point the term transport length has been dropped several times, and I know it is the topic of Davy & Lague 2009, but the reader needs an explanation earlier how this transport length relates to sediment transport as the volume per unit area per second that most are familiar with. I propose to state this early, and its relation to Shields number, because then it is obvious why the entire section 2 is about that number. Now the relation only comes in 275 eq. 18, which does not help readability. If only a functional relation is provided that would already help, for example the inverse of equation 21 (solved for q_s) or something. Or provide parts of section 2.2 first, for example line 241-244 explains part of the story already.
Table 1 The reference to the empirical equation of Nielsen is unclear. This is a book on coastal boundary layers and sediment transport and Nielsen worked on coastal bedforms. Not only is it unclear which equation is used here, but also is it unclear why this had to replace Soulsby's equation. This deserves a place at least in the supplementary information
151-160 insightful paragraph concerning two concepts between which the difference is not understood by a whole lot of people
173 perhaps mention that d50 is in mm in this equation, hence the factor 1000
165-196 yes, complicated (not complex) indeed, and the reader certainly needs a figure here showing the resulting theta_r,i and the shields curve not accounting for hiding effects for the different methods (for example as my fig 1-3 in my 2002 paper). Please make such a figure for a sediment in your dataset, or multiple figures if they cannot be plotted together.
245 mention that this assumes the law of the wall, which is fine, but differs from the linear velocity profile derived from measurements in gravel beds and the double-averaged reynolds equations, which we also assume between the roughness elements (Vollmer Kleinhans as cited) and therefore would apply to all sediment sizes below D84. Assuming a log profile means that deviations are ascribed later to the hiding or grain-size dependent entrainment model. Please explicate this here or elsewhere. Furthermore, this equation assumes that the roughness is z_0, while we have indications that the saltation layer thickness actually adds to the roughness (Kleinhans et al. 2017). Assuming this is not the case also affects the empirical coefficients later.
285 on a similar note, this adjustment could also be necessitated by a deviation from the logarithmic velocity profile. Furthermore, it could be necessitated from the three-dimensional structure of the grains on the bed surface as shown by Kirchner et al. 1990 and shown to have a huge effect on the hiding function by Kleinhans & Vollmer (2008 we were on a similar path as you here but family matters took over and we never published this as a paper so I am happy you are doing something like this now).
All this is fine, we know the system is complex and we need to neglect certain feedbacks otherwise we have an underdetermined mathematical system to fit on limited data, so I think I understand sufficiently that, and why, you make these choices, but they need to be stated and made clear to the reader. Also, this needs to be discussed.Fig 2a a power function was fitted here (which makes sense) but was the condition of homoscedasticity valid enough for this data (normal distribution of points on a double log scale)? If not, are those high sigma cases affecting the function very much?
376 I am relieved that F does not matter that much, or I would be inclined to ask why the entirely artificial 2 mm distinction between sand and gravel was used rather than a geometrical measure such as the pore-filling size (Frings et al. 2008). (Don't take this point too serious.)
388 I would prefer to have Fig S2 in the paper, possibly expanded with earlier equations referred to here so that it is visualized for the reader.
391 and 523 rather than reporting R^2, it might be better to report significance because with a large number of points a low R^2 may still be significant. As you also state "Our model is slightly more complex than Wilcock and Crowe (2003) but has lower residuals", it makes sense to calculate the significance which would account for the larger number of variables in your model.
Fig 3 is shown far too small and a colour graph would be better. This is an important graph and a nice result.
446 and the strong trend (fig. 4a) is reduced (compare fig 5a).
498 to be fair to Shvidchenko, while he did not fit a function he certainly considered the possible dependence on the grain size distribution, because he designed his tests with narrow and wide distributions and with skewed distributions. I am, in fact, quite certain that a future expansion to your functions should include skewness, because a skewed distribution puts the various grain sizes at different elevations (Kirchner's concept but not quantified by him, see Kleinhans and Vollmer 2008) which must affect their hiding function.
511 but also the pressure fluctuations into the bed which may entrain the finest sediments (Vollmer) and angularity differences between size classes and so on, and a hiding function hides/parameterizes effects of changes in the boundary layer structure (Vollmer) and the turbulence forces on the different grain weights (Kleinhans & Van Rijn). Better state here than in final paragraph of the discussion.
549 this needs a reference, and I suggest the elegant work of Ferguson (2007, 2012)
577 not only roughness, but also density effects on turbulence damping as you also state in line 604. Better state here I think. EH's data is of fine sediment at high Shields number so I wonder whether this was important (Wright and Parker use a modified Engelund Hansen relation for density effects if I remember correctly). See, for example, Van Rijn 2007 and Van Maren (2009 and earlier refs therein) for larger effects of density. This might well be relevant for catastrophic overloading of rivers and mudflows.
598 Really De Leeuw? this finding goes back to the 1960s, for example Vanoni also expressed various things as a function of Froude number.
604 a reference to Winterwerp (2001) is deserved who worked on this long before Wright and Parker
607 not only near-bed turbulence, but also in-bed pressure fluctuations
616 not only Yager et al but also earlier work by Carling, Ikeda Seal-Paola, and others including myself (Kleinhans et al 2002 and refs therein)
622 Kleinhans and Van Rijn 2002 explicitly considered hindering in their semi-empirical sediment transport predictor. I acknowledge it is primitive...
680 the online repository shows a seemingly different European funding scheme or project, which also explains why you mention the landslides early in this paper.
Table S3: multiple variables in the last columns deserve a better visualization. Perhaps multicolumn on a landscape page?
REFERENCESDe Haas, T., Kleinhans, M. G., Carbonneau, P. E., Rubensdotter, L., & Hauber, E. (2015). Surface morphology of fans in the high-Arctic periglacial environment of Svalbard: Controls and processes. Earth-Science Reviews, 146, 163-182. https://doi.org/10.1016/j.earscirev.2015.04.004
Ferguson, R. (2007), Flow resistance equations for gravel and boulder bed streams, Water Resour. Res., 43, W05427, https://doi.org/10.1029/2006WR005422
Ferguson, R. I. (2012), River channel slope, flow resistance, and gravel entrainment thresholds, Water Resour. Res., 48, W05517, https://doi.org/10.1029/2011WR010850
Frings, R. M., Kleinhans, M. G., & Vollmer, S. (2008). Discriminating between pore-filling load and bed-structure load: a new porosity-based method, exemplified for the river Rhine. Sedimentology, 55(6), 1571-1593.
Kirchner, J. W., W. E. Dietrich, F. Iseya, and H. Ikeda (1990), The variability of critical shear stress, friction angle, and grain protrusion in water worked sediments, Sedimentology, 37, 647–672
Kleinhans, M. G., & van Rijn, L. C. (2002). Stochastic prediction of sediment transport in sand-gravel bed rivers. Journal of Hydraulic Engineering, 128(4), 412-425.
Kleinhans, M. G., Wilbers, A. W. E., de Swaaf, A., & van den Berg, J. H. (2002). Sediment supply-limited bedforms in sand--gravel bed rivers. Journal of Sedimentary Research, 72(5), 629-640. https://www.researchgate.net/publication/46623817_Sediment_Supply-Limited_Bedforms_in_Sand-Gravel_Bed_Rivers
Kleinhans, M. G. (2005). Upstream sediment input effects on experimental dune trough scour in sediment mixtures. Journal of geophysical research. Earth surface, 110(F4), F04S06. https://doi.org/10.1029/2004JF000169
Van Maren, D. S., Winterwerp, J. C., Wu, B. S., & Zhou, J. J. (2009). Modelling hyperconcentrated flow in the Yellow River. Earth Surface Processes and Landforms, 34(4), 596-612.
Vollmer, S., & Kleinhans, M. G. (2007). Effects of particle exposure, near-bed velocity and pressure fluctuations on incipient motion of particle-size mixtures. In River, Coastal and Estuarine Morphodynamics conference Universiteit van Twente.
https://www.researchgate.net/publication/46688490_Effects_of_particle_exposure_near-bed_velocity_and_pressure_fluctuations_on_incipient_motion_of_particle-size_mixtures
Also see https://ris.utwente.nl/ws/portalfiles/portal/22398629/Pages_from_9781439856567_preview_1_.pdfKleinhans, M. G., Leuven, J. R. F. W., Braat, L., & Baar, A. W. (2017). Scour holes and ripples occur below the hydraulic smooth to rough transition of movable beds. Sedimentology, 64(5), 1381-1401. https://doi.org/10.1111/sed.12358
Parker, G. P., and P. C. Klingeman (1982), On why gravel bed streams are paved, Water Resour. Res., 18, 1409–1423.
Parker, G. P., and P. R. Wilcock (1993), Sediment feed and recirculating flumes: Fundamental difference, J. Hydraul. Eng., 119, 1192–1204.
Winterwerp JC. 2001. Stratication effects by cohesive and noncohesive sediment. Journal of Geophysical Research 106(C10):22.559–22.574
Citation: https://doi.org/10.5194/egusphere-2025-1271-RC1
Data sets
Supporting data tables and Python scripts for the paper: "Improving a multi-grain size total sediment load model through a new standardized reference shear stress for incipient motion and an adjusted saltation height description" Marine Le Minor https://doi.org/10.5281/zenodo.15043113
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