the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Jul 2025
Spatial variability in bedload transport rates determined by river pattern
Abstract. Local spatial patterns in flow hydraulics generate temporal variations in bedload transport rates. The nature of this local spatial variability changes as larger spatial scales are considered. Here, we investigate the hypothesis that spatial variability in bedload transport is a function of river pattern defined at the reach scale. A high-resolution system-scale DEM, which fuses bathymetric and topographic surveys, is used for two-dimensional hydraulic modelling to predict distributions of flow depth, velocity and shear stress. From this modelling, we predict bedload transport rates in four contiguous reaches with different (meandering, wandering, braided, deltaic) river patterns. Spatial and frequency distributions of bedload transport rate reveal distinct signatures associated with each river pattern. The results enable the real-world variance in the continuum of river patterns and bedload transport to be characterised, with implications for assessing channel change from, for example, anthropogenic modification and restoration.
- Preprint
(1646 KB) - Metadata XML
-
Supplement
(337 KB) - BibTeX
- EndNote
Status: final response (author comments only)
-
RC1: 'Comment on egusphere-2025-2722', Anonymous Referee #1, 14 Jul 2025
In the paper, the authors run simplified hydraulic simulations over several reaches of a river, calculate bedload transport rates using a shear-stress based equation, and investigating the spatial variability of the transport rates. The main take-away message of the paper seems to be that a focus on intrinsic fluctuations in transport rate are unwarranted and that, instead, variations are caused by differences in planform pattern (line 142).
In my opinion, the paper lacks quality in all relevant areas. The author seem to be only partially aware of the relevant literature. The motivation of the study is unconvincing. The research question, expectation, and the approach are not well described and argued. The modeling is not set up in a clear approach to answer a well-posed research question. Methods are insufficiently described. The models are simplified, and an awareness of the consequences of the modeling choices for the interpretation seems to be lacking (and is not discussed). Moreover, the model outcomes seem to be to me a direct consequence of the modelling assumptions, and are therefore neither surprising nor novel. The analysis is largely qualitative and speculative. A major claim is made that is not supported either by the results or by the analysis. I might miss something major here, but in that case, there is a strong need for better communication.
Here are some more detailed points
1) In the modeling approach, bedload transport is related to shear stress using a standard equation. The critical shear stress seems to have been set constant for the entire modeling domain (not totally clear from the method description). Sediment continuity is not accounted for (i.e., sediment transport rates at a location are independent of those upstream and downstream, erosion and deposition does not occur). As a result, bedload transport rates directly follow local shear stress. Given the equation, this can lead to either a linear scaling with discharge (for shear stresses high above the threshold), or a non-linear equation (for shear stresses close to the threshold). This is what the authors report in Fig. 5, and on what they build their main interpretation. In essence, single threat reaches show a shear stress distributions where the majority of locations has a shear stress high above the threshold, while the other planforms show progressively increasing fractions close to the threshold. This makes sense; as water spreads out of larger areas, the average flow depth, informing shear stress, decreases.
2) I do not think it is possible to conclude that spatial variations in shear stress (assumed to determine bedload transport rates directly) take dominance over internally-driven fluctuations based on the model results (line 142). All you can say is that geometry caused spatial differences are of similar order (or not) as transport rate fluctuations observed at a cross section, given the simulations in your chosen river reaches. Here are some reasons behind that statement: (i) The model does not include any small-scale processes that have been argued to drive transport rate fluctuations, including, for example, turbulent fluctuations, burst processes, granular processes, or particle impacts. It therefore cannot inform about the relative importance of these processes. (ii) The model does not include any sub- and between-reach variability and complexity of, for example, grain size distributions, shape, density, and so on, or vegetation, and biological activity. These, too, have been argued to contribute to transport rate fluctuations (e.g., Chen & Stone, WRR 2008, doi:10.1029/2006WR005483). (iii) The model does not include any non-linear interactions at the sub-reach scale, for example, spatio-temporal grain size sorting that may lead to patch formation (e.g., Monsalve et al. 2016, doi:10.1002/2015WR017694), the organization of grains into moving bedforms (e.g., Hamamori, 1962), or cyclic or non-linear erosion and deposition driven autogenically (e.g., Recking, 2014, http://dx.doi.org/10.1016/j.jher.2013.08.005) or by geometric variations (e.g., Cook et al., 2020, DOI: 10.1002/esp.4993). Again, these have been argued to contribute to transport rate fluctuations, as exemplified in the mentioned papers.
3) I think there is a need for a better rooting of the study in available literature, both in terms of the types of models that are available, and in terms of the knowledge on transport rate fluctuations that is out there (both for the grain and the reach scale). Further, to go beyond the specific case study needs a clear conceptual framework, and a stringent scientific approach. For example, the study and approach need to be clearly framed between the three different points of views of spatial variability in transport rates at a given time, the fluctuations in transport rate for a steady flow at a cross section, and those fluctuations over time at a cross section for varying flow conditions (e.g., hysteresis). And how these three relate both conceptually (there are available mathematical frameworks) and within the context of the study. Similarly, fluctuations can be driven by internal processes, by sediment supply to a point, or by variations in forcing (discharge, turbulence). Your model does not take into account sediment continuity, which is a major assumption that relates both to the space vs time question, and to the potential causes of transport rate fluctuations.
It may be possible to refocus the study, looking at velocity and shear stress distributions, and how they could affect transport rates and reach-scale simplified modelling. There is not a huge amount of literature on this. An example is by Barbour et al., GRL, 2009, doi:10.1029/2008GL035786.
Structure: currently all the methods are in various appendices, which is a very uncommon way to structure a paper. Please move the methods into a method section between the introduction and the results.
18-20 describe the results wrt variance, as well as the implications
22-38 research on bedload transport rate fluctuations has a history going back to the 1930ies. Most of the literature cited here is from the past few years, with only a few earlier papers mentioned (and most of those published after 2000). I suggest to honor the long history of the topic with some of the key earlier citations.
54 add ‘e.g.’ to these citations, maybe acknowledge some of the many other authors who have worked on this.
61 what does ABTA stand for? That’s just the fraction of area where local shear stress exceeds the local threshold, correct? In the methods, you mention three different grain size fractions; which one is used for the calculation here?
62 please define symbols (Q_50 here, but also elsewhere)
62 a description of the classification into planform types and a definition of these types are missing.
70 you could add a map of the threshold of motion here, in case you took into account its spatial variation.
77 how did you establish significance? Please describe the appropriate statistical tests (in the method section) and their outcomes.
84 I am confused by this. When reading the method section, I get the impression that the same grain size distribution was applied to all reaches. How, then, did you calculated a variation with grain size?
90 what does it mean, they are close to linear? How did you measure the concavity of the relationships?
123 Ok, yet sediment mixtures behave in different way, for example hiding-exposure relationships. Even in your qualitative discussion, you can go way beyond this.
128 how did you calculate discharge here? Is that the discharge in a pixel, i.e., essentially the product of water depth and flow velocity?
135 Am I missing something, or is this essentially what you put into the model? Given a distribution of shear stress, the main thing your model seems to do (see eq. 1) is to truncate this distribution at the threshold of motion, and then transform it in a non-linear way (power function with exponent 1.5). The interesting question here is now: under what circumstances do you obtain the scaling relationship close to linear and at what does the non-linear scaling prevail. That, too, can be easily obtained from the transport equation. For a transport equation with an exponent of 1.5, transport rates are linear in discharge for discharge above the threshold (this can easily be shown, e.g., Rickenmann, WRR, 2001). So, the observed linear scaling occurs for reaches where the discharge is far above the threshold in most places, while the non-linear scaling occurs for reaches that are close to the threshold of motion in most cases. I think the other patterns can be interpreted in a similar way.
142 sorry to give a strong objection here: you have not demonstrated this at all and a statement with such a strength is neither justified from your study not from the literature. (i) Your simplified model does not allow an assessment of the importance of intrinsic fluctuations, since it does not include the relevant generation mechanisms, (ii) fluctuations in transport rates are observed also in controlled (and sometime very simple) environments. The 2D flume experiments of Ancey are an example of that (and many other reported experiments). (iii) Multiple sources for transport have already been identified in the literature. These include processes at the grain scale (not modelled here, including for example: turbulent fluctuations and eddy formation, variations in grain size and shape, as well as their distributions, non-linear feedbacks between stationary and moving grains, non-linear feedbacks between moving grains, grain mobilization, roughness, and local flow properties), and at the reach scale (partially assessed here, but also differential grain sorting, separation of the transport path from the path of fastest flow, continuity of sediment and the interactions of erosion, deposition and transport), but also those arising from continuity, and non-linear mixing of particular effects.
In addition, spatial and temporal variability is not the same in most practical cases, yet this forms a basic assumption of your interpretation. This warrants a broader discussion.
182 the criteria used for classification into different planform patterns should be described somewhere.
195 This needs more details, describe the algorithm that you used and the solver.
196 This needs more details. Please describe your approach to calibration procedure. Especially the part where the model output was compared to data is insufficiently described. Did you optimize some stats? Which ones? How did you deal with spatio-temporal variability?
203 the way I understand the description here is that sediment continuity is not honoured, and bedload transport rates are a simple function of the hydraulics in a particular location, correct?
211 do I understand this correctly that the critical shear stress is a constant for the entire study?
Citation: https://doi.org/10.5194/egusphere-2025-2722-RC1 -
RC2: 'Comment on egusphere-2025-2722', Anonymous Referee #2, 19 Aug 2025
The manuscript addresses an important and often overlooked topic in fluvial geomorphology: the link between river patterns and modes of sediment transport. This is of great interest for our community, and the authors frame an excellent research question. However, I find that the current version of the paper does not yet provide sufficiently robust or meaningful findings to support publication in its present form.
The attempt to analyze four river types along the same rivers is interesting and potentially powerful. However, the main result presented—that sediment fluxes decrease downstream—is not particularly surprising and does not, in itself, represent a significant contribution. The hydrological and grain-size simplifications adopted in the simulations could be acceptable, but they would need to be explored more thoroughly. For example:
- Why does sediment transport decrease downstream? Is this driven mainly by slope reduction?
- What is the role of grain-size fining, and at which scales or reaches does it become relevant?
Furthermore, only one sediment transport formula is applied. Considering the well-known uncertainties and differences in assumptions across formulas, a comparative analysis with several approaches would substantially strengthen the work.
The aspect of the study that I found most promising is the analysis of active transport width. These results deserve much more detailed discussion, ideally supported by maps showing changes across river types and return-period discharges. Such maps would also benefit from comparisons among different transport equations, which incorporate different assumptions about critical mobility. For instance, I find it difficult to accept that a braided river would show only minor changes in active transport width from Tr50 to Tr100. If this is indeed the case, it requires a clear explanation. I would expect such behavior from a sinuous or meandering system, but not from a braided one.
Additional analyses could further enrich the manuscript:
- Providing information on armoring conditions in different reaches.
- Characterizing grain-size variability across active channel elements (e.g., bars vs. incised channels), which is particularly relevant for gravel-bed braided rivers but also for some meandering systems. I acknowledge the difficulty of collecting such data, but addressing the research question posed here requires grappling with exactly these kinds of details and assumptions regarding sediment entrainment and critical discharges.
I also found the methods section excessively dry and underdeveloped. Since this is not a multidisciplinary journal, the methods must be described with enough detail for specialists to properly assess the assumptions made. For example, the criteria used to classify the four river types are presented with too little detail. Such information is crucial for interpreting sediment transport processes and linking them to river morphology.
I recommend at least a major revision of the manuscript or a re-submission. Additional simulations, methodological comparisons, and more in-depth analyses of the link between sediment transport and river morphology are needed before this paper can be considered for publication
Citation: https://doi.org/10.5194/egusphere-2025-2722-RC2
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 308 | 37 | 15 | 360 | 21 | 14 | 27 |
- HTML: 308
- PDF: 37
- XML: 15
- Total: 360
- Supplement: 21
- BibTeX: 14
- EndNote: 27
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1