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.
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- RC1: 'Comment on egusphere-2025-2722', Anonymous Referee #1, 14 Jul 2025
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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 -
AC1: 'Comment on egusphere-2025-2722', Richard Williams, 16 Sep 2025
We would like to thank both reviewers for their detailed comments on our manuscript. Below, we provide a combined response to both reviewers’ comments.
FRAMING
First, it is apparent from the reviews that we didn’t frame our investigation sufficiently clearly in both the abstract and introduction. We note that both reviewers agree that we are addressing a fundamental research question that is important in the discipline. To some extent, our results may appear intuitive, but we are not aware of any literature that has provided empirical or modelling data to answer our hypothesis, although there has been conjecture regarding the issue. We are confident that our approach generates results that support our hypothesis and confirm such conjecture. Our modelling approach is deliberately and necessarily simplified but such approaches, including foundational reduced complexity / cellular-automata models, have been effectively applied in fluvial geomorphology to address foundational questions, from which further investigations have often subsequently been conducted that have added in further process representation. Reviewer 1 takes issue with our model formulation which implies that we need to better explain our simplified approach to convince readers of its validity, prior to presenting our results. We propose to reposition our investigation by rewriting both the abstract and introduction. At this stage, we propose the following revised abstract:
Spatial variability in gravel-bed river bedload transport rates is generated by spatial patterns in flow hydraulics and bed material grain-size. Here, we consider reaches of different channel pattern types that are sufficiently large to generate frequency distributions of point bed shear stress that are characteristic of that channel pattern. Four such distributions, taken from contiguous reaches of the Bislak River, the Philippines, are used to test the hypothesis that spatial variability in bedload transport is a function of reach scale river pattern. Flow depth, velocity and shear stress were calculated using two-dimensional hydraulic modelling over a high-resolution system-scale DEM which fuses bathymetric and topographic surveys. A simplified approach is taken, using constant water discharge and a single grain-size across the reach, to isolate the effect of channel pattern on bedload transport. From the hydraulic modelling, we predict relative bedload transport rates in the four reaches (meandering, wandering, braided, deltaic). Spatial maps and frequency distributions of bedload transport reveal distinct signatures associated with each river pattern, which remain consistent when we vary grain size from D16 to D84. This first-order association between channel pattern and bedload transport rates has implications for understanding the real-world variance in the continuum of river patterns, with implications for assessing channel change resulting from both natural and anthropogenic drivers.
We propose to rewrite the first three paragraphs of the introduction so that the rationale behind our investigation is clearer from the outset. First, we will start with a paragraph on how spatial variability in reach-scale topography and hydraulics control bedload movement, which itself is suggested to be a function of channel morphology. We will acknowledge that there are better data available on bedload temporal variability but that there is a need to investigate large-scale spatial variability in bedload both to fully understand temporally unsteady transport and to link transport to morphological dynamics. We will then review how simplified (e.g. reduced complexity, including cellular automata) approaches enable process-complexity to be stripped back to test one hypothesis.
MODELLING APPROACH
We agree that more sophisticated modelling approaches area available but we seek to explain the first-order hydraulic control over transport rates. One alternative approach would be to represent a spatially variable grain size mix. Observational datasets are emerging at the system-scale (e.g. Ribet et al., 2025) but these data are not available for the Bislak river. Incorporating such data could be the next logical step in addressing this research question and we propose to add this topic to our revised discussion. However, although we do not vary grain size spatially, we do test the sensitivity of our approach with D16 and D84 grain sizes and find that the spatial patterns remain consistent. The representation of spatially variable grain sizes to represent armouring is therefore likely to make the frequency distribution slightly more “fuzzy” but not to change the overall signal. Another step in sophistication would be to develop a morphodynamic model. We have separately undertaken some such modelling for part of the study area in the current paper, and encountered considerable uncertainty arising from e.g. unknown upstream sediment influx boundary conditions, and unknown sediment supply rates along the river. We conclude that increasing the complexity of our modelling at this stage would introduce spurious precision to our results without affecting our ability to test the hypothesis in the paper; in fact, such un-tested complexity may well obscure our insights into fundamental process controls.
PAPER FORMAT
We consider that our paper provides a conceptual contribution to a fundamental and important question in fluvial geomorphology, that has been designed to test a single hypothesis and to provide the basis for further research. We thus formatted our manuscript for an ESurf Letter, which has <2500 words in the main text and a description of the methods in an appendix, as detailed at https://www.earth-surface-dynamics.net/about/manuscript_types.html and https://www.earth-surface-dynamics.net/about/manuscript_types/esurf_letters.html. We acknowledge that we edited the methods down too much to fit an overall 2500 word limit and now realise that we have an allowance of a further 3000 words for the methods. We propose to rewrite the methods section to provide an expanded explanation of the methods that will likely be in the 2500-3000 word range. This revised methods appendix will respond to all relevant reviewer comments asking for clarity on our methods (e.g. information on hydraulic model calibration, more detail on channel pattern classification).
CRITICAL SHEAR STRESS
We can confirm that the critical shear stress was set to be constant across the model domain (using Equation 2). We can also confirm that the two-dimensional hydraulic model predicts spatially variable shear stress for each model cell. We considered different grain sizes (D16, D50, D84) for our calculations and the critical shear stress was different for each grain size. For each scenario, we used the same grain size across the model domain. As noted above, we considered different grain sizes to assess the sensitivity of the differences in bedload transport that we observed between different river patterns. We agree that a next step would be to consider spatially variable grain size and hence critical shear stress. As noted above, without extensive grain-size data across the reaches, any estimation of grain-size spatial variation would reduce our ability to assess the hypothesis presented in the paper. Our contribution was intended to enable us to present a fundamental concept and to provide a first-order assessment of its validity. Variable grain size would be a wonderful addition for someone to make in the future.
DISCUSSION
We are grateful for reviewer 2’s suggestions of how we could further explore hydrological and grain size simplifications and propose to address these in our revised discussion. We will make a histogram of slopes between adjacent cells in the downstream direction for each river pattern to assess the frequency distribution of slopes. We expect a down-river reduction in the median slope and will assess the variability in these data. With respect to grain size, we will expand our commentary on grain size mixtures in section 3.1. Within the simplified experimental framework that we adopt, we consider D16 to D84 to be a relatively wide range. If D84 is controlling bedload entrainment, due to hiding and protrusion effects, then the results for D16 and D50 are effectively showing the effects of reducing grain size or of changing the degree of armouring present in the river. Once again, using constant grain sizes is a necessary simplification given that grain-size distributions and the degree of armouring are likely to vary within and between reaches, and from our own field observations we know that grain sorting within this river is complex, as has been extensively reported from other gravel-bed rivers worldwide. However, importantly, all grain sizes show similar spatial patterns within each river reach.
FURTHER POINTS OF CLARIFICATION:
- ABTA stands for Active Bedload Transport Area. This acronym is defined in Figure 2 and we apologise that it was not clearly defined in the text
- Flow frequencies: Q2, Q50 and Q100 refer to the 50%, 2% and 1% annual exceedance probability high flow events.
- River pattern: River patterns were mapped and classified using the River Styles Framework, reported in Tolentino et al (2022). We referred to this in the methods (section A1.1) and Figure 1. We apologise that this reference was missed off the reference list and it can be found below. We will expand on our determination of river pattern in the extended methods section.
Reviewer 1 made a series of comments on specific lines. We will address all the comments that seek clarity and further methodological detail.
REFERENCES
Ribet, L., Liébault, F., Borgniet, L., Deschâtres, M., and Melun, G.: Surface grain-size mapping of braided channels from SfM photogrammetry, Earth Surf. Dynam., 13, 607–627, https://doi.org/10.5194/esurf-13-607-2025, 2025.
Tolentino, P.L.M., Perez, J.E.G., Guardian, E.L., Boothroyd, R.J., Hoey, T.B., Williams, R.D., Fryirs, K.A., Brierley, G.J., David, C.P.C.: River Styles and stream power analysis reveal the diversity of fluvial morphology in a Philippine tropical catchment, Geoscience Letters, 9, https://doi.org/10.1186/s40562-022-00211-4, 2022.
Citation: https://doi.org/10.5194/egusphere-2025-2722-AC1
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- 1
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?