Modelling braided river morphodynamics using a particle travel length framework

Kasprak, Alan; Brasington, James; Hafen, Konrad; Williams, Richard D.; Wheaton, Joseph M.

doi:https://doi.org/10.5194/esurf-7-247-2019

Articles | Volume 7, issue 1

https://doi.org/10.5194/esurf-7-247-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/esurf-7-247-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 7, issue 1

Research article

|

14 Mar 2019

Research article |

| 14 Mar 2019

Modelling braided river morphodynamics using a particle travel length framework

Alan Kasprak, James Brasington, Konrad Hafen, Richard D. Williams, and Joseph M. Wheaton

Download

Final revised paper (published on 14 Mar 2019)
Preprint (discussion started on 13 Apr 2018)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

- Printer-friendly version

- Supplement

RC1: 'Modelling braided river morphodynamics using a particle travel length framework', Anonymous Referee #1, 06 May 2018
- AC1: 'Response to AR1', Alan Kasprak, 22 Jun 2018
RC2: 'Review of esurf-2018-17', Anonymous Referee #2, 13 May 2018
- AC2: 'Response to AR2', Alan Kasprak, 22 Jun 2018
RC3: 'Review of ESURF-2018-17', Anonymous Referee #3, 16 May 2018
- AC3: 'Response to AR3', Alan Kasprak, 22 Jun 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Alan Kasprak on behalf of the Authors (17 Jul 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (17 Jul 2018) by Jens Turowski

RR by Anonymous Referee #1 (29 Jul 2018)

RR by Anonymous Referee #3 (05 Aug 2018)

Suggestions for revision or reasons for rejection

Overview
This paper presents a new morpho-dynamic modelling approach, whereby sediment transport is simulated through particle travel lengths algorithm rather than the more traditional flow-field and gravity-driven sediment algorithms. The model is applied to two case-study river reaches over different time scales.

Evaluation
The paper is well-written and logically structured. The approach is novel and appears quite promising, both in terms of flexibility and initial results. I very much like the concept of the paper, and I think this revised manuscript can be can be published after a few additional minor changes and clarifications.

Comments/questions
1) The strangest element of the model is the assumption that event erosion is independent of event duration (p10 ln1-3). Imagine two scenarios: scenario A is a three-day flood of 200 m3/s; scenario B consist of three one-day flood events of the same discharge, but separated by a short period of low flow. In the authors' approach, scenario B will result in three times as much erosion as scenario A. This seems counter-intuitive.
Nonetheless, the authors obtain seemingly reasonable results for their single event simulations on the River Rees and multiple event simulations on the River Feshie. This is especially notable since the authors “did not attempt to scale or correct estimates of bed sediment erosion as a function of flood duration” (p10 ln3). However, their method does introduce a dependency on event discretization or the choice of event magnitude threshold, discretizing multiple sub-events for the same simulations would simply result in more erosion and more geomorphic change.
Indeed, with their discretized hydrograph simulations the authors observe more erosion over a wider area than with the single discharge simulation (p19 ln21-24). This is not surprising, since the discretized hydrograph effectively consists of three “events” whereas the single discharge representation consists of one “event”. Since event erosion is independent of event duration (p10 ln1-3), it is to be expected that adding two “events” as part of the discretization will result in more erosion. As the added events are of smaller magnitude (representing the rising and falling limbs of the hydrograph) there is no tripling of the erosion. A further discretization, representing more points on the hydrograph would result in more erosion still.
Can the authors elaborate on the further implications for the seemingly odd assumption that event erosion is independent of event duration?

2) The authors’ bank erosion mechanism is not fully clear, and could be descried and illustrated in more detail.

2a)The authors state that “the model calculates the slope of all cells in the model domain […]. Cells that exceed a user-defined slope criterion […] are then identified as candidate cells for undergoing bank erosion” (p10 ln14-20). As this occurs for all cells in the model domain, this seems to suggest that bank erosion can occur on any cell of the model domain, i.e. not just on the banks, but potentially also on the river bed or on the floodplain. Is there any selecting that the bank cells have to be dry and be bordering a wet cell?

2b) The bank erosion algorithm introduces a couple of seemingly arbitrary choices: erosion area threshold (30 cells), shear stress sampling area (3x5 window), average shear stress exclusion threshold (50 N/m2). Has there been any sensitivity analysis to investigate the impact of these arbitrary value choices? For the erosion area threshold the authors indicate that 30 cells produced good agreement with observed erosion patches (p10 ln28-29). Are the other choices equally calibrated to the observed field-data? Or are they based on other considerations? Would any deviation from these seemingly arbitrary values result in notably different results, or in numerical instability? Are these values likely to need adjusting for each River?

2c) Equation 11, determines the number of cells from which material will be removed during bank erosion? What is the basis for this equation? How was it derived? Why is shear stress divided by 3? Why is slope divided by 15? Is the division by 15realted to the size of the shear stress window (3x5)? If so, does it matter that not all cells in that window are necessarily included in the shear stress calculation.

2d) It is not clear how the red area (Fig 2.4) is derived, nor is it fully clear how the volume of erosion is determined. The number of cells in the red area, i.e. n, is determined using equation 11. But I do not understand how the location of these cells is determined.
I raised the lack of clarity on this issue in my initial review. In their response the authors note that “ the values within the brown cells (Panel 4A, Figure 4 [presumably the authors meant Fig 2]) correspond to the computed extents around those cells where bank erosion occurs – essentially, the brown cells are ‘padded’ by this value, and the cells falling within that padding window undergo bank erosion, which produces the red polygon in Panel 4. We have clarified this approach on page 11.”
I do not think the authors’ clarification on page 11 is very clear, nor is Fig 2. First of all, the title for fig 2.4A suggests that the values given are “erosion values”, not “the computed extents around those cells where bank erosion occurs”. Further, the text indicates that “material is removed from cells working in a direction opposite the bank cells' aspect” (p11 ln13), but in that case it is not clear how the red area can extend in two directions beyond the brown cells that river bank make up the end points of bank erosion patch (fig 2.4). Also it is not clear from which cells in the brown patch one would start to identify the n red cells. Presumably I would get a different cluster of n red cells if I start allocating them from the upstream end than if I were to start from the downstream end.
Finally, material is removed from the n cells in the red area. The text states that “eroded cells are reduced in elevation to a level equal to that of the lowest cell in the initial neighbourhood surrounding the bank cell”. Presumable this is a 3x3 neigbourhood, although this is not specified. Moreover, it is not clear if this refers to the neighbourhood of the eroding bank cell (i.e. red cell, fig 2.4) or the neighbourhood of the original bank cell (i.e. brown cell).
In short, based on the description in the manuscript and associated figures, I would not be able to recreate the authors’ bank erosion algorithm. I could, of course, look at their open source code to have all these things clarified, but that is beside the point.
Could the authors please expand the description of their bank erosion algorithm, or maybe provide a clearer illustration of its working?

2e) During bank erosion when “eroded sediment is immediately transported downstream” (p11 ln 15), does that affect bed erosion capacity? In other words: is bed scour adjusted (reduced) when bank erosion occurs?

Minor edits:
p6 ln 4: The mentions of (e.g., x) and (e.g., y) are redundant.

p6 ln 5: The phrase about rotation of the elevation model grid better fits with the description of the grid (p6 ln 12, 13)

p10 ln28: 60m2 --> 120 m2

p11 ln5: number of cells specified by Eq.(10) --> number of cells specified by Eq.(11).
The authors have indicated in their response to my earlier comment that there was nothing wrong with this equation reference. However, Eq.(10) does not specify a number of cells (it specifies a shear velocity), whilst Eq.(11) does.

p15 ln8: (Kasprak et al., 2017) is not included in the reference list

p22 ln27: Delt3DThis --> Delft3D. This

p28 ln7: et al --> et al.

all text: modeling --> modelling
(I believe EGU follows UK English spelling)

fig 2: It is somewhat confusing that subfigure 3A is placed next to subfigure 2. Intuitively one would expect each of the detail views to be associated with the workflow view to the left of it. It is for 1, 3B and 4, but not for 3A.
In their response to my earlier comment about this, the authors indicated that they agree, and have added arrows linking the sub-figures with their appropriate panels in Figure 3 to avoid confusion. This appears to not be the case.

figs 7-11: Text too small to read comfortably in many subpanels (axis labels, axis values, legends, scale bars)

fig 8: Include same subpanels as fig 7,9,11

Hide

RR by Anonymous Referee #2 (20 Aug 2018)

Suggestions for revision or reasons for rejection

The authors have done a generally good job of attending to previous review comments but there remain several issues with the present version that should be addressed. I will discuss those first, then list smaller/minor page by page things warranting corrections.
1. In the abstract (and later in the paper) the notion of representing hydrographs as a series of steady states is misleading – it continues to imply a duration associated with each steady state (note that I fully understand how time is removed from the calculations), and it implies that this expediency is at the root of the computational time saving over CFD type approaches. The implication is that by chopping event hydrographs down into smaller and smaller blocks the approach might converge on a CFD result. But that is never done in the paper – the example provided from the Rees is actually three events back to back – it is not a single event hydrograph split in 3 time blocks.
Indeed, a key (unstated) assumption of the approach is that each event modelled has adequate duration to allow the bedload to get to its destination – so you can see that breaking events up into smaller and smaller intervals will ultimately badly overcook the results, not give them greater precision. While I appreciate that this is never actually done, the paper hints that it could be.
2. On page 9 there are two things that niggle me. The first is that Montgomery’s event averaged relation (eqn 7) is applied to the event peak discharge then assumed to be representative of the whole event – so all of sudden event averaged Qb becomes Qb at peak discharge, and ditto for bedload advection speed. What Eqn 7 is really predicting at the event peak is the active layer thickness. The second is that Eqn 8 is not the MPM formula – the scaling coefficient (8) is missing as are the density terms. The net result is that a factor of ~ 0.4 is missing from the equation. Hopefully this was an omission in the text and not the model.
3. Section 2.5. The input boundary condition option used needs to specified for each model run. What was done in the cases of the first event in a series or for single events, like the first Rees example – since there is not a preceding event calculation?
Also,what was done at the lateral boundaries? It reads like bedload was allowed to diffuse across them but was not returned (e.g. on the opposite side) so the modelling should progressively lose sediment mass.
4. Two things on page 19. First, on line 18, the notion of altering the model timestep is misleading (as discussed in 1. above). The example used is actually a multipeak event, but is dominated by the big middle one. Note on line 20, 254 should be 259 (as elsewhere).
5. At the top of page 21, again, the assumption needs to be stated that the undisclosed event duration provides adequate time for the bedload to get to its destination. It would be a good idea to calculate this as an assumption check.
6. On page 22, there are potential implications of the upstream BC that require discussion. Around about line 12 it is important to say which upstream boundary condition is imposed. Also, I would like to see some discussion around how the sequencing of events impacts the results – for example, a large event before a small one will deliver a large wad of bedload into the top of the reach for the small event - promoting deposition there. It is mentioned that the top 25 m of the reach is not analysed but that is because of the hydraulic boundary condition issue. Surely the sequencing of events will affect the net apparent change between the first and last event in the Feshie sequence? I suggest a plot of mean bed level vs time to explore this?
7. Section 5.1, which discusses emergent behaviour, really needs to discuss the emergent scour behaviour that develops. Given only a relatively small number of iterations (i.e. 185 events in the period 2003-2013), the tendency to scour, degrade, and simplify the channel network is quite notable (e.g. -8.07 elevation fall is very severe and quite unrealistic). While this is noted on page 22 (around line 25) with reference to the Singh et al Delft3D run, it doesn’t mention that the Singh et al run also produced unrealistic results. So this issue appears to be being swept under the carpet whereas it really shows that the model in its present form is not to be trusted for predicting decadal or longer scale morphological evolution. While this is discussed some more on page 30, and explanations are offered, it seems pretty clear that the main channel has gotten into a (scour, increased flow capture, increased shear stress, increased ) feedback loop.

Page/by page comments:
P5, L 26: Need to say that Delft3D was run in 2D depth-averaged mode. Also, I suggest shifting the sentence on lines 9-12 of P6 to here.
P7, L1-4: Needs some edits. Also, give units of m to the Ks values.
P7, L11-12: Need to say at event timescales rather than coarser time intervals. The model is never being run at “coarser time intervals”. The events are assumed to have undetermined duration. See also comment 1 above.
P7, L26-27: Sorry, but I’ve never heard of a braided river being exhausted of bedload through a hydrograph. This might be reasonable for suspended load. I suspect latency issues created by the upstream bedload feed boundary condition is something better to evaluate (see 6 above).
P8, L20: Needs to read Grad Qs. But also, why talk about Qs here then jump across to using Qb in Eqns 7 and 8?
P9, L 7: Need to say that Qb is the average unit mass-based bedload during the event.
P 9, eqn 8: give the dimensionally correct version of the MP-M formula.
P13, L17: Mode of what?
P13, L20: Suggestion only, but I struggle to see that ST is particularly informative here, as it really weights the average sinuosity of individual channels (which is a useful measure of the morphological evolution) by the braiding index. In other words, if you use ST you don’t know if it’s due to a sinuosity change or a BI change.
P13, L28: It’s not large differences in the metric, it’s large non-zero values (and say what -values indicate and what +values indicate).
P15, L24: Say 0.5 m grid models – otherwise it suggests models accurate to 0.5 m in elevation.
P16, L31: The model roughness parameter is the Nikuradse roughness length, ks.
P17, all of section 4.1.1: This is confusing and needs to be written. On P 7 you say you calculate ks off grainsize, then here you first suggest you derived this by trial error (i.e. by calibration), then finally you say you just used Williams et al’s calibration result. Is it that you used an initial grainsize-based value of ks, saw no reason to change this during calibration runs, and this aligned with what Williams et al got?
P 20, L4: I’m curious – how much of the bed was mobile at 20 m3/s? Was that a good estimate based on the more detailed results coming from the model (which evaluates Tc everywhere)?
P25, L6-8: It seems hardly surprising that the big 259 m3/s event dominated compared to the “pups” that came before and after it – particularly considering the threshold of motion influence. So I see no reason for the speculation that follows. I suggest deleting.
P27, L22: I disagree that it replicates the magnitude, rather, it produces similar.
P27, L 24: It would be helpful to say if Williams et al thresholded their model results as done in this paper – so that that apples are being compared with apples.
P32: I suggest acknowledging the referees!

Referee Report: PDF

Hide

ED: Reconsider after major revisions (30 Aug 2018) by Jens Turowski

AR by Alan Kasprak on behalf of the Authors (20 Nov 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (28 Nov 2018) by Jens Turowski

RR by Anonymous Referee #3 (14 Dec 2018)

Suggestions for revision or reasons for rejection

Overview
This paper presents a new morphodynamic modelling approach, whereby flow is modelled at the event-scale and sediment transport is simulated through a particle travel lengths algorithm rather than the more traditional flow-field and gravity-driven sediment algorithms. The model is applied to two case-study river reaches over different time scales.

Evaluation
The authors have addressed my main concerns from the previous iterations. I think the paper is publishable following a few minor corrections corresponding to a couple of minor issues, as listed below.

Minor issues
1) Be explicit about origin of model parameter values
The authors have not formally calibrated the model. But they have somehow qualitatively tuned some of their equations to “obtain the best possible agreement with areas of bank erosion delineated from successive DEMs on both the Feshie and the Rees Rivers” (author’s response to one of my previous comments). I would like the authors to be a bit more explicit about this in the text. For example: What is the basis for setting k equal to 8 (p9 ln28)? Is it part of the same loose calibration, or are there other reasons? Similarly, explicitly mention that “Equation 11 is not physically based, and was derived through qualitative calibration, whereby the values used in Equation 11 are simply reflective of the best qualitative correspondence between modelled and field-derived estimates of areas undergoing bank retreat”.

2) Explicitly mention handling of sediment import for each experiment
The authors indicate that sediment import is user-specified and can be set in one of three ways (equal to the volume of sediment export during the preceding event; percent of sediment export during the preceding event; or specified via a text file sedigraph timeseries) (p14 ln18). However, it is not clear which of those three is used for the simulations described in the paper. Section 4.3 (particle length case study) contains an explicit mention that “in all simulations we employed an equilibrium sediment budget” (p23 ln13), but it is not clear if this applies to all simulations in the particle length case study, or if this applies to all other case studies too. Presumably the other case studies (Sections 4.1., 4.2, 4.4) did not apply a equilibrium sediment budget since they were able to compute net volumetric erosion (under equilibrium this would not happen: volumetric erosion would equal volumetric deposition, and the net difference would be zero). In any case, please explicitly state how sediment import was handled in each of the case studies.

p13 ln9: e.g. --> i.e.

p13 ln12: e.g. --> i.e.

p30 ln 30: three discrete events --> multiple discrete events

Fig 7: The first four entries in the data table under subpanel A contain numbers in brackets. Please add an explanation to the figure caption to indicate what these mean

Fig 8: In an earlier review I had requested that this figure be laid out in the same style as Figs 7, 9 and 11. The authors are reluctant to do so because of duplication of information already contained in subpanels A,B and D from Figure 7. Instead, they provide rather focus on new information equivalent to what is shown in subpanels C and E from figure 7. However, in doing so, they omit the equivalent information equivalent to subpanels F and G, i.e. they omit the spatial map of modelled braiding mechanisms (F), and their volumetric contributions in relation to the observed mechanisms (G). I think this information would be useful, to see how much or how little of a difference the 3-point discretization makes to the attribution of braiding mechanisms, relative to the 1-point discretization. Can the authors please add an equivalent to subpanels F and G to Figure 8?
I still think that the easiest and most consistent way to do this is to follow the same layout as Fig 7, 9, 11, even if that duplicates some of the information displayed – but I’m not too bothered if they authors prefer a different layout.

Hide

ED: Publish subject to minor revisions (review by editor) (17 Dec 2018) by Jens Turowski

AR by Alan Kasprak on behalf of the Authors (20 Dec 2018) Author's response Manuscript

ED: Publish subject to technical corrections (03 Jan 2019) by Jens Turowski

ED: Publish subject to technical corrections (04 Jan 2019) by Tom Coulthard (Editor)

AR by Alan Kasprak on behalf of the Authors (28 Jan 2019) Author's response Manuscript

Short summary

We present a modelling framework for the prediction of gravel-bed braided river evolution. The model is unique in that it simplifies sediment transport through the use of empirically-derived relationships between channel form and flood-scale particle transport distances, or path lengths, which ultimately allow for longer duration model runs with reduced computational demand. We use field surveys on two braided rivers to validate the model at the event, annual, and decadal timescales.