We would like to begin by thanking the editor and the three academics who participated in the discussion of our manuscript, in particular the two anonymous reviewers.  We appreciate the time that you have all taken to look over our manuscript and provide feedback which will help to improve our work.

Below we provide a brief response to each of the comments from the discussion beginning with the suggestions from the two anonymous reviewers.  A more detailed response will be provided at the time of resubmission.

Reviewer Comment 1:

We thank the reviewer for their overall positivity about our aims and the quality of our writing, however we accept that the reviewer has a number of concerns regarding the manuscript as originally presented.   Below we quote the comments of the reviewer along with an individual response to each:

“Line 1-5: Although I'm pleased to see this article, I was not very satisfied when I read the abstract because you did not highlight your core points. Firstly, you merely inform everyone that you have undertaken such a work, but you do not explain why it is necessary to do it, or what new and interesting contributions it can offer. Secondly, when you state "unlike previous agent-based models, we are able to…" it tends to emphasize the contributions of the model too heavily, in fact, the innovations regarding the model have already been published (e.g. Robson, D 2023; GRL).”

We accept that we have not provided significant motivation for the work in the abstract and will remedy this in a revised submission.

“Line 54-57: Firstly, your work is meaningful, it reports the dynamic processes of barchan swarms under unidirectional as well as bimodal winds. However, the content fails to capture the reader's interest because it overly emphasizes the importance of your model, thereby neglecting the insights this model could provide into the dynamic mechanisms of barchan swarms. Second, you said that your model can also simulate the formation of asymmetric bedforms under the influence of variable wind regimes. Is this simulation result accurate? Can it be verified in the field? I believe that there is a significant difference between the simulation and observed results in the field, at least, it cannot represent all cases.”

Thank you for acknowledging the meaning of our work and for pointing out that we do not emphasise enough its relevance to a general reader, we will address this in our revisions.  On the second point, we have previously shown in Robson and Baas GRL (2023) that our model can reproduce asymmetry growth similar to the Bagnold model in the case of bimodal winds with acute angular separation and similar to the Tsoar model in the case of obtuse angular separation.  The same dependence of the growth mode on the angular distance between modes of wind regime has previously been shown in Parteli et al. Aeolian Research (2014) and Lv et al. Environmental Earth Sciences (2016).  For acute angular separation of modes, our results are very similar to Parteli et al and we will include this in supplementary material during the revision.  We have also observed very similar behaviour in real world barchan swarms, especially south of Akjoujt, Mauritania in which the wind regime displays two distinct modes separated by a large acute angle.

However, we do accept that the growth of asymmetry according to the Tsoar model with obtuse angular separation is somewhat less pronounced that in the other works, this is because the asymmetry observed to arise with obtuse separation in the other simulations is the significant longitudinal extension of one of the horns (and eventually a transition to a seif or linear dune), our model can capture some of the initial stages of such an asymmetry growth, but is not able to capture the extreme extension of the horns after some time.  In the revision we will make this fact more obvious and provide explicit examples in supplementary material.

“Line 202-204: Although you have accounted for the distribution of dune asymmetry, I found that the simulation may not reflect the morphological characteristics of barchan swarm in the real world.”

“Line 205-207: Can you provide some photos? I would like to see real, similar evidence, which might be more convincing.”

“Line 450: For the angular separation of the wind direction, the asymmetry between the left and right horns of the Barchan dunes should be significant, but in your simulation results, I see that it is almost symmetrical.”

In the revision we will more explicitly compare the distributions of asymmetry in real-world swarms compared to the simulated ones to address these points.

“Line 289-355：For the result of bimodal simulations, I think they need to be discussed. First of all, under bidirectional wind conditions, it is difficult for barchan dunes to reach or maintain a stable state. Secondly, with wind at an angle, the horns of crescent-shaped dunes are very asymmetrical. I noticed that in Figure 14, the horns of many dunes are nearly symmetrical in size, which clearly is not reasonable. Lastly, under multi-directional wind conditions, transverse sand ridges would form on the windward side facing the airflow, but I found that your simulation results did not show this; instead, they more closely resemble small chains of crescent-shaped dunes.”

As above, we will include in the revision an explicit comparison of the asymmetry distribution observed in real-world swarms together with our simulations.  On the point of a transition of barchans to other forms of aeolian bedform, it is true that our model (and all agent-based models of barchas) would be unable to capture such a transition since this would require the introduction of new types of agents and rules governing the metamorphosis between the different classes.  This is something we are considering as a future development of our work, however, in the current case we believe that there is already sufficient scope in our model to merit publication.  We will add discussion along these lines into the revised manuscript.

Reviewer Comment 2

“The manuscript "Barchan swarm dynamics from a two-flank agent-based model" presents simulations of barchan fields (or swarm) under different wind and boundary condition using a simplified model of dune interactions. Although the collective dynamics of dune fields is a relevant and interesting problem, the authors didn't properly validate the agent-based model before moving on to complex scenarios. Of course, a simple exploratory-type model can sometimes be very valuable in shedding light on a complex problem. However, the authors don't emphasize this aspect sufficiently and we get the impression that this is a solved problem. In particular, there is no discussion of the many approximations and assumptions underlying their approach, and how their work could be improved using physical models.

As pointed out in detail below, the manuscript can benefit from a more in-depth discussion of the assumptions and approximations, as well as existing literature on physical dune models. In addition, the fact that mass might not be conserved in their model should be addressed in detail.”

Thank you for your time in reading our manuscript, we will endeavour to provide a more explicit description of model assumptions and limitations in the revised manuscript, such assumptions are necessary to simplify the dynamics of large systems such as barchan swarms which are untractable for more involved models.  We do not agree that the model has not been properly validated, in Robson and Baas GRL (2023) we have already described the phenomenology of our model for many simple cases and how this compares to other types of modelling as well as observations.  In particular, in the supplementary material of that work (referred to in the paper), we provide an analysis comparing the relative success of all existing barchan agent-based models at reproducing collisions from both water-tank and cellular automaton simulations.

“1. Section 2.2. The dune mass balance equation (Eq.2) is not validated neither here nor in the original paper (Robson and Bass, 2023). I know this is a published model, but a lack of validation with either data or physical models has to be discussed. For example, the physical model in Duran et al. ESPL (2010) clearly shows that the outflux from a barchan horn is function of the influx (perhaps because the horn width depends on the influx). In contrast, in the model presented by the authors the outflux is just proportional to the saturated flux q_sat.”

The dune mass balance equation used in this model is a well-known expression which we did not create, but was first suggested in Hersen et al Phys. Rev. Lett. (2004) based upon numerical simulations and has subsequently been used in the agent-based model of Worman et al. Geology (2013).  However, we accept that the scaling of influx and outflux reported in Duran et al. ESPL (2010) is also well-known.  In fact, we had already included the possibility of setting the outflux using the relation from that work in the code of our model.  We did not, however, use this expression since it is not so obvious how to partition the outflux between the two flanks of the dune.  In fact, the best way we could think of doing it was to use the scaling relation of horn-width and total width which we already used in the manuscript and which was inspired by Hersen et al. (2004).  We will test this alternative expression for the outflux to see how it impacts the simulations and discuss any differences in the revised manuscript.

“2. Section 2.2. The central parameter of the model (q_shift) is completely phenomenological and unconstrained -- btw this would have been the perfect application of physical models simulating the evolution of asymmetrical barchans in unidirectional winds. This parameter is introduced to simulate a lateral transfer of mass between the two flanks. However, this cannot be the case because there is no mass exchange between the two sides of a barchan (from symmetry, the transversal flux q_y at the central dune slice is 0). In fact, the arms become more equal because of an imbalance between the sand captured and emitted (q_out and q_in). The somewhat arbitrary nature of this parameter and its implication should be addressed in detail when introducing the model and also at the end of the introduction and the discussion section. This would help the reader differentiate between physical and phenomenological aspects of the model and thus the results.”

We agree the q_shift is an unconstrained parameter describing a phenomenological process within the model.  However, we believe that the fact that a small range of the parameter is able to explain a wide range of observed properties of both collisions and swarm-scale properties suggests that it may be close to representing a physical process in reality, this is something we aim to explore in the future.  We do not agree that the flux at the central dune slice is 0, particularly since this assertion is, as you say, based upon the symmetry.  Thus, we see no reason to prevent this from being non-zero in the case of asymmetric dunes.  Furthermore, as we have said, this parameter pertains not only to flux on the surface of the dune, but also to internal restructuring of the barchan shape (e.g. if material accumulates on one side rather than the other then there may be some avalanching in the transverse direction from one flank to the other).  Such processes have not been well-understood thus far, and so we are unable to rely on existing physical models.  We will, however, as the reviewer suggests make it more clear in the revised manuscript that this is a phenomenological parameter which relates to a physical process that is not yet properly modelled.

“3. Sections 2.3 and 2.4. The outcome of calving and collisions is not validated (not even in the original 2023 paper). The authors could at least compare it to the physical simulations of dune collisions in Duran et al. 2005, 2009 and 2011, and existing water dune experiments.”

Validation of the outcomes of collisions from simulations and water experiments was in fact provided in the supplementary material of the original 2023 paper (and mentioned in that paper) and is available open access at the following link https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023GL105182

“4. In particular, the spontaneous calving of large asymmetric dunes is not obvious at all. Following Eq.(2), the dune would become symmetric again after a given time. The authors should discuss the effects of their assumptions in the model outcome, e.g. what would happen if calving is ignored/suppressed?”

We cannot completely suppress calving of large barchans since at some point the two-flank shape of the agents stops being a valid geometry.  However, such a point is rarely reached and, as discussed in the manuscript, the overall rate of calving is low, and mostly occurs during a collision.

“5. What is "fragmentation" in Fig.2? I couldn't find a definition. Similarly with "exchange". Also, why there is no fragmentation when q_shift = 0?”

Thank you for pointing this out, we will include definitions in the revision.

“6. The authors should include a figure defining the different parts of the barchan and also the different outcomes from collisions. I know some of this was already included in their previous paper, but it is very difficult to follow this one without some visual guide.”

We will include this as well.

“7. One thing I found very strange was the spatial decrease of dune density for a constant average dune width (Figs. 3 and 9). I mean, if the average dune width (and thus volume) is constant spatially, then a decrease in the number of dunes suggest sand is not conserved. The authors must check that their equations conserve the mass. For example, in Duran et al. (2011), the cover fraction of dunes (dune area/total area) was constant downwind, which is consistent with mass conservation.”

Mass is conserved, but the production of small, short-lived dunes during some fragmentation collisions means that mass contained in dunes decreases in favour of free flux when these dunes become too small and disappear.  In fact, in Duran et al. (2011) dune number density decreased as the inverse square of downwind distance while the width increased linearly with downwind distance, thus the mass (equivalent to volume which is proportional to the cube of the width) contained in dunes increased linearly with downwind distance which must have been compensated for by a decrease in the available free sand flux.  Thus in both our model and the existing models, mass conservation results only from an interchange of sediment contained in dunes and flowing as free flux.  There is no reason a priori to expect mass conservation in dunes given that these are open rather than closed systems as would be the case with periodic boundary conditions. We will include discussion on this in the revision.

“8. Furthermore, even if mass is somehow conserved in their model, the authors should discuss the meaning of a dune field model where dune density continuously decrease, which implies dunes eventually disappear downwind.”

We will add a discussion on this.  In fact, decreasing density and eventual disappearance was something that Bagnold (1941) suggested should happen unless there were additional sediment supplies at the transverse boundaries of the swarm which could provide additional material.

“9. It would be interesting to calculate the PDF of dune width. In one of their previous papers they presented a mean-field model that captured real distributions using a similar set of collision outcomes. How that compares with the explicit simulations shown here?”

We will include these distributions in the revised manuscript, we did not in the original since we were focusing on showing novel results and we observe distributions that are log-normal as has been reported elsewhere.

“10. Finally, the authors should discuss the pros and cons of the different approaches. For example, Duran et al. (2011) simulated dune fields by leveraging the results of physical dune simulations but reducing the outcome of collisions to only two dunes (for simplicity), which clearly wasn't enough to capture the spatial uniformity. Here, on the other hand, the authors introduce purely phenomenological relations and are able to reproduce the uniformity of real fields for some conditions. This should help clarifying the open issues and next steps within the topic.”

We agree with this comment that such a discussion would be useful and will add to the revised manuscript.

Comment 1

“We thoroughly enjoyed reading your preprint and are excited about the prospect of using your model to explore dune swarm dynamics.”

Thank you, we look forward to seeing what can be done in the future!

“We would like to take the opportunity this format offers to address a point you raise in your manuscript. Specifically, you state that shifting upwind boundary conditions does not result in a transient/local increase in dune-interaction density, but rather to a gradual relaxation to a new steady state, which you contend is contrary to the results of Marvin et al. (2023). Here, we argue that model results appear, in fact, to support the findings of Marvin et al. (2023).

First and foremost, the comparison is not of apples to apples. Although your simulations run long enough for dune width and number to stabilize, small, isolated dunes that are not in equilibrium with the system are constantly fed at the upwind boundary. Thus, when averaged over the whole domain, dune pattern statistics reflect some average over the whole pattern transition, from disequilibrium, to adjusting, to equilibrated. In contrast, Marvin et al. (2023) do not consider field-averaged pattern statistics, but how pattern statistics would vary spatially downwind. Their results suggest that dune-interaction density, under the conditions of your simulation, should first increase then decrease in the downwind direction (similar to the example in their Figure 3E) – once the whole dune field is formed and pattern statistics have equilibrated downwind. Although it is difficult for us to assess quantitatively whether it is the case, your model does seem to produce a local increase in dune interactions around 2-5 km (e.g., your Figure 1).

This subtle misrepresentation of the Marvin et al. (2023) findings is reflected in a few places in the preprint:”

“- At line 258-262: you state that the portion of the dune field between 0-3 km is where the greatest change in density occurs, resulting from the change in boundary conditions, and that according to Marvin et al. (2023) it is also where we should expect the highest rate of collisions. However, the expectation from Marvin et al. (2023) would be for dune density to first increase so dunes can start exchanging sand; only at that point (in space) would the spatial density of dune interactions start increasing. In fact, your finding that dune-interaction density is highest where dune density is highest is consistent with the finding of Marvin et al. (2023) that the background level of dune interactions increases with decreasing dune spacing.”

“- At line 283-286: the observed gradual relaxation in average number of collisions with time is not inconsistent with the results of Marvin et al. (2023). The results of Marvin et al. (2023) suggest that, once your domain is full of dunes and the number of dunes in the domain has plateaued, the spatial density of dune interactions should increase and then decrease downwind, with the local enhancement in dune-interaction density reflecting the pattern’s response to upwind changes in boundary conditions. In your model, you feed small, isolated dunes, which then interact downwind to, over time, start forming an equilibrated swarm further downwind. Thus, at early model epochs, the domain only contains small, isolated dunes (low number of interactions). As time progresses, those dunes migrate downwind and start interacting, increasing the number of interactions present in the whole domain, until they reach some equilibrated pattern, at which point the dunes migrate downwind without changing pattern statistics anymore. At that point in time, pattern statistics averaged over the whole domain have plateaued, but a spatial increase and then decrease in dune-interaction density in the downwind direction could still (and in fact does seem to) exist, at least qualitatively consistent with Marvin et al. (2023).”

“- At line 439-447: Again here, your statements compare the time evolution of domain-averaged dune pattern statistics to results that instead pertain to the spatial evolution of local dune pattern statistics at a given point in time. This difference in what is actually measured in the two studies seems to reconcile their results.”

It is indeed true that the results we presented in the current manuscript relate to spatial averaged statistics which is not what was reported in your work.  However, all of the results we observed (even when considering collision statistics at a single point in space) showed that the local rate of collisions was simply a function of the local dune density.  Thus, in locations where the change in boundary conditions leads to a decrease in the local dune density we expect a decrease in the rate of collisions.  Our understanding of the results of Marvin et al. (2023) was that any change in boundary conditions would first lead to an increase in the rate of interactions before then adjusting to a new equilibrium.  Therefore, it is our understanding that at a location subject to a change in boundary conditions leading to a decrease in dune density, Marvin et al. (2023) would predict a small rise in the rate of interactions firstly before a decrease to the new equilibrium, whereas in our simulations we would see only the decrease to the new equilibrium and not the short-lived increase.  It may be worth having further discussion on this point before the revision of the manuscript and we will be in touch to discuss this.

“Second, we note an even subtler difference that might result in qualitatively but not quantitatively similar results between the two studies. All collisions are interactions, but not all interactions are collisions. Marvin et al. (2023) adopt the definition of Day and Kocurek (2018) for a dune interaction, i.e., any location where two adjacent dune crestlines approach each other within 10% of the field-average dune spacing is counted as a dune interaction. Whereas somewhat arbitrary, this threshold is used as a proxy to define where crestlines are close enough for dunes to exchange sand with one another. This is in contrast with your quantification of collisions, which you define as any point where a dune center of mass (CoM) impinges upon the footprint of another dune.”

We definitely agree that not all interactions are collisions.  Unfortunately however, it would be much more difficult to determine the density of long-range interactions such as through flux exchange, although it could be done.  There is also something of an issue in defining where long-range interactions take place since they are, by definition, non-local.  Thus if two dunes were interacting over a distance then one could imagine a number of ways of defining “where” that interaction was taking place e.g. at the upwind dune, at the downwind dune, the average position of the interacting dunes etc. It is not obvious which of these conventions would be the best to use but it is clear that the choice would have a significant impact on any measure of local interaction density.  

“In summary, we believe that your results are at least qualitatively consistent with those of Marvin et al. (2023), contrary to what is currently stated in the preprint. Showing this would require considering spatial changes in interaction density once dune number in the domain has equilibrated rather than the time evolution of domain-averaged pattern statistics. We suspect that such an analysis would reconcile both studies qualitatively. A quantitative comparison would further require the consideration of dune interactions (per Day and Kocurek, 2018) rather than just collisions.

Again, we are excited about what your model will teach us about dune swarm dynamics and are thankful for your consideration of our recent results in your manuscript!

Best regards,

Colin Marvin and Mathieu Lapôtre”

Thank you again for the time you have taken to read our work, we look forward to seeing how we can continue to progress our understanding of dune-systems together.

Dominic T Robson and Andreas CW Baas