Mobilisation thresholds for coral rubble and consequences for windows of reef recovery

Kenyon, Tania M.; Harris, Daniel; Baldock, Tom; Callaghan, David; Doropoulos, Christopher; Webb, Gregory; Newman, Steven P.; Mumby, Peter J.

doi:https://doi.org/10.5194/bg-2023-2

Preprints

https://doi.org/10.5194/bg-2023-2

Preprints

16 Feb 2023

| 16 Feb 2023

Status: a revised version of this preprint was accepted for the journal BG and is expected to appear here in due course.

Mobilisation thresholds for coral rubble and consequences for windows of reef recovery

Tania M. Kenyon, Daniel Harris, Tom Baldock, David Callaghan, Christopher Doropoulos, Gregory Webb, Steven P. Newman, and Peter J. Mumby

Abstract. The proportional cover of rubble on reefs is predicted to increase as disturbances increase in intensity and frequency. Unstable rubble can kill coral recruits and impair binding processes that consolidate rubble into a stable substrate for coral recruitment. A clearer understanding of the mechanisms of inhibited coral recovery on rubble requires characterisation of the hydrodynamic conditions that trigger rubble mobilisation. Here, we investigated rubble mobilisation under regular wave conditions in a wave flume and irregular wave conditions in-situ on a coral reef in the Maldives. We examined how changes in near-bed wave orbital velocity influenced the likelihood of rubble motion (e.g., rocking) and transport (by walking, sliding or flipping). Rubble mobilisation was considered as a function of rubble length, branchiness (branched vs. unbranched), and underlying substrate (rubble vs. sand). Rubble was more likely to be transported if ieces were small (4–8 cm) and had no branches, and rubble travelled slightly greater distances (~2 cm) per day on substrates composed of sand than rubble. The effect of near-bed wave orbital velocity on rubble mobilisation was comparable between flume and reef observations. Rubble had a 50 % and 90 % chance of transport when near-bed wave orbital velocities reached 0.30 m/s and 0.43 m/s, respectively, in the wave flume, and 0.34 m/s and 0.55 m/s, respectively, on the reef. Importantly, the probability of rubble transport per day declined over 3-day deployments in the field, suggesting rubble had settled into more hydrodynamically-stable positions or snagged on the first day of deployment. We expect that settled or snagged rubble may have been mobilised more commonly in locations with higher energy and more variable wave environments. Our results show that rubble beds comprised of small rubble pieces and/or pieces with fewer branches are likely to be more unstable. Such rubble beds are likely to have shorter windows of recovery (stability) between mobilisation events, and thus be good candidates for rubble stabilisation interventions to enhance coral recruitment and binding.

Received: 11 Jan 2023 – Discussion started: 16 Feb 2023

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Tania M. Kenyon et al.

Status: closed

RC1:
'Comment on bg-2023-2', Anonymous Referee #1, 14 Mar 2023

General comments:
This well-written study presents work empirically determining the threshold of mobilisation for individual rubble pieces of varying shapes and sizes, and on different substrate types and slopes, in both controlled and field settings (the Maldives). Rubble movement is relevant because it impacts coral recovery, and many threats to coral (e.g. destructive fishing, storms, bleaching) result in coral breakage and/or death. These pieces become “rubble” of various sizes and shapes. The experiments are clever and thorough, designed to elucidate the probability of rubble ‘rocking’ or various types of ‘transport’ (walk/slide/flip). Unsurprisingly, the authors found similar mobilisation thresholds in the wave flume and in the field, and that the probability of rubble mobilisation increases with higher velocity. Also as common sense and previous work would suggest, it decreases as: (i) rubble size increases; (ii) morphological complexity/’branchiness’ (of both the rubble and of the substrate type) increases; and (iii) as the slope angle decreases (and the contribution of gravity subsequently decreases). Interlocking and ‘settling’ of rubble was a strong inhibitor of mobilisation.
Specific comments
While the authors did find some some nuanced results (e.g. larger rubble is more likely to settle into sand) and differences between the northeastern and western monsoon seasons, overall, their results seem a very sophisticated experimental demonstration of what common sense would predict. While sentences in the Abstract (l 19-21) and Introduction (l 37-40) suggest relevance for managers of reefs that exhibit a significant increase in rubble cover, there is no discussion of what managers can actually do once they have the information presented herein. While there is mention of “rubble stabilisation interventions to enhance coral recruitment and binding,” it’s unclear that the results from this work would actually be needed to predict the likelihood of natural rubble stabilisation and recovery beyond simple first principles. I suggest the discussion at least address potential management relevance, including context for discussions for rubble stabilization, budget needed vs. scale of the problem, etc.
No technical corrections.

Citation: https://doi.org/10.5194/bg-2023-2-RC1
- AC1: 'Reply on RC1', Tania Kenyon, 21 Jun 2023
  
  RC1: 'Comment on bg-2023-2', Anonymous Referee #1, 14 Mar 2023 reply
  General comments:
  This well-written study presents work empirically determining the threshold of mobilisation for individual rubble pieces of varying shapes and sizes, and on different substrate types and slopes, in both controlled and field settings (the Maldives). Rubble movement is relevant because it impacts coral recovery, and many threats to coral (e.g. destructive fishing, storms, bleaching) result in coral breakage and/or death. These pieces become “rubble” of various sizes and shapes. The experiments are clever and thorough, designed to elucidate the probability of rubble ‘rocking’ or various types of ‘transport’ (walk/slide/flip). Unsurprisingly, the authors found similar mobilisation thresholds in the wave flume and in the field, and that the probability of rubble mobilisation increases with higher velocity. Also as common sense and previous work would suggest, it decreases as: (i) rubble size increases; (ii) morphological complexity/’branchiness’ (of both the rubble and of the substrate type) increases; and (iii) as the slope angle decreases (and the contribution of gravity subsequently decreases). Interlocking and ‘settling’ of rubble was a strong inhibitor of mobilisation.
  Specific comments
  While the authors did find some some nuanced results (e.g. larger rubble is more likely to settle into sand) and differences between the northeastern and western monsoon seasons, overall, their results seem a very sophisticated experimental demonstration of what common sense would predict. While sentences in the Abstract (l 19-21) and Introduction (l 37-40) suggest relevance for managers of reefs that exhibit a significant increase in rubble cover, there is no discussion of what managers can actually do once they have the information presented herein. While there is mention of “rubble stabilisation interventions to enhance coral recruitment and binding,” it’s unclear that the results from this work would actually be needed to predict the likelihood of natural rubble stabilisation and recovery beyond simple first principles. I suggest the discussion at least address potential management relevance, including context for discussions for rubble stabilization, budget needed vs. scale of the problem, etc.
  No technical corrections.
  Our response:
  We thank Reviewer 1 for their review of the manuscript and are pleased that they found the results to be novel yet intuitive. We thank the reviewer for their comment regarding highlighting potential management relevance, which is a valuable addition to the manuscript. A revised manuscript can include reference to management relevance in the introduction (as before), and in the discussion. Such an addition is pasted below.
  “Implications for management
  These results provide information toward improved management of damaged reefs with high rubble cover. Broadly, rubble stabilisation interventions might be considered at lower mobilisation thresholds if a rubble bed is comprised mostly of small, lighter pieces, which is more commonly the case with anthropogenic disturbances such as ship groundings, human trampling, coastal armouring and blast fishing (Masucci et al. 2021, Kenyon et al. 2022). More comprehensively, the mobilisation estimates reported here can be used in modelling frameworks that predict the frequency of everyday rubble mobilisation in a certain location, based on a modelled time series of wave climate estimates, e.g., model for the Great Barrier Reef (Roelfsema et al. 2020). Reefs or areas of reefs at higher risk of frequent rubble mobilisation can be prioritised for rubble stabilisation interventions. These predictions can be improved through consideration of the discussion points above, e.g., bathymetry, rubble quantity and morphology (based on surrounding coral cover and diversity), water quality and bioerosion. The scale of reef degradation and subsequent intervention methods is vast, putting pressure on reef restoration budgets. While the issue of implementing reef restoration at scale is investigated, tools that allow managers to prioritise reefs which are particularly vulnerable to rubble mobilisation, and thus longer recovery times, are essential.”
  
  Citation: https://doi.org/10.5194/bg-2023-2-AC1
RC2:
'Comment on bg-2023-2', Anonymous Referee #2, 31 May 2023

General comments
This manuscript describes an interesting study of movement of coral rubble under waves. The lab and field measurements of rubble movement seem to have been generally well-executed, the combination of lab and field measurements is informative, the figures show interesting patterns, and the datasets have a lot of potential. While I think the manuscript has potential to ultimately be a nice contribution, I do have serious concerns about aspects of the analysis and the way some of the methods and results are presented in this submission. My major concerns are around the treatment of wave period, which is very different (factor of up to 10) in the lab versus in the field, and the use of orbital velocity as the hydrodynamic parameter against which rubble movement is plotted and assessed.
The physics of rubble motion under waves isn’t fully explained in the manuscript so I provide some background here. The total force on an object under waves is the sum of two components: the inertial force and the drag force. The drag force is proportional to orbital velocity squared and dominates only if the orbital excursion is substantially larger than the size of the object (Keulegan Carpenter number KC>1). From my back-of-the-envelope calculations this seems to be the case in much of the field data presented. However, if the orbital excursion is smaller than the object size (KC<1), the inertial force is the dominant force on the obstacle. The inertial force is proportion to the fluid ACCELERATION, which is the orbital velocity multiplied by the wave frequency (2*pi /PERIOD). By my calculations the inertial force should be the dominant force for many of the lab flume conditions. The wave period is therefore a critical parameter for this problem, in addition to the orbital velocity.
Because of the very different wave periods between the lab and the field, comparisons between the two datasets need to be done very carefully/cautiously. Additionally, in the lab flume, it seems the period was changed (somewhat arbitrarily when breaking was observed), but the combinations of wave height and period are not reported in the manuscript. A table of the combinations of conditions in the lab flume experiments needs to be reported, along with corresponding bottom orbital excursions, velocities, accelerations. This will allow comparison of orbital excursions with rubble sizes which will inform as to whether drag (proportional to velocity squared) or inertial force (proportional to acceleration) is the relevant force. Ideally, the probability of movement would be plotted against a measure of the total force rather than velocity. There is a nice paper by Viehman et al. (2018) that lays out these forces on rubble. It is cited briefly in the introduction, but I think it could be a useful reference for sorting out this issue of dominant forces.
The figures are generally well-constructed and the manuscript text is well-organized and generally well-written.
I provide a few specific comments below, but I have not provided line-by-line comments at this point because of the critical major issues described above.
Specific comments
Abstract lines 10-15, and corresponding sections of the text. Comparisons rubble motion in lab and field studies with respect to orbital velocities are flawed, due to the reasons outlined above in my general comments. Also, rubble size is an important determinant of when motion occurs, so I didn’t understand why a single probability of motion at a single velocity was reported.
Diagram – the statement that rubble is mobilized for orbital velocities greater than 0.4 m/s is too simplistic since we know (and the results show) there is a strong dependence on rubble size. There will also be a dependence on wave period for some rubble size classes and wave conditions due to inertial force being the dominant force.
Page 6, line 5-10. A table of wave conditions in the flume (height, period, water depth) is needed. The description of how wave period was increased when waves started to break seems very arbitrary. Changing the wave period for the same wave height will alter the orbital velocity, orbital excursion, and acceleration.
P6, Line 17-20. Linear wave theory is generally used to estimate bottom orbital velocities, accelerations, excursions. The approach described here (Soulsby cosine approximation) is non-standard and I didn’t understand why it was used in preference to linear wave theory.
P6, Line 19-20. The last statement on this page is very concerning: “Wave orbital velocities obtained in the flume were comparable to those measured in the field, hence scaling of the analyses was not required.” As I explained above, the forces on the rubble are the relevant quantity that should be compared in the lab vs the field, and related to rubble motion. The velocities can be the same but if other important parameters are different (e.g., wave period) then direct comparisons of laboratory and field results will not be possible. Careful consideration of scaling is always required when relating lab flume experiments and the field situation.
P8. Line 10. Unclear that the shallow water approximation is valid here for computing wavenumber k. There is readily available code available to calculate k from frequency and depth using the general/complete linear wave theory dispersion relation.
P8. Iine 32. Unclear what is meant by peak wave orbital velocity here. Do you mean the maximum 30-min significant wave height over the 3-day period? This is not truly the peak wave orbital velocity, which would require going back to the original time series for each burst.
P9. Results. Wave periods need to be reported and used appropriately in the analysis!
Fig 4. Bottom orbital excursion and accelerations should be shown also, for the reasons outlined in my General Comments

Citation: https://doi.org/10.5194/bg-2023-2-RC2
- AC2: 'Reply on RC2', Tania Kenyon, 21 Jun 2023
  
  We have included our response to RC2 as an attachment as the formatting for equations etc. would not copy across to the response box correctly.
  
  Citation: https://doi.org/10.5194/bg-2023-2-AC2

Status: closed

RC1:
'Comment on bg-2023-2', Anonymous Referee #1, 14 Mar 2023

General comments:
This well-written study presents work empirically determining the threshold of mobilisation for individual rubble pieces of varying shapes and sizes, and on different substrate types and slopes, in both controlled and field settings (the Maldives). Rubble movement is relevant because it impacts coral recovery, and many threats to coral (e.g. destructive fishing, storms, bleaching) result in coral breakage and/or death. These pieces become “rubble” of various sizes and shapes. The experiments are clever and thorough, designed to elucidate the probability of rubble ‘rocking’ or various types of ‘transport’ (walk/slide/flip). Unsurprisingly, the authors found similar mobilisation thresholds in the wave flume and in the field, and that the probability of rubble mobilisation increases with higher velocity. Also as common sense and previous work would suggest, it decreases as: (i) rubble size increases; (ii) morphological complexity/’branchiness’ (of both the rubble and of the substrate type) increases; and (iii) as the slope angle decreases (and the contribution of gravity subsequently decreases). Interlocking and ‘settling’ of rubble was a strong inhibitor of mobilisation.
Specific comments
While the authors did find some some nuanced results (e.g. larger rubble is more likely to settle into sand) and differences between the northeastern and western monsoon seasons, overall, their results seem a very sophisticated experimental demonstration of what common sense would predict. While sentences in the Abstract (l 19-21) and Introduction (l 37-40) suggest relevance for managers of reefs that exhibit a significant increase in rubble cover, there is no discussion of what managers can actually do once they have the information presented herein. While there is mention of “rubble stabilisation interventions to enhance coral recruitment and binding,” it’s unclear that the results from this work would actually be needed to predict the likelihood of natural rubble stabilisation and recovery beyond simple first principles. I suggest the discussion at least address potential management relevance, including context for discussions for rubble stabilization, budget needed vs. scale of the problem, etc.
No technical corrections.

Citation: https://doi.org/10.5194/bg-2023-2-RC1
- AC1: 'Reply on RC1', Tania Kenyon, 21 Jun 2023
  
  RC1: 'Comment on bg-2023-2', Anonymous Referee #1, 14 Mar 2023 reply
  General comments:
  This well-written study presents work empirically determining the threshold of mobilisation for individual rubble pieces of varying shapes and sizes, and on different substrate types and slopes, in both controlled and field settings (the Maldives). Rubble movement is relevant because it impacts coral recovery, and many threats to coral (e.g. destructive fishing, storms, bleaching) result in coral breakage and/or death. These pieces become “rubble” of various sizes and shapes. The experiments are clever and thorough, designed to elucidate the probability of rubble ‘rocking’ or various types of ‘transport’ (walk/slide/flip). Unsurprisingly, the authors found similar mobilisation thresholds in the wave flume and in the field, and that the probability of rubble mobilisation increases with higher velocity. Also as common sense and previous work would suggest, it decreases as: (i) rubble size increases; (ii) morphological complexity/’branchiness’ (of both the rubble and of the substrate type) increases; and (iii) as the slope angle decreases (and the contribution of gravity subsequently decreases). Interlocking and ‘settling’ of rubble was a strong inhibitor of mobilisation.
  Specific comments
  While the authors did find some some nuanced results (e.g. larger rubble is more likely to settle into sand) and differences between the northeastern and western monsoon seasons, overall, their results seem a very sophisticated experimental demonstration of what common sense would predict. While sentences in the Abstract (l 19-21) and Introduction (l 37-40) suggest relevance for managers of reefs that exhibit a significant increase in rubble cover, there is no discussion of what managers can actually do once they have the information presented herein. While there is mention of “rubble stabilisation interventions to enhance coral recruitment and binding,” it’s unclear that the results from this work would actually be needed to predict the likelihood of natural rubble stabilisation and recovery beyond simple first principles. I suggest the discussion at least address potential management relevance, including context for discussions for rubble stabilization, budget needed vs. scale of the problem, etc.
  No technical corrections.
  Our response:
  We thank Reviewer 1 for their review of the manuscript and are pleased that they found the results to be novel yet intuitive. We thank the reviewer for their comment regarding highlighting potential management relevance, which is a valuable addition to the manuscript. A revised manuscript can include reference to management relevance in the introduction (as before), and in the discussion. Such an addition is pasted below.
  “Implications for management
  These results provide information toward improved management of damaged reefs with high rubble cover. Broadly, rubble stabilisation interventions might be considered at lower mobilisation thresholds if a rubble bed is comprised mostly of small, lighter pieces, which is more commonly the case with anthropogenic disturbances such as ship groundings, human trampling, coastal armouring and blast fishing (Masucci et al. 2021, Kenyon et al. 2022). More comprehensively, the mobilisation estimates reported here can be used in modelling frameworks that predict the frequency of everyday rubble mobilisation in a certain location, based on a modelled time series of wave climate estimates, e.g., model for the Great Barrier Reef (Roelfsema et al. 2020). Reefs or areas of reefs at higher risk of frequent rubble mobilisation can be prioritised for rubble stabilisation interventions. These predictions can be improved through consideration of the discussion points above, e.g., bathymetry, rubble quantity and morphology (based on surrounding coral cover and diversity), water quality and bioerosion. The scale of reef degradation and subsequent intervention methods is vast, putting pressure on reef restoration budgets. While the issue of implementing reef restoration at scale is investigated, tools that allow managers to prioritise reefs which are particularly vulnerable to rubble mobilisation, and thus longer recovery times, are essential.”
  
  Citation: https://doi.org/10.5194/bg-2023-2-AC1
RC2:
'Comment on bg-2023-2', Anonymous Referee #2, 31 May 2023

General comments
This manuscript describes an interesting study of movement of coral rubble under waves. The lab and field measurements of rubble movement seem to have been generally well-executed, the combination of lab and field measurements is informative, the figures show interesting patterns, and the datasets have a lot of potential. While I think the manuscript has potential to ultimately be a nice contribution, I do have serious concerns about aspects of the analysis and the way some of the methods and results are presented in this submission. My major concerns are around the treatment of wave period, which is very different (factor of up to 10) in the lab versus in the field, and the use of orbital velocity as the hydrodynamic parameter against which rubble movement is plotted and assessed.
The physics of rubble motion under waves isn’t fully explained in the manuscript so I provide some background here. The total force on an object under waves is the sum of two components: the inertial force and the drag force. The drag force is proportional to orbital velocity squared and dominates only if the orbital excursion is substantially larger than the size of the object (Keulegan Carpenter number KC>1). From my back-of-the-envelope calculations this seems to be the case in much of the field data presented. However, if the orbital excursion is smaller than the object size (KC<1), the inertial force is the dominant force on the obstacle. The inertial force is proportion to the fluid ACCELERATION, which is the orbital velocity multiplied by the wave frequency (2*pi /PERIOD). By my calculations the inertial force should be the dominant force for many of the lab flume conditions. The wave period is therefore a critical parameter for this problem, in addition to the orbital velocity.
Because of the very different wave periods between the lab and the field, comparisons between the two datasets need to be done very carefully/cautiously. Additionally, in the lab flume, it seems the period was changed (somewhat arbitrarily when breaking was observed), but the combinations of wave height and period are not reported in the manuscript. A table of the combinations of conditions in the lab flume experiments needs to be reported, along with corresponding bottom orbital excursions, velocities, accelerations. This will allow comparison of orbital excursions with rubble sizes which will inform as to whether drag (proportional to velocity squared) or inertial force (proportional to acceleration) is the relevant force. Ideally, the probability of movement would be plotted against a measure of the total force rather than velocity. There is a nice paper by Viehman et al. (2018) that lays out these forces on rubble. It is cited briefly in the introduction, but I think it could be a useful reference for sorting out this issue of dominant forces.
The figures are generally well-constructed and the manuscript text is well-organized and generally well-written.
I provide a few specific comments below, but I have not provided line-by-line comments at this point because of the critical major issues described above.
Specific comments
Abstract lines 10-15, and corresponding sections of the text. Comparisons rubble motion in lab and field studies with respect to orbital velocities are flawed, due to the reasons outlined above in my general comments. Also, rubble size is an important determinant of when motion occurs, so I didn’t understand why a single probability of motion at a single velocity was reported.
Diagram – the statement that rubble is mobilized for orbital velocities greater than 0.4 m/s is too simplistic since we know (and the results show) there is a strong dependence on rubble size. There will also be a dependence on wave period for some rubble size classes and wave conditions due to inertial force being the dominant force.
Page 6, line 5-10. A table of wave conditions in the flume (height, period, water depth) is needed. The description of how wave period was increased when waves started to break seems very arbitrary. Changing the wave period for the same wave height will alter the orbital velocity, orbital excursion, and acceleration.
P6, Line 17-20. Linear wave theory is generally used to estimate bottom orbital velocities, accelerations, excursions. The approach described here (Soulsby cosine approximation) is non-standard and I didn’t understand why it was used in preference to linear wave theory.
P6, Line 19-20. The last statement on this page is very concerning: “Wave orbital velocities obtained in the flume were comparable to those measured in the field, hence scaling of the analyses was not required.” As I explained above, the forces on the rubble are the relevant quantity that should be compared in the lab vs the field, and related to rubble motion. The velocities can be the same but if other important parameters are different (e.g., wave period) then direct comparisons of laboratory and field results will not be possible. Careful consideration of scaling is always required when relating lab flume experiments and the field situation.
P8. Line 10. Unclear that the shallow water approximation is valid here for computing wavenumber k. There is readily available code available to calculate k from frequency and depth using the general/complete linear wave theory dispersion relation.
P8. Iine 32. Unclear what is meant by peak wave orbital velocity here. Do you mean the maximum 30-min significant wave height over the 3-day period? This is not truly the peak wave orbital velocity, which would require going back to the original time series for each burst.
P9. Results. Wave periods need to be reported and used appropriately in the analysis!
Fig 4. Bottom orbital excursion and accelerations should be shown also, for the reasons outlined in my General Comments

Citation: https://doi.org/10.5194/bg-2023-2-RC2
- AC2: 'Reply on RC2', Tania Kenyon, 21 Jun 2023
  
  We have included our response to RC2 as an attachment as the formatting for equations etc. would not copy across to the response box correctly.
  
  Citation: https://doi.org/10.5194/bg-2023-2-AC2

Tania M. Kenyon et al.

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https://doi.org/10.5194/bg-2023-2-supplement

Tania M. Kenyon et al.

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The movement of rubble on coral reefs can lead to persistent unstable rubble beds that hinder reef recovery. To identify where such rubble beds are, we need to know the minimum flow velocity that will move rubble. We tested this and found that rubble moved more if pieces were small and had no branches. Rubble had a 50% chance of being moved when flow velocities reached ~0.35 m/s. Rubble beds that experience frequent movement would be good candidates for rubble stabilisation interventions.


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