the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Submitted as: development and technical paper 15 Jan 2021
Submitted as: development and technical paper | 15 Jan 2021
A discrete interaction numerical model for coagulation and fragmentation of marine detritic particulate matter
- 1Institut des sciences de la mer de Rimouski, UQAR, Québec-Océan, Rimouski (Quebec), Canada
- 2Instituto Antártico Argentino, Buenos Aires, Argentina
- 3Centro Austral de Investigaciones Científicas (CADIC-CONICET), Ushuaia, Argentina
- 4Universidad Nacional de Tierra del Fuego, Ushuaia, Argentina
- 5ArcticNet, Québec-Océan, Université Laval,(Quebec), Canada
- 1Institut des sciences de la mer de Rimouski, UQAR, Québec-Océan, Rimouski (Quebec), Canada
- 2Instituto Antártico Argentino, Buenos Aires, Argentina
- 3Centro Austral de Investigaciones Científicas (CADIC-CONICET), Ushuaia, Argentina
- 4Universidad Nacional de Tierra del Fuego, Ushuaia, Argentina
- 5ArcticNet, Québec-Océan, Université Laval,(Quebec), Canada
Abstract. A simplified model, representing the dynamics of marine organic particles in a given size range experiencing coagulation and fragmentation reactions is developed. The framework is based on a discrete size spectrum on which reactions act to exchange properties between different particle sizes. The reactions are prescribed according to triplets interactions. Coagulation combines two particle sizes to yield a third one, while fragmentation breaks a given particle size into two (i.e. the inverse of the coagulation reaction). The complete set of reactions is given by all the permutations of two particle sizes associated with a third one. Since, by design, some reactions yield particle sizes that are outside the resolved size range of the spectrum, a closure is developed to take into account this unresolved range and satisfy global constraints such as mass conservation. In order to minimize the number of tracers required to apply this model to an Ocean General Circulation Model focus is placed on the robustness of the model to the particle size resolution. Thus, numerical experiments were designed to study the dependence of the results on i) the number of particle size bins used to discretize a given size range (i.e. the resolution) and ii) the type of discretization (i.e. linear vs nonlinear). The results demonstrate that in a linearly size discretized configuration, the model is independent of the resolution. However, important biases are observed in a nonlinear discretization. A first attempt to mitigate the effect of nonlinearity of the size spectrum is then presented and shows significant improvement in reducing the observed biases.
Gwenaëlle Gremion et al.
Status: final response (author comments only)
-
CEC1: 'Comment on gmd-2020-423', Astrid Kerkweg, 26 Feb 2021
Dear authors,
in my role as Executive editor of GMD, I would like to bring to your attention our Editorial version 1.2:
https://www.geosci-model-dev.net/12/2215/2019/
This highlights some requirements of papers published in GMD, which is also available on the GMD website in the ‘Manuscript Types’ section:
http://www.geoscientific-model-development.net/submission/manuscript_types.html
In particular, please note that for your paper, the following requirement has not been met in the Discussions paper:
- "The main paper must give the model name and version number (or other unique identifier) in the title."
Please add a name and a version number of the model you are publishing here in the title upon your revised submission to GMD. Note, that a name or acroynm and version number make your model much easier referencable.
Yours,
Astrid Kerkweg
-
AC1: 'Reply on CEC1', Gwenaelle Gremion, 26 Mar 2021
We would like to thank Astrid Kerkweg, Executive editor of GMD, for bringing to our attention that our contribution title was not properly following the editorial rules.
- "The main paper must give the model name and version number (or other unique identifier) in the title."
Even if we consider that our parameterization may not justify a model name and version, we agree to modify our title as :
A discrete interaction numerical model for coagulation and fragmentation of marine detritic particulate matter (Coagfrag V.1)We hope that this adjustment, alongside the improvement we propose in response to reviewers’ comments and suggestions will meet your expectations for publication.
Sincerely yours,
Gwenaëlle Gremion, on behalf of all co-authors.
-
RC1: 'Comment on gmd-2020-423', Anonymous Referee #1, 26 Feb 2021
The present paper aims to include the process of particle coagulation and fragmentation into an OGCM. Particle coagulation is a challenging process to model as it requires the inclusion of many compartments, representing the spectrum of aggregated particle sizes. So far, no real attempt has been made to incorporate this process explicitly into the larger scale biogeochemical models. I believe this is an important step in biological oceanography due to its importance in carbon flux estimations.
Ideally, one would include a total of N tracer compartments, N representing the maximum amount of individual cells or particles a single aggregated floc can contain. However, due to computational restrictions, including N tracers in an OGCM is not feasible. This paper aims to address this problem by reducing the particle size resolution (i.e. reducing the amount of tracers). More importantly, the modelling approach is flexible to allow a nonlinear size distribution, which is more suited to the biological process.
It is encouraging that attempts are being made to incorporate this process into an OGCM and I believe this paper certainly has merit. I would recommend publication subject to addressing the minor concerns raised below.
- Firstly, I was surprised to see links to the cloud microphysics field had not been made. These spectral bin models are used frequently e.g. Khain et al 2004 and a discussion is warranted.
- Line 375 states “But, the sensitivity of our model outcomes to many arbitrary constant parameters needs to be profoundly investigated”. This is an extremely pertinent point and I think at least a basic sensitivity analysis should be conducted.
- Regarding the penalty function: while I appreciate the simplicity used to reconcile the errors arising from nonlinearity, more tests should be carried out to confirm the applicability of the parameter choices used in the function.
- The work aims to replace the simplified coagulation parameterizations currently used in OGCMs, which use several detritus compartments. While I completely agree that the approach used here is a positive step, it would be useful to demonstrate exactly why the model developed here is preferable beyond the current discussion given in the introduction. Is there evidence showing that carbon fluxes are estimated more accurately using this type of method? Can a simple experiment be carried out to show the shortfalls of the other approaches? There is going to be a computational penalty for including more tracers, so it should be shown that the sacrifice is worth it.
- Takeuchi et al. 2019 finds aggregates are bounded in size by the Kolmogorov length scale. Rather than using an arbitrary upper bound, this characteristic could be used to inform the choice of upper bound.
Khain, A., Pokrovsky, A., Pinsky, M., Seifert, A. and Phillips, V., 2004. Simulation of effects of atmospheric aerosols on deep turbulent convective clouds using a spectral microphysics mixed-phase cumulus cloud model. Part I: Model description and possible applications. Journal of the atmospheric sciences, 61(24), pp.2963-2982.
Takeuchi, M., Doubell, M.J., Jackson, G.A., Yukawa, M., Sagara, Y. and Yamazaki, H., 2019. Turbulence mediates marine aggregate formation and destruction in the upper ocean. Scientific reports, 9(1), pp.1-8.
-
AC2: 'Reply on RC1', Gwenaelle Gremion, 26 Mar 2021
We would like to thank the first anonymous referee for the time he/she spent to review our manuscript with very helpful comments that will certainly improve the quality of our work. We include the comments from the referee and our responses below. We hope that this version, alongside the improvement related to the second reviewer will meet your expectations for publication.
Sincerely yours,
Gwenaëlle Gremion, on behalf of all co-authors.
------ Firstly, I was surprised to see links to the cloud microphysics field had not been made. These spectral bin models are used frequently e.g. Khain et al 2004 and a discussion is warranted.
We do agree that some concepts used in our study come from aerosol physics. We recognize this when we refer to the seminal work of Gelbard et al. (1980) on aerosol coagulation, but we agree that a short discussion on more contemporary work in this field is relevant and will be added. We thank the reviewer for its suggestion.
- Line 375 states “But, the sensitivity of our model outcomes to many arbitrary constant parameters needs to be profoundly investigated”. This is an extremely pertinent point and I think at least a basic sensitivity analysis should be conducted.
We fully agree with the reviewer that a thorough sensitivity analysis must be conducted. However, the main objective of our manuscript is to present a numerical framework representing coagulation and fragmentation based on discrete interaction and to test its consistency and robustness with respect to the spectral resolution and discretization. This is specified at p. 3 lines 73-76: “a formulation is sought that will attenuate the dependence of the results to the size discretization resolution. Numerical experiments are designed to study the dependence of the results on i) the number of size bins used to discretize a given size range (i.e. the resolution) and ii) the type of discretization (i.e. linear vs nonlinear)“. Although we are considering applications in biogeochemical modeling, what is presented remains general in scope. Carrying sensitivity analyses was also purposely left out because it is lengthy when properly done and that we currently have 31 pages already. Again, we agree that it is important and it is currently being done in a working manuscript.
- Regarding the penalty function: while I appreciate the simplicity used to reconcile the errors arising from nonlinearity, more tests should be carried out to confirm the applicability of the parameter choices used in the function.
The penalty function was empirically set up to demonstrate that it is required to correct for the asymmetry between the reactions. Following this idea, parameters were chosen by trial-and-error to achieve an arbitrary satisfactory reduction of the asymmetry. However, as mentioned in p. 22, lines 347-350, a more systematic inquiry of the resolution and non-linearity dependence is needed (which is ongoing and will be the subject of a subsequent paper) to find either an exact or empirical formulation of the penalty function.
- The work aims to replace the simplified coagulation parameterizations currently used in OGCMs, which use several detritus compartments. While I completely agree that the approach used here is a positive step, it would be useful to demonstrate exactly why the model developed here is preferable beyond the current discussion given in the introduction. Is there evidence showing that carbon fluxes are estimated more accurately using this type of method? Can a simple experiment be carried out to show the shortfalls of the other approaches? There is going to be a computational penalty for including more tracers, so it should be shown that the sacrifice is worth it.
OGCMs that use many detritus compartments do not necessarily take into account coagulation. This requires that the detritus variables react together, which is not the case to our knowledge. Our ultimate objective is to explicitly implement the coagulation and fragmentation reactions in NPZD models coupled to OGCMs, with a number of detritus variables that is as low as possible.
In some OGCM-BGC models, a depth-dependent function is prescribed to account for the degradation of organic matter as it sinks to the ocean floor and transformed into dissolved organic carbon p. 2 line 52: “Gloege et al. (2017), e.g. exponential decay, Martin’s curve, ballast hypothesis“. However, this cannot be viewed as an explicit parameterization of coagulation-fragmentation reactions. Other OGCM-BGC models consider numerous detritic variables, but they do not use the coagulation-fragmentation reaction results as a determinant of the size representation of their detritus variables. For example in Butenschön et al. (2016), detritus are only split up in size classes, related to size-specific primary or secondary producers variables, for which they are the terminal variable (where they end up when dead). In this example, once the material ends up in those detritic variables it is not able to move from one size class to another. They can however move from a particulate variable to a dissolved one. Thereafter, this matter is exported to the seafloor according to the size-dependent settling velocity. In our work, the particulate matter when placed in a size-specific detritic variable is able to move from one size bin to another following coagulation and fragmentation reactions. Once coupled to a BGC model, this will vary as a function of depth and time. To sum up, size-detritic variables will not be considered as terminal variables of the particulate matter, and matter dynamics and export rates will be fluctuating depending on the biological and physical environment.
Therefore, we then think that our approach will provide new carbon export patterns in NPZD models that ultimately will be compared with the depth-dependent degradation functions of the organic matter as reference. Indeed those functions are representative of what is observed in the ocean, as they are based on field results. Although this is a really stimulating and important question, we are however unable, in the current state of our research, to carry out any experiment of comparison. This requires additional work, such as the implementation of parameters known to be variating with size (coagulation and fragmentation), and a parameterization with a physical and biological environment. This is precisely stated in the manuscript (p.24 line 385): “Ultimately, when reliably parameterized, this model will be coupled to an upper trophic level ecological model and OGCMs that will enable addressing further questions related to the fate of particle evolution with depth.”
- Takeuchi et al. 2019 finds aggregates are bounded in size by the Kolmogorov length scale. Rather than using an arbitrary upper bound, this characteristic could be used to inform the choice of upper bound.
This is true that the Kolmogorov length scale constrains the upper bound of particle sizes and we thank the reviewer for pointing out a recent study about this. However, there are also evidences that some phytoplankton species (e.g. Melosira Arctica) can form ~20 cm-long strands that reach the seafloor thousands of meters below the surface (Boetius et al, 2013). Despite its importance, prescribing an upper bound is beyond the scope of our paper which is to develop a numerical framework that is robust and that can be adapted to practical applications. There are multiple ways to represent the effects of turbulence in and those will be discussed in a subsequent study.
References
Boetius, A., Albrecht, S., Bakker, K., Bienhold, C., Felden, J., Fernández-Méndez, M., Hendricks, S., Katlein, C., Lalande, C., Krumpen, T., et al.: Export of algal biomass from the melting Arctic sea ice, Science, 339, 1430–1432, https://doi.org/10.1126/science.1231346, 2013.
Butenschön, M., Clark, J., Aldridge, J. N., Allen, J. I., Artioli, Y., Blackford, J., Bruggeman, J., Cazenave, P., Ciavatta, S., Kay, S., Lessin, G., van Leeuwen, S., van der Molen, J., de Mora, L., Polimene, L., Sailley, S., Stephens, N., and Torres, R.: ERSEM 15.06: a generic model for marine biogeochemistry and the ecosystem dynamics of the lower trophic levels, Geosci. Model Dev., 9, 1293–1339, https://doi.org/10.5194/gmd-9-1293-2016, 2016.
-
RC2: 'Comment on gmd-2020-423', Anonymous Referee #2, 08 Mar 2021
In this paper, a model representing the dynamics of marine organic particles by coalescence and fragmentation is developed. Coagulation and fragmentation are key microphysical processes in cloud and aerosol physics, since they affect size distribution of aerosols and droplets. In explicit models at cloud scale, coagulation is usually modelled by solving the kinetic collection or Smoluchowski equation (Pruppacher and Klett, 1997), or by using the stochastic approach with Monte Carlo methods (Shima, 2009). The coalescence process for multiple components has also been addressed in previous works, by treating unactivated aerosols and cloud droplets in a joint two-dimensional size distribution (Bottt, 2000).
The aim of this work is to implement an explicit treatment of the coagulation-fragmentation processes in order to avoid parameterizations. Within the approach adopted by the authors, the particle size distribution is discretized into size bins, with a discretization that can be linear or non-linear. The final aim is to incorporate this processes into Ocean General Circulation Models by solving a set of differential kinetic equations for each size bin.
I recommend publication of this paper after some minor revision considering the following:
- Bin microphysical models for coagulation are widely used in cloud and aerosol physics. There are many studies that addressed this problem and some excellent reviews (Jacobson, M.Z., 2005; Khain et al., 2015). I would suggest the authors to cite and briefly discuss some papers from these research areas. This can help place the current work in a more general context, and exhibit the advances compared with studies from other fields.
- In Eqs. (8) and (9), the triplet operator that represents both coagulation and fragmentation for a given bin, should be discussed in more detailed. It is clear from Eq (9), that the increase in the number of particles in bin k is proportional the product of particles number concentrations in bins i and j. However, the coagulation and fragmentations rates (coagulation kernels) from Table 2 are considered constant, and not depending on particle radius, chemical composition or terminal velocity of the particles.
- The mechanisms for particle coagulation are not emphasized or discussed. For example, in Jackson (2001) three mechanisms for particle coagulation are discussed: Brownian diffusion, shear (laminar and turbulent), and differential sedimentation. It is not clear if coagulation and fragmentation rates are considered constant just to check the performance of the algorithm, or as some kind of approximation for different physical processes like differential sedimentation.
- In page 14, line 218, it is written that “Coagulation of particles belonging to bins 1 μm and 10 μm would ideally produce particle size 11 μm”, which is in general not true for the radius of the resulting particles after coagulation.
- In the discussion of simulation results, authors stated that “coagulation leads to a reduction of Cp in small size bins and an increase in larger ones for both LR and HR, resulting in a linearly increasing distribution of Cp over the resolved size range”. And “fragmentation yields a reduction of Cp in larger size bins to the benefit of an increase in the small ones”, as in general expected. However, it could be interesting to check further the performance of the model for the coagulation case only, by comparing the results obtained from the kinetic equations developed by the authors with analytical solutions of the Smoluchowski equation for a constant coagulation kernel (for example).
References:
BOTT, Andreas. A flux method for the numerical solution of the stochastic collection equation: Extension to two-dimensional particle distributions. Journal of the atmospheric sciences, 2000, vol. 57, no 2, p. 284-294.
JACOBSON, Mark Z.; JACOBSON, Mark Z. Fundamentals of atmospheric modeling. Cambridge university press, 2005.
Khain, A. P., Beheng, K. D., Heymsfield, A., Korolev, A., Krichak, S. O., Levin, Z., ... & Yano, J. I. (2015). Representation of microphysical processes in cloudâresolving models: Spectral (bin) microphysics versus bulk parameterization. Reviews of Geophysics, 53(2), 247-322.
PRUPPACHER, Hans R.; KLETT, James D. Microphysics of Clouds and Precipitation: Reprinted 1980. Springer Science & Business Media, 2012.
SHIMA, Shin-ichiro, et al. The superâdroplet method for the numerical simulation of clouds and precipitation: A particleâbased and probabilistic microphysics model coupled with a nonâhydrostatic model. Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, applied meteorology and physical oceanography, 2009, vol. 135, no 642, p. 1307-1320.
-
AC3: 'Reply on RC2', Gwenaelle Gremion, 26 Mar 2021
We would like to thank the second anonymous referee for the time he/she spent to review our manuscript with very helpful comments that will certainly improve the quality of our work. We include the comments from the referee and our responses. We hope that this version, alongside the improvement related to the first reviewer will meet your expectations for publication.
Sincerely yours,
Gwenaëlle Gremion, on behalf of all co-authors.-----
- Bin microphysical models for coagulation are widely used in cloud and aerosol physics. There are many studies that addressed this problem and some excellent reviews (Jacobson, M.Z., 2005; Khain et al., 2015). I would suggest the authors to cite and briefly discuss some papers from these research areas. This can help place the current work in a more general context, and exhibit the advances compared with studies from other fields.
This comment echoes Reviewer 1’s first comment. We do agree that some concepts used in our study come from aerosol physics. We recognize this when we refer to the seminal work of Gelbard et al. (1980) on aerosol coagulation, but we agree that a short discussion on more contemporary work in this field is relevant and will be added. We thank the reviewer for its suggestion.
- In Eqs. (8) and (9), the triplet operator that represents both coagulation and fragmentation for a given bin, should be discussed in more detailed. It is clear from Eq (9), that the increase in the number of particles in bin k is proportional the product of particles number concentrations in bins i and j. However, the coagulation and fragmentations rates (coagulation kernels) from Table 2 are considered constant, and not depending on particle radius, chemical composition or terminal velocity of the particles.
Coagulation and fragmentation rates depend on particle size through a number of different processes and our model takes this into account. To better reflect this, we have modified the equations describing our model (mainly Equations 8-9) so that they use size-dependent coagulation and fragmentation rates, and we briefly summarise how these rates depend on size, citing relevant literature. It is only when we design the numerical experiments that those rates are set constant, to facilitate the interpretation of the results and the assessment of robustness to resolution and discretisation.
- The mechanisms for particle coagulation are not emphasized or discussed. For example, in Jackson (2001) three mechanisms for particle coagulation are discussed: Brownian diffusion, shear (laminar and turbulent), and differential sedimentation. It is not clear if coagulation and fragmentation rates are considered constant just to check the performance of the algorithm, or as some kind of approximation for different physical processes like differential sedimentation.
We agree with the reviewer that it was not clear from the manuscript whether the model was only applicable with constant rates and whether or not we recognized that there are well-known mechanisms and well-described formulations that exist. In response to the previous comment, we will revise the model formulation by adding size-dependent rates, including coagulation. Shortly after, we will recall the mechanisms driving particle collision and coagulation, namely Brownian motion, shear and differential sedimentation. It is only when we describe the numerical experiments that we will set these rates to constant values and say why we choose to do so.
- In page 14, line 218, it is written that “Coagulation of particles belonging to bins 1 μm and 10 μm would ideally produce particle size 11 μm”, which is in general not true for the radius of the resulting particles after coagulation.
We are thankful that this point was raised, as we did not precise, indeed, that this rule applied when considering size as the particles’ volume. We will correct this statement by referring to volume (in μm3) instead of the one-dimensional size (in μm).
- In the discussion of simulation results, authors stated that “coagulation leads to a reduction of Cp in small size bins and an increase in larger ones for both LR and HR, resulting in a linearly increasing distribution of Cp over the resolved size range”. And “fragmentation yields a reduction of Cp in larger size bins to the benefit of an increase in the small ones”, as in general expected. However, it could be interesting to check further the performance of the model for the coagulation case only, by comparing the results obtained from the kinetic equations developed by the authors with analytical solutions of the Smoluchowski equation for a constant coagulation kernel (for example).
Good point, thank you. We made a formal comparison between Smoluchowski’s approach and ours that will be presented in the revised version. In essence, there exists very few differences between the two. If we put aside the closure for the unresolved range, the only difference resides in the fact that Smoluchowski’s formulation is in terms of number of particles, while ours is in terms of concentration. This slightly modifies the evolution equation since the total concentration is conserved for a given reaction in our setup while the total number of particles is not conserved in Smoluchowski’s (two particles are combined to yield a single new one). Nevertheless the two formulations are equivalent and, in this context, it is difficult to imagine a setup that would allow a comparison outside of a simple bookkeeping between concentration and number of particles.
Gwenaëlle Gremion et al.
Model code and software
Source code and user manual of the Coagfrag Model (Version Version 1) Gremion, G. and Nadeau, L.-P. https://doi.org/10.5281/zenodo.4432896
Gwenaëlle Gremion et al.
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 263 | 81 | 17 | 361 | 2 | 4 |
- HTML: 263
- PDF: 81
- XML: 17
- Total: 361
- BibTeX: 2
- EndNote: 4
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1