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the Creative Commons Attribution 4.0 License.
| 04 Nov 2024
SISSOMA (v1): modelling marine aggregate dynamics from production to export
Abstract. A mechanistic approach linking the population dynamics of plankton communities to the export of detrital material to the oceans interior, remains a largely unresolved component of global bio-geochemical models. We propose that the self-similarity of aggregation provides a tractable modelling framework for simulating the dynamics and sinking speed of natural marine particle aggregates. It provides a means to track both size and excess density of aggregates as they are formed and transformed by aggregation, degradation and fragmentation processes. A self-similarity parameter a in the range 1.8 to 2.1 is well supported by direct observations drawn from an extensive database of aggregate size and sinking speed. We provide a simple model, SISSOMA, that uses a 2 dimensional state-space representation of aggregate dynamics for which we conduct sensitivity analyses for the self-similarity parameter, stickiness, turbulent dissipation rate and the production rate of primary particles. The model provides size and density resolved estimates of the export flux of detrital material generated by a diverse community of primary producers. While open to improvement in several aspects, the model compares well with observations of aggregate size spectra covering the global ocean.
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RC1: 'Comment on egusphere-2024-2520', Anonymous Referee #1, 14 Dec 2024
The manuscript by Visser et al. introduces the modeling framework “Sissoma,” which offers a valuable approach to better estimate the excess density and sinking velocity of marine aggregates by considering fragmentation and aggregation processes. A noteworthy strength of the framework is its ability to incorporate various primary particle properties, enabling the model outcomes (e.g., aggregate numbers, sizes, and excess density) to be linked directly to specific primary producers. This is a promising contribution to the field.
The manuscript is technically robust and well-written, making it a pleasure to read. However, in most sections, the authors appear to overstate the implications of their model results by using absolute statements that are not fully supported by the presented evidence (see the first major comment below). There are also many statements made that need references throughout the manuscript. Additionally, the discussion would benefit from greater integration with existing literature, particularly through comparisons with other modeling approaches that have explored similar approaches, including those used in Earth System Models (e.g., doi.org/10.5194/bg-17-1765-2020 ).
If the authors prefer to retain these strong claims, I would recommend providing a more detailed comparison between the model results and actual measurements. So far, the authors are only comparing ranges. Comparisons could be achieved, for instance, by leveraging databases such as Ecopart to start with comparisons of aggregate properties. That said, I believe the manuscript would stand out even more by adopting a more measured tone, which would make its conclusions appear even more credible and impactful.
Major comments:
(1) The authors should address the absolute statements made throughout the manuscript. For instance, the claim that “the model compares well with observations of aggregate size spectra covering the global ocean” is not accurate. The paper does not present direct comparisons between modeling results and measurements; only ranges are compared. Similarly, the statement that “a mechanistic approach linking the population dynamics of plankton communities to the export of detrital material to the ocean’s interior remains a largely unresolved component of global biogeochemical models” is broadly true but somewhat misleading in this context. The manuscript does not provide this mechanistic link. Upon first reading, this statement led me to expect a population dynamics model coupled with fractal theory, which is not the case. Similar statements are made throughout the manuscript and should be adjusted accordingly.
(2) The manuscript is not the first to apply fractal theory to the aggregation and fragmentation of marine aggregates. The authors should more clearly articulate the novelty of their approach and specify where similar methods have been employed in the existing literature (particularly in the introduction and discussion). Within the manuscript mostly the studies that focus on the basic theories that are covered.
(3) The ocean features a stratified water column which influences the excess density of aggregates. Numerous studies from various laboratories have demonstrated these effects, particularly around pycnoclines (e.g. below mixed layer depth), as well as in the linear stratification commonly observed throughout the ocean. While I don’t believe it is necessary to incorporate these aspects into the model at this stage, a discussion of this limitation would improve the manuscript.
(4) The authors focus on the excess density of aggregates which integrates the solid hydrated density and porosity of aggregates and is a typical approach taken. However, measurements of the last decades indicate that these two parameters (porosity+solid hydrated density) have their own specific composition-dependent variability that is difficult to estimate through the holistic approach taken. These limitations should be addressed in more detail, so far the porosity is only measured briefly in the discussion and solid-hydrated density is not covered at all.
(5) As a recommendation: Throughout the text, the authors mention properties that are difficult to measure. As a researcher with a focus on experimental approaches to studying marine aggregates, I believe it would be a valuable addition to the manuscript to highlight which parameters should be measured in more detail in future.
Line specific comments:
Line 120: A reference is missing that shows that the particle size spectra produced from roller tanks are not representative of natural aggregate communities. Also: I find the term “natural aggregate communities” confusing and would just refer to natural aggregates.
Line 119: Throughout the manuscript, the authors occasionally use "particles" to refer to aggregates and at other times to primary particles. While this usage is not necessarily incorrect (depending on the definition), it can be confusing for the reader. I recommend clearly distinguishing the terminology between primary particles and aggregates to improve clarity.
Equation 8: A short name for the individual terms next to the equation would make it easier for the reader to following the different processes.
Figures
In my opinion, the authors could make the paper more accessible to a broader readership by simplifying the figures. The axes should directly represent the variables being displayed, and the captions should be concise and clear, avoiding unnecessary complexity. Figure 1, in particular, appears somewhat random, as it simply demonstrates that Stokes’ law with a constant excess density does not predict sinking velocity accurately—an observation already established in the literature. I would expect this figure to show an improvement in the settling-velocity prediction, which is currently missing.
Comment on the code provided
I have tested the code provided by the authors in Matlab Mathworks 2024a and the main function is operational, but the batch files are not (e.g. output file expA.mat is not existing) and the batchRun misses the parameter definition. Overall, the code is well documented which I appreciate.
Citation: https://doi.org/10.5194/egusphere-2024-2520-RC1 -
AC2: 'Reply on RC1', Andre Visser, 06 Feb 2025
We very much appreciate the reviewers time and effort in reviewing our work, and providing insightful feed back. Much of this feedback will be incorporated in an update manuscript. Below is a detailed accounting of our responses to the reviewers comments (included in italics)
- Referee 1 makes the following points
- The authors should address the absolute statements made throughout the manuscript. For instance, the claim that “the model compares well with observations of aggregate size spectra covering the global ocean” is not accurate. The paper does not present direct comparisons between modeling results and measurements; only ranges are compared. Similarly, the statement that “a mechanistic approach linking the population dynamics of plankton communities to the export of detrital material to the ocean’s interior remains a largely unresolved component of global biogeochemical models” is broadly true but somewhat misleading in this context. The manuscript does not provide this mechanistic link. Upon first reading, this statement led me to expect a population dynamics model coupled with fractal theory, which is not the case. Similar statements are made throughout the manuscript and should be adjusted accordingly.
We concede that we were perhaps a bit over enthusiastic in our wording and will adjust the revised ms accordingly. There have been similar approaches used before, that we have reference, but the list was perhaps not complete. This is being corrected.
While we are certainly aware of the need for a full validation of the model, in this instance, we thought it also important to verify the approach against macroscopic properties of observed aggregate communities. Specifically, the model results fall within observed ranges of aggregate size spectra, notably without the requirement of model calibration, is a strong indicator that the model captures the underlying dynamics.
The coupling between the aggregate and plankton dynamic is alluded to and is currently being conducted – coupling SISSOMA with NUM – a size and trait based model describing plankton dynamics. We will adjust our language accordingly.- The manuscript is not the first to apply fractal theory to the aggregation and fragmentation of marine aggregates. The authors should more clearly articulate the novelty of their approach and specify where similar methods have been employed in the existing literature (particularly in the introduction and discussion). Within the manuscript mostly the studies that focus on the basic theories that are covered.
The fundamental difference between SISSOMA and existing theories and models is that it does NOT treat fractal dimension as a fundamental property of aggregates. Rather it considers the aggregation process to be self-similar, which, in the absence of degradation and fragmentation would lead to aggregates with uniform fractal dimension. However, with degradation and fragmentation, the conservation of fractal dimension is violated. SISSOMA allows for more natural representations of degradation and fragmentation that are not constrained by an assumed conservation of fractal dimension. This is now made clear in the discussion.
One aspect where we are expanding our discussion is in comparison with some of the operational models that are being used to estimate export flux on a global scale. A particular issue we take up is the concept of “mean primary particle characteristics” that is central to many such models, and meshes with the concept we introduce of a “proto” aggregate. In our context, this represents characteristic aggregates that are rapidly produced by small, slowly sinking aggregates whose dynamics are largely determined by production, aggregation and degradation. These “proto” aggregates then grow through a dynamic controlled by aggregation, fragmentation and sinking. This separation of dominant dynamic balances that SISSOMA reveals would be very instructive in parameterizing flux modules that can be imbedded into global simulations.- The ocean features a stratified water column which influences the excess density of aggregates. Numerous studies from various laboratories have demonstrated these effects, particularly around pycnoclines (e.g. below mixed layer depth), as well as in the linear stratification commonly observed throughout the ocean. While I don’t believe it is necessary to incorporate these aspects into the model at this stage, a discussion of this limitation would improve the manuscript.
This will be mentioned in conjunction with our discussion on how the model can be recast to give vertical resolution. A stratified water column impacting aggregate excess density and sinking velocity would be a natural extension of this. This is not really a limitation of the model, it is just not implemeted in this version, which is purposefully kept a simple as possible.
- The authors focus on the excess density of aggregates which integrates the solid hydrated density and porosity of aggregates and is a typical approach taken. However, measurements of the last decades indicate that these two parameters (porosity+solid hydrated density) have their own specific composition-dependent variability that is difficult to estimate through the holistic approach taken. These limitations should be addressed in more detail, so far the porosity is only measured briefly in the discussion and solid-hydrated density is not covered at all.
We are confined in the model to consider aggregate parameters that are hydrodynamically relevant. In this, there is a linear dimension and an excess density that together determine sinking speed. We treat porosity simply as the volume of the aggregate that is occupied by interstitial water. We are mindful that the precise composition of the aggregate is much more nuanced. We do, for instance mention the different kinds of compounds that aggregates are composed of, and these can have different degradation rates. We can expand this discussion somewhat.
- As a recommendation: Throughout the text, the authors mention properties that are difficult to measure. As a researcher with a focus on experimental approaches to studying marine aggregates, I believe it would be a valuable addition to the manuscript to highlight which parameters should be measured in more detail in future.
All of the control parameters – stickiness, fragmentation rate, degradation rate – require better quantification. Of these, fragmentation is perhaps the least well know, and it is suspected that it plays an important role in controlling how large aggregates grow. Degradation & remineralization is also more nuanced that previously thought. The new observations (https://doi.org/10.1038/s41586-024-07850-x) indicate that globally, only about 10 to 30% of carbon in sinking aggregates is remineralized by resident microbes – the other 70 to 90% being presumably mediated by “free living” microbes and metazoan flux feeders.Line specific comments:
- Line 120: A reference is missing that shows that the particle size spectra produced from roller tanks are not representative of natural aggregate communities.
The Jackson et al reference in the preceding sentence should cover this. - Also: I find the term “natural aggregate communities” confusing and would just refer to natural aggregates.
A size spectrum is NOT a property of a natural aggregate, rather it is a property of the aggregate community. It is actually important to emphasize that the entire aggregate community is dynamic, being shaped by aggregation fragmentation and degradation, and export flux is a consequence of this dynamic. - Line 119: Throughout the manuscript, the authors occasionally use "particles" to refer to aggregates and at other times to primary particles. While this usage is not necessarily incorrect (depending on the definition), it can be confusing for the reader. I recommend clearly distinguishing the terminology between primary particles and aggregates to improve clarity.
Will use aggregate exclusively except when referring to primary particles. - Equation 8: A short name for the individual terms next to the equation would make it easier for the reader to following the different processes.
This is a bit tricky given the journal layout. - In my opinion, the authors could make the paper more accessible to a broader readership by simplifying the figures. The axes should directly represent the variables being displayed, and the captions should be concise and clear, avoiding unnecessary complexity. Figure 1, in particular, appears somewhat random, as it simply demonstrates that Stokes’ law with a constant excess density does not predict sinking velocity accurately—an observation already established in the literature. I would expect this figure to show an improvement in the settling-velocity prediction, which is currently missing.
We are not quite sure what this refers to. Figure 1 is a sketch of the various processes considered in the ms. Does this refer to Figure 2? This does show that using a constant excess density does not predict sinking velocity, but it shows so much more. It also shows that while excess density is in general a decreasing function of aggregate size (due to increasing porosity) there is still variability that can be traced bac to the variable density of primary particles. It also indicates a natural transformation of aggregate characteristics that is exploited in the model structure.
We will fix the batch files so that the demonstrations and documentation match.
Citation: https://doi.org/10.5194/egusphere-2024-2520-AC2
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AC2: 'Reply on RC1', Andre Visser, 06 Feb 2025
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RC2: 'Comment on egusphere-2024-2520', Anonymous Referee #2, 02 Jan 2025
Visser et al. present a new model that simulates two properties of marine aggregates, size and excess density, and thereby a time-varying sinking speed of the detritus.
The model is embedded in a zero-dimensional setup representing the well-mixed upper 50m of the ocean. It is forced by external input of particle production, and provides export flux through the bottom of the model domain. The model's sensitivity to particle input, their stickiness, turbulent dissipation rate and the self-similarity parameter, which defines the scaling of aggregate size, is explored.The approach itself seems very interesting and thorough, and worthwhile to be explored in a larger context, for example, one-dimensional or even global models. However, I have some concerns and suggestions regarding the presentation of the model and its validation. The way the model is presented now is quite theoretical and abstract, which, in my opinion, makes it difficult to access for empirical scientists and perhaps even for (large-scale) modellers. In particular, I would suggest to improve the paper on the following points:
(1) In parts of the "empirical" literature people often refer to the "optical" diameter or ESD. In section 1 I was wondering to what "r" (the "linear dimension" of equation 1) refers to: is it the optical or the "solid" radius? Likewise, I was wondering how volume "v" of equation (3) is being calculated - is it based on "r" cubed? A bit clarification on this point would be helpful.
(2) The self-similarity parameter "a" is introduced in equation 1, and this parameter, together with another parameter "b" seem to be essential for the paper. While, to my understanding, "a" seems to be a more abstract parameter, closely related to the theory of fractals, the autors later introduce "b", whose range is estimated from from an impressive compilation of observations of excess density vs. radius (Table 1 and lines 104ff ).
To my understanding, b=3-a (or a=3-b); if this is indeed the case, I would suggest to state this clearly.
Moreover, if indeed a=3-b I wonder how the authors arrive at "a" between 1.8-2.0 (e.g., line 107, 2.1 in line 114 and the abstract). I understand that this value of "a" is derived from "b" between 1.2 to 1.0 in the work by Iversen and Ploug (2010). In that paper, however, I find three values for the slope of the regression of excess density to size (Fig 3), namely 1.21 (diatom aggregates), 1.39 (E. huxleyi aggregates), and 1.05 (mixed aggregates); i.e., rounded, one would arrive at a range of 1 to 1.4, resulting in "a" between 1.6 to 2. In line 107, and throughout the paper the authors, however, refer to a range for the self similarity parameter of 1.8 to 2. In Table 1, however, the values are listet as 1.01, 1.13 and 1.20. This is somehow confusing.(3) Figures 3 and 4 to my opinion are quite complex, with little relation to the "real" world. While I can understand the usefulness of the scale transformations of the x- and y-axes, I think that non-transformed axes (radius, porosity) would really enhance that readability of the paper, and make it accessible for a broader community. This applies especially for the lower panel of that figure (sinking speed), which may be of great interest to many observing and modeling scientists.
(4) Besides aggregation, which is based on mechanistic principles, the model also contains assumptions and/or parameterisation of other processes, such as particle growth, fragmentation, and dissolution/remineralisation. Some of the related parameters may be quite uncertain. This is partly mentioned in the paper (which I appreciate very much). However, at least with regard to potential users of the model, I would suggest to more clearly identify the often uncertain parameters, that will have to be specified by modelers, in Table 2. This could be done by separating the state variables, derived or interim properties (E.g., N(x,z), F(x,z) or beta) from the parameters one has to specify before a model run (e.g., alpha, fragmentation rate) in the table.
(5) In the abstract the authors state that "While open to improvement in several aspects, the model compares well with observations of aggregate size spectra covering the global ocean." - Did I miss something? As far as I can see, no comparisons to observations have been made?
(6) I assume once aggregation kicks in, produces large and/or dense, fast aggregates which quickly sink out of the surface layer, this would have feedback effects on the productivity. Has this been taken into account?
Minor comments/typos:
line 155 variables
line 163 Is rho_0 really in [kg m^-1]?
line 242 "The same holds true for increasing turbulence and stickiness, both of which increase the rate of large, fast-sinking aggregate formation." - But turbulence also affects fragmentation? Is there any way to disentangle the effects?
line 266 "The organic components itself is ..." - Check grammar.
line 389 remineralizationCitation: https://doi.org/10.5194/egusphere-2024-2520-RC2 -
AC1: 'Reply on RC2', Andre Visser, 06 Feb 2025
We very much appreciate the reviewers time and effort in revieing our work, and providing insightful feed back. Much of this feedback will be incorporated in an update manuscript. Below is a detailed accounting of our responses to the reviewers comments (included in italics)
Referee 2 suggests the following specfic points
- In parts of the "empirical" literature people often refer to the "optical" diameter or ESD. In section 1 I was wondering to what "r" (the "linear dimension" of equation 1) refers to: is it the optical or the "solid" radius? Likewise, I was wondering how volume "v" of equation (3) is being calculated - is it based on "r" cubed? A bit clarification on this point would be helpful.
The radius is technically the hydrodynamic linear dimension that appears in the modified Stokes law and Reynold number. It s closest to the the solid radius and is related to the volume by 4/3 pi r^3. (This is specified in the parameter Table)
- The self-similarity parameter "a" is introduced in equation 1, and this parameter, together with another parameter "b" seem to be essential for the paper. While, to my understanding, "a" seems to be a more abstract parameter, closely related to the theory of fractals, the autors later introduce "b", whose range is estimated from from an impressive compilation of observations of excess density vs. radius (Table 1 and lines 104ff ). To my understanding, b=3-a (or a=3-b); if this is indeed the case, I would suggest to state this clearly.
Actually, b = a – 3 and a = 3 + b. (a is a positive number, while b is a negative number). The key parameter for the model is “a”, and while it may be somewhat abstract, it’s value can be inferred from size-density relationship for an aggregate community under special conditions – i.e. no degradation and no fragmentation. The closest to these conditions are relatively fresh aggregates reported by Iversen and Ploug (2010).
- Moreover, if indeed a=3-b I wonder how the authors arrive at "a" between 1.8-2.0 (e.g., line 107, 2.1 in line 114 and the abstract). I understand that this value of "a" is derived from "b" between 1.2 to 1.0 in the work by Iversen and Ploug (2010). In that paper, however, I find three values for the slope of the regression of excess density to size (Fig 3), namely 1.21 (diatom aggregates), 1.39 (E. huxleyi aggregates), and 1.05 (mixed aggregates); i.e., rounded, one would arrive at a range of 1 to 1.4, resulting in "a" between 1.6 to 2. In line 107, and throughout the paper the authors, however, refer to a range for the self similarity parameter of 1.8 to 2. In Table 1, however, the values are listet as 1.01, 1.13 and 1.20. This is somehow confusing.
Firstly, there seems to be an error in the slope estimates given in Iversen and Ploug (2010) in their caption for Figure 3. This can be deduced from examining their fig 3.B; the steepest slope is for the solid line b = - 1.21 (diatoms) while that for E. huxleyi (dotted line) is depicted as shallower but reported as a steeper slope b = -1.39. In our analysis, we used the original observations from Iversen and Ploug (2010) which can be found in the submitted database, to re-estimate the slope as b = -1.01. The slope values reported in Table 2 are b = -1.01, -1.13 and -1.20 respectively corresponding to values of a = 1.99, 1.87 and 1.80 respectively, ie in the range 1.8 to 2.0.
- Figures 3 and 4 to my opinion are quite complex, with little relation to the "real" world. While I can understand the usefulness of the scale transformations of the x- and y-axes, I think that non-transformed axes (radius, porosity) would really enhance that readability of the paper, and make it accessible for a broader community. This applies especially for the lower panel of that figure (sinking speed), which may be of great interest to many observing and modeling scientists.
The figures are also intended to illustrate the model architecture to modelers. We have re-worked the axes and captions to make this clearer. The plot that the reviewer asks for is actually a 3 dimensional relationship and will be supplied in the appendix as additional information.
- Besides aggregation, which is based on mechanistic principles, the model also contains assumptions and/or parameterisation of other processes, such as particle growth, fragmentation, and dissolution/remineralisation. Some of the related parameters may be quite uncertain. This is partly mentioned in the paper (which I appreciate very much). However, at least with regard to potential users of the model, I would suggest to more clearly identify the often uncertain parameters, that will have to be specified by modelers, in Table 2. This could be done by separating the state variables, derived or interim properties (E.g., N(x,z), F(x,z) or beta) from the parameters one has to specify before a model run (e.g., alpha, fragmentation rate) in the table.
This will be done in the revised ms.
- In the abstract the authors state that "While open to improvement in several aspects, the model compares well with observations of aggregate size spectra covering the global ocean." - Did I miss something? As far as I can see, no comparisons to observations have been made?
This is now reworded. The comparison is only with the aggregate size-spectrum slope
- I assume once aggregation kicks in, produces large and/or dense, fast aggregates which quickly sink out of the surface layer, this would have feedback effects on the productivity. Has this been taken into account?
In this version we have no feedbacks to nutrient cycling. We are currently coupling the model to the NUM model – a trait and size based description of plankton dynamics. In this there will be a coupling between particle sinking, nutrient dynamics and seasonal cycling.
Citation: https://doi.org/10.5194/egusphere-2024-2520-AC1
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AC1: 'Reply on RC2', Andre Visser, 06 Feb 2025
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