the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Aug 2025
Computational library for the Nutrient-Unicellular-Multicellular plankton modeling framework v. 1.0
Abstract. The Nutrient-Unicellular-Multicellular (NUM) model is a trait-based model of unicellular and multicellular plankton that uses body size as the main structuring variable for community composition. The distinguishing feature is that body size is used for structuring predator-prey interactions and to scale all parameters. For unicellular plankton, trophic strategies across the full range from osmotrophy, phototrophy, phagotrophy and mixotrophy, are an emergent outcome of the model. Another distinguishing feature is that the multicellular component, represented by copepods, includes ontogeny, which is crucial in shaping population dynamics. In addition, the framework encompasses a nutrient pool consisting of nitrogen, silica and dissolved organic carbon (DOC) which interacts dynamically with the plankton community in three model setups: a chemostat simulating the photic zone, a water-column, and a global setup. Here we present a user-friendly Fortran-Matlab library which makes the NUM model accessible as a practical tool for marine ecologists or biogeochemical modellers. The model output is validated with in situ and satellite data and demonstrates its applicability in chemostat, water-column, and global setups.
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Status: open (until 02 Oct 2025)
- RC1: 'Comment on egusphere-2025-755', Anonymous Referee #1, 09 Sep 2025 reply
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CC1: 'Comment on egusphere-2025-755', Ben Ward, 15 Sep 2025
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Review of
Computational library for the Nutrient-Unicellular-Multicellular plankton modeling framework v. 1.0
By Papapostolou, Almgren, Hansen, Kandylas, Serra-Pompei, Visser and Andersen
The submitted manuscript presents a significant development of the Nutrient-Unicellular-Multicellular (NUM) plankton modelling framework. This includes the extension of the physical framework to global, water column and modelling environments, and the addition of a diatom functional group. A unique feature of this global model is the emergence of different trophic strategies as a function of organism traits and environmental conditions.
The model is calibrated against multiple datasets, but there is some ambiguity regarding the spatial resoloution of the assimilated data (see comments). Nonetheless, the model reproduces important global-scale patterns of plankton biomass, nutrient fields and net primary production with some accuracy.
I found the paper to be well written, subject to some corrections, as suggested in an annotated copy of the submitted pdf. Of these suggestions, I have highlighted a few of the more important points below.
- Please could the authors say a little more about what they mean by “first principles"? I am not convinced that all the phytoplankton parameters are derived purely from physical constraints, but it is possible the authors mean something different. Regardless off this, the authors later step back from this ambition slightly, stating on Line 282 that "All parameters of the plankton groups are based on first principles or cross-species comparisons". The latter is more realistic and this qualifier should be included throughout.
- Section 3.4 suggests that there is no non-advective export of Si included in the model (i.e. particulate Si does not sink. This seems very unrealistic, and potentially an important omission. I did not see any indication that living diatoms had a sinking speed. Please could the authors clarify and justify this choice.
- When discussing or plotting size spectra, could the authors please use the length dimension instead of (or as well as) mass. It is much, much easier for readers to understand how big the organisms are in terms of diameter. I have no idea how big a 0.01 µg C plankton is.
- After reading the ms I was unsure if these first three data types shown in equation 21 are spatially resolved or a single global mean. Much of the text suggests the latter, but if this is not clear from the description in section 3.9. This requires clarification.
- I expect that the low N and Si concentrations in the ocean surface are better explained by unrealistically efficient nutrient uptake by phytoplankton, rather than underestimated external supply. For surface Si, the inclusion of unrealistically small diatoms could certainly contribute to this.
- Please use micromolar units for nutrient concentrations (and possibly biomass), which are much more standard in ocean biogeochemistry.
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- 1
Review of "Computational library for the Nutrient-Unicellular-Multicellular
Plankton modeling framework v. 1.0" by Papapostolou et al.
General evaluation
The authors describe a library for their Nutrient-Unicellular-Multicellular (NUM) model, which can be used from Matlab. The ms describes the model and compares predictions with observations and provides a few hints how it can be used. The NUM model is advertised as a tool for ecological modellers without a biogeochemical or physical background.
The model is built on principles and assumptions similar to previous plankton ecosystem models but does not appear to achieve a similar performance as similarly or less complex global ocean models representing the current state of the art. While this is OK given the focus on simplicity, I see several problems both with the ms and the model itself. To begin with, the authors vastly overstate the novelty and scientific rigor of the model or understate the current state of the art. For example, this is neither the first nor the only model built on size-based parametrisation of multiple phytoplankton and zooplankton groups, the same holds for mixotrophy, and many of the underlying assumptions are not based on first principles, contrary to what is written in the ms. Related to this is a lack of consideration of and comparison with the pertinent literature. Further, essential information about the model is either missing or difficult to access, e.g., how the transport matrix was extracted and from which model, or how the model was calibrated. Given the many deficiencies of the model (basically any current model) I find it inappropriate to advertise the use by modellers without biogeochemical or physical background, as this background is essential for a meaningful application. Finally, the model is strongly nudged towards bottom concentrations of N and Si. As it stands, this not only makes the (essential) analysis of mass balance extremely difficult, which is further complicated by fluxes to unresolved compartments (higher trophic levels), but also put into the question the interpretation of and conclusions drawn from the model results. These issues, in particular the ability to check the mass balance, must resolved to make this ms publishable.
Another, though comparatively minor, problem is the choice of Matlab as the high-level interface. This restricts the use to those who have access to a Matlab license. More importantly, however, Matlab has repeatedly introduced backwards-incompatible changes, making older programs difficult or impossible to use with recent Matlab versions, e.g., the ROMS-AGRIF toolbox. This is difficult to deal with also because Matlab is not open source. Thus, for future developments, I would suggest to switch to open-source software, e.g., Python or R, both of which have advanced numerical integration packages and can be used with Fortran.
Specific evaluation
In the Abstract, l4: "The distinguishing feature is that body size is used for structuring predator-prey interactions and to scale all parameters". This makes it sound as if this was new or specific to the presented model, but the same concept has been employed previously by Ward and Follows (2016) and Ward et al. (2012: L&O 57), and is was also outlined in Andersen et al. (2015: JPR 37).
Several statements in the Introduction regarding the current state of the art are misleading at the very least:
l20: "focus on phytoplankton" This is not quite correct, ESMs generally focus on export and most of them place similar focus on phytoplankton and zooplankton, e.g., PISCESv2 (Aumont et al, 2015, GMD 8) has 2 phyto and 2 zoo groups and COBALTv2 (Dunne et al., 2020, JAMES 12) has 3 each. In fact, I am not aware of a current Earth system model merely treating zooplankton as a closure term (l22). Some global modelling studies even focus specifically on zooplankton, for example Prowe et al., (2012: Progr. Oceanogr. 101; 2019: L&O 64) and Ward et al., (2012). In particular, Ward et al., (2012) and Prowe et al., (2019) appear also highly relevant for the present manuscript and should be discussed/contrasted with the present model, also Ward and Follows (2016). There are likely more. Without relating the present to previous models is will be very difficult to assess the usefulness of the present study.
l21: "fast turnover rates mean that they have the highest loss rates to the biological carbon pump": This is not true, the fast turnover rates characterise quick recycling in the microbial loop. Only export enters the biological pump and this is largely channelled through zooplankton.
l32: "most eukaryotic plankton are neither phytoplankton or zooplankton but mixotrophic jacks-of-all-trades": This is not correct. While many species are indeed mixotrophs, most members of the groups of major importance to the biological pump and higher trophic levels, i.e., diatoms, coccolithophorids, copepods, are indeed predominantly autotrophs or heterotrophs. Mixotrophy is best established for dinoflagellates and photosynthetic bacteria and even there one trophic mode is usually dominant and the other restricted to some auxiliary processes, meaning that, with few exceptions, the classification as functional autotrophs and heterotrophs is still valid and useful. Also, the ability to switch between autotrophy and heterotrophy seems to be a rare exception. This is a problem in models representing mixotrophy, including the one under consideration here, since they assume that this switching is a regular feature of mixotrophy.
l36: "sufficient representation of the functions of marine planktonic food webs ... requires a representation of the mixotrophic nature of eukaryotic plankton": This statement, while I have seen it quite often already in several forms, has never been substantiated. Just that a phenomenon exists and is not represented in models does not mean that it is important, even though it may have strong effects in the model (and several modelling studies have shown that this is the case). Either remove this statement or at least tone in down.
The NUM library and model description (Sections 2 and 3) is very difficult to follow, at least in part because many model equations are collected, without equation numbers, in tables in Appendix B. Several statements are either not correct, unclear, or misleading.
l78: "All the setups are derived from a global transport matrix": Where does this transport matrix (TM) come from? How was it extracted and from which model? TM extraction is not a trivial task and only very few researchers can do this currently. Thus, some details are required here (or at least somewhere in the model description). Also missing is the temporal and spatial resolution of the TM.
l82: "DOC, nitrogen, and silicate": Unclear why these have been chosen. What about P and Fe?
l109: "The vacuole requires a silica shell": No, it only requires a cell wall. The vacuole is not unique to diatoms but fairly common in other groups as well, e.g., green algae.
l107: "This trait allows them to increase their volume per carbon without additional nutrient demands, which in turn leads to lowered predation pressure": This statement, while frequently encountered in the literature, lacks observational support and should be toned down. In fact, diatoms seem to be the preferred food for many copepod species, and their success appears more related to their high growth rates rather than predation avoidance.
l119: "spring blooms are controlled by a time lag between the maximum consumption by adult copepods and the rise of juveniles (Vidal and Smith, 1986)": This is not what Vidal and Smith wrote. What they did write is that the development of one herbivores (copepods) community was affected by this time lag, not that of the (phytoplankton) spring bloom. Interestingly for the present work, they also wrote that "growth rates of planktonic crustaceans must not be scaled just on the basis of body size", which is what current size-based models do, including the present. I think discussing this kind of caveats of allometric scaling is essential for the advancement of size-based models. Sweeping these problems under the carpet is only going to aggravate problems in the future.
l125: "representative populations": Representative of what?
l129: "we have used a single POM group": Unclear: Does this mean only one size class?
l160: "comply": does not make sense, use a better word, e.g., allow for
l167: "they [diatoms] have a lowered predation risk": They are the preferred prey of many copepods (see above).
l196: "To avoid unnecessary respiration, the cell regulates the actual uptakes jX from the encountered uptakes jenc.X to maximize cell division rate under the constraint of a fixed C:N:Si stoichiometry": According to Table B1 this seems to be a simple law of the minimum, dictated by the fixed-stoichiometry assumption and should be described as such. The formulation "to maximize cell division rate" is misleading.
l247 and Eq. (19): What is the vertical resolution? This equation will exert a very strong relaxation on the whole ocean grid, including the surface layer, which is usually much thinner than the bottom layer, and there the gradient with respect to the bottom concentration will be strongest also.
l282: "All parameters ... are based on first principles or cross-species comparisons": This is simply not true. For example, representing temperature dependence by one or more Q10s is not based on first principles and also often does not hold among species, and the same applies to prey preference, viral lysis, etc. In fact, very little of the theory (assumptions) behind the present model has a sound empirical foundation, which should be obvious from the above and below comments.
l289: "Lower higher": Unclear which one, lower or higher?
l291: "We calibrate by minimizing the error between average modeled and observed values": How was this done? Did you account for possible correlations between the three calibrated parameters or among the variables used in the cost function?
Eq. (21): What are Q and P?
l296: "three sites that represent markedly different environments": Which sites are these? They are never identified.
l310: "innocuous": makes no sense. Did you mean simple?
caption Fig. 4: "all fluxes into POM are directly mineralized into dissolved silicate": The arrow through (1 – γ2) in the right panel points to POM. Should it not point to Si? How are the fluxes to higher trophic levels accounted for? For example, what happens to the N going into HTL?
This, together with the nudging (Eq. 19), raises questions regarding mass balance. Checking mass balance is essential for asserting the internal consistency and integrity of numerical models. Models employing nudging or fluxes into unresolved compartments thus need to provide special tools for accounting for the fluxes implied by the nudging and outside of the model domain. Without these, the NUM library will be completely useless.
caption Fig. 5: "Sheldon size distributions": It should be explained briefly what this is.
Results:
l325: "with a weak effect on the biomass distributions": This is difficult to believe, owing to the very strong effect on surface nutrients according to Eq. (19).
l330: "(3.8)": What does this number refer to?
l375: "diatoms can also take up dissolved DOC and therefore a fraction of their biomass will be categorized as bacteria": This is very confusing. On l365 it is stated and Fig. 4 (right) indicates that diatoms are obligate autotrophs, i.e., do not use DOC. Table B1 also does not specify which parameters apply to which groups, so this should be clarified and/or the statements and Fig. 4 corrected regarding diatoms.
l379: "The copepod community is dominated by active copepods in higher latitudes (Fig. 13b) and by passive (ambushing) copepods in oligotrophic gyres": This is the opposite of what has been reported by Prowe et al. (2019). What differences between the two models could be responsible for this difference?
l382: "In the Equatorial Pacific though, passive copepods dominate, possibly because there small primary producers are more common ..., whose size is preferred by these copepods": This does not appear to make sense. Ambush feeding is effective only for motile prey, which is why ambush-feeding copepods are usually relatively large, carnivorous species with a preference for large prey.
l407: "In less seasonal environments, the absence of advection appears to result in too low production": Vertical mixing in oligotrophic regions is often driven by internal waves. Are these included in the 1D simulations?
l421: "generalists combine phototrophy (yellow lines) for carbon uptake with predation (red lines) for nitrogen": Why do they not just use the carbon contained in their prey?
Fig. 14: Please add labels (global, water column, chemostat) to the panels.
Fig. 15: axis label missing for the x-axes
Discussion:
l434: "Overall the NUM model is an intermediate-complexity model laboratory for ecological simulations that is accessible to marine ecologists without biogeochemical or physical oceanography background": Given the many deficiencies of the present model and the general lack of consensus about the formulation of the plankton-ecosystem components of ocean models, I find it inappropriate to advertise the use by people without the scientific training required for a meaningful employment of this kind of tool.
l449: "a deeper production maximum": This is most likely a model artefact (these have never been observed), resulting from the assumption of a fixed stoichiometry and Chl:C ratio. Models with variable Chl:C ratio generate deep chlorophyll maxima but these are not associated with production maxima.
l449: "the global simulation reproduces the deep maximum less accurately": In order to assess the accuracy of a model feature, it must be compared with observations, not other model configurations, but this is not done here.
l455: "This finding points to the importance of a better understanding of plankton’s ability to maintain a position in the photic zone despite vertical mixing": I don't think so. Mixing losses apply identically to other unicellular species as well. Much more likely it is a misrepresentation of the microbial loop.
l463: "The smallest diatoms are predominantly osmoheterotrophs (bacteria)": No, diatoms (of any size) are not bacteria.
l469: "We conjecture that the absence of large diatoms is due to mixing losses": See above comment for l455
l477: "the model produces global patterns of biomass, production, and surface nutrients reasonably": This statement is in stark contrast to what is shown in Figs. 8, 10, 11.
l514: "what mechanism provides diatoms a faster cell division rate than other phototrophic plankton": This has been linked to the energetic efficiency of a siliceous cell wall (Martin-Jézéquel et al., 2000: J. Phycol. 36)
Appendix B:
Please add equation numbers to the equations in the tables.
Appendix F:
Fig. F3: Please add labels in the panels and units to the colour bars. It could also be helpful to use a 2-column layout. Also, the numbers on the colour bars are nonsensical, indicating negative concentrations. There is only one white area (in panel b) and it is unclear why it is white and not green (as 0.01 should be according to the colour bar).