the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Sep 2026
Quantifying parameter-induced uncertainty and evaluating the effects of model simplification in a marine biogeochemical model
Abstract. Marine biogeochemical models are widely used to investigate plankton ecosystem dynamics and biogeochemical cycling. However, their increasing complexity makes large ensemble analyses of parameter-induced uncertainty computationally demanding. Model simplification can reduce computational cost, but it may also modify how parameter perturbations propagate through ecological and biogeochemical processes. This study examines whether model simplification affects not only mean-state behaviour, but also the magnitude and time-depth distribution of parameter-induced uncertainty. We used the one-dimensional vertical configuration of the Eco3M-MED-V1b model at the DYFAMED station in the northwestern Mediterranean Sea, and compared the full-complexity (FULL) version with two simplified versions: MOD1, designed to preserve the state variables, and MOD2, designed to preserve a set of key ecosystem indicators. A common 512-member Sobol low-discrepancy ensemble was generated by perturbing 30 parameters shared by the three model versions, allowing direct comparison under identical parameter perturbations. The results show that parameter-induced uncertainty in FULL is concentrated in ecologically important periods and depths, including the upper productive layer, near the nutricline, the deep chlorophyll maximum, and during the spring bloom and summer stratification. Model simplification did not systematically increase or decrease uncertainty; instead, its effects varied among variables, ecosystem indicators, periods and depths. MOD1 broadly preserved the main time–depth distribution of uncertainty in the state variables, whereas MOD2 generally preserved the uncertainty magnitude of most ecosystem indicators. However, similar uncertainty magnitudes in indicators integrated over the whole year or water column may mask local differences occurring during specific periods or within specific depth ranges. Diagnostics used to guide model evaluation or simplification should therefore be defined a priori according to the scientific question and intended application. Uncertainty analysis can also help identify complementary diagnostics.
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Status: open (until 03 Nov 2026)
- RC1: 'Comment on egusphere-2026-5134', Nabir Mamnun, 07 Oct 2026 reply
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RC2: 'Comment on egusphere-2026-5134', Anonymous Referee #2, 13 Oct 2026
reply
Review of the manuscript “Quantifying parameter-induced uncertainty and evaluating the effects of model simplification in a marine biogeochemical model” by Yutong Zhang et al.
General comment
The work provides the results of comparing effects of parameters variability on biogeochemical (BGC) models at different complexity levels, providing insights on the use of simplified models to generate parameter-based ensembles. Results are obtained using a 1-dimensional (1D) model simulating one year at the Mediterranean DYFAMED stations.
The manuscript is well written and, even if in 1D application, the results on the effects of the use of simplified models are relevant for the scientific community, as the computational cost of complex BGC models is a current issue for ensemble applications in 3-dimensional (3D) domains. In my opinion, the manuscript is worth to be published but some aspects need to be revised better clarifying the framework of “simplified models” and some minor issues has to be addressed.Major points
I see a single major aspect to be addressed in the manuscript: to clarify as much as possible the “simplified models” strategy adopted in this work.- The clarification on the simplification strategy should start from the introduction, where the authors could dedicate more space to possible strategies adopted for BGC model simplification. For instance, BGC models can be simplified by reducing the number of simulated processes, the number of variables, and also by resolving them at lower resolution.
- Having identified possible simplification strategies, it should be easier for the reader to identify the ones that are applied in the present work. These should be clearly stated in the introduction and specified in the materials and methods section referring to the possible strategies introduced in the introduction.
- If possible, it could be useful for the reader to have the differences of MOD1 and MOD2 with respect to FULL graphically illustrated in Fig. 1.
- The simplifications are described in section 2.1.2 referring to Zhang et al. (2026) and declaring that MOD1 is designed to preserve all the state variables while MOD to preserve selected model indicators. If the method by Zhang et al. (2026) quantifies the effectiveness of MOD1 and MOD2 in preserving variables and state indicators, this information should be provided here to the reader (before discussing the parameter-induced variability). To have a better framework for the later results in the manuscript, it could be relevant to have an indication on how much MOD1, MOD2 and FULL agree when using the reference parameters or the same parameters (supplementary materials S4 could be informative on this).
Knowing the fidelity degree of MOD1 and MOD2 in reproducing FULL, would help in understanding how much the differences emerging when applying parameter-induced variability are related to intrinsic model differences. - The discussion could also address the theme of simplification choices made in this work with respect to other potential strategies. It would be also relevant to stress even more that results on parameter-induced variability are strongly dependent on the simplification strategy as well as on the BGC processes of the studied area (open-sea or coastal processes dominated regions, eutrophic or oligotrophic regimes).
- A minor aspect related to the simplifications concerns the number of parameters. In the present work, 30 parameters – the ones common to the three models – are varied to generate the simulation ensembles. How many parameters are removed in MOD1 and MOD2 with respect to FULL? Among the removed parameters in MOD1 and MOD2, are there some common ones (removed both in MOD1 and MOD2)? Declaring the number of removed parameters could offer the authors the possibility to discuss a potential compensation effect: less parameters in MOD1 and MOD2 have to represent the dynamic of FULL, which is based on a larger number of parameters, implying that the reduced number of parameters in the simplified models should account for some missing parameter or process. This could also allow to discuss that a larger impact of the variability of the parameters on the ensemble spread in the simplified models could be related to the larger information that is contained in the parameters of the simplified models (as the parameters could potentially compensating for the missing ones).
Minor points
There are some minor corrections that, in my opinion, would help to improve the manuscript clarity and readability:- If feasible, I suggest to enlarge the font size in figures. Figure labelling is relatively small and could be difficult to read.
- A couple of sentences seem a bit generic or not necessary and can be removed or better specified:
L 20 “specially when coupled with atmosphere and ocean circulation models”. In general, the first sentence of the Introduction can be modified to highlight that marine BGC models are used in a number of 3D applications, while, in my opinion, the fact that they are used to study marine ecosystem, plankton food web dynamics and biogeochemical cycles is quite an implicit description of BGC models.
L 37-38 The lower computational costs of simplified BGC models is somehow assured by the simplification itself. The authors could introduce previous papers on simplified BGC models more in a cost-benefit framework. Assuming that having reduced the computational costs had impacts on the model fidelity, have previous works demonstrated that loss on fidelity and lower computational costs can be efficiently balanced? - L 80 PFT is already defined at L 29.
- L 99 As the manuscript is totally focused on 1D applications, consider moving the information on potential computational-cost reduction in 3D applications to the discussion.
- In Table 1 the main changes due to simplification are presented as potential changes, as the effects are frequently introduced by “can”. I would expect that the impact of simplification on MOD1 and MOD2 fidelity are already quantified or verified (see also Major point above).
- Section 2.3 (L 120-123) The first part of the section could be shortened as the definition of the approach is previously defined.
- Section 2.3 (L 124-126) The description of the simulation settings should be more specific, in particular on the definition of forcings, initial and boundary conditions. For instance, are the forcings representative of a specific year (I suppose 2003)? Boundary and initial conditions are obtained from observations, models, literature values? These details are needed to assure the reproducibility of the results and, if not specified in the manuscript, can be provided as a reference to a previous published paper that use the same settings.
Partially related to this, I suggest to state in the Introduction that simulations are applied at the DYFAMED station in the Mediterranean Sea. This would give the reader a more focused context and better introduce the comparison with DYFAMED observations. Indeed, the comparison with DYFAMED observations is described in Section 2.2, before Section 2.3 where it is mentioned for the first time (apart the abstract) that the 1D model configuration is aimed at simulating DYFAMED conditions. - L 128 “(n=30)” It is maybe unnecessary to use this mathematical terminology, since “n” is not used later in the manuscript. The number of parameters can be defined directly in the sentence “to a subset of 30 parameters”. The same approach can be used for the number of WC, MC and UC parameters: “11 well-constrained (WC), 15 moderately-constrained, and 4 uncertain (UC) as defined in Zhang et al. (2026).
Avoiding unnecessary mathematical terms can help the manuscript readability. - L 144 Similarly to the previous point, “(κi)” could be probably removed, as its meaning and use is self-consistently defined in appendix A4.
- Consider removing “using Sobol sequence” in the title of section 2.3.2, to keep the title short while not repeating the type of approach that it is already well mentioned and described in the main text.
- L 169 The symbol m ̂ for the reference simulation is already mentioned at L 129.
- Eq 4 To highlight the meaning of φ(log_10〖∆^S)〗, it can be written as log_10〖〖(∆〗^S/∆^FULL)〗.
- Before describing the results, it would be useful to have a synthetic description of the main seasonal processes typical of the DYFAMED area (sequence of mixing and stratification that causes surface blooms and deep chlorophyll maximum) or, more generally, of the Mediterranean Sea. This would help the reader that is not familiar with seasonal BGC dynamics in Mediterranean in the interpretation of the results. The description of DYFAMED/Mediterranean BGC processes can be inserted in the introduction or before presenting results and can refer to previous published works to keep it relatively short.
- Section 3.1.2 In the comparison with the observations, it is often discussed if the observations are within or close to the model ensemble envelop. Even if in this case the comparison with the observations is not meant to be a validation of the model and the aim is not to design a model that is closest as possible to the observations, I suggest describing the results the other way round. For instance, “the ensemble envelop is close/contains the model observations. This would more in line with the usual approach of evaluating how much a model is close to the observations (and not the opposite).
- In the caption of Fig. 3, how the ranges to define the observation uncertainty envelope (3% and 15%) were chosen? Do they refer to typical observation errors?
- Throughout the manuscript, terms like “upper layer” are used. Sometimes it would be better to use depths (e.g., 0-30 m) to define the extension of the layers, helping a non-familiar reader to locate the described results.
- L 290 The use of “biological variables” sounds a little weird to me, I would be more familiar with “living-compartment variables”.
- In the caption of Table 6, it would be helpful to mention also here that the relative differences are expressed as %.
- L 345 The first sentence of the discussion seems to present generalized results. I think that it would be useful to stress at the beginning of the discussion that the results are strongly linked to the model, settings and simplification strategies adopted in the present work.
- The title of section 4.3 anticipates the result, and I suggest to make it more concise and general.
- In section 4.3 it is mentioned that the use of indicators can mask the differences due to simplification, and my impression is that this is described uniquely as an issue. However, it could be also considered as a benefit in terms of simplified model fidelity when focusing on indicators that do not need to be investigated on relatively detailed temporal or spatial scales.
- In my opinion, section 4.4 is a bit out of context, as implications on surrogate models are not central in the present work. I suggest removing it or limiting the discussion on implications for surrogate models to a few sentences.
- I suggest mentioning also in the Conclusions that the results have been obtained with model settings representing DYFAMED station in the Mediterranean Sea.
Citation: https://doi.org/10.5194/egusphere-2026-5134-RC2
Model code and software
Eco3M-MED model source code Melika Baklouti https://github.com/Eco3M/Eco3M
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- 1
This study examines if reducing a marine biogeochemical model changes not only the mean state but also the magnitude and the time–depth distribution of parameter-induced uncertainty. The authors use a 512-member Sobol parameter ensemble for the Eco3M-MED-V1b model and for two reduced versions, in a 1DV configuration at DYFAMED. The question is useful, because reduced models are cheaper options for ensemble simulations and uncertainty quantification. The manuscript is well written and the figures are clear and detailed.
S1 gives not much more information than Section 2.1.1 (Description of Eco3M-MED-V1b model). I think the authors can move S1 into the main text. However, what missing here is model setup documentation. I suggest to add a description of the physics, the initial and boundary conditions, the grid and the time step (in the Supplement is also fine).
Each run covers two years with the same annual forcing, and the first year is removed as spin-up. After only one year of spin-up, the deep water probably still reflects the initial conditions, which are similar for all members. So the small spread in the deep layers and in oxygen may be due to the short spin-up run and perhaps not to low parameter sensitivity. This could affect the results for the deep layers, oxygen and deep carbon export. I suggest to add a short discussion on how the short spin-up and the initial conditions may affect these results.
The 30 perturbed parameters are a subset of the parameters “shared” by all three versions. The authors explain well how these parameters are grouped by confidence level (well-constrained, moderately-constrained and uncertain) and how their ranges are defined. But, they do not explain why these 30 parameters were chosen and not the other “shared” parameters. For example, were they selected based on a sensitivity analysis, on expert knowledge, or on some other criterion? It would also help to give the total number of parameters in each version (FULL, MOD1 and MOD2), and how many of them are “shared”. In addition, Table 1 lists the processes removed in MOD1 and MOD2, but not the parameters that belong to these processes. A list of these parameters could be useful for readers, perhaps in the Supplement.
The parameters of the removed processes are kept fixed in FULL. So the experiment shows how the uncertainty of the “shared” parameters propagates through each version, not the full parameter uncertainty of FULL. The authors mention this in the discussion, but the abstract and conclusions say that the simplified versions "broadly" or "generally preserved" the uncertainty of FULL, which reads more general. The FULL uncertainty for oxygen and export may be underestimated, because the processes that are removed in the simplified versions (for example nitrification and the faecal-pellet pathway) are directly related to oxygen and export. I suggest to make this limitation clear in the abstract and conclusions, and to discuss how it may affect the oxygen and export results. I think it would be worth to run one additional FULL ensemble that also perturbs all parameters. This is optional, but it would show how much of the FULL uncertainty is lost when switching to a reduced model.
It is not clear if the parameters of MOD1 and MOD2 were retuned after the reduction. If not, the median shifts (for example in carbon export and bacterial production) may be partly because of that. Speaking of this, I am also curious whether the authors tuned the parameter values for DYFAMED.
The annual bacterial production seems to be about five times higher than the primary production (Fig. 6 and Fig. S4). Could the authors explain why bacterial production is do high compare to primary production? I suggest also adding a discussion of how bacterial production is defined and why it is much higher than primary production.
I was struggling to find a clear answer to question (iii) in the manuscript, about how the uncertainty propagates towards higher trophic levels. The discussion only says that the results "suggest a possible propagation". I think the current analysis presented in the manuscript can not well answer the questions. However, I think the study is already solid and gives useful results even without question (iii), so I suggest to remove it.
The main recommendation of the study is that the diagnostics "should be defined a priori". I agree, but it is too general. It was already the starting point of the objective-specific framework in Zhang et al. (2026). So what is new here compared to that study? Also, the next sentence says that uncertainty analysis can also help to identify complementary diagnostics (a posteriori). Is this not in contradiction with the first sentence? Could the authors explain what they mean here?
The simplified versions save about 15–23% of the computational time (L98–99). So, with the same cost of a 512-member FULL ensemble, one can run about 670 MOD2 members. The computational cost is one of the main motivations of the study, so I am curious if this saving is really important in practice. Could the authors explain for which applications (for example 3D simulations) this saving can make a real difference?
Fig. 5: The colour ranges are not the same between the rows, so it is hard to compare the panels, and some of the colours are also saturated. I think using the same colour range would show the differences better.