Review of the manuscript “Simultaneous versus sequential estimation of biogeochemical and physical parameters in coupled marine ecosystem models” by Kern et al. 

Summary: The study advertises automatized parameter optimization in coupled biogeochemical ocean modelling in a 1-dimensional framework. The authors highlight uncertainties in both, physical and biogeochemical model parameters. They obtain best results in fitting these parameters simultaneously when reproducing the mean seasonal cycle of biogeochemical observations at two observing stations (BATS and HOTS). 

Major Comments:

The study addresses important aspects in biogeochemical ocean modelling and all the work is greatly appreciated. The study is generally well written and organized. Still, I would suggest some clarifications and more discussion on the aspects outlined below in the specific comments. I am particularly puzzled about seemingly strong nutrient budget differences between the different parameter fits at station HOTS, which should be explained in more detail, and I am not 100% sure how sinking of organic matter is treated. Further, the manuscript might benefit from being more concise to enhance readability and attract a wider audience (e.g. it might not be necessary to start with the most general form in the “Optimization Methodology”  and all BATS subsections could be merged to avoid repetition (same for HOTS); some parts might well be moved to an Appendix).

Specific comments:

Ln 6: please add that a 1-dimensional model has been used

Ln 9: replace “observational data” by “the observed mean seasonal cycle” 

Ln 11: I find the word “prediction” misleading because the tuned models have not been tested for predicting independent data but the authors rather refer to the mean seasonal cycle used for parameter fitting. Better: “simultaneous estimation results in a closer fit to the observed seasonal cycle of biogeochemical tracers”

Introduction

Ln 21ff: How was the conclusion drawn that “sequential parameter tuning in coupled models may not produce accurate predictions”? My understanding so far was that in case the effects of certain parameters compensate it might well make sense to keep some of them on fixed predefined values  (cf. Matear, 1995, Löptien & Dietze, 2021). Could this apply here?

Ln 25: I suggest to reformulate. I don’t see that “the potential benefits” are “quantified” – especially in the context of the foregoing sentence - because there is no prediction or test on independent observational data. I would rather say that the goodness of fit of the different approaches is explored with respect to the mean seasonal cycle on two locations. 

Ln 26: Add 1-dimensional

Ln 35: Please add that this refers to the mean seasonal cycle.

Ln 42: replace “with the data from BATS and HOTS” by “with the observed mean seasonal cycle of selected biogeochemical tracers at BATS and HOTS”

Optimization Methodology

As I understood, the method depends on some random sampling of the parameters. Would a repetition lead to different results? 

Ln 66: Why not write right away which objective function has been used instead of providing a general formulation? (if needed you could refer to Kern et al. 2024 for the generalized form)

Ln 92: Could you be more specific? “… the initial search is truncated based on the available computational resources.“

Ln 96/97 Maybe mention already here how Nsamp and Ntop were chosen (or refer to page 19 which feels a bit repetitive)?

Ln 151: How were “the most sensitive BGC parameters” chosen? (refer to Section 5?)

Physical Scenarios

To me the title “Physical scenarios” is somewhat misleading because I (and maybe others) associate “scenarios” with climate change or management scenarios while this just refers to two different locations.

Ln 238: Again, I find “physical scenarios” somewhat misleading here. Better? “locations”

Ln 244: better replace “scenario”

Ln 247: better replace “these physical scenarios”

Ln 248: How was the model initialized? Why are sinking velocity and boundary control parameters included  as part of the physical model (as stated on page 15, ln 311)? Since the study investigates the separation of physical and biogeochemical parameter tuning, this point deserves attention. 

Bermuda Atlantic time-series (BATS)

Ln 261: I find “trend” misleading when referring to a seasonal cycle 

Ln 263: It would be nice to see some numbers here. 

Ln 264: I would appreciate a short description of the typical seasonal cycle. 

Ln 265: What is meant by “annual trend”? 

Ln 268: Has significance been tested? Otherwise please reword. It would be nice to see some number (e.g. % relative to the observed mean)

Ln 271: How was the model initialized and how come that the nutrient content in the water column is generally over-estimated (is this related to the bottom boundary relaxation?)? 

Ln 271: I believe “over-predicted” should be “overestimated“

Hawaii Ocean time-series (HOTS)

The nutrient budgets seem visually rather different. Is this related to bottom boundary relaxation? So, is this here defined to be related to the physical model or did I get this wrong? 

Ln 304: “increase the accuracy of the model” should rather be something like “enhance the fit to the mean seasonal cycle”.

Parameter Sensitivity Analysis

The authors might  consider to move this part to an Appendix (same for the Twin Experiments).

Ln 311: this did not become clear to me – has “sinking velocity” of organic matter been optimized as part of the physical model? What is the rationale behind this? I would particularly be interested in more details, because foregoing studies considered this parameter to be important (cf. Taucher & Oschlies, 2011 or Kriest & Oschlies, 2008)

Ln 318: How were the parameter ranges determined? 

Ln 332: How much do the base line parameters for BATS and HOTS differ?

Page 20 - Bermuda Atlantic Time Series

It might be nice to move this part to the first Bermuda Atlantic time-series (BATS)-Section. 

Ln 428: How do temperature and salinity profiles look like compared to the observations? 

Page 21 - Hawaii Ocean Time Series

Same here - it might be nice to move this part to the first section on HOTS. 

How much do the biogeochemical parameters for BATS and HOTS differ after optimization and what does this mean for global biogeochemical models? (cf. Schartau & Oschlies, 2003)

Ln 450: How do temperature and salinity profiles look like compared to the observations? 

Page 22 - Conclusions (& Discussion): 

The results of the presented study seem somewhat contradictory to earlier findings where it has been shown that biogeochemical model parameters can be tuned to compensate for ocean model differences - which can be problematic when it comes to projections (Löptien & Dietze, 2019; Pasquier et al. 2023). I would be very interested in some thoughts on this. Also, it has been stated early on that the multitude of poorly known biogeochemical model parameters might lead to overfitting (e.g. Matear, 1995). I fully understand that the study/model design and lack of observational data makes testing of the presented models on independent observations difficult  - still some discussion on overfitting and strategies for (future) model testing would be beneficial. Finally, it should be mentioned that the obtained results might well depend on parameter choice, location and objective function. It is particularly worth mentioning that even the physical model parameters were fitted on selected biogeochemical observations while temperature and salinity (as I understood it) were not considered.  

Ln 466: remove “scenario”

Ln 470: I find it confusing  to talk about “trends” when it comes to the seasonal cycle

References: 

Kern, S., McGuinn, M. E., Smith, K. M., Pinardi, N., Niemeyer, K. E., Lovenduski, N. S., & Hamlington, P. E. (2024). Computationally efficient parameter estimation for high-dimensional ocean biogeochemical models. Geoscientific Model Development Discussions, 2023, 1-34.

Kriest, I., & Oschlies, A. (2008). On the treatment of particulate organic matter sinking in large-scale models of marine biogeochemical cycles. Biogeosciences, 5(1), 55-72.

Löptien, U., & Dietze, H. (2017). Effects of parameter indeterminacy in pelagic biogeochemical modules of Earth System Models on projections into a warming future: The scale of the problem. Global Biogeochemical Cycles, 31(7), 1155-1172.

Löptien, U., & Dietze, H. (2019). Reciprocal bias compensation and ensuing uncertainties in model-based climate projections: pelagic biogeochemistry versus ocean mixing. Biogeosciences, 16(9), 1865-1881.

Matear, R. J. (1995). Parameter optimization and analysis of ecosystem models using simulated annealing: A case study at Station P.

Pasquier, B., Holzer, M., Chamberlain, M. A., Matear, R. J., Bindoff, N. L., & Primeau, F. W. (2023). Optimal parameters for the ocean's nutrient, carbon, and oxygen cycles compensate for circulation biases but replumb the biological pump. Biogeosciences, 20(14), 2985-3009.

Schartau, M., & Oschlies, A. (2003). Simultaneous data-based optimization of a 1D-ecosystem model at three locations in the North Atlantic: Part II—Standing stocks and nitrogen fluxes.

Taucher, J., & Oschlies, A. (2011). Can we predict the direction of marine primary production change under global warming?. Geophysical Research Letters, 38(2).

Review

This study investigates the optimisation of physical and biogeochemical parameters independently, sequentially, and simultaneously and concludes that the combined optimisation approach performs best. The topic is important and relevant, and the results could make a valuable contribution to the field. However, to strengthen the paper and make the conclusions more convincing, I suggest the following improvements.

Major Comments

1. Demonstrate simultaneous optimisation in the twin experiment

The paper’s central claim is that simultaneously optimising physical and biogeochemical parameters provides the best outcome. To clearly demonstrate this, I recommend expanding the twin experiment to explicitly include this combined optimisation case. Showing results in an idealised setting would help clarify both the advantages and potential challenges of the approach, thereby making the BATS and HOTS applications more robust and convincing.

2. Investigate parameter correlations and identifiability

A more thorough analysis of parameter correlations would significantly strengthen the paper. Earlier work (e.g. Matear 1995) showed that many biogeochemical model parameters are highly correlated and thus cannot be independently determined. Is this also the case for your BFM17 model? Figure 6 shows that two biogeochemical parameters are correlated and not uniquely determined. Related to point (1), simultaneously optimising physical and biogeochemical parameters may amplify these correlations. Quantifying and discussing these relationships would provide valuable insight into parameter uniqueness and the robustness of the optimisation results.

3. Address potential overfitting and define acceptable-fit criteria

For real observational data, the goal should not be a perfect fit to the data, as the model is an approximation of reality. The optimisation framework should therefore incorporate a notion of what constitutes an “acceptable” fit to the data. Overfitting could lead to unrealistic model behaviour when small perturbations occur (e.g., minor changes in mesoscale upwelling). Defining an appropriate tolerance level or misfit threshold would make the results more physically and statistically robust.

4. Clarify and evaluate the mesoscale upwelling parameterisation

The physical model uses an idealised parameterisation of mesoscale upwelling and downwelling. Please provide evidence, references, or justification for representing mesoscale variability in this way. It would also strengthen the paper to assess whether the optimised results are consistent with known or observed seasonal variations in mesoscale activity. This evaluation would help determine whether the model’s physical representation is realistic and whether the optimised parameters remain physically meaningful.

Specific Comments

Line 70: Please clarify what is considered an acceptable fit to the data. Does a normalised RMS error of 1 define this threshold?

Model constraints: Are any constraints applied to the model parameters beyond the prescribed range limits?

Cycle enforcement: Is an annual repeating cycle imposed on the simulated fields? If so, how is this implemented?

Line 115: It is unsurprising that the conjugate gradient approach fails here; stochastic methods such as simulated annealing are typically more robust in complex optimisation problems.

Line 155: Is the settling velocity depth-dependent? Please clarify.

Line 165: Add clarification that at both sites, the Ekman velocities are all negative.

Line 169: Do you have evidence or references supporting the chosen parameterisation of eddy vertical velocities?

Table 1: The September values are notably large—can you provide a physical explanation for this?

Line 235: What is the model time step used in the simulations?

Figure 6: If two parameters are highly correlated, why attempt to optimise both? Consider removing one and instead testing the 13th parameter previously identified as significant.

Line 370: Why not use twin experiments to directly compare independent, sequential, and simultaneous optimisation performance?

Table 4: What constitutes an acceptable fit (e.g., RMS = 1)? What would overfitting look like in this context?

Figure 7: Does the seasonal behaviour of W_e make physical sense? For example, does eddy activity exhibit seasonal variation? The minimum in September (Fig. 7c) coincides with a large value in Table 1—please comment. Similar behaviour appears in Fig. 8c; again, some discussion would be useful.

Reference

Matear, R.J. (1995).  Parameter optimization and analysis of ecosystem models using simulated annealing: A case study at Station P. Journal of Marine Research, 53, 571–607.