Argon Saturation in a Suite of Coupled General Ocean Circulation Biogeochemical Models off Mauretania

Dietze, Heiner; Löptien, Ulrike

doi:https://doi.org/10.5194/egusphere-2024-918

Preprints

https://doi.org/10.5194/egusphere-2024-918

Preprints

03 May 2024

| 03 May 2024

Argon Saturation in a Suite of Coupled General Ocean Circulation Biogeochemical Models off Mauretania

Heiner Dietze and Ulrike Löptien

Abstract. Numerical coupled ocean circulation biogeochemical modules are routinely employed in Earth System Models that provide projections into our warming future to the Intergovernmental Panel on Climate Change (IPCC). Previous studies have shown that a major source of uncertainties in the biogeochemical ocean component is the yet unacquainted vertical, or rather diapycnal, ocean mixing. The representation of diapycnal mixing in models is effected by several factors, among them are the (poorly constrained) parameter choices of the background diffusivity, the choice of the underlying advection numerics and the spatial discretization. This study adds to the discussion by exploring these effects in a suite of regional coupled ocean circulation biogeochemical model configurations. The configurations comprise the Atlantic Ocean off Mauretania – a region renown for its complex ocean circulation driven by seasonal wind patterns, coastal upwelling and peculiar mode water eddies featuring toxically low levels of dissolved oxygen. By exploiting simulated argon saturation as a proxy for effective mixing we show that the resolution effect beyond mesoscale on diapycnal mixing is comparable to other infamous spurious effects, such as the choice of advection numerics or a change of the background diffusivity within 20–40 %.

Received: 27 Mar 2024 – Discussion started: 03 May 2024

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

Download & links

Preprint (PDF, 7929 KB)

Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
Preprint (7929 KB)

Download & links

The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

Journal article(s) based on this preprint

05 Mar 2025

Mixing, spatial resolution and argon saturation in a suite of coupled general ocean circulation biogeochemical models off Mauritania

Heiner Dietze and Ulrike Löptien

Biogeosciences, 22, 1215–1236, https://doi.org/10.5194/bg-22-1215-2025,https://doi.org/10.5194/bg-22-1215-2025, 2025

Short summary

Heiner Dietze and Ulrike Löptien

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-918', Anonymous Referee #1, 06 May 2024

Review of Dietze and Löptien’s “Argon Saturation in a Suite of Coupled General Ocean Circulation Biogeochemical Models off Mauretania” (manuscript #: 2024-918)

General comments:

The authors of this manuscript examine the model-simulated inaccuracies in diapycnal mixing that cannot be explained by the horizontal resolution near Mauretania and find that it’s comparable to advection numerics and choices of background diffusivity by making use of argon saturation as a proxy for effective mixing. I can appreciate how much time and effort that went into this work but I have some reservations about publishing this manuscript as is. One concern that I have is that there is no comparison of the effective diapycnal mixing with other methods, like that of Holmes et al. (2021) or potentially separating out the spurious contribution to compare with a method like that developed in Ilıcak (2016)'s "Quantifying spatial distribution of spurious mixing in ocean models”. I understand the authors just want to have a relative measure to rank their model configurations with their effective mixing against one another but without knowing whether their method is properly quantifying the effective mixing, the ranking could be misleading. For example, the authors include the mixed layer in their calculations of the effective mixing, despite how there are known confounding effects on the effective mixing. The second issue is that the authors try to connect Ekman pumping/suction to effective diapycnal mixing without explaining the relationship between the diapycnal advection and diapycnal mixing in the Ekman layer. The third issue is that the model spin-up time may suffice for many applications of model experiments, but they are investigating a signal that is so small that the rate at which their model diagnostics are changing at the time they are evaluating them may be relevant to the significance of the small differences they’re finding. I suggest major revisions. Specific comments are listed below:

Specific comments:

Line 3: The authors say “unacquainted vertical” by which they are referring to “diapycnal” but that way of describing diapycnal sounds more literary than it sounds like it has specificity; did the authors use AI to help them write this abstract?

Lines 38-39: The canonical reference for uncertainties in representation of diapycnal mixing (not just vertical) is MacKinnon et al. (2017)’s “Climate Process Team on Internal-Wave Driven Ocean Mixing” even though there’s also shear-driven and other mixing

Line 45: This seems like more “coupled” reasoning than circular because the biogeochemical modules can potentially be developed to be more realistic without developing the diapycnal diffusivity modules, but of course the biogeochemical variables depend upon the diapycnal diffusivities. It’s difficult to point to new model innovations in ESMs that don’t have this coupling problem. Your argument seems analogous to saying that assimilating sea-ice concentrations with the goal of improving the sea surface properties is circular reasoning because our sea-ice modules are imperfect. In any case, without improvements in the biogeochemical modules, the information propagated by the assimilation of biogeochemical variables may not inform the diapycnal diffusivities as much as the biogeochemical parameters themselves, which is the problem you’re pointing out. This would certainly be the case with the Green’s function-based approach of ECCO-Darwin (see Carroll et al. (2020)’s “The ECCO-Darwin Data-assimilative Global Ocean Biogeochemistry Model: Estimates of Seasonal to Multi-decadal Surface Ocean pCO2 and Air-sea CO2 Flux”) because the physical variables aren’t changed in their formulation; only the biogeochemical parameters are altered. I believe the proposal by Trossman et al. (2022) is that the ECCO-Darwin and ECCO setups could be used in an iterative process to incrementally improve the biogeochemical parameters and the physical parameters, respectively, but this is even more computationally expensive than the current process and may require a different process for sequential data assimilation systems, which they present unique issues with in their appendix. Additional evidence that this could work comes from Skakala et al. (2022)’s “The impact of ocean biogeochemistry on physics and its consequences for modelling shelf seas,” where it was shown that assimilation of a suite of biogeochemical variables had an impact on the diapycnal diffusivities beyond that of physical variables.

Lines 63-64: Will this always be the case? The atmospheric community seems to have come up with a solution to advection numerics in McGraw et al. (2024)’s “Preserving Tracer Correlations in Moment‐Based Atmospheric Transport Models”. Also, is it possible that spurious diapycnal mixing is the result of spurious vertical advection sometimes? This certainly happens when you perform sequential assimilation (see: Pilo et al. (2018)’s “Impact of data assimilation on vertical velocities in an eddy resolving ocean model”).

Lines 81-82: Isn’t there also the effect of surface disequilibrium at the time of water mass formation (e.g., when subduction occurs) that needs to be accounted for? Both the nonlinearity of solubility in the presence of mixing and surface disequilibrium effect cause apparent oxygen utilization to be different from true oxygen utilization, for example. So the argon tracer needs to be injected below the mixed layer such that it doesn’t get obducted throughout the experiment. Also, argon can’t be injected into the ocean to derive diapycnal diffusivities from observations (unless the background levels are well-known) because there are significant background levels of argon in the ocean, which will eventually render it another exotic tracer on top of the ones Ledwell used. I mention this because it was noted that argon could be used as a proxy for effective diapycnal mixing in both models and observations in the text.

Line 150: I understand not wanting to compete with Jason Momoa in Google searches by dubbing your model’s acronym MOMOA, but you’re going to compete with the Museum of Modern Art in New York City instead. In any case, the model and its tracer conservation properties won’t be as much of a problem as they would be if the authors chose another model like HYCOM. And the model domain is reasonable, considering problems with boundary conditions that can occur.

Line 169: You say that there are 55 geopotential levels in all model configurations here but in Table 1, it says there are 72 grid points in an undefined dimension. The caption of Table 1 only mentions zonal and meridional directions but there is a third dimension listed for the number of grid points. Is that dimension time or is one of your instances of vertical dimensions inaccurate (i.e., in Table 1 or on Line 169)?

Line 186: For future equilibrations of biogeochemical variables, you could consider using anther method like the one by Khatiwala (2024)’s “Efficient spin-up of Earth System Models using sequence acceleration”

Line 189: I would argue that use of COREv2 forcing is no longer considered standard, as JRA55-do has supplanted COREv2 in OMIP2 and ERA5 is also commonly used

Lines 201-203: If you’re interested in the evolution of each of the model configurations, then you should be assessing metrics that are related to the time rate of change, not averages

Lines 205-206: One year of spin-up is common amongst published high-resolution model simulations (based on the global kinetic energy metric you seem to be using) because the initial shock is essentially adjusted away but the model’s climatological state is still being approached asymptotically. That would need at least several more years to achieve. It may take much longer to equilibrate potential energy, which includes available potential energy relevant to the eddying circulation, but to first order using kinetic energy may be good enough.

Table 2: Continuing on from my previous comments, please include the time rate of change (linear slope of a regression against time, for example) of the Delta Ar[%] metric you include the average of in this table. That would help the reader see whether these values are close enough to what they would be in a more well-spun-up state. Also, why are you including the mixed layer in your calculations when Argon is not a conservative tracer near the sea surface and diapycnal mixing is not very meaningful within a bulk mixed layer? Are you not using a bulk mixed layer?

Lines 234-236: Again, because penetrating solar radiation, bubble entrainment, and possibly other processes affect Delta Ar[%], why are you including the mixed layer in your calculations?

Lines 266-268: This is qualitatively accurate. However, it can be noted that there are in-situ estimates of eddy kinetic energy compared with high-resolution model simulations in the literature, like those presented in Luecke et al. (2020)’s “Statistical Comparisons of Temperature Variance and Kinetic Energy in Global Ocean Models and Observations: Results From Mesoscale to Internal Wave Frequencies”. Also, along-track SWOT data resolves the higher wavenumbers and there are preliminary results that much more of the spectrum is resolved with SWOT. I’m not suggesting that you perform a comparison with in-situ (e.g., moored) or SWOT data. This is just something to be aware of.

Figure 3: It’s curious that the relatively warm SST feature near 18W, 21N in the High configuration is completely absent in Coarse, except for what seems like a separate merging feature near the upper part of the domain plotted here. The rest of the figure comparison looks like the High configuration’s SST was coarse-grained.

Table 3 and Figure 6: Okay, the higher the resolution, the greater the Ekman pumping/suction there is in its mean and variability, but how come you’re spending time on this when you’re not relating it to the effective diapycnal mixing? You’re relating how resolving the wind stress curl and upper-ocean features to diapycnal fluxes of tracer properties within the Ekman layer, which has more to do with advection. It’s possible, however, that, by conversation of volume in your model, diapycnal mixing will counter advective diapycnal fluxes but you are not showing this.

Lines 313-319: The differences in domain-averaged Delta Ar[%] amounting to <0.1% with the same back diffusivities (equivalent to increasing the background diffusivity from 20% to 40%) may not be significant/detectable here once you consider the rate at which Delta Ar[%] and/or global kinetic energy is changing as the simulations are spinning-up. It appears that in Figure 7d that the seasonal variability and trend in (Delta?) Ar[%] may be larger than the difference across High and Coarse. So it’s unclear whether the comparisons you make with the comparable effect of varying the background diffusivity and/or numerical advection scheme will hold up if your model was spun up more. A decrease in Delta Ar[%] from using a background diffusivity of 0.14 cm^2 s^-1 to 0.16 cm^2 s^-1 suggests varying rates of spin-up across different background diffusivities, for instance.

Minor corrections:
Line 4: “effected” should be “affected”
Lines 43 and 668: Trossmann should be Trossman
Line 209: “… effects associated to our…” should be “… effects associated with our…”
Line 233: “… that would allows for…” should be “… that would allow for…”
Line 261: “… starts to contributes to…” should be “… starts to contribute to…”
Line 295: “looses” should be “loses”
Line 419: Steven Griffith should be Stephen Griffies, I believe; Eric Galbreith should be Eric Galbraith

Citation: https://doi.org/10.5194/egusphere-2024-918-RC1
- AC1: 'Reply on RC1', Heiner Dietze, 16 Jun 2024
  
  We are really grateful for the reviewer's time and effort and very helpful comments. Please find our comprehensive point-by-point response in the supplement .
  
  Citation: https://doi.org/10.5194/egusphere-2024-918-AC1
RC2:
'Comment on egusphere-2024-918', Anonymous Referee #2, 14 Oct 2024
Review of “Argon Saturation in a Suite of Coupled General Ocean Circulation
Biogeochemical Models off Mauretania” by Dietze and Löptien

Summary:
The main finding of this paper is that diapycnal mixing, a key source of uncertainty in ocean models, is strongly influenced by factors such as model resolution, advection schemes, and background diffusivity. Using Argon saturation as a proxy, the study shows that the effect of differences in resolution is comparable to that of other factors. This study highlights the ongoing challenge of accurately representing ocean mixing in models used for climate projections. I found this manuscript concise and well-written. However, some clarifications in methods and a few minor corrections are needed before publication. I suggest minor revisions. Please see the general comments and specific comments below.

General comments:
Consider changing the title to highlight the key findings or purpose of this study. The current title is concise, but it could be refined for better focus and impact.

While the rationale for using a 3-year simulation period is clear in terms of model spin-up and avoiding equilibrium, I have concerns about the potential influence of spurious effects from the closed boundaries on the region of interest. Could the authors provide diagnostics or an analysis that evaluates how far spurious effects, such as reflected waves or boundary-induced disturbances, propagate into the domain over the 3-year period? This would help confirm whether the region of interest remains unaffected.

Detailed comments:
Line 134: What is the horizontal resolution of MOMSO? Is it 50 km as shown in Fig. 1?

Line 165: “resolutions” should be “resolution.”

Line 169: I have a question regarding the vertical grid description in line 169, where it is mentioned that the model uses 55 vertical levels but 72 vertical grid points in Table 1. Could you kindly clarify this aspect? Is the difference in grid points due to the use of staggered grids, boundary conditions, or another feature of the model's vertical discretization? If there is a specific reason for this configuration, I would appreciate further details as a reader.

Figure 1 caption: Panel (c) and panel (d) don’t show vertical resolution, right? Am I missing anything?

Line 188: I believe “affect” would be better than “effect” here.

Line 225: It seems to me that equation (1) is incorrect. Since delta_Ar = Ar - Ar_sat, why do we need to subtract 100% in this equation? This might be a typo, but if not, please check the calculations presented in this study. Or am I missing anything?

Line 229: Could the authors elaborate on why mixing always causes an increase in saturation? Wouldn't the sign of the change in saturation depend on the temperature before and after mixing, given that Argon saturation is a non-linear function of temperature?

Line 229: There is a typo. Change “his” to “is.”

Line 233: “Allows” should be “allow.”

Line 266: There is an extra parenthesis.

Line 295: “loses” should replace “looses.”
Citation: https://doi.org/10.5194/egusphere-2024-918-RC2
- AC2: 'Reply on RC2', Heiner Dietze, 28 Oct 2024
  
  We would like to thank the reviewer for the encouragement and constructive comments. A detailed point-to-point response is provided below (the reviewer comments are displayed in bold, followed by our answers in italics).
  Summary:
  
  The main finding of this paper is that diapycnal mixing, a key source of uncertainty in ocean models, is strongly influenced by factors such as model resolution, advection schemes, and background diffusivity. Using Argon saturation as a proxy, the study shows that the effect of differences in resolution is comparable to that of other factors. This study highlights the ongoing challenge of accurately representing ocean mixing in models used for climate projections. I found this manuscript concise and well-written. However, some clarifications in methods and a few minor corrections are needed before publication. I suggest minor revisions. Please see the general comments and specific comments below.
  
  General comments:
  
  1. Consider changing the title to highlight the key findings or purpose of this study. The current title is concise, but it could be refined for better focus and impact.
  Thank you! We will change the title to: “Mixing, Spatial Resolution and Argon Saturation in a Suite of Coupled General Ocean Circulation Biogeochemical Model Configurations off Mauretania.”
  
  2. While the rationale for using a 3-year simulation period is clear in terms of model spin-up and avoiding equilibrium, I have concerns about the potential influence of spurious effects from the closed boundaries on the region of interest. Could the authors provide diagnostics or an analysis that evaluates how far spurious effects, such as reflected waves or boundary-induced disturbances, propagate into the domain over the 3-year period? This would help confirm whether the region of interest remains unaffected.
  The reviewer is right in pointing out that regional model configurations are inevitably affected by the choice of the spatial boundary conditions and that some discussion is needed as to what extend this may affect our results. This is especially true for the northern and southern boundaries of our configuration, where in reality the adjacent subpolar gyre and equatorial ocean are affecting water mass transformations that we do not account for in our setup.
  In response to the reviewer's concern, we will put the results of an additional model experiment in which we estimate the time elapsed since a water parcel was in contact with the boundaries into the revised version of the manuscript. Figure 1 (added as a supplement to this reply) shows preliminary results of such a model experiment with such a specific, modified age tracer (or artificial clock). The respective model simulation was integrated for 30 years. The artificial clock counts the time since starting the model simulation everywhere in the model domain, except for at the northern, southern and western model boundaries where it is continuously reset to 0. The red contour line encircles that area where water parcels below the thermocline have, on average, not been in contact with the boundaries for more than three years. We conclude that the high-resolution region of our interest is rather undisturbed by coditions at the boundaries – even at the end of a three-year run.
  Detailed comments:
  
  1. Line 134: What is the horizontal resolution of MOMSO? Is it 50 km as shown in Fig. 1?
  MOMSO has a resolution of less than 11km (https://gmd.copernicus.org/articles/13/71/2020/). The highest-resolution version of MOMA has a resolution of 1.5km in the high-resolution model domain (Table 1). We will make this more clear in the revised version of the manuscript.
  2. Line 165: “resolutions” should be “resolution.”
  
  Yes, thank you!
  3. Line 169: I have a question regarding the vertical grid description in line 169, where it is mentioned that the model uses 55 vertical levels but 72 vertical grid points in Table 1. Could you kindly clarify this aspect? Is the difference in grid points due to the use of staggered grids, boundary conditions, or another feature of the model's vertical discretization? If there is a specific reason for this configuration, I would appreciate further details as a reader.
  Sorry. Ln. 169 is wrong. There are 72 vertical levels.
  4. Figure 1 caption: Panel (c) and panel (d) don’t show vertical resolution, right? Am I missing anything?
  You are correct. We will adjust the wording without using the confusing “respectively” construct.
  5. Line 188: I believe “affect” would be better than “effect” here.
  Thank you. We will replace “effect” with “drive”.
  6. Line 225: It seems to me that equation (1) is incorrect. Since delta_Ar = Ar - Ar_sat, why do we need to subtract 100% in this equation? This might be a typo, but if not, please check the calculations presented in this study. Or am I missing anything?
  No, you are right! This is a typo. Thank you! Equation (1) defining the Argon oversaturation in units percent should read: \Delta Ar = 100\% \times (\frac{Ar}{Ar_{sat}} \times 100\% - 1), i.e. the little delta should be replaced by Ar.
  7. Line 229: Could the authors elaborate on why mixing always causes an increase in saturation? Wouldn't the sign of the change in saturation depend on the temperature before and after mixing, given that Argon saturation is a non-linear function of temperature?
  
  Thank you, this makes sense. We will add an elaborated explanation in the revised version of the manuscript. Something along the lines: A mixed water-parcel will always carry a higher argon saturation than the arithmetic mean of the original parcels since the saturation curves are convex over the entire range of oceanic temperatures (and salinities).
  8. Line 229: There is a typo. Change “his” to “is.”
  
  9. Line 233: “Allows” should be “allow.”
  
  10. Line 266: There is an extra parenthesis.
  
  11. Line 295: “loses” should replace “looses.”
  
  Thank you. We will fix 8., 9., 10., 11. as suggested.
  
  Citation: https://doi.org/10.5194/egusphere-2024-918-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-918', Anonymous Referee #1, 06 May 2024

Review of Dietze and Löptien’s “Argon Saturation in a Suite of Coupled General Ocean Circulation Biogeochemical Models off Mauretania” (manuscript #: 2024-918)

General comments:

The authors of this manuscript examine the model-simulated inaccuracies in diapycnal mixing that cannot be explained by the horizontal resolution near Mauretania and find that it’s comparable to advection numerics and choices of background diffusivity by making use of argon saturation as a proxy for effective mixing. I can appreciate how much time and effort that went into this work but I have some reservations about publishing this manuscript as is. One concern that I have is that there is no comparison of the effective diapycnal mixing with other methods, like that of Holmes et al. (2021) or potentially separating out the spurious contribution to compare with a method like that developed in Ilıcak (2016)'s "Quantifying spatial distribution of spurious mixing in ocean models”. I understand the authors just want to have a relative measure to rank their model configurations with their effective mixing against one another but without knowing whether their method is properly quantifying the effective mixing, the ranking could be misleading. For example, the authors include the mixed layer in their calculations of the effective mixing, despite how there are known confounding effects on the effective mixing. The second issue is that the authors try to connect Ekman pumping/suction to effective diapycnal mixing without explaining the relationship between the diapycnal advection and diapycnal mixing in the Ekman layer. The third issue is that the model spin-up time may suffice for many applications of model experiments, but they are investigating a signal that is so small that the rate at which their model diagnostics are changing at the time they are evaluating them may be relevant to the significance of the small differences they’re finding. I suggest major revisions. Specific comments are listed below:

Specific comments:

Line 3: The authors say “unacquainted vertical” by which they are referring to “diapycnal” but that way of describing diapycnal sounds more literary than it sounds like it has specificity; did the authors use AI to help them write this abstract?

Lines 38-39: The canonical reference for uncertainties in representation of diapycnal mixing (not just vertical) is MacKinnon et al. (2017)’s “Climate Process Team on Internal-Wave Driven Ocean Mixing” even though there’s also shear-driven and other mixing

Line 45: This seems like more “coupled” reasoning than circular because the biogeochemical modules can potentially be developed to be more realistic without developing the diapycnal diffusivity modules, but of course the biogeochemical variables depend upon the diapycnal diffusivities. It’s difficult to point to new model innovations in ESMs that don’t have this coupling problem. Your argument seems analogous to saying that assimilating sea-ice concentrations with the goal of improving the sea surface properties is circular reasoning because our sea-ice modules are imperfect. In any case, without improvements in the biogeochemical modules, the information propagated by the assimilation of biogeochemical variables may not inform the diapycnal diffusivities as much as the biogeochemical parameters themselves, which is the problem you’re pointing out. This would certainly be the case with the Green’s function-based approach of ECCO-Darwin (see Carroll et al. (2020)’s “The ECCO-Darwin Data-assimilative Global Ocean Biogeochemistry Model: Estimates of Seasonal to Multi-decadal Surface Ocean pCO2 and Air-sea CO2 Flux”) because the physical variables aren’t changed in their formulation; only the biogeochemical parameters are altered. I believe the proposal by Trossman et al. (2022) is that the ECCO-Darwin and ECCO setups could be used in an iterative process to incrementally improve the biogeochemical parameters and the physical parameters, respectively, but this is even more computationally expensive than the current process and may require a different process for sequential data assimilation systems, which they present unique issues with in their appendix. Additional evidence that this could work comes from Skakala et al. (2022)’s “The impact of ocean biogeochemistry on physics and its consequences for modelling shelf seas,” where it was shown that assimilation of a suite of biogeochemical variables had an impact on the diapycnal diffusivities beyond that of physical variables.

Lines 63-64: Will this always be the case? The atmospheric community seems to have come up with a solution to advection numerics in McGraw et al. (2024)’s “Preserving Tracer Correlations in Moment‐Based Atmospheric Transport Models”. Also, is it possible that spurious diapycnal mixing is the result of spurious vertical advection sometimes? This certainly happens when you perform sequential assimilation (see: Pilo et al. (2018)’s “Impact of data assimilation on vertical velocities in an eddy resolving ocean model”).

Lines 81-82: Isn’t there also the effect of surface disequilibrium at the time of water mass formation (e.g., when subduction occurs) that needs to be accounted for? Both the nonlinearity of solubility in the presence of mixing and surface disequilibrium effect cause apparent oxygen utilization to be different from true oxygen utilization, for example. So the argon tracer needs to be injected below the mixed layer such that it doesn’t get obducted throughout the experiment. Also, argon can’t be injected into the ocean to derive diapycnal diffusivities from observations (unless the background levels are well-known) because there are significant background levels of argon in the ocean, which will eventually render it another exotic tracer on top of the ones Ledwell used. I mention this because it was noted that argon could be used as a proxy for effective diapycnal mixing in both models and observations in the text.

Line 150: I understand not wanting to compete with Jason Momoa in Google searches by dubbing your model’s acronym MOMOA, but you’re going to compete with the Museum of Modern Art in New York City instead. In any case, the model and its tracer conservation properties won’t be as much of a problem as they would be if the authors chose another model like HYCOM. And the model domain is reasonable, considering problems with boundary conditions that can occur.

Line 169: You say that there are 55 geopotential levels in all model configurations here but in Table 1, it says there are 72 grid points in an undefined dimension. The caption of Table 1 only mentions zonal and meridional directions but there is a third dimension listed for the number of grid points. Is that dimension time or is one of your instances of vertical dimensions inaccurate (i.e., in Table 1 or on Line 169)?

Line 186: For future equilibrations of biogeochemical variables, you could consider using anther method like the one by Khatiwala (2024)’s “Efficient spin-up of Earth System Models using sequence acceleration”

Line 189: I would argue that use of COREv2 forcing is no longer considered standard, as JRA55-do has supplanted COREv2 in OMIP2 and ERA5 is also commonly used

Lines 201-203: If you’re interested in the evolution of each of the model configurations, then you should be assessing metrics that are related to the time rate of change, not averages

Lines 205-206: One year of spin-up is common amongst published high-resolution model simulations (based on the global kinetic energy metric you seem to be using) because the initial shock is essentially adjusted away but the model’s climatological state is still being approached asymptotically. That would need at least several more years to achieve. It may take much longer to equilibrate potential energy, which includes available potential energy relevant to the eddying circulation, but to first order using kinetic energy may be good enough.

Table 2: Continuing on from my previous comments, please include the time rate of change (linear slope of a regression against time, for example) of the Delta Ar[%] metric you include the average of in this table. That would help the reader see whether these values are close enough to what they would be in a more well-spun-up state. Also, why are you including the mixed layer in your calculations when Argon is not a conservative tracer near the sea surface and diapycnal mixing is not very meaningful within a bulk mixed layer? Are you not using a bulk mixed layer?

Lines 234-236: Again, because penetrating solar radiation, bubble entrainment, and possibly other processes affect Delta Ar[%], why are you including the mixed layer in your calculations?

Lines 266-268: This is qualitatively accurate. However, it can be noted that there are in-situ estimates of eddy kinetic energy compared with high-resolution model simulations in the literature, like those presented in Luecke et al. (2020)’s “Statistical Comparisons of Temperature Variance and Kinetic Energy in Global Ocean Models and Observations: Results From Mesoscale to Internal Wave Frequencies”. Also, along-track SWOT data resolves the higher wavenumbers and there are preliminary results that much more of the spectrum is resolved with SWOT. I’m not suggesting that you perform a comparison with in-situ (e.g., moored) or SWOT data. This is just something to be aware of.

Figure 3: It’s curious that the relatively warm SST feature near 18W, 21N in the High configuration is completely absent in Coarse, except for what seems like a separate merging feature near the upper part of the domain plotted here. The rest of the figure comparison looks like the High configuration’s SST was coarse-grained.

Table 3 and Figure 6: Okay, the higher the resolution, the greater the Ekman pumping/suction there is in its mean and variability, but how come you’re spending time on this when you’re not relating it to the effective diapycnal mixing? You’re relating how resolving the wind stress curl and upper-ocean features to diapycnal fluxes of tracer properties within the Ekman layer, which has more to do with advection. It’s possible, however, that, by conversation of volume in your model, diapycnal mixing will counter advective diapycnal fluxes but you are not showing this.

Lines 313-319: The differences in domain-averaged Delta Ar[%] amounting to <0.1% with the same back diffusivities (equivalent to increasing the background diffusivity from 20% to 40%) may not be significant/detectable here once you consider the rate at which Delta Ar[%] and/or global kinetic energy is changing as the simulations are spinning-up. It appears that in Figure 7d that the seasonal variability and trend in (Delta?) Ar[%] may be larger than the difference across High and Coarse. So it’s unclear whether the comparisons you make with the comparable effect of varying the background diffusivity and/or numerical advection scheme will hold up if your model was spun up more. A decrease in Delta Ar[%] from using a background diffusivity of 0.14 cm^2 s^-1 to 0.16 cm^2 s^-1 suggests varying rates of spin-up across different background diffusivities, for instance.

Minor corrections:
Line 4: “effected” should be “affected”
Lines 43 and 668: Trossmann should be Trossman
Line 209: “… effects associated to our…” should be “… effects associated with our…”
Line 233: “… that would allows for…” should be “… that would allow for…”
Line 261: “… starts to contributes to…” should be “… starts to contribute to…”
Line 295: “looses” should be “loses”
Line 419: Steven Griffith should be Stephen Griffies, I believe; Eric Galbreith should be Eric Galbraith

Citation: https://doi.org/10.5194/egusphere-2024-918-RC1
- AC1: 'Reply on RC1', Heiner Dietze, 16 Jun 2024
  
  We are really grateful for the reviewer's time and effort and very helpful comments. Please find our comprehensive point-by-point response in the supplement .
  
  Citation: https://doi.org/10.5194/egusphere-2024-918-AC1
RC2:
'Comment on egusphere-2024-918', Anonymous Referee #2, 14 Oct 2024
Review of “Argon Saturation in a Suite of Coupled General Ocean Circulation
Biogeochemical Models off Mauretania” by Dietze and Löptien

Summary:
The main finding of this paper is that diapycnal mixing, a key source of uncertainty in ocean models, is strongly influenced by factors such as model resolution, advection schemes, and background diffusivity. Using Argon saturation as a proxy, the study shows that the effect of differences in resolution is comparable to that of other factors. This study highlights the ongoing challenge of accurately representing ocean mixing in models used for climate projections. I found this manuscript concise and well-written. However, some clarifications in methods and a few minor corrections are needed before publication. I suggest minor revisions. Please see the general comments and specific comments below.

General comments:
Consider changing the title to highlight the key findings or purpose of this study. The current title is concise, but it could be refined for better focus and impact.

While the rationale for using a 3-year simulation period is clear in terms of model spin-up and avoiding equilibrium, I have concerns about the potential influence of spurious effects from the closed boundaries on the region of interest. Could the authors provide diagnostics or an analysis that evaluates how far spurious effects, such as reflected waves or boundary-induced disturbances, propagate into the domain over the 3-year period? This would help confirm whether the region of interest remains unaffected.

Detailed comments:
Line 134: What is the horizontal resolution of MOMSO? Is it 50 km as shown in Fig. 1?

Line 165: “resolutions” should be “resolution.”

Line 169: I have a question regarding the vertical grid description in line 169, where it is mentioned that the model uses 55 vertical levels but 72 vertical grid points in Table 1. Could you kindly clarify this aspect? Is the difference in grid points due to the use of staggered grids, boundary conditions, or another feature of the model's vertical discretization? If there is a specific reason for this configuration, I would appreciate further details as a reader.

Figure 1 caption: Panel (c) and panel (d) don’t show vertical resolution, right? Am I missing anything?

Line 188: I believe “affect” would be better than “effect” here.

Line 225: It seems to me that equation (1) is incorrect. Since delta_Ar = Ar - Ar_sat, why do we need to subtract 100% in this equation? This might be a typo, but if not, please check the calculations presented in this study. Or am I missing anything?

Line 229: Could the authors elaborate on why mixing always causes an increase in saturation? Wouldn't the sign of the change in saturation depend on the temperature before and after mixing, given that Argon saturation is a non-linear function of temperature?

Line 229: There is a typo. Change “his” to “is.”

Line 233: “Allows” should be “allow.”

Line 266: There is an extra parenthesis.

Line 295: “loses” should replace “looses.”
Citation: https://doi.org/10.5194/egusphere-2024-918-RC2
- AC2: 'Reply on RC2', Heiner Dietze, 28 Oct 2024
  
  We would like to thank the reviewer for the encouragement and constructive comments. A detailed point-to-point response is provided below (the reviewer comments are displayed in bold, followed by our answers in italics).
  Summary:
  
  The main finding of this paper is that diapycnal mixing, a key source of uncertainty in ocean models, is strongly influenced by factors such as model resolution, advection schemes, and background diffusivity. Using Argon saturation as a proxy, the study shows that the effect of differences in resolution is comparable to that of other factors. This study highlights the ongoing challenge of accurately representing ocean mixing in models used for climate projections. I found this manuscript concise and well-written. However, some clarifications in methods and a few minor corrections are needed before publication. I suggest minor revisions. Please see the general comments and specific comments below.
  
  General comments:
  
  1. Consider changing the title to highlight the key findings or purpose of this study. The current title is concise, but it could be refined for better focus and impact.
  Thank you! We will change the title to: “Mixing, Spatial Resolution and Argon Saturation in a Suite of Coupled General Ocean Circulation Biogeochemical Model Configurations off Mauretania.”
  
  2. While the rationale for using a 3-year simulation period is clear in terms of model spin-up and avoiding equilibrium, I have concerns about the potential influence of spurious effects from the closed boundaries on the region of interest. Could the authors provide diagnostics or an analysis that evaluates how far spurious effects, such as reflected waves or boundary-induced disturbances, propagate into the domain over the 3-year period? This would help confirm whether the region of interest remains unaffected.
  The reviewer is right in pointing out that regional model configurations are inevitably affected by the choice of the spatial boundary conditions and that some discussion is needed as to what extend this may affect our results. This is especially true for the northern and southern boundaries of our configuration, where in reality the adjacent subpolar gyre and equatorial ocean are affecting water mass transformations that we do not account for in our setup.
  In response to the reviewer's concern, we will put the results of an additional model experiment in which we estimate the time elapsed since a water parcel was in contact with the boundaries into the revised version of the manuscript. Figure 1 (added as a supplement to this reply) shows preliminary results of such a model experiment with such a specific, modified age tracer (or artificial clock). The respective model simulation was integrated for 30 years. The artificial clock counts the time since starting the model simulation everywhere in the model domain, except for at the northern, southern and western model boundaries where it is continuously reset to 0. The red contour line encircles that area where water parcels below the thermocline have, on average, not been in contact with the boundaries for more than three years. We conclude that the high-resolution region of our interest is rather undisturbed by coditions at the boundaries – even at the end of a three-year run.
  Detailed comments:
  
  1. Line 134: What is the horizontal resolution of MOMSO? Is it 50 km as shown in Fig. 1?
  MOMSO has a resolution of less than 11km (https://gmd.copernicus.org/articles/13/71/2020/). The highest-resolution version of MOMA has a resolution of 1.5km in the high-resolution model domain (Table 1). We will make this more clear in the revised version of the manuscript.
  2. Line 165: “resolutions” should be “resolution.”
  
  Yes, thank you!
  3. Line 169: I have a question regarding the vertical grid description in line 169, where it is mentioned that the model uses 55 vertical levels but 72 vertical grid points in Table 1. Could you kindly clarify this aspect? Is the difference in grid points due to the use of staggered grids, boundary conditions, or another feature of the model's vertical discretization? If there is a specific reason for this configuration, I would appreciate further details as a reader.
  Sorry. Ln. 169 is wrong. There are 72 vertical levels.
  4. Figure 1 caption: Panel (c) and panel (d) don’t show vertical resolution, right? Am I missing anything?
  You are correct. We will adjust the wording without using the confusing “respectively” construct.
  5. Line 188: I believe “affect” would be better than “effect” here.
  Thank you. We will replace “effect” with “drive”.
  6. Line 225: It seems to me that equation (1) is incorrect. Since delta_Ar = Ar - Ar_sat, why do we need to subtract 100% in this equation? This might be a typo, but if not, please check the calculations presented in this study. Or am I missing anything?
  No, you are right! This is a typo. Thank you! Equation (1) defining the Argon oversaturation in units percent should read: \Delta Ar = 100\% \times (\frac{Ar}{Ar_{sat}} \times 100\% - 1), i.e. the little delta should be replaced by Ar.
  7. Line 229: Could the authors elaborate on why mixing always causes an increase in saturation? Wouldn't the sign of the change in saturation depend on the temperature before and after mixing, given that Argon saturation is a non-linear function of temperature?
  
  Thank you, this makes sense. We will add an elaborated explanation in the revised version of the manuscript. Something along the lines: A mixed water-parcel will always carry a higher argon saturation than the arithmetic mean of the original parcels since the saturation curves are convex over the entire range of oceanic temperatures (and salinities).
  8. Line 229: There is a typo. Change “his” to “is.”
  
  9. Line 233: “Allows” should be “allow.”
  
  10. Line 266: There is an extra parenthesis.
  
  11. Line 295: “loses” should replace “looses.”
  
  Thank you. We will fix 8., 9., 10., 11. as suggested.
  
  Citation: https://doi.org/10.5194/egusphere-2024-918-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (31 Oct 2024) by Olivier Sulpis

AR by Heiner Dietze on behalf of the Authors (05 Dec 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (09 Dec 2024) by Olivier Sulpis

RR by Anonymous Referee #1 (12 Dec 2024)

Suggestions for revision or reasons for rejection

General comments:

The authors of this manuscript examine the model-simulated inaccuracies in diapycnal mixing that cannot be explained by the horizontal resolution near Mauretania and find that it’s comparable to advection numerics and choices of background diffusivity by making use of argon saturation as a proxy for effective mixing. The method makes use of Argo saturation and is simpler than previous methods for detecting spurious diapycnal mixing, except is somewhat similar (in signal detection capability and complexity) to that of Holmes et al. (2021). The distinction between using Argon saturation for diagnostic purposes (spurious diapycnal mixing) as opposed to constraining mixing parameters in ocean models in a data assimilation application needs to be better clarified because there are long passages in the introduction's text that seem to suggest that the authors are going to choose Argo saturation over, for example, biogeochemical tracers, which are used (e.g., in a submitted paper by Ellison et al.) for the other application. This manuscript further points out nuances with using Argo saturation as a proxy for diapycnal mixing, such as the fact that equilibrating air-sea fluxes can erase oversaturation signals, which makes Argo saturation less than perfect for diagnosing spurious diapycnal mixing. But in the way the authors experiments are designed (e.g., using different background diffusivities), their conclusions can be drawn. I suggest technical revisions. Specific comments are listed below:

Specific comments:

Line 21: “erroneous” is still spelled incorrectly (currently spelled “erroeneous”)

Line 68: “… so complex that the essence…” should have an exampled cited such as “… so complex (e.g., Ilıcak (2016)) that the essence…” where Ilıcak (2016) is Ilıcak's "Quantifying spatial distribution of spurious mixing in ocean models" in Ocean Modelling

Line 81: Before the sentence, “The relatively novel approach…” the authors should insert a sentence like, “While argon saturation is poorly observed, especially when compared with the observational coverage of biogeochemical tracers, for example, this study makes use of argon saturation as a model diagnostic, not a data constraint.” I suggest this because the reader may get the idea that Argo saturation is used as a data constraint to calculate ocean mixing parameters with the previous discussion about how studies have done that to date, and if one wants to ultimately use observations of Argo saturation to guide ocean mixing, they will only have a single transect going south from Alaska, a couple of zonal transects in the equatorial Atlantic Ocean, and a couple of meridional transects in the equatorial Atlantic Ocean of Argo concentrations in the World Ocean Database. This seems like the best place to clarify that Argon saturation is used here more for diagnostic purposes of spurious diapycnal mixing in ocean models.

Line 205: “… integration time of maximal three years) which constrains potentially spurious effects…” should be “… integration time of a maximum of three years) which limits potentially spurious effects…”

Line 230: “…can be indicative for spurious dispersion).” should be “… can be indicative of spurious dispersion).”

Lines 335-336: The sentence, “We suspect that the same holds…” can be deleted because it doesn’t add anything (just speculation).

Line 393: The authors are missing an end parenthesis: “(Porcupine Abyssal Plain and POMME region, respectively).”

Referee Report: PDF

Hide

ED: Publish subject to technical corrections (16 Dec 2024) by Olivier Sulpis

AR by Heiner Dietze on behalf of the Authors (17 Dec 2024) Manuscript

Journal article(s) based on this preprint

05 Mar 2025

Mixing, spatial resolution and argon saturation in a suite of coupled general ocean circulation biogeochemical models off Mauritania

Heiner Dietze and Ulrike Löptien

Biogeosciences, 22, 1215–1236, https://doi.org/10.5194/bg-22-1215-2025,https://doi.org/10.5194/bg-22-1215-2025, 2025

Short summary

Heiner Dietze and Ulrike Löptien

Viewed

Total article views: 818 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	BibTeX	EndNote
484	162	172	818	33	28

HTML: 484
PDF: 162
XML: 172
Total: 818
BibTeX: 33
EndNote: 28

Views and downloads (calculated since 03 May 2024)

Month	HTML	PDF	XML	Total
May 2024	152	46	8	206
Jun 2024	62	15	6	83
Jul 2024	56	17	5	78
Aug 2024	34	9	7	50
Sep 2024	33	12	2	47
Oct 2024	68	17	2	87
Nov 2024	12	6	0	18
Dec 2024	17	16	33	66
Jan 2025	26	10	50	86
Feb 2025	18	14	45	77
Mar 2025	6	14	20

Cumulative views and downloads (calculated since 03 May 2024)

Month	HTML	PDF	XML	Total
May 2024	152	46	8	206
Jun 2024	62	15	6	83
Jul 2024	56	17	5	78
Aug 2024	34	9	7	50
Sep 2024	33	12	2	47
Oct 2024	68	17	2	87
Nov 2024	12	6	0	18
Dec 2024	17	16	33	66
Jan 2025	26	10	50	86
Feb 2025	18	14	45	77
Mar 2025	6	14	20

Viewed (geographical distribution)

Total article views: 783 (including HTML, PDF, and XML) Thereof 783 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 05 Mar 2025

Download

The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

Preprint (7929 KB)
Metadata XML

Short summary

We introduce argon saturation as a prognostic variable in a suite of coupled general ocean circulation biogeochemical models off Mauretania. Our results indicate that the effect of increasing the spatial horizontal model resolutions from 12 km to 1.5 km leads to changes comparable to other infamous spurious effects of state-of-the-art numerical advection numerics.


Total:	0
HTML:	0
PDF:	0
XML:	0