the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
NeverWorld2: An idealized model hierarchy to investigate ocean mesoscale eddies across resolutions
- 1Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, CO
- 2University of Colorado, Department of Applied Mathematics, Boulder, CO
- 3Courant Institute, New York University, New York, NY
- 4Woods Hole Oceanographic Institution, Woods Hole, MA
- 5Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ
- 6NOAA Geophysical Fluid Dynamics Laboratory, Princeton, NJ
- 7Department of Earth, Environmental, and Planetary Sciences, Brown University, Providence, RI
- 8Department of the Geophysical Sciences, The University of Chicago, Chicago, IL
- 9Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, UK
- 1Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, CO
- 2University of Colorado, Department of Applied Mathematics, Boulder, CO
- 3Courant Institute, New York University, New York, NY
- 4Woods Hole Oceanographic Institution, Woods Hole, MA
- 5Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ
- 6NOAA Geophysical Fluid Dynamics Laboratory, Princeton, NJ
- 7Department of Earth, Environmental, and Planetary Sciences, Brown University, Providence, RI
- 8Department of the Geophysical Sciences, The University of Chicago, Chicago, IL
- 9Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, UK
Abstract. We describe an idealized primitive equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans, and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the equator, and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally have diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest, and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.
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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.
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Preprint
(7068 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Gustavo Marques et al.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-186', Anonymous Referee #1, 24 May 2022
Summary
This paper is supposed to serve as an introduction to a model configuration, grid resolution hierarchy, and to datasets for use by the community (lines 231–232). The model hierarchy (NeverWorld2) is reasonably well-described. It consists of a two-hemisphere basin with a southern reentrant channel realized using the adiabatic layered mode of MOM6. The idealized setup is similar to a number of previous iterations on the idea, although its use of adiabatic layer coordinates and analytically specified topography make the setup well suited for its intended use, which is to understand mesoscale eddy parameterizations and the impact of resolution on mesoscale eddy dynamics. To this end, the model hierarchy consists of four resolutions ranging in powers of two from 1/4º to 1/32º. The bulk of the manuscript is devoted to model description and comparison of the solutions at different resolutions.
The NeverWorld2 model hierarchy promises to be a useful tool for understanding mesoscale dynamics and I appreciate that the authors are releasing and documenting it. The manuscript is well-written and approachable overall, although there are some points that could be clarified and a some changes (discussed below) that would make the paper more useful and understandable. Perhaps the papers most significant shortcoming as an “introduction to datasets” is that the datasets themselves are not actually described, nor is a useable link or pointer to them provided to the reader. There is a statement in the “code and data availability” section that the dataset will be publicly available via Open Storage Network, but there’s no indication of when or how they can be accessed. Information on the contents of the datasets beyond that they’ll include “initial conditions and restart files” would also be useful. For example, it would be nice to know if the available data will also include mean fields, derived quantities (e.g., EKE, fluxes), and snapshots.
Other than the lack of discussion of datasets, most of my concerns relate to claims/demonstrations of convergence with resolution (see major comments below). I think the paper is quite publishable if these issues can be addressed. My sense is that the required revisions lie in the grey area between “major” and “minor”—I selected “major” but would not argue if the editor dropped it to “minor.”
Major comments
There several attempts to argue that the 1/32º version is converged or approaching convergence, but a number are confusing or not convincing.
- On the bottom of page 10 it is mentioned that the strength of the western boundary currents and their extensions decrease slightly with resolution. This seems rather unexpected: the transport of the WBC extensions is dominated by recirculation gyres that are largely eddy-driven. One expects that they would become stronger rather than weaker as resolution increases. Figures 9 and 10 indeed show substantial increases with resolution in the KE at the latitudes of the WBC extensions, so it’s not clear where the claim that the strength of the extensions decreases with resolution comes from. The figure referenced in support (figure 5) merely shows SSH at 50 cm intervals, so it’s impossible to tell what the WBCs are doing from this figure.
- Lines 201–202: The fact that the APE change from 1/16º to 1/32º is the smallest is used to suggest that the model is approaching convergence. However, a simple fit the APE curve shows that the APE is inversely proportional to the logarithm of the number of grid cells (in 1D). This means that the APE change after every doubling will be smaller than the previous doubling, but that the APE change will converge to zero very slowly with resolution.
- The fact that the KE at scales greater than 1/4º appears to stabilize is a better metric of convergence than the APE change, although the fact that it’s still increasing around 40ºS calls the convergence into questions. On the other hand, since the model hierarchy is designed to study mesoscale eddies, it would be more useful to know if the mesoscales (rather than the large scales), are converging. For this, a band-pass spatial filter with cutoffs several times larger and smaller than the local deformation radius would be more convincing.
- The fact that the spectra (figure 13) are collapsing onto each other is probably the most convincing indicator of convergence, such that it might be better to concentrate more on the spectra. A number of the aspects of the spectra are confusing, however.
- The spectra are supposed to be of EKE but are computed from the meridional velocity only. Unless the velocity is isotropic (unlikely in the presence of PV gradients), this would not necessarily give the EKE spectrum.
- The spectra are listed as being “at” several fixed latitudes. Are they zonal spectra or radial spectra?
- The fact that the spectra at 15ºN and 50ºS follow inertial-range scaling all the way to the highest wavenumber is somewhat surprising. The forward cascade dissipates enstrophy, so there should be at least a few wavenumbers in the enstrophy dissipation regime, but it seems like the cascade is dissipation-less all the way to the end.
Minor comments
- Line 87 and the rest of the page: The manuscript doesn’t really provide an analysis of energetics, beyond tabulating the amount of energy in KE and APE in various ways. The conversion, transport, and generation terms in equations (6) and (7) are both standard and never used in the rest of the paper. At the moment they seem like filler and could be removed.
- Lines 92–94: If the Coriolis terms do not actually vanish in a point-wise manner, they should be included in equation (6) if that equation is retained (but see above).
- Lines 117–118: The idealized Scotia Arc is cute, but does it actually do anything? It may make the topography more “realistic” but there’s nothing realistic about the topography in this model. The arc’s appearance in an otherwise highly idealized model gives the impression that it’s an important feature, but its impact is never discussed.
- Figures 4 & 5: The insets should be described in the captions.
- Figure 7: The contour spacing for SSH (50 cm) is too coarse to see detail of anything other than the circumpolar current. The entirety of each gyre is represented by a single contour, which doesn’t make it a very useful diagnostic. Further, the f/H contours aren’t mentioned in the text and don’t seem to add anything (the topography is shown in figure 1a) except to clutter up the figure.
- Line 178: How are “emergent features” defined? This phrase appears to include features such as southern ocean stratification and the vertical extent of jets, but not features such as tropical thermocline depth and the strength of the WBCs and circumpolar jet.
- Lines 205–210: Given that time mean energy has already been discussed, switching the definition of “mean” to mean “scales larger than 1/4º” is confusing terminology. Something like “large scale energy” and “small scale energy” would be better. (“Mesoscale energy” implemented using a band-pass filter would be even better.)
- Line 228: “Basin-scale” would be more accurate/clear than “pseudo-global”.
Minor issues (garmmar, typos, etc)
- Lines 30–31: The last sentence of this paragraph makes it seem like there’s going to be a description of “recent mesoscale parameterizations … with novel momentum closures” but the paragraph simply ends after this sentence.
- Line 44: “The broad configuration is similar” should be “The configuration is broadly similar” (unless there’s some distinction between a broad configuration and a narrow configuration I’m missing).
- Line 68: “we here write” â “here we write”
- Line 87: “and in subsequent papers.” What will happen in subsequent papers? It seems like there should be more after “papers”.
- Lines 176–177: “features are converging” should be “features converge” to match the tense of the rest of the sentence.
- Line 180: “the outcropping of interfaces” â “the interface outcrops”
- Line 246: There appears to be an unresolved reference following Bachman et al., 2017.
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AC2: 'Reply on RC1', Gustavo Marques, 02 Aug 2022
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/egusphere-2022-186/egusphere-2022-186-AC2-supplement.pdf
- AC3: 'Reply on AC2', Gustavo Marques, 04 Aug 2022
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RC2: 'Comment on egusphere-2022-186', Takaya Uchida, 29 May 2022
Marques et al. introduce a new purely adiabatic primitive equation model which is computationally cheap and easy to run. As they note, a cheap and versatile model to test mesoscale eddy parametrizations has indeed long been a needed tool for the ocean modeling community and their configuration would be a great resource for the community. NeverWorld2 (NW2) being part of the MOM6 module also provides confidence in the stability of their model. The manuscript is well written and I only provide minor points listed below.
- Some discussion regarding how computationally cheap NW2 is compared to a non-adiabatic, isopycnal primitive equation model where the equation of state for density is linear (e.g. the density linearly depending only on temperature without salinity) would be nice to have. While I understand the adiabatic nature of NW2 allows the user to focus on the dynamics and isolate mesoscale processes, a non-adiabatic isopycnal model is closer to reality, also allowing for a surface mixed layer.
- Figure 13: Is any tapering applied prior to taking the Fourier transform to make the data periodic?
-
AC1: 'Reply on RC2', Gustavo Marques, 02 Aug 2022
We are grateful to Dr. Takaya Uchida for taking the time to carefully read the manuscript and provide thoughtful comments.
Below are our detailed responses (in bold) to all the comments.
Marques et al. introduce a new purely adiabatic primitive equation model which is computationally cheap and easy to run. As they note, a cheap and versatile model to test mesoscale eddy parametrizations has indeed long been a needed tool for the ocean modeling community and their configuration would be a great resource for the community. NeverWorld2 (NW2) being part of the MOM6 module also provides confidence in the stability of their model. The manuscript is well written and I only provide minor points listed below.
- Some discussion regarding how computationally cheap NW2 is compared to a non-adiabatic, isopycnal primitive equation model where the equation of state for density is linear (e.g. the density linearly depending only on temperature without salinity) would be nice to have. While I understand the adiabatic nature of NW2 allows the user to focus on the dynamics and isolate mesoscale processes, a non-adiabatic isopycnal model is closer to reality, also allowing for a surface mixed layer.
We appreciate the reviewer’s comment on this point. We have made the choice of using an adiabatic model to indeed isolate the effects of mesoscale eddies. Unfortunately, we cannot give the exact cost of running NW2 in the diabatic mode because this configuration does not exist. The main reason for using an adiabatic configuration is that the model achieves an equilibrated state significantly faster than with a diabatic mode. It would take 1000’s years for the deep ocean to equilibrate in a diabatic setup, while we were able to achieve this in 10’s years for the ¼ degree configuration. Thus, roughly, the cost of NW2 is 100x less than that of a diabatic run. In addition, running the model in the diabatic mode would require an increased number of vertical levels to represent the surface boundary layer, which would make the model more computationally expensive.
- Figure 13: Is any tapering applied prior to taking the Fourier transform to make the data periodic?
Thank you for the question. Yes, when computing the spectra we use the XRFT Python package (https://xrft.readthedocs.io/en/latest/) with a Hann window to taper the data. Since the data are not periodic and influenced by boundary effects, we also cut off 2.5 degrees from the Western and Eastern boundaries before computing the spectra. We added text to the caption of Figure 13 and additional discussion of the spectra at the end of Section 5 to address these points.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-186', Anonymous Referee #1, 24 May 2022
Summary
This paper is supposed to serve as an introduction to a model configuration, grid resolution hierarchy, and to datasets for use by the community (lines 231–232). The model hierarchy (NeverWorld2) is reasonably well-described. It consists of a two-hemisphere basin with a southern reentrant channel realized using the adiabatic layered mode of MOM6. The idealized setup is similar to a number of previous iterations on the idea, although its use of adiabatic layer coordinates and analytically specified topography make the setup well suited for its intended use, which is to understand mesoscale eddy parameterizations and the impact of resolution on mesoscale eddy dynamics. To this end, the model hierarchy consists of four resolutions ranging in powers of two from 1/4º to 1/32º. The bulk of the manuscript is devoted to model description and comparison of the solutions at different resolutions.
The NeverWorld2 model hierarchy promises to be a useful tool for understanding mesoscale dynamics and I appreciate that the authors are releasing and documenting it. The manuscript is well-written and approachable overall, although there are some points that could be clarified and a some changes (discussed below) that would make the paper more useful and understandable. Perhaps the papers most significant shortcoming as an “introduction to datasets” is that the datasets themselves are not actually described, nor is a useable link or pointer to them provided to the reader. There is a statement in the “code and data availability” section that the dataset will be publicly available via Open Storage Network, but there’s no indication of when or how they can be accessed. Information on the contents of the datasets beyond that they’ll include “initial conditions and restart files” would also be useful. For example, it would be nice to know if the available data will also include mean fields, derived quantities (e.g., EKE, fluxes), and snapshots.
Other than the lack of discussion of datasets, most of my concerns relate to claims/demonstrations of convergence with resolution (see major comments below). I think the paper is quite publishable if these issues can be addressed. My sense is that the required revisions lie in the grey area between “major” and “minor”—I selected “major” but would not argue if the editor dropped it to “minor.”
Major comments
There several attempts to argue that the 1/32º version is converged or approaching convergence, but a number are confusing or not convincing.
- On the bottom of page 10 it is mentioned that the strength of the western boundary currents and their extensions decrease slightly with resolution. This seems rather unexpected: the transport of the WBC extensions is dominated by recirculation gyres that are largely eddy-driven. One expects that they would become stronger rather than weaker as resolution increases. Figures 9 and 10 indeed show substantial increases with resolution in the KE at the latitudes of the WBC extensions, so it’s not clear where the claim that the strength of the extensions decreases with resolution comes from. The figure referenced in support (figure 5) merely shows SSH at 50 cm intervals, so it’s impossible to tell what the WBCs are doing from this figure.
- Lines 201–202: The fact that the APE change from 1/16º to 1/32º is the smallest is used to suggest that the model is approaching convergence. However, a simple fit the APE curve shows that the APE is inversely proportional to the logarithm of the number of grid cells (in 1D). This means that the APE change after every doubling will be smaller than the previous doubling, but that the APE change will converge to zero very slowly with resolution.
- The fact that the KE at scales greater than 1/4º appears to stabilize is a better metric of convergence than the APE change, although the fact that it’s still increasing around 40ºS calls the convergence into questions. On the other hand, since the model hierarchy is designed to study mesoscale eddies, it would be more useful to know if the mesoscales (rather than the large scales), are converging. For this, a band-pass spatial filter with cutoffs several times larger and smaller than the local deformation radius would be more convincing.
- The fact that the spectra (figure 13) are collapsing onto each other is probably the most convincing indicator of convergence, such that it might be better to concentrate more on the spectra. A number of the aspects of the spectra are confusing, however.
- The spectra are supposed to be of EKE but are computed from the meridional velocity only. Unless the velocity is isotropic (unlikely in the presence of PV gradients), this would not necessarily give the EKE spectrum.
- The spectra are listed as being “at” several fixed latitudes. Are they zonal spectra or radial spectra?
- The fact that the spectra at 15ºN and 50ºS follow inertial-range scaling all the way to the highest wavenumber is somewhat surprising. The forward cascade dissipates enstrophy, so there should be at least a few wavenumbers in the enstrophy dissipation regime, but it seems like the cascade is dissipation-less all the way to the end.
Minor comments
- Line 87 and the rest of the page: The manuscript doesn’t really provide an analysis of energetics, beyond tabulating the amount of energy in KE and APE in various ways. The conversion, transport, and generation terms in equations (6) and (7) are both standard and never used in the rest of the paper. At the moment they seem like filler and could be removed.
- Lines 92–94: If the Coriolis terms do not actually vanish in a point-wise manner, they should be included in equation (6) if that equation is retained (but see above).
- Lines 117–118: The idealized Scotia Arc is cute, but does it actually do anything? It may make the topography more “realistic” but there’s nothing realistic about the topography in this model. The arc’s appearance in an otherwise highly idealized model gives the impression that it’s an important feature, but its impact is never discussed.
- Figures 4 & 5: The insets should be described in the captions.
- Figure 7: The contour spacing for SSH (50 cm) is too coarse to see detail of anything other than the circumpolar current. The entirety of each gyre is represented by a single contour, which doesn’t make it a very useful diagnostic. Further, the f/H contours aren’t mentioned in the text and don’t seem to add anything (the topography is shown in figure 1a) except to clutter up the figure.
- Line 178: How are “emergent features” defined? This phrase appears to include features such as southern ocean stratification and the vertical extent of jets, but not features such as tropical thermocline depth and the strength of the WBCs and circumpolar jet.
- Lines 205–210: Given that time mean energy has already been discussed, switching the definition of “mean” to mean “scales larger than 1/4º” is confusing terminology. Something like “large scale energy” and “small scale energy” would be better. (“Mesoscale energy” implemented using a band-pass filter would be even better.)
- Line 228: “Basin-scale” would be more accurate/clear than “pseudo-global”.
Minor issues (garmmar, typos, etc)
- Lines 30–31: The last sentence of this paragraph makes it seem like there’s going to be a description of “recent mesoscale parameterizations … with novel momentum closures” but the paragraph simply ends after this sentence.
- Line 44: “The broad configuration is similar” should be “The configuration is broadly similar” (unless there’s some distinction between a broad configuration and a narrow configuration I’m missing).
- Line 68: “we here write” â “here we write”
- Line 87: “and in subsequent papers.” What will happen in subsequent papers? It seems like there should be more after “papers”.
- Lines 176–177: “features are converging” should be “features converge” to match the tense of the rest of the sentence.
- Line 180: “the outcropping of interfaces” â “the interface outcrops”
- Line 246: There appears to be an unresolved reference following Bachman et al., 2017.
-
AC2: 'Reply on RC1', Gustavo Marques, 02 Aug 2022
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/egusphere-2022-186/egusphere-2022-186-AC2-supplement.pdf
- AC3: 'Reply on AC2', Gustavo Marques, 04 Aug 2022
-
RC2: 'Comment on egusphere-2022-186', Takaya Uchida, 29 May 2022
Marques et al. introduce a new purely adiabatic primitive equation model which is computationally cheap and easy to run. As they note, a cheap and versatile model to test mesoscale eddy parametrizations has indeed long been a needed tool for the ocean modeling community and their configuration would be a great resource for the community. NeverWorld2 (NW2) being part of the MOM6 module also provides confidence in the stability of their model. The manuscript is well written and I only provide minor points listed below.
- Some discussion regarding how computationally cheap NW2 is compared to a non-adiabatic, isopycnal primitive equation model where the equation of state for density is linear (e.g. the density linearly depending only on temperature without salinity) would be nice to have. While I understand the adiabatic nature of NW2 allows the user to focus on the dynamics and isolate mesoscale processes, a non-adiabatic isopycnal model is closer to reality, also allowing for a surface mixed layer.
- Figure 13: Is any tapering applied prior to taking the Fourier transform to make the data periodic?
-
AC1: 'Reply on RC2', Gustavo Marques, 02 Aug 2022
We are grateful to Dr. Takaya Uchida for taking the time to carefully read the manuscript and provide thoughtful comments.
Below are our detailed responses (in bold) to all the comments.
Marques et al. introduce a new purely adiabatic primitive equation model which is computationally cheap and easy to run. As they note, a cheap and versatile model to test mesoscale eddy parametrizations has indeed long been a needed tool for the ocean modeling community and their configuration would be a great resource for the community. NeverWorld2 (NW2) being part of the MOM6 module also provides confidence in the stability of their model. The manuscript is well written and I only provide minor points listed below.
- Some discussion regarding how computationally cheap NW2 is compared to a non-adiabatic, isopycnal primitive equation model where the equation of state for density is linear (e.g. the density linearly depending only on temperature without salinity) would be nice to have. While I understand the adiabatic nature of NW2 allows the user to focus on the dynamics and isolate mesoscale processes, a non-adiabatic isopycnal model is closer to reality, also allowing for a surface mixed layer.
We appreciate the reviewer’s comment on this point. We have made the choice of using an adiabatic model to indeed isolate the effects of mesoscale eddies. Unfortunately, we cannot give the exact cost of running NW2 in the diabatic mode because this configuration does not exist. The main reason for using an adiabatic configuration is that the model achieves an equilibrated state significantly faster than with a diabatic mode. It would take 1000’s years for the deep ocean to equilibrate in a diabatic setup, while we were able to achieve this in 10’s years for the ¼ degree configuration. Thus, roughly, the cost of NW2 is 100x less than that of a diabatic run. In addition, running the model in the diabatic mode would require an increased number of vertical levels to represent the surface boundary layer, which would make the model more computationally expensive.
- Figure 13: Is any tapering applied prior to taking the Fourier transform to make the data periodic?
Thank you for the question. Yes, when computing the spectra we use the XRFT Python package (https://xrft.readthedocs.io/en/latest/) with a Hann window to taper the data. Since the data are not periodic and influenced by boundary effects, we also cut off 2.5 degrees from the Western and Eastern boundaries before computing the spectra. We added text to the caption of Figure 13 and additional discussion of the spectra at the end of Section 5 to address these points.
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Gustavo Marques et al.
Gustavo Marques et al.
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