Wind-Forced Submesoscale Symmetric Instability around Deep Convection in the Northwestern Mediterranean Sea

Round 1

Reviewer 1 Report

In the manuscript "Wind-forced submesoscale symmetric instability around deep convection in the NW Mediterranean Sea", Bosse et al. use numerous glider measurements in the Gulf of Lion as well as the output of a numerical model to show the importance of submesoscale instabilities in deep water convection.

This is a timely contribution and it brings the attention of the community to the importance of processes that occur on smaller scales that are not usually sampled in regions of deep water formation and, ultimately, in long-term predictions of climate models.

I recommend publication after minor corrections.

Some comments regarding the methods:

1 - I am sure the authors are aware that there will be potential critics on the diagnostics of symmetric instabilities with a 1 km resolution model (or even with the resolution of the gliders). Nonetheless, I believe the estimates are robust.  The authors do acknowledge that they are resolving the upper bound of the mesoscale, so there will be questions about how well can this reproduce SI. 

 

2 - Equation 1 shows an estimate of the frictional buoyancy flux, where the authors use Me as the Ekman transport and suggest that this was calculated according to Thomas and Lee 2005. It seems as though the authors do not take into account the surface geostrophic vorticity in their estimate of the Ekman transport, as done in Thomas and Lee 2005. The pattern in Figure 7b suggests that this is indeed the case, as the patches of large frictional buoyancy flux seem to be associated with surface buoyancy gradients and not surface, geostrophic relative vorticity gradients.  Perhaps the inclusion of the surface geostrophic relative vorticity would yield even larger values of the fricional PV flux.

 

Author Response

Please find attached my detailed response to your comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments on Bosse et al. (2021) submitted to Fluids

General comments

In this manuscript, the authors diagnosed the Ertel potential vorticity (PV) in the Northwest Mediterranean Sea through combing glider observations and a high-resolution numerical model.  Based on the PV-based criterion of symmetric instability, i.e. negative PV, they futher investigated the possible occurrence of symmetric instability and its connection with down-front wind forcing.  Additionally, they also suggested that vertical circulations associated with wind-forced symmetric instability may play an important role for the ventilation of intermediate layers, phytoplankton growth and carbon export.  Overall, the story of this manuscript well organized, the analysis methods are standard, and most of the results are expected by theories.  As it stands, I think this manuscript is suitable for publishing in Fluids.  However, before acceptance, several important issues have to be properly adressed or clarified.  My detailed comments are as follows and I hope them will be helpful for the authors to improve their manuscript.  

Major comments

1. My first concern is the geostrophic approximation in the PV calculation using glider data (Lines 203-206).  As the authors mentioned in the Introduction (also in Figure 4), the submesoscale fronts are characterized by order one Rossby numbers.  This means that for submesoscales, the nonlinear term (or horizontal advection term) in the momentum equations becomes as important as the Coriolis term.  In a most recent observational paper by Zhang et al. (2021), the authors have demonstrated that the ageostrophic kinematic energy should not be neglected for submesoscale currents.  From this point, is your geostrophic approximation used in the PV calculation really valid?  Although in Figure 6, the authors attempt to demonstrate the validness of geostrophic approximation through showing a case in the model, I can still not be convinced.  Therefore, I think the authors should do more work to clarify this important issue, especially considerring that the way you did is contradictory to the concept of submesoscale (i.e. order one Rossby number).           
2. My second concern is whether the 1-km resolution model can really resolve the process of symmetric instability. A numerical simulation with a given horizontal resolution can correctly resolve the physics of wavelengths of at least 5 times this resolution (Lévy et al. 2012).  This means that the effective resolution of 1-km simulation is only 5 km, which is larger than the estimated horizontal length scale of the symmetric instability (i.e. 3.3 km, Lines 449-452).  Furthermore, according to Bachman et al. (2017), timescales of symmetric instability ranges from one minute to

an hour.  So, I am not sure what is the temporal resolution of your model outputs and wheter can it resolve the short time scale of symmetric instability.  As the results of model simulation is another foundation of your paper (in addition to glider observations), I sugget the authors clarify the above issue more clearly and carefully.  

Minor comments

1. Line 2 in the abstract: “NW Mediterranean”-->> “Northwest Mediterranean” ?
2. Lines 45-47: I also recommend reading Zhang et al. (2015) and Li et al. (2017), which directly demonstrated the important role of SCVs in water mass transports.
3. Line 68: For “internal deformation radius”, do you mean the first baroclinic deformation radius?  Because the submesoscales have order one Rossby number and Richardson number, it means that their Burger numer is also order one.  In this sense, the horizontal scale of submesoscales is comparable with the so called internal deformation radius(i.e. Rd=NH/f).  
4. Line 69: I also suggest referring to the observational work of Zhang et al. (2021), which directly quantified the vertical velocity associated with submesoscales.
5. Lines 89-91: The horizontal and time scales mentioned here are much larger than the estimates in Bachman et al. (2017).  Please double check these references.  Note that the horizontal scale of negative PV patchs is not the scale of symmetric instability (overturning cell).  They are totally different concepts.
6. Line 162: “internal deformation radius”-->>“first baroclinic deformation radius”?
7. Figure 3: I do not find the “(c) Comparison of the total model and glider-like PV estimates of qN”.  Panels (c, f, i) are missing.  
8. Line 377: “similar amplitude than”-->>”similar amplitude with”?
9. Lines 436-438: I do not think the scale of symmetric instability is determined by the typical mesoscale.  The scale of negative PV patchs and the scale of symmetric instability are two different things.  Please also refer to my minor comment 5.
10. Figure 10: Please clarify what do the color shading and black vectors mean ?
11. Line 521: How do you obtain the T’and w’ ?  Do they also contain the contributions from mixed-layer baroclinic instability, which is an important generation mechanism of submesoscales that can also cause large positive w’T’ (see Zhang et al., 2021).  I suggest explaining this point more clearly.     
12. Lines 557-560: The large vertical velocity can be caused by many other mechanisms such as strain-induced frontogenesis and mixed-layer instability etc.  So, based on the large vertical velocity, one cannot say whether the model can resolve the symmetric instability or not.  

 

References

Lévy M, Resplandy L, Klein P, Capet X, Iovino D, Éthé C (2012b) Grid degradation of submesoscale resolving ocean models: benefits for offline passive tracer transport. Ocean Modelling, 48, 1-9.

Zhang, Z., X. Zhang, B. Qiu, W. Zhao, C. Zhou, X. Huang, and J. Tian (2021): Submesoscale currents in the subtropical upper ocean observed by two-year long high-resolution mooring arrays. J. Phys. Oceanogr., 51(1), 187–206, DOI: 10.1175/JPO-D-20-0100.1

Zhang, Z., P. Li, L. Xu, C. Li, W. Zhao, J. Tian, and T. Qu (2015), Subthermocline eddies observed by rapid-sampling Argo floats in the subtropical northwestern Pacific Ocean in Spring 2014, Geophys. Res. Lett., 42(8), 6438-6445.

Li, C., Z. Zhang, W. Zhao, and J. Tian (2017), A statistical study on the subthermocline submesoscale eddies in the northwestern Pacific Ocean based on Argo data, J. Geophys. Res., 122 (5), 3586-3598, doi: 10.1002/ 2016JC012561.

Bachman, S. D., Fox‐Kemper, B., Taylor, J. R., & Thomas, L. (2017). Parameterization of frontal symmetric instabilities. I: Theory for resolved fronts. Ocean Modelling, 109, 72-95.

Author Response

Please find attached my detailed response to your comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have well addressed my previous concerns.  Now, I only have one minor comment that should be addressed before acceptance. 

Minor point

LInes 529-530: The authors should make it more explicit how you calculated the w' and T', which is useful information for readers.  

Author Response

Thanks for rising this last point that we overlooked. We now provide more details on where w' and T' come from :

"Considering vertical displacements w' of O(10-100 m/day) roughly estimated from the subduction of phytoplankton below the mixed layer in O(1km) cross-front patches"

"Along isopycnal temperature and salinity anomalies T'/S' associated with interleaving could also be observed with the order of magnitude of 0.2°C/0.05 (see for instance Figure 5 or 11)."