Review of "Ocean 2D eddy energy fluxes from small mesoscale processes 

with SWOT"

By E. Carli, R. Morrow, O. Vergara, R. Chevrier and L. Renault

This article diagnoses the potential improvements in the restitution of geostrophic eddy dynamics 

in the Agulhas current system from the new SWOT satellite mission.

It uses subsampled outputs of the MITgcm 1/48deg LLCC4320 global ocean model (LLC10) with the SWOT simulator 

to compares  the eddy dynamics representation when using current altimetry products  and SWOT.

The Agulhas current region is used as one of the most turbulent regions of the world oceans.

An innovative artificial intelligence processing (U-Net) trained with a model of the North Atlantic

appears promising for the reduction of random noise in the Agulhas Current system.

Observable wavelengths of 15 to 20 km are retrieved  for sea surface height 

and also for high-order eddy diagnostics such as EKE and strain.

A specific attention is given on key processes of the region: 

turbulence in the Agulhas retroflection, Natal Pulses, frontal eddies...

A coarse graining technique is used to investigate the energy cascades for two scales (60km and 150 km).

This is a very good article which uses the opportunity of the SWOT mission to revisit 

important eddy processes in the Agulhas region.

It shows the limitations in the current altimetry products and the potential improvements for the new mission.

Even not trained in the region, the U-Net denoising method appears promising 

in mitigating the KarIn random error.

Specific comments

Line 113: "(Rocha et al., 2016). (Rocha et al., 2016)"

citation doubled

Line 125: "Arbic et al. (2022)"

citet instead of citep 

Line 201: "KarIn random noise"

please define KarIn in the text

Line 250: "which the noise to signal ratio (NSR) reaches one."

please refer to equation (1)

Equation (6): 

can you defined how the bars are computed ?

Line 301: "mean surface geostrophic EKE over this 1-year period,"

One year is a bit short for a mean surface geostrophic EKE here.

This is why EKE pattern in Figure 3 is quite patchy.

... but I think this is the limitation of using LLC10 ?

Line 350: "these smaller-scale features"

They are actually called "submesoscale frontal eddies" or "shear eddies"

Figure 5: What is the definition of the cross-terms ?

Table 1: Values of strain for PseudoDUACS are quite large compared to Figure 3.

Is this due to the specific locations of the boxes ?

Line 370 : "sub-mesoscale barotropic anomalies"

no. these are (baroclinic) submesoscale frontal eddies generated by barotropic instabilities.

Figure 7: if the figure is dominated by the propagagtion of Natal Pulses, one possibility would 

be to do the statistics in absence of Natal Pulses (as in Tedesco et al., 2019).

Line 545: 

"direct cascade ad scales"

"direct cascade at scales"

This paper investigates ocean dynamics at different scales in the Agulhas current system, a region of important interocean exchange of heat and energy. The authors analyze different eddy diagnostics in the Agulhas Current region and quantify the contributions from the larger mesoscales observable today, and the smaller scales to be observed with the recently launched NASA-CNES Surface Water and Ocean Topography (SWOT) wide-swath altimeter mission. The paper presents surface geostrophic diagnostics of eddy kinetic energy, strain, and energy cascades estimated from modeled sea surface height fields of the MITGCM / LLC4320 simulation subsampled at 1/10 degree. The authors also used a coarse-graining technique to investigate the horizontal cascade of energy and observed that the wavelength range where the inverse cascade occurs is biased towards larger mesoscale wavelengths with today's altimetric sampling. To calculate the projected sampling of the eddy diagnostics under the SWOT swaths, the authors used the CNES-NASA simulator to include the satellite position and realistic noise. They also implemented a neural network noise mitigation method to reduce the residual SWOT random error before calculating eddy diagnostics. The paper presents the observability of the ocean eddy diagnostics before and after the U-net de-noising treatment of the residual KarIn random error.

This paper presents valuable results of what SWOT could bring to the scientific community in terms of small-scale altimetric observation and it would benefit from some examination in the methodology and discussion. I recommend the minor revision before acceptance for publication.

Major comments

L210: Systematic errors such as satellite roll, and phase errors, could be much bigger sources of error on SSH than Karin random error. Can the authors elaborate on the reason why they choose to focus on Karin random error on SSH data and observable wavelengths in SSH, eddy kinetic energy, and strain rate?

L391-L395 The paper's findings don't seem to align with Sasaki et al. (2014)'s research regarding the energy feeding dynamics between different mesoscale EKE during various seasons. If the paper doesn't adequately address this discrepancy, it could be a point of critique.

L233-244 U-Net's General Application: The authors show that U-net performs well even with different models and in different zones, leading to similar Root Mean Square Error (RMSE) and variance of SSH residuals. This indicates the potential universal applicability of the U-net method across various regions and circumstances. While the authors show U-Net's promise, the discussion lacks a thorough analysis of why U-Net performs similarly across various regions and models. It’s not clear how U-Net achieves this consistency, which might lead to skepticism about the broad application of U-Net in other environments. Moreover, the potential improvements that could be achieved by training U-Net specifically for different regions could be discussed in more detail.

Minor comments

L70: “multi-multi mission”  “multi-mission information”?

L125: … and an offset on the atmosphere forcing fields (by 6 hours) (Arbic et al., 2022).

L290 define how the u bar and v bar are calculated.

L383 The study found that Natal Pulses, despite being the strongest events in terms of Eddy Kinetic Energy (EKE), had only a small impact on the strain, particularly on the pseudo-DUACS strain. This could be criticized if it contradicts the existing understanding of the effects of Natal Pulses on ocean dynamics or if the paper does not provide a sufficient explanation for this finding.

4.2 SWOT Observability: The authors employ the U-net noise mitigation technique and assess its impact on different models. Despite the efficacy of the U-net method, it does slightly underestimate the signal amplitude. Also, there is no clear discussion on the limitations of using the U-net technique and the reasons behind its efficacy.