Implementation of the Optical Flow to Estimate the Propagation of Eddies in the South Atlantic Ocean

Round 1

Reviewer 1 Report

 

The optical flow method is applied to pairs of consecutive sea surface height maps producing a nearly 30-year long record. The paper is well written with clear illustrations. Here my suggestions to help increase interests from the ocean community:

Can the authors comment on the estimated spatial resolution of the resulting velocities, expected from both the application of the O-F methodology and the evolving resolution (number of satellites) of the SSH maps ? Can the authors comment about the O-F aperture problem (i.e. only motions across feature/eaddy gradients can be estimated) and also about the cost-function constraints used in the present study ? Can the author compare their use and assumptions of the O-F and the technique proposed by Piterbarg (2009)
Piterbarg, L.I., 2009. A simple method for computing velocities from tracer observations and a model output. Applied mathematical modelling, 33(9), pp.3693-3704.

Can the authors provide results over the last 15 years, to benefit an imrpoved satellite spatio-temporal coverage ?

Can the authors provide comparisons with velocities derived from the latest mean dynamic topography estimates ?

Can the authors possibly provide information about the estimated velocities associated to cyclones vs anti-cyclones, and estimates of the velocity distribution with the size of the eddies ?

Can the authors possibly comment about the joint use of SSH and SST maps ?

 

Author Response

We are very grateful to the reviewer for his/her time, constructive comments, and helpful suggestions. We have tried to address all comments accordingly. The Section 2 (Methods) has been substantially revised, which, we hope, improves the clarity of the manuscript. Our answers to the reviewer's comments are presented below following the subtitle "Authors". All changes we have introduced to the text are highlighted by blue color in the manuscript file.

Reviewer: The optical flow method is applied to pairs of consecutive sea surface height maps producing a nearly 30-year long record. The paper is well written with clear illustrations. Here my suggestions to help increase interests from the ocean community:

Can the authors comment on the estimated spatial resolution of the resulting velocities, expected from both the application of the O-F methodology and the evolving resolution (number of satellites) of the SSH maps?

Authors: The resulting velocities are obtained on the same 1/4-degree grid as the SSH maps. The resolution of these velocities depends on the patch size and on the effective resolution of SSH maps. The larger the patch size, the smoother the velocities are. Because we use the patch size of 5x5, the spacing between (u,v) estimates based on non-overlapping patches is 1.25 degrees. This is smaller than the effective resolution of SSH maps everywhere in the domain (which is not equal to 1/4-degree).

In the revised version of the manuscript, we provide a discussion of the effective resolution of SSH maps, as well as the impact of satellite constellation on the effective resolution in lines 119-127 (Section 2.1). In the following Section 2.2, we also include the following sentences: “For the grid spacing of 1/4° and the patch size of 5x5 pixels, the spacing between the estimates of u(u, v) based on non-overlapping W is 1.25°. This is less than the effective spatial resolution of SSH maps everywhere within the domain.” (lines 182-185).

Reviewer: Can the authors comment about the O-F aperture problem (i.e. only motions across feature/eddy gradients can be estimated) and also about the cost-function constraints used in the present study?

Authors: The aperture problem is resolved by applying the Lucas-Kanade method. We have modified the Section 2.2 to explicitly address this question (see lines 164-182). Regarding the cost function, equation (5) of the revised manuscript is the solution for the least-squares error of equation (3), that is the cost function is the sum over the patch W of the square of equation (3).

Reviewer: Can the author compare their use and assumptions of the O-F and the technique proposed by Piterbarg (2009)?

Piterbarg, L.I., 2009. A simple method for computing velocities from tracer observations and a model output. Applied mathematical modelling, 33(9), pp.3693-3704.

Authors: We thank the reviewer for bringing this interesting paper to our attention. However, we think that the method of Piterbarg is totally different, and it is not possible to make an apple-to-apple comparison. This method is to combine the model output and observations of a continuously distributed TRACER with forcing. In our case, SSH is not a tracer, but a dynamical property. We do not have any preliminary (background) estimate of the velocity field. The velocity field is obtained from the evolving texture of SSH maps. In this respect, the optical flow method can be compared to the maximum cross-correlation analysis, as we do in Section 4.

Reviewer: Can the authors provide results over the last 15 years, to benefit an improved satellite spatio-temporal coverage?

Authors: In lines 121-127 of the revised manuscript, we included the following sentences: “Due to the filtering properties of the optimal interpolation, the SSH maps have the effective spatial resolution ranging from about 400 km at 10°S to 100 km at 60°S and the effective temporal resolution varying between 14 – 45 days [42]. Although the number of simultaneously flying altimeter satellites has varied with time, it has been reported that the impact of satellite constellation on the effective spatial resolution is modest, with a globally averaged gain of resolution of ∼5% in maps constructed with three altimeters compared with two altimeters [42].”. Because of this, there is no significant difference between the velocities averaged over 1993-2021 and the ones averaged over the last 15 years.

Reviewer: Can the authors provide comparisons with velocities derived from the latest mean dynamic topography estimates?

Authors: The initial version of the manuscript did not make it clear that SSH we used in this study is the sum of mean dynamic topography and sea level anomalies. In the revised manuscript, we clarify this point in the first paragraph of Section 2.1 (lines 113-115): “The SSH above the geoid is the sum of the MDT-CNES-CLS22 mean dynamic topography [40] over the 1993-2012 period and sea level anomaly with respect to the mean sea surface.” Please note that the comparison presented in Fig. 5 uses the time-mean SSH (the caption of Fig. 5 has been corrected).

Reviewer: Can the authors possibly provide information about the estimated velocities associated to cyclones vs anti-cyclones, and estimates of the velocity distribution with the size of the eddies?

Authors: In the revised version of the manuscript, we clarify that: “Like the space-time lagged correlation analysis of [21,22], the OF method cannot distinguish various forms of eddy variability, e.g., isolated cyclones and anticyclones, planetary waves, meanders, fronts, etc..” (lines 68-71). In several places of the manuscript, we also state that the OF method provides a description of eddy propagation velocities in the Eulerian frame of reference, as opposed to the Lagrangian description of individual eddies.

Reviewer: Can the authors possibly comment about the joint use of SSH and SST maps?

Authors: As we mention in the Introduction (lines 66-67), the optical flow technique has been applied to SST images. However, we are not familiar with, nor we have worked on the application of the method to combine SSH and SST maps. This could be a subject for a follow-on study.

Reviewer 2 Report

Mesoscale eddies have long been a prominent topic in physical oceanography, playing a crucial role in global-scale matter and energy redistribution. In this study, the authors implemented the optical flow technique, a computer vision method, to map the pathways of mesoscale eddies in the South Atlantic Ocean. While various methods exist for eddy tracking, the proposed approach in this article is particularly intriguing. Notably, the optical flow method allows for the temporal evolution of eddy motion, which proves useful in regions with strong ocean currents. The research article is well-written, providing detailed data and comprehensive arguments. With some minor revisions, I recommend its publication in the journal "Remote Sensing."

General Comments:

1. The article's overall review of previous research is weak, as many important viewpoints lack references, resulting in only 39 cited references throughout the paper. This is insufficient for a research topic like mesoscale eddies. Please refer to my following explanations for specific details. However, I have only provided a portion, and the authors need to enhance the paper further through their own efforts.

2. Lines 139-140: “We compute the optical flow between the pairs of SSH maps separated by 10 days (Dt = 10 days).” The satellite observations used in this study provide daily data, so why is Dt set to 10 days instead of 1 day?

“We assume that (i) the SSH change over Dt is relatively small...”. Additionally, the authors assume that the change in SSH over dt is small, and for this condition to hold, dt should be as small as possible.

3. Line 153: “W is nxn, and in this study, n is 5, with a horizontal resolution of 1/4, thus the distance from ocean grid points to the coastal boundary is at least 2.5°. Figure 1 in the paper shows that many eddies are located at a distance from the coastal boundary that is less than 2.5 degrees. Has the author considered this issue?

Minor Comments:

1. Lines 35-37: “This type of ocean variability is usually termed as mesoscale eddies, where the generic term 'eddies' includes vortices, meanders, fronts, filaments, and planetary Rossby waves." In Sun et al. (2021), the type of eddy you mentioned is referred to as "transient mesoscale eddy.” It might be beneficial for the authors to refer to this terminology and consider incorporating it into their study.

Reference: Sun W, Yang J, Tan W, Liu Y, Zhao B, He Y, et al. Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean. Acta Oceanol Sin. (2021) 40: 1-16. doi: 10.1007/s13131-021-1881-4 2.

Lines 42-44: “They carry properties horizontally and redistribute them vertically, contribute to the climatically meaningful meridional heat transport, drive regional sea level changes, influence shipping routes and fisheries, etc.” I agree with your point that mesoscale eddies indeed have these important roles. However, I believe it is necessary for the authors to include references to these relevant studies. Numerous research papers are available in this field, such as Zhang et al. (2014), Dong et al. (2014), etc.

References:

Dong C, McWilliams JC, Liu Y, Chen D. Global heat and salt transports by eddy movement. Nat. Commun. (2014) 5: 1-6. doi: 10.1038/ncomms4294

Zhang Z, Wang W, Qiu B. Oceanic mass transport by mesoscale eddies. Science. (2014) 345: 322-4. doi: 10.1126/science.1252418

3. Lines 49-53: The authors reviewed the optical flow (OW) method and wavelet analysis (WA) method, but in fact, Nencioli et al. (2010) proposed the “vorticity gradient” (VG) method, and comparative studies have been conducted between the OW method, WA method, and VG method. It was found that the VG method has advantages in eddy detection, and it has been widely used in the study of mesoscale eddies (Liu et al., 2012; Sun et al., 2021).

References:

Liu Y, Dong C, Guan Y, Chen D, McWilliams J, Nencioli F. Eddy analysis in the subtropical zonal band of the North Pacific Ocean. Deep Sea Res. (2012) 68: 54-67. doi: 10.1016/j.dsr.2012.06.001

Nencioli F, Dong C, Dickey T, Washburn L, McWilliams JC. A vector geometry-based eddy detection algorithm and its application to a high-resolution numerical model product and high-frequency radar surface velocities in the Southern California Bight. J. Atmos. Oceanic Technol. (2010) 27: 564-79. doi: 10.1175/2009JTECHO725.1

Author Response

We are very grateful to the reviewer for his/her time, constructive comments, and helpful suggestions. We have tried to address all comments accordingly. The Section 2 (Methods) has been substantially revised, which, we hope, improves the clarity of the manuscript. Our answers to the reviewer's comments are presented below following the subtitle "Authors". All changes we have introduced to the text are highlighted by blue color in the manuscript file.

Reviewer: General Comments

1. The article's overall review of previous research is weak, as many important viewpoints lack references, resulting in only 39 cited references throughout the paper. This is insufficient for a research topic like mesoscale eddies. Please refer to my following explanations for specific details. However, I have only provided a portion, and the authors need to enhance the paper further through their own efforts.

Authors: We thank the reviewer for providing additional references on the topic of mesoscale eddies. We have included all of them and added some more in the revision. This is indeed a very rich topic, and this manuscript is not meant to provide an all-inclusive overview, but we have tried to include the main studies of eddy detection and tracking.

Reviewer: 2. Lines 139-140: “We compute the optical flow between the pairs of SSH maps separated by 10 days (Dt = 10 days).” The satellite observations used in this study provide daily data, so why is Dt set to 10 days instead of 1 day?

“We assume that (i) the SSH change over Dt is relatively small...”. Additionally, the authors assume that the change in SSH over dt is small, and for this condition to hold, dt should be as small as possible.

Authors: Because of the filtering properties of the optimal interpolation the SSH maps are very smooth in time. In the revised version of the manuscript, we have included a discussion of the effective spatial and temporal resolutions of SSH maps (lines 121-127). Note that the smallest repeat period of altimeter satellites (excluding crossover points) is about 10 days. The effective temporal resolution varies between 14-45 days, so while Dt = 10 days is computationally less expensive, it is still less than the effective temporal resolution.

Reviewer: 3. Line 153: “W is nxn, and in this study, n is 5, with a horizontal resolution of 1/4, thus the distance from ocean grid points to the coastal boundary is at least 2.5°. Figure 1 in the paper shows that many eddies are located at a distance from the coastal boundary that is less than 2.5 degrees. Has the author considered this issue?

Authors: We thank the reviewer for this comment, and we agree that the manuscript needs to clarify this issue. In the revised version of the manuscript (lines 181-185), we include the following sentences, which we hope address the issue: “Any land and out-of-bound pixels falling within W are discarded, reducing the number of equations in (4). For the grid spacing of 1/4° and the patch size of 5x5 pixels, the spacing between the estimates of u(u, v) based on non-overlapping W is 1.25°. This is less than the effective spatial resolution of SSH maps everywhere within the domain.” Because patches overlap and u(u, v) is estimated at each grid point (1/4-degree spacing between the grid nodes), this means that the distance between land and a grid point with an estimate of u(u, v) can be less than 1.25 degrees.

Reviewer: Minor Comments

1. Lines 35-37: “This type of ocean variability is usually termed as mesoscale eddies, where the generic term 'eddies' includes vortices, meanders, fronts, filaments, and planetary Rossby waves." In Sun et al. (2021), the type of eddy you mentioned is referred to as "transient mesoscale eddy.” It might be beneficial for the authors to refer to this terminology and consider incorporating it into their study.

Reference: Sun W, Yang J, Tan W, Liu Y, Zhao B, He Y, et al. Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean. Acta Oceanol Sin. (2021) 40: 1-16. doi: 10.1007/s13131-021-1881-4 2.

Authors: We thank the reviewer for this suggestion. We have adapted the term “transient mesoscale eddies” throughout the manuscript where applicable.

Reviewer: Lines 42-44: “They carry properties horizontally and redistribute them vertically, contribute to the climatically meaningful meridional heat transport, drive regional sea level changes, influence shipping routes and fisheries, etc.” I agree with your point that mesoscale eddies indeed have these important roles. However, I believe it is necessary for the authors to include references to these relevant studies. Numerous research papers are available in this field, such as Zhang et al. (2014), Dong et al. (2014), etc.

References:

Dong C, McWilliams JC, Liu Y, Chen D. Global heat and salt transports by eddy movement. Nat. Commun. (2014) 5: 1-6. doi: 10.1038/ncomms4294

Zhang Z, Wang W, Qiu B. Oceanic mass transport by mesoscale eddies. Science. (2014) 345: 322-4. doi: 10.1126/science.1252418

Authors: These references and some more have been added to the revised manuscript. We thank the reviewer for mentioning them.

Reviewer: 3. Lines 49-53: The authors reviewed the optical flow (OW) method and wavelet analysis (WA) method, but in fact, Nencioli et al. (2010) proposed the “vorticity gradient” (VG) method, and comparative studies have been conducted between the OW method, WA method, and VG method. It was found that the VG method has advantages in eddy detection, and it has been widely used in the study of mesoscale eddies (Liu et al., 2012; Sun et al., 2021).

Authors: We agree with the reviewer. In the revised manuscript, we have modified the review of prior work by including the following sentence (lines 49-52): “Existing techniques include the Okubo-Weiss method [9-12], algorithms based on the geometry of velocity vectors and streamlines [13-17], a hybrid geometric Okubo-Weiss method [18], a wavelet-based approach [19,20], and an objective method based on geodesic transport theory [21].”

Reviewer: References

Liu Y, Dong C, Guan Y, Chen D, McWilliams J, Nencioli F. Eddy analysis in the subtropical zonal band of the North Pacific Ocean. Deep Sea Res. (2012) 68: 54-67. doi: 10.1016/j.dsr.2012.06.001

Nencioli F, Dong C, Dickey T, Washburn L, McWilliams JC. A vector geometry-based eddy detection algorithm and its application to a high-resolution numerical model product and high-frequency radar surface velocities in the Southern California Bight. J. Atmos. Oceanic Technol. (2010) 27: 564-79. doi: 10.1175/2009JTECHO725.1

Authors: These references have been included in the revision.

Reviewer 3 Report

The authors present very nice results on the application of a computer vision technique to satellite altimetry data to estimate the direction and speed of eddies in the South Atlantic Ocean. This work is very important as mesoscale eddies play a crucial role in heat transport and strongly influence the mean state of the ocean. The manuscript is well written, the structure follows a logical order and the figures are of high quality and clear. I congratulate the authors for their efforts, which will be very much appreciated by the scientific community. The paper should definitely be published but requires some corrections which are listed below.

  

Major comments

 1. Please review the transport estimates mentioned in lines 89-90. The estimate of the MC transport (60–90 Sv) seems to be too high. Recent studies suggest that the MC transport is approximately 30–40 Sv based on direct velocity measurements as well as numerical simulations [Piola et al., 2013; Frey et al., 2021; Combes and Matano, 2014]. Please also provide the range of the BC transport estimates.

Combes, V., & Matano, R. P. (2014). A two-way nested simulation of the oceanic circulation in the Southwestern Atlantic. Journal of Geophysical Research: Oceans, 119, 731–756. https://doi.org/10.1002/2013JC009498

Frey, D. I., Piola, A. R., Krechik, V. A., Fofanov, D. V., Morozov, E. G., Silvestrova, K. P., et al. (2021). Direct measurements of the Malvinas Current velocity structure. Journal of Geophysical Research: Oceans, 126, e2020JC016727. https://doi.org/10.1029/2020JC016727

Piola, A. R., Franco, B. C., Palma, E. D., & Saraceno, M. (2013). Multiple jets in the Malvinas Current. Journal of Geophysical Research: Oceans, 118, 2107–2117. https://doi.org/10.1002/jgrc.20170

 

2. In line 120, you write that you use each 10th SSH map to reduce the computational cost, which seems reasonable. However, have you tested that your method gives the same result if you use, for example, every 5th or 15th SSH map? Also note that not all modern satellite altimeters have a period of approximately 10 days

 

3. There are gaps in data south of 55S in all SSH and SSH-derived maps. Is this because of sea ice cover? To my knowledge, satellite altimetry does provide data for this area, but maybe not for the entire 30-year long period

  

Minor comments

Line 91. Both the Brazil and the Malvinas Currents collide

Currents => currents

Figure 2a. All axis and color scale labels are too small, please increase the font size.

Figure 4. Please mention which bottom topography data you have used. Is it GEBCO2023 or another database? You may want to add several bathymetry contours (200, 4000 m) to show the shelf break and continental slope clearly. The classic blue-white color palette for bathymetry seems better to me.

Line 448. the OF method CAN be used

Author Response

We are very grateful to the reviewer for his/her time, constructive comments, and helpful suggestions. We have tried to address all comments accordingly. The Section 2 (Methods) has been substantially revised, which, we hope, improves the clarity of the manuscript. Our answers to the reviewer's comments are presented below following the subtitle "Authors". All changes we have introduced to the text are highlighted by blue color in the manuscript file.

Reviewer: Major comments

1. Please review the transport estimates mentioned in lines 89-90. The estimate of the MC transport (60–90 Sv) seems to be too high. Recent studies suggest that the MC transport is approximately 30–40 Sv based on direct velocity measurements as well as numerical simulations [Piola et al., 2013; Frey et al., 2021; Combes and Matano, 2014]. Please also provide the range of the BC transport estimates.

Combes, V., & Matano, R. P. (2014). A two-way nested simulation of the oceanic circulation in the Southwestern Atlantic. Journal of Geophysical Research: Oceans, 119, 731–756. https://doi.org/10.1002/2013JC009498

Frey, D. I., Piola, A. R., Krechik, V. A., Fofanov, D. V., Morozov, E. G., Silvestrova, K. P., et al. (2021). Direct measurements of the Malvinas Current velocity structure. Journal of Geophysical Research: Oceans, 126, e2020JC016727. https://doi.org/10.1029/2020JC016727

Piola, A. R., Franco, B. C., Palma, E. D., & Saraceno, M. (2013). Multiple jets in the Malvinas Current. Journal of Geophysical Research: Oceans, 118, 2107–2117. https://doi.org/10.1002/jgrc.20170

Authors: We thank the reviewer for bringing more recent estimates of the MC transport to our attention. We have included the suggested references and modified the text accordingly (see lines 89-92). We have also included one of the recent estimates of the Brazil Current transport at 34.5S from Chidichimo et al (2021).

Reviewer: 2. In line 120, you write that you use each 10th SSH map to reduce the computational cost, which seems reasonable. However, have you tested that your method gives the same result if you use, for example, every 5th or 15th SSH map? Also note that not all modern satellite altimeters have a period of approximately 10 days

Authors: There is no significant difference if we use every 5th or even every single SSH map, at least within the study domain. In the revised manuscript, we have discussed the effective resolution of SSH maps (lines 121-127). This is true that not all altimeter satellites have the repeat period of ~10 days, but this is the shortest period. So, we think that making Dt < 10 days is an overkill, while making Dt >=15 days could be at the edge of or exceed the effective temporal resolution in some places. 

Reviewer: 3. There are gaps in data south of 55S in all SSH and SSH-derived maps. Is this because of sea ice cover? To my knowledge, satellite altimetry does provide data for this area, but maybe not for the entire 30-year long period

Authors: Yes, this is because of seasonal sea ice cover. We have included the following sentence in the caption of Fig. 1 of the revised manuscript: “The blank areas are places with data gaps due to seasonal sea ice cover.” This is true that altimetry provides data when sea ice is not present. However, because we low-pass filter the data to remove the seasonal, interannual and longer-term variations, we disregard the areas with data gaps. These areas do not represent a significant portion of our study domain.

Reviewer: Minor comments

Line 91. Both the Brazil and the Malvinas Currents collide

Currents => currents

Authors: Corrected.

Reviewer: Figure 2a. All axis and color scale labels are too small, please increase the font size.

Authors: The font size has been increased.

Reviewer: Figure 4. Please mention which bottom topography data you have used. Is it GEBCO2023 or another database? You may want to add several bathymetry contours (200, 4000 m) to show the shelf break and continental slope clearly. The classic blue-white color palette for bathymetry seems better to me.

Authors: To plot maps, we used M_Map toolbox for Matlab by Rich Pawlowicz (www.eoas.ubc.ca/~rich/map.html), which uses ETOPO2 Global Relief Model. The caption of Fig. 4 now mentions that. We have also added 200-m and 4000-m bathymetry contours and changed the colormap in Fig. 4.

Reviewer: Line 448. the OF method CAN be used

Authors: Corrected. Thank you!