the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Dec 2022
A robust framework for comparing Lagrangian and gridded Eulerian velocity fields: an example application to surface drifters and altimetry-derived surface currents
Abstract. A novel framework for comparing Lagrangian and gridded Eulerian velocity fields is proposed. The method involves three steps that individually leverage the strengths of each reference frame to provide robust intercomparisons, while also allowing the user to adapt the individual steps to the process of interest. The utility of the methodology is then demonstrated by applying it to a comparison between a set of 34 Lagrangian surface drifters deployed on the continental shelf around the southern tip of Greenland and Eulerian altimetry-derived surface currents with and without Ekman velocities. We conclude that the methodology sufficiently addresses differences between the reference frames and accurately identifies errors when they exist. This result enables us to conclude that the altimetry-derived surface currents accurately resolve the important components of the shelf circulation around the southern tip of Greenland and can be used to track pathways of fresh water around Greenland.
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RC1: 'Comment on egusphere-2022-1450', Anonymous Referee #1, 09 Feb 2023
general comments
The authors propose a more comprehensive approach for evaluating and intercomparing different Eulerian gridded surface current products against Lagrangian drifting data. It consists in evaluating gridded Eulerian products in 3 independent steps: a direct comparison of model velocities to drifter velocities, a comparison in the Eulerian frame of reference by transforming Lagrangian drifting velocities onto a Eulerian grid, and finally a comparison in the Lagrangian framework through the generation of model trajectories from eulerian velocities. These approaches are not novel as suggested in the title as each one is widely applied in the community but not necessarily altogether in one same study as done here. A novelty however is the complementary assessment of products using along and across shore velocities.
The authors illustrate the approach with a case study around Greenland comparing two altimetry-derived surface velocity products (geostrophy and geostophy+ekman), and conclude that both products reproduce well the shelf circulation of the region without entering too much in the detail as to why. The tone of the paper is ambitious, yet the manuscript does not contain major advances, and I feel that the manuscript would require significant modification for reaching the objectives it sets itself.
specific comments
A concluding sentence of the introduction highlights the model errors in the region as a justification for such study, yet no model have been included in the investigation, solely altimetry derived products. The regional analysis system TOPAZ4 was included in step1 as a reference point, but not carried across in the following steps which is regrettable. One main purpose of carrying out such intercomparison work is to assess the skill of operational systems. Previous studies have evaluated altimetry products with operationnel systems (e.g. Dagestad and Rohrs, 2019). It would therefore be very valuable to assess TOPAZ4 in all 3 steps.
The manuscript would benefit from a more exhaustive review of work carried out on the topic (and in the region), so to highlight the state of the art, present their limitation to justify the proposed approach.
For step1, the methodology suggests to select the closest gridded product point to compare with the observation (daily average). I disagree with this approach and would recommend to interpolate the product value at the point of observation. It is not clear what resolution TOPAZ4 is, and for an approach to be robust a methodology should also be provided when comparing products of different resolution.
It is not clear how across and along shelf velocity are calculated, (this could be illustrated in figure1). The author mention smoothing the bathymetry, but without further detail (which bathymetry product, is the bathymetry common to all products?), how is the distance to the coast calculated? The authors introduce frequency spectrum analysis but do not carry it out in this study.
Comments for step2:
Lagrangian velocity is transformed onto Eulerian grid for comparison. The result is a map of average velocity for each gridcell wherethrough drifter travelled for the period that the drifter covered. The spatial averaging is well explained and clear, what is not so clear is how the eulerian gridded product velocities have been selected to confront with each transformed lagrangian velocity. Let say if velocity values for a drifter travelling a given cell covers the temporal window not centered on the time window of the daily average gridded product, how is this addressed?
A map of mean velocity vectors for each product, together with differences in magnitude and direction are proposed to evaluate the skill of products for the different subregions of the shelf. It would be interesting to measure second order statistics so to get a better feel of the product behaviour, and put uncertainties on the values (e.g. on skill score like Revelard et al. 2021).
Comments for step3:
Statistics are done for the Liu skill score. A score that sets to 0 the negative values. Mean values of this skill score do not take into account the negative values, and may not be so robust when intercomparing models. Other studies have suggested alternative statistics for the skill score distribution such as the proportion of score > 0.6 (Revelard et al. 2021), which may be more informative.
No information is given for the particle tracking software used.
Overall point for the case study:
This study investigates altimetry derived products for the Greenland shelf, with an assessment of Ekman component on improving the representation of shelf circulation. The study would benefit from a more in depth study of the processes. For example, evaluating the altimetry tracks, in particular their angle relative to meridional/zonal component, which could explain the better resolution of one component relative to the other. Relative to Ekman, questions are raised to explain why it may perform better than other regions. The Ekman component of the product could be assessed by investigating wind patterns of the regions, and see if a better parameterisation would improve results.
A paragraph is missing in the discussion wherein the 3 steps are brought together and their complementarity illustrated, as such it feels like 3 independent steps.
The study does not address approaches raised in the community such as for example particle ensemble releases with diffusion terms to account uncertainties.
I feel that the manuscript would be better pitched if the authors stated that they used a complementary approach to validate surface current (here geo and geo + ekman) illustrated with their Greenland case study, rather than presenting it as a new framework.
Citation: https://doi.org/10.5194/egusphere-2022-1450-RC1 -
AC1: 'Reply on RC1', Arthur Coquereau, 28 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1450/egusphere-2022-1450-AC1-supplement.pdf
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AC1: 'Reply on RC1', Arthur Coquereau, 28 May 2023
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RC2: 'Comment on egusphere-2022-1450', Anonymous Referee #2, 06 Apr 2023
A robust framework for comparing Lagrangian and gridded Eulerian velocity fields: an example application to surface drifters and altimetry-derived surface currents
By A. Coquereau and N.P. Foukal
General comments
The paper seems to have two goals. One is to propose a new method, another is to validate the satellite velocities on the southern Greenland shelf as the authors make it clear they have a special interest in this region. Rather than being a thorough methods paper, it seems like that authors needed to validate satellite data in this region and part of a process study paper was rewritten as methods paper. Right now these goals seems to be add odds, presenting an objective examination of the skill of a method, versus having a clear interest in the satellite data to come through the validation. This shows in several ways. The only gridded Eulerian data considered is satellite data. This is specified in the title, but needs to be clearer throughout the text. Some Lagrangian methods to deal with data are also not considered. The area where the data is compared is very limited, and is more or less confined to one type of flow regime (a fast boundary current). There are also issues with the latitude (rossby radius and oneven bin sizes) direction of shelf versus the grid. Nearly all aspects of time and variability are ignored, but are a main interest in studies of ocean currents. If this is to be a true methods paper then these issues needs to be addressed and the methods needs to be shown for a more widely representative area.
Line by line comments
Line 12. “A fluid parcel trajectory“
Line 13. Please rephrase. It’s not the physical systems that needs to be constrained, but the observations of.
Lines 40-45. What is completely missing from these questions is the time aspect. How well do methods 1 and 2 do in varying conditions/seasons? In 3, how well is variability captured? Since a large part of oceanographic research is not to understand the mean field, but to explain changes and trends, this is not something that should be neglected.
Lines 63 to 69. It is not clear whether the described example applies to Fig 1. If it does, it would be helpful to zoom out in Fig 1 so one can more clearly see the shelf break and the chosen angles.
A question about this method. By limiting the comparison to discrete grid points, one might introduce artificial mismatched in the comparison. For example, if there is a clear front, or other dividing line between two flow regimes, the nearest grid point may be on the other side of the dividing line while the slightly further grid point may be in the same regime as the Lagrangian measurement. Allowing for interpolation between grid points would remote such artificial mismatches.
Lines 70 to 74. While several of the comparisons are definitely useful, none of them are actually done in this paper.
Lines 76 to 78. An important method that is left out here is clustering based on the Lagrangian data density (Koszalka and LaCasce, 2010). This is important because the data density itself provides important information on the flow field, not only in terms of fast and slow, but also in terms of convergence and divergence. This covers also the description of the problems in lines 81 through 83. However, the clustering method is more elegant than the methods proposed here, because it is not bound to fixed cell sizes.
Line 119-120. Rephrase the sentence “gridded Eulerian field” versus “time-averaged Eulerian field”. I’m assuming the authors are still referring to Lagrangian data (density), but it’s not clear from the sentence.
Line 137. Ect… Or, in the case of multiple trajectories, dispersion.
Line 142. More attention could be given to describe what is good or acceptable skill score is here and elsewhere.
Fig 3. Is the black dot at the start indicating a skill score of 0, or is it the start of the trajectory. In the latter case I suggest using a different symbol.
Lines 172-189. While this is an interesting data set, it is very limited in time and space. Therefore it may not be the best to test these method. See also earlier comments regarding the time aspect that needs to be considered.
Line 193 and 205. Would specify more clearly that the original satellite data does not have a daily resolution. The return period of a satellite over a certain track is 10 days. Therefore it is also not clear what the 6-hour resolution could add in information. What additional data would be included in this product that provides information on this time scale?
Lines 244 and onwards. The reader would be helped with interpretation of these results if the authors first gave an explanation on what values represent poor, medium, good and excellent skill scores. Also, what significance level is used to determine if correlations are significant?
Lines 248 to 268. The difference in skill between zonal and meridional velocities is worrisome. If the explanation by the authors is correct, this suggests that the area used is not ideally suited to test this method. It would be more convincing to test the methods with regular boxes (either by design or at lower latitudes) and away from a shelf that is aligned with one direction of the grid.
Line 286. If there is good reason, than it’s not surprising. Please rephrase this section.
Fig 5. There quite a number of points with very low skill score and low correlation, which is worrisome and not commented on by the authors.
Fig 6 and line 300. The difference in magnitude of some of these vectors is extremely larger. I am not surprised velocities from altimetry are lower, as a lot of averaging and filtering is applied to this data. I do not subscribe to the authors’ interpretation that a factor 2 difference in magnitude is acceptable or very good.
Line 314 to 315. See the general comment on competing interests or focus in the paper. The large differences in the comparison should not be accepted because the authors have a special interest in the shelf break.
Line 326. Variance is not addressed.
Line 370. Are skill scores of 0.55 really “particularly good”? Please keep in mind that these were also calculated for a very limited data set.
Line 386. “remarkably capable” is somewhat overstated given also lines 403- 406.
Line 407. “remain confident of tracking exchange” . There aspect of exchange is not addressed nor was it validated. Again, it shows a competing interest for the focus of the paper.
Lines 417 to end. This is indeed a very large caveat and needs to be addressed. See also other comments.
Citation: https://doi.org/10.5194/egusphere-2022-1450-RC2 -
AC2: 'Reply on RC2', Arthur Coquereau, 28 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1450/egusphere-2022-1450-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Arthur Coquereau, 28 May 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-1450', Anonymous Referee #1, 09 Feb 2023
general comments
The authors propose a more comprehensive approach for evaluating and intercomparing different Eulerian gridded surface current products against Lagrangian drifting data. It consists in evaluating gridded Eulerian products in 3 independent steps: a direct comparison of model velocities to drifter velocities, a comparison in the Eulerian frame of reference by transforming Lagrangian drifting velocities onto a Eulerian grid, and finally a comparison in the Lagrangian framework through the generation of model trajectories from eulerian velocities. These approaches are not novel as suggested in the title as each one is widely applied in the community but not necessarily altogether in one same study as done here. A novelty however is the complementary assessment of products using along and across shore velocities.
The authors illustrate the approach with a case study around Greenland comparing two altimetry-derived surface velocity products (geostrophy and geostophy+ekman), and conclude that both products reproduce well the shelf circulation of the region without entering too much in the detail as to why. The tone of the paper is ambitious, yet the manuscript does not contain major advances, and I feel that the manuscript would require significant modification for reaching the objectives it sets itself.
specific comments
A concluding sentence of the introduction highlights the model errors in the region as a justification for such study, yet no model have been included in the investigation, solely altimetry derived products. The regional analysis system TOPAZ4 was included in step1 as a reference point, but not carried across in the following steps which is regrettable. One main purpose of carrying out such intercomparison work is to assess the skill of operational systems. Previous studies have evaluated altimetry products with operationnel systems (e.g. Dagestad and Rohrs, 2019). It would therefore be very valuable to assess TOPAZ4 in all 3 steps.
The manuscript would benefit from a more exhaustive review of work carried out on the topic (and in the region), so to highlight the state of the art, present their limitation to justify the proposed approach.
For step1, the methodology suggests to select the closest gridded product point to compare with the observation (daily average). I disagree with this approach and would recommend to interpolate the product value at the point of observation. It is not clear what resolution TOPAZ4 is, and for an approach to be robust a methodology should also be provided when comparing products of different resolution.
It is not clear how across and along shelf velocity are calculated, (this could be illustrated in figure1). The author mention smoothing the bathymetry, but without further detail (which bathymetry product, is the bathymetry common to all products?), how is the distance to the coast calculated? The authors introduce frequency spectrum analysis but do not carry it out in this study.
Comments for step2:
Lagrangian velocity is transformed onto Eulerian grid for comparison. The result is a map of average velocity for each gridcell wherethrough drifter travelled for the period that the drifter covered. The spatial averaging is well explained and clear, what is not so clear is how the eulerian gridded product velocities have been selected to confront with each transformed lagrangian velocity. Let say if velocity values for a drifter travelling a given cell covers the temporal window not centered on the time window of the daily average gridded product, how is this addressed?
A map of mean velocity vectors for each product, together with differences in magnitude and direction are proposed to evaluate the skill of products for the different subregions of the shelf. It would be interesting to measure second order statistics so to get a better feel of the product behaviour, and put uncertainties on the values (e.g. on skill score like Revelard et al. 2021).
Comments for step3:
Statistics are done for the Liu skill score. A score that sets to 0 the negative values. Mean values of this skill score do not take into account the negative values, and may not be so robust when intercomparing models. Other studies have suggested alternative statistics for the skill score distribution such as the proportion of score > 0.6 (Revelard et al. 2021), which may be more informative.
No information is given for the particle tracking software used.
Overall point for the case study:
This study investigates altimetry derived products for the Greenland shelf, with an assessment of Ekman component on improving the representation of shelf circulation. The study would benefit from a more in depth study of the processes. For example, evaluating the altimetry tracks, in particular their angle relative to meridional/zonal component, which could explain the better resolution of one component relative to the other. Relative to Ekman, questions are raised to explain why it may perform better than other regions. The Ekman component of the product could be assessed by investigating wind patterns of the regions, and see if a better parameterisation would improve results.
A paragraph is missing in the discussion wherein the 3 steps are brought together and their complementarity illustrated, as such it feels like 3 independent steps.
The study does not address approaches raised in the community such as for example particle ensemble releases with diffusion terms to account uncertainties.
I feel that the manuscript would be better pitched if the authors stated that they used a complementary approach to validate surface current (here geo and geo + ekman) illustrated with their Greenland case study, rather than presenting it as a new framework.
Citation: https://doi.org/10.5194/egusphere-2022-1450-RC1 -
AC1: 'Reply on RC1', Arthur Coquereau, 28 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1450/egusphere-2022-1450-AC1-supplement.pdf
-
AC1: 'Reply on RC1', Arthur Coquereau, 28 May 2023
-
RC2: 'Comment on egusphere-2022-1450', Anonymous Referee #2, 06 Apr 2023
A robust framework for comparing Lagrangian and gridded Eulerian velocity fields: an example application to surface drifters and altimetry-derived surface currents
By A. Coquereau and N.P. Foukal
General comments
The paper seems to have two goals. One is to propose a new method, another is to validate the satellite velocities on the southern Greenland shelf as the authors make it clear they have a special interest in this region. Rather than being a thorough methods paper, it seems like that authors needed to validate satellite data in this region and part of a process study paper was rewritten as methods paper. Right now these goals seems to be add odds, presenting an objective examination of the skill of a method, versus having a clear interest in the satellite data to come through the validation. This shows in several ways. The only gridded Eulerian data considered is satellite data. This is specified in the title, but needs to be clearer throughout the text. Some Lagrangian methods to deal with data are also not considered. The area where the data is compared is very limited, and is more or less confined to one type of flow regime (a fast boundary current). There are also issues with the latitude (rossby radius and oneven bin sizes) direction of shelf versus the grid. Nearly all aspects of time and variability are ignored, but are a main interest in studies of ocean currents. If this is to be a true methods paper then these issues needs to be addressed and the methods needs to be shown for a more widely representative area.
Line by line comments
Line 12. “A fluid parcel trajectory“
Line 13. Please rephrase. It’s not the physical systems that needs to be constrained, but the observations of.
Lines 40-45. What is completely missing from these questions is the time aspect. How well do methods 1 and 2 do in varying conditions/seasons? In 3, how well is variability captured? Since a large part of oceanographic research is not to understand the mean field, but to explain changes and trends, this is not something that should be neglected.
Lines 63 to 69. It is not clear whether the described example applies to Fig 1. If it does, it would be helpful to zoom out in Fig 1 so one can more clearly see the shelf break and the chosen angles.
A question about this method. By limiting the comparison to discrete grid points, one might introduce artificial mismatched in the comparison. For example, if there is a clear front, or other dividing line between two flow regimes, the nearest grid point may be on the other side of the dividing line while the slightly further grid point may be in the same regime as the Lagrangian measurement. Allowing for interpolation between grid points would remote such artificial mismatches.
Lines 70 to 74. While several of the comparisons are definitely useful, none of them are actually done in this paper.
Lines 76 to 78. An important method that is left out here is clustering based on the Lagrangian data density (Koszalka and LaCasce, 2010). This is important because the data density itself provides important information on the flow field, not only in terms of fast and slow, but also in terms of convergence and divergence. This covers also the description of the problems in lines 81 through 83. However, the clustering method is more elegant than the methods proposed here, because it is not bound to fixed cell sizes.
Line 119-120. Rephrase the sentence “gridded Eulerian field” versus “time-averaged Eulerian field”. I’m assuming the authors are still referring to Lagrangian data (density), but it’s not clear from the sentence.
Line 137. Ect… Or, in the case of multiple trajectories, dispersion.
Line 142. More attention could be given to describe what is good or acceptable skill score is here and elsewhere.
Fig 3. Is the black dot at the start indicating a skill score of 0, or is it the start of the trajectory. In the latter case I suggest using a different symbol.
Lines 172-189. While this is an interesting data set, it is very limited in time and space. Therefore it may not be the best to test these method. See also earlier comments regarding the time aspect that needs to be considered.
Line 193 and 205. Would specify more clearly that the original satellite data does not have a daily resolution. The return period of a satellite over a certain track is 10 days. Therefore it is also not clear what the 6-hour resolution could add in information. What additional data would be included in this product that provides information on this time scale?
Lines 244 and onwards. The reader would be helped with interpretation of these results if the authors first gave an explanation on what values represent poor, medium, good and excellent skill scores. Also, what significance level is used to determine if correlations are significant?
Lines 248 to 268. The difference in skill between zonal and meridional velocities is worrisome. If the explanation by the authors is correct, this suggests that the area used is not ideally suited to test this method. It would be more convincing to test the methods with regular boxes (either by design or at lower latitudes) and away from a shelf that is aligned with one direction of the grid.
Line 286. If there is good reason, than it’s not surprising. Please rephrase this section.
Fig 5. There quite a number of points with very low skill score and low correlation, which is worrisome and not commented on by the authors.
Fig 6 and line 300. The difference in magnitude of some of these vectors is extremely larger. I am not surprised velocities from altimetry are lower, as a lot of averaging and filtering is applied to this data. I do not subscribe to the authors’ interpretation that a factor 2 difference in magnitude is acceptable or very good.
Line 314 to 315. See the general comment on competing interests or focus in the paper. The large differences in the comparison should not be accepted because the authors have a special interest in the shelf break.
Line 326. Variance is not addressed.
Line 370. Are skill scores of 0.55 really “particularly good”? Please keep in mind that these were also calculated for a very limited data set.
Line 386. “remarkably capable” is somewhat overstated given also lines 403- 406.
Line 407. “remain confident of tracking exchange” . There aspect of exchange is not addressed nor was it validated. Again, it shows a competing interest for the focus of the paper.
Lines 417 to end. This is indeed a very large caveat and needs to be addressed. See also other comments.
Citation: https://doi.org/10.5194/egusphere-2022-1450-RC2 -
AC2: 'Reply on RC2', Arthur Coquereau, 28 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1450/egusphere-2022-1450-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Arthur Coquereau, 28 May 2023
Peer review completion
Journal article(s) based on this preprint
Data sets
Global Ocean Gridded L4 Sea Surface Heights And Derived Variables Nrt EU Copernicus Marine Service https://doi.org/10.48670/moi-00149
Global Total Surface and 15m Current (COPERNICUS-GLOBCURRENT) from Altimetric Geostrophic Current and Modeled Ekman Current Processing EU Copernicus Marine Service https://doi.org/10.48670/moi-00049
Arctic Ocean Physics Analysis and Forecast Sakov, P., Counillon, F., Bertino, L., Lisæter, K. A., Oke, P. R. and Korablev, A. https://doi.org/10.48670/moi-00001
Global Drifter Program quality-controlled 6-hour interpolated data Lumpkin, R. and Centurioni, L. https://doi.org/10.25921/7ntx-z961
Global Ocean Gridded L 4 Sea Surface Heights And Derived Variables Reprocessed 1993 Ongoing EU Copernicus Marine Service https://doi.org/10.48670/moi-00148
Global Total Surface and 15m Current (COPERNICUS-GLOBCURRENT) from Altimetric Geostrophic Current and Modeled Ekman 440 Current Reprocessing EU Copernicus Marine Service https://doi.org/10.48670/moi-00050
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Arthur Coquereau
Nicholas P. Foukal
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(15957 KB) - Metadata XML
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Supplement
(6111 KB) - BibTeX
- EndNote
- Final revised paper