the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Improved global sea surface height and currents maps from remote sensing and in situ observations
- 1Collecte Localisation Satellites, 31520 Ramonville-Saint-Agne, France
- 2Datlas, 38400 Saint Martin d’Hères, France
- 3Centre National d'Études Spatiales, 31400 Toulouse, France
- 4Centre de Topographie des Océans et de l’Hydrosphère, Laboratoire d’Etudes en Géophysique et Océanographie Spatiale, CNRS, CNES, IRD, Université Toulouse III, Toulouse, France
- 1Collecte Localisation Satellites, 31520 Ramonville-Saint-Agne, France
- 2Datlas, 38400 Saint Martin d’Hères, France
- 3Centre National d'Études Spatiales, 31400 Toulouse, France
- 4Centre de Topographie des Océans et de l’Hydrosphère, Laboratoire d’Etudes en Géophysique et Océanographie Spatiale, CNRS, CNES, IRD, Université Toulouse III, Toulouse, France
Abstract. We present a new gridded sea surface height and current dataset produced by combining observations from nadir altimeters and drifting buoys. This product is based on a multiscale & multivariate mapping approach that offers the possibility to improve the physical content of gridded products by combining the data from various platforms and in resolving a broader spectrum of ocean surface dynamic than in the current operational mapping system. The dataset covers the entire global ocean and spans from 2016-07-01 to 2020-06-30. The multiscale approach decomposes the observed signal into different physical contributions. In the present study, we simultaneously estimate the mesoscale ocean circulations as well as part of the equatorial wave dynamics (e.g., tropical instability and Poincaré waves). The multivariate approach is able to exploit the geostrophic signature resulting from the synergy of altimetry and drifter observations. Sea level observations in Arctic leads are also used in the merging to improve the surface circulation in this poorly mapped region. A quality assessment of this new product is proposed against the DUACS operational product distributed in the Copernicus Marine Service. We show that the multiscale & multivariate mapping approach offers promising perspectives for reconstructing the ocean surface circulation: leads observations contribute to improve the coverage in delivering gap free maps in the Arctic; drifters observations help to refine the mapping in regions of intense dynamics where the temporal sampling must be accurate enough to properly map the rapid mesoscale dynamics; overall, the geostrophic circulation is better mapped in the new product, with mapping errors significantly reduced in regions of high variability and in the equatorial band; the effective resolution of this new product is hence between 5 % and 10 % finer than the Copernicus product.
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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
(3541 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.
Journal article(s) based on this preprint
Maxime Ballarotta et al.
Interactive discussion
Status: closed
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RC1: 'Comment on essd-2022-181', Anonymous Referee #1, 31 Aug 2022
General Comments
This paper begins by presenting a new gridding method for producing maps of currents and sea surface height by combining data from altimeters and measurements from drifting buoys.
The method was already proposed in a previous work published by one of the authors of this paper and tested using an Observing System Simulation Experiment (OSSE) and Observing System Experiment (OSE). Here the method is applied for the first time to real data and the results appear to be quite interesting.
In its current form, the article also includes a very long description of the mapping method that has already been published, which, at the same time, is also too short for readers unfamiliar with the mathematical details of the discussion. My suggestion is to move section 2.2 (methods) to an appendix leaving in the main text only a qualitative introduction to the two gridding methods. This will also give the opportunity to add some missing information, such as, for example, justify the choice of covariance function or the limit to 1000 observations, which I assume is the result of several trials.
The major merit of this paper is to propose the combined use of al the useful and available data (altimeters and drifters) to obtain an improved product for the global ocean circulation also in view of the future missions based on large swath technologies. Even if the actual improvement of the currents and seal level is not very impressive, I am convinced that the method and the strategy of using data form very different platforms is more than promising. In this sense, I would also be curious to know how far this new interpolation method is from being used in an operational context such as CMEMS.
Overall, I would say that it is a good paper that deserves to be published doing some revisions as suggested in this review
Recommendation: minor to major revisions
Specific Comments
Section 2.1, table 1: date interval in the table “20160115-20200630” please put a space or any other kind of separator between year month and day (this applies for all the dates in the paper). In the same table also add “degrees” in the spatial coverage line. And also define AOML.
Section 2.1.1 line 79-80: Add a reference.
Section 2.1.1 figure 1: How many altimeters are included in these 7 days period?
Section 2.1.2, line 89: The reference to Prandi et al. is not in the references section. This is not the only missed reference, please check the reference section.
Section 2.1.2: probably some of the readers might be interested in understanding how the altimeter can measure sea level in ice-covered areas. Can you add few words about this?
Section 2.1.3: Really a lot of model-based corrections! How much better is this geostrophic estimate than using geostrophic currents directly derived from models from their sea level elevation estimates (when produced)?
Section 2.1.3, figure 3: no drifters in the Mediterranean Sea in 2019?
Section 2.2.1, line 143: Duced et al 2000 in not in the reference section
Section 2.2.1, it would be interesting to see the covariance function. Also, Arhan and Colin de Verdière (1985) in not in the reference list. Definitely the reference section needs to be carefully reviewed!
Section 2.2.1, line 176: “(in this study N=3”. The second parathesis is missing.
Section 2.2.1, lines 221-222: “the result strongly relies on the choice of covariance models”. Once again, if this choice is so important, I suggest to show your choice.
Section 3.1, line 290: “geostrophic current anomaly data from AOML drifter database” How “geostrophic currents” are computed from drifter (by the way lagrangian) velocities?
Section 3.1, line 293-294: what is the criterion used to select the 20% to be excluded?
Section 3.2, line 315: the mentioned “geostrophic velocity errors” refers to the intensity or to a specific component?
Section 3.2, lines 333-334: The criterion used to determine the effective resolution is not justified. If not an explanation at least a reference is needed. Moreover, can the slope of the PSD contribute to determine the effective resolution?
Figure 6: Why not show the two variance maps as well?
Table 4: Perhaps you need more digits to appreciate differences of less than 1%? Is that reasonable? Why can you say 0.0% for the Arctic and -0.8 for the equatorial belt when you read the same numbers in columns 2 and 3? Of course, this question applies also for the other tables.
Section 4.2.1, Geostrophic current quality: “Overall, MIOST surface velocities are slightly closer to drifter velocities than the DUACS surface velocities.” can it be said that MIOST is closer to the drifters also because it applies a kind of assimilation of them?
Table 6: It would probably be interesting to show the error for velocity intensity as well.
Section 5: Ubelmann et al (2020, 2021): 2020 or 2016? Once again control the reference section.
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AC1: 'Reply on RC1', Maxime Ballarotta, 15 Dec 2022
The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2022-181/essd-2022-181-AC1-supplement.pdf
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AC1: 'Reply on RC1', Maxime Ballarotta, 15 Dec 2022
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RC2: 'Comment on essd-2022-181', Anonymous Referee #2, 01 Nov 2022
This manuscript presents a new gridded sea surface height and current dataset produced by combining observations from nadir altimeters and drifting buoys. The application of the MIOST solution is extended to the simultaneous mapping of equatorial waves and mesoscale circulation from real observations. These results pave the way for the exploration of new types of ocean signals that may eventually be mapped from remote sensing and in situ observations.
In the introduction section, it is better to review and summarize different global gridded sea surface current datasets that already exist. Also, Further highlight the differences and advantages between this data set and other previous data sets.
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AC2: 'Reply on RC2', Maxime Ballarotta, 15 Dec 2022
The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2022-181/essd-2022-181-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Maxime Ballarotta, 15 Dec 2022
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RC3: 'Comment on essd-2022-181', Anonymous Referee #3, 16 Nov 2022
Review of the MS by Ballarotta et al. (essd-2022-181)
The MS makes a significant step in reconstruction of gridded global sea level and surface currents over extended range of scales, based on fusing the data from different sources. While Level-3 altimetry is the main data source, known problems related to anisotropy of sampling density in along-track and cross-track directions are gradually solved by inclusion of independent surface drifter data. From methodical point of view, classical optimal interpolation scheme, used in the operational DUACS setup, is extended in the experimental MIOST method. The new method allows inclusion of theoretical knowledge of the involved processes (i.e. geostrophy, divergent and high-frequency ageostrophy, dispersion relations of basic wave types etc) based on the wavelet decomposition of original physical state vectors into scale-dependent components in the time-space domain. Such an approach is promising.
Practical study is made on the basis of data from three sources: CMEMS Global Altimeter SLA products, experimental Arctic leads Altimeter SLA products, and drifter trajectories related to the AOML Drifters’ geostrophic velocity product. Drifter data were not used in the equatorial strip.
While overall material of the MS is clear, interesting and worth publishing, I give some comments which may be taken into account when preparing the final MS.1. The MS involves a number of issues from physical oceanography, but their presentation is rather fragmentary. There could be an outline of the scales and main features of the processes that are considered in the methods and results, perhaps in the introduction or in the beginning of sub-sections of section 2.2.2 (see the next comment). For example, it could be noted, that slow Rossby waves are solved already within geostrophy, but faster equatorial waves (TIW and Poincaré) benefit from direct inclusion of their dispersion relations.
2. The section “2.2.2 A multiscale & multivariate mapping approach” is too technical. The section start with noting the oversampling problem (lines 168-173) is not helpful and could be skipped. The section could briefly summarize the motivation by Ubelmann et al. (2021) written in the Plain Language Summary. The list in lines 175-179 /1) geostrophy and equatorial waves: 2) Tropical Instability Waves (TIW) and 3) Poincaré waves/ could be elaborated and explained; it could be also harmonized with caption of Figure 7 and equations 20, 21. I propose that in the beginning of each approach of inclusion of analytical expressions, description of specific oceanographic processes could be given together with references to the basic literature.
3. Presentation of matrix-vector operations in lines 178-222 is exactly copied from the paper by Ubelmann et al. (2021). Such repetition is not necessary. The section could be condensed and explained for the user who is not intending to make own implementation or development of the method, but rather interested to understand the basic steps behind the new gridded data sets. It seems that the key equations are 9, 10 and 15. Regarding (10), it could be explicitly written that index k (1...3) presents different type of physics as stated earlier. Type of the wavelet decomposition (line 189, but also 240, 253) is not clear and could be explained
4. The section of geostrophy component in lines 225-255 is again a direct copy from Ubelmann et al. (2021). It is necessary for the next parts of the MS. Still, it can be modified for better readability. For example, more physics like quasi-geostrophic motions, including Rossby waves (later referenced in line 373), could be noted.
5. Compared to Ubelmann et al. (2021), the MS presents new approach for two types of equatorial waves. Since earlier in lines 175-179 these waves were indexed k=2 and k=3, then dispersion relations Eq (21) should be split into two, with appropriate indexes. Literature references to the dispersion relations should be given.
6. Reasons for excluding the drifter data in the equatorial zone (lines 294-296) are not clear; are the drifter data too noisy to evaluate equatorial waves, or some other reasons.
7. Description of experiments (lines 296-299) does not agree with the Table 3; data from Copernicus Marine Service referred in the text are not in the table.
8. Vorticity results are presented without any explanation (line 344, Fig. 5). Why we need them, are we interested in eddies etc?
9. Theoretical dispersion curves in Fig. 7 are not labeled. Their main features are not explained and/or referenced in the text.Technical issues
a) The title starts with “Improved global sea surface height and currents maps...”. Although comparison with the existing sea level maps (E.U. Copernicus Marine Service (product reference SEALEVEL_GLO_PHY_L3_MY_008_062) show some improvement during the 4 years test period, in my understanding it is not yet finally clear whether the new method is also an improved method in statistical sense.
b) Lines 22-23 state that “this new product is proposed against the DUACS operational product distributed in the Copernicus Marine Service.” The wording may create a feeling of contradiction, but in essence, the new method is meant to be used in further development of CMEMS.
c) Line 28: “effective resolution” remains unclear in the abstract, although it is well presented in the main text.
d) There is a number of unexplained abbreviations like AVISO, DUACS, MIOST, AOML, SWOT.
e) The name DUACS in the section 2.2.1 heading (line 140) is not informative. The section presents optimal interpolation used in the operational setup.
f) Line 256 should have reference to Fig. 4a and 4c (not the whole Fig. 4), since westward propagating graphs (Fig. 4b and 4d) are introduced in the next section.
g) Lines 376-378 (caption of Fig. 7) lacks the notation, which curves correspond to Kelvin, Yanai, Rossby and Poincaré waves.
h) There should be space between the number and the unit (lines 386-389, 412, 414 and so on).
i) Naming of the experiments should be unified throughout the MS. There are EXP01 to EXP03 listed in Table 3, but other names are given in the captions of Figs. 8-14.
j) Reference list could be extended to include basic papers in physical oceanography, relevant to the altimetry development issues.
k) References should be ordered according to the journal rules (alphabetically), presently there are flaws. Paper by Le Guillou lacks reference to the publication year.-
AC3: 'Reply on RC3', Maxime Ballarotta, 15 Dec 2022
The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2022-181/essd-2022-181-AC3-supplement.pdf
-
AC3: 'Reply on RC3', Maxime Ballarotta, 15 Dec 2022
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on essd-2022-181', Anonymous Referee #1, 31 Aug 2022
General Comments
This paper begins by presenting a new gridding method for producing maps of currents and sea surface height by combining data from altimeters and measurements from drifting buoys.
The method was already proposed in a previous work published by one of the authors of this paper and tested using an Observing System Simulation Experiment (OSSE) and Observing System Experiment (OSE). Here the method is applied for the first time to real data and the results appear to be quite interesting.
In its current form, the article also includes a very long description of the mapping method that has already been published, which, at the same time, is also too short for readers unfamiliar with the mathematical details of the discussion. My suggestion is to move section 2.2 (methods) to an appendix leaving in the main text only a qualitative introduction to the two gridding methods. This will also give the opportunity to add some missing information, such as, for example, justify the choice of covariance function or the limit to 1000 observations, which I assume is the result of several trials.
The major merit of this paper is to propose the combined use of al the useful and available data (altimeters and drifters) to obtain an improved product for the global ocean circulation also in view of the future missions based on large swath technologies. Even if the actual improvement of the currents and seal level is not very impressive, I am convinced that the method and the strategy of using data form very different platforms is more than promising. In this sense, I would also be curious to know how far this new interpolation method is from being used in an operational context such as CMEMS.
Overall, I would say that it is a good paper that deserves to be published doing some revisions as suggested in this review
Recommendation: minor to major revisions
Specific Comments
Section 2.1, table 1: date interval in the table “20160115-20200630” please put a space or any other kind of separator between year month and day (this applies for all the dates in the paper). In the same table also add “degrees” in the spatial coverage line. And also define AOML.
Section 2.1.1 line 79-80: Add a reference.
Section 2.1.1 figure 1: How many altimeters are included in these 7 days period?
Section 2.1.2, line 89: The reference to Prandi et al. is not in the references section. This is not the only missed reference, please check the reference section.
Section 2.1.2: probably some of the readers might be interested in understanding how the altimeter can measure sea level in ice-covered areas. Can you add few words about this?
Section 2.1.3: Really a lot of model-based corrections! How much better is this geostrophic estimate than using geostrophic currents directly derived from models from their sea level elevation estimates (when produced)?
Section 2.1.3, figure 3: no drifters in the Mediterranean Sea in 2019?
Section 2.2.1, line 143: Duced et al 2000 in not in the reference section
Section 2.2.1, it would be interesting to see the covariance function. Also, Arhan and Colin de Verdière (1985) in not in the reference list. Definitely the reference section needs to be carefully reviewed!
Section 2.2.1, line 176: “(in this study N=3”. The second parathesis is missing.
Section 2.2.1, lines 221-222: “the result strongly relies on the choice of covariance models”. Once again, if this choice is so important, I suggest to show your choice.
Section 3.1, line 290: “geostrophic current anomaly data from AOML drifter database” How “geostrophic currents” are computed from drifter (by the way lagrangian) velocities?
Section 3.1, line 293-294: what is the criterion used to select the 20% to be excluded?
Section 3.2, line 315: the mentioned “geostrophic velocity errors” refers to the intensity or to a specific component?
Section 3.2, lines 333-334: The criterion used to determine the effective resolution is not justified. If not an explanation at least a reference is needed. Moreover, can the slope of the PSD contribute to determine the effective resolution?
Figure 6: Why not show the two variance maps as well?
Table 4: Perhaps you need more digits to appreciate differences of less than 1%? Is that reasonable? Why can you say 0.0% for the Arctic and -0.8 for the equatorial belt when you read the same numbers in columns 2 and 3? Of course, this question applies also for the other tables.
Section 4.2.1, Geostrophic current quality: “Overall, MIOST surface velocities are slightly closer to drifter velocities than the DUACS surface velocities.” can it be said that MIOST is closer to the drifters also because it applies a kind of assimilation of them?
Table 6: It would probably be interesting to show the error for velocity intensity as well.
Section 5: Ubelmann et al (2020, 2021): 2020 or 2016? Once again control the reference section.
-
AC1: 'Reply on RC1', Maxime Ballarotta, 15 Dec 2022
The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2022-181/essd-2022-181-AC1-supplement.pdf
-
AC1: 'Reply on RC1', Maxime Ballarotta, 15 Dec 2022
-
RC2: 'Comment on essd-2022-181', Anonymous Referee #2, 01 Nov 2022
This manuscript presents a new gridded sea surface height and current dataset produced by combining observations from nadir altimeters and drifting buoys. The application of the MIOST solution is extended to the simultaneous mapping of equatorial waves and mesoscale circulation from real observations. These results pave the way for the exploration of new types of ocean signals that may eventually be mapped from remote sensing and in situ observations.
In the introduction section, it is better to review and summarize different global gridded sea surface current datasets that already exist. Also, Further highlight the differences and advantages between this data set and other previous data sets.
-
AC2: 'Reply on RC2', Maxime Ballarotta, 15 Dec 2022
The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2022-181/essd-2022-181-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Maxime Ballarotta, 15 Dec 2022
-
RC3: 'Comment on essd-2022-181', Anonymous Referee #3, 16 Nov 2022
Review of the MS by Ballarotta et al. (essd-2022-181)
The MS makes a significant step in reconstruction of gridded global sea level and surface currents over extended range of scales, based on fusing the data from different sources. While Level-3 altimetry is the main data source, known problems related to anisotropy of sampling density in along-track and cross-track directions are gradually solved by inclusion of independent surface drifter data. From methodical point of view, classical optimal interpolation scheme, used in the operational DUACS setup, is extended in the experimental MIOST method. The new method allows inclusion of theoretical knowledge of the involved processes (i.e. geostrophy, divergent and high-frequency ageostrophy, dispersion relations of basic wave types etc) based on the wavelet decomposition of original physical state vectors into scale-dependent components in the time-space domain. Such an approach is promising.
Practical study is made on the basis of data from three sources: CMEMS Global Altimeter SLA products, experimental Arctic leads Altimeter SLA products, and drifter trajectories related to the AOML Drifters’ geostrophic velocity product. Drifter data were not used in the equatorial strip.
While overall material of the MS is clear, interesting and worth publishing, I give some comments which may be taken into account when preparing the final MS.1. The MS involves a number of issues from physical oceanography, but their presentation is rather fragmentary. There could be an outline of the scales and main features of the processes that are considered in the methods and results, perhaps in the introduction or in the beginning of sub-sections of section 2.2.2 (see the next comment). For example, it could be noted, that slow Rossby waves are solved already within geostrophy, but faster equatorial waves (TIW and Poincaré) benefit from direct inclusion of their dispersion relations.
2. The section “2.2.2 A multiscale & multivariate mapping approach” is too technical. The section start with noting the oversampling problem (lines 168-173) is not helpful and could be skipped. The section could briefly summarize the motivation by Ubelmann et al. (2021) written in the Plain Language Summary. The list in lines 175-179 /1) geostrophy and equatorial waves: 2) Tropical Instability Waves (TIW) and 3) Poincaré waves/ could be elaborated and explained; it could be also harmonized with caption of Figure 7 and equations 20, 21. I propose that in the beginning of each approach of inclusion of analytical expressions, description of specific oceanographic processes could be given together with references to the basic literature.
3. Presentation of matrix-vector operations in lines 178-222 is exactly copied from the paper by Ubelmann et al. (2021). Such repetition is not necessary. The section could be condensed and explained for the user who is not intending to make own implementation or development of the method, but rather interested to understand the basic steps behind the new gridded data sets. It seems that the key equations are 9, 10 and 15. Regarding (10), it could be explicitly written that index k (1...3) presents different type of physics as stated earlier. Type of the wavelet decomposition (line 189, but also 240, 253) is not clear and could be explained
4. The section of geostrophy component in lines 225-255 is again a direct copy from Ubelmann et al. (2021). It is necessary for the next parts of the MS. Still, it can be modified for better readability. For example, more physics like quasi-geostrophic motions, including Rossby waves (later referenced in line 373), could be noted.
5. Compared to Ubelmann et al. (2021), the MS presents new approach for two types of equatorial waves. Since earlier in lines 175-179 these waves were indexed k=2 and k=3, then dispersion relations Eq (21) should be split into two, with appropriate indexes. Literature references to the dispersion relations should be given.
6. Reasons for excluding the drifter data in the equatorial zone (lines 294-296) are not clear; are the drifter data too noisy to evaluate equatorial waves, or some other reasons.
7. Description of experiments (lines 296-299) does not agree with the Table 3; data from Copernicus Marine Service referred in the text are not in the table.
8. Vorticity results are presented without any explanation (line 344, Fig. 5). Why we need them, are we interested in eddies etc?
9. Theoretical dispersion curves in Fig. 7 are not labeled. Their main features are not explained and/or referenced in the text.Technical issues
a) The title starts with “Improved global sea surface height and currents maps...”. Although comparison with the existing sea level maps (E.U. Copernicus Marine Service (product reference SEALEVEL_GLO_PHY_L3_MY_008_062) show some improvement during the 4 years test period, in my understanding it is not yet finally clear whether the new method is also an improved method in statistical sense.
b) Lines 22-23 state that “this new product is proposed against the DUACS operational product distributed in the Copernicus Marine Service.” The wording may create a feeling of contradiction, but in essence, the new method is meant to be used in further development of CMEMS.
c) Line 28: “effective resolution” remains unclear in the abstract, although it is well presented in the main text.
d) There is a number of unexplained abbreviations like AVISO, DUACS, MIOST, AOML, SWOT.
e) The name DUACS in the section 2.2.1 heading (line 140) is not informative. The section presents optimal interpolation used in the operational setup.
f) Line 256 should have reference to Fig. 4a and 4c (not the whole Fig. 4), since westward propagating graphs (Fig. 4b and 4d) are introduced in the next section.
g) Lines 376-378 (caption of Fig. 7) lacks the notation, which curves correspond to Kelvin, Yanai, Rossby and Poincaré waves.
h) There should be space between the number and the unit (lines 386-389, 412, 414 and so on).
i) Naming of the experiments should be unified throughout the MS. There are EXP01 to EXP03 listed in Table 3, but other names are given in the captions of Figs. 8-14.
j) Reference list could be extended to include basic papers in physical oceanography, relevant to the altimetry development issues.
k) References should be ordered according to the journal rules (alphabetically), presently there are flaws. Paper by Le Guillou lacks reference to the publication year.-
AC3: 'Reply on RC3', Maxime Ballarotta, 15 Dec 2022
The comment was uploaded in the form of a supplement: https://essd.copernicus.org/preprints/essd-2022-181/essd-2022-181-AC3-supplement.pdf
-
AC3: 'Reply on RC3', Maxime Ballarotta, 15 Dec 2022
Peer review completion
Journal article(s) based on this preprint
Maxime Ballarotta et al.
Data sets
Gridded Sea Level Height and geostrophic velocities computed with Multiscale Interpolation combining altimetry and drifters Maxime Ballarotta, C. Ubelmann, P. Veillard, P. Prandi, H. Etienne, S. Mulet, Y. Faugère, G. Dibarboure, R. Morrow & N. Picot https://doi.org/10.24400/527896/a01-2022.009
Maxime Ballarotta et al.
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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.
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