Producing SWOT measurements with a multiscale data assimilation system during the prelaunch field campaign

Li, Zhijin; Archer, Matthew R.; Wang, Jinbo; Fu, Lee-Lueng

doi:https://doi.org/10.5194/egusphere-2022-1399

Preprints

https://doi.org/10.5194/egusphere-2022-1399

Preprints

20 Dec 2022

| 20 Dec 2022

Producing SWOT measurements with a multiscale data assimilation system during the prelaunch field campaign

Zhijin Li, Matthew R. Archer, Jinbo Wang, and Lee-Lueng Fu

Abstract. A data assimilation system for a high-resolution model has been developed to address the opportunities and challenges posed by the upcoming Surface Water and Ocean Topography (SWOT) satellite mission. This developed system is based on a three-dimensional variational data assimilation scheme (3DVAR), which is computationally highly efficient and thus can be applied to a very high-resolution model. A crucial consideration of the system is to use a multiscale data assimilation approach (MSDA) to first assimilate routinely available observations, including conventional satellite altimetry, sea surface temperature (SST) and salinity (SSS), and temperature/salinity vertical profiles, to constrain large scales and large mesoscales. High-resolution (dense) observations and future SWOT measurements can then be effectively and seamlessly assimilated to constrain the smaller scales. The 3DVAR is extended to assimilate observations over a time interval, which specifically enhances the efficacy of the assimilation of satellite along-track altimetry observations, which are limited by large repeat time intervals. Using this system, a reanalysis dataset was produced for the SWOT pre-launch field campaign that took place in the California Current System from September through December, 2019. An evaluation of this system with assimilated and withheld data demonstrates its ability to effectively utilize both routine and campaign observations to produce sea surface heights with the accuracy close to that required by SWOT. These results suggest a promising avenue for data assimilation development in the SWOT altimetry era, which will need the capability of jointly assimilating existing routine observations with SWOT measurements to resolve small-scale ocean processes.

Received: 06 Dec 2022 – Discussion started: 20 Dec 2022

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Zhijin Li, Matthew R. Archer, Jinbo Wang, and Lee-Lueng Fu

Status: closed

RC1:
'Comment on egusphere-2022-1399', Anonymous Referee #1, 17 Feb 2023

Review of manuscript egusphere-2022-1399
Title: Producing SWOT measurements with a multiscale data assimilation system during the prelaunch field campaign.
General comments
I see the document has a DOI number, so I am not sure if this review is for recommendation for publication. But I read and review the manuscript as if it were. I read this manuscript with great interest, especially given the expertise of the listed first author on 3DVAR and multiscale data assimilation. Although the manuscript is generally well written, I found that it contains several points that need to be addressed and for which I cannot make a recommendation for publication.
I was anticipating the system to be used for the assimilation of simulated SWOT (lines 26-27 in the abstract), but that did not happen. The only dense observations assimilated in this manuscript were microwave SST. There was no assessment of the extent to which the assimilation was able to accurately correct spatial features resolved by the model. No one can really tell if this system will be effective for SWOT data, which I presume is the real target of the method.
The authors could have applied their method to the dense S-MODE field campaign data which was available at the time of this study.
The title is misleading and needs to be revised. As it stands, it conveys the idea that a multiscale data assimilation produces SWOT measurements. That statement cannot be true or even substantiated. Data assimilation has a specific use of words, and “measurements” commonly refer or relate to “observations”. Data assimilation produces an analysis or analysis increments, and thus in essence cannot and does not produce measurements, much less pre-launch SWOT measurements. What is the real meaning of the title?
The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
Specific comments
The system provides only a very modest 14% reduction in RMSD for SSH (lines 530-534).
An 11-day data window for 3DVAR is very unrealistic, even with inflated observation errors for those observations that are distant in time from the analysis time. No reason is provided to justify the choice.
The authors claim “a significant reduction in the forecast errors at all depths for both temperature and salinity when compared to the NODA run (not shown)”, lines 570-571. How can the reader assess or verify this significant reduction in forecast error if it is not shown? The backdrop of this information is a 14% error reduction in SSH at analysis time. The authors should have presented the results a that show the significant reduction in forecast error at all depths.
I am not sure why HYCOM is relevant to the discussion in the manuscript.

Citation: https://doi.org/10.5194/egusphere-2022-1399-RC1
- AC1: 'Reply on RC1', Zhijin Li, 09 Apr 2023
  
  The replies were given by the first author of the manuscript. The replies are in the bold font.
  General comments
  I see the document has a DOI number, so I am not sure if this review is for recommendation for publication. But I read and review the manuscript as if it were. I read this manuscript with great interest, especially given the expertise of the listed first author on 3DVAR and multiscale data assimilation. Although the manuscript is generally well written, I found that it contains several points that need to be addressed and for which I cannot make a recommendation for publication.
  I was anticipating the system to be used for the assimilation of simulated SWOT (lines 26-27 in the abstract), but that did not happen. The only dense observations assimilated in this manuscript were microwave SST. There was no assessment of the extent to which the assimilation was able to accurately correct spatial features resolved by the model. No one can really tell if this system will be effective for SWOT data, which I presume is the real target of the method.
  The authors could have applied their method to the dense S-MODE field campaign data which was available at the time of this study.
  The title is misleading and needs to be revised. As it stands, it conveys the idea that a multiscale data assimilation produces SWOT measurements. That statement cannot be true or even substantiated. Data assimilation has a specific use of words, and “measurements” commonly refer or relate to “observations”. Data assimilation produces an analysis or analysis increments, and thus in essence cannot and does not produce measurements, much less pre-launch SWOT measurements. What is the real meaning of the title?
  The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
  Reply: Thank you very much for reviewing the manuscript and the thoughtful and insightful comments.
  We agree that the title was misleading. It has been changed to “Simulating SWOT measurements with a multiscale data assimilation system during the prelaunch field campaign”.
  We thank the reviewer for suggesting to apply the system to S-MODE field campaigns, which we plan to do.
  The motivation of this manuscript is to assimilate very localized observations and see if we can generate SSH variability that SWOT aims to measure. The results suggested that we can assimilate localized observations after we appropriately assimilate observations from current observing networks, and it should be possible that we can assimilate SWOT measurements along with T/S vertical profiles in the future, although we agree that we cannot tell yet whether the system can effectively assimilate SWOT measurements. However, we believe that we need to learn more about SWOT measurements before we can assimilate them beyond traditional nadir altimetry measurements.
  A few field campaigns are going on now at some locations around the global ocean, aiming for SWOT Cal/Val and/or to understand SWOT measurements. Thus, another important motivation of this manuscript is to provide a reference for DA efforts associated with those SWOT Cal/Val field campaigns.
  In the manuscript, we repeatedly claimed that the DA scheme is 3DVAR. The cost function was defined over a time window, because it is needed to deriving the error associated with the difference between DA and sampling time. The 4DVAR scheme is mentioned for reminding the readers that this is not 4DVAR, because we did not use model forecast but persistency forecast in the cost function. We have revised the relevant paragraphs for more clearly making this point.
  In 3DVAR, we understand that it is impossible to deal with the error associated with the difference between DA and sampling time as 4DVAR does. However, we tried to add something that can mitigate the impact of this error in 3DVAR as much as possible. It is not a solution but a useful technique.
  We had emphasized that the used 3DVAR is of similarities to FGAT in the manuscript, even in the introduction. We also emphasized the difference from FGAT, that is, the error associated with the difference between DA and sampling time was formulated and estimated. In particular, it was easy to implement in any 3DVAR. Thus, we added a derivation and explanation, which should help readers to understand and use. However, we agree that we should delete all the words that make the 3DVAR method sound innovative. We have checked the entire manuscript and deleted the relevant words, that is , extent, extended and extension.
  
  Specific comments
  The system provides only a very modest 14% reduction in RMSD for SSH (lines 530-534).
  Reply: We agree that a reduction of 14% is not necessary to be significant. We have checked the manuscript and deleted “significant”.
  An 11-day data window for 3DVAR is very unrealistic, even with inflated observation errors for those observations that are distant in time from the analysis time. No reason is provided to justify the choice.
  Reply: It was empirically chosen. The major consideration is about the scales that large scale DA to constrain and the density of along-track altimetry measurements (see Fig. 3). It can be adjusted, but we used 11 days based on our past experience.
  The authors claim “a significant reduction in the forecast errors at all depths for both temperature and salinity when compared to the NODA run (not shown)”, lines 570-571. How can the reader assess or verify this significant reduction in forecast error if it is not shown? The backdrop of this information is a 14% error reduction in SSH at analysis time. The authors should have presented the results a that show the significant reduction in forecast error at all depths.
  Reply: We agree that it could be misleading to call the reduction to be significant. We have checked it in the entire manuscript and have deleted it
  I am not sure why HYCOM is relevant to the discussion in the manuscript.
  Reply: HYCOM data sets are used for the model lateral boundary conditions and also for comparisons.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC1
- AC3: 'Reply on RC1', Zhijin Li, 09 Apr 2023
  
  RC1 Comment
  The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
  Reply: We revised the manuscript in response to this comment.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC3
- AC4: 'Reply on RC1', Zhijin Li, 09 Apr 2023
  
  RC1 Comment
  The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
  Reply: We revised the section that describes the 3DVAR algorithm in response to this major comment. The revised section was submitted as Supplement.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC4
RC2:
'Comment on egusphere-2022-1399', Anonymous Referee #2, 17 Mar 2023

The ms. presents an ocean data assimilation system and its use in a pre-launch field campaign for SWOT in the California Current System.
The topic is timely and original in that it addresses the problem of simultaneous estimation of multiple ocean scales (multiscale DA), in particular the fusion via DA of routine observational constraints with very local observational constraints from a field campaign. However, the ms. does not address this central issue with sufficient focus, precision and detail.
The ms. describes the experimental protocol and offers an illustration, at times reasonably convincing, of the capabilities of the DA scheme without and with assimilated field data in addition to routine observations. However, it suffers from numerous shortcomings that detract from both the understanding of the approach (especially its important details) and its ultimate credibility.
Several key concepts are only vaguely explained or not at all, and/or their merits are not convincingly and quantitatively demonstrated:

- The successive assimilation of different scales in separate steps - since the assimilated observations are different at each step, this comes back to doing everything in one step with a block-diagonal B matrix: is it reasonable to assume that prior uncertainties on the various scales are uncoupled/uncorrelated to each other?

- The modeling of multivariate uncertainties in B and the associated notion of B-scaling (nondimensionalization), which directly control the topology of the descent space of the variational algorithm. And, if the assimilation is univariate, how do you apply dynamical balances and avoid the problems listed at the bottom of page 20?

- The (multiscale) localization, how it is applied, the sensitivity of results to localization.

- How is the R matrix set for gridded data? Do you consider observational uncertainties at each gridpoint as independent/uncorrelated to each other? Couldn't that lead to overfitting?

- The descent algorithm itself and how it imposes a cost function form and limits the options available for four-dimensional inversion. For instance, the so-called "sampling time error" is only an error insofar as the approximation page 12 line 282 is made -- do alternate formulations exist in the literature for the 4D extension of 3D-Var?

- The choice of linear modelling of the "sampling time error" in (4) and its calibration (only a vague hint on lines 397-398 on page 16).
As it stands, I consider the scientific value and innovative character of this ms. to be extremely modest.
For these reasons, I cannot recommend publication of this manuscript in its current state. Alternatively, the editor might consider that pending a very substantial revision of content, form and focus, the ms. might reach a state acceptable to this particular journal.
Given the extent of my general comments above, I will not give a detailed list of smaller comments. This will be for a second round if the Editor decides to give this ms. a chance.

Citation: https://doi.org/10.5194/egusphere-2022-1399-RC2
- AC2: 'Reply on RC2', Zhijin Li, 09 Apr 2023
  
  The replies were given by the first author of the manuscript. The replies are in the bold font.
  Reply
  The ms. presents an ocean data assimilation system and its use in a pre-launch field campaign for SWOT in the California Current System.
  The topic is timely and original in that it addresses the problem of simultaneous estimation of multiple ocean scales (multiscale DA), in particular the fusion via DA of routine observational constraints with very local observational constraints from a field campaign. However, the ms. does not address this central issue with sufficient focus, precision and detail.
  The ms. describes the experimental protocol and offers an illustration, at times reasonably convincing, of the capabilities of the DA scheme without and with assimilated field data in addition to routine observations. However, it suffers from numerous shortcomings that detract from both the understanding of the approach (especially its important details) and its ultimate credibility.
  Reply: Thank you very much for reviewing the manuscript and the thoughtful and insightful comments.
  Several key concepts are only vaguely explained or not at all, and/or their merits are not convincingly and quantitatively demonstrated:
  
  - The successive assimilation of different scales in separate steps - since the assimilated observations are different at each step, this comes back to doing everything in one step with a block-diagonal B matrix: is it reasonable to assume that prior uncertainties on the various scales are uncoupled/uncorrelated to each other?
  Reply: Yes, it is reasonable. It has long been known that the correlations between different scales is zero if the background error is homogeneous and isotropic. It can be traced back to the classic Wiener-Khinchin theorem.
  -The modeling of multivariate uncertainties in B and the associated notion of B-scaling (nondimensionalization), which directly control the topology of the descent space of the variational algorithm. And, if the assimilation is univariate, how do you apply dynamical balances and avoid the problems listed at the bottom of page 20?
  Reply: This is an important question. Yes, the dynamical balance used was described in Li et al. (2008a), which was cited in the manuscript. In MSDA, we emphasize that the dynamical balance become scale dependent.
  
  - The (multiscale) localization, how it is applied, the sensitivity of results to localization.
  Reply: We do not use localization. The background error correlations were given according to decorrelation length scales. The correlations have been compact.
  
  - How is the R matrix set for gridded data? Do you consider observational uncertainties at each gridpoint as independent/uncorrelated to each other? Couldn't that lead to overfitting?
  Reply: This is an important point. We assimilated the gridded data only in the large-scale DA. The DA spatial scale is close to the gridded data scale, so that the representation error is small. This is one major motivation of using MSDA.
  
  - The descent algorithm itself and how it imposes a cost function form and limits the options available for four-dimensional inversion. For instance, the so-called "sampling time error" is only an error insofar as the approximation page 12 line 282 is made -- do alternate formulations exist in the literature for the 4D extension of 3D-Var?
  Reply: There are different practical ways to assimilate observations over a time window. 4DVAR is ideal. Because of difficulties and demanding computational costs with 4DVAR for high resolution models, we used 3DVAR but tried to assimilate observations over a time window in a more reasonable way, while we understand that it could not match 4DVAR.
  
  - The choice of linear modelling of the "sampling time error" in (4) and its calibration (only a vague hint on lines 397-398 on page 16).
  Reply. We agree. It was not optimal and could be better estimated.
  As it stands, I consider the scientific value and innovative character of this ms. to be extremely modest.
  Reply: We agree. The manuscript basically aimed to provide a reference for researchers who work on DA with high resolutions models and on assimilation of spatially localized observations.
  For these reasons, I cannot recommend publication of this manuscript in its current state. Alternatively, the editor might consider that pending a very substantial revision of content, form and focus, the ms. might reach a state acceptable to this particular journal.
  Given the extent of my general comments above, I will not give a detailed list of smaller comments. This will be for a second round if the Editor decides to give this ms. a chance.
  Reply: Thank you.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC2

Status: closed

RC1:
'Comment on egusphere-2022-1399', Anonymous Referee #1, 17 Feb 2023

Review of manuscript egusphere-2022-1399
Title: Producing SWOT measurements with a multiscale data assimilation system during the prelaunch field campaign.
General comments
I see the document has a DOI number, so I am not sure if this review is for recommendation for publication. But I read and review the manuscript as if it were. I read this manuscript with great interest, especially given the expertise of the listed first author on 3DVAR and multiscale data assimilation. Although the manuscript is generally well written, I found that it contains several points that need to be addressed and for which I cannot make a recommendation for publication.
I was anticipating the system to be used for the assimilation of simulated SWOT (lines 26-27 in the abstract), but that did not happen. The only dense observations assimilated in this manuscript were microwave SST. There was no assessment of the extent to which the assimilation was able to accurately correct spatial features resolved by the model. No one can really tell if this system will be effective for SWOT data, which I presume is the real target of the method.
The authors could have applied their method to the dense S-MODE field campaign data which was available at the time of this study.
The title is misleading and needs to be revised. As it stands, it conveys the idea that a multiscale data assimilation produces SWOT measurements. That statement cannot be true or even substantiated. Data assimilation has a specific use of words, and “measurements” commonly refer or relate to “observations”. Data assimilation produces an analysis or analysis increments, and thus in essence cannot and does not produce measurements, much less pre-launch SWOT measurements. What is the real meaning of the title?
The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
Specific comments
The system provides only a very modest 14% reduction in RMSD for SSH (lines 530-534).
An 11-day data window for 3DVAR is very unrealistic, even with inflated observation errors for those observations that are distant in time from the analysis time. No reason is provided to justify the choice.
The authors claim “a significant reduction in the forecast errors at all depths for both temperature and salinity when compared to the NODA run (not shown)”, lines 570-571. How can the reader assess or verify this significant reduction in forecast error if it is not shown? The backdrop of this information is a 14% error reduction in SSH at analysis time. The authors should have presented the results a that show the significant reduction in forecast error at all depths.
I am not sure why HYCOM is relevant to the discussion in the manuscript.

Citation: https://doi.org/10.5194/egusphere-2022-1399-RC1
- AC1: 'Reply on RC1', Zhijin Li, 09 Apr 2023
  
  The replies were given by the first author of the manuscript. The replies are in the bold font.
  General comments
  I see the document has a DOI number, so I am not sure if this review is for recommendation for publication. But I read and review the manuscript as if it were. I read this manuscript with great interest, especially given the expertise of the listed first author on 3DVAR and multiscale data assimilation. Although the manuscript is generally well written, I found that it contains several points that need to be addressed and for which I cannot make a recommendation for publication.
  I was anticipating the system to be used for the assimilation of simulated SWOT (lines 26-27 in the abstract), but that did not happen. The only dense observations assimilated in this manuscript were microwave SST. There was no assessment of the extent to which the assimilation was able to accurately correct spatial features resolved by the model. No one can really tell if this system will be effective for SWOT data, which I presume is the real target of the method.
  The authors could have applied their method to the dense S-MODE field campaign data which was available at the time of this study.
  The title is misleading and needs to be revised. As it stands, it conveys the idea that a multiscale data assimilation produces SWOT measurements. That statement cannot be true or even substantiated. Data assimilation has a specific use of words, and “measurements” commonly refer or relate to “observations”. Data assimilation produces an analysis or analysis increments, and thus in essence cannot and does not produce measurements, much less pre-launch SWOT measurements. What is the real meaning of the title?
  The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
  Reply: Thank you very much for reviewing the manuscript and the thoughtful and insightful comments.
  We agree that the title was misleading. It has been changed to “Simulating SWOT measurements with a multiscale data assimilation system during the prelaunch field campaign”.
  We thank the reviewer for suggesting to apply the system to S-MODE field campaigns, which we plan to do.
  The motivation of this manuscript is to assimilate very localized observations and see if we can generate SSH variability that SWOT aims to measure. The results suggested that we can assimilate localized observations after we appropriately assimilate observations from current observing networks, and it should be possible that we can assimilate SWOT measurements along with T/S vertical profiles in the future, although we agree that we cannot tell yet whether the system can effectively assimilate SWOT measurements. However, we believe that we need to learn more about SWOT measurements before we can assimilate them beyond traditional nadir altimetry measurements.
  A few field campaigns are going on now at some locations around the global ocean, aiming for SWOT Cal/Val and/or to understand SWOT measurements. Thus, another important motivation of this manuscript is to provide a reference for DA efforts associated with those SWOT Cal/Val field campaigns.
  In the manuscript, we repeatedly claimed that the DA scheme is 3DVAR. The cost function was defined over a time window, because it is needed to deriving the error associated with the difference between DA and sampling time. The 4DVAR scheme is mentioned for reminding the readers that this is not 4DVAR, because we did not use model forecast but persistency forecast in the cost function. We have revised the relevant paragraphs for more clearly making this point.
  In 3DVAR, we understand that it is impossible to deal with the error associated with the difference between DA and sampling time as 4DVAR does. However, we tried to add something that can mitigate the impact of this error in 3DVAR as much as possible. It is not a solution but a useful technique.
  We had emphasized that the used 3DVAR is of similarities to FGAT in the manuscript, even in the introduction. We also emphasized the difference from FGAT, that is, the error associated with the difference between DA and sampling time was formulated and estimated. In particular, it was easy to implement in any 3DVAR. Thus, we added a derivation and explanation, which should help readers to understand and use. However, we agree that we should delete all the words that make the 3DVAR method sound innovative. We have checked the entire manuscript and deleted the relevant words, that is , extent, extended and extension.
  
  Specific comments
  The system provides only a very modest 14% reduction in RMSD for SSH (lines 530-534).
  Reply: We agree that a reduction of 14% is not necessary to be significant. We have checked the manuscript and deleted “significant”.
  An 11-day data window for 3DVAR is very unrealistic, even with inflated observation errors for those observations that are distant in time from the analysis time. No reason is provided to justify the choice.
  Reply: It was empirically chosen. The major consideration is about the scales that large scale DA to constrain and the density of along-track altimetry measurements (see Fig. 3). It can be adjusted, but we used 11 days based on our past experience.
  The authors claim “a significant reduction in the forecast errors at all depths for both temperature and salinity when compared to the NODA run (not shown)”, lines 570-571. How can the reader assess or verify this significant reduction in forecast error if it is not shown? The backdrop of this information is a 14% error reduction in SSH at analysis time. The authors should have presented the results a that show the significant reduction in forecast error at all depths.
  Reply: We agree that it could be misleading to call the reduction to be significant. We have checked it in the entire manuscript and have deleted it
  I am not sure why HYCOM is relevant to the discussion in the manuscript.
  Reply: HYCOM data sets are used for the model lateral boundary conditions and also for comparisons.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC1
- AC3: 'Reply on RC1', Zhijin Li, 09 Apr 2023
  
  RC1 Comment
  The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
  Reply: We revised the manuscript in response to this comment.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC3
- AC4: 'Reply on RC1', Zhijin Li, 09 Apr 2023
  
  RC1 Comment
  The authors make a bold claim in the manuscript that they have “extended” the 3DVAR algorithm (section 3) by including time distributed observations in the cost function, and inflating their associated observation error due to the “sampling time error”. First, this is nothing new or different than FGAT: even though innovations are calculated in time, collocated observations cannot be assimilated simultaneously. Second, analysis increments are still being computed only at the analysis time, so the corrections are not applied at the time of the observations that is different from the analysis time. This is due to the nature of 3DVAR and its static covariance. I thus don’t understand why the authors claim this is an extension of 3DVAR. The authors also liken their cost function to and consider it to be a reduced 4DVAR cost function. The similarity of the const functions should not be a basis for comparison, even via reduction, of 3DVAR and 4DVAR. Their respective cost functions are minimized under different constraints. In 4DVAR, those constraints include strong or weak model dynamics, and in 3DVAR there is no dynamical constraints. The authors should avoid making such confusing comparisons. The method proposed in section 3 is nothing but a MS3DVAR with FGAT.
  Reply: We revised the section that describes the 3DVAR algorithm in response to this major comment. The revised section was submitted as Supplement.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC4
RC2:
'Comment on egusphere-2022-1399', Anonymous Referee #2, 17 Mar 2023

The ms. presents an ocean data assimilation system and its use in a pre-launch field campaign for SWOT in the California Current System.
The topic is timely and original in that it addresses the problem of simultaneous estimation of multiple ocean scales (multiscale DA), in particular the fusion via DA of routine observational constraints with very local observational constraints from a field campaign. However, the ms. does not address this central issue with sufficient focus, precision and detail.
The ms. describes the experimental protocol and offers an illustration, at times reasonably convincing, of the capabilities of the DA scheme without and with assimilated field data in addition to routine observations. However, it suffers from numerous shortcomings that detract from both the understanding of the approach (especially its important details) and its ultimate credibility.
Several key concepts are only vaguely explained or not at all, and/or their merits are not convincingly and quantitatively demonstrated:

- The successive assimilation of different scales in separate steps - since the assimilated observations are different at each step, this comes back to doing everything in one step with a block-diagonal B matrix: is it reasonable to assume that prior uncertainties on the various scales are uncoupled/uncorrelated to each other?

- The modeling of multivariate uncertainties in B and the associated notion of B-scaling (nondimensionalization), which directly control the topology of the descent space of the variational algorithm. And, if the assimilation is univariate, how do you apply dynamical balances and avoid the problems listed at the bottom of page 20?

- The (multiscale) localization, how it is applied, the sensitivity of results to localization.

- How is the R matrix set for gridded data? Do you consider observational uncertainties at each gridpoint as independent/uncorrelated to each other? Couldn't that lead to overfitting?

- The descent algorithm itself and how it imposes a cost function form and limits the options available for four-dimensional inversion. For instance, the so-called "sampling time error" is only an error insofar as the approximation page 12 line 282 is made -- do alternate formulations exist in the literature for the 4D extension of 3D-Var?

- The choice of linear modelling of the "sampling time error" in (4) and its calibration (only a vague hint on lines 397-398 on page 16).
As it stands, I consider the scientific value and innovative character of this ms. to be extremely modest.
For these reasons, I cannot recommend publication of this manuscript in its current state. Alternatively, the editor might consider that pending a very substantial revision of content, form and focus, the ms. might reach a state acceptable to this particular journal.
Given the extent of my general comments above, I will not give a detailed list of smaller comments. This will be for a second round if the Editor decides to give this ms. a chance.

Citation: https://doi.org/10.5194/egusphere-2022-1399-RC2
- AC2: 'Reply on RC2', Zhijin Li, 09 Apr 2023
  
  The replies were given by the first author of the manuscript. The replies are in the bold font.
  Reply
  The ms. presents an ocean data assimilation system and its use in a pre-launch field campaign for SWOT in the California Current System.
  The topic is timely and original in that it addresses the problem of simultaneous estimation of multiple ocean scales (multiscale DA), in particular the fusion via DA of routine observational constraints with very local observational constraints from a field campaign. However, the ms. does not address this central issue with sufficient focus, precision and detail.
  The ms. describes the experimental protocol and offers an illustration, at times reasonably convincing, of the capabilities of the DA scheme without and with assimilated field data in addition to routine observations. However, it suffers from numerous shortcomings that detract from both the understanding of the approach (especially its important details) and its ultimate credibility.
  Reply: Thank you very much for reviewing the manuscript and the thoughtful and insightful comments.
  Several key concepts are only vaguely explained or not at all, and/or their merits are not convincingly and quantitatively demonstrated:
  
  - The successive assimilation of different scales in separate steps - since the assimilated observations are different at each step, this comes back to doing everything in one step with a block-diagonal B matrix: is it reasonable to assume that prior uncertainties on the various scales are uncoupled/uncorrelated to each other?
  Reply: Yes, it is reasonable. It has long been known that the correlations between different scales is zero if the background error is homogeneous and isotropic. It can be traced back to the classic Wiener-Khinchin theorem.
  -The modeling of multivariate uncertainties in B and the associated notion of B-scaling (nondimensionalization), which directly control the topology of the descent space of the variational algorithm. And, if the assimilation is univariate, how do you apply dynamical balances and avoid the problems listed at the bottom of page 20?
  Reply: This is an important question. Yes, the dynamical balance used was described in Li et al. (2008a), which was cited in the manuscript. In MSDA, we emphasize that the dynamical balance become scale dependent.
  
  - The (multiscale) localization, how it is applied, the sensitivity of results to localization.
  Reply: We do not use localization. The background error correlations were given according to decorrelation length scales. The correlations have been compact.
  
  - How is the R matrix set for gridded data? Do you consider observational uncertainties at each gridpoint as independent/uncorrelated to each other? Couldn't that lead to overfitting?
  Reply: This is an important point. We assimilated the gridded data only in the large-scale DA. The DA spatial scale is close to the gridded data scale, so that the representation error is small. This is one major motivation of using MSDA.
  
  - The descent algorithm itself and how it imposes a cost function form and limits the options available for four-dimensional inversion. For instance, the so-called "sampling time error" is only an error insofar as the approximation page 12 line 282 is made -- do alternate formulations exist in the literature for the 4D extension of 3D-Var?
  Reply: There are different practical ways to assimilate observations over a time window. 4DVAR is ideal. Because of difficulties and demanding computational costs with 4DVAR for high resolution models, we used 3DVAR but tried to assimilate observations over a time window in a more reasonable way, while we understand that it could not match 4DVAR.
  
  - The choice of linear modelling of the "sampling time error" in (4) and its calibration (only a vague hint on lines 397-398 on page 16).
  Reply. We agree. It was not optimal and could be better estimated.
  As it stands, I consider the scientific value and innovative character of this ms. to be extremely modest.
  Reply: We agree. The manuscript basically aimed to provide a reference for researchers who work on DA with high resolutions models and on assimilation of spatially localized observations.
  For these reasons, I cannot recommend publication of this manuscript in its current state. Alternatively, the editor might consider that pending a very substantial revision of content, form and focus, the ms. might reach a state acceptable to this particular journal.
  Given the extent of my general comments above, I will not give a detailed list of smaller comments. This will be for a second round if the Editor decides to give this ms. a chance.
  Reply: Thank you.
  
  Citation: https://doi.org/10.5194/egusphere-2022-1399-AC2

Zhijin Li, Matthew R. Archer, Jinbo Wang, and Lee-Lueng Fu

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Short summary

The Surface Water and Ocean Topography (SWOT) satellite mission will carry a new-generation altimeter to measure sea surface height in two-dimensions at unprecedented spatial resolution. An integration of SWOT measurements into an oceanic numerical model will improve our oceanic prediction in spatial resolution and accuracy. It has been demonstrated that the methodology used is ready to integrate SWOT measurements into the model, and the result may be used to interpret SWOT measurements.


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