Comparison of Mean Dynamic Topography Modeling from Multivariate Objective Analysis and Rigorous Least Squares Method

Round 1

Reviewer 1 Report

This manuscript looks at a geodetic approach to evaluating mean dynamic topography estimates using two different “filtering” techniques. The manuscript uses much of the information in the three papers listed below, just in a slightly revised way and for an expanded number of study areas. The first 5 authors of this manuscript appear across these three papers published within the last 12 months. The techniques, datasets for MSS and geoid are identical or updated from previous work. The presentation in terms of Tables and Figures is also very similar (and in the current manuscript likely has units in Table 2 incorrect -> not cm/s, otherwise the results are physically implausible with current speeds of up to 3-5 m/s!!!).   I find the presentation of results is simplistic in the extreme and does not quantify at all how accurate the recovered MDT is compared to independent hydrographic/oceanographic information nor ocean model data.

The manuscript looks also to be written with a cut-paste from the other manuscripts, making this version at some stages unintelligible as I had to read the three papers below to understand some of the technique formulation. There are many grammatical errors that would need editorial revision. The techniques and approaches are not fully described, as mentioned above I had to read the other papers to figure out what was done, and even then, I am not clear. For example, what reference system and zero tide system are used. DTU MSS comes in both topex ellipsoid or GRS80 ellipsoid. What filtering wavelengths were used and at what stages; the time periods of the various datasets (given in the other three references).

 

A more publishable paper would be to compare geodetic approaches to computing MDT with oceanographic approaches – some suggested references below. And to derive ocean dynamic quantities of relevance to truly verify if there is oceanographic meaningful improvement. The use of rms statistics just disguises the oceanography. And a better appreciation of the wider literature is required, there was a bias towards literature published within a small circle of collaborators.

 

The Figures are too small to show any significant results. One can see that the largest discrepancies typically occur where there are boundary currents and other ocean dynamic features. It would be better to look at sections across the boundary current, in mid-gyre regions and along repeat hydrographic sections such as WOCE, tide gauge information along coastlines, etc. Even looking at transport volume closures around a basin would give some information on any biases present in the geodetic approaches.  And if ocean models are to be used, then there are far better choices that provide significantly more detail to evaluate the MDT estimates.

 

 

Three papers:

Wu et al. 2021. Mean Dynamic Topography Modeling Based on Optimal Interpolation from Satellite Gravimetry and Altimetry Data. Appl.Sci., 11, 5286 – uses Objective Analysis approach in the Kuroshio region.

 

Shi et al. 2022. Spectrally Consistent Mean Dynamic Topography by Combining Mean Sea Surface and Global Geopotential Model Through a Least Squares-Based Approach. Front. Earth Sci. 10:795935 – uses least-squares approach and has results for the Gulf Stream region.

 

Wu et al. 2022. Coastal Mean Dynamic Topography Recovery Based on Multivariate Objective Analysis by Combining Data from Synthetic Aperture Radar Altimeter. Remote Sens. 14, 240. – uses Objective Analysis with results for the Kuroshio region.

 

 

 

Some additional References

Thomson and Emery, Data Analysis Methods in Physical Oceanography, 3^rd Ed, 2014. Elsevier; Chs 4 and 5.

 

Bowen et al. 2002. Extracting Multiyear Surface Currents from Sequential Thermal Imagery Using the Maximum Cross-Correlation Technique, JAOT,19(10): 1665-1676.

 

Wilkin et al. 2002. Mapping mesoscale currents by optimal interpolation of satellite radiometer and altimeter data, Ocean Dynamics, 52(3):95-103.

 

Ridgway et al. 2002. Ocean Interpolation by Four-Dimensional Weighted Least Squares—Application to the Waters around Australasia, JAOT, Vol. 19(9): 1357–1375.

 

Deng et al. 2009. Assessment of Geoid Models Offshore Western Australia Using In-Situ Measurements, Journal of Coastal Research, Vol. 25(3), pp. 581-588.

 

Mintourakis et al. 2019. Evaluation of ocean circulation models in the computation of the mean dynamic topography for geodetic applications. Case study in the Greek seas, J.Geod.Sci, 9, 154-173.

 

 

Rezvani et al. 2021. Estimating vertical land motion and residual altimeter systematic errors using a Kalman-based approach. Journal of Geophysical Research: Oceans, 126, e2020JC017106.

Author Response

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Reviewer 2 Report

The manuscript "Comparison of Mean Dynamic Topography Modeling from Multivariate Objective Analysis and Rigorous Least Squares Method" expertly expands on the topic of mean dynamic topography (MDT) modeling in which the authors have established themselves through their previous publications. Due to the direct physical connection between the MDT and the geostrophic current velocities of the oceans, the discussed topic can be considered highly relevant in view of the global climate change of the planet. The article is prepared at a high professional level and its theoretical basis is based on enough relevant literary sources. The obtained results are sufficiently presented and discussed.

Formal comments:

* Page 3; equation (2): I consider it necessary to emphasize that $\overline{\varTheta}$ and $\overline{\lambda }$ represent the MDT values at the nodes. Please include a reminder.

* Page 3, 4; equations (3), (4), (5): It is not clear from the text how equation (3) becomes equations (4) or (5). How was the unknown parameter $X_{cs3}$ eliminated? Where did it disappear?

* Page 4, lines 7-8: It is not true that "$Q$ and $P$ represent covariance matrix and variance matrix,...". $Q$ is the cofactor matrix and $P$ is the weight matrix. I think readers would appreciate information on how was determined the matrices $P$, $Q$, and the variance of unit weight $\sigma$.

* Page 3-5; equations (3)-(9): It is very confusing if the same symbol is used within the same article to denote different mathematical variables with different content. In this case, the symbol $A$ denotes:
 

- coefficient matrix (also called design, information, or Jacobian matrix) in the equations (3), (4), (5) a (6),  

- covariance matrix of the observations in equations (7), (8) a (9). In view of the continuity with previous publications and the clarity of the interpreted mathematical background, I recommend using the customary notation, for example $J$, for the Jacobian (coefficient) matrix.

* Figures (2), (3), (5), (6): Longitudes $\lambda$ are unreadable.

Author Response

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Reviewer 3 Report

The rigorous least squares method (LS) and the multivariate objective analysis method (MOA) have been demonstrated superior over the traditional filtering-based methods in mean dynamic topography computation, but the community lacks a comparison between the LS and MOA methods. With numerical computations in four typical study areas, the performance of the two methods was compared and evaluated using ocean numerical models and geostrophic velocities in this study. Results of these experiments are useful in selecting computation methods for the mean dynamic topography. The manuscript is well written, logically organized, and thus are appropriate for publication in Remote Sensing. The only concern I would like to raise is that discussions about the scientific mechanisms behind the outperformance of the LS method should be enhanced.

Author Response

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