# Key Factors for Improving the Resolution of Mapped Sea Surface Height from Multi-Satellite Altimeters in the South China Sea

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Datasets

- New altimetry standards and geophysical corrections were used to improve the accuracy of sea level anomaly (SLA) content. The regional mean sea level (MSL) trend and regional deviation was affected.
- The new ‘internal tide’ correction was used to improve the mesoscale signal mapping.
- The new mean sea level (non-repetitive and recent tasks) or mean profile (repetitive task) was used to improve the accuracy of SLA and regional deviation.
- The new mean dynamic topography (MDT) was used to improve the geostrophic current and regional deviation.
- The mesoscale signal on the L4 products were improved by using the improved mapping parameters.

#### 2.2. A Two-Dimensional Variational Method

## 3. Results

#### 3.1. Signal Proportion of Different Scales in the Background

#### 3.2. Evaluation of Accuracy

#### 3.2.1. Remote Sensing Evaluation

#### 3.2.2. In Situ Evaluation

#### 3.2.3. Along-Track Satellite Evaluation

#### 3.3. Evaluation of Effective Resolution

## 4. Discussion

#### 4.1. Signal Composition in Background Field and Associated Error

#### 4.2. Filtering Effect of Correlation Coefficient Scale in Variational Method

#### 4.3. The Scale of Effective Resolution Compared with Eddy Radius

#### 4.4. The Restriction of HYCOM and the Advantages of 2DVAR

- There is limited historical sampling data, leading to inaccurate assimilation of height field results.
- Non-steric sea surface heights in the altimeter data cannot be assimilated.
- The set of an assimilation thresholds is defined as the noise level of the satellite altimeter (currently set to 4 cm), which restricts the merging of small-scale information.

- The matrix deformation avoids inversion of the background error covariance matrix and can be minimized over the entire grid domain, and is therefore suitable for solving high-resolution problems with a large number of grid points.
- The processing methods of the background error covariance matrix and observation error covariance matrix are more flexible than those of the other models; this flexibility is convenient for simplifying and introducing dynamic constraints.
- Using the observation operator H, it is easy to merge the observation data of different properties.

#### 4.5. Limitations and Future Work

**R**

_{s}=

**R**

_{m}+

**R**

_{e}, the observation error covariance matrix

**R**

_{s}consists of measurement

**R**

_{m}and evolutionary error covariance matrices

**R**

_{e}) to address the difference between observation time and mapping time [12]. In addition, the wide-swath Surface Water and Ocean Topography (SWOT) mission was launched on 15 December 2022. As a result, the findings of this study can be extended to resolve small-scale features in maps derived using data from new multi-satellite altimeters, including SWOT data [34]. The multi-scale data merging will be tried to improve further the ER of merged maps in the future [35].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ubelmann, C.; Dibarboure, G.; Gaultier, L.; Ponte, A.L.S.; Ardhuin, F.; Ballarotta, M.; Faugére, Y. Reconstructing Ocean Surface Current Combining Altimetry and Future Spaceborne Doppler Data. J. Geophys. Res. Ocean.
**2021**, 126, e2020JC016560. [Google Scholar] [CrossRef] - Mulet, S.; Rio, M.; Etienne, H.; Artana, C.; Cancet, M.; Dibarboure, G.; Feng, H.; Husson, R.; Picot, N.; Strub, C.P.A.P. The new CNES-CLS18 global mean dynamic topography. Ocean Sci.
**2021**, 17, 789. [Google Scholar] [CrossRef] - Elipot, S.; Lumpkin, R.; Perez, R.C.; Lilly, J.M.; Early, J.J.; Sykulski, A.M. A global surface drifter data set at hourly resolution. J. Geophys. Res. Ocean.
**2016**, 121, 2937–2966. [Google Scholar] - Abdalla, S.; Kolahchi, A.A.; Ablain, M.; Adusumilli, S.; Bhowmick, S.A.; Alou-Font, E.; Amarouche, L.; Andersen, O.B.; Antich, H.; Aouf, L.; et al. Altimetry for the future: Building on 25 years of progress. Adv. Space Res.
**2021**, 68, 319–363. [Google Scholar] [CrossRef] - Wang, G.; Wu, L.; Mei, W.; Xie, S.P. Ocean currents show global intensification of weak tropical cyclones. Nature
**2022**, 611, 496–500. [Google Scholar] [CrossRef] [PubMed] - Davis, R.; Talley, L.; Roemmich, D.; Owens, B.; Rudnick, D.; Toole, J.; Weller, R.; McPhaden, M.; Barth, J. 100 Years of Progress in Ocean Observing Systems. Meteorol. Monogr.
**2018**, 59, 1–46. [Google Scholar] [CrossRef] - Zilberman, N.; Roemmich, D.; Gille, S.; Gilson, J. Estimating the Velocity and Transport of Western Boundary Current Systems: A Case Study of the East Australian Current near Brisbane. J. Atmos. Ocean. Technol.
**2018**, 35, 1313–1329. [Google Scholar] [CrossRef] - Charney, J.; Flierl, G. Oceanic analogues of large scale atmospheric motions. In Evolution of Physical Oceanoaraphy; Warren, B., Wunsch, C., Eds.; MIT Press: Cambridge, MA, USA, 1981; pp. 502–546. [Google Scholar]
- Yu, H.; Li, J.; Wu, K.; Wang, Z.; Yu, H.; Zhang, S.; Hou, Y.; Kelly, R.M. A global high-resolution ocean wave model improved by assimilating the satellite altimeter significant wave height. Int. J. Appl. Earth Obs. Geoinf.
**2018**, 70, 43–50. [Google Scholar] [CrossRef] - Detlef, S.; Anny, C. Satellite Altimetry Over Oceans and Land Surfaces. Aeronaut. J.
**2019**, 123, 1297–1298. [Google Scholar] [CrossRef] - Archer, M.R.; Li, Z.; Fu, L.L. Increasing the Space–Time Resolution of Mapped Sea Surface Height from Altimetry. J. Geophys. Res. Ocean.
**2020**, 125, 2019JC015878. [Google Scholar] [CrossRef] - Liu, L.; Jiang, X.; Fei, J.; Li, Z. Development and evaluation of a new merged sea surface height product from multi-satellite altimeters. Chin. Sci. Bull.
**2020**, 65, 1888–1897. [Google Scholar] [CrossRef] - Chelton, D.B.; Schlax, M.G.; Samelson, R.M. Global observations of nonlinear mesoscale eddies. Prog. Oceanogr.
**2011**, 91, 167–216. [Google Scholar] [CrossRef] - Chelton, D.; Dibarboure, G.; Pujol, M.I.; Taburet, G.; Schlax, M.G. The Spatial Resolution of AVISO Gridded Sea Surface Height Fields; OSTST: Lake Constance, Germany, 2014; pp. 28–31. Available online: https://meetings.aviso.altimetry.fr/fileadmin/user_upload/tx_ausyclsseminar/files/29Red0900-1_OSTST_Chelton.pdf (accessed on 30 March 2022).
- Ubelmann, C.; Klein, P.; Fu, L. Dynamic Interpolation of Sea Surface Height and Potential Applications for Future High-Resolution Altimetry Mapping. J. Atmos. Ocean. Technol.
**2015**, 32, 177–184. [Google Scholar] [CrossRef] - Chen, G.; Hou, Y.; Chu, X. Mesoscale eddies in the South China Sea: Mean properties, spatiotemporal variability, and impact on thermohaline structure. J. Geophys. Res.
**2011**, 116, C06018. [Google Scholar] [CrossRef] - Wang, G.; Su, J.; Chu, P.C. Mesoscale eddies in the South China Sea observed with altimeter data. Geophys. Res. Lett.
**2003**, 30, 2121. [Google Scholar] [CrossRef] - Roberts-Jones, J.; Bovis, K.; Martin, M.J.; McLaren, A. Estimating background error covariance parameters and assessing their impact in the OSTIA system. Remote Sens. Environ.
**2016**, 176, 117–138. [Google Scholar] [CrossRef] - Pegliasco, C.; Chaigneau, A.; Morrow, R.; Dumas, F. Detection and tracking of mesoscale eddies in the Mediterranean Sea: A comparison between the Sea Level Anomaly and the Absolute Dynamic Topography fields. Adv. Space Res.
**2021**, 68, 401–419. [Google Scholar] [CrossRef] - Jiang, X.; Liu, L.; Li, Z.; Liu, L.; Sian, K.T.C.L.; Dong, C. A Two-Dimensional Variational Scheme for Merging Multiple Satellite Altimetry Data and Eddy Analysis. Remote Sens.
**2022**, 14, 3026. [Google Scholar] [CrossRef] - Taburet, G.; Pujol, M.; SL-TAC Team. QUID for Sea Level TAC DUACS Products. Available online: https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-SL-QUID-008-032-068.pdf (accessed on 5 April 2023).
- Ballarotta, M.; Ubelmann, C.; Pujol, M.I.; Taburet, G.; Fournier, F.; Legeais, J.F.; Faugere, Y.; Delepoulle, A.; Chelton, D.; Dibarboure, G.; et al. On the resolutions of ocean altimetry maps. Ocean Sci.
**2019**, 15, 1091–1109. [Google Scholar] [CrossRef] - Lewis, J.M.; Lakshmivarahan, S.; Maryada, S.K.R. Placement of Observations for Variational Data Assimilation: Application to Burgers’ Equation and Seiche Phenomenon. In Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications; Park, S.K., Xu, L., Eds.; Springer: Cham, Switzerland, 2021; Volume IV, pp. 259–275. [Google Scholar] [CrossRef]
- JPL MUR MEaSUREs Project. GHRSST Level 4 MUR Global Foundation Sea Surface Temperature Analysis, Version 4.1; PO.DAAC: Pasadena, CA, USA, 2015. [Google Scholar] [CrossRef]
- Lumpkin, R.; Centurioni, L. Global Drifter Program Quality-Controlled 6-Hour Interpolated Data from Ocean Surface Drifting Buoys. NOAA National Centers for Environmental Information. Dataset. 2019. Available online: https://www.aoml.noaa.gov/phod/gdp/ (accessed on 30 March 2022).
- Pujol, M.; Egrave, F.; Re, Y.; Taburet, G.; Dupuy, S.E.; Phanie; Pelloquin, C.; Ablain, M.; Picot, N. DUACS DT2014: The new multi-mission altimeter data set reprocessed over 20 years. Ocean Sci.
**2016**, 12, 1067–1090. [Google Scholar] [CrossRef] - Gaspari, G.; Cohn, S.E. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc.
**1999**, 125, 723–757. [Google Scholar] [CrossRef] - Li, Z.; Cheng, X.; Gustafson, W.I., Jr.; Vogelmann, A.M. Spectral characteristics of background error covariance and multiscale data assimilation. Int. J. Numer. Methods Fluids
**2016**, 82, 1035–1048. [Google Scholar] [CrossRef] - Daley, R. Atmospheric data assimilation. In Cambridge Atmospheric and Space Science Series; Cambridge University Press: Cambridge, UK, 1991. [Google Scholar]
- Gaube, P.; Chelton, D.B.; Samelson, R.M.; Schlax, M.G.; O’Neill, L.W. Satellite Observations of mesoscale Eddy-Induced Ekman Pumping. J. Phys. Oceanogr.
**2015**, 45, 104–132. [Google Scholar] [CrossRef] - Hausmann, U.; Czaja, A. The observed signature of mesoscale eddies in sea surface temperature and the associated heat transport. Deep. Sea Res. Part I Oceanogr. Res. Pap.
**2012**, 70, 60–72. [Google Scholar] [CrossRef] - Zhang, Z.; Zhao, W.; Tian, J.; Yang, Q.; Qu, T. Spatial structure and temporal variability of the zonal flow in the Luzon Strait (Article). J. Geophys. Res. Ocean.
**2015**, 120, 759–776. [Google Scholar] [CrossRef] - Liu, Y.; Tian, F.; Chen, G. Statistical characterization of sea surface temperature over mesoscale eddies in the south China sea. Period. Ocean. Univ. China
**2020**, 50, 146–156. [Google Scholar] [CrossRef] - Morrow, R.; Fu, L.; Ardhuin, F.; Benkiran, M.; Chapron, B.; Cosme, E.; D’Ovidio, F.; Farrar, J.T.; Gille, S.; Lapeyre, G.; et al. Global Observations of Fine-Scale Ocean Surface Topography with the Surface Water and Ocean Topography (SWOT) Mission. Front. Mar. Sci.
**2019**, 6, 232. [Google Scholar] [CrossRef] - Li, Z.; Wang, J.; Fu, L. An Observing System Simulation Experiment for Ocean State Estimation to Assess the Performance of the SWOT Mission: Part 1—A Twin Experiment. J. Geophys. Res. Ocean.
**2019**, 124, 4838–4855. [Google Scholar] [CrossRef]

**Figure 1.**The correlation length scale and its Gaussian-fit distribution of the 2DVAR and AVISO maps with different background time windows.

**Figure 2.**Proportion of error energy at different scales of background errors with the 2DVAR and AVISO methods with different background time average windows.

**Figure 3.**MUR sea surface temperature (SST) and the inversion of geostrophic current from merged absolute dynamic topography (ADT): (

**a**) 2DVAR, (

**b**) HYCOM, (

**c**) 1/8° AVISO, and (

**d**) 1/4° AVISO on 7 July 2018.

**Figure 4.**Absolute dynamic topography (ADT) maps of 2DVAR, HYCOM, 1/8° AVISO, and 1/4° AVISO (sorted by column) with the drifting buoy path. The days are (

**a**) 29 May, (

**b**) 30 May, (

**c**) 31 May, (

**d**) 1 June, and (

**e**) 2 June 2018 (sorted by row, respectively). Blue line: drift path of the buoy on the focal days; red line, drift path during the two days before and after. The arrow indicates the geostrophic vectors from the middle moment of the focal day.

**Figure 5.**Geostrophic velocity scatter plot and linear regression curve of (

**a**) 2DVAR, (

**b**) HYCOM, (

**c**) 1/8° AVISO, and (

**d**) 1/4° AVISO with the drifting buoy. The slope of the dotted black dot is 1. Equation y on the upper left corner represents linear regression curve which is the dotted line colored in red. R is the correlation of linear regression coefficients. C is the correlation coefficient between the merged map and the drifting buoy data, and the root mean square deviation (RMSD) between the merged map and the drifting buoy data.

**Figure 6.**Root mean square error (RMSE) on the satellite track of merged absolute dynamic topography (ADT) compared with S3A (

**a**–

**d**) and J3 (

**e**–

**h**) satellite along-track data: (

**a**,

**e**) 2DVAR, (

**b**,

**f**) HYCOM, (

**c**,

**g**) 1/8° AVISO, and (

**d**,

**h**) 1/4° AVISO. Note that the color scale for each map is differ from each other for the uniform of colors.

**Figure 7.**Correlations between the merged maps: (

**a**,

**e**) 2DVAR, (

**b**) HYCOM, (

**c**) 1/8° AVISO, (

**d**) 1/4° AVISO, and S3A (

**a**–

**d**) and J3 (

**e**–

**h**) satellite along-track data. The ratio of the black dotted line is 1; C is the coefficient of correlation; the red dotted line is the linear regression curve; y represents its equation; and R is the coefficient of correlation for linear regression.

**Figure 8.**The absolute dynamic topography (ADT) sequence (

**a**) from merged maps along the along-track points of satellite J3 on 9 July. The red and blue dashed lines are the separation position between different tracks. The J3 satellite track in the South China Sea (SCS) for 9 July (

**b**); red dotted line). The sequence P1–6 indicates the direction of movement of different parts of the satellite tracks and corresponds to the sequence of the sampling fragments separated by the red and blue dashed lines.

**Figure 9.**The power spectral density (PSD) that calculated by (

**a**) subtraction and (

**b**) non-subtraction of the J3 data (except for the gray line in (

**a**), it was the origin data of J3 satellite) from the four merged maps (2DVAR, HYCOM, 1/8° AVISO, and 1/4°AVISO). (

**c**) Effective resolution (ER) and (

**d**) useful resolution (UR) of the four merged maps based on NSR and ER, respectively on 9 July.

**Figure 10.**(

**a**–

**d**) Effective resolution (ER) and (

**e**–

**h**) useful resolution UR of the four merged models of (

**a**,

**e**) 2DVAR, (

**b**,

**f**) HYCOM, (

**c**,

**g**) 1/8° AVISO, and (

**d**,

**h**) 1/4°AVISO in the South China Sea (SCS) and nearby waters used S3A satellite data as true values; the darker the color is, the larger the ER or UR value is.

**Figure 11.**The frequency wavelength power spectral density (PSD) values of the four merged maps. Due to the different spatial map resolutions, the coordinate range of each spectrum was different.

**Table 1.**Variance and effective resolution (ER) of regional Europe products. The first column is the variance of the differences between 1/8° DT2021 regional Europe product and SARAL-DP/ALtika independent along-track measurements from 2016 to 2019. In parenthesis, variance reduction (in %) compared with the results obtained with the 1/4° DT2021 Global product. The second column is the spatial ER of the 1/8° DUACS-DT2018 product in the regional European seas. In parenthesis, average resolution over the basin.

European Seas | Variance [cm^{2}] | Effective Resolution [km] |
---|---|---|

Black Sea | 14.4 (−0.94%) | 100 to 150 (~130) |

Mediterranean Sea | 15.3 (−4.25%) | 90 to 160 (~130) |

**Table 2.**The accuracy of 4 models. The root mean square error (RMSE, in cm) for entire map compared with along-track S3A and J3 satellite L3 data, and the mean error index score S for entire map of each product compared with 2DVAR.

Experiments/ Models | RMSE [cm] | S | ||
---|---|---|---|---|

S3A | J3 | S3A | J3 | |

2DVAR | 0.0299 | 0.0340 | / | / |

HYCOM | 1.5946 | 0.5189 | 0.8987 | 0.9421 |

1/8° AVISO | 0.0678 | 0.0688 | 0.6658 | 0.7070 |

1/4° AVISO | 0.0396 | 0.0414 | 0.1125 | 0.2313 |

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## Share and Cite

**MDPI and ACS Style**

Liu, L.; Zhang, X.; Fei, J.; Li, Z.; Shi, W.; Wang, H.; Jiang, X.; Zhang, Z.; Lv, X.
Key Factors for Improving the Resolution of Mapped Sea Surface Height from Multi-Satellite Altimeters in the South China Sea. *Remote Sens.* **2023**, *15*, 4275.
https://doi.org/10.3390/rs15174275

**AMA Style**

Liu L, Zhang X, Fei J, Li Z, Shi W, Wang H, Jiang X, Zhang Z, Lv X.
Key Factors for Improving the Resolution of Mapped Sea Surface Height from Multi-Satellite Altimeters in the South China Sea. *Remote Sensing*. 2023; 15(17):4275.
https://doi.org/10.3390/rs15174275

**Chicago/Turabian Style**

Liu, Lei, Xiaoya Zhang, Jianfang Fei, Zhijin Li, Wenli Shi, Huizan Wang, Xingliang Jiang, Ze Zhang, and Xianyu Lv.
2023. "Key Factors for Improving the Resolution of Mapped Sea Surface Height from Multi-Satellite Altimeters in the South China Sea" *Remote Sensing* 15, no. 17: 4275.
https://doi.org/10.3390/rs15174275