**5. Conclusions**

The analyses have shown that the ER of the 2DVAR mapped altimetry data is approximately 130 km, while it is approximately 250 km for both the 1/8◦ and 1/4◦ AVISO mapped data products. The factors for increasing the effective resolution was then examined. Both the 2DVAR and AVISO OI methods were formulated based on optimal estimation theory, and they are equivalent to each other [15]. The differences arise only from their implementation.

It was shown that the differences in the effective resolution result from the difference in the chosen background states and thus the associated background error. In the 2DVAR method, the mapped SSH of the previous day was used as the background state, while a 25 yeas mean used as the background state in the AVISO OI method. Thus, the background error with the 2DVAR method are relatively dominated by meso- and small-scale signals. In contrast, the background error with the AVISO OI method is the anomalies from the 25 year mean, and thus it includes large-scale signals, such as interannual and seasonal variabilities. The large-scale signals leads to a larger correlation length scale. A large correlation length scale imposes stronger filtering effect on the merged maps. Thus, the large correlation length scale is the main reason for a low effective resolution with 1/4◦ AVISO, even with a finer spatial grid of 1/8◦ AVISO and 1/12◦ HYCOM.

**Author Contributions:** Conceptualization, L.L. and J.F.; methodology, X.Z. and X.J.; validation, Z.L.; formal analysis, X.Z. and L.L.; investigation, X.Z. and L.L.; data curation, W.S., H.W. and X.L.; writing—original draft preparation, X.Z. and L.L.; writing—review and editing, X.Z., L.L. and Z.Z.; visualization, L.L. and X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the National Natural Science Foundation of China (42192552, 41775053 and 42022033) and the National Key Research and Development Program of China (2019YFC1510001).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The 1/4◦AVISO data, J3 and S3A Levle-3 data were downloaded from E.U. Copernicus Marine Environment Monitoring Service, available online: https://resources. marine.copernicus.eu (accessed on 22 January 2022). The MUR SST data were downloaded from Jet Propulsion Laboratory: https://coastwatch.pfeg.noaa.gov/erddap/griddap/jplMURSST41.html (accessed on 9 July 2022). The drifter data were support from GDP, available online: https://www. aoml.noaa.gov/phod/gdp/ (accessed on 30 March 2022). The 1/8◦AVISO data, 2DVAR data and HYCOM data in this study is available at Zenodo (https://doi.org/10.5281/zenodo.7578466 (accessed on 7 July 2022)). Figures were made with MATLAB version 2021b, available under the MATLAB license at https://www.mathworks.com/ (accessed on 15 December 2022).

**Acknowledgments:** The authors are grateful to three anonymous reviewers for their constructive comments on this work and recommending several beneficial references. The authors thank Xiaolei ZOU and Xiaochun WANG for their help in improving the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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