## 4 Summary  
In this study, we take advantage of multiple SAR images over the North Atlantic to investigate the joint retrieval performance of wind vector and line-of-sight current velocity using a Bayesian approach. To achieve this purpose, the NRCS and Doppler information of SAR images, representing backscattering magnitude and phase of radar return, are combined in the inversion scheme, along with a priori wind information. A series of correction steps are first carried out to obtain the geophysical component of the  
Figure 9: Comparison of retrieved oceanic current with reference dataset. (**a**) SAR-derived radial current velocity on 26 September 2019 overlapped with the trajectory of drifters (solid line in red). (**b**) Sea surface current velocity vector observed by HF radar on 26 September 2019. (**c**) Pointwise comparison of drifter measured radial velocity versus SAR-derived current velocity with the comparison metrics annotated in the plot. Note that all the collocation pairs between SAR and drifters are included in panel (**c**) to generate the scatter plot. Doppler centroid from SAR estimates. This includes the removal of scalloping effect and antenna miss-pointing based on land coverage. The performance of the inversion scheme combining NRCS, DCA, and the model winds is then evaluated with respect to in situ buoy measurements. The metrics indicate a slight improvement in comparison to the inversion results with the input of Doppler information. For sea surface current inversion, the study introduces the use of the CDOP model to estimate and correct Doppler frequency shifts induced by sea surface wind and waves. This correction mechanism is found to enhance the accuracy of ocean current inversion. The results highlight the consistency of velocities obtained through S-1 inversion with high-frequency ground-based radar observations. Furthermore, the spatial distribution characteristics of ocean currents can be effectively derived through this innovative integration of S-1 data, offering valuable insights into oceanographic dynamics. The Doppler information of SAR images can certainly play a role in relevant geophysical fields [27]. However, there are some deviations in certain regions that can be attributed to a couple of reasons. For example, the partial land coverage across the swath width may result in inconsistency in Doppler corrections. In addition, the DCA included in the cost function of the inversion scheme combines the wind and current contribution, which might lead to a bias in the retrieval results. Thus, how to take into account this combination and a possible extension over the polar regions will be the focus of our following work [28]. Conceptualization, H.L. ; Formal analysis, J.S. ; Investigation, H.L. and W.L. ; Writing--original draft, J.S. and H.L. ; Writing--review & editing, H.L., W.L. and Y.H. ; Supervision, Y.H.. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Science Foundation of China under grants 42027805 and 42006163. Not applicable. **Data Availability Statement**: Copernicus Sentinel-1 data are used and are publicly available via [[https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)]([https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)) (accessed on 10 November 2023), the buoy winds are available via [[https://www.ndbc.noaa.gov/](https://www.ndbc.noaa.gov/)]([https://www.ndbc.noaa.gov/](https://www.ndbc.noaa.gov/))(accessed on 10 November 2023), the high-frequency radar current measurements are available via [[https://hrhret-tds.ucsd.edu/](https://hrhret-tds.ucsd.edu/)]([https://hrhret-tds.ucsd.edu/](https://hrhret-tds.ucsd.edu/)) (accessed on 10 November 2023), and the dritter current velocity products are available via [[https://www.aoml.noaa.gov/phod/gdp/index.php](https://www.aoml.noaa.gov/phod/gdp/index.php)]([https://www.aoml.noaa.gov/phod/gdp/index.php](https://www.aoml.noaa.gov/phod/gdp/index.php)) (accessed on 10 November 2023).