## 2 Study Area and Data Processing
### Data and Processing  
Altimetry allows eddies to be observed by measuring sea surface heights, where currents rotate around local highs and lows due to a geostrophic balance between pressure gradient forces and kurtosis acceleration. In this study, we use the Mesoscale Eddy Trajectory Atlas product (META3.2 DT allsat), which can be accessed from [[https://www.aviso.altimetry.fr](https://www.aviso.altimetry.fr)]([https://www.aviso.altimetry.fr](https://www.aviso.altimetry.fr)) (accessed on 21 September 2023) [27]. More specifically, this refers to the multimission altimetry-derived eddy trajectories in version 3.2 DT (for delayed-time), computed with upstream data from the \"all satellites\" constellation maps distributed by the Copernicus Marine Environmental Monitoring Service (CMEMS). The product provides anticyclonic and cyclonic eddies detected from the multimission altimetry datasets, with their location, contours, amplitude, radius speed, and associated metadata, which was produced by SSALTO/DUACS and distributed by AVISO+ with support from CNES, in collaboration with IMEDEA. The atlas was downloaded on 21 September 2023, and covers the period from January 1993 to February 2022. The algorithm used for the product is derived from [PERSON] et al. [28] and further described in [PERSON] et al. [29]. The dataset employed in this study spans a period of 20 years, from 2002 to 2021, which is sufficient to establish and validate the model dedicated to reconstruction of the vertical TA profiles. Similar to the dataset selection in  
Figure 1: Schematic map of the ocean circulation, and the mean surface geostrophic sea water velocity for 2022 in m/s. This has been conducted using E.U. Copernicus Marine Service Information; [[https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/description](https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/description)]([https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/description](https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/description)), accessed on 21 July 2023.  
article [30], this paper has chosen mesoscale eddies with tracking trajectories lasting longer than 10 days to ensure more stable data. The dataset has been accordingly divided into the two types, cyclonic eddies (CEs) and anticyclonic eddies (AEs). Vertical eddy thermal information could be observed with Argo profiles thanks to the Argo project. The Argo project and its data have contributed to the study and development of marine science [31], which provide a large number of vertical CTD (conductivity, temperature, and depth) profiles from the upper 2000 m of the ice-free global ocean and currents from intermediate depths [13]. The delayed mode Argo float profiles were collected and made freely available by the International Argo Program and the national programs that contribute to it ([[https://www.seanoe.org/data/00311/42182/](https://www.seanoe.org/data/00311/42182/)]([https://www.seanoe.org/data/00311/42182/](https://www.seanoe.org/data/00311/42182/)) ), accessed on 1 March 2023. The Argo Program is part of the Global Ocean Observing System. Figure 2 shows the Argo array statistics within the study area on a randomly selected day. All data collected by Argo floats are publicly available in near real-time via the Global Data Assembly Centers (GDAC) in Brest (France) and Monterey (California) after an automated quality control. Additionally, the China Argo Real-Time Data Centre synchronises with the GDAC data server every two days to provide quality-controlled data. In this study, the Argo profile data of the interested area from January 2002 to December 2021 are chosen, and they are downloaded from [[ftp://data.argo.org.cn/pub/ARGO/](ftp://data.argo.org.cn/pub/ARGO/)]([ftp://data.argo.org.cn/pub/ARGO/](ftp://data.argo.org.cn/pub/ARGO/)), accessed on 1 March 2023. Before using the profile data, it is necessary to control quality to ensure the research results are more reliable.