They likely make use of lots of computer time but they are NOT "based on models". They are based on direct measurements of ocean temperatures. From the linked study paper.
2.
Data and methods Data are obtained from in situ measurements made available through the World Ocean Database. The instruments used to collect data include expendable bathythermographs (XBTs), Argo profiles (Argo, 2022), conductivity/temperature/depth instruments, mechanical bathythermographs (MBTs), bottles, moorings, and gliders (Boyer et al., 2018). Each of these instruments has an associated accuracy that may vary over time or with geographical location (Abraham et al., 2013; Cowley et al., 2021). Efforts have been made by the scientific community to improve the accuracy of these instruments. Although the source data are the same for the two groups, the gap-filling approach and many other data processing techniques are different. As an example, XBT biases have been corrected for IAP by Cheng et al. (2014) and for NCEI by Levitus et al. (2009). The newly available corrections for bottle and MBT data (Gouretski and Cheng, 2020; Gouretski et al., 2022) have not been incorporated; instead, MBT biases have been corrected for NCEI by Levitus et al. (2009) and for IAP by Ishii and Kimoto (2009). Besides, a reanalysis data is used for the Mediterranean Sea (CMS-MEDREA). The CMS-MEDREA assimilated XBT, CTD, Argo profiles, integrating data from CMS and SeaDataNet (
SeaDataNet - SeaDataNet) and, CMS satellite along track sea level anomaly (Escudier et al., 2021). The 0–2000 m SC index is calculated as in Cheng et al. (2020) for each month (t) over the 3D (x, y, z) ocean salinity field:
View attachment 747762, (1) where (x, y, z) are the three dimensions of latitude, longitude, and depth; Vhigh is the salinity averaged over high-salinity regions (Vhigh) where salinity is higher than the climatological global median Sclim; and Vlow is the salinity averaged over low-salinity regions (Vlow) where salinity is lower than the climatological global median Sclim. Sclim, Vhigh and Vlow are all determined on the basis of the climatological salinity field during 1960–2017. All data collected in the World Ocean Database (Boyer et al., 2018) are used to calculate the SC index, including real-time Argo observations. Ocean stratification is calculated as in Li et al. (2020a), computed as the squared buoyancy frequency:
View attachment 747763 , (2) where , ρ and σn denote the sea water density, local potential g density anomaly, and gravitational acceleration, respectively; and N, the Brunt–Väisälä frequency, represents the intrinsic frequency of internal waves.
Now don't you feel stupid? All you had to do was actually take a look - just like you told me to do. Don't you get tired of embarrassing yourself like this?