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ADVANCING EARTH 
AND SPACE SCIENCES 
Journal of Geophysical Research: Oceans 
10.1029/2023JC019937 
where w is the vertical velocity, N” is the Brunt-Väisälä frequency, f is the Coriolis parameter, h denotes the 
horizontal components and Q is the forcing associated with different processes: kinematic deformation, turbulent 
buoyancy and turbulent momentum. Buongiorno Nardelli et al. (2018) and Buongiorno Nardelli (2020a) provide 
an extensive introduction to the method and the equations used to retrieve the horizontal and vertical currents. 
OMEGABD is available on the same regular global grid and has the same time resolution as ARMOR3D. On the 
vertical scale, it differs from ARMOR3D since it has a finer resolution from the surface down to 1,500 m (75 
depth levels). 
This product has been extensively validated before its release through the Copernicus Marine Service (Buon- 
ziorno Nardelli, 2020b), as also detailed in Buongiorno Nardelli (2020a). The global RMS differences for the 
horizontal components attain approximately around 0.10 m s”' at 15 and 0.06 m s”' at 1,000 m depth with distinct 
geographical variations. Larger discrepancies are expected in the equatorial zone and coastal areas making the 
product only suited for open ocean application (Buongiorno Nardelli, 2020a). Given their relatively small 
magnitude, vertical velocities cannot be measured in the open ocean (order of 1-100 m d7'). Consequently, the 
validation of the vertical velocity in OMEGA3D faces limitations due to the absence of direct observational 
benchmarks. The validation of OMEGA3D was thus obtained by indirect assessment of the divergent components 
of the quasi-geostrophic horizontal currents and by intercomparison with available model re-analysis data. 
B3uongiorno Nardelli (2020a) compared the vertical velocities with the output of two ocean climate reanalysis 
systems that contain vertical velocity time series of comparable length (SODAv3.4.2 and ECCOv4r4). The large- 
scale patterns and range of values found in the averaged velocities are quite similar among the three products, 
ihough OMEGA3D shows higher variance, mostly driven by mesoscale signals that are not resolved in lower 
'‚esolution products such as ECCOv4r4. Maximum absolute mean values reach around 2 m d7'. Areas dominated 
by large-scale, wind-driven upwelling at high latitudes and by downwelling at mid-latitudes are consistently 
identified in the three products, with values rarely exceeding 0.5 m ah 
For the calculation of the water mass formation using the thermodynamic approach, we use the ECMWF 
Reanalysis v5 (ERAS5) data set (Hersbach et al., 2023) provided by the Copernicus Climate Change Service 
(C3S). ERAS5 is the fifth generation of the ECMWF reanalysis for the global climate and weather and covers the 
periods from 1959 to the present. We use the gridded product with %° resolution on single levels from 1993 to 
2018. We further use hourly data and average them as daily values regarding the evaporation and precipitation 
rates and all components that are necessary to calculate the total heat fluxes. 
2.2. Identification of SPMW and Volume Calculation 
The high vertical homogeneity of SPMW manifests itself through low values of an approximated estimate of the 
potential vorticity (PV) (only including the effect of stratification). PV can be used as a proxy to identify SPMW 
in the isopycnal layers (Brambilla & Talley, 2008). We calculated PV following Brambilla and Talley (2008) as: 
PV — 
A 
pp öz 
(2) 
where fis the Coriolis parameter, and p is the density referenced to the midpoint of the depth interval z. Using a 
similar criterion as in Brambilla and Talley (2008), we identify SPMW as water that has a PV lower than 
80x 1071? m} 87. However, different from their work, we consider only the amount of SPMW below the mixed 
layer depth since we are interested in the part of SPMW that potentially leaves the mixed layer and might 
eventually contributes to the deep water formation. This minimum in PV is found in the density range 09 = 27.05- 
27.55 kg m, in the upper 1,000 m of the water column (Figures 1c and 1d). Before calculating PV, we inter- 
polated all the ARMOR3D profiles on a vertical grid of 5 m. 
Che choice of a specific PV minimum value to identify SPMW is rather arbitrary. For example, Brambilla and 
Talley (2008) used PV values between 40 and 100 x 107'* m”' s7' found in the density range 09 = 27.3- 
27.5 kg m. Petit et al. (2021) used a PV value below 40 x 107? m‘ s7' for the identification of SPMW across 
the Iceland Basin that occupies the same density range 09 = 27.3-27.5 kg m. The choice of the upper bound 
69 = 27.05 kg m in our study serves to include into our analysis the formation and transformation of lighter 
variety of SPMW near the Porcupine Bank and Bay of Biscay in the eastern North Atlantic. These regions also 
show low PV below 80 x 107!? m-! s7!( Figure 1). Brambilla et al. (2008) analyzed the density range 604 = 27.05- 
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