Le 
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ADVANCING EARTH 
AND SPACE SCIENCES 
Journal of Geophysical Research: Oceans 
10.1029/2023JC019937 
masses of the Southern Ocean (Karstensen & Quadfasel, 2002) and numerical model results for the North 
Atlantic (Marshall et al., 1999). 
2.3.1. Kinematic Approach 
With the kinematic approach, we calculated the rate at which a water parcel crosses the mixed layer base toward 
the ocean's interior (Marshall et al., 1999). This combines the vertical and horizontal velocities from the 
OMEGAB3D data set along with associated estimates of MLD. To determine the net subduction rates (Sr) as 
defined in Equation 3, we integrated the vertical and horizontal volume fluxes across the instantaneous mixed 
layer base over a complete annual cycle using weekly OMEGA3D velocities. Additionally, we accounted for 
changes in the mixed layer volume by addressing variations of the MLD over time, which is referred to as 
‘“entrainment/detrainment” (Figure 2a). 
oh 
Sr=—+7W, .‚Vh+w,; 
(3) 
where h is the mixed layer depth, and @, and w, are the velocity components at the base of the mixed layer. 
The resulting positive rates are the subduction rates, while the negatives are the obduction rates. It is important to 
stress that no “perfect” assessment of subduction/obduction rates can be based on Eulerian approaches, as true 
water mass transformation evaluation would imply tracking the fate of individual water parcel along Lagrangian 
ırajectories. Other operational definitions of net subduction have been thus adopted in the literature (see also 
Xwon et al., 2013; Marshall, 1997) often limiting to the fluxes across a time-invariant winter maximum mixed 
‚ayer (e.g., Buongiorno Nardelli et al., 2018). In those cases, only the exchange rate to the main pycnocline is 
considered. Significant differences can be expected with respect to the instantaneous approach followed here, 
most likely due to diapycnal processes that occur within the seasonal pycnocline (Kwon et al., 2013; Nishikawa 
et al., 2010). 
Since OMEGA3D has a different vertical resolution than ARMOR3D, the MLD used for the kinematic approach 
needs to be re-estimated. We estimate the instantaneous MLD as the depth at which a density difference of 
0.03 kg m is found with respect to the density at the surface (see also Buongiorno Nardelli et al., 2017; de Boyer 
Montegut et al., 2004). Then, we compute the volumetric flow rate across the mixed layer base by estimating 
separately the contribution of the horizontal, vertical and entrainment terms, respectively. Instantaneous values 
are then integrated between December of the previous year and November of the follow-up year to analyze the 
interannual variations in the spatial patterns and intensity of the subduction rates. The yearly mean net sub- 
duction/obduction rates focus on predefined density bins to identify and track specific water mass changes. 
Specifically, as for the volume calculation, we have divided the density range into five isopycnal bins of 
0.1 kg m width, covering the density range between 07 = 27.05 and 27.55 kg m *. Using yearly net subduction 
estimates we aim at quantifying the amount of water that is transferred from the upper boundary layer to the 
interior ocean over one complete destratification/stratification annual cycle (Stommel, 1979). 
2.3.2. Thermodynamic Approach 
The transfer of water into the thermocline must be supported by the formation of surface water through heat and 
freshwater fluxes (Karstensen & Quadfasel, 2002; Marshall et al., 1999). With the thermodynamic approach, this 
ıransformation is estimated using the buoyancy fluxes calculated from ERA5. The convergence/divergence of 
"his transformation flux yields to creation/destruction of water masses by air-sea fluxes (Marshall et al., 1999). To 
quantify the transformation rates, we calculated first the buoyancy fluxes (kg m s7') from the heat and 
freshwater fluxes as follows: 
bf = —a 2 + BE P)S 
(4) 
where the coefficient of thermal expansion of seawater (a in °C '), the haline contraction coefficient (ß), the heat 
capacity of seawater (c, in J kg‘ °C7') and surface salinity (S) are derived from ARMOR3D data. The surface 
net heat flux (0,.. in W m”) and the net freshwater fluxes, expressed as evaporation minus precipitation (E-P in 
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