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ADVANCING EARTH 
AND SPACE SCIENCES 
Journal of Geophysical Research: Oceans 
10.1029/2023JC019937 
the Copernicus Marine Service. The data sets are combined with a reanalysis data set for the air-sea fluxes, ERA5 
(Dee et al., 2011) from the European Center for Medium-Range Weather Forecasts (ECMWF). We utilize these 
observation-based data to describe the rates and changes in the formation process of SPMW and investigate their 
potential impact on the local volume and distribution of SPMW. When discussing “formation” in our study, we 
‚efer to both the formation resulting from the divergence of diapycnal fluxes caused by air-sea interaction 
(thermodynamic approach) and the volume transport of water from the mixed layer to the ocean's interior through 
subduction (kinematic approach). We thus aim at extending previous analyses. These either focused only on the 
mean state of the SPMW (Brambilla et al., 2008; Brambilla & Talley, 2008) and were based on a limited amount 
of data from the winter season, or limited to specific regions and periods (de Boisseson et al., 2012; Stendardo 
et al., 2015). While others considered only the thermodynamic estimates (e.g., Petit et al., 2021). 
2. Data and Methods 
2.1. Data Sets 
To analyze the spatial and temporal variability of the SPMW's volume, we use a multi-observation global ocean 3D 
data set (ARMOR3D, 2021) that is distributed by the Copernicus Marine Service (Guinehut et al., 2012; Mulet 
et al., 2012). ARMOR3D covers the period from 1993 to the present. The period chosen in this study is 1993-2018. 
which is the time range in common with the other data sets used for this analysis and presented in this section. 
ARMOR3D provides hydrographic properties like temperature, salinity, geostrophic velocities and mixed layer 
depth. We use delayed time mode (DT) data on a global regular grid resolved at %°. The vertical range is from the 
surface down to a depth of 5,500 m. The data set incorporates 50 vertical levels with finer resolution in the upper 
1,500 m of the water column (between 5 and 100 m) and coarser resolution below (between 250 and 500 m). For 
our study, we use the weekly resolution, which represents a weekly value centered on Wednesdays. 
ARMOR3D is a combination of in situ observations and satellite data processed in three steps. Details on the data 
processing can be found in Guinehut et al. (2012). Major steps involve statistical regressions to retrieve synthetic 
T/S fields from the surface down to 1,500 m. These fields are combined in a second step with the available in situ 
„rofiles for T and S using an optimal interpolation algorithm. The outcome of this second processing step is the 
ARMOR3D combined fields for the upper 1,500 m of the water column. In the final step, the 3D fields are 
expanded to the water column below 1,500 m incorporating T/S fields from seasonal World Ocean Atlas 2018 
'WOA18) climatology. The advantage of ARMOR3D over other gridded data sets that simply interpolate in situ 
profiles (e.g., EN4) lies in this multi-step combination of in situ observations and satellite data that in our opinion 
allows to significantly increase the accuracy and effective resolution of the reconstructed fields. According to the 
Quality Information Document from the Copernicus Marine Service (ARMOR3D, 2021) temperature at 10 m has 
a root mean square (RMS) error from 0.6°C to 1.1°C, where the lower value corresponds to the best RMS over the 
Argo period (2003-2018), whereas the upper value corresponds to RMS over the pre-Argo period (1993-2003). 
At 100 m the RMS goes from 0.8°C to 1.4°C and at 1,000 m from 0.2°C to 0.5°C. Salinity RMS at 10 m goes from 
0.1 to 0.2, at 100 m from 0.1 to 0.15 and at 1,000 m from 0.02 to 0.07. Regarding the geostrophic currents, the 
Quality Information Document (ARMOR3D, 2021) explains that the velocities are slightly too barotropic with a 
bias in the zonal component on the period from 1998 to 2017 of around 0.0006 m s”' and in the meridional 
component close to zero. The RMS differences are around 0.064 m s”' for the zonal component and 0.052 ms” 
for the meridional component. Finally, the mixed layer depth (MLD) has an RMS of 29 m. 
For the calculation of the water mass formation using the kinematic approach, we consider an observation-based 
data set of 3D ocean currents. This product, named OMEGA3D (Buongiorno Nardelli, 2020b), is based on the 
application of a quasi-geostrophic diagnostic model to ARMOR3D data and is also distributed by the Copernicus 
Marine Service. It covers the period from 1993 to 2018 and provides 3D fields of vertical and horizontal currents 
estimated through a diagnostic model based on a diabatic version of the Omega equation (Buongiorno Nar- 
delli, 2020a; Giordani et al., 2006): 
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