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1. AAIW is defined by the low salinity tongue, and spiciness is defined by salinity anomaly along isopycnal surfaces, so that one can use salinity or spiciness to trace AAIW. Here we use WOA18 data downloaded from https://www.nodc.noaa.gov/OC5/woa18/woa18data.html, and the results are shown in Figure 2, one can trace AAIW with different tracers, including the absolute salinity (panel a), the spiciness (panel b), the distance from the origin (defined by the temperature and salinity at 30oS and 50 m below the sea surface) (panel c), and the spicity (panel d).
2. As observed in Schmitt (1981), density ratio was 1.89 and 1.95 for the South and North Center Water stations. Using World Ocean Circulation Experiment (WOCE) database (https://cchdo.ucsd.edu/), we find two stations: (17.4oS, 30.8oW) in Section A17 and (24.5oN, 36.7oW) in Section A05-2, nearest to those in Schmitt (1981), to calculate the density ratio.
3. In the Arctic Ocean, we used temperature and salinity data acquired with Ice-Tethered Profiler (ITP), downloaded from https://www.whoi.edu/page.do?pid=28866. With the vertical resolution of 0.25 m, the data enables us to examine the small-scale structures, i.e. diffusive convection staircases. The ITP4 station is located at (79.0oN, 142.5oW) in the Canada Basin, where a stack of staircases exists in the upper layer of a water mass, called as Antarctic Water (Figure 3(a)) (Padman and Dillon, 1987).
