# Interpolation of TALK Below the Deepest Mixed Layer

Below the mixed layer, TALK can be interpolated by piecewise linear regression as a function of potential temperature () and salinity (S):

TALK = a + bθ + cS (1)

One regression was performed in each of the two layers: from the winter time mixed layer down to 1000 m, and below 1000 m. The cutoff at 1000 m reflects the mean depth of the TALK maximum. The coefficients were calculated for each profile, interpolated to the 3-D grid using the Generic Mapping Tools (GMT) software (Wessel and Smith 1995), and applied to climatological temperature and salinity (Levitus and Boyer 1994a,b; Levitus et al. 1994) to compute TALK. Uncertainty associated with this interpolation procedure in the Indian, Pacific, and Atlantic Oceans is respectively estimated to be ±8.4 µmol/kg, ±10.2 µmol/kg, and ±4.6 µmol/kg in the upper 1000 m, and ±4.8 µmol/kg, ±9.1 µmol/kg, and ±5.9 µmol/kg at depths below 1000 m. The mean uncertainty associated with the TALK interpolation procedure in the global ocean below the mixed layer is estimated to be ±5.5 µmol/kg.