Under Arctic pack ice, a cold, fresh meltwater layer sits above a halocline, below which warmer, saltier Atlantic-derived water intrudes. This probe descends through a modelled water column where temperature and salinity relax exponentially from their surface values to deep values over the "mixed-layer depth" you set:
S(z) = S_deep − (S_deep − S_surf)·e^(−z / L)
T(z) = T_surf + (T_deep − T_surf)·(1 − e^(−z / L))
The surface water sits at its local freezing point (water in contact with ice cannot be colder than this):
T_f(S) ≈ −0.054·S (linear seawater freezing-point approximation)
Density is a simplified linear equation of state (colder + saltier ⇒ denser, the mechanism that drives polar brine rejection and deep convection):
ρ(T,S) ≈ 1000 + 0.78·S − 0.15·T − 0.0002·T² [kg/m³]
Sound speed uses the Mackenzie (1981) empirical formula, valid for −2–30 °C, 25–40 psu, 0–8000 m depth:
c = 1448.96 + 4.591T − 0.05304T² + 0.0002374T³
+ 1.340(S−35) + 0.0163z + 1.675e−7z²
− 0.01025T(S−35) − 7.139e−13Tz³