Bindoff and McDougall  proposed three processes for interpreting the observed changes: pure warming, pure freshening and pure heave, involving their respective change in atmospheric forcing in the water mass source region. The first two are related to heat and freshwater fluxes, changing the water mass characteristics, and the third one is related to wind stress curl, renewal rates of water masses or internal waves. The relative strength of each process, in terms of percentage variance explained (Aw, Af and Ah, where w, f and h stand for warming, freshening and heave, respectively), can be estimated solving the following equations [Bindoff and McDougall, 1994]:
where ρ−1ρ′∣z is the density anomaly at fixed pressure, N′ is the change in pressure of a neutral density surface, ∣z denotes changes on isobars, ∣n denotes changes along isoneutrals, and Rρ (Rρ = αθz/βSz) is the stability ratio defined from the thermal expansion and the haline contraction coefficients, α and β, respectively, and the vertical gradients of temperature and salinity, θz and Sz. Although Equation (2) is an ill-posed system, the proportion of the variance explained by each process can be assessed by making the assumption that only a single process is acting and applying an inverse method. We have distinguished four pressure regimes where a single process tends to dominate (Figure 4). In Regime I (350–600 db), corresponding to the lower levels of NACW, pure freshening explains more than 95% of the variance, suggesting water mass modification at the outcropping region. This result is expected based on the shift of the θ/S relationship shown in Figure 3a. Between 600 and 900 db (Regime II), the observed changes can be explained by pure heave and by pure freshening in Regime III (900–1200 db), both statistically significant at the 90% level. At deeper layers (Regime IV) the percentage of the overall variance resolved drops. However, pure heave explains 60–90% of the signal over the deepest levels of intermediate waters and NADW.