We consider anomalies of annually averaged quantities from the control runs of CCSM4 and GFDL-ESM2M to diagnose "deterministic" (i.e., slow) behavior, and monthly averaged quantities to diagnose what the slow dynamics see as stochastic forcing. We find that the deterministic dynamics of AMOC, in both models, can be described by: the streamfunction (minus the Ekman component; &psi_NoEk hereafter), ocean temperature (T) and salinity (S) at upper 700m and deep 1500-2000m levels. We found timescales of surface heat flux and fresh water flux to be too short to be included in a deterministic (and predictable) description of AMOC on annual timescales; rather, they appear to be only related to the stochastic (unpredictable) forcing of AMOC.
Despite that the basic dynamical behavior of these models appears to be fundamentally different, i.e., to consist of internal (ESM2M) vs. forced behavior (CCSM4), S and T are highly coupled at both upper and lower levels of the ocean, with the leading principal component time series of these quantities strongly correlated (68-98%). Furthermore, the analysis of the dynamical modes yields consistent relationships between S, T, and &psi_NoEk in these models allowing us to identify the common predictable components in those models.