Fig. 3: Stochastic bifurcation of the Atlantic Meridional Overturning Circulation (AMOC).

a Temporal evolution of the AMOC in the \({{EXP}}_{2110}\) categorized into 3 groups based on the last 50-year (2261–2310) average of AMOC strength. Three groups are named collapse, uncertain, and recovery group, and consist of 17, 2, and 9 ensemble members, respectively. Thin and thick lines represent all ensemble members and their mean in each group, respectively. The thick green line shows the ensemble mean. b Temporal evolution of the AMOC stability indicator (\(\Delta {F}_{{ov}}\); see Methods) in the \({{EXP}}_{2110}\). The y-axis represents the ensemble rank, sorted in ascending order based on the last 50-year average of AMOC strength in (a). For example, the ensemble members with the weakest and strongest AMOC strength in the last 50 years are assigned rank 1 and 28 (bottom and top of the y-axis), respectively. c Same format as (b), but for each member’s deviation from the ensemble mean (i.e., stochastic noise, represented by the symbol \({{\boldsymbol{\delta }}}\)). The physical quantity in (c) is the boreal winter (January-February-March; JFM) averaged surface density flux integrated over the Labrador-Irminger Sea (LIS, black contour in e). The blue dots in (b–d) indicate the timing of \(\Delta {F}_{{ov}}=0\) for each ensemble within the collapse group. d Same as c, but accumulated over time (named as “cumulative stochastic noise” and represented by the symbol \({{{\boldsymbol{\delta }}}}^{{{\boldsymbol{cum}}}}\)). e–g Collapse group mean of the cumulative stochastic noise until the timing of \(\Delta {F}_{{ov}}=0\) in each member (17 blue dots in d). The physical quantities in e–g are the winter density flux, evaporation, and sea level pressure with 1000-hPa wind (sky-blue vectors), respectively. The black contours in g are climatological winter sea level pressure (zonal mean removed) of 0, −5, −10, and −15 hPa. Hatchings and the solid vectors indicate statistically significant response at the 95% confidence level.