Fig. 4: The tipping modulation experiment with varying freshwater forcing rate using LOVECLIM.

a The tipping point (left blue side) and the delayed tipping timing (right orange side) compared to the static tipping point along r for collapse. b The average change rate of AMOC intensity during the collapse. The LOVECLIM experiment result (thick blue line), estimated stationary response (thick orange line), and reproduced changing rate based on the analytical formulation using Eq. (13) (thick yellow line). c and d are the same as a and b, respectively, but for the recovery. For d, the analytical formulation for recovery (Eq. (14)) was adopted instead of collapse (Eq. (13)). For all subpanels, examples of estimated freshwater flux forcing (FWF) rates are marked (Table 1). Four examples, DO events (gray shading), MWP-1A (dashed yellow line), Greenland ice sheet runoff for 2003–2016 from the GRACE dataset (dashed orange line), and 2017–2100 from the CMIP6 SSP5-8.5 scenario output (dashed red line) are plotted.