We use the standard version of IPSL-CM6A-LR (Boucher et al., 2020). The ocean component of IPSL-CM6A-LR is the NEMO oceanic model Version 3.6. The dynhpg.F90 file is a modified version of the routine that implements the flow-field correction method, and the namelist_ORCA1_cfg is the modified namelist used to activate the flow field correction, set the parameters, and read the input temperature, salinity, and mask. The mask specifies the region where this method is applied. To implement this method using the IPSL coupled model, consider following these steps: 1. Install the standard configuration in a path 2. Copy the provided dynhpg.F90 in modipsl/modeles/NEMOGCM/CONFIG/ORCA1_LIM3_PISCES/MY_SRC 3. Compile 3. Copy and modify the namelist_ORCA1_cfg in modipsl/config/IPSLCM6/testffc/PARAM The input conservative temperature (in degC), absolute salinity (in g/kg), and mask are provided to the model for the flow field correction are available in the following files: data_sal_sa_1.5LFC.nc (salinity) data_sal_sa_weak1.5LFC.nc (salinity) data_tem_bigthetao_1.5LFC.nc (temperature) data_tem_bigthetao_weak1.5LFC.nc (temperature) rhdmsk_data_bothBC2.v2.nc (mask) Note that data_sal_sa_1.5LFC.nc and data_tem_bigthetao_1.5LFC.nc are used to constrain the AMOC to the strong state in Jiang et al., (2023). data_sal_sa_weak1.5LFC.nc and data_tem_bigthetao_weak1.5LFC.nc are used to constrain it to the weak state in Jiang et al., (2023). Finally, some of the main simulated outputs are given. All the outputs are the annual mean ensemble mean (3 members) data lasting for 100 years. The initial states of the 3 members are sampled in the years of 1850, 2000 and 2080 of the CMIP6 piControl simulation available on ESGF, corresponding to neutral, strong, and weak AMOC states respectively. heatc_strong_3runs_1Y.nc (ocean heat content in J/m2) sos_strong_3runs_1Y.nc (sea surface salinity in psu) tos_strong_3runs_1Y.nc (sea surface temperature in degC) precip_strong_3runs_1Y.nc (precipitation in kg/(s*m2)) diaptrW_strong_3runs_1Y.nc (meridional streamfunction in Sv) slp_strong_3runs_1Y.nc (sea level pressure in Pa) geop500_strong_3runs_1Y.nc (geopotential height at 500 hPa in m) nettop0_strong_3runs_1Y.nc (clear-sky solar radiation at the top of atmosphere in W/m2) nettop_strong_3runs_1Y.nc (net downward flux at the top of atmosphere in W/m2) t2m_strong_3runs_1Y.nc (air temperature at 2-m in K) vitu850_strong_3runs_1Y.nc (zonal wind at 850 hPa in m/s) cld_strong_3runs_1Y.nc (low-level and high-level cloudiness, unitless) tauuo_strong_3runs_1Y.nc (surface downward stress in the x-direction in N/m2) tauvo_strong_3runs_1Y.nc (surface downward stress in the y-direction in N/m2) The files listed above are the results from simulations where the AMOC is constrained to the strong state (i.e., using the input data_tem_bigthetao_1.5LFC.nc and data_sal_sa_1.5LFC.nc). Similarly, the same fields from simulations where the AMOC is constrained to the weak state (i.e., using the input data_tem_bigthetao_weak1.5LFC.nc and data_sal_sa_weak1.5LFC.nc) are: heatc_weak_3runs_1Y.nc (ocean heat content in J/m2) sos_weak_3runs_1Y.nc (sea surface salinity in psu) tos_weak_3runs_1Y.nc (sea surface temperature in degC) precip_weak_3runs_1Y.nc (precipitation in kg/(s*m2)) diaptrW_weak_3runs_1Y.nc (meridional streamfunction in Sv) slp_weak_3runs_1Y.nc (sea level pressure in Pa) geop500_weak_3runs_1Y.nc (geopotential height at 500 hPa in m) nettop0_weak_3runs_1Y.nc (clear-sky solar radiation at the top of atmosphere in W/m2) nettop_weak_3runs_1Y.nc (net downward flux at the top of atmosphere in W/m2) t2m_weak_3runs_1Y.nc (air temperature at 2-m in K) vitu850_weak_3runs_1Y.nc (zonal wind at 850 hPa in m/s) cld_weak_3runs_1Y.nc (low-level and high-level cloudiness, unitless) tauuo_weak_3runs_1Y.nc (surface downward stress in the x-direction in N/m2) tauvo_weak_3runs_1Y.nc (surface downward stress in the y-direction in N/m2)