Supplementary Information for the manuscript The stability of an evolving Atlantic meridional overturning circulation Wei Liu*1,2, Zhengyu Liu3,2 and Aixue Hu4 1 Key Laboratory of Meteorological Disaster of Ministry of Education, School of Marine Sciences, Nanjing University of Information Science & Technology, Nanjing, China 2 3 4 Center for Climatic Research, University of Wisconsin-Madison, USA Lab. Climate, Ocean and Atmosphere Studies, Peking University, Beijing, China Climate and Global Dynamics Division, National Center for Atmospheric Research, Boulder, Colorado, USA 1. Models The state-of-the-art CGCMs used in this study are two versions of the National Center for Atmospheric Research (NCAR) Community Climate System Model version 3 (CCSM3): a standard T42 version, i.e., CCSM3 T42 [Collins et al., 2006] and a lowresolution T31 version, i.e., CCSM3 T31 [Yeager et al., 2006]. In both versions, the atmosphere, ocean, sea ice and land components are the Community Atmospheric Model version 3 (CAM3), the Parallel Ocean Program (POP), the Community Sea Ice Model version 5 (CSIM5) and the Community Land Model version 3 (CLM3), respectively. In particular, for the atmospheric component, two models employ T42 and T31 spectral truncations, respectively. For the land component, CCSM3 T31 includes dynamic vegetation in CLM3. In the ocean and sea ice components, CCSM3 T42 adopts an x1ocn * Corresponding Author: W.Liu, Address: 1225 W. Dayton St., 1143, Madison, WI, 53706 Email address: wliu5@wisc.edu 1 grid (nominally 1°) with 40 vertical levels in ocean while CCSM3 T31 adopts an x3ocn grid (nominally 3°) with 25 vertical levels in ocean. Benefited from rotating the North Pole to Greenland, resolutions of the ocean and ice components in both models become significantly finer towards Greenland, so that narrow straits or passages around the Arctic and the North Atlantic, such as the Fram Strait and the Canadian Arctic Archipelago (CAA), are well resolved. 2. The sensitivity of Mov to the reference salinity S0 Fig. S1 shows the evolution of the reference salinity S0 (the Atlantic basin mean salinity) in three simulations. Here, by choosing the Atlantic basin mean salinity as the reference salinity, we define the freshwater with a clear physical meaning: the water with salinity lower than the reference salinity means the “freshwater” relative to the Atlantic basin. To examine the sensitivity of Mov on the time dependency of S0, we re-calculate the freshwater transports in Fig. 2 by using a constant S0 as the reference salinity. In particular, this constant S0 is selected as the global mean salinity under different climates (34.7psu in OBS and OBS; 36.5psu in LGM). As shown in Fig. S4, a switch of S0 causes little changes in MovS, MovN and in turn ΔMov. It only leads to some variations in MovFRA and MovBAR in the OBS simulation, which further compensate with each other and hardly affect the total freshwater transport across the northern boundary (MovN). 3. The northern boundary in the calculation of Mov Fig. S2 shows that, besides the Labrador Sea, deep-water also is formatted in the Greenland, Iceland and Norwegian (GIN) Seas area (between 60-80oN). Therefore, it is 2 reasonable to include the GIN Seas area in a generalized Atlantic basin for examining the freshwater transport Mov and associated feedback. In the study, we select the northern boundary as the boundary between the Arctic and the North Atlantic by following the definition in many previous researches [e.g., Aagaard and Carmack, 1989; Serreze et al., 2006; Holland et al., 2007; Jahn et al., 2010]. From these researches, the freshwater exchange between the Arctic and the North Atlantic is mainly through the three passages: the Fram Strait, the CAA and the western shelf of the Barents Sea. As a result, these three passages constitute the northern boundary in our study. Fig. S3b shows the domain of the Arctic Ocean (pick colored), as well as the northern boundary in form of three passages (black solid lines) in CCSM3, which is consistent with previous studies [e.g., Aagaard and Carmack, 1989; Serreze et al., 2006; Holland et al., 2007; Jahn et al., 2010]. Seen from Fig. S3b, these three subsections are not purely zonal. The location of subsections and the split-up between subsections naturally comply with the geostrophic constraints (Fig. S3a). Besides, the hydrologic characteristics (Fig.s S7 and R8) and the ocean dynamics are quite different across three subsections. Therefore, it is reasonable to calculate Mov at the northern boundary by adding three separate subsection estimates with three different zonal averages for velocity and salinity. The physical meaning for this calculation is that, based on uniform reference salinity (the Atlantic basin mean salinity), M ov at each subsection represents the contribution of “freshwater” (relative to the Atlantic basin) carried by the overturning flow across this subsection. The sum of three Mov is then MovN, the total amount of freshwater carried through the northern boundary. On the other hand, if we treat the northern boundary as “one” section and calculate MovN by making an 3 average over three subsections for π£ and π , we will mess up the hydrologic and dynamic characteristics among three subsections. As a result, MovN will include the term such as Μ Μ Μ Μ Μ π£′π ′, i.e., the product of deviations in π£ and π among three subsections. In another word, the barotropic transports over the three subsections of the northern section then would project on MazN (see the definition of MazN in the following text). 4. The basin-integrated freshwater budget Derivations below generally follow Drijfhout et al. [2010] but in the context of this study. For a Boussinesq ocean the vertically-integrated continuity equation is in form of the literature [Griffies et al., 2004] π η,t = − ∫−π» ππ§∇ β π’ + ππ€ + πππ π£ (S-1) where π» is the depth of the ocean, π is the free surface elevation, π’ is the horizontal velocity vector, ππ€ is the volume flux per unit per unit horizontal area of fresh water crossing the sea surface. πππ π£ is a rest term. Integrated over the Atlantic between two boundaries, V,t = β¬π π£ππ₯ππ§ − β¬π π£ππ₯ππ§ − πΈππ πΌ + π ππ π (S-2) π π where ππ and ππ denote the southern and northern boundaries, respectively. The subscripts ππ and ππ indicate the integration along ππ and ππ , between where the continent terminates. πΈππ πΌ is the net evaporation over the basin and V is the water volume, which is the sum of evaporation (E), precipitation (-P), runoff (R) and sea ice change (I). π ππ π is the integrated rest term. As a result, Eq. (S-2) can be written as 4 V,t = ππ − ππ − πΈππ πΌ + π ππ π where ππ = β¬π π£ππ₯ππ§ π (S-3) and ππ = β¬π π£ππ₯ππ§ , respectively denoting the barotropic π transport at boundaries of ππ and ππ . Here, considering the realistic complex boundary between the North Atlantic and the Arctic, the barotropic transport ππ is comprised of three components, respectively via the Fram Strait, the CAA and the western shelf of the Barents Sea, i.e., ππ = β¬πΉπ π΄ π£ππππ§ + β¬πΆπ΄π΄ π£ππππ§ + β¬π΅π΄π π£ππππ§ (S-4) where the subscripts πΉπ π΄, πΆπ΄π΄ and π΅π΄π indicate the integration over a transection along the direction of the Fram Strait, the CAA and the western shelf of the Barents Sea where the continent terminates, respectively. π£ denotes the normal velocity at each section. Meanwhile, the vertically-integrated equation for salinity S reads π η π π π ,t ∫−π» ππ§π,π‘ + π»+π ∫−π» ππ§π = ∫−π» ππ§∇ β (ππ’) − ∫−π» ππ§∇πΉ + π + πππ π (S-5) where πΉ is the flux from small-scale mixing ; π is a source term and πππ π is a rest term. Integrated over the Atlantic between ππ and ππ , ∫π΄π‘π π,π‘ ππ + V,t ππ΄π‘π = β¬π π£πππ₯ππ§ − β¬π π£πππ₯ππ§ + ππΌπ + ππππ πΆπΈ + π ππ π (S-6) π π where MIX denotes the contribution by small-scale mixing and π ππ π is the integrated rest term. Similar to Eq. (S-4), β¬π π£πππ₯ππ§ = β¬πΉπ π΄ π£πππππ§ + β¬πΆπ΄π΄ π£πππππ§ + β¬π΅π΄π π£πππππ§ (S-7) π We choose ππ΄π‘π = π0 = 34.7ππ π’ , then this salt budget becomes an equivalent freshwater budget in which all terms can be expressed in Sverdrups: 5 1 1 0 0 1 − π ∫π΄π‘π π,π‘ ππ − V,t = − π β¬π π£πππ₯ππ§ + π β¬π π£πππ₯ππ§ +ππΌππ0 + ππππ πΆπΈπ0 + π ππ π0 π 0 π (S-8) 1 where ππππ πΆπΈπ0 = − π ππππ πΆπΈ = −πΈππ πΌ ∗ , πΈππ πΌ ∗ is the equivalent water flux 0 1 through the ocean surface. ππΌππ0 = − π ππΌπ and π ππ π = πππ π ππ π , where πππ is the 0 weighted averaged salinity of the cross-land mixed water. Then π π ππ π0 = − πππ π ππ π = (1 + πππ −π0 π0 0 ) π ππ π = −(1 + π)π ππ π (S-9) Since π = π(0.01), ππ ππ π0 is a small term that can be added to the large mixing term (ππππ₯ ) in form of ππππ₯ = ππΌππ0 −ππ ππ π (S-10) As a result, Eq. (S-8) can be written as −ππ‘ππππ − V,t = ππ − ππ + ππππ₯ − π ππ π − πΈππ πΌ ∗ (S-11) where ππ‘ππππ , ππ and ππ are the trend term of freshwater transport and the total freshwater transports at boundaries of ππ and ππ , respectively in form of 1 ππ‘ππππ = π ∫π΄π‘π π,π‘ ππ 0 (S-12) 1 ππ = − π β¬π π£πππ₯ππ§ (S-13) 0 π 1 ππ = − π β¬π π£πππ₯ππ§ (S-14) 0 π Here, it is notable that Eqs. (S-11) and Eq. (S-3) take different forms in various numerical models. For those models employing a freshwater flux (named the FWF models therein), such as the GFDL CM2.1 model, in which the freshwater flux changes the salinity of a sea-water parcel by changing its volume while keeping its salt context constant. As a 6 result, πΈππ πΌ ∗ = 0 in Eq. (S-11) but πΈππ πΌ is kept in Eq. (S-3), so Eq. (S-11) degenerates as −ππ‘ππππ − V,t = ππ − ππ + ππππ₯ − π ππ π (S-15) By combining Eq. (S-3) with Eq. (S-15), we obtain πΈππ πΌ = ππ − ππ + ππ − ππ + ππππ₯ + ππ‘ππππ (S-16) On the other hand, for those models using a virtual salt flux (named the VSF models therein), such as the CCSM3 models (T42 and T31) in this study, the virtual salt flux changes the salinity of a sea-water parcel by changing its salt content while keeping its volume constant. As a result, πΈππ πΌ = π,π‘ = π ππ π = 0 in Eq. (S-3) but πΈππ πΌ ∗ is kept in Eq. (S-11). So Eq. (S-3) degenerates as ππ − ππ = 0 (S-17) By combining Eq. (S-11) with Eq. (S-17), we obtain πΈππ πΌ ∗ = ππ − ππ + ππΌπ+ππ‘ππππ (S-18) Furthermore, the meridional velocity and salinity in ππ and ππ can be written as π£ = 〈π£〉 + π£′ and π = 〈π 〉 + π ′, where 〈π£〉 and 〈π 〉 denote mean velocity and salinity along the section of boundaries of ππ and ππ , π£′ and π ′ are deviations from their means. (1) For the FWT models, we average on Eq. (S-16) over a sufficient long time for a quasi-steady state so that ππ‘ππππ ≈ 0. By keeping the original symbols for the time mean variables, and using the overbars for temporal average, we obtain ∗ ∗ πΈπ ππΌ = πππ£π − πππ£π + πππ§π − πππ§π + ππ − ππ + ππππ₯ (S-19) where 1 ∗ πππ£π = − π β¬π 〈π£Μ 〉〈π Μ 〉ππ₯ππ§ (S-20) 0 π 7 1 ∗ πππ£π = − π β¬π 〈π£Μ 〉〈π Μ 〉ππ₯ππ§ (S-21) 0 π 1 πππ§π = − π β¬π Μ Μ Μ Μ Μ π£ ′ π ′ππ₯ππ§ (S-22) 1 πππ§π = − π β¬π Μ Μ Μ Μ Μ π£ ′ π ′ππ₯ππ§ (S-23) 0 0 π π In particular, the transports πππ£π and πππ§π can be written as ∗ ∗ ∗ ∗ πππ£π = πππ£πΉπ π΄ + πππ£πΆπ΄π΄ + πππ£π΅π΄π (S-24) πππ§π = πππ§πΉπ π΄ + πππ§πΆπ΄π΄ + πππ§π΅π΄π (S-25) ∗ ∗ ∗ (πππ§πΉπ π΄ ) , πππ£πΆπ΄π΄ (πππ§πΆπ΄π΄ ) and πππ£π΅π΄π (πππ§π΅π΄π ) are the overturning where πππ£πΉπ π΄ ∗ (azimuthal) components of πππ£π (πππ§π ) along the Fram Strait, the CAA and the western shelf of the Barents Sea, respectively. These transports can be written as 1 ∗ πππ£πΉπ π΄ = − π β¬πΉπ π΄〈π£Μ 〉〈π Μ 〉ππππ§ 0 1 ∗ πππ£πΆπ΄π΄ = − π β¬πΆπ΄π΄〈π£Μ 〉〈π Μ 〉ππππ§ 0 1 ∗ πππ£π΅π΄π = − π β¬π΅π΄π 〈π£Μ 〉〈π Μ 〉ππππ§ 0 1 πππ§πΉπ π΄ = − π β¬πΉπ π΄ Μ Μ Μ Μ Μ π£ ′ π ′ππππ§ 0 1 πππ§πΆπ΄π΄ = − π β¬πΆπ΄π΄ Μ Μ Μ Μ Μ π£ ′ π ′ππππ§ 0 1 πππ§π΅π΄π = − π β¬π΅π΄π Μ Μ Μ Μ Μ π£ ′ π ′ππππ§ 0 (S-26) (S-27) (S-28) (S-29) (S-30) (S-31) ∗ ∗ ∗ Here, we define βπππ£ = πππ£π − πππ£π as the AMOC induced freshwater transport and βππππ‘π = ππ − ππ as the net barotropic transport across the Atlantic basin. So Eq. (S-19) becomes ∗ πΈππ πΌ = βπππ£ + πππ§π − πππ§π + βππππ‘π + ππππ₯ 8 (S-32) Finally, we make π ππ = ππππ₯ , rewrite πΈππ πΌ as [πΈπππ‘ ] where [.] denote a basin-wide averaging and obtain ∗ [πΈπππ‘ ] = βπππ£ + πππ§π − πππ§π + βππππ‘π + π ππ (S-33) (2) For the VSF models, we average on Eq. (S-18) over a long period for a quasisteady state, and similarly we obtain πΈππ πΌ ∗ = ππ − ππ + ππΌπ (S-34) Since ππ − ππ = 0, we re-write Eq. (S-34) as πΈππ πΌ ∗ = πππ£π − πππ£π + πππ§π − πππ§π + ππΌπ (S-35) where πππ£π and πππ§π are the overturning and azimuthal freshwater transport at boundaries of ππ (ππ ) of the Atlantic basin, respectively in form of 1 πππ£π = − π β¬π 〈π£Μ 〉(〈π Μ 〉 − π0 )ππ₯ππ§ π 0 1 πππ£π = − π β¬π 〈π£Μ 〉(〈π Μ 〉 − π0 )ππ₯ππ§ π 0 (S-36) (S-37) In particular, the transports πππ£π can be written as πππ£π = πππ£πΉπ π΄ + πππ£πΆπ΄π΄ + πππ£π΅π΄π (S-38) where πππ£πΉπ π΄ , πππ£πΆπ΄π΄ and πππ£π΅π΄π are the overturning components of πππ£π along the Fram Strait, the CAA and the western shelf of the Barents Sea, respectively. In particular, they can be written as πππ£πΉπ π΄ = − 1 π0 β¬πΉπ π΄〈π£Μ 〉(〈π Μ 〉 − π0 )ππππ§ (S-39) 1 πππ£πΆπ΄π΄ = − π β¬πΆπ΄π΄〈π£Μ 〉(〈π Μ 〉 − π0 )ππππ§ (S-40) 0 1 πππ£π΅π΄π = − π β¬π΅π΄π 〈π£Μ 〉(〈π Μ 〉 − π0 )ππππ§ (S-41) 0 9 Finally, we make π ππ = ππΌπ, rewrite πΈππ πΌ ∗ as [πΈπππ‘ ] where [.] denote a basin-wide averaging and obtain [πΈπππ‘ ] = βπππ£ + πππ§π − πππ§π + π ππ (S-42) where βπππ£ = πππ£π − πππ£π , denoting the net meridional freshwater transport across the ∗ Atlantic basin. It is worth noting here, since ππ = ππ , βπππ£ = βπππ£ in the VFS models, ∗ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ πΏ = πβπ ππ£ ⁄ππ = πβπππ£ ⁄ππ in three simulations of this study. 5. The sensitivity of L to the averaging period of ψ and ΔMov Fig. S5 is the same as Fig. 3 except that πΜ and Μ Μ Μ Μ Μ Μ Μ βπππ£ are taken as the 100-year mean of ψ and ΔMov in the calculation of L. Comparing with Fig. 3, L has a nosier pattern in Fig. S5. However, the general characteristics of L are highly similar between Fig. 3 and Fig. S5, i.e., L is mostly positive in OBS and LGM but appears as negative during year 1600-3600 in CBS, which demonstrates that sign of L is not sensitive to the averaging period of ψ and ΔMov as long as it is beyond the inter-decadal time scale. 6. Changes in MovS and MovN during hosing Fig. S6 focuses on explaining the evolution pattern of MovS in the OBS, CBS and LGM simulations. Under the present day climate, MovS in OBS and CBS exhibit a similar saddle-like evolution pattern. This is because, with increasing freshwater forcing, the NADW outflow at 34oS is greatly diluted from its formation area while the overlapping surface and thermocline water has a minor salinity change in the first ~1500 years (Fig. S6a and b). So the AMOC exports more freshwater via its lower branch, making MovS alter from positive (freshwater convergence) to negative (freshwater divergence). After 10 that, either the NADW or the upper ocean water gets freshened, and the AMOC rapidly slows down, approaching collapse. Combination of both factors leads to a reduced freshwater export or even a freshwater import. Under the LGM climate, the freshwater import MovS mono-decreases to zero and switches into freshwater export at the maximum hosing, which mainly results from the freshening of the surface and thermocline water at 34oS (Fig. S6c). Meanwhile, to explain the evolution pattern of MovN, we further examine the along section mean salinity and normal velocity profiles at three sections. Under the present day climate (OBS and CBS), for the Atlantic basin, there are inflow (<~400m) at Fram Strait, outflow (<~400m) at the western Barents Sea and inflow (<~200m) at the CAA (Fig. S8). With increasing freshwater input, changes in Mov at each section are listed as below: 1) The Fram Strait: in the beginning of hosing, the inflow carries “freshwater” relative to the Atlantic basin, i.e., a freshwater import in both cases. During hosing, the inflow becomes shallower and weaker, with a small change in the salinity difference between the inflow and the Atlantic basin (Fig. S7a and d). As a result, the freshwater imports reduce in both cases. Comparing with CBS, the inflow in OBS has a greater reduction with hosing (Fig. S8a and d), which then induces a larger drop in the freshwater import (Fig. 2g and h). 2) The western Barents Sea: in the beginning of hosing, the outflow in OBS (CBS) induces a freshwater export in the upper 100m (60m) and a freshwater import in 100460m (60-460m). By integrating Mov over the whole depth, the outflow induces a freshwater export in OBS but a freshwater import in CBS. During hosing, the outflow becomes shallower and weaker (Fig. S8b and e), however, the salinity difference between 11 the outflow and the Atlantic basin grows larger towards the maximum hosing (Fig. S7b and e). As a result, the freshwater export rapidly increases in OBS, and the freshwater import switches to a freshwater export in CBS. Towards the maxing hosing, the increasing rates of freshwater exports become smaller in both cases (Fig. 2g and h). 3) The CAA: in the beginning of hosing, the inflow carries “freshwater” relative to the Atlantic basin, i.e., a freshwater import in both cases. Note that this flow is much weaker than those across the Fram Strait and the western Barents Sea, together with a relative small salinity change during hosing (Fig. S8c and f). Therefore, Mov at the CAA has little variations in both cases (Fig. 2g and h). For the LGM simulation, the CAA and the Barents Sea are closed in the model. At the Fram Strait, the water is “fresh” relative to the Atlantic basin. For the Atlantic basin, there is an outflow in the upper 600m and a deep inflow below in the beginning of hosing. By integrating Mov over the whole depth, the total flow induces a freshwater export. During hosing, both the inflow and the outflow get shallower (Fig. S8g), and the vertical salinity gradient increases (Fig. S7g), leading to a small change in Mov across the Fram Strait (Fig. 2f). 7. The issue of the barotropic transport First, the choice of S0 equal to the Atlantic basin mean salinity enables the barotropic transports across the southern and northern boundaries of the Atlantic to mostly cancel with each other. Therefore, ΔMov has little contribution from the barotropic transport [Liu and Liu, 2012]. Besides, the barotropic transport induced by S0 only slightly modifies MovS in 12 magnitude but does not change the sign of MovS. Fig. S9a shows two versions of two MovS in OBS: one contains no barotropic transport by using S0 that is equal to the sectionaverage salinity at 34oS [Drijfhout et al., 2010] while the other is from Fig. 2b, which utilizes the Atlantic basin mean as S0 and contains some barotropic transports. Obviously, the contribution from the barotropic transport is so small that both MovS share a highly similar pattern. Finally, we need to clarify that there is no barotropic transport contributing to Mov in the CBS and LGM simulations because of the closure of the Bering Strait. This is similar to the case in Rahmstorf [1996], in which no depth-integrated flow through Bering Strait is allowed. 13 Reference Aagaard, K., and E. C. Carmack (1989), The role of sea ice and other fresh water in the Arctic Circulation, J. Geophys. Res., 94, 14485–14498. Collins, W. D., et al. (2006), The Community Climate System Model version 3 (CCSM3), J. Climate, 19, 2122–2143. Drijfhout, S. S., et al. (2010), The stability of the MOC as diagnosed from model projections for pre-industrial, present and future climates, Clim. Dyn., 37, 15751586, DOI:10.1007/s00382-010-0930-z. Griffies S. M., et al. (2004), A technical guide to MOM4, NOAA/GFDL, pp 337. Holland, M. M., et al. (2007), Projected changes in Arctic Ocean freshwater budgets, J. Geophys. Res., 112, G04S55, doi:10.1029/2006JG000354. Jahn, A., et al. (2010), A tracer study of the Arctic Ocean’s liquid fresh- water export variability, J. Geophys. Res., 115, C07015, doi:10.1029/2009JC005873. Liu, W., and Z. Liu (2012), A diagnostic indicator of the stability of the Atlantic Meridional Overturning Circulation in CCSM3, J. Climate, doi:10.1175/JCLI-D-1100681.1, in press. Rahmstorf, S. (1996), On the freshwater forcing and transport of the Atlantic thermohaline circulation, Clim. Dyn., 12, 799–811. Serreze, M. C., et al. (2006), The large-scale freshwater cycle of the Arctic, J. Geophys. Res., 111, C11010, doi:10.1029/2005JC003424. Yeager, S. G., et al. (2006), The low-resolution CCSM3, J. Climate, 19, 2545–2566. 14 Figure captions Fig. S1. Evolution of the Atlantic basin mean salinity in the (a) OBS, (b) CBS and (c) LGM simulations, in which the Atlantic basin mean salinity is shown as a 20-year mean. The global mean salinity (gray dashed line) for each climate is included in the figure, which equals to 34.7psu in OBS and OBS, and equals to 36.5psu in LGM. Fig. S2. The meridional streamfunction (contour in Sv) in the Atlantic and the Arctic for the state without hosing in the (a) OBS, (b) CBS and (c) LGM simulations, with the upper 1,000 m of the ocean stretched. The contour interval of the meridional streamfunction is 4 Sv, with blue shading for negative values and red shading for positive values. No shading is applied between -2Sv and 2Sv. The northern boundary of the Atlantic basin is around 80oN, which is denoted by the green dashed line. Fig. S3. (a) Bathymetry map in CCSM3 T42 to the north of 45oN (in unit of meter). (b) The basin index of CCSM3 T42 to the north of 45oN. The Arctic Ocean is connected with the Atlantic via three passages (black solid lines), respectively the CAA, the Fram Strait and the western shelf of the Barents Sea. These three passages are composed of the northern boundary of the Atlantic basin. Fig. S4. (left panel) The Atlantic freshwater transports in the OBS simulation, as calculated from a time-evolving S0 and a constant S0 = 34.7psu. (a) Evolution of the net AMOC-induced freshwater transport ΔMov (evolving S0, red; constant S0, black). (b) Evolution of the AMOC-induced freshwater transports at the southern (MovS, evolving S0, blue; constant S0, green) and northern (MovN, evolving S0, orange; constant S0, brown) boundaries. (c) Evolution of the MovN components, i.e., the liquid overturning freshwater transports across the Fram Strait (MovFRA, evolving S0, 15 magenta; constant S0, maroon), the CAA (MovCAA, evolving S0, purple; constant S0, violet) and the western shelf of the Barents Sea (MovBAR, evolving S0, cyan; constant S0, navy). (middle panel) The same as the left panel except for the CBS simulation. (right panel) The same as the top two plots in the left panel except for the LGM simulation, with a constant S0 = 36.5psu as the reference salinity. All the freshwater transports are calculated from monthly model output and also shown as a 20-year mean. Fig. S5. (left panel) Evolution of the generalized AMOC stability indicator L in the (a) OBS, (c) CBS and (e) LGM simulations. Gray lines denote the moments of the maximum freshwater forcing in each simulation, respectively. (right panel) Hysteresis diagrams of the indicator L in the (b) OBS, (d) CBS and (f) LGM simulations. In all the plots, the cyan/magenta dots represent the phase of freshwater forcing increase (decrease) in these simulations. In the calculation of L, πΜ and Μ Μ Μ Μ Μ Μ Μ βπππ£ are taken as the 100-year mean of ψ and ΔMov for eliminating the AMOC inter-decadal variability. Fig. S6. Vertical profiles of the zonal mean Atlantic salinity at 34oS from three states in the (a) OBS, (b) CBS and (c) LGM simulations, with the upper 1000m amplified. Salinity in each state is calculated as a 20-year mean. In OBS, the three states are year 0-20, year 1400-1420 and year 2200-2220, respectively. In CBS, the three states are year 0-20, year 1600-1620 and year 2100-2120, respectively. In LGM, the three states are year 0-20, year 1000-1020 and year 2000-2000, respectively. Fig. S7. Similar to Fig. S6, expect for the vertical profiles of the along-section mean salinity at three passages (the northern boundary) from three states (a)-(c) OBS, (d)(f) CBS and (g) LGM simulations. The reference salinity is shown in dashed line. The 16 CAA and the Barents Sea is closed in the LGM so that only the salinity profile at the Fram Strait is shown in the LGM simulation. Fig. S8. Similar to Fig. S7, expect for the along-section mean normal velocity. Note that the velocity is negative if it is in the opposite normal direction of the section. Fig. S9. (a) MovS in the OBS simulation, as calculated from S0 that equals to the Atlantic basin mean salinity (blue) and S0 that equals to the section-averaged salinity at 34oS (red). (b) Evolution of various S0 in the OBS simulation, which equals to the Atlantic basin mean salinity (blue) and the section-average salinity at 34oS (red), respectively. ΔMov is calculated from monthly model output and also shown as a 20-year mean. 17 Fig. S1 18 Fig. S2 19 Fig. S3 20 Fig. S4 21 Fig. S5 22 Fig. S6 23 Fig. S7 24 Fig. S8 25 Fig. S9 26