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 𝑣 and 𝑠, we will mess up the hydrologic and dynamic
characteristics among three subsections. As a result, MovN will include the term such as
̅̅̅̅̅
𝑣′𝑠′, i.e., the product of deviations in 𝑣 and 𝑠 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]
𝜂
η,t = − ∫−𝐻 𝑑𝑧∇ ∙ 𝑢 + 𝑞𝑤 + 𝑟𝑒𝑠𝑣
(S-1)
where 𝐻 is the depth of the ocean, 𝜂 is the free surface elevation, 𝑢 is the horizontal
velocity vector, 𝑞𝑤 is the volume flux per unit per unit horizontal area of fresh water
crossing the sea surface. 𝑟𝑒𝑠𝑣 is a rest term.
Integrated over the Atlantic between two boundaries,
V,t = ∬𝜃 𝑣𝑑𝑥𝑑𝑧 − ∬𝜃 𝑣𝑑𝑥𝑑𝑧 − 𝐸𝑃𝑅𝐼 + 𝑅𝑒𝑠𝑉 (S-2)
𝑆
𝑁
where 𝜃𝑠 and 𝜃𝑁 denote the southern and northern boundaries, respectively. The
subscripts 𝜃𝑠 and 𝜃𝑁 indicate the integration along 𝜃𝑠 and 𝜃𝑁 , between where the
continent terminates. 𝐸𝑃𝑅𝐼 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). 𝑅𝑒𝑠𝑉 is the integrated rest term. As a result, Eq. (S-2) can be written as
4
V,t = 𝑇𝑆 − 𝑇𝑁 − 𝐸𝑃𝑅𝐼 + 𝑅𝑒𝑠𝑉
where 𝑇𝑆 = ∬𝜃 𝑣𝑑𝑥𝑑𝑧
𝑆
(S-3)
and 𝑇𝑁 = ∬𝜃 𝑣𝑑𝑥𝑑𝑧 , respectively denoting the barotropic
𝑁
transport at boundaries of 𝜃𝑆 and 𝜃𝑁 .
Here, considering the realistic complex boundary between the North Atlantic and the
Arctic, the barotropic transport 𝑇𝑁 is comprised of three components, respectively via the
Fram Strait, the CAA and the western shelf of the Barents Sea, i.e.,
𝑇𝑁 = ∬𝐹𝑅𝐴 𝑣𝑑𝑙𝑑𝑧 + ∬𝐶𝐴𝐴 𝑣𝑑𝑙𝑑𝑧 + ∬𝐵𝐴𝑅 𝑣𝑑𝑙𝑑𝑧 (S-4)
where the subscripts 𝐹𝑅𝐴, 𝐶𝐴𝐴 and 𝐵𝐴𝑅 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. 𝑣 denotes the normal velocity at each section.
Meanwhile, the vertically-integrated equation for salinity S reads
𝜂
η
𝜂
𝜂
𝜂
,t
∫−𝐻 𝑑𝑧𝑆,𝑡 + 𝐻+𝜂 ∫−𝐻 𝑑𝑧𝑆 = ∫−𝐻 𝑑𝑧∇ ∙ (𝑆𝑢) − ∫−𝐻 𝑑𝑧∇𝐹 + 𝑆 + 𝑟𝑒𝑠𝑠 (S-5)
where 𝐹 is the flux from small-scale mixing ; 𝑆 is a source term and 𝑟𝑒𝑠𝑠 is a rest term.
Integrated over the Atlantic between 𝜃𝑆 and 𝜃𝑁 ,
∫𝐴𝑡𝑙 𝑆,𝑡 𝑑𝑉 + V,t 𝑆𝐴𝑡𝑙 = ∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 − ∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 + 𝑀𝐼𝑋 + 𝑆𝑂𝑈𝑅𝐶𝐸 + 𝑅𝑒𝑠𝑆 (S-6)
𝑆
𝑁
where MIX denotes the contribution by small-scale mixing and 𝑅𝑒𝑠𝑆 is the integrated rest
term. Similar to Eq. (S-4),
∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 = ∬𝐹𝑅𝐴 𝑣𝑆𝑑𝑙𝑑𝑧 + ∬𝐶𝐴𝐴 𝑣𝑆𝑑𝑙𝑑𝑧 + ∬𝐵𝐴𝑅 𝑣𝑆𝑑𝑙𝑑𝑧 (S-7)
𝑁
We choose 𝑆𝐴𝑡𝑙 = 𝑆0 = 34.7𝑝𝑠𝑢 , then this salt budget becomes an equivalent
freshwater budget in which all terms can be expressed in Sverdrups:
5
1
1
0
0
1
− 𝑆 ∫𝐴𝑡𝑙 𝑆,𝑡 𝑑𝑉 − V,t = − 𝑆 ∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 + 𝑆 ∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 +𝑀𝐼𝑋𝑆0 + 𝑆𝑂𝑈𝑅𝐶𝐸𝑆0 + 𝑅𝑒𝑠𝑆0
𝑆
0
𝑁
(S-8)
1
where 𝑆𝑂𝑈𝑅𝐶𝐸𝑆0 = − 𝑆 𝑆𝑂𝑈𝑅𝐶𝐸 = −𝐸𝑃𝑅𝐼 ∗ , 𝐸𝑃𝑅𝐼 ∗ is the equivalent water flux
0
1
through the ocean surface. 𝑀𝐼𝑋𝑆0 = − 𝑆 𝑀𝐼𝑋 and 𝑅𝑒𝑠𝑆 = 𝑆𝑐𝑙 𝑅𝑒𝑠𝑉 , where 𝑆𝑐𝑙 is the
0
weighted averaged salinity of the cross-land mixed water. Then
𝑆
𝑅𝑒𝑠𝑆0 = − 𝑆𝑐𝑙 𝑅𝑒𝑠𝑉 = (1 +
𝑆𝑐𝑙 −𝑆0
𝑆0
0
) 𝑅𝑒𝑠𝑉 = −(1 + 𝜀)𝑅𝑒𝑠𝑉 (S-9)
Since 𝜀 = 𝑂(0.01), 𝜀𝑅𝑒𝑠𝑆0 is a small term that can be added to the large mixing term
(𝑀𝑚𝑖𝑥 ) in form of
𝑀𝑚𝑖𝑥 = 𝑀𝐼𝑋𝑆0 −𝜀𝑅𝑒𝑠𝑉 (S-10)
As a result, Eq. (S-8) can be written as
−𝑀𝑡𝑟𝑒𝑛𝑑 − V,t = 𝑀𝑆 − 𝑀𝑁 + 𝑀𝑚𝑖𝑥 − 𝑅𝑒𝑠𝑉 − 𝐸𝑃𝑅𝐼 ∗
(S-11)
where 𝑀𝑡𝑟𝑒𝑛𝑑 , 𝑀𝑆 and 𝑀𝑁 are the trend term of freshwater transport and the total
freshwater transports at boundaries of 𝜃𝑆 and 𝜃𝑁 , respectively in form of
1
𝑀𝑡𝑟𝑒𝑛𝑑 = 𝑆 ∫𝐴𝑡𝑙 𝑆,𝑡 𝑑𝑉
0
(S-12)
1
𝑀𝑆 = − 𝑆 ∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 (S-13)
0
𝑆
1
𝑀𝑁 = − 𝑆 ∬𝜃 𝑣𝑆𝑑𝑥𝑑𝑧 (S-14)
0
𝑁
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, 𝐸𝑃𝑅𝐼 ∗ = 0 in Eq. (S-11) but 𝐸𝑃𝑅𝐼 is kept in Eq. (S-3), so Eq. (S-11) degenerates
as
−𝑀𝑡𝑟𝑒𝑛𝑑 − V,t = 𝑀𝑆 − 𝑀𝑁 + 𝑀𝑚𝑖𝑥 − 𝑅𝑒𝑠𝑉 (S-15)
By combining Eq. (S-3) with Eq. (S-15), we obtain
𝐸𝑃𝑅𝐼 = 𝑀𝑆 − 𝑀𝑁 + 𝑇𝑆 − 𝑇𝑁 + 𝑀𝑚𝑖𝑥 + 𝑀𝑡𝑟𝑒𝑛𝑑 (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, 𝐸𝑃𝑅𝐼 = 𝑉,𝑡 = 𝑅𝑒𝑠𝑉 = 0 in Eq. (S-3) but 𝐸𝑃𝑅𝐼 ∗ is kept in
Eq. (S-11). So Eq. (S-3) degenerates as
𝑇𝑆 − 𝑇𝑁 = 0
(S-17)
By combining Eq. (S-11) with Eq. (S-17), we obtain
𝐸𝑃𝑅𝐼 ∗ = 𝑀𝑆 − 𝑀𝑁 + 𝑀𝐼𝑋+𝑀𝑡𝑟𝑒𝑛𝑑
(S-18)
Furthermore, the meridional velocity and salinity in 𝑀𝑆 and 𝑀𝑁 can be written as 𝑣 =
⟨𝑣⟩ + 𝑣′ and 𝑠 = ⟨𝑠⟩ + 𝑠′, where ⟨𝑣⟩ and ⟨𝑠⟩ denote mean velocity and salinity along the
section of boundaries of 𝜃𝑆 and 𝜃𝑁 , 𝑣′ and 𝑠′ 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 𝑀𝑡𝑟𝑒𝑛𝑑 ≈ 0. By keeping the original symbols for the time mean
variables, and using the overbars for temporal average, we obtain
∗
∗
𝐸𝑅𝑃𝐼 = 𝑀𝑜𝑣𝑆
− 𝑀𝑜𝑣𝑁
+ 𝑀𝑎𝑧𝑆 − 𝑀𝑎𝑧𝑁 + 𝑇𝑆 − 𝑇𝑁 + 𝑀𝑚𝑖𝑥 (S-19)
where
1
∗
𝑀𝑜𝑣𝑆
= − 𝑆 ∬𝜃 ⟨𝑣̅ ⟩⟨𝑠̅⟩𝑑𝑥𝑑𝑧 (S-20)
0
𝑆
7
1
∗
𝑀𝑜𝑣𝑁
= − 𝑆 ∬𝜃 ⟨𝑣̅ ⟩⟨𝑠̅⟩𝑑𝑥𝑑𝑧 (S-21)
0
𝑁
1
𝑀𝑎𝑧𝑆 = − 𝑆 ∬𝜃 ̅̅̅̅̅
𝑣 ′ 𝑠′𝑑𝑥𝑑𝑧
(S-22)
1
𝑀𝑎𝑧𝑁 = − 𝑆 ∬𝜃 ̅̅̅̅̅
𝑣 ′ 𝑠′𝑑𝑥𝑑𝑧
(S-23)
0
0
𝑆
𝑁
In particular, the transports 𝑀𝑜𝑣𝑁 and 𝑀𝑎𝑧𝑁 can be written as
∗
∗
∗
∗
𝑀𝑜𝑣𝑁
= 𝑀𝑜𝑣𝐹𝑅𝐴
+ 𝑀𝑜𝑣𝐶𝐴𝐴
+ 𝑀𝑜𝑣𝐵𝐴𝑅
(S-24)
𝑀𝑎𝑧𝑁 = 𝑀𝑎𝑧𝐹𝑅𝐴 + 𝑀𝑎𝑧𝐶𝐴𝐴 + 𝑀𝑎𝑧𝐵𝐴𝑅 (S-25)
∗
∗
∗
(𝑀𝑎𝑧𝐹𝑅𝐴 ) , 𝑀𝑜𝑣𝐶𝐴𝐴
(𝑀𝑎𝑧𝐶𝐴𝐴 ) and 𝑀𝑜𝑣𝐵𝐴𝑅
(𝑀𝑎𝑧𝐵𝐴𝑅 ) are the overturning
where 𝑀𝑜𝑣𝐹𝑅𝐴
∗
(azimuthal) components of 𝑀𝑜𝑣𝑁
(𝑀𝑎𝑧𝑁 ) along the Fram Strait, the CAA and the western
shelf of the Barents Sea, respectively. These transports can be written as
1
∗
𝑀𝑜𝑣𝐹𝑅𝐴
= − 𝑆 ∬𝐹𝑅𝐴⟨𝑣̅ ⟩⟨𝑠̅ ⟩𝑑𝑙𝑑𝑧
0
1
∗
𝑀𝑜𝑣𝐶𝐴𝐴
= − 𝑆 ∬𝐶𝐴𝐴⟨𝑣̅ ⟩⟨𝑠̅⟩𝑑𝑙𝑑𝑧
0
1
∗
𝑀𝑜𝑣𝐵𝐴𝑅
= − 𝑆 ∬𝐵𝐴𝑅⟨𝑣̅ ⟩⟨𝑠̅⟩𝑑𝑙𝑑𝑧
0
1
𝑀𝑎𝑧𝐹𝑅𝐴 = − 𝑆 ∬𝐹𝑅𝐴 ̅̅̅̅̅
𝑣 ′ 𝑠′𝑑𝑙𝑑𝑧
0
1
𝑀𝑎𝑧𝐶𝐴𝐴 = − 𝑆 ∬𝐶𝐴𝐴 ̅̅̅̅̅
𝑣 ′ 𝑠′𝑑𝑙𝑑𝑧
0
1
𝑀𝑎𝑧𝐵𝐴𝑅 = − 𝑆 ∬𝐵𝐴𝑅 ̅̅̅̅̅
𝑣 ′ 𝑠′𝑑𝑙𝑑𝑧
0
(S-26)
(S-27)
(S-28)
(S-29)
(S-30)
(S-31)
∗
∗
∗
Here, we define ∆𝑀𝑜𝑣
= 𝑀𝑜𝑣𝑆
− 𝑀𝑜𝑣𝑁
as the AMOC induced freshwater transport and
∆𝑇𝑏𝑎𝑡𝑝 = 𝑇𝑆 − 𝑇𝑁 as the net barotropic transport across the Atlantic basin. So Eq. (S-19)
becomes
∗
𝐸𝑃𝑅𝐼 = ∆𝑀𝑜𝑣
+ 𝑀𝑎𝑧𝑆 − 𝑀𝑎𝑧𝑁 + ∆𝑇𝑏𝑎𝑡𝑝 + 𝑀𝑚𝑖𝑥
8
(S-32)
Finally, we make 𝑅𝑒𝑠 = 𝑀𝑚𝑖𝑥 , rewrite 𝐸𝑃𝑅𝐼 as [𝐸𝑛𝑒𝑡 ] where [.] denote a basin-wide
averaging and obtain
∗
[𝐸𝑛𝑒𝑡 ] = ∆𝑀𝑜𝑣
+ 𝑀𝑎𝑧𝑆 − 𝑀𝑎𝑧𝑁 + ∆𝑇𝑏𝑎𝑡𝑝 + 𝑅𝑒𝑠 (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
𝐸𝑃𝑅𝐼 ∗ = 𝑀𝑆 − 𝑀𝑁 + 𝑀𝐼𝑋
(S-34)
Since 𝑇𝑆 − 𝑇𝑁 = 0, we re-write Eq. (S-34) as
𝐸𝑃𝑅𝐼 ∗ = 𝑀𝑜𝑣𝑆 − 𝑀𝑜𝑣𝑁 + 𝑀𝑎𝑧𝑆 − 𝑀𝑎𝑧𝑁 + 𝑀𝐼𝑋
(S-35)
where 𝑀𝑜𝑣𝑆 and 𝑀𝑎𝑧𝑆 are the overturning and azimuthal freshwater transport at
boundaries of 𝜃𝑆 (𝜃𝑁 ) of the Atlantic basin, respectively in form of
1
𝑀𝑜𝑣𝑆 = − 𝑆 ∬𝜃 ⟨𝑣̅ ⟩(⟨𝑠̅⟩ − 𝑆0 )𝑑𝑥𝑑𝑧
𝑆
0
1
𝑀𝑜𝑣𝑁 = − 𝑆 ∬𝜃 ⟨𝑣̅ ⟩(⟨𝑠̅ ⟩ − 𝑆0 )𝑑𝑥𝑑𝑧
𝑁
0
(S-36)
(S-37)
In particular, the transports 𝑀𝑜𝑣𝑁 can be written as
𝑀𝑜𝑣𝑁 = 𝑀𝑜𝑣𝐹𝑅𝐴 + 𝑀𝑜𝑣𝐶𝐴𝐴 + 𝑀𝑜𝑣𝐵𝐴𝑅 (S-38)
where 𝑀𝑜𝑣𝐹𝑅𝐴 , 𝑀𝑜𝑣𝐶𝐴𝐴 and 𝑀𝑜𝑣𝐵𝐴𝑅 are the overturning components of 𝑀𝑜𝑣𝑁 along the
Fram Strait, the CAA and the western shelf of the Barents Sea, respectively. In particular,
they can be written as
𝑀𝑜𝑣𝐹𝑅𝐴 = −
1
𝑆0
∬𝐹𝑅𝐴⟨𝑣̅ ⟩(⟨𝑠̅⟩ − 𝑆0 )𝑑𝑙𝑑𝑧 (S-39)
1
𝑀𝑜𝑣𝐶𝐴𝐴 = − 𝑆 ∬𝐶𝐴𝐴⟨𝑣̅ ⟩(⟨𝑠̅⟩ − 𝑆0 )𝑑𝑙𝑑𝑧 (S-40)
0
1
𝑀𝑜𝑣𝐵𝐴𝑅 = − 𝑆 ∬𝐵𝐴𝑅⟨𝑣̅ ⟩(⟨𝑠̅⟩ − 𝑆0 )𝑑𝑙𝑑𝑧 (S-41)
0
9
Finally, we make 𝑅𝑒𝑠 = 𝑀𝐼𝑋, rewrite 𝐸𝑃𝑅𝐼 ∗ as [𝐸𝑛𝑒𝑡 ] where [.] denote a basin-wide
averaging and obtain
[𝐸𝑛𝑒𝑡 ] = ∆𝑀𝑜𝑣 + 𝑀𝑎𝑧𝑆 − 𝑀𝑎𝑧𝑁 + 𝑅𝑒𝑠 (S-42)
where ∆𝑀𝑜𝑣 = 𝑀𝑜𝑣𝑆 − 𝑀𝑜𝑣𝑁 , denoting the net meridional freshwater transport across the
∗
Atlantic basin. It is worth noting here, since 𝑇𝑆 = 𝑇𝑁 , ∆𝑀𝑜𝑣 = ∆𝑀𝑜𝑣
in the VFS models,
∗
̅
̅̅̅̅̅̅̅
̅̅̅̅̅̅̅ ̅
𝐿 = 𝜕∆𝑀
𝑜𝑣 ⁄𝜕𝜓 = 𝜕∆𝑀𝑜𝑣 ⁄𝜕𝜓 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 𝜓̅ and ̅̅̅̅̅̅̅
∆𝑀𝑜𝑣 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, 𝜓̅ and ̅̅̅̅̅̅̅
∆𝑀𝑜𝑣 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