In the format provided by the authors and unedited.
Contribution of topographically-generated submesoscale
1
turbulence to Southern Ocean overturning
2
Xiaozhou Ruan
1
, Andrew F. Thompson
1
, Mar M. Flexas
1
& Janet Sprintall
2
3
1
Environmental Science & Engineering, California Institute of Technology
4
2
Scripps Institution of Oceanography, University of California, San Diego
5
Supplementary material
6
1. Estimates for water mass transformation rates:
7
The water mass transformation rate can be expressed, following Marshall et al. (1999), using a
8
diapycnal velocity
̃
e
, as
9
T
=
−
∫∫
A
̃
e
·
n
b
dA
=
∫∫
A
∇·
F
b
|∇
b
|
dA.
(1)
Here
b
=
−
g
(
ρ
−
ρ
0
)
/ρ
0
is the buoyancy and
ρ
0
is a reference density,
A
is the area of a buoy-
10
ancy surface across which the diapycnal transport is measured,
n
b
is the unit vector normal to the
11
isopycnal and
F
b
is the turbulent buoyancy flux. It has been argued that the vertical buoyancy flux
12
scales with the dissipation rate as
Γ
, where
Γ
is the mixing efficiency (Osborn 1980). Thus, the
13
buoyancy flux divergence can be estimated as
Γ
/h
where
h
is the thickness of the bottom mixed
14
layer (BML); this assumes that the buoyancy flux vanishes at the solid bottom. Using a mixing
15
efficiency
Γ=0
.
2
, a typical bottom mixed layer thickness
h
=100
m and a local vertical stratifi-
16
cation
N
2
=
∂b
∂z
=10
−
6
s
−
2
, the diapycnal velocity can be estimated as
2
×
10
−
4
ms
−
1
, or
∼
20 m
17
day
−
1
. Considering a 5 km-wide boundary current (associated with the southern boundary of the
18
1
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1
ACC) that flows along the continental slope for a distance of 500 km in southern Drake Passage
19
(Fig. S4; Orsi
et al
. 1995),
A
is
2
.
5
×
10
9
m
2
. Using equation (5), this yields a local water mass
20
transformation rate of 0.5 Sv. We acknowledge that the mixing efficiency,
Γ
, is uncertain in this
21
area, nevertheless, this likely remains an underestimate since only the shear-induced mechanism is
22
accounted for here.
23
The use of the vertical buoyancy gradient
N
2
assumes that the diapycnal mixing and asso-
24
ciated water mass modification is a local, one-dimensional (vertical) process, which relies on the
25
rapid export of modified water into the interior. McDougall and Ferrari (2017) hypothesize that
26
water masses may be modified and upwell in boundary layers over sloping topography. In this
27
case,
N
2
should be replaced by the lateral buoyancy gradient across the continental slope. Esti-
28
mating this value across multiple glider sections gives a value of roughly
5
×
10
−
8
s
−
2
(Fig. 1c).
29
This smaller buoyancy gradient suggests a local diapycnal velocity 20 times larger than the pre-
30
vious estimate using the vertical buoyancy gradient. We note that the lateral buoyancy gradient is
31
a more challenging quantity to estimate, especially if the incropping of density surfaces is hetero-
32
geneous along the slope (see, for instance, Fig. 4 in Thompson and Heywood, 2008). Now we
33
estimate the area of relevant buoyancy surfaces
A
within the BML using the BML thickness of 100
34
m and a longitudinal distance of 500 km along Southern Drake Passage which yields
A
= 5
×
10
7
35
m
2
. The water mass transformation rate can be thus estimated to be 0.2 Sv. It is important to
36
note that, according to the hypothesis, the excessive (upwelling) diapycnal volume flux along the
37
bottom boundary layers has to be largely compensated by diapycnal downwelling in the stratified
38
mixed layers globally. While the estimates above are associated with some uncertainty, they are
39
2
sufficiently large to warrant further investigation.
40
2. Extrapolation to the circumpolar Southern Ocean using numerical model output:
41
In order to estimate the circumpolar relevance of the proposed mechanism, we turn to output from
42
a high-resolution global numerical model to examine the interactions between ACC fronts and
43
major topographic features in the Southern Ocean.
44
LLC4320 is a global ocean and sea ice simulation that represents full-depth ocean processes.
45
The simulation is based on a Latitude/Longitude/polar-Cap (LLC) configuration of the MIT gen-
46
eral circulation model (MITgcm; Marshall
et al
. 1997; Hill
et al
. 2007). The LLC grid has 13
47
square tiles with 4320 grid points on each side (hereafter called LLC4320) and 90 vertical levels
48
for a total grid count of 2:21010. Horizontal grid spacing ranges from 0.75 km near Antarctica
49
to 2.2 km at the Equator and vertical levels have 1-m thickness near the surface to better resolve
50
the diurnal cycle. The simulation is initialized from a data-constrained global ocean and sea ice
51
solution provided by the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2)
52
project (Menemenlis
et al
. 2005, 2008; Losch
et al
. 2010), and includes atmospheric pressure and
53
tidal forcing (Menemenlis
et al
. 2014). The inclusion of tides allows for successful reproduction of
54
shelf-slope dynamics and water mass modification (Flexas
et al
. 2015). Surface boundary condi-
55
tions are from the European Center for Medium-Range Weather Forecasts (ECMWF) atmospheric
56
operational model analysis, starting in 2011. The sections shown in Figure S4 correspond to a
57
snapshot of LLC4320 on 29/11/2011.
58
Assuming that there are strong interactions between deep-reaching ACC currents and sloping
59
3
bottom topography near the Kerguelen Plateau, Campbell Plateau, Drake Passage and ridges and
60
fracture zones in the South Pacific and Atlantic, as seen in Figure S4, then a conservative estimate
61
for
A
in equation (5) would be
2
.
5
×
10
10
m
2
(an average of 5km-wide narrow front is assumed).
62
This area estimation would yield a global transformation of LCDW of 5 Sv for the local vertical
63
process. For the along-bottom diapycnal upwelling framework, we estimate the area
A
to be
64
5
×
10
8
m
2
which yields a transformation rate of 2 Sv (with the possible compensating downwelling
65
neglected).
66
4
I6
I8
P14
P18
67
Figure S1
: Salinity distributions from WOCE transects (summer measurements) I6, I8, P14
68
and P18 (Orsi and Whitworth 2005). The purple colors highlight that Lower Circumpolar
69
Deep Water (characterized by a salinity maximum) incrops on the Antarctic continental slope
70
and deeper topographic features broadly around Antarctica. Neutral density surfaces are
71
indicated as black contours.
72
5
73
74
Figure S2
: Statistics of bottom mixed layer (BML) thickness (m) based on a
∆
0.02 kg m
−
3
75
threshold (blue) and a
∆
0.005 kg m
−
3
threshold (yellow).
76
6
(
C
)
(
C
)
(
C
)
(
C
)
77
Figure S3
: Two transect examples of CDW being close to (left panels; Transect 5) and away
78
from (right panels; Transect 8) the slope. (Upper panels) Potential temperature sections.
79
Isothermals are labeled every 0.5
◦
C. The 2
◦
C contour roughly defines the location of the
80
7
Bdy. The 0
◦
C isotherm (in bold black) marks the front separating warm CDW from cold
81
shelf water. (Middle panels)
Θ
/S diagram of glider data colored by depth (in meters). (Lower
82
panels) Positive Ertel PV (in magenta) over all data sampled for each given transect (in gray).
83
8
a
b
c
d
a
b
c
d
84
Figure S4
: Zonal velocity snapshots across topographic features in the Southern Ocean
85
from a high-resolution numerical model (See model introduction in Supplementary Mate-
86
rial). Transects a, b, c and d correspond to Northern and Southern Kerguelen Plateau, Camp-
87
bell Plateau (including the Macquarie Ridge) and Drake Passage. White contours in the
88
upper panel are the climatological frontal positions in the Southern Ocean (Orsi
et al
. 1995)
89
and black straight lines correspond to the transects from which zonal velocity snapshots
90
are shown below. Black contours in the lower four panels are zonal velocities (eastward,
91
positive, solid lines). Contour levels are from 0.1m/s to 0.5m/s with a 0.1m/s interval. Deep-
92
reaching fast boundary currents (some with bottom velocity intensification) interacting with
93
sloping topography can be seen widely in the Southern Ocean across the chosen major topo-
94
graphic features.
95
9
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11