of 11
Submesoscale
Eddy
Contribution
to
Ocean
Vertical
Heat
Flux
Diagnosed
From
Airborne
Observations
Hector
S.
Torres
1
,
Alexander
Wineteer
1
,
Ernesto
Rodriguez
1
,
Patrice
Klein
1,2,3
,
Andrew
F.
Thompson
2
,
Dragana
Perkovic‐Martin
1
,
Jeroen
Molemaker
4
,
Delphine
Hypolite
4
,
Jöern
Callies
2
,
J.
Thomas
Farrar
5
,
Eric
D’Asaro
6
,
and
Mara
A.
Freilich
7
1
Jet
Propulsion
Laboratory,
California
Institute
of
Technology,
Pasadena,
CA,
USA,
2
Environmental
Science
and
Engineering,
California
Institute
of
Technology,
Pasadena,
CA,
USA,
3
LMD‐IPSL,
ENS,
PSL
Université,
Ecole
Polytechnique,
Sorbonne
Université,
CNRS,
Paris,
France,
4
Atmospheric
and
Oceanic
Sciences,
University
of
California
Los
Angeles,
Los
Angeles,
CA,
USA,
5
Woods
Hole
Oceanographic
Institution,
Woods
Hole,
MA,
USA,
6
Applied
Physics
Laboratory,
University
of
Washington,
Seattle,
WA,
USA,
7
Department
of
Earth,
Environmental
and
Planetary
Sciences
and
Division
of
Applied
Mathematics,
University
of
Brown,
Providence,
RI,
USA
Abstract
Submesoscale
eddies
(those
smaller
than
50
km)
are
ubiquitous
throughout
the
ocean,
as
revealed
by
satellite
infrared
images.
Diagnosing
their
impact
on
ocean
energetics
from
observations
remains
a
challenge.
This
study
analyzes
a
turbulent
field
of
submesoscale
eddies
using
airborne
observations
of
surface
currents
and
sea
surface
temperature,
with
high
spatial
resolution,
collected
during
the
S‐MODE
experiment
in
October
2022.
Assuming
surface
current
divergence
and
temperature
are
homogeneous
down
to
30
m
depth,
we
show
that
more
than
80%
of
the
upward
vertical
heat
fluxes,
reaching
227
W
m
2
,
is
explained
by
the
smallest
resolved
eddies,
with
a
size
smaller
than
15
km.
This
result
emphasizes
the
contribution
of
small‐scale
eddies,
poorly
represented
in
numerical
models,
to
the
ocean
heat
budget
and,
therefore,
to
the
climate
system.
Plain
Language
Summary
Vertical
heat
transport
is
a
key
mechanism
that
regulates
ocean
heat
storage
and,
therefore,
the
Earth's
climate.
Using
airborne
observations
with
very
high
spatial
resolution,
the
present
study
shows
that
the
upward
vertical
heat
fluxes
explained
by
ocean
submesoscales
smaller
than
15
km
are
greater
than
those
due
to
larger
eddies.
This
highlights
the
contribution
of
small
oceanic
scales,
poorly
resolved
in
previous
studies,
to
the
Earth's
climate
system.
1.
Introduction
Ocean
submesoscale
eddies
(with
a
size
smaller
than
50
km)
were
observed
from
sun
glitter
during
the
Space
Shuttle
mission
in
1968
(Figure
1a
)
and,
later
on,
in
infra‐red
and
ocean
color
satellite
images.
Over
the
past
15
years,
numerical
models
have
shown
that
submesoscale
eddies
may
arise
through
baroclinic
instability
linked
to
temperature
(density)
fronts.
The
tendency
for
these
submesoscale
eddies
to
restratify
the
surface
ocean
is
directly
linked
to
an
upward
(positive)
vertical
heat
flux.
The
link
between
submesoscale
restratification
and
vertical
heat
flux
was
first
identified
by
Fox‐Kemper
et
al.
(
2008
)
and
subsequently
corroborated
by
numerous
studies
(McWilliams,
2016
;
Siegelman,
2020
;
Siegelman
et
al.,
2020
;
Su
et
al.,
2018
,
2020
;
Taylor
&
Thomp-
son,
2023
;
Yu
et
al.,
2019
),
particularly
in
the
California
Current
System
(Torres
et
al.,
2022
).
However,
at
the
scale
of
an
individual
submesoscale
eddy,
the
sign
of
these
heat
fluxes
exhibits
significant
spatial
variability
(Taylor
&
Thompson,
2023
;
Torres
et
al.,
2022
).
From
all
these
studies,
submesoscale
eddies
may
explain
most
of
the
upward
vertical
heat
fluxes
in
the
upper
ocean,
highlighting
their
impact
on
the
climate
system.
These
results
were
one
of
the
primary
motivations
for
the
S‐MODE
experiment
(“Sub‐Mesoscale
Ocean
Dynamics
Experiment”)
carried
out
in
the
California
Current
System
(CCS)
(Farrar
et
al.,
2024
)
(Figure
1b
).
During
S‐MODE,
airborne
observations
of
surface
currents
and
sea
surface
temperature
(SST)
were
collected
concurrently
from
the
Doppler
Scatterometer
(DopplerScatt)
and
Long‐Wave
Infrared
camera
(MOSES),
respectively,
onboard
the
same
plane.
The
spatial
resolution
of
both
the
surface
currents
and
SST
(
250
m)
is
such
that
vertical
heat
fluxes
(VHF)
can
be
diagnosed
as
the
correlation
between
SST
and
divergence
of
surface
currents
down
to
scales
of
1
km,
assuming
temperature
and
divergence
are
homogeneous
down
to
a
given
depth.
The
present
study
analyzes
the
airborne
observations
collected
by
four
research
flights
over
three
days
in
October
2022.
The
domain
observed
by
the
airborne
experiment
(50
×
100
km)
covered
a
large
horizontal
scale
range
in
RESEARCH
LETTER
10.1029/2024GL112278
Key
Points:
Airborne
observations
reveal
the
contribution
of
coherent
submesoscale
eddies
to
ocean
turbulence
Phase
relationship
between
SST
and
divergence
at
submesoscale
leads
to
upward
vertical
heat
fluxes
A
large
part
of
the
upward
vertical
heat
fluxes
is
principally
explained
by
eddies
with
a
size
smaller
than
15
km
Supporting
Information:
Supporting
Information
may
be
found
in
the
online
version
of
this
article.
Correspondence
to:
H.
S.
Torres,
Hector.Torres.Gutierrez@jpl.nasa.gov
Citation:
Torres,
H.
S.,
Wineteer,
A.,
Rodriguez,
E.,
Klein,
P.,
Thompson,
A.
F.,
Perkovic‐
Martin,
D.,
et
al.
(2025).
Submesoscale
eddy
contribution
to
ocean
vertical
heat
flux
diagnosed
from
airborne
observations.
Geophysical
Research
Letters
,
52
,
e2024GL112278.
https://doi.org/10.1029/
2024GL112278
Received
4
SEP
2024
Accepted
19
DEC
2024
Author
Contributions:
Conceptualization:
Hector
S.
Torres,
Patrice
Klein
Data
curation:
Hector
S.
Torres
Formal
analysis:
Hector
S.
Torres
Investigation:
Hector
S.
Torres,
Alexander
Wineteer,
Ernesto
Rodriguez,
Patrice
Klein,
Andrew
F.
Thompson,
Dragana
Perkovic‐Martin,
Jeroen
Molemaker,
Delphine
Hypolite,
Jöern
Callies,
J.
Thomas
Farrar,
Eric
D’Asaro,
Mara
A.
Freilich
Methodology:
Hector
S.
Torres
Software:
Hector
S.
Torres
Validation:
Hector
S.
Torres,
Alexander
Wineteer,
Ernesto
Rodriguez,
Jeroen
Molemaker,
Delphine
Hypolite
Visualization:
Hector
S.
Torres
©
2025.
The
Author(s).
This
is
an
open
access
article
under
the
terms
of
the
Creative
Commons
Attribution‐NonCommercial‐NoDerivs
License,
which
permits
use
and
distribution
in
any
medium,
provided
the
original
work
is
properly
cited,
the
use
is
non‐commercial
and
no
modifications
or
adaptations
are
made.
TORRES
ET
AL.
1
of
11
the
surface
ocean,
from
1
to
50
km.
The
present
study
tests
the
hypothesis
that
VHF
are
mostly
explained
by
scales
smaller
than
15
km.
2.
Data
and
Methods
2.1.
Airborne
Remote
Sensing:
The
DopplerScatt
and
MOSES
Instruments
DopplerScatt
is
a
Ka‐band
Doppler
Scatterometer
operating
from
a
plane.
The
instrument
provides
vector
surface
currents
at
a
200
m
spatial
resolution
posting
across
a
25
km
swath
and
with
random
noise
of
0.04
m
s
1
(Rodri-
guez,
2018
;
Rodríguez
et
al.,
2020
;
Wineteer
et
al.,
2020
).
Torres
et
al.
(
2024
)
reported
an
error
in
the
velocity
gradients
(vorticity
and
divergence)
of
0.2
f
o
when
a
Gaussian
smoother
with
spatial
averaging
scale
of
1
km
is
used.
The
Multi‐Scale
Observation
System
of
the
Ocean
Surface
(MOSES)
flew
onboard
the
same
plane
as
Dop-
plerScatt.
It
operates
in
the
Long
Wave
Infrared
(LWIR)
spectrum
(9
12
.
5
μ
m)
and
features
a
camera,
capturing
images
at
640
×
512
pixels
which
translates
into
a
10
m
resolution
along
a
wide‐swath
of
5.4
km
at
28,000
ft
of
altitude.
The
accuracy
of
the
measurements
is
0.1
K.
The
MOSES
camera
was
angled
10
degrees
off‐
nadir
to
align
with
the
DopplerScatt
system.
Systematic
cross‐track
instrumental
biases
were
detected
and
Writing
original
draft:
Hector
S.
Torres,
Alexander
Wineteer,
Patrice
Klein
Writing
review
&
editing:
Hector
S.
Torres,
Alexander
Wineteer,
Ernesto
Rodriguez,
Patrice
Klein,
Andrew
F.
Thompson,
Dragana
Perkovic‐Martin,
Jeroen
Molemaker,
Delphine
Hypolite,
Jöern
Callies,
J.
Thomas
Farrar,
Eric
D’Asaro,
Mara
A.
Freilich
Figure
1.
A
multiscale
view
of
the
ocean.
(a)
Photograph
taken
off
the
northeastern
seaboard
of
the
United
States
in
October
1984
during
the
Space
Shuttle
mission
STS‐41G
(Munk
et
al.,
2000
).
(b)
Sea
surface
temperature
(color)
from
VIIRS
at
04:00
UTC
and
contours
of
SSHA
from
AVISO
(white
contours
every
3
cm)
on
26
October
2022.
The
red
polygon
in
panel
(b)
marks
the
S‐MODE
study
domain.
The
black
rectangle
in
panel
(b)
identifies
the
area
explored
by
DopplerScatt
and
MOSES.
Panel
(c)
displays
the
area,
100
×
50‐km,
covered
by
the
“King
Air
B200”
on
October
26
16:04
UTC,
highlighting
the
synergy
between
MOSES
(SST
in
color)
and
the
DopplerScatt
(high‐pass,
<
15
km,
surface
currents
as
contours).
Geophysical
Research
Letters
10.1029/2024GL112278
TORRES
ET
AL.
2
of
11
19448007, 2025, 2, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2024GL112278, Wiley Online Library on [21/01/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
removed
from
MOSES
data
by
binning
measured
SST
as
a
function
of
swath
position
over
multiple
flight
lines.
The
resulting
mean
multi‐flight
systematic
cross‐track
error
was
then
subtracted.
The
mean
SST
for
each
flight
was
calibrated
to
match
measurements
from
satellite
SST
data
from
VIIRS
over
the
same
region.
2.2.
In
Situ
Observations
Valuable
in‐situ
validations
of
the
airborne
data
were
carried
out
by
using
observations
made
by
the
MV
Bold
Horizon
in
the
2022.
The
ship‐based
sampling
contributes
to
validate
the
ocean
features
observed
by
remote
sensing.
Here,
we
report
the
observations
made
by
Eco‐CTD
during
October
26.
Additionally,
airborne‐based
vertical
velocity
estimations
were
validated
using
Lagrangian
floats
(D’Asaro,
2003
),
in
water‐following
mode,
deployed
in
October
26.
Particularly,
we
report
the
in‐situ
observations
along
a
prominent
frontal
feature
captured
by
airborne
observations.
2.3.
The
S‐MODE
Experiment
The
DopplerScatt
and
MOSES
instruments
were
utilized
during
the
S‐MODE
experiment
(a
NASA
Earth
Ventures
Suborbital‐3
experiment)
along
with
a
large
contingent
of
in‐situ
platforms.
The
multi‐scale
observa-
tional
platforms
aim
to
test
the
hypothesis
that
submesoscale
eddies
make
important
contributions
to
the
vertical
exchange
of
climate‐
and
biological‐relevant
properties
in
the
upper
ocean
(Farrar
et
al.,
2020
,
2024
).
A
concomitant
goal
in
testing
the
hypothesis
is
to
examine
the
relationship
between
surface
velocity
and
temper-
ature.
The
S‐MODE
experiment
consisted
of
three
campaigns
all
conducted
approximately
100
km
west
of
San
Francisco
during
2021–2023
fall
and
spring.
The
present
study
utilized
the
subset
of
data
corresponding
to
October
2022
(Figures
1b
and
1c
).
The
research
flight
conducted
by
the
King
Air
B200
plane,
with
DopplerScatt
and
MOSES
onboard,
covered
an
area
of
50
×
100
km
in
approximately
four
hours,
allowing
a
quasi‐synoptic
view
of
submesoscale
turbulence
(Torres
et
al.,
2024
).
One
research
flight
per
day
was
carried
out
on
October
23
and
October
24
(both
flights
starting
at
16:04
UTC),
and
two
flights
on
October
26,
starting
respectively
at
16:04
UTC
and
21:44
UTC.
DopplerScatt
and
MOSES
repeatedly
collected
data
over
multiple
parallel
lines
125
km
in
length,
separated
by
4
km,
to
image
an
area
roughly
50
×
100
km
in
4
hr
(Torres
et
al.,
2024
).
As
noted
by
Rodriguez
(
2018
)
and
Torres
et
al.
(
2024
),
this
overlapped
sampling
enabled
the
reduction
of
measurement
noise
and
improved
the
estimates
of
vorticity
and
divergence.
Because
of
the
different
spatial
resolution
of
MOSES
and
DopplerScatt
instruments,
10
m
and
200
m,
respectively,
MOSES
SST
was
binned
to
the
DopplerScatt
grid
to
have
data
collocated
in
space
and
time
(see
in
Supporting
Information
S1
for
details)
(Figure
1c
).
Two
mesoscale
eddies
were
observed
by
satellite
altimetry
in
October
2022
and
were
associated
with
an
unstable
front
in
between,
observed
by
satellite
infrared
images
(Figure
1b
)
(see
in
Supporting
Information
S1
).
The
contribution
of
the
mesoscale
eddy
field
has
been
removed
by
from
the
DopplerScatt
observations
and
SST
by
linearly
detrending
the
data,
as
described
in
Supporting
Information
S1
.
2.4.
Methods
The
DopplerScatt
high‐pass
surface
currents
were
decomposed
into
a
rotational
component
v
ψ
and
a
divergent
component
v
χ
such
that:
v
=
v
ψ
+
v
χ
,
where
v
ψ
=
ˆ
k
×
h
ψ
with
ψ
the
streamfunction,
and
v
χ
=
h
χ
with
χ
the
velocity
potential.
h
is
the
horizontal
gradient
operator.
The
rotational
component
identifies
eddies
through
the
streamfunction
(or
streamisolines).
Taking
the
vertical
component
of
the
curl
of
v
=
v
ψ
+
v
χ
,
we
get
2
h
ψ
=
ζ
,
where
ζ
=
v
x
u
y
is
the
relative
vorticity.
Similarly,
taking
the
divergence
of
v
=
v
ψ
+
v
χ
,
we
get
2
h
χ
=
δ
,
where
δ
=
u
x
+
v
y
is
the
horizontal
velocity
divergence.
We
have
used
the
methodology
developed
by
Li
et
al.
(
2006
)
to
solve
the
Helmholtz
decomposition,
in
particular
to
diagnose
the
streamfunction,
with
double
periodic
boundary
conditions
through
double
mirroring
the
domain.
Observations
of
surface
currents
and
SST
at
the
submesoscale
motivated
our
study
to
assess
their
impact
on
the
vertical
heat
fluxes
in
the
ocean
interior
averaged
over
the
four
flights
and
the
whole
domain
covered
by
the
airborne
experiment.
These
fluxes
(VHF)
at
a
given
depth
are
given
by
V
H
F
=
ρ
o
C
p
W
θ
,
(
1
)
Geophysical
Research
Letters
10.1029/2024GL112278
TORRES
ET
AL.
3
of
11
19448007, 2025, 2, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2024GL112278, Wiley Online Library on [21/01/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License