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Climate change impacts on nesting and internesting leatherback sea turtles using 3D animated computational fluid dynamics and finite volume heat transfer

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Abstract and Figures

Shifting suitable range limits under global warming will threaten many species. Modeling and mapping these potential range shifts is important for conservation. As global warming will introduce new sets of abiotic conditions, predictive empirical niche models may not perform well and the best method to model a specie's projected range shifts may be to model their fundamental niche with a biophysical mechanistic niche model. However, this class of model requires many physiological parameters that are difficult to measure for species not easily kept in captivity. It is also difficult to estimate these parameters for marine species given the interactions among their in-water motion, metabolism, and heat transfer. To surmount these difficulties, we use our previously verified novel technique combining 3D digital design, computational fluid dynamics, and finite volume heat transfer modeling to find animal core temperatures. We then use this method to build a fundamental niche map for internesting and nesting leatherback sea turtles (. Dermochelys coriacea). With these niche maps we analyze three main nesting areas. We show that global warming poses a large overheating risk to leatherbacks in Southeast Asia, a slight risk to leatherbacks in the West Atlantic and a low risk to leatherbacks in the East Atlantic. We also show that the impact may be less on leatherbacks that shift their nesting location or who are smaller. Methods such these are important to produce efficiently and economically accurate maps of regions that will become inhospitable to species under global warming conditions.
Content may be subject to copyright.
Ecological
Modelling
320
(2016)
231–240
Contents
lists
available
at
ScienceDirect
Ecological
Modelling
journa
l
h
om
epa
ge:
www.elsevier.com/locate/ecolmodel
Climate
change
impacts
on
nesting
and
internesting
leatherback
sea
turtles
using
3D
animated
computational
fluid
dynamics
and
finite
volume
heat
transfer
Peter
N.
Dudleya,,1,
Riccardo
Bonazzab,
Warren
P.
Portera
aUniversity
of
Wisconsin-Madison,
Department
of
Zoology,
250
N.
Mills
Street,
Madison,
WI
53706,
United
States
bUniversity
of
Wisconsin-Madison,
Engineering
Physics,
1415
Engineering
Drive,
Madison,
WI
53706,
United
States
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
27
May
2015
Received
in
revised
form
16
October
2015
Accepted
18
October
2015
Available
online
11
November
2015
Keywords:
Biophysical
ecology
Climate
change
Global
warming
Leatherback
Niche
model
Sea
turtle
a
b
s
t
r
a
c
t
Shifting
suitable
range
limits
under
global
warming
will
threaten
many
species.
Modeling
and
mapping
these
potential
range
shifts
is
important
for
conservation.
As
global
warming
will
introduce
new
sets
of
abiotic
conditions,
predictive
empirical
niche
models
may
not
perform
well
and
the
best
method
to
model
a
specie’s
projected
range
shifts
may
be
to
model
their
fundamental
niche
with
a
biophysical
mechanistic
niche
model.
However,
this
class
of
model
requires
many
physiological
parameters
that
are
difficult
to
measure
for
species
not
easily
kept
in
captivity.
It
is
also
difficult
to
estimate
these
parameters
for
marine
species
given
the
interactions
among
their
in-water
motion,
metabolism,
and
heat
transfer.
To
surmount
these
difficulties,
we
use
our
previously
verified
novel
technique
combining
3D
digital
design,
computational
fluid
dynamics,
and
finite
volume
heat
transfer
modeling
to
find
animal
core
temperatures.
We
then
use
this
method
to
build
a
fundamental
niche
map
for
internesting
and
nesting
leatherback
sea
turtles
(Dermochelys
coriacea).
With
these
niche
maps
we
analyze
three
main
nesting
areas.
We
show
that
global
warming
poses
a
large
overheating
risk
to
leatherbacks
in
Southeast
Asia,
a
slight
risk
to
leatherbacks
in
the
West
Atlantic
and
a
low
risk
to
leatherbacks
in
the
East
Atlantic.
We
also
show
that
the
impact
may
be
less
on
leatherbacks
that
shift
their
nesting
location
or
who
are
smaller.
Methods
such
these
are
important
to
produce
efficiently
and
economically
accurate
maps
of
regions
that
will
become
inhospitable
to
species
under
global
warming
conditions.
©
2015
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
Global
warming
poses
a
large
extinction
risk
for
many
species
(Thomas
et
al.,
2004).
A
species’
inability
to
shift
its
current
range
to
match
the
future
suitable
range
accounts
for
much
of
the
extinc-
tion
risk
(Parmesan
and
Yohe,
2003).
Therefore,
mangers
and
conservationists
will
likely
need
accurate
range
shift
predictions
to
successfully
address
the
global
warming
threat
to
their
focal
species.
For
leatherback
sea
turtles
(Dermochelys
coriacea)
estimat-
ing
new
suitable
ranges
is
quite
complex.
The
first
difficulty
is
that
leatherbacks
are
gigantotherms,
endothermic
poikilotherms,
whose
large
body
size
traps
waste
heat
thus
elevating
their
core
temperature
(Paladino
et
al.,
1990).
This
effect
means
that
leatherbacks
are
neither
thermal
conformers
nor
regulators
and
Corresponding
author.
E-mail
address:
pndphd@gmail.com
(P.N.
Dudley).
1Present
Address:
Southwest
Fisheries
Science
Center,
110
Shaffer
Road,
Santa
Cruz,
CA
95060,
United
States.
thus
makes
predicting
their
core
body
temperature
difficult.
The
second
difficulty
is
their
complex
life
history.
They
have
the
largest
range
of
any
reptile
(Saba,
2013)
and
are
biphasic
(nesting
on
land
and
living
in
the
water).
Thus,
global
warming
will
affect
leatherbacks
over
a
wide
geographic
range
as
well
as
in
two
dis-
tinct
environments.
Hence,
there
is
not
only
a
need
to
determine
the
leatherback’s
marine
distribution
(National
Marine
Fisheries
Service
and
U.S.
Fish
and
Wildlife
Service,
1992)
but
also
potential
future
nesting
locations
(Fuentes
et
al.,
2012).
Despite
the
logistic
difficulties
of
tracking
leatherbacks
given
their
pelagic
life
history,
scientists
have
tracked
this
species
for
over
three
decades
and
are
now
producing
studies
with
hundreds
of
tracks
(Fossette
et
al.,
2014).
While
these
studies
can
provide
infor-
mation
on
the
lower
thermal
limits
of
leatherbacks,
they
cannot
analyze
the
potential
future
threat
of
increased
water
temperatures
in
the
leatherback’s
equatorial
ranges
because
water
temperatures
as
high
as
those
under
climate
change
do
not
yet
occur.
In
addi-
tion
to
higher
temperatures,
global
warming
may
introduce
new
combinations
of
abiotic
conditions,
thus
the
best
method
to
model
leatherbacks’
response
to
climate
change
may
be
to
model
their
http://dx.doi.org/10.1016/j.ecolmodel.2015.10.012
0304-3800/©
2015
Elsevier
B.V.
All
rights
reserved.
232
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
fundamental
niche
using
a
biophysical
mechanistic
niche
model
(Kearney
and
Porter,
2009;
Porter
et
al.,
2002).
However,
this
class
of
model
requires
many
physiological
parameters
that
are
difficult
to
measure
for
leatherbacks
as
they
are
not
easily
kept
in
cap-
tivity
(Jones
et
al.,
2011).
Since
leatherbacks
are
marine
species,
it
is
also
difficult
to
estimate
these
parameters
given
the
interac-
tion
between
their
in-water
motion,
metabolism,
and
heat
transfer
(Boisclair
and
Tang,
1993).
In
our
earlier
work
we
avoided
these
difficulties
by
sim-
ply
making
reasonable
assumptions
about
missing
physiological
parameters
and
simplifying
assumptions
about
the
leatherbacks
physiology
in
general
(Dudley
and
Porter,
2014).
In
this
current
work,
we
attempt
to
address
and
overcome
these
difficulties
by
using
an
animated,
3D
computational
fluid
dynamics
(CFD)
simu-
lation
and
a
numerical
internal
heat
transfer
model.
Our
previous
work
showed
how
CFD
simulations
can
match
the
forces
on
and
heat
transfer
from
complex
animal
shapes
in
wind
tunnel
exper-
iments
(Dudley
et
al.,
2013).
In
later
work
we
then
demonstrated
that,
using
only
stroke
frequency,
ambient
water
temperature
and
an
allometric
relation
for
resting
metabolic
rate
(RMR),
this
method
is
able
to
accurately
predict
leatherback
core
temperatures
in
a
lab-
oratory
environment
(Dudley
et
al.,
2014).
Thus,
by
combining
the
data
from
our
CDF
model
(power,
heat
transfer
coefficients,
infrared
(IR)
absorption
and
radiation,
and
internal
temperature
profiles)
with
global
climate
models
(GCMs)
we
can
predict
regions
within
the
leatherback’s
current
marine
and
terrestrial
range
that
may
become
inaccessible
under
global
warming
conditions.
We
exam-
ine
potential
shifts
in
nesting
and
internesting
time
and,
range,
as
well
as
body
geometry
and
size.
To
our
knowledge,
this
is
the
first
projection
of
the
fundamental
niche
of
an
organism
using
this
high
level
of
detail,
which
can
only
come
from
CFD
and
numerical
heat
transfer
models
(Dudley
et
al.,
2013).
2.
Methods
2.1.
Outline
The
modeling
process
has
three
steps
and
each
of
these
steps
is
done
for
the
leatherback
while
it
is
in
the
marine
environment
(“internesting
phase”)
and
while
it
is
on
land
laying
eggs
(“nesting
phase”).
The
first
step
(“CFD
simulation
step”)
uses
CFD
to
calcu-
late
heat
transfer
coefficients
from
the
leatherback,
and,
for
the
internesting
phase,
power
required
to
maintain
a
set
swimming
speed.
The
second
step
(“heat
transfer
simulation
step”)
takes
the
results
of
the
first
step
and
uses
them
in
a
heat
transfer
model
to
calculate
the
leatherback’s
core
temperature
given
varying
envi-
ronmental
conditions.
The
third
step
(“niche
model
step”)
takes
the
relations
between
environmental
conditions
and
leatherback
core
temperature
and
combines
those
with
climate
models
to
produce
maps
of
leatherback
core
temperatures
under
two
climate
change
scenarios.
Fig.
1
is
a
diagram
of
the
modeling
approach.
2.2.
Internesting
phase
2.2.1.
CFD
simulation
step
We
drew
five
different
anatomically
realistic
adult
leatherbacks
in
a
non-uniform
rational
basis
splines
(NURBS)
format
using
com-
mercial
3D
design
software
(MoI).
NURBS
are
2D
irregular
surfaces
that
can
produce
realistic
3D
models
of
biological
forms.
The
five
different
models
are:
one
with
the
largest
curved
carapace
length
(CCL)
to
curved
carapace
width
(CCW)
ratio
(1.5)
and
the
longest
CCL
(171
cm)
(called
long
narrow
(LN));
one
with
the
smallest
ratio
(1.2)
and
the
longest
CCL
(called
long
wide
(LW));
one
with
the
largest
ratio
and
the
smallest
CCL
(128)
(called
short
narrow
(SN));
one
with
the
smallest
ratio
and
the
smallest
CCL
(called
short
wide
Fig.
1.
A
diagram
of
the
modeling
procedure.
The
procedure
is
divided
into
three
steps
(CFD,
heat
transfer,
and
niche
model)
each
done
on
two
different
phases
(internesting
and
nesting).
The
computational
fluid
dynamic
(CFD)
step
produces
heat
transfer
coefficients
and
work
(in
the
internesting
phase).
The
heat
transfer
step
produces
a
function
of
environmental
conditions
(water
temperature
(Tw),
air
temperature
(Ta),
land
temperature
(Tl),
radiant
temperature
(Tr),
and
air
velocity
(va))
which
predicts
the
turtle’s
core
temperature,
or
change
in
core
temperature
during
the
nesting
phase
(in
water
(Tcw)
and
on
land
(Tcl)).
The
niche
model
phase
uses
the
previously
established
relations
to
map
the
turtle’s
core
temperature
under
climate
change.
(SW));
and
one
which
had
an
average
ratio
(1.4)
and
an
average
CCL
(150
cm)
(called
average
(Av))
(see
Fig.
A.1
and
Table
A.1
in
Appendix
S1
in
Supporting
Information).
These
leatherbacks
would
weigh
approximately
477
kg,
633
kg,
201
kg,
266
kg,
and
337
kg
respectively.
The
ratios
and
lengths
are
based
on
data
from
three
sources
(James
et
al.,
2007;
“Jupiter
Island
sea
turtle
taging
project
(JISTTP),”
2012;
Médicci
et
al.,
2011).
This
size
range
more
than
covers
the
typical
standard
deviation
observed
in
CCLs
of
sampled
leatherbacks
(typically
less
than
10
cm).
The
flipper
length
scaled
with
CCL
and
not
with
CCW
(Walker,
2010).
We
placed
one
side
of
the
model
in
a
virtual
half
cylinder
with
buffer
distances
of
approx-
imately
4
m
between
the
turtle’s
flipper
tip
and
the
cylinder’s
wall,
which
is
adequate
space
to
not
affect
the
stroke
mechanics.
The
plane
dividing
the
cylinder
in
half
also
divides
the
turtle
along
the
midsagittal
plane.
Using
half
the
turtle
and
a
symmetry
boundary
condition
on
the
plane
bisecting
the
turtle
increases
computational
efficiency
by
only
solving
the
fluid
dynamics
around
one
half
of
the
turtle.
This
setup
resulted
in
volumes
ranging
from
440
to
1450
m3
depending
on
the
size
of
the
turtle.
We
meshed
all
the
fluid
domains
with
tetragons
(a
standard
choice
for
an
unstructured
computa-
tional
grid
in
CFD).
All
domains
contained
approximately
150,000
elements
which
is
adequate
to
produce
accurate
results
(Dudley
et
al.,
2014).
We
use
a
commercial
CFD
program,
ANSYS
Fluent
(ANSYS,
Inc.,
Cecil
Township,
Pennsylvania,
USA),
We
wrote
a
supplemen-
tal
program
using
Fluent’s
“DEFINE
GRID
MOTION”
macro,
which
describes
the
leatherbacks’
swimming
motion
(additional
details
Dudley
et
al.,
2014).
To
mimic
a
turtle’s
flipper
motion,
we
used
ImageJ
software
(National
Institutes
of
Health,
Bethesda,
Mary-
land,
USA)
to
analyze
frames
from
publicly
available
video
of
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
233
leatherbacks
freely
swimming.
The
flipper
had
four
zones.
The
14%
of
the
flipper
closest
to
the
shoulder
was
the
transition
zone
from
no
motion
to
steady
roll
(flipper
moving
dorsally
to
ventrally)
and
yaw
(flipper
moving
posteriorly
to
anteriorly).
The
next
22%
of
the
flipper
was
the
transition
zone
from
steady
roll
and
yaw
to
steady
roll,
yaw,
and
pitch
(flipper
twisting).
The
next
21%
of
the
flipper
was
a
zone
of
constant
roll,
yaw,
and
pitch.
The
last
43%
of
the
flip-
per
was
the
transition
zone
from
steady
roll,
yaw,
and
pitch
to
roll,
yaw,
pitch,
and
bend
(flexing
of
the
flipper
in
the
roll
plane).
The
stroke
had
four
phases.
There
was
a
down
stroke
(32.3%
of
stroke
period,
0.95
radians
of
roll,
0.00
radians
of
pitch,
0.15
radians
of
yaw,
and
0.00
radians
of
bend),
a
turn
at
the
bottom
and
at
the
top
of
the
stroke
(17.0%
of
stroke
period
for
each,
0.00
radians
of
total
roll,
±2.40
radians
of
pitch,
0.00
radians
of
total
yaw,
and
±0.80
radians
of
bend),
and
an
up
stroke
(33.7%
of
stroke
period,
0.95
radians
of
roll,
0.00
radians
of
pitch,
0.15
radians
of
yaw,
and
0.00
radians
of
bend).
To
prevent
discontinuities
in
the
motion,
we
programmed
smooth
transitions
into
the
top
and
bottom
phases.
To
correctly
position
the
flipper,
there
was
also
a
0.5
s
setup
time.
To
set
the
internesting
swimming
velocity
we
averaged
64
records
of
leatherbacks
swimming
during
their
internesting
phase
(Byrne
et
al.,
2009;
Eckert,
2002;
Hughes
et
al.,
1998;
Lambardi
et
al.,
2008;
Luschi
et
al.,
2003;
Shillinger
et
al.,
2008).
Most
of
these
stud-
ies
measured
the
turtles’
speed
by
satellite
tracking,
however,
one
study
used
ultramarine
velocity
recorders
(UVRs)
on
five
turtles
to
measure
actual
swim
speed
(Eckert,
2002).
Given
the
small
dif-
ference
between
the
two
measurement
methods
(less
than
14%),
the
small
sample
size
using
UVRs
and
that
average
current
effects
should
be
small
since
leatherbacks
orient
randomly
with
respect
to
current
(Galli
et
al.,
2012),
we
used
the
average
of
all
64
as
the
internesting
swim
speed
(0.53
m/s).
The
stroke
periods
for
the
leatherbacks
to
produce
this
speed
were
2.01
s,
2.19
s,
1.63
s,
1.72
s,
and
1.81
s
for
LN,
LW,
SN,
SW,
and
Av
respectively.
The
simulation
used
the
kω
shear
stress
transport
(SST)
model
in
Fluent,
with
a
constant
velocity
inlet
(0.53
m/s)
and
a
zero
pres-
sure
outlet.
The
kω
SST
model
provides
accurate
near
“wall”
performance
(i.e.
flow
around
the
turtle’s
body)
as
well
as
accurate
free
stream
performance
(i.e.
flow
away
from
the
turtle’s
body).
The
virtual
fluid
the
turtle
swam
in
had
the
properties
of
seawater
(density:
1015
kg/m3,
specific
heat:
4053
J/kg
K,
thermal
conductiv-
ity:
0.6
W/m
K
and
viscosity:
9.68
×
103kg/m
s).
We
set
the
time
step
to
0.001
s
and
ran
the
simulation
for
one
full
stroke
cycle.
We
know
from
our
previous
work
that
this
time
step
is
short
enough
to
produce
accurate
results.
In
all
analyses,
we
removed
the
initial
500
setup
steps.
We
calculated
average
thrust,
work,
and
flipper
and
body
heat
transfer
coefficients.
To
translate
the
work
done
on
the
fluid
into
expended
energy,
we
used
the
aerobic
efficiency
of
tortoise
muscle
(35%;
Woledge,
1968).
2.2.2.
Heat
transfer
simulation
step
The
internal
model
is
the
same
model
we
used
in
our
previ-
ous
work
except
scaled
to
each
leatherback’s
size
(Dudley
et
al.,
2014).
Details
of
the
model
are
in
our
previous
work
but,
in
brief,
we
divided
the
inertial
region
into
insulating
blubber,
muscle/internal
viscera,
and
counter
current
heat
exchanger
regions.
We
found
nec-
essary
thermal
properties
for
all
of
these
regions
in
the
literature
(Table
A.2).
The
internal
thermal
conductivity
varied
with
tempera-
ture
to
simulate
vasoconstriction
and
vasodilation
given
cold
or
hot
temperatures.
We
set
a
resting
metabolic
rate
from
an
allometric
relation
(Wallace
and
Jones,
2008)
and
scaled
that
with
temper-
ature
according
to
a
Boltzmann
factor.
The
external
heat
transfer
coefficients
came
from
our
swimming
simulations
described
above.
We
calculate
the
core
temperature
by
taking
the
average
tempera-
ture
of
the
body
region
inside
the
insulating
blubber
region.
The
resting
metabolic
rate
(RMR)
scales
with
core
tempera-
ture
and
we
are
attempting
to
determine
actual
core
temperature,
therefore
assigning
a
metabolic
rate
to
the
internal
simulation
is
problematic.
Therefore,
we
ran
several
simulations
for
a
single
ambient
water
temperature.
Each
of
these
simulations
had
a
dif-
ferent
metabolic
rate
corresponding
to
a
different
thermal
gradient
(ranging
from
2C
to
18 C).
For
each
set
of
simulations,
we
then
have
two
relations.
One
relation
is
the
guessed
thermal
gradient
between
the
turtle’s
core
and
the
environment
vs.
metabolic
rate
and
the
other
is
the
simulated
thermal
gradient
vs.
metabolic
rate.
The
actual
thermal
gradient
for
a
given
ambient
temperature
is
when
the
guessed
thermal
gradient
equals
the
simulated
thermal
gradient.
2.2.3.
Niche
model
step
Using
the
relations
between
ambient
water
temperature
and
core
leatherback
temperature
from
the
internal
swimming
simula-
tion,
we
developed
a
marine
niche
model
program
for
leatherback
turtles.
The
niche-modeling
program
uses
the
relations
we
found
in
the
CFD
simulations
to
determine
the
core
temperature
based
on
the
ambient
water
temperature.
Consistent
with
observations,
our
leatherbacks
spend
90
percent
of
their
time
stroking
and
10
percent
gliding
(Southwood
et
al.,
2005).
As
a
leatherback
can
decrease
its
ambient
temperature
by
diving
deeper,
longer
and
more
frequently,
if
a
leatherback
in
a
certain
area
would
have
a
core
temperature
above
a
goal
temperature
of
29 C
it
could
access
colder
water
by
diving
deeper,
longer,
or
more
often
up
to
a
limit.
Based
on
liter-
ature
on
internesting
leatherback
dive
profiles,
we
set
the
depth
and
time
limit
to
be
two
standard
deviations
above
the
average
dive
depth
and
time
(115
m
and
17
min
respectively).
We
removed
from
the
calculation
for
depth
limit
any
study
where
the
author
suggested
that
shallow
water
capped
the
dive
profiles.
We
set
the
surface
recovery
time
to
be
the
average
of
the
minimums
observed
(30
s)
(Eckert
et
al.,
1996,
1989,
1986;
Eguchi
et
al.,
2006;
Fossette
et
al.,
2010,
2008,
2007;
Reina
et
al.,
2005;
Southwood
et
al.,
2005,
1999;
Wallace
et
al.,
2005).
While
leatherbacks
are
capable
of
div-
ing
longer/deeper
than
this,
we
are
attempting
to
set
a
limit
on
their
average
behavior
not
any
individual
behavior.
Based
on
Knutti
et
al.,
we
selected
four
global
climate
mod-
els
(GCMs)
from
the
CMIP5
multi-model
ensemble
to
use
as
the
climate
inputs
for
our
niche
model
(2010).
We
selected
high
performing
models
that
had
the
outputs
we
needed.
As
ocean
tem-
perature
is
the
most
influential
environment
variable
in
our
model
the
highest
performing
models
are
those
with
the
least
sea
sur-
face
temperature
bias
in
hindcasts
(Wang
et
al.,
2014).
The
four
models
are
the
Met
Office
Hadley
Centre’s
Hadley
Center
Global
Environment
Model,
version
2
(Earth
System)
(HadGEM2-ES),
the
Institute
Pierre-Simon
Laplace’s
Earth
System
Model
for
the
5th
IPCC
report
(mid-resolution)
(IPSL-CM5A-MR),
The
University
of
Tokyo’s
Atmosphere
and
Ocean
Research
Institute,
National
Insti-
tute
for
Environmental
Studies,
and
Japan
Agency
for
Marine-Earth
Science
and
Technology’s
Model
for
Interdisciplinary
Research
on
Climate
(MIROC5),
and
the
low
resolution
Max
Planck
Institute
for
Meteorology’s
Earth
System
Model
(MPI-ESM-LR).
We
selected
the
monthly
average
data
sets
from
January
2006
to
December
2095
for
relative
concentration
pathway
(RCP)
4.5
(a
stabiliz-
ing
scenario)
(Clarke
et
al.,
2007;
Smith
and
Wigley,
2006;
Wise
et
al.,
2009)
and
8.5
(’business
as
usual’)
(Riahi
et
al.,
2007).
We
set
the
internesting
region
to
be
areas
within
200
km
of
shore
which
should
encompass
the
regions
leatherbacks
occupy
during
internesting
behavior
(Almeida
et
al.,
2011;
Eckert
et
al.,
2006).
We
calculated
the
leatherbacks
core
temperature
by
running
our
niche
model
with
each
GCM
individually
before
analyzing
the
results.
This
method
allows
us
to
average
the
results
from
the
four
GCMs
to
find
the
average
core
temperature
in
regions
as
well
as
look
at
the
range
of
core
temperatures
different
CGMs
produce.
We
then
graphed
a
10
year
moving
average
of
the
core
temperatures
to
remove
annual
fluctuations
and
display
long
tern
trends.
234
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
2.3.
Nesting
phase
2.3.1.
CFD
simulation
step
We
setup
the
land
model’s
fluid
dynamics
component
to
cal-
culate
the
heat
transfer
coefficients
of
the
leatherback’s
body
and
flipper
at
different
wind
speeds.
For
this
model,
we
added
a
plane
below
the
plastron
of
the
leatherback
to
simulate
the
ground.
The
ground
covered
24%
of
the
leatherback’s
surface
area.
We
enclosed
this
geometry
in
a
virtual
half
pipe
with
5
m
buffers
around
the
leatherback.
We
meshed
the
leatherback
virtual
pipe
environment
with
1.2
million
elements
using
a
combination
of
tetrahedrons,
pyramids
and
wedges.
The
simulation
used
the
kω
SST
model
with
a
variable
velocity
inlet
(0.1–20.0
m/s)
and
a
zero
pressure
outlet.
2.3.2.
Heat
transfer
simulation
step
The
internal
land
model
geometry
was
similar
to
the
swimming
geometry
with
the
exception
that
we
divided
the
surface
area
into
three
areas.
The
bottom
area
exchanged
heat
with
the
ground
by
conduction.
This
portion
of
the
plastron
and
the
bottom
of
the
flip-
per
accounted
for
33%
of
the
leatherback’s
surface
area.
The
middle
area
exchanged
heat
by
convection
with
the
air
and
infrared
(IR)
radiation
with
the
ground
and
accounted
for
22%
of
the
surface
area.
The
top
portion
exchanged
heat
through
convection
with
the
air
and
IR
radiation
with
the
sky
and
accounted
for
the
remaining
55%
of
the
surface
area.
We
set
the
IR
temperature
of
the
ground
to
that
of
the
ambient
temperature
multiplied
by
sand’s
emissivity.
We
set
the
IR
temperature
of
the
sky
using
the
Swinbank
rela-
tion
(Swinbank,
1963).
Our
previous,
more
simplified
model
had
demonstrated
that
evaporative
cooling
has
little
effect,
thus
we
neglected
it
(Dudley
and
Porter,
2014).
The
internal
heat
genera-
tion
used
metabolic
rates
of
nesting
leatherbacks
(1.05
W/kg
when
crawling
(Paladino
et
al.,
1996,
1990),
1.38
W/kg
when
digging
and
covering
(Paladino
et
al.,
1990),
and
0.15
when
laying
(Lutcavage
et
al.,
1990;
Paladino
et
al.,
1996)).
The
nesting
timetable
was
3
min
to
crawl
up,
22
min
to
dig,
15
min
to
lay,
45
min
to
cover,
and
8
min
to
return
(Carr
and
Ogren,
1959).
We
set
the
initial
temperature
of
all
leatherbacks
to
29.85 C
and
set
air
and
land
temperatures
relative
to
this
initial
temperature.
Preliminary
runs
showed
that
core
temperature
on
an
absolute
scale
made
little
difference
in
temperature
increase
and
that
difference
between
the
initial
core
temperature
and
ambient
was
the
important
factor.
We
ran
the
Av
internal
model
for
five
different
air
temperatures,
five
different
wind
speeds,
and
nine
different
land
temperatures
for
a
total
of
225
combinations.
This
number
of
points
proved
to
give
excessive
res-
olution
and
so
we
ran
the
remaining
four
leatherbacks
with
three
different
air
temperatures,
three
different
wind
speeds,
and
three
different
land
temperatures
for
a
total
of
27
combinations.
2.3.3.
Niche
model
step
The
land
niche
model
used
the
255
or
27
element
matrix
to
interpolate
the
temperature
increase
a
leatherback
would
experi-
ence
in
a
given
region.
We
used
the
same
four
models
as
the
marine
niche
model
taking
monthly
averages
for
soil
temperature,
daily
minimum
temperature,
and
wind
velocity.
We
took
the
nearest
marine
core
temperatures
to
each
of
the
land
cells.
We
only
exam-
ined
land
areas
that
directly
bordered
water.
We
again
graph
a
10
year
moving
average.
3.
Results
3.1.
Marine
simulation
From
the
marine
CFD
simulation
we
calculated
power
and
heat
transfer
coefficients.
The
power
profile
was
similar
for
all
five
mor-
phologies.
There
was
a
rise
in
power
output
during
the
down
phase,
a
spike
in
power
in
the
middle
of
the
bottom
phase,
a
spike
followed
Fig.
2.
The
pressure
contours
on
the
Av
leatherback
as
it
moves
through
one
stroke
period.
Black
arrows
indicate
the
direction
of
the
image
sequence.
The
other
4
sizes
of
turtle
show
similar
patterns.
by
a
plateau
during
the
up
phase,
and
a
spike
in
power
in
the
mid-
dle
of
the
top
phase
(Fig.
A.2).
For
the
average
power
during
the
stroke,
the
LN
had
the
largest
while
the
SW
had
the
smallest
(Fig.
A.3).
Note
that
LN
and
SN
used
more
power
to
swim
at
the
same
speed
than
LW
and
SW
respectively.
This
difference
is
because
the
narrowing
of
the
carapace
moves
the
flippers
closer
together
and
reduces
their
propeller
efficiency
(useful
power/available
power).
Also
note
that
attempting
to
calculate
power
by
using
the
force
nec-
essary
to
overcome
static
drag
would
have
underestimated
power
output
by
50%
even
given
a
low
15%
propeller
efficiency.
Our
cal-
culated
propeller
efficiency
in
the
simulation
(work
that
moves
the
turtle
forward
divided
by
the
work
turtle
does
on
the
fluid)
is
16.7%
which
is
similar
to
other
studies
(Feldkamp,
1987;
Webb,
1971).
Examining
the
Av
leatherback’s
pressure
profile
during
the
stroke,
it
is
evident
that
most
of
the
power
comes
from
the
flipper’s
distal
region
(Fig.
2).
For
the
heat
transfer
coefficient,
there
is
a
relatively
stable
coefficient
for
the
body
and
a
changing
coefficient
on
the
flipper.
The
flipper
heat
transfer
coefficient
is
highest
during
the
down
stroke
and
lowest
during
the
bottom
portion
of
the
stroke.
The
Av
leatherback
had
the
highest
coefficients
while
the
SN
had
the
low-
est
(Fig.
A.3).
The
heat
flux
through
the
skin
as
the
Av
leatherback
moves
through
its
stroke
shows
higher
heat
fluxes
in
the
flipper’s
distal
region
and
in
the
lateral
portion
of
the
carapace
posterior
to
the
flipper.
Since
these
simulations
only
get
the
heat
transfer
coef-
ficient,
the
leatherback
skin
is
set
at
a
constant
temperature
and
the
actual
leatherback’s
heat
flux
(below)
will
differ.
The
internal
simulation
produced
a
relation
for
each
of
the
five
leatherbacks
between
ambient
temperature
and
leatherback
core
temperature
(Fig.
3).
SN
and
SW
had
the
lowest
core
temperature
for
a
given
ambient
temperature,
Av
was
slightly
above
them,
and
LW
and
LN
were
warmer
still
and
close
together.
The
shallow
slope
of
the
graphs
around
20 C
is
due
to
the
leatherback
controlling
its
core
conduction
through
vasoconstriction
and
dilation.
In
these
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
235
Fig.
3.
The
core
body
temperature
of
a
swimming
leatherback
given
the
ambient
water
temperature
and
morphology
(long
wide
(LW),
long
narrow
(LN),
short
wide
(SW),
short
narrow
(SN),
and
average
(Av).
The
bold,
horizontal,
black
line
demarks
the
critical
thermal
maximum
(CTM)
while
the
dotted
lines
demark
the
standard
deviation
in
the
CTM
measurement.
simulations,
the
highest
heat
flux
through
the
skin
is
around
the
soft
tissue
of
the
shoulder
regions.
The
Marine
niche
model
produces
1080
maps
(one
for
each
month
from
January
2006
to
December
2095)
for
a
given
set
of
conditions.
As
an
example
we
show
a
map
of
the
Av
leatherback’s
core
temperature
using
the
HadGEM2-ES
RCP8.5
inputs
for
August
2095
(Fig.
4)
(All
niche
maps
in
NetCDF
format
are
archived
with
Dataverse
(http://dx.doi.org/10.7910/DVN/4JHFYA)).
The
orange
to
red
areas
on
the
map
indicate
regions
where
the
leatherbacks
are
within
one
standard
deviation
of
their
critical
thermal
maximum
(CTM)
(40.2
±
1.3 C)
(Drake
and
Spotila,
2002)
and
the
black
areas
are
where
they
are
above
one
standard
deviation
of
their
CTM.
Looking
at
the
condition
of
the
Av
leatherback
during
local
nesting
seasons
at
some
specific
areas
(Fig.
5)
with
large
leatherback
nesting
populations
(French
Guiana
and
Suriname
(FG&S)
(nesting
March–July),
Gabon
and
Congo
(G&C)
(nesting
November–February),
and
West
Papua,
Indonesia
(WP)
(nesting
May–September)),
we
see
that
leatherback
internesting
core
tem-
peratures
will
increase.
Only
WP
under
RCP8.5
shows
overlap
Fig.
4.
The
core
temperature
of
an
Av
internesting
leatherback
using
the
HadGEM2-
ES
RCP8.5
inputs
during
August
2095.
Areas
in
orange
to
red
are
areas
where
the
leatherback’s
core
temperature
is
within
one
standard
deviation
of
the
CTM.
The
calculation
only
extends
from
40N
thru
40S.
Fig.
5.
The
three
regions
specifically
analyzed
in
this
study.
In
the
plate
containing
Papua
the
west
most
polygon
is
the
site
initially
considered
while
the
east
most
site
is
used
to
examine
the
effects
of
shifting
nesting
grounds
on
leatherback
core
temperatures.
236
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
Fig.
6.
The
Av
internesting
leatherback’s
core
temperature
in
a
given
region
from
2006
to
2095
for
two
climate
change
scenarios.
The
graphs
are
the
10
year
moving
averages
for
the
relevant
nesting
months
at
each
location
(French
Guiana
and
Suriname
(FG&S)
(nesting
March–July),
Gabon
and
Congo
(G&C)
(nesting
November–February),
and
West
Papua
(WP)
(nesting
May–September)).
The
“Avg.”
line
is
the
average
core
temperature
across
the
four
climate
models.
The
“Max/Min”
dashed
lines
represent
the
maximum
and
minimum
core
temperatures
found
among
the
four
models.
The
size
dotted
lines
represent
the
maximum
temperature
found
among
the
four
models
for
the
LW
turtle
and
the
minimum
temperature
found
among
the
four
models
for
the
SN
turtle.
The
gray
band
represents
the
leatherbacks
CTM
range
(39.8–41.5 C).
between
the
leatherback’s
CTM
and
the
range
of
the
ten
year
mov-
ing
average
of
the
niche
models
calculated
core
temperature.
None
of
the
scenarios
show
the
average
from
all
four
models
reaching
the
CTM
zone
by
the
2095
mark
(which
is
the
average
of
2085–2095)
(Fig.
6).
3.2.
Terrestrial
simulation
The
terrestrial
niche
model
produces
another
1080
maps
(one
for
each
month)
for
a
given
set
of
conditions
(All
niche
maps
in
NetCDF
format
are
archived
with
Dataverse
(http://dx.doi.org/10.
7910/DVN/4JHFYA)).
A
leatherback
heats
up
while
nesting
except
during
the
laying
portion
where
the
low
metabolic
rate
allows
it
to
cool.
Again,
like
the
swimming
turtle,
the
highest
heat
flux
was
around
the
shoulder
area.
Our
terrestrial
data
in
our
three
regions
of
interest
yield
similar
results
to
the
marine
niche
map
(Fig.
7).
As
might
be
expected
each
nesting
core
temperature
graph
matches
its
corresponding
internesting
graph
in
shape
but
is
a
few
degrees
higher.
Two
strategies
leatherback
populations
in
WP
could
use
as
refuges
are
changing
location
and
changing
nesting
time.
We
ana-
lyzed
those
two
options.
Changing
the
nesting
time
(shifting
the
nesting
season
later
or
earlier
by
two
months)
offers
no
substantial
relief;
location
change
(nesting
north
of
Papua
New
Guinea)
pro-
vides
some
relief
(Fig.
8).
Figs.
6
and
7
also
show
that
leatherbacks
of
smaller
size
are
better
equipped
to
deal
with
the
increasing
ambient
temperatures.
The
LW
leatherback
is
in
distress
in
places
outside
of
WP.
For
example,
the
range
of
the
nesting
niche
model
outputs
for
the
LW
leatherback
overlaps
the
CTM
in
FG&S
under
both
RCP4.5
and
8.5
(Fig.
9).
4.
Discussion
This
study
shows
that
using
3D
CFD
in
conjunction
with
a
bio-
physical
niche
model
is
a
useful
method
to
model
future
ranges
under
projected
global
climate
change
scenarios.
For
animals
with
complex
and
difficult-to-measure
physiologic
characteristics,
or
for
animals
whose
physiological
data
are
expensive
to
collect,
this
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
237
Fig.
7.
The
Av
nesting
leatherback’s
core
temperature
in
a
given
region
from
2006
to
2095
for
two
climate
change
scenarios.
The
graphs
are
the
10
year
moving
averages
for
the
relevant
nesting
months
at
each
location
(French
Guiana
and
Suriname
(FG&S)
(nesting
March–July),
Gabon
and
Congo
(G&C)
(nesting
November–February),
and
West
Papua
(WP)
(nesting
May–September)).
The
“Avg.”
line
is
the
average
core
temperature
across
the
four
climate
models.
The
“Max/Min”
dashed
lines
represent
the
maximum
and
minimum
core
temperatures
found
among
the
four
models.
The
size
dotted
lines
represent
the
maximum
temperature
found
among
the
four
models
for
the
LW
turtle
and
the
minimum
temperature
found
among
the
four
models
for
the
SN
turtle.
The
gray
band
represents
the
leatherbacks
CTM
range
(39.8–41.5 C).
Fig.
8.
A
comparison
between
the
nesting
core
temperatures
of
leatherback
using
current
nesting
timing
and
location
in
WP
and
alternative
timing
and
the
alternative
location.
Fig.
5
shows
the
alternative
location.
method
proved
a
useful
alternative
for
gathering
accurate
physio-
logical
data.
In
comparison
to
an
empirical
niche
model
this
method
is
superior
especially
considering
global
warming
because
form-
ing
an
empirical
niche
map
for
novel
conditions
requires
complex
statistical
methods
and
may
still
be
inappropriate
or
inaccurate
(Dormann,
2007;
Kearney
et
al.,
2008).
Using
the
leatherback
sea
turtle,
we
showed
how
these
physiological
data
can
be
used
to
pre-
dict
an
animal’s
future
fundamental
niche
and
projected
range
shift
under
global
warming
conditions.
Our
results
show
that
global
warming,
especially
if
mitiga-
tion
efforts
are
not
successful,
will
be
damaging
for
leatherbacks
particularly
in
Southeast
Asia.
While
all
leatherback
internesting
core
temperatures
will
increase,
in
the
three
regions
we
exam-
ined,
only
those
in
Southeast
Asia
will
likely
approach
their
CTM.
For
larger
leatherbacks,
FG&S
nesting
populations
will
also
expe-
rience
some
thermal
distress
especially
under
RCP
8.5.
We
also
see
from
our
results
that
leatherbacks
in
WP
could
shift
their
nes-
ting
location
and
find
refuge
from
increased
temperatures.
Also
238
P.N.
Dudley
et
al.
/
Ecological
Modelling
320
(2016)
231–240
Fig.
9.
The
LW
nesting
leatherback’s
core
temperature
in
French
Guiana
and
Suri-
name
(FG&S)
from
2006
to
2095
for
two
climate
change
scenarios.
The
graphs
are
the
10
year
moving
averages
for
the
relevant
nesting
months
in
FG&S
(nes-
ting
March–July).
The
“Avg.”
line
is
the
average
core
temperature
across
the
four
climate
models.
The
“Max/Min”
dashed
lines
represent
the
maximum
and
mini-
mum
core
temperatures
found
among
the
four
models.
The
gray
band
represents
the
leatherbacks
CTM
range
(39.8–41.5 C).
smaller
leatherbacks
have
much
lower
body
temperatures
in
gen-
eral
which
may
be
an
advantage
to
them
in
the
future.
While
the
body
size
of
the
population
could
decrease
in
response
to
increased
temperatures,
observed
cases
of
rapid
decreases
in
body
size
are
in
species
with
shorter
generation
times
(Grant
and
Grant,
2002;
Heimsath
et
al.,
2003;
Jackson
et
al.,
2001;
Shackell
et
al.,
2010).
These
predictions
are
conservative
in
some
respects
but
leatherbacks
may
also
be
able
to
compensate
for
higher
tem-
peratures
in
ways
not
considered
in
the
model.
The
results
are
conservative
particularly
in
the
terrestrial
phase.
Our
model
used
the
average
monthly
minimum
temperature,
and
an
efficient
nes-
ting
schedule.
If
leatherbacks
nest
slower
or
on
a
warmer
day
or
time
of
day,
especially
if
the
sun
is
up