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Absolute gravity observations in Norway (1993–2014) for glacial isostatic adjustment studies: The influence of gravitational loading effects on secular gravity trends

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We have compiled and analyzed FG5 absolute gravity observations between 1993 and 2014 at 21 gravity sites in Norway, and explore to what extent these observations are applicable for glacial isostatic adjustment (GIA) studies. Where available, raw gravity observations are consistently reprocessed. Furthermore, refined gravitational corrections due to ocean tide loading and non-tidal ocean loading, as well as atmospheric and global hydrological mass variations are computed. Secular gravity trends are computed using both standard and refined corrections and subsequently compared with modeled gravity rates based on a GIA model. We find that the refined gravitational corrections mainly improve rates where GIA, according to model results, is not the dominating signal. Consequently, these rates may still be considered unreliable for constraining GIA models, which we trace to continued lack of a correction for the effect of local hydrology, shortcomings in our refined modeling of gravitational effects, and scarcity of observations. Finally, a subset of standard and refined gravity rates mainly reflecting GIA is used to estimate ratios between gravity and height rates of change by ordinary and weighted linear regression. Relations based on both standard and refined gravity rates are within the uncertainty of a recent modeled result.
Content may be subject to copyright.
Journal
of
Geodynamics
102
(2016)
83–94
Contents
lists
available
at
ScienceDirect
Journal
of
Geodynamics
jou
rn
al
hom
ep
age:
http://www.elsevier.com/locate/jog
Absolute
gravity
observations
in
Norway
(1993–2014)
for
glacial
isostatic
adjustment
studies:
The
influence
of
gravitational
loading
effects
on
secular
gravity
trends
Vegard
Ophauga,,
Kristian
Breilia,b,
Christian
Gerlacha,c,
Jon
Glenn
Omholt
Gjevestada,
Dagny
Iren
Lysakerb,
Ove
Christian
Dahl
Omangb,
Bjørn
Ragnvald
Pettersena
aDepartment
of
Mathematical
Sciences
and
Technology,
Norwegian
University
of
Life
Sciences
(NMBU), ˚
As,
Norway
bGeodetic
Institute,
Norwegian
Mapping
Authority,
Hønefoss,
Norway
cCommission
of
Geodesy
and
Glaciology,
Bavarian
Academy
of
Sciences
and
Humanities,
Munich,
Germany
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
16
April
2016
Received
in
revised
form
4
August
2016
Accepted
10
September
2016
Available
online
24
September
2016
Keywords:
Absolute
gravity
Ocean
tide
loading
Non-tidal
ocean
loading
Atmospheric
effect
Global
hydrological
effect
Time-variable
gravity
Land
uplift
Glacial
isostatic
adjustment
Gravity-to-height
ratios
a
b
s
t
r
a
c
t
We
have
compiled
and
analyzed
FG5
absolute
gravity
observations
between
1993
and
2014
at
21
gravity
sites
in
Norway,
and
explore
to
what
extent
these
observations
are
applicable
for
glacial
isostatic
adjust-
ment
(GIA)
studies.
Where
available,
raw
gravity
observations
are
consistently
reprocessed.
Furthermore,
refined
gravitational
corrections
due
to
ocean
tide
loading
and
non-tidal
ocean
loading,
as
well
as
atmo-
spheric
and
global
hydrological
mass
variations
are
computed.
Secular
gravity
trends
are
computed
using
both
standard
and
refined
corrections
and
subsequently
compared
with
modeled
gravity
rates
based
on
a
GIA
model.
We
find
that
the
refined
gravitational
corrections
mainly
improve
rates
where
GIA,
according
to
model
results,
is
not
the
dominating
signal.
Consequently,
these
rates
may
still
be
considered
unreli-
able
for
constraining
GIA
models,
which
we
trace
to
continued
lack
of
a
correction
for
the
effect
of
local
hydrology,
shortcomings
in
our
refined
modeling
of
gravitational
effects,
and
scarcity
of
observations.
Finally,
a
subset
of
standard
and
refined
gravity
rates
mainly
reflecting
GIA
is
used
to
estimate
ratios
between
gravity
and
height
rates
of
change
by
ordinary
and
weighted
linear
regression.
Relations
based
on
both
standard
and
refined
gravity
rates
are
within
the
uncertainty
of
a
recent
modeled
result.
©
2016
The
Authors.
Published
by
Elsevier
Ltd.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
Gravimetry
considers
the
observation
or
measurement
of
grav-
ity.
It
may
be
spaceborne,
air-
and
shipborne,
or
ground-based
(terrestrial),
where
latter
observations
may
be
used
to
validate
results
from
the
first
(e.g., ˇ
Sprlák
et
al.,
2015).
Observing
temporal
gravity
changes,
and
thus
changes
in
the
Earth’s
density
distribu-
tion,
gives
insight
into
a
range
of
geophysical
phenomena,
e.g.,
Earth
tides,
Chandler
wobble,
core,
mantle
and
tectonic
processes
(Torge
and
Müller,
2012),
sea-level
change
(e.g.,
Simpson
et
al.,
2013),
the
hydrological
cycle
(e.g.,
Pálinkáˇ
s
et
al.,
2012),
and
cryospheric
mass
variations
(e.g.,
Breili
and
Rolstad,
2009;
Arneitz
et
al.,
2013).
Long-term
temporal
gravity
changes
can
be
observed
by
repeated
absolute
gravimetry,
with
an
accuracy
of
0.5
Gal
yr1(where
1
Gal
=
108ms2)
after
10
years
of
annual
observations
(Van
Camp
et
al.,
2016).
Corresponding
author.
E-mail
address:
vegard.ophaug@nmbu.no
(V.
Ophaug).
As
opposed
to
space-geodetic
observation
techniques
such
as
Global
Navigation
Satellite
Systems
(GNSS),
absolute
gravity
(AG)
is
independent
of
the
terrestrial
reference
frame,
and
may
thus
be
used
to
assess
it
(e.g.,
Mazzotti
et
al.,
2011;
Collilieux
et
al.,
2014).
Furthermore,
AG
is
particularly
suitable
for
monitoring
long-term
vertical
deformation
(Van
Camp
et
al.,
2011)
caused
by,
e.g.,
glacial
isostatic
adjustment
(GIA)
in
North
America
(e.g.,
Lambert
et
al.,
2006)
and
Fennoscandia
(e.g.,
Steffen
et
al.,
2009;
Pettersen,
2011;
Müller
et
al.,
2012;
Timmen
et
al.,
2011,
2015;
Nordman
et
al.,
2014),
alongside
GNSS
(e.g.,
Milne
et
al.,
2001;
Vestøl,
2006).
Sasagawa
(1989)
reviewed
the
required
time
span
of
gravity
observations
for
determining
a
secular
gravity
trend
with
desired
accuracy,
given
by
˙
g=g12
TN
1
N
,
(1)
where
˙
gis
the
trend
uncertainty,
gis
the
uncertainty
of
individ-
ual
gravity
observations,
T
is
the
time
in
years,
and
N
the
number
of
observations.
Eq.
(1)
assumes
evenly
distributed
observations
with
known
uncertainties
and
a
true
Gaussian
distribution.
Steffen
http://dx.doi.org/10.1016/j.jog.2016.09.001
0264-3707/©
2016
The
Authors.
Published
by
Elsevier
Ltd.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.
0/).
84
V.
Ophaug
et
al.
/
Journal
of
Geodynamics
102
(2016)
83–94
Fig.
1.
AG
sites
in
Norway.
Blue
sites
have
been
observed
more
than
once.
The
contour
lines
show
modeled
gravity
rates
(Gal
yr1)
from
the
preliminary
NKG2016GIA
prel0306
GIA
model
(H.
Steffen,
personal
communication,
2016).
(For
interpretation
of
the
references
to
colour
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
and
Wu
(2011)
further
state
that
a
secular
gravity
trend
should
be
known
within
an
uncertainty
of
±0.5
Gal
yr1for
crustal
defor-
mation
studies,
which,
by
Eq.
(1),
should
be
achieved
by
five
to
six
years
of
annual
gravity
observations
with
g
1
2
Gal.
In
1990,
the
Nordic
Geodetic
Commission
(NKG,
http://www.
nordicgeodeticcommission.com/)
began
establishing
a
geodetic
network
for
monitoring
crustal
deformations
and
sea-level
changes
in
Fennoscandia
and
Svalbard.
As
part
of
this
initiative,
the
first
AG
observations
with
modern
instruments
were
performed
in
Norway
in
1991
and
1992
(Roland,
1998).
Between
1991-1995,
several
AG
campaigns
were
conducted
in
Fennoscandia
and
Svalbard
(Roland,
1998).
Breili
et
al.
(2010)
established
an
AG
reference
frame
for
Norway
including
16
gravity
sites.
Since
then,
it
has
been
extended
to
include
21
sites,
as
shown
in
Fig.
1
and
Table
1.
Gravity
sites
marked
in
blue
have
been
observed
more
than
once,
thus
only
VEGA
is
excluded
from
the
set
of
candidates
for
trend
computation.
There
exist
single
observations
at
a
few
other
sites,
but
these
are
less
likely
to
be
revisited
and
are
therefore
not
considered
in
our
work.
The
observation
time
spans
are
5
years
or
longer
for
18
of
the
21
sites
(Table
1).
Unfortunately,
some
gravity
sites
show
uneven
obser-
vation
distributions,
with
typically
larger
gaps
between
initial
and
later
observations.
Thus
we
interpret
Eq.
(1)
as
a
best-case
scenario
for
our
data
sets.
The
present
crustal
movements
of
Fennoscandia
are
largely
due
to
the
viscoelastic
process
of
GIA
(or
postglacial
rebound),
which
has
been
monitored
by
geodetic
techniques
(e.g.,
Milne
et
al.,
2001;
Lidberg
et
al.,
2010;
Kierulf
et
al.,
2014;
Steffen
and
Wu,
2011).
The
GIA
pattern
of
Fennoscandia
is
shown
in
Fig.
1.
This
work
presents
results
from
two
decades
of
AG
observations
in
Norway,
and
an
attempt
is
made
to
derive
empirical
secular
grav-
ity
trends
based
on
these
data.
Our
main
goal
is
to
explore
to
what
extent
the
gravity
trends
are
applicable
for
GIA
studies.
A
prerequi-
site
for
this
goal
is
a
homogenization
of
the
gravity
trends
through
a
consistent
analysis
of
the
AG
data.
This
is
done
by
investigating
to
what
extent
the
gravity
trends
reflect
GIA
or
other
geophysical
processes.
Ideally,
careful
reduction
of
other
geophysical
processes
will
ultimately
give
the
pure
GIA
signal.
Therefore,
we
compute
refined
ocean
loading,
atmospheric,
and
global
hydrological
effects
on
gravity,
and
explore
how
these
affect
the
trends.
Finally,
the
rela-
tion
between
gravity
and
height
rates
of
change
is
investigated.
The
presented
gravity
values
serve
as
a
Norwegian
contribution
to
the
Fennoscandian
AG
project
of
the
Working
Group
on
Geodynamics
of
the
NKG,
which
aims
to
combine
all
Fennoscandian
AG
data
in
a
joint
analysis
on
postglacial
gravity
change
for
the
region.
Section
2
covers
fundamentals
of
the
AG
processing
scheme,
where
Sections
2.1
and
2.2
concern
the
refined
modeling
of
ocean,
atmospheric
and
hydrological
effects
on
gravity.
Secular
gravity
trends
are
computed
in
Section
3,
and
a
subset
of
reliable
trends
are
used
for
determining
ratios
between
the
rates
of
change
of
gravity
and
height.
Results
are
discussed
in
Section
4,
while
Section
5
con-
cludes
the
work
with
recommendations
for
future
AG
observations
in
Norway.
2.
Processing
absolute
gravity
All
AG
observations
in
this
work
were
made
with
the
FG5
(Niebauer
et
al.,
1995)
absolute
gravimeter,
which
has
an
accu-
racy
of
1–2
Gal.
It
is
ballistic,
i.e.,
it
applies
the
free-fall
principle,
where
a
test
mass
is
dropped
in
vacuum.
A
laser
interferometer
and
atomic
clock
are
used
to
obtain
time-distance
pairs,
and
New-
ton’s
equations
of
motion
are
solved
to
obtain
the
acceleration.
A
typical
observation
campaign
lasts
1–2
days,
including
several
hourly
gravity
sets
where
a
set
consists
of
50-100
drops
of
the
test
mass.
With
few
exceptions,
we
have
used
observations
made
dur-
ing
the
same
season
(between
May
and
September),
so
as
to
reduce
seasonal
effects
(e.g.,
the
influence
of
surface
snow
cover
during
winter).
To
minimize
computational
biases,
we
have
adopted
a
com-
mon
processing
scheme
for
the
data
analysis,
ensuring
consistency
with
respect
to
model
and
setup
parameters.
All
raw
gravity
obser-
vations
have
been
reprocessed
using
the
g9
software
(Micro-g
LaCoste,
2012),
developed
by
Micro-g
LaCoste
and
bundled
with
the
instrument.
Vertical
transfer
of
the
measured
gravity
value
is
done
using
the
vertical
gravity
gradient,
which
has
been
determined
at
each
gravity
site
using
the
LaCoste
&
Romberg
G-761
relative
gravimeter,
see
Table
1.
All
AG
observations
in
this
work
are
given
at
a
reference
height
of
120
cm,
close
to
a
point
where
the
influence
of
the
gradient
uncertainty
on
the
FG5
is
almost
zero
(Timmen,
2010).
The
most
important
time-variable
components
of
the
raw
grav-
ity
value
are
reduced
in
the
software
by
various
models,
i.e.,
variations
due
to
solid
Earth
and
ocean
tides,
polar
motion,
ocean
loading,
and
atmospheric
mass
(Timmen,
2010).
The
atmospheric
correction
is
determined
by
observed
barometric
pressure
during
the
observations,
which
was
done
at
all
sites
except
Hammerfest
in
2006.488,
where
the
barometer
failed,
and
pressure
observa-
tions
transferred
from
a
nearby
weather
station
were
used
instead
(Breili
et
al.,
2010).
Corrections
for
polar
motion
were
computed
using
final
polar
coordinates
from
the
International
Earth
Rotation
and
Reference
Systems
Service
(IERS),
at
http://datacenter.iers.org.
The
bulk
of
observations
presented
here
were
made
with
the
FG5-226
AG
meter
of
the
Norwegian
University
of
Life
Sciences
(NMBU).
The
rubidium
(Rb)
frequency
standard
of
the
FG5-226
has
been
calibrated
(i.e.,
compared
with
a
stable
reference
signal)
at
convenience
since
its
acquisition
in
April
2004,
and
on
a
reg-
ular
basis
using
a
portable
Rb
reference
since
the
oscillator
was
replaced
in
May
2007.
We
have
observed
it
to
vary
within
a
range
of
0.02
Hz
(where
0.01
Hz
roughly
corresponds
to
2
Gal).
While
Gitlein
(2009)
reports
a
linear
drift
of
the
FG5-220
Rb
frequency,
the
FG5-226
Rb
frequency
development
is
non-linear,
see
Fig.
2.
A
stable
frequency
was
observed
with
the
original
oscillator,
while
the
frequency
changed
by
∼−0.005
Hz
during
the
first
year
after
its
replacement.
Then
it
was
stable
within
0.002
Hz
until
a
large
V.
Ophaug
et
al.
/
Journal
of
Geodynamics
102
(2016)
83–94
85
Table
1
Absolute
gravity
sites
in
Norway,
gravity
gradients,
and
observation
spans.
Site
Code
ϕ
()
()
H
(m)
g/Ha(Gal
cm1)
tgb(yrs)
ngc
Andøya
ANDO
69.278
16.009
370
4.04
±
0.01
6.0
5
Bodø
Asylhaugen BODB
67.288
14.434
68
3.31
±
0.01
4.0
4
Bodø
Bankgata
BODA
67.280
14.395
13
2.64
±
0.02
5.1
4
Hammerfest
HAMM
70.662
23.676
17
3.14
±
0.01
4.0
2
Honningsvåg
HONN
70.977
25.965
20
3.54
±
0.01
4.9
5
Hønefoss
AA
HONA
60.124
10.364
108
2.23
±
0.04
16.7
2
Hønefoss
AB
HONB
60.167
10.389
604
3.11
±
0.02
16.7
4
Hønefoss
AC HONC
60.143
10.250
120
2.80
±
0.02
15.9
12
Jondal
2 JON2
60.286
6.246
52
2.53
±
0.03
9.0
2
Kautokeino
KAUT
69.022
23.020
388
3.08
±
0.01
4.9
5
Kollsnes
1
KOL1
60.559
4.836
10
2.67
±
0.01
7.7
2
Kollsnes
2
KOL2
60.557
4.828
3
2.80
±
0.02
7.7
2
Stavanger
AA
STVA
59.018
5.599
55
2.86
±
0.08
15.2
7
Tromsø
TROM
69.663
18.940
103
3.34
±
0.01 15.9
8
Trondheim
AA
TRDA
63.455
10.446
27
2.95
±
0.01
14.8
10
Trysil
AB
TRYB
61.423
12.381
693
3.85
±
0.01
16.8
7
Trysil
AC
TRYC
61.423
12.381
693
3.85
±
0.01
18.0
17
Vågstranda
AA VAGA
62.613
7.275
38
3.03
±
0.01
7.2
4
Vega
VEGA
65.673
11.964
12
3.44
±
0.01
1
˚
Alesund ALES
62.476
6.199
145
2.90
±
0.01
7.0
5
˚
As
NMBU
NMBU
59.666
10.778
95
2.94
±
0.01
9.9
10
aDetermined
by
repeated
observations
of
the
gravity
difference
between
the
floor
marker
and
1.4
m
above
it.
bNumber
of
years.
cNumber
of
campaigns.
Fig.
2.
Calibration
of
the
FG5-226
Rb
oscillator.
The
vertical
bar
denotes
the
oscillator
replacement
(May
2007).
frequency
offset
of
0.02
Hz
was
observed
during
the
2013
cam-
paign
in
Ny- ˚
Alesund
in
Svalbard.
This
large
offset
was
due
to
a
helium
leakage
from
the
co-located
superconducting
gravimeter
which
penetrated
the
Rb
cell.
Subsequent
frequency
calibrations
indicate
that
it
has
slowly
returned
to
the
level
prior
to
the
helium
contamination.
Mäkinen
et
al.
(2015)
discuss
the
effect
of
helium
contamination
on
Rb
frequency
references,
and
underline
that
large
offsets
are
unproblematic
as
long
as
they
are
known
and
corrected
for.
For
every
observation
epoch
we
have
chosen
to
use
the
cali-
brated
frequency
value
closest
in
time.
We
have
also
used
AG
observations
performed
by
other
agen-
cies
and
instruments,
see
Table
2.
Raw
observations
by
LM
at
TRYB,
TRYC
and
VAGA
in
2007
have
been
reprocessed
using
the
above
procedure.
Observations
by
IfE
and
BKG,
reported
in
Gitlein
(2009),
are
given
at
120
cm
and
125
cm
reference
heights,
respectively.
Remaining
observations
by
NOAA
and
BKG,
reported
in
Roland
(1998),
are
given
at
a
reference
height
of
100
cm.
When
needed,
the
observations
were
transferred
to
the
120
cm
reference
height
in
two
steps.
First,
the
original
gradient
value
was
used
to
transfer
gravity
from
the
original
reference
height
(100
or
125
cm)
to
the
actual
measurement
height.
In
turn,
the
new
gravity
gradients
pre-
sented
in
this
work
(Table
1)
were
used
to
transfer
gravity
from
the
actual
measurement
height
to
the
new
reference
height
of
120
cm.
The
total
uncertainty
of
an
observed
gravity
value
is
composed
of
the
gravity
measurement
precision
g,
system
errors
SYS,
setup
error
SETUP,
and
vertical
transfer
(gradient)
error
g/H(Niebauer
et
al.,
1995).
SYS includes
(i)
instrumental
errors
(laser,
clock,
sys-
tem
model)
and
(ii)
modeling
errors
(barometer,
polar
motion,
Earth
tide,
ocean
loading).
Using
formal
error
propagation
and
thereby
assuming
the
error
terms
are
uncorrelated,
the
total
uncer-
tainty
tot is
given
by
tot =2
g+
2
SYS +
2
SETUP +g/H×
HTRANS2,
(2)
where
HTRANS is
the
difference
between
actual
measurement
height
(top
of
the
drop)
and
reference
height.
The
measurement
precision
gis
the
standard
deviation
of
the
mean
of
all
sets,
i.e.,
the
set
to
set
scatter
SET divided
by
the
square
root
of
the
number
of
sets.
We
take
SYS
1.6
Gal
as
given
in
g9
by
the
manufacturer.
Instead
of
the
SETUP =
1.0
Gal
estimate
suggested
in
g9,
however,
we
adopt
the
more
conservative
SETUP =
1.6
Gal
estimate
of
Van
Camp
et
al.
(2005).
We
investigated
the
stability
of
the
FG5-226
by
checking
for
time-variable
instrument
offsets,
trends
or
drift.
Fig.
3
shows
the
gravity
time
series
using
all
sufficiently
long
FG5-226
gravity
cam-
paigns
at
its
home
site,
NMBU.
The
mean
gravity
value
has
been
subtracted
from
each
observation,
and
the
observations
have
been
corrected
for
GIA
using
a
recent
modeled
linear
rate
of
change
in
gravity, ˙
gM,
as
described
in
Section
3.
We
observe
the
remaining
secular
gravity
trend
to
be
0.0
±
0.1
Gal
yr1and
insignificant.
A
similar
conclusion
can
be
drawn
from
Fig.
4,
which
shows
the
grav-
ity
time
series
using
FG5-226
observations
at
all
gravity
sites
where
more
than
one
observation
is
available.
Here,
the
mean
gravity
value
of
each
site
has
been
removed
from
GIA-corrected
site
obser-
vations,
giving
several
time
series
which
are
ultimately
plotted
in
the
same
figure.
Again
we
observe
an
insignificant
remaining
grav-
ity
trend
of
0.1
±
0.4
Gal
yr1.
Furthermore,
we
do
not
observe
any
nonlinear
structure
in
neither
Fig.
3
nor
Fig.
4.
We
therefore
con-
clude
that
the
FG5-226
has
no
significant
drift,
which
suggests
it
has
been
stable
throughout
the
observation
span
of
this
work.
86
V.
Ophaug
et
al.
/
Journal
of
Geodynamics
102
(2016)
83–94
Table
2
FG5-generation
of
absolute
gravimeters
used
in
Norway
1993–2014.
Instrument
Agency
Reference
FG5-226
(2004–2014)
Norwegian
University
of
Life
Sciences
(NMBU), ˚
As,
Norway
This
work
FG5-233
(2007)
Lantmäteriet
(LM),
Gävle,
Sweden
FG5-220
(2003–2007) Institut
für
Erdmessung
(IfE),
Leibniz
Universität
Hannover,
Germany
(Roland,
1998)
FG5-101
(1993–1998),
FG5-301
(2003)
Bundesamt
für
Kartographie
und
Geodäsie
(BKG),
Frankfurt,
Germany
(Gitlein,
2009)
FG5-102
(1993),
FG5-111
(1995,
1997)
National
Oceanic
and
Atmospheric
Administration
(NOAA),
Silver
Spring,
Maryland,
USA
G.
Sasagawa,
personal
communication,
2005
Fig.
3.
Stability
of
the
FG5-226
AG
meter
for
the
2004–2015
period,
as
derived
from
all
repeated
gravity
observations
at
NMBU.
The
gravity
time
series
is
reduced
for
the
site-specific
mean
value
and
GIA
trend,
thus
showing
residual
temporal
variations
including
instrumental
drift
only.
Standard
g9
gravity
estimates
g0and
uncertainties
are
shown
in
the
supplementary
data
Table
S1.
2.1.
Ocean
loading
effects
The
majority
of
the
AG
sites
in
Norway
are
located
within
2
km
of
the
coast
(see
Fig.
1).
It
has
been
previously
shown
that
these
stations
may
be
strongly
influenced
by
ocean
tide
loading
(OTL)
(e.g.,
Lysaker
et
al.,
2008;
Breili,
2009;
Breili
et
al.,
2010).
In
addition,
non-tidal
variation
of
sea
level
due
to
low
barometric
pressure
and
strong
winds
may
affect
gravity
(Olsson
et
al.,
2009).
OTL
and
non-tidal
loading
(NTL)
have
different
characteristics.
Along
the
Norwegian
coast,
OTL
may
introduce
deterministic
semi-
diurnal
patterns
with
amplitudes
of
several
Gal
in
time
series
of
gravity
(Lysaker
et
al.,
2008).
As
a
result,
the
variation
of
the
set
to
set
scatter
of
a
gravity
campaign
may
increase
if
appropriate
OTL
corrections
are
not
applied.
Furthermore,
the
campaign
averages
and
derived
secular
trends
may
be
biased
(Timmen
et
al.,
2015).
This
is
particularly
relevant
for
short
campaigns
not
covering
an
integer
multiple
of
the
dominating
tidal
periods.
NTL,
on
the
other
hand,
is
non-deterministic
and
non-periodic;
hence,
corrections
must
be
computed
from
observations.
As
NTL
may
be
close
to
con-
stant
during
a
campaign,
its
impact
on
gravity
is
difficult
to
infer
from
inspection
of
the
set
to
set
scatter
alone.
In
the
following
we
investigate
different
OTL
corrections
and
identify
OTL
models
that
are
most
successful
in
reducing
the
cam-
paign
set
to
set
scatter
(SET).
In
general,
OTL
corrections
are
easily
computed
from
pre-
determined
amplitude
and
phase
coefficients
for
sinusoids
with
frequencies
matching
the
major
tidal
constituents
(Petit
and
Fig.
4.
Stability
of
the
FG5-226
AG
meter
for
the
2005–2014
period,
as
derived
from
repeated
gravity
observations
at
20
different
sites.
The
gravity
time
series
of
each
station
is
reduced
for
the
site-specific
mean
value
and
GIA
trend,
thus
showing
residual
temporal
variations
including
instrumental
drift
only.
Luzum,
2010,
Ch.
7).
The
coefficients
are
computed
by
convolving
global
ocean
tide
(GOT)
models
with
Green’s
functions
formed
by
load
Love
numbers
(Farrell,
1972),
and
are
available
through
M.S.
Bos
and
H.-G.
Scherneck’s
Ocean
tide
loading
provider
at
http://
holt.oso.chalmers.se/loading/.
This
procedure
is
also
implemented
in
g9,
and
for
our
standard
gravity
estimates
(g0,
see
Table
S1),
OTL
was
computed
with
the
FES2004
GOT
model
(Lyard
et
al.,
2006),
with
the
exception
of
KAUT
and
TRYB/TRYC,
where
no
OTL
effect
was
computed
due
to
their
inland
locations.
An
important
difference
between
g9
and
the
OTL
provider
is
that
the
latter
refines
the
spatial
resolution
of
the
GOT
model
gradually
towards
the
observation
point
and
checks
whether
new
GOT
cells
are
located
on
land
or
sea
(Penna
et
al.,
2008).
g9
also
refines
the
GOT
model
towards
the
observation
point,
but
does
no
land/sea
check
of
the
new
cells
(O.
Francis,
personal
communication,
2016).
With
coefficients
from
the
OTL
provider
we
have
explored
a
suite
of
GOT
models,
i.e.,
FES2004,
CSR4.0
(Eanes,
1994),
DTU10
(Cheng
and
Andersen,
2010),
EOT11
(Savcenko
and
Bosch,
2011),
GOT4.8
(Ray,
1999),
NAO99b
(Matsumoto
et
al.,
2000),
OSU12
(Fok
et
al.,
2012),
Schwiderski
(Schwiderski,
1980),
and
TPXO7.2
(Egbert
and
Erofeeva,
2002).
These
models
were
chosen
as
they
represent
the
latest
release
from
each
group
available
at
the
OTL
provider.
Lysaker
et
al.
(2008)
showed
that
careful
local
modeling
of
the
OTL
correction
(direct
Newtonian
and
displacement
of
the
observ-
ing
point
due
to
load)
corresponded
better
with
the
OTL
signal
at
selected
high-latitude
coastal
stations
in
Norway
than
did
the
effect
computed
from
GOT
models.
Thus
for
FES2012
(produced
by
Nov-
eltis,
Legos,
and
CLS
Space
Oceanography
Division
and
distributed
V.
Ophaug
et
al.
/
Journal
of
Geodynamics
102
(2016)
83–94
87
Table
3
The
gravitational
and
loading
effects
of
a
one-meter
sea-level
anomaly
within
10
km
of
coastal
gravity
sites
in
Norway,
and
the
amplitude
of
the
M2
tidal
constituent
for
the
attraction
component.
All
in
Gal.
Code
Gravitation
due
to
a
1
m
sea-level
anomaly
Loading
due
to
a
1
m
sea-level
anomaly
Amplitude
of
M2
(attraction
only)
ANDO
3.4
0.20
3.7
BODB
0.6
0.22
1.1
BODA
0.3
0.25
0.8
HAMM
3.1
0.13
3.0
HONN
6.4
0.28
5.9
JON2
4.8
0.16
1.5
KOL1
0.3
0.29
0.1
KOL2
0.5
0.30
0.2
STVA
1.5
0.26
0.2
TROM
1.4
0.14
1.6
TRDA
2.6
0.27
2.1
VAGA
4.2
0.21
3.2
VEGA
0.1
0.17
0.6
ALES
9.8
0.26
6.9
by
Aviso,
with
support
from
CNES,
at
http://www.aviso.altimetry.
fr)
as
well
as
NAO99b,
we
investigate
OTL
corrections
as
computed
by
an
in-house
software.
The
routines
closely
follow
methods
used
by
the
OTL
provider,
although
with
two
important
distinctions.
First,
we
have
used
a
higher-resolution
coastline
provided
by
the
Norwegian
Mapping
Authority
(NMA),
with
a
level
of
detail
corresponding
to
national
maps
in
scale
1:50,000,
and
termed
the
N50
coastline
hereafter.
It
is
complete
and
includes
all
islands
and
reefs
along
the
Norwegian
coast
with
an
area
greater
than
20,000
m2.
Second,
our
software
allows
for
choosing
which
regions
are
to
be
included
in
the
convolution.
We
have
used
this
function-
ality
to
investigate
the
effect
of
replacing
the
GOT
model
with
predicted
tides
based
on
tide-gauge
observations
when
comput-
ing
the
attraction
from
the
tides
in
the
local
zone.
The
local
zone
is
here
defined
as
the
area
within
10
km
of
the
gravity
site.
The
method
is
a
development
of
the
one
demonstrated
by
Lysaker
et
al.
(2008).
By
this
approach
the
gravitational
effect
of
the
local
tides
was
modeled
by
(i)
dividing
the
local
zone
into
spherical
sectors,
(ii)
assigning
to
each
sector
a
uniform
layer
of
water
correspond-
ing
to
sea
level
as
observed
by
a
local
tide
gauge,
(iii)
computing
the
attraction
from
each
sector,
(iv)
eliminating
sectors
on
land,
and
(v)
add
together
the
contributions
from
the
individual
ocean
sectors.
The
size
of
the
spherical
sectors
was
adjusted
depending
on
the
distance
from
the
observation
point,
i.e.,
the
length
of
the
outer
arc
was
set
to
25,
50,
and
200
m
in
the
zones
0–500,
500–1000,
and
1000–10,000
m
from
the
observation
point,
respectively.
Each
sec-
tor
was
classified
as
land
or
ocean
by
comparing
the
sector
midpoint
coordinates
with
the
N50
coastline.
In
this
work,
NTL
is
the
combined
effect
of
gravitational
attrac-
tion
and
loading
of
the
seabed
due
to
non-tidal
variations
in
sea
level.
The
gravitational
attraction
component
was
modeled
by
the
above
procedure,
using
spherical
sectors
with
a
water
thickness
equal
to
the
difference
between
actual
and
predicted
sea
level
as
observed
by
a
local
tide
gauge.
For
the
loading
components,
we
assumed
that
sea
level
responds
like
an
inverted
barometer
(IB,
static
atmospheric
loading
effect).
This
implies
that
sea
level
vari-
ation
due
to
changing
atmospheric
pressure
does
not
induce
any
loading
on
the
sea
floor.
Thus,
before
computing
the
loading
effect,
observed
sea
level
was
corrected
for
the
IB
effect
using
Wunsch
and
Stammer
(1997,
Eq.
(1)).
We
have
computed
refined
OTL
and
NTL
corrections
at
14
coastal
gravity
sites
in
Norway
(Table
3),
with
remaining
sites
excluded
due
to
their
inland
locations.
The
gravitational
and
loading
effects
of
a
one-meter
sea-level
anomaly
at
the
coastal
gravity
sites
is
shown
in
Table
3,
where
the
actual
gravitational
effect
may
be
found
by
scaling
the
one-meter
effect
with
the
actual
sea-level
anomaly.
We
have
used
tide-gauge
records
from
the
NMA
database,
with
a
sampling
rate
of
10
minutes
and
all
observations
referring
to
present
mean
sea
level
(1996-2014
inclusive).
Unfortunately,
there
are
no
tide
gauges
within
the
local
zones
of
JON2,
KOL1,
KOL2,
VEGA,
and
VAGA.
For
these
sites,
sea
level
was
derived
by
applying
site-specific
scale
factors
and
time
delays
to
observations
from
the
nearest
tide
gauge.
The
scale
factors
and
time
delays
were
obtained
from
the
tide
and
sea-level
web
service
of
the
NMA
at
http://www.
kartverket.no/en/sehavniva/.
For
each
gravity
site,
we
identify
the
ocean
loading
corrections
that
reduce
SET as
much
as
possible,
combining
all
OTL
and
NTL
corrections.
Table
4
shows
the
average
percentage
reduction
in
SET
for
each
site.
We
note
that
STVA
and
JON2
stand
out
with
low
reduc-
tions.
For
STVA,
this
is
due
to
a
weak
OTL
signal
related
to
a
M2
amphidromic
point
in
the
North
Sea,
giving
a
locally
low
tidal
range
(0.32
m
between
mean
high
and
mean
low
tide).
At
JON2
the
aver-
age
is
strongly
influenced
by
the
2005.482
campaign,
which
has
a
low
SET of
1.2
Gal.
When
applied
to
this
campaign,
SET increases
for
several
OTL
corrections,
resulting
in
a
negative
reduction
of
SET.
With
few
exceptions,
the
OTL
corrections
computed
by
g9
reduce
SET less
than
the
corrections
computed
by
the
OTL
provider
or
the
in-house
software.
This
also
holds
for
FES2004
as
used
by
both
g9
and
the
OTL
provider.
Table
4
suggests
that
N50
improves
the
fit
between
obser-
vations
and
models
at
several
sites
(e.g.,
NAO99b(N50)
com-
pared
with
NAO99b(OTLP),
and
FES2012(N50)
compared
with
FES2004(OTLP)).
Largest
improvements
are
found
at
HONN
and
HAMM
for
NAO99b
and
FES2012,
and
at
TRDA
and
VAGA
for
NAO99b.
For
these
combinations,
the
N50
coastline
reduces
SET by
7.5%
to
22.5%.
We
expect
coastline
accuracy
to
have
largest
influ-
ence
on
gravity
sites
that
are
in
immediate
vicinity
of
the
ocean.
Indeed
the
sites
showing
the
largest
improvements
are
also
among
those
closest
to
the
ocean,
e.g.,
HAMM
and
HONN
(75
m).
For
most
stations
we
observe
further
improvement
when
the
N50
coastline
is
combined
with
local
tide-gauge
observations.
The
change
in
reduced
SET ranges
from
0.5%
to
3.7%
for
NAO99b,
and
from
0%
to
21.3%
for
FES2012.
Both
TRDA
and
JON2
are
located
inside
fjords.
Comparing
NAO99b
and
FES2012
at
these
sites,
the
largest
effect
of
introducing
tide-gauge
observations
is
seen
for
the
latter,
suggesting
that
FES2012
does
not
capture
the
tidal
regime
in
these
fjords.
Choosing
a
best-performing
model
is
challenging,
as
their
per-
formance
depends
on
the
gravity
site.
Considering
all
models,
NAO99b
and
FES2012
in
combination
with
the
N50
coastline
per-
form
best
at
9
out
of
14
sites.
Corrections
from
the
OTL
provider
give
the
best
results
at
BODA,
VEGA,
KOL1,
JON2,
and
STVA,
where
all
sites
but
JON2
have
in
com-
mon
that
the
M2
amplitude
of
the
attraction
component
is
less
than
1
Gal
(see
Table
3).
This
suggests
that
careful
modeling
of
the
local
zone
is
important
mainly
at
sites
with
a
strong
attraction
component.
Table
S1
shows
the
final
ocean
loading
corrections
for
all
coastal
gravity
campaigns,
together
with
standard
and
refined
set
to
set
scatters
and
the
chosen
ocean
loading
model.
As
the
standard
grav-
ity
estimates
from
g9,
g0,
have
already
been
corrected
for
OTL
(g0
OTL),
we
present
the
change
in
OTL
correction,
i.e.,
ıgOTL =
gOTL
g0
OTL,
to
ease
the
application
of
the
refined
OTL
correc-
tion
gOTL.
NTL
is
not
treated
in
g9;
hence,
the
complete
correction
is
listed
as
gNTL.
Typically,
OTL
and
NTL
contribute
to
a
campaign
gravity
value
by
a
few
tenths
of
a
Gal,
although
some
corrections
reach
2
Gal.
The
refined
OTL
correction
ranges
from
0.55
Gal
(STVA
2006.855)
to
1.81
Gal
(ALES
2006.384),
while
the
new
NTL
88
V.
Ophaug
et
al.</