Geoscience Reference
In-Depth Information
slightly modified IB hypothesis. If there is a net increase or decrease in the mass
of air above the oceans, the seafloor experiences a uniform pressure
Δ
P
o
acting
everywhere on the ocean bottom surface:
ocean
[
r
,
r
)
]
ϑ
d
ϑ
d
λ
P
(
t
)
−
P
ref
(
cos
Δ
P
o
=
.
(8)
ϑ
ϑ
d
λ
cos
d
ocean
The IB model above is adequate to describe the sea height variations with periods
longer than 5-20 days but is not accurate enough for shorter periods. Wunsch and
Stammer (
2010
) showed that the (non-equilibrium) diurnal and sub-diurnal ocean
tides imply that the global oceanic response is certainly not an IB at shorter periods.
Following Petrov and Boy (
2004
), the integrals in Eqs. (
1
), (
2
) and (
3
), can be split
up into land and ocean contributions, thus an IB correction for the oceanic portion
can be applied:
+
Δ
P
o
ocean
r
,
r
)
]
U
r
(
r
,
t
)
=
[
P
(
t
)
−
P
ref
(
G
r
(ψ)
ds
G
r
(ψ)
ds
,
(9)
land
land
[
+
Δ
P
o
ocean
r
,
r
)
]
U
e
(
r
,
t
)
=
P
(
t
)
−
P
ref
(
G
h
(ψ)
sin
α
rr
ds
G
h
(ψ)
sin
α
rr
ds
,
(10)
land
[
+
Δ
P
o
ocean
r
,
r
)
]
U
n
(
r
,
t
)
=
P
(
t
)
−
P
ref
(
G
h
(ψ)
cos
α
rr
ds
G
h
(ψ)
cos
α
rr
ds
,
(11)
λ
.
In order to calculate the displacements using Eqs. (
9
)-(
11
), the following physical
information is required:
ϑ
d
ϑ
where
ds
=
cos
d
r
,
•
Global surface pressure
. The parameter
P
can be derived from data from
a Numerical Weather Model (NWM), e.g. from those of the European Centre
for Medium-range Weather Forecasts (ECMWF) and the National Centers for
Environmental Prediction (NCEP). Both centers provide the data every 3 or 6h
with various spatial resolutions.
(
t
)
r
)
•
Reference pressure
.
P
ref
(
can be determined by long-termaveraging of surface
pressure data. Schuh et al. (
2009
) thoroughly review various methods for the
definition of reference pressure for geodetic applications and they propose a new
method that is called the Global Reference Pressure (GRP) which is based on the
application of pressure level data instead.
•
Green's functions and Load Love Numbers
. The vertical and horizontal Green's
functions
(
G
r
(ψ)
and
G
h
(ψ))
are used as weighting factors for surface pressure
r
,
r
)
]
anomaly data
[
P
(
t
)
−
P
ref
(
. In the definition of the Green's functions, high
