Geoscience Reference
In-Depth Information
degree LLN are required. Farrell (
1972
) suggest to compute the LLN values up to
degree
n
=
10000.
•
Land-sea mask
. For separation of the integration over land and the oceans, appro-
priate land-sea masks should be provided. Topography models can be used to
generate land-sea masks with various spatial resolutions.
Surface pressure data of the ECMWF or NCEP are known to contain signals
associated with the diurnal
S
1
(
atmospheric tides. Unfor-
tunately, the representation of these tides is significantly distorted owing to the sam-
pling interval of 6 hours of most numerical weather models. This particularly holds
for the
S
2
(
p
)
and semi-diurnal
S
2
(
p
)
tide (van den Dool et al.
1997
; Petrov and Boy
2004
), which is located
exactly at the Nyquist frequency of 2 cycles/day and, thus, cannot be modeled cor-
rectly. Ponte and Ray (
2002
) suggested to remove the diurnal and semi-diurnal tidal
power from the six-hourly atmospheric pressure fields and re-calculate them using
a harmonic model. This leads to the calculation of the displacement corrections in
three steps:
p
)
1. Calculate non-tidal loading displacements using pressure fields in which the tidal
signals have been removed (Sect.
2.1.1
).
2. Calculate tidal loading displacements using a gridded global model of pressure
tides (Sect.
2.1.2
).
3. Calculate total loading displacements by summing both non-tidal and tidal load-
ing displacements.
2.1.1 Non-Tidal Loading Displacements
Petrov and Boy (
2004
) removed the diurnal and semi-diurnal tidal power from the
six-hourly atmospheric pressure fields by subtracting gridpoint-wise sinusoids with
the frequencies 1 and 2 cycles/day, that were estimated from several years of six-
hourly surface pressure data. As amplitude and phase of sub-daily tidal variations
are only quasi-harmonic quantities and might change considerably over time, this
approach cannot account for the full
S
1
(
pressure variations. Moreover,
it also neglects the seasonal modulation of atmospheric tides, which is manifested in
spectral domain as small side lobes around themain frequencies of 1 and 2 cycles/day.
However, it has been shown that such an approach is appropriate for correcting APL
effects at globally distributed VLBI sites (Petrov and Boy
2004
). Most importantly,
it is well suited for the operational calculations because it can also be used for real-
time applications. An alternative method has been applied by Tregoning and van
Dam (
2005
), who convolved the plain pressure data and then employed a low-pass
filter on the time series of the displacements. Note that both approaches only aim at
removing the
S
1
(
p
)
and
S
2
(
p
)
tidal signals as they are contained in the six-hourly
data, regardless of whether their representation in the undersampled meteorological
data is accurate or not. Another possibility is the determination of a sinusoidal model
from three-hourly numerical weather model data which is then removed from the
surface pressure data.
p
)
and
S
2
(
p
)
