Geoscience Reference
In-Depth Information
The coefficients of zero and first degree are set to zero due to the choice of the
coordinate system. GRACE is insensitive to degree-one coefficients (geocenter).
Estimates of C
20
(oblateness) coefficients from GRACE are not very reliable; they
were replaced by SLR-derived solutions. Since we are interested in the monthly
changes, the averaged field over 10 years was subtracted from the GRACE monthly
Stokes coefficients. GIA
1
correction was also applied according to Paulson et al.
(
2007
) model. Finally, the results were converted to the surface mass changes in
terms of equivalent water height (EWH) level (cm), according to Wahr et al. (
1998
)
X
60
X
n
2n
C
1
1
C
k
n
2ap
ave
3p
w
h.';;t/
D
W
n
.C
nm
.t/ cosm
n
D
2
m
D
0
C
S
nm
.t/ sin m/P
n
.sin '/;
(3.2)
here C
nm
.t/, S
nm
.t/ are normalized Stokes coefficient differences with respect
to the mean (model); p
ave
and p
w
are average densities of the Earth and seawater,
respectively; k
n
is the load Love number of degree n;andW
n
is a filter coefficient.
All spectral filter coefficients in Eq. (
3.2
) were set to one, so we did not apply any
filtering except MSSA.
3.2.2
Multichannel Singular Spectrum Analysis Method
Filtering of GRACE data is needed, because they contain meridional error - stripes.
Such errors are primarily due to the fact that GRACE satellites are in the same polar
orbit and satellite-to-satellite tracking only observes along-track direction, causing
the gravity field inversion problem to be near singular.
The orbital and instrument errors are correlated in the resonant orders of the
spherical harmonic Stokes coefficients, causing the so-called stripes high-spatial-
frequency errors. An unfiltered map, obtained as the difference between January
2003 and January 2013 initial data, is shown in Fig.
3.1
.
Different authors use a variety of filtering methods to minimize stripes and
reduce noises in the GRACE monthly gravity field solutions. Among them are
Gaussian filtering with symmetric and asymmetric Gaussian function (Han et al.
2005
), Wiener (Klees et al.
2007
) and regularizing (Kusche et al.
2009
) filters,
whose coefficients depend on degree and order, and de-striping/smoothing (Duan
et al.
2009
; Guo et al.
2010
; Swenson and Wahr
2006
) filters, operating to remove
the anomalously large values from the resonant orders of the Stokes coefficients.
1
Glacial isostatic adjustment (GIA), related to the restoration of isostatic equilibrium, is especially
large in Canada and Scandinavia due to the release of massive ice sheets located there 20,000 years
ago.
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