Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models

By Jürgen Kusche. 2007

415 citations recorded by the source corpus.

We discuss a new method for approximately decorrelating and non-isotropically filtering the monthly gravity fields provided by the gravity recovery and climate experiment (GRACE) twin-satellite mission. The procedure is more efficient than conventional Gaussian-type isotropic filters in reducing stripes and spurious patterns, while retaining the signal magnitudes. One of the problems that users of GRACE level 2 monthly gravity field solutions fight is the effect of increasing noise in higher frequencies. Simply truncating the spherical harmonic solution at low degrees causes the loss of a significant portion of signal, which is not an option if one is interested in geophysical phenomena on a scale of few hundred to few thousand km. The common approach is to filter the published solutions, that is to convolve them with an isotropic kernel that allows an interpretation as smoothed averaging. The downside of this approach is an amplitude bias and the fact that it neither accounts for the variable data density that increases towards the poles where the orbits converge nor for the anisotropic error correlation structure that the solutions exhibit. Here a relatively simple regularization procedure will be outlined, which allows one to take the latter two effects into account, on the basis of published level 2 products. This leads to a series of approximate decorrelation transformations applied to the monthly solutions, which enable a successive smoothing to reduce the noise in the higher frequencies. This smoothing effect may be used to generate solutions that behave, on average over all possible directions, very close to Gaussian-type filtered ones. The localizing and smoothing properties of our non-isotropic kernels are compared with Gaussian kernels in terms of the kernel variance and the resulting amplitude bias for a standard signal. Examples involving real GRACE level 2 fields as well as geophysical models are used to demonstrate the techniques. With the new method, we find that the characteristic striping pattern in the GRACE solutions are much more reduced than Gaussian-filtered solutions of comparable signal amplitude and root mean square.

Subfields: Astronomy and Astrophysics, Molecular Biology, Oceanography

View Paper: https://www.semanticscholar.org/paper/0be3173209808e527cdc67e81580a60a534c32bc

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Citations in the corpus

On the postprocessing removal of correlated errors in GRACE temporal gravity field solutions (2009, methodology): “Kusche (2007) turned out to be a simplified case of Klees et al. (2008).”
Thin plate spline interpolation (2019, methodology): “…of a region S0 of the surface of the Earth and a thin plate spline interpolation from the boundary, where the data is given, to the interior was carried out and the result is compared to the global Gaussian smoothed standard solution and to the global application of the Kusche filter (Kusche 2007).”
Deriving daily snapshots of the Earth's gravity field from GRACE L1B data using Kalman filtering (2009, methodology): “Therefore, to both GFZ-RL04 solutions a non-isotropic decorrelation filter (DDK) [see Kusche, 2007] was applied.”
Antarctica, Greenland and Gulf of Alaska land-ice evolution from an iterated GRACE global mascon solution (2013, methodology): “…ŝk ¼ ATWA 1 ATr ŝkþ1¼ ~sk þ ŝk h̃kþ1¼ P 1hh LT ATWA 1þLP 1hh LTh i 1 ŝkþ1: 8>>>< >>>: ð9Þ This is now in the form of an anisotropic, non-symmetric (ANS) filter (Kusche, 2007) that acts upon an unfiltered Stokes state, ŝkþ1, to produce a filtered Stokes state, ~skþ1, ~skþ1 ¼ P 1ss N 1 þ P…”
Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model (2009, methodology): “In the Kusche (2007) method, the GRACE error covariance matrix used in the construction of the decorrelating kernel is created synthetically, using one month of GRACE twinspacecraft orbits and a simplified method for mapping the K-band inter-satellite ranging observations into the spherical harmonic”
The design of an optimal filter for monthly GRACE gravity models (2008, background): “They may be taken from the multiinstitutional Estimating the Circulation and Climate of the Ocean (ECCO) project (Fukumori et al. 2000), the Global Land Data Assimilation System (GLDAS) (Rodell et al. 2004), or the Land Dynamics (LaD) model (Milly & Shmakin 2002) to name a few.”
What Can be Expected from the GRACE-FO Laser Ranging Interferometer for Earth Science Applications? (2016, neutral): “1998), the so-called DDK filtering (Kusche 2007), or the destriping method by Swenson and Wahr (2006).”