1 Approximate decorrelation and non- isotropic smoothing of time-variable GRACE gravity field models J ü rgen Kusche , Roland Schmidt with input from Susanna Werth, Roelof Rietbroek GFZ Potsdam IUGG 2007, Perugia, GS002
Dec 30, 2015
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Approximate decorrelation and non-isotropic smoothing of time-variable
GRACE gravity field models
Jürgen Kusche, Roland Schmidt
with input fromSusanna Werth, Roelof Rietbroek
GFZ Potsdam
IUGG 2007, Perugia, GS002
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Outline of the talk
• GRACE fields exhibit artefacts (“stripes”) which may be seen as a realization of spatially correlated noise - smoothing and/or “de-striping” is required
• Theory: Discussion of ways to decorrelate (“de-stripe”) the noise in GRACE solutions (including method from Swenson-Wahr 2006 (SW06) and a new method)
• Theory: The scaling (bias) problem
• Results: De-striped GFZ GRACE RL4 fields, surface mass grids, and a time series of basin-averaged GRACE-derived OBP ( talk in JGS001)
• Conclusions
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Stripes in GRACE solutions
NS-oriented artefacts
gravity field determination =ill-posed problem
Stochastic (noise) and deterministic (background model) errors cause unphysical oscillations
RMS variability of 40 GFZ RL04 monthly solutions in
2/03-12/06 relative to their mean (7-10/04 and
12/06 excluded), Gaussian 550km
Surface Mass
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• degree-dependent (isotropic)• Gauss (Jekeli 1981, Wahr & al 1998), Gauss-Weierstrass (Freeden 1998), Hanning (Jekeli 1981), Blackman (Schmidt & al 2006), CuP (Fengler & al 2006)
• degree- and order-dependent• modified Gauss (Han 2005)• removing single coefficients based on hypothesis testing (Sasgen & al 2005)
• full non-isotropic (general two-point kernel)• constrained fields (Tikhonov)• empirical signal decorrelation combined with Gaussian (Swenson & Wahr 2006)• empirical error decorrelation and Tikhonov smoothing (Kusche 2007)
Issues • de-striping property• amplitude damping (bias) and phase lags• interpretability• optimality criteria, multiresolution properties
Filter Methods for GRACE-L2 Products
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• combine approximate error decorrelation and Tikhonov smoothing (Kusche 2007)• scaled dense synthetic, “smooth” normal matrix for 1 month• synthetic, smooth signal variance model from Hydrology + Ocean circulation• damping “on normal equation level”
This work
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LAT=60oCross-sections
N-S direction (o)
W-E direction (*)
Impulse response
Filter Properties
This work
LAT=0o
Distance from kernel center
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This work Swenson and Wahr (2006)
black circle = Gaussian 500km
Impulse response
Filter Properties
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• ratio between filtered and exact basin average
• depends on • filter• shape of basin• signal within and outside basin
All smoothed GRACE-based functionals, global maps or basin averages, are systematically biased low
Scaling (bias) problem
• damping of the global rms
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Relative bias from true and filtered signal, including hydrology
apparent phase lag
Scaling (bias) problem
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Relative bias from true and filtered signal, hydrology removed
400km: 56%
Scaling (bias) problem
year
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Comparison of filters based upon variance and standard scaling bias
Comparison Gaussian – This Work
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Gaussian Filter
RMS variability of 40 GFZ RL04 monthly solutions in 2/03-12/06 relative to their mean (7-10/04 and 12/06 excluded)
Further “de-striping” reduced amplitude (biased towards zero)
Left: Gaussian 500km, Right: Gaussian 550km
wrms=3.85cm
Surface MassGeoid
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Empirical signal decorrelation according to Swenson and Wahr
(2006)
Filter > l=10, Gaussian 400km
RMS variability of 40 GFZ RL04 monthlySolutions in 2/03-12/06 relative to theirMean (7-10/04 and 12/06 excluded)
wrms=3.76cm
Decorrelation – Swenson and Wahr 2006
Surface Mass
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RMS variability of 40 GFZ RL04 monthly solutions in2/03-12/06 relative to their mean (7-10/04 and 12/06 excluded)
Left and right: approx. decorrelated using 8/03 orbits and LaD+ECCOfor W-matrix (up to deg/ord = 70), a = 10E+14
wrms=3.83cm
Decorrelation – This Work
Surface MassGeoid
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BOTH are decorrelated/smoothed using the SAME operator, i.e.8/03 orbits and LaD+ECCO for W-matrix (up to deg/ord = 70), a = 10E+14
Approx. (GRACE) decorrelation does not distort hydrology model
wrms=3.85cmwrms=2.30cm
Decorrelation – This Work
Surface Mass – GRACESurface Mass - WGHM
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DFG-Mass Transport project STREMP See talk by L. Fenoglio et al in JSG001
Regional Averaging
GRACE “raw” time series of mass change over the Mediterraneanby different methods
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• Stripes in GRACE solutions still visible; although RL04 improvement over earlier releases
• Best strategy: remove during processing (but perfect de-aliasing impossible)
• Second-best strategy: post-processing using error correlation model (here: from an arbitrary GRACE- or GRACE-type orbit + a-priori model information)
• Proposed technique removed stripes much more effectively compared to Gaussian; simultaneously smoothing (“amplitude bias”) is comparable to Gaussian
• Use for mass transport studies (hydrology, ocean); higher resolution at comparable damping
Conclusions
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Decorrelation – This Work
Full W-matrixOrder/parity only
RMS variability of 40 GFZ RL04 monthly solutions in2/03-12/06 relative to their mean (7-10/04 and 12/06 excluded)
Approximately decorrelated using 8/03 orbits and LaD+ECCOfor W-matrix (up to deg/ord = 70), a = 10E+14
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Decorrelation – This Work
W-matrix based on syntheticnormals from orbit 8/03
W-matrix based on covariancematrix for 8/03 GFZ-RL04
RMS variability of 40 GFZ RL04 monthly solutions in
2/03-12/06 relative to their mean (7-10/04 and 12/06 excluded)
Apriori model information for W-matrix (70,70) from LaD+ECCO, a = 10E+14
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Filtering Regularization
eq.
interpretation
estimate of x estimate of x
reduces variance
yes yes
introduces bias
yes (“scaling factor”)
yes
alternative interpretatio
n
unbiased estimate of averaged x
no
required processing
L2 data L1 data (but…)
LSx̂Wx̂
LS
1T11T x̂WyA)RAA(x̂
Decorrelation – This Work
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Filtering Regularization
parameter tuning
S/N geophysical signals /GRACE
(Wiener/”optimal”)
S/N geophysical signals/ GRACE (LSC)
ordata-driven (GCV,VCE)
latitude-dependence
no (but…) automatically
anisotropic decorrelatio
nno (but…) automatically
geometric interpretatio
nyes no
Decorrelation – This Work