Bert Wouters

1
Improved Accuracy of GRACE Solutions Through EOF
Filtering of Spherical Harmonics

• Bert Wouters Ejo Schrama
• Bert.Wouters_at_tudelft.nl
• DEOS TU Delft

GRACE Science Team Meeting
October 15-17, 2007
2
Overview
1st

• Basics of EOF theory
• Filter Method
• Results
• Modelled data
• Conclusions

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EOF decomposition

• Empirical Orthogonal Functions
• decomposition of a signal y(x,t) in orthogonal
  basis functions eigenvectors Ej(x) of data
  covariance matrix
• to each eigenvector Ej belongs a time mode aj(t)
• rebuild data by selected EOFs
• y(x,t)Saj(t). Ej(x)

See e.g. Preisendorfer (1989) Principal
Component analysis in Meteorology and oceanography
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EOF decomposition

• Applied successfully to maps of GRACE equivalent
  water height, e.g.
• Chambers (2006)
• Schrama et al. (2007)
• Rangelova et al. (2007)
• Apply EOF method directly to SH coefficients

1st
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Method overview
1st

• 54 GRACE solutions CSR RL04
• Series of Stokes coefficients Clm (t) and Slm (t)
  for fixed order m
• Apply EOF decomposition to the series
• Test principal component for temporal randomness
  Kolmogorov-Smirnov test
• Rebuild series of Stokes Clm (t) and Slm (t)
  coefficients using selected EOF modes

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EOF decomposition of order m0 series
1st
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Method Kolmogorov-Smirnov test
1st

• Test principal components aj(t) of EOF modes for
  temporal randomness Kolmogorov-Smirnov test
• Fourier transform to obtain power density
  spectrum
• Compare cumulative distribution function (CDF)
  with CDF of random distributed population
• Find maximum distance D between CDFs
• Reject EOF if D lt DKS2

m0
m44
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Method Kolmogorov-Smirnov test
1st
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Results
1st
500 km Gaussian
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Results
1st
350 km Gaussian
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Results
1st
0 km Gaussian
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Some statistics

• Remove annual and semi-annual signal
• RMS of residual is upper bound for GRACE errors
  (Wahr et al., 2004)

1st
  no filter EOF filter SW
350 km 43.5 21.1 21.1 mm
500 km 23.7 16.7 17.7 mm
SWSwenson and Wahr, 2006.
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Test on modeled data
1st

• Combination of GLDAS (hydrology) and JASON-1
  corrected with WOA05 (54 months)
• Filter reduces RMS of signal only slightly
• The longer the timeseries, the more signal is
  retained (27 months 36.8 mm at 0 km)

  model filtered
0 km 43.4 39.9 mm
350 km 30.3 29 mm
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1st
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Trends 2003 mid 2007 (350 km)
1st
EOF filter Swenson Wahr (2006)
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Conclusions

• EOF filtering of spherical harmonics effective
  filtering method
• Separates random signal from non-random in SH
• effectiveness increases as more GRACE solutions
  become available
• Stripes significantly reduced, geophysical
  signal only slightly attenuated
• Episodic events more difficult to separate

1st
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?

• Questions

Bert.Wouters_at_tudelft.nl
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  no filter m ordered l ordered
350 km 43.5 21.1 22.6 mm
500 km 23.7 16.7 17.8 mm
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