Time-variable gravity field determination from GRACE-FO data at - - PowerPoint PPT Presentation

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Time-variable gravity field determination from GRACE-FO data at - - PowerPoint PPT Presentation

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Time-variable gravity field determination from GRACE-FO data at AIUB Martin Lasser 1 , Ulrich Meyer 1 , Daniel Arnold 1 , Adrian J aggi 1 1 Astronomical Institute, University of Bern, Switzerland GRACE & GRACE-FO Science Team Meeting Oct.

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SLIDE 1

Time-variable gravity field determination from GRACE-FO data at AIUB

Martin Lasser1, Ulrich Meyer1, Daniel Arnold1, Adrian J¨ aggi1

1Astronomical Institute, University of Bern, Switzerland

GRACE & GRACE-FO Science Team Meeting

  • Oct. 8-10, 2019

Pasadena, California

Astronomical Institute, University of Bern AIUB

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SLIDE 2
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Content

Kinematic orbits of GRACE-FO satellites Stochastic behaviour of kinematic positions Empirical modelling Inter-satellite link Impact on gravity field determination

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Astronomical Institute, University of Bern AIUB

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Observations

Credit: DLR

GPS Inter-satellite link absolute relative 3-dim 1-dim lower precision very high precision

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Astronomical Institute, University of Bern AIUB

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SLIDE 4
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Kinematic orbits of GRACE-FO satellites

LEO precise orbit determination from GPS data

  • 10 s sampling (full sampling used in processing)
  • undifferenced PPP solution
  • fixing zero-difference ambiguities to integers

→ CODE (Center of Orbit Determination in Europe) phase biases → CODE ambiguity-fixed clocks

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SLIDE 5
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Integer-fixing of carrier phase ambiguities

SLR residuals for 2018-11 (in comparison with float) SV type mean [mm]

  • std. dev [mm]

GRACE-C float 3.1 18.6 GRACE-D float

  • 4.5

16.8 GRACE-C fixed 4.3 10.6 GRACE-D fixed 1.0 12.0

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SLIDE 6
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Integer-fixing of carrier phase ambiguities

SLR residuals for 2018-11 (in comparison with float) SV type mean [mm]

  • std. dev [mm]

GRACE-C float 3.1 18.6 GRACE-D float

  • 4.5

16.8 GRACE-C fixed 4.3 10.6 GRACE-D fixed 1.0 12.0 K-band range validation of kinematic positions → Individual arcs feature less scattering

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Astronomical Institute, University of Bern AIUB

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SLIDE 7
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Stochastic behaviour of kinematic positions

  • SST-hl tracking geometry varies between poles and the equator
  • Epoch-wise covariance information from kinematic PPP:

mainly 2/rev; important information on observation quality

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Astronomical Institute, University of Bern AIUB

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SLIDE 8
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Stochastic behaviour of kinematic positions

  • SST-hl tracking geometry varies between poles and the equator
  • Epoch-wise covariance information from kinematic PPP:

mainly 2/rev; important information on observation quality

Slide 6 of 16

Astronomical Institute, University of Bern AIUB

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SLIDE 9
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Stochastic behaviour of kinematic positions

  • SST-hl tracking geometry varies between poles and the equator
  • Epoch-wise covariance information from kinematic PPP:

mainly 2/rev; important information on observation quality

  • Ambiguities feature the correlation between epochs

→ Full covariance matrix from PPP (at least in principle) → Integer-fixed: almost no correlations

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SLIDE 10
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Empirical modelling

Non linear least squares: x = x0 + (ATPA)−1ATPδl → The observations enter via δl = o − c

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SLIDE 11
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Empirical modelling

Non linear least squares: x = x0 + (ATPA)−1ATPδl → The observations enter via δl = o − c

Slide 7 of 16

Astronomical Institute, University of Bern AIUB

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SLIDE 12
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Empirical modelling

Non linear least squares: x = x0 + (ATPA)−1ATPδl → The observations enter via δl = o − c

  • Residuals feature observation noise (o)
  • And mismodelings from the computed component (c)

→ c contains the full a priori force model (gravity field, tides, AOD, accelerometer, ...)

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SLIDE 13
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Empirical modelling

Non linear least squares: x = x0 + (ATPA)−1ATPδl → The observations enter via δl = o − c

Slide 8 of 16

Astronomical Institute, University of Bern AIUB

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SLIDE 14
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Empirical covariance estimation

  • Set up (constrained) piecewise constant accelerations

(strategy used at AIUB) In case of a stationary process

  • Estimate a mean covariance function from the residuals e.

cov(∆tk) = 1 n

n

  • i=0

e(ti)e(ti + ∆tk)

  • Variance/covariance matrix has a symmetric Toeplitz-structure

and the individual elements only depend on the distance in time. → Mean covariance function for each month → Length of correlation 100 min

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SLIDE 15
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Inter-satellite link

The inter-satellite link is much more precise → dominates the resulting gravity field signal → 5 s sampling for K-band, 2 s sampling for LRI

  • Assign one factor to weight K-band

→ extended to weight based on its arc-wise residual RMS

  • Set up constrained PCA to model stochastic behaviour

(mainly a 2/rev signal)

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Inter-satellite link

The inter-satellite link is much more precise → dominates the resulting gravity field signal → 5 s sampling for K-band, 2 s sampling for LRI

  • Assign one factor to weight K-band

→ extended to weight based on its arc-wise residual RMS

  • Set up constrained PCA to model stochastic behaviour

(mainly a 2/rev signal)

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SLIDE 17
  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Inter-satellite link

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Inter-satellite link

  • Large

distance in time between reference epoch of background field and

  • bservations

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Impact on gravity field determination

  • Formal errors are

too optimistic

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Impact on gravity field determination

  • Slight improvement

due to better characterisation of range-rate data

  • Noise in

background force field modelled through PCA only

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Impact on gravity field determination

  • Noise in

background force field mainly characterised due to GPS contribution

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Impact on gravity field determination

  • Formal errors in

higher degrees realistic

  • Low degrees require

further inspection

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  • M. Lasser, U. Meyer, D. Arnold, A. J¨

aggi: Status of GFO data processing at AIUB GRACE & GRACE-FO Science Team Meeting, Oct. 8-10, 2019, Pasadena, California

Summary

  • Integer-fixing of carrier phase ambiguities closer to K-band
  • Empirical noise modelling via GPS improves formal errors

→ Extend the procedure to K-band/Laser link

  • Processing strategy tested on GRACE-FO

→ (At some point) reprocess GRACE time series

Thank you for your attention.

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Astronomical Institute, University of Bern AIUB