Real-time Dynamic MRI using Kalman Filtered Compressed Sensing
Kalman filtered daily GRACE gravity field solutions in...
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![Page 1: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/1.jpg)
S C I E N C E P A S S I O N T E C H N O L O G Y
u www.tugraz.at
Kalman filtered daily GRACE gravity field
solutions in near real-time – first steps
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr
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EGSIEM near real-time (NRT) service
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr2
As part of EGSIEM (European Gravity Service for Improved Emergency
Management) a tech demonstrator for near real-time gravity products will be
established
Scope: daily gravity field solutions with five day delay
Operations will be run at GFZ and Graz University of Technology
Regional and global solutions
Evaluation with GNSS loading at University of Luxembourg
Horizon 2020
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Daily gravity field solutions from GRACE
Additional information is introduced in form of a process model
Prediction based on spatio-temporal correlations from geophysical models
Solution is weighted mean between GRACE observations and prediction
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr3
𝑡 − 2
GRACE Kalman Filter
(Kurtenbach et al. 2012)
GRACE obs. 𝑙𝑡−1
𝑡 − 1 𝑡
… …
GRACE obs. 𝑙𝑡
![Page 4: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/4.jpg)
Post processing results – ITSG-Grace2016
GRACE time series (2002 to 2016) processed and continually updated
5053 daily solutions (4258 days with GRACE contribution)
Process model derived from WGHM (hydrosphere) and ESA ESM (residual
atmosphere/ocean)
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr4
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Post processing results – ITSG-Grace2016
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr5
WGHM - 2006-04-15
CSR RL05 2006-04 (350km Gaussian filter)
ITSG-Grace2016 daily - 2006-04-15
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Post processing results – ITSG-Grace2016
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr6
Bazias, RO
Danube floods 2006
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Post-processing allows for fixed interval smoothing
Kalman filter runs in forward and backward direction
Minimum variance average of both time series
Implemented as RTS smoother (Rauch et al. 1965)
Adapted daily gravity field processing scheme:
Rapid GNSS constellation and Earth orientation
forward only filtering → increased high frequency noise
RTS smoother replaced by fixed-lag smoother
Nominal solution delay allows for 1-2 lag epochs
Smoothing algorithms
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr7
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Smoothing algorithms
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr8
Danube basin area mean time series
(annual, trend removed)
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Smoothing algorithms
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr9
PSD of Danube area mean time series
Even one lag epoch reduces
high frequency noise
M2
Basin repeat-cycle
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Conclusion and outlook
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr10
GRACE can provide information for much shorter time spans than the
standard monthly solutions
Reduced latency will enable monitoring of floods and droughts as they
occur
EGSIEM near real-time operational test run starts in 2017
Global and regional daily GRACE gravity fields with 5 days latency
Check out www.egsiem.eu for updates
ITSG-Grace2016 solutions available under ifg.tugraz.at/ITSG-Grace2016
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ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr11
EGSIEM is funded by the Horizon 2020
Framework Programme of the European Union
under grant agreement No 637010.
Discharge data provided by the Global Runoff
Data Centre, 56068 Koblenz, Germany
Acknowledgements
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Daily gravity field solutions from GRACE
GRACE data coverage:
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr12
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Daily gravity field solutions from GRACE
Monthly
GRACE data coverage:
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr13
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Daily gravity field solutions from GRACE
Weekly
GRACE data coverage:
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr14
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Daily gravity field solutions from GRACE
Limited spatial
sampling
Hig
h s
patial sam
plin
g
Daily
GRACE data coverage:
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr15
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Daily gravity field solutions from GRACE
Limited spatial
sampling
Hig
h s
patial sam
plin
g
GRACE contribution
limited to order ~15
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr16
![Page 17: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/17.jpg)
Daily gravity field solutions from GRACE
Limited spatial
sampling
Hig
h s
patial sam
plin
g
GRACE alone cannot observe
the full gravity field signal
GRACE contribution
limited to order ~15
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr17
![Page 18: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/18.jpg)
Additional information is introduced in form of a process model
Prediction based on spatio-temporal correlations from geophysical models
Solution is weighted mean between GRACE observations and prediction
Daily gravity field solutions from GRACE
𝑡 − 2
GRACE Kalman Filter
(Kurtenbach et al. 2012)
GRACE obs. 𝑙𝑡−1
𝑡 − 1 𝑡
… …
GRACE obs. 𝑙𝑡
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr18
![Page 19: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/19.jpg)
Post processing results – ITSG-Grace2016
GRACE time series (2002 to 2016) processed and continually updated
5053 daily solutions (4258 days with GRACE contribution)
Process model derived from WGHM (hydrosphere) and ESA ESM (residual
atmosphere/ocean)
GRACE processing details: Klinger et al. - Towards a new ITSG-Grace release:
improvements within the processing chain, Session G4.2 - Wednesday, 9am
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr19
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Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr20
![Page 21: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/21.jpg)
Post processing results – ITSG-Grace2016
Danube floods
2006
Bazias,
RO
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr21
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Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr22
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Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr23
![Page 24: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/24.jpg)
Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr24
![Page 25: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/25.jpg)
Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr25
![Page 26: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/26.jpg)
Post processing results – ITSG-Grace2016
Bazias,RO
Danube floods 2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr26
![Page 27: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/27.jpg)
Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr27
![Page 28: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/28.jpg)
Post processing results – ITSG-Grace2016
Bazias,
RO
Danube floods
2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr28
![Page 29: Kalman filtered daily GRACE gravity field solutions in ...lps16.esa.int/posterfiles/paper1874/ESA_LPS2016_supplementary.pdf · Kalman filtered daily GRACE gravity field solutions](https://reader031.fdocuments.net/reader031/viewer/2022022109/5c4571a593f3c34c4b2992e8/html5/thumbnails/29.jpg)
Post processing results – ITSG-Grace2016
Bazias, RO
Danube floods 2006
ESA LPS2016 - 09.05.2016 - 13.05.2016
Andreas Kvas, Torsten Mayer-Gürr29