u ifg.tugraz.at
(1) Institute of Geodesy, Graz University of Technology
(2) GFZ German Research Centre for Geosciences
S C I E N C E P A S S I O N T E C H N O L O G Y
Error budget of GRACE gravity field recovery –
a simulation study
Torsten Mayer-Guerr1, Henryk Dobslaw2, Andreas Kvas1, and Lea Poropat2
GRACE/GRACE-FO Science Team Meeting 2018
2018-10-10
2 Torsten Mayer-Gürr et. al.
Motivation
Real data analysis
Detecting anomalous effects, improving parametrization
Simulation study
Understanding underlying processes, separation
3 Torsten Mayer-Gürr et. al.
Simulation scenario
Simulated world
Gravity field (max. degree 120)
Static gravity field: GOCO05s
Time variable part: ESA ESM AOHIS
Tides: JPL DE421
Earth tides: IERS2010
Ocean tides: FES2014b
Non-conservative forces
Radiation pressure JPL421
Albedo CERES
Drag JB 2008
Instrument data
One month of data (2006-01)
Integrated orbit is fitted to real GRACE orbit
Attitude: Taken from GRACE star camera
Realistic instrument noise
KBR phases: white noise with 2.8 μm/s with 0.1 s sampling,
=> range rate: CNR low pass/derivation filter applied
ACC along, radial: 1 + 0.005𝑓 ∙ 10−10 m/𝑠2/ 𝐻𝑧
cross: 1 + 0.1𝑓 ∙ 10−9 m/𝑠2/ 𝐻𝑧
SCA white noise with 0.1 mrad
POD white noise with 3 cm per axis with 300 s sampling
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Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Residuals (range rate)
Gravity field
Power spectral density (PSD)
ITSG-Grace2018 processing
Parameter:
Spherical harmonics
degree 2..120
Accelerometer bias:
6 hour cubic splines
Satellite states
Daily
Weight matrix P:
Estimated error covariance
3 hour blocks
Improved weight
matrix by analyizing
the residuals
Background models
Background models
5 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
6 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS ESA ESM AOHIS
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b FES2014b
Scenario: Instrument noise only
Perfect dealiasing/background models
Very old (inaccurate) static field
7 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS ESA ESM AOHIS
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b FES2014b
Scenario: Instrument noise only
Perfect dealiasing/background models
Very old (inaccurate) static field
EGM96 – GOCO05s
8 Torsten Mayer-Gürr et. al.
Gravity field recovery: Instrument noise only
degree variances Range rate residuals PSD
baseline
simulation
Differentiated
KBR noise
Integrated
ACC noise
Instrument noise only
Baseline can be reached
Even with EGM96 as background model
(Solution is independent of reference model)
Linearization is not an issue
9 Torsten Mayer-Gürr et. al.
Gravity field recovery: Instrument noise only
degree variances Range rate residuals PSD
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Gravity field recovery: Instrument noise only
degree variances Range rate residuals PSD
Real data
ITSG2018
11 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS ESA ESM AOHIS
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b FES2014b
12 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS AO + ESM error
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b EOT11a
Realistic scenario: Full aliasing
Only atmosphere and ocean signals are reduced
AOD model is not perfect
Ocean tide model is not perfect
13 Torsten Mayer-Gürr et. al.
Gravity field recovery: Instrument noise only
degree variances Range rate residuals PSD
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Gravity field recovery: Full aliasing
degree variances Range rate residuals PSD
Full aliasing
Recovered gravity field and residuals and field
show realistic error behavior
real residuals and solution accuracy can be explained by
this simulation
15 Torsten Mayer-Gürr et. al.
Gravity field recovery: Full aliasing
degree variances Range rate residuals PSD
Improvement of the solution
Co-estimation of constrained daily gravity field solutions
(degree 40, background model uncertainties as constrained)
12:15: Andreas Kvas et. al.:
Incorporation of background model uncertainties into
the gravity field recovery process
16 Torsten Mayer-Gürr et. al.
Gravity field recovery: Full aliasing + Daily Kalman estimates
degree variances Range rate residuals PSD
Full aliasing + Daily Kalman estimates
Daily estimates improves the monthly gravity field
and the post-fit residuals
17 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS AO + error
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b EOT11a
18 Torsten Mayer-Gürr et. al.
Gravity field recovery
Instrument data Least squares adjustment
∆ 𝑥 = 𝐴𝑇𝑃𝐴 −1𝐴𝑇𝑃∆𝑙
Gravity field
Residuals (range rate)
Power spectral density (PSD)
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS AO + error
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b FES2014b
Scenario: AOD errors
Assumption:
ocean tide model can be improved in future
Here: ocean tide model is error free
19 Torsten Mayer-Gürr et. al.
Gravity field recovery: Full aliasing
degree variances Range rate residuals PSD
20 Torsten Mayer-Gürr et. al.
Gravity field recovery: AOD errors
degree variances Range rate residuals PSD
21 Torsten Mayer-Gürr et. al.
Gravity field recovery: AOD errors + Daily Kalman estimates
degree variances Range rate residuals PSD
AOD errors + Daily Kalman estimates
Large improvement
but large subdaily signal remains in the residuals
Daily estimates cannot replace good dealiasing models
Torsten Mayer-Gürr et. al.22
Next generation missions:
GRACE + Second pair (Bender constellation)
Torsten Mayer-Gürr et. al.23
Simulation scenario
Additional inclined satellite pair
Inclination: 70° Altitude: 429 km
Distance: ~120 km
Same forces and same noise models
Background models
ForcesSimulated world
(„True“ Earth)
Background models
in the recovery
Static gravity field GOCO05s EGM96
Time variable part ESA ESM AOHIS AO + error
Direct tides JPL DE421 JPL DE421
Earth tides IERS2010 IERS2010
Ocean tides FES2014b EOT11a
24 Torsten Mayer-Gürr et. al.
GRACE: full aliasing
25 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing
Additional second pair
Solution is robust against aliasing errors
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GRACE + Bender: full aliasing + daily Kalman estimates
Daily Kalman estimates
Slightly improvement in degree 30…60
Slightly worse in degree 2..20 (???)
Improved formal errors in the low degrees
27 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing
Wiese approach
Wiese et. al. (2011): Estimating low resolution
gravity fields at short time intervals to reduce
temporal aliasing errors,
https://doi.org/10.1016/j.asr.2011.05.027
Daily normals
Daily parameter elimination of low degrees
Accumulation to monthly
=> solve high degrees
Accumulation of full normals to monthly
Subtract solution of high degrees
Solve normals (only part of low degrees)
28 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing + Wiese approach
Wiese approach
Wiese et. al. (2011): Estimating low resolution
gravity fields at short time intervals to reduce
temporal aliasing errors,
https://doi.org/10.1016/j.asr.2011.05.027
Daily normals
Daily parameter elimination of low degrees
Accumulation to monthly
=> solve high degrees
Accumulation of full normals to monthly
Subtract solution of high degrees
Solve normals (only part of low degrees)
Daily
degree 30
29 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing + Wiese approach
Wiese approach
Wiese et. al. (2011): Estimating low resolution
gravity fields at short time intervals to reduce
temporal aliasing errors,
https://doi.org/10.1016/j.asr.2011.05.027
Daily normals
Daily parameter elimination of low degrees
Accumulation to monthly
=> solve high degrees
Accumulation of full normals to monthly
Subtract solution of high degrees
Solve normals (only part of low degrees)
Daily
degree 20
30 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing + Wiese approach
Wiese approach
Wiese et. al. (2011): Estimating low resolution
gravity fields at short time intervals to reduce
temporal aliasing errors,
https://doi.org/10.1016/j.asr.2011.05.027
Daily normals
Daily parameter elimination of low degrees
Accumulation to monthly
=> solve high degrees
Accumulation of full normals to monthly
Subtract solution of high degrees
Solve normals (only part of low degrees)
Daily
degree 10
31 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing
32 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing + daily Kalman estimates
Daily Kalman estimates
Are dealiasing models (AOD) still needed?
33 Torsten Mayer-Gürr et. al.
GRACE + Bender: full aliasing + daily Kalman estimates - AOD
Daily Kalman estimates
Are dealiasing models (AOD) still needed?
Torsten Mayer-Gürr et. al.34
Summary
GRACE
Real solution accuracy and real range rate residuals can be explained by simulation
Most of the error sources are understood
Taylorpoint for linearization is not an issue
Errors in the background models are major contributors to the total error budget
Co-estimation of daily gravity fields improve the solutions
Good dealiasing models are still needed
Bender constellation
Additional satellite pair improves the solution significantly
Daily co-estimation needs more fine tuning (Kalman and Wiese)
Good dealiasing models are still needed
u ifg.tugraz.at
(1) Institute of Geodesy, Graz University of Technology
(2) GFZ German Research Centre for Geosciences
S C I E N C E P A S S I O N T E C H N O L O G Y
Error budget of GRACE gravity field recovery –
a simulation study
Torsten Mayer-Guerr1, Henryk Dobslaw2, Andreas Kvas1, and Lea Poropat2
GRACE/GRACE-FO Science Team Meeting 2018
2018-10-10