institut für erdmessung (ife), leibniz universität hannover, germany quality assessment of goce...
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Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany
Quality Assessment of GOCE Gradients
Phillip Brieden, Jürgen Müller
living planet symposium28 June – 2 July 2010 | Bergen | Norway
Introduction
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Power Spectral Density (PSD)of GOCE GG
CorrectData?
Contents
Filtering of GGT L1b datao Why ?o The Methodo Results
Two Validation Methods
1)Reference Gradient approach
2)Cross-Over (XO) approachBasic ideasResults based in real GOCE data
Conclusions
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Hanover is part of the official Cal/Val team of ESA. data access preliminary results!
> 0.5 E
Comparison in Gradiometer Reference Frame: Measured GG – GPM (e.g. EGM 08)
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Quality Assessment at the level of some mE
1 E=
10-9 1/s²
GOCE Gravity Gradients
long-wavelength errors(caused by accelerometer-drift)
validation within MBW filtering is necessary!
MBW: between 0.005 and 0.1 Hz
0 E
Filtering GGT Components - The Idea
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
+
GOCE
GPM
high-pass
low-pass
Filtering - Used Filter
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Finite Impulse Response filter (FIR) Butterworth-filter
o high-pass (GOCE)o low-pass (GPM)o cut-off frequency: 5 mHz
filtering and combination in time domain!
Additional filtering of the combined informationo Butterworth-filter againo cut-off frequency: 50 mHz spherical harmonic
degree l ≈ 270 GOCE-only gravity field solutions up to degree ~250
Filtering – Result (1)
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
high-pass filtered GOCE
low-passfiltered EGM08
GOCEmeasurements
MBW
Filtering – Result (2)
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
time series used for analyses
time series used for analyses
Selection of best cut-off frequency?
filtering result
difference:GOCE – filter result
GOCEmeasurements
Reference Gradients from Gravity Anomalies (Reference Gradient Approach)
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
terrestrial data (incl. airborne gravimetry and satellite altimetry) of well-surveyed regional areas combined with global geopotential model (GPM)
Δg´ = ΔgG – ΔgM – ΔgRTM
Reference Gradient ApproachThe Evaluation Area
regional area: reference values (3D grid) availableo residual values related to a GPM + terrestrial datao altitude interval: 5 kmo resolution: 6 min
latitude φ:40.05° - 54.95°
longitude λ:00.05° - 19.95°
altitude:
230.0 km - 280.0 km
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Reference Gradient ApproachCalculation of the Differences
regional area: reference values (3D grid) availableo residual values related to a GPM + terrestrial datao altitude interval: 5 kmo resolution: 6 min
select GOCE data across the regional area 3D-spline interpolation of reference gradients (Tij) in
gradiometer position restore-part of the reference gradients into the
interpolation point & restore-step Tij Vij
analysis of the differences:
analysis for each trackliving planet symposium 28 June – 2 July 2010 | Bergen | Norway
ΔVijRG = Vij
GOCE – VijRefGrad
Reference Gradient ApproachDifferences ΔVij
RG
differences ΔVijRG [E]
• color-coded (different scales!)• mean value reduced (each track)
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Reference Gradient ApproachPSD of GG-differences for all track pieces
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
average of PSDs
GOCE requirements
spherical harmonic
degree l ≈ 270
The Cross-Over (XO) Approach
Basic ideaIdentical measurement position identical gravity gradient: Vij,1 = Vij,2
Attention!No repeated measurement positions!
differences in attitude and altitude that have to be reduced
GPM used for reduction
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
xy
z
xyz
gravity gradient differences in XO to be analyzed
ij = {xx, xy, xz, yy, yz, zz}ΔVijXO = Vij
1 – Vij2 – redij
GPM
Cross-Over (XO) ApproachResults (1)
Statistical resultso Set up a threshold of maximum difference in all XOso Percentage of differences that exceed the thresholdo Distinction for each GGT component
main diagonal components
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
tensor component threshold [mE] percentage of XO-point differences that exceed
the threshold
XX 15 0.25 %
YY 15 0.64 %
ZZ 15 5.44 %
Cross-Over (XO) ApproachResults (2)
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
[mE]
Almost all ‘outliers’ have differences near the threshold XO-approach is very suitable for GOCE data validation Good data quality of GOCE gravity gradients
GGT component: XXthreshold: 11 mE‘outliers’: 0.66 %
GGT component: XXthreshold: 11 mE‘outliers’: 0.66 %
Conclusions
Longer-wavelength errors require a filtering of GG measurementso replacement of long wavelength by GPM information selection ‘the best’ cut-off frequency
Reference Gradient Approacho results perfectly meet the requirements
Cross-Over (XO) Approacho only scattered unevenly distributed outliers
Both approaches… confirm the somewhat higher noise level of Vzz compared to the
other main diagonal components Vxx and Vyy
suitable for the validation of GOCE GG confirm the very good quality of GOCE GG
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
good data quality
Additional Slides
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Differences Along One Track Crossing the Evaluation Area
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
Different GPMs XO-Results
living planet symposium 28 June – 2 July 2010 | Bergen | Norway
different max-degree no significant differences
tensor component
threshold [mE]
percentage of XO-point differences that exceed the threshold
EGM08degree… ITG-Grace2010s
degree 180360 180
XX 15 0.25 % 0.25 % 0.24 %
YY 15 0.64 % 0.63 % 0.62 %
ZZ 15 5.44 % 5.39 % 5.38 %
XZ 15 3.75 % 3.86 % 3.81 %
XX 11 0.66 % 0.69 % 0.61 %
YY 11 2.56 % 2.61 % 2.57 %
ZZ 11 15.59 % 15.61 % 15.33 %
XZ 11 12.54 % 12.75 % 12.43 %
Cut-off frequencies: 5 mHz - lower line50 mHz - upper line
Different Cut-Off Frequencies
living planet symposium 28 June – 2 July 2010 | Bergen | Norway