Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany

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


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)


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


+

GOCE

GPM

high-pass

low-pass

Filtering - Used Filter


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)


high-pass filtered GOCE

low-passfiltered EGM08

GOCEmeasurements

MBW

Filtering – Result (2)


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)


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


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)


Reference Gradient ApproachPSD of GG-differences for all track pieces


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


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


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)


[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


good data quality

Additional Slides


Differences Along One Track Crossing the Evaluation Area


Different GPMs XO-Results


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


Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany

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