Quality Assessment of GOCE Gradients
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Quality Assessment of GOCE Gradients Phillip Brieden , Jürgen Müller living planet symposium 28 June – 2 July 2010 | Bergen | Norway. Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany. Introduction. Power Spectral Density (PSD ) of GOCE GG. Correct Data?. Contents.

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Institut f r erdmessung ife leibniz universit t hannover germany

Quality Assessment of GOCE GradientsPhillip Brieden, Jürgen Müllerliving planet symposium28 June – 2 July 2010 | Bergen | Norway

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


Introduction
Introduction

Power Spectral Density (PSD)of GOCE GG

CorrectData?

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Contents
Contents

  • Filtering of GGT L1b data

    • Why ?

    • The Method

    • Results

  • Two Validation Methods

    • Reference Gradient approach

    • Cross-Over (XO) approach

    • Basic ideas

    • Results based in real GOCE data

  • Conclusions

  • Hanover is part of the official Cal/Val team of ESA.

  • data access

  • preliminary results!

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Comparison in gradiometer reference frame measured gg gpm e g egm 08
Comparison in Gradiometer Reference Frame: Measured GG – GPM (e.g. EGM 08)

> 0.5 E

GOCE Gravity Gradients

validation within MBW filtering is necessary!

long-wavelength errors(caused by accelerometer-drift)

1 E=10-9 1/s²

MBW: between 0.005 and 0.1 Hz

0 E

 Quality Assessment at the level of some mE

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Filtering ggt components the idea
Filtering GGT Components - The Idea GPM (e.g. EGM 08)

GOCE

high-pass

+

GPM

low-pass

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Filtering used filter
Filtering - Used Filter GPM (e.g. EGM 08)

  • Finite Impulse Response filter (FIR)

  • Butterworth-filter

    • high-pass (GOCE)

    • low-pass (GPM)

    • cut-off frequency: 5 mHz

       filtering and combination in time domain!

  • Additional filtering of the combined information

    • Butterworth-filter again

    • cut-off frequency: 50 mHz spherical harmonic degree l ≈ 270

    • GOCE-only gravity field solutions up to degree ~250

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Filtering result 1
Filtering – Result (1) GPM (e.g. EGM 08)

GOCE

measurements

high-pass filtered GOCE

low-passfiltered EGM08

MBW

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Filtering result 2
Filtering – Result (2) GPM (e.g. EGM 08)

GOCE

measurements

filtering result

time series used for analyses

difference:

GOCE – filter result

  • Selection of best cut-off frequency?

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Reference gradients from gravity anomalies reference gradient approach
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

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Reference gradient approach the evaluation area
Reference Gradient Approach Gradient Approach)The Evaluation Area

  • regional area: reference values (3D grid) available

    • residual values related to a GPM + terrestrial data

    • altitude interval: 5 km

    • 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 approach calculation of the differences
Reference Gradient Approach Gradient Approach)Calculation of the Differences

  • regional area: reference values (3D grid) available

    • residual values related to a GPM + terrestrial data

    • altitude interval: 5 km

    • 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 track

ΔVijRG= VijGOCE – VijRefGrad

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Reference gradient approach differences v ij rg
Reference Gradient Approach Gradient Approach)Differences ΔVijRG

  • differences ΔVijRG [E]

    • color-coded (different scales!)

    • mean value reduced (each track)

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Reference gradient approach psd of gg differences for all track pieces

spherical harmonic degree l ≈ 270 Gradient Approach)

Reference Gradient ApproachPSD of GG-differences for all track pieces

average of PSDs

GOCE requirements

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


The cross over xo approach
The Cross-Over (XO) Approach Gradient Approach)

Basic idea

Identical 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

gravity gradient differences in XO  to be analyzed

ij = {xx, xy, xz, yy, yz, zz}

ΔVijXO = Vij1 – Vij2 – redijGPM

living planet symposium 28 June – 2 July 2010 | Bergen | Norway

y

x

z

x

y

z


Cross over xo approach results 1
Cross-Over (XO) Approach Gradient Approach)Results (1)

  • Statistical results

    • Set up a threshold of maximum difference in all XOs

    • Percentage of differences that exceed the threshold

    • Distinction for each GGT component main diagonal components

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Cross over xo approach results 2
Cross-Over (XO) Approach Gradient Approach)Results (2)

GGT component: XXthreshold: 11 mE

‘outliers’: 0.66 %

[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

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Conclusions
Conclusions Gradient Approach)

  • Longer-wavelength errors require a filtering of GG measurements

    • replacement of long wavelength by GPM information

    • selection ‘the best’ cut-off frequency

  • Reference Gradient Approach

    • results perfectly meet the requirements

  • Cross-Over (XO) Approach

    • 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

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Additional slides
Additional Slides Gradient Approach)

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Differences along one track crossing the evaluation area
Differences Along One Track Crossing the Evaluation Area Gradient Approach)

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Different gpms xo results

Cut-off frequencies: Gradient Approach) 5 mHz - lower line50 mHz - upper line

Different GPMs XO-Results

different max-degree  no significant differences

living planet symposium 28 June – 2 July 2010 | Bergen | Norway


Different cut off frequencies
Different Cut-Off Frequencies Gradient Approach)

living planet symposium 28 June – 2 July 2010 | Bergen | Norway