Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany Quality Assessment of GOCE Gradients Phillip Brieden, Jürgen Müller living planet symposium 28 June – 2 July 2010 | Bergen | Norway

Introduction living planet symposium 28 June – 2 July 2010 | Bergen | Norway Power Spectral Density (PSD) of GOCE GG Correct Data?

Contents  Filtering of GGT L1b data o Why ? o The Method o Results  Two Validation Methods 1)Reference Gradient approach 2)Cross-Over (XO) approach  Basic ideas  Results 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 = /s² GOCE Gravity Gradients long-wavelength errors (caused by accelerometer-drift) validation within MBW  filtering is necessary! MBW: between 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 information o Butterworth-filter again o 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-pass filtered EGM08 GOCE measurements MBW

Filtering – Result (2) living planet symposium 28 June – 2 July 2010 | Bergen | Norway time series used for analyses  Selection of best cut-off frequency? filtering result difference: GOCE – filter result GOCE measurements

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´ = Δg G – Δg M – Δg RTM

Reference Gradient Approach The Evaluation Area  regional area: reference values (3D grid) available o residual values related to a GPM + terrestrial data o altitude interval:5 km o resolution:6 min latitude φ: 40.05° ° longitude λ: 00.05° ° altitude: km km living planet symposium 28 June – 2 July 2010 | Bergen | Norway

Reference Gradient Approach Calculation of the Differences  regional area: reference values (3D grid) available o residual values related to a GPM + terrestrial data o altitude interval:5 km o resolution:6 min  select GOCE data across the regional area  3D-spline interpolation of reference gradients (T ij ) in gradiometer position  restore-part of the reference gradients into the interpolation point & restore-step T ij  V ij  analysis of the differences:  analysis for each track living planet symposium 28 June – 2 July 2010 | Bergen | Norway ΔV ij RG = V ij GOCE – V ij RefGrad

Reference Gradient Approach Differences ΔV ij RG differences ΔV ij RG [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 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 idea Identical measurement position  identical gravity gradient: V ij,1 = V ij,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 x y z xy z gravity gradient differences in XO  to be analyzed ij = {xx, xy, xz, yy, yz, zz} ΔV ij XO = V ij 1 – V ij 2 – red ij GPM

Cross-Over (XO) Approach Results (1)  Statistical results o Set up a threshold of maximum difference in all XOs o Percentage of differences that exceed the threshold o Distinction for each GGT component  main diagonal components living planet symposium 28 June – 2 July 2010 | Bergen | Norway tensor componentthreshold [mE] percentage of XO-point differences that exceed the threshold XX % YY % ZZ %

Cross-Over (XO) Approach Results (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: XX threshold: 11 mE ‘outliers’: 0.66 % GGT component: XX threshold: 11 mE ‘outliers’: 0.66 %

Conclusions  Longer-wavelength errors require a filtering of GG measurements o replacement of long wavelength by GPM information  selection ‘the best’ cut-off frequency  Reference Gradient Approach o results perfectly meet the requirements  Cross-Over (XO) Approach o only scattered unevenly distributed outliers  Both approaches…  confirm the somewhat higher noise level of V zz compared to the other main diagonal components V xx and V yy  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 EGM08 degree… ITG-Grace2010s degree XX % 0.24 % YY %0.63 %0.62 % ZZ %5.39 %5.38 % XZ %3.86 %3.81 % XX %0.69 %0.61 % YY %2.61 %2.57 % ZZ %15.61 %15.33 % XZ %12.75 %12.43 % Cut-off frequencies: 5 mHz - lower line 50 mHz - upper line

Different Cut-Off Frequencies living planet symposium 28 June – 2 July 2010 | Bergen | Norway