Refining regional gravity field solutions with GOCE gravity gradients for cryospheric

investigations

D. Rieser *, R. Pail, A. I. Sharov

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Contents

• Introduction

• Gradients for regional Geoid computations

• Coping with noise

• Solution strategies

• Geoid computation

• Problems

• Summary

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Introduction

• Background and motivation

– Project ICEAGE

• Arctic snow- and ice cover variations and relations to gravity

• Sharov et al.: Variations of the Arctic ice-snow cover in nonhomogenous geopotential (oral, 30.06.,11:40)

• Gisinger et al.: Ice mass change versus gravity-local models and GOCE's contribution (poster, 30.06, 16:00)

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Introduction

• Contributions of GOCE to regional gravity field

– Gradients as in-situ observations

– Beneficial dense data distribution

– Combination with other data types

• terrestrial (gravity anomalies, e.g. ArcGP)

• gravity models (EGM2008)

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• Least Squares Collocation

– Prediction

– Gravity quantity as functional of disturbing potential T

– Covariance function

Gradients for regional Geoid computations

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Gradients for regional Geoid computations

• Approach following Tscherning (1993)

– Covariances as combination of base functions

– All covariances up to 2nd order derivatives of the disturbing potential (i.e. gradients)

– Advantage:

• Covariances can be rotated in arbitrary reference frame

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Gradients for regional Geoid computations

• Characteristics of GOCE gradients observations

– Observations in Gradiometer Reference Frame (GRF)

– Assumption of uncorrelated gradients in GRF

– Gradients suffering from coloured noise

– Vxy and Vyz tensor components badly deteriorated

Error PSD from ESA E2E-simulation (before GOCE launch)

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Coping with noise

• Filtering of coloured noise by applying Wiener filter method (Migliaccio et al., 2004)

– Signal t consisting of signal s + noise n

– Wiener filter in spectral domain

– Filtered signal in time domain

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• Covariance function of the filter error

– Requirement: stationary signal (valid only in Local Orbit Reference Frame LORF)

– Problem: rotation of gradients from GRF to LORF unfavorable (Vxy, Vyz)

Coping with noise

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Solution strategies

• Strategy 1

– Gradients in GRF

– Filtering in GRF

• not allowed in strict sense

– Cll rotated to GRF

– Cnn set up in GRF

– Csl for signals in Local North Oriented Frame (LNOF) and gradientsin GRF

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Solution strategies

• Strategy 2

– Rotate gradient tensor toLORF

• a-priori replacement ofless accurate tensor components with EGM

– Filtering in LORF

– Set up of Cnn in GRF and rotation to LORF

• a-priori covariance propagation for replacedcomponents from EGM

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Solution strategies

• Noise covariance propagation GRF LORF

– GRF: uncorrelated gradient tensor components

– LORF: correlation through rotation

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Geoid computation

• GOCE data:

– 01. November 2009 – 30. November 2009

– Reduced up to D/O 49by EGM2008

– 5 sec sampling

– Region: 53° – 79° E 73° – 78° N

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Geoid computation

• Filtering of gradients

– Noise PSD Quicklook

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Geoid computation

• Noise-free scenario:

– Vzz gradients simulated from EGM2008 on real orbit (D/O 50to250)

EGM2008 reference LSC with VzzDifference to EGM2008 reference Standard deviation

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Geoid computation

• Geoid solution from real Vxx, Vyy and Vzz components

Strategy 1 Strategy 2

Sta

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rd

devi

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iffer

enc

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o re

fere

nce

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Geoid computation

• ‚Terrestrial‘ data

– Gravity anomalies simulated from EGM2008 (~ ArcGP)

– D/O 50 to 250

– = 3 mgal

– 0.25° X 0.25° grid

Standard deviation

Difference to reference

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Geoid computation

• Combination of GOCE and terrestrial data

– Vxx, Vyy and Vzz gradients (filtered in GRF)

– Gravity anomalies (D/O 50 to 250, = 3 mGal)

Standard deviation

Difference to reference

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Geoid computation

Standard deviation

Difference to reference

com

bine

dg

on

ly

grad

ient

s on

ly

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Problems

• Downward continuation of gradients unstable

– Ground data necessary

• Global covariance model

– Valid for g (ground) and gradients (GOCE altitude)

• Assumptions

– Strategy 1:

• Wiener filtering in non-stationary GRF

– Strategy 2:

• Noise-covariance information from a-priori Wiener filtering in GRF

• Replacement of real gradients with EGM information

Empirical and EGM2008 model covariance function for g (D/O 50 to

250)

Empirical and EGM2008 model covariance function for V ZZ (D/O 50 to 250) at

h=245km

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Summary

• GOCE gravity gradients can be used as in-situ observations

• Reduction of noise by applying Wiener filtering

• Different solution strategies lead to similar results

– Assumptions inevitable

• Combination of GOCE gradients with terrestrial data improves the solution in medium wavelengths

D. Rieser *, R. Pail, A. I. Sharov

Thank you for your attention