C.C.Tscherning, Niels Bohr Institute, University of Copenhagen

.

Improvement of Least-Squares Collocation error estimates

using local GOCE Tzz signal standard deviations.

Hotine-Marussi Symposium, Rome, June 2013

GOCE

Hotine-Marussi Symposium, Rome, June 2013

GOCE Tzz (-ITG_Grace 2010s to 36), mean of 1 deg. Blocks, E.U.

Hotine-Marussi Symposium, Rome, June 2013

Use of Gradients:

• Contribution to determination of coefficients and error estimates of Spherical Harmonic Models

• Estimation of global grids of gravity anomalies or gradients at satellite (mean) altitude, at 10 km height or on ground level + error-estimates, see e.g.

• “Global grids of gravity anomalies and vertical gravity gradients at 10 km altitude from GOCE gradient data and polar gravity, by D.N. Arabelos, M. Reguzzoni and C.C.Tscherning”, submitted, 2013”, http://cct.gfy.ku.dk/publ_cct/cct2208g.pdf

• Error estimates not satisfactory – reason for this presentation.

Hotine-Marussi Symposium, Rome, June 2013

PURPOSE OF ERROR ESTIMATES

(1) an indicator of the quality of an observed or estimated quantity

(2) for the use of data in a data assimilation procedure such as estimating ocean current velocities or an EGM

(3) in simulation studies and

(4) for gross-error detection

Hotine-Marussi Symposium, Rome, June 2013

ERROR ESTIMATES FROM LEAST-SQUARES COLLOCATION

Generally an isotropic covariance function or reproducing kernel valid for a certain region is used.

Local variations are not accounte for !

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ERROR ESTIMATES OF HEIGHT ANOMALIES FROM GRAVITY, units: m.

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ERROR ESTIMATES + IMPROVEMENTS

(1) Only show location of data

(2) Sometimes quality of data

(3) Influence of different data types

(4) But may be improved knowing local signal standard deviation or (rms)

Hotine-Marussi Symposium, Rome, June 2013

Example of local improvement of error estimates

Hotine-Marussi Symposium, Rome, June 2013

Gravity anomalies from GOCE Tzz & EGM2008 to 512. (ITG-Grace2010c to 36 subtracted everywhere), units: mgal.

Differences and LSC error estimates

Hotine-Marussi Symposium, Rome, June 2013

Differences gravity fromGOCE Tzz- EGM2008 to 512 and LSC error estimates.

GOCE Tzz RMS in 1 deg. blocks and scaled error estimates

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GOCE Tzz RMS (E.U.) and scaled error estimates (mgal). Now error-estimates show how error varies.

Global scaling using GOCE Tzz RMS in 1 deg. Blocks.

Hotine-Marussi Symposium, Rome, June 2013

GOCE Tzz (-ITG-GRACE2010c to 36) RMS (E.U)

Global scaling possibel ?

Hotine-Marussi Symposium, Rome, June 2013

LSC error estimates of predicted reduced gravity in 20x20 blocks from GOCE Tzz.

Global scaling of LSC error estimates in 1x1 deg blocks.

Hotine-Marussi Symposium, Rome, June 2013

Scaled error-estimates of predicted reduced gravity anomalies.

Conclusion

It is planned to use the procedure in order to provide error-estimates of the global 0.125 deg. gravity anomaly grids predicted from GOCE Tzz.

Problems remaining:How should the local signal standard deviations be computed in case of a local

bias ? Should the root-mean-square variation be used ? Should the scaling be done

regionally or by using the global root-mean-square variation ? In both cases the bias is small due to the subtraction of for example the ITG-

Grace 2010s field or other Earth Gravity Models to the same maximal degree..

The scaling of LSC derived error-estimates improves the estimates, so that the variation of the error due to changing local signal standard deviation is seen.

Same procedure may be used e.g. on error-estimates associated with spherical harmonic models of the gravity field and in many other cases !

Hotine-Marussi Symposium, Rome, June 2013