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ARCGICE WP 4.3 Recommendations for inclusion of GOCE data C.C.Tscherning & S.Laxon C.C.Tscherning, UCPH, S.Laxon, UCLA, 2006-10-20 1

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The GOCE satellite level 2 products will be produced of the High Level processing Facility, (HPF). The main products of importance for ARCGICE are: EGM_GCF_2 the spherical harmonic series EGM_GVC_2 the associated error-covariance matrix, EGG_NOM_2 gravity gradients in the gradiometer reference frame (GRF). EGG_TRF_2 gravity gradients in a local North- oriented frame. SST_PSO_2 precise science orbit, including rotation matrix information. DATA C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 2

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All these data may contribute to the determination of an enhanced geoid enhanced estimates of associated error-estimates error correlations. Enhanced Arctic products C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 3

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Directly used in the geoid computation in the remove-restore step. The variance-covariance matrix must be used so that the error information is correctly propagated into the geoid error-estimates and error-covariances. Use of spherical harmonic coefficients C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 4

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At the moment only the error-variances of the estimated coefficients are used in order to produce so-called error-degree-variances. The use of the full variance-covariance matrix is complicated, and its integration into the geoid-estimation process is difficult. Use of error-covariances C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 5

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The covariance function of the residual gravity anomalies (obtained in the remove- restore process) will include some information related to the coefficient errors. Use of error-covariances C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 6

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The coefficients may also be used to improve the identification of biases in individual gravity surveys. Identification of Biases in surveys C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 7

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The gravity gradients include the same information as the spherical harmonic coefficients in areas of moderately varying gravity. In areas with larger gravity variations (such as over trenches) they may include extra information. (Better signal-to-noise ratio). Use of the gravity gradients. C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 8

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Directly used in the geoid computation in the remove-restore step. The variance-covariance matrix must be used so that the error information is correctly propagated into the geoid error-estimates and error-covariances. Areas identified by computing the difference between observed values and values of the gradients computed from the spherical harmonic series. Use of spherical harmonic coefficients C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 9

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The gravity gradients may directly be used in the geoid estimation using such methods as Least- Squares-Collocation (LSC). The use may require changes in existing software, where spherical approximation is used. Availability of ground gravity data is important for “tuning” the “down-ward” continuation inherent in the regularisation process (where data at satellite altitude is combined with data on the ground). Direct use of Gradients C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 10

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GOCE products may be used to compute an improved geoid in the Arctic Ocean. Spherical harmonic coefficients and gravity gradients may be used. The use of the gravity gradients will primarily help in reducing the error in the region south of 84o latitude. Require improvements in existing software so that the variance-covariance information of the coefficients may be properly propagated into the geoid estimation process. Conclusion C.C.Tscherning, UCPH, S.Laxon, UCL, 2006.10-20. 11

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