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

C.C.Tscherning, Niels Bohr Institute, University of Copenhagen. Improvement of Least -Squares Collocation error estimates using local GOCE Tzz signal standard deviations. . GOCE. GOCE Tzz (-ITG_Grace 2010s to 36), mean of 1 deg. Blocks, E.U. Use of Gradients:.

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

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  1. C.C.Tscherning, Niels Bohr Institute, University of Copenhagen Improvement of Least-Squares Collocation errorestimates usinglocal GOCE Tzz signal standard deviations. Hotine-Marussi Symposium, Rome, June 2013 .

  2. GOCE Hotine-Marussi Symposium, Rome, June 2013

  3. GOCE Tzz (-ITG_Grace 2010s to 36), mean of 1 deg. Blocks, E.U. Hotine-Marussi Symposium, Rome, June 2013

  4. 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. Reguzzoniand 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

  5. PURPOSE OF ERROR ESTIMATES • an indicator of the quality of an observed or estimated quantity • 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

  6. 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 ! Hotine-Marussi Symposium, Rome, June 2013

  7. ERROR ESTIMATES OF HEIGHT ANOMALIES FROM GRAVITY, units: m. Hotine-Marussi Symposium, Rome, June 2013

  8. ERROR ESTIMATES + IMPROVEMENTS • Only show location of data • Sometimes quality of data • Influence of different data types • But may be improved knowing local signal standard deviation or (rms) Hotine-Marussi Symposium, Rome, June 2013

  9. Example of localimprovement of errorestimates Gravityanomalies from GOCE Tzz & EGM2008 to 512. (ITG-Grace2010c to 36 subtracted everywhere), units: mgal. Hotine-Marussi Symposium, Rome, June 2013

  10. Differences and LSC errorestimates Differences gravityfromGOCETzz- EGM2008 to 512 and LSC errorestimates. Hotine-Marussi Symposium, Rome, June 2013

  11. GOCE Tzz RMS in 1 deg. blocks and scalederrorestimates GOCE Tzz RMS (E.U.) and scaled error estimates (mgal). Now error-estimates show how error varies. Hotine-Marussi Symposium, Rome, June 2013

  12. Global scaling using GOCE Tzz RMS in 1 deg. Blocks. GOCE Tzz (-ITG-GRACE2010c to 36) RMS (E.U) Hotine-Marussi Symposium, Rome, June 2013

  13. Global scaling possibel ? LSC error estimates of predicted reduced gravity in 20x20 blocks from GOCE Tzz. Hotine-Marussi Symposium, Rome, June 2013

  14. Global scaling of LSC error estimates in 1x1 deg blocks. Scaled error-estimates of predicted reduced gravity anomalies. Hotine-Marussi Symposium, Rome, June 2013

  15. 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

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