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D.N. Arabelos, M. Reguzzoni and C.C.Tscherning HPF Progress Meeting # 26, München, Feb. 20-21, 2013. Global grids of gravity anomalies and vertical gravity.

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Presentation on theme: "D.N. Arabelos, M. Reguzzoni and C.C.Tscherning HPF Progress Meeting # 26, München, Feb. 20-21, 2013. Global grids of gravity anomalies and vertical gravity."— Presentation transcript:

1 D.N. Arabelos, M. Reguzzoni and C.C.Tscherning HPF Progress Meeting # 26, München, Feb. 20-21, 2013. Global grids of gravity anomalies and vertical gravity gradients at 10 km altitude from GOCE gradient data 2009-2011 and polar gravity

2 PURPOSE Progress Meeting # 26, München, Feb. 20-21, 2013. Promote the use of GOCE products by producing (new) grids of gravity anomalies and vertical gravity gradients at 10 km altitude. Possible improvement compared to the the HPF product of grids at zero height derived from the EGM’s. Observed gradients may contain more information than expressed through an EGM. Grid values may be improved using polar gravity.

3 Data used. Progress Meeting # 26, München, Feb. 20-21, 2013. TRF data 2009-2011 Polar gravity – but not Antarctic gravity. ITG-GRACE2010s (remove/restore)* EGM2008, GOCE DIR2 (control data). Data selected closest to mid-points of 10’ cells and 1/8 deg cells.** * permits spherical approximation in local areas, help in polar caps. ** nearly all cells filled !

4 Products: gridded gravity anomalies and vertical gradients, 10 km. Progress Meeting # 26, München, Feb. 20-21, 2013. Grids produced in 162 20x20 deg blocks with 10’ spacing. Error-estimates in grids with 1 deg spacing.

5 Use of Least-Squares Collocation (LSC). Progress Meeting # 26, München, Feb. 20-21, 2013. 1.Covariance estimation (from reduced data) 2.Selection of analytic representation 3.Selection of data in 25 x 25 deg. block 4.Creation of (upper triangular part of) normal equations 5.Solution of equations (Cholesky) 6.Prediction, comparison with EGM2008 to 512 and error-estimation in 1 deg. Grid. 7.Prediction of 10’ grids.

6 Covariance estimation (from reduced data),+analytic fitting Progress Meeting # 26, München, Feb. 20-21, 2013. Empirical (from EGM08, h=0), analytic, Analytic from GOCE vertical gradients.

7 Best data selection Progress Meeting # 26, München, Feb. 20-21, 2013. Numbe r of data Spacing (degree) Data type Mean difference Standard deviation Mean error estimate 224640.166T zz -0.59.736.92 449290.166T zz +T yy -0.49.656.85 379710.125T zz -0.59.166.79 Prediction of EGM08 derived gravity anomalies at 10 km, mgal Tzz with 0.125 deg. spacing selected.

8 Computational considerations with geocol19. Progress Meeting # 26, München, Feb. 20-21, 2013. Processor22 4 N3797122464 CHsss 05 1040741832 10676427098381 15789829627793 20696626427469 25722128367748 30747628948300 OMP Processing time for 20x20 block, N=number of data,CH=chunk block size. Time depends on rate of disk transfer.

9 Data noise standard deviation selection Progress Meeting # 26, München, Feb. 20-21, 2013. Prediction of EGM08 derived gravity anomalies at 10 km, block 73 Tzz with 0.02 EU noise st.dev. selected. Noise (EU)Dg (mgal)T zz (EU) Observed- predicted Error estimates Observed-predictedError estimates Standard deviationMean valueStandard deviationMean value 0.0307.417.673.283.06 0.0207.307.223.262.99 0.0107.446.523.292.88 0.0087.626.323.332.84 0.0058.405.753.522.76 0.0039.285.403.772.65 EGM08-DIR27.58 3.53

10 Prediction, comparison with EGM08 to 512 st.dev. gravity anomalies. Progress Meeting # 26, München, Feb. 20-21, 2013.

11 Prediction, comparison with EGM08 to 512 vert. gravity gradients (EU). Progress Meeting # 26, München, Feb. 20-21, 2013.

12 Comparison of st.dev. differences LSC, DIR2 wrt. EGM08. LSC inferior at middle latitudes due to less data used (?). Progress Meeting # 26, München, Feb. 20-21, 2013.

13 dg from TRF Tzz at 10 km (mgal). Progress Meeting # 26, München, Feb. 20-21, 2013.

14 dg at 10 km from EGM2008 to 512 (mgal). Progress Meeting # 26, München, Feb. 20-21, 2013.

15 TRF Tzz at satellite height (EU). Progress Meeting # 26, München, Feb. 20-21, 2013.

16 Transfer of results and further work. Progress Meeting # 26, München, Feb. 20-21, 2013. 1.Grids of gravity anomalies and vertical gradients transferred to POLIMI 2.Production to be repeated with POLIMI data and associated error-correlation functions. 3.Investigation using more data at middle latitudes 4.Smoothing of discontinuities at block boundaries 5.Use of MPI instead of OMP on several servers

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