REeal data AnaLysis GOCE Gravity field determination from GOCE

Transcription

1 REeal data AnaLysis GOCE Gravity field determination from GOCE J.M. Brockmann 1, O. Baur 3, J. Cai 3, A. Eicker 2, B. Kargoll 1, I. Krasbutter 1, J. Kusche 2, T. Mayer-Gürr 2, J. Schall 2, W.-D. Schuh 1, A. Shabanloui 2, N. Sneeuw Institute of Geodesy and Geoinformation Theoretical Geodesy University of Bonn 2 Institute of Geodesy and Geoinformation Astronomical Physical Mathematical Geodesy University of Bonn 3 Institute of Geodesy University of Stuttgart BMBF Geotechnologien Statusseminar: Erfassung des Systems Erde aus dem Weltraum III Bonn, 04/10/2010

2 Content 1 Motivation 2 Gravity field determination within REAL GOCE Satellite-to-Satellite Tracking (SST) Satellite-gravity-gradiometry (SGG) 2 3 First gravity field solutions derived from GOCE 4 Summary and Outlook

3 Sensors for gravity field determination The whole satellite is the sensor! c ESA 3 But three main sensor observations to be scientificly processed for gravity field determination: GPS tracking (SST) Gradiometry (SGG) star tracker (STR) c ESA

4 From observations to the gravity field geolocated gravity gradients satellite orbits gradiometer orientation + + V (r, θ, λ) = 4 + +gradient error information +orbit error information lmax l a l+1 X GM X (clm cos (mλ) + slm sin (mλ)) Plm (cosθ), (1) a l=0 r m=0 spherical harmonic coeficients + accuracies geoid heights + accuracies geoidegm2008.dat (min= , max= , avg= , rms= ) geoidvariance.dat (min= , max= , avg= , rms= ) 9 log10 degree degree 9 10 log m sin cos sin mm cos

5 SST observations Satellite-to-Satellite tracking in high low mode: The Instrument: The Principle: c GOCE Projektbu ro 1 X 1 r = F = g(clm, slm ) + Fi (2) m m i Original measurements: I GPS Code observations I GPS Phase observations Pseudo observations for GFR: I kinematic satellite positions (ITRF, x, y, z), σ 20mm I covariance matrix (GPS geometry) 5 I source a) HPF/EGG-C: SST PSO I source b) orbit determination in REAL GOCE (IGG-APMG) I Approaches within REAL GOCE: integral equation approach, acceleration approach, energy balance approach I Sensitivity: long wavelength part, s/h degree 2 to 100 I Contribution: within a combined GOCE-only model d/o 2-25 Long wavelength GOCE models will never be competitive to GRACE!

6 GOCE SST real data performance 2 months compared to GRACE/CHAMP (7 years): degree variance without (near) zonals (m) ITG Grace2010s energy balance (EGG C) AIUB CHAMP03S integral equation (IGG APMG) spherical harmonic degree l 6 solid: degree variance from difference to ITG-Grace2010s, dashed: degree variance from formal errors

7 SGG observations Satellite-gravity-gradiometry: The Instrument: The Principle: Original measurements: I accelerations of the six accelerometers c ESA 2 Vxx T = 4Vxy Vxz I I I c ESA Vxy Vyy Vyz 3 Vxz Vyz 5 Vzz (3) Pseudo observations for GFR: I 6 differential accelerations I high temporal auto correlations in the gradients I as calibrated gravity gradients Vij 7 I source: ESA HPF/EGG-C: EGG NOM REAL GOCE approaches: in situ time-wise approach, in situ short arc approach, in situ invariant approach Sensitivity: short wavelength part Contribution: within a combined GOCE-only model d/o ( future?)

8 Stochastic Characteristics of SGG Data Estimated SGG noise as time series: Spectral characteristics of SGG noise: Vzz (E) :00:00 measured - GRS80 (mean reduced) computed - GRS80 (mean reduced) measured-computed (mean reduced) 01:00:00 02:00:00 03:00:00 04:00:00 time on 01-Nov-2009 I measured mean & GRS reduced Vzz gradient I computed mean & GRS reduced Vzz gradient (EIGEN5C) I estimated mean reduced Vzz noise (measured-computed) I signal and noise have the same order of magnitude I flat spectra only within the MBW I two gradient components with very high noise levels (Vxy, Vyz ) I sharp peaks at k per revolution (k = 1, 2,... ) I noise level MBW: 8mE/ Hz for Vxx, Vyy & 12mE/ Hz for Vxz, Vzz I worse Vzz performance not understood

9 Time-Wise Approach (IGG-TG) gap-less part of independent gradients as equidistant time series: optimized digital ARMA filter cascades to decorrelate gradient observation equations: simulated gradients xx 3.09e e e e e e e e e-06 04:00:00 06:00:00 08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 17:59:59 20:00:00 Observation equations: 1. potential in EFRF cf. (1) 2. 2nd derivative according to λ, θ 3. rotation to GRF (earth rotation, error-free STR) (l + v = Ax)GRF 4. application of decorrelation filters to obs. eqs. (Fl + Fv = FAx)GRF ` 5. Final obs. eqs.: l + v = A x GRF, Q l l = I Solution process: 1. Least-Squares solution 2. using tailored parallel iterative solver (PCGMA, conjugate gradients) 3. combination of SGG with SST NEQ 4. stabilisation using Kaula s rule 5. optimal weighting using VCE 6. iterative refinement of filter cascades

10 Short-Arc Approach (IGG-APMG) analysis of short arcs (length of 15 min): full variance covariance information per short arc: 10 Observation equations per short arc: 1. short arcs assumed to be uncorrelated 2. long wavelength error modeled with a bias parameter 3. 2 nd derivative of (1) according to x, y, z 4. rotation with STR data to GRF Solution process: 1. Least-Squares solution 2. assembling of arc-wise full NEQ 3. stabilisation using priori information 4. optimal weighting using VCE 5. local refinement with local base functions

11 Invariants Approach (GIS) rotational invariants of gravity gradients combination of tensor elements: Invariant I 2 on 02-Nov-2009 main diagonal GGs only: 11 Observation equations (STR independent): 1. I 2 = 1 `V 2 2 xx +Vyy 2 +V zz 2 Vxy 2 V xz 2 V yz 2 2. Variance propagation of GG error model to invariants 3. neglecting correlations among GGs 4. Σ I2 I 2 = P P J ij Σ Vij V ij J T ij i x,y,z j x,y,z 1 5. inserting Σ Vij V ij = F T F Vij Vij Solution process: 1. Least-Squares solution 2. Tailored parallel processing scheme 3. High performance computing with OpenMP and MPI 4. Stabilisation with a priori information 5. Optimal regularization

12 GOCE SGG real data performance GOCE SGG performance (1-2 months) compared to EIGEN5C: degree variance without (near) zonals (m) EIGEN5C ITG Grace2010s 1 month SGG (IGG APMG) 2 months SGG (IGG TG) spherical harmonic degree l solid: degree variance from difference to EIGEN5C, dashed: degree variance from formal errors

13 Overview of methods within REAL GOCE In general, there are three independet methods to determine the gravity field model from GOCE within REAL GOCE: SST general functional model stochastic model IGG-TG preprocessed in HPF energy balance geometry of GPS constellation IGG-APMG short arcs integral equation geometry of GPS constellation, refinement with emp. covarince function 13 GIS acceleration approach numerical differenciation variance-covariance information of kinematic GOCE orbit of GOCE orbit (GPS constellation) SGG general functional model stochastic model IGG-TG time series 2 nd derivative of potential in GRF ARMA filter cascades, decorrelation for V xx, V yy, V zz of continuous, gap-less time series IGG-APMG short arcs 2 nd derivative of potential in GRF empirical covariance matrix, empirical for V xx, V yy, V zz parameters/arc, independence of arcs GIS time series rotational invariants of the propergation of gradient error model gradient tensor to invariants

14 Links in the gravity field processing groups Cooperations within the gravity field processing groups: IGG-TG GIS: Stochastic model for gradients (for error propagation to invariants) IGG-APMG IGG-TG: alternative SST normal equation matrix for combination 14 GIS IGG-TG, IGG-APMG: STR independent solution IGG-TG IGG-APMG: stochastic model analysis, filter vs. covariance function ALL ALL: outlier information, quality information on gradients ALL ALL: mutual validation of results

15 GOCE-only model performance GOCE performance (1-2 months) compared to EIGEN5C: degree variance without (near) zonals (m) EIGEN5C GOCE only (II) GOCE only (I) Kaula s rule spherical harmonic degree l 15 solid: degree variance from difference to EIGEN5C, dashed: degree variance from formal errors

16 GOCE-only model performance Geoid heights compared to ITG-Grace2010s (d/o 150): [m/s^2] sector min max mean rms [ ] [m] [m] [m] [m] ± ±

17 GOCE-only model performance Geoid heights compared to EIGEN5C (d/o 200): [m/s^2] sector min max mean rms [ ] [m] [m] [m] [m] ± ±

18 Gain of GOCE Gain of the current GOCE models: degree 10 log 10 degree 10 log sin cos sin cos With only two months of data: consistent set of spherical harmonic coefficients d/o GRACE improvement d/o 140+ Improvement of combined models in regions w. low-quality terrestrial data Lot s of effort in stochastic modeling: High quality variance/covariance matrix Good reflection of errors by the VCM Formal errors are meaningful There will be huge improvements with more GOCE data!

19 Summary and Outlook Summary: Processing of real data started within REAL GOCE First results from all three approaches Processed until now: November (and December) 2009 (data released by ESA) For details on the three approaches: See posters! All milestones which are due until today have been achieved Work to achive other milestones is in progress Outlook: Understand the new observation type in more detail Processing of a longer time span Regional refinements of global solution 19