1. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Overview of GOCE Gradiometer Cal/Val Activities J. Bouman, P. Brieden, G. Catastini, S. Cesare, R. Floberghagen, B. Frommknecht, R. Haagmans, M. Kern, D. Lamarre, J. Müller, G. Plank, S. Rispens, C. Stummer, C.C. Tscherning, M. Veicherts, P. Visser

2. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway GOCE Cal/Val LP Symposium 2010 The in-flight calibration of the GOCE gradiometer (Cesare et al) Alternative in-flight calibration of the gradiometer using ESA's L-Method (Lamarre and Kern) Quality assessment of GOCE gradients (Müller and Brieden) A methodology to use terrestrial gravity data sets for regional validation of GOCE products in central Europe (Schäfer et al) First results using ESA's internal calibration method GRADNET (Kern et al) External calibration of GOCE differential accelerations (Rispens) Validation of GOCE with terrestrial gravity data in Norway (Gerlach and Pettersen) External calibration of the GOCE gravity gradients at the High-Level Processing Facility (Bouman et al)

3. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway 6 accelerometers measure in 3 orthogonal directions Each accelerometer has two ultra-sensitive axes and one less-sensitive axis OAG: One-Axis Gradiometer GRF: Gradiometer Reference Frame Gradiometer

4. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Ideal accelerometer measurements:  Gravity gradients  Rotational terms  Drag, solar radiation pressure, thruster action, …  Vibrations, self-gravity, … Common and differential accelerations  Common = sum averaged  drag etc  Differential = differences averaged  gravity gradients and rotational terms Pair of two accelerometers is OAG (One-Axis Gradiometer) Single accelerometer and pairs

5. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway 1.different scale factors 2.axes are not perfectly aligned 3.sensitive axes are not mutually perpendicular 4.internal dynamics 5.accelerometers do not occupy their nominal positions 6.origins of the 3 OAGRFs do not coincide and their axes are not aligned 7.gradiometer configuration is time-varying Measurements with a real gradiometer have errors due to: Real gradiometer measurements

6. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Acceleration measured by the accelerometer A i : a i = true acceleration a’ i = measured acceleration [K] i = scale factor matrix [dR] i = rotation matrix (misalignment) [dS] i = accelerometer inter-axis coupling matrix [K2] i = quadratic factor matrix b i = bias n i = noise Real gradiometer measurements

7. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway 1.On-ground verification 2.In-flight accelerometer calibration Quadratic factors Calibration parameters (matrix) Accelerometer or satellite shaking 3.External calibration and validation Accelerations or gravity gradients External gravity data and models GOCE Calibration Steps

8. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Verification of design/manufacturing tolerances and of stability (e.g. K2) One-Axis Gradiometer (OAG) baselines were measured on ground and these values are used in flight On-ground verification

9. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Two operations: Quadratic factor (K2) adjustment Scale factor, coupling & misalignment determination  Baseline method  ESA L-method  GRADNET In-flight calibration

10. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Feed-back loop non-linear a = K 0 + K 1 V + K 2 V 2 + … Physically reduce K2 to zero (acceptable level) by test mass position adjustment Test mass shaking In-flight calibration: quadratic factors

11. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway For each OAG, common and differential:  Couplings  Misalignments  Scale factors 54 calibration parameters (3*18) Relation between measured and corrected common & differential accelerations for one OAG (ij = 14, 25, 36): In-flight calibration: Inverse calibration matrices Three 6x6 calibration matrices M ij (scale factors, misalignments & couplings). Inverse calibration matrices MI ij must be known to recover actual accelerations from the measured ones.

12. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Calibration matrices for each OAG determined separately (iterative process) Satellite shaking enables relative calibration (all ICM elements except common scale factors) Star sensor data used to determine 9 absolute (common) scale factors Empirical relation between scale factors needed In-flight calibration: baseline method

13. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Equations in GRF instead of OAG (72 parameters) 54 parameters are estimated Co-estimate STR – gradiometer misalignment 1.Relative scale factors, relative positions and relative misalignments 2.One absolute scale factor, misalignment with respect to star tracker ESA-L & baseline ICMs agree except for large differences in common scale factors In-flight calibration: ESA-L method

14. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Accelerometers form a gradiometer network Use redundancy within the network ESA-L & GRADNET agree well Gradiometer scale factors stable to better than 10 -3 In-flight calibration: GRADNET x (GRF) y (GRF) z (GRF) (a 3x + a 6x ) / 2 = (a 1x + a 4x ) / 2

15. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway External calibration of accelerations External calibration and validation of gravity gradients (GOCE Cal/Val Team)  Global gravity field models  Using GOCE GPS data  Using terrestrial gravity data  Validation in crossovers External calibration

16. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway Use GG from model to calibrate GOCE GG GG scale factor determined up to 10 -3 level External calibration: Global gravity field models GOCE Model

17. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway External calibration GOCE GPS and terrestrial gravity data GOCE GPS data  Estimation of global 80 x 80 gravity field combining GOCE GPS data and GGs  GG scale factors co-estimated Terrestrial gravity data For each track in area GG SF estimated

18. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway External calibration Validation in crossovers (XO) Basic idea Identical measurement position → identical gravity gradient: V ij,1 = V ij,2 Tasks Interpolation of XO position and GG measurement along time series Reduction of altitude and attitude effects in measurements XO-differences fit very well with GG noise level V XX, V YY : 98% < 15 mE V ZZ : 98% < 25 mE

19. Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway GOCE calibration is done in 3 steps:  On-ground verification  In-flight calibration  External calibration and validation Absolute calibration requires reliable standard: not trivial Result:  Gravity gradient data of good quality  Improved gravity field information GOCE Calibration Splinter Meeting: Thursday 10 AM, Room Bøygen, Grieghallen Summary