Traitement des données de GRACE Mesures GPS et KBR R. Biancale (1), S. Bruinsma (1), J.-M. Lemoine (1), S. Loyer (2), F. Perosanz (1), G. Balmino (1), F. Flechtner (3), R. Schmidt (3), Ul. Meyer (3) (1) (2) (3) CNES/GRGS, Toulouse, France Noveltis, Ramonville Saint-Agne, France GeoForschungsZentrum, Potsdam, Germany Journées "Gravimétrie spatiale" Paris, 11-12 mai 2005 GRACE GRACE 2 satellites co-orbitant lancement : mars 2002 orbite polaire, circulaire altitude moyenne ~470 km Accéléromètres (Super-STAR) GPS : phases et pseudo-distances KBR : mesures de phase entre les deux satellites Î distance ambiguë Données de niveau 1B Î vitesse relative fournies par JPL (5 sec) Î accélération relative JPL, CSR & GFZ utilisent la vitesse relative seule ⇒Étude pour utiliser les autres observables (CNES) Principles of the GRACE gravity field mapping mission SST observables in the high-low & low-low modes GPS Satellites SST-hl- n SST-ll Density Anomaly Earth Performances prédites : erreur cumulée sur le géoïde … mais les performances de GRACE ne sont pas atteintes ! Sensitivity Analysis : RMS of linear perturbations Inter-satellite range perturbations per s. h. coefficient for periods < 1 day starting from 10 µm (log scale in m) Inter-satellite range-rate perturbations per s. h. coefficient for periods < 1 day starting from 0.1 µm/s (log scale in m/s) Comparison of projected orbit perturbations generated by the EIGEN-GRACE02S gravity field model in terms of range and range-rate inter-satellite perturbations, according to each degree and order of the spherical harmonic expansion up to degree 120. It shows a much more powerful signal for range measurements, in the considered intervals of sensitivity . Sensitivity ratio in orbit perturbations : range vs. range-rate Range (20 µm) / Range-Rate (0.3 µm/s ) Range (3 µm) / Range-Rate (0.3 µm/s ) % % The sensitivity ratio of calibrated (through noise) perturbation amplitudes of inter-satellite perturbations is given here, per spherical harmonic coefficient, as: (range/σrange) / (range-rate/σrange-rate) in %. It shows that, even for a 20 µm noise in range measurements, range perturbations are up to 40% more sensitive, particularly in the sectorial band, than range-rate perturbations when assuminging a noise level of 0.3 µm/s on the derived inter-satellite velocity. Covariance Analysis ( analytical linear theory) δ(l,m) % This figure compares errors of spherical harmonic coefficients estimated (by covariance analysis) from K-band range measurements and from range-rate measurements between GRACE-A and -B satellites (with white noise respectively of 20 µm and 0.3 µm/s). It represents the ratio δ(l,m) in % such as : δ(l,m) = { [σrange(l,m) - σrange-rate(l,m)] / σrange-rate(l,m) } x 100 It is remartkable that the wide negative sectorial band of coefficients (δ(l,m) < 0) corresponds to coefficients for which formal errors estimated from range data are less than those estimated from range-rate data. Away from this band, range-rate data induce smaller errors (up to 600% for harmonics of high degree and of low order). First conclusion : Range and range-rate observables may be combined : they carry different information strength vs. (l,m) … it may even be best to also use accelerations But : There are discontinuities in the range Î parameterization Each differentiation : - multiplies the signal by the frequency - amplifies the noise Computation of inter-satellite range-rate and acceleration by the CNES-GRGS team from 5s sampled level-1B data Biased range 1. Editing , Smoothing (optional) 2. Adjust & Remove 1/rev, 2/rev,…k/rev terms Lagrange derivation operator (e.g. degree 5) (in moving window) Smoothing (optional) - Restore periodic part of velocity 3. Lagrange derivation operator (in moving window) Smoothing (optional) - Restore periodic part of acceleration meas. rms (Level-1b) : 12 µm in orbit processing over one day arc (Aug. 14th, 2003) Range rate σ(l-1B – GRGS) = 0.1 µm/s rms (Level-1b) : 0.24 µm/s rms (GRGS) : 0.19 µm/s Acceleration σ(L-1b – GRGS) = 80 nm/s2 rms (Level-1b) : 92 nm/s2 rms (GRGS) : 34 nm/s2 Comparison of first and second derivatives of K-band range data Parameterization of K-band data K-band biased range, range-rate and range-acceleration data can be used concomitantly in orbit processing and gravity field model adjustment. But empirical parameters should be introduced to account for non stable behaviour of the K-band instrument at low frequency. We have tried 2 strategies of parameterization: 1) a bias, a slope, once per revolution and twice per revolution periodic terms each 90 mn; twice per rev. sine and cosine terms once per rev. sine and cosine terms slope bias 90 mn 2) a bias, a slope, even a quadratic term each 15 mn. quadratic term slope bias 15 mn In both cases, continuity constraints are applied between each consecutive interval, except when phase breaks occur. Moreover, the same parameters are used at the different levels of data derivation ; for example, a slope parameter in range is interpreted as bias in range-rate, or a quadratic term in range is interpreted as bias in range-acceleration. K-band residuals after adjustment of biases per 15 mn Systematic data processing … … but : gaps in K-band data coverage ! Example in August 2003 Example of monthly solutions : August 2003 August 2003 CNES Range-rate August 2003 GFZ Range-rate Solutions sur 30 j Août 2003 "vitesse" Í GFZ CNESÎ Solutions sur 30 j Août 2003 CNES Í "vitesse" "distance"Î Solution sur 10 j 3-13 Août 2003 CNES "vitesse" CONCLUSIONS 1. Génération de nos propres quantités dérivées (meilleure qualité que les données JPL) 2. Utilisation séparée/conjointe : de la vitesse de la distance de l'accélération + GPS (combinaison : mise au point système de pondération) 3. Solutions mensuelles : Août 2002- juillet 2004 4. Solution moyenne : champ "statique" sur cette période 5. Solutions décadaires : lorsque la couverture le permet