GRACE processing at TU Graz

Transcription

1 S C I E N C E P A S S I O N T E C H N O L O G Y GRACE processing at TU Graz Torsten Mayer-Gürr, Saniya Behzadpour, Andreas Kvas, Matthias Ellmer, Beate Klinger, Norbert Zehentner, and Sebastian Strasser Institute of Geodesy Graz University of Technology COST-G meeting, Bern u ifg.tugraz.at

2 ITSG-Grace2018 (Almost) complete reprocessed GRACE time series. Static gravity field degree/order 200 trend + annual signal full normal equations in SINEX format Unconstrained monthly solutions degree/order 60, 96, 120 full normal equations in SINEX format Daily Kalman filtered solutions degree/order 40 ifg.tugraz.at DOI /ICGEM

3 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 3

4 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 4

5 Covariance matrix of reduced obervations 5

6 Time series of postfit residuals KBR Range Rate Residuals are clearly correlated! 6

7 Covariance matrix of reduced observations Ca observations per month Size: ca. 2 TerraByte Divide into smaller blocks (max. 3 hours length = 2160 epochs) P 1 = ll = Correlations between blocks are ignored 7

8 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T KBR & ACC noise (stationary) Background models uncertanties Variance propagated to range rates SCA noise Variance propagated to range rates 8

9 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T KBR & ACC noise (stationary) Iterative procedure 1. Apriori covariance matrix 2. Solution via Least Squares Adjustment 3. Variance factor (amplitude) for each frequency via Variance Component Estimation (VCE) Toeplitz matrix Covariance function Power Spectral density (PSD) 9

10 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T KBR & ACC noise (stationary) Iterative procedure 1. Apriori covariance matrix 2. Solution via Least Squares Adjustment 3. Variance factor (amplitude) for each frequency via Variance Component Estimation (VCE) Toeplitz matrix Covariance function Power Spectral density (PSD) Ellmer, Matthias (2018): Contributions to GRACE Gravity Field Recovery, Doctoral dissertation, Graz University of Technology, Graz, Austria. DOI: /

11 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T SCA noise Variance propagated to range rates Antenna offset correction computed using level-1b orientation data (RL03). increase opening angle α: increase noise AOC α Variance propagation Stationary noise for star camera observations. Orientation uncertainties propagation to antenna offset correction. Ellmer, Matthias (2018): Contributions to GRACE Gravity Field Recovery, Doctoral dissertation, Graz University of Technology, Graz, Austria. DOI: /

12 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T Background models uncertanties Variance propagation to range rates AOD1B is given as series of spherical harmonics (degree 180) every 3 hours For variance propagation: Only daily mean (degree 40) are considered Vector of daily spherical harmonics x AOD = x 1 x 2 x 31 Covariance matrix: block Toeplitz matrix Σ AOD = Σ 11 Σ 12 Σ 13 T Σ 12 Σ 11 T Σ 12 T T Σ 13 Σ 12 Σ 11 12

13 The Updated ESA Earth System Model atmosphere ocean hydrology ice Solid earth Dobslaw et al estimation of the errors in the AO component 13

14 The Perturbed De-Aliasing Model for ESA ESM Atmosphere Ocean Dobslaw et al

15 The Perturbed De-Aliasing Model for ESA ESM Atmosphere Ocean Estimation of signal/error covariance matrix from 10 years of simulated data Σ AOD = 1 n n i= 1 x i x T i Assumption of stationary noise Temporal correlations are modelled as autoregressive (AR) process of order 3 Dobslaw et al

16 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T Background models uncertanties Variance propagation to range rates AOD1B is given as series of spherical harmonics (degree 180) every 3 hours For variance propagation: Only daily mean (degree 40) are considered Vector of daily spherical harmonics x AOD = x 1 x 2 x 31 Σ AOD = Covariance matrix: block Toeplitz matrix Σ 11 Σ 12 Σ 13 T Σ 12 Σ 11 T Σ 12 T T Σ 13 Σ 12 Σ 11 For variance propagation: Integration of spherical harmonics to range rates (Design matrix A) 16

17 Evaluation Using GRACE Data Quiet ocean RMS: No model uncert.: 21.2 cm EWH Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T ITSG2018 w/o model uncertainties 17

18 Evaluation Using GRACE Data Quiet ocean RMS: No model uncert.: 21.2 cm EWH Model uncert. considered: 13.3 cm EWH 37% RMS reduction Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T ITSG model uncertainties considered 18

19 Covariance matrix of reduced observations Covariance matrix Σ Δl = Σ KBR + BΣ SCA B T + AΣ AOD A T Background models uncertanties Variance propagation to range rates AOD1B is given as series of spherical harmonics (degree 180) every 3 hours For variance propagation: Only daily mean (degree 40) are considered Vector of daily spherical harmonics x AOD = x 1 x 2 x 31 Σ AOD = Covariance matrix: block Toeplitz matrix Σ 11 Σ 12 Σ 13 T Σ 12 Σ 11 T Σ 12 T T Σ 13 Σ 12 Σ 11 For variance propagation: Integration of spherical harmonics to range rates (Design matrix A) 22

20 S C I E N C E P A S S I O N T E C H N O L O G Y Incorporation of Background Model Uncertainties into the Gravity Field Recovery Process Andreas Kvas, Saniya Behzadpour, Matthias Ellmer, Beate Klinger, Sebastian Strasser, Norbert Zehentner, Torsten Mayer-Gürr Institute of Geodesy Graz University of Technology GSTM , Potsdam u ifg.tugraz.at

21 Gravity Field Recovery with Model Errors x gravity field parameters y model parameters evaluated using model output contaminated with (random) errors l = f(x, y) l = f x, y m = f m (x) y m = y t + y e y e ~ N(0, Σ y m ) linearization wrt to x observation equations covariance propagation Σ(e)? f m l = f m x 0 + ቤ x x x 0 + l f m x 0 = AΔx + e Σ e = Σ l + BΣ y m B T x 0, y m least squares adjustment B = f ቤ y x0, y m x = x 0 + A T PA 1 (A T PΔl) T 1 P = Σ l + BΣ y m B 24

22 Gravity Field Recovery with Model Errors Alternative Approach x gravity field parameters y model parameters l = f(x, y) linearization wrt to x and y f l = f x 0, y m + ቤ x x x f 0 + ቤ y y y 0 + add pseudo-observations blocked normal equations l f x 0, y m = AΔx + BΔy + e Σ(e) = Σ l 0 = IΔy + v Σ v = Σ(y m ) A T Σ l 1 A A T Σ l 1 B B T Σ l 1 1 B + Σ y m Δx Δy = AT Σ l 1 Δl B T Σ l 1 Δl least squares adjustment x = x 0 + A T PA 1 (A T PΔl) some tedious matrix algebra T 1 P = Σ l + BΣ y m B 25

23 Gravity Field Recovery with Model Errors Model uncertainties can be incorporated on both observation and parameter level Either augmentation of the covariance matrix of observations, or extension of the parameter space to include model corrections Δl = AΔx + e Δl = AΔx + BΔy + e Σ(e) = Σ l Σ e = Σ l + BΣ y m B T 0 = IΔy + v Σ v = Σ(y m ) For GRACE AOD errors applications as additional is preferable term to extend the parameter space Co-estimation of daily solutions Stationarity in theof covariance model errors matrix <= identical result => can be exploited to reduce computational demand with Σ AOD as constraint y e assumed stationary Σ y m has Toeplitz structure By e (observation level) non-stationary, depends on satellite position In this study, only dealiasing model errors are considered Stochastic properties are drawn from the ESA ESM aoerror sample time series Covariance structure is approximated by fitting an autoregressive model (AR) of order three to the time series 26

24 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 27

25 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 28

26 Updated background models 29

27 Background models Force models ITSG-Grace2016 ITSG-Grace2018 Static field + annual + trend GOCO05s Internal GRACE+GOCE 2017 Atmosphere + Ocean AOD1B RL05 AOD1B RL06 Hydrology - LSDM (submonthly part) Astronomical tides JPL DE421 JPL DE421 Earth tides IERS2010 IERS2010 Ocean tides EOT11a FES2014b + GRACE estimates Atmospheric tides van Dam, Ray 2010 (S1, S2) AOD1B RL06 Pole tides IERS2010 IERS2010 (linear mean pole) Ocean pole tides Desai 2004 Desai 2004 (linear mean pole) Non-Conservative forces Accelerometer L1B Accelerometer L1B Relativistic effects IERS2010 IERS

28 Background models Force models Static field + annual + trend Atmosphere + Ocean ITSG-Grace2016 GOCO05s AOD1B RL05 Hydrology - Astronomical tides Earth tides Ocean tides JPL DE421 IERS2010 EOT11a Atmospheric tides van Dam, Ray 2010 (S1, S2) Pole tides IERS2010 Ocean pole tides Desai 2004 Non-Conservative forces Relativistic effects Accelerometer L1B IERS

29 Background models Force models ITSG-Grace2016 ITSG-Grace2018 Static field + annual + trend GOCO05s Internal GRACE+GOCE 2017 Atmosphere + Ocean AOD1B RL05 AOD1B RL06 Hydrology - LSDM (submonthly part) Astronomical tides JPL DE421 JPL DE421 Earth tides IERS2010 IERS2010 Ocean tides EOT11a FES2014b + GRACE estimates Atmospheric tides van Dam, Ray 2010 (S1, S2) AOD1B RL06 Pole tides IERS2010 IERS2010 (linear mean pole) Ocean pole tides Desai 2004 Desai 2004 (linear mean pole) Non-Conservative forces Accelerometer L1B Accelerometer L1B Relativistic effects IERS2010 IERS

30 Background models Force models ITSG-Grace2016 ITSG-Grace2018 Static field + annual + trend GOCO05s Internal GRACE+GOCE 2017 Atmosphere + Ocean AOD1B RL05 AOD1B RL06 Hydrology - LSDM (submonthly part) Astronomical tides JPL DE421 JPL DE421 LDSM Hydrology model - reduced by annual, trend Earth tides IERS2010 IERS2010 Ocean tides EOT11a - reduced FES2014b by monthly + GRACE mean estimates only submonthly part used as dealiasing Atmospheric tides van Dam, Ray 2010 (S1, S2) AOD1B RL06 Defintion of GRACE monthly not changed (contains full monthly hydrological signal) Pole tides IERS2010 IERS2010 (linear mean pole) Ocean pole tides Desai 2004 Desai 2004 (linear mean pole) Non-Conservative forces Accelerometer L1B Accelerometer L1B Relativistic effects IERS2010 IERS

31 Background models Force models ITSG-Grace2016 ITSG-Grace2018 Static field + annual + trend GOCO05s Internal GRACE+GOCE 2017 Atmosphere + Ocean AOD1B RL05 AOD1B RL06 Hydrology - LSDM (submonthly part) Astronomical tides JPL DE421 JPL DE421 Earth tides IERS2010 IERS2010 Ocean tides EOT11a FES2014b + GRACE estimates Atmospheric tides van Dam, Ray 2010 (S1, S2) AOD1B RL06 Pole tides IERS2010 IERS2010 (linear mean pole) Ocean pole tides Desai 2004 Desai 2004 (linear mean pole) Non-Conservative forces Accelerometer L1B Accelerometer L1B Relativistic effects IERS2010 IERS

32 Estimated ocean tides from GRACE data Complete GRACE time series Full normals: tides+daily+annual+trend Constrained towards FES2014b Contains atmospheric and ocean tides Introduced as new background model Q1 O1 Mm P1 N2 Mf S1 M2 Mtm K1 S2 cos sin cos sin cos sin 35

33 Estimated ocean tides from GRACE data Complete GRACE time series Full normals: tides+daily+annual+trend Q1 Constrained towards FES2014b Contains atmospheric and ocean tides Introduced as new background model M2 (GRACE estimates relative to FES2014b) O1 Mm P1 N2 Mf S1 M2 Mtm K1 S2 cos sin cos sin cos sin 36

34 Estimated ocean tides from GRACE data Complete GRACE time series Full normals: tides+daily+annual+trend Q1 Constrained towards FES2014b Contains atmospheric and ocean tides Introduced as new background model S1 (GRACE estimates relative to FES2014b) O1 Mm P1 N2 Mf S1 M2 Mtm K1 S2 cos sin cos sin cos sin 37

35 Background models Force models ITSG-Grace2016 ITSG-Grace2018 Static field + annual + trend GOCO05s Internal GRACE+GOCE 2017 Atmosphere + Ocean AOD1B RL05 AOD1B RL06 Hydrology - LSDM (submonthly part) Astronomical tides JPL DE421 JPL DE421 Earth tides IERS2010 IERS2010 Ocean tides EOT11a FES2014b + GRACE estimates Atmospheric tides van Dam, Ray 2010 (S1, S2) AOD1B RL06 Pole tides IERS2010 IERS2010 (linear mean pole) Ocean pole tides Desai 2004 Desai 2004 (linear mean pole) Non-Conservative forces Accelerometer L1B Accelerometer L1B Relativistic effects IERS2010 IERS

36 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 39

37 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 40

38 Parametrization 41

39 Parametrization Gravity field Monthly spherical harmonics (degree = 60, 96, 120) Daily spherical harmonics (degree = 40), constrained Orbit Daily satellite state (position, velocity) Accelerometer Bias per axis: cubic splines with 6 hour knot interval Daily full 3x3 scale matrix: scale, rotation, shear KBR antennca center (x, y) Monthly Beate Klinger and Torsten Mayer-Gürr (2016): The role of accelerometer data calibration within GRACE gravity field recovery: Results from ITSG-Grace2016, Advances in space research, 1597, DOI /j.asr

40 KBR Antenna Center 43

41 Parametrization Gravity field Monthly spherical harmonics (degree = 60, 96, 120) Daily spherical harmonics (degree = 40), constrained Orbit Daily satellite state (position, velocity) Accelerometer Bias per axis: cubic splines with 6 hour knot interval Daily full 3x3 scale matrix: scale, rotation, shear KBR antennca center (x, y) Monthly Parametrization of special events (sun-shadow crossing, sun intrusion into star camera) Signal events are identified beforehand in the monthly time series. For each event the middle time is selected + Time margin. disturbance range rate signals at each event using polynomial (degree 11). The monthly variation of each signal: uniform cubic B-splines Beate Klinger and Torsten Mayer-Gürr (2016): The role of accelerometer data calibration within GRACE gravity field recovery: Results from ITSG-Grace2016, Advances in space research, 1597, DOI /j.asr GSTM-2018: Saniya Behzadpour et. al.: Reducing systematic errors in the GRACE observations using parametric models Paper is in preparation 44

42 Residuals (argument of latitude versus time) Equator Time One revolution North pole Equator South pole Equator 45

43 Residuals (argument of latitude versus time) Sun shadow crossing 46

44 Residuals (argument of latitude versus time) Sun intrusion into star camera baffle Sun shadow crossing 47

45 Residuals (argument of latitude versus time) 48

46 Residuals (argument of latitude versus time) 49

47 Residuals (argument of latitude versus time) 50

48 Residuals (argument of latitude versus time) 51

49 Processing at TU Graz Level2: Monthly gravity fields Postfit residuals Least squares adjustment xˆ = Design matrix: Parametrization T 1 1 T 1 ( A A) A l ll ll Weight matrix: Inverse of the covariance matrix of reduced observations Reduced observations: Observed computed (Background models) 52

50 References Matthias Ellmer (2018): Contributions to GRACE Gravity Field Recovery, Doctoral dissertation, Graz University of Technology, Graz, Austria. DOI: / Beate Klinger (2018): A contribution to GRACE time-variable gravity field recovery: Improved Level-1B data preprocessing methodologies, Doctoral dissertation, Graz University of Technology, Graz, Austria. Matthias Ellmer, Torsten Mayer-Gürr (2017): High precision dynamic orbit integration for spaceborne gravimetry in view of GRACE Follow-on, Advances in space research, DOI /j.asr Norbert Zehentner (2017): Kinematic orbit positioning applying the raw observation approach to observe time variable gravity, Doctoral dissertation, Graz University of Technology, Graz, Austria. Beate Klinger and Torsten Mayer-Gürr (2016): The role of accelerometer data calibration within GRACE gravity field recovery: Results from ITSG-Grace2016, Advances in space research, 1597, DOI /j.asr Norbert Zehentner and Torsten Mayer-Gürr (2015): Precise orbit determination based on raw GPS measurements, Journal of geodesy, 90: 275. DOI /s