Satellite Gravity: GRACE & GOCE
Srinivas Bettadpur, Associate Professor, Dept of Aerospace Engineering & Engineering Mechanics and Center for Space Research University of Texas at Austin
Airborne Gravimetry for Geodesy – Summer School Silver Springs, MD, USA (May 23-27, 2016) Presentation Viewpoint
• Global gravity field models derived from satellite data serve as a long-wavelength reference, to support the interpretation of in situ data. – While this may not be literally exact, it serves as basis for the flow of this presentation
• Therefore, I choose to classify the audience engagement with satellite gravity data into three levels: – Level-3: Start with “satellite-only” fields – resolution ≈ 300-100 km – Level-2: Start with Inter-technique data fusion • GOCE, GRACE, GRACE-FO, GNSS-tracking of low Earth orbiters, etc – Level-1: Process mission datasets at “lower” levels (metrology) Level-3 Use of Global Satellite Models Level-3: Many global models available… Level-3: Broad User Guidelines… • Many global models are available.
• All models provide spherical harmonic coefficients
– Nmax ranges from 180 to 280 – Data span ranges from 3 years to 12 years – Infinite variety of analyst noise
• Spatio-Temporal Error Characteristics – Low Degrees – Generally very well determined – Mid Degrees – Strongly influenced by analyst choices in data fusion – High Degrees – Recognizable/unique error characteristics
• A typical Level-3 User will, therefore, put in most effort in the recognition of (and accounting for) these unique error patterns. The GGM05 Model Suite
• GGM05S – A “GRACE-only” model • Outcome of CSR_RL05 monthly time-variable gravity models • Unconstrained estimates to d/o 180 • GGM05G – A “GRACE+GOCE” model • Coefficients of a “smooth” (EGM08-like) field adjusted using band-pass filtered (10-50 mHz) GOCE data (XX+XZ+YY+ZZ). • Polar gap filled with synthetic gradients derived from 150x150 GGM05S at 200-km altitude • Added GGM05S after extensive experimentation with relative weights of GRACE and GOCE – trading long-wavelength benefits relative to short wavelength artifacts • GGM05C – A GRACE + GOCE + DTU13 GGM05S
Ten-year combination of GRACE monthly estimates (March 2003 to April 2013)
Gravity anomalies from GGM05S to degree/order 180 (100 km smoothing) GGM05G
Combine GGM05S with GOCE + polar gap fill from GGM05S
Gravity anomalies from GGM05G to degree/order 240 (50 km smoothing) Variations Relative to EGM08
(Pavlis et al. 2012) Image on left shows, in addition to the land gravity corrections:
1. Corrections to potential MDT built into EGM08 (evident in Southern Oceans) 2. GRACE-related artifacts (≈2-4 cm) evident over mid-Pacific 3. Near coastal artifacts (≈10 cm) arise likely from the transition between three datasets across the coasts in EGM2008 Smoothed Surface Gravity Test Statistics
No solution is best everywhere, though all show improvement in areas where no gravity data was available for EGM2008 GRAV-D data comparisons show little discrimination between models Level-3 User would carry out further analysis at spatial scales of typical interest to this audience GOCO05S
MDT residuals before spectral filtering (no smoothing). Color scale runs ± 35 cm
GGM05G GOCO05S
MDT residuals after spectral filtering (no smoothing). Color scale runs ± 35 cm
GGM05G No need any longer to use GRACE-only models for this purpose Level-3: A Way Forward
• Choose one (or many) candidate global field(s) – Use fields derived using both GRACE and GOCE datasets. – No reason any more to use any (current-day) GRACE-only fields • (High-resolution time-variable signals due to ice-loss are “few-mm”)
• For the local region of interest, empirically build error covariance – By inspection – Upon comparison with in situ data
• Use, thereafter, the global models with your own error estimates Level-2: Build your own ‘satellite-only’ field
Ingredients Needed: Estimates and covariance matrices for individual datasets from each satellite gravity mission
And then on to the concerns of Level-3 user… Level-2: GRACE Variations
• Variable Data Quality: – 2003-2010: Flight platform was most stable; relatively constant altitude. • Exclude certain durations with very poor ground-track coverage – Post-2010: Strike a balance between poor environmental control and lower altitude (higher noise at wavelengths shorter than ≈ 500 km, compared to earlier in mission).
• Formal covariance certainly does NOT reflect true errors in the mean field harmonics – For tuning GGM05G errors, a very “engineering” approach was adopted – We think we have a way to do this is a formally correct way in next Release-06 (due Spring/Summer 2017)
• Stray issues – Choice of the degree-2 harmonics should be solveable
Level-2: GOCE Variations
• Variable Data Sensitivity – GOCE mission identifies spans with variable extent of instrument calibration and with lowering altitude
• Consider treating each component of the gravity gradient independently, for its regional information contribution
• Handle polar gap “carefully” – This may scare the space-geodesists more than it does the physical geodesists Level-2 Work: Covariance Tuning & Relative Weighting Level-1: To the basics… Level-1: Checklist • Global or Local Solutions? Go for global solutions
• Do I need a supercomputer? Wouldn’t hurt, as it allows for rapid parameteric experiments – Each processing by itself is not too onerous computationally
• Differential Corrections with Variational Equations and a spherical harmonic model will work. – All roads lead to the same place with unconstrained solutions – “striations” with GRACE, and “orange-peel” with GRACE+GOCE – Regularization or stabilization are the only meaningful game-changers in this domain, for purposes of needs of this audience.
• Specialized software is needed, and is considerable effort to assemble. – Some knowledge of aerospace systems will be needed, as well. – Data screening requires a LOT of effort Oct 2004 Year:2004 DOY:304 From:65000 sec To:69000 sec
Editing Orbits kbr residuals
Before Extra Editing
Post-fir kbr residuals Starting Early in the Space Age
• The Pear-Shape of the Earth (1959) was estimated from studies of the orbits of Vanguard-1 satellites.
From: O’Keefe, Eckels & Squires, Science, New Series, Vol. 129, No. 3348 (Feb 27, 1959) pp 565-566 Over the next four decades, a wide variety of techniques of observing orbital motion of near-Earth satellites were used to determine and analyze the variations in Earth’s gravity field:
Optical Measurements Radar and Radio Ranging Satellite Laser Ranging Global Positioning System Radar Altimetry Status Just Before GRACE
• 30+ years of analysis of terrestrial tracking data: – Hemispheric scale estimates, used as validation/constraints on climate models – Formulation: Short-arc, Precision Orbit Determination, with numerical adjustment of model parameters
Figure 1, Cheng & Tapley (JGR v 109, Sep 2004)
GIA + Atmosphere + Hydrology + Glaciers + … 20 years later 500 km 89° 5+2+2 years Rockot (via DLR)
3 x 1.3 x 0.9 m Otherwise “perfect” record No panel 440 kg GRM Gradio Aristoteles 0.2 µ/s (& better) < 1 cm SLR/GPS TIDES GAMES …. GRACE Measurement Concept Gravity Observations & Orbits
Potential Observations of satellite motion Altimetry and analysis of perturbations (Seasat to OSTM) U
(Lageos 1/2, and (TDRSS, Doris) other geodetic sats) Doppler SLR/GPS
Acceleration Velocity Position Gravimetry g = ∇ U ∫ g ∫∫ g
Earth’s gravity field variation spectrum ranges from sub-diurnal to millenial time-scales, and is visible at all spatial (local to global) wavelengths.
Variations are caused by external (luni-solar tides) and internal (GOCE) (oceans, atmosphere, ice, elastic Earth) influences, and can be regular Gradiometry Gradients (tides), irregular (climate), or episodic (earthquakes). G = ∇ g Measurement of higher derivatives of gravity provides better determination of small spatial-scale features. GRACE: Mission Concept
GPS Satellites
Nominal separation Ground-based GPS Receiver
Mass anomaly (fixed or moving) GRACE: Mission Concept
GPS Satellites
Leading satellite - approaching the anomaly - feels Ground-based a greater gravitational attraction: GPS Receiver Separation Increases
Mass anomaly GRACE: Mission Concept
GPS Satellites
Trailing satellite - also approaching the mass Ground-based anomaly - accelerates and catches up: GPS Receiver Decreasing Separation
Mass anomaly GRACE: Mission Concept
GPS Satellites
Leading satellite is far from the anomaly, and is Ground-based not affected by it; while the trailing satellite - having just GPS Receiver passed the anomaly - is being tugged backwards: Increasing Separation.
Mass anomaly GRACE: Mission Concept
GPS Satellites
Trailing satellite catches back up with leading satellite but the ‘signature’ of mass ‘lump’ has been observed in K-band range data Ground-based GPS Receiver
Mass anomaly KBR Signal Content
Full KBR Range - Bias
Cubic Spline Residual (30 second knots)
Topography Along Groundtrack
(glk/jpl) GRACE Mission Science Goals High resolution, mean & time variable gravity field mapping for Earth System Science applications. Mission Systems Instruments • HAIRS (JPL/SSL/APL) • SuperSTAR (ONERA) • Star Cameras (DTU) • GPS Receiver (JPL) Satellite (JPL/Astrium) Launcher (DLR/Eurockot) Operations (DLR/GSOC) Science (CSR/JPL/GFZ) Orbit Launched: March 17, 2002 Initial Altitude: 500 km Inclination: 89 deg Eccentricity: ~0.001 Separation Distance: ~220 km Lifetime: 5 years Non-Repeat Ground Track, Earth Pointed, 3-Axis Stable The Satellites Orders of Magnitude Virtually all of this signal is due to the phase difference between the two satellites traveling in eccentric orbits.
Various Perturbations
Gravitational Sat-to-Sat Sat-to-Sat Sat-to-Sat Effect Acceleration Range Range-Rate Acceleration
Moon 1.04E-6 3.2 mm 7.8 micron/s 15 nm/s^2
Sun 9.95E-7 1.6 mm 5.9 micron/s 7.3 nm/s^2
Solid Earth 1.96E-7 0.13 mm 0.27 micron/s 0.7 nm/s^2 Tides
Ocean Tides 7.41E-8 122 microns 0.6 micron/s 5 nm/s^2
Atmosphere + non-tidal 3.33E-8 10 microns 0.12 micron/s 1 nm/s^2 Oceans
GRACE Signal 7.50E-8 127 microns 0.7 micron/s 5.4 nm/s^2 Time-Averaged Gravity From Space
9.8 m/s2
9.78 – 9.832 m/s2 equator-to-pole
Permanent deviations from gravity of an oblate spheroid reflect crustal/tectonic structure, and are ≈ ± 100 micro-g at Earth surface (4th & 5th decimal places in “g”)
Acceleration Units: 1 milli-Gal = 10-5 m/s2 ≈ 1 micro-g; 100 mGal = 1 mm/s2
Color scale from WGM2012/BGI The Known Variations
• Largest time variations are due to planetary perturbations and solid tides, and generally well-known.
• Ocean tides (top-right) are known (to a large extent) from radar altimetry and in situ measurements.
• Non-tidal atmospheric and ocean variations (bottom-right) are less-well known (measurements and models)
• NOTES: – Images drawn to Nmax = 100 (and hence the “smeared” appearance), and show RMS about the mean within one month (April 2010). – Atmospheric/Oceanic variations are quite variable from month-to-month; and are shown without the thermal (S2) variations. New Observations from GRACE
What is left? Hydrological and Ice-Sheet variations (along with errors in tides, atmosphere, oceans, etc)
This mass re-distribution measurement gives insights into their causative climate processes.
These processes could not be observed uniformly globally, at this scale, before GRACE.
Compare the ±6 nano-g scale of this animation with Acceleration Units: 1 micro-Gal = 10-8 m/s2; or 1 nano-g the ±100 micro-g for the static field;
Relative Accelerations on GRACE s/c These are inter-satellite acceleration residuals with respect to the background gravity field accelerations.
Continental hydrology and ice-sheet changes are the most conspicuous omissions from the background models, and hence most visible in data residuals.
Late mission (Nov 2013, right) residuals show the growing ice-mass loss compared to the early mission residuals (Nov 2002, top).
While relative accelerations are shown for geographic specificity, we adjust gravity models to relative range-rate – fitting to ≈20 nm/s at low frequencies, and 200 nm/s at high frequencies Observation Geometry Distribution of Data in a Bin
Location of all data for calendar year 2008 is shown All GRACE Data in a Bin
Each vertical “pass” represents one visit (70-80 seconds) to this bin Within each pass, data is well approximated by a line or a quadratic Trend within each pass is part of an overall, long-period signal during that orbit Representing Time Variability in the Bin
Considerable variation within one month (largely part of the annual signal) Outliers are also evident. A “quiet” bin Sub-Seasonal Variations: A Simulation
Note arrows, showing location of large, rapid soil-moisture variations that are missed by GRACE due to orbital coverage – This is Motivation for a future GRACE constellation. Schematic For Data Analysis Processing Schematic
Mean gravity
Location of GRACE Time-series products created in measurements Feb 2004 ground processing
F
Consolidate Level-2 Level-1 Intersatellite Range regionally or Processing δρgrav - ρall Processing Accelerometry globally Attitude GPS Ranging
Fgrav δ δMass or Grav δPressure All “known” gravitational influences are removed using geophysical models Gravity change Map products created in (Feb 2004 - mean) derived from other data ground processing
It should be emphasized that GRACE provides mass “anomalies” relative to a long-term average The Dynamical System
• Parametrized Modeling of Orbit Dynamics
• Physics: Newtonian Mechanics * • Gravitational & non-gravitational accelerations • State of the System defined by – Position & Velocity; and – Suite of models for grav & non-grav accelerations • System Parameters are: – Initial position & velocity at some epoch – Parameters within models for grav & non-grav accelerations – Other “nuisance” parameters • Propagation using numerical integration techniques – Non-linear system includes sophisticated models for orbit dynamics – Propagate non-linear state AS WELL AS variational equations
* With relativistic corrections The Observations
• Observations: Measurements of instantaneous position or velocity relative to an observatory: e.g. – Distances from terrestrial observatories • using radio or laser techniques – GPS ranging – GRACE inter-satellite ranging
• Differential Corrections, with iterations – Estimate corrections to nominal values of System Parameters – Linearized least-squares, using variational equations – Multi-sensor data fusion – Optimal Weighting
Piecewise Constant Representation
• The continuous spatial and temporal spectrum of natural mass flux processes is represented by piece-wise constant models.
• For each time “piece”, the gravity field of the Earth is represented by the coefficients of a spherical harmonic expansion.
• The GRACE project deliverable is a time-sequence of such harmonic coefficients – Presently, we deliver monthly products – Representations other than the spherical harmonic coefficients are popular. Background Gravity Model Science from the mission is a conjunction of Estimates and the errors of Omission and Commission in the Background Gravity Model
Estimate
GRACE Obs Predicted Obs Resolution & Accuracy Elements in Data Reduction
All strategies to extract mass anomalies from GRACE data have these elements in common, though they may be mixed in various ways:
1. Relationship between range (or its derivatives) and the in situ gravitational potential 2. Downward continuation method, suitably stabilized 3. Inversion from gravitational potential to mass anomalies 4. Error reduction methodologies
For GRACE data products, the latter two are the responsibility of the users. For GRACE-FO, a nominal mass anomaly dataset will be produced by the mission. User interpretation must depend on a knowledge of background models. GRACE & the User
Payoff Satellite data Complete flexibility Level-1 Skills High resolution data - Aerospace Engg (10 Hz versus 0.2 Hz) - Filtering/Data Proc Need to “learn” the instruments Level-1 data Optimally adapted, Level-2 Skills regionally tailored science - Geodesy Adaptive spatio/temporal resolution - Geodynamics Gravity Alternative methods/Error reduction Models Level-3 Skills Adaptability in science applications - Geophysics Post-proc Error reduction - Geodesy Mass Flux Est Dual One-Way Ranging System Dual One-Way Range Measurement
Image from GRACE at GFZ Layout in Satellite
Z acc
X acc
Y acc K-Band Ranging System
Leading Satellite Trailing Satellite 32 GHz 15 cm 15 cm Horn Horn KaKa Down Down KaKa Down Down ConverterConverter ConverterConverter L1 24 GHz L1 L2 L2 Ka Ka USO Ka Ka USO XX’’mtrmtr XX’’mtrmtr
GPS Rcvr GPS Rcvr
10 Hz K/Ka Band Phase; 1 Hz GPS L1/L2
GPS Receiver is the nerve center for the instrument: • Extracts K/Ka band phase data; • Extracts GPS phase data; • Processes star camera images • Provides time reference for satellites Dual One-Way Range Concept Sat-1 Sat-2
• Each one-way phase measurement is similar to GPS phase measurement • Dual-frequency (24 & 32 GHz) measurements • The range-change (& hence gravity) information is implicit in the time-of-flight • Derivatives of range are numerically obtained in data pre-processing Raw K-Band Phase Data
Level-1 Processing Required (not necessarily in this order): Unwrap phase & identify all breaks Register data from both s/c to common GPS epoch Make dual-one-way range combination Outlier identification & normal-pointing At the end of Level-1 Processing
10 Hz Level-1A data has been reduced to 5-sec Level-1B data
After the “Known” effects are removed…
Effects of the a priori static and time-variable gravity; as well as non- gravitational influences have been removed. These “residuals” form the basis of piece-wise gravity adjustment visualized earlier as “new” signals. Sheard et al. 2012 (J. of Geodesy December 2012, Volume 86, Issue 12, pp 1083-1095) SuperSTAR Accelerometer Sensor Axes Operating Principle
• Electrostatic Suspension of proof mass – Proof mass: 72 g, 5x5x1 cm, Titanium Alloy – Held motionless relative to an electrode cage – Proof-mass to cage displacement detection by high resolution capacitive sensors – Electrostatic levitation keep the proof mass centered within the cage – Restoring voltage needed on the cage is a measure of the proof-mass acceleration in 6 d.o.f • Measures both linear & angular accelerations What the Accelerometer Measures
CG offset is Actively Controlled the “twangs” desired signal
Pending Verification
Work in Progress in Validation Phase Verification by (affects s/c configuration) analysis General Remarks, in closing… Orbital Geometry
Key angles relative to “Earth-fixed” processes are:
Argument of Latitude
Node relative to Greenwich
Image: http://www.orbitessera.com Orbit Perturbation Spectrum
GRACE mission measurement b/w
≈ 1 cpr ≈ n cpr amplitudes decrease as perturbation frequencies increase --> Local (RTN) Frame (GRACE) In-plane (a, e, ω, M) Pathway for perturbations observed by GRACE error susceptibility
amplitudes decrease as perturbation frequencies increase --> Orbital Elements Secular 1/perigee Resonances M-dailies n-cpr (early techniques) Early Ground Based Tracking Space-Based Tracking & Later In-plane & Out-of-plane (e, ω, and I, Ω) (later, GPS-based, methods observed low n-cpr) Observational limitations led to “lumped-harmonic” or inseparability effects Observation Spectrum
Global Regional Variability Variability
Secular Resonant m-Dailies Sub-Rev
Large-Amplitude Small-Amplitude Perturbations Perturbations
Long-period stability Very high precision of measurements is measurements are difficult to assure required Overview
• User may engage with “satellite-only” mean Earth gravity field models at several levels, with differing effort.
• Regional use of global satellite-only fields today clearly benefits from dedicated error analysis efforts.
• Available satellite-only fields are useful for guiding strategies for combination of heterogeneous datasets across overlapping spatial domains (e.g. coastal blending in case of EGM08) – This should be even more useful as the spatial resolution improves with next- generation satellite-only mean fields.
Looking Ahead
• Next generation (RL06) products, due out in Spring/Summer 2017, should present improved mean field – Formal error calibration – Including contributions from data collected at lowest altitudes – Reduction of systematic errors
• LRI data from GRACE-FO mission should contribute meaningfully to the mean field estimates.
Thank you for your attention… OPTIONAL: Validation of Gravity Fields Basics • Gravity field has been parametrized, modeled, and estimated from the GRACE data. – Following discussion is carried out in terms of a gravity field estimated as a piecewise constant, spherical harmonic coefficient set. – Can be easily extended to other parametrization strategies
• Some common methods – INTERNAL: • Data residuals after fit • Statistical consistency • Visualization & sanity checks – EXTERNAL: • Low degree harmonic comparisons with SLR & EOP • Ocean circulation comparisons at long wavelengths • Inter-comparisons with output from geophysical models • (If you are lucky) Regional comparisons with in situ data INTERNAL: Data Residuals: Check if residuals are clustered in regions of large signal
INTERNAL: Visualizing the formal errors
This is useful for assessments of effects of evolution of mission geometry and data collection strategies.
INTERNAL: Statistics of the Gravity Field Overview • In GRACE data processing, say we estimate one set of geopotential harmonic coefficients for each month of data.
• We define the “Variability” as deviations from ensemble average, that is:
• We visualize the variability in several ways: – Scatter: Degree root sum-squared of the spherical harmonic variability
– Sequences, montages or movies of maps of the variability
Signal
Each point above is a root sum-squares averaged over M individual fields. The Y-axis should be in units of the geopotential harmonics, but multiplication by ae converts it to units of geoid height. The Y-axis then represents contribution to global RMS from terms of each degree (there is sound statistical basis for this). Degree “Error” Statistics Degree/Order Distribution of Error
Launch until May-2003 2003-07 until 2010-12 2011-Jan until present Early months limited by Best quality products Limited by absence of the star camera noise thermal control Calibrated Errors (& Covariances)
A power-law relationship between residual scatter and formal errors is derived, separately for each span.
The formal error covariance matrix is inflated using this power law.
The standard deviations are delivered to archives. Functionals of the Potential
The estimated geopotential harmonics are hardly ever mapped geographically in the units of potential. Common functionals of geopotential, used for mapping, are shown in the table below.
Quantity Units Remarks
Geoid Height mm of geoid meters for static field
Gravity Anomaly nanoGal microGal for static field
Equivalent Water Layer cm of water --
Gravity Gradients microEU milliEU for static field
Mass Density Layer kg/m2 Use GT for basin averages
Radial Loading Displacement mm --
Geoid height requires simple multiplication of the variability by ae, invoking Bruns’ formula. All others need degree-dependent operations. Spectral Operators Geoid Height
Gravity Anomaly
Equivalent Water Layer
Radial Gradient
Mass Density Layer
Radial Displacement follows from Each quantity, therefore, emphasizes a different part of the error spectrum The next set of images show variability for the month (RL04) of May, 2010, for n=60, smoothed to 400 km, and Variability is defined relative to 2010 mean
Different quantities and different smoothings can highlight problems in different parts of the spectrum
INTERNAL: Visualizations of the data and the fields EXTERNAL: Low degree harmonics C20 from GRACE and SLR GRACE estimates dominated by long-period aliases
EXTERNAL: Ocean circulation
Each month’s gravity field should be able to stand on its own, as a good model of the Earth’s gravity field. This is a quick sanity check of the quality.
Other such tests could be envisaged… EGM08 – Zonal (no smoothing) Test Statistics (Ocean Circulation)
Correlation of geostrophic currents computed from various geoid models with the circulation from ARGO data (Roemmich & Gilson 2009, via Kosempa and Chambers 2012; relative to 2000 m; courtesy of D. Chambers) Gravity solution Zonal Meridional GGM05S (GRACE only) 0.83 0.37 EGM2008 0.86 0.44 GOCE only (XX+YY+ZZ+XZ) 0.88 0.49 GGM05G (GRACE+GOCE) 0.88 0.51 GOCO05S (GRACE+GOCE+Reg) 0.88 0.55 EIGEN6C4 (GRACE+GOCE+Terr) 0.88 0.55
• Tests to 180x180 with 300 km smoothing, and is at its limit of usefulness • Up-weighting GRACE improves the meridional correlations at the long wavelengths, but increase the striations at short wavelengths While the example here was illustrated for a mean Earth gravity field model, it works well for discovering problems in monthly fields, as well… EXTERNAL: Comparisons with geophysical model output
This works very well visually when working at a global scale. On regional scales, this is far less certain. But by this time, you are no longer only validating – you are engaged in geophysical analysis. GRACE satellite monitoring of large depletion in water storage in response to the 2011 drought in Texas
There is wide divergence among the model predictions of soil moisture. Combination of improvements in modeling & in situ data Long et al. 2013 are needed to correctly disaggregate the Geophysical Research Letters total. Volume 40, Issue 13, pages 3395-3401, 3 JUL 2013 DOI: 10.1002/grl.50655 http://onlinelibrary.wiley.com/doi/10.1002/grl.50655/full#grl50655-fig-0003