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)
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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
Ten-year combination of GRACE monthly estimates (March 2003 to April 2013)
Gravity anomalies from GGM05S to degree/order 180 (100 km smoothing)
GGM05S
Combine GGM05S with GOCE + polar gap fill from GGM05S
Gravity anomalies from GGM05G to degree/order 240 (50 km smoothing)
GGM05G
Variations Relative to EGM08
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
(Pavlis et al. 2012)
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
Presenter
Presentation Notes
GRAV-D data shows little discrimination between models.
GOCO05S
GGM05G
MDT residuals before spectral filtering (no smoothing). Color scale runs ± 35 cm
GOCO05S
GGM05G
MDT residuals after spectral filtering (no smoothing). Color scale runs ± 35 cm
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
GGM05G, not regularized, runs off from geoid at about degree 210, while GOCO05S, regularized, loses power at about the same place Error calibration at higher degrees consistent with differences, closer to more recent GRACE/GOCE models than EIGEN6C3, which should be a good sign Differences at mid degrees probably reflect different weighting of GRACE vs GOCE
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
Editing Orbits kbr residuals
Post-fir kbr residuals
Oct 2004 Year:2004 DOY:304
From:65000 sec To:69000 sec
Before Extra Editing
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
Presenter
Presentation Notes
Newton can be invoked again, to see how gravity could be measured from space. The Earth’s gravity field would determine the accelerations acting on an Earth orbiter, and would thus influence its trajectory. If we could observe its trajectory, we could measure the gravitational influences acting on the satellite. Almost as soon as the first satellite was launched, analysis of its trajectory led to estimates of the shape of the Earth’s gravity field. There is a four decade history of analysis of multiple Earth orbiting satellites trajectories to determine the Earth’s gravity field, using several methods. For example… This is applicable not just to Earth, but to the planetary orbiters as well.
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
GIA + Atmosphere + Hydrology + Glaciers + …
Figure 1, Cheng & Tapley (JGR v 109, Sep 2004)
Presenter
Presentation Notes
This page summarizes the state of the art just before GRACE flew. The right panel shows the names & orbital orientations of some of the notable satellites - tracking whose trajectory from ground contributed in this arena. The panel on left shows J2 - A hemispheric scale parameter of Earth’s gravity - observed very accurately, over 30+ years ! As rich as this piece of information was, it was still only the hemispheric scale. It could not give the spatial detail you saw in the animation. Yet, there was considerable multi-disciplinary Earth science expertise built into its interpretation. Black points are estimates. Blue line is the seasonal signal - ascribed to the atmospheric/seasonal variations. Red line is the inter-annual, plus secular, plus cryospheric, plus GIA etc.
20 years later
500 km 89° 5+2+2 years
Rockot (via DLR)
3 x 1.3 x 0.9 m No panel 440 kg
0.2 µ/s (& better) < 1 cm SLR/GPS
Otherwise “perfect” record
GRM Gradio
Aristoteles TIDES
GAMES ….
GRACE
Measurement Concept
(GOCE)
Gravity Observations & Orbits
(Seasat to OSTM)
Acceleration g = ∇ U
Potential U
Gradients G = ∇ g
Velocity
∫ g
Position
∫∫ g
Altimetry
Gravimetry
Gradiometry
Doppler SLR/GPS
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 (oceans, atmosphere, ice, elastic Earth) influences, and can be regular (tides), irregular (climate), or episodic (earthquakes). Measurement of higher derivatives of gravity provides better determination of small spatial-scale features.
(Lageos 1/2, and other geodetic sats) (TDRSS, Doris)
Observations of satellite motion and analysis of perturbations
Ground-based GPS Receiver
GPS Satellites
Nominal separation
Mass anomaly (fixed or moving)
GRACE: Mission Concept
Presenter
Presentation Notes
In order to observe the mass anomalies, we try to observe the orbital path of satellites. Flying two satellites and measuring the relative distance - as in the GRACE concept - gives us a good chance to do it globally, continuously, and with very high accuracy. Each satellite follows a path that is as well known as the “well-known” parts of the gravitational influences. We depict by “mass anomaly” the part that we do not yet know, and talk about its influence on the path of the two satellites - RELATIVE TO EXPECTATIONS.
Ground-based GPS Receiver
Leading satellite - approaching the anomaly - feels a greater gravitational attraction:
Separation Increases
GPS Satellites
Mass anomaly
GRACE: Mission Concept
Ground-based GPS Receiver
Trailing satellite - also approaching the mass anomaly - accelerates and catches up:
Decreasing Separation
GPS Satellites
Mass anomaly
GRACE: Mission Concept
Ground-based GPS Receiver
Leading satellite is far from the anomaly, and is not affected by it; while the trailing satellite - having just
passed the anomaly - is being tugged backwards: Increasing Separation.
GPS Satellites
Mass anomaly
GRACE: Mission Concept
Ground-based GPS Receiver
Trailing satellite catches back up with leading satellite but the ‘signature’ of
mass ‘lump’ has been observed in K-band range data
GPS Satellites
Mass anomaly
GRACE: Mission Concept
KBR Signal Content
Full KBR Range - Bias
Cubic Spline Residual (30 second knots)
Topography Along Groundtrack
(glk/jpl)
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
Science Goals High resolution, mean & time variable gravity field mapping for Earth System Science applications.
GRACE Mission
The Satellites
Orders of Magnitude
Virtually all of this signal is due to the phase difference between the two satellites traveling in eccentric orbits.
Effect Gravitational Acceleration
Sat-to-Sat Range
Sat-to-Sat Range-Rate
Sat-to-Sat 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 Tides 1.96E-7 0.13 mm 0.27 micron/s 0.7 nm/s^2
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.
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 the ±100 micro-g for the static field;
New Observations from GRACE
Acceleration Units: 1 micro-Gal = 10-8 m/s2; or 1 nano-g
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).
Relative Accelerations on GRACE s/c
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
Flight Data Intersatellite Range Accelerometry Attitude GPS Ranging
Level-1 Processing ρall
Fnon-grav
δρgrav -
Time-series products created in ground processing
Level-2 Processing
Consolidate regionally or
globally
δGrav δMass or δPressure
Map products created in ground processing
<Grav>
Gravity change (Feb 2004 - mean)
Mean gravity
Location of GRACE measurements Feb 2004
Fgrav
All “known” gravitational influences are removed using geophysical models derived from other data
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
Predicted Obs GRACE Obs
Estimate
Science from the mission is a conjunction of Estimates and the errors of Omission and Commission in the Background Gravity Model
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.
Adaptability in science applications Post-proc Error reduction
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
Ka Down Converter Ka Down Converter
USO Ka X’mtr
Ka X’mtr
GPS Rcvr
15 cm Horn
L1 L2
Ka Down Converter Ka Down Converter
USO Ka X’mtr Ka
X’mtr
GPS Rcvr
15 cm Horn
L1 L2
24 GHz
32 GHz Trailing Satellite
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)
• 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
desired signal
CG offset is Actively Controlled the “twangs”
Verification by analysis
Pending Verification
Work in Progress in Validation Phase
(affects s/c configuration)
General Remarks, in closing…
Image: http://www.orbitessera.com
Orbital Geometry
Key angles relative to “Earth-fixed” processes are: Argument of Latitude Node relative to Greenwich
Orbit Perturbation Spectrum
1/perigee Secular Resonances n-cpr M-dailies
≈ 1 cpr ≈ n cpr Local (RTN) Frame
(GRACE)
Orbital Elements (early techniques)
In-plane (a, e, ω, M) perturbations observed by GRACE
In-plane & Out-of-plane (e, ω, and I, Ω) (later, GPS-based, methods observed low n-cpr)
amplitudes decrease as perturbation frequencies increase -->
amplitudes decrease as perturbation frequencies increase -->
Observational limitations led to “lumped-harmonic” or inseparability effects
Early Ground Based Tracking Space-Based Tracking & Later
GRACE mission measurement b/w
Pathway for error
susceptibility
Observation Spectrum
Secular Resonant m-Dailies Sub-Rev
Global Variability
Regional Variability
Large-Amplitude Perturbations
Small-Amplitude Perturbations
Long-period stability of measurements is difficult to assure
Very high precision measurements are 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
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).
Signal
Degree “Error” Statistics
Degree/Order Distribution of Error
Launch until May-2003 Early months limited by the star camera noise
2003-07 until 2010-12 Best quality products
2011-Jan until present Limited by absence of 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
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.
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.
Spectral Operators
Radial Displacement follows from
Mass Density Layer
Radial Gradient
Equivalent Water Layer
Gravity Anomaly
Geoid Height
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)
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)
Test Statistics (Ocean Circulation)
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 are needed to correctly disaggregate the total.