Error characteristics estimated from CHAMP, GRACE and GOCE derived geoids and from altimetry derived mean dynamic topography E. Schrama TU Delft, DEOS e-mail: [email protected]
Jan 18, 2016
Error characteristics estimated from CHAMP, GRACE and GOCE derived
geoids and from altimetry derived mean dynamic topography
E. Schrama
TU Delft, DEOS
e-mail: [email protected]
Contents
• Static Gravity
• Mean circulation inversion problem
• Satellite altimetry
• Temporal Gravity
• Conclusions
Static gravity
• Existing gravity field solutions
• New gravity missions
• Gravity mission performance
• Cumulative geoid errors
• Characteristics of errors
Existing gravity solutions• Satellite geodesy
– Range/Doppler observations– Model/observe non-conservative accerations– large linear equations solvers– Sensitivity in lower degrees, resonances
• Physical geodesy– Terrestrial gravity data, altimetric g– Relative local geoid improvement wrt global models – Surface integral relations – Sensitivity at short wavelengths
• Quality determined by: data noise, coverage, combination
New gravity missions
• Measuring (rather than modeling) non-conservative forces (CHAMP concept)
• Low-low satellite to satellite tracking (GRACE concept)
• Observation of differential accelerations in orbit: (GOCE concept)
• New gravity surveys (airborne gravity projects)
Gravity mission performance
0 20 40 60 80 100 120 140 160 180 20010
-14
10-12
10-10
10-8
10-6
10-4
Degree l
Co
eff
icie
nt
rms
by
de
gre
e
Bouman & Visser
Cumulative geoid errors
T = 1 yearSID 2000 report
Characteristics of errors • All calculations so far considered geoid errors to
by isotropic and homogeneous.• We only considered commission errors, and did
not average spatially (beta operator) • In reality there is only one static gravity field• Data subset solution Tailored cases.• Optimal data combination is a non-trivial problem.
• The temporal gravity field is an error source for GOCE.
EGM96 geoid error map
Lemoine et al
Mean Circulation
• Hydrographic inversion– density gradients and tracer properties– geostrophic balance
• Dynamic topography examples– Hydrography– Satellite Altimetry
Hydrographic inversion• thermal wind equations
• conservation tracers
• geostrophic balance
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zo
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Dynamic Topography from hydrographic inversion
Le Grand,1998
Dynamic topography from altimetry
JPL web site
Satellite Altimetry
• System accuracy
• Averaging the mean sea level
• Mesoscale variability
• Gulf stream wall detection
• Sampling characteristics
• Correlated Noise
• Correlated Signals
System accuracy
• definition of the reference frame (?)• orbits (Laser+Doris, GPS, Altimeter) (2 - 2.5 cm)• accuracy/stability of the instrument (5 mm)• accuracy of environmental corrections
(troposphere, ionosphere, EM-bias) ( 1.5 cm )• accuracy of geophysical corrections ( 3 cm )
– tides (ocean, earth, load, pole), inverse barometer
• Net system accuracy: 4-5 cm for T/P
Averaging the mean sea level• GOCE: 12 months, GRACE: 60 months.• White noise fades out as a sqrt(N) process • If you had 300 T/P cycles then
– 5 cm r.m.s. goes down to 0.3 cm
– 30 cm r.m.s. goes down to 1.7 cm
• Spatial averaging helps to reduce this error. • Yet we can’t average further than the required
resolution of the geoid.
Mesoscale variability map
JPL web site
Gulf stream wall detection
Lillibridge et al
Gulfstream T/P in COFS model
Lillibridge et al
Gulfstream T/P + ERS2 in COFS
Lillibridge et al
Infrared Gulfstream
Lillibridge et al
Gulf stream velocity (ERS-2)
DEOS (Vossepoel?)
Sampling the sea level
• Gravity mapping orbits
• Repeat track orbits
• Sun synchronous
• Frozen orbits
• Repeat length vs intertrack spacing
122
T/P sampling
121
120
119
Topex/Poseidon groundtrack
Examples systematic errors
• Errors that are definitely not white are:– reference frame
• stability
• definition issues
– instrument biases– geographical correlated orbit errors– tides aliasing– inverse barometer
Examples of time correlated SLA
• Equatorial Rossby and Kelvin waves
• ENSO
• Annual behavior
• Tides
• Internal tides
Equatorial Kelvin and Rossby wavesEquator: 2.8 m/s 20 N: 8.5 cm/s
El Niño 1997-1998
Four seasons (Annual cycle)
JPL web site
M2 tide
Internal tides
• Hawaiian Island chain is formed on a sub-surface ridge
• wave hits ridge (perpendicular)
• energy radiates away from ridge
Temporal gravity
• Current situation
• Overview processes
• Challenges
• Separation Signals/Noise
Current situation
• Currently observed in the lower degree and orders• Signal approximately at the 1e-10 level• Traditional observations by SLR: Lageos I + II,
Stella, Starlette, GFZ, Champ• Various geodynamic processes are responsible for
changes in the gravity field.• Increased spatial resolution by the new proposed
missions
Source: NRC 1997
Table 2.1 Geodynamical processes and their predicted effect on the gravity field (from Chao, 1994).Static value of J2 is 1.083x10-3, static value of J3 is -2.533x10-6.
source temporal scale amplitude (peak-to-peak)J2 (10-10) J3 (10-10)
solid Earth tides long period up to 20 ?diurnal 0 0semi-diurnal 0 0
ocean tides all tidal periods Up to 4atmosphere IB days/seasonal/interannual 8 (peak) 10 (peak)
3 (annual) 5 (annual)1 (interannual) 1 (interannual)
atmosphere NIB days/seasonal/interannual 15 (peak) 20 (peak)5 (annual) 6 (annual)2 (interannual) 2 (interannual)
snow seasonal/interannual 2 (annual) 1rain seasonal/interannual 1 (annual) 1.7glaciers secular 0.02 per year 0.01 per yearreservoirs cumulative since 1950 -0.4 0.3ice sheets secular ? ?groundwater seasonal/secular ? ?sea level secular 0.03 per year -0.02 per yearocean circulation seasonal/interannual ? ?earthquakes episodic 0.5 (’64 Alaska) 0.3 (’60 Chile)
cumulative secular (‘77-’90) -0.002 per year 0.008 (peak)postglacial rebound secular -0.3 per year ?tidal braking secular -0.005 per year 0mantle convection/ tectonics secular ? ?core activity secular ? ?
Temporal gravity and geodynamic processes (Chao,1994)
Challenges• Extreme sensitivity of low-low satellite to satellite tracking in
the lower degree and orders (till L=70)
• The entire gravity field can be solved for after 30 days of data, temporal variations can be observed
• It opens the possibility to study e.g.: – the continental water balance
– ocean bottom pressure observations.
• Open questions: – How do you separate between signals.
– How do you suppress nuisance signals
Surface mass layer to geoid
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• Model
• Purpose: convert equivalent water heights (h) to geoid undulations (dN)
Properties Kernel function
0 5 10 15 20 25 30 35 40 45 5010
-3
10-2
10-1
100
degree
ratio
dN
/dH
Geophysical contamination
• Approximately 1 - 1.5 mbar error (now-cast) is typical ECMWF and NCEP (Velicogna et al, 2001)
• averaging over space and time helps to drive down this error, better than 0.3 mbar is unlikely.
• Some regions are poorly mapped (South Pole) and the errors will be larger
• The low degree and orders are more affected and probably the gravity performance curves are too optimistic (see kernel function)
Other Temporal gravity issues
• Unclear how to separate different signals ( criteria: location, spatial patterns? EOF? Other?)
• Accuracy tidal models (3 cm rms currently)?• Aliasing of S1/S2 radiational tides in sun-
synchronous orbits used for gravity missions• Edge effects near coastal boundaries• Data gaps
Round up
• Gravity missions: new missions discussed and their error characteristics, isotropy, homogeneity.
• Mean circulation: thermal wind, tracers, assimilation of observations, results from exiting approaches
• Satellite altimetry: typical results averaging and sampling in oceanic areas with high mesoscale signal, a sample of the scientific progress since 1992.
• Temporal gravity: current research and processes that are visible, contamination with geophysical signals, separation of individual signals and noise