Error characteristics estimated from CHAMP, GRACE and GOCE derived

geoids and from altimetry derived mean dynamic topography

E. Schrama

TU Delft, DEOS

e-mail: schrama@geo.tudelft.nl

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

ref

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ref

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zo

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Cv

x

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ug

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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