Error characteristics estimated from CHAMP, GRACE and GOCE derived geoids and from altimetry derived mean dynamic topography E. Schrama TU Delft, DEOS.

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

z

zo

ref

z

zo

vdzxf

gzv

udzyf

gzu

0

0

)(

)(

),,,().().().(

tzyxqz

Cw

y

Cv

x

Cu

....

....

ug

f

y

vg

f

x

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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nmapp

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)1(3

,),(

• 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