E. Schrama TU Delft, DEOS e-mail: schrama@geo.tudelft.nl 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 Bouman & Visser

Cumulative geoid errors SID 2000 report T = 1 year

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 Dynamic topography examples density gradients and tracer properties geostrophic balance Dynamic topography examples Hydrography Satellite Altimetry

Hydrographic inversion thermal wind equations conservation tracers geostrophic balance

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

T/P sampling 119 121 120 122

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 waves Equator: 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

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 Model Purpose: convert equivalent water heights (h) to geoid undulations (dN)

Properties Kernel function

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