Bathymetry from Space: Present and Future David Sandwell and Walter Smith. The deep oceans are largely unexplored. Satellite altimetry provides: - a direct measurement of vertical deflection and gravity - an indirect measurement of bathymetry and roughness.
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and coastal tides - ionosphere and troposphere delay
are NOT limitations.
of 4 improvement in marine gravity/bathymetry in:
(t < 50 yr)
[Sandwell et al., 2001, http:topex.ucsd.edu/marine_grav/white_paper.pdf]
poor ship coverage + high sea state + mesoscale variabilityneed higher precision altimeter and 6-year mission
remove long- geoid from raw altimetry using best available geoid models (e.g., GRACE).
take along-track derivative to convert height to slope.
combine along-track slopes from all available satellite altimeters to form north and east slope grids.
Current altimeters provide ~3 x higher noise in the east slope than in the north slope because of their high inclination orbits.
use Laplace equation to convert slopes to gravity anomaly.
restore long- gravity model.
l =15 km
ocean depth = 4 km
attenuation = 0.18
satellite altitude = 200 km
attenuation = 4.1 x 10-37
assemble available ship soundings and construct a long-( > 160 km) depth model.(NGDC & SIO maintain non-proprietary ship soundings.)
remove > 160 km from gravity grid.
downward continue gravity to mean ocean depth.
calibrate the topography-to-gravity ratio along ship tracks.
multiply residual gravity by calibration factor.
restore long- depth grid.
ionosphere and troposphere delay are NOT limitations
Suppose we want to improve resolution from 25 km to 15 km.
must reduce noise by e-5/3 = 5 times
waves are ~ 3 m rms
1 mrad = 1 cm accuracy over 10 km (1.4 s)
Topex 1 Hz noise is ~ 4 cm
need 16 repeats to reduce noise to 1 cm
each repeat is 1.5 yr so we need 24 years of data!!
need more precise altimeter
Wave height noise can be reduced to 1 mrad
in just 6 years if the altimeter range precision is
2 times better than Topex.
tides are shallow water waves
tide model error for
1mrad slope error
area of ocean covered
wave height noise
62˚ retrograde orbit ?
Improved range precision -- A factor of 2 or more improvement in altimeter range precision, with respect to Geosat and Topex, is needed to reduce the noise due to ocean waves.
Fine cross-track spacing and long mission duration -- A ground track spacing of 6 km or less is required (non-repeat orbit for at least 1.2 years). The Geosat Geodetic Mission (1.5 years) provides a single mapping of the oceans at ~5 km track spacing. Since the measurement noise scales as the square root of the number of independent measurements, a 6-year mission would reduce the error by another factor of 2.
Moderate inclination -- Current non-repeat-orbit altimeter data have high inclination (72˚ Geosat, 82˚ ERS) and thus poor accuracy of the E-W slope at the equator. An inclination of 62˚ (retrograde) is optimal for science, geometry, and wave noise?
Near-shore tracking -- Need to track the ocean surface close to shore (~5 km), and acquire the surface soon after leaving land.