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.along-track slope
combine along-track slopes from all available satellite altimeters to form north and east slope grids.north and east slope
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. altimeters to form north and east slope grids.
restore long- gravity model.gravity anomaly
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- altimeters to form north and east slope grids.( > 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.bathymetry
downward continuation altimeters to form north and east slope grids.
ionosphere and troposphere delay are NOT limitationsfundamental limitations
Suppose we want to improve resolution from 25 km to 15 km. altimeters to form north and east slope grids.downward continuation
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 altimeters to form north and east slope grids.
Wave height noise can be reduced to 1 mrad
in just 6 years if the altimeter range precision is
2 times better than Topex.
d altimeters to form north and east slope grids.coastal tides
tides are shallow water waves
tide model error for
1mrad slope error
area of ocean covered altimeters to form north and east slope grids.
wave height noise
62˚ retrograde orbit ?what is the optimal inclination?
Improved range precision altimeters to form north and east slope grids. -- 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.Mission Requirements