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Bathymetry from Space: Present and Future David Sandwell and Walter Smith

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- The deep oceans are largely unexplored.
- Satellite altimetry provides:
- - a direct measurement of vertical deflection and gravity
- - an indirect measurement of bathymetry and roughness.

- The important altimeters are Geosat and ERS-1.
- The main limitations are: downward continuation, ocean waves
and coastal tides - ionosphere and troposphere delay

are NOT limitations.

- A non-repeat orbit altimeter mission could achieve a factor
of 4 improvement in marine gravity/bathymetry in:

- - 24 years for a Topex-class altimeter
- - 6 years for a delay-doppler altimeter

commercial and

military applications

solid earth

science

new altimeter

mission

ABYSS

proposal

climate

(t < 50 yr)

NASA ESE

planetary

exploration

[Sandwell et al., 2001, http:topex.ucsd.edu/marine_grav/white_paper.pdf]

global topography

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.

north slope

y

east 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.

downward continuation

ocean waves

coastal tides

ionosphere and troposphere delay are NOT limitations

Suppose we want to improve resolution from 25 km to 15 km.

signal

present noise

desired noise

1/l 5/3l

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.

d

tides are shallow water waves

tide model error for

1mrad slope error

(T=1/2 day)

wavelength

ocean surface

slope

tide height

mrad

mrad

mrad

area of ocean covered

orthogonal tracks

wave height noise

science targets

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.