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Smith2005-Bathymetry from Satellite altimetry

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Bathymetry from satellite altimetry: Present and
future
Conference Paper · February 2005
DOI: 10.1109/OCEANS.2005.1640160 · Source: IEEE Xplore
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Bathymetry From Satellite Altimetry: Present And Future
Walter H. F. Smith
U.S. National Oceanic and Atmospheric Administration
Silver Spring Maryland
David T. Sandwell
Scripps Institution of Oceanography
La Jolla, California
R. Keith Raney
Johns Hopkins University Applied Physics Laboratory
Laurel Maryland
Abstract - Bathymetric survey lines cover the remote ocean
basins about as sparsely as the Interstate Highway System covers
the United States.
Therefore the most complete global
bathymetric models employ reconnaissance deep sea bottom
topography (“bathymetry from space”) combining conventional
acoustic soundings with detailed marine gravity field information
derived from densely spaced satellite altimeter profiles of sea
surface slope. Gravity and bathymetry may be correlated over
spatial scales (half-wavelengths) of roughly 5 to 80 km. The
vertical precision and horizontal resolution of derived
bathymetry depends on the signal-to-noise characteristics of the
satellite altimetry over the correlated band.
Comparison between gravity anomalies derived from
existing satellite altimeter data and gravity anomalies measured
with shipboard gravimeters shows root-mean-square differences
around 5 milliGals (mGal) and spectral coherency (signal
exceeding noise) for half-wavelengths longer than about 13 km.
Reconnaissance bathymetry estimates derived from these data
have a similar scale of resolution (roughly 15 km half
wavelength) and vertical errors of approximately 125 to 250
meters, depending on conditions such as regional water depth
and the spectrum of the local topographic signal. The most
challenging error situation is predicting the summit depth of a
narrow and steep seamount rising from deep water. In the area
of the USS San Francisco collision, for example, the altimetric
bathymetry map shows a ridge with a local summit at 278 meters
depth near the crash site, rising from a regional background
depth of more than 3000 m of water. Landsat imagery near the
crash site suggests that the seamount the San Francisco hit is
probably shallower than 40 m at its summit.
State-of-the-art shipboard gravimetry has an error level
around 1 mGal, and cross-spectral comparisons of shipboard
measurements of gravity and bathymetry show coherency down
to half wavelengths as short as 5 km. Thus if a new mission could
reduce the error in gravity maps derived from satellite altimetry
by as much as a factor of five, one could expect significant
improvements in the horizontal resolution and vertical error of
estimated reconnaissance bathymetry.
While the error
propagation from gravity to estimated bathymetry depends on
the local conditions as above, we can expect a five-fold reduction
in the bathymetry error from a five-fold reduction in gravity
error.
Recent advances in altimetry – the delay-Doppler technology
– make this five-fold gain readily achievable with a low-cost
mission. The limiting error in altimetry of sea surface slopes is
random noise in the altimeter’s range measurement, and the
delay-Doppler altimeter is superior to conventional altimeters in
this respect by a factor of at least two. The mission should have
an orbit with a ground track pattern that does not repeat for at
least 1.2 to 1.5 years or so, in order to obtain dense spatial
sampling to support short-wavelength horizontal resolution.
Thus a 5 to 6 year mission would yield four-fold data
redundancy, reducing the error another factor of two. An
additional noise reduction factor of roughly 1-1/4 or so can be
gained by choosing an optimal orbital inclination.
I. THE NEED FOR GLOBALLY UNIFORM
BATHYMETRY
Bathymetry is foundational data, providing basic
infrastructure for scientific, economic, educational,
managerial, and political work. Surface and submarine
navigation, communications cable and pipeline route planning,
resource exploration, habitat management, and territorial
claims under the Law of the Sea all require reliable
bathymetric maps to be available on demand.
A variety of applications also require ocean-basin-wide or
global-scale bathymetric information with a geographically
uniform level of detail. Examples include
•
Understanding the geologic processes responsible for
ocean floor features unexplained by simple plate
tectonics, such as abyssal hills, seamounts,
microplates, and propagating rifts.
•
Improving tsunami hazard forecast accuracy by
mapping the deep ocean topography that steers
tsunami wave energy.
•
Determining the effects of bathymetry and seafloor
roughness on ocean circulation, mixing, climate, and
biological communities, habitats, and mobility.
II. THE ROLE OF SATELLITE ALTIMETRY
Despite the fundamental nature of bathymetry, we have
much better maps of Earth’s Moon, Mars, Venus and some
asteroid surfaces than we have of Earth’s ocean floors.
Seafloor maps are inadequate for many of the purposes above
because there has been no systematic ocean mapping effort.
Existing surveys cover only a small fraction of the ocean floor
and in an irregular pattern.
The most detailed mapping possible would employ ships
or robotic vehicles equipped with acoustic swath mapping
systems, but a complete survey would take hundreds of years
of vessel time at a cost of billions of dollars [1]. In shallow
areas the bottom may be visible to airborne or spaceborne
optical or hyperspectral sensors, but these systems are useful
only in water depths less than several tens of meters, at best.
The only technique for globally uniform reconnaissance
of deep-sea bottom topography is spaceborne radar altimetry
of ocean surface height anomalies. These anomalies combine
a time-invariant signal reflecting the equipotential of the
Earth’s gravity field with other, mostly time-varying, signals
associated with tides, currents and eddies, climatic
fluctuations, and other physical oceanographic signals. The
bathymetric signal is expressed in short-spatial scale (less than
80 km half-wavelength) and time-invariant sea surface slopes,
and this signal is readily distinguished from other
oceanographic signals such as El Niño and the dynamics of
basin circulation.
III. FACTORS LIMITING RESOLUTION
Decades of marine geophysical research have confirmed
that in the deep-sea, where sediments are thin, bottom
topography is usually well-correlated with sea surface gravity
anomalies over a band of horizontal wavelengths. At the
largest scales, “isostatic compensation” attenuates the
gravitational attraction of the seafloor topography, cancelling
it by adding an opposite attraction caused by compensating
masses at greater depth. This attenuation is spread over a
band of wavelengths generally longer than 160 km but with
details depending on the mechanical strength of the
lithosphere [2, 3]. As a consequence, satellite altimeter data
can most usefully be applied to mapping of smaller sized
features, such as seamounts, abyssal hills, and the seafloor
topography built by the seafloor spreading process [4, 5].
The shortest resolvable scale depends ultimately on the
signal-to-noise ratio in the satellite altimeter data at spatial
scales shorter than 80 km. The sea floor topography spectrum
tends to be red, due to its quasi-fractal nature and finite
variance. The gravitational attraction at the sea surface
produced by the seafloor topography is further reddened by
“upward continuation”, which attenuates anomalies by a factor
exp[-2πd/L], where d is the mean depth between sea surface
and sea floor, and L is the full-wavelength of the topographic
signal. Thus the signal of interest diminishes rapidly as the
horizontal scale of a feature shrinks to approach the typical
depth in the deep ocean, on the order of 5 km.
Inversion of gravity data to estimate bathymetry requires
the inverse operation of downward continuation, producing
exponential growth of amplitude with decreasing wavelength.
To prevent the estimate from being swamped by noise one
must limit the estimation to a band of wavelengths. The
shortest scale in the band is somewhat variable, as the best
possible resolution is achieved by designing the roll-off of the
band-pass filter to consider the spectra of the signals to be
resolved and the error processes in satellite altimeter data at
the scales of interest. Reference [2] discusses the optimization
of the filter roll-off and the factors limiting resolution in detail.
IV. THE CURRENT SITUATION
To be bathymetrically useful, an altimeter mission must
collect data over a network of ground tracks sufficiently dense
to resolve signals at half-wavelengths shorter than 80 km.
Two such missions have been flown, the U.S. Navy’s GeoSat
Geodetic Mission of 1985-86, and the European Space
Agency’s ERS-1 Mission Phases E and F of 1994-95.
Combining these data one obtains a sea surface gravity field
which shows high correlation with shipborne gravimetry at
half-wavelengths longer than 12 km. Root-mean-square
differences between satellite altimeter gravity models and
shipborne gravimetry suggest that the typical sea surface slope
error in the models is around 3 micro-radians.
These data have been combined with publicly available
conventional bathymetric survey data to estimate global
reconnaissance bathymetry [4]. The results show good
correlation with truth data at half-wavelengths longer than 13
km. Differences between estimated and true point values are
less than 100 m about 50% of the time, but errors can exceed
250 m in areas of very rugged topography and/or very sparse
control sounding data.
An example of a rugged area with poor control is the
Caroline Islands region of Micronesia in the Western Pacific,
where the USS San Francisco nuclear submarine ran into a
seamount in January of 2005. The altimetry-based estimate
([4], version 8.2, November, 2000) shows a ridge with
summits shallower than 300 m. Later inspection of a Landsat7 image in the area suggests that depth may be less than 50 m
near the collision site.
It seems then that altimetrically-estimated bathymetry
performs worst where it is needed most: in areas of rugged
topography with poor ground-truth sounding control.
However, this is a consequence of the noise level in the
currently available data, which necessitates filtering the
estimated depths to wavelengths longer than about 25 km. In
rugged areas there is significant topographic variation at
shorter scales, and so the filtered estimate under-predicts
seamount summits. A new mission with a lower noise level
would need less filtering, resulting in a product much more
faithful to the actual topography.
V. A FUTURE MISSION?
We have been researching for some years the possibility
of a future mission. At present it seems that the delay-Doppler
altimeter [6] offers the best way forward. This device
employs signal-processing innovations from synthetic aperture
radar in a nadir-looking ocean height instrument, achieving
several advantages over the conventional instruments used to
date.
First, the instrument has lower random noise level, by a
factor of 2 in calm seas and more than 2 in rough seas.
Operating this instrument for 5 to 6 years, as opposed to the 11
months of the ERS-1 or 18 months of the Geosat mapping
campaigns, would cut the noise level in the resolved gravity
field by a factor of at least 4 (16 in variance); optimizing the
orbital inclination would achieve further gains. This reduced
noise level would immediately improve the resolution and
reduce the error in estimated bathymetry by comparable
amounts.
Second, the delay-Doppler instrument yields finer spatial
sampling in the direction of flight. This can support finer
spatial resolution of sea surface slope for gravity and
bathymetry. Importantly, it can also support smarter surface
tracking, so that the instrument can acquire data much closer
to shore than a conventional instrument.
Third, the delay-Doppler instrument achieves these
performance gains by making smarter use of the returned radar
energy, and this also results in much greater efficiency. These
gains permit instrument power levels to be reduced, leading to
small and lightweight electronics with very long expected life
at modest cost.
The website [7] describes a mission scenario with links to
some additional information, including a mission design study
[8] and some animations demonstrating the recovery of
mesoscale oceanography from a geodetic orbit and the
sensitivity of tsunami propagation to deep-water bathymetry.
A mission to achieve these goals could be realized now at a
cost under $100M.
Because ocean bathymetry is a
fundamental measurement of our planet, there is a broad
spectrum of interest from government, the research
community, industry, and the general public.
It is important to stress here that a low-cost and focused
mission design with a simple instrument package would be
multi-purpose, and simultaneously so. The bathymetric
measurement goal is essentially a gravity measurement goal,
and so the mission will furnish knowledge of the marine
gravity field. This knowledge is directly useful in geophysical
studies, in resource exploration, and in inertial navigation.
The gravity and bathymetry application requires only a
low-noise measurement on a densely spaced network of
ground tracks, such as from an orbit that does not repeat for at
least a year. The temporal sequence with which those ground
tracks are overflown is irrelevant to the bathymetry mission,
and so the orbit can be designed for any desired sampling of
tides or mesoscale ocean signals. In particular, though “nonrepeat” it can be rich in “near repeats” and thereby furnish
observations of the mesoscale ocean eddies.
Because the necessary measurement is band-limited,
absolute accuracy of the total sea-surface height, or long-term
stability in that absolute accuracy, are not required. This
makes the instrument package much cheaper and simpler than
those of missions like TOPEX or Jason, which are designed to
monitor climate variability signals such as El Niño and global
sea level rise.
It should be noted that radar altimetry of the ocean
surface, by measuring the sea surface shape anomalies caused
by gravity anomalies, measures gravity at sea level. Gravity at
sea level suffers only about 4 km of upward continuation from
the sea floor to the sea surface, and so resolves bathymetric
signals. Space gravity missions such as the Gravity Recovery
And Climate Experiment (GRACE) measure gravity at orbital
altitude, 400 km above the sea floor, where upward
continuation wipes out the bathymetric signal. Thus advances
in global ocean mapping will require a new altimeter mission;
they will not come from missions such as GRACE.
ACKNOWLEDGMENTS
This mission concept has matured through its
development as a NASA ESSP-3 proposal in 2001 (“ABYSS:
Altimetric Bathymetry from Surface Slopes”), in a
NASA/NOAA/NSF
funded
workshop
in
2002
(http://www.igpp.ucsd.edu/bathymetry_workshop),
Navy
workshops in 2003 and 2005, and articles in the 2004
“Bathymetry from Space” issue of Oceanography
(http://www.tos.org/oceanography/issues/issue_archive/17_1.h
tml). Further discussion of the mission concept, resolving
power, and applications to tsunami and seismic hazard, ocean
circulation, ocean mixing, climate modeling, and the UN Law
of the Sea can be found in peer-reviewed articles in
Oceanography volume 17, number 1.
A website
(http://topex.ucsd.edu/concept) holds additional supporting
materials, including animated demonstrations of the effect of
bathymetry in tsunami propagation and of the recovery of
mesoscale
eddies
from
a
non-repeat
orbit
(http://www.tos.org/oceanography/issues/issue_archive/17_1.h
tml). The views, opinions and findings contained in this
document are those of the authors and should not be construed
as an official U.S. Government position, policy or decision.
REFERE NCES
[1] M. J. Carron, P. R. Vogt, and W.-Y. Jung, “A proposed
international long-term project to systematically map the
world’s ocean floors from beach to trench: GOMaP
(Global Ocean Mapping Program)”, Intl. Hydr. Rev. 2(3),
49-55, 2001.
[2] W. H. F. Smith and D. T. Sandwell, “Bathymetric
prediction from dense satellite altimetry and sparse
shipboard bathymetry”, J. Geophys. Res., vol. 99 (B11),
pp. 21803-21824, November, 1994.
[3] W. H. F. Smith, “Seafloor tectonic fabric from satellite
altimetry”, Annu. Rev. Earth Planet. Sci., vol. 26, pp. 697738, 1998.
[4] W. H. F. Smith and D. T. Sandwell, “Global seafloor
topography from satellite altimetry and ship depth
View publication stats
[5]
[6]
[7]
[8]
soundings”, Science, vol. 277, pp. 1956-1962, 26
September 1997.
J. A. Goff, W. H. F. Smith, and K. M. Marks, “The
contributions of abyssal hill morphology and noise to
altimetric gravity fabric”, Oceanography, vol. 17 (1), pp.
24-37, March, 2004.
R. K. Raney, “The delay Doppler radar altimeter”, IEEE
Transactions on Geoscience and Remote Sensing 36 (5),
1578-1588, 1998.
http://topex.ucsd.edu/concept
R. K. Raney, W. H. F. Smith, and D. T. Sandwell,
“Abyss-Lite: A high-resolution gravimetric and
bathymetric
mission
(AIAA-2004-6006)”,
in
Proceedings, Space-2004, AIAA, San Diego, CA, 2004.
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