Bathymetry from satellite altimetry: present and future

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.