A Bathymetry from Space mission is simultaneously an ocean mesoscale observing mission.
In the early days of satellite altimetry when little was known about sea surface height anomaly signals, altimeter missions were designed to be either "geodetic" or "oceanographic", but it was thought that one mission could not be both at once. Geodetic missions, like a bathymetry from space mission, have non-repeating ground tracks, while oceanographic missions have traditionally had "exact-repeat" orbits that periodically revisit a limited set of widely spaced ground tracks. It was thought that exact repeat sampling was required to observe the subtle height changes of dynamical oceangraphy in the presence of large static geoid gradients.
Decades of experience with altimetry have given us detailed knowledge of the spatial and temporal scales of correlation of various sea surface height signals of interest, and so it is now possible for a "geodetic" orbit to furnish "oceanographic" information such as observations of the mesoscale eddy field. To prove this, we look at the April 1994 to March 1995 time period, when Topex was in a 10-day exact repeat orbit and ERS-1 was in a geodetic orbit, and we recover the mesoscale eddy field associated with the Gulf Stream current in the Northwest Atlantic. The results are shown in the following animation
The upper right shows the eddy field resolved by Topex, the upper left by ERS-1, the lower left by both combined. The lower right shows the difference between the Topex and ERS-1 (upper right and left) results, and the ground tracks that sampled the fields. The differences (lower right) are mostly confined to the gaps not covered by Topex tracks (stationary black lines), that is, the geodetic orbit is sampling eddies that the exact-repeat orbit cannot see.
This data recovery works so well for two reasons. First, the space- and time-scales of correlation of the mesoscale eddy field are well-known (Jacobs, G., JOURNAL OF GEOPHYSICAL RESEARCH-OCEANS 106 (C9): 19581-19595 SEP 15 2001), and so it is possible to design an operator which will extract the signal having these characteristics from orbit ground track patterns of any type. Second, long experience with altimetry has furnished a mean sea surface which is well-known at mesoscale wavelengths, obviating the original reason for requiring exact-repeat ground tracks.
The above movie demonstrates something else meant to test the use of a simple altimeter for bathymetry from space. Topex set the "gold standard" in satellite altimetry of absolutely accurate sea surface height by having a dual-frequency altimeter and a passive microwave radiometer. These features allowed simultaneous in situ measurement of the radar path delays caused by the ionosphere and water vapor in the troposphere, so that the Topex radar measurement could be turned into an absolute sea surface height. ERS-1 was a single-frequency altimeter, so it did not measure the ionosphere delay directly. It did carry a radiometer, but we have not used that data in the above movie. Instead we used model, rather than in situ, corrections for the ionosphere and wet troposphere radar delays, in order to simulate the mesoscale eddy recovery achievable with a low-cost Bathymetry from Space mission having only a one-frequency altimeter and no radiometer.
As the movie shows, this works. This is because the ionosphere and troposphere delays have spatial scales of correlation that are much longer than the mesoscale signal. This demonstrates two important things, one pertaining to the geodetic mission goal of Bathymetry from Space and the other to the oceanographic goal of observing mesoscale eddies. The mesoscale observations work without these in situ corrections because the mesoscale signal is one of relative height anomalies, not absolute heights. The lack of in situ corrections introduces no error at mesoscale wavelengths, demonstrating that these corrections have longer spatial scales of correlation. This also shows that these corrections are irrelevant to Bathymetry from Space, where we need to improve the recovery of sea surface slopes at scales much shorter than mesoscale wavelengths.