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I am aware that techniques exist for measuring surface currents using HF radar, either fromland-based installationsor from space.
How do these work? I have assumed in the past that it's some sort of doppler system, but if I'm right about that, how are currents separated out from waves?
I'm not familiar with land-based methods, but for global measurements, one method is to use satellite altimetry (I'm more familiar with the geodesy side, but many of the same satellites are used). I think many of the current methods interpolate global or regional currents from a sparse network of buoys. As more radar satellites are launched, however, satellite measurements of sea surface currents will become more common.
Global-scale satellite-based radar altimetry measures the average elevation of the ocean's surface over a few kilometers (the exact amount depends on the wavelength of the radar band being used). Over this distance, waves cancel out, so the measurement is accurate to within a few centimeters. (This is aided by using the motion of the satellite to enhance the image, referred to as Synthetic Aperture Radar (SAR).)
Surface currents in the ocean are directly related to the slope of the ocean's surface. (Again, at the scales we're working with, wind-formed waves cancel out.)
Once you have an accurate snapshot of the elevation of the ocean, you can calculate the direction and magnitude of the surface currents. (Note that this isonlythe surface currents! Deep ocean currents are different matter altogether.)
This is also how we coarsely map the ocean floor from space. (For example, Sandwell & Smith's extensive work:http://topex.ucsd.edu/WWW_html/mar_topo.html)
The average elevation of the ocean's surface with respect to center of the Earth follows the geoid (by definition).
Seamounts on the ocean floor cause a preturbation in the geoid above them. Water effectively "bunches up" around seamounts (or rather, the surface of gravitational equipotential "bunches up" above the seamount).
By repeatedly measuring the oceans surface (over several years) we can remove the effect of surface currents and get an accurate picture of what the geoid looks like over the ocean. You can then use this to predict water depths over the oceans on a spatial scale of ~1 kilometer.
In fact, to calculate surface currents, you need this information to begin with. The surface currents are calculated as deviations from this measurement of the geoid.
Joe Kington has provided an excellent answer re sensing from space. Torbjørn T. pointed out in a comment that the site that I linked for context actually has a good explanation... so after blushing slightly, I shall summarise it here. People with more specialist knowledge are, of course, welcome to elaborate or correct any misunderstanding. Incidentally, it came as a surprise to me to realise that the land-based and space-based methods are entirely different techniques - so perhaps this should have been two questions.
There's a good explanation athttp://www.codar.com/intro_hf_radar.shtml. In summary:
The surface of the sea, complete with waves, acts in a manner analogous to a diffraction grating. When illuminated with HF radar, only a specific frequency is returned in the direction of the transmitter, and that specific frequency corresponds to waves of a particular wavelength that are travelling directly towards or away from the transmitter. This wavelength is one that is always present in the ocean (and, presumably, always present at some level in every direction of travel?).
Assuming deep water, because we know the wavelength and frequency of the wave, we can calculate its speed. We can also obtain its speed from doppler shift in the radar return. Any difference between the two must be due to surface currents.
