# How do they measure sub-centimeter wave height on a moon of Saturn?

Michael Stevens from V-Sauce has a video called The Mandelbrot Set on a different channel. At 12:56 he says:

There’s a moon of Saturn that has liquid hydrocarbon lakes that literally have waves that are only like a fraction of a centimeter large, but, you could surf that, right?

While Michael occasionally does indeed say things that appear to be wrong I'm guessing he got this correct.

How are waves a fraction of a centimeter tall measured on a moon of Saturn? How is the existence of these waves either measured or deduced?

According to the Wikipedia page on Titan, that data was deduced from Cassini.

On December 21, 2008, Cassini passed directly over Ontario Lacus and observed specular reflection in radar. The strength of the reflection saturated the probe's receiver, indicating that the lake level did not vary by more than 3 mm (implying either that surface winds were minimal, or the lake's hydrocarbon fluid is viscous).

That claim cites two sources:

newscientist.com (definitely not a primary source)

Harvard ADSABS which does appear to be a primary source analysis of Cassini data. However, I don't have time right now to see what peer-review made of this analysis.

Cassini RADAR altimetry data collected on the 49th flyby of Titan (2008 December 21) over Ontario Lacus in Titan's south polar region provides strong evidence for an extremely smooth surface, with less than 3 mm rms surface height variation over the 100m-wide Fresnel zone. Histograms of the raw radar echoes imply a mirror-like specular reflection of the transmitted signal. Such an echo is possible only if the surface is extremely flat relative to our 2.2-cm wavelength. The 3 mm upper bound follows from analyzing the strength of the specular return, which declines exponentially with increasing surface height variance. In this experiment, the strength of the echo was larger than expected, severely saturating the receiver. We developed a method to partially correct the echoes for the distortion incurred. While the implied mm-scale smoothness is not proof that the surface is liquid, it is unlikely that a solid surface is so smooth.

From the abstract, it seems they are deriving this conclusion indirectly, but I'm not educated enough in this area to personally vouch for the methods.

• That's interesting, thank you. So these describe an upper limit on roughness and are consistent with both very small waves and no waves, and they don't describe evidence that waves exist. – uhoh Dec 20 '18 at 22:12