How thick is sea ice and how do we know?
nsidc.org
nsidc.org
It's also a bit confusing to me. Sonar can't measure thickness. It only measures the distance between the sub and the bottom of the ice. Altimeters likewise only measure the height.
I suppose if the maps are comprehensive enough and you overlay them, you can get a thickness. However, the computer models appear to be looking at ice age and surface temperature, not sonar or altimeter mapping.
Surface temperature seems like the sort of thing that would be well tracked if satellites are capable of taking those measurements. Ice age seems like something they'd probably need human run surveys for.
Surface temp is done via IR satellite imagery, although clouds will muck the readings.
A small penetrator with built in radio could conceivably make it through a lot of ice sheet depth and relay all of the data back.
Optical methods could penetrate a certain thickness of ice and give us absorbance / reflectance spectra.
Sonar should be able to measure the distance from the sub to the ocean floor and the sub to the bottom of the ice above it. Add them together and you get the distance from the ice to the ocean floor.
With those two datapoints it should be possible to get an accurate estimate of the ice thickness.