So it is not as significant a factor as compared to a glacier or an ice cap, which are thousands of feet thick. Sea ice extent has a bigger fluctuation than sea ice thickness, so it is a better measure of seasonal change. A few years ago we had the situation where a bunch of sea ice had been pushed by winds into a constricted passage. The news was full of claims that sea ice was getting thicker, but in fact it was a localized effect and did not represent am increase in the system wide volume of ice formation.

We did have a laser range finding satellite up there for a few years:

https://en.wikipedia.org/wiki/ICESat

Good info here:

http://nsidc.org/cryosphere/sotc/sea_ice.html

the following image is from NSIDC: