Since the draft of latest +1000 pages US Climate Assessment completely ignores volume as a dimension of Arctic sea ice - probably assuming constant thickness during satellite era - I'll start here a series of findings to give evidence sea ice volume is not an unknown thing to science.

To be fair, the search term 'sea ice thickness' appears once in Chapter 12, Tribal, Indigenous, and Native Lands and Resources

Scientists across the Arctic have documented regional warming over the past few decades at twice the global rate, and indigenous Arctic communities have been observing the changes in their daily lives. This warming is accompanied by significant reductions in sea ice thickness and extent, increased permafrost thaw, more extreme weather and severe storms, changes in seasonal ice melt/freeze of lakes and rivers, water temperature, flooding patterns, erosion, and snowfall timing and type

Later this spring the series will result in a comment to the draft and hopefully the key message with a projection of an ice free Arctic earliest in the middle of the century got revised.

Here is the first part of the series, a paper presented for discussion earlier this week, written by V. A. Alexeev, V. V. Ivanov, R. Kwok and L. H. Smedsrud and titled: North Atlantic warming and declining volume of arctic sea ice, [full text] The article tries to estimate the effect of the recent North Atlantic warming on the ice melting processes happening at the outlet of the Arctic Ocean near Fram Strait, Svalbard and Franz Joseph Land.

Abstract: Long-term thinning of arctic sea ice over the last few decades has resulted in significant declines in the coverage of thick multi-year ice accompanied by a proportional increase in thinner first-year ice. This change is often attributed to changes in the arctic atmosphere, both in composition and large-scale circulation, and greater inflow of warmer Pacific water through the Bering Strait.

The Atlantic Water (AW) entering the Arctic through Fram Strait has often been considered less important because of strong stratification in the Arctic Ocean and the deeper location of AW compared to Pacific water. In our combined examination of oceanographic measurements and satellite observations of ice concentration and thickness, we find evidence that AW has a direct impact on the thinning of arctic sea ice downstream of Svalbard Archipelago. The affected area extends as far as Severnaya Zemlya Archipelago.

The imprints of AW appear as local minima in sea ice thickness; ice thickness is significantly less than that expected of first-year ice. Our lower-end conservative estimates indicate that the recent AW warming episode could have contributed up to 150–200 km³ of sea ice melt per year, which would constitute about 20% of the total 900 km³yr⁻¹ negative trend in sea ice volume since 2004.