Uncertainties in thickness estimates of floating ice when applying buoyancy assumption

The largest impediment to accurately measuring changes in ice volume, both of land origin and sea ice, is with uncertainties in ice thickness estimates. Since the satellite era, the extent and seasonality of sea ice and the location and size of ice shelves and icebergs is quite well known; but those satellites provide only a two-dimensional representation of a three-dimensional entity. Surface elevation measurements by air- or space-borne altimeters provide an estimate of the ice or snow–air interface above a reference surface, the freeboard. In the case of floating ice the reference surface is usually the open water surface. Computing the thickness and subsequently volume of floating ice from altimetry data relies critically on the validity of the parameters used when converting surface elevation measurements into ice thickness. The underlying assumption is that ice and ocean are in hydrostatic equilibrium derived from the buoyancy principle first described by Archimedes in ‘On floating bodies’ proposition 5 discovered in 212 B.C. In this study we present a numerical analysis of the most widely used formula to compute ice thickness from freeboard measurements. We are investigating the errors associated with reasonable uncertainty estimates of the parameters of the buoyancy conversion when applied to surface elevation estimates in the Antarctic marine cryosphere.