Phase-sensitive Radar Observations of Strain and Compaction in Dry Firn

We present phase-sensitive radar data collected at a number of sites on Ronne Ice Shelf, Antarctica. The phase information in the received signal enables us to track rather precisely the vertical motion of reflectors over the period of the observations (about one year in this case). We assume that the most prominent reflections originate from discrete horizons within the firn/ice, so that reflector motion can be equated to material motion. Within the upper 100 m of the firn/ice we expect to see a component of reflector motion related to firn compaction. However, the dominant signature over much of this depth range arises from vertical strain, which appears to affect ice and firn identically. With the vertical strain removed, the residual layer motion gives us a consistent picture of compaction at all sites, implying that the compaction process is independent of the stress regime. We argue that this should indeed be the case (to a good approximation), because typical horizontal normal stresses are much smaller that the hydrostatic pressure, so represent only a small perturbation to the isotropic stress that drives the volume change of the firn. "Sorge's Law" now gives us a simple model for the residual layer motion, from which we could estimate the long-term mean surface accumulation rate if we knew the density profile, or vice versa. In practice we know neither, but we do have observations of accumulation over a single year, measurements of density in the upper few metres and knowledge that at depth the density tends towards that of solid ice. Using the latter two pieces of information we can make an "a priori" estimate of the density profile, with an associated uncertainty, then use inverse theory to calculate the combination of densities and accumulation rate that are most likely to explain the observed layer motion. We find high spatial variability in the long-term mean accumulation rates derived in this manner, although regional averages are surprisingly close to the values measured over one year.