Firn Compaction Rate Calculator

Firn is snow that has survived at least one melt season and is partway through its conversion into glacial ice. Density climbs from roughly 300 to 400 kg/m3 at the surface, through a mechanical packing regime that ends near the critical density of 550 kg/m3, into a sintering and plastic creep regime, and finally past pore close-off near 830 kg/m3 to bubbly ice at about 917 kg/m3. The exponential form used here follows from assuming that densification proceeds at a rate proportional to the remaining pore space, so the density deficit between ice and firn decays geometrically with accumulated load. Because load accumulates at the rate A, depth enters the exponent as k times z divided by A. The rate constant k carries an Arrhenius factor, which is why a site at -20 degrees C densifies several times faster than one at -50 degrees C. Typical close-off depths run 50 to 70 m on the warm, high-accumulation flanks of Greenland and 95 to 120 m at cold, low-accumulation East Antarctic domes such as Dome C and Vostok. Firn air contents of 20 to 40 cubic meters per square meter are common. The single-stage formulation used here is a simplification of the published two-stage scheme, so close-off depths computed at very low accumulation rates are unreliable. Melt layers, wind crusts, and depth-dependent activation energies are not represented at all.

The empirical foundation was laid in 1930 and 1931, when Ernst Sorge, overwintering at Eismitte on the Greenland ice sheet during Alfred Wegener's expedition, hand-dug a pit roughly 15 m deep and measured a smooth, continuous increase of density with depth. Henri Bader later formalised the observation as Sorge's law: at a site in steady state the density-depth profile is fixed in time, so a single core reveals the whole densification trajectory. That principle made firn profiles from individual boreholes interpretable as process curves rather than site curiosities. Deep coring after the Second World War supplied the data set that empirical models needed. The US Army Cold Regions Research and Engineering Laboratory drilled at Site 2 in Greenland in the late 1950s, at Camp Century in 1966, and at Byrd Station in Antarctica in 1968, spanning a wide range of temperature and accumulation. In 1980 Michael Herron and Chester Langway published a two-stage empirical model in the Journal of Glaciology, split at 550 kg/m3 and fitted to profiles from seventeen polar sites, with reported activation energies of 10160 and 21400 calories per mole for the two stages. Later physically based schemes, and the FirnMICE model intercomparison published in 2017, refined transient behaviour, driven largely by the need to correct satellite altimetry for changing firn thickness.