Doomed descent? How fast sulphate signals diffuse in the EPICA Dome C ice column

Abstract. The loss of climate information due to smoothing of ionic impurity signals in ice provides a strong motivation for understanding their diffusion rates at ice-core sites. By analysing sulphate signals in the EPICA Dome C (EDC) core, recent studies estimated the vertical profile of effective diffusivity D_eff at that site. However, D_eff crudely approximates the local diffusivity D in the ice, it being a nonuniform-weighted average of D over large intervals. We formulate the mathematical inversion for retrieving the D profile from observed signals, which reconciles the findings of the earlier studies as well as elucidating the averaging approximation. Inversion for EDC sulphate reveals a rapid decrease in D through the firn layer – from ≈ 10^–6 m² yr^–1 at the surface to ≈ 1.7 × 10^–8 m² yr^–1 at the firn-ice transition (≈ 100 m depth, ≈ 2.5 ka), followed by a gradual decline to ≈ 10^–10 m² yr^–1 through 100–2700 m (2.5–390 ka). This profile enables new interpretation of sulphate transport in the EDC column. We propose vapour diffusion of H₂SO₄ through interconnecting air pores as the cause of the high firn diffusivity. By evaluating the mechanisms controlling D below the firn (diffusion through ice crystals, liquid veins and grain boundaries and diffusion arising from interfacial motion), we infer a dominant partitioning of signals immediately below the firn to a connected vein system, and progressive smoothing of vein signals by Gibbs–Thomson diffusion down to ≈ 2000 m depth, which leaves more and more of the remaining signals to grain boundaries. We conclude that those sulphate signals that survive the initial fast diffusion in the firn to “punch through” to its base might survive into deep ice, and that EDC sulphate preserves a strongly filtered history of volcanic and climatic forcing that underrepresents changes and events shorter than a few years. For the Beyond EPICA – Oldest Ice and Million Year Ice Core drilling sites on Little Dome C, calculations assuming a diffusivity profile like our EDC profile and not exceeding 10^–10 m² yr^–1 in ice older than 450 ka constrain the sulphate diffusion length in ice 1–2 Ma old to 2 cm at most, and probably as low as ≈ 1 cm, for atmospheric-sourced signals that experienced only diffusion and mechanical shortening in the column.