Response times of ice-sheet surface heights to changes in the rate of Antarctic firn compaction caused by accumulation and temperature variations

Variations in accumulation rate A(s)(t) and temperature T-s(t) at the surface of firn cause changes in the rate of firn compaction (FC) and surface height H(t) that do not involve changes in mass, and therefore need to be accounted for in deriving mass changes from measured H(t). As the effects of changes in A(s)(t) and T-s(t) propagate into the firn, the FC rate is affected with a highly variable and complex response time. The H(t) during measurement periods depend on the history of A(s)(t) and T-s(t) prior to the measurements. Consequently, knowledge of firn response times to climate perturbations is important to estimate the required length of the time series of A(s)(t) and T-s(t) used in FC models. We use our numerical FC model, which is time-dependent on both temperature and accumulation rate, to examine the response times of both H(t) and the rates of change dH(t)/dt to variations in A(s)(t) and T-s(t) using sample perturbations and climate data for selected sites in Antarctica. Our results show that the response times for dH(t)/dt, which are of particular interest, are much shorter than the responses of H(t). Typical response times of dH(t)/dt are from several years to <20 years. The response times are faster in warmer and higher-accumulation areas such as Byrd Station, West Antarctica (4 years), and slower in colder and lower-accumulation areas such as Vostok, East Antarctica (18 years). The response times to temperature are much faster (0.9 year at Byrd and 2.2 years at Vostok), but the corresponding height changes persist much longer. The associated variations in firn density are significantly preserved in the density depth profiles. For typical fluctuations of surface weather, the Ts(()t) from satellite observations since 1982 and A(s)(t) from meteorological data since 1979 are essentially of sufficient length to correct for FC height changes for measurements beginning in 1992.