Statistics of firn closure: a simulation study

Abstract

AbstractThe trapping of bubbles of air in polar ice has provided a unique record of past atmospheric composition. However, the interpretation of measured concentrations depends on the statistics of the trapping process. Measurements of trace atmospheric constituents whose concentrations are changing steadily can be interpreted in terms of an “effective age” of the gas which differs from the age of the ice by a delay which corresponds to the mean trapping time. The statistics of bubble trapping can be modelled as a percolation model which is one of a class of models whose transitions are characterized by large critical fluctuations. These critical fluctuations cause an intrinsic sample-to-sample variability in the delay time and thus in the effective age. Monte Carlo simulations using a lattice model of the firn are presented, showing the effect of finite sample size on the age distribution of trapped gas. For samples containing more than about 103–104bubbles, the simulations indicate that the range of variability is small compared to the average duration of the trapping process.