1Centre for Australian Weather and Climate Research, CSIRO Marine and Atmospheric Research, Aspendale, Victoria, Australia
2MASCOS, University of Melbourne, 3010, Victoria, Australia
3School of Earth Sciences, University of Melbourne, 3010, Victoria, Australia
4Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Juliane Maries vej 30, 2100 Copenhagen, Denmark
5College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis OR 97331, USA
Abstract. Firn air transport models are used to interpret measurements of the composition of air in firn and bubbles trapped in ice in order to reconstruct past atmospheric composition. The diffusivity profile in the firn is usually calibrated by comparing modelled and measured concentrations for tracers with known atmospheric history. However, in some cases this is an under-determined inverse problem, often with multiple solutions giving an adequate fit to the data (this is known as equifinality). Here we describe a method to estimate the firn diffusivity profile that allows multiple solutions to be identified, in order to quantify the uncertainty in diffusivity due to equifinality. We then look at how well different combinations of tracers constrain the firn diffusivity profile. Tracers with rapid atmospheric variations like CH3CCl3, HFCs and 14CO2 are most useful for constraining molecular diffusivity, while δ15N2 is useful for constraining parameters related to convective mixing near the surface. When errors in the observations are small and Gaussian, three carefully selected tracers are able to constrain the molecular diffusivity profile well with minimal equifinality. However, with realistic data errors or additional processes to constrain, there is benefit to including as many tracers as possible to reduce the uncertainties. We calculate CO2 age distributions and their spectral widths with uncertainties for five firn sites (NEEM, DE08-2, DSSW20K, South Pole 1995 and South Pole 2001) with quite different characteristics and tracers available for calibration. We recommend moving away from the use of a single firn model with one calibrated parameter set to infer atmospheric histories, and instead suggest using multiple parameter sets, preferably with multiple representations of uncertain processes, to allow quantification of the uncertainties.