How well do different tracers constrain the firn diffusivity profile?

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 most 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 &delta:¹⁵N₂ 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 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 assist in quantification of the uncertainties.