ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-13-1485-2013 How well do different tracers constrain the firn diffusivity profile? Trudinger C. M. 1 Enting I. G. 2 Rayner P. J. 3 Etheridge D. M. 1 Buizert C. 4 5 Rubino M. 1 4 Krummel P. B. 1 Blunier T. 4 Centre for Australian Weather and Climate Research, CSIRO Marine and Atmospheric Research, Aspendale, Victoria, Australia MASCOS, University of Melbourne, 3010, Victoria, Australia School of Earth Sciences, University of Melbourne, 3010, Victoria, Australia Centre for Ice and Climate, Niels Bohr Institute, University of Copenhagen, Juliane Maries vej 30, 2100 Copenhagen, Denmark College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis OR 97331, USA 06 02 2013 13 3 1485 1510 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/13/1485/2013/acp-13-1485-2013.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/13/1485/2013/acp-13-1485-2013.pdf

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 CH<sub>3</sub>CCl<sub>3</sub>, HFCs and <sup>14</sup>CO<sub>2</sub> are most useful for constraining molecular diffusivity, while &delta:<sup>15</sup>N<sub>2</sub> 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 CO<sub>2</sub> 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.

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