ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-9-8447-2009 The effect of nonlinearity in CO<sub>2</sub> heating rates on the attribution of stratospheric ozone and temperature changes Jonsson A. I. 1 Fomichev V. I. 2 Shepherd T. G. 1 Department of Physics, University of Toronto, Toronto, Ontario, Canada ESSE, York University, Toronto, Ontario, Canada 05 11 2009 9 21 8447 8452 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/9/8447/2009/acp-9-8447-2009.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/9/8447/2009/acp-9-8447-2009.pdf

An analysis of the attribution of past and future changes in stratospheric ozone and temperature to anthropogenic forcings is presented. The analysis is an extension of the study of Shepherd and Jonsson (2008) who analyzed chemistry-climate simulations from the Canadian Middle Atmosphere Model (CMAM) and attributed both past and future changes to changes in the external forcings, i.e. the abundances of ozone-depleting substances (ODS) and well-mixed greenhouse gases. The current study is based on a new CMAM dataset and includes two important changes. First, we account for the nonlinear radiative response to changes in CO<sub>2</sub>. It is shown that over centennial time scales the radiative response in the upper stratosphere to CO<sub>2</sub> changes is significantly nonlinear and that failure to account for this effect leads to a significant error in the attribution. To our knowledge this nonlinearity has not been considered before in attribution analysis, including multiple linear regression studies. For the regression analysis presented here the nonlinearity was taken into account by using CO<sub>2</sub> heating rate, rather than CO<sub>2</sub> abundance, as the explanatory variable. This approach yields considerable corrections to the results of the previous study and can be recommended to other researchers. Second, an error in the way the CO<sub>2</sub> forcing changes are implemented in the CMAM was corrected, which significantly affects the results for the recent past. As the radiation scheme, based on Fomichev et al. (1998), is used in several other models we provide some description of the problem and how it was fixed.

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