ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-11-921-2011 Technical Note: Propagating correlations in atmospheric inversions using different Kalman update smoothers Tang J. 1 2 Zhuang Q. 1 2 3 Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN, USA Purdue Climate Change Research Center, West Lafayette, IN, USA Department of Agronomy, Purdue University, West Lafayette, IN, USA 02 02 2011 11 3 921 929 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/11/921/2011/acp-11-921-2011.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/11/921/2011/acp-11-921-2011.pdf

The scheme to propagate correlations between on-line and off-line state variables in atmospheric inversions using the fixed-lag Kalman smoother proposed in Bruhwiler et al. (2005) is explained as a process to impose a balanced constraint on the on-line state variables. It is then extended to the fixed-lag ensemble square root Kalman smoother and fixed-lag square root sigma-point Kalman smoother, allowing us to treat nonlinear observation operators easily. Further, to constrain the posterior fluxes within their feasible ranges, the constrained fixed-lag Kalman smoother is presented and the variable transform technique is proposed for the other two smoothers. Comparisons between various methods and observational data are conducted using a synthetic inversion of atmospheric CH<sub>4</sub> fluxes. The results indicate that our developed methods are good alternatives to existing methods for conducting sequential inversion of atmospheric trace gases. It is also shown that the benefit to include the correlations between on-line and off-line state variables is case dependent.

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