ACPD Atmospheric Chemistry and Physics Discussions ACPD 1680-7375 Copernicus GmbH Göttingen, Germany 10.5194/acpd-10-19219-2010 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 16 08 2010 10 8 19219 19245 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-discuss.net/10/19219/2010/acpd-10-19219-2010.html The full text article is available as a PDF file from http://www.atmos-chem-phys-discuss.net/10/19219/2010/acpd-10-19219-2010.pdf

Propagating correlations between on-line and off-line state variables in the problem of sequential inversion of surface fluxes for atmospheric CH<sub4</sub> is investigated with the fixed-lag Kalman smoother, the fixed-lag ensemble square root Kalman smoother and the fixed-lag square root sigma-point Kalman smoother. The formulae for the fixed-lag Kalman smoother in Bruhwiler et al. (2005) are further developed with a more concise representation of the posterior covariance. Extension to the fixed-lag ensemble square root Kalman smoother and fixed-lag square root sigma-point Kalman smoother allows us to treat nonlinear observation operators easily. To constrain the posterior fluxes within their feasible ranges, the constrained fixed-lag Kalman smoother is also presented, and the variable transform technique is implemented for the other two smoothers. Results with synthetic inversion of CH<sub4</sub> fluxes 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 of including the correlation between on-line and off-line state variables is case dependent.

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