Atmospheric Chemistry and Physics www.atmos-chem-phys.net 1680-7316 1680-7324 5 10 2005 10.5194/acp-5-2691-2005 http://www.atmos-chem-phys.net/5/2691/2005/ http://www.atmos-chem-phys.net/5/2691/2005/acp-5-2691-2005.html http://www.atmos-chem-phys.net/5/2691/2005/acp-5-2691-2005.pdf 2691 2702 2005-10-18 An improved Kalman Smoother for atmospheric inversions L. M. P. Bruhwiler A. M. Michalak W. Peters D. F. Baker P. Tans NOAA Climate Monitoring and Diagnostics Laboratory, Boulder, Colorado, USA Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Michigan, USA Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, USA National Center for Atmospheric Research, Boulder, Colorado, USA We explore the use of a fixed-lag Kalman smoother for sequential estimation of atmospheric carbon dioxide fluxes. This technique takes advantage of the fact that most of the information about the spatial distribution of sources and sinks is observable within a few months to half of a year of emission. After this period, the spatial structure of sources is diluted by transport and cannot significantly constrain flux estimates. We therefore describe an estimation technique that steps through the observations sequentially, using only the subset of observations and modeled transport fields that most strongly constrain the fluxes at a particular time step. Estimates of each set of fluxes are sequentially updated multiple times, using measurements taken at different times, and the estimates and their uncertainties are shown to quickly converge. Final flux estimates are incorporated into the background state of CO₂ and transported forward in time, and the final flux uncertainties and covariances are taken into account when estimating the covariances of the fluxes still being estimated. The computational demands of this technique are greatly reduced in comparison to the standard Bayesian synthesis technique where all observations are used at once with transport fields spanning the entire period of the observations. It therefore becomes possible to solve larger inverse problems with more observations and for fluxes discretized at finer spatial scales. We also discuss the differences between running the inversion simultaneously with the transport model and running it entirely off-line with pre-calculated transport fields. We find that the latter can be done with minimal error if time series of transport fields of adequate length are pre-calculated.