An improved Kalman Smoother for atmospheric inversions

L. M. P. Bruhwiler, A. M. Michalak, W. Peters, D. F. Baker, P. Tans
2005 Atmospheric Chemistry and Physics  
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 struc-5 ture of sources is diluted by transport and cannot significantly constrain flux estimates. We therefore describe an estimation technique that steps through
more » ... hat 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, 10 and the estimates and their uncertainties are shown to quickly converge. Final flux estimates are incorporated into the background state of CO 2 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 synthe-15 sis 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 20 find that the latter can be done with minimal error if time series of transport fields of adequate length are pre-calculated. One approach that has been used over recent years to quantify the atmospheric car-1892 ACPD Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Print Version Interactive Discussion 25 comparatively simple and do not require much computational expense, however, they do not result in information about seasonal cycles. A more complex approach that does yield seasonal cycles of sources and sinks is the cyclo-stationary approach. Multi-year monthly average observations and a state vec-1893 ACPD Abstract ACPD Abstract ACPD Abstract 25 1898 Abstract ACPD Abstract ACPD
doi:10.5194/acp-5-2691-2005 fatcat:kts57hzunjau3aldnxj3xbwkyi