Background error covariance estimation for atmospheric CO₂ data assimilation

Abstract

[1] In any data assimilation framework, the background error covariance statistics play the critical role of filtering the observed information and determining the quality of the analysis. For atmospheric CO 2 data assimilation, however, the background errors cannot be prescribed via traditional forecast or ensemble-based techniques as these fail to account for the uncertainties in the carbon emissions and uptake, or for the errors associated with the CO 2 transport model. We propose an approach where the differences between two modeled CO 2 concentration fields, based on different but plausible CO 2 flux distributions and atmospheric transport models, are used as a proxy for the statistics of the background errors. The resulting error statistics: (1) vary regionally and seasonally to better capture the uncertainty in the background CO 2 field, and (2) have a positive impact on the analysis estimates by allowing observations to adjust predictions over large areas. A state-of-the-art four-dimensional variational (4D-VAR) system developed at the European Centre for Medium-Range Weather Forecasts (ECMWF) is used to illustrate the impact of the proposed approach for characterizing background error statistics on atmospheric CO 2 concentration estimates. Observations from the Greenhouse gases Observing SATellite "IBUKI" (GOSAT) are assimilated into the ECMWF 4D-VAR system along with meteorological variables, using both the new error statistics and those based on a traditional forecast-based technique. Evaluation of the four-dimensional CO 2 fields against independent CO 2 observations confirms that the performance of the data assimilation system improves substantially in the summer, when significant variability and uncertainty in the fluxes are present.

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Ensemble Kalman filter implementations based on shrinkage covariance matrix estimation

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