Background error statistics for assimilation of atmospheric CO2

The modeling and specification of the background error covariance structure are important elements in any data assimilation system, where the background errors represent the uncertainty associated with the latest available forecast from the system. For Numerical Weather Prediction (NWP) applications, approximate information about the background error statistics can be obtained from the model forecasts, using several techniques involving either analyzing forecasts of varying lengths, or by generating an ensemble of forecasts. These techniques, however, are not appropriate for CO2 (or other atmospheric trace gas) assimilation applications as they fail to 1) optimally capture the spatial and temporal statistics of the errors associated with the background CO2 field, which result from uncertainties in both CO2 fluxes and CO2 transport, and 2) generate error statistics that are independent of the observation density. In this presentation, we propose a novel method for parameterizing the background error covariance, based on directly quantifying the regional spatial variability of the background CO2 field. Since the 'true' background CO2 field is unknown, it is assumed that the difference between modeled CO2 concentrations from two global models is statistically representative of the background errors. By choosing models that differ both in terms of their prescribed fluxes and their atmospheric transport, we demonstrate that this new approach can generate error statistics that are more appropriate for CO2 data assimilation. The resulting error statistics 1) vary regionally and seasonally to better capture the changing degree of variability in the background CO2 field, and 2) are independent of the observation density. The new background error statistics are implemented in the ECMWF 4DVAR system for generating global 4D fields of atmospheric CO2 concentrations constrained using radiance observations from the Atmospheric Infrared Sounder (AIRS). The new error statistics were found to be correlated over longer distances than those previously assumed in the ECMWF 4DVAR system, implying that when the AIRS observations are assimilated to inform the 4D CO2 fields, the information is used to reduce errors over a larger domain. Validation of these 4D fields using independent CO2 observations from NOAA/ESRL aircraft sampling sites also highlight the potential benefits of using the proposed approach over conventional techniques.