Influence of CO₂ observations on the optimized CO₂ flux in an ensemble Kalman filter

Abstract. In this study, the effect of CO₂ observations on an analysis of surface CO₂ flux was calculated using an influence matrix in the CarbonTracker, which is an inverse modeling system for estimating surface CO₂ flux based on an ensemble Kalman filter. The influence matrix represents a sensitivity of the analysis to observations. The experimental period was from January 2000 to December 2009. The diagonal element of the influence matrix (i.e., analysis sensitivity) is globally 4.8% on average, which implies that the analysis extracts 4.8% of the information from the observations and 95.2% from the background each assimilation cycle. Because the surface CO₂ flux in each week is optimized by 5 weeks of observations, the cumulative impact over 5 weeks is 19.1%, much greater than 4.8%. The analysis sensitivity is inversely proportional to the number of observations used in the assimilation, which is distinctly apparent in continuous observation categories with a sufficient number of observations. The time series of the globally averaged analysis sensitivities shows seasonal variations, with greater sensitivities in summer and lower sensitivities in winter, which is attributed to the surface CO₂ flux uncertainty. The time-averaged analysis sensitivities in the Northern Hemisphere are greater than those in the tropics and the Southern Hemisphere. The trace of the influence matrix (i.e., information content) is a measure of the total information extracted from the observations. The information content indicates an imbalance between the observation coverage in North America and that in other regions. Approximately half of the total observational information is provided by continuous observations, mainly from North America, which indicates that continuous observations are the most informative and that comprehensive coverage of additional observations in other regions is necessary to estimate the surface CO₂ flux in these areas as accurately as in North America.