A priori covariance estimation for CO₂ and CH₄ retrievals

We derive the a priori covariance matrices of CO₂ and CH ₄ for the retrieval of their profiles and columns from satellite spectral data. The monthly a priori covariance matrices of CO₂ and CH₄ at each grid cell (0.5° × 0.5°) on the globe are calculated using simulated data from the atmospheric tracer transport model. The a priori covariance matrix is defined as the sum of the bias and noise components, where the bias is obtained from the difference in seasonal cycle between simulated data and observation-based reference data, and the noise is defined as synoptic and interannual variations. The use of simulated data as well as observation-based reference data enables realistic variance and covariance values to be obtained for each temporal component. The seasonal bias is approximately 2 ppm for CO₂ and 20 ppb for CH₄. A large difference in synoptic variations is obtained between simulated and reference data over the source region, especially over land. The interannual variances derived from the reference data show maximum values (4 ppm² for CO₂ and 220 ppb² for CH₄) in northern midlatitudes. Global data sets of a priori covariance matrices for CO ₂ and CH₄ are now available for the retrieval of concentrations using satellite spectral data. Furthermore, the data set has the potential to be applied in studies in other fields, including estimates of CO₂ flux error using inverse modeling and planning for ground-based observation networks.