Estimating CO 2 sources and sinks from atmospheric mixing ratio measurements using a global inversion of atmospheric transport

This report describes algorithmic details used to estimate the spatio-temporal distribution of CO 2 sources/sinks from atmospheric concentration measurements.The algorithm extents that used in Rdenbeck et al. (2003) in the following ways:Higher time resolution.The inversion uses individual mixing ratio measurements (rather than monthly mean concentrations): Either individual flask pair averages, or hourly values from continuous analyzers.Correspondingly, also the time resolution of fluxes was increased (to daily flux values).In order to combine weekly and hourly data, a data density weighting is applied.Generalized process-oriented flux model.All the a-priori information is supplied in the form of a statistical linear 'flux model'.Using this formulation, it is more easy to specify a-priori constraints based on direct process understanding in a flexible and transparent way.At the same time, the prominence of a-priori constraints can be reduced to a minimum.The 'flux model' indirectly determines a-priori correlations (both spatial and temporal), a spatio/temporal weighting, and an overall scaling.Iterative solution.Because of the higher time resolution, the number of knowns and unknowns is increased to a level that the minimization cannot be done via the analytical matrix expressions.Therefore, an iterative algorithm is used to find the cost function minimum, even though the problem is still linear.As additional advantage, more flexibility is gained, because atmospheric transport is simulated 'on-line' (rather than being fixed as soon as transport basis functions have been pre-computed), such that choices like data selection can easily be changed.As disadvantage, each run takes considerable amounts of CPU time.A-posteriori (co)variances can be calculated for a number of selected scalar quantities.Besides the general description of the mathematical algorithm, specific implementation details and results for the case of CO 2 are presented.i