Application of Geostatistical Inverse Modeling to Gridscale Estimation of CO2 Surface Fluxes

A geostatistical inversion algorithm is applied to the recovery of CO₂ fluxes on a 3.75^o latitude by 5.0^o longitude scale. The geostatistical approach to inverse modeling is a Bayesian approach in which the prior probability density function is specified based on an assumed form for the spatial and/or temporal correlation of the function to be estimated. This differs from traditional Bayesian approaches to atmospheric inverse modeling, where the prior information is in the form of initial surface flux estimates for given regions or gridcells. In geostatistical inverse modeling, the degree to which values of an unknown function (in this case, surface fluxes) at two points are expected to be correlated is defined as a function of the separation distance in space or in time between these two points. The parameters describing this correlation, such as, for example, the variance of the process and its correlation length, are also estimated as part of the inversion. In addition, flux estimates are not subject to some of the limitations associated with traditional Bayesian inversions, such as potential biases created by the choice of prior fluxes and aggregation error resulting from the use of large regions with prescribed flux patterns. Results show that CO₂ surface flux variations can be recovered on a significantly smaller scale than that imposed by regional synthesis inversions, with posterior flux covariances indicating that these variations are well supported by the available observations.