On the use of satellite-derived CH₄ : CO₂ columns in a joint inversion of CH₄ and CO₂ fluxes

Abstract. We present a method for assimilating total column CH₄ : CO₂ ratio measurements from satellites for inverse modeling of CH₄ and CO₂ fluxes using the variational approach. Unlike conventional approaches, in which retrieved CH₄ : CO₂ are multiplied by model-derived total column CO₂ and only the resulting CH₄ is assimilated, our method assimilates the ratio of CH₄ and CO₂ directly and is therefore called the ratio method. It is a dual tracer inversion, in which surface fluxes of CH₄ and CO₂ are optimized simultaneously. The optimization of CO₂ fluxes turns the hard constraint of prescribing model-derived CO₂ fields into a weak constraint on CO₂, which allows us to account for uncertainties in CO₂. The method has been successfully tested in a synthetic inversion setup. We show that the ratio method is able to reproduce assumed true CH₄ and CO₂ fluxes starting from a prior, which is derived by perturbing the true fluxes randomly. We compare the performance of the ratio method with that of the traditional proxy approach and the use of only surface measurements for estimating CH₄ fluxes. Our results confirm that the optimized CH₄ fluxes are sensitive to the treatment of CO₂, and that hard constraints on CO₂ may significantly compromise results that are obtained for CH₄. We find that the relative performance of ratio and proxy methods have a regional dependence. The ratio method performs better than the proxy method in regions where the CO₂ fluxes are most uncertain. However, both ratio and proxy methods perform better than the surface-measurement-only inversion, confirming the potential of spaceborne measurements for accurately determining fluxes of CH₄ and other greenhouse gases (GHGs).