Efficient computation of global high-resolution Jacobian matrices for analytical inversions of satellite observations of greenhouse gases: Application to the Integrated Methane Inversion (IMI) version 2.3

Abstract. Dense satellite observations of atmospheric composition call for global high-resolution inversions to infer surface fluxes from the observations, using a chemical transport model (CTM) as forward model to relate the fluxes to the observed concentrations. The inversion can be done analytically when the relationship of surface fluxes to the observable atmospheric concentrations is linear. The main cost of analytical inversions is the explicit construction of the Jacobian matrix describing the CTM sensitivity of atmospheric concentrations to the gridded surface fluxes (state vector elements) and requiring perturbation simulations for all individual state vector elements. This cost has so far limited global analytical inversions to coarse resolution (~200 km) despite the availability of fine-resolution (~10 km) satellite observations. Here we show how the stretched-grid capability of the high-performance GEOS-Chem CTM (GCHP) operating on a cubed-sphere grid can considerably reduce the computational and storage costs of global Jacobian construction by achieving high resolution in the near-field of the state vector elements (target face) while gradually relaxing to coarse resolution at the antipode. Application to a stretch factor of 10 on the C36 cubed-sphere GCHP grid (C36S10) enables generation of a compact global Jacobian archive at 25-km resolution with 100 times lower computational and storage costs than a regular-grid C360 GCHP with global quasi-uniform 25-km resolution. We have implemented this capability in the Integrated Methane Inversion (IMI) version 2.3. Beyond its use for global inversions, the precomputed C36S10 Jacobian matrix archive can be used for regional inversions, which in the IMI rely on a nested rectilinear grid with boundary conditions at the edges. Conservative remapping of the stretched-grid Jacobian archive to the rectilinear grid reduces the cost of these regional inversions by an order of magnitude by skipping the Jacobian calculation. We demonstrate this capability with a 1-month regional inversion of TROPOMI methane satellite data over the South-Central US where the remapped C36S10 Jacobian reproduces closely the standard IMI results (posterior fluxes) at 0.25°×0.3125° resolution.