Higher-Efficiency Inverse Atmospheric Modelling by Virtue of a Global Hexagonal Mesh

Emission sources and sinks of long-lived greenhouse gases (GHGs), such as CO2 and N2O, can be localized and scaled by inversely modelling existing distributions of these tracers in the atmosphere. This is particularly useful for monitoring GHG emissions at a global level, for comparison, for instance, with the national inventory reports of the United Nations Framework Convention on Climate Change (UNFCCC).

To achieve inverse transport numerically, multiple approaches can be taken, notably variational data assimilation. This involves the optimization of the Bayesian cost function accounting for prior state errors and observation errors. Variational data assimilation can be implemented by adjoint modelling. This method is based on the modification of the tracer transport equations of general circulation models (GCMs). The transpose of the tangent-linear operator, called the “adjoint”, is applied to find the initial sources and sinks. Eulerian backtracking, also called “retro-transport”, is a simplified approach to adjoint modelling, where the roles of updraughts and entrainment are switched with downdraughts and detrainment, respectively, and vice versa (Hourdin et al., 2005a).

In our presented work, we implement both the adjoint method for inverse modelling (Lions, 1971; Marchuk, 1974, 1982) and the retro-transport method put forth by Hourdin et al. (2005a). Our newfound approach consists of adapting these methods to a hexagonal mesh. For this, we use the DYNAMICO dynamical core of the the Laboratoire de Météorologie Dynamique-Zoom (LMDZ) GCM, which computes forward-in-time transport equations on a hexagonal mesh (Dubos et al., 2015). We add routines to DYNAMICO’s source code for the adjoint method, and alter the direction of fluxes to implement Eulerian backtracking.

The hexagonal mesh permits to reduce the computational cost traditionally attributed to inverse atmospheric modelling. Without the decreasing cell size as we approach the poles in a regular lon-lat grid, a hexagonal mesh covers the globe with a smaller number of nearly fixed-size cells. This directly reduces the size of input data and the number of operations. Further, the hexagonal mesh allows modellers to bypass the need for nonlinear cell-treatment at the poles of a regular lon-lat grid, increasing the accuracy of the retro-transport approximation. The increased computational efficiency of the hexagonal mesh paves the way for higher horizontal resolutions for global atmospheric inversion.