A variational approach for optimal diffusivity identification in firns

Trace gas measurements in interstitial air from polar firn allow to reconstruct their atmospheric concentration time trends over the last 50 to 100 years. This provides a unique way to reconstruct the recent anthropogenic impact on atmospheric composition. Converting depth-concentration profiles in firn into atmospheric concentration histories requires models of trace gas transport in firn. A fundamental parameter of these models is firn diffusivity. Here we propose a new method to evaluate the diffusivity of polar firns using automatic control analysis techniques. More precisely, the diffusivity identification is formulated as an optimization problem in terms of partial differential equations (PDE). The proposed theorems generally apply to transport phenomena in non-homogeneous media (space-dependent coefficients), a variational approach is proposed and the optimization problem is solved with an adjoint-based gradient-descent algorithm.