CMCC Webinar

Speaker
Giovanni Conti, CMCC – CSP Division
Moderator
Carla Cardinali, CMCC – CSP Division

Novel ideas in the field of Data Assimilation (DA) are presented here. The ideas will cover various aspects of the DA field, starting from its mathematical formulation and the numerical representation (the application) selected to the construction of adaptive diagnostic tools that are verifying and measuring the quality and robustness of such a system.

First an extended deterministic physical nudging scheme will be introduced that incorporates two essential components: the background and observation information together with the assumed observation R and model error G co- variance matrix. These are the main components of classical data assimilation schemes. In particular, the first ideas presented here, proposes a data assimi- lation system that does not rely on the Bayesian framework. Instead, the data assimilation system is transformed into a boundary problem characterized by an initial and final condition. The relation between the Langevin and Fokker- Planck equations is leveraged to formulate the data assimilation problem in the probability space and extend the scheme in the coordinate space. The inclusion of background information arises from the recognition that the matrix G acts as a diffusion matrix in the Fokker-Planck equation, which is linked to the noise modulation in the corresponding Langevin equation. Instead, the observation error covariance matrix R, is taken into account by solving a Kolmogorov back- ward problem related to the boundary condition formulation. Notably, the final condition can be represented by a Gaussian function with a covariance matrix corresponding to R, the observation error covariance matrix. This dynamic treatment of the initial and final conditions simulates the DA problem.