Theoretical and practical aspects of data assimilation for air pollution models

The assimilation of observational data into comprehensive transport-chemistry models is a very intensive computational process. Variational methods (3D-Var, 4D-Var) or Kalman filter based algorithms may be used in the data assimilation process in order to provide an optimal analysis of the state of the atmosphere.; We present the theoretical framework and address some of the issues of combining the information provided by the observations of the chemical species and the atmospheric models to improve our understanding of the current state of the atmosphere.; From the family of linear-implicit solvers we analyze Rosenbrock methods and present efficient implementations of the adjoint model in the presence of stiff chemical reactions. In the data assimilation context, it is shown that coupling the transport and chemistry computations may have advantages over the traditional operator splitting approach. Software support is developed for the automatic generation of the adjoint code. An adjoint sensitivity analysis is presented and further applied to the problem of the adaptive location of the observational system and area targeting.; Practical issues related with modeling errors in data assimilation are presented using a Kalman filter for a stratospheric methane circulation model with chemistry. The influence of the chemical reactions and the influence of the initial error and model error on the assimilation results together with filter divergence issues are discussed. The continuum equations of the conditional mean of the state and error covariance matrix are presented for a general nonlinear advection-chemistry model.