Sequential data assimilation algorithms for air quality monitoring models based on a weak-constraint variational principle

Abstract

A data assimilation problem for unsteady models is considered as a sequence of coupled inverse problems of reconstruction of the space-time structure of the state functions with various sets of measurement data. The data assimilation is carried out jointly with the identification of an additional unknown function, which is interpreted as a function of model uncertainty. A variational principle serves as the basis for constructing the algorithms. Various versions of the algorithms are presented and analyzed. Based on the principle of the residual, a computationally efficient algorithm for data assimilation in a locally one-dimensional case is constructed. A theoretical estimate of its performance is obtained. This algorithm is one of the main components of a data assimilation system based on a splitting scheme for unsteady three-dimensional transport and transformation models of atmospheric chemistry.