Adjoint sensitivity analysis of regional air quality models

The task of providing an optimal analysis of the state of the atmosphere requires the development of efficient computational tools that facilitate an efficient integration of observational data into models. In a variational approach the data assimilation problem is posed as a minimization problem, which requires the sensitivity (derivatives) of a cost functional with respect to problem parameters. The direct decoupled method has been extensively applied for sensitivity studies of air pollution. Adjoint sensitivity is a complementary approach which efficiently calculates the derivatives of a functional with respect to a large number of parameters. In this paper, we discuss the mathematical foundations of the adjoint sensitivity method applied to air pollution models, and present a complete set of computational tools for performing three-dimensional adjoint sensitivity studies. Numerical examples show that three-dimensional adjoint sensitivity analysis provides information on influence areas, which cannot be obtained solely by an inverse analysis of the meteorological fields. Several illustrative data assimilation results in a twin experiments framework, as well as the assimilation of a real data set are also presented.