Variational methods of data assimilation and inverse problems for studying the atmosphere, ocean, and environment

Methods for the combined use of mathematical models and observational data for studying and forecasting the evolution of the natural processes in the atmosphere, ocean and environment are presented. Variational principles for estimation of the functionals defined on a set of the functions of state, parameters and sources of the models of processes are the theoretical background. Mathematical models with allowance for uncertainties are considered as constraints to the class of functions. The main attention is paid to methods of successive data assimilation and to the inverse problems.