Adjoint Equations and Methods of Variational Data Assimilation in Problems of Geophysical Hydrodynamics

The current state of research in the field of adjoint equations and variational assimilation of observational data for the ocean dynamics model developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences is presented. The technology of four-dimensional variational data assimilation (4D-Var) is based on the multicomponent splitting of the mathematical model of ocean dynamics and minimization of the cost functional associated with observational data by solving an optimality system including adjoint equations and covariance matrices of observational errors and the background errors. Efficient algorithms for solving variational data assimilation problems based on modern iterative processes with a special choice of iterative parameters, as well as algorithms for studying the sensitivity of model characteristics to observational data errors, are proposed. The methodology is illustrated for the Black Sea hydrothermodynamics model with variational data assimilation for reconstructing heat fluxes on the sea surface.