Second-Order Methods in Variational Data Assimilation

The chapter presents the second-order methods in variational data assimilation. The algorithms to compute the Hessian of the cost function are discussed, the second-order adjoint method among them. General sensitivity analysis for the optimality system is presented. Using the Hessian, the sensitivity of the optimal solution and its functionals is studied with respect to observations and uncertainties in model parameters. Numerical examples for joint state and parameter estimation for a sea thermodynamics model are presented.