Inner-Loop Stopping Criteria for Incremental Four-Dimensional Variational Data Assimilation

Incremental four-dimensional variational data assimilation is a method that solves the assimilation problem by minimizing a sequence of approximate “inner-loop” functions. In any implementation of such a scheme a decision must be made as to how accurately to solve each of the inner minimization problems. In this paper recently developed theory is applied to derive a new stopping criterion for the inner-loop minimizations, which guarantees convergence of the outer loops. This new criterion is shown to give improved convergence compared with other commonly used inner-loop stopping criteria.