An inverse ocean modeling system

The implementation of a system for variational assimilation of data into ocean models is described. The system is modular: the ocean dynamics may be changed by replacing subroutines for the tangent-linear forward model and for the adjoint model. The assimilation is `weak': the ocean dynamics need not be satisfied exactly. An iterative algorithm within the system enables the solution of nonlinear assimilation problems. There is a suite of diagnostics including posterior error statistics, term balances and array assessment. The system has been in development for over a decade, and has been used in conjunction with a variety of oceanic, atmospheric and coupled models, with real data in quantity. The algorithms used in these applications, and the particular scientific assumptions and results, have been reported elsewhere. The emphasis in this article is on the implementation. This is a considerable challenge, both in the scale and complexity of the calculations, over and above those of the underlying ocean model. The vehicle for this presentation is a `toy' model, defined by a single nonlinear equation of motion. Code for real models is available at an anonymous ftp site. Components of the code are matched here in detail to stages of the assimilation algorithm and the diagnostics. Options are given for preconditioning, parallelization, memory management and other performance issues. Resource requirements, from computing speed through preconditioning effort to algebraic derivation, are also discussed in detail. Several applications are reviewed with the emphasis, again, on implementation. (C) 2001 Publisher by Elsevier Sciencs Ltd.