A new representation of data‐assimilation methods: The PALM flow‐charting approach

We introduce a new graphical representation for data‐assimilation methods which allows the visualization of the following items: control spaces, dual spaces, elementary operators and flow charts, for the computation of the gradient of the cost function. It is illustrated on a large variety of data‐assimilation methods used in meteorology and oceanography: three‐dimensional variational, four‐dimensional (4‐D) variational, 4D‐dual, Kalman filters, incremental formulations, formulations with imperfect models, addition of weak constraints, and reductions of the control space, etc. The flow‐charting approach is a powerful tool for decomposing a data‐assimilation method into elementary steps, for pointing out the elementary steps common to several methods or for building new and more efficient algorithms. In addition to the use of a common system of notation for assimilation methods, flow charting allows different algorithms to be easily compared, and is a necessary step prior to the development of any operational suite coupling data and models through one or several assimilation methods. This approach has been successfully followed to design a universal coupler called PALM (Projet d'Assimilation par Logiciel Multi‐méthodes) for the purpose of operational oceanography in the framework of the MERCATOR project.