Data assimilation at the oceanic mesoscale: A review

Methods used to estimate the state of the ocean and its temporal variations with special focus on the mesoscale (the eddy scale) are examined and illustrated. There are two broad categories of methods, although mixed approaches can be found. The "statistical methods" are first discussed. It is shown that these methods are robust and can help assimilate the routinely available ocean observations (typically, satellite altimetry and surface temperature), with the help of order-reduction methods which are still open to debate, especially as far as the inference of the deep circulation is concerned. Among the possible simplifications, recent developments around the adaptive filter and representor approaches attempt to address the facts that oceanic eddy-resolving problems are usually of very high dimension, and that the knowledge of process and observational noise statistics is poor. The sophisticated "variational methods" lack an error theory, but are more flexible in efficiently assimilating various data kinds, and can help study the sensitivity to various controls. Examples of strategies using both types of methods in sequence are also given.