DATA ASSIMILATION IN THE LOW NOISE, ACCURATE OBSERVATION REGIME WITH APPLICATION TO THE KUROSHIO CURRENT

On-line data assimilation techniques such as ensemble Kalman filters and particle filters tend to loose accu- racy dramatically when presented with an unlikely observation. Such an observation may be caused by an unusually large measurement error or reflect a rare fluctuation in the dynamics of the system. Over a long enough span of time it becomes likely that one or several of these events will occur. In some cases they are signatures of the most interesting features of the underlying system and their prediction becomes the primary focus of the data assimilation procedure. The Kuroshio current that runs along the eastern coast of Japan is an example of just such a system. It undergoes infrequent but dramatic changes of state between a small meander during which the current remains close to the coast of Japan, and a large meander during which the current bulges away from the coast. Because of the important role that the Kuroshio plays in distributing heat and salinity in the surrounding region, prediction of these transitions is of acute interest. Here we propose several data assimilation strategies capable of efficiently handling rare events such as the transitions of the Kuroshio current in situations where both the stochastic forcing on the system and the observational noise are small. In this regime, large deviation theory can be used to understand why standard filtering methods fail and guide the design of the more effective data assimilation techniques suggested here. These techniques are tested on the Kuroshio and shown to perform much better than standard filtering methods.