*Nonlin. Proc. in Geophys.*

A pair of chaotic dynamical systems can synchronize when loosely coupled in a variety of ways. It is suggested that the synchronization phenomenon, with one system representing ``truth" and the other system representing ``model," provides a new approach to data assimilation in high-dimensional systems, reminiscent of Carl Jung's notion of synchronicity between matter and mind. One is led to search for low-dimensional subspaces through which the two systems can be synchronously coupled, such as a subspace defined by a small number of local bred vectors. Using a pair of 2-layer quasigeostrophic channel models, the efficacy of a bred vector basis for data assimilation can thus be compared to that of other bases.

It is argued that the synchronization approach differs qualitatively from any of the standard approaches to data assimilation. An equation for synchronously coupled dynamical systems can be obtained for continuous data assimilation in a linearized model, with coupling strength given in terms of observation and background errors in the usual way, and with observation error taken to correspond to noise in the coupling channel. Background error is computed from an assumption of stationarity of the probability distribution function (PDF) that satisfies the corresponding Fokker-Planck equation, for the case of a perfect model. An optimal coupling, in contrast, can be defined as one that minimizes the spread of the PDF. The analysis demonstrates that the synchronization approach to computing the optimal coupling for the full nonlinear model can improve upon more empirical methods in the vicinity of regime transitions.

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