Data assimilation as synchronization of truth and model: Experiments with the three-variable Lorenz system

The potential use of chaos synchronization techniques in data assimilation for numerical weather prediction models is explored by coupling a Lorenz three-variable system that represents "truth" to another that represents "the model." By adding realistic "noise" to observations of the master system, an optimal value of the coupling strength was clearly identifiable. Coupling only the γ variable yielded the best results for a wide range of higher coupling strengths. Coupling along dynamically chosen directions identified by either singular or bred vectors could improve upon simpler chaos synchronization schemes. Generalized synchronization (with the parameter r of the slave system different from that of the master) could be easily achieved, as indicated by the synchronization of two identical slave systems coupled to the same master, but the slaves only provided partial information about regime changes in the master. A comparison with a standard data assimilation technique, three-dimensional variational analysis (3DVAR), demonstrated that this scheme is slightly more effective in producing an accurate analysis than the simpler synchronization scheme. Higher growth rates of bred vectors from both the master and the slave anticipated the location and size of error spikes in both 3DVAR and synchronization. With less frequent observations, synchronization using time-interpolated observational increments was competitive with 3DVAR. Adaptive synchronization, with a coupling parameter proportional to the bred vector growth rate, was successful in reducing episodes of large error growth. These results suggest that a hybrid chaos synchronization-data assimilation approach may provide an avenue to improve and extend the period for accurate weather prediction.