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 here through experiments with the Lorenz 3-variable model. Our experiments show that synchronization takes for a wide range (over two orders of magnitude) in the coupling coefficient. We compare a coupling scheme based on coupling along the direction of either bred vector or singular vector. Our results suggest that coupling along dynamically chosen directions has the potential to improve current chaos synchronization schemes. Experiments on "generalized synchronization" (GS) were performed by letting one of the parameters in the slave equation differ from those that guide the master's dynamics. We find that GS is easier to attain than identical synchronization even with low coupling strengths but the slaves provide only partial information about the master. A direct comparison with a standard data assimilation technique, 3-Dimensional Variational Analysis (3D-Var), demonstrates that this scheme is slightly more effective in producing an accurate analysis than the simpler synchronization scheme. We note that higher growth rates of bred vectors from both the master and the slave anticipate the location and size of error spikes in both 3D-Var and synchronization, whereas the more advanced data assimilation method of Kalman Filtering, yielding the most accurate analyses, avoids large error spikes through the use of adaptive weights. Adaptive synchronization, with a coupling parameter proportional to the bred vector, succeeds in reducing episodes of large error growth. Our results suggest that a hybrid chaos synchronization-data assimilation approach may provide an avenue to improve and extend the period for accurate weather prediction.