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 y 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.
The SPEEDO global climate model (an atmosphere model coupled to a land and an ocean/sea-ice model with about 250.000 degrees of freedom) is used to investigate the merits of a new multi-model ensemble approach to the climate prediction problem in a perfect model setting. Two imperfect models are generated by perturbing parameters. Connection terms are introduced that synchronize the two models on a common solution, referred to as the supermodel solution. A synchronization-based learning algorithm is applied to the supermodel through the introduction of an update rule for the connection coefficients. Connection coefficients cease updating when synchronization errors between the supermodel and solutions of the "true" equations vanish. These final connection coefficients define the supermodel. Different supermodel solutions, but with equivalent performance, are found depending on the initial values of the connection coefficients during learning. The supermodels have a climatology and a climate response to a CO increase in the atmosphere that is closer to the truth as compared to the imperfect models and the standard multi-model ensemble average, showing the potential of the supermodel approach to improve climate predictions.
While synchronized chaos is familiar in low-order systems, the relevance of this paradigm to natural phenomena and spatially extended systems is questionable because of the time lags introduced by finite signal propagation speeds. A form of partially synchronized chaos is here demonstrated in a low-order numerical model of the coupled large-scale atmospheric circulation patterns in the northern and southern hemispheres. The model is constructed using a Green's function method to represent the time-lagged boundary forcing of the flow in each hemisphere by Rossby waves emanating from the opposite hemisphere. The two hemispheric subsystems are semiautonomous because Rossby waves cannot penetrate the tropics except in narrow longitudinal bands where the background winds are westerly. Each hemisphere has previously been described by a 10-variable model, derived from a spectral truncation of the barotropic vorticity equation. The model exhibits dynamical regimes corresponding to ''blocked'' and ''zonal'' atmospheric flow patterns in the hemisphere. Applying the same spectral truncation to the Green's functions that define the coupling, we construct a 28-variable model of the coupled flow on a planet with simplified geometry and background wind field. Partial synchronization is manifest in a significant tendency for the two hemispheric subsystems to occupy the same regime simultaneously. This tendency is observed in actual meteorological data. Partial synchronization of this form can be viewed as an extension of on-off intermittency in a system with a synchronization manifold, to a region of parameter space that is far from the bifurcation point at which this manifold loses stability.
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