Theoretical Basis and Application of an Analogue- Dynamical Model in the Lorenz System

The theoretical basis and application of an analogue-dynamical model (ADM) in the Lorenz systemis studied. The ADM can effectively combine statistical and dynamical methods in which the small disturbanceof the current initial value superimposed on the historical analogue reference state can be regarded as aprediction objective. Primary analyses show that under the condition of appending disturbances in modelparameters, the model errors of ADM are much smaller than those of the pure dynamical model (PDM).The characteristics of predictability on the ADM in the Lorenz system are analyzed in phase space byconducting case studies and global experiments. The results show that the ADM can quite effectivelyreduce prediction errors and prolong the valid time of the prediction in most situations in contrastto the PDM, but when model errors are considerably small, the latter will be superior to the former.To overcome such a problem, the multi-reference-state updating can be applied to introduce theinformation of multi-analogue and update analogue and can exhibit exciting performance in the ADM.