Based On Nonlinear Time Series Analysis Method Of Nonlinear System Characteristics

Recently the development of Nonlinear Science received more and more attention from scientific society. Most problems in Meteorology are nonlinear problems, and the shortage of research of nonlinear problems became the main reason why the precision of weather forecasts is far from enough. Thus sloving problems in Atmospheric science using new theory and new methods in Nonlinear Science became one of the most important aspect in nowdays advances of meteorology. Although some progress obtained in the study of nonlinear time series, because of the nonliearity, multi-hierarchy, and nonstationarity of climatic system, those methods use in research of time series falls short of demands. Because the atmospheric system is a chaotic dynamic system, any small fluctuations in the beginning would cause big mistakes in the prediction, and further more, gives a quite different result.The integrality and correctiveness of initial value remain a big problem we faced in prediction. The study of nonlinearity and complexity of atmospheric system concentrates on the problem of predictability. In this paper we focus on the research of the sensitivity of nonlinear system's initial values and get result based on the state of the art Nonlinear Science as follows:1) In this paper we introduced Empirical Mode Decomposition(EMD) method, and study the sensitivity of Lorenz system's intial value. Decompose time series of Lorenz system's x variable through EMD under the circumstances of different initial flucatuations; compare the trivial differences of sensitivity of each IMF components, and try to figure out from which level the IMF components of Lorenz system separate first, e.g. low frequency or high frequency. In this paper we study the sensitivity of initial values of Lorenz system and found that the sensitvity of intial value is a general character of nonliear phenomenon. Since the sensitivity of intial values of Chaotic system, small fluctuations in intial value would cause big difference in future state. Moreover, with time pass by, the difference increased. Different intial value corresponds to different sensitivity, e.g. the speed of error amplification in initial value is different with different initial value, and thus the selection of intial value became an important aspect in the research of climatic system predicability. The speeds of seperation of IMF components are faster than the original ones, this result are in good accordance with former conclusions that short-range weather forecasts are possible while the long-range ones are impossible. We also analyzed the one or several IMF components of low layers and find that the information contains in lower layer IMF components are less than higher layers and contribute little to short-range climate prediction. However, the most likely tendency of big scale atmospheric circulation, e.g. long-range climate estimation is possible. These conclusions have certain guidence to the study of predicability of climatic system.2) We all knows that the origin of the error exist in weather prediction is the uncertainty of initial values and the incomplete of models while the basic ones is the chaotic characteristics of atompeheric process. Also we analyzed the development of errors in chaotic system's initial value. However, beacause of the interact of different spatio-temporal scales lies in atmospheric system, the understanding of the rules governs the error development in atmospheric system is far from enough. Since the climate system is a multi-hierarchical comlex open system, and most of our observational data are the output of low level system, if we can filter the information from high levels from the low levels system's output became the main problem need to be solved. In this paper we introduces a two-level model, analyzed the time series of low level through EMD method and try to find if it can reflect the information lies in high level systems. Research result indicates that, the information of high level systems are comprised in the time series of the low level systems, in other words, shows that EMD and Hilber transformation are good methods in the detection of informaiton of notable levels in climate system.3) The Climatic prediction methods already in existence all have the mathematic assumption that the time series processsed are linear and stationry, while this is not true for observational data. In this paper we construct a new forecast model, e.g. first use Empirical Mode Decompostion (EMD) to transform climatic time series into stationary one and obtain a series of Intrinsic Mode Function (IMF), then we use MGF model to get the first time prediction value of eaceh components, and on the base of OSR model, through direct or non-direct fit of some prediction value, finally we construct two scheme to enhance the ability of prediction. Experiment of classic climatic time series indicate that, the predictability of stationary IMF components, especially character IMF component are higher, this finding have good guidance to the prediction of the trend of the original time series. This model shows a new effectvie way to the prediction(estimation) of climate and enrich the Theory of hierarchical Climatic system.