Research On Fractal On Fractal Characteristics Of The Stream Flow Time Series

Stream flows are sorts of nonlinear time series, description and exploration exactly about which have straight relations with water resources exploitation and utilization efficiently. Based on fractal and other nonlinear theories, aimed at the characteristics of stream flow evolvement, some works have be done such as distilling, comparing, analyzing, modeling and computing on certain nonlinear characteristics about stream flow evolvement. The main results of this paper are as follows:(1) Basis statistic characteristics of the stream flow time series are analyzed. Kolmogorov-Smirnov is introduced to test random normal nature of the stream flow fluctuation. The results indicate that the distributing forms have distinct difference with the departure degree about normal school. Through frequency distributing, stream flows are proved having the fractal distributing characteristic of"pinnacle and large trail".(2) Stream flow nonlinearity is identified through Bispectrum analysis. The results shows that the stream flow time series of the Yellow River and the Yangtse River are nonlinearity. For non-symetry systems, Bispectrum can token nonlinear characteristics completely. So high steps accumulated measures are kinds of exact and effective method to study systemetic nonlinearity.(3) Long-range relativity and dimensions about the stream flows are analyzed. Based on time series long relativities, detrended fluctuation analysis based on certain non-symmetry cycle models is advanced to identify the relativity and index fixity of the months flow time series in the Yellow River and the Yangtse River main streams. The results indicate that the two main streams have long-range relativities and the indexes are larger than 0.5 and even the degree in the Yellow River is higher than the Yangtse River. Months flow time series of every hydrological station has the characteristic of slow raise, quick fall in annual cycle. Larger the catchment areas are, stranger the relativity is. So the long-range relativity shows clear cumulated domino offect. Larger the scales of the hydrology system are, higher stability it is. Then according to the index, the fractal dimensions of the object are calculated and the results validate the stream flow is of comparability and index fixty.(4) Long memory about the stream flows evolution is researched. To analyze, understand flow structure, and estimate the trend and the long memory has important effects on hydrology system and its future movement. So a kind of flow decomposes analysis based on Liu switch has been put forward and then R/S is used to test the long memory of the fore-and-aft decomposed time series. The results indicate that the change of the stream flow has large relations with precipitation and climate changes. At the same time, long memory series have been proved the long memory is being in the stream flow fluctuation, which can be explained through the durative of structure switches in reason and deeply makes clear that it is very important to structure decomposing before series analysis.(5) Multi-fractal characteristics of the stream flow are analyzed. Compared to single fractal, multi-fractal is better to depict asymmetry in the process of the stream flow evolution. MF-DFA is used to analyze the multi-fractal characteristics in the stream flow and the formation is discussed. The conclusion shows that the flow time series in the Yellow River and the Yangtse River main streams present obvious multi-fractal characteristics, which is the outcomes of long relativities and the large trails. It breaks a new path for quantitive analysis on deepen water system evolution rules.(6) Aimed at the stream flow nonlinearity, the nearest adjacent chaos forecast model has been established to analyze the flow process in the Yellow River and the Yangtse River main streams and the satisfied precision is received. Then based on the model tracking the attracted dot in phase-spaces efficiently and catching useful information in the original dates well, the average square errors change is found through adding adjacent dots deeply to test the forecast effects. The results indicate that the method can reflects the general trend of the stream flow truly, which provides a new method to estimate the nonlinearity of time series.