Studies On Chaos Theory And Its Application In Hydrological Time Series

The hydrological processes have been described by regular methods of internal determinacy orexternal randomness or both of them for a long time. In fact, hydrology system is dominated by theobjective factors, such as weather, geography and human activities, with combination ofdeterminacy and randomness. In this paper, in order to analyze the chaotic characteristics of themonthly precipitation from bielahong hydrology station in Sanjiang Plain, the groundwater depthfrom some farms of Sanjiang Plain and from Qiqihaer livestock breeding farm, the monthlydissolved oxygen of water quality from liuyuan hydrological station in the Nenjiang River, thestream-flow from shihuiyao hydrological station in Nenjiang River and from Dashankouhydrological station in Kaidou River of Bositeng Lake, the phase space was reconstructed at first.Then the diagnosis of chaotic characteristics of all hydrological time series was conducted and theresearch of chaotic prediction was done.The methods of state space parameters were discussed in detail. Time delay was chosendependently by using autocorrelation function method and the average cycle method of orbits,while reconstruct dimension was obtained by G-P saturation correlation dimension method andfalse nearest neighbor percentage method in dependently. Time delay and reconstruct dimensionwere obtained by C-C method and non-bias multiple autocorrelation function method at the sametime. The works laid a solid foundation for the diagnosis of chaotic characteristics of allhydrological time series.The paper applied many analysis methods, such as the power spectrum method, the principalcomponents analytical method, the phase portrait method, the Poincare section method, andcalculated the characteristics, i.e., the saturated correlation dimension, the maximal Lyapunovexponent and the Kotmogorov entropy, to analyze the chaotic characteristics of all hydrologicaltime series from every aspect. The results showed there is more or less chaos in these hydrologicaltime series.The saturation correlation dimension method was improved by setting Theiler-Windows basedon the suggestion of specialist in some documents for more accuracy. The conventional Wolfmethod which calculates maximal Lyapuonv exponent was improved, in which confines theevolution angle between new vector and original vector to avoid the distortion.Then, on the basis of above analysis, the paper established the local adding-weight linearregression forecasting model based on degree of incidence and the forecasting model of chaosbased on wavelet neural network. The results of prediction showed that the two forecasting modelare rational on theories, the precision and the result of assessment are satisfied. The history of chaos theory is short and the time of its application research in hydrology isdecades. Because the complexity of chaos and hydrology system, though the development oftheory and its application in hydrology was fast, the research is very superficial. Under theuncertain condition of hydrology system, the research of chaos application is very prospect.