Nonlinear Characteristics Identification And Analysis For River Runoff Time Series

The study of the regularity for the daily runoff time series is the prerequisite and foundation in hydrochemistry and development using of water resource, modeling towards planning and management of river basins. Hydrological process is a suquence course; however, runoff series is a complex, discrete and nonlinear data. A large number of random factors, such as data noise and the length of data, would have an effect on the mathematic model establish and predictions. For a long time, people analyse and study runoff fluctuation frequency and evolution process using the traditional method based on the phase-space reconstruction. Based on the previse research methods and theoretical results, some newly nonlinear time series theory and analyzes methods:the zero-one (0-1) test algorithm, recurrence plot and recurrence quantification analysis (RQA) theory, and complex network reconstruction theory, is put forward in which the chaos theory is combined to compute, discuss and slove on the river runoff. Case studies of daily discharges of Yangtze River (Hankou station, Yichang station and Pingshan station) in china and Umpqua River in America (Elkton station) are implemented. The main research contents and research achievement of this paper are as follows:1. This paper presents a new effective algorithm for chaos detection in time series named0-1test fo chaos. The advantages of the method is that it can applies directly to time series data and phase space reconstruction is not necessary. Moreover, the non-chaotic and chaotic characteristic can be decided by means of the parameters Kc approaching asymptotically either to zero or one. Case studies of Logistic map, daily runoff series of Jinsha River in China and Umpqua River in America are implemented. The chaotic characteristics are identified and verified by using the0-1test algorithm. Then, based on the phase space reconstruction, nonlinear dynamic methods are employed, for example correlation dimension method, Lyapunov exponent method and Kolmogorov entropy. The comparison results show the effectiveness and reliability of the0-1test algorithm. The results from these methods provide cross-verification and confirmation of the existence of a mild low-dimensional chaos in the two daily runoff time series.2. Natural runoff dynamics is an outcome of complex nonlinear and multi-scale phenomena, integrated together in some coherent manner. Based on chaos theory and the phase space reconstruction theory, daily runoff series of Jinsha River in china and Umpqua River in America are used for this study at different timescales (one day,1/3month and one month). This paper calculates the asymptotic growth rate Kc by the0-1test algorithm and its variation with timescales are explored firstly. Then phase space reconstruction are adopted for the runoff series, three discrimination indexes, correlation dimension, Lyapunov exponent and Kolmogorov entropy, are used:An attempt is made to identify the existence of chaos and the intensity of nonlinear behavior at three characteristic time scales. A comparison of results reveals the relationship of the timescales and the intensity of nonlinearity is not very obvious, no clear variation is found between the asymptotic growth rate and the timescale, the embedded dimension decrease as the timescales increase. However, largest Lyapunov exponent and Kolmogorov entropy increases with the increase of the timescale.3. The method of recurrence plot and order pattant recurrence plot are proposed to get dynamic characteristics property of hydrological time series, which is based on reconstruction phase space. After structuring recurrence plots for Brownian movement, the Lorenz system and periodic sequence (Logisticc map and sine function), the recurrence plots of daily runoff time series at different timescale were studied quantitatively. Through the analysis of fluctuation patterns and identification of deterninacy, the certainty and uncertainty components were identified in the runoff time series. Then, the Recurrence quantification analysis (RQA) is used for characterizing complexity analysis of runoff series, the recurrence plot and recurrence parameters of five different runoff series are compared. The results show the analysis method is a valid effective means for ranoff fluctuation pattern and evolution rule.4. This paper introduced a new method for model of complex networks based on renormalization from a time series-Complex Network based on Phase Space. It is used in hydrology and water resources research, the method has offered an interesting new angle on analyses of the hydrological time series. Prior studies on the statistical properties of network topotogy, shows that the constructed complex network model contained inherent characteristics of the time series in its structure. Specifically, a set of periodic data and noisy series could be transformed into a deteminate networks and stochastic networks, respectively, and the chaotic complex networks typically show the properties of small-world and scale-free property involved in unstable periodic trajectories. Then the study focused on the construction of complex network of dialy runoff seires in Yangtze River at different hydrological station. The complex network characteristic of the runoff time series is discussed. Then the community-detection algorithm based on K-means clustering is proposed and detecting the community structure of the complex network of runoff time series. We investigate the correspondence between the dynamics of runoff time series and the node fluctuation patterns distribution of complex network. And the characteristics of different space scale diarly runoff series are depicted by the network parameters, including average degree, graph density, modularity, number of communities, average clustering coefficient, and average path lengh, number of shortest paths, average neighborhood overlap and average embeddness. This is a great reference value of modeling and prediction of runoff series from the prospective of network.