Nonlinear analysis of river flow time sequences

Within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed. In light of these ideas we study the dynamics which control the behavior over time of river flow, investigating the existence of a low‐dimension deterministic component. The present article follows the research undertaken in the work of Porporato and Ridolfi [1996a] in which some clues as to the existence of chaos were collected. Particular emphasis is given here to the problem of noise and to nonlinear prediction. With regard to the latter, the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown.

[1]  Luca Ridolfi,et al.  Clues to the existence of deterministic chaos in river flow , 1996 .

[2]  Upmanu Lall,et al.  Nonlinear dynamics and the Great Salt Lake: A predictable indicator of regional climate , 1996 .

[3]  Giuseppe Rega,et al.  An exploration of chaos , 1996 .

[4]  Upmanu Lall,et al.  Nonlinear Dynamics of the Great Salt Lake: Nonparametric Short-Term Forecasting , 1996 .

[5]  Upmanu Lall,et al.  Nonlinear Dynamics of the Great Salt Lake: Dimension Estimation , 1996 .

[6]  A. Porporato,et al.  ANALYSIS OF RANDOMLY SAMPLED DATA USING FUZZY AND NONLINEAR TECHNIQUES , 1996 .

[7]  Upmanu Lall,et al.  The Great Salt Lake: A Barometer of Low-Frequency Climatic Variability , 1995 .

[8]  A. Mees,et al.  On selecting models for nonlinear time series , 1995 .

[9]  A. Rinaldo,et al.  Can One Gauge the Shape of a Basin , 1995 .

[10]  S. Peckham.  New Results for Self‐Similar Trees with Applications to River Networks , 1995 .

[11]  V. F. Pisarenko,et al.  Statistical estimation of the correlation dimension , 1995 .

[12]  M. Paluš.  Testing for nonlinearity using redundancies: quantitative and qualitative aspects , 1994, comp-gas/9406002.

[13]  J. Theiler,et al.  Generalized redundancies for time series analysis , 1994, comp-gas/9405006.

[14]  P. Claps,et al.  Conceptually-based univariate stochastic modelling of river runoff , 1995 .

[15]  Mike E. Davies,et al.  Noise reduction schemes for chaotic time series , 1994 .

[16]  F. Busse.  An exploration of chaos: J. Argyris, G. Faust and M. Haase, Elsevier, Amsterdam, 1994, 722 pp., ISBN 0-444-82002-7 (hardbound), 0-444-82003-5 (paperback) , 1994 .

[17]  Milan Paluš,et al.  Testing for Nonlinearity in Weather Records , 1994 .

[18]  R. Vio,et al.  Luminosity Variations of 3C 345: Is There Any Evidence of Low-dimensional Chaos? , 1994 .

[19]  Anastasios A. Tsonis,et al.  Searching for determinism in observed data: a review of the issues involved , 1994 .

[20]  K. Judd.  Estimating dimension from small samples , 1994 .

[21]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[22]  G. Kember,et al.  Forecasting river flow using nonlinear dynamics , 1993 .

[23]  Daw,et al.  Role of low-pass filtering in the process of attractor reconstruction from experimental chaotic time series. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Schreiber,et al.  Extremely simple nonlinear noise-reduction method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  P. Grassberger,et al.  On noise reduction methods for chaotic data. , 1993, Chaos.

[26]  Takayasu,et al.  Water erosion as a fractal growth process. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Eric R. Ziegel,et al.  Developments in Time Series Analysis , 1993 .

[28]  Gerd Pfister,et al.  Comparison of algorithms calculating optimal embedding parameters for delay time coordinates , 1992 .

[29]  J. Maquet,et al.  Construction of phenomenological models from numerical scalar time series , 1992 .

[30]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

[31]  T. Sauer.  A noise reduction method for signals from nonlinear systems , 1992 .

[32]  Julien Clinton Sprott,et al.  Extraction of dynamical equations from chaotic data , 1992 .

[33]  J. Elsner,et al.  Nonlinear prediction as a way of distinguishing chaos from random fractal sequences , 1992, Nature.

[34]  Guan-Hsong Hsu,et al.  SNR perfomance of a noise reduction algorithm applied to coarsely sampled chaotic data , 1992 .

[35]  James B. Elsner,et al.  Predicting time series using a neural network as a method of distinguishing chaos from noise , 1992 .

[36]  W. Ditto,et al.  Chaos: From Theory to Applications , 1992 .

[37]  Anastasios A. Tsonis,et al.  Nonlinear Prediction, Chaos, and Noise. , 1992 .

[38]  M. Casdagli.  Chaos and Deterministic Versus Stochastic Non‐Linear Modelling , 1992 .

[39]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[40]  P. Grassberger,et al.  A simple noise-reduction method for real data , 1991 .

[41]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[42]  E. Lorenz.  Dimension of weather and climate attractors , 1991, Nature.

[43]  J. Theiler.  Some Comments on the Correlation Dimension of 1/fαNoise , 1991 .

[44]  K. Pawelzik,et al.  Optimal Embeddings of Chaotic Attractors from Topological Considerations , 1991 .

[45]  P. Linsay.  An efficient method of forecasting chaotic time series using linear interpolation , 1991 .

[46]  M. Mundt,et al.  Chaos in the sunspot cycle: Analysis and Prediction , 1991 .

[47]  J. D. Farmer,et al.  Optimal shadowing and noise reduction , 1991 .

[48]  J. D. Farmer,et al.  A Theory of State Space Reconstruction in the Presence of Noise , 1991 .

[49]  Breeden,et al.  Reconstructing equations of motion from experimental data with unobserved variables. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[50]  Grebogi,et al.  Shadowing of physical trajectories in chaotic dynamics: Containment and refinement. , 1990, Physical review letters.

[51]  Stephen M. Hammel,et al.  A noise reduction method for chaotic systems , 1990 .

[52]  P. Grassberger.  An optimized box-assisted algorithm for fractal dimensions , 1990 .

[53]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[54]  Pfister,et al.  Attractor reconstruction from filtered chaotic time series. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[55]  Konstantine P. Georgakakos,et al.  Evidence of Deterministic Chaos in the Pulse of Storm Rainfall. , 1990 .

[56]  James A. Yorke,et al.  Noise Reduction: Finding the Simplest Dynamical System Consistent with the Data , 1989 .

[57]  Ranvir Singh,et al.  Watershed Planning and Analysis in Action , 1990 .

[58]  N. F. Jr. Hunter,et al.  Application of nonlinear time series models to driven systems , 1990 .

[59]  H. Schuster,et al.  Proper choice of the time delay for the analysis of chaotic time series , 1989 .

[60]  Peter Grassberger,et al.  Information content and predictability of lumped and distributed dynamical systems , 1989 .

[61]  Konstantine P. Georgakakos,et al.  Chaos in rainfall , 1989 .

[62]  Martin Casdagli,et al.  Nonlinear prediction of chaotic time series , 1989 .

[63]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .

[64]  J. Havstad,et al.  Attractor dimension of nonstationary dynamical systems from small data sets. , 1989, Physical review. A, General physics.

[65]  J. Doyne Farmer,et al.  Exploiting Chaos to Predict the Future and Reduce Noise , 1989 .

[66]  Agnessa Babloyantz,et al.  A comparative study of the experimental quantification of deterministic chaos , 1988 .

[67]  Yorke,et al.  Noise reduction in dynamical systems. , 1988, Physical review. A, General physics.

[68]  J. Elsner,et al.  The weather attractor over very short timescales , 1988, Nature.

[69]  Broggi,et al.  Dimension increase in filtered chaotic signals. , 1988, Physical review letters.

[70]  S. Yakowitz,et al.  Rainfall-runoff forecasting methods, old and new , 1987 .

[71]  Theiler,et al.  Efficient algorithm for estimating the correlation dimension from a set of discrete points. , 1987, Physical review. A, General physics.

[72]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[73]  秦 浩起,et al.  Characterization of Strange Attractor (カオスとその周辺(基研長期研究会報告)) , 1987 .

[74]  S. Yakowitz,et al.  Nearest‐neighbor methods for nonparametric rainfall‐runoff forecasting , 1987 .

[75]  Swinney,et al.  Strange attractors in weakly turbulent Couette-Taylor flow. , 1987, Physical review. A, General physics.

[76]  James P. Crutchfield,et al.  Equations of Motion from a Data Series , 1987, Complex Syst..

[77]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[78]  A. Provenzale,et al.  A search for chaotic behavior in large and mesoscale motions in the Pacific Ocean , 1986 .

[79]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[80]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[81]  G. Nicolis,et al.  Is there a climatic attractor? , 1984, Nature.

[82]  James P. Crutchfield,et al.  Low-dimensional chaos in a hydrodynamic system , 1983 .

[83]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[84]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[85]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[86]  Peter K. Kitanidis,et al.  Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty , 1980 .

[87]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[88]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[89]  M. Priestley.  STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSIS , 1980 .

[90]  D. H. Pilgrim.  Travel Times and Nonlinearity of Flood Runoff From Tracer Measurements on a Small Watershed , 1976 .

[91]  E. Lorenz.  Atmospheric Predictability as Revealed by Naturally Occurring Analogues , 1969 .