Does the river run wild? Assessing chaos in hydrological systems

Abstract The standing debate over whether hydrological systems are deterministic or stochastic has been taken to a new level by controversial applications of chaos mathematics. This paper reviews the procedure, constraints, and past usage of a popular chaos time series analysis method, correlation integral analysis, in hydrology and adds a new analysis of daily streamflow from a pristine watershed. Significant problems with the use of correlation integral analysis (CIA) were found to include a continued reliance on the original algorithm even though it was corrected subsequently and failure to consider the physics underlying mathematical results. The new analysis of daily streamflow reported here found no attractor with D ⩽5. Phase randomization of the Fourier Transform of streamflow was used to provide a better stochastic surrogate than an Autoregressive Moving Average (ARMA) model or gaussian noise for distinguishing between chaotic and stochastic dynamics.

[1]  Klaus Fraedrich,et al.  Estimating the Dimensions of Weather and Climate Attractors , 1986 .

[2]  I. Rodríguez‐Iturbe,et al.  Reply [to “Comment on ‘Chaos in rainfall’ by I. Rodriguez-Iturbe et al.”] , 1990 .

[3]  Ignacio Rodriguez-Iturbe,et al.  A Possible Explanation for Low Correlation Dimension Estimates for the Atmosphere , 1993 .

[4]  Klaus Fraedrich,et al.  Estimating Weather and Climate Predictability on Attractors , 1987 .

[5]  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 .

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

[7]  P. Grassberger.  Do climatic attractors exist? , 1986, Nature.

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

[9]  J. Costa.  Effects of Agriculture on Erosion and Sedimentation in the Piedmont Province, Maryland , 1975 .

[10]  Christopher Essex,et al.  The climate attractor over short timescales , 1987, Nature.

[11]  Robert B. Jacobson,et al.  Stratigraphy and Recent evolution of Maryland Piedmont flood plains , 1986 .

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

[13]  Konstantine P. Georgakakos,et al.  Estimating the Dimension of Weather and Climate Attractors: Important Issues about the Procedure and Interpretation , 1993 .

[14]  D. Newland.  An introduction to random vibrations and spectral analysis , 1975 .

[15]  X. Zeng,et al.  Estimating the fractal dimension and the predictability of the atmosphere , 1992 .

[16]  E. Lorenz.  Atmospheric predictability experiments with a large numerical model , 1982 .

[17]  A. Fraser.  Reconstructing attractors from scalar time series: A comparison of singular system and redundancy criteria , 1989 .

[18]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[19]  Mark S. Seyfried,et al.  Searching for chaotic dynamics in snowmelt runoff , 1991 .

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

[21]  Renzo Rosso,et al.  Comment on “Chaos in rainfall” by I. Rodriguez‐Iturbe et al. , 1990 .

[22]  Harry W. Henderson,et al.  Obtaining Attractor Dimensions from Meteorological Time Series , 1988 .

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

[24]  A. Jayawardena,et al.  Analysis and prediction of chaos in rainfall and stream flow time series , 1994 .

[25]  Siegfried D. Schubert,et al.  Dynamical Predictability in a Simple General Circulation Model: Average Error Growth. , 1989 .

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

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

[28]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

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

[30]  X. Zeng,et al.  What does a low-dimensional weather attractor mean? , 1993 .

[31]  Edward N. Lorenz,et al.  Can chaos and intransitivity lead to interannual variability , 1990 .