On embedding dimensions and their use to detect deterministic chaos in hydrological processes

D. Koutsoyiannis, On embedding dimensions and their use to detect deterministic chaos in hydrological processes, Hydrofractals '03, An international conference on fractals in hydrosciences, Monte Verita, Ascona, Switzerland, doi:10.13140/RG.2.2.16920.60165, ETH Zurich, MIT, Université Pierre et Marie Curie, 2003.



Studies of dynamical systems have demonstrated that simple nonlinear systems with low-dimensional deterministic dynamics may yield irregular trajectories with random appearance. This led many to investigate the inverse, i.e. to try to detect the presence of low dimensional determinism in time series formerly regarded as outcomes of stochastic systems. A typical method used in many such investigations is time delay embedding and correlation dimension. This method, however, may be misleading if applied to hydrological time series. Specifically, it is shown that specific peculiarities of hydrological processes on fine time scales, such as asymmetric, J-shaped distribution functions, intermittency, and high autocorrelations, are synergistic factors that can lead to misleading conclusions regarding presence of (low-dimensional) deterministic chaos. In addition, the required size to accurately estimate chaotic descriptors of hydrological processes is quantified by statistical reasoning and it is shown that such a size is not met in hydrological records. All these arguments are demonstrated using appropriately synthesized theoretical examples. Finally, in light of the theoretical analyses and arguments, typical real-world hydrometeorological time series, such as relative humidity, rainfall, and runoff, are explored and none of them is found to indicate the presence of low-dimensional chaos.

PDF Full text:

See also: http://dx.doi.org/10.13140/RG.2.2.16920.60165

Related works:

Other works that reference this work (this list might be obsolete):

1. Howard, D., and M.A. Edwards, Enhancing chance discovery: Dimensions, strategies and tools, Knowledge-Based Intelligent Information and Engineering Systems, Pt 2, 3214, 793-799, 2004.

Tagged under: Determinism vs. stochasticity