On the quest for chaotic attractors in hydrological processes

D. Koutsoyiannis, On the quest for chaotic attractors in hydrological processes, Hydrological Sciences Journal, 51 (6), 1065–1091, doi:10.1623/hysj.51.6.1065, 2006.



In the last two decades, several researchers have claimed to have discovered low-dimensional determinism in hydrological processes, such as rainfall and runoff, using methods of chaotic analysis. Such results, however, have been criticized by others. In an attempt to offer additional insights into this discussion, it is shown here that in some cases merely the careful application of concepts of dynamical systems, without doing any calculation, provides strong indications that hydrological processes cannot be (low-dimensional) deterministic chaotic. Furthermore, it is shown that specific peculiarities of hydrological processes on fine timescales, 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 recovery of a hypothetical attractor from a time series is put as a statistical estimation problem whose study allows, among others, quantification of the required sample size; this appears to be so huge that it prohibits any accurate estimation even with the largest available 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 chaos.

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See also: http://dx.doi.org/10.1623/hysj.51.6.1065

Our works referenced by this work:

1. D. Koutsoyiannis, H. Yao, and A. Georgakakos, Multiyear behaviour and monthly simulation and forecasting of the Nile River flow, European Geosciences Union General Assembly 2006, Geophysical Research Abstracts, Vol. 8, Vienna, 05046, doi:10.13140/RG.2.2.33645.38888, European Geosciences Union, 2006.

Our works that reference this work:

1. D. Koutsoyiannis, H. Yao, and A. Georgakakos, Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods, Hydrological Sciences Journal, 53 (1), 142–164, doi:10.1623/hysj.53.1.142, 2008.
2. D. Koutsoyiannis, A random walk on water, Hydrology and Earth System Sciences, 14, 585–601, doi:10.5194/hess-14-585-2010, 2010.
3. S.M. Papalexiou, D. Koutsoyiannis, and A. Montanari, Can a simple stochastic model generate rich patterns of rainfall events?, Journal of Hydrology, 411 (3-4), 279–289, 2011.
4. G. Tsekouras, and D. Koutsoyiannis, Stochastic analysis and simulation of hydrometeorological processes associated with wind and solar energy, Renewable Energy, 63, 624–633, doi:10.1016/j.renene.2013.10.018, 2014.
5. D. Koutsoyiannis, P. Dimitriadis, F. Lombardo, and S. Stevens, From fractals to stochastics: Seeking theoretical consistency in analysis of geophysical data, Advances in Nonlinear Geosciences, edited by A.A. Tsonis, 237–278, doi:10.1007/978-3-319-58895-7_14, Springer, 2018.
6. D. Koutsoyiannis, and Z. W. Kundzewicz, Atmospheric temperature and CO₂: Hen-or-egg causality?, Sci, 2 (4), 83, doi:10.3390/sci2040083, 2020.
7. D. Koutsoyiannis, C. Onof, A. Christofides, and Z. W. Kundzewicz, Revisiting causality using stochastics: 1.Theory, Proceedings of The Royal Society A, 478 (2261), 20210835, doi:10.1098/rspa.2021.0835, 2022.

Works that cite this document: View on Google Scholar or ResearchGate

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

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Tagged under: Determinism vs. stochasticity, Papers initially rejected, Stochastics