Climate change, the Hurst phenomenon, and hydrological statistics

D. Koutsoyiannis, Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, doi:10.1623/hysj., 2003.



The intensive research of the recent years on climate change has led to the strong conclusion that climate has always, through the planet history, changed irregularly on all time scales. Climate changes are closely related to the Hurst phenomenon, which has been detected in many long hydroclimatic time series and is stochastically equivalent with a simple scaling behaviour of climate variability over timescale. The climate variability, anthropogenic or natural, increases the uncertainty of the hydrologic processes. It is shown that hydrologic statistics, the branch of hydrology that deals with uncertainty, in its current state is not consistent with the varying character of climate. Typical statistics used in hydrology such as means, variances, cross- and auto-correlations and Hurst coefficients, and the variability thereof, are revisited under the hypothesis of a varying climate following a simple scaling law, and new estimators are studied which in many cases differ dramatically from the classic ones. The new statistical framework is applied to real-world examples for typical tasks such as estimation and hypothesis testing where again the results depart significantly from those of the classic statistics.

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Alternative names for Hurst phenomenon are Hurst effect, Joseph effect, Long term persistence, Long range dependence, Scaling behaviour (in time), Multi-scale fluctuation, Hurst-Kolmogorov pragmaticity, etc.

Erratum: The runoff of the Boeotikos Kephisos catchment (Fig. 3, p. 7, and p. 21, first full paragraph) should be corrected to volume units, i.e. cubic hectometers (instead of millimeters).

Our works referenced by this work:

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Our works that reference this work:

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40. T. Iliopoulou, and D. Koutsoyiannis, Revealing hidden persistence in maximum rainfall records, Hydrological Sciences Journal, 64 (14), 1673–1689, doi:10.1080/02626667.2019.1657578, 2019.
41. T. Iliopoulou, and D. Koutsoyiannis, Projecting the future of rainfall extremes: better classic than trendy, Journal of Hydrology, 588, doi:10.1016/j.jhydrol.2020.125005, 2020.
42. Z. W. Kundzewicz, I. Pińskwar, and D. Koutsoyiannis, Variability of global mean annual temperature is significantly influenced by the rhythm of ocean-atmosphere oscillations, Science of the Total Environment, 747, 141256, doi:10.1016/j.scitotenv.2020.141256, 2020.
43. P. Dimitriadis, D. Koutsoyiannis, T. Iliopoulou, and P. Papanicolaou, A global-scale investigation of stochastic similarities in marginal distribution and dependence structure of key hydrological-cycle processes, Hydrology, 8 (2), 59, doi:10.3390/hydrology8020059, 2021.
44. D. Koutsoyiannis, and P. Dimitriadis, Towards generic simulation for demanding stochastic processes, Sci, 3, 34, doi:10.3390/sci3030034, 2021.
45. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023.

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86. Merz, B., T. Maurer and K. Kaiser, Wie gut können wir vergangene und zukünftige Veränderungen des Wasserhaushalts quantifizieren? [How well can we quantify past and future changes of the water cycle?], Hydrologie und Wasserbewirtschaftung, 5, 244-256, DOI: 10.5675/HyWa_2012,5_1, 2012.
87. Musa, M., and K. Ibrahim, Existence of long memory in ozone time series, Sains Malaysiana, 41 (11), 1367-1376, 2012.
88. Bard, A., B. Renard et M. Lang, Tendances observées sur les régimes hydrologiques de l’Arc Alpin [Observed Trends in the hydrologic regime of Alpine catchments], Houille Blanche, (1), 38-43, 2012.
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92. Kumar, S., V. Merwade, J. L. Kinter III and D. Niyogi, Evaluation of temperature and precipitation trends and long-term persistence in CMIP5 20th century climate simulations, Journal of Climate, 26 (12), 4168-4185, 2013.
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96. Lacombe, G., V. Smakhtin and C. Hoanh, Wetting tendency in the Central Mekong Basin consistent with climate change-induced atmospheric disturbances already observed in East Asia, Theoretical and Applied Climatology, 111 (1-2), 251-263, 2013.
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Tagged under: Course bibliography: Stochastic methods, Climate stochastics, Hurst-Kolmogorov dynamics, Papers initially rejected, Stochastics, Uncertainty