P.E. O’Connell, D. Koutsoyiannis, H. F. Lins, Y. Markonis, A. Montanari, and T.A. Cohn, The scientific legacy of Harold Edwin Hurst (1880 – 1978), *Hydrological Sciences Journal*, 61 (9), 1571–1590, doi:10.1080/02626667.2015.1125998, 2016.

[doc_id=1593]

[English]

Emanating from his remarkable characterization of long-term variability in geophysical records in the early 1950s, Hurst’s scientific legacy to hydrology and other disciplines is explored. A statistical explanation of the so-called ‘Hurst Phenomenon’ did not emerge until 1968 when Mandelbrot and co-authors proposed fractional Gaussian noise based on the hypothesis of infinite memory. A vibrant hydrological literature ensued where alternative modelling representations were explored and debated eg ARMA models, the Broken Line model, shifting mean models with no memory, FARIMA models, and Hurst-Kolmogorov dynamics, acknowledging a link with the work of Kolmogorov in 1940. The diffusion of Hurst’s work beyond hydrology is summarized by discipline and citations, showing that he arguably has the largest scientific footprint of any hydrologist in the last century. Its particular relevance to the modelling of long-term climatic variability in the era of climate change is discussed. Links to various long-term modes of variability in the climate system, driven by fluctuations in sea surface temperatures and ocean dynamics, are explored. A physical explanation of the Hurst Phenomenon in hydrology remains as a challenge for future research.

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**See also:**
http://dx.doi.org/10.1080/02626667.2015.1125998

**Our works referenced by this work:**

1. | D. Koutsoyiannis, The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47 (4), 573–595, doi:10.1080/02626660209492961, 2002. |

2. | D. Koutsoyiannis, Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, doi:10.1623/hysj.48.1.3.43481, 2003. |

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7. | D. Koutsoyiannis, and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, Academic Press, Oxford, 2011. |

8. | D. Koutsoyiannis, Hurst-Kolmogorov dynamics and uncertainty, Journal of the American Water Resources Association, 47 (3), 481–495, doi:10.1111/j.1752-1688.2011.00543.x, 2011. |

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10. | D. Koutsoyiannis, Hydrology and Change, Hydrological Sciences Journal, 58 (6), 1177–1197, doi:10.1080/02626667.2013.804626, 2013. |

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13. | D. Koutsoyiannis, and A. Montanari, Negligent killing of scientific concepts: the stationarity case, Hydrological Sciences Journal, 60 (7-8), 1174–1183, doi:10.1080/02626667.2014.959959, 2015. |

14. | D. Koutsoyiannis, and S.M. Papalexiou, Extreme rainfall: Global perspective, Handbook of Applied Hydrology, Second Edition, edited by V.P. Singh, 74.1–74.16, McGraw-Hill, New York, 2017. |

**Our works that reference this work:**

1. | Y. Markonis, and D. Koutsoyiannis, Scale-dependence of persistence in precipitation records, Nature Climate Change, 6, 399–401, doi:10.1038/nclimate2894, 2016. |

2. | A. Tegos, H. Tyralis, D. Koutsoyiannis, and K. H. Hamed, An R function for the estimation of trend signifcance under the scaling hypothesis- application in PET parametric annual time series, Open Water Journal, 4 (1), 66–71, 6, 2017. |

3. | T. Iliopoulou, S.M. Papalexiou, Y. Markonis, and D. Koutsoyiannis, Revisiting long-range dependence in annual precipitation, Journal of Hydrology, 556, 891–900, doi:10.1016/j.jhydrol.2016.04.015, 2018. |

4. | P. Dimitriadis, and D. Koutsoyiannis, Stochastic synthesis approximating any process dependence and distribution, Stochastic Environmental Research & Risk Assessment, 32 (6), 1493–1515, doi:10.1007/s00477-018-1540-2, 2018. |

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. | H. Tyralis, P. Dimitriadis, D. Koutsoyiannis, P.E. O’Connell, K. Tzouka, and T. Iliopoulou, On the long-range dependence properties of annual precipitation using a global network of instrumental measurements, Advances in Water Resources, 111, 301–318, doi:10.1016/j.advwatres.2017.11.010, 2018. |

7. | I. Tsoukalas, C. Makropoulos, and D. Koutsoyiannis, Simulation of stochastic processes exhibiting any-range dependence and arbitrary marginal distributions, Water Resources Research, 54 (11), 9484–9513, doi:10.1029/2017WR022462, 2018. |

8. | I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation structure, Journal of Hydrology, 575, 354–380, doi:10.1016/j.jhydrol.2019.05.017, 2019. |

9. | P. Dimitriadis, K. Tzouka, D. Koutsoyiannis, H. Tyralis, A. Kalamioti, E. Lerias, and P. Voudouris, Stochastic investigation of long-term persistence in two-dimensional images of rocks, Spatial Statistics, 29, 177–191, doi:10.1016/j.spasta.2018.11.002, 2019. |

10. | T. Iliopoulou, C. Aguilar , B. Arheimer, M. Bermúdez, N. Bezak, A. Ficchi, D. Koutsoyiannis, J. Parajka, M. J. Polo, G. Thirel, and A. Montanari, A large sample analysis of European rivers on seasonal river flow correlation and its physical drivers, Hydrology and Earth System Sciences, 23, 73–91, doi:10.5194/hess-23-73-2019, 2019. |

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13. | D. Koutsoyiannis, Simple stochastic simulation of time irreversible and reversible processes, Hydrological Sciences Journal, 65 (4), 536–551, doi:10.1080/02626667.2019.1705302, 2020. |

14. | D. Koutsoyiannis, Revisiting the global hydrological cycle: is it intensifying?, Hydrology and Earth System Sciences, 24, 3899–3932, doi:10.5194/hess-24-3899-2020, 2020. |

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1. | Vogel, M., Stochastic watershed models for hydrologic risk management, Water Security, doi:10.1016/j.wasec.2017.06.001, 2017. |

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Hurst-Kolmogorov dynamics,
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Scaling,
Stochastics