D. Koutsoyiannis, An entropic-stochastic representation of rainfall intermittency: The origin of clustering and persistence, *Water Resources Research*, 42 (1), W01401, doi:10.1029/2005WR004175, 2006.

[doc_id=675]

[English]

The well-established physical and mathematical principle of maximum entropy, interpreted as maximum uncertainty, is used to explain the observed dependence properties of the rainfall occurrence process, including the clustering behavior and persistence. The conditions used for the maximization of entropy are as simple as possible, i.e. that the rainfall processes is intermittent with dependent occurrences. Intermittency is quantified by the probability that a time interval is dry, and dependence is quantified by the probability that two consecutive intervals are dry. These two probabilities are used as constraints in a multiple scale entropy maximization framework, which determines any conditional or unconditional probability of any sequence of dry and wet intervals at any time scale. Thus, the rainfall occurrence process including its dependence structure is described by only two parameters. This dependence structure appears to be non-Markovian. Application of this theoretical framework to the rainfall data set of Athens indicates good agreement of theoretical predictions and empirical data at the entire range of scales for which probabilities dry and wet can be estimated (from one hour to several months).

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http://dx.doi.org/10.1029/2005WR004175

**Our works referenced by this work:**

1. | D. Koutsoyiannis, D. Kozonis, and A. Manetas, A mathematical framework for studying rainfall intensity-duration-frequency relationships, Journal of Hydrology, 206 (1-2), 118–135, doi:10.1016/S0022-1694(98)00097-3, 1998. |

2. | D. Koutsoyiannis, Coupling stochastic models of different time scales, Water Resources Research, 37 (2), 379–391, doi:10.1029/2000WR900200, 2001. |

3. | D. Koutsoyiannis, and C. Onof, Rainfall disaggregation using adjusting procedures on a Poisson cluster model, Journal of Hydrology, 246, 109–122, 2001. |

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

5. | D. Koutsoyiannis, C. Onof, and H. S. Wheater, Multivariate rainfall disaggregation at a fine timescale, Water Resources Research, 39 (7), 1173, doi:10.1029/2002WR001600, 2003. |

6. | D. Koutsoyiannis, Statistics of extremes and estimation of extreme rainfall, 1, Theoretical investigation, Hydrological Sciences Journal, 49 (4), 575–590, doi:10.1623/hysj.49.4.575.54430, 2004. |

7. | D. Koutsoyiannis, Statistics of extremes and estimation of extreme rainfall, 2, Empirical investigation of long rainfall records, Hydrological Sciences Journal, 49 (4), 591–610, doi:10.1623/hysj.49.4.591.54424, 2004. |

8. | D. Koutsoyiannis, Uncertainty, entropy, scaling and hydrological stochastics, 1, Marginal distributional properties of hydrological processes and state scaling, Hydrological Sciences Journal, 50 (3), 381–404, doi:10.1623/hysj.50.3.381.65031, 2005. |

9. | D. Koutsoyiannis, Uncertainty, entropy, scaling and hydrological stochastics, 2, Time dependence of hydrological processes and time scaling, Hydrological Sciences Journal, 50 (3), 405–426, doi:10.1623/hysj.50.3.405.65028, 2005. |

**Our works that reference this work:**

1. | D. Koutsoyiannis, C. Makropoulos, A. Langousis, S. Baki, A. Efstratiadis, A. Christofides, G. Karavokiros, and N. Mamassis, Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability, Hydrology and Earth System Sciences, 13, 247–257, doi:10.5194/hess-13-247-2009, 2009. |

2. | D. Koutsoyiannis, and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, doi:10.1016/B978-0-444-53199-5.00027-0, Academic Press, Oxford, 2011. |

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. | D. Koutsoyiannis, Physics of uncertainty, the Gibbs paradox and indistinguishable particles, Studies in History and Philosophy of Modern Physics, 44, 480–489, doi:10.1016/j.shpsb.2013.08.007, 2013. |

5. | D. Koutsoyiannis, Entropy: from thermodynamics to hydrology, Entropy, 16 (3), 1287–1314, doi:10.3390/e16031287, 2014. |

6. | 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. |

7. | F. Lombardo, E. Volpi, D. Koutsoyiannis, and F. Serinaldi, A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall, Water Resources Research, 53 (6), 4586–4605, doi:10.1002/2017WR020529, 2017. |

8. | 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. |

9. | 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. |

10. | D. Koutsoyiannis, and P. Dimitriadis, Towards generic simulation for demanding stochastic processes, Sci, 3, 34, doi:10.3390/sci3030034, 2021. |

11. | P. Kossieris, I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Generic framework for downscaling statistical quantities at fine time-scales and its perspectives towards cost-effective enrichment of water demand records, Water, 13 (23), 3429, doi:10.3390/w13233429, 2021. |

12. | D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 2, ISBN: 978-618-85370-0-2, 346 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2022. |

13. | T. Iliopoulou, N. Malamos, and D. Koutsoyiannis, Regional ombrian curves: Design rainfall estimation for a spatially diverse rainfall regime, Hydrology, 9 (5), 67, doi:10.3390/hydrology9050067, 2022. |

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2. | Langousis, A., and D. Veneziano, Intensity-duration-frequency curves from scaling representations of rainfall, Water Resources Research, 43(2), W02422, 2007. |

3. | #Stockwell, D., Niche Modeling: Predictions from Statistical Distributions, Chapman & Hall, Boka Raton, USA, 2007. |

4. | Wang, J.Y., B.T. Anderson and G.D. Salvucci, Stochastic modeling of daily summertime rainfall over the southwestern United States. Part II: Intraseasonal variability, Journal of Hydrometeorology, 8(4), 938-951, 2007. |

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6. | Raynal, J.A., Comparison of the method of the principle of maximum entropy for the estimation of parameters of the extreme value type I distribution, Informacion Tecnologica, 19(2), 103-112, 2008. |

7. | Molini, A., G. G. Katul, and A. Porporato, Revisiting rainfall clustering and intermittency across different climatic regimes, Water Resour. Res., 45, W11403, doi:10.1029/2008WR007352, 2009. |

8. | #Montesarchio, V., and F. Napolitano, A single-site rainfall disaggregation model based on entropy, International Workshop Advances in Statistical Hydrology, International Association of Hydrological Sciences (IAHS/STAHY), Taormina, Italy, 2010. |

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16. | Jameson, A.R., M.L. Larsen and A.B. Kostinski, Disdrometer network observations of finescale spatial-temporal clustering in rain, Journal of the Atmospheric Sciences, 72 (4), 1648-1666, 10.1175/JAS-D-14-0136.1, 2015. |

**Tagged under:**
Entropy,
Rainfall models