I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Stochastic periodic autoregressive to anything (SPARTA): Modelling and simulation of cyclostationary processes with arbitrary marginal distributions, *Water Resources Research*, 54 (1), 161–185, WRCR23047, doi:10.1002/2017WR021394, 2018.

[doc_id=1746]

[English]

Stochastic models in hydrology traditionally aim at reproducing the empirically derived statistical characteristics of the observed data rather than any specific distribution model that attempts to describe the usually non-Gaussian statistical behavior of the associated processes. SPARTA (Stochastic Periodic AutoRegressive To Anything) offers an alternative and novel approach which allows the explicit representation of each process of interest with any distribution model, while simultaneously establishes dependence patterns that cannot be fully captured by the typical linear stochastic schemes. Cornerstone of the proposed approach is the Nataf joint-distribution model, which is related with the Gaussian copula, combined with Gaussian periodic autoregressive processes. In order to obtain the target stochastic structure, we have also developed a computationally simple and efficient algorithm, based on a hybrid Monte-Carlo procedure that is used to approximate the required equivalent correlation coefficients. Theoretical and practical benefits of the proposed method, contrasted to outcomes from widely used stochastic models, are demonstrated by means of real-world as well as hypothetical monthly simulation examples involving both univariate and multivariate time series.

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**Additional material:**

- Historical data for Evinos and Mornos reservoirs (26 KB)
- Pre-print (2330 KB)

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**Our works that reference this work:**

1. | I. Tsoukalas, C. Makropoulos, and A. Efstratiadis, Stochastic simulation of periodic processes with arbitrary marginal distributions, 15th International Conference on Environmental Science and Technology (CEST2017), Rhodes, Global Network on Environmental Science and Technology, 2017. |

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3. | I. Tsoukalas, S.M. Papalexiou, A. Efstratiadis, and C. Makropoulos, A cautionary note on the reproduction of dependencies through linear stochastic models with non-Gaussian white noise, Water, 10 (6), 771, doi:10.3390/w10060771, 2018. |

4. | 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. |

5. | P. Kossieris, and C. Makropoulos, Exploring the statistical and distributional properties of residential water demand at fine time scales, Water, 10 (10), 1481, doi:10.3390/w10101481, 2018. |

6. | C. Rebolho, V. Andréassian, I. Tsoukalas, et A. Efstratiadis, La crue du Loing de Juin 2016 était-elle exceptionnelle?, De la prévision des crues à la gestion de crise, Avignon, Société Hydrotechnique de France, 2018. |

7. | 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. |

8. | P. Kossieris, I. Tsoukalas, C. Makropoulos, and D. Savic, Simulating marginal and dependence behaviour of water demand processes at any fine time scale, Water, 11 (5), 885, doi:10.3390/w11050885, 2019. |

9. | C. Makropoulos, and D. Savic, Urban hydroinformatics: past, present and future, Water, 11 (10), 1959, doi:10.3390/w11101959, 2019. |

10. | D. Nikolopoulos, G. Moraitis, D. Bouziotas, A. Lykou, G. Karavokiros, and C. Makropoulos, Cyber-physical stress-testing platform for water distribution networks, Journal of Environmental Engineering, 146 (7), 04020061, doi:10.1061/(ASCE)EE.1943-7870.0001722, 2020. |

11. | I. Tsoukalas, P. Kossieris, and C. Makropoulos, Simulation of non-Gaussian correlated random variables, stochastic processes and random fields: Introducing the anySim R-Package for environmental applications and beyond, Water, 12 (6), 1645, doi:10.3390/w12061645, 2020. |

12. | H. Elsayed, S. Djordjević, D. Savic, I. Tsoukalas, and C. Makropoulos, The Nile water-food-energy nexus under uncertainty: Impacts of the Grand Ethiopian Renaissance Dam, Journal of Water Resources Planning and Management - ASCE, 146 (11), 04020085, doi:10.1061/(ASCE)WR.1943-5452.0001285, 2020. |

13. | A. Efstratiadis, I. Tsoukalas, and D. Koutsoyiannis, Generalized storage-reliability-yield framework for hydroelectric reservoirs, Hydrological Sciences Journal, 2021. |

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

1. | Papalexiou, S. M., Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency, Advances in Water Resources, 115, 234-252, doi:10.1016/j.advwatres.2018.02.013, 2018. |

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5. | Nazemi, A., M. Zaerpour, and E. Hassanzadeh, Uncertainty in bottom-up vulnerability assessments of water supply systems due to regional streamflow generation under changing conditions, Journal of Water Resources Planning and Management, 146(2), doi:10.1061/(ASCE)WR.1943-5452.0001149, 2020. |

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7. | Dutta, R., and R. Maity, Temporal networks based approach for non‐stationary hydroclimatic modelling and its demonstration with streamflow prediction, Water Resources Research, 56(8), e2020WR027086, doi:10.1029/2020WR027086, 2020. |

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