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.

[doc_id=1950]

[English]

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf’s joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h.

**
Full text
**
(6862 KB)

**See also:**
https://www.mdpi.com/2073-4441/11/5/885

**Our works referenced by this work:**

1. | D. Koutsoyiannis, A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series, Water Resources Research, 36 (6), 1519–1533, doi:10.1029/2000WR900044, 2000. |

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

3. | 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. |

4. | 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. |

5. | P. Dimitriadis, and D. Koutsoyiannis, Climacogram versus autocovariance and power spectrum in stochastic modelling for Markovian and Hurst–Kolmogorov processes, Stochastic Environmental Research & Risk Assessment, 29 (6), 1649–1669, doi:10.1007/s00477-015-1023-7, 2015. |

6. | S.M. Papalexiou, and D. Koutsoyiannis, A global survey on the seasonal variation of the marginal distribution of daily precipitation, Advances in Water Resources, 94, 131–145, doi:10.1016/j.advwatres.2016.05.005, 2016. |

7. | E. Creaco, P. Kossieris, L. Vamvakeridou-Lyroudia, C. Makropoulos, Z. Kapelan, and D. Savic, Parameterizing residential water demand pulse models through smart meter readings, Environmental Modelling and Software, 80, 33–40, 2016. |

8. | P. Kossieris, C. Makropoulos, E. Creaco, L. Vamvakeridou-Lyroudia, and D. Savic, Assessing the applicability of the Bartlett-Lewis model in simulating residential water demands, Procedia Engineering, 154, 123–131, 2016. |

9. | 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. |

10. | 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. |

11. | 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. |

12. | 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. |

13. | 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. |

14. | 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. |

**Our works that reference this work:**

1. | 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. |

2. | 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. |

3. | 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. |

4. | 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. |

5. | 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. |

6. | K.-K. Drakaki, G.-K. Sakki, I. Tsoukalas, P. Kossieris, and A. Efstratiadis, Day-ahead energy production in small hydropower plants: uncertainty-aware forecasts through effective coupling of knowledge and data, Advances in Geosciences, 56, 155–162, doi:10.5194/adgeo-56-155-2022, 2022. |

**Tagged under:**
Stochastics,
Urban water