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.

[doc_id=18]

[English]

A generalized framework for single-variate and multivariate simulation and forecasting problems in stochastic hydrology is proposed. It is appropriate for short-term or long-term memory processes and preserves the Hurst coefficient even in multivariate processes with a different Hurst coefficient in each location. Simultaneously, it explicitly preserves the coefficients of skewness of the processes. The proposed framework incorporates short memory (autoregressive - moving average) and long memory (fractional Gaussian noise) models, considering them as special instances of a parametrically defined generalized autocovariance function, more comprehensive than those used in these classes of models. The generalized autocovariance function is then implemented in a generalized moving average generating scheme that yields a new time symmetric (backward-forward) representation, whose advantages are studied. Fast algorithms for computation of internal parameters of the generating scheme are developed, appropriate for problems including even thousands of such parameters. The proposed generating scheme is also adapted through a generalized methodology to perform in forecast mode, in addition to simulation mode. Finally, a specific form of the model for problems where the autocorrelation function can be defined only for a certain finite number of lags is also studied. Several illustrations are included to clarify the features and the performance of the components of the proposed framework.

**See also:**
http://dx.doi.org/10.1029/2000WR900044

**Our works referenced by this work:**

1. | D. Koutsoyiannis, and E. Foufoula-Georgiou, A scaling model of storm hyetograph, Water Resources Research, 29 (7), 2345–2361, doi:10.1029/93WR00395, 1993. |

2. | D. Koutsoyiannis, and A. Manetas, Simple disaggregation by accurate adjusting procedures, Water Resources Research, 32 (7), 2105–2117, doi:10.1029/96WR00488, 1996. |

3. | D. Koutsoyiannis, Optimal decomposition of covariance matrices for multivariate stochastic models in hydrology, Water Resources Research, 35 (4), 1219–1229, doi:10.1029/1998WR900093, 1999. |

4. | D. Koutsoyiannis, An advanced method for preserving skewness in single-variate, multivariate and disaggregation models in stochastic hydrology, 24th General Assembly of the European Geophysical Society, Geophysical Research Abstracts, Vol. 1, The Hague, 346, doi:10.13140/RG.2.1.1749.2725, European Geophysical Society, 1999. |

**Our works that reference this work:**

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

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, A. Efstratiadis, and G. Karavokiros, A decision support tool for the management of multi-reservoir systems, Journal of the American Water Resources Association, 38 (4), 945–958, doi:10.1111/j.1752-1688.2002.tb05536.x, 2002. |

4. | I. Nalbantis, E. Rozos, G. M. T. Tentes, A. Efstratiadis, and D. Koutsoyiannis, Integrating groundwater models within a decision support system, Proceedings of the 5th International Conference of European Water Resources Association: "Water Resources Management in the Era of Transition", edited by G. Tsakiris, Athens, 279–286, European Water Resources Association, 2002. |

5. | 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. |

6. | D. Koutsoyiannis, and A. Economou, Evaluation of the parameterization-simulation-optimization approach for the control of reservoir systems, Water Resources Research, 39 (6), 1170, doi:10.1029/2003WR002148, 2003. |

7. | D. Koutsoyiannis, G. Karavokiros, A. Efstratiadis, N. Mamassis, A. Koukouvinos, and A. Christofides, A decision support system for the management of the water resource system of Athens, Physics and Chemistry of the Earth, 28 (14-15), 599–609, doi:10.1016/S1474-7065(03)00106-2, 2003. |

8. | D. Koutsoyiannis, and A. Efstratiadis, Experience from the development of decision support systems for the management of large-scale hydrosystems of Greece, Proceedings of the Workshop "Water Resources Studies in Cyprus", edited by E. Sidiropoulos and I. Iakovidis, Nikosia, 159–180, Water Development Department of Cyprus, Aristotle University of Thessaloniki, Thessaloniki, 2003. |

9. | A. Efstratiadis, D. Koutsoyiannis, and D. Xenos, Minimizing water cost in the water resource management of Athens, Urban Water Journal, 1 (1), 3–15, doi:10.1080/15730620410001732099, 2004. |

10. | 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. |

11. | A. Christofides, A. Efstratiadis, D. Koutsoyiannis, G.-F. Sargentis, and K. Hadjibiros, Resolving conflicting objectives in the management of the Plastiras Lake: can we quantify beauty?, Hydrology and Earth System Sciences, 9 (5), 507–515, doi:10.5194/hess-9-507-2005, 2005. |

12. | A. Langousis, and D. Koutsoyiannis, A stochastic methodology for generation of seasonal time series reproducing overyear scaling behaviour, Journal of Hydrology, 322, 138–154, 2006. |

13. | D. Koutsoyiannis, Nonstationarity versus scaling in hydrology, Journal of Hydrology, 324, 239–254, doi:10.1016/j.jhydrol.2005.09.022, 2006. |

14. | D. Koutsoyiannis, A. Efstratiadis, and K. Georgakakos, Uncertainty assessment of future hydroclimatic predictions: A comparison of probabilistic and scenario-based approaches, Journal of Hydrometeorology, 8 (3), 261–281, doi:10.1175/JHM576.1, 2007. |

15. | D. Koutsoyiannis, H. Yao, and A. Georgakakos, Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods, Hydrological Sciences Journal, 53 (1), 142–164, doi:10.1623/hysj.53.1.142, 2008. |

16. | E. Rozos, and D. Koutsoyiannis, Error analysis of a multi-cell groundwater model, Journal of Hydrology, 392 (1-2), 22–30, 2010. |

17. | 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. |

18. | 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. |

19. | D. Koutsoyiannis, A. Paschalis, and N. Theodoratos, Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields, Journal of Hydrology, 398 (1-2), 91–100, doi:10.1016/j.jhydrol.2010.12.012, 2011. |

20. | 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. |

21. | C. Ioannou, G. Tsekouras, A. Efstratiadis, and D. Koutsoyiannis, Stochastic analysis and simulation of hydrometeorological processes for optimizing hybrid renewable energy systems, Proceedings of the 2nd Hellenic Concerence on Dams and Reservoirs, Athens, Zappeion, doi:10.13140/RG.2.1.3787.0327, Hellenic Commission on Large Dams, 2013. |

22. | G. Tsekouras, and D. Koutsoyiannis, Stochastic analysis and simulation of hydrometeorological processes associated with wind and solar energy, Renewable Energy, 63, 624–633, doi:10.1016/j.renene.2013.10.018, 2014. |

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

24. | A. Efstratiadis, Y. Dialynas, S. Kozanis, and D. Koutsoyiannis, A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence, Environmental Modelling and Software, 62, 139–152, doi:10.1016/j.envsoft.2014.08.017, 2014. |

25. | A. Efstratiadis, I. Nalbantis, and D. Koutsoyiannis, Hydrological modelling of temporally-varying catchments: Facets of change and the value of information, Hydrological Sciences Journal, 60 (7-8), 1438–1461, doi:10.1080/02626667.2014.982123, 2015. |

26. | I. Tsoukalas, and C. Makropoulos, Multiobjective optimisation on a budget: Exploring surrogate modelling for robust multi-reservoir rules generation under hydrological uncertainty, Environmental Modelling and Software, 69, 396–413, doi:10.1016/j.envsoft.2014.09.023, 2015. |

27. | I. Tsoukalas, and C. Makropoulos, A surrogate based optimization approach for the development of uncertainty-aware reservoir operational rules: the case of Nestos hydrosystem, Water Resources Management, 29 (13), 4719–4734, doi:10.1007/s11269-015-1086-8, 2015. |

28. | D. Koutsoyiannis, Generic and parsimonious stochastic modelling for hydrology and beyond, Hydrological Sciences Journal, 61 (2), 225–244, doi:10.1080/02626667.2015.1016950, 2016. |

29. | P. Dimitriadis, D. Koutsoyiannis, and P. Papanicolaou, Stochastic similarities between the microscale of turbulence and hydrometeorological processes, Hydrological Sciences Journal, 61 (9), 1623–1640, doi:10.1080/02626667.2015.1085988, 2016. |

30. | P. Kossieris, C. Makropoulos, C. Onof, and D. Koutsoyiannis, A rainfall disaggregation scheme for sub-hourly time scales: Coupling a Bartlett-Lewis based model with adjusting procedures, Journal of Hydrology, 556, 980–992, doi:10.1016/j.jhydrol.2016.07.015, 2018. |

31. | 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. |

32. | 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. |

33. | 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. |

34. | 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. |

35. | 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. |

36. | D. Koutsoyiannis, Knowable moments for high-order stochastic characterization and modelling of hydrological processes, Hydrological Sciences Journal, 64 (1), 19–33, doi:10.1080/02626667.2018.1556794, 2019. |

37. | D. Koutsoyiannis, Time’s arrow in stochastic characterization and simulation of atmospheric and hydrological processes, Hydrological Sciences Journal, 64 (9), 1013–1037, doi:10.1080/02626667.2019.1600700, 2019. |

38. | 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. |

39. | G.-F. Sargentis, R. Ioannidis, G. Karakatsanis, S. Sigourou, N. D. Lagaros, and D. Koutsoyiannis, The development of the Athens water supply system and inferences for optimizing the scale of water infrastructures, Sustainability, 11 (9), 2657, doi:10.3390/su11092657, 2019. |

40. | 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. |

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. | 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. |

43. | A. Efstratiadis, I. Tsoukalas, and D. Koutsoyiannis, Generalized storage-reliability-yield framework for hydroelectric reservoirs, Hydrological Sciences Journal, 66 (4), 580–599, doi:10.1080/02626667.2021.1886299, 2021. |

44. | 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. |

45. | L. Katikas, P. Dimitriadis, D. Koutsoyiannis, T. Kontos, and P. Kyriakidis, A stochastic simulation scheme for the long-term persistence, heavy-tailed and double periodic behavior of observational and reanalysis wind time-series, Applied Energy, 295, 116873, doi:10.1016/j.apenergy.2021.116873, 2021. |

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

47. | 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. |

48. | T. Iliopoulou, P. Dimitriadis, A. Siganou, D. Markantonis, K. Moraiti, M. Nikolinakou, I. Meletopoulos, N. Mamassis, D. Koutsoyiannis, and G.-F. Sargentis, Modern use of traditional rainwater harvesting practices: An assessment of cisterns’ water supply potential in West Mani, Greece, Heritage, 5 (4), 2944–2954, doi:10.3390/heritage5040152, 2022. |

49. | 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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1. | Clifford, N.J., Hydrology: the changing paradigm, Progress in Physical Geography, 26(2), 290-301, 2002. |

2. | Ochoa-Rivera, J.C., R. Garcia-Bartual and J. Andreu, Multivariate synthetic streamflow generation using a hybrid model based on artificial neural networks, Hydrology & Earth System Siences, 6 (4), 641-654, 2002. |

3. | Gneiting, T., and M. Schlather, Stochastic models that separate fractal dimension and the Hurst effect, Society for Industrial and Applied Mathematics Review, 46(2), 269-282, 2004. |

4. | Srinivas, V.V., and K. Srinivasan, Hybrid moving block bootstrap for stochastic simulation of multi-site multi-season streamflows, Journal of Hydrology, 302(1-4), 307-330, 2005. |

5. | Cohn, T.A., and H. F. Lins, Nature's style: Naturally trendy, Geophysical Research Letters, 32(23), art. no. L23402, 2005. |

6. | Srinivas, V. V., and K. Srinivasan, Hybrid matched-block bootstrap for stochastic simulation of multiseason streamflows, Journal of Hydrology, 329(1-2), 1-15, 2006. |

7. | Muniandy, S.V., and R. Uning, Characterization of exchange rate regimes based on scaling and correlation properties of volatility for ASEAN-5 countries, Physica A - Statistical Mechanics and its Applications, 371(2), 585-598, 2006. |

8. | Wong, H., W.-c. Ip, R. Zhang and J. Xia, Non-parametric time series models for hydrological forecasting, Journal of Hydrology, 332(3-4), 337-347, 2007. |

9. | Ochoa-Rivera, J.C., J. Andreu and R. Garcia-Bartual, Influence of inflows modeling on management simulation of water resources system, Journal of Water Resources Planning and Management, 133(2), 106-116, 2007. |

10. | Mackey, R., Rhodes Fairbridge and the idea that the solar system regulates the Earth's climate, Journal of Coastal Research, Special Issue 50, Proceedings ICS2007, 955-968, 2007. |

11. | #Chen, Y.Q., R, Sun and A. Zhou, An overview of fractional order signal processing (FOSP) techniques, Proc. ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 1205-1222, 2007. |

12. | Hamed, K.H., Trend detection in hydrologic data: The Mann-Kendall trend test under the scaling hypothesis, Journal of Hydrology, 349(3-4), 350-363, 2008. |

13. | Yang, Z.P., W.X. Lu, Y.Q. Long and P. Li, Application and comparison of two prediction models for groundwater levels: A case study in Western Jilin Province, China, Journal of Arid Environments, 73 (4-5), 487-492, 2009. |

14. | Hamed, K.H., Enhancing the effectiveness of prewhitening in trend analysis of hydrologic data, Journal of Hydrology, 368(1-4), 143-155, 2009. |

15. | Wang, D., V. P. Singh, Y.-s. Zhu and J.-c. Wu, Stochastic observation error and uncertainty in water quality evaluation, Advances in Water Resources, 32 (10), 1526-1534, 2009. |

16. | Wang, W., S. Hu and Y. Li, Wavelet transform method for synthetic generation of daily streamflow, Water Resources Management, 25, (1), 41-57, DOI: 10.1007/s11269-010-9686-9, 2011. |

17. | Srivastav, R. K., K. Srinivasan and K. P. Sudheer, Simulation-optimization framework for multi-season hybrid stochastic models, Journal of Hydrology, 404 (3-4), 209-225, 2011. |

18. | #Kulasiri, D., Computational Modelling of Multi-Scale Non-Fickian Dispersion in Porous Media - An Approach Based on Stochastic Calculus, InTech, ISBN 978-953-307-726-0, 231 pp., 2011. |

19. | Henley, B. J., M. A. Thyer, G. Kuczera, and S. W. Franks, Climate-informed stochastic hydrological modeling: Incorporating decadal-scale variability using paleo data, Water Resour. Res., 47, W11509, doi: 10.1029/2010WR010034, 2011. |

20. | Hamed, K. H., A probabilistic approach to calculating the reliability of over-year storage reservoirs with persistent Gaussian inflow, Journal of Hydrology, 448-449, 93-99, 2012. |

21. | Lee. T., Serial dependence properties in multivariate streamflow simulation with independent decomposition analysis, Hydrological Processes, 26 (7), 961-972, 2012. |

22. | Boukharouba, K., Annual stream flow simulation by ARMA processes and prediction by Kalman filter, Arab J. Geosci., 6 (7), 2193-2201, 2013. |

23. | De Michele, C., and M. Ignaccolo, New perspectives on rainfall from a discrete view, Hydrological Processes, 10.1002/hyp.9782, 2013. |

24. | #Kulasiri, D., Non-fickian Solute Transport in Porous Media, A Mechanistic and Stochastic Theory, Springer-Verlag Berlin Heidelberg, 2013. |

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27. | Nigam, R., S. Nigam and S.K. Mittal, The river runoff forecast based on the modeling of time series, Russian Meteorology and Hydrology, 39 (11), 750-761, 2014. |

28. | Nigam, R., S. Nigam and S.K. Mittal, Stochastic modelling of rainfall and runoff phenomenon: A time series approach review, International Journal of Hydrology Science and Technology, 4 (2), 81-109, 2014. |

29. | Marković, Đ., J. Plavšić, N. Ilich and S. Ilić, Non-parametric stochastic generation of streamflow series at multiple locations, Water Resources Management, 29(13), 4787-4801, 10.1007/s11269-015-1090-z, 2015. |

30. | Bekri, E., M. Disse, P. Yannopoulos, Optimizing water allocation under uncertain system conditions in Alfeios River Basin (Greece), Part A: Two-stage stochastic programming model with deterministic boundary intervals, Water, 7(10), 5305-5344, doi:10.3390/w7105305, 2015. |

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**Tagged under:**
Course bibliography: Stochastic methods,
Hurst-Kolmogorov dynamics,
Stochastics,
Uncertainty