Coupling stochastic models of different time scales

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



A methodology is proposed for coupling stochastic models of hydrologic processes applying to different timescales so that time series generated by the different models be consistent. Given two multivariate time series, generated by two separate (unrelated) stochastic models of the same hydrologic process, each applying to a different timescale, a transformation is developed (referred to as a coupling transformation) that appropriately modifies the time series of the lower-level (finer) timescale so that this series becomes consistent with the time series of the higher-level (coarser) timescale without affecting the second-order stochastic structure of the former and also establishes appropriate correlations between the two time series. The coupling transformation is based on a developed generalized mathematical proposition, which ensures preservation of marginal and joint second-order statistics and of linear relationships between lower- and higher-level processes. Several specific forms of the coupling transformation are studied, from the simplest single variate to the full multivariate. In addition, techniques for evaluating parameters of the coupling transformation based on second-order moments of the lower-level process are studied. Furthermore, two methods are proposed to enable preservation of the skewness of the processes, in addition to that of second-order statistics. The overall methodology can be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal timescales, as well as problems involving finer timescales (e.g. daily - hourly), with the only requirement that a specific stochastic model is available for each involved time scale. The performance of the methodology is demonstrated by means of a detailed numerical example.

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Our works referenced by this work:

1. D. Koutsoyiannis, A nonlinear disaggregation method with a reduced parameter set for simulation of hydrologic series, Water Resources Research, 28 (12), 3175–3191, doi:10.1029/92WR01299, 1992.
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Our works that reference this work:

1. D. Koutsoyiannis, and C. Onof, Rainfall disaggregation using adjusting procedures on a Poisson cluster model, Journal of Hydrology, 246, 109–122, 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.
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4. 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.
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6. 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.
7. A. Efstratiadis, D. Koutsoyiannis, and D. Xenos, Minimising water cost in the water resource management of Athens, Urban Water Journal, 1 (1), 3–15, 2004.
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9. 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.
10. 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.
11. D. Koutsoyiannis, and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, Academic Press, Oxford, 2011.
12. 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.
13. F. Lombardo, E. Volpi, and D. Koutsoyiannis, Rainfall downscaling in time: Theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades, Hydrological Sciences Journal, 57 (6), 1052–1066, 2012.
14. E. Rozos, and C. Makropoulos, Source to tap urban water cycle modelling, Environmental Modelling and Software, 41, 139–150, doi:10.1016/j.envsoft.2012.11.015, Elsevier, 1 March 2013.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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, doi:10.1016/j.jhydrol.2016.07.015, 2016.
21. F. Lombardo, E. Volpi, D. Koutsoyiannis, and F. Serinaldi , A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall, Water Resources Research, doi:10.1002/2017WR020529, 2017.

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Tagged under: Course bibliography: Stochastic methods, Stochastic disaggregation, Stochastics