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.

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[English]

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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See also: http://dx.doi.org/10.1029/2000WR900200

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.
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, 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.

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.
3. 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.
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.
5. 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.
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, Minimizing water cost in the water resource management of Athens, Urban Water Journal, 1 (1), 3–15, doi:10.1080/15730620410001732099, 2004.
8. 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.
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, doi:10.1016/B978-0-444-53199-5.00027-0, 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. 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.
21. 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.
22. 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.
23. 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.
24. 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.
25. 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.
26. D. Koutsoyiannis, and P. Dimitriadis, Towards generic simulation for demanding stochastic processes, Sci, 3, 34, doi:10.3390/sci3030034, 2021.
27. 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. Sharma, A., and R. O'Neill, A nonparametric approach for representing interannual dependence in monthly streamflow sequences, Water Resources Research, 38(7), art. no. 1100, 2002.
2. von Asmuth, J.R., M.F.P. Bierkens and K. Maas, Transfer function-noise modeling in continuous time using predefined impulse response functions, Water Rersoures Research, 38 (12), art. no. 1287, 2002.
3. Bojilova, E.K., Disaggregation modelling of spring discharges, International Journal of Speleology, 33(1/4), 65-72, 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. von Asmuth, J.R., and M.F.P. Bierkens, Modeling irregularly spaced residual series as a continuous stochastic process, Water Resources Research, 41(12), art. no. W12404, 2005.
6. Srinivas, V.V., and K. Srinivasan, Hybrid matched-block bootstrap for stochastic simulation of multiseason streamflows, Journal of Hydrology, 329(1-2), 2006.
7. Wu, S.-J., Y.-K. Tung and J.-C. Yang, Stochastic generation of hourly rainstorm events, Stochastic Environmental Research and Risk Assessment, 21(2), 195-212, 2006.
8. Schoups, G., C.L. Addams, J.L. Minjares and S.M. Gorelick, Reliable conjunctive use rules for sustainable irrigated agriculture and reservoir spill control, Water Resources Research, 42(12), W12406, 2006.
9. Debele, B., R. Srinivasan and J. Yves Parlange, Accuracy evaluation of weather data generation and disaggregation methods at finer timescales, Advances in Water Resources, 30(5), 1286-1300, 2007.
10. Prairie, J., B. Rajagopalan, U. Lall and T. Fulp, A stochastic nonparametric technique for space-time disaggregation of streamflows, Water Resources Research, 43(3), W03432, 2007.
11. Prairie, J.R., and B. Rajagopalan, A basin wide stochastic salinity model, Journal of Hydrology, 344(1-2), 43-54, 2007.
12. Wang, Q.J., and R.J. Nathan, A method for coupling daily and monthly time scales in stochastic generation of rainfall series, Journal of Hydrology, 346(3-4), 122-130, 2007.
13. #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, 2008.
14. #Sun, R., Y. Chen and Q. Li, The modeling and prediction of Great Salt Lake elevation time series based on ARFIMA, Proc. ASME 2007 Intern. Design Engineering Technical Conferences & Computers and Information in Engineering Conf., 1349-1359, 2008.
15. Prairie, J., K. Nowak, B. Rajagopalan, U. Lall and T. Fulp, A stochastic nonparametric approach for streamflow generation combining observational and paleoreconstructed data, Water Resources Research, 44 (6), W06423, 2008.
16. Klein, B., A. Schumann and M. Pahlow, Application of multivariate statistical methods in flood protection planning for river basins: The river Unstrut case study, Wasser Wirtschaft, 98 (11), 29-34, 2008.
17. Debele, B., R. Srinivasan and J.Y. Parlange, Hourly analyses of hydrological and water quality simulations using the ESWAT model, Water Resources Management, 23 (2), 303-324, 2009.
18. #Sharma, A., F. Johnson, R. Mehrotra and S. Westra, Simulating climate change impacts at the catchment scale: the need for GCM nested bias correction and stochastic downscaling, International Workshop Advances in Statistical Hydrology, International Association of Hydrological Sciences (IAHS/STAHY), Taormina, Italy, 2010.
19. Chen, J., F. P. Brissette and R. Leconte, A daily stochastic weather generator for preserving low-frequency of climate variability, Journal of Hydrology, 388 (3-4), 480-490, 2010.
20. #Streng, H., and Y. Chen, The modeling of Great Salt Lake elevation time series based on ARFIMA with stable innovations, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, 4 (PART B), 1137-1145, 2010.
21. #Sheng, H., N. Zaveri, Y. Chen and A. Zhou, Analysis of electrochemical noise (ECN) of Ti02 nanoparticles coated Ti-6AL-4V in simulated biofluids using Fractional Order Signal Processing (FOSP) techniques, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, 4 (PART B), 1157-1171, 2010.
22. #Zagona, E., K. Nowak, R. Balaji, C. Jerla, and J. Prairie, Riverware’s integrated modeling and analysis tools for long-term planning under uncertainty, Proceedings of the 2nd Joint Federal Interagency Conference on Sedimentation and Hydrologic Modeling, Las Vegas, Nevada, USA, 2010.
23. #Sharma, A., and R. Mehrotra, Rainfall Generation, in Rainfall: State of the Science (eds F. Y. Testik and M. Gebremichael), American Geophysical Union, Washington, DC, 10.1029/2010GM000973, 2010.
24. Sheng, H., and Y.Q. Chen, FARIMA with stable innovations model of Great Salt Lake elevation time series, Signal Processing, 91 (3), 553-561, doi:10.1016/j.sigpro.2010.01.023, 2011.
25. #Klein, B., A. H. Schumann and M. Pahlow, Copulas – New Risk Assessment Methodology for Dam Safety, Flood Risk Assessment and Management, 149-185, DOI: 10.1007/978-90-481-9917-4_8, Springer, 2011.
26. Ndiritu, J., A variable length block bootstrap for multi-site synthetic streamflow generation, Hydrol. Sci. J., 56 (3), 362-379, 2011.
27. Johnson, F., and A. Sharma, Accounting for interannual variability: A comparison of options for water resources climate change impact assessments, Water Resources Research, 47, W04508, DOI: 10.1029/2010WR009272, 2011.
28. 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.
29. Kalra, A., and S. Ahmad, Evaluating changes and estimating seasonal precipitation for the Colorado River Basin using a stochastic nonparametric disaggregation technique, Water Resources Research, 47, W05555, doi: 10.1029/2010WR009118, 2011.
30. #Ye, X., X. Xia, J. Zhang and Y.-Q. Chen, Characterizing long memories in electric water heater power consumption time series, AFRICON, 2011, Victoria Falls, Livingstone, Zambia, DOI: 10.1109/AFRCON.2011.6072104, 2011.
31. #Sheng, H., Y.Q. Chen and T.S. Qiu, Fractional Processes and Fractional-Order Signal Processing, Techniques and Applications, Springer, London, DOI: 10.1007/978-1-4471-2233-3, 2012.
32. Johnson, F., and A. Sharma, A nesting model for bias correction of variability at multiple time scales in general circulation model precipitation simulations, Water Resour. Res., doi: 10.1029/2011WR010464, 2012.
33. Chakraborty, S., D. M. Denis and A. Sherring, Development of time series autoregressive model for prediction of rainfall and runoff in Kelo Watershed Chhattisgarh, International Journal of Advances in Engineering Science and Technology, 2 (2), 153-162, 2013.
34. Ilich, N., An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series, Hydrological Sciences Journal, 59 (1), 85-98, 2014.
35. Paschalis, A., P. Molnar, S. Fatichi and P. Burlando, On temporal stochastic modeling of precipitation, nesting models across scales, Advances in Water Resources, 63, 152-166, 2014.
36. Johnson, F., and A. Sharma, What are the impacts of bias correction on future drought projections?, Journal of Hydrology, 525, 472-485, 2015.
37. Chen, L., V.P. Singh, S. Guo, J. Zhou and J. Zhang, Copula-based method for multisite monthly and daily streamflow simulation, Journal of Hydrology, 528, 369-384, 2015.
38. 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.
39. Bekri, E., M. Disse, P. Yannopoulos, Optimizing water allocation under uncertain system conditions in Alfeios River Basin (Greece), Part B: Fuzzy-boundary intervals combined with multi-stage stochastic programming Model, Water, 7(10), 6427-6466, doi:10.3390/w7116427, 2015.

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