Generic and parsimonious stochastic modelling for hydrology and beyond

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.



The old principle of parsimonious modelling of natural processes has regained its importance in the last few years. The inevitability of uncertainty and risk, and the value of stochastic modelling in dealing with them, are also again appreciated, after a period of growing hopes for radical reduction of uncertainty. Yet in stochastic modelling of natural processes several families of models are used which are often non-parsimonious, unnatural or artificial, theoretically unjustified and, eventually, unnecessary. Here we develop a general methodology for more theoretically justified stochastic processes, which evolve in continuous time and stem from maximum entropy production considerations. The discrete-time properties thereof are theoretically derived from the continuous-time ones and a general simulation methodology in discrete time is built, which explicitly handles the effects of discretization and truncation. Some additional modelling issues are discussed with focus on model identification and fitting, which are often made using inappropriate methods.

Full text is only available to the NTUA network due to copyright restrictions

PDF Additional material:

See also:


The first 50 copies of the paper are available for free at:

Our works referenced by this work:

1. 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.
2. 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.
3. D. Koutsoyiannis, Coupling stochastic models of different time scales, Water Resources Research, 37 (2), 379–391, doi:10.1029/2000WR900200, 2001.
4. D. Koutsoyiannis, The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47 (4), 573–595, doi:10.1080/02626660209492961, 2002.
5. D. Koutsoyiannis, Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, doi:10.1623/hysj., 2003.
6. 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.
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, Uncertainty, entropy, scaling and hydrological stochastics, 1, Marginal distributional properties of hydrological processes and state scaling, Hydrological Sciences Journal, 50 (3), 381–404, doi:10.1623/hysj.50.3.381.65031, 2005.
9. 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.
10. 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.
11. 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.
12. D. Koutsoyiannis, and A. Montanari, Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resources Research, 43 (5), W05429, doi:10.1029/2006WR005592, 2007.
13. 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.
14. D. Koutsoyiannis, C. Makropoulos, A. Langousis, S. Baki, A. Efstratiadis, A. Christofides, G. Karavokiros, and N. Mamassis, Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability, Hydrology and Earth System Sciences, 13, 247–257, doi:10.5194/hess-13-247-2009, 2009.
15. D. Koutsoyiannis, A random walk on water, Hydrology and Earth System Sciences, 14, 585–601, doi:10.5194/hess-14-585-2010, 2010.
16. H. Tyralis, and D. Koutsoyiannis, Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process, Stochastic Environmental Research & Risk Assessment, 25 (1), 21–33, 2011.
17. D. Koutsoyiannis, Hurst-Kolmogorov dynamics as a result of extremal entropy production, Physica A: Statistical Mechanics and its Applications, 390 (8), 1424–1432, doi:10.1016/j.physa.2010.12.035, 2011.
18. 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.
19. 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.
20. A. Montanari, and D. Koutsoyiannis, A blueprint for process-based modeling of uncertain hydrological systems, Water Resources Research, 48, W09555, doi:10.1029/2011WR011412, 2012.
21. Y. Markonis, and D. Koutsoyiannis, Climatic variability over time scales spanning nine orders of magnitude: Connecting Milankovitch cycles with Hurst–Kolmogorov dynamics, Surveys in Geophysics, 34 (2), 181–207, doi:10.1007/s10712-012-9208-9, 2013.
22. D. Koutsoyiannis, Encolpion of stochastics: Fundamentals of stochastic processes, doi:10.13140/RG.2.2.10956.82564, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, 2013.
23. D. Koutsoyiannis, Hydrology and Change, Hydrological Sciences Journal, 58 (6), 1177–1197, doi:10.1080/02626667.2013.804626, 2013.
24. A. Montanari, G. Young, H. H. G. Savenije, D. Hughes, T. Wagener, L. L. Ren, D. Koutsoyiannis, C. Cudennec, E. Toth, S. Grimaldi, G. Blöschl, M. Sivapalan, K. Beven, H. Gupta, M. Hipsey, B. Schaefli, B. Arheimer, E. Boegh, S. J. Schymanski, G. Di Baldassarre, B. Yu, P. Hubert, Y. Huang, A. Schumann, D. Post, V. Srinivasan, C. Harman, S. Thompson, M. Rogger, A. Viglione, H. McMillan, G. Characklis, Z. Pang, and V. Belyaev, “Panta Rhei – Everything Flows”, Change in Hydrology and Society – The IAHS Scientific Decade 2013-2022, Hydrological Sciences Journal, 58 (6), 1256–1275, doi:10.1080/02626667.2013.809088, 2013.
25. F. Lombardo, E. Volpi, D. Koutsoyiannis, and S.M. Papalexiou, Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology, Hydrology and Earth System Sciences, 18, 243–255, doi:10.5194/hess-18-243-2014, 2014.
26. H. Tyralis, and D. Koutsoyiannis, A Bayesian statistical model for deriving the predictive distribution of hydroclimatic variables, Climate Dynamics, 42 (11-12), 2867–2883, doi:10.1007/s00382-013-1804-y, 2014.
27. D. Koutsoyiannis, Entropy: from thermodynamics to hydrology, Entropy, 16 (3), 1287–1314, doi:10.3390/e16031287, 2014.
28. 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.
29. 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.

Our works that reference this work:

1. P. Dimitriadis, D. Koutsoyiannis, and K. Tzouka, Predictability in dice motion: how does it differ from hydrometeorological processes?, Hydrological Sciences Journal, 61 (9), 1611–1622, doi:10.1080/02626667.2015.1034128, 2016.
2. 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.
3. C. Pappas, M.D. Mahecha, D.C. Frank, F. Babst, and D. Koutsoyiannis, Ecosystem functioning is enveloped by hydrometeorological variability, Nature Ecology & Evolution, 1, 1263–1270, doi:10.1038/s41559-017-0277-5, 2017.
4. D. Koutsoyiannis, Entropy production in stochastics, Entropy, 19 (11), 581, doi:10.3390/e19110581, 2017.
5. P. Dimitriadis, and D. Koutsoyiannis, Stochastic synthesis approximating any process dependence and distribution, Stochastic Environmental Research & Risk Assessment, doi:10.1007/s00477-018-1540-2, 2018.
6. 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.
7. I. Tsoukalas, C. Makropoulos, and D. Koutsoyiannis, Simulation of stochastic processes exhibiting any-range dependence and arbitrary marginal distributions, Water Resources Research, doi:10.1029/2017WR022462, 2018.
8. E. Klousakou, M. Chalakatevaki, P. Dimitriadis, T. Iliopoulou, R. Ioannidis, G. Karakatsanis, A. Efstratiadis, N. Mamassis, R. Tomani, E. Chardavellas, and D. Koutsoyiannis, A preliminary stochastic analysis of the uncertainty of natural processes related to renewable energy resources, Advances in Geosciences, 45, 193–199, doi:10.5194/adgeo-45-193-2018, 2018.

Works that cite this document: View on Google Scholar or ResearchGate

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

1. Serinaldi, F., Can we tell more than we can know? The limits of bivariate drought analyses in the United States, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-015-1124-3, 2015.
2. Bardsley, E., A finite mixture approach to univariate data simulation with moment matching, Environmental Modelling & Software, 90, 27-33, doi:10.1016/j.envsoft.2016.11.019, 2017.

Tagged under: Hurst-Kolmogorov dynamics, Most recent works, Scaling, Stochastics, Uncertainty