D. Koutsoyiannis, A random walk on water, *Hydrology and Earth System Sciences*, 14, 585–601, doi:10.5194/hess-14-585-2010, 2010.

[doc_id=923]

[English]

According to the traditional notion of randomness and uncertainty, natural phenomena are separated into two mutually exclusive components, random (or stochastic) and deterministic. Within this dichotomous logic, the deterministic part supposedly represents cause-effect relationships and, thus, is physics and science (the “good”), whereas randomness has little relationship with science and no relationship with understanding (the “evil”). Here I argue that such views should be reconsidered by admitting that uncertainty is an intrinsic property of nature, that causality implies dependence of natural processes in time, thus suggesting predictability, but even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon. On these premises it is possible to shape a consistent stochastic representation of natural processes, in which predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components. Deciding which of the two dominates is simply a matter of specifying the time horizon and scale of the prediction. Long horizons of prediction are inevitably associated with high uncertainty, whose quantification relies on the long-term stochastic properties of the processes.

**
Full text
**
(4499 KB)

**Additional material:**

- The toy model in Excel (57 KB)
- The toy model in Excel, slightly modified by Jeremy Shiers (54 KB)
- Discussion version (HESSD, 6, 6611–6658, 2009), for reading on screen (5409 KB)
- Discussion version (HESSD, 6, 6611–6658, 2009), for print (5408 KB)
- Discussion version, Preprint (867 KB)
- 'Hydrology as emergence', Comment by Steven Weijs (331 KB)
- A first reaction to the comment by Steven Weijs, by D. Koutsoyiannis (257 KB)
- 'Additional remarks on the Comment by Steven Weijs', by D. Koutsoyiannis (276 KB)
- Review by Willie Soon (262 KB)
- Reply to Willie Soon’s review (274 KB)
- 'Stochastics embracing determinism and randomness', Review by Antonis Koussis (271 KB)
- 'Embracing the ideas about further research', Reply to the review by Antonis Koussis (253 KB)
- 'Alternatives to probability', Review by Alberto Montanari (265 KB)
- 'On alternatives to probability', Reply to the review by Alberto Montanari (284 KB)

**See also:**
http://dx.doi.org/10.5194/hess-14-585-2010

**Related works:**

- [doc_id=896] Predecessor talk (Henry Darcy Medal Lecture)

**Remarks:**

Blog posts and discussions can be seen in Outside the Cube, Climate Science: Roger Pielke Sr., Retread Resources Blog, William M. Briggs, Niche Modeling 1, Niche Modeling 2, The Blackboard 1, The Blackboard 2, The Blackboard 3, Climate Audit, Bart Verheggen's weblog.

Erratum in p. 589, left column, around the middle: the line "Eq. (1) (but not in Eq. (1), which represents..." should read "Eq. (2) (but not in Eq. (1), which represents...".

**Our works referenced by this work:**

1. | D. Koutsoyiannis, On the quest for chaotic attractors in hydrological processes, Hydrological Sciences Journal, 51 (6), 1065–1091, doi:10.1623/hysj.51.6.1065, 2006. |

2. | 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. |

3. | D. Koutsoyiannis, A. Montanari, H. F. Lins, and T.A. Cohn, Climate, hydrology and freshwater: towards an interactive incorporation of hydrological experience into climate research—DISCUSSION of “The implications of projected climate change for freshwater resources and their management”, Hydrological Sciences Journal, 54 (2), 394–405, doi:10.1623/hysj.54.2.394, 2009. |

**Our works that reference this work:**

1. | G. G. Anagnostopoulos, D. Koutsoyiannis, A. Christofides, A. Efstratiadis, and N. Mamassis, A comparison of local and aggregated climate model outputs with observed data, Hydrological Sciences Journal, 55 (7), 1094–1110, doi:10.1080/02626667.2010.513518, 2010. |

2. | D. Koutsoyiannis, and A. Langousis, Precipitation, Treatise on Water Science, edited by P. Wilderer and S. Uhlenbrook, 2, 27–78, Academic Press, Oxford, 2011. |

3. | 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. |

4. | 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, 2011. |

5. | 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. |

6. | A. Christofides, and D. Koutsoyiannis, Causality in climate and hydrology, European Geosciences Union General Assembly 2011, Geophysical Research Abstracts, Vol. 13, Vienna, EGU2011-7440, doi:10.13140/RG.2.2.33776.46082, European Geosciences Union, 2011. |

7. | D. Koutsoyiannis, A. Christofides, A. Efstratiadis, G. G. Anagnostopoulos, and N. Mamassis, Scientific dialogue on climate: is it giving black eyes or opening closed eyes? Reply to “A black eye for the Hydrological Sciences Journal” by D. Huard, Hydrological Sciences Journal, 56 (7), 1334–1339, doi:10.1080/02626667.2011.610759, 2011. |

8. | 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. |

9. | 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. |

10. | 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. |

11. | D. Koutsoyiannis, Hydrology and Change, Hydrological Sciences Journal, 58 (6), 1177–1197, doi:10.1080/02626667.2013.804626, 2013. |

12. | 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. |

13. | 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. |

14. | 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. |

15. | D. Koutsoyiannis, Reconciling hydrology with engineering, Hydrology Research, 45 (1), 2–22, doi:10.2166/nh.2013.092, 2014. |

16. | C. Pappas, S.M. Papalexiou, and D. Koutsoyiannis, A quick gap-filling of missing hydrometeorological data, Journal of Geophysical Research-Atmospheres, 119 (15), 9290–9300, doi:10.1002/2014JD021633, 2014. |

17. | A. Montanari, and D. Koutsoyiannis, Modeling and mitigating natural hazards: Stationarity is immortal!, Water Resources Research, 50 (12), 9748–9756, doi:10.1002/2014WR016092, 2014. |

18. | D. Koutsoyiannis, and A. Montanari, Negligent killing of scientific concepts: the stationarity case, Hydrological Sciences Journal, 60 (7-8), 1174–1183, doi:10.1080/02626667.2014.959959, 2015. |

19. | 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. |

20. | 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. |

21. | 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. |

22. | I. Deligiannis, P. Dimitriadis, Ο. Daskalou, Y. Dimakos, and D. Koutsoyiannis, Global investigation of double periodicity οf hourly wind speed for stochastic simulation; application in Greece, Energy Procedia, 97, 278–285, doi:10.1016/j.egypro.2016.10.001, 2016. |

23. | G. Koudouris, P. Dimitriadis, T. Iliopoulou, N. Mamassis, and D. Koutsoyiannis, Investigation on the stochastic nature of the solar radiation process, Energy Procedia, 125, 398–404, 2017. |

24. | D. Koutsoyiannis, Entropy production in stochastics, Entropy, 19 (11), 581, doi:10.3390/e19110581, 2017. |

25. | 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. |

26. | 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. |

27. | H. Tyralis, P. Dimitriadis, D. Koutsoyiannis, P.E. O’Connell, K. Tzouka, and T. Iliopoulou, On the long-range dependence properties of annual precipitation using a global network of instrumental measurements, Advances in Water Resources, 111, 301–318, doi:10.1016/j.advwatres.2017.11.010, 2018. |

28. | 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. |

29. | G. Koudouris, P. Dimitriadis, T. Iliopoulou, N. Mamassis, and D. Koutsoyiannis, A stochastic model for the hourly solar radiation process for application in renewable resources management, Advances in Geosciences, 45, 139–145, doi:10.5194/adgeo-45-139-2018, 2018. |

30. | P. Dimitriadis, K. Tzouka, D. Koutsoyiannis, H. Tyralis, A. Kalamioti, E. Lerias, and P. Voudouris, Stochastic investigation of long-term persistence in two-dimensional images of rocks, Spatial Statistics, 29, 177–191, doi:10.1016/j.spasta.2018.11.002, 2019. |

31. | G. Papacharalampous, H. Tyralis, and D. Koutsoyiannis, Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes, Stochastic Environmental Research & Risk Assessment, doi:10.1007/s00477-018-1638-6, 2019. |

32. | 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. |

33. | D. Koutsoyiannis, Time’s arrow in stochastic characterization and simulation of atmospheric and hydrological processes, Hydrological Sciences Journal, doi:10.1080/02626667.2019.1600700, 2019. |

34. | T. Iliopoulou, and D. Koutsoyiannis, Revealing hidden persistence in maximum rainfall records, Hydrological Sciences Journal, doi:10.1080/02626667.2019.1657578, 2019. |

**
Works that cite this document:
**
View on
Google Scholar,
ResearchGate
or
ResearchGate (additional)

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

1. | Blöschl, G., and A. Montanari, Climate change impacts - throwing the dice?, Hydrological Processes, DOI:10.1002/hyp.7574, 24(3), 374-381, 2010. |

2. | Alila, Y., R. Hudson, P. K. Kuraś, M. Schnorbus, and K. Rasouli, Reply to comment by Jack Lewis et al. on “Forests and floods: A new paradigm sheds light on age-old controversies,” Water Resour. Res., 46, W05802, doi:10.1029/2009WR009028, 2010. |

3. | #Weijs, S., and N. van de Giesen, Information theory, uncertainty and risk for evaluating hydrologic forecasts, International Workshop Advances in Statistical Hydrology, International Association of Hydrological Sciences (IAHS/STAHY), Taormina, Italy, 2010. |

4. | Weijs, S. V., G. Schoups and N. van de Giesen, Why hydrological forecasts should be evaluated using information theory, Hydrol. Earth Syst. Sci., 14, 2545-2558, doi: 10.5194/hess-14-2545-2010, 2010. |

5. | Ward, J. D., A. D. Werner, W. P. Nel, and S. Beecham, The influence of constrained fossil fuel emissions scenarios on climate and water resource projections, Hydrology and Earth System Sciences, 15, 1879-1893, 2011. |

6. | Peel, M. C., and G. Blöschl, Hydrological modelling in a changing world, Progress in Physical Geography, 35 (2), 249-261, 2011. |

7. | Fildes, R., and N. Kourentzes, Validation and forecasting accuracy in models of climate change, International Journal of Forecasting, 27(4), 968-995, 2011. |

8. | Wagener, T., and A. Montanari, Convergence of approaches toward reducing uncertainty in predictions in ungauged basins, Water Resources Research, 47, W06301, doi: 10.1029/2010WR009469, 2011. |

9. | Frank, P. Imposed and neglected uncertainty in the global average surface air temperature index, Energy and Environment, 22 (4), 407-424, 2011. |

10. | #Allen, P.G., What (if anything) can econometric forecasters learn from meteorologists (and vice versa)?, 31st International Symposium on Forecasting , Prague, Czech Republic, 2011. |

11. | Gudmundsson, L., L. M. Tallaksen, K. Stahl, and A. K. Fleig, Low-frequency variability of European runoff, Hydrol. Earth Syst. Sci., 15, 2853-2869, doi: 10.5194/hess-15-2853-2011, 2011. |

12. | Castellarin, A., and A. Pistocchi, An analysis of change in alpine annual maximum discharges: implications for the selection of design discharges, Hydrological Processes, 21 (2), 139-168, 2012. |

13. | Pianosi, F. and L. Raso, Dynamic modeling of predictive uncertainty by regression on absolute errors, Water Resour. Res., 48, W03516, doi: 10.1029/2011WR010603, 2012. |

14. | Montanari, A., Hydrology of the Po River: looking for changing patterns in river discharge, Hydrol. Earth Syst. Sci., 16, 3739-3747, 2012. |

15. | #Rianna, M., E. Ridolfi, L. Lorino, L. Alfonso, V. Montesarchio, G. Di Baldassarre, F. Russo and F. Napolitano, Definition of homogeneous regions through entropy theory, 3rd STAHY International Workshop on Statistical Methods for Hydrology and Water Resources Management, Tunis, Tunisia, 2012. |

16. | #Bierkens, M. F. P., and F. C. van Geer, Stochastic Hydrology, Utrecht University, 2012. |

17. | Ramos, M. H., S. J. van Andel and F. Pappenberger, Do probabilistic forecasts lead to better decisions?, Hydrol. Earth Syst. Sci., 17, 2219-2232, 10.5194/hess-17-2219-2013, 2013. |

18. | Beven, K., So how much of your error is epistemic? Lessons from Japan and Italy, Hydrological Processes, 27 (11), 1677-168, 2013. |

19. | Soja, G., J. Züger, M. Knoflacher, P. Kinner and A.-M. Soja, Climate impacts on water balance of a shallow steppe lake in Eastern Austria (Lake Neusiedl), Journal of Hydrology, 480, 115-124, 2013. |

20. | Renard, B., K. Kochanek, M. Lang, F. Garavaglia, E. Paquet, L. Neppel, K. Najib, J. Carreau, P. Arnaud, Y. Aubert, F. Borchi, J.-M. Soubeyroux, S. Jourdain, J.-M. Veysseire, E. Sauquet, T. Cipriani and A. Auffray, Data-based comparison of frequency analysis methods: a general framework, Water Resources Research, 49 (2), 825-843,10.1002/wrcr.20087, 2013. |

21. | Hrachowitz, M., H.H.G. Savenije, G. Blöschl, J.J. McDonnell, M. Sivapalan, J.W. Pomeroy, B. Arheimer, T. Blume, M.P. Clark, U. Ehret, F. Fenicia, J.E. Freer, A. Gelfan, H.V. Gupta, D.A. Hughes, R.W. Hut, A. Montanari, S. Pande, D. Tetzlaff, P.A. Troch, S. Uhlenbrook, T. Wagener, H.C. Winsemius, R.A. Woods, E. Zehe, and C. Cudennec, A decade of Predictions in Ungauged Basins (PUB) — a review, Hydrological Sciences Journal, 58(6), 1198-1255, 2013. |

22. | Thompson, S. E., M. Sivapalan, C. J. Harman, V. Srinivasan, M. R. Hipsey, P. Reed, A. Montanari and G. and Blöschl, Developing predictive insight into changing water systems: use-inspired hydrologic science for the Anthropocene, Hydrol. Earth Syst. Sci., 17, 5013-5039, 2013. |

23. | Beven, K., and P. Young, A guide to good practice in modelling semantics for authors and referees, Water Resources Research, 10.1002/wrcr.20393, 2013. |

24. | Legates, D. R., W. Soon, W. M. Briggs and C. Monckton of Brenchley, Climate consensus and ‘misinformation’: a rejoinder to agnotology, scientific consensus, and the teaching and learning of climate change, Science & Education, 10.1007/s11191-013-9647-9, 2013. |

25. | #Loukas, A., and L. Vasiliades, Review of applied methods for flood-frequency analysis in a changing environment in Greece, In: A review of applied methods in Europe for flood-frequency analysis in a changing environment, Floodfreq COST action ES0901: European procedures for flood frequency estimation (ed. by H. Madsen et al.), Centre for Ecology & Hydrology, Wallingford, UK, 2013. |

26. | Serinaldi, F., L. Zunino and O. Rosso, Complexity–entropy analysis of daily stream flow time series in the continental United States, Stochastic Environmental Research and Risk Assessment, 28 (7), 1685-1708, 2014. |

27. | Szolgayova, E., G. Laaha, G. Blöschl and C. Bucher, Factors influencing long range dependence in streamflow of European rivers, Hydrological Processes, 28 (4), 1573-1586, 2014. |

28. | Ehret, U., H. V. Gupta, M. Sivapalan, S. V. Weijs, S. J. Schymanski, G. Blöschl, A. N. Gelfan, C. Harman, A. Kleidon, T. A. Bogaard, D. Wang, T. Wagener, U. Scherer, E. Zehe, M. F. P. Bierkens, G. Di Baldassarre, J. Parajka, L. P. H. van Beek, A. van Griensven, M. C. Westhoff and H. C. Winsemius, Advancing catchment hydrology to deal with predictions under change, Hydrol. Earth Syst. Sci., 18, 649-671, 2014. |

29. | Honti, M., A. Scheidegger, and C. Stamm, The importance of hydrological uncertainty assessment methods in climate change impact studies, Hydrology and Earth System Sciences, 18, 3301-3317, 10.5194/hess-18-3301-2014, 2014. |

30. | Ridley, D., and P. Ngnepieba, Antithetic time series analysis and the CompanyX data, Journal of the Royal Statistical Society: Series A (Statistics in Society), 177 (1), 83–94, 2014. |

31. | Berghuijs, W. R., R. A. Woods and M. Hrachowitz, A precipitation shift from snow towards rain leads to a decrease in streamflow, Nature Climate Change, 10.1038/nclimate2246, 2014. |

32. | Lazri, M., S. Ameur and J. M. Brucker, Analysis of the time trends of precipitation over Mediterranean region, I.J. Information Engineering and Electronic Business, 4, 38-44, 10.5815/ijieeb.2014.04.06, 2014. |

33. | Tsonis, A., Randomness: a property of the mathematical and physical systems, Hydrological Sciences Journal, 2014. |

34. | Beven, K., and P. Smith, Concepts of information content and likelihood in parameter calibration for hydrological simulation models, Journal of Hydrologic Engineering, 20 (1), 10.1061/(ASCE)HE.1943-5584.0000991, art. no. A4014010, 2015. |

35. | Odongo, V.O., C. van der Tol, P.R. van Oel, F.M. Meins, R. Becht, J. Onyando and Z.B. Su, Characterisation of hydroclimatological trends and variability in the Lake Naivasha basin, Kenya, Hydrological Processes, 29 (15), 3276-3293, 10.1002/hyp.10443, 2015. |

36. | Tsonis, A.A., Randomness: a property of the mathematical and physical systems, Hydrological Sciences Journal, 10.1080/02626667.2014.992434, 2015. |

37. | Pechlivanidis, I.G., B. Jackson, H. McMillan and H.V. Gupta, Robust informational entropy-based descriptors of flow in catchment hydrology, Hydrological Sciences Journal, 10.1080/02626667.2014.983516, 2015. |

38. | 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. |

39. | Di Baldassarre, G., L. Brandimarte, and K. Beven, The seventh facet of uncertainty: wrong assumptions, unknowns and surprises in the dynamics of human-water systems, Hydrological Sciences Journal, doi:10.1080/02626667.2015.1091460, 2015. |

**Tagged under:**
Hurst-Kolmogorov dynamics,
Course bibliography: Hydrometeorology,
Course bibliography: Stochastic methods,
Climate stochastics,
Determinism vs. stochasticity,
Works discussed in weblogs,
Entropy,
Scaling,
Stochastics,
Uncertainty