Nonstationarity versus scaling in hydrology

D. Koutsoyiannis, Nonstationarity versus scaling in hydrology, Journal of Hydrology, 324, 239–254, 2006.



The perception of a changing climate, which impacts also hydrological processes, is now generally admitted. However, the way of handling the changing nature of climate in hydrologic practice and especially in hydrological statistics has not become clear so far. The most common modelling approach is to assume that long-term trends, which have been found to be omnipresent in long hydrological time series, are "deterministic" components of the time series and the processes represented by the time series are nonstationary. In this paper, it is maintained that this approach is contradictory in its rationale and even in the terminology it uses. As a result, it may imply misleading perception of phenomena and estimate of uncertainty. Besides, it is maintained that a stochastic approach hypothesizing stationarity and simultaneously admitting a scaling behaviour reproduces climatic trends (considering them as large-scale fluctuations) in a manner that is logically consistent, easy to apply and free of paradoxical results about uncertainty.

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Our works referenced by this work:

1. I. Nalbantis, N. Mamassis, et D. Koutsoyiannis, Le phénomène recent de sécheresse persistante et l' alimentation en eau de la cité d' Athènes, Publications de l'Association Internationale de Climatologie, 6eme Colloque International de Climatologie, edité par P. Maheras, Thessaloniki, 6, 123–132, doi:10.13140/RG.2.1.4430.1041, Association Internationale de Climatologie, Aix-en-Provence Cedex, France, 1993.
2. D. Koutsoyiannis, A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series, Water Resources Research, 36 (6), 1519–1533, 2000.
3. D. Koutsoyiannis, The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47 (4), 573–595, doi:10.1080/02626660209492961, 2002.
4. D. Koutsoyiannis, Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, doi:10.1623/hysj., 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, Climate change certainty versus climate uncertainty and inferences in hydrological studies and water resources management (solicited), European Geosciences Union General Assembly 2004, Geophysical Research Abstracts, Vol. 6, Nice, doi:10.13140/RG.2.2.12726.29764, European Geosciences Union, 2004.
7. E. Rozos, A. Efstratiadis, I. Nalbantis, and D. Koutsoyiannis, Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows, Hydrological Sciences Journal, 49 (5), 819–842, doi:10.1623/hysj.49.5.819.55130, 2004.
8. D. Koutsoyiannis, The water resource management of Athens in the perspective of the Olympic Games, The Olympic Games Athens 2004 and the National Technical University of Athens, edited by K. Moutzouris, Athens, 17–27, doi:10.13140/RG.2.2.35480.39680, National Technical University of Athens, 2004.
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. D. Koutsoyiannis, A toy model of climatic variability with scaling behaviour, Journal of Hydrology, 322, 25–48, 2006.

Our works that reference this work:

1. 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.
2. 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.
3. C. Cudennec, C. Leduc, and D. Koutsoyiannis, Dryland hydrology in Mediterranean regions -- a review, Hydrological Sciences Journal, 52 (6), 1077–1087, doi:10.1623/hysj.52.6.1077, 2007.
4. D. Koutsoyiannis, A. Efstratiadis, N. Mamassis, and A. Christofides, On the credibility of climate predictions, Hydrological Sciences Journal, 53 (4), 671–684, 2008.
5. 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.
6. 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.
7. 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.
8. 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.
9. P.E. O’Connell, D. Koutsoyiannis, H. F. Lins, Y. Markonis, A. Montanari, and T.A. Cohn, The scientific legacy of Harold Edwin Hurst (1880 – 1978), Hydrological Sciences Journal, 61 (9), 1571–1590, doi:10.1080/02626667.2015.1125998, 2016.

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

1. Ellis, C., and C. Hudson, Scale-adjusted volatility and the Dow Jones index, Physica A: Statistical Mechanics and its Applications, 378(2), 374-386, 2007.
2. #Stockwell, D., Niche Modeling: Predictions from Statistical Distributions, Chapman & Hall, Boka Raton, USA, 2007.
3. #Iimi, A., Estimating global climate change impacts on hydropower projects: Applications in India, Sri Lanka and Vietnam, World Bank Policy Research Working Paper No. 4344, 2007.
4. 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.
5. Rybski, D., A. Bunde and H. von Storch, Long-term memory in 1000-year simulated temperature records, Journal of Geophysical Research-Atmospheres, 113(D2), D02106, 2008.
6. Rutten, M.M., N. van de Giesen, M. Baptist, J. Icke and W. Uijttewaal, Seasonal forecast of cooling water problems in the River Rhine, Hydrological Processes, 22(7), 1037-1045, 2008.
7. Khaliq, M.N., T.B.M.J. Ouarda, P. Gachon and L. Sushama, Temporal evolution of low-flow regimes in Canadian rivers, Water Resources Research, 44 (8), W08436, 2008.
8. Daniell, T.M., The Tao of hydrology and water resources: Some philosophical thoughts, Australian Journal of Water Resources, 12 (3), 189-204, 2008.
9. Rybski, D., and A. Bunde, On the detection of trends in long-term correlated records, Physica A, 388 (8), 1687-1695, 2009.
10. Hamed, K.H., Exact distribution of the Mann-Kendall trend test statistic for persistent data, Journal of Hydrology, 365(1-2), 86-94, 2009.
11. Hamed, K.H., Enhancing the effectiveness of prewhitening in trend analysis of hydrologic data, Journal of Hydrology, 368(1-4), 143-155, 2009.
12. Khaliq, M., T. Ouarda, and P. Gachon, Identification of temporal trends in annual and seasonal low flows occurring in Canadian rivers: The effect of short- and long-term persistence, Journal of Hydrology, 369(1-2), 183-197, 2009.
13. Déry, S. J., K. Stahl, R. D. Moore, P. H. Whitfield, B. Menounos, and J. E. Burford, Detection of runoff timing changes in pluvial, nival, and glacial rivers of western Canada, Water Resour. Res., 45, W04426, doi:10.1029/2008WR006975, 2009.
14. Hamed, K. H., Effect of persistence on the significance of Kendall’s tau as a measure of correlation between natural time series, The European Physical Journal, 174 (1), 65-79, 2009.
15. Bordi, I., K. Fraedrich, and A. Sutera, Observed drought and wetness trends in Europe: an update, Hydrol. Earth Syst. Sci., 13, 1519-1530, 2009.
16. Villarini, G., F. Serinaldi, J. A. Smith, and W. F. Krajewski, On the stationarity of annual flood peaks in the continental United States during the 20th century, Water Resour. Res., 45, W08417, doi:10.1029/2008WR007645, 2009.
17. #Zhang, H., N. Wang and K. Dong, Return Intervals Analysis of the Hong Kong Stock Market, 2009 International Conference on Computational Intelligence and Natural Computing, Art. no. 5231145, 262-265, 2009.
18. Fatichi, S., S. M. Barbosa, E. Caporali and M. E. Silva, Deterministic versus stochastic trends: Detection and challenges, Journal Of Geophysical Research-Atmospheres, 114, D18121, doi:10.1029/2009JD011960, 2009.
19. #Baroang, K. M., M, Hellmuth and P. Block, Identifying uncertainty and defining risk in the context of the WWDR-4, Prepared for the World Water Assessment Programme, International Research Institute for Climate and Society, Earth Institute, Columbia University, 2009.
20. Ehsanzadeh, E., and K. Adamowski, Trends in timing of low stream flows in Canada: impact of autocorrelation and long-term persistence, Hydrological Processes, 24, 970–980, 2010.
21. Hossain, F., I. Jeyachandran and R. Pielke Sr., Dam safety effects due to human alteration of extreme precipitation, Water Resources Research, 46, W03301, doi:10.1029/2009WR007704, 2010.
22. Villarini, G., J. A. Smith and F. Napolitano, Nonstationary modeling of a long record of rainfall and temperature over Rome, Advances in Water Resources, 33 (10), 1256-1267, doi: 10.1016/j.advwatres.2010.03.013, 2010.
23. Gedikli, A., H. Aksoy, N. E. Unal and A. Kehagias, Modified dynamic programming approach for offline segmentation of long hydrometeorological time series, Stochastic Environmental Research and Risk Assessment, 24 (5), 547-557, 2010.
24. Rybski, D., H. D. Rozenfeld and J. P. Kropp, Quantifying long-range correlations in complex networks beyond nearest neighbors, EPL, 90, 28002, 2010.
25. Villarini, G., and J. A. Smith, Flood peak distributions for the eastern United States, Water Resour. Res., 46, W06504, doi:10.1029/2009WR008395, 2010.
26. Gautam, M. R., K. Acharya and M. K. Tuladhar, Upward trend of streamflow and precipitation in a small, non-snow-fed, mountainous watershed in Nepal, Journal of Hydrology, 387 (3-4), 304-311, 2010.
27. Dong, K. Q., P. J. Shang and H. Zhang, The multi-dependent Hurst exponent in traffic time series, Applied Mechanics and Materials, 20-23, 346-351, 2010.
28. Liu, Z. M., H. Zhang and K. Q. Dong, A new method to determine the periodicity of time series, Applied Mechanics and Materials, 26-28, 535-538, 2010.
29. Stahl, K., H. Hisdal, J. Hannaford, L. M. Tallaksen, H. A. J. van Lanen, E. Sauquet, S. Demuth, M. Fendekova, and J. Jódar, Streamflow trends in Europe: evidence from a dataset of near-natural catchments, Hydrol. Earth Syst. Sci., 14, 2367-2382, doi:10.5194/hess-14-2367-2010, 2010.
30. Fan, J., W. Q. Li, H. Zhang and K.Q. Dong, Return intervals analysis of the sunspot time series, Applied Mechanics and Materials, 29, 1144-1149, 2010.
31. #Mudelsee, M., Climate Time Series Analysis: Classical Statistical and Bootstrap Methods, 473 pp., Springer, Dordrecht, 2010.
32. Khaliq M. N., and P. Gachon, Pacific decadal oscillation climate variability and temporal pattern of winter flows in Northwestern North America, Journal of Hydrometeorology, 11 (4), 917-933, 2010.
33. Wang, N., Y. Li and H. Zhang, Hurst Exponent Estimation Based on Moving Average Method, Advances in Wireless Networks and Information Systems, 72, 137-142, doi: 10.1007/978-3-642-14350-2_17, 2010.
34. #Rybski, D., A. Bunde, S. Havlin, J. W. Kantelhardt and E. Koscielny-Bunde, Detrended fluctuation studies of long-term persistence and multifractality of precipitation and river runoff records, in: In Extremis: Disruptive Events and Trends in Climate and Hydrology, J. Kropp and H.-J. Schellnhuber (Eds.), Springer, 400 pp., 2010.
35. #Hodgkins, G.A., Historical changes in annual peak flows in Maine and implications for flood-frequency analyses, U.S. Geological Survey Fact Sheet 2010–3034,, 2010.
36. Kottegoda, N.T., L. Natale and E. Raiteri, Simulation of climatic series with nonstationary trends and periodicities, Journal of Hydrology, 398 (1-2), 33-43, 2011.
37. Caloiero, T., R. Coscarelli, E. Ferrari and M. Mancini, Trend detection of annual and seasonal rainfall in Calabria (Southern Italy), International Journal of Climatology, 31 (1), 44-56, 2011.
38. Barbosa, S. M., Testing for deterministic trends in global sea surface temperature, Journal of Climate, 24 (10), 2516-2522, 2011.
39. Villarini, G., J. A. Smith, F. Serinaldi and A. A. Ntelekos, Analyses of seasonal and annual maximum daily discharge records for Central Europe, Journal of Hydrology, 399 (3-4), 299-312, 2011.
40. Villarini, G., J. A. Smith, M. L. Baeck, R. Vitolo, D. B. Stephenson and W. F. Krajewski, On the frequency of heavy rainfall for the midwest of the United States, Journal of Hydrology, 400 (1-2), 103-120, 2011.
41. Love, J. J.: Secular trends in storm-level geomagnetic activity, Annales Geophysicae, 29, 251-262, 2011.
42. Villarini, G., J. A. Smith, A. A. Ntelekos, and U. Schwarz, Annual maximum and peaks-over-threshold analyses of daily rainfall accumulations for Austria, J. Geophys. Res., 116, D05103, doi: 10.1029/2010JD015038, 2011.
43. Villarini, G., J. A. Smith, M. L. Baeck, and W. F. Krajewski, Examining flood frequency distributions in the Midwest U.S., Journal of the American Water Resources Association, 47(3), 447-463, 2011.
44. Napolitano, G., F. Serinaldi and L. See, Impact of EMD decomposition and random initialisation of weights in ANN hindcasting of daily stream flow series: an empirical examination, Journal of Hydrology, 406 (3-4), 199-214, 2011.
45. Hodgkins, G. A., and R. W. Dudley, Historical summer base flow and stormflow trends for New England rivers, Water Resour. Res., 47, W07528, doi: 10.1029/2010WR009109, 2011.
46. Shohami, D., U. Dayan, and E. Morin, Warming and drying of the eastern Mediterranean: Additional evidence from trend analysis, J. Geophys. Res., 116, D22101, doi: 10.1029/2011JD016004, 2011.
47. #Grimaldi, S., S.-C. Kao, A. Castellarin, S. M. Papalexiou, A. Viglione, F. Laio, H. Aksoy and A. Gedikli, Statistical Hydrology, In: Treatise on Water Science (ed. by P. Wilderer), 2, 479–517, Academic Press, Oxford, 2011.
48. Villarini, G., J. A. Smith, F. Serinaldi, A. A. Ntelekos and U. Schwarz, Analyses of extreme flooding in Austria over the period 1951–2006, International Journal of Climatology, 32 (8), 1178-1192, 2012.
49. Villarini, G., Analyses of annual and seasonal maximum daily rainfall accumulations for Ukraine, Moldova, and Romania, International Journal of Climatology, 32 (14), 2213-2226, 2012.
50. Ehsanzadeh, E., G.. van der Kamp and C. Spence, The impact of climatic variability and change in the hydroclimatology of Lake Winnipeg watershed, Hydrological Processes, 26 (18), 2802-2813, 2012.
51. Bakker, A. M. R., and B. J. J. M. van den Hurk, Estimation of persistence and trends in geostrophic wind speed for the assessment of wind energy yields in Northwest Europe, Climate Dynamics, 39 (3-4), 767-782, 2012.
52. #Machiwal, D., and M. K. Jha, Analysis of trends in low-flow time series of Canadian rivers, Hydrologic Time Series Analysis: Theory and Practice, Springer, Netherlands, 201-221, 2012.
53. Prokoph, A., J. Adamowski and K. Adamowski, Influence of the 11 year solar cycle on annual streamflow maxima in Southern Canada, Journal of Hydrology, 442–443, 55-62, 2012.
54. #Safford, H. D., G. D. Hayward, N. E. Heller and J. A. Wiens, Historical ecology, climate change, and resource management: Can the past still inform the future?, Historical Environmental Variation in Conservation and Natural Resource Management (ed. by J. A. Wiens, G. D. Hayward, H. D. Safford and C. Giffen), 46-62, Wiley-Blackwell, Chichester, UK, 2012.
55. #WWAP (World Water Assessment Programme), The United Nations World Water Development, Report 4: Managing Water under Uncertainty and Risk, UNESCO, Paris, 2012.
56. Panda, D. K., A. Mishra and A. Kumar, Quantification of trends in groundwater levels of Gujarat in western India, Hydrological Sciences Journal, 57 (7), 1325–1336, 2012.
57. Bakker, A., J. Coelingh and B. van den Hurk, Long-term trends in the wind supply in the Netherlands, Proceedings EWEA 2012 Annual Event, Copenhagen, Denmark, 2012.
58. Janža, M., Impact assessment of projected climate change on the hydrological regime in the SE Alps, Upper Soča River basin, Slovenia, Natural Hazards, 67 (3), 1025-1043, 2013.
59. Rougé, C., Y. Ge and X. Cai, Detecting gradual and abrupt changes in hydrological records, Advances in Water Resources, 53, 33-44, 2013.
60. Villarini, G., and J. A. Smith, Flooding in Texas: Examination of temporal changes and impacts of tropical cyclones, Journal of the American Water Resources Association, 10.1111/jawr.12042, 2013.
61. Yusof, F., I. L. Kane and Z. Yusop, Structural break or long memory: an empirical survey on daily rainfall data sets across Malaysia, Hydrol. Earth Syst. Sci., 17, 1311-1318, 2013.
62. Hodgkins, G. A., The importance of record length in estimating the magnitude of climatic changes: an example using 175 years of lake ice-out dates in New England, Climatic Change, 10.1007/s10584-013-0766-8, 2013.
63. 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.
64. Clarke, R. T., How should trends in hydrological extremes be estimated?, Water Resources Research, 10.1002/wrcr.20485, 2013.
65. Debabrata Das and R. Srinivasan, Variation of temperature and rainfall in India, International Journal of Advances in Engineering & Technology, 6 (4), 1803-1812, 2013.
66. #Wood, A. W., and G. Sreckovic, The sustainability of Pacific Northwest Hydropower Generation in the context of nonstationarity and renewable energy growth, Climate Vulnerability: Understanding and Addressing Threats to Essential Resources, Pielke, R. (editor), 5, 177-194, Elsevier Science, 2013.
67. Kane, I. L., and F. Yusof, Assessment of risk of rainfall events with a hybrid of ARFIMA-GARCH, Modern Applied Science, 7 (12), 78-89, 2013.
68. Barros, A. P., Y. Duan, J. Brun and M. A. Medina Jr, Flood nonstationarity in the Southeast and Mid-Atlantic regions of the United States, Journal of Hydrologic Engineering, 19 (10), 10.1061/(ASCE)HE.1943-5584.0000955, 2014.
69. Chu, M., A. Ghulam, J. H. Knouft and Z. Pan, A hydrologic data screening procedure for exploring monotonic trends and shifts in rainfall and runoff patterns, Journal of the American Water Resources Association, 50 (4), 928-942, 2014.
70. Benkhaled, A., H. Higgins, F. Chebana and A. Necir, Frequency analysis of annual maximum suspended sediment concentrations in Abiod wadi, Biskra (Algeria), Hydrological Processes, 28 (12), 3841-3854, 2014.
71. Markovic, D., and M. Koch, Long-term variations and temporal scaling of hydroclimatic time series with focus on the German part of the Elbe River Basin, Hydrological Processes, 28 (4), 2202-2211, 2014.
72. Fleming, S. W., A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series, Hydrological Sciences Journal, 59 (1), 73–84, 2014.
73. Panagoulia, D., P. Economou and C. Caroni, Stationary and nonstationary generalized extreme value modelling of extreme precipitation over a mountainous area under climate change, Environmetrics, 25 (1), 29-43, 2014.
74. Li, D., H. Xie and L. Xiong, Temporal change analysis based on data characteristics and nonparametric test, Water Resources Management, 28 (1), 227-240, 2014.
75. Kędra, M., Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains), Journal of Hydrology, 509, 474-503, 2014.
76. Graf, R., Reference statistics for the structure of measurement series of groundwater levels (Wielkopolska Lowland - western Poland), Hydrological Sciences Journal, 10.1080/02626667.2014.905689, 2014.
77. 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.
78. Sagarika, S., A. Kalra and S. Ahmad, Evaluating the effect of persistence on long-term trends and analyzing step changes in streamflows of the continental United States, Journal of Hydrology, 10.1016/j.jhydrol.2014.05.002, 2014.
79. Guzman, J. A., M. L. Chu, P. J.Starks, D. N. Moriasi, J. L. Steiner, C. A. Fiebrich and A. G. McCombs, Upper Washita River experimental watersheds: Data screening procedure for data quality assurance, Journal of Environmental Quality, 43, 1250-1261, 2014.
80. #Detzel, D. H. M., and M. R. M. Mine, Trends in hydrological series: methods and application, 11th International Conference on Hydroscience & Engineering, Hamburg, Germany, 2014.
81. Bozzi, S., G. Passoni,P. Bernardara,N. Gouta and A. Arnaud, Roughness and discharge uncertainty in 1D water level calculations, Environmental Modeling & Assessment, 10.1007/s10666-014-9430-6, 2014.
82. Zhang, Q., X. Gu, V. P. Singh, M. Xiao and C.-Y. Xu, Stationarity of annual flood peaks during 1951-2010 in the Pearl River basin, China, Journal of Hydrology, 10.1016/j.jhydrol.2014.10.028, 2014.
83. Mondal, A., and P.P. Mujumdar, Return levels of hydrologic droughts under climate change, Advances in Water Resources, 75, 67-79, 2015.
84. Lopez-de-la-Cruz, J., and F. Frances, Low-Frequency climate variability in the non-stationary modeling of flood regimes in the Sinaloa and Presidio San Pedro hydrologic regions, Tecnologia Y Ciencias Del Agua, 5 (4), 79-101 , 2014.
85. Verdon-Kidd, D. C. and A. S. Kiem, Non–stationarity in annual maxima rainfall across Australia – implications for Intensity–Frequency–Duration (IFD) relationships, Hydrology and Earth System Sciences Discussions, 12, 3449-3475, doi:10.5194/hessd-12-3449-2015, 2015.
86. Serinaldi, F., and C.G. Kilsby, Stationarity is undead: Uncertainty dominates the distribution of extremes, Advances in Water Resources, 77, 17-36, 2015.
87. Steinschneider, S., and U. Lall, A hierarchical Bayesian regional model for nonstationary precipitation extremes in Northern California conditioned on tropical moisture exports, Water Resources Research, 51 (3), 1472-1492, 2015.
88. Tan, X.Z., and T.Y. Gan, Nonstationary analysis of annual maximum streamflow of Canada, Journal of Climate, 28 (5) 1788-1805, 10.1175/JCLI-D-14-00538.1, 2015.
89. 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.
90. Hu, Y. M., Z.M. Liang, X.L. Jiang and H. Bu, Non-stationary hydrological frequency analysis based on the reconstruction of extreme hydrological series, Proc. IAHS, 371, 163-166, 10.5194/piahs-371-163-2015, 2015.
91. Bayazit, M., Nonstationarity of hydrological records and recent trends in trend analysis: a state-of-the-art review, Environmental Processes, 2 (3), 527-542, 10.1007/s40710-015-0081-7, 2015.

Tagged under: Course bibliography: Stochastic methods, Climate stochastics, Determinism vs. stochasticity, Hurst-Kolmogorov dynamics, Scaling, Uncertainty