Climate change, the Hurst phenomenon, and hydrological statistics

D. Koutsoyiannis, Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, doi:10.1623/hysj., 2003.



The intensive research of the recent years on climate change has led to the strong conclusion that climate has always, through the planet history, changed irregularly on all time scales. Climate changes are closely related to the Hurst phenomenon, which has been detected in many long hydroclimatic time series and is stochastically equivalent with a simple scaling behaviour of climate variability over timescale. The climate variability, anthropogenic or natural, increases the uncertainty of the hydrologic processes. It is shown that hydrologic statistics, the branch of hydrology that deals with uncertainty, in its current state is not consistent with the varying character of climate. Typical statistics used in hydrology such as means, variances, cross- and auto-correlations and Hurst coefficients, and the variability thereof, are revisited under the hypothesis of a varying climate following a simple scaling law, and new estimators are studied which in many cases differ dramatically from the classic ones. The new statistical framework is applied to real-world examples for typical tasks such as estimation and hypothesis testing where again the results depart significantly from those of the classic statistics.

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Alternative names for Hurst phenomenon are Hurst effect, Joseph effect, Long term persistence, Long range dependence, Scaling behaviour (in time), Multi-scale fluctuation, Hurst-Kolmogorov pragmaticity, etc.

Erratum: The runoff of the Boeotikos Kephisos catchment (Fig. 3, p. 7, and p. 21, first full paragraph) should be corrected to volume units, i.e. cubic hectometers (instead of millimeters).

Our works referenced by this work:

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Our works that reference this work:

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27. 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.
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84. #Schumann, A., Gumbel Distribution, ARMA, Copulas – The importance of stochastic tools for water management, 3rd STAHY International Workshop on Statistical Methods for Hydrology and Water Resources Management, Tunis, Tunisia, 2012.
85. #Rice, K. C., and R. M. Hirsch, Spatial and temporal trends in runoff at long-term streamgages within and near the Chesapeake Bay Watershed, U.S. Geological Survey Scientific Investigations Report 2012–5151, 56 pp., 2012.
86. Merz, B., T. Maurer and K. Kaiser, Wie gut können wir vergangene und zukünftige Veränderungen des Wasserhaushalts quantifizieren? [How well can we quantify past and future changes of the water cycle?], Hydrologie und Wasserbewirtschaftung, 5, 244-256, DOI: 10.5675/HyWa_2012,5_1, 2012.
87. Musa, M., and K. Ibrahim, Existence of long memory in ozone time series, Sains Malaysiana, 41 (11), 1367-1376, 2012.
88. Bard, A., B. Renard et M. Lang, Tendances observées sur les régimes hydrologiques de l’Arc Alpin [Observed Trends in the hydrologic regime of Alpine catchments], Houille Blanche, (1), 38-43, 2012.
89. Resta, M., Hurst exponent and its applications in time-series analysis, Recent Patents on Computer Science, 5 (3), 211-219, 2012.
90. Ye, X., X. Xia, J. Zhang and Y. Chen, Effects of trends and seasonalities on robustness of the Hurst parameter estimators, Signal Processing, IET, 6 (9), 849-856, 2012.
91. 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.
92. Kumar, S., V. Merwade, J. L. Kinter III and D. Niyogi, Evaluation of temperature and precipitation trends and long-term persistence in CMIP5 20th century climate simulations, Journal of Climate, 26 (12), 4168-4185, 2013.
93. Hannaford, J., G. Buys, K. Stahl and L. M. Tallaksen, The influence of decadal-scale variability on trends in long European streamflow records, Hydrol. Earth Syst. Sci., 17, 2717-2733, 10.5194/hess-17-2717-2013, 2013.
94. #Alexandridis, A. K., and A. D. Zapranis, Weather Derivatives: Modeling and Pricing Weather-Related Risk, Springer, New York, 2013.
95. Zeng, X., D. Wang, J. Wu and X. Chen, Reliability analysis of the groundwater conceptual model, Human and Ecological Risk Assessment, 19 (2), 515-525, 2013.
96. Lacombe, G., V. Smakhtin and C. Hoanh, Wetting tendency in the Central Mekong Basin consistent with climate change-induced atmospheric disturbances already observed in East Asia, Theoretical and Applied Climatology, 111 (1-2), 251-263, 2013.
97. 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.
98. Fleming, S. W., and D. J. Sauchyn, Availability, volatility, stability, and teleconnectivity changes in prairie water supply from Canadian Rocky Mountain sources over the last millennium, Water Resources Research, 49 (1), 64-74, 2013.
99. Navarro, X., F. Porée, A. Beuchée and G. Carrault, Performance analysis of Hurst exponent estimators using surrogate-data and fractional lognormal noise models: Application to breathing signals from preterm infants, Digital Signal Processing, 10.1016/j.dsp.2013.04.007, 2013.
100. #Jones, M. R., S. Blenkinsop, H. J. Fowler, D. B. Stephenson and C. G. Kilsby, Generalized additive modelling of daily precipitation extremes and their climatic drivers, NCAR Technical Note 501+STR, National Center for Atmospheric Research, Boulder, Colorado, USA, 2013.
101. Kirchner, J.W. and C. Neal, Universal fractal scaling in stream chemistry and its implications for solute transport and water quality trend detection, Proceedings of the National Academy of Sciences (PNAS), 110 (30), 12213-12218, 2013.
102. #Ercan, A., M. L. Kavvas and R. Abbasov, Long-range dependence and ARFIMA models, Long-Range Dependence and Sea Level Forecasting, Springer International Publishing, 10.1007/978-3-319-01505-7_2, 2013.
103. #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.
104. Steinschneider, S., and C. Brown, Casey, A semiparametric multivariate, multi-site weather generator with low-frequency variability for use in climate risk assessments, Water Resources Research, 10.1002/wrcr.20528, 2013.
105. Rocheta, E., M. Sugiyanto, F. Johnson, J. Evans and A. Sharma, How well do general circulation models represent low frequency rainfall variability?, Water Resources Research, 50 (3), 2108-2123, 2014.
106. 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.
107. Dinpashoh, Y., R. Mirabbasi, D. Jhajharia, H. Abianeh and A. Mostafaeipour, Effect of short term and long-term persistence on identification of temporal trends, J. Hydrol. Eng., 19(3), 617–625, 2014.
108. Lacombe, G., and M. McCartney, Uncovering consistencies in Indian rainfall trends observed over the last half century, Climatic Change, 10.1007/s10584-013-1036-5, 2014.
109. Condon, L. E., and R. M. Maxwell, Groundwater-fed irrigation impacts spatially distributed temporal scaling behavior of the natural system: a spatio-temporal framework for understanding water management impacts, Environmental Research Letters, 9 (3), 034009, 2014.
110. Ghadage, A., S. Balan and S. Shelke, Performance analysis different filters for noise removal of underwater bathymetric data, International Journal of Application or Innovation in Engineering & Management, 3 (3), 339-344, 2014.
111. #Kalra, A., S. Sagarika and S. Ahmad, Investigation of the linkages between oceanic atmospheric variability and continental U.S. streamflow, ASCE World Water and Environmental Resources Congress, Portland, OR., USA, 2014.
112. 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.
113. 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.
114. Fatichi, S., and V. Y. Ivanov, Interannual variability of evapotranspiration and vegetation productivity, Water Resources Research, 50 (4), 3275-3294, 2014.
115. Ribeiro, L., N. Kretschmer, J. Nascimento, A. Buxo, T. Roetting, G. Soto, M. Señoret, J. Oyarzún, H. Maturana and R. Oyarzún, Evaluating piezometric trends using the Mann-Kendall test on the alluvial aquifers of the Elqui river basin, Chile, Hydrological Sciences Journal, 10.1080/02626667.2014.945936, 2014.
116. Stonevičius, E., G. Valiuškevičius, E. Rimkus and J. Kažys, Climate induced changes of Lithuanian rivers runoff in 1960–2009, Water Resources, 41 (5), 592-603, 2014.
117. Yao, Y., S. Zhao, Y. Zhang, K. Jia and M. Liu, Spatial and decadal variations in potential evapotranspiration of China based on reanalysis datasets during 1982–2010, Atmosphere, 5(4), 737-754, 2014.
118. Setty, V. A., and A. S. Sharma, Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2014.10.016, 2014.
119. Franzke, C.L.E., S.M. Osprey, P. Davini and N.W. Watkins, A dynamical systems explanation of the Hurst effect and atmospheric low-frequency variability, Scientific Reports, 5, art. no. 9068, 10.1038/srep09068, 2015.
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121. Razavi, S., A. Elshorbagy, H. Wheater and D. Sauchyn, Toward understanding nonstationarity in climate and hydrology through tree ring proxy records, Water Resources Research, 51 (3), 1813-1830, 2015.
122. Machado, J.A.T., Fractional order description of DNA, Applied Mathematical Modelling, 39 (14), 4095-4102, 2015.
123. Kalra, A., S. Sagarika and S. Ahmad, Spatial and temporal evaluation of hydroclimatic variables in the Colorado river basin, World Environmental and Water Resources Congress 2015: Floods, Droughts, and Ecosystems - Proceedings of the 2015 World Environmental and Water Resources Congress, 1118-1127, 2015.
124. 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.
125. Serinaldi, F., and C.G. Kilsby, The importance of prewhitening in change point analysis under persistence, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-015-1041-5, 2015.
126. Kundzewicz, Z.W. Farewell, HSJ!—address from the retiring editor, Hydrological Sciences Journal, 10.1080/02626667.2015.1058627, 2015.
127. Tenreiro Machado, J.A., Fractional dynamics in the Rayleigh’s piston, Communications in Nonlinear Science and Numerical Simulation, 10.1016/j.cnsns.2015.07.009, 2015.
128. Hu, Z., Q. Li, X. Chen, Z. Teng, C. Chen, G. Yin and Y. Zhang, Climate changes in temperature and precipitation extremes in an alpine grassland of Central Asia, Theoretical and Applied Climatology, 10.1007/s00704-015-1568-x, 2015.
129. Munshi, J., A robust test for OLS trends in daily temperature data, Social Science Research Network, doi:10.2139/ssrn.2631298, 2015.
130. Müller, R., and N. Schütze, Multi-objective optimization of multi-purpose multi-reservoir systems under high reliability constraints, Environmental Earth Sciences, 75:1278, doi:10.1007/s12665-016-6076-5, 2016.

Tagged under: Course bibliography: Stochastic methods, Climate stochastics, Hurst-Kolmogorov dynamics, Papers initially rejected, Stochastics, Uncertainty