2,723
Views
51
CrossRef citations to date
0
Altmetric
Special issue: Facets of Uncertainty

The scientific legacy of Harold Edwin Hurst (1880–1978)

, , , , &
Pages 1571-1590 | Received 12 Jan 2015, Accepted 25 Nov 2015, Published online: 04 May 2016

References

  • Anis, A.A. and Lloyd, E.H., 1953. On the range of partial sums of a finite number of independent normal variates. Biometrika, 40 (1–2), 35–42. doi:10.1093/biomet/40.1-2.35
  • Arneodo, A., et al., 1996. Wavelet based fractal analysis of DNA sequences. Physica D: Nonlinear Phenomena, Measures of Spatio-Temporal Dynamics, 96, 291–320. doi:10.1016/0167-2789(96)00029-2
  • Baillie, R.T., 1996. Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73 (1), 5–59. doi:10.1016/0304-4076(95)01732-1
  • Ballerini, R. and Boes, D.C., 1985. Hurst behavior of shifting level processes. Water Resources Research, 21 (11), 1642–1648. doi:10.1029/WR021i011p01642
  • Barnard, G.A., 1956. Discussion of H. E. Hurst, 1956. On methods of using long-term storage in reservoirs. Proceedings of Institute Civil Engineering, 5 (5), 552–553.
  • Benzi, R., et al., 1982. Stochastic resonance in climatic change. Tellus, 34 (1), 10–16. doi:10.1111/tus.1982.34.issue-1
  • Beran, J., 1994. Statistics for long-memory processes. Florida: CRC Press, 315 pp.
  • Bhattacharya, R.N., Gupta, V.K., and Waymire, E., 1983. The Hurst effect under trends. Journal of Applied Probability, 20, 649–662. doi:10.2307/3213900
  • Bindoff, N.L., et al., 2013. Detection and attribution of climate change: from global to regional. In: T.F. Stocker, et al., eds. Climate change 2013: the physical science basis. Contribution of working group I to the fifth assessment report of the intergovernmental panel on climate change. Cambridge, United Kingdom: Cambridge University Press.
  • Blender, R., Fraedrich, K., and Hunt, B., 2006. Millennial climate variability: GCM‐simulation and Greenland ice cores. Geophysical Research Letters, 33 (L04710). doi:10.1029/2005GL024919
  • Bloomfield, P., 1992. Trends in global temperature. Climatic Change, 21 (1), 1–16. doi:10.1007/BF00143250
  • Boes, D.C. and Salas, J.D., 1978. Nonstationarity of the mean and the Hurst phenomenon. Water Resources Research, 14 (1), 135–143. doi:10.1029/WR014i001p00135
  • Borland, L., 1998. Microscopic dynamics of the nonlinear Fokker-Planck equation: a phenomenological model. Physical Review E, 57 (6), 6634–6642. doi:10.1103/PhysRevE.57.6634
  • Box, G.E. and Jenkins, G.M., 1970. Time series analysis, forecasting and control. San Francisco: Holden-Day, 537 pp.
  • Bras, R.L. and Rodriguez-Iturbe, I., 1985. Random functions and hydrology. London: Courier Dover Publications, 559 pp.
  • Cohn, T.A. and Lins, H.F., 2005. Nature’s style: naturally trendy. Geophysical Researcher Letters, 32 (L23402). doi:10.1029/2005GL024476
  • Dijkstra, H.A. and Ghil, M., 2005. Low‐frequency variability of the large‐scale ocean circulation: a dynamical systems approach. Reviews of Geophysics, 43 (3). doi:10.1029/2002RG000122
  • Ellaway, P.H., 1978. Cumulative sum technique and its application to the analysis of peristimulus time histograms. Electroencephalography and Clinical Neurophysiology, 45, 302–304. doi:10.1016/0013-4694(78)90017-2
  • Eltahir, E.A., 1996. El Niño and the natural variability in the flow of the Nile River. Water Resources Research, 32 (1), 131–137. doi:10.1029/95WR02968
  • Enfield, D.B., Mestas‐Nuñez, A.M., and Trimble, P.J., 2001. The Atlantic multidecadal oscillation and its relation to rainfall and river flows in the continental US. Geophysical Research Letters, 28 (10), 2077–2080. doi:10.1029/2000GL012745
  • Feller, W., 1951. The asymptotic distribution of the range of sums of independent random variables. Annals Mathematical Statistics, 22, 427–432. doi:10.1214/aoms/1177729589
  • Fiering, M.B., 1967. Streamflow synthesis. Cambridge, MA: Harvard University Press.
  • Fraedrich, K., 2002. Fickian diffusion and Newtonian cooling: a concept for noise induced climate variability with long-term memory? Stochastics and Dynamics, 2 (3), 403–412. doi:10.1142/S0219493702000492
  • Fraedrich, K. and Blender, R., 2003. Scaling of atmosphere and ocean temperature correlations in observations and climate models. Physical Review Letters, 90 (10), 108501. doi:10.1103/PhysRevLett.90.108501
  • Fraedrich, K., Blender, R., and Zhu, X., 2009. Continuum climate variability: long-term memory, scaling, and 1/f-noise. International Journal of Modern Physics B, 23 (28–29), 5403–5416. doi:10.1142/S0217979209063729
  • Fraedrich, K., Luksch, U., and Blender, R., 2004. 1∕f model for long-time memory of the ocean surface temperature. Physical Review E, 70 (3), 037301. doi:10.1103/PhysRevE.70.037301
  • Franzke, C., 2010. Long-range dependence and climate noise characteristics of Antarctic temperature data. Journal of Climate, 23, 6074–6081. doi:10.1175/2010JCLI3654.1
  • Frost, V.S. and Melamed, B., 1994. Traffic modelling for telecommunications networks. Communications Magazine, IEEE, 32 (3), 70–81. doi:10.1017/S0022112062000518
  • Garcia, L.E., Dawdy, D.R., and Mejia, J.M., 1972. Long memory monthly streamflow simulation by a broken line model. Water Resources Research, 8 (4), 1100–1105. doi:10.1029/WR008i004p01100
  • Ghil, M. and Childress, S., 1987. Topics in geophysical fluid dynamics: atmospheric dynamics, dynamo theory and climate dynamics. New York: Springer, 480 pp.
  • Granger, C.W., 1980. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 14 (2), 227–238. doi:10.1016/0304-4076(80)90092-5
  • Granger, C.W. and Joyeux, R., 1980. An introduction to long‐memory time series models and fractional differencing. Journal of Time Series Analysis, 1 (1), 15–29. doi:10.1111/j.1467-9892.1980.tb00297.x
  • Greene, M.T. and Fielitz, B.D., 1977. Long-term dependence in common stock returns. Journal of Financial Economics, 4 (3), 339–349. doi:10.1016/0304-405X(77)90006-X
  • Halley, J.M., 1996. Ecology, evolution and 1f-noise. Trends in Ecology and Evolution, 11 (1), 33–37. doi:10.1016/0169-5347(96)81067-6
  • Hartmann, D.L., et al., 2013. Observations: atmosphere and surface. In: T.F. Stocker, et al., eds. Climate change 2013: the physical science basis. Contribution of working group I to the fifth assessment report of the intergovernmental panel on climate change. Cambridge, United Kingdom: Cambridge University Press.
  • Hasselman, K., 1976. Stochastic climate variability. Tellus, 28, 473–485.
  • Hereford, R., Webb, R.H., and Graham, S., 2002. Precipitation history of the Colorado Plateau region, 1900–2000 (p. 4). U.S. Geological Survey Fact Sheet 119-02. Reston, VA: U.S. Geological Survey, 4 pp.
  • Hipel, K.W. and McLeod, A.I., 1978a. Preservation of the rescaled adjusted range: 3. Fractional Gaussian noise algorithms. Water Resources Research, 14 (3), 509–516. doi:10.1029/WR014i003p00509
  • Hipel, K.W. and McLeod, A.I., 1978b. Preservation of the rescaled adjusted range: 2. Simulation studies using Box‐Jenkins Models. Water Resources Research, 14 (3), 509–516. doi:10.1029/WR014i003p00509
  • Hipel, K.W., McLeod, A.I., and Lennox, W.C., 1977. Advances in Box‐Jenkins modeling: 1. Model construction. Water Resources Research, 13 (3), 567–575. doi:10.1029/WR013i003p00567
  • Hosking, J.R.M., 1981. Fractional differencing. Biometrika, 68 (1), 165–176. doi:10.1093/biomet/68.1.165
  • Hosking, J.R.M., 1984. Modeling persistence in hydrological time series using fractional differencing. Water Resources Researcher, 20 (12), 1898–1908. doi:10.1029/WR020i012p01898
  • Hurrell, J.W. and Van Loon, H., 1997. Decadal variations in climate associated with the North Atlantic Oscillation. Climatic change at high elevation sites. Netherlands: Springer, 36 301–306.
  • Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Transactions of the American Social Civil Engineering, 116, 770–808.
  • Hurst, H.E., 1956. Methods of using long-term storage in reservoirs: I. Proceedings Institution of Civil Engineers, 5, 519–543.
  • Hurst, H.E., 1957. A suggested statistical model of some time series which occur in nature. Nature, 180, 494. doi:10.1038/180494a0
  • Huybers, P. and Curry, W., 2006. Links between annual, Milankovitch and continuum temperature variability. Nature, 441 (7091), 329–332. doi:10.1038/nature04745
  • IPCC, 2013. Summary for policymakers. In: T.F. Stocker, et al., eds. Climate change 2013: the physical science basis. Contribution of working group I to the fifth assessment report of the intergovernmental panel on climate change. Cambridge, United Kingdom: Cambridge University Press.
  • Jiang, T., et al., 2005. Yangtze Delta floods and droughts of the last millennium: Abrupt changes and long term memory. Theoretical and Applied Climatology, 82 (3–4), 131–141. doi:10.1007/s00704-005-0125-4
  • Jones, P.D., et al., 1998. Millennial temperature reconstructions. Boulder, CO: IGBP PAGES/World Data Center-A for Paleoclimatology Data Contribution Series #1998-039, NOAA/NGDC, Paleoclimatology Program.
  • Kantelhardt, J.W., et al., 2006. Long‐term persistence and multifractality of precipitation and river runoff records. Journal of Geophysical Research: Atmospheres (1984–2012), 111 (D1). doi:10.1029/2005JD005881
  • Klemeš, V., 1974. The Hurst phenomenon: a puzzle? Water Resources Researcher, 10 (4), 675–688. doi:10.1029/WR010i004p00675
  • Klemeš, V., 1978. Physically based stochastic hydrologic analysis. Advances in Hydroscience, 11, 285–355.
  • Kobayashi, M. and Musha, T., 1982. 1/f fluctuation of heartbeat period. IEEE Transactions on Biomedical Engineering BME, 29, 456–457. doi:10.1109/TBME.1982.324972
  • Kolmogorov, A.N., 1940. Wienersche Spiralen und einige andere interessante Kurven in Hilbertschen Raum. Dokl Akad Nauk URSS, 26, 115–118.
  • Kolmogorov, A.N., 1962. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. Journal of Fluid Mechanics, 13 (01), 82–85. doi:10.1017/S0022112062000518
  • Koscielny-Bunde, E., et al., 1998. Indication of a universal persistence law governing atmospheric variability. Physical Review Letters, 81 (3), 729. doi:10.1103/PhysRevLett.81.729
  • Koutsoyiannis, D., 2002. The Hurst phenomenon and fractional Gaussian noise made easy. Hydrological Sciences Journal, 47 (4), 573–595. doi:10.1080/02626660209492961
  • Koutsoyiannis, D., 2003. Climate change, the Hurst phenomenon, and hydrological statistics. Hydrological Sciences Journal, 48, 3–24. doi:10.1623/hysj.48.1.3.43481
  • Koutsoyiannis, D., 2006a. Nonstationarity versus scaling in hydrology. Journal of Hydrology, 324 (1–4), 239–254. doi:10.1016/j.jhydrol.2005.09.022
  • Koutsoyiannis, D., 2006b. A toy model of climatic variability with scaling behaviour. Journal of Hydrology, 322 (1–4), 25–48. doi:10.1016/j.jhydrol.2005.02.030
  • Koutsoyiannis, D., 2011. Hurst-Kolmogorov dynamics and uncertainty. JAWRA Journal of the American Water Resources Association, 47, 481–495. doi:10.1111/j.1752-1688.2011.00543.x
  • Koutsoyiannis, D., 2013. Hydrology and change. Hydrological Sciences Journal, 58 (6), 1177–1197. doi:10.1080/02626667.2013.804626
  • Koutsoyiannis, D., 2014. Entropy: from thermodynamics to hydrology. Entropy, 16 (3), 1287–1314. doi:10.3390/e16031287
  • Koutsoyiannis, D., Efstratiadis, A., and Georgakakos, K.P., 2007. Uncertainty assessment of future hydroclimatic predictions: a comparison of probabilistic and scenario-based approaches. Journal of Hydrometeorology, 8 (3), 261–281
  • Koutsoyiannis, D. and Langousis, A., 2011. Precipitation. In: P. Wilderer and S. Uhlenbrook, Eds. Treatise on water science. Vol. 2. Oxford: Academic Press, 27–78.
  • Koutsoyiannis, D. and Montanari, A., 2007. Statistical analysis of hydroclimatic time series: uncertainty and insights. Water Resources Research, 43 (5), W05429. doi:10.1029/2006WR005592
  • Koutsoyiannis, D. and Montanari, A., 2015. Negligent killing of scientific concepts: the stationarity case. Hydrological Sciences Journal, 60, 1174–1183. doi:10.1080/02626667.2014.959959
  • Koutsoyiannis, D. and Papalexiou, S.M., 2016. Extreme rainfall: global perspective, chapter 75. In: V. Singh, eds. Chow’s handbook of applied hydrology, 2nd ed. New York: McGRAW-HILL Professional.
  • Kraus, E.B., 1956. Secular changes of tropical rainfall regimes. Secular variations of east‐coast rainfall regimes. Quarterly Journal of the Royal Meteorological Society, 82 (353), 358–361. doi:10.1002/(ISSN)1477-870X
  • Lamb, H.H., 1965. Discussion of H.E. Hurst (1965): a method of simulating time series occurring in nature”. Medmenham: Proc. Reser. Yield Symp., Water Resources Association, D1.7–D1.8.
  • Lamb, H.H., 1966. Climate in the 1960’s. The Geographical Journal, 132 (2), 183–212. doi:10.2307/1792334
  • Langbein, W.B., 1956. Discussion of Hurst (1956). Proceedings of Institution of Civil Engineers, 5 (5), 565.
  • Leith, C.E., 1973. The standard error of time-average estimates of climatic means. Journal of Applied Meteorology, 12 (6), 1066–1069. doi:10.1175/1520-0450(1973)012<1066:TSEOTA>2.0.CO;2
  • Leland, W.E., et al., 1993. On the self-similar nature of Ethernet traffic. ACM SIGCOMM Computer Communication Review, 23 (4), 183–193. doi:10.1145/167954
  • Leland, W.E., et al., 1994. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking, 2, 1–15. doi:10.1109/90.282603
  • Lennartz, S. and Bunde, A., 2009. Trend evaluation in records with long-term memory: application to global warming. Geophysical Researcher Letters, 36 (L16706). doi:10.1029/2009GL039516
  • Lins, H.F. and Cohn, T.A., 2011. Stationarity: wanted dead or alive? JAWRA Journal of the American Water Resources Association, 47 (3), 475–480. doi:10.1111/j.1752-1688.2011.00542.x
  • Lloyd, E.H., 1967. Stochastic reservoir theory. In: V.T. Chow ed. Advance hydroscience. New York: Academic Press Inc., vol. 4, 281–339.
  • Lo, A.W., 1991. Long-term memory in stock market prices. Econometrica, 59, 1279–1313. doi:10.2307/2938368
  • Magi, A., et al., 2010. A shifting level model algorithm that identifies aberrations in array-CGH data. Biostatistics, 11 (2), 265–280. doi:10.1093/biostatistics/kxp051
  • Mandelbrot, B.B., 1963. The variation of speculative prices. Journal of Business, 38, 394, 419.
  • Mandelbrot, B.B., 1965. Une classe de processus stochastiques homothétiques a soi: application à la loi climatoloique de H. E. Hurst. C R Academic Sciences Paris, 260, 3274–3276.
  • Mandelbrot, B.B., 1966. Forecasts of future prices, unbiased markets and Martingale models. The Journal of Business, 39, 242–255. doi:10.1086/jb.1966.39.issue-S1
  • Mandelbrot, B.B., 1967. The variation of some other speculative prices. The Journal of Business, 40, 393–413. doi:10.1086/jb.1967.40.issue-4
  • Mandelbrot, B.B., 1971. A fast fractional Gaussian noise generator. Water Resources Research, 7 (3), 543–553. doi:10.1029/WR007i003p00543
  • Mandelbrot, B.B., 1977. The Fractal geometry of nature. New York: W. H Freeman, 468 pp.
  • Mandelbrot, B.B. and Van Ness, J.W., 1968. Fractional Brownian motions, fractional noises and applications. SIAM Reviews, 10 (4), 422–437. doi:10.1137/1010093
  • Mandelbrot, B.B. and Wallis, J.R., 1968. Noah, Joseph, and operational hydrology. Water Resources Researcher, 4 (5), 909–918. doi:10.1029/WR004i005p00909
  • Mandelbrot, B.B. and Wallis, J.R., 1969a. Computer experiments with fractional Gaussian noises: part 1, rescaled ranges and spectra. Water Resources Research, 5 (1), 228–241. doi:10.1029/WR005i001p00228
  • Mandelbrot, B.B. and Wallis, J.R., 1969b. Computer experiments with fractional Gaussian noises: part 2, rescaled ranges and spectra. Water Resources Research, 5 (1), 242–259. doi:10.1029/WR005i001p00242
  • Mandelbrot, B.B. and Wallis, J.R., 1969c. Computer experiments with fractional Gaussian noises: mathematical appendix. Water Resources Research, 5 (1), 260–267. doi:10.1029/WR005i001p00260
  • Mandelbrot, B.B. and Wallis, J.R., 1969d. Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence. Water Resources Research, 5 (5), 967–988. doi:10.1029/WR005i005p00967
  • Mandelbrot, B.B. and Wallis, J.R., 1969e. Some long‐run properties of geophysical records. Water Resources Researcher, 5 (2), 321–340. doi:10.1029/WR005i002p00321
  • Mann, M.E., 2011. On long range dependence in global surface temperature series. Climatic Change, 107, 267–276. doi:10.1007/s10584-010-9998-z
  • Mantua, N.J. and Hare, S.R., 2002. The Pacific decadal oscillation. Journal of Oceanography, 58 (1), 35–44. doi:10.1023/A:1015820616384
  • Markonis, Y. and Koutsoyiannis, D., 2013. 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
  • Matalas, N.C. and Huzzen, C.S., 1967. A property of the range of partial sums. Paper Presented at the International Hydrology Symposium, 4, 252.
  • Matalas, N.C. and Wallis, J.R., 1971. Statistical properties of multivariate fractional noise processes. Water Resources Research, 7 (6), 1460–1468. doi:10.1029/WR007i006p01460
  • Mejia, J.M., Rodriguez‐Iturbe, I., and Dawdy, D.R., 1972. Streamflow simulation: 2. The broken line process as a potential model for hydrologic simulation. Water Resources Research, 8 (4), 931–941. doi:10.1029/WR008i004p00931
  • Mesa, O.J., Gupta, V.K., and O’Connell, P.E., 2012. Dynamical system exploration of the Hurst phenomenon in simple climate models. In: A.S. Sharma, et al., Eds. Extreme events and natural hazards: the complexity perspective. Washington, DC: American Geophysical Union, 209–229.
  • Meyers, S.R. and Hinnov, L.A., 2010. Northern hemisphere glaciation and the evolution of Plio‐Pleistocene climate noise. Paleoceanography, 25 (3), PA3207. doi:10.1029/2009PA001834
  • Mills, T.C., 2010. ‘Skinning a cat’: alternative models of representing temperature trends. Climatic Change, 101, 415–426. doi:10.1007/s10584-010-9801-1
  • Milly, P.C.D., et al., 2008. Stationarity is dead: whither water management? Science, 319, 573–574. doi:10.1126/science.1151915
  • Montanari, A., 2003. Long-range dependence in hydrology. In: P. Doukhan, G. Oppenheim, and M. Taqqu, eds. Theory and applications of long-range dependence. Boston: Birkhauser, 461–472.
  • Montanari, A. and Koutsoyiannis, D., 2014. Modeling and mitigating natural hazards: stationarity is immortal!. Water Resources Research, 50 (12), 9748–9756. doi:10.1002/2014WR016092
  • Montanari, A., Rosso, R., and Taqqu, M.S., 1996. Some long-run properties of rainfall records in Italy. Journal of Geophysical Research: Atmospheres, 101 (D23), 29431–29438. doi:10.1029/96JD02512
  • Montanari, A., Rosso, R., and Taqqu, M.S., 1997. Fractionally differenced ARIMA models applied to hydrologic time series: identification, estimation, and simulation. Water Resources Research, 33 (5), 1035–1044. doi:10.1029/97WR00043
  • Moran, P.A., 1964. On the range of cumulative sums. Annals of the Institute of Statistical Mathematics, 16 (1), 109–112. doi:10.1007/BF02868565
  • Moran, P.A.P., 1959. The theory of storage. London: Methuen.
  • Mudelsee, M., 2007. Long memory of rivers from spatial aggregation. Water Resources Research, 43 (1), W01202. doi:10.1029/2006WR005721
  • Nagatani, T., 1993. Power-law distribution and 1/f noise of waiting time near traffic-jam threshold. Journal of the Physical Society of Japan, 62 (8), 2533–2536. doi:10.1143/JPSJ.62.2533
  • National Research Council, 1991. Opportunities in the hydrologic sciences, 21. Washington, DC: National Academy Press.
  • O’Connell, P.E., 1974a. A simple stochastic modelling of Hurst’s Law. In: T. Ciriani, U. Maione, and J.R. Wallis, eds., Proceeding of the international symposium on mathematical models in hydrology. Warsaw: IAHS Publ. No. 100, 169–187.
  • O’Connell, P.E. 1974b. Stochastic Modelling of Long-term Persistence in Streamflow Sequences. Thesis (PhD). Imperial College, University of London.
  • O’Connell, P.E., 1976. Discussion of ‘Skew inputs and the Hurst effect’ by A. A. Anis and E. H. Lloyd. Journal of Hydrology, 31, 85–191.
  • O’Connell, P.E., 1977. ARIMA models in synthetic hydrology. In: Proceeding of the workshop on mathematical models for surface water hydrology. IBM Scientific Centre, Pisa: John Wiley and Sons, 51–68.
  • Paillard, D., 2001. Glacial cycles: toward a new paradigm. Reviews of Geophysics, 39 (3), 325–346. doi:10.1029/2000RG000091
  • Papoulis, A., 1991. Probability, random variables, and stochastic processes. New York: McGraw-Hill, 666pp.
  • Peng, C.-K., et al., 1992. Long-range correlations in nucleotide sequences. Nature, 356, 168–170. doi:10.1038/356168a0
  • Peng, C.K., et al., 1994. Mosaic organization of DNA nucleotides. Physical Review E, 49 (2), 1685. doi:10.1103/PhysRevE.49.1685
  • Piper, B.S., Plinston, D.T., and Sutcliffe, J.V., 1986. The water balance of Lake Victoria. Hydrological Sciences Journal, 31, 25–37. doi:10.1080/02626668609491025
  • Potter, K.W., 1975. Comment on ‘The Hurst phenomenon: a puzzle?’ by V. Klemeš. Water Resources Research, 11 (2), 373–374. doi:10.1029/WR011i002p00373
  • Potter, K.W., 1979. Annual precipitation in the northeast United States: long memory, short memory, or no memory? Water Resources Research, 15 (2), 340–346. doi:10.1029/WR015i002p00340
  • Rial, J.A., et al., 2004. Nonlinearities, feedbacks, and critical thresholds within the earth’s climate system. Climatic Change, 65, 11–38. doi:10.1023/B:CLIM.0000037493.89489.3f
  • Rocheta, E., et al., 2014. How well do general circulation models represent low‐frequency rainfall variability? Water Resources Research, 50 (3), 2108–2123. doi:10.1002/2012WR013085
  • Rodriguez‐Iturbe, I., Mejia, J.M., and Dawdy, D.R., 1972. Streamflow simulation: 1. A new look at Markovian models, fractional Gaussian noise, and crossing theory. Water Resources Research, 8 (4), 921–930. doi:10.1029/WR008i004p00921
  • Ruzmaikin, A., Feynman, J., and Robinson, P., 1994. Long-term persistence of solar activity. Sol Physical, 149, 395–403. doi:10.1007/BF00690625
  • Rybski, D., et al., 2006. Long‐term persistence in climate and the detection problem. Geophysical Research Letters, 33 (6). doi:10.1029/2005GL025591
  • Sadler, P.M., 1981. Sediment accumulation rates and the completeness of stratigraphic sections. Journal of Geology, 89 (5), 569–584. doi:10.1086/628623
  • Salas, J.D. and Boes, D.C., 1980. Shifting level modelling of hydrologic series. Advances in Water Resources, 3, 59–63. doi:10.1016/0309-1708(80)90028-7
  • Salas, J.D., et al., 1979. Hurst phenomenon as a pre-asymptotic behavior. Journal of Hydrology, 44 (1–2), 1–15. doi:10.1016/0022-1694(79)90143-4
  • Salas, J.D., Obeysekera, J.B., and Boes, D.C., 1981. Modeling of the equatorial lakes outflows. In: V.P. Singh, ed., Statistical analysis of rainfall and runoff, proceedings of the international symp. on rainfall-runoff modeling. Littleton, CO: Water Resources Publications, WRP, 431–440.
  • Sene, K.J. and Plinston, D.T., 1994. A review and update of the hydrology of Lake Victoria in East Africa. Hydrological Sciences Journal, 39 (1), 47–63. doi:10.1080/02626669409492719
  • Solari, M.E. and Anis, A.A., 1957. The mean and variance of the maximum of the adjusted partial sums of a finite number of independent normal variates. The Annals of Mathematical Statistics, 28 (3), 706–716.
  • Srokosz, M., et al., 2012. Past, present, and future changes in the Atlantic meridional overturning circulation. Bulletin of the American Meteorological Society, 93 (11), 1663–1676. doi:10.1175/BAMS-D-11-00151.1
  • Sutcliffe, J.V., et al., 2015. Harold Edwin Hurst: the Nile and Egypt, past and future. Hydrological Sciences Journal, (this issue). doi:10.1080/02626667.2015.1019508
  • Sutcliffe, J.V. and Parks, Y.P., 1999. The hydrology of the Nile. Wallingford, UK: IAHS Spec. Publ. No. 5, IAHS Press.
  • Sveinsson, O.G.B., et al., 2003. Modeling the dynamics of long-term variability of hydroclimatic processes. Journal of Hydrometeorology, 4, 489–505. doi:10.1175/1525-7541(2003)004<0489:MTDOLV>2.0.CO;2
  • Todini, E. and O’Connell, P.E., 1979. Hydrological simulation of Lake Nasser. Volume I. Analysis and results. Pisa: IBM Italy Scientific Centres/Institute of Hydrology.
  • Tung, -K.-K. and Zhou, J., 2013. Using data to attribute episodes of warming and cooling in instrumental records. Proceedings of the National Academy of Sciences, 110, 2058–2063. doi:10.1073/pasa:.1212471110
  • USGS, 2004. Climatic fluctuations, drought, and flow in the Colorado River Basin. USGS Fact Sheet 2004-3062 [Internet]. Reston, VA: USGS. Available from http://pubs.usgs.gov/fs/2004/3062
  • U.S. Water Resources Council, 1981. Guidelines for determining flood flow frequency, Bulletin 17-B of the Hydrology Subcommittee. Reston, VA: U.S. Geological Survey, 183 pp.
  • U.S. Water Resources Council, 1981. Guidelines for determining flood flow frequency, Bulletin 17-B of the Hydrology Subcommittee. Reston, VA: U.S. Geological Survey, 183 pp.
  • Van Vliet, K.M., Van Der Ziel, A., and Schmidt, R.R., 1980. Temperature‐fluctuation noise of thin films supported by a substrate. Journal of Applied Physics, 51 (6), 2947–2956. doi:10.1063/1.328104
  • Vogel, R.M., Tsai, Y., and Limbrunne, J.F., 1998. The regional persistence and variability of annual streamflow in the United States. Water Resources Research, 34 (12), 3445–3459. doi:10.1029/98WR02523
  • Voss, R.F. and Clarke, J., 1975. “1/f noise” in music and speech. Nature, 258, 317–318. doi:10.1038/258317a0
  • Voss, R.F. and Clarke, J., 1976. Flicker (1/f) noise: equilibrium temperature and resistance fluctuations. Physical Review B, 13 (2), 556–573. doi:10.1103/PhysRevB.13.556
  • Wallis, J.R. and O’Connell, P.E., 1973. Firm reservoir yield—how reliable are historic hydrological records? Hydrological Sciences Journal, 18 (3), 347–365. doi:10.1080/02626667309494046
  • Wang, C. and Zhang, L., 2013. Multidecadal ocean temperature and salinity variability in the tropical North Atlantic: linking with the AMO, AMOC, and subtropical cell. Journal of Climate, 26 (16), 6137–6162. doi:10.1175/JCLI-D-12-00721.1
  • Wu, Z., et al., 2011. On the time varying trend in global-mean surface temperature. Climate Dynamics, 37, 759–773. doi:10.1007/s00382-011-1128-8
  • Zhang, Y., Wallace, J.M., and Battisti, D.S., 1997. ENSO-like interdecadal variability: 1900-93. Journal of Climate, 10 (5), 1004–1020. doi:10.1175/1520-0442(1997)010<1004:ELIV>2.0.CO;2
  • Zhou, J. and Tung, -K.-K., 2013. Deducing multidecadal anthropogenic global warming trends using multiple regression analysis. Journal Atmospheric Sciences, 70, 3–8. doi:10.1175/JAS-D-12-0208.1
  • Zorita, E., Stocker, T.F., and von Storch, H., 2008. How unusual is the recent series of warm years? Geophysical Researcher Letters, 35 (L24706). doi:10.1029/2008GL036228

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.