Nonstationarity in Flood Time Series
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 7
Abstract
Flood hazard and arising risks due to associated vulnerabilities still appear to be among the common problems in today’s hydrology in spite of highly motivated assessments and increasing knowledge and awareness as well as targeted measures for mitigation, preparedness, and emergency management. Beside the role of overall inaction, deficiencies in precautionary actions and presence of natural barriers and inaccurate or incomplete approaches in flood studies towards estimating flood magnitudes and frequencies are also assumed to have considerable impacts on limited control against the flood phenomenon. Prevalent claims about the invalidity of the stationarity assumption in hydrologic studies indicate any ignorance of nonstationarity as potential sources of ineffective flood assessments and the associated improper actions. The presented study investigates potential impacts and relative significance of observed trends on the magnitude and frequency of floods through comparisons performed over stationary and nonstationary flood frequency analyses. Results indicate slightly significant discrepancies between the estimates from both the stationary and nonstationary analyses by potentially pointing out to the arising needs for considering the nonstationarity in flood studies.
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Acknowledgments
The financial support provided by TÜBİTAK, The Scientific and Technological Research Council of Turkey, through the project numbered 110M375 is gratefully acknowledged.
References
Adamowski, K., and Bocci, C. (2001). “Geostatistical regional trend detection in river flow data.” Hydrol. Process., 15(18), 3331–3341.
Akaike, H. (1974). “A new look at the statistical model identification.” IEEE Trans. Autom. Control, 19(6), 716–723.
Baker, V. R., Webb, R. H., and House, P. K. (2001). “The scientific and societal value of paleoflood hydrology.” Ancient floods, modern hazards: Principles and applications of paleoflood hydrology, P. K. House, R. H. Webb, V. R. Baker, and D. R. Levish, eds., American Geophysical Union, Washington, DC.
Bartl, S., Schümberg, S., and Deutsch, M. (2009). “Revising time series of the Elbe river discharge for flood frequency determination at gauge Dresden.” Nat. Hazards Earth Syst. Sci., 9(6), 1805–1814.
Berger, J. O. (1985). “Statistical decision theory and Bayesian analysis.” Springer Series in Statistics, 2nd Ed., Springer, New York.
Cameron, D., Beven, K., and Naden, P. (2000). “Flood frequency estimation by continuous simulation under climate change (with uncertainty).” Hydrol. Earth Syst. Sci., 4(3), 393–405.
Cannon, A. J. (2010). “A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology.” Hydrol. Process., 24(6), 673–685.
Cannon, A. J. (2011). GEV conditional density estimation network, Package ‘GEVcdn’ v.1.0.3, 〈http://cran.r-project.org/web/packages/GEVcdn/〉 (Dec. 1, 2011).
Cayan, D. R., Redmond, K. T., and Riddle, L. G. (1999). “ENSO and hydrologic extremes in the western United States.” J. Clim., 12(9), 2881–2893.
Changnon, S. A., and Kunkel, K. E. (1995). “Climate-related fluctuation in Midwestern floods during 1921–1985.” J. Water Resour. Plann. Manage., 326–334.
Chow, V. T. (1964). “Statistical and probability analysis of hydrologic data, part I: Frequency analysis.” Handbook of applied hydrology, McGraw Hill, New York, 8.1–8.42.
Cigizoglu, H. K., Bayazit, M., and Onoz, B. (2005). “Trends in the maximum, mean, and low flows of Turkish rivers.”J. Hydrometeorol., 6(3), 280–290.
Coles, S. (2001). An introduction to statistical modeling of extreme values, Springer, London.
Cox, D. R., Isham, V. S., and Northrop, P. J. (2002). “Floods: Some probabilistic and statistical approaches.” Philos. Trans. R. Soc. London, Ser. A, 360(1796), 1389–1408.
Cunderlik, J. M., and Burn, D. H. (2002). “Local and regional trends in monthly maximum flows in southern British Columbia.” Can. Water Resour. J., 27(2), 191–212.
Cunderlik, J. M., and Burn, D. H. (2003). “Nonstationary pooled flood frequency analysis.” J. Hydrol., 276(1–4), 210–223.
Cunderlik, J. M., and Ouarda, T. B. M. J. (2006). “Regional flood-duration-frequency modeling in the changing environment.” J. Hydrol., 318(1–4), 276–291.
Douglas, E. M., Vogel, R. M., and Kroll, C. N. (2000). “Trends in floods and low flows in the United States: Impact of spatial correlation.” J. Hydrol., 240(1–2), 90–105.
El Adlouni, S., Ouarda, T. B. M. J., Zhang, X., Roy, R., and Bobée, B. (2007). “Generalized maximum likelihood estimators for the nonstationary generalized extreme value model.” Water Resour. Res., 43(3), W03410.
Fisher, R. A. (1929). “Moments and product moments of sampling distributions.” Proc. Londan Math. Soc., s2-30(1), 199–238.
Fujihara, Y., Tanaka, K., Watanabe, T., Nagano, T., and Kojiri, T. (2008). “Assessing the impacts of climate change on the water resources of the Seyhan River Basin in Turkey: Use of dynamically downscaled data for hydrologic simulations.” J. Hydrol., 353(1–2), 33–48.
Gardner, M. W., and Dorling, S. R. (1998). “Artificial neural networks (the multilayer perceptron)—A review of applications in the atmospheric sciences.” Atmos. Environ., 32(14–15), 2627–2636.
Gilroy, K. L., and McCuen, R. H. (2012). “A nonstationary flood frequency analysis method to adjust for future climate change and urbanization.” J. Hydrol., 414–415, 40–48.
Haan, C. T. (1977). Statistical methods in hydrology, Iowa State University Press, Ames, IA.
Hamed, K. H. (2008). “Trend detection in hydrologic data: The Mann–Kendall trend test under the scaling hypothesis.” J. Hydrol., 349(3–4), 350–363.
Hirabayashi, Y., Kanae, S., Emori, S., Oki, T., and Kimoto, M. (2008). “Global projections of changing risks of floods and droughts in a changing climate.” Hydrol. Sci. J., 53(4), 754–772.
Hirsch, R. M., and Ryberg, K. R. (2012). “Has the magnitude of floods across the USA changed with global levels?” Hydrolog. Sci. J., 57(1), 1–9.
Hosking, J. R. M. (1990). “L-moments: Analysis and estimation of distributions using linear combinations of order statistics.” J. R. Stat. Soc. Ser. B, 52(1), 105–124.
Hsieh, W. W., and Tang, B. (1998). “Applying neural network models to prediction and data analysis in meteorology and oceanography.” Bull. Amer. Meteor. Soc., 79(9), 1855–1870.
Hundecha, Y., St-Hilaire, A., Ouarda, T. B. M. J., and El-Adlouni, S. (2008). “A nonstationary extreme value analysis for the assessment of changes in extreme annual wind speed over the Gulf of St. Lawrence, Canada.” J. Appl. Meteorol. Climatol., 47(11), 2745–2759.
Hurvich, C. M., and Tsai, C. (1989). “Regression and time series model selection in small samples.” Biometrika, 76(2), 297–307.
Intergovernmental Panel for Climate Change (IPCC). (2001). Climate change 2001: Impacts, adaptation and vulnerability, Cambridge University Press, New York.
Intergovernmental Panel for Climate Change (IPCC). (2007). Climate change 2007: Working Group II report—Impacts, adaptation and vulnerability, Cambridge University Press, New York.
Jain, S., and Lall, U. (2001). “Floods in a changing climate: does the past represent the future?” Water Resour. Res., 37(12), 3193–3205.
Jenkinson, A. F. (1955). “The frequency distribution of the annula maximum (or minimum) of meteorological elements.” Q. J. R. Meteorolog. Soc., 81(348), 158–171.
Kendall, M. G. (1975). Rank correlation methods, Griffin, London.
Khaliq, M., Ouarda, T. B. M. J., Ondo, J.-C., Gachon, P., and Bobée, B. (2006). “Frequency analysis of a sequence of dependent and/or nonstationary hydrometeorological observations: A review.” J. Hydrol., 329(3–4), 534–552.
Kharin, V. V., and Zwiers, F. W. (2004). “Estimating extremes in transient climate change simulations.” J. Clim., 18(8), 1156–1173.
Kite, G. W. (1977). Frequency and risk analysis in hydrology, Water Resources Publications, Fort Collins, CO.
Kwon, H.-H., Brown, C., and Lall, U. (2008). “Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling.” Geophys. Res. Lett., 35(5), L05404.
Leclerc, M., and Ouarda, T. B. M. J. (2007). “Nonstationary regional flood frequency analysis at ungauged sites.” J. Hydrol., 343(3–4), 254–265.
Lins, H. F., and Slack, J. R. (1999). “Streamflow trends in the United States.” Geophys. Res. Lett., 26(2), 227–230.
Loukas, A., and Quick, M. C. (1996). “Effect of climate change on hydrologic regime of two climatically different watersheds.” J. Hydrol. Eng., 77–87.
Loukas, A., and Quick, M. C. (1999). “The effect of climate change on floods in British Columbia.” Nordic Hydrology, 30(3), 231–256.
Madsen, H., Lawrence, D., Lang, M., Martinkova, M., and Kjeldsen, T. R. (2013). A review of applied methods in Europe for flood-frequency analysis in a changing environment, Centre for Ecology & Hydrology (CEH), Wallingford, U.K.
Madsen, H., and Rosbjerg, D. (1997). “Generalized least squares and empirical Bayes estimation in regional partial duration series index-flood modeling.” Water Resour. Res., 33(4), 771–782.
Mann, H. B. (1945). “Non-parametric tests against trend.” Econometrica, 13(3), 245–259.
Martins, E. S., and Stedinger, J. R. (2000). “Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data.” Water Resour. Res., 36(3), 737–744.
McCuen, R. H. (2003). Modeling hydrologic change: Statistical methods, CRC Press LLC, Boca Raton, FL.
Met Office. (2011). Climate: Observations, projections and impacts—Turkey, Exeter, Devon, U.K.
Milly, P. C. D., et al. (2008). “Climate change—Stationarity is dead: Whither water management?” Science, 319(5863), 573–574.
Milly, P. C. D., Wetherald, R. T., Dunne, K. A., and Delworth, T. L. (2002). “Increasing risk of great floods in a changing climate.” Nature, 415(6871), 514–517.
Moriasi, D. N., Arnold, J. G., Van Liew, M. W., Bingner, R. L., Harmel, R. D., and Veith, T. L. (2007). “Model evaluation guidelines for systematic quantification of accuracy in watershed simulations.” Trans. ASABE, 50(3), 885–900.
Nguyen, V. T. V. (2002). “On modeling of extreme hydrologic processes.” Proc., Int. Workshop on Non-Structural Measures for Water Management Problems, UNESCO, Paris, 167–180.
Önöz, B., and Bayazıt, M. (1995). “Best-fit distributions of largest available flood samples.” J. Hydrol., 167(1–4), 195–208.
Önöz, B., and Bayazıt, M. (2003). “Power of the statistical tests for trend detection.” Turk. J. Eng. Environ. Sci., 27(4), 247–251.
Onuşluel, G., and Harmancıoğlu, N. (2002). “Su kaynaklı doğal afet: Taşkın.” Türkiye Mühendislik Haberleri, Su-II, TMMOB İnşaat Mühendisleri Odası, 421–422-423[47/2002], 131–132.
Ouarda, T. B. M. J., and El-Adlouni, S. (2011). “Bayesian nonstationary frequency analysis of hydrological variables.” J. Am. Water Resour. Assoc., 47(3), 496–505.
Raff, D. A., Pruitt, T., and Brekke, L. D. (2009). “A framework for assessing flood frequency based on climate projection information.” Hydrol. Earth Syst. Sci., 13(11), 2119–2136.
Rao, A. R., and Hamed, H. H. (2000). Flood frequency analysis, CRC Press, Boca Raton, FL.
R Core Team. (2014). “A language and environment for statistical computing.” R Foundation for Statistical Computing, Vienna, Austria, 〈http://www.R-project.org〉 (Apr. 15, 2014).
Reed, D. W., Jakob, D., and Robson, A. J. (1999). “Statistical procedures for flood frequency estimation.” Flood estimation handbook, Vol. 3, A. J. Robson and D. W. Reed, eds., Institute of Hydrology, Wallingford, U.K., 338.
Renard, B., et al. (2008). “Regional methods for trend detection: assessing field significance and regional consistency.” Water Resour. Res., 44(8), W08419.
Reynard, N., Crooks, S., Wilby, R., and Kay, A. (2004). “Climate change and flood frequency in the UK.” Proc., 39th Defra Flood and Coastal Management Conf., 11.1.1–11.1.12.
Robson, A. J., Jones, T. K., Reed, D. W., and Bayliss, A. C. (1998). “A study of national trend and variation in UK floods.” Int. J. Clim., 18(2), 165–182.
Salmi, T., Määttä, A., Anttila, P., Ruoho-Airola, T., and Amnell, T. (2002). “Detecting trends of annual values of atmospheric pollutants by the Mann-Kendall test and Sen’s slope estimates—The Excel template application MAKESENS.” Publications on Air Quality No. 31, Rep. code FMI-AQ-31, Finnish Meteorological Institute, Helsinki, Finland.
Schwarz, G. (1978). “Estimating the dimension of a model.” Ann. Stat., 6(2), 461–464.
Sen, P. K. (1968). “Estimates of the regression coefficient based on Kendall’s Tau.” J. Am. Stat. Assoc., 63(324), 1379–1389.
Singh, K. P. (1980). “Regional and sample skew values in flood frequency analysis of streams in Illinois.” Illinois State Water Survey, Champaign, IL.
Singh, V. P. (1987). Regional flood frequency analysis, D. Reidel Publishing, Dordrecht, Netherlands.
Singh, V. P., Wang, S. X., and Zhang, L. (2005). “Frequency analysis of nonidentically distributed hydrologic flood data.” J. Hydrol., 307(1–4), 175–195.
Smith, R. L. (1985). “Maximum likelihood estimation in a class of non-regular cases.” Biometrika, 72(1), 67–90.
Stedinger, J. R., Vogel, R. M., and Foufoula-Georgiou, E. (1993). “Frequency analysis of extreme events.” Chapter 18, Handbook of hydrology, D. R. Maidment, ed., Vol. II, McGraw-Hill, New York, 18.1–18.66.
Strupczewski, W. G., and Kaczmarek, Z. (2001). “Non stationary approach to at-site flood frequency modelling 2: Weighted least squares estimation.” J. Hydrol., 248(1–4), 143–151.
Strupczewski, W. G., Kochanek, K., Feluch, W., Bogdanowicz, E., and Singh, V. P. (2009). “On seasonal approach to nonstationary flood frequency analysis.” Phys. Chem. Earth , 34(10–12), 612–618.
Strupczewski, W. G., Singh, V. P., and Feluch, W. (2001a). “Non stationary approach to at-site flood frequency modelling 1: Maximum likelihood estimation.” J. Hydrol., 248(1–4), 123–142.
Strupczewski, W. G., Singh, V. P., and Mitosek, H. T. (2001b). “Non-stationary approach to at-site flood frequency modelling 3: Flood analysis of Polish rivers.” J. Hydrol., 248(1–4), 143–151.
Thiele, T. N. (1903). Theory of observations, Charles & Edwin Layton, London, 160.
Villarini, G., Smith, J. A., and Napolitano, F. (2010). “Nonstationary modeling of a long record of rainfall and temperature over Rome.” Adv. Water Resour., 33(10), 1256–1267.
Villarini, G., Smith, J. A., Serinaldi, F., Bales, J., Bates, P. D., and Krajewski, W. F. (2009). “Flood frequency analysis for nonstationary annual peak records in an urban drainage basin.” Adv. Water Resour., 32(8), 1255–1266.
Wang, Q. (1990). “Unbiased estimation of probability weighted moments and partial probability weighted moments from systematic and historical flood information and their application to estimating the GEV distribution.” J. Hydrol., 120(1–4), 115–124.
Wang, X. L., Trewin, B., Feng, Y., and Jones, D. (2013). “Historical changes in Australian temperature extremes as inferred from extreme value distribution analysis.” Geophys. Res. Lett., 40(3), 573–578.
Westmacott, J. R., and Burn, D. H. (1997). “Climate change effects on the hydrologic regime within the Churchill–Nelson River Basin.” J. Hydrol., 202(1–4), 263–279.
Wilks, D. S. (1993). “Comparison of three parameter probability distributions for representing annual extreme and partial duration precipitation series.” Water Resour. Res., 29(10), 3543–3549.
Yevjevich, V. (1972). Probability and statistics in hydrology, Water Resources Publications, Fort Collins, CO.
Zhang, X., Harvey, K. D., Hogg, W. D., and Yuzyk, T. R. (2001). “Trends in Canadian streamflow.” Water Resour. Res., 37(4), 987–998.
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Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 7 • July 2014
Pages: 1349 - 1360
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Mar 12, 2013
Accepted: Oct 15, 2013
Published online: Oct 17, 2013
Discussion open until: Mar 17, 2014
Published in print: Jul 1, 2014
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