The influence of non-stationarity in extreme hydrological events on flood frequency estimation

  • 1 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia.
  • 2 Vienna University of Technology, Institute of Hydraulic Engineering and Water Resources Management, Karlsplatz 13/222, A-1040 Vienna, Austria.

Abstract

Substantial evidence shows that the frequency of hydrological extremes has been changing and is likely to continue to change in the near future. Non-stationary models for flood frequency analyses are one method of accounting for these changes in estimating design values. The objective of the present study is to compare four models in terms of goodness of fit, their uncertainties, the parameter estimation methods and the implications for estimating flood quantiles. Stationary and non-stationary models using the GEV distribution were considered, with parameters dependent on time and on annual precipitation. Furthermore, in order to study the influence of the parameter estimation approach on the results, the maximum likelihood (MLE) and Bayesian Monte Carlo Markov chain (MCMC) methods were compared. The methods were tested for two gauging stations in Slovenia that exhibit significantly increasing trends in annual maximum (AM) discharge series. The comparison of the models suggests that the stationary model tends to underestimate flood quantiles relative to the non-stationary models in recent years. The model with annual precipitation as a covariate exhibits the best goodness-of-fit performance. For a 10% increase in annual precipitation, the 10-year flood increases by 8%. Use of the model for design purposes requires scenarios of future annual precipitation. It is argued that these may be obtained more reliably than scenarios of extreme event precipitation which makes the proposed model more practically useful than alternative models.

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  • Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 6, 716–723.

  • ARSO, 2010. Hydrological report on the floods in days, between 23rd and 27th of December 2010. MOP ARSO, Ljubljana, 1–14. (In Slovenian.)

  • ARSO, 2012. Hydrological report on floods in days, between 4th and 6th of November 2012. MOP ARSO, Ljubljana, 1–15. (In Slovenian.)

  • ARSO, 2015a. http://vode.arso.gov.si/hidarhiv/pov_arhiv_tab.php. Accessed: 9.9.2015.

  • ARSO, 2015b. http://meteo.arso.gov.si/met/sl/app/webmet/. Accessed: 16.9.2015.

  • Bates, B.C., Chandler, R.E., Charles, S.P., Campbell, E.P., 2010. Assessment of apparent nonstationarity in time series of annual inflow, daily precipitation, and atmospheric circulation indices: A case study from southwest Western Australia. Water Resources Resource, 46, 1–15.

  • Bezak, N., Brilly, M., Šraj, M., 2015a. Flood frequency analyses, statistical trends and seasonality analyses of discharge data: a case study of the Litija station on the Sava River. Journal of Flood Risk Management. doi: 10.1111/jfr3.12118.

  • Bezak, N., Horvat, A., Šraj, M., 2015b. Analysis of flood events in Slovenian streams. Journal of Hydrology and Hydromechanics, 63, 134–144.

  • Blöschl, G., Montanari, A., 2010. Climate change impacts—throwing the dice? Hydrological Processes, 24, 374–381.

  • Blöschl, G. et al., 2015. Increasing river floods: fiction or reality? WIREs Water. doi: 10.1002/wat2.1079.

  • Bormann, H., Pinter, N., Elfert, S., 2011. Hydrological signatures of flood trends on German rivers: flood frequencies, flood heights and specific stages. Journal of Hydrology, 404, 1–2, 50–66.

  • Cheng, L., AghaKouchak, A., Gilleland, E., Katz, R.W., 2014. Non-stationary extreme value analysis in a changing climate. Climatic Change, 127, 353–369.

  • Coles, S., 2001. An Introduction to Statistical Modeling of Extreme Values. Springer, London.

  • Cunderlik, J.M., Ouarda, T., 2009. Trends in the timing and magnitude of floods in Canada. Journal of Hydrology, 375, 3–4, 471–480.

  • Delgado, J.M., Apel, H., Merz, B., 2010. Flood trends and variability in the Mekong river. Hydrology and Earth System Sciences, 14, 3, 407–418.

  • Delgado, J.M., Merz, B., Apel, H., 2014. Projecting flood hazard under climate change: an alternative approach to model chains. Natural Hazards and Earth System Science, 14, 6, 1579–1589.

  • Douglas, E.M., Vogel, R.M., Kroll, C.N., 2000. Trends in floods and low flows in the United States: impact of spatial correlation. Journal of Hydrology, 240, 1–2, 90–105.

  • El Adlouni, S., Ouarda, T.B.M.J., Zhang, X., Roy, R., Bobee, B., 2007. Generalized maximum likelihood estimators for the non stationary generalized extreme value model. Water Resources Research, 43, W03410.

  • Finch, W.H., French, B.F., 2012. Parameter estimation with mixture item response theory models: A Monte Carlo comparison of maximum likelihood and Bayesian methods. Journal of Modern Applied Statistical Methods, 11, 1, 167–178.

  • Frantar, P., Hrvatin, M., 2005. Discharge regimes in Slovenia from 1971 to 2000. Geografski vestnik, 77, 115–127. (In Slovenian.)

  • Frantar, P., Nadbath, M., Ulaga, F., 2008. Water balance impact factors. In: Frantar, P. (Ed.): Water Balance of Slovenia 1971–2000. MOP ARSO, Ljubljana, pp. 15–27.

  • Gaál, L., Szolgay, J., Kohnová, S., Parajka, J., Merz, R., Viglione, A., Blöschl, G., 2012. Flood timescales: Understanding the interplay of climate and catchment processes through comparative hydrology. Water Resources Research, 48, W04511.

  • Gilleland, E., Katz, R.W., 2011. New software to analyze how extremes change over time. Eos, 92, 2, 13–14.

  • Gilroy, K.L., McCuen, R.H., 2012. A nonstationary flood frequency analysis method to adjust for future climate change and urbanization. Journal of Hydrology, 414–415, 40–48.

  • Groisman, P.Y., Knight, R.W., Easterling, D.R., Karl, T.R., Hegerl, G.C., Razuvaev, V.N., 2005. Trends in intense precipitation in the climate record. Journal of Climatology, 18, 1326–1350.

  • Gül, G., Aşıkoğlu, Ö., Gül, A., Gülçem Yaşoğlu, F., Benzeden, E., 2014. Nonstationarity in flood time series. Journal of Hydrologic Engineering, 19, 7, 1349–1360.

  • Hall, J. et al., 2014. Understanding flood regime changes in Europe: a state-of-the-art assessment. Hydrology and Earth System Sciences, 18, 7, 2735–2772.

  • Jones, P.D., New, M., Parker, D.E., Martin, S., Rigor, I.G., 1999. Surface air temperature and its changes over the past 150 years. Reviews of Geophysics, 37, 2, 173–199.

  • Katz, R.W., Parlange, M.B., Naveau, P., 2002. Statistics of extremes in hydrology. Advances in Water Resources, 25, 1287–1304.

  • Kendall, M.G., 1975. Multivariate Analysis. London, Griffin.

  • Khaliq, M.N., Ouarda, T.B.M.J., Ondo, J.C., Gachon, P., Bobee, B., 2006. Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: a review. Journal of Hydrology, 329, 3–4, 534–552.

  • Kjeldsen et al., 2014. Documentary evidence of past floods in Europe and their utility in flood frequency estimation. Journal of Hydrology, 517, 963–973.

  • Kobold, M., Ulaga, F., Trcek, R., Lalic, B., Sušnik, M., Polajnar, J., Robic, M., 2005. High waters in August 2005. MOP ARSO, Ljubljana, pp. 1–21. (In Slovenian.)

  • Kobold, M., Dolinar, M., Frantar, P., 2012. Changes of water regime due to the climate change and anthropogenic influences. In: Proc. The first conference on waters in Slovenia, 22.3.2012, Ljubljana, pp. 7–22. (In Slovenian.)

  • Kuczera, G., 1996. Correlated rating curve error in flood frequency inference. Water Resources Research, 32, 7, 2119–2127.

  • Kundzewicz, Z.W., Graczyk, D., Maurer, T., Pinskwar, I., Radziejewski, M., Svensson, C., Szwed, M., 2005. Trend detection in river flow series: 1. Annual maximum flow. Hydrological Sciences Journal, 50, 5, 797–810.

  • Labat, D., Godderis, Y., Probst, J.L., Guyot, J.L., 2004. Evidence for global runoff increase related to climate warming. Advances in Water Resources, 27, 6, 631–642.

  • Ljung, G.M., Box, G.E.P., 1978. On a measure of a lack of fit in time series models. Biometrika, 65, 2, 297–303.

  • Lopez, J., Frances, F., 2013. Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates. Hydrol. Earth Syst. Sci., 17, 3189–3203.

  • McLeod, A.I., 2011. Kendall: Kendall rank correlation and Mann-Kendall trend test. R package version 2.2. http://CRAN.R-project.org/package=Kendall.

  • Mediero et al., 2015. Identification of coherent flood regions across Europe by using the longest streamflow records. Journal of Hydrology, 528, 341–360.

  • Menih, M., Bezak, N., Šraj, M., 2015. The influence of the climate variability on the results of the flood frequency analyses: a case study of the Litija station on the Sava River. SZGG, Ljubljana, 23–34. (In Slovenian.)

  • Merz, B., Vorogushyn, S., Uhlemann, S., Delgado, J., Hundecha, Y., 2012. HESS Opinions: “More efforts and scientific rigour are needed to attribute trends in flood time series”. Hydrol. Earth Syst. Sci., 16, 1379–1387.

  • Milly, P.C.D., Betancourt, J., Falkenmark, M., Hirsch, R.M., Kundzewicz, Z.W., Lettenmaier, D.P., Stouffer, R.J., 2008. Stationarity is dead: Whither water management. Science, 319, 573–574.

  • Montanari, A., Koutsoyiannis, D., 2014. Modeling and mitigating natural hazards: Stationarity is immortal! Water Resources Research, 50, 12, 9748–9756.

  • Obeysekera, J., Salas, J.D., 2014. Quantifying the uncertanty of design floods under nonstationary conditions. Journal of Hydrologic Engineering, 19, 1438–1446.

  • Pachauri, R.K., Allen, M.R., Barros, V.R., Broome, J., Cramer, W., Christ, R., ... & van Vuuren, D., 2014. Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. IPCC, Geneva, Switzerland.

  • Perdigão, R.A.P., Blöschl, G., 2014. Spatiotemporal flood sensitivity to annual precipitation: Evidence for landscape-climate coevolution, Water Resour. Res., 50, 5492–5509.

  • Polajnar, J., 2007. High waters in Slovenia in 2006. Ujma, 21, 42–44. (In Slovenian.)

  • Prosdocimi, I., Kjeldsen, T.R., Svensson, C., 2014. Non-stationarity in annual and seasonal series of peak flow and precipitation in the UK. Nat. Hazards Earth Syst. Sci., 14, 1125–1144.

  • Prosdocimi, I., Kjeldsen, T.R., Miller, J.D., 2015. Detection and attribution of urbanization effect on flood extremes using nonstationary flood-frequency models. Water Resources Research, 51, 4244–4262.

  • R Core Team, 2013. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.

  • Robson, A.J., Jones, T.K., Reed, D.W., Bayliss, A.C., 1998. A study of national trend and variation in UK floods. International Journal of Climatology, 18, 2, 165–182.

  • Rosbjerg, D., Blöschl, G., Burn, D.H., Castellarin, A., Croke, B., DiBaldassarre, G., Iacobellis, V., Kjeldsen, T.R., Kuczera, G., Merz, R., Montanari, A., Morris, D., Ouarda, T.B.M.J., Ren, L., Rogger, M., Salinas, J.L, Toth, E., Viglione, A., 2013. Prediction of floods in ungauged basins. Chapter 9. In: Blöschl, G., Sivapalan, M., Wagener, T., Viglione, A., Savenije, H. (Eds.): Runoff Prediction in Ungauged Basins - Synthesis across Processes, Places and Scales. Cambridge University Press, Cambridge, UK, pp. 135–162.

  • Salas, J.D., Obeysekera, J., 2014. Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. Journal of Hydrologic Engineering, 19, 554–568.

  • Singh, J., Singh, T., Vittal, H., Karmakar, S., 2013. Nonstationary frequency estimation of flood extremes. In: Proc. of Hydro 2013 International, 4–6.12.2013, IT Madras, India, pp. 3–16.

  • Sivapalan, M., Blöschl, G., 2015. Time scale interactions and the coevolution of humans and water. Water Resour. Res., 51, 6988–7022.

  • Stahl, K., Hisdal, H., Hannaford, J., Tallaksen, L.M., van Lanen, H.A.J., Sauquet, E., Demuth, S., Fendekova, M., Jodar, J., 2010. Streamflow trends in Europe: evidence from a dataset of near-natural catchments. Hydrology and Earth System Sciences, 14, 12, 2367–2382.

  • Strupczewski, W.G., Singh, V.P., Feluch, W., 2001. Nonstationary approach to at – site flood frequency modelling I. Maximum likelihood estimation. Journal of Hydrology, 248, 123–142.

  • Viglione, A., Blöschl, G., 2009. On the role of storm duration in the mapping of rainfall to flood return periods. Hydrology and Earth System Sciences, 13, 205–216.

  • Viglione, A., Merz, R., Blöschl, G., 2009. On the role of the runoff coefficient in the mapping of rainfall to flood return periods. Hydrology and Earth System Sciences, 13, 5, 577–593.

  • Viglione, A., Merz, R., Salinas, J.L., Blöschl, G., 2013. Flood frequency hydrology: 3. A Bayesian analysis. Water Resources Research, 49, 675–692.

  • Villarini, G., Smith, J.A., Serinaldi, F., Bales, J., Bates, P.D., Krajewski, W.F., 2009. Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Advances in Water Resources, 32, 8, 1255–1266.

  • Vogel, R.M., Yaindl, C., Walter, M., 2011. Nonstationarity: Flood magnification and recurrence reduction factors in the United States. Journal of American Water Resources Association, 47, 464–474.

  • Wilby, R.L., Quinn, N.W., 2013. Reconstructing multi-decadal variations in fluvial flood risk using atmospheric circulation patterns. Journal of Hydrology, 487, 109–121.

  • Wobus, C., Lawson, M., Jones, R., Smith, J., Martinich, J., 2014. Estimating monetary damages from flooding in the United States under a changing climate. Journal of Flood Risk Management, 7, 217–229.

  • Yue, S., Pilon, P., Cavadias, G., 2002. Power of the Mann-Kendall and Spearman’s rho test for detecting monotonic trends in hydrological series. Journal of Hydrology, 259, 254–271.

  • Zhang, X.B., Harvey, K.D., Hogg, W.D., Yuzyk, T.R., 2001. Trends in Canadian streamflow. Water Resources Research, 37, 4, 987–998.

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