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Non Stationary Analysis of Extreme Events

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Abstract

Traditional approaches to the analysis of extreme hydrological series are based on the stationarity assumption for the underlying processes, namely that the probability distribution of the hydrological variable does not change with time. Over the last decade however, a growing interest has arisen both from a scientific as well as engineering point of view, toward the development of tools able to cope with the apparent non stationary features (either natural or anthropogenic) observed in many hydrological processes. Though most of the works deal with extreme precipitation and floods, less attention has been devoted to modeling droughts under non stationarity paradigm. In the paper, a brief review of the available tools for modeling non stationary series is presented. An extension of such methodologies to drought lenght modeling is developed, taking into account the non stationary nature of the underlying series and/or of the threshold level used for drought definition. An example of application of the developed methods to four precipitation series in Sicily, Italy, exhibiting different degrees of trends is also presented.

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References

  • Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Pubblications, Inc., New York

    Google Scholar 

  • Agilan V, Umamahesh N (2017) Non-stationary rainfall intensity-duration-frequency relationship: a comparison between annual maximum and partial duration series. Water Resour Manag 31(6):1825–1841

    Article  Google Scholar 

  • Aissaoui-Fqayeh I, El-Adlouni S, Ouarda T, St-Hilaire A, et al. (2009) Non-stationary lognormal model development anf comparison with non-stationary gev model. Hydrol Sci J 54(6):1141–1156

    Article  Google Scholar 

  • Bonaccorso B, Peres D, Cancelliere A, Rossi G (2013) Large scale probabilistic drought characterization over europe. Water Resour Manag 27(6):1675–1692

    Article  Google Scholar 

  • Bonaccorso B, Peres D, Castano A, Cancelliere A (2015) Spi-based probabilistic analysis of drought areal extent in sicily. Water Resour Manag 29(2):459–470

    Article  Google Scholar 

  • Bowles D, James W, Kottegoda N (1987) Initial model choice: An operational comparison of stochastic streamflow models for drought. Water Resour Manag 1(1):3–15

    Article  Google Scholar 

  • Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting. Springer Verlag, New York

    Book  Google Scholar 

  • Cancelliere A, Salas JD (2004) Drought length properties for periodic-stochastic hydrologic data. Water Resour Res 40(2):

  • Cancelliere A, Salas JD (2010) Drought probabilities and return period for annual streamflows series. J Hydrol 391(1):77–89

    Article  Google Scholar 

  • Coles S, Bawa J, Trenner L, Dorazio P (2001) An introduction to statistical modeling of extreme values, vol 208. Springer,

  • Cooley D (2013) Return periods and return levels under climate change. Extremes in a Changing Climate, Springer, pp 97–114

  • Delgado J, Merz B, Apel H (2014) Projecting flood hazard under climate change: an alternative approach to model chains. Nat Hazards Earth Syst Sci 14(6):1579–1589

    Article  Google Scholar 

  • Delgado JM, Apel H, Merz B (2010) Flood trends and variability in the mekong river. Hydrol Earth Syst Sci 14(3):407–418

    Article  Google Scholar 

  • Du T, Xiong L, Xu C-Y, Gippel C, Guo S, Liu P (2015) Return period and risk analysis of nonstationary low-flow series under climate change. J Hydrol 527:234–250

    Article  Google Scholar 

  • Duan K, Mei Y (2014) Comparison of meteorological, hydrological and agricultural drought responses to climate change and uncertainty assessment. Water Resour Manag 28(14):5039–5054

    Article  Google Scholar 

  • El Adlouni S, Ouarda TBMJ, Zhang X, Roy R, Bobée B (2007). Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resour Res 43 (3)

  • Field CB, Barros V, Stocker TF, Dahe Q, Dokken DJ, Ebi KL, Mastrandrea MD, Mach KJ, Plattner G-K, Allen SK et al (2013) Managing the risks of extreme events and disasters to advance climate change adaptation: Special report of the Intergovernmental Panel on Climate Change

  • Fuller WE (1914) Flood flows. ASCE

  • Gilleland E, Ribatet M, Stephenson AG (2013) A software review for extreme value analysis. Extremes 16(1):103–119

    Article  Google Scholar 

  • Griffis VW, Stedinger JR (2007) Incorporating climate change and variability into bulletin 17b lp3 model. World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat, pp 1–8

  • Gül GO, Aşıkoğlu ÖL, Gül A, Gülçem Yaşoğlu F, Benzeden E (2014) Nonstationarity in flood time series. J Hydrol Eng 19(7):1349–1360

    Article  Google Scholar 

  • Haro D, Solera A, Paredes J, Andreu J (2014) Methodology for drought risk assessment in within-year regulated reservoir systems. application to the orbigo river system (Spain). Water Resour Manag 28(11):3801–3814

    Article  Google Scholar 

  • Katz RW (2013) Statistical methods for nonstationary extremes. Extremes in a Changing Climate, Springer, pp 15–37

  • Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Adv Water Resour 25(8):1287–1304

    Article  Google Scholar 

  • Khaliq M, Ouarda T, Ondo J-C, Gachon P, Bobée B (2006) Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review. J Hydrol 329(3):534–552

    Article  Google Scholar 

  • Kundzewicz ZW (2011) Nonstationarity in water resources - Central European perspective. J Am Water Resour Assoc 47(3):550–562

    Article  Google Scholar 

  • Li J, Wang Y, Li SF, Hu R (2015) A nonstationary standardized precipitation index incorporating climate indices as covariates. J Geophys Res Atmos 120(23):12,082–12,095 2015JD023920

    Article  Google Scholar 

  • Llamas J, Siddiqui M (1969) Runs of precipitation series. Hydrology paper 33. Colorado State University, Fort Collins, Colorado

    Google Scholar 

  • López J, Francés F (2013) Non-stationary flood frequency analysis in continental spanish rivers, using climate and reservoir indices as external covariates. Hydrol Earth Syst Sci 17(8):3189

    Article  Google Scholar 

  • Mohammed R, Scholz M, Zounemat-Kermani M (2017) Temporal hydrologic alterations coupled with climate variability and drought for transboundary river basins. Water Resour Manag 31(5):1489–1502

    Article  Google Scholar 

  • Mondal A, Mujumdar P (2015) Return levels of hydrologic droughts under climate change. Adv Water Resour 75:67–79

    Article  Google Scholar 

  • Mood A, Graybill F, Boes D (1974) Introduction to the theory of statistics. McGraw-Hill, New York

    Google Scholar 

  • Nalbantis I, Tsakiris G (2009) Assessment of hydrological drought revisited. Water Resour Manag 23(5):881–897

    Article  Google Scholar 

  • Prosdocimi I, Kjeldsen T, 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

    Article  Google Scholar 

  • Raff DA, Pruitt T, Brekke LD (2009) A framework for assessing flood frequency based on climate projection information. Hydrol Earth Syst Sci 13(11):2119–2136

    Article  Google Scholar 

  • Razmi A, Golian S, Zahmatkesh Z (2017) Non-stationary frequency analysis of extreme water level: Application of annual maximum series and peak-over threshold approaches. Water Resour Manag 31(7):2065–2083

    Article  Google Scholar 

  • Rossi G, Benedini M, Tsakiris G, Giakoumakis S (1992) On regional drought estimation and analysis. Water Resour Manag 6(4):249–277

    Article  Google Scholar 

  • Rossi G, Cancelliere A (2013) Managing drought risk in water supply systems in europe: a review. Int J Water Resour Dev 29(2):272–289

    Article  Google Scholar 

  • Russo S, Dosio A, Sterl A, Barbosa P, Vogt J (2013) Projection of occurrence of extreme dry-wet years and seasons in europe with stationary and nonstationary standardized precipitation indices. J Geophys Res Atmos 118(14):7628–7639

    Article  Google Scholar 

  • Salas JD, Obeysekera J (2014) Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. J Hydrol Eng 19(3):554–568

    Article  Google Scholar 

  • Serinaldi F (2015) Dismissing return periods!. Stoch Env Res Risk A 29(4):1179–1189

    Article  Google Scholar 

  • Sharma T (1997) Estimation of drought severity on independent and dependent hydrologic series. Water Resour Manag 11(1):35–49

    Article  Google Scholar 

  • Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt K, Tignor M, Miller H et al (2007) Ipcc, 2007: summary for policymakers. Climate change, pp 93–129

  • Šraj M, Viglione A, Parajka J, Blöschl G (2016) The influence of non-stationarity in extreme hydrological events on flood frequency estimation. J Hydrol Hydromechanics 64(4):426–437

    Google Scholar 

  • Stedinger JR, Griffis VW (2011) Getting from here to where? flood frequency analysis and climate1. J Amer Water Works Assoc 47(3):506–513

    Article  Google Scholar 

  • Strupczewski W, Singh V, Feluch W (2001) Non-stationary approach to at-site flood frequency modelling i. maximum likelihood estimation. J Hydrol 248(1):123–142

    Article  Google Scholar 

  • Sveinsson OG, Salas JD, Boes DC (2005) Prediction of extreme events in hydrologic processes that exhibit abrupt shifting patterns. J Hydrol Eng 10(4):315–326

    Article  Google Scholar 

  • Tsakiris G, Kordalis N, Tigkas D, Tsakiris V, Vangelis H (2016) Analysing drought severity and areal extent by 2d archimedean copulas. Water Resour Manag 30(15):5723–5735

    Article  Google Scholar 

  • Tsakiris G, Nalbantis I, Vangelis H, Verbeiren B, Huysmans M, Tychon B, Jacquemin I, Canters F, Vanderhaegen S, Engelen G, Poelmans L, De Becker P, Batelaan O (2013) A system-based paradigm of drought analysis for operational management. Water Resour Manag 27(15):5281–5297

    Article  Google Scholar 

  • Tsakiris G, Pangalou D, Vangelis H (2007) Regional drought assessment based on the reconnaissance drought index (rdi). Water Resour Manag 21(5):821–833

    Article  Google Scholar 

  • Vangelis H, Spiliotis M, Tsakiris G (2010) Drought severity assessment based on bivariate probability analysis. Water Resour Manag 25(1):357–371

    Article  Google Scholar 

  • Villarini G, Smith JA, Napolitano F (2010) Nonstationary modeling of a long record of rainfall and temperature over rome. Adv Water Resour 33(10):1256–1267

    Article  Google Scholar 

  • Villarini G, Smith JA, Serinaldi F, Bales J, Bates PD, Krajewski WF (2009) Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Adv Water Resour 32(8):1255–1266

    Article  Google Scholar 

  • Volpi E, Fiori A, Grimaldi S, Lombardo F, Koutsoyiannis D (2015) One hundred years of return period: Strengths and limitations. Water Resour Res 51(10):8570–8585

    Article  Google Scholar 

  • Wang Y, Li J, Feng P, Hu R (2015) A time-dependent drought index for non-stationary precipitation series. Water Resour Manag 29(15):5631–5647

    Article  Google Scholar 

  • Xiong L, Du T, Xu C-YB, Guo SC, Jiang C, Gippel C (2015) Non-stationary annual maximum flood frequency analysis using the norming constants method to consider non-stationarity in the annual daily flow series. Water Resour Manag 29(10):3615–3633

    Article  Google Scholar 

  • Zargar A, Sadiq R, Khan F (2014) Uncertainty-driven characterization of climate change effects on drought frequency using enhanced spi. Water Resour Manag 28(1):15–40

    Article  Google Scholar 

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Correspondence to Antonino Cancelliere.

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Cancelliere, A. Non Stationary Analysis of Extreme Events. Water Resour Manage 31, 3097–3110 (2017). https://doi.org/10.1007/s11269-017-1724-4

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