On some aspects of peaks-over-threshold modeling of floods under nonstationarity using climate covariates

详细信息    查看全文

• 作者：Artur Tiago Silva ; Mauro Naghettini…
• 关键词：Flood frequency analysis ; Peaks ; over ; threshold ; Nonstationarity ; Design life level
• 刊名：Stochastic Environmental Research and Risk Assessment (SERRA)
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：30
• 期：1
• 页码：207-224
• 全文大小：1,146 KB
• 参考文献：Abers RN (2007) Organizing for governance: building collaboration in Brazilian river basins. World Dev 35(8):1450–1463CrossRef
  Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723CrossRef
  Balkema A, de Haan L (1974) Residual life time at great age. Ann Probab 2(5):792–804CrossRef
  Barreiro M (2010) Influence of ENSO and the South Atlantic Ocean on climate predictability over Southeastern South America. Clim Dynam 35(7–8):1493–1508CrossRef
  Bernardara P, Mazas F, Kergadallan X, Hamm L (2014) A two-step framework for over-threshold modelling of environmental extremes. Nat Hazards Earth Syst Sci 14(3):635–647CrossRef
  Bhunya P, Singh R, Berndtsson R, Panda S (2012) Flood analysis using generalized logistic models in partial duration series. J Hydrol 420:59–71CrossRef
  Bhunya P, Berndtsson R, Jain SK, Kumar R (2013) Flood analysis using negative binomial and Generalized Pareto models in partial duration series (PDS). J Hydrol 497:121–132CrossRef
  Bras RL (1990) Hydrology: an introduction to hydrologic science. Addison-Wesley, Reading
  Casella G, Berger RL (1990) Statistical inference, vol 70. Duxbury Press, Belmont
  Chavez-Demoulin V, Davison AC (2005) Generalized additive modelling of sample extremes. J R Stat Soc C 54(1):207–222CrossRef
  Cheng L, AghaKouchak A, Gilleland E, Katz RW (2014) Non-stationary extreme value analysis in a changing climate. Clim Change 127(2):353–369CrossRef
  Chow V, Maidment D, Mays L, et al. (1988) Applied hydrology. McGraw-Hill series in water resources and environmental engineering. McGraw-Hill, New York
  Clarke R (2007) Hydrological prediction in a non-stationary world. Hydrol Earth Syst Sc 11(1):408–414. doi:10.​5194/​hess-11-408-2007 CrossRef
  Coles S (2010) An introduction to statistical modeling of extreme values. Springer, London
  Cooley D (2009) Extreme value analysis and the study of climate change. Clim Change 97(1–2):77–83CrossRef
  Cooley D (2013) Return periods and return levels under climate change. In: Extremes in a changing climate, Springer, London, pp 97–114
  Cordero A, Medeiros P (2003) Estimativa da curva chave de Blumenau. In: XV Simpósio Brasileiro de Recursos Hídricos
  Correia FN (1983) Métodos de análise e determinação de caudais de cheia. Laboratório Nacional de Engenharia Civil, Lisbon
  Cunnane C (1979) A note on the Poisson assumption in partial duration series models. Water Resour Res 15(2):489–494CrossRef
  Davison A, Ramesh N (2000) Local likelihood smoothing of sample extremes. J R Stat Soc B 62(1):191–208CrossRef
  Davison A, Smith R (1990) Models for exceedances over high thresholds. J R Stat Soc B 52(3):393–442
  Davison AC (2003) Statistical models. Cambridge University Press, CambridgeCrossRef
  Delgado J, Apel H, Merz B (2010) Flood trends and variability in the Mekong river. Hydrol Earth Syst Sci 14(3):407–418CrossRef
  Eastoe EF, Tawn JA (2010) Statistical models for overdispersion in the frequency of peaks over threshold data for a flow series. Water Resour Res 46(2):W02510. doi:10.​1029/​2009WR007757
  Ekanayake S, Cruise J (1993) Comparisons of Weibull-and exponential-based partial duration stochastic flood models. Stoch Hydrol Hydraul 7(4):283–297CrossRef
  Fernandes W, Naghettini M, Loschi R (2010) A bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions. Stoch Environ Res Risk Assess 24(8):1127–1143CrossRef
  Fisher R, Tippett L (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. In: Mathematical proceedings of the Cambridge Philosophical Society, vol 24. Cambridge University Press, Cambridge, pp 180–190
  Frank B (2003) Uma história das enchentes e seus ensinamentos, vol 20. Edifurb, Blumenau, pp 15–62
  Gnedenko B (1943) Sur la distribution limite du terme maximum d’une série aléatoire. Ann Math 44(3):423–453CrossRef
  Grimm AM (2011) Interannual climate variability in south america: impacts on seasonal precipitation, extreme events, and possible effects of climate change. Stoch Environ Res Risk Assess 25(4):537–554CrossRef
  Grimm AM, Tedeschi RG (2009) ENSO and extreme rainfall events in South America. J Clim 22(7):1589–1609CrossRef
  Grimm AM, Barros VR, Doyle ME (2000) limate variability in southern south america associated with el niño and la niñ a events. J Clim 13(1):35–58CrossRef
  Gringorten II (1963) A plotting rule for extreme probability paper. J Geophys Res 68(3):813–814CrossRef
  Hastie TJ, Tibshiran RJ (1990) Generalized additive models, vol 43. CRC Press, London
  Heffernan JE, Stephenson A, Gilleland E (2013) Ismev: an introduction to statistical modeling of extreme values. R Package Version 1:39
  Hundecha Y, St-Hilaire A, Ouarda T, El Adlouni S, Gachon P (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 Clim 47(11):2745–2759CrossRef
  Jakob D (2013) Nonstationarity in extremes and engineering design. In: Extremes in a changing climate. Springer, London, pp 363–417
  Jin EK, Kinter JL III, Wang B, Park CK, Kang IS, Kirtman B, Kug JS, Kumar A, Luo JJ, Schemm J et al (2008) Current status of enso prediction skill in coupled ocean-atmosphere models. Clim Dyn 31(6):647–664CrossRef
  Katz RW (2013) Statistical methods for nonstationary extremes. In: Extremes in a changing climate. Springer, London, pp 15–37
  Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Adv Water Resour 25(8):1287–1304CrossRef
  Kirby W (1969) On the random occurrence of major floods. Water Resour Res 5(4):778–784CrossRef
  Lang M, Ouarda T, Bobée B (1999) Towards operational guidelines for over-threshold modeling. J Hydrol 225(3–4):103–117CrossRef
  Lee T, Ouarda T (2010) Long-term prediction of precipitation and hydrologic extremes with nonstationary oscillation processes. J Geophys Res (1984–2012) 115(D13)
  Lima CH, Lall U, Jebara T, Barnston AG (2009) Statistical prediction of ENSO from subsurface sea temperature using a nonlinear dimensionality reduction. J Clim 22(17):4501–4519CrossRef
  Lopez 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):3189–3203CrossRef
  Madsen H, Rasmussen PF, Rosbjerg D (1997) Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: 1. At-site modeling. Water Resour Res 33(4):747–757CrossRef
  Martins ESP, Clarke RT (1993) Likelihood-based confidence intervals for estimating floods with given return periods. J Hydrol 147(1):61–81CrossRef
  McCullagh P, Nelder JA (1989) Generalized linear models (Monographs on statistics and applied probability 37). Chapman Hall, London
  Milly P, Betancourt J, Falkenmark M, Hirsch R, Kundzewicz Z, Lettenmaier D, Stouffer R (2008) Stationarity is dead: whither water management? Science 319(5863):573CrossRef
  Naghettini M, Pinto E (2007) Hidrologia estatística. CPRM, Belo Horizonte
  NERC (1975) Flood Studies Report, vol I. Natural Environment Research Council
  Nery JT, Baldo MC, Martins MdLOF (2000) O comportamento da precipitação na Bacia do Itajaí. Acta Sci-Technol 22(5):1429–1435
  Obeysekera J, Salas JD (2014) Quantifying the uncertainty of design floods under nonstationary conditions. J Hydrol Eng 19(7):1438–1446CrossRef
  Olsen JR, Lambert JH, Haimes YY (1998) Risk of extreme events under nonstationary conditions. Risk Anal 18(4):497–510CrossRef
  Önöz B, Bayazit M (2001) Effect of the occurrence process of the peaks over threshold on the flood estimates. J Hydrol 244(1):86–96CrossRef
  Ouarda T, El-Adlouni S (2011) Bayesian nonstationary frequency analysis of hydrological variables. J Am Water Resour Assoc 47(3):496–505CrossRef
  Parey S, Malek F, Laurent C, Dacunha-Castelle D (2007) Trends and climate evolution: Statistical approach for very high temperatures in france. Clim change 81(3–4):331–352CrossRef
  Parey S, Hoang TTH, Dacunha-Castelle D (2010) Different ways to compute temperature return levels in the climate change context. Environmetrics 21(7–8):698–718CrossRef
  Pauli F, Coles S (2001) Penalized likelihood inference in extreme value analyses. J Appl Stat 28(5):547–560CrossRef
  Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3(1):119–131CrossRef
  R Core Team (2012) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna. http://​www.​R-project.​org/​ , ISBN 3-900051-07-0
  Rayner N, Parker D, Horton E, Folland C, Alexander L, Rowell D, Kent E, Kaplan A (2003) Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J Geophys Res: Atmospheres (1984–2012) 108(D14)
  Renard B, Lang M, Bois P (2006) Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data. Stoch Environ Res Risk Assess 21(2):97–112CrossRef
  Renard B, Sun X, Lang M (2013) Bayesian methods for non-stationary extreme value analysis. In: Extremes in a changing climate, Springer, London, pp 39–95
  Rootzén H, Katz RW (2013) Design life level: quantifying risk in a changing climate. Water Resour Res 49(9):5964–5972CrossRef
  Rosbjerg D, Rasmussen F (1991) Modelling of exceedances in partial duration series. In: Proceeding of the international hydrology and water resources symposium, national conference publication—Institute of Engineers, vol 3, pp 755–760
  Rosbjerg D, Madsen H, Rasmussen PF (1992) Prediction in partial duration series with generalized Pareto-distributed exceedances. Water Resour Res 28(11):3001–3010CrossRef
  Salas JD, Obeysekera J (2014) Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. J Hydrol Eng 19(3):554–566CrossRef
  Serinaldi F (2013) On the relationship between the index of dispersion and Allan factor and their power for testing the poisson assumption. Stoch Environ Res Risk Assess 27(7):1773–1782
  Serinaldi F (2014) Dismissing return periods! Stoch Environ Res Risk Assess 1–11
  Serinaldi F, Kilsby CG (2015) Stationarity is undead: uncertainty dominates the distribution of extremes. Adv Wat Resour 77:17–36CrossRef
  Shane R, Lynn W (1964) Mathematical model for flood risk evaluation. J Hydr Eng Div 90(HY 6):4119–4122
  Silva AT, Portela MM, Naghettini M (2014) On peaks-over-threshold modeling of floods with zero-inflated poisson arrivals under stationarity and nonstationarity. Stoch Environ Res Risk Assess 28(6):1587–1599
  Tachini M (2010) Avaliação de danos associados às inundações no município de Blumenau. PhD thesis, Universidade Federal de Santa Catarina
  Tramblay Y, Neppel L, Carreau J, Najib K (2013) Non-stationary frequency analysis of heavy rainfall events in southern France. Hydrol Sci J 58(2):280–294CrossRef
  Trenberth KE (1997) The definition of El Niño. Bull Am Meteorol Soc 78(12):2771–2777
  Ward PJ, Eisner S, Flörke M, Dettinger MD, Kummu M (2014) Annual flood sensitivities to El Niño-Southern Oscillation at the global scale. Hydrol Earth Syst Sci 18(1):47–66. doi:10.​5194/​hess-18-47-2014 CrossRef
  Wigley TM (1988) The effect of changing climate on the frequency of absolute extreme events. Clim Monit 17(1–2):44–55
  Wigley TM (2009) The effect of changing climate on the frequency of absolute extreme events. Clim Change 97(1–2):67–76CrossRef
  Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J R Stat Soc B 73(1):3–36CrossRef
  Yee TW (2014) VGAM: Vector generalized linear and additive models. http://​CRAN.​R-project.​org/​package=​VGAM , r package version 0.9-4
  Yee TW, Stephenson AG (2007) Vector generalized linear and additive extreme value models. Extremes 10(1–2):1–19CrossRef
  Zelenhasic E (1970) Theoretical probability distributions for flood peaks. Hydrology paper 42, Colorado State University, Fort Collins
  
• 作者单位：Artur Tiago Silva (1)
  Mauro Naghettini (2)
  Maria Manuela Portela (1)
  
  1. CEris, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
  2. Department of Hydraulics and Water Resources Engineering, Federal University of Minas Gerais, Belo Horizonte, Brazil
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Environment
  Mathematical Applications in Environmental Science
  Mathematical Applications in Geosciences
  Probability Theory and Stochastic Processes
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Numerical and Computational Methods in Engineering
  Waste Water Technology, Water Pollution Control, Water Management and Aquatic Pollution
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-3259

文摘

This paper discusses some aspects of flood frequency analysis using the peaks-over-threshold model with Poisson arrivals and generalized Pareto (GP) distributed peak magnitudes under nonstationarity, using climate covariates. The discussion topics were motivated by a case study on the influence of El Niño–Southern Oscillation on the flood regime in the Itajaí river basin, in Southern Brazil. The Niño3.4 (DJF) index is used as a covariate in nonstationary estimates of the Poisson and GP distributions scale parameters. Prior to the positing of parametric dependence functions, a preliminary data-driven analysis was carried out using nonparametric regression models to estimate the dependence of the parameters on the covariate. Model fits were evaluated using asymptotic likelihood ratio tests, AIC, and Q–Q plots. Results show statistically significant and complex dependence relationships with the covariate on both nonstationary parameters. The nonstationary flood hazard measure design life level (DLL) was used to compare the relative performances of stationary and nonstationary models in quantifying flood hazard over the period of records. Uncertainty analyses were carried out in every step of the application using the delta method.