A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions

Stochastic Environmental Research and Risk Assessment

Volumn 24, Issue 8, 2010, Pages 1127-1143

  Fernandes, Wilson ^a   Naghettini, Mauro ^a   Loschi, Rosângela ^a  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

Bayesian analysis; Flood frequency; Hydrologic extreme events; Probable maximum flood

Indexed keywords

APPLICATION EXAMPLES; BAYESIAN; BAYESIAN ANALYSIS; BAYESIAN APPROACHES; BAYESIAN FRAMEWORKS; BAYESIAN THEORY; CALIFORNIA , USA; EXPLORATORY STUDIES; EXTREME FLOOD; FLOOD FLOW; FLOOD FREQUENCY; FLOOD FREQUENCY ANALYSIS; FLUVIAL PROCESS; FREQUENCY ANALYSIS; HISTORICAL FLOODS; HYDROLOGIC EXTREMES; HYDROLOGICAL VARIABLES; LIKELIHOOD FUNCTIONS; LOGICAL CONTEXTS; MAXIMUM FLOWS; PRIOR DISTRIBUTION; PRIOR INFORMATION; PROBABLE MAXIMUM FLOODS; REFERENCE VALUES; RELIABLE ESTIMATES; RIVER BASINS; THEORETICAL LIMITS;

BAYESIAN NETWORKS; DISTRIBUTION FUNCTIONS; FLOOD CONTROL; FLOODS; RESERVOIRS (WATER);

UNCERTAINTY ANALYSIS;

BAYESIAN ANALYSIS; EXTREME EVENT; FLOOD FREQUENCY; FLOODING; PROBABILITY DENSITY FUNCTION; RIVER BASIN; RIVER DISCHARGE;

CALIFORNIA; FOLSOM LAKE; UNITED STATES;

EID: 78650076181     PISSN: 14363240     EISSN: 14363259     Source Type: Journal    
DOI: 10.1007/s00477-010-0365-4     Document Type: Article

References (54)

1. Baker VR (1987) Paleoflood hydrology and extraordinary flood events. J Hydrol 96: 79-99.
2. Baker VR (2003) A bright future for old flows: origin, status and future of paleoflood hydrology. In: Thorndycraft VR, Benito G, Barriendos M, Llasat MC (eds) Proceedings of 2002 PHEFRA workshop-palaeofloods, historical floods and climatic variability: applications in flood risk assessment, Chap 2, pp 13-18. http://www. ccma. csic. es/dpts/suelos/hidro/images/chapter_02_phefra. pdf.
3. Baker VR, Webb RH, House PK (2002) The scientific and societal value of paleoflood hydrology. In: House PK, Webb RH, Baker VR, Levish DR (eds) Ancient floods, modern hazards, principles and applications of paleoflood hydrology. American Geophysical Union Water Science and Application Series, Washington, pp 1-19.
4. Bernardara P, Schertzer D, Sauquet E, Tchiguirisnkaia I, Lang M (2008) The flood probability distribution tail: how heavy is it? Stoch Environ Res Risk Assess 22: 107-122. doi: 10. 1007/s00477-006-0101-2.
5. Botero BA (2006) Estimación de crecidas de alto período de retorno mediante funciones de distribución con límite superior e información no sistemática. PhD Thesis, Universidad Politécnica de Valéncia, Spain.
6. Coles SG, Powell EA (1996) Bayesian methods in extreme value modeling: a review and new developments. Int Stat Rev 64(1): 119-136.
7. Dawdy DR, Lettenmaier DP (1987) Initiative for risk-based flood design. J Hydrol Eng 113(8): 1041-1051.
8. Dubler JR, Grigg NS (1996) Dam safety policy for spillway design floods. J Prof Issues Eng Educ Pract 122(4): 163-169.
9. Elíasson J (1997) A statistical model for extreme precipitation. Water Resour Res 33(3): 449-455.
10. Enzel Y, Ely LL, House PK, Baker VR, Webb RH (1993) Paleoflood evidence for a natural upper bound to flood magnitudes in the Colorado River Basin. Water Resour Res 29(7): 2287-2297.
11. FEMA-Federal Emergency Management Agency (2004) Federal guidelines for dam safety: selecting and accommodating inflow design floods for dams. The Interagency Committee of the U. S. Department of Homeland Security, Washington, DC.
12. Francés F (2001) Incorporating non-systematic information to flood frequency analysis using the maximum likelihood estimation method. In: Glade T, Albini P, Francés F (eds) The use of historical data in natural hazard assessments, Chapter B: Flooding. Kluwer Academic Publishers, Dordrecht, pp 89-99.
13. Francés F, Botero BA (2003) Probable maximum flood estimation using systematic and non-systematic information. In: Thorndycraft VR, Benito G, Barriendos M, Lllasat MC (eds) Proceedings of 2002 PHEFRA workshop-palaefloods, historical floods and climatic variability: applications in flood risk assessment, Chap 34, pp. 223-229. http://www. ccma. csic. es/dpts/suelos/hidro/images/chapter_34_phefra. pdf.
14. Francés F, Salas JD, Boes DC (1994) Flood frequency analysis with systematic and historical or paleoflood data based on the two parameter general extreme values models. Water Resour Res 30(6): 1653-1664.
15. Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov chain Monte Carlo in practice. Chapman & Hall/CRC, London, UK.
16. Hershfield DM (1965) Method for estimating maximum probable precipitation. J Am Waterworks Assoc 57: 965-972.
17. Hirsch RM, Stedinger JR (1987) Plotting positions for historical floods and their precision. Water Resour Res 23(4): 715-727.
18. Hirschboeck K (2003) Floods, paleofloods, and droughts: insights from the upper tails. In: CLIVAR/PAGES/IPCC Workshop-a multi-millennia perspective on droughts and implications for the future, Tucson, AZ. Available at http://ipcc-wg1. ucar. edu/meeting/Drght/materials/abstracts/Hirschboeck. pdf.
19. Horton RE (1936) Hydrologic conditions as affecting the results of the application of methods of frequency analysis to flood records. U. S. Geol. Surv Water Supply Paper No. 771, pp 433-449.
20. Hosking JRM, Wallis JR (1997) Regional frequency analysis-an approach based on L-moments. Cambridge University Press, Cambridge.
21. Houghton J (1978) Birth of a parent: the Wakeby distribution for modeling flood flows. Water Resour Res 15(6): 1361-1372.
22. IACWD-Interagency Advisory Committee on Water Data (1985) Feasibility of assigning a probability to the probable maximum flood. Office of Water Coordination, Washington, DC.
23. ICOLD-International Commission of Large Dams (1987) Bulletin 59-dam safety guidelines, Paris, France.
24. Jacoby Y, Grodek T, Enzel Y, Porat N, McDonald EV, Dahan O (2008) Late holocene upper bounds of flood magnitudes and twentieth century large floods in the ungauged, hyperarid alluvial Nahal Arava, Israel. Geomorphology 95(3-4): 274-294.
25. Kanda J (1981) A new extreme value distribution with lower and upper limits for earthquake motions and wind speeds. Theor Appl Mech 31: 351-360.
26. Klemeš V (1987) Hydrological and engineering relevance of flood frequency analysis. In: Proceedings of international symposium on flood frequency risk analysis-regional flood frequency analysis, Baton Rouge, LA. D. Reidel Publishing Company, Boston, MA, pp 1-18.
27. Klemeš V (1993) Probability of extreme hydrometeorological events-a different approach. In: Proceedings of Yokohama symposium on extreme hydrological events: precipitation, floods and droughts. IAHS Publ. 213, pp 167-176.
28. Koutsoyiannis D (1999) A probabilistic view of Hershfield's method for estimating probable maximum precipitation. Water Resour Res 35(4): 1313-1322.
29. Lunn DJ, Thomas A, Best N, Spiegelhalter D (2000) WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Stat Comput 10: 325-337.
30. Martins ES, Stedinger JR (2000) Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resour Res 36(3): 737-744.
31. McRobbie A (2004) The Bayesian view of extreme events. In: Proceedings of Henderson colloquium: designing for the consequences of hazards. The Institution of Structural Engineers, London, UK. Available at http://www. istructe. org/IABSE/db/599. asp.
32. Micevski T, Kuczera G (2009) Combining site and regional flood information using a Bayesian Monte Carlo approach. Water Resour Res 45: W04405. doi: 10. 1029/2008WR007173.
33. Migon HS, Gamerman D (1999) Statistical inference: an integrated approach. Hodder Arnold, London.
34. Nathan RJ, Weinmann PE (2001) Estimation of large and extreme floods for medium and large catchments: book VI. Australian rainfall and runoff-a guide to flood estimation, 4th edn. Engineers Australia, National Committee for Water Engineering, Australia.
35. Naulet R (2002) Utilisation de l'information des crues historiques pour une meilleure prédétermination du risque d'inondation. Application au bassin de l'Ardèche à Vallon Pont-d'Arc et St-Martin d'Ardèche. PhD Thesis, INRS-ETE, Grenoble, France.
36. NRC-National Research Council (1999) Improving American river flood frequency analysis. National Academy Press, Washington, DC.
37. O'Connell DRH, Ostenaa DA, Levish DR, Klinger RE (2002) Bayesian flood frequency analysis with paleohydrologic bound data. Water Resour Res 38(5): 16. 1-16. 13.
38. Reis D, Stedinger JR (2005) Bayesian MCMC flood frequency analysis with historical information. J Hydrol 313: 97-116.
39. 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: 97-112. doi: 10. 1007/s00477-006-0047-4.
40. Sisson SA, Pericchi LR, Coles SG (2006) A case for reassessment of the risks of extreme hydrological hazards in the Caribbean. Stoch Environ Res Risk Assess 20: 296-306. doi: 10. 1007/s00477-005-0246-4.
41. Slade JJ (1936) An asymmetric probability function. Trans Am Soc Civ Eng, vol 101, Paper No. 1924, pp 35-61.
42. Stedinger JR, Cohn TA (1986) Flood frequency analysis with historical and paleoflood information. Water Resour Res 22(5): 785-793.
43. Stedinger JR, Heath DC, Thompson K (1989) Risk analysis for dam safety evaluation. Report TCN 87-653 prep. for the U. S. Army Corps of Engineers.
44. Takara K, Loebis J (1996) Frequency analysis introducing probable maximum hydrologic events: preliminary studies in Japan and in Indonesia. In: Proceedings of international symposium on comparative research on hydrology and water resources in Southeast Asia and the Pacific. Indonesian National Committee for International Hydrological Programme, pp 67-76.
45. Takara K, Tosa K (1999) Storm and flood frequency analysis using PMP/PMF estimates. Proc. International symposium on floods and droughts, Nanjing, China, pp 7-17, IHP-V Technical Documents in Hydrology No. 4, UNESCO Jakarta Office, Hohai University Press.
46. USACE-United States Army Corps of Engineers (2001) American River Basin, California, Folsom Dam and Lake Revised PMF Study-Hydrology Office Report. U. S. Army Corps of Engineers, Sacramento District, CA.
47. USBR-United States Bureau of Reclamation. (2004) Hydrologic hazard curve estimating procedures. Research Report DSO-04-08, U. S. Bureau of Reclamation, Denver, CO.
48. USBR-United States Bureau of Reclamation (2002) Flood hazard analysis, Folsom Dam Central Valley Project. Flood Hydrology Group, Denver, CO.
49. USNRC-U. S. Nuclear Regulatory Commission (1977) Design Basis Floods for Nuclear Power Plants. Regulatory Guide 1. 59, Washington, DC.
50. Vick SG (2002) Degrees of belief-subjective probability and engineering judgment. ASCE Press, Reston, VA.
51. Vogel RM, Matalas NC, England JF, Castellarin A (2007) As assessment of exceedance probabilities of envelope curves. Water Resour Res 43(7), W07403. doi: 10. 1029/2006WR005586.
52. WMO-World Meteorological Organization (1986) Manual for estimation of probable maximum precipitation, 269 pp. Operational Hydrology Report 1, WMO 332, Geneva, Switzerland.
53. Yevjevich V (1968) Misconceptions in hydrology and their consequences. Water Resour Res 4(2): 225-232.
54. Yevjevich V, Harmancioglu NB (1987) Some reflections on the future of hydrology. In: Proceedings of Rome symposium on water for the future: hydrology in perspective, IAHS Publ. 164. International Association of Hydrological Sciences, Wallingford, UK, pp 405-414.