Dynamic flood modeling: Combining Hurst and Gumbel's approach

Environmetrics

Volumn 20, Issue 1, 2009, Pages 32-52

  Charpentier, Arthur ^a   Sibaï, David ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b Ecole Nationale de la Statistique et de l'Administration Economique   (France)

Author keywords

ACD models; Bivariate point process; Frequency analysis

Indexed keywords

FLOOD; FREQUENCY ANALYSIS; HYDROLOGICAL MODELING;

EID: 60249088571     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.909     Document Type: Article

References (47)

1. Albert JRG, Baxter LA. 1995. Applications of the EM algorithm to the analysis of life length data. Applied Statistics 44: 323-341.
2. Bachelier L. 1900. Théorie de la spéculation. Annales scientifiques de l'Ecole Normale Supérieure 3(17): 21-86.
3. Barlow RE, Proschan F. 1965. Mathematical Theory of Reliability. J. Wiley & Sons. Reprinted (1996) SIAM, Philadelphia, PA.
4. Beirlant J, Goegebeur Y, Segers J, Teugels J. 2004. Statistics of Extremes - Theory and Applications. Wiley: New York.
5. Bernstein PL. 1993. Capital Ideas: The Improbable Origins Of Modern Wall Street. John Wiley & Sons: New York.
6. Boes DC, Salas JD. 1978. Nonstationarity of the mean and the Hurst phenomenon. Water Resources Research 14(1): 135-143.
7. Cheung YW. 1993. Long memory in foreign-exchange rates. Journal of Business and Economic Statistics 11: 93-102.
8. Chukova S, Dimitrov B. 1992. On distributions almost having the almost lack of memory property. Journal of Applied Probability 29: 691-698.
9. David HA, Moeschberger ML. 1978. Theory of Competing Risks. Griffin: London.
10. Davis DR, Duckstein L, Fogel MM. 1976. Uncertainty in thereturn period of maximum hydrologic events: a Bayesian approach. Journal of Hydrology 31: 8195.
11. Embrechts P, Klüppelberg C, Mikosch T. 1997. Modelling Extremal Events: for Insurance and Finance. Springer Verlag: Berlin.
12. Engle RF, Russell JR. 1998. Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica 66: 1127-1162.
13. Engle RF, Lunde A. 2003. Trades and quotes: a bivariate point process. Journal of Financial Econometrics 1: 159-188.
14. Foufoula-Georgiou E. 1999. On scaling theories of space-time rainfall: some recent results and open problems. In Stochastic Methods in Hydrology, Barndorff-Nielsen, Gupta, Pérez-Abreu, Waymire (eds). Wolrd Scientific.
15. Franks SW, Kuczera G. 2002. Flood frequency analysis: evidence and implications of secular climate variability, New South Wales. Water Resources Research 38(5): 1062.
16. Greene M, Fielitz B. 1977. Long term dependence in common stock returns. Journal of Financial Econometrics 4: 339-349.
17. Gumbel EJ. 1941. The return period of flood flows. The Annals of Mathematical Statistics 12: 163-190.
18. Gumbel E. 1958. Statistics of Extreme. Columbia University Press: New York.
19. Hosking JRM. 1981. Fractional differencing. Biometrika 68: 165-176.
20. Hosking JRM. 1984. Testing whether the shape parameter is zero in the generalized Extreme-Value Distribution. Biometrika 71: 367-374.
21. Hurst HE. 1951. Long-term storage capacity of reservoirs. Transanctions of the American Society of Civil Engineers 116: 770-799.
22. Kelly KS, Krzysztofowicz R. 2000. Precipitation uncertainty processor for probabilistic river stage forecasting. Water Resources Research 36: 2643-2653.
23. Kelly KS, Krzysztofowicz R. 2001. Hydrologic uncertainty processor for probabilistic river stage forecasting: precipitation dependent model. Journal of Hydrology 249: 46-68.
24. Klemes V. 1974. The Hurst phenomenon: a puzzle? Water Resources Research 10(4): 675-688.
25. Koscielny-Bunde E, Kantelhardt JW, Braun P, Bunde A, Havlin S. 2006. Long-term persistence and multifractality of river runoff records. Journal of Hydrology 322: 120-137.
26. Liu C, Rubin DB. 1994. The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika 81: 633-648.
27. Lloyd EH. 1970. Occurrence interval in the presence of persistence. Journal of Hydrology 10: 291298.
28. Lo AW. 1991. Long term memory in stock market prices. Econometrica 59: 1276-1313.
29. Mandelbrot BB, Van Ness JW. 1968. Fractional Brownian motions, fractional noises and applications. SIAM Rev 10: 422-437.
30. Mandelbrot B, Wallis JR. 1968. Noah, Joseph and operational hydrology. Water Ressources Research 4: 909-918.
31. Martins ESPR, Clarke RT. 1993. Likelihood-based confidence intervals for estimating floods with given return periods. Journal of Hydrology 147: 61-81.
32. McCullagh P, Nelder JA. 1988. Generalized Linear Models. Chapman and Hall: London.
33. Nelson DB. 1991. Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59: 347-370.
34. NERC. 1975. Flood Studies Report Vol 1 - Hydrological Studies. Natural Environment Research Council, London.
35. Pandey G, Lovejoy S, Schertzer D. 1998. Multifractal analysis of daily river flows including extremes for basins of five to two million square kilometres, one day to 75 years. Journal of Hydrology 208: 62-81.
36. Pelletier JD, Turcotte DL. 1997. Long-range persistence in climatological and hydrological time series: analysis, modeling and application to drought hazard assessment. Journal of Hydrology 203: 198-208.
37. Potter K. 1976. Evidence for nonstationarity as a physical explanation of the Hurst phenomenon. Water Resources Research 12(5): 1047-1052.
38. Prentice RL, Kalbfleisch JD, Peterson AW, Flournoy N, Farewell VT, Breslow NE. 1978. The analysis of failure times in the presence of competing risks. Biometrics 34: 541-554.
39. Probst JL, Tardy Y. 1987. Long range streamflow and world continental runoff fluctuations since the beginning of this century. Journal of Hydrology 94: 289-311.
40. Puente CE. 1996. A new approach to hydrologic modeling: derived distributions revisited. Journal of Hydrology 187: 65-80.
41. Salas J, Boes D, Pegram G, Yevjevich V. 1979. Hurst phenomenon as a pre-asymptotic behavior. Journal of Hydrology 44: 1-15.
42. Sveinsson O, Salas JD, Boes DC, Pielke RA. 2003. Modeling the dynamics of long term variability of hydroclimatic processes. Journal of Hydrometeorology 4: 489-505.
43. Sveinsson O, Salas JD, Boes DC. 2005. Prediction of extreme events in hydrologic processes that exhibit abrupt shifting patterns. ASCE Journal of Hydrologic Engineering 10(4): 315-326.
44. Thyer M, Kuczera G. 2000. Modeling long term persistence in hydroclimatic time series using a hidden Markov model. Water Resources Research 36(11): 3301-3310.
45. Titterington D, Smith A, Makov U. 1985. Statistical Analysis of Finite Mixture Distributions. Wiley: New York.
46. Todorovic P, Zelenhasic E. 1970. A stochastic model for flood analysis. Water Resource 6: 1641-1648.
47. Todorovic P, Rousselle J. 1970. Some problems of flood analysis. Water Resource 7: 1144-115.