Statistical Properties of Partial Duration Series and Its Implication on Regional Frequency Analysis
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 7
Abstract
The use of partial duration series (PDS) in hydrological application includes the difficulty in determining the exceedance threshold or the number of average peaks per year () used to define extreme events from observation. The difficulty is exacerbated when the PDS is used in the context of regional frequency analysis; however, there are only limited studies to address this difficulty. This study aims to investigate the determination of an optimum regional value of for the North Island of New Zealand by examining the performance of the PDS when used in a regional frequency analysis (RFA). The suitability of a number of frequency distributions to be used in the regional frequency is examined. The results confirmed that the generalized Pareto (GP) best described the PDS in the study area. The results also show that the best PDS/GP performance is obtained when the value of is equal to 5.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like express thanks to the editor, Dr. Rao S. Govindaraju, and the reviewers for their valuable comments which greatly improved the quality of this paper.
References
Adamowski, K. (2000). “Regional analysis of annual maximum and partial duration flood data by nonparametric and L-moment methods.” J. Hydrol., 229(3–4), 219–231.
Begueria, S. (2005). “Uncertianties in partial duration series modelling of extremes related to the choice of thereshold value.” J. Hydrol., 303, 215–230.
Birikundavyi, S., and Rousselle, J. (1997). “Use of partial duration series for single-station and regional analysis of floods.” J. Hydrol. Eng., 68–75.
Bobee, B., Cavadias, G., Ashkar, F., Bernier, J., and Rasmussen, P. (1993). “Towards a systematic approach to comparing distributions used in flood frequency analysis.” J. Hydrol., 142(1–4), 121–136.
Buishand, T. A. (1989). “The PDS method with a fixed number of peaks.” J. Hydrol., 109(1–2), 1–9.
Claps, P., and Laio, F. (2003). “Can continuous streamflow data support flood frequency analysis? An alternative to the partial duration series approach.” Water Resour. Res., 39(8).
Cunnane, C. (1973). “A particular comparison of annual maximum and partial duration series methods of flood frequency prediction.” J. Hydrol., 18(3–4), 257–271.
Cunnane, C. (1979). “A note on the Poisson assumption in partial duration series models.” Water Resour. Res., 15(2), 489–494.
Cunnane, C. (1985). “Factors affecting choice of distribution for flood series.” Hydrol. Sci. J., 30(1), 3–36.
Cunnane, C. (1988). “Methods and merits of regional flood frequency analysis.” J. Hydrol., 100(1–3), 269–290.
Das, S., and Cunnane, C. (2010). “Examination of homogeneity of selected Irish pooling groups.” Hydrol. Earth Syst. Sci., 7, 5099–5130.
Foufoula-Georgiou, E., and Lettenmaier, D. P. (1987). “Continuous-time versus discrete-time point process models for rainfall occurrence series.” Water Resour. Res., 23, 875–884.
Fowler, A. M., and Hennessy, K. J. (1995). “Potential impacts of global warming on the frequency and magnitude of heavy precipitation.” Nat. Hazards, 11(3), 283–303.
Fowler, H. J., and Kilsby, C. G. (2003a). “Implications of changes in seasonal and annual extreme rainfall.” Geophys. Res. Lett., 30(13), 1720–1724.
Fowler, H. J., and Kilsby, C. G. (2003b). “A regional frequency analysis of United Kingdom extreme rainfall from 1961 to 2000.” Int. J. Climatol., 23(11), 1313–1334.
Haddad, K., Rahman, A., and Green, J. (2011). “Design rainfall estimation in Australia: A case study using L moments and generalized least squares regression.” Stochastic Environ. Res. Risk Assess., 25(6), 815–825.
Hosking, J. R. M., and Wallis, J. R. (1987). “Parameter and quantile estimation for the generalized pareto distribution.” Technometrics, 29(3).
Hosking, J. R. M., and Wallis, J. R. (1993). “Some statistic useful in regional frequency analysis.” Water Resour. Res., 29(2), 271–281.
Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis: An approach based on L-moments. Cambridge University Press, Cambridge, U.K.
Insurance Council of New Zealand. (2005). “Current issues: The cost of weather losses: Claims history.” NZ Insurance Council, Wellington, 〈http://www.icnz./org.nz/current/wx.php〉.
Jaiswal, R. K., Goel, N. K., Singh, P., and Thomas, T. (2003). “L-moment based flood frequency modelling.” J. Inst. Eng. (India) Civ. Eng. Div., 84, 6–10.
Madsen, H., Pearson, C. P., and Rosbjerg, D. (1997). “Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: Regional modelling.” Water Resour. Res., 33(4), 759–769.
Madsen, H., Rosbjerg, D., and Harremoes, P. (1994). “PDS-modelling and regional Bayesian estimation of extreme rainfalls.” Nord. Hydrol., 25(4), 279–300.
McKerchar, A. I. (1991). “Regional flood frequency analysis for small New Zealand basins: Mean annual flood estimation.” J. Hydrol. N. Z., 30(2), 65–75.
Meng, F., Li, J., and Gao, L. (2007). “ERM-POT model for quantifying operational risk for Chinese commercial banks.” Lecture notes in computer science, Y. Shi, ed., Springer, Berlin Heildbreg, Berlin, Germany.
Mohssen, M. (2009). “Partial duration series in the annual domain.” 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, R. S. Anderssen, R. D. Braddock, and L. T. H. Newham, eds., Cairns, Australia.
Moreno, J. I. L., Vicente-Serrano, S. M., Martínez, M. A., Beguería, S., and Kenawya, A. (2010). “Trends in daily precipitation on the north eastern Iberian Peninsula, 1955–2006.” Int. J. Climatol., 30(7), 1026–1041.
Mosley, M. P. (1981). “Delimitation of New Zealand hydrologic regions.” J. Hydrol., 49(1), 173–192.
Norbiato, D., Borga, M., Sangati, M., and Zanon, F. (2007). “Regional frequency analysis of extreme precipitation in the eastern Italian Alps and the August 29, 2003 flash flood.” J. Hydrol., 345(3–4), 149–166.
Pearson, C. P. (1991). “New Zealand regional flood frequency analysis using L-moments.” J. Hydrol., 30(2), 53–64.
Pearson, C. P., and Henderson, R. D. (1998). “Frequency distributions of annual maximum storm rainfalls in New Zealand.” J. Hydrol., 37(1), 19–33.
Pham, H. X., Asaad, Y. S., and Bruce, M. (2013). “Statistical properties of partial duration series: Case study of North Island, New Zealand.” J. Hydrol. Eng., 807–815.
Potter, K. W., and Lettenmaier, D. P. (1990). “A comparison of regional flood frequency estimation methods using bootstrap statistics.” Water Resour. Res., 26(3), 415–424.
Saf, B. (2009). “Regional flood frequency analysis using L-moments for the West Mediterranean region of Turkey.” Water Resour. Manage., 23(3), 531–551.
Saf, B. (2010). “Assessment of the effects of discordant sites on regional flood frequency analysis.” J. Hydrol., 380(3–4), 362–375.
Shinyie, W. L., and Ismail, N. (2012). “Analysis of -year return level for partial duration rainfall series.” Sains Malays., 41(11), 1389–1401.
Takeuchi, K. (1984). “Annual maximum series and partial duration series - Evaluation of Langbien's formula and Chow's discussion.” J. Hydrol., 68, 275–284.
Thompson, C. S., and Tomlinson, A. I. (1993). “Probable maximum precipitation in New Zealand for small areas and short durations.” J. Hydrol., 31(2), 78–90.
Trefry, C. M., Watkins, D. W., and Johnson, D. (2005). “Regional rainfall frequency analysis for the state of Michigan.” J. Hydrol. Eng., 437–449.
Veneziano, D., Langousis, A., and Furcolo, P. (2006). “Multifractality and rainfall extremes: A review.” Water Resour. Res., 42, W06D15.
Wilks, D. S. (1993). “Comparison of three-parameter probability distributions for representing annual extreme and partial duration precipitation series.” Water Resour. Res., 29(10), 3543–3549.
Yang, T., et al. (2010). “Regional frequency analysis and spatio-temporal pattern characterization of rainfall extremes in the Pearl River Basin, China.” J. Hydrol., 380(3–4), 386–405.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 7 • July 2014
Pages: 1471 - 1480
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Mar 2, 2013
Accepted: Sep 30, 2013
Published online: Oct 11, 2013
Discussion open until: Mar 11, 2014
Published in print: Jul 1, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.