• Ahmad, M. I., Sinclair C. D. , and Spurr B. D. , 1988a: Assessment of flood frequency models using empirical distribution function statistics. Water Resour. Res., 24, 13231328, doi:10.1029/WR024i008p01323.

    • Search Google Scholar
    • Export Citation
  • Ahmad, M. I., Sinclair C. D. , and Werritty A. , 1988b: Log-logistic flood frequency analysis. J. Hydrol., 98, 205224, doi:10.1016/0022-1694(88)90015-7.

    • Search Google Scholar
    • Export Citation
  • Akaike, H., 1974: A new look at the statistical model identification. IEEE Trans. Autom. Control, 19, 716723, doi:10.1109/TAC.1974.1100705.

    • Search Google Scholar
    • Export Citation
  • Alila, Y., and Mtiraoui A. , 2002: Implications of heterogeneous flood-frequency distributions on traditional stream-discharge prediction techniques. Hydrol. Processes, 16, 10651084, doi:10.1002/hyp.346.

    • Search Google Scholar
    • Export Citation
  • Arnell, N. W., Beran M. , and Hosking J. R. M. , 1986: Unbiased plotting positions for the general extreme value distribution. J. Hydrol., 86, 5969, doi:10.1016/0022-1694(86)90006-5.

    • Search Google Scholar
    • Export Citation
  • Ashkar, F., and Ouarda T. B. M. J. , 1996: On some methods of fitting the generalized Pareto distribution. J. Hydrol., 177, 117141, doi:10.1016/0022-1694(95)02793-9.

    • Search Google Scholar
    • Export Citation
  • Ashkar, F., and Ouarda T. B. M. J. , 1998: Approximate confidence intervals for quantiles of gamma and generalized gamma distributions. J. Hydrol. Eng., 3, 4351, doi:10.1061/(ASCE)1084-0699(1998)3:1(43).

    • Search Google Scholar
    • Export Citation
  • Calenda, G., Mancini C. P. , and Volpi E. , 2009: Selection of the probabilistic model of extreme floods: The case of the River Tiber in Rome. J. Hydrol., 371, 111, doi:10.1016/j.jhydrol.2009.03.010.

    • Search Google Scholar
    • Export Citation
  • Cameron, D., Beven K. , and Tawn J. , 2000: Modelling extreme rainfalls using a modified random pulse Bartlett–Lewis stochastic rainfall model (with uncertainty). Adv. Water Resour., 24, 203211, doi:10.1016/S0309-1708(00)00042-7.

    • Search Google Scholar
    • Export Citation
  • Carreau, J., Naveau P. , and Sauquet E. , 2009: A statistical rainfall-runoff mixture model with heavy-tailed components. Water Resour. Res., 45, W10437, doi:10.1029/2009WR007880.

    • Search Google Scholar
    • Export Citation
  • Carta, J. A., and Ramírez P. , 2007: Use of finite mixture distribution models in the analysis of wind energy in the Canarian Archipelago. Energy Convers. Manage., 48, 281291, doi:10.1016/j.enconman.2006.04.004.

    • Search Google Scholar
    • Export Citation
  • Chebana, F., and Ouarda T. B. M. J. , 2008: Depth and homogeneity in regional flood frequency analysis. Water Resour. Res., 44, W11422, doi:10.1029/2007WR006771.

    • Search Google Scholar
    • Export Citation
  • Chen, J., Brissette F. P. , and Leconte R. , 2010: A daily stochastic weather generator for preserving low-frequency of climate variability. J. Hydrol., 388, 480490, doi:10.1016/j.jhydrol.2010.05.032.

    • Search Google Scholar
    • Export Citation
  • El-Adlouni, S., and Ouarda T. B. M. J. , 2009: Joint Bayesian model selection and parameter estimation of the generalized extreme value model with covariates using birth-death Markov chain Monte Carlo. Water Resour. Res., 45, W06403, doi:10.1029/2007WR006427.

    • Search Google Scholar
    • Export Citation
  • El-Adlouni, S., Ouarda T. B. M. J. , Zhang X. , Roy R. , and Bobée B. , 2007: Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resour. Res., 43, W03410, doi:10.1029/2005WR004545.

    • Search Google Scholar
    • Export Citation
  • Erişoǧlu, Ü., Erişoǧlu M. , and Erol H. , 2011: A mixture model of two different distributions approach to the analysis of heterogeneous survival data. Int. J. Comput. Math. Sci., 5, 7579.

    • Search Google Scholar
    • Export Citation
  • Escalante-Sandoval, C., 1998: Multivariate extreme value distribution with mixed Gumbel marginals. J. Amer. Water Resour. Assoc., 34, 321333, doi:10.1111/j.1752-1688.1998.tb04138.x.

    • Search Google Scholar
    • Export Citation
  • Evin, G., Merleau J. , and Perreault L. , 2011: Two-component mixtures of normal, gamma, and Gumbel distributions for hydrological applications. Water Resour. Res., 47, W08525, doi:10.1029/2010WR010266.

    • Search Google Scholar
    • Export Citation
  • Geem, Z. W., Kim J. H. , and Loganathan G. V. , 2001: A new heuristic optimization algorithm: Harmony search. Simulation, 76, 6068, doi:10.1177/003754970107600201.

    • Search Google Scholar
    • Export Citation
  • Goldberg, D. E., 1989: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 432 pp.

  • Hamed, K., and Rao A. R. , 2010: Flood Frequency Analysis. Taylor and Francis, 376 pp.

  • Hassanzadeh, Y., Abdi A. , Talatahari S. , and Singh V. , 2011: Meta-heuristic algorithms for hydrologic frequency analysis. Water Resour. Manage., 25, 18551879, doi:10.1007/s11269-011-9778-1.

    • Search Google Scholar
    • Export Citation
  • Heo, J. H., Kho Y. W. , Shin H. , Kim S. , and Kim T. , 2008: Regression equations of probability plot correlation coefficient test statistics from several probability distributions. J. Hydrol., 355, 115, doi:10.1016/j.jhydrol.2008.01.027.

    • Search Google Scholar
    • Export Citation
  • Hu, Y.-M., Liang Z.-M. , Liu Y.-W. , Zeng X.-F. , and Wang D. , 2015: Uncertainty assessment of estimation of hydrological design values. Stochastic Environ. Res. Risk Assess., 29, 501511, doi:10.1007/s00477-014-0979-z.

    • Search Google Scholar
    • Export Citation
  • Hundecha, Y., St-Hilaire A. , Ouarda T. B. M. J. , El Adlouni S. , and 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. Meteor. Climatol., 47, 27452759, doi:10.1175/2008JAMC1665.1.

    • Search Google Scholar
    • Export Citation
  • Hundecha, Y., Pahlow M. , and Schumann A. , 2009: Modeling of daily precipitation at multiple locations using a mixture of distributions to characterize the extremes. Water Resour. Res., 45, W12412, doi:10.1029/2008WR007453.

    • Search Google Scholar
    • Export Citation
  • Katz, R. W., 1999: Extreme value theory for precipitation: Sensitivity analysis for climate change. Adv. Water Resour., 23, 133139, doi:10.1016/S0309-1708(99)00017-2.

    • Search Google Scholar
    • Export Citation
  • Katz, R. W., and Zheng X. , 1999: Mixture model for overdispersion of precipitation. J. Climate, 12, 25282537, doi:10.1175/1520-0442(1999)012<2528:MMFOOP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Katz, R. W., Parlange M. B. , and Naveau P. , 2002: Statistics of extremes in hydrology. Adv. Water Resour., 25, 12871304, doi:10.1016/S0309-1708(02)00056-8.

    • Search Google Scholar
    • Export Citation
  • Kennedy, J., and Eberhart R. , 1995: Particle swarm optimization. Proc. Int. Conf. on Neural Networks, Vol. 4, Perth, WA, Australia, IEEE, 1942–1948, doi:10.1109/ICNN.1995.488968.

  • Kim, K., and Coauthors, 2000: Survey report of water resource management method development in 1999: Drawing Korean probability rainfall map. Korea Institute of Civil Engineering Tech. Rep.

  • Kleiber, W., Katz R. W. , and Rajagopalan B. , 2012: Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes. Water Resour. Res., 48, W01523, doi:10.1029/2011WR011105.

    • Search Google Scholar
    • Export Citation
  • Kwon, H. H., Khalil A. F. , and Siegfried T. , 2008: Analysis of extreme summer rainfall using climate teleconnections and typhoon characteristics in South Korea. J. Amer. Water Resour. Assoc., 44, 436448, doi:10.1111/j.1752-1688.2008.00173.x.

    • Search Google Scholar
    • Export Citation
  • Leclerc, M., and Ouarda T. B. M. J. , 2007: Non-stationary regional flood frequency analysis at ungauged sites. J. Hydrol., 343, 254265, doi:10.1016/j.jhydrol.2007.06.021.

    • Search Google Scholar
    • Export Citation
  • Lee, T., and Ouarda T. B. M. J. , 2010: Long-term prediction of precipitation and hydrologic extremes with nonstationary oscillation processes. J. Geophys. Res., 115, D13107, doi:10.1029/2009JD012801.

    • Search Google Scholar
    • Export Citation
  • Lee, T., and Jeong C. , 2014: Frequency analysis of nonidentically distributed hydrometeorological extremes associated with large-scale climate variability applied to South Korea. J. Appl. Meteor. Climatol., 53, 11931212, doi:10.1175/JAMC-D-13-0200.1.

    • Search Google Scholar
    • Export Citation
  • Li, Z. Z., and Zhang Y. , 2011: Application of Gaussian mixture model and estimator to radar-based weather parameter estimations. IEEE Geosci. Remote Sens. Lett., 8, 10411045, doi:10.1109/LGRS.2011.2151250.

    • Search Google Scholar
    • Export Citation
  • Martins, E. S., and Stedinger J. R. , 2000: Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resour. Res., 36, 737744, doi:10.1029/1999WR900330.

    • Search Google Scholar
    • Export Citation
  • Masina, M., and Lamberti A. , 2013: A nonstationary analysis for the northern Adriatic extreme sea levels. J. Geophys. Res. Oceans, 118, 39994016, doi:10.1002/jgrc.20313.

    • Search Google Scholar
    • Export Citation
  • McLachlan, G. J., and Peel D. , 2000: Finite Mixture Models. Wiley, 456 pp.

  • Mitchell, M., 1998: An Introduction to Genetic Algorithms. MIT Press, 221 pp.

  • Nadarajah, S., and Choi D. , 2007: Maximum daily rainfall in South Korea. J. Earth Syst. Sci., 116, 311320, doi:10.1007/s12040-007-0028-0.

    • Search Google Scholar
    • Export Citation
  • Ouarda, T. B. M. J., and Shu C. , 2009: Regional low-flow frequency analysis using single and ensemble artificial neural networks. Water Resour. Res., 45, W11428, doi:10.1029/2008WR007196.

    • Search Google Scholar
    • Export Citation
  • Ouarda, T. B. M. J., and El-Adlouni S. , 2011: Bayesian nonstationary frequency analysis of hydrological variables. J. Amer. Water Resour. Assoc., 47, 496505, doi:10.1111/j.1752-1688.2011.00544.x.

    • Search Google Scholar
    • Export Citation
  • Overeem, A., Buishand A. , and Holleman I. , 2008: Rainfall depth-duration-frequency curves and their uncertainties. J. Hydrol., 348, 124134, doi:10.1016/j.jhydrol.2007.09.044.

    • Search Google Scholar
    • Export Citation
  • Park, J.-S., Kang H.-S. , Lee Y. S. , and Kim M.-K. , 2011: Changes in the extreme daily rainfall in South Korea. Int. J. Climatol., 31, 22902299, doi:10.1002/joc.2236.

    • Search Google Scholar
    • Export Citation
  • Phien, H. N., and Jivajirajah T. , 1984: Fitting annual rainfall an annual streamflow by two transformed Gamma distributions. Water SA, 10, 65–74.

  • Rossi, F., Fiorentino M. , and Versace P. , 1984: Two-component extreme value distribution for flood frequency analysis. Water Resour. Res., 20, 847856, doi:10.1029/WR020i007p00847.

    • Search Google Scholar
    • Export Citation
  • Russo, S., Dosio A. , Sterl A. , Barbosa P. , and 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, 76287639, doi:10.1002/jgrd.50571.

    • Search Google Scholar
    • Export Citation
  • Schaefli, B., Talamba D. B. , and Musy A. , 2007: Quantifying hydrological modeling errors through a mixture of normal distributions. J. Hydrol., 332, 303315, doi:10.1016/j.jhydrol.2006.07.005.

    • Search Google Scholar
    • Export Citation
  • Shin, J.-Y., Heo J.-H. , Jeong C. , and Lee T. , 2014: Meta-heuristic maximum likelihood parameter estimation of the mixture normal distribution for hydro-meteorological variables. Stochastic Environ. Res. Risk Assess., 28, 347358, doi:10.1007/s00477-013-0753-7.

    • Search Google Scholar
    • Export Citation
  • Singh, V. P., Wang S. , and Zhang L. , 2005: Frequency analysis of nonidentically distributed hydrologic flood data. J. Hydrol., 307, 175195, doi:10.1016/j.jhydrol.2004.10.029.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., Villarini G. , and Baeck M. L. , 2011: Mixture distributions and the hydroclimatology of extreme rainfall and flooding in the eastern United States. J. Hydrometeor., 12, 294309, doi:10.1175/2010JHM1242.1.

    • Search Google Scholar
    • Export Citation
  • Strupczewski, W. G., Kochanek K. , Bogdanowicz E. , and Markiewicz I. , 2012: On seasonal approach to flood frequency modelling. Part I: Two-component distribution revisited. Hydrol. Processes, 26, 705716, doi:10.1002/hyp.8179.

    • Search Google Scholar
    • Export Citation
  • Sun, A. Y., Morris A. P. , and Mohanty S. , 2009: Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques. Water Resour. Res., 45, W07424, doi:10.1029/2008WR007443.

    • Search Google Scholar
    • Export Citation
  • Tramblay, Y., St-Hilaire A. , and Ouarda T. B. M. J. , 2008: Frequency analysis of maximum annual suspended sediment concentrations in North America. Hydrol. Sci. J., 53, 236252, doi:10.1623/hysj.53.1.236.

    • Search Google Scholar
    • Export Citation
  • Vogel, R. M., 1986: Probability plot correlation coefficient test for the normal, lognormal and Gumbel distributional hypotheses. Water Resour. Res., 22, 587590, doi:10.1029/WR022i004p00587.

    • Search Google Scholar
    • Export Citation
  • Vrac, M., and Naveau P. , 2007: Stochastic downscaling of precipitation: From dry events to heavy rainfalls. Water Resour. Res., 43, W07402, doi:10.1029/2006WR005308; Corrigendum, 44, W05702, doi:10.1029/2008WR007083.

    • Search Google Scholar
    • Export Citation
  • Waylen, P., and Woo M.-K. , 1983: Annual floods in southwestern British Columbia, Canada. J. Hydrol., 62, 95105, doi:10.1016/0022-1694(83)90096-3.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., and Wilby R. L. , 1999: The weather generation game: A review of stochastic weather models. Prog. Phys. Geogr., 23, 329357, doi:10.1177/030913339902300302.

    • Search Google Scholar
    • Export Citation
  • Wójcik, R., Troch P. A. , Stricker H. , Torfs P. , Wood E. , Su H. , and Su Z. , 2006: Mixtures of Gaussians for uncertainty description in bivariate latent heat flux proxies. J. Hydrometeor., 7, 330345, doi:10.1175/JHM491.1.

    • Search Google Scholar
    • Export Citation
  • Yoo, C., Jung K. S. , and Kim T. W. , 2005: Rainfall frequency analysis using a mixed Gamma distribution: Evaluation of the global warming effect on daily rainfall. Hydrol. Processes, 19, 38513861, doi:10.1002/hyp.5985.

    • Search Google Scholar
    • Export Citation
  • Yoon, P., Kim T.-W. , Yang J.-S. , and Lee S.-O. , 2012: Estimating quantiles of extreme rainfall using a mixed Gumbel distribution model. J. Korea Water Resour. Assoc., 45, 263274, doi:10.3741/JKWRA.2012.45.3.263.

    • Search Google Scholar
    • Export Citation
  • Yoon, P., Kim T.-W. , and Yoo C. , 2013: Rainfall frequency analysis using a mixed GEV distribution: A case study for annual maximum rainfalls in South Korea. Stochastic Environ. Res. Risk Assess., 27, 11431153, doi:10.1007/s00477-012-0650-5.

    • Search Google Scholar
    • Export Citation
  • Yoon, S., Jeong C. , and Lee T. , 2013: Application of harmony search to design storm estimation from probability distribution models. J. Appl. Math., 2013, 932943, doi:10.1155/2013/932943.

    • Search Google Scholar
    • Export Citation
  • Yue, S., Ouarda T. B. M. J. , Bobée B. , Legendre P. , and Bruneau P. , 1999: The Gumbel mixed model for flood frequency analysis. J. Hydrol., 226, 88100, doi:10.1016/S0022-1694(99)00168-7.

    • Search Google Scholar
    • Export Citation
  • Yue, S., Ouarda T. B. M. J. , and Bobée B. , 2001: A review of bivariate gamma distributions for hydrological application. J. Hydrol., 246, 118, doi:10.1016/S0022-1694(01)00374-2.

    • Search Google Scholar
    • Export Citation
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Heterogeneous Mixture Distributions for Modeling Multisource Extreme Rainfalls

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  • 1 Institute Center for Water Advanced Technology and Environmental Research, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates
  • | 2 Department of Civil Engineering, ERI, Gyeongsang National University, Jinju, South Korea
  • | 3 Institute Center for Water Advanced Technology and Environmental Research, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates
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Abstract

Frequency analysis has been widely applied to investigate the behavior and characteristics of hydrometeorological variables. Hydrometeorological variables occasionally show mixture distributions when multiple generating phenomena cause the extreme events to occur. In such cases, a mixture distribution should be applied. Past studies on mixture distributions assumed that they are drawn from the same probability density functions. In fact, many hydrometeorological variables can consist of different types of probability density functions. Research on heterogeneous mixture distributions can lead to improvements in understanding the behavior and characteristics of hydrometeorological variables and in the capacity to model them properly. In the present study heterogeneous mixture distributions are developed to model extreme hydrometeorological events. To fit heterogeneous mixture distributions, the authors present an extension of the metaheuristic maximum likelihood approach. The performance of the parameter estimation method employed was verified through simulation tests. The fits of nonmixture, homogeneous mixture, and heterogeneous mixture distributions were evaluated through the application to a real-world case study of the extreme rainfall events of South Korea. Results indicate that the heterogeneous mixture distribution is a good alternative when sources possessing dissimilar statistical characteristics influence extreme hydrometeorological variables.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JHM-D-14-0130.s1.

Corresponding author address: Taesam Lee, Assistant Professor, Department of Civil Engineering, Gyeongsang National University, ERI, 501 Jinju-daero, Jinju, Gyeongsangnam-do 660-701, South Korea. E-mail: tae3lee@gnu.ac.kr

Abstract

Frequency analysis has been widely applied to investigate the behavior and characteristics of hydrometeorological variables. Hydrometeorological variables occasionally show mixture distributions when multiple generating phenomena cause the extreme events to occur. In such cases, a mixture distribution should be applied. Past studies on mixture distributions assumed that they are drawn from the same probability density functions. In fact, many hydrometeorological variables can consist of different types of probability density functions. Research on heterogeneous mixture distributions can lead to improvements in understanding the behavior and characteristics of hydrometeorological variables and in the capacity to model them properly. In the present study heterogeneous mixture distributions are developed to model extreme hydrometeorological events. To fit heterogeneous mixture distributions, the authors present an extension of the metaheuristic maximum likelihood approach. The performance of the parameter estimation method employed was verified through simulation tests. The fits of nonmixture, homogeneous mixture, and heterogeneous mixture distributions were evaluated through the application to a real-world case study of the extreme rainfall events of South Korea. Results indicate that the heterogeneous mixture distribution is a good alternative when sources possessing dissimilar statistical characteristics influence extreme hydrometeorological variables.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JHM-D-14-0130.s1.

Corresponding author address: Taesam Lee, Assistant Professor, Department of Civil Engineering, Gyeongsang National University, ERI, 501 Jinju-daero, Jinju, Gyeongsangnam-do 660-701, South Korea. E-mail: tae3lee@gnu.ac.kr

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