Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events

1. At-site modeling

Henrik Madsen, Peter F. Rasmussen, Dan Rosbjerg

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Two different models for analyzing extreme hydrologic events, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a generalized Pareto distribution for modeling threshold exceedances corresponding to a generalized extreme value distribution for annual maxima. The performance of the two models in terms of the uncertainty of the T-year event estimator is evaluated in the cases of estimation with, respectively, the maximum likelihood (ML) method, the method of moments (MOM), and the method of probability weighted moments (PWM). In the case of ML estimation, the PDS model provides the most efficient T-year event estimator. In the cases of MOM and PWM estimation, the PDS model is generally preferable for negative shape parameters, whereas the AMS model yields the most efficient estimator for positive shape parameters. A comparison of the considered methods reveals that in general, one should use the PDS model with MOM estimation for negative shape parameters, the PDS model with exponentially distributed exceedances if the shape parameter is close to zero, the AMS model with MOM estimation for moderately positive shape parameters, and the PDS model with ML estimation for large positive shape parameters. Since heavy-tailed distributions, corresponding to negative shape parameters, are far the most common in hydrology, the PDS model generally is to be preferred for at-site quantile estimation.
    Original languageEnglish
    JournalWater Resources Research
    Volume33
    Issue number4
    Pages (from-to)747-757
    ISSN0043-1397
    DOIs
    Publication statusPublished - 1997

    Cite this

    @article{0cea971d201d4466a1dacfaad7c9a61c,
    title = "Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: 1. At-site modeling",
    abstract = "Two different models for analyzing extreme hydrologic events, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a generalized Pareto distribution for modeling threshold exceedances corresponding to a generalized extreme value distribution for annual maxima. The performance of the two models in terms of the uncertainty of the T-year event estimator is evaluated in the cases of estimation with, respectively, the maximum likelihood (ML) method, the method of moments (MOM), and the method of probability weighted moments (PWM). In the case of ML estimation, the PDS model provides the most efficient T-year event estimator. In the cases of MOM and PWM estimation, the PDS model is generally preferable for negative shape parameters, whereas the AMS model yields the most efficient estimator for positive shape parameters. A comparison of the considered methods reveals that in general, one should use the PDS model with MOM estimation for negative shape parameters, the PDS model with exponentially distributed exceedances if the shape parameter is close to zero, the AMS model with MOM estimation for moderately positive shape parameters, and the PDS model with ML estimation for large positive shape parameters. Since heavy-tailed distributions, corresponding to negative shape parameters, are far the most common in hydrology, the PDS model generally is to be preferred for at-site quantile estimation.",
    author = "Henrik Madsen and Rasmussen, {Peter F.} and Dan Rosbjerg",
    year = "1997",
    doi = "10.1029/96WR03848",
    language = "English",
    volume = "33",
    pages = "747--757",
    journal = "Water Resources Research",
    issn = "0043-1397",
    publisher = "Wiley-Blackwell",
    number = "4",

    }

    Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events : 1. At-site modeling. / Madsen, Henrik; Rasmussen, Peter F.; Rosbjerg, Dan.

    In: Water Resources Research, Vol. 33, No. 4, 1997, p. 747-757.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events

    T2 - 1. At-site modeling

    AU - Madsen, Henrik

    AU - Rasmussen, Peter F.

    AU - Rosbjerg, Dan

    PY - 1997

    Y1 - 1997

    N2 - Two different models for analyzing extreme hydrologic events, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a generalized Pareto distribution for modeling threshold exceedances corresponding to a generalized extreme value distribution for annual maxima. The performance of the two models in terms of the uncertainty of the T-year event estimator is evaluated in the cases of estimation with, respectively, the maximum likelihood (ML) method, the method of moments (MOM), and the method of probability weighted moments (PWM). In the case of ML estimation, the PDS model provides the most efficient T-year event estimator. In the cases of MOM and PWM estimation, the PDS model is generally preferable for negative shape parameters, whereas the AMS model yields the most efficient estimator for positive shape parameters. A comparison of the considered methods reveals that in general, one should use the PDS model with MOM estimation for negative shape parameters, the PDS model with exponentially distributed exceedances if the shape parameter is close to zero, the AMS model with MOM estimation for moderately positive shape parameters, and the PDS model with ML estimation for large positive shape parameters. Since heavy-tailed distributions, corresponding to negative shape parameters, are far the most common in hydrology, the PDS model generally is to be preferred for at-site quantile estimation.

    AB - Two different models for analyzing extreme hydrologic events, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a generalized Pareto distribution for modeling threshold exceedances corresponding to a generalized extreme value distribution for annual maxima. The performance of the two models in terms of the uncertainty of the T-year event estimator is evaluated in the cases of estimation with, respectively, the maximum likelihood (ML) method, the method of moments (MOM), and the method of probability weighted moments (PWM). In the case of ML estimation, the PDS model provides the most efficient T-year event estimator. In the cases of MOM and PWM estimation, the PDS model is generally preferable for negative shape parameters, whereas the AMS model yields the most efficient estimator for positive shape parameters. A comparison of the considered methods reveals that in general, one should use the PDS model with MOM estimation for negative shape parameters, the PDS model with exponentially distributed exceedances if the shape parameter is close to zero, the AMS model with MOM estimation for moderately positive shape parameters, and the PDS model with ML estimation for large positive shape parameters. Since heavy-tailed distributions, corresponding to negative shape parameters, are far the most common in hydrology, the PDS model generally is to be preferred for at-site quantile estimation.

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    SN - 0043-1397

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