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Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: 1. At‐site modeling
Author(s) -
Madsen Henrik,
Rasmussen Peter F.,
Rosbjerg Dan
Publication year - 1997
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/96wr03848
Subject(s) - generalized pareto distribution , quantile , estimator , mathematics , series (stratigraphy) , extreme value theory , generalized extreme value distribution , statistics , method of moments (probability theory) , maxima , shape parameter , biology , art history , art , paleontology , performance art
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.