Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: 1. At‐site modeling

Abstract

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.

Detection and attribution of urbanization effect on flood extremes using nonstationary flood‐frequency models

“…Beside block maxima, peaks-over-the threshold series (POT), also known as a Partial Duration Series (PDS), are frequently used to assess the behavior of extreme events [see Madsen et al, 1997;Lang et al, 1999]. It can be shown that a connection exists between the models typically used to estimate flood frequency using either block maxima or the POT series, and both methods would asymptotically lead to equivalent inference.…”

“…It can be shown that a connection exists between the models typically used to estimate flood frequency using either block maxima or the POT series, and both methods would asymptotically lead to equivalent inference. The performance of different estimation methods applied to block maxima and POT series are discussed in Madsen et al [1997]. The analysis of threshold exceedances would potentially be a better tool to detect and attribute the effect of different variables on the high-flow properties as this would ensure that a larger number of data points (all characterizing the extremal part of the distribution) are used to investigate the effects of the variables on high flows.…”

Estimating extreme dry‐spell risk in the middle Ebro valley (northeastern Spain): a comparative analysis of partial duration series with a general Pareto distribution and annual maxima series with a Gumbel distribution

“…This value should be low enough to ensure the inclusion of as much relevant information as possible, without violating the assumption of independence of the peaks. Various methods have been proposed to determine the most appropriate lower bound (Ashkar and Rouselle, 1987;Madsen et al, 1997a). However, Beguería (2003) has shown that the parameters and quantile estimations vary randomly with the threshold value, and no single value is entirely adequate.…”

A direct analysis of flood interval probability using approximately 100-year streamflow datasets

“…Various pds have been fitted to PS discharges including exponential (Cunnane 1973, Madsen et al 1997 and log Pearson 3 (Jayasuriya and Mein 1985). The generalized Pareto (GP) pd is a popular choice with its merits demonstrated in the late 1920s (Fisher andTippet 1928 cited in Ribatet et al 2007).…”