Flood frequency analysis with systematic and historical or paleoflood data based on the two‐parameter general extreme value models

Abstract

Historical and paleoflood data have become an important source of information for flood frequency analysis. A number of studies have been proposed in the literature regarding the value of historical and paleoflood information for estimating flood quarttiles. These studies have been generally based on computer simulation experiments. In this paper the value of using systematic and historical/paleoflood data relative to using systematic records alone is examined analytically by comparing the asymptotic variances of flood quantiles assuming a two-parameter general extreme value marginal distribution, type 1 and type 2 censored data, and maximum likelihood estimation method. The results of this study indicate that the value of historical and paleoflood data for estimating flood quarttiles can be small or large depending on only three factors: the relative magnitudes of the length of the systematic record (N) and the length of the historical period (M); the return period (T) of the flood quanti!e of interest; and the return period (H) of the threshold level of perception. For instance, for N --50, M = 50 and T = 500, the statistical gain for type 2 censoring becomes significantly larger than for type 1 censoring as H becomes greater than 100 years. In addition, computer experiments have shown that the results regarding the statistical gain based on asymptotic considerations are valid for the usual sample sizes. 1Now at books, damage reports (for instance, records of bridge repairs), unpublished written records, and verbal communication from the general public. Paleoflood data are generally obtained from the botanical evidence left by past floods through corrosion scars, adventitious sprouts, ring anomalies, and vegetation age distribution [Hupp, 1986, 1988] and from paleostage indicators such as silt lines [O'Connor et al., 1986], scour lines [Jarrett and Malde, 1987], and slackwater deposits [Kochel and Baker, 1988]. Both historical and paleoflood information can provide data in various forms such as the magnitude and date of one or more large floods and the occurrence of one or more floo.ds greater than a certain threshold value. The combination of historical and paleoflood data can provide the most accurate information of the magnitude and frequency of extreme floods occurring prior to the systematic period [Fuertsch, 1992]. Frequency analysis of flood data arising from systematic, historical, and paleoflood records has been proposed by several investigators. A review of the literature on this subject has been made by Stedinger and Baker [1987]. Empirical and nonparametric methods for determining flood quantiles have been suggested by many [e.g., Benson, 1950; USWRC, 1982; Hirsch and Stedinger, 1987; Hirsch, 1987; Adamowski and Feluch, 1990; Guo and Cunnane, 1991; also J. D. Salas and B. Fernandez, Plotting position formulas based on systematic, historical and paleoflood data, submitted to Journal of Hydrology, 1993]. Likewise, parametric methods based on the method of moments estimation and the log Pearson type 3 ...

Quantitative historical hydrology in Europe

“…1). Generally, this minimum flood level required to assure documentary evidence of flooding is related with a perception threshold to which the contemporary society was susceptible in terms of damage or social disruption (Stedinger and Cohn, 1986;Francés et al, 1994). This perception threshold is frequently related to a flood water level within urban zones and build-ings with distinct characteristics (e.g.…”

“…For instance, flooding of the Aranjuez Royal gardens (Spain) is produced when the River Tagus overtopped the river banks during discharges exceeding 300 m 3 s −1 (Benito et al, 2003a). A list of k i observations above an arbitrary specified discharge threshold X i in n i years is similar to the analysis of partial duration series (data censored above threshold; Stedinger and Cohn, 1986;Francés et al, 1994;Francés, 2001). Statistically it is important to confirm that years with lack of a historical flood record really corresponded to flows smaller than the discharge threshold X i .…”

FEH Local: Improving flood estimates using historical data

“…with the rarity associated to the target design event), but reaches a minimum at some value of T. In general this minimum is reached when T is such that X 0 corresponds to the Q T quantile, for example T=100 when X 0 corresponds to the 99 th percentile of the distribution, or T=10 when X 0 corresponds to the 90 th percentile. In [14] this property is described by means of the asymptotic variances of GEV parent distributions. Although not proved in a mathematical way, this seems to hold for the simulation study in this paper.…”

Rainfall-runoff modelling and palaeoflood hydrology applied to reconstruct centennial scale records of flooding and aquifer recharge in ungauged ephemeral rivers

“…The stratigraphic record is assumed to be complete for each flood exceeding the threshold of discharge at the palaeoflood site. As such, palaeoflood information can be treated as censored data, which can be handled efficiently by appropriate statistical methods (Stedinger and Cohn, 1986;Francés et al, 1994). Frequency analysis of a 500-yr flood record introduces the question of flood stationarity, since cyclic and systematic climatic and land-use conditions may affect the assumption of statistical parametric models on which the random variable (flood discharge) is independent and identically distributed (see discussion in Redmond et al, 2002;Francés, 2004 The associated FFA curves are shown in Fig.…”