No 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are valid for the usual sample sizes. 1Now at books, damage reports (for instance, records of bridge repairs), unpublished written records, and verbal communication from the general public.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 ...

Abstract. Regional frequency analyses based on index flood procedures have been used within the hydrologic community since 1960. It appears that when the index flood method was first suggested, the index flood was taken to be the at-site population mean, which, in turn, in the last two or three decades, has been estimated by the at-site sample mean. The objectives of this paper are to investigate the consequences of replacing a population characteristic with its sample counterpart and to propose an analytically correct regional model dubbed as the population index flood (PIF) method. In this method the homogeneity of the region is embedded in the structure of the parameter space of the underlying distribution model. Simulation experiments are conducted to test the proposed PIF method based on the generalized extreme value distribution with parameters estimated using the method of maximum likelihood (MLE) and the method of probabilityweighted moments (PWM). Furthermore, in the simulation experiments the PIF method is compared with the Hosking and Wallis [1997] regional estimation scheme (HW scheme). Comparing among all index flood methods investigated herein, the PIF method with parameters estimated using MLE provides the best overall results for the 0.95 and the 0.99 quantiles in terms of both bias and root-mean-square error for moderate to sufficiently large sample sizes, but for the 0.995 quantile the HW scheme seems to perform best for the investigated sample sizes.

The stochastic analysis, modeling, and simulation of climatic and hydrologic processes such as precipitation, streamflow, and sea surface temperature have usually been based on assumed stationarity or randomness of the process under consideration. However, empirical evidence of many hydroclimatic data shows temporal variability involving trends, oscillatory behavior, and sudden shifts. While many studies have been made for detecting and testing the statistical significance of these special characteristics, the probabilistic framework for modeling the temporal dynamics of such processes appears to be lacking. In this paper a family of stochastic models that can be used to capture the dynamics of abrupt shifts in hydroclimatic time series is proposed. The applicability of such ''shifting mean models'' are illustrated by using time series data of annual Pacific decadal oscillation (PDO) indices and annual streamflows of the Niger River.

The Yule-Walker equations for ARMA (p, q) models with periodic parameters are derived from which moment estimates can be obtained. Specifically, for the case of ARMA (p, 1) models, the periodic autoregressive parameters can be found by solving a system of linear equations, while the periodic moving average parameters satisfy a system of equations which can be solved iteratively. Particular examples are given and comparisons are made between the proposed moment estimates and estimates given previously.