Design events with specified flood risk

Abstract

A maximum likelihood or method of moments estimate of the 99 percentile of a flood flow distribution is the traditional choice for the 100-year design flood event in flood plain planning. Because such estimates ignore the small-sample properties of quantile estimators, the resulting design event values will be exceeded with a probability in excess of that intended. For a sample size of 16 the estimated 100-year flood is, in expectation, the 50-year flood. Bayesian and classical statistical approaches can be used to develop design flood values which, given available hydrologic information, will (on average) be exceeded with the specified 1% design probability. Bias in estimates of expected flood damages and procedures for using regional information at gauged and ungauged sites are discussed. INTRODUCTIONIn flood plain planning, flood plain mapping, and levee and flood control reservoir design, a single estimate of the 100year flood event (and perhaps the 10-, 50-, and 500-year events) often serves as the design event upon which a design and management policy are based. The traditional approach for selecting such design values has been to use a statistically efficient or minimum variance estimate of the 99 percentile of the flood flow distribution [Benson, 1968; Water Resources Council (Hydrology Committee), 1976, pp. 1-20; Kite, 1977]. Such estimates are most often variations of the method of moments or maximum likelihood parameterestimation methods. Other investigators, adopting a Bayesian point of view, have developed the posterior distribution for future flood flows; these distributions integrate the natural variability of flood flows and one's uncertainty concerning the parameters of that distribution [Shane and Gaver, 1970; Wood, 1978; Wood and Rodriguez-Iturbe, 1975a; Woad et al., 1974; Vicens et al., 1975; Benjamin and Cornell, 1970, p. 640]. Some work has even incorporated model uncertainty into the analysis [Wood and Rodriquez-Iturbe, 1975b; Bodo and Unny, 1976; Bogardi et al., 1977]. Classical analogues of the Bayesian approach have been presented by Moran [1957], Beard [1960, 1974 (Appendix A), 1978], Hardison and Jennings [1972], and Thomas [1948]. On the other hand, Wood [1978] and Kuczera [1982a, b] formulated a Bayesian analog of the classical approach. These four approaches for obtaining design flood flow values result from different interpretations of the hydrologic information requirements of flood plain planning studies and the use of different statistical philosophies for developing design flood values which meet those requirements; there is considerable controversy and confusion among practitioners concerning the appropriate procedure for estimating design floods [Jackson, 1981; Thomas, 1976]. It seems that what planners and legal statutes often ask for from statistical hydrologists is a design flood value xp ø which, given the available regional hydrologic and geomorphologic information, will be exceeded with an allowable or design probability of 1 -p. Then a flood control or flood management...

Comprehensive at‐site flood frequency analysis using Monte Carlo Bayesian inference

“…Even though the true flood model is lognormal, the t probability model should be used in estimating the design flood. When n and the exceedance probability are small, (7) can yield a substantially more conservative estimate than classical quantile estimators [Stedinger, 1983]. However, as n increases, m and s converge to their true values and t n _ 1 converges to the normal distribution.…”

“…However, the practical value of (19) is limited by the fact that the integral (18) may not necessarily be bounded for some of the probability distributions used in flood frequency analysis [Stedinger, 1983]. Such situations may be detected by computing the asymptotic coefficient of variation of the estimate (19).…”

“…The Bayesian distribution of an annual maximum flood q is obtained by application of the total probability theorem, yielding the pdf a(qID) = f(qll)(llD) (6) The integral (6) yields the expected pdf of q given the data D. Stedinger [1983] refers to this distribution as the design flood distribution.…”

Application of Bayesian approach to hydrological frequency analysis

“…One of the most attractive advantages of the Bayesian approach is that it couples prior information with sample information to provide a theoretically consistent framework for integrating systematic flow records with regional and hydrologic information within a unit framework, and allows the explicit modeling estimation uncertainties arising from both the flood frequency model and its parameters [18][19][20]. Wood and Rodriguez-Iturbe developed procedures for analyzing and accounting for both statistical uncertainty of competing flood frequency models and parameter uncertainty for the individual models, and then considered the problem of uncertainty among flood frequency models within a Bayesian analysis [21,22].…”

Brief Communication: Likelihood of societal preparedness for global change: trend detection

“…A type II error in the context of an infrastructure decision implies under-preparedness, which is often an error much more costly to society than the type I error (overpreparedness), which the NHST focuses on. Note that type II errors corresponding to under-preparedness are paramount, even in a stationary world as was rigorously shown by Stedinger (1982) for risks posed by floods. For example, the physical implication of a Type I or overpreparedness error in adaptation decisions for flood management is wasted money on unneeded infrastructure.…”