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Censoring - 42 Improving American River Flood Frequency Analyses Censoring below a threshold can be an effective way to account for the fact that commonly assumed parametric distributions (such as the log-Pearson type III distribution) may be inadequate to fit the "true" distribution at a given site. At the very low end, the fact that use of annual flood data (i.e., the largest peak flow in a year) can result in inclusion in the data set peak flows that are clearly not associated with floods. Floods associated with distinctly different hydrometeorological processes, such as hurricanes, convective storms, and rain-on-snow, can lead to complex distributional shapes. In some cases, it is clear that certain mechanisms do not produce large floods, and peak discharges associated with these mechanisms can be separated in the analysis. (In the case of the American River, peak discharges at late spring or early summer snowmelt events are excluded from the analysis.) It is also possible to use mixture models in the analysis or highly parameterized distributions (such as the Wakeby) that have complex shapes. These techniques suffer from estimation problems caused by the large number of parameters. It may be preferable to resort instead to methods for censoring the data set below some threshold. Although censoring reduces the quantity of sample data, Monte Carlo results indicate that censoring can actually improve estimation efficiency (Wang, 1997). The practice of low censoring effectively allows the analyst to place the estimation focus where it belongs, on the upper tail of the distribution (NRC, 1988). There are several approaches that can be used in estimation with data censored below a given threshold. Non-parametric approaches avoid the assumption of a specific distribution function. Parametric approaches are based on an assumed distribution either for the entire population or for exceedances of a specified threshold. Non-parametric estimation methods, which typically use kernel-based estimators of the density or quantile function, can be applied to estimation of the upper tail ofa distribution (Moon and Lall, 1994). Particularly appropriate is the use of kernel functions with bounded support, as only the data values falling within a fmite range. of an estimated quantile have a bearing on the resulting estimate. Breiman and Stone (1985) give a non-parametric method for tail modeling, which essentially involves fitting a quadratic rnodel to the upper part of the data. Non- parametric methods in general, and especially kernel-based methods, are often criticized when they are used for extrapolation beyond the range of the data; but extrapolation beyond the data poses problems for all methods of estimation. The committee did not explore the application of non-parametric methods to the American River data because such an approach would diverge significantly from the Bulletin 17-B guidelines. There are several estimation methods that can be applied to fit a chosen distribution, such as the log-Pearson type III, to values exceeding a given threshold. The method of maximum likelihood is efficient for many distributions (Leese, 1973; Stedinger and Cohn, 1986), but it often has convergence problems for the log- Pearson type Ill. Alternative methods include distributional truncation (see Durrans, 1996); partial probability weighted moments (Wang, 1990,1996; Kroll and Stedinger, 1996); probability plot regression (Kroll and Stedinger, 1996); LH-moments (Wang, 1997); and the Expected Moments Algorithm (Cohn et a!., 1997). The last method