The stationarity assumption

Viessman et al. (1977, p. 158) noted that “usually, the length of record as well as the design life for an engineering project are relatively short compared with ge­ologic history and tend to temper, if not justify, the assumption of stationarity.” On the other hand, Klemes (1986) noted that there are many known causes for nonstationarity ranging from the dynamics of the earth’s motion to human- caused changes in land use. In this context, Klemes (1986) reasons that the notion of a 100-year flood has no meaning in terms of average return period, and thus the 100-year flood is really a reference for design rather than a true reflection of the frequency of an event.

3.9.2 Summary comments

The original premise for the use of hydrologic frequency analysis was to find the optimal project size to provide a certain protection level economically, and the quality of the optimization is a function of the accuracy of the estimated flood level. The preceding discussions in this section have indicated that the accuracy of hydrologic frequency estimates may not be high. For example, Beard (1987) reported that the net result of studies of uncertainties of flood frequency analy­sis is that standard errors of estimated flood magnitudes are very high—on the order of 10 to 50 percent depending on the stream characteristics and amount of data available.

Even worse, the assumptions of hydrologic frequency analysis, namely, stationarity and homogeneous, representative data, and good statistical

modeling—not extrapolating too far beyond the range of the data—may be violated or stretched in common practice. This can lead to illogical results such as the crossing of pre — and post-change frequency curves illustrated in Fig. 3.8, and the use of such illogical results is based on “a subconscious hope that nature can be cheated and the simple logic of mathematical manipulations can be substituted for the hidden logic of the external world” (Klemes, 1986).

Given the many potential problems with hydrologic frequency analysis, what should be done? Klemes (1986) suggested that if hydrologic frequency theorists were good engineers, they would adopt the simplest procedures and try to stan­dardize them in view of the following facts:

1. The differences in things such as plotting positions, parameter-estimation methods, and even the distribution types, may not matter much in design optimization (Slack et al., 1975). Beard (1987) noted that no matter how reli­able flood frequency estimates are, the actual risk cannot be changed. Thus the benefits from protection essentially are a function of investment and are independent of uncertainties in estimating flood frequencies. Moderate changes in protection or zoning do not change net benefits greatly; i. e., the benefit function has a broad, flat peak (Beard, 1987).

2. There are scores of other uncertain factors in the design that must be settled, but in a rather arbitrary manner, so the whole concept of optimization must be taken as merely an expedient design procedure. The material covered in Chaps. 4, 6, 7, and 8 of this book provide methods to consider the other uncertain factors and improve the optimization procedure.

3. Flood frequency analysis is just one convenient way of rationalizing the old engineering concept of a safety factor rather than a statement of hydrologic truth.

Essentially, the U. S. Water Resources Council (1967) was acting in a manner similar to Klemes’ approach in that a standardized procedure was developed and later improved (Interagency Advisory Committee on Water Data, 1982). However, rather than selecting and standardizing a simple procedure, the rel­atively more complex log-Pearson type 3 procedure was selected. Beard (1987) suggested that the U. S. Water Resources Council methods are the best currently available but leave much to be desired.

Given are the significant independent peak discharges measured on the Saddle River at Lodi, NJ, for two 18-year periods 1948-1965 and 1970-1987. The Saddle River at Lodi has a drainage area of 54.6 mi2 primarily in Bergen County. The total data record for peak discharge at this gauge is as follows: 1924-1937 annual peak only, 1938-1987 all peaks above a specified base value, 1988-1989 annual peak only (data are missing for 1966, 1968, and 1969, hence the odd data periods).

3.1 Determine the annual maximum series.

3.2 Plot the annual maximum series on normal, lognormal, and Gumbel probability papers.

3.3 Calculate the first four product moments and L-moments based on the given peak — flow data in both the original and logarithmic scales.

3.4 Use the frequency-factor approach to the Gumbel, lognormal, and log-Pearson type 3 distributions to determine the 5-, 25-, 50-, and 100-year flood peaks.

3.5 Based on the L-moments obtained in Problem 3.3, determine the 5-, 25-, 50-, and 100-year flood peaks using Gumbel, generalized extreme value (GEV), and lognor­mal distributions.

3.6 Determine the best-fit distribution for the annual maximum peak discharge series based on the probability-plot correlation coefficient, the two model relia­bility indices, and L-moment ratio diagram.

3.7 Establish the 95 percent confidence interval for the frequency curve derived based on lognormal and log-Pearson type 3 distribution models.