Use of historical information in hydrologic frequency analysis
Use of information about historical floods, i.e. extreme floods that occurred prior to systematic gauging, can often substantially improve the precision of flood quantile estimates. Such information can be retrieved from archives, newspapers, interviews with local residents, or by use of paleohydrologic and dendohydrologic traces. Various statistical techniques for incorporating historical information into frequency analyses are discussed in this review paper. The basic hypothesis in the statistical modeling of historical information is that a certain perception water level exists and that during a given historical period preceding the period of gauging, all exceedances of this level have been recorded, be it in newpapers, in people's memory, or trough traces in the catchment such as sediment deposits or traces on trees. No information is available on floods that did not exceed the perception threshold. It is further assumed that a period of systematic gauging is available. Figure 1 illustrates this situation. The U.S. Water Resources Council (1982) recommended the use of the method of adjusted moments for fitting the log Pearson type III distribution. A weighting factor is applied to the data below the threshold observed during the gauged period to account for the missing data below the threshold in the historical period. Several studies have pointed out that the method of adjusted moments is inefficient. Maximum likelihood estimators based on partially censored data have been shown to be much more efficient and to provide a practical framework for incorporating imprecise and categorical data. Unfortunately, for some of the most common 3-parameter distributions used in hydrology, the maximum likelihood method poses numerical problems. Recently, some authors have proposed use of the method of expected moments, a variant of the method of adjusted moments which gives less weight to observations below the threshold. According to preliminary studies, estimators based on expected moments are almost as efficient as maximum likelihood estimators, but have the advantage of avoiding the numerical problems related to the maximization of likelihood functions. Several studies have emphasized the potential gain in estimation accuracy with the use of historical information. Because historical floods by definition are large, their introduction in a flood frequency analysis can have a major impact on estimates of rare floods. This is particularly true when 3-parameter distributions are considered. Moreover, use of historical information is a means to increase the representativity of a outlier in the systematic data. For example, an extreme outlier will not get the same weight in the analysis if one can state with certainty that it is the largest flood in, say, 200 years, and not only the largest flood in, say, 20 years of systematic gauging. Historical data are generally imprecise, and their inaccuracy should be properly accounted for in the analysis. However, even with substantial uncertainty in the data, the use of historical information is a viable means to improve estimates of rare floods.