Low‐flow analysis with a conditional Weibull Tail Model

Estimates of low‐flow quantiles, such as the 7‐day, 10‐year low flow, which are usually obtained by statistical modeling of observed data series, are widely used in water quality management. This paper presents a conditional modeling approach to low‐flow analysis that employs only those data values which are less than or equal to a ceiling value. Modeling in this fashion has been motivated by the observation that annual low flows may derive from mixed processes and by the subjective nature of graphical methods, such as those employed by the U.S. Geological Survey, which are often employed in such cases. Results of Monte Carlo experiments demonstrate that the conditional modeling approach yields a low‐flow quantile estimator whose bias and RMSE are comparable to more conventional modeling approaches of fitting a classical textbook probability distribution on the basis of all observed data values, even when the underlying population is of a “well‐behaved” form. Since the complex forms of mixed low‐flow data distributions are not capable of being represented by classical textbook distributions and since the conditional modeling approach performs comparably to those models even when the data derive from well‐behaved probability distributions, these results imply that the conditional modeling approach is worthy of consideration for use by hydrologists. The conditional modeling approach also leads rather naturally to a scheme, much like that used in index flood methods, whereby a regional low‐flow estimator might be devised. An application of the conditional modeling approach to 48 low‐flow data series in Alabama is presented.