Some recommendations for hydrological use of the two-parameter Weibull model

The Weibull (WEI) distribution is suitable for studying a wide variety of hydrological phenomena. We discuss some properties of this model that make it appropriate for hydrological applications. We then present some estimation techniques for this distribution, based on generalized probability weighted moments (GPWM), generalized moments (GM), and maximum likelihood (ML). Some comparisons are given of the different estimators. Although the GPWM method may in some situations lead to a slight gain in quantile estimation accuracy, the ML method is the one to be generally recommended. Constructing confidence intervals (CI's) for quantiles of a hydrological variable is a means of assessing the precision of quantile estimates. Inaccurate methods for calculating such CI's have been used, although more accurate techniques may be available. We review and recommend specific methods for calculating such CI's for the two-parameter WEI model.