Treatment of Zeroes in Tail Modeling of Low Flows

Abstract

The presence of zeroes in a record of low flows usually has been interpreted as being indicative of a stream that goes dry during some periods. However, in some instances, zeroes may appear in a gauging record simply because the actual discharge was below a measurement threshold. For example, in some regions it is sometimes true that the lower limit of a stream gauge is above the true stream bottom, and any (censored) discharges not registered by the gauges are recorded as zeroes. This paper presents a comparison of alternative methods for treatment of zeroes in low-flow estimation procedures when tail models are employed for modeling purposes. Simulation experiments indicate that a Weibull tail model, as fitted using a likelihood-based method for inclusion of censored data, is the best estimator of the 10-year low-flow quantile when zeroes in a data set have arisen as a consequence of censoring. When zeroes in a data set exist because the stream is an ephemeral one, a lognormal mixed tail model fitted using maximum likelihood is the best performer. When one is not sure whether zeroes in a data set are real, it is recommended that the 10-year low-flow quantile be estimated by treating the zeroes as censored values and performing the estimation using the Weibull tail model fitted using maximum likelihood.