Variability of Empirical Flow Quantiles

Abstract

Empirical quantiles constitute a simple alternative for estimating flow values for which there is a specified nonexceedance probability. The standard error of empirical quantile estimators is a measure of the variability to be expected about the numerical estimates obtained from flow records. It is shown in this work that the standard error of empirical flow quantiles is a function of: (1) The specified probability level associated with a particular quantile; (2) the sample size used in the estimation; and (3) the probability density function governing the realization of flow variates. An example using a series of annual runoff from 1904–1986 in the American River at Folsom Reservoir, California, shows that empirical flow quantiles are efficient, i.e., have standard errors of estimates not exceeding 10% of the actual quantile value when the return periods involved are less than 100 years and the flow record is moderately large. Results from Monte Carlo simulations indicate that the approximate expression for standard error of the empirical quantile derived in this work is accurate to within ±10% of population values.