| The method of L-moments is the recommended method for fitting the three
parameters (location, scale and shape) of a Generalised Logistic (GLO) distribution when
conducting flood frequency analyses in the UK. This paper examines the sampling uncertainty of
quantile estimates obtained using the GLO distribution for single site analysis using the
median to estimate the location parameter. Analytical expressions for the mean and variance
of the quantile estimates were derived, based on asymptotic theory. This has involved deriving
expressions for the covariance between the sampling median (location parameter) and the
quantiles of the estimated unit-median GLO distribution (growth curve). The accuracy of the
asymptotic approximations for many of these intermediate results and for the quantile estimates
was investigated by comparing the approximations to the outcome of a series of Monte Carlo
experiments. The approximations were found to be adequate for GLO shape parameter values
between –0.35 and 0.25, which is an interval that includes the shape parameter estimates for
most British catchments. An investigation into the contribution of different components to
the total uncertainty showed that for large returns periods, the variance of the growth curve
is larger than the contribution of the median. Therefore, statistical methods using regional
information to estimate the growth curve should be considered when estimating design events at
large return periods.
Keywords: flood frequency analysis, Flood Estimation Handbook, single site, annual
maximum series, Generalised Logistic Distribution, uncertainty |