Uncorrelated measurement error in flood frequency inference

Abstract

When measurement error (ME) is present, the true value of the annual maximum discharge and of the censoring threshold discharge is unknown. The impact of using estimated rather than true discharges on the inference of flood quantiles is considered. The likelihood function is formulated for data which consist of annual maximum discharges (systematic data) and occurrences of floods above some threshold discharge (binomial‐censored data). The formulation makes explicit allowance for the corruption of discharges by statistically independent ME. This formulation can be used to get maximum likelihood estimates or perform a Bayesian analysis. A limited sampling experiment was conducted to assess the performance of two‐parameter lognormal maximum likelihood quantile estimators in the presence of simple uncorreiated discontinuous ME. It was found that ME reduces the information content of systematic and binomial‐censored data with the reduction being greatest for distributions with low coefficients of variation. When only using systematic data it was found that the performance of estimators making allowance for ME was, at best, only modestly better than that of estimators ignoring ME. The principal finding, however, was that the performance of maximum likelihood estimators using binomial‐censored data but ignoring ME can be substantially worse than that of estimators making explicit allowance for ME. In fact, the loss in performance can be so great that in some cases, it may be preferable to ignore the binomial‐censored data. Finally, it is shown that a Bayesian analysis of flood data affected by ME provides insights not offered by maximum likelihood estimation. When the threshold discharge is in error, the posterior distribution of the lognormal parameters can become bimodal as the length of the binomial‐censored record increases, indicating an inconsistency between the information in the systematic and binomial‐censored data.