The bias of the maximum likelihood estimates of flood quantiles based solely on the largest historical records

Abstract

The common practice to improve the assessments of design (upper) quantiles of annual flow maxima distribution is incorporating historical data into flood frequency estimates, which in general are greater than the systematic flood maxima records. A big body of literature was dedicated to this issue showing the advantages and constraints of this approach, but the research was not concentrated on the largest floods which for many reasons cannot be treated in the same way as less important ones. Assuming that only few (k) largest flood peaks in the specified time period (M) are known we applied maximum likelihood censoring type II method to estimate a hundred-year flow quantile. The relative bias supported by the relative root mean square error of the estimates were evaluated in numerical simulation experiments for different values of k and M performed under true and false distribution assumptions. The main and surprising result of the experiments is that in case of a false model assumption the estimation of the upper tail quantiles based on few largest floods in a given period can provide comparable or even better estimates in the sense of the relative bias and relative root mean square error than the estimation for the whole sample.Encouraged by the results of numerical experiments in the aspect of historical heavily censored samples we found that it might be reasonable to use this approach in a situation where all elements of the series of observation are known, but the upper tail of the distribution (in our case, F = 0.99 quantile) will be assessed using only the largest records. The results are presented in the case study research.