Are parsimonious FF models more reliable than true ones? I. Accuracy of quantiles and moments estimation (AQME) - Method of assessment
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Distribution/Estimation (D/E) procedures were tested for their ability to reproduce the upper tail of a Flood Parent Distribution (FPD). The study was designed to investigate the cognitive limitations of at-site flood frequency modelling (FFM) and to provide the guidance for choosing a D/E procedure for a given hydrological regime and available sample size. Moments (MOM), L-moments (LMM) and maximum likelihood (MLM) were used as alternative methods. This study consists of two parts. The first part describes the methodology and the second part a comparative assessment of the performance of various parsimonious models versus an FPD. The study is based on a simulation experiment in which the Wakeby distribution serves as a FPD and forty D/E procedures are included in the search in respect to the estimation of upper quantiles and moments. The bias and relative root mean square error were used for the assessment of the relative performance of alternative procedures D/E of the distributions and methods of fitting for estimating upper quantiles for both given values of the Wakeby parameters and sample size. The percentage of successful estimations for every D/E was recorded, pointing to the limitations in the application of a D/E for given values of the Wakeby parameters and sample size, and it serves both to improve the efficiency of existing parameter and quantile estimation algorithms and to define tasks for future work. Inclusion of the moment estimation brings out the problem of the inverse-power distributions called here the Limited Existence of Moments (LEM) distributions, such as Wakeby, generalized extreme value and generalized log-logistic distributions. For these distributions, depending on the sample size and the estimation method, the percentage of samples for which an r-order moment exists may be lower than the percentage of successful parameter estimation got by LMM or MLM. The use of LEM distributions means considerable limitation or eve a farewell to the moments and method of moments in flood frequency analysis.
