Testing a numerically-analytical method for prediction design maxima discharges of floods using plotting position formulas: the river Uzh case, the “Uzhhorod” gauging station data

Abstract

There are a lot of analytical probability distributions that might be used to predict peak discharges of floods. However, there is no proper theoretical or another similar justification for choosing an appropriate parametric probability distribution to predict peak discharges of floods by using observed data. As a permissible hypothesis, any of recommended probability distributions can be considered providing it meets the given statistical criteria and other considerations for the adequacy of simulation are taken into account. In turn, more than seventeen plotting position formulas have been proposed. They provide a non-parametric means to estimate the observed data probability distribution. Using a plotting position formula, a plot of the estimated values from a theoretical parametric probability distribution can be compared with the observed data.The choice of a better plotting position formula for fitting the different probability distributions has been discussed many times in hydrology and statistical literature. However, no specific criterion for choosing these formulas has been proposed yet. Perhaps there is no need for such a criterion. Maybe, the diversity of estimates that can be obtained due to these formulas matters more. Due to the diversity of the different plotting position estimates, from the point of view of informational entropy, different plotting position formulas enable revealing epistemic (non-stochastic or subjective) uncertainty in predictions of hydrological extremes.Results of calculating empirical annual probabilities of exceedance observed maxima discharge employing various plotting position formulas show that increasing the predicting horizon toward low probable and more extreme events increases the divergence between the estimates obtained using the different plotting position formulas. Therefore, it is reasonable to assume that this divergence may be extrapolated to predict design maxima discharges of floods based on empirical estimates of plotting position probabilities.This paper proposes a numerically-analytical method using such an extrapolation. It is based on using different plotting position formulas, numerical calculations of plotting position probabilities, and extrapolation of the divergence between the obtained estimates. The method is tested in predicting the maxima discharges of 0.5% and 1% annual probability of exceedance for the Uzh River flowing in the Transcarpathia region, the hydrological station “Uzhhorod” data.