On the instabilities of estimated distributions of the POT (Peak Over Threshold) low flow characteristics

In a certain stream gauge profile, consider the low flow flows determined with the POT (Peak Over Threshold) method. Each of the flows can be described by three characteristics – deficit, duration and minimal flow. Values of the three-dimensional random variable depend on the choice of truncation level Qg (threshold flow) – POT method parameter. It is typically assumed that the threshold level is included within the range from Q95% to Q60% (Tallaksen, van Lanen 2004). However, in computational practice the Qg value is determined at the level of either Q90% to Q70%. This choice is made mainly from the hydrological (not statistical) point of view. In this paper the influence of the threshold flow on the form of estimated distributions of each of the above three characteristics is considered. The following distributions are chosen: − GEV (generalised extreme value distribution) – while examining the distribution of extremes; − log-normal – in the non-extreme case. In each of the examined stream gauge profiles the following algorithm was used: 1. from the curve of duration sums, two flow values Q90% and Q55% are chosen 2. for each flow from the range (Q90%, Q55%), using the Zelenhasić method (1987), a three-dimensional sequence is determined of observed deficits, durations and minimal flow values; 3. for each of the one-dimensional sequences, the parameters of the above distributions are estimated. The variability of the estimated quantiles and their intervals of confidence were shown with the example of three gauge profiles – Kuripapango (New Zealand), Bogusław (Prosna) and Bystrzyca Kłodzka (Nysa Kłodzka).