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2 2022

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Probability Function Estimation for the Maximum Precipitation Model Using Kernel Estimators

Karczewski Maciej, Kaźmierczak Bartosz, Michalski Andrzej, Kuchar Leszek

Rocznik Ochrona Środowiska

2022

Tom 24

260--275

The distribution of maximum rainfall level is not a homogeneous phenomenon and is often characterised by multimodality and often the phenomenon of the heavy right-hand tail. Modelling this phenomenon using classic probability distributions leads to ignoring multimodality, thus underestimating or overestimating the predicted values in the tail tails – the most important from the point of view of safe dimensioning of drainage systems. To avoid the difficulties mentioned above, a non-parametric kernel estimator method of maximum precipitation density function was used (in the example of rainfall data from a selected station in Poland). The methodology proposed in the paper (for use on any rainfall data from other meteorological stations) will allow the development of more reliable local models of maximum precipitation.

Quantile estimation of probability distributions for maximum daily precipitation and short time series of observational data for engineering design

Kuchar Leszek, Broszkiewicz-Suwaj Ewa

Environment Protection Engineering

2022

Vol. 48, nr 1

35--50

Knowledge of the distribution quantiles of precipitation maximum amounts is required in many fields concerning engineering design or hydrological risk assessment. When the number of observation years is small, it is not possible to fit the probability distribution function to maximum values and to calculate quantiles. This paper presents a procedure for calculating the quantiles of the probability distribution of daily precipitation maximums over a year using stochastic convergence of distributions. The distribution series of random variables, defined based on the cut-off sample with the elimination of the smallest values, made it possible to determine the quantiles for times series of order α of the distribution. These values were approximated by a function from the exponential class and then extrapolated to obtain quantiles for the distribution of maxima. The resulting quantile estimates, for short time series, were corrected using the kurtosis of the data used for estimation, which leads to a very large error reduction.