On the possibility of using the empirical distribution function to quantify the probability of exceeding the water color standards
A.V. Yalaletdinova, M.A. Malkova, L.V. Enikeеva, E.A. Kantor
Section: Methodology and research methods. Models and forecasts
We found that the nature of the distribution of water color values within a year depends on seasonality. Therefore, to take into account the above, further analysis of the distribution of the indicator was carried out for each month. The analysis of water color distributions for January, May, July and October is given as an example. Variation series were plotted and empirical water color distribution functions were calculated for each month. It is revealed that the laws of water color distribution do not correspond to normal and log-normal distributions, but are approximated quite accurately by polynomials (theoretical distribution function). For the obtained polynomials, the domains of definition of the values of the argument x,
at which they have all the properties of the distribution function (continuously increase on the interval [0; 1]) are revealed. The hypotheses about the laws of water color distribution tested using Kolmogorov–Smirnov test were confirmed. The methodology used and the resulting water color distribution functions made it possible to calculate the probabilities of an indicator exceeding the specified values, for example, exceeding the standard (20 degrees) for all months. Thus, in January, the probability of not exceeding the standard will is 0.792, in July – 0.562, in October – 0.809, while in May the probability of not exceeding the water color standard is 0.091. Knowledge of the law of water color distribution, taking into account the seasonal characteristics of the studied process, allows to assess the risks of exceeding normative values by the indicator and to use it for making decisions on ensuring normative water quality in terms of color.
Keywords: water quality, water color, empirical distribution function, theoretical distribution function, Kolmogorov–Smirnov test, event probability
Article published in number 4 for 2024 DOI: 10.25750/1995-4301-2024-4-073-082
ISSN 1995-4301
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