Forecasting the design maxima water discharges of floods on the Latorica river according to the data of the Mukachevo gauging station using plotting position formulas
DOI:
https://doi.org/10.32347/2411-4049.2024.3.123-140Keywords:
annual exceedance probability, design maxima discharge, epistemic uncertainty, extrapolation, flood, forecasting, observation data, parametric probability distributions, plotting position formulas, rank-weighted estimatesAbstract
This article presents the results of forecasting design maxima discharges on the Latorica River within Mukachevo town based on hydrological observation data at the “Mukachevo” gauging station using plotting position formulas. While solving the task, a novel non-parametric method of forecasting using observation data is applied. The method includes extrapolating the discrepancy (divergence, disagreement) between the estimates of the statistical annual probabilities of exceedance obtained by different plotting position formulas. The task is considered in the frame of the stationarity hypothesis of the maximum river flow employing a time series of maximal discharges of the Latorica River observed at the “Mukachevo” gauging station from 1947 to 1999.
We involved the thirteen plotting position formulas. There was no specific criterion for choosing them to solve the task. All applied formulas were considered admissible options, and results obtained after using them – expert judgments reflecting decision-makers’ predisposition to more cautious or less expensive decision options in flood management strategies.
The epistemic uncertainty of the different plotting positions was reduced by employing the Fishburn rule. According to this rule, the significance of various plotting positions was given by arranging their estimates in descending order of importance of their values under decision-making. Depending on the selected significance option assignment of the different plotting position formulas, such rank-weighted estimates of the design peak discharges (each of them for annual exceedance probability 1%, 0.5%, and 0.2%) were computed: (1) the rank-weighted upper bound estimate (sup-estimate) corresponding to the predisposition to more cautious decision options; (2) the rank-weighted lower bound estimate (inf-estimate) corresponding to the predisposition to less expensive decision options. As possible control theoretical alternatives for forecasting design maximal discharges considered were five parametric probability distributions: 1) the Kritskyi-Menkel three-parameter gamma distribution; 2) Pearson’s type III distribution; 3) the Extreme value type I distribution (Gumbell’s type I distribution); 4) the Logarithmic Pearson type III distribution; and 5) the Two-parameters logarithmic-normal distribution. The population statistical parameters for these parametric probability distributions were estimated from the sample statistics by the method of moments.
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