Open AccessAnalysis of Maximum Runoff Volumes with Different Time Durations of Flood Waves: A Case Study on Topl’a River in Slovakia
Author(s) -
Veronika Bačová Mitková,
Pavla Pekárová
Publication year - 2019
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.179
H-Index - 26
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/362/1/012013
Subject(s) - gumbel distribution , flood myth , copula (linguistics) , hydrology (agriculture) , mathematics , joint probability distribution , statistics , range (aeronautics) , surface runoff , return period , generalized extreme value distribution , extreme value theory , bivariate analysis , log normal distribution , environmental science , geography , geology , geotechnical engineering , ecology , archaeology , biology , materials science , composite material , econometrics
In applied hydrology, it is problematic to assign the flood wave volume values with a certain probability of exceedance to given corresponding T -year discharges. This dependence is highly irregular, and requires knowledge the flood wave course of the given probability. For this reason, this work deals with the determination of the annual maximum discharge volumes on the Topl’a River for the time duration of 2-, 5-, 10- , and 15 -days (V tmax ). The series of 84 years (1931-2015) mean daily discharges of the Topl’a River at Hanušovce above Topl’a station was used as input data to calculate the maximum annual volumes of runoff of the Topl’a River. Subsequently, the theoretical curves of exceedance of the maximal discharge volumes V tmax were determined by the Log-Pearson distribution of the Type III. This type of probability distribution is used to estimate maximum (extreme) values across a range of natural processes. The results showed relatively small differences in estimated T -year volumes when compared to other types of theoretical distribution functions used in hydrological extreme analyses in Slovakia (Gamma, Log-normal, etc.). The second part of our work was focused on the bivariate analysis of the relationship between T -year maximum volumes with different duration and peak discharges by the three Archimedean copula functions (Clayton, Gumbel-Hougaard and Frank). The LPIII distribution was used as marginal probability distribution function. Subsequently joint and conditional return periods of the T -year maximum annual flows and T -year maximum volumes with different time duration were calculated. The first one defines joint return periods as the return periods using one random variable equalling or exceeding a certain magnitude and/or using another random variable equalling or exceeding another certain magnitude. The second one is conditional return periods for one random variable, given that another random variable equals or exceeds a specific magnitude.