Flood frequency estimation for the design of hydraulic structures is usually performed as a univariate analysis of flood event magnitudes. However, recent studies show that for accurate return period estimation of the flood events, the dependence and the correlation pattern among flood attribute characteristics, such as peak discharge, volume and duration should be taken into account in a multivariate framework. The primary goal of this study is to compare univariate and joint bivariate return periods of floods that all rely on different probability concepts in Yermasoyia watershed, Cyprus. Pairs of peak discharge with corresponding flood volumes are estimated and compared using annual maximum series (AMS) and peaks over threshold (POT) approaches. The Lyne-Hollick recursive digital filter is applied to separate baseflow from quick flow and to subsequently estimate flood volumes from the quick flow timeseries. Marginal distributions of flood peaks and volumes are examined and used for the estimation of typical design periods. The dependence between peak discharges and volumes is then assessed by an exploratory data analysis using K-plots and Chi-plots, and the consistency of their relationship is quantified by Kendall's correlation coefficient. Copulas from Archimedean, Elliptical and Extreme Value families are fitted using a pseudo-likelihood estimation method, verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic and evaluated according to the corrected Akaike Information Criterion. The selected copula functions and the corresponding joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results indicate the importance of the bivariate analysis in the estimation of design return period of the hydraulic structures.
The objective of this study is to compare univariate and joint bivariate return periods of extreme precipitation that all rely on different probability concepts in selected meteorological stations in Cyprus. Pairs of maximum rainfall depths with corresponding durations are estimated and compared using annual maximum series (AMS) for the complete period of the analysis and 30-year subsets for selected data periods. Marginal distributions of extreme precipitation are examined and used for the estimation of typical design periods. The dependence between extreme rainfall and duration is then assessed by an exploratory data analysis using K-plots and Chi-plots and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical, and Extreme Value families are fitted using a pseudo-likelihood estimation method, evaluated according to the corrected Akaike Information Criterion and verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic. The selected copula functions and the corresponding conditional and joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results highlight the effect of sample size on univariate and bivariate rainfall frequency analysis for hydraulic engineering design practices.
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