The study is focused on the analysis and statistical evaluation of the joint probability of the occurrence of hydrological variables such as peak discharge (Q), volume (V) and duration (t). In our case study, we focus on the bivariate statistical analysis of these hydrological variables of the Danube River in Bratislava gauging station, during the period of 1876-2013. The study presents the methodology of the bivariate statistical analysis, choice of appropriate marginal distributions and appropriate copula functions in representing the joint distribution. Finally, the joint return periods and conditional return periods for some hydrological pairs (Q-V, V-t, Q-t) were calculated. The approach using copulas can reproduce a wide range of correlation (nonlinear) frequently observed in hydrology. Results of this study provide comprehensive information about flood where a devastating effect may be increased in the case where its three basic components (or at least two of them) Q, V and t have the same significance.
Flood frequency analysis is usually performed as a univariate analysis of flood peaks using a suitable theoretical probability distribution of the annual maximum flood peaks or peak over threshold values. However, other flood attributes, such as flood volume and duration, are necessary for the design of hydrotechnical projects, too. In this study, the suitability of various copula families for a bivariate analysis of peak discharges and flood volumes has been tested. Streamflow data from selected gauging stations along the whole Danube River have been used. Kendall’s rank correlation coefficient (tau) quantifies the dependence between flood peak discharge and flood volume settings. The methodology is applied to two different data samples: 1) annual maximum flood (AMF) peaks combined with annual maximum flow volumes of fixed durations at 5, 10, 15, 20, 25, 30 and 60 days, respectively (which can be regarded as a regime analysis of the dependence between the extremes of both variables in a given year), and 2) annual maximum flood (AMF) peaks with corresponding flood volumes (which is a typical choice for engineering studies). The bivariate modelling of the extracted peak discharge - flood volume couples is achieved with the use of the Ali-Mikhail-Haq (AMH), Clayton, Frank, Joe, Gumbel, Hüsler-Reiss, Galambos, Tawn, Normal, Plackett and FGM copula families. Scatterplots of the observed and simulated peak discharge - flood volume pairs and goodness-of-fit tests have been used to assess the overall applicability of the copulas as well as observing any changes in suitable models along the Danube River. The results indicate that for the second data sampling method, almost all of the considered Archimedean class copula families perform better than the other copula families selected for this study, and that for the first method, only the upper-tail-flat copulas excel (except for the AMH copula due to its inability to model stronger relationships).
Cardinal Josef Beran leads a procession with the skull of Saint Adalbert of Prague in a fragmented segment from film weekly newsreel. The procession starts at Saint Vitus Cathedral at Prague Castle and walks through the Gate of Giants. Cardinal Beran blesses the remains of Saint Adalbert of Prague on Hradčany Square in Prague.
Writer Josef Štefan Kubín in a garden. Kubín accepts a bouquet of flowers on the occasion of his 100th birthday in Dobříš Chateau in a segment from Československý filmový týdeník (Czechoslovak Film Weekly Newsreel) 1964, issue no. 42.