Primerjava med klasičnimi univariatnimi verjetnostnimi analizami in bivariatnimi z uporabo funkcijekopula

Šraj, Mojca (author), Bezak, Nejc (author), Brilly, Mitja (author)

Verjetnostne analize so osnova za določanje projektnih pretokov. Običajno se pri analizah upošteva le ena spremenljivka, večinoma letna konica pretoka. Ker pa so hidrološki pojavi določeni z več medsebojno odvisnimi spremenljivkami, je pri analizah smiseln multivariaten pristop. Primer takega postopka je funkcija kopula. Klasične, univariatne verjetnostne analize so še vedno predpogoj za izvedbo analiz z uporabo funkcije kopula. Bivariatno verjetnostno analizo z uporabo funkcije kopula smo naredili za letne konice pretokov in pripadajoče volumne vodomerne postaje Litija na reki Savi. Uporabili smo tri funkcije kopula iz Arhimedove družine in parametre ocenili s pomočjo Kendallovega koeficienta korelacije (metoda momentov). Izračunali smo skupne povratne dobe in jih primerjali z univariatnimi povratnimi dobami. Ugotovili smo, da razlike med povratnimi dobami niso zanemarljivo majhne. Pri dogodku iz leta 1990, ki je bil največji v opazovanem obdobju, povratna doba TAND znaša 92 let, TOR pa 17 let. Univariatni povratni dobi konic in volumnov pa ležita v območju med omenjenima povratnima dobama. S pomočjo statističnih in grafičnih kriterijev ustreznosti smo ugotovili, da kopula Gumbel-Hougaard za obravnavani primer izkazuje boljše rezultate kot kopula Clayton ali kopula Frank.

• Language: Slovenian
• Keywords: funkcija kopula, bivariatne analize, Kendallov koeficient korelacije, Arhimedova družina kopul, skupna povratna doba OR, skupna povratna doba AND
• Work type: Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo
• Year: 2013
• Number of pages: 37-48
• Numbering: 26
• PID: 20.500.12556/RUL-83436
• ISSN: 1581-0267
• Publication date in RUL: 28.05.2020

Secondary language

• Language: English
• Title: Comparison between classical univariate frequency analysis and bivariate analysis with copula

Abstract

Frequency analyses are a basis for designing discharge estimations. Univariate flood frequency analyses are usually applied in hydrological practice. Hydrological processes are multivariate, however multivariate analyses are needed. Copula function can be used for multivariate modelling. Classical univariate flood frequency analyses are a precondition for the copula analyses. Flood frequency analyses were made on the annual maximum series data from gauging station Litija on the Sava River. Three copulas from the Archimedean family were used; parameters were estimated with method of moments (based on the Kendall correlation coefficient). Some joint return periods were calculated and compared with the univarite return periods. Differences between return periods were not negligible. In the case of a flood event in 1990, which was the largest in the observed period, TAND was 92 years and TOR was 17 years. Univariate return periods lay between these two values. Statistical and graphical performance measures were used to choose the best fit copula function. Gumbel-Hougaard copula gave better results than Clayton and Frank copulas.

• Keywords: copula function, bivariate analyses, Kendall’s correlation coefficient, Archimedean copula family, joint return period OR, joint return period AND