Verjetnostna analiza visokovodnih konic z metodo vrednosti nad izbranim pragom in z metodo letnih maksimumov : diplomska naloga

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

Poplave so redek in izredno dinamičen pojav. V Sloveniji se poplave praviloma dogajajo zaradi intenzivnih padavin. Za zmanjšanje ogroženosti pred poplavami izvajamo aktivne in pasivne ukrepe, za katere potrebujemo verjetnostne analize visokih vod. Ker lahko poplave ogrožajo tudi človeška življenja, je potrebno verjetnostne analize izvesti kvalitetno in zanesljivo. Verjetnostna analiza visokih vod se najpogosteje dela z metodo letnih maksimumov ali z metodo vrednosti konic nad izbrano mejno vrednostjo - pragom (POT metodo). Metoda letnih maksimumov je precej enostavna za uporabo, medtem ko je pri POT metodi potrebno izbrati ustrezne pogoje neodvisnosti in določiti primerno vrednost praga. Prav zaradi teh lastnosti se POT metoda v praksi uporablja redkeje kot metoda letnih maksimumov. Pri POT analizi upoštevamo vse dogodke nad določeno vrednostjo praga. Pri metodi letnih maksimumov vzorec sestavljajo le največji letni pretoki. V diplomski nalogi je najprej predstavljeno teoretično ozadje obeh metod ter njune prednosti in slabosti. Sledi opis statističnih testov, ki se lahko uporabijo za določitev najustreznejše porazdelitvene funkcije ali testiranje hipotez in enačbe, s katerimi lahko določimo intervale zaupanja za ocenjene vrednosti pretokov. V praktičnem delu naloge smo za vodomerno postajo Litija 1 na reki Savi naredili verjetnostno analizo visokovodnih konic z metodo letnih maksimumov in s POT metodo. Pri verjetnostni analizi smo uporabili različne najpogosteje uporabljene porazdelitvene funkcije in tri različne načine ocenjevanja parametrov porazdelitev: metodo momentov, metodo L-momentov in metodo največjega verjetja. POT metodo smo naredili za različne vrednosti praga in analizirali vpliv vrednosti praga na rezultate. Z uporabo testov smo določili porazdelitveno funkcijo in metodo ocenjevanja parametrov, ki sta dali najboljše rezultate. Na podlagi priporočil različnih tujih avtorjev, smo poskušali določiti optimalno vrednost praga. Rezultate POT metode in metode letnih maksimumov smo primerjali in ugotovili, da je POT metoda dala boljše rezultate kot metoda letnih maksimumov. Pri metodi letnih maksimumov se je za najbolj učinkovito izkazala logaritemsko Pearsonova porazdelitev tipa 3, kjer so bili parametri ocenjeni z metodo L-momentov. Rezultati metode L-momentov so bili pri večini porazdelitev boljši, kot rezultati metode momentov in metode največjega verjetja.

• Language: Slovenian
• Keywords: gradbeništvo, UNI, HS, POT metoda, verjetnostna analiza, visoke vode
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Place of publishing: Ljubljana
• Publisher: [N. Bezak]
• Year: 2012
• Number of pages: XII, 106 str.
• PID: 20.500.12556/RUL-32640
• UDC: 519.21:551.577:627.51(043.2)
• COBISS.SI-ID: 5956193
• Publication date in RUL: 10.07.2015

Secondary language

• Language: English
• Title: Flood frequency analysis with peaks over threshold method and annual maximum series method

Abstract

Floods are natural and dynamic phenomenon. Floods in Slovenia are mostly caused by intensive rainfall. Active and passive flood mitigations are performed to lower flood threat. Floods can endanger human lives, therefore effective and quality flood frequency analysis are important and in addition they are also precondition for flood mitigations. Flood frequency analysis can be carried out with annual maximum series method or peaks over threshold method. The main advantage of annual maximum series method is simplicity. Independence criterion and threshold selection are two important properties of POT method. Due to these difficulties POT method remains unpopular and underemployed in the practice of design flood estimation. POT sample is compounded from all peaks above a certain threshold level. Annual maximum series sample contains only maximum flood of each year. First part of graduation thesis consist theoretical background of partial duration and annual maximum series methods. Goodness of fit tests which can be used for testing hypothesis and distributions comparison are introduced. Confidence intervals are also discussed in thesis. In practical part of thesis flood frequency analysis are performed. Data from gauging station Litija 1 on river Sava was used for analysis. Some frequently used probability distributions and three different parameter estimation techniques were used. Method of moments, method of L-moments and maximum likelihood method were applied to Litija 1 data. POT analyses were carried out for different threshold values and influence of threshold selection on analysis results was discussed. Goodness of fit tests were used for determination of the best fit distribution and for comparison of parameter estimation techniques. We tried to define the optimal threshold value. Analyses results were compared and we find out that POT method gave better results as annual maximum series method. Log-Pearson type 3 distribution with parameters estimated with method of L-moments gave the best fit to data. Method of L-moments gave better results in most of the applied probability distributions as method of moments and maximum likelihood method.