Modeliranje stohastičke strukture karakteristika velikih voda dobijenih iz serija pikova iznad praga

Abstract

Na formiranje velikih voda utiˇcu mnogobrojni i medusobno uslovljeni ˇcinioci, pa se one najˇceˇs´ce opisuju u domenu verovatno´ce pojave. Merodavne velike vode, izraˇzene kroz protoke, zapremine, trajanja talasa i sliˇcno, uobiˇcajeno se dobijaju analizom verovatno´ce pojave na godiˇsnjem nivou, preteˇzno metodom godiˇsnjih ek- strema. Medutim, unutar godine su mogu´ce pojave ve´ceg broja znaˇcajnih poplavnih talasa koji se koriste u analizi verovatno´ce metodom pikova iznad praga. Karakteristike velikih voda dobijaju se iz nizova dnevnih protoka. U disertaciji se pored osnovnih nizova karakteristika uvode u razmatranje i agregacije od dve ili viˇse uzastopnih vrednosti. To su veliˇcine sluˇcajnog karaktera i mogu se obuhvatiti zbirnim nazivom karakteristike strukture velikih voda. Predmet istraˇzivanja u disertaciji su informacije o strukturi pojave velikih voda koje se mogu izvesti iz nizova dnevnih protoka uvodenjem razliˇcitih karakteristika velikih voda kao sluˇcajnih veliˇcina i analizom njihove verovatno´ce pojave. Hipoteza disertacije je da se upotrebom parcijalnih serija tj. pikova iznad praga, kroz koncept sluˇcajnih procesa, analiziraju elementi procesa velikih voda, odnosno njihove strukture i da sve ekstremne vrednosti (vrhovi poplavnih talasa, zapremine talasa velikih voda) nose informaciju o pojavi velikih voda. Cilj istraˇzivanja je da se na velike vode primeni metodologija analize pomo´cu prekidnih sluˇcajnih procesa proˇsirenjem postupaka iz metode pikova. Na karakteri- stikama velikih voda definiˇsu se dogadaji koji se mogu opisati sluˇcajnim procesima. Zadatak je da se verovatno´ce dogadaja opiˇsu funkcijama raspodele i ostvari de- taljniji uvid u strukturu velikih voda primenom prekidnih sluˇcajnih procesa. Primena postavljenih hipoteza i predloˇzenih metoda i postupaka analize stoha- stiˇcke strukture velikih voda prikazana je na podacima o srednjim dnevnim proto- cima na hidrometrijskoj stanici Bezdan na reci Dunav, za period od 1931. do 2009. godine. Disertacija je organizovana u ˇcetiri celine. Prvu ˇcini Uvod, gde je opisan znaˇcaj prouˇcavanja velikih voda, postavljeni ciljevi disertacije i dat prikaz pristupa i me- toda stohastiˇcke analize velikih voda. Druga celina se bavi teorijskim osnovama za predloˇzenu metodologiju stohastiˇckog modeliranja karakteristika velikih voda. Nju ˇcine tri glave – od druge do ˇcetvrte. Maksimalna godiˇsnja zapremina talasa velikih voda, trajanje talasa i trajanje ciklusa kao sluˇcajni procesi razmatraju se u glavi 2. Metoda pikova iznad praga za analizu maksimalnih godiˇsnjih protoka prikazana je u glavi 3, a karakteristike velikih voda koje se mogu definisati na serijama pikova iznad praga u glavi 4. Tre´cu celinu predstavlja test primer modeliranja stohastiˇcke strukture velikih voda prikazan u glavi 5. Poslednja, ˇcetvrta celina, je ˇsesta glava sa zakljuˇccima. U poglavljima o teorijskim osnovama prvo je predstavljen pregled poznatih kon- cepata za stohastiˇcku analizu. Predstavljene su metode analize i njihova tipizacija. Ukazano je na pretpostavke koje dovode do metoda koje se predlaˇzu u disertaciji. Dat je osvrt i na standardnu proceduru statistiˇcke analize velikih voda...

There are number of factors that influence flood occurrence. Many of them are interdependent. Because of their random nature, floods are usually analysed using stochastic models. The most widespread approach in estimating a design-flood is based on the annual maximum series (AMS) of flood discharges. The design-flood is usually defined in terms of a peak-discharge-value, but it may also be defined in terms of its volume or its duration. Another approach is the peak-over-threshold method (POT). As there might be a number of flood occurrences within a year, only those ones whose peaks exceed a given threshold level are used to define flood characteristics in the POT. These floods form a partial duration series. Datasets of flood characteristics are derived from the daily mean flow data. In addition to the basic (raw) datasets of the considered flood characteristic (a peak discharge, a flood duration, a flood volume, a number of flood occurrences within a specified interval, a time duration between the two floods, etc.), datasets derived through aggregation of two or more consecutive members of the basic series are also considered in this dissertation. Members of the derived datasets are also random variables. Together with the corresponding raw data they are termed flood structure characteristics. The dissertation, thus deals with the information about the flood structure that might be deduced from the daily mean flow data through the introduction of flood characteristics and the analysis of their probability distributions using different stoc- hastic models. The main hypothesis is that all relevant information about the floods and their structure are inherent in the values of the flood characteristics that exceed given threshold, i.e. in the partial duration series of flood characteristics. The dissertation aims at applying the theory of intermittent stochastic processes on the series of flood structure characteristics with procedures extended from the peak-over-threshold methods. To do this, probabilities of chosen events should be described with appropriate distribution functions. The data used to check the va- lidity of the posed hypothesis and the applied methodology are obtained from the mean daily series for the Bezdan gauging station on the Danube River in Serbia. These data refer to the 79-years long period, i.e. to the period 1931-2009. The dissertation has four parts that are organised in six chapters. The first part is Chapter 1 Introduction. In this part, the importance of the flood analysis is outlined, aims and objectives of the study are set forth and the stochastic appro- ach to the problem of the flood analysis is presented along with the description of available stochastic models. In the second part, which contains the following three chapters, theoretical bases of the proposed methodology for the description and pre- diction of the flood behaviour are given. The annual maximal volume of the flood, the flood duration and the flood cycle duration are defined as stochastic processes in Chapter 2. The peak-over-threshold method in the analysis of the flood peak discharges is described in Chapter 3, while Chapter 4 presents how the other flood characteristics are defined and derived from the partial duration series of the flood peak discharges. The proposed methodology for modelling stochastic structure of flood characteristics, derived from the peak-over-threshold series, is tested against the 79-years record of mean flow data from the gauging station Bezdan on the Da- nube River in the third part of the dissertation (Chapter 5). The most important conclusions from this study are summarised in the forth part (Chapter 6).