Modeliranje stohastičke strukture karakteristika velikih voda dobijenih iz serija pikova iznad praga
Modelling of stohastic structure of flood characteristics derived from peaks over threshold series
Докторанд
Pavlović, DragutinМентор
Despotović, JovanЧланови комисије
Plavšić, JasnaJevremović, Vesna
Radić, Zoran
Dašić, Tina
Метаподаци
Приказ свих података о дисертацијиСажетак
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 durati...on 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).