Analiza rizika od poplava pomoću prekidnih slučajnih procesa

Abstract

Probabilističko opisivanje veli¬kih voda ima važnu ulogu u hidrotehničkim i vodoprivrednim studijama i projektima koji se bave rizikom od poplava. Osnovni alat za ovaj zadatak je statistička analiza velikih voda, kojom se za određeni protok velike vode vezuje njegova verovatnoća pojave. U tim analizama postoje neizve¬snosti koje najvećim delom potiču od nedovoljnih raspoloživih podataka osmatranja i nepoznavanja raspodele verovatnoće velikih voda. Ove neizvesnosti se ne mogu izbeći, ali je njihovo poznavanje veoma značajno kako bi se omogućilo da se sagledaju ograničenja projektovanih rešenja ili da se, uzimanjem neizvesnosti u obzir, dođe do boljih rešenja. Fokus disertacije su neizvesnosti u oceni velikih voda metodom prekoračenja preko praga (POT metoda), koja je zasnovana na prekidnim slučajnim procesima i predstavlja alter¬nativu standardnom postupku statističke analize godišnjih maksimuma protoka. Iako se ova metoda povremeno nalazila u fokusu istraživača, do sada nije postojalo si¬stematsko razmatranje njene efikasnosti sa gledišta neizvesnosti. Rezultati retkih prethodnih istraživanja nisu bili opšteg karaktera i bili su ograničeni na pojedine slučajeve metode POT. U okviru ove disertacije sistematizovana su dosa¬dašnja saznanja u određi¬vanju neizvesnosti velikih voda metodom POT i izvr¬šeno je vrednovanje odre¬đe¬nih pretpostavki u postupcima proračuna. Obuh¬va¬ćeni su svi relevantni modeli par¬ci¬jalnih serija i postavljen je jedinstven originalni mate¬matički okvir za izvođenje izraza za pokazatelje neizvesnosti u oceni kvantila i verovatnoće velikih voda (pristrasnost, standardna greška, interval poverenja kvantila velikih voda). Metodologija je ilustrovana na većem broju primera uz diskusiju o primenljivosti i efi¬kasnosti pojedinih modela. Disertacija dakle predlaže zaokruženu metodolo¬gi¬ju za celovitu probabilističku analizu velikih voda pomoću metode POT.

Probabilistic characterisation of floods is an important task in water resources management studies and projects addressing flood risks. Main tool for this task is the flood frequency analysis, by which a probability of occurrence is attributed to a ceratin flood flow. A range of uncertainties is inherent in the flood frequency analysis, mostly stemming from limited observational data and lack of knowledge on parent probability distributions. These uncertainties cannot be avoided, but knowing their rainges is very important so that they could be considered in the planning and design process. The focus of the dissertation are the uncertainties in flood frequency assessment by the peaks over threshold (POT) method (or partial duration series method), which is founded in the intermittent stochastic processes and represents an alternative to the standard flood frequency analysis of annual maximum floods. Although the POT method has been occasionally in the focus of hydrologic research, there has been no systematic consideration of its efficiency in terms of uncertainties. Results of rare previous studies were not generalized and were limited to particular cases of the POT method. Within this dissertation, the existing knowledge on uncertainties in floods estimated by the POT method has been systematized and certain assumptions in the calculation procedures have been evaluated. All pertinent POT models used in practice are analysed and the consistent and original mathematical framework for deriving analytical expressions for uncertainty measures (bias, standard errors and confidence intervals of flood quantiles) in the flood frequency estimation is developed. The entire methodology is illustrated with a number of examples, with discussion on the applicability and efficiency of particular POT models. The dissertation therefore proposes the methodology for a complete probabilistic analysis of floods based on the POT method.