Modelling of Stohastic Structure of Flood Characteristics Derived From Peaks Over Threshold Series

Na formiranje velikih voda utiču mnogobrojni i međusobno uslovljeni ćinioci, pa se one najčešće opisuju u domenu verovatnoće pojave. Merodavne velike vode, izražene kroz protoke, zapremine, trajanja talasa i slično, uobičajeno se dobijaju analizom verovatnoće pojave na godišnjem nivou, pretežno metodom godišnjih ekstrema. Međutim, unutar godine su moguće pojave većeg broja značajnih poplavnih talasa koji se koriste u analizi verovatnoće 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 više uzastopnih vrednosti. To su veličine slučajnog karaktera i mogu se obuhvatiti zbirnim nazivom karakteristike strukture velikih voda. Predmet istraživanja u disertaciji su informacije o strukturi pojave velikih voda koje se mogu izvesti iz nizova dnevnih protoka uvodenjem različitih karakteristika velikih voda kao slučajnih veličina i analizom njihove verovatnoće pojave. Hipoteza disertacije je da se upotrebom parcijalnih serija tj. pikova iznad praga, kroz koncept slučajnih 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 istraživanja je da se na velike vode primeni metodologija analize pomoću prekidnih slučajnih procesa proširenjem postupaka iz metode pikova. Na karakteristikama velikih voda definišu se dogadaji koji se mogu opisati slučajnim procesima. Zadatak je da se verovatnoće dogadaja opišu funkcijama raspodele i ostvari detaljniji uvid u strukturu velikih voda primenom prekidnih slučajnih procesa. Primena postavljenih hipoteza i predloženih metoda i postupaka analize stohastičke strukture velikih voda prikazana je na podacima o srednjim dnevnim protocima na hidrometrijskoj stanici Bezdan na reci Dunav, za period od 1931. do 2009. godine. Disertacija je organizovana u četiri celine. Prvu čini Uvod, gde je opisan značaj proučavanja velikih voda, postavljeni ciljevi disertacije i dat prikaz pristupa i metoda stohastičke analize velikih voda. Druga celina se bavi teorijskim osnovama za predloženu metodologiju stohastičkog modeliranja karakteristika velikih voda. Nju čine tri glave – od druge do četvrte. Maksimalna godišnja zapremina talasa velikih voda, trajanje talasa i trajanje ciklusa kao slučajni procesi razmatraju se u glavi 2. Metoda pikova iznad praga za analizu maksimalnih godišnjih protoka prikazana je u glavi 3, a karakteristike velikih voda koje se mogu definisati na serijama pikova iznad praga u glavi 4. Treću celinu predstavlja test primer modeliranja stohastičke strukture velikih voda prikazan u glavi 5. Poslednja, četvrta celina, je šesta glava sa zaključcima. U poglavljima o teorijskim osnovama prvo je predstavljen pregled poznatih koncepata za stohastičku analizu. Predstavljene su metode analize i njihova tipizacija. Ukazano je na pretpostavke koje dovode do metoda koje se predlažu u disertaciji. Dat je osvrt i na standardnu proceduru statističke analize velikih voda. Kroz raspravu o maksimalnoj godišnjoj zapremini talasa velike vode koji prekoračuje izabrani prag protoka, postavljene su osnovne stohastičke relacije. Koncepcija analize je da se pri stohastičkoj analizi slučajne veličine, u opštem slučaju bilo koje karakteristike velikih voda, proučavaju: a) broj dogadaja u intervalu vremena, b) trajanje ciklusa izmedu dva, tri ili više uzastopnih dogadaja, c) broj dogadaja u intervalima vrednosti karakteristike, d) vrednosti karakteristika pri jednom, dva ili više uzastopnih dogadaja, e) maksimalne vrednosti karakteristike u vremenskom intervalu. Osnovu teorije predstavljaju postulati o broju prekida (promeni stanja procesa) po vremenu i po zapremini talasa (stavke a) i c)). Iz ovih postulata sledi da njima odgovarajući sistemi diferencijalnih jednačina imaju rešenje koje eksplicitno zavisi od funkcija intenziteta javljanja. Da bi se sistem jednačina rečio, uzimajući u obzir opravdane pretpostavke, usvojeni su oblici funkcija intenziteta koji vode ka binomnom, Puasonovom ili negativnom binomnom zakonu verovatnoće broja dogadaja odnosno prekida u procesu. Ovi oblici su dokazani u dosadašnjoj primeni metode pikova iznad praga. Neprekidne raspodele dužina vremenskog perioda izmedu dva ili više uzastopnih dogadaja i vrednosti karakteristika pri jednom ili više uzastopnih dogadaja (stavkeb) i d)) modelirane su prema eksponencijalnoj, Vejbulovoj ili Pareto raspodeli. U disertaciji se razmatra i rekurentni model koji modelira raspodele agregiranih – udruženih karakteristika preko funkcije intenziteta osnovnog niza, sa oblikom koji odgovara Vejbulovoj raspodeli osnovnog niza karakteristike, i diskretne raspodele broja javljanja. Zatim se, u posebnom poglavlju, daje prikaz klasične metode pikova iznad praga, koja je poseban slučaj prethodno pomenute metodologije, jer koristi u zaključivanju samo deo prethodno iznesenih teorijskih postavki. Radi računarskog formalizovanja postupaka analize podataka, u posebnom poglavlju su dati principi i šeme za tretiranje nizova srednjih dnevnih protoka kao bi se na njima formirali nizovi karakteristika velikih voda po principu prekoračenja izabranog praga. Obuhvaćena je metodologija formiranja kako osnovnih nizova, tako i njihovih agregacija. Metodologija za modeliranje stohastičke strukture velikih voda dobijenih iz serija pikova iznad praga prikazana je na podacima o srednjim dnevnim protocima na reci Dunav za hidrometrijsku stanicu Bezdan. Podaci su iz 79 godina, od 1931. do 2009. godine. Karakteristike velikih voda koje su razmatrane su zapremine talasa velikih voda iznad praga, trajanja prekoračenja, trajanja ciklusa i pikovi protoka. Za raspodele izabranih karakteristika velikih voda, ustanovljeno je da od teorijskih neprekidnih raspodela za veličine prekoračenja, zadovoljavajuće slaganje u većini slučajeva (za većinu baznih protoka) ima Vejbulova raspodela. Prilagodenjem osnovnog niza karakteristike Vejbulovom raspodelom može se posredno doći do modela za funkciju intenziteta broja javljanja, odnosno do njenog integrala. Diskretne raspodele za broj javljanja su drugačije za razne veličine, te mogu biti bilo koje od tri navedene (binomna, Puasonova ili negativna binomna). Predloženi rekurentni modeli raspodela karakteristika i njihovih agregacija, počivaju na postulatima Markova za prekide u vremenu i po vrednosti karakteristike, kao i na nezavisnoti te dve vrste prekida. Modeli se zasnivaju na funkciji intenziteta broja javljanja osnovnog niza, sa oblikom koji odgovara Vejbulovoj raspodeli osnovnog niza karakteristike, i vrednosti parametra karakteristici odgovarajuće diskretne raspodele broja javljanja. Ono što je opšti zaključak je da iako predloženi rekurentni modeli za raspodelu karakteristike formalno imaju opravdanje, proračun jednog od parametara iz raspodele broja javljanja (za koji se prepostavlja da je konstantan, a pokazano je da iz realnih nizova nije) često ne daje dobro slaganje empirijskih i teorijskih raspodela. Zato je predložen postupak kojim se vrši prilagodenje drugom metodom, koja unosi dodatnu složenost u proračune, ali poboljšava slaganje osmotrenih podataka i modela. Kao završetak testiranja daje se prikaz rezulatata analize maksimalnih vrednosti karakteristike na godišnjem nivou (što odgovara dogadaju e)).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 validity 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 prediction 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 Danube 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). An overview of the known concepts of stochastic modelling is given in the theoretical part of the dissertation. The types of methods are systematised and assumptions that lead to methods proposed in the dissertation are drawn. The standard procedure for statistical analysis of floods is also discussed. The basic stochastic relations are introduced through the discussion of the annual maximum volumes of floods that exceed the selected threshold for the discharge. The proposed methodological approach to the stochastic modelling of any flood characteristic includes the following analyses the analysis of: a) a number of occurrences in a time interval, b) a cycle duration or a time between two, three or more consecutive events, c) a number of occurrences in an interval measured in the units of the characteristic variable, d) the value of the flood characteristic in a single event or its cumulative value in two, three or more consecutive events, e) the maximum flood characteristic value in a time interval. A number of interruptions over time and by the flood volume are the postulates of the proposed theory. These postulates imply that the result of the corresponding system of the two differential equations depends on the shape of functions of the occurrence. To solve the system of equations according to all relevant assumptions for the given variable, only those shapes of the intensity function that lead to the binomial, Poisson and negative binomial probability distributions for the number of occurrences or interruptions are considered. The use of these shapes was already proven in the applications of the peak-over-threshold method. Continuous distribution functions of the time periods between two or more con- secutive events and cumulative values of the flood characteristics in two or more consecutive events (items b) and d)) are modelled by exponential, Weibull or Pareto distributions. A recurrence model for the distributions of the aggregated flood characteristics is also considered in the dissertation. The model consists of the discrete distribution for the number of occurrences and the type of the intensity function that corresponds to the Weibull distribution for the base data-series from which the flood characteristic is derived. Consequently, it is shown in a separate chapter, that the traditional peak-overthreshold method is simply a special case of the proposed methodology, i.e. that it is based only on the selected assumptions. For the sake of easier handling of large amounts of data, the basic principles and schemes of the computer procedures that are used for derivation of the partial duration series of the flood characteristics and their aggregates are presented in a separate chapter. The methodology for modelling of stochastic structure of flood characteristics derived from peak-over-threshold series was tested against mean daily flow data from the Bezdan gauging station on the Danube River in Serbia. The data refer to the 79-years long record, i.e. from the period 1931-2009. The analysed flood characteristics are: excess flood volumes and excess flood discharges along with the associated event and cycle durations. For the majority of chosen threshold values the Weibull distribution function provides the best fitting with the exceed values of the chosen flood characteristic. The fitting of the starting partial duration series to the Weibull distribution allows one to define, indirectly, the intensity function of the process and its integral. The proposed recurrence models for distributions of flood characteristics andtheir aggregates rest on the Markov theory both for the time and characteristic value intermissions, as well as on the assumption that the two types of intermittence are independent. The models are based on the occurrence intensity function with the shape corresponding to the Weibull distribution for the starting partial duration series and the parameter of the discrete distribution for the number of occurrences of the considered flood characteristic. The overall conclusion is that there is formal justification for the application of the proposed recurrence model. However, the parameter of the discrete distribution sometimes does not lead to satisfactory fitted results (theoretically, parameter is supposed to be constant, but data records show that it is variable). Due to this conclusion, a modification of the method for parameter determination is introduced to achieve a better fit. However, the modification makes the calculations more complicated than expected. The testing ends with the analysis of annual maximum values (the item e)) of the chosen flood characteristics.M71, UDK 624:556(043.3), teza javno odbranjena 27.12.2013. godine na Građevinskom fakultetu Univerziteta u Beogradu, Mentori: v.prof. Jovan Despotović, dipl.građ.inž. i doc. Jasna Plavšić, dipl.građ.inž., (Gradevinski fakultet Univerziteta u Beogradu). Ostali članovi komisije: v.prof. Vesna Jevremović, dipl.matematičar (Matematički fakultet Univerziteta u Beogradu), doc.dr. Zoran Radić, dipl.grad.inž, (Gradevinski fakultet Univerziteta u Beogradu), doc.dr. Tina Dašić, dipl.grad.inž, (Gradevinski fakultet Univerziteta u Beogradu

Modelling of stohastic structure of flood characteristics derived from peaks over threshold series

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)

Statistička analiza maksimalnih kratkotrajnih kiša metodom godišnjih ekstrema

The analysis of short duration rainfall for one rain gauge station is presented in the paper. The most commonly used theoretical probability distributions are considered as regards the domain of their applicability. The outlier identification and replacement is proposed according to the US and Australian practices. In addition to the analysis of probability distribution of rainfall depth, the necessity is emphasized to analyze temporal distribution of rainfall intensity. The beta distribution is used to describe the distribution of rainfall intensity. Finally, the need for regional short duration rainfall analysis is introduced with basic steps for its implementation.Analiza je data za jednu pluviografsku stanicu. Prikazane su najčešće primenjivane teorijske funkcije raspodele i naglašeni domeni njihove primene. Predložena identifikacija i zamena izuzetaka je prema američkim i australijskim iskustvima. Insistirano je na konceptu analize verovatnoće pojave visine padavina i analizi neravnomernosti intenziteta padavina tokom trajanja kiše. Za opis verovatnoće oblika kiše korišćena je beta raspodela. Na kraju je naglašena potreba regionalne analize maksimalnih kratkotrajnih kiša i izloženi su elementi neophodni da bi se ista realizovala

Prostorne analize jakih kiša kratkog trajanja na teritoriji Srbije

Heavy rain aerial analyses in Serbia are based on data from 26 pluviometrique stations, 435 rain-gauges, long series of maximal daily data for Belgrade and rainfall which caused the exteme floods in Serbia. It is shown that existing practice based on local data sets is hyghly uncertain and new approach based on regional data analyses is proposed.Zbornik radova Građevinskog fakultet

New Krivelj River Tunnel Derivation Around Veliki Krivelj Flotation Waste Heap

REZIME Potreba za povećanjem kapaciteta flotacijske deponije borskog rudnika u Velikom Krivelju za posledicu ima izvestan slom konstrukcije postojeće tunelske derivacije Kriveljske reke koja ide po dnu deponije. U tekstu se prikazuje odabrano rešenje za novu tunelsku derivaciju pravcem pored deponije. Prikazane su osnovne karakteristike tunela, skretne brane na Kriveljskoj reci kao i sigurnosnog preliva brane sa slapištem. Ovim rešenjem se, uz druge potrebne objekte i mere, obezbeđuje buduće tehnološko funkcionisanje proizvodnje bakra i pratećih metala.ABSTRACT Enlagement of existing Bor mines flotation tailing landfields at Veliki Krivelj site leads to inevitable structure collapse of the Kriveljska river tunnel derivation, since that the tunnel lies on the landfield invert. This report depicts final design of the new tunnel derivation traced out of the landfill. Characteristics of the tunnel, diversion dam at the tunnel intake and its safety spillway are presented. The tunnel design, along with other structures design and management decisions, enables future techological integrity of copper and trace metals production in Bor municipality

Analize zavisnosti visina padavina od nadmorskih visina na prostoru Srbije

Analyses of ellevations influences on precipitations in Serbia are based on data from 26 pluviometrique stations, and 437 rain-gauges. Influences are studied for yearly averages, maximal daily data, and heavy rain durations from 10 minutes to 24 hours. For heavy rains elevation influences on main statistics (averages, coefficient of variations and skewness) and design rains (return period 100 years) are analysed. It is shown that range of elevations in Serbia is not wide, so other factors (as the stocastic rain characteristics) are predominant. It is sugested that avalilable metheorological radars data must be detailed studies and used in hydrological practice for the improvement of precipitations prediction and real-time floods forecasting in Serbia.Ubrzani razvoj brzine procesuiranja i kapaciteta memorija računara omogućili su uvođenje hidroloških modela sa distribuiranim parametrima i proračune prostornih karakteristika u okviru GIS-orijentisanih modela. Pri modeliranju se često iz literature preuzimaju određene relacije bez prethodne provere na podacima sa konkretnog sliva. Padavine predstavljaju glavne ulaze hidroloških modela, pa su pouzdane analize prostornog i visinskog rasporeda kiša od presudnog uticaja na krajnje rezultate. Cilj ovog rada je da utvrdi da li je na prostoru Srbije opravdano vršiti korekcije padavina u funkciji promena nadmorske visine. Analize su obuhvatile podatke sa 26 glavnih meteoroloških stanica koje verno reprezentuju visinske odnose na prostoru čitave Srbije. U analize su uključeni podaci o prosečnim godišnjim padavinama, statistike (srednje vrednosti, koeficijenti varijacije i koeficijenti asimetrije) jakih kiša kratkih trajanja, kao i računske vrednosti jakih kiša povratnog perioda 100 godina (verovatnoće pojave 1%) za trajanja u rasponu od 10 minuta do 1 dan. Pored toga ispitana je i zavisnost prosečnih godišnjih padavina sa računskim jednodnevnim padavinama. Zaključeno je da globalno posmatrano na prostoru Srbije nema opravdanja da se uvode korekcije padavina sa nadmorskom visinom, a preporučeno da se kod modeliranja, korišćenjem maksimalno raspoloživih lokalnih podataka merenja, karakter veze ispita i utvrde relacije na svakom konkretnom slivu.Zbornik radova Građevinskog fakultet

Statistička analiza maksimalnih kratkotrajnih kiša metodom godišnjih ekstrema

The analysis of short duration rainfall for one rain gauge station is presented in the paper. The most commonly used theoretical probability distributions are considered as regards the domain of their applicability. The outlier identification and replacement is proposed according to the US and Australian practices. In addition to the analysis of probability distribution of rainfall depth, the necessity is emphasized to analyze temporal distribution of rainfall intensity. The beta distribution is used to describe the distribution of rainfall intensity. Finally, the need for regional short duration rainfall analysis is introduced with basic steps for its implementation.Analiza je data za jednu pluviografsku stanicu. Prikazane su najčešće primenjivane teorijske funkcije raspodele i naglašeni domeni njihove primene. Predložena identifikacija i zamena izuzetaka je prema američkim i australijskim iskustvima. Insistirano je na konceptu analize verovatnoće pojave visine padavina i analizi neravnomernosti intenziteta padavina tokom trajanja kiše. Za opis verovatnoće oblika kiše korišćena je beta raspodela. Na kraju je naglašena potreba regionalne analize maksimalnih kratkotrajnih kiša i izloženi su elementi neophodni da bi se ista realizovala

Concept of polycentricity—the differences between development policies and spatial reality

Contemporary scientific literature and strategic documents suggest the concept of polycentricity as a key factor and the aim of regional development policies. One of the aims of this study is to analyze spatial relations between the nodal regions and to determine (calculate) the level of polycentricity in the region of Vojvodina (Northern Serbia). By quantifying spatial relations in the region (using selected methods), we pointed out the relevance of regional development policies, i.e., the extent to which the proposed measures for reducing regional inequalities are in line with the direction of contemporary spatial relations in the region of Vojvodina. We have used four different methodological tools: rank-size rule, urban primacy index, index of functional centrality, and commuting patterns (levels of functional dependence). The obtained results identified the existence of morphological polycentricity, but also the growing domination of the cities of Novi Sad and Belgrade in regulating and managing spatial and functional relations in the region of Vojvodina. These results are not completely in line with the development directions declared in the strategic documents. Our approach focuses on assessing the influence of the main nodal (sub)centers in managing further spatial and functional relations in the region of Vojvodina

Multivariate and multi-scale generator based on non-parametric stochastic algorithms

A method for generating combined multivariate time series at multiple locations and at different time scales is presented. The procedure is based on three steps: first, the Monte Carlo method generation of data with statistical properties as close as possible to the observed series; second, the rearrangement of the order of simulated data in the series to achieve target correlations; and third, the permutation of series for correlation adjustment between consecutive years. The method is non-parametric and retains, to a satisfactory degree, the properties of the observed time series at the selected simulation time scale and at coarser time scales. The new approach is tested on two case studies, where it is applied to the log-transformed streamflow and precipitation at weekly and monthly time scales. Special attention is given to the extrapolation of non-parametric cumulative frequency distributions in their tail zones. The results show a good agreement of stochastic properties between the simulated and observed data. For example, for one of the case studies, the average relative errors of the observed and simulated weekly precipitation and streamflow statistics (up to skewness coefficient) are in the range of 0.1–9.2% and 0–5.4%, respectively.This is the submitted version of the article: Đ. Marković, S. Ilić, D. Pavlović, J. Plavšić, and N. Ilich, ‘Multivariate and multi-scale generator based on non-parametric stochastic algorithms’, Journal of Hydroinformatics, vol. 21, no. 6, pp. 1102–1117, Nov. 2019, [https://doi.org/10.2166/hydro.2019.071

Merenje protoka na kratkim objektima u hidraulički neregularnim uslovima na primeru HE 'Đerdap 2'

Hydraulic conditions at short structures in most cases prevents the existence of cross sections with parallel streamlines and fully developed turbulent flow profile. In such conditions the flow measurement is rather challenging. In spite of recent developments in flow measuring methods, there is no universal device that can be used in inappropriate hydraulic conditions with adequate accuracy. This paper gives the overview of the contemporary flow measuring methods with the focus on its usability in hydraulically difficult conditions. As a case study, the problem of flow measurements at the intake of the aggregates of Hydroelectric Power Plant (HE) 'Djerdap 2' is presented. Due to its position in Danube and leftovers of preconstruction works in river bed, there is a significant incoming angle of the water to the HE 'Djerdap' turbines. The streamlines angle is larger at the Serbian side then at the Rumanian side, resulting the worse efficiency of the Serbian turbines. To analyze the effect of the curved incoming stream to the turbine performance, the true flowrate has to be measured. Since the Kaplan's short turbines were used and no regular cross section where flow can be measured using standard methods exists, available measuring methods for velocity field measurement were analyzed in this paper. For selected method based on electromagnetic velocity measurement devices, the field check was performed and presented. The paper concludes with the assessment of accuracy and total costs for selected flow measurement method.Merenje protoka na objektima gde ne postoje uslovi za formiranje pravolinijskog razvijenog turbulentnog strujanja predstavlja poseban izazov. I pored značajnog napretka u razvoju merne tehnike, ne postoji univerzalna metoda kojom je moguće izmeriti protok sa u napred poznatom tačnošću. U ovom radu je napravljen presek trenutno raspoloživih metoda sa osvrtom na njihovu upotrebljivost u složenim uslovima kao što je slučaj prostornog rasporeda brzina. Kao primer, razmatran je problem merenja protoka na zahvatima agregata hidroelektrane HE 'Đerdap 2'. Zbog asimetričnog položaja elektrane u odnosu na maticu toka reke Dunava, kao i zbog toga što radovi na čišćenju dna uzvodno od brane nisu sprovedeni do kraja, voda na turbine dotiče pod izvesnim uglom. Taj ugao je veći kod turbina bližih sredini brane (kod srpskih turbina) dok je kod turbina postavljenih uz levu obalu (rumunsku) zanemarljiv. Da bi se analizirao uticaj kosog dostrujavanja na rad turbina, neophodno je izmeriti protoke. Kako su kod primenjenih kratkih cevnih agregata loši hidraulički uslovi za kvalitetno merenje protoka standardnim metodama, u radu se analiziraju moguće varijante snimanja prostornog rasporeda brzina. Za slučaj korišćenja elektormagnetnih sondi, obavljena je i provera uticaj a smetnji od strane magnetnog polja generatora. Na kraju, procenjena je moguća tačnost merenja protoka kao i cena takvog sistema