Hrvatske vode
 
Koincidencija velikih voda Save i Drine
Coincidence of flood waves in the Sava and Drina Rivers

Stevan Prohaska1, Aleksandra Ilić2

Sažetak/Abstract: 

U radu je prikazana teorijska osnova za definiranje koincidencije velikih voda u zoni značajnog međusobnog utjecaja glavne rijeke i pritoke. Prikazane su matematičke osnove i procedure za definiranje linija istih vjerojatnosti pojave, kao i linija vjerojatnosti prekoračenja dvije slučajne varijable. Za slučaj složenog riječnog sustava, ograničenog s dva ulazna profila (na glavnoj rijeci i pritoci) i jednog izlaznog (na glavnoj rijeci), bez značajnog utjecaja dotoka s međusliva, definirane su relevantne konstelacije (kombinacije) maksimalnih godišnjih protoka i njegovih odgovarajućih (sinkronih) vrijednosti protoka na ostalim ulazno/izlaznim profilima. Precizirani su pravci praktičnog korištenja definiranih zavisnosti koincidencija velikih voda, a to su:

a) definiranje mjerodavnih protoka za ekonomsko-optimalni proračun linija nivoa vodnog lica u zoni međusobnog utjecaja glavne rijeke i pritoke,

b) definiranje mjerodavnih velikih voda različitih vjerojatnosti pojave na sektoru glavne rijeke, nizvodno od ušća pritoke, ako su poznati samo protoci na dva ulazna profila (na glavnoj rijeci i pritoci),

c) ocjena statističke značajnosti povijesnih i prognoziranih poplava.

Rezultati primjene navedene procedure proračuna koincidencije velikih voda prikazani su za sektor rijeke Save, od vodomjerne postaje Županja do vodomjerne postaje Sremska Mitrovica, s uključivanjem donjeg toka rijeke Drine, od vodomjerne postaje Radalj do ušća u Savu. Rad je, numerički i grafički, ilustriran rezultatima proračuna pod a), b) i c), za navedeni sektor rijeka Save i Drine.

 

The paper presents a theoretical basis for defining the coincidence of flood waves in the zone of significant interaction between the mainstem and its tributary. It shows the mathematical bases and procedures for defining the lines of same probabilities of occurrence and the lines of probabilities of exceedance for two random variables. In the case of a complex river system, limited by two inlet profiles (on the mainstem and its tributary) and one outlet profile (on the mainstem), without a significant influence of inflow from the inter-catchment, the relevant constellations (combinations) of maximum annual discharges and their corresponding (synchronous) discharge values on other inlet/outlet profiles were determined. The following practical uses of the defined dependences of flood wave coincidences were determined:

a) Definition of design discharges for economically optimal calculation of water table lines in the zone of interaction between the mainstem and its tributary;

b) Definition of design floods of different probabilities of occurrence on the mainstem section downstream of the tributary mouth, if only the discharges on two inlet profiles (on the mainstem and its tributary) are known;

c) Assessment of the statistical significance of historical and forecast floods.

The application results of this procedure of the calculation of flood coincidences are presented for the section of the Sava River from the gauging station Županja to the gauging station Sremska Mitrovica, with the inclusion of the Lower Drina River from the gauging station Radalj to its confluence with the Sava River. The calculation results mentioned under points a), b) and c) for these Sava and Drina sections are used for numerical and graphic illustration of the paper.

Kategorija: 
Izvorni (originalni) znanstveni članak / Original Scientific Paper
Ključne riječi/Key words: 

koincidencija velikih voda, linije istih vjerojatnosti pojave, vjerojatnosti prekoračenja, statistička značajnost poplave

flood coincidence, same probability of occurrence, exceedance probability, statistical significance of floods

Podaci o autorima/Authors affiliations: 

1Institut za vodoprivredu „Jaroslav Černi“, Jaroslava Černog 80, 11000 Beograd, Srbija, stevan.prohaska@jcerni.co.rs

 

2Građevinsko-arhitektonski fakultet, Aleksandra Medvedeva 14, 18000 Niš, Srbija, aleksandra-ilic @gaf.ni.ac.rs

Literatura/References: 

Abramowitz, M.; Stegun, A. I. (1972): Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, INC., New York.

 

Prohaska, S.; Marjanović, N.; Čabrić, M. (1978.): Dvoparametarsko definiranje velikih voda, Vode Vojvodine, Novi Sad.

 

Prohaska, S. (1983.): Koincidencija velikih voda donje Save sa velikim vodama Dunava i Drine, Vode Vojvodine, Novi Sad.

 

Prohaska S.; Isailović D.; Srna P., Marčetić I. (1999.): The Danube and its Basin – A Hydrological Monograph Follow-up volume IV, Coincidence of Flood Flow of the Danube River and its Tributaries, Regional Cooperation of the Danube Countries in the Frame of the International Hydrological Programme of UNESCO, pp 1-187, Water Research Institute Bratislava, Slovakia.

 

Prohaska S. (2006.) Hidrologija II deo, Institut za vodoprivredu “Jaroslav Černi”, Rudarsko-geološki fakultet i RHMZ Srbije, Beograd.

 

Prohaska S.; Ilić A. (2008.): Coincidence of the Probability of Flood Waves, International Conference „Planning and Management of Water Resources Systems“, Organized to celebrate the 50th anniversary of the scientific and educational work, and the 75th birthday of Prof. dr Miloradov Milorad, 25-27 September 2008, Novi Sad, pp. 171-183.

 

Prohaska S.; Ilic A.; Majkic B. (2008.): Multiplecoincidence of flood waves on the main river and its tributaries, IOP Electronic Journal, IOP Conf. Series: Earth and Environmental Science 4 (2008) 012013, rad na 8 str., 2008. doi: 10.1088/1755-1307/4/1/012013

 

Prohaska S.; Ilić A.; Majkić B.; Orlić A.; Stanić Ž. (2009.): Postupak za definiranje višedimenzionalnih vjerojatnosti pojave poplava na složenim riječnim sustavima, Monografija «Upravljanje vodnim resursima Srbije ‘09», Institut za vodoprivredu «Jaroslav Černi», Beograd, ISBN 978-86-82565-24-6, str. 215-232.

 

Prohaska S.; Ilic A. (2010.): Coincidence of Flood Flow of the Danube River and Its Tributaries, (In: Mitja Brilly (Ed.): Hydrological Processes of the Danube River Basin - Perspectives from the Danubian Countries), Publisher: Springer, ISBN 978-90-481-3422-9, Book Chapter 6, p. 175-226. DOI: 10.1007/978-90-481-3423-6_6

 

Prohaska S.; Ilić A.; Bartoš Divac, V. (2010.): Tehničko rješenje: Nova metoda za definisanje višestruke koincidencije poplavnih talasa na složenim rečnim sistemima. Baza privredne komore Beograda.

 

Yevjevich, V. (1972.): Probability and Statistics in Hydrology; Water Resources Publications, Fort Collins, Colo. U.S.A. Yevjevich, V. (1972.): Stochastic Processes in Hydrology; Water Resources Publications, Fort Collins, Colo. U.S.A.