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Hidrološka analiza za 2015. godinu

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RHMZ Srbije Sektor za hidroloki osmatraki sistem i analize Odeljenje za hidroloke analize Republiki hidrometeoroloki zavodRepublika Srbija

Analiza hidroloke situacije na glavnim slivovima na teritoriji Republike Srbije za 2015. godinu

Za analizu hidroloke situacije u 2015. godini korieni su podaci sa hidrolokih stanica na Dunavu, Tisi, Savi i Velikoj Moravi. Izbor je uinjen sa ciljem da se dobije slika o hidrolokoj situaciji na svim veim rekama koje najvee koliine vode dobijaju sa razliitih geografskih regiona (Centralna Evropa i Alpi, Karpati i Balkansko poluostrvo).Kao ulazni parametar vodnog bilansa, prvo su analizirane zalihe vode u snegu na slivu Dunava do Namaroa i na slivu Tise do Segedina za 2015. godinu (slike 1 i 2 izvor: Orszgos Vzjelz Szolglat Hydroinfo, http://www.hydroinfo.hu).

Slika 1: Zalihe vode u snenom pokrivau na Dunavu do Namaroa

Slika 2: Zalihe vode u snenom pokrivau na Tisi do SegedinaNa osnovu podataka o zalihama vode u snenom pokrivau, moe se zakljuiti da su na slivu Dunava do Namaroa, zalihe vode u snenom pokrivau u prvih 5 meseci 2015. godine bile ispod proseka (sem u drugoj dekadi februara), dok su na slivu Tise do Segedina bile znatno ispod proseka.Nepovoljni ulazni elementi vodnog bilansa tokom 2015. godine, osim smanjenih zaliha vode u snenom pokrivau na kraju zimskog perioda, manifestovale su se i kroz padavine, koje su bile ispod proseka u periodu januar - decembar na slivu Dunava, Tise i Save van nae i na naoj teritoriji. Rezultat toga je smanjeni dotok u rena korita tokom druge polovine 2015. godine, tako da su se vrednosti protoka vode kretale ispod i znatno ispod prosenih.Na teritoriji Republike Srbije, za hidroloku analizu korieni su podaci sa stanica Bezdan i Smederevo na Dunavu, Senta na Tisi, Sremska Mitrovica na Savi i Ljubievski Most na Velikoj Moravi (na slici 3 je grafiki prikaz lokacija hidrolokih stanica).Podaci koji su korieni za hidroloku analizu su: istorijski podaci za ukupan period merenja zakljuno sa 2015. godinom i podaci za 2015. godinu.

Slika 3: Grafiki prikaz lokacija hidrolokih stanica

Reka Dunava) Hidroloka stanica Bezdan

Na hidrogramu (slika 4) prikazane su raunske vrednosti protoka za 2015. godinu, kao i karakteristini protoci reke Dunav u profilu hidroloke stanice Bezdan.

Slika 4: Uporedni hidrogram ekstremnih, srednjih i godinjih protoka za reku Dunav u profilu hidroloke stanice Bezdan

Na osnovu hidrograma i podataka o protocima u profilu hidroloke stanice Bezdan, moe se konstatovati da su do sredine juna protoci varirali oko viegodinjeg proseka. U periodu od sredine juna do sredine oktobra moemo rei da je bio nepovoljan hidroloki reim sa vrednostima protoka ispod vrednosti protoka viegodinjeg proseka. U drugoj i treoj dekadi oktobra dolazi do porasta vrednosti protoka oko viegodinjeg proseka, da bi zatim dolo do pada vrednosti protoka ispod viegodinjeg protoka i pribliavanja anvelopi minimuma, kada je zabeleena i minimalna vrednost protoka, 18. novembra - Qmin,god = 1050 m3/s. Maksimalni protok zabeleen je 28. maja i iznosio je Qmax,god = 4220 m3/s.

Sa ciljem dobijanja dodatnih informacija i zbog potvrivanja prethodnih navoda izvreno je poreenje ukupno proteklih voda (sumarne krive zapremine srednjemesenih protoka - slika 5), iz kojih moemo zakljuiti da je 2015. godina do jula bila oko viegodinjeg proseka, a period od avgusta do kraja godine bio je manje vodan u odnosu na viegodinji prosek.

Slika 5: Sumarne krive zapremine srednjemesenih protoka za reku Dunav u profilu hidroloke stanice Bezdan

Izvrena je dodatna analiza srednjemesenih protoka, a na slici 6 su prikazani srednjemeseni protoci za 2015. godinu i raunski srednjemeseni protoci karakteristinih verovatnoa pojave.

Slika 6: Verovatnoe obezbeenosti srednjemesenih protoka za hidroloku stanicu Bezdan

Prema statistikoj analizi u profilu hidroloke stanice Bezdan (slika 6), protoci su se u periodu jul - septembar pribliili obezbeenosti 95%, to bi u domenu malih voda odgovaralo povratnom periodu od 20 godina.

b) Hidroloka stanica SmederevoZa deonicu toka Dunava, nizvodno od uliva Save i Tise, analizirani su podaci za hidroloku stanicu Smederevo koji su prikazani na hidrogramu na slici 7.

Slika 7: Uporedni hidrogram ekstremnih, srednjih i godinjih protoka za reku Dunav u profilu hidroloke stanice SmederevoAnalizom dijagrama na slici 7 moe se konstatovati da su vrednosti protoka na hidrolokoj stanici Smederevo tokom prve polovine 2015. godine varirale oko viegodinjeg proseka. Poetkom juna dolazi do pada vrednosti protoka, tako da u periodu od sredine juna do sredine oktobra moemo rei da je bio nepovoljan hidroloki reim tj. vrednosti protoka su bile ispod viegodinjeg proseka. U drugoj polovini oktobra dolo je do porasta protoka koji su bili iznad viegodinjeg proseka. Zatim u novembru, vrednosti protoka su opet opale ispod viegodinjeg proseka, gde su varirale do kraja godine. Minimalni godinji protok zabeleen je 26. septembra 2015. godine i iznosio je Qmin,god = 2520 m3/s. Maksimalni godinji protok zabeleen je 2. juna i iznosio je Qmax,god = 8640 m3/s.

Konaan zakljuak se moe izvesti i na osnovu uvida u sumarne krive zapremine srednjemesenih protoka (slika 8). Slika 8: Sumarne krive zapremine protoka za reku Dunav u profilu hidroloke stanice Smederevo

U profilu hidroloke stanice Smederevo sumarna kriva zapremine do maja 2015. godine imala je vrednosti oko viegodinjeg proseka. Za period od juna do kraja godine, moemo konstatovati da je bio manje vodan u odnosu na viegodinji prosek.

Na slici 9 prikazani su srednjemeseni protoci za 2015. godinu i raunski srednjemeseni protoci karakteristinih verovatnoa pojave u profilu hidroloke stanice Smederevo. Protoci u julu su se kretali izmeu obezbeenosti 80% i 95%, dok su se u avgustu, septembru i decembru pribliili obezbeenosti 80%, to u domenu malih voda odgovara povratnom periodu od 5 godina.

Slika 9: Verovatnoe obezbeenosti srednjemesenih protoka za hidrloku stanicu Smederevo

Reka Tisaa) Hidroloka stanica SentaNa slici 10 prikazan je hidrogram reke Tise za 2015. godinu u profilu hidroloke stanice Senta sa odgovarajuim anvelopama i viegodinjim prosekom protoka.

Slika 10: Uporedni hidrogram ekstremnih, srednjih i godinjih protoka za reku Tisu u profilu hidroloke stanice Senta

Na osnovu hidrograma prikazanih na slici 10 i podataka o protocima kod hidroloke stanice Senta izmerenih u 2015. godini, moe se pouzdano tvrditi da se radi o nepovoljnom hidrolokom reimu, jer su protoci bili ispod prosenih vrednosti, uz manje odstupanje poetkom februara i decembra kada su blago prevazili liniju viegodinjih proseka. Najmanji protok je zabeleen 14. avgusta i iznosio je Qmin,god= 140 m3/s, a najvei 29. januara i iznosio je Qmax,god = 1320 m3/s. Za potvrdu prethodnih navoda izvreno je poreenje sumarnih kriva zapremine srednjemesenih protoka prikazanih na slici 11.

Slika 11: Sumarne krive zapremine protoka za reku Tisu u profilu hidroloke stanice Senta

Sa dijagrama na slici 11 moe se zakljuiti da je sumarna kriva zapremine protoka za 2015. godinu znatno ispod viegodinjeg srednjemesenih proseka.

Na slici 12 su prikazani su srednjemeseni protoci za 2015. godinu i raunski srednjemeseni protoci karakteristinih verovatnoa pojave. Slika 12: Verovatnoe obezbeenosti srednjemesenih protoka za hidrloku stanicu Senta

Prema statistikoj analizi protoci u periodu jul - septembar su se pribliili obezbeenosti od 95%, to u domenu malih voda odgovara povratnom periodu od 20 godina.

Reka Savaa) Hidroloka stanica Sremska Mitrovica

Na slici 13 prikazan je hidrogram reke Save za 2015. godinu u profilu hidroloke stanice Sremska Mitrovica sa odgovarajuim anvelopama i viegodinjim prosekom protoka.

Slika 13: Uporedni hidrogram ekstremnih, srednjih i godinjih protoka za reku Savu u profilu hidroloke stanice Sremska MitrovicaNa osnovu hidrograma prikazanih na slici 13 moe se konstatovati da su se poetkom 2015. godine i sve do polovine aprila vrednosti protoka kretale oko i iznad prosenih viegodinjih vrednosti protoka. Od sredine aprila do druge dekade maja, vrednosti protoka su se kretale ispod viegodinjeg proseka tako da je u tom periodu bio nepovoljan hidroloki reim. U poslednjoj dekadi maja dolo je do porasta vrednosti protoka iznad viegodinjeg proseka, posle ega je usledio pad tako da su protoci u periodu od druge dekade juna do polovine oktobra imali vrednosti ispod viegodinjeg proseka, tj. bio je nepovoljan hidroloki reim. Minimalni protok u 2015. godini zabeleen je 19. avgusta i iznosio je Qmin, god = 347 m3/s. Od sredine oktobra do poetka novembra protoci su se kretali iznad prosenih viegodinjih, zatim je dolo do opadanja vrednosti protoka i nastavljen je nepovoljan hidroloki reim do kraja godine. Maksimalni protok za 2015. godinu, Qmax, god = 3770 m3/s, je zabeleen 7. marta 2015. godine.

Na osnovu dijagrama sumarnih krivih zapremine protekle vode (slika 14), moe se konstatovati da je do oktobra, 2015. godina bila vodnija u odnosu na viegodinji prosek. Mesec novembar je bio u okviru viegodinjeg proseka, a u decembru je bilo manje vodno u odnosu na viegodinji prosek.

Slika 14: Sumarne krive zapremine protoka za reku Savu u profilu hidroloke stanice Sremska Mitrovica

Na osnovu statistikih analiza srednjemesenih protoka (slika 15), u profilu hidroloke stanice Sremska Mitrovica protoci su se u periodu jul - septembar pribliili obezbeenosti 80%, to u domenu malih voda odgovara povratnom periodu od 5 godina.

Slika 15. Verovatnoe obezbeenosti srednjemesenih protoka za hidrolokoj stanici Sremska Mitrovica

Reka Velika Moravaa) Hidroloka stanica Ljubievski MostNa slici 16 prikazani su hidrogrami Velike Morave za 2015. godinu u profilu hidroloke stanice Ljubievski Most sa odgovarajuim anvelopama i viegodinjim prosekom.

Slika 16: Uporedni hidrogram ekstremnih, srednjih i godinjih protoka za reku Veliku Moravu u profilu hidroloke stanice Ljubievski Most

Analizom hidrograma prikazanih na slici 16 moe se zakljuiti da su u prvih pet meseci protoci na hidrolokoj stanici Ljubievski Most bili iznad prosenih viegodinjih vrednosti, posle ega je dolo do njihovog naglog opadanja, da bi u drugoj polovini godine bili ispod prosenih vrednosti. U maju su se kretali oko prosenih vrednosti, a u drugoj polovini godine su se pribliili anvelopi minimalnih godinjih protoka. Minimalni protok zabeleen je 9. oktobra i iznosio je Qmin, god = 47 m3/s, a maksimalni protok zabeleen je 3. aprila i bio je Qmax, god = 1710 m3/s.Moe se zakljuiti da je nepovoljan hidroloki reim trajao od maja do kraja godine, ali je porast protoka koji se javio poetkom godine, doprineo poboljanju hidrolokog reima u prvih 5 meseci.

Slika 17: Sumarne krive zapremine protoka u profilu hidroloke stanice Ljubievski Most

Na osnovu sumarnih kriva srednjemesenih protoka za hidroloku stanicu Ljubievski Most (slika 17), moe se zakljuiti da je 2015. bila vodnija od viegodinjeg proseka, emu su doprineli protoci vei od viegodinjih proseka zabeleeni u prvih pet meseci 2015. godine.

Na slici 18 su prikazani srednjemeseni protoci za 2015. godinu i statistiki obraeni srednjemnjseni protoci karakteristinih verovatnoama pojave.

Slika 18. Verovatnoe obezbeenosti srednjemesenih protoka za h.s. Ljubievski Most

Prema statistikoj analizi u profilu hidroloke stanice Ljubievski most (slika 18.), protoci u periodu jun-oktobar bili oko obezbeenosti od 80%, to u domenu malih voda odgovara povratnom periodu od 5 godina, osim u oktobru kada su bili na nivou obezbeenosti izmeu 30% i 50%.

ZAKLJUAK

Na osnovu dijagrama uporednih hidrograma za reke Dunav, Tisu i Savu (slika 19), moemo konstatovati da je u toku prve polovine godine zabeleeno 5 veih porasta protoka, kada su se protoci kretali oko srednjih viegodinjih protoka.

Slika 19: Uporedni hidrogram za reke Dunav, Tisu i Savu za 2015. godinu

U drugoj polovini godine, protoci su bili u opadanju i stagnaciji (manji porasti su registrovani krajem oktobra, krajem novembra i poetkom decembra) i kretali su se uglavnom ispod srednjih viegodinjih proseka sa pribliavanjem anvelopi minimuma.

Na kraju, moe se zakljuiti da je prva polovina 2015. godine u hidrolokom smislu bila prosena, a druga polovina malovodna, ali ne ekstremno suna. Proseni meseni protoci u periodu jul - septembar bili su u domenu malih voda, povratnog perioda od 5 do 20 godina.

Sedmodnevne vrednosti zaliha vode u snenom pokrivau na Dunavu do Namaroa2005JanuarFebruarMartAprilMaj4.3993.1536.849000000000000210.7712.58413.01215.70517.14818.16617.65200000000000111.4529999999999998.657.14299999999999985.85799999999999975.00699999999999975.03399999999999983.39199999999999992006JanuarFebruarMartAprilMaj13.14115.13599999999999914.93099999999999914.63115.4415.9520.20400000000000119.62399999999999915.15900000000000118.35518.25199999999999917.92200000000000111.5879999999999997.34499999999999986.09400000000000035.5243.25599999999999982.58800000000000012015JanuarFebruarMartAprilMaj4.51999999999999965.534.40000000000000044.786.569.02999999999999948.277.587.036.715.845.897.15.75.014.11000000000000033.18prosekJanuarFebruarMartAprilMaj66.57.27.88.19999999999999938.699999999999999399.510109.8000000000000007987.5765.44.8Zalihe vode (km3)

Sedmodnevne vrednosti zaliha vode u snenom pokrivau na Tisi do Segedina2005JanuarFebruarMartAprilMaj0.6251.4823.9152.63499999999999985.796.927.28099999999999977.20399999999999979.05300000000000088.89600000000000086.1173.43599999999999992.38200000000000011.0790.493999999999999990.4370.2512006JanuarFebruarMartAprilMaj4.7584.46699999999999965.32599999999999966.03399999999999985.9445.85599999999999996.47900000000000016.4074.36500000000000025.79300000000000015.925.5163.43500000000000011.3470.7550.527000000000000020.173999999999999996.0000000000000001E-32015JanuarFebruarMartAprilMaj1.09000000000000011.061.581.081.042.161.861.250.850.830.670.450.579999999999999960.270.154.1000000000000002E-20prosekJanuarFebruarMartAprilMaj22.52.833.644.24.54.3432.41.30.80.50.30.20.1Zalihe vode (km3)

Hidrogrami, anvelope i viegodinji prosekProtok 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4200542006420074200842009420104201142012420134201442015420164201742018420194202042021420224202342024420254202642027420284202942030420314203242033420344203542036420374203842039420404204142042420434204442045420464204742048420494205042051420524205342054420554205642057420584205942060420614206242063420644206542066420674206842069420704207142072420734207442075420764207742078420794208042081420824208342084420854208642087420884208942090420914209242093420944209542096420974209842099421004210142102421034210442105421064210742108421094211042111421124211342114421154211642117421184211942120421214212242123421244212542126421274212842129421304213142132421334213442135421364213742138421394214042141421424214342144421454214642147421484214942150421514215242153421544215542156421574215842159421604216142162421634216442165421664216742168421694217042171421724217342174421754217642177421784217942180421814218242183421844218542186421874218842189421904219142192421934219442195421964219742198421994220042201422024220342204422054220642207422084220942210422114221242213422144221542216422174221842219422204222142222422234222442225422264222742228422294223042231422324223342234422354223642237422384223942240422414224242243422444224542246422474224842249422504225142252422534225442255422564225742258422594226042261422624226342264422654226642267422684226942270422714227242273422744227542276422774227842279422804228142282422834228442285422864228742288422894229042291422924229342294422954229642297422984229942300423014230242303423044230542306423074230842309423104231142312423134231442315423164231742318423194232042321423224232342324423254232642327423284232942330423314233242333423344233542336423374233842339423404234142342423434234442345423464234742348423494235042351423524235342354423554235642357423584235942360423614236242363423644236542366423674236842369836047404180380035203320316030202890278026802590250224302350228022202150209020301980192018601800174516901630158015201460141013451290123511701080962742Protok (m3/s)

Sumarne (kumulativne) krive zapremine srednjemesenog protoka - za viegodinji period i 2015. godinuSum_kriva_vieg.IIIIIIIVVVIVIIVIIIIXXXIXII5253.265454400005210302.74919963870316782.19775163869424188.65313434837731807.27631194836439347.84921620642946752.31400980641853068.14342580641858014.5999620644862463.36348046447566885.88893956123571936.426557161234Sum_kriva_20157499.5212773.37618719.42399999999925588.22399999999833918.04799999999541253.40799999999645779.90399999999549556.44799999999752874.20799999999956998.94399999999660238.94399999999664015.487999999998V [10^6] (m3)

10%IIIIIIIVVVIVIIVIIIIXXXIXII26732923338841253858409340313543270623002466270630%IIIIIIIVVVIVIIVIIIIXXXIXII21262329271132163123312231122658211918481871211150%IIIIIIIVVVIVIIVIIIIXXXIXII18351991232427182729267426102190180515901579178880%IIIIIIIVVVIVIIVIIIIXXXIXII14761550181820882241219619811620141812511246138395%IIIIIIIVVVIVIIVIIIIXXXIXII1224122214401636189619191533122711469971032109599%IIIIIIIVVVIVIIVIIIIXXXIXII106099911831337167017721239977969823903905protok 2015280021802220265031102830169014101280154012501410aps mes minIIIIIIIVVVIVIIVIIIIXXXIXII89581096096011701320929784791742790854Q sr mes (m3/s)

Hidrogrami, anvelope i viegodinji prosekProtok 2015420054200642007420084200942010420114201242013420144201542016420174201842019420204202142022420234202442025420264202742028420294203042031420324203342034420354203642037420384203942040420414204242043420444204542046420474204842049420504205142052420534205442055420564205742058420594206042061420624206342064420654206642067420684206942070420714207242073420744207542076420774207842079420804208142082420834208442085420864208742088420894209042091420924209342094420954209642097420984209942100421014210242103421044210542106421074210842109421104211142112421134211442115421164211742118421194212042121421224212342124421254212642127421284212942130421314213242133421344213542136421374213842139421404214142142421434214442145421464214742148421494215042151421524215342154421554215642157421584215942160421614216242163421644216542166421674216842169421704217142172421734217442175421764217742178421794218042181421824218342184421854218642187421884218942190421914219242193421944219542196421974219842199422004220142202422034220442205422064220742208422094221042211422124221342214422154221642217422184221942220422214222242223422244222542226422274222842229422304223142232422334223442235422364223742238422394224042241422424224342244422454224642247422484224942250422514225242253422544225542256422574225842259422604226142262422634226442265422664226742268422694227042271422724227342274422754227642277422784227942280422814228242283422844228542286422874228842289422904229142292422934229442295422964229742298422994230042301423024230342304423054230642307423084230942310423114231242313423144231542316423174231842319423204232142322423234232442325423264232742328423294233042331423324233342334423354233642337423384233942340423414234242343423444234542346423474234842349423504235142352423534235442355423564235742358423594236042361423624236342364423654236642367423684236949304730444043904140406041304360456048004850498053405860641067607020713071407190745077407960794079908040808081208070795078807670754075207480750075107520738071506930668065306450629061606030601059005820569054705450544053105340544057806280672070107220740075507810803082208290825080207690750073607080675065406440618059905730556053205260518050604880503053105550565059006330657068307230744074507320710069706890670063706150606061406170622062406270629063506400637062505940566054305230509050205110512053005450549055105620577059306030613061105970581056205410527051705220526051905190516054506020676074407940828085208600864085508270784073606780616055305210500048504780474048104700449044504490434041904170423042404190425043204610476048204850464043104090385037203470342033803390341034003390337033403200310030103020299029802980298029502970297029902980298029802950298030002960295030003020301030002980297029402870279027402730266026402600260026502700281029503070317031503090300028402770270027402740278028002730269026102640283030603200313030402970292028102690270027102750273027102660261025602520254026102770300033503360336034003350334033903210312031703220318033003430369042104550461048605160537056305670570056905730564055005230488045004290419039003710357034603390335032903160305030202990290028602850286028302830281028302890292031303360372043204740477045804090385036103620390042904820498047904510413038303540341033403330334032503200312031003060307030703080309031003050302030403030Anvelopa min4200542006420074200842009420104201142012420134201442015420164201742018420194202042021420224202342024420254202642027420284202942030420314203242033420344203542036420374203842039420404204142042420434204442045420464204742048420494205042051420524205342054420554205642057420584205942060420614206242063420644206542066420674206842069420704207142072420734207442075420764207742078420794208042081420824208342084420854208642087420884208942090420914209242093420944209542096420974209842099421004210142102421034210442105421064210742108421094211042111421124211342114421154211642117421184211942120421214212242123421244212542126421274212842129421304213142132421334213442135421364213742138421394214042141421424214342144421454214642147421484214942150421514215242153421544215542156421574215842159421604216142162421634216442165421664216742168421694217042171421724217342174421754217642177421784217942180421814218242183421844218542186421874218842189421904219142192421934219442195421964219742198421994220042201422024220342204422054220642207422084220942210422114221242213422144221542216422174221842219422204222142222422234222442225422264222742228422294223042231422324223342234422354223642237422384223942240422414224242243422444224542246422474224842249422504225142252422534225442255422564225742258422594226042261422624226342264422654226642267422684226942270422714227242273422744227542276422774227842279422804228142282422834228442285422864228742288422894229042291422924229342294422954229642297422984229942300423014230242303423044230542306423074230842309423104231142312423134231442315423164231742318423194232042321423224232342324423254232642327423284232942330423314233242333423344233542336423374233842339423404234142342423434234442345423464234742348423494235042351423524235342354423554235642357423584235942360423614236242363423644236542366423674236842369178418081928200020852274227424391914178917881789178617841781177916131607206221412141222822282254225522542254206220622141225423802035231523422201237820822376213123282310226122482255231120612061231222532379237923292473232922952307220826712363245423702363232223152315230923152315230923092315233623632363237025462920327435383891374833213447338033783315324233403340332032903364.323393.357342034403440350035903315376638883866.3483712360334263426331332183606299635723604360438563499349934883467349934993488347834673478342534883499347834363446377534513644358136443643353028693449309834493395321429632598240424112554237723603104347834553143294927052703237724702061246124612900237723842377238423362342240423092309229523022315219321812193214621932170215821342123212321342181218121812181218121132158219323122193218121702158213421582158217021702193210621582181196519772061198919891977197719891994198919771806179418411558154015401558154915581812154915401540152315231498151515231515151515321426141014021410141015231523187218921934190319131934191318721872153215321515154918521855192419441944193418921913190318921872187218821903174115581872155815581850155818701860185018421830183018201800178017801780178017801770177017601750184018401836182418121800180018001790182418521870188018801860184018201800178017801800186019591660178818031788160916051846183817241831181718101803181018031810181018101810181718241838187419032040204920402040204020322016199220672175205820321976193618241800181618321840Viegodinji prosek42005420064200742008420094201042011420124201342014420154201642017420184201942020420214202242023420244202542026420274202842029420304203142032420334203442035420364203742038420394204042041420424204342044420454204642047420484204942050420514205242053420544205542056420574205842059420604206142062420634206442065420664206742068420694207042071420724207342074420754207642077420784207942080420814208242083420844208542086420874208842089420904209142092420934209442095420964209742098420994210042101421024210342104421054210642107421084210942110421114211242113421144211542116421174211842119421204212142122421234212442125421264212742128421294213042131421324213342134421354213642137421384213942140421414214242143421444214542146421474214842149421504215142152421534215442155421564215742158421594216042161421624216342164421654216642167421684216942170421714217242173421744217542176421774217842179421804218142182421834218442185421864218742188421894219042191421924219342194421954219642197421984219942200422014220242203422044220542206422074220842209422104221142212422134221442215422164221742218422194222042221422224222342224422254222642227422284222942230422314223242233422344223542236422374223842239422404224142242422434224442245422464224742248422494225042251422524225342254422554225642257422584225942260422614226242263422644226542266422674226842269422704227142272422734227442275422764227742278422794228042281422824228342284422854228642287422884228942290422914229242293422944229542296422974229842299423004230142302423034230442305423064230742308423094231042311423124231342314423154231642317423184231942320423214232242323423244232542326423274232842329423304233142332423334233442335423364233742338423394234042341423424234342344423454234642347423484234942350423514235242353423544235542356423574235842359423604236142362423634236442365423664236742368423695273.02461428571415305.94034285714325360.02107142857135399.0754571428575406.7638571428575393.51209999999995403.26857142857175367.70731428571435315.34041428571445253.03930000000045267.88948571428595250.18328571428545227.80218571428585236.51364285714325189.02990000000055125.60538571428615058.21041428571434992.58181428571425004.86648571428584963.1436714285714922.89867142857115005.4951857142865012.45597142857155025.39402857142895004.37269999999995013.69082857142894954.06695714285715015.5331142857145073.1979857142865083.68381428571415057.28870000000015130.29732857142885097.05862857142895058.26668571428585084.43552857142825095.19565714285735048.93201428571415042.33947142857145075.60774285714255103.60382857142855151.08491428571415229.2322285714295287.72575714285725337.08635714285725396.56984285714325437.07039999999965484.61038571428625589.9906857142865580.93672857142885601.25150000000035643.81045714285765716.49802857142825763.98925819.45934285714255809.61311428571395809.25479999999975839.89251428571425843.44635714285695865.37168571428545859.45701428571465883.09125714285715900.94961428571425914.41910000000016020.25108571428616081.28222857142836167.26097142857186251.72728571428626288.84707142857136300.74634285714276301.17715714285716315.17465714285756310.59389999999986286.38092857142876315.3614571428576322.07409999999986276.58784285714326278.49998571428576282.73691428571426286.15197142857146335.59715714285726439.99405714285696478.35919999999996507.75198571428616550.62784285714326622.94902857142826654.72561428571416744.57924285714316831.94589999999976929.43054285714247005.55289999999977109.69207142857167198.24094285714277265.5547142857147359.5819857142867434.21014285714327488.27829999999997523.19130000000047506.86165714285747531.15735714285717535.47128571428587562.79635714285727591.98021428571437582.30820000000047586.55221428571447595.27535714285757589.01004285714327584.37092857142857577.34379999999967561.66497142857137557.11842857142897499.03899999999987506.09708571428567487.02292857142867450.34607142857117425.92839999999987380.95070000000037345.54370000000027301.99712857142827269.62991428571427208.74281428571437163.49785714285747112.68900000000037084.6655857142867067.4344857142867034.90375714285716993.63987142857156986.42142857142886991.90331428571436947.39800000000016925.76045714285746921.99778571428586866.03727142857136865.7563428571436798.90422857142866799.11192857142856738.53077142857186720.40868571428566693.21478571428546683.03385714285746684.04975714285686660.69162857142876603.59438571428566574.66357142857126516.7827571428576510.21282857142896507.60184285714336546.10635714285676519.51325714285766495.07412857142846460.02747142857156415.38578571428576371.96128571428566305.40154285714296286.65117142857166205.52284285714276194.66038571428546156.64634285714336109.87618571428546043.42425714285676001.36484285714325939.67922857142826003.20928571428616008.58637142857155991.47248571428556019.28920000000026014.19998571428555997.59284285714336016.61761428571396002.85980000000025995.31630000000045970.61772857142845930.48785714285715963.51244285714265906.76235714285765904.15048571428545816.18317142857185745.50952857142875749.96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42005420064200742008420094201042011420124201342014420154201642017420184201942020420214202242023420244202542026420274202842029420304203142032420334203442035420364203742038420394204042041420424204342044420454204642047420484204942050420514205242053420544205542056420574205842059420604206142062420634206442065420664206742068420694207042071420724207342074420754207642077420784207942080420814208242083420844208542086420874208842089420904209142092420934209442095420964209742098420994210042101421024210342104421054210642107421084210942110421114211242113421144211542116421174211842119421204212142122421234212442125421264212742128421294213042131421324213342134421354213642137421384213942140421414214242143421444214542146421474214842149421504215142152421534215442155421564215742158421594216042161421624216342164421654216642167421684216942170421714217242173421744217542176421774217842179421804218142182421834218442185421864218742188421894219042191421924219342194421954219642197421984219942200422014220242203422044220542206422074220842209422104221142212422134221442215422164221742218422194222042221422224222342224422254222642227422284222942230422314223242233422344223542236422374223842239422404224142242422434224442245422464224742248422494225042251422524225342254422554225642257422584225942260422614226242263422644226542266422674226842269422704227142272422734227442275422764227742278422794228042281422824228342284422854228642287422884228942290422914229242293422944229542296422974229842299423004230142302423034230442305423064230742308423094231042311423124231342314423154231642317423184231942320423214232242323423244232542326423274232842329423304233142332423334233442335423364233742338423394234042341423424234342344423454234642347423484234942350423514235242353423544235542356423574235842359423604236142362423634236442365423664236742368423695200513850754984485247004563.5430542513952.537823692.534643278323632243200319431823140312230923050303230082984296629302918291828762864282228222804279827982786278627262684267826782654264826422630261225942594256425402534252225042498249824982498248024682468245624502444243824262426242624202420241424142414240824022402239623962384238423842384236623602354234823482348234823422342233023302324231823182300230023002288228822882282227022582252225222462240223422342228222822222222219821982192216821682114211421142108209620842084206620602054205420542048204820422042203620252025202020202015201020102005200019901990198019801970196519601960195519501940194019401930192519201920192019101910191019051905189518851885188518801880187518751875187018651865185518451845184518451845184518401835183518301825182518251815181018101805180518001795179017851785178017801775177017651760176017551745174017351735173517201710170517051700170016851680168016751670166016451645164016401640163516351630162516251625161516101605160016001600160015951595159515951595159015901585158515801580157515751575157515751575157015701565156515651565156015601560156015551555155515501550155015501545153515351535153015301525152515001495149514851480147514451445144514401440143514251420141014051405140513951395139513701365135513551350135013451340133513351335133013001300129012801268126812601252125212521244124012321228122012121212120411841184117611761172116811641148113611321124112411201100110011001092107610721068106010561044Protok (m3/s)

Sumarne (kumulativne) krive zapremine srednjemesenog protoka - za viegodinji period i 2015. godinuSum_kriva_vieg.IIIIIIIVVVIVIIVIIIIXXXIXII13866.45810676362628414.14801774543645418.51616203635165485.61262981818483563.62126938182399602.129195345449113289.78693599997124339.75822341815134046.74127927271143752.32860465453155304.6110050909168773.87959854546Sum_kriva_201516793.56799999999932929.63199999999850607.07267144.03200000000782893.02400000000597019.423999999999106018.848113732.64120938.4132401.95199999999141266.592150828.48000000001V [10^6] (m3)

10%IIIIIIIVVVIVIIVIIIIXXXIXII714274288624103829203848072716007511952586398728630%IIIIIIIVVVIVIIVIIIIXXXIXII57796176709084237526671357784686407840474791577850%IIIIIIIVVVIVIIVIIIIXXXIXII49635349617772736555572949153930348434063992487480%IIIIIIIVVVIVIIVIIIIXXXIXII38514129493257255264446737742942270726213069365095%IIIIIIIVVVIVIIVIIIIXXXIXII29893117396145384280354629182213212820762467271799%IIIIIIIVVVIVIIVIIIIXXXIXII239123903277371435982929233617271735172420992084protok 2015627064406600638058805450336028802780428034203570aps mes min160720352309299623602061196514101402155816051800Q sr mes (m3/s)

Hidrogrami, anvelope i viegodinji prosekProtok 201541640416414164241643416444164541646416474164841649416504165141652416534165441655416564165741658416594166041661416624166341664416654166641667416684166941670416714167241673416744167541676416774167841679416804168141682416834168441685416864168741688416894169041691416924169341694416954169641697416984169941700417014170241703417044170541706417074170841709417104171141712417134171441715417164171741718417194172041721417224172341724417254172641727417284172941730417314173241733417344173541736417374173841739417404174141742417434174441745417464174741748417494175041751417524175341754417554175641757417584175941760417614176241763417644176541766417674176841769417704177141772417734177441775417764177741778417794178041781417824178341784417854178641787417884178941790417914179241793417944179541796417974179841799418004180141802418034180441805418064180741808418094181041811418124181341814418154181641817418184181941820418214182241823418244182541826418274182841829418304183141832418334183441835418364183741838418394184041841418424184341844418454184641847418484184941850418514185241853418544185541856418574185841859418604186141862418634186441865418664186741868418694187041871418724187341874418754187641877418784187941880418814188241883418844188541886418874188841889418904189141892418934189441895418964189741898418994190041901419024190341904419054190641907419084190941910419114191241913419144191541916419174191841919419204192141922419234192441925419264192741928419294193041931419324193341934419354193641937419384193941940419414194241943419444194541946419474194841949419504195141952419534195441955419564195741958419594196041961419624196341964419654196641967419684196941970419714197241973419744197541976419774197841979419804198141982419834198441985419864198741988419894199041991419924199341994419954199641997419984199942000420014200242003420046846195644844134103963823793853793794465876647157647737537067067918541050120012701300132013201310129012301170114011601170115011301080103096289383376070666860458056054053653051151450450452951959369378184698910801220131013201300126011701070976906846781758717670651610606604604595582539476476482492476479577660761857915924887865850809785752716705724757748713685785895938908842767693666626613648696763809865956993992941911870810725725759741708716741716667658617632570562562668817976104010401050911783668582474474474458387321300290270270371430444420402430461480410394360335430562524456391374298284260261261261237237237210200190184209181182181209182209208234210182210210210208165175180175159163168155155150145140150143142155143142154171175165181213220215194207213187181171176176174171165180170171176171166171161166176174175180170173170170175180185180201195195205227235235245240240225220215230260275250285305320295310310335375395415420365365330315308300270280291261274268282271265290310295297320319304304300305310320544917115012501310122010809108097748621010115011901140985879802734644590557512507457452447438398388388373378378377357367362Anvelopa min4164041641416424164341644416454164641647416484164941650416514165241653416544165541656416574165841659416604166141662416634166441665416664166741668416694167041671416724167341674416754167641677416784167941680416814168241683416844168541686416874168841689416904169141692416934169441695416964169741698416994170041701417024170341704417054170641707417084170941710417114171241713417144171541716417174171841719417204172141722417234172441725417264172741728417294173041731417324173341734417354173641737417384173941740417414174241743417444174541746417474174841749417504175141752417534175441755417564175741758417594176041761417624176341764417654176641767417684176941770417714177241773417744177541776417774177841779417804178141782417834178441785417864178741788417894179041791417924179341794417954179641797417984179941800418014180241803418044180541806418074180841809418104181141812418134181441815418164181741818418194182041821418224182341824418254182641827418284182941830418314183241833418344183541836418374183841839418404184141842418434184441845418464184741848418494185041851418524185341854418554185641857418584185941860418614186241863418644186541866418674186841869418704187141872418734187441875418764187741878418794188041881418824188341884418854188641887418884188941890418914189241893418944189541896418974189841899419004190141902419034190441905419064190741908419094191041911419124191341914419154191641917419184191941920419214192241923419244192541926419274192841929419304193141932419334193441935419364193741938419394194041941419424194341944419454194641947419484194941950419514195241953419544195541956419574195841959419604196141962419634196441965419664196741968419694197041971419724197341974419754197641977419784197941980419814198241983419844198541986419874198841989419904199141992419934199441995419964199741998419994200042001420024200342004130130120115110100105909090909096908080808094110110115126132126136136128136138140140139142145147147147147147126105105105105105105105105105105105160130150180190210220230234236240230225225225225240205220220230240240240220230210200180200230210160140200220190150287285287307317324327350370371.851396.858999999999983373093373373623623372803102401501802001802201801301201402302703503202902101801902302903303203102902802602502502502402402402502502272452602452602502402402402302302002402151552302302202202102101892112301891631951891331951631639016316919521819519516919516916916916316017016913394.215114594.513913794.2135909094.3174171162133151149147147951519515313516013116095959590140100100100961361319696961201209094.312011094.294.21201221221221351221221221281291221201201201201201201201201201201201201201101101101101101108511094110110110110110110110110110110110110110110120120120120120120120120120120120120120120120130130130130130130130120120120130130130130130130130140140120130176173172172174176175164165151151151140155155158164173178170170170170181178178136152136170170160160150150150150150150140Viegodinji prosek4164041641416424164341644416454164641647416484164941650416514165241653416544165541656416574165841659416604166141662416634166441665416664166741668416694167041671416724167341674416754167641677416784167941680416814168241683416844168541686416874168841689416904169141692416934169441695416964169741698416994170041701417024170341704417054170641707417084170941710417114171241713417144171541716417174171841719417204172141722417234172441725417264172741728417294173041731417324173341734417354173641737417384173941740417414174241743417444174541746417474174841749417504175141752417534175441755417564175741758417594176041761417624176341764417654176641767417684176941770417714177241773417744177541776417774177841779417804178141782417834178441785417864178741788417894179041791417924179341794417954179641797417984179941800418014180241803418044180541806418074180841809418104181141812418134181441815418164181741818418194182041821418224182341824418254182641827418284182941830418314183241833418344183541836418374183841839418404184141842418434184441845418464184741848418494185041851418524185341854418554185641857418584185941860418614186241863418644186541866418674186841869418704187141872418734187441875418764187741878418794188041881418824188341884418854188641887418884188941890418914189241893418944189541896418974189841899419004190141902419034190441905419064190741908419094191041911419124191341914419154191641917419184191941920419214192241923419244192541926419274192841929419304193141932419334193441935419364193741938419394194041941419424194341944419454194641947419484194941950419514195241953419544195541956419574195841959419604196141962419634196441965419664196741968419694197041971419724197341974419754197641977419784197941980419814198241983419844198541986419874198841989419904199141992419934199441995419964199741998419994200042001420024200342004697.58823529411768714.96470588235297733.42642352941175751.85919999999999754.73570588235293756.96508235294118757.01214117647055748.47348235294123744.03818823529411737.44995294117643734.81805882352944724.16212941176468715.26801176470588704.56212941176466694.3975058823529691.56212941176466692.95331764705884688.85335294117647691.28864705882359679.40629411764701678.45335294117649676.06067058823533669.89861176470583662.83169411764709662.67409411764709663.33518823529414666.61610588235294677.40514117647058697.4263411764706702.05149411764705710.64436470588237705.06935294117648697.51662352941173699.22514117647063702.47628235294121706.75969411764709707.43785882352938703.75478823529409704.88911764705881701.13125882352938711.08420000000001731.04890588235298745.87075294117642767.44095294117642781.61052941176467797.35201176470594809.68669411764711826.28749411764704845.29989411764711862.07561176470585871.56589411764708882.6011882352941891.97928235294114901.95704705882349913.19385882352947916.59257647058826912.92278823529409925.08797647058827937.72342352941178974.07469411764703996.169364705882341009.77647058823531024.23529411764711047.83707058823531079.11063529411761102.02402352941181124.95392941176461149.38984705882351162.0056941176471168.18008235294111181.13616470588231188.68565882352941198.79500000000011198.04456470588231206.82390588235281206.04885882352941209.705882352941212091224.11521237.15637647058821250.24448235294111262.88707058823521277.8172941176471285.64437647058821290.99317647058821290.88577647058831304.52107058823531311.55788235294111314.99165882352941322.15205882352941333.07058823529411350.49411764705881370.28384705882351383.70688235294121398.05049411764711413.28578823529411437.23875294117651447.88089411764711459.63354117647051475.05707058823531486.04541493.38359999999991494.70672941176461497.53035294117651503.07152941176471502.87404705882361507.25967058823541505.69757647058831506.90931764705871501.56085882352931493.28632941176471493.08384705882351481.48618823529411482.45497647058821475.70682352941181470.49511764705881470.59207058823541458.69411764705891444.68714117647051435.32243529411771424.25184705882361408.31067058823531395.19207058823531375.32556470588221365.2508941176471350.57796470588231332.58972941176471313.85624705882361294.19665882352931275.44855294117661265.3450117647061244.18917647058831230.10931764705881217.8832941176471204.87664705882341189.68437647058821169.39635294117651145.75347058823541126.47095294117641108.32443529411761088.53310588235291076.2807882352941062.17385882352941047.44705882352951040.76470588235291040.08235294117641038.83643529411761026.29143529411771018.40923529411761005.3694235294117993.82847058823529987.79376470588238978.58570588235295966.61590588235299951.0785647058824941.66365882352943930.09388235294114922.0444235294118911.79632941176476911.40996470588232911.70742352941181904.06338823529416903.03903529411764899.21461176470586895.72049411764704895.09128235294122891.20892941176476885.87951764705883878.67544705882358871.51425882352942868.84855294117642862.91184705882358853.57647058823534842.82352941176475834.03529411764703833.64705882352939822.57647058823534815.94117647058829813.6470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max416404164141642416434164441645416464164741648416494165041651416524165341654416554165641657416584165941660416614166241663416644166541666416674166841669416704167141672416734167441675416764167741678416794168041681416824168341684416854168641687416884168941690416914169241693416944169541696416974169841699417004170141702417034170441705417064170741708417094171041711417124171341714417154171641717417184171941720417214172241723417244172541726417274172841729417304173141732417334173441735417364173741738417394174041741417424174341744417454174641747417484174941750417514175241753417544175541756417574175841759417604176141762417634176441765417664176741768417694177041771417724177341774417754177641777417784177941780417814178241783417844178541786417874178841789417904179141792417934179441795417964179741798417994180041801418024180341804418054180641807418084180941810418114181241813418144181541816418174181841819418204182141822418234182441825418264182741828418294183041831418324183341834418354183641837418384183941840418414184241843418444184541846418474184841849418504185141852418534185441855418564185741858418594186041861418624186341864418654186641867418684186941870418714187241873418744187541876418774187841879418804188141882418834188441885418864188741888418894189041891418924189341894418954189641897418984189941900419014190241903419044190541906419074190841909419104191141912419134191441915419164191741918419194192041921419224192341924419254192641927419284192941930419314193241933419344193541936419374193841939419404194141942419434194441945419464194741948419494195041951419524195341954419554195641957419584195941960419614196241963419644196541966419674196841969419704197141972419734197441975419764197741978419794198041981419824198341984419854198641987419884198941990419914199241993419944199541996419974199841999420004200142002420034200424902480249024502420240023802350232022902270225022702300232023502360235023202270224021702090208021402240233023402410240023902390233023702270225123032311232323342340235123592318238124122470252125972587258125452560260026302650264026702620268027602840288028802880291030603200283026802670267026502640264026502650267028503053307029083061307528792825280027802750272027102700271029203050316032003320334033803400358036603700370037303700364036103691369437183694367236563635361435833542350834453395334132573238319031903200323032603290331033103290343032503230320031303050295029803080310031603220327033203340336034103470348034403360329032103160312030803060306030603060308031203170322032503270327032703270325032203160311030803040300029402900280027202660263025702550253024902460242024002370234022902240219021202070202019602000204020401980192019502030210021702210219021402080209021202140216021402130214021202130214021602120213521002085207520852075200019851935188518601810170015501640156815461529149414101400145016001690173017601740174017601820188019201950202020702140223022002080202019501880179016501530153015701570156016901710169016201510138013801380138013701330128013101340137014001460151015501580162017301810188019502010207021302180224022902360244025002580261026202610260025802560253024902450240023402290221021802220227022902300231022902250221021802415238423132203210619841910186618511861186618511870192019501980198019701980197019902010204021002160224023002330237024002410 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4164041641416424164341644416454164641647416484164941650416514165241653416544165541656416574165841659416604166141662416634166441665416664166741668416694167041671416724167341674416754167641677416784167941680416814168241683416844168541686416874168841689416904169141692416934169441695416964169741698416994170041701417024170341704417054170641707417084170941710417114171241713417144171541716417174171841719417204172141722417234172441725417264172741728417294173041731417324173341734417354173641737417384173941740417414174241743417444174541746417474174841749417504175141752417534175441755417564175741758417594176041761417624176341764417654176641767417684176941770417714177241773417744177541776417774177841779417804178141782417834178441785417864178741788417894179041791417924179341794417954179641797417984179941800418014180241803418044180541806418074180841809418104181141812418134181441815418164181741818418194182041821418224182341824418254182641827418284182941830418314183241833418344183541836418374183841839418404184141842418434184441845418464184741848418494185041851418524185341854418554185641857418584185941860418614186241863418644186541866418674186841869418704187141872418734187441875418764187741878418794188041881418824188341884418854188641887418884188941890418914189241893418944189541896418974189841899419004190141902419034190441905419064190741908419094191041911419124191341914419154191641917419184191941920419214192241923419244192541926419274192841929419304193141932419334193441935419364193741938419394194041941419424194341944419454194641947419484194941950419514195241953419544195541956419574195841959419604196141962419634196441965419664196741968419694197041971419724197341974419754197641977419784197941980419814198241983419844198541986419874198841989419904199141992419934199441995419964199741998419994200042001420024200342004836047404180380035203320316030202890278026802590250224302350228022202150209020301980192018601800174516901630158015201460141013451290123511701080962742Protok (m3/s)

Sumarne (kumulativne) krive zapremine srednjemesenog protoka - za viegodinji period i 2015. godinuSum_kriva_vieg.IIIIIIIVVVIVIIVIIIIXXXIXII1914.46830613333443867.35173653333377093.908649599993610919.67284159999914152.85790186666816479.47665386666618384.39328959999719780.9594261333320925.36048213332822126.26840746666123699.64027946666125566.265450666662Sum_kriva_20152011.47843922.64639999999966118.93440000000018086.262399999999610111.13279999999911420.09279999999912113.79839999999812574.48319999999913028.08319999999913791.42719999999815020.03519999999816715.462399999997V [10^6] (m3)

0.1IIIIIIIVVVIVIIVIIIIXXXIXII1327141719392392191215681318959714763101913000.3IIIIIIIVVVIVIIVIIIIXXXIXII872101014321732134410108156024955106158340.5IIIIIIIVVVIVIIVIIIIXXXIXII6407781127135510517525894403843854506120.8IIIIIIIVVVIVIIVIIIIXXXIXII3784887298797064763542702572452903700.95IIIIIIIVVVIVIIVIIIIXXXIXII2202964515564813132211721761582042280.99135185286363347223149119128109158150protok 2015751790820759756505259172175285474633aps mes min801051401201809090908594120136Q sr mes (m3/s)

Hidrogrami, anvelope i viegodinji prosek 201342005420064200742008420094201042011420124201342014420154201642017420184201942020420214202242023420244202542026420274202842029420304203142032420334203442035420364203742