72531631 Analiza Velikih i Malih Voda

8/12/2019 72531631 Analiza Velikih i Malih Voda

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SVEUILITE U ZAGREBUGRAEVINSKI FAKULTETPOSLIJEDIPLOMSKI STUDIJSMJER:HidrotehnikaKOLEGIJ:Hidrolo i!a " oda#rana $o la%l!aAkademska god. 2010. / 2011.

ANALIZA VELIKIH I &ALIH V'(A

St de!t: " #a$o Ma%&!a' M":2()

*ag%e#' % +a! 20


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Hidrologija odabrana poglavlja_____________________________________________________

SA(R)A*

1 ANALIZA JAKIH OBORINA .......................................................................................................... 4

1.1 Openito ..................................................................................................................................... 41.2 Metodoloki postupci o !"de k!"tkot!"#ni$ #"ki$ o o!in" .......................................................... %

1.2.1 &!i'"!n" o !"d" '#e!eni$ o o!in" ...................................................................................... (

1.2.2 )o!'i!"n#e ni*o+" k"!"kte!isti,ni$ +!i#ednosti inten*i+ni$ o o!in" ................................... -

1.2. An"li*" +#e!o#"tnosti po#"+e '"ksi'"lni$ inten*itet" ....................................................... 11

1.2.4 /e0ini!"n#e H & I &3 k!i+ul#" ......................................................................................... 12

1. &!osto!n" !"spod#el" #"ki$ ki" ................................................................................................. 1%

2 5LIK5 O/5 ............................................................................................................................... 1%

2.1 Openito .................................................................................................................................. 1%2.2 &!o!",un '"ksi'"lni$ p!otok" n" i*u,eni' sli+o+i'" ............................................................ 1-

2. &!o!",un '"ksi'"lni$ p!otok" n" nedo+ol#no i*u,eni' sli+o+i'" ......................................... 16

2.4 &!o!",un '"ksi'"lni$ p!otok" n" sli+o+i'" e* p!o'"t!"n#" ................................................ 16

&RO&A7A8IJA &O&LA NIH ALO A .................................................................................... 29

.1 Hid!oloki 'odeli p!op":"ci#e +odno: +"l" ............................................................................ 2%

.2 K+"*ist"cion"!n" 'etod" .......................................................................................................... 2-

. &!op":"ci#" k!o* "ku'ul"ci#u .................................................................................................. 9

.4 Metod" Muskin:u' .................................................................................................................. 4 MAL5 O/5 .................................................................................................................................. %

4.1 Openito ................................................................................................................................... %

4.2 Ope $id!oloke *n","#ke po#"+" '"li$ +od" .......................................................................... -

4. ;t"tisti,k" "n"li*" '"li$ +od" .................................................................................................. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


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, ANALIZA *AKIH 'B'RINA

,-, '$.enito

A!a$&,a & -%o+ekt&%a!+e &d%ote !& k& o#+ekata & s sta a ,a -%a $+a!+e od!&m%es %s&ma ,a t&+e a+ kao $a,! e$& &! -odatke o o#o%&!ama. O#$& & t&$a,a mog #&t& %$o %a,$& &t&' s t&m da se &! e!+e%sko+ -%aks& da!as ko%&ste

s$&+ede3&: -o &+es!& -oda & o-a e!& o#o%&!a' ge!e%&%a!e se%&+e o#o%&!a' o#o%&!-%&ka,a!e o#$&k sk -a k%& $+a &!te!,&tet4t%a+a!+e4-o %at!& -e%&od 5ITP6 &-%o+ekt!e o#o%&!e.

Po &+es!& -oda & o-a e!& o#o%&!a' -ose#!o o!& +ak& &!te!,&teta' s os!o a,a 7o%m&%a!+e osta$a t%& t&-a $a,a. Dak$e' -% & !a ede!& t&-' t+. -o &+es!& -oda &o &,m+e%e!&m o#o%&!ama' &, o%!& +e & !e,ao#&$a,!& e$eme!t s ake &d%o$o8kea!a$&,e o#o%&!a. S & osta$& t&-o & $a,a &, ede!& s &, !+ega' a &$+ &m +e dat&odgo o%e !a to ko+a 3e -ada$&!a dat& k%&t& !e %8!e -%otoke &$& k%&t& !e,a-%em&!e & o#$&ke &d%og%ama ot+e a!+a kako #& se adek at!&m

&d%ote !& k&m o#+ektom &$& ,a atom %eag&%a$o !a !e-o o$+!e -os$+ed& etak og t&-a o#o%&!a.

Pod -o+mom 9+aka k&8a ' &d%o$o8ko+ -%aks&' o#& !o se -od%a, m&+e a+k%atkot%a+!e' &!te!,& !e o#o%&!e &+e +e t%a+a!+e od 1 m&! te do 2; sata.

K%a+!+& &$+ a!a$&,e +ak& o#o%&!a +e da se do#&+e ,a &s!ost &!te!,&teti 5&$& &s&!aH6 4 t%a+a!+et k 4 -o %at!& -e%&od o#o%&!eP 5it k P 4 k%& $+e6. Po %at!& -e%&odP'od!os!o +e%o+at!ost -o+a e o#o%&!a %a,$& &tog &!te!,&teta +e a !a kod o +e!e

e$&k& oda s ma!+& s$& o a gd+e !&s %8e!a o &ta!+a o#o%&!a t+. -%otoka.K%& $+eit k P 5Ht k P6 s em-&%&+ske k%& $+e ko+e +e +ed&!o mog 3e &,%ad&t& !aos!o -o &+es!& m+e%e!& -odataka o o#o%&!ama -omo3 om#%og%a7a' ao!e 3e #&t& k a$&tet!&+e od%e


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Hidrologija odabrana poglavlja_____________________________________________________ 4. Od !&,a o#o%&!sk& -odataka t%a & se da # d sta &o!a%!&.=esta &o!a%!ost ko+ ,%ok + &d%ok$&matske -%om+e!e od%a a a se -%ekot%e!do a' -e%&od& !ost& & s$.>. O#o%&!sk& -oda & mo%a+ #&t& me< so#!o !e,a &s!&. I,me< o#o%&!sk&e-&,oda ,et& -%o%a ! !e #& sm+e$a -osto+at& stat&st& k& ,!a a+!ako%e$a &+a.?. =&,o & -odataka m+e%e!& -ada$&!a mo%a+ #&t& do o$+!o d g&. =ekeg%e8ke ko+e se +a $+a+ kod stat&st& ke a!a$&,e 7 !k &+a s d $+&!e !&,a o &ta!+a.-. Ekst%em!e %&+ed!ost& o#o%&!a s$&+ede s-e &7& !e 7 !k &+e %as-od+e$e

+e%o+at!ost&. I,#o% !a+#o$+e d &+e -%&$agod#e %8& se 24testom & testomKo$mogo%o a. *a -%o +e! -a%ameta%a ko%&ste se %a,$& &t& k%&te%&+& kao metodamome!ata' metoda !a+ma!+& k ad%ata' &td.

*a-&s om#%og%a7a -%edsta $+a s ma%! $&!&+ -a$e o#o%&!eH = H(t) ' te +e&!te!,&tet k&8ei !ekom %eme! t :

dt dH

i = (1)dok +e +ed!ad #a s ma%!e $&!&+e:

=t

idt H 9

(2)

P%os+e !& &!te!,&tet k&8e ko!a !om %eme!skom &!te% a$ t 3e -%ema (1)#&t&:

t H

i= (3)

gd+e +e H -%&%ast &s&!e k&8e %eme! t.

G%a7& k& -%&ka, &!te!,&teta 7 !k &+& %eme!a se !a,& a &+etog%am' ko+& se!a+ e83e ko!st% &%a &stog%amskom o#$&k ' -%& em &!te% a$& d&sk%et&,a &

t mog #&t& &ste &$& %a,$& &te 8&%&!e. Ako t 0 do#& a se ko!t&! &%a!a $&!&+a sa +ed!ad #om (1) .

,-/ &etodolo0ki $o1t2$3i o#rade kratkotra!nih !akih o#orina

Sta!da%d!& -ost -ak o#%ad& %e &ma k%atkot%a+!& +ak& o#o%&!a s %de7&!&%a!+aHTP 5ITP6 k%& $+a ,a !ek oda#%a! -$ &og%a7sk -osta+ sasto+&se s$&+ede3&m ka%akte%&st& !&m ko%a &ma:a) d&g&ta$&,a &+a & -%&ma%!a o#%ada -$ &og%a7sk& ,a-&sa %eg&st%&%a!& !&-odataka o -a$&m o#o%&!ama'b) 7o%m&%a!+e !&,o a ka%akte%&st& !& %&+ed!ost& &!te!,& !& o#o%&!a %a,$& &ta t%a+a!+a & &s-&t& a!+e !+& o e omoge!ost&'c) a!a$&,a +e%o+at!ost& -o+a e ka%akte%&st& !& %&+ed!ost& maks&ma$!& &s&5&!te!,&teta6 o#o%&!a ko%&8te!+em &8e t&-o a k%& $+a %as-od+e$e' te test&%a!+est -!+a -%&$agod#e em-&%&+sk&m %&+ed!ost&ma'd) de7&!&%a!+eHTP 5ITP6 k%& $+a !a teme$+ a!a$&,a st -!+a -%&$agod#e &8et&-o a tak & k%& $+a & test&%a!+em st -!+a !+& o a -%&$ago


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Hidrologija odabrana poglavlja_____________________________________________________ e) s-o%ed#a do#& e!& %&+ed!ost& maks&ma$!& &s&!a 5&!te!,&teta6 o#o%&!aoda#%a!& t%a+a!+a s %e, $tat&ma e e!t a$!& -%et od!& o#%ada !aa!a$&,&%a!o+ -%edmet!o+ -osta+&' kao & !a -osta+ama sa 8&%eg %eg&o!a$!og-%osto%a te !+& o a e%&7&ka &+a.

,-/-,+ri4arna o#rada 4!erenih o#orina

S aka a!a$&,a -$+ sko a ,a-o &!+e -%&ma%!om o#%adom om#%og%a7sk& t%aka'd&g&ta$&,a &+om o#o%&!a & &,d a+a!+em ka%akte%&st& !& ko$& &!a o#o%&!oda#%a!e %eme!ske &!te% a$e o#%ada %as-o! od >' 10' 1>' ...' ?0 m&!.' 2'(' ...' do 2; sata. O a+ -ost -ak se mo e od%a,&t& !a to !ost sek !da%!&o#%ada & a!a$&,a' -od ko+&ma se -od%a, m&+e a !&, kom-$eks!& o#%adaos!o !& -odataka o &!te!,&tet&ma o#o%&!a ,a -ot%e#e &8& &d%o$o8k& &osta$& a!a$&,a.

K$as& a! -%&st - tom ,adatk da!as se %+e8a a !a !a &! da se d&g&ta$&,a &+om

-$ &og%a7sk& ,a-&sa ko+e g$a !om %8&Dravni hidrometeorolo ki !avodos&g %a a !&, >4m&! t!& ,a-&sa s -odatkom o ko$& &!& o#o%&!a %eg&st%&%a!o+ tom %eme!skom &!te% a$ . P%&+e #&$o kak & da$+!+& o#%ada %eg&st%&%a-odataka o &!te!,&tet -a$& o#o%&!a' ! !o +e -%o est& s-o%ed#%eg&st%&%a!& d!e !& o#o%&!a -o -$ &og%a7 & -o k$as& !om k&8om+e% ' te &da$+!+& a!a$&,a &sk$+ &t& !e%e-%e,e!tat& !e god&!e 5god&!e s -%e &8e -%ek&da %ad -$ &og%a7a & -%e e$&k&m %a,$&kama %eg&st%a &+& -$ &og%a7sk&8om+e%!& -odataka6' te od&t& %a !a o !ek&m s sta !&m g%e8kama %eg&st%a &+&' ako tak e -osto+e.

=a os!o d&g&ta$&,&%a!& !&,o a -odataka o >4m&! t!&m %eg&st%&%a!&mo#o%&!ama %8& se &,d a+a!+e %&+ed!ost& &!te!,& !& o#o%&!a d $+& t%a+a!+a' -

em se o#& !o &,a#&% t%a+a!+a od 10' 20' (0' ;0 & >0 m&! ta' te 1'2';'?'12'1@& 2; sata. P%o#$em &,d a+a!+a o#o%&!a !&+e tako +ed!osta a! kako se mo da!aoko &!&. =a&me' -%&$&kom &,d a+a!+a !a+&!te!,& !&+& o#o%&!a %a,$& &t%a+a!+a t&+ekom !eke s$o e!e k&8e ! !o +e od&t& %a !a o -%o#$emod%e4m&! t!& &!te% a$ !a+k%a3a %eme!ska d&sk%et&,a &+a -%& -%&ma%!oo#%ad& 4 d&g&ta$&,a &+& -$ &og%a7sk& ,a-&sa' a o#%adom se s k es& !o &,d a+a+-a$e ko$& &!e o#o%&!a s akom od >4m&! t!& &!te% a$a' !a+ +e%o+at!&+e +e dame< &,d o+e!&m !a+ e3&m -oda &ma !&+e & do&sta !a+ e3& >4m&! t!& &!te!,&tetko+& se st a%!o -o+a &o. S&g %!o +e da se od!os !a ,a-a e!e s k es& !e >4m&! t!e %&+ed!ost& -o+a &$o & !eko >4m&! t!o %a,do#$+e s +o8 ekst%em!&+&m

%&+ed!ost&ma od!os !a %eg&st%&%a!e. =o' s o#,&%om !a metodo$og&+-%&ma%!e o#%ade' -odatak o tom &!te!,&tet !&+e mogao #&t& ,a#&$+e e! &,%a,$oga 8to !&+e to !o %eme!sk& -ao ! ta% oda#%a!og s$&+eda >4m&! t!&%a,do#$+a. Ut+e a+ tog -od +e!+& a!+a st a%!o -a$& & %eg&st%&%a!& o#o%&!!a+ e3& +e kod s-ome! tog >4m&! t!og &!te% a$a' a s&g %!o se os+e3a & kodd% g& k%a3& t%a+a!+a 4 !-%. 104m&! t!& . S -o%astom %eme!a t%a+a!+a's-ome! ta se s sta !a g%e8ka od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (


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Hidrologija odabrana poglavlja_____________________________________________________ &!te!,&teta o#o%&!a ! ta% !eke !e,a &s!e k&8!e e-&,ode m&!&ma$&,&%a' tako da

%$o #%,o -osta+e m&!o%!a. S-ome! t& #& se -%o#$em mogao %&+e8&t&' od!os!o +o8 &8e m&!&ma$&,&%at&' !a !a &! da se -%&$&kom d&g&ta$&,a &+e s a+a k%%a,do#$+e d&sk%et&,a &+e 5!-%. 1 m&! ta6.

P%&$&kom ko!st% k &+eHTP 5ITP6 k%& $+a & o tom se deta$+ t%e#a od&t& %a !a' &to !a !a &! da se -%&$&kom &,+ed!a e!+a s-ome! t& 7 !k &+a ko%&ste o!e7 !k &+e ko+e -%&$&kom &,+ed!a e!+a !e sma!+ + $a,!o -%o%a !ate

%&+ed!ost& ,a s-ome! ta k%atka > & 104m&! t!a %a,do#$+a' e3 +e ak &-o e$+!o da s tom &!te% a$ odst -a!+a s o+e!e 7 !k &+e &,+ed!a e!+a ko+eda+ & 104tak e3e %&+ed!ost& -a$& o#o%&!a 5kod >4m&! t!& &!te!&teta &

&8e6 kod t& !a+k%a3& t%a+a!+a. =&kako !&s -%& at$+& e 7 !k &+e &,+ed!a e!+#e, o#,&%a kako se do#%o -%&$ago


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Hidrologija odabrana poglavlja_____________________________________________________ !&s %sto ,as!o a!e !a -%&! &-&ma matemat& ke stat&st&ke. S d% ge st%a!e'teo%&+a ekst%em!& %&+ed!ost& da+e -o ,da!e %e, $tate samo ,a -o+a e ma$e

+e%o+at!ost& +a $+a!+a.

D &+e metode ko+e !&s o-te%e3e!e !a ede!&m !edosta &ma s metoda kodko+e se od%e< + k a%t&$& se%&+a god&8!+& maks&m ma & a!a$&,aP$T se%&+a.

K a%t&$& s %&+ed!ost& ko+e %e & 1 god&! mo e seko%&st&t& -o,!ata e,a La!g#e&!a:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


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TP$T 0.> god' ? T 1.1? god'TP$T 1.0 god' ? T 1.>@ god.

S !a ede!&m ko%ek &+ama ,aT ' %&+ed!ost& ,a 7 s ' -%ema ( ) da!e st -5(6. U st - 5;6 s %&+ed!ost& -%ema Je!k&!so! .

O,!aka

Po %at!&-e%&od

Sta!da%d&,&%a!o 7

T 5god&!a6 I,%a,( ) Je!k&!so!

516 526 5(6 5;6FM1 0.> 40.?@ 40.@0FM2 1.0 40.002 0.02FM( 4 4 0.))G1 2 0.() 0.;0G2 > 1.>0 1.>>

FM; 10 2.2> 2.(2Ta#li3a ,7 Po %at!& -e%&od& god&8!+& ekst%ema

Em-&%&+ske to ke se tako>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6


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S e%ma! +e ,ak$+ &o da +e st a%!o -%os+e !o t%a+a!+e -o+ed&!& o#o%&!a' ko+es &d d!e !& o#o%&!a #&$e o,!a e!e od%e


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Ta#li3a =7 Do!+e g%a!& e &!te!,& !& o#o%&!a s ko+&m se $a,& sek !da%!eo#%ade

=a e$& &! kas!&+e -%o%a !at& %&+ed!ost& ka%akte%&st& !& maks&ma$!&s&!a 5&!te!,&teta6 o#o%&!a &, tako 7o%m&%a!& se%&+a &ma & e$& &!a -%aga' a

esta$ost -o+a a &!te!,& !& o#o%&!a &,!ad tako oda#%a!og -%aga. U tom

s$ a+ -ose#a! -%o#$em -%edsta $+a & g$a !om !ekom-$et!a %eg&st%a &+ao#o%&!a' -a se tako & s$ a+ kad s %eg&st%&%a!& god&8!+& ekst%em!&&!te!,&tet& %a,$& &t& t%a+a!+a' t&+ekom -o+ed&!& god&!a +a $+a !edostatak%eg&st%&%a!& &!te!,& !& o#o%&!a &,!ad oda#%a!og -%aga. U s&t a &+ama kadase !a8&m +et&ma %as-o$a e s -%os+ek %eda e$& &!e s ega oko >0 -$ &og%a7sk& %eg&st%&%a!& o#o%&!a' to -%edsta $+a o,#&$+! -%e-%ek ko%&8tetak & se%&+a -odataka. Ta+ se -%o#$em -%aks& mo e d+e$om& !o -%e $adat& !a!a &! da se ko%&ste mod&7& &%a!e POT se%&+e' kod ko+& +e k -a! #%o+ $a!o ase%&+e +ed!ak #%o+ a!a$&,&%a!& god&!a. =a ta+ se !a &! da$+!+e o#%ade

k$+ +e e3& #%o+ !a+&!te!,& !&+& o#o%&!a 5!eo &s!o ko+o+ s god&!&%eg&st%&%a!e6 od!os !a se%&+ god&8!+& maks&m ma' a$& !a tak se%&+-%eko%a e!+a &ma ma!+& t+e a+ #%o+ !e%eg&st%&%a!& o#o%&!a e3& od -o et!ooda#%a!og -%aga.

Ut %4god&8!+eg -o %at!og -e%&oda &

esta$&+& &ma+ !e8to -o e3a!e %&+ed!ost& od!os !a %e, $tate do#& e!ea!a$&,om se%&+a god&8!+& maks&m ma. P%& %+e


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Hidrologija odabrana poglavlja_____________________________________________________ !&,o a $a,!& -odataka6 !asto+& -%e $adat& ko%&8te!+em !a-%&+ed oda#%a!ogt&-a %as-od+e$e ,a koga +e !a teme$+ -%o ede!& %a!&+& test&%a!+a t %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 12


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Slika ,7 "&$ amo a k$as&7&ka &+a o#o%&!a

Da!as se m+esto esta$ost& e, od& -o %at!& -e%&od +a $+a!+a 5P6. O! sede7&!&%a kao -%os+e a! &!te% a$ %eme!a 5 god&!ama6 tokom ko+eg 3e se +eda!- t +a &t& o#o%&!a e3a &$& +ed!aka od%e' >0' 100' 200' >00 &1000 god&!a' mada -o+ed&!& a to%&' s -%a om' !e -%&ka, + %e, $tate ,a-o %at!e -e%&ode -%eko 100 god&!a.

Slika /7 P%&m+e% PtkP & &tkP k%& $+e ,a k&8om+e%! sta!& T ,$a

it k P &$&Pt k P k%& $+e mog #&t& -%&ka,a!e a!a$&t& kom o#$&k &$& mog #&t& dat

samo g%a7& k&. G%a7& k& -%&ka, #e, a!a$&t& kog de7&!&%a!+a od!osa o#& a+e! +ako se it k P k%& $+e 7o%m&%a+ ,a t%a+a!+e k&8et k od m&!&ma$!o > &$& 10 m&! ta do2; sata. P%e-o% ka +e' dak$e' da se od o+e!o t%et&%a+ 7&,& k& %a,$& &te -ada$&!e st&m da +e g%a!& a t%a+a!+a o & k&8a &,me< 1 & 2 sata.

Kod a!a$&t& k& &,%a,a ,ait k P k%& $+e -ost -ak +e taka da se ,a &,a#%a!e-o %at!e -e%&ode !a$a,& a!a$&t& k& od!os &,me< &!te!,&teta -ada &!a & !+& o ogt%a+a!+a. P%& tome +e mog 3e %ad&t& tako da se od o+e!o de7&!&%a a!a$&t& k& &,%a,i = :(t k) ) ,a s ak& -o %at!& -e%&odP -ose#!o. *a o aka !a &! %ada M Q e!-%ed$a e s$&+ede3e a!a$&t& ke &,%a,e:

bt

ai

k +=

,a t k 2 (9)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1


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k d

t ci = ,a t k 2 (;)

-%& em se -a%amet%&a b c &d od%e< + -%&m+e!om &8est% ke %eg%es&+e -oteo%&+& !a+ma!+& k ad%ata. %$o esto se a!a$&t& k& &,%a,& ,ait k P k%& $+ede7&!&%a+ !e samo ,a +eda! -o %at!& -e%&odP !ego ,a s e -o %at!e -e%&odeo# a3e!e a!a$&,om. U tom s$ a+ !a+ e83e se ko%&st& s$&+ede3& &,%a,:

ck

b

t aT

i = (1,)

Os&m &,%a,a 5106 -%aks& se ko%&ste & #%o+!& d% g& kao !a -%&m+e%:

k t baT

i+

= (11)

k

d

t ecT i += (12)

ik

g

t h fT

i+

= (13)

Po8to +e -%et od!o !eko$&ko !a %ata !ag$a8e!o da s it k P 5Pt k P6 k%& $+eem-&%&+ske' -%&$&kom !+& o e &,%ade mo%a se &mat& !a m & s % a !+& o oko%&8te!+a ,#og toga se od%e< + g%a!& e t%a+a!+a k&8et k & -o %at!& -e%&odP

! ta% ko+& seit k P k%& $+e de7&!&%a+ . =a -%&m+e%' ako seit k P k%& $+e de7&!&%a+

,a -ot%e#e g%ad!+e & d&me!,&o!&%a!+a ka!a$&,a &+sk& s sta a ma!+& !ase$+a' ko+&ma s -%ete !o stam#e!& o#+ekt&' t%e#a ,et& o#,&% t%a+a!+a k&8e od >m&! ta do 1 sata' a -o %at!e -e%&ode od 0.2> do > god&!a. *a -ot%e#e-o$+o-%& %ed!e od od!+e %a,mat%a!+e t%e#a ,et& -o %8&! s$& a kao & -adte%e!a ko+& d&kt&%a+ %&+eme ko! e!t%a &+e -a -%ema tome & t%a+a!+e k&8e' s t&mda &,#o% -o %at!og -e%&oda mo%a &3& od > do 2> god&!a. Kod ma$& -%&%od!&s$& o a ,a -ot%e# d&me!,&o!&%a!+a mosto a & -%o- sta !a odoto &ma'%a,m&8$+a!+a e,a!a s &,#o%om t%a+a!+a k&8e &de!t& !a s kao & kod-o$+o-%& %ed!& -o %8&!a' a -o %at!& -e%&od& s o#& !o e3& & k%e3 se od 10 do100 god&!a' -o8to !a e$&ke ode tak & -o %at!& -e%&oda t%e#ad&me!,&o!&%at& o#+ekte od od!+e.

" d 3& da +e m%e a o#& !& k&8om+e%a da$eko g 83a od m%e e a tomatsk&sta!& a' %a,%a>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 14


15/50

Hidrologija odabrana poglavlja_____________________________________________________ d!e !e k&8e -o %at!og -e%&oda P. *a od%e =


16/50


e$&k od s a+a sta!+e kad %&+e !o ko%&to &8e !&+e sta!+ da s od-%o od& !&, od!&m tokom' -a do$a,& do -%e$&+e a!+a & 8teta od e$&k& oda.

e$&ka oda +e ekst%em!a -o+a a de7&!&%a!a odosta+em' sek !d!&m-%ot+e a!+em &$& o$ me!om od%e


17/50

Hidrologija odabrana poglavlja_____________________________________________________ ,ad% a a!+e o#o%&!a !a s$& o#$&k s!+e !og -ok%& a a. Po%astomtem-e%at %e do$a,& do to-$+e!+a s!&+ega -a' o &s!o o !+ego o+ ko$& &!& !a s$& &&!te!,&tet to-$+e!+a' do$a,& do -o e3a!a ot+e a!+a. Po+a ama e$&k& oda-ogod + odgo a%a+ 3& geo$o8k& sasta s$& a 5!e-%o- s!ost6' to-og%a7sk&

+et& 5 e$&k koe7& &+e!t ko! e!t%&%a!ost& s$& a & e$&k& -ado & s$& a6' sto#%as$ost& 5s$a#a o#%a


18/50


=eo- od!o +e da %e$at& !a s%ed!+a k ad%at!a odst -a!+a stat&st& k&-a%ameta%a !e # d e3a od 10 ' 8to se %a !a:4 ,a s%ed!+ %&+ed!ost: %&&

nQ =

(14)

4 ,a koe7& &+e!t a%&+a &+e: %&&' %n(

' (v

v' v

+=

(1 )

4 ,a koe7& &+e!t as&met%&+e: ( ) %&&c)c* %n

+v

(v' " ++=

(19)gd+e s :

/ 4 s%ed!+a %&+ed!ost se%&+e maks&ma$!& god&8!+& -%otoka/ ma B 4 sta!da%d!a de &+a &+a se%&+a/ ma @v 4 koe7& &+e!t a%&+a &+e se%&+a/ ma @& 4 koe7& &+e!t as&met%&+e se%&+e/ ma n 4 k -a! #%o+ $a!o a se%&+e/ ma

%eme!ska se%&+a mo e se smat%at& %e-%e,e!tat& !om ako o# a3a #a% d a- !a &k$ sa & ako %e$at& !e s%ed!+e g%e8ke -%&ka,a!& -a%ameta%a5maks&ma$!& -%otoka6 ,ado o$+a a+ -osta $+e!& +et.

Em-&%&+ska 7 !k &+a %as-od+e$eP( ) s$ a+!e a%&+a#$e * -%edsta $+a ,ako!-%om+e!e esta$ost& doga


19/50


Po %at!& -e%&od m4tog $a!a !&, &,%a !a se:! P %

T =

Ako +e se%&+a 7o%m&%a!a ko%&8te!+em samo +ed!oga -odatka god&!& 5!-%.maks&ma$!& god&8!+& -%otok6' tada se -o %at!o %a,do#$+e &,%a a a god&!ama.

*a od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 16


20/50


2. Metode ko+e se teme$+e !a ko%&8te!+ &sk st e!& o &s!& g$a !&e$eme!ata ot+e a!+a & &m#e!&ka ko+& ga +et + .

*#og s$o e!ost& &d%o$o8k& -%o esa' -%aks& se o#& !o ko%&st&-o+ed!osta $+e!a s ema 7o%m&%a!+a ot+e a!+a 4 %a &o!a$!a metoda & metoda

m+et!oga +ed&!& !og &d%og%ama. P%& -%o%a ! e$&k& oda t%e#a #&t&eoma o-%e,a!' -a +e da$eko &!ko &t&+e o%ga!&,&%at& -%& %eme!a -%omat%a!+a

& m+e%e!+a &$+ do#& a!+a -o ,da!&+ega +ed&!& !og &d%og%ama !aa!a$&,&%a!om s$& .

D% ga g% -a metoda' !a+ e3em #%o+ s$ a+e a' &ma %ed k &+sk& ka%akte% &-%edsta $+a %ed k &+ maks&ma$!og mod $a ot+e a!+a s -o e3a!+em -o %8&!es$& a &$& %eme!a dot+e a!+a. P%&m+e!a +ed!e &$& d% ge g% -e metoda !&+e +as!ode7&!&%a!a' a$& se mo e %e3& da ,a s$& o e > -, km 2 ' od!os!o ma$e s$& o e'metode teme$+e!e !a ge!et& ko+ teo%&+& ot+e a!+a &ma+ ,!a a+! -%ed!ost.Og%a!& e!+e sm&s$ -%&m+e!e %a &o!a$!e metode samo !a ma$e s$& o e

-os$+ed& a +e &!+e!& e da o a metoda !e o# a3a e7ekt %eta%da &+e ,#ogak m $&%a!+a ode !a -o %8&!& s$& a & -%et-osta $+a +ed!ak o#o%&! !a s$& .=a&me' 8to +e e3& s$& to +e & te e od% & a -%et-osta ka o mog 3!ost&e$&m&!a &+e e7ekta ,ad% a a!+a ode & ko!sta!t!ost& o#o%&!a.

*a e3e s$& o e -%o%a ! maks&ma$!& -%otoka se teme$+& !a s&m $&%a!+ot+e a!+a ode !a s$& !om -od% + . P%o%a ! se ,as!& a !a odgo a%a+ 3em-%o+ekt&%a!om -$+ sk & !a teme$+ -%et-osta $+e!e ko!7&g %a &+e %+e8e!+a.=o%ma$!o' os!o !& -%ed +et ,a -o ,da!e %e, $tate s do#%& $a,!& -oda &. Us$ a+ ko%&8te!+a s&m $a &+sk& te !&ka to s -%&+e s ega &d%o$o8k& -oda &-oda & o # d 3&m ka%akte%&st&kama s$& !oga -od% +a.

Os&m %a &o!a$!e metode -osto+& +o8 !&, d% g& $&te%at %& & -%aks& ko%&8te!metoda ,a -%o%a ! maks&ma$!& -%otoka kao !-%.: SQS metoda' metoda

+ed&!& !og &d%og%ama' metoda &,ok%o!a' te #%o+!e &sk st e!e metode.Os!o !a -%ed!ost SQS metode od!os !a %a &o!a$! +e !e$&!ea%a! od!os-a$e & otek$e o#o%&!e -a se mo e +e%!&+e os$&kat& -%&%oda! -%o es.

= +R'+AGA;I*A +'+LAVNIH VAL'VA

P%o-aga &+a -o-$a !& a$o a +e -%o es ko+&m se de7&!&%a+ ka%akte%&st&ke-o-$a !& a$o a !a $oka &+& !&, od!o od !eke ak m $a &+e &$& !a !eko+!&, od!o+ d&o!& & %&+e !og toka' a !a os!o -o,!at& -o-$a !& a$o a !a

, od!o+ d&o!& &. E7ekt t+e a+a -%osto%a ak m $a &+e 5&$& ak m $a &+sk&ka%akte%&st&ka d&o!& e %&+e !og toka6 +e mod&7&ka &+a -o,!at& od!& a$o a !a

$a, ak m $a &+ &$& !a , od!o+ d&o!& & %&+e !og toka. Kada se de7&!&%a+ka%akte%&st&ke od!og a$a !a &,$a, &, !eke -osto+e3e &$& -%o+ekt&%a!eak m $a &+e' ta+ -%o es se !a,& a -%o-aga &+a od!og a$a k%o, ak m $a &+ .S -%ot!o tome' kada +e -ot%e#!o de7&!&%at& ka%akte%&st&ke od!og a$a !a!&, od!om -%o7&$ !eke d&o!& e %&+e !og toka' a !a os!o -o,!atog od!og

a$a !a , od!om -%o7&$ te d&o!& e' ta+ -%o es se !a,& a -%o-aga &+a od!og

a$a d %&+e !og toka. *#og toga' -%o-aga &+a -o-$a !& a$o a se g% #od&+e$& d &+e g% -e: 5&6 -%o-aga &+ -o-$a !& a$o a d -%&%od!& odotoka &ka!a$a & 5&&6 -%o-aga &+ -o-$a !& a$o a k%o, ak m $a &+e.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 29


21/50


Dak$e' -od -o+mom mode$a -%o-aga &+e -o-$a !& a$o a -od%a, m&+e a+ se-ost - & & metode ko+e se ko%&ste &d%o$og&+& ,a -%o%a ! !a-%edo a!+a

od!og a$a d toka' &$& k%o, ak m $a &+ sm&s$ -%o%a !a %eme!a!+ego og -o+a $+& a!+a & o#$&ka -o-$a !og a$a. Kod -%&%od!& odotoka &ka!a$a' kao & ak m $a &+a' -%& -%o$ask -o-$a !& a$o a' od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 21


22/50


t+e a+ %eg $a &+sk& %ado a s$& 5-%es&+e a!+e %&+e !k%& &!a' &sk$+ e!+e %ete! &+a &,g%ad!+om !as&-a d toka &s$.6 !a +ete - to a!+a & t%a!s7o%ma &+e -o-$a !& a$o a'-&ta!+e &,#o%a ak m $a &+a s$& 5$oka &+e & ,a-%em&!eak m $a &+skog -%osto%a ,a -%&+em -o-$a !& a$o a6' s

&$+em maks&ma$!og #$a e!+a -o-$a !og a$a do$&!&!&, od!o'd&me!,&o!&%a!+e !as&-a ,a s-%+e a a!+e &,$&+e a!+a e$&k&

oda.

A!a$&,e -o+a e e$&k& oda 4 -o-$a !& a$o a & !+& o e -%o-aga &+e k%o,ak m $a &+e' tako


23/50


Uko$&ko se -%osto%!o st% +a!+e ,am+e!& $&!&+sk&m & ako se ed od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2


24/50


Slika 7 P%&m+e!a Sa&!t4 e!a!to & +ed!ad #&

S&stem Sa&!t4 e!a!to & +ed!ad #& mo e se %&+e8&t& !a s$+ede3e !a &!e:4 a!a$&t& k& , do- !ske -%et-osta ke'4 ! me%& k& , do- !ske -%et-osta ke'4 &d%a $& k&m mode$&ma'4 &d%o$o8k&m mode$&ma.

I,#o% o-t&ma$!e metode -%o%a !a ,a &s& o ka%akte% -%o#$ema' %as-o$o & &m$a,!&m -oda &ma & o %as-o$o & &m s%edst &ma ,a o#a $+a!+e -%o%a !a

5-%&m+e!om %a !a$a &$& % !o6.

P% & od o a et&%& !a &!a e,a! +e ,a &!teg%&%a!+e os!o !& d&7e%e! &+a$!& +ed!ad #& 5$&!ea%&,a &+ Sa&!t4 e!a!to & +ed!ad #&6' dok d% g& -%edsta $+a

!+& o o ! me%& ko %+e8a a!+e 5metoda ka%akte%&st&ka' metoda ko!a !&-%&%a8ta+a & d%.6. Od matemat& k& metoda -%o%a !a' !a+,!a a+!&+a +e metodaka%akte%&st&ka & metoda ko!a !& -%&%asta. Metoda ka%akte%&st&ka !&+e -ogod!a,a -%o%a !e e,a!e ,a -%&%od!e toko e. Metode ko!a !& -%&%asta s!a+-ogod!&+e ,a -%o%a !e o e %ste' a do & +e$e s - ! a7&%ma &+ s-%&m+e!om %a !a$a &d%a $& k&m -%o%a !&ma. "&t metode ko!a !&-%&%asta $e & tome 8to se d&7e%e! &+a$& os!o !&m +ed!ad #ama ,am+e!+ +d&7e%e! &+ama 4 ko!a !&m -%&%ast&ma.

&d%a $& k& -%o%a !& te e!+a ode -%&%od!&m toko &ma mog #&t& &, %8-%&m+e!om ! me%& kog &$& 7&,&ka$!og mode$a. U &, +es!&m' -ose#!o s$o e!&m

s$ a+e &ma' -%&m+e!+ + se -a%a$e$!o & ! me%& k& & 7&,&ka$!& mode$&' s t&mse %e, $tat& do#& e!& -o +ed!om &$& d% gom mode$ do- !+ + & s$ e ,ata%&%a!+e' s-o%e


25/50

Hidrologija odabrana poglavlja_____________________________________________________ o#a as-ekta & -%edsta $+a+ %e, $tat -%$& !og %+e8a a!+a o#+e +ed!ad #ek%eta!+a 4 d&!am& ke +ed!ad #e & +ed!ad #e ko!t&! &teta.

P%o#$em t%a!s7o%ma &+e se mo e %&+e8&t& & -omo3 mode$a +ed!osta !est% kt %e' &+& se -a%amet%& od%e< + !a #a,& -%omot%e!& a$o a' & ko+&-%edsta $+a+ -o+ed!osta $+e!o %+e8e!+e os!o !& d&7e%e! &+a$!& +ed!ad #&ga!+a. O e metode s $&te%at %& -o,!ate -od !a,& om &d%o$o8ke metode,a -%o%a ! t%a!s7o%ma &+e -o-$a !& a$o a. P%& tome se -o$a,& od-%et-osta ke da se -%otok %&+e !om ko%&t m&+e!+a -ost -!o' & da +e,a-%em&!a ode ko%&t !a -%omat%a!o+ d&o!& & %&+e !og toka 7 !k &+a samo

$a,a 5dotoka6 &$&/& &,$a,a 5ot+e a!+a6.

3.1 Hidrolo0ki 4odeli $ro$a a3i!e %odno %ala

Eg,akt!e matemat& ke metode &d%a $& k& -%o%a !a e,a!& ,a-%o a a!+e - to a!+a & t%a!s7o%ma &+e -o-$a !& a$o a -%&%od!&m

toko &ma %$o s s$o e!e -%&m+e!& +e% ,a t&+e a+ %$o k a$&tet!e $a,!e-odatke. *#og toga' !asta$e s t, . &! e!+e%ske 4 &d%o$o8ke metode ko+e +o8&+ek !&s &,g #&$e s o+ ,!a a+' -o8to omog 3 + da se %e$at& !o $ako & #%,o

do>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2%


26/50


-a s$&+ed&:

Q xt

#

= (4)

Qt

0

= (2 )

DinamiJka 0ednadbaG

*a!ema%& a!+em &!e% &+a$!og $a!a & $a!a ko+& o# a3a t+e a+ -%om+e!e#%,&!ske &s&!e +ed!ad #a 2; -o-%&ma o#$&k:

ed 1 1 xh =

(29)

Kako +e -o de7&!& &+&

x 3

1 xh

d =

(2;)

d&!am& ka +ed!ad #a se t%a!s7o%m&%a Q e, +e +ed!ad # :

' 0

1 x 3

e 2

2

==

(3,)

od!os!o ,a &s!ost

( ) 3 QQ = (31)

Kako +e & ,a-%em&!a %&+e !og ko%&ta 7 !k &+a &s- !+e!ost& %&+e !og ko%&taodom' s$&+ed& da +e & 3 3 0 0 = . I, o oga se mo e ,ak$+ &t& da +e & ,a-%em&!a

7 !k &+a -%otoka' 8to se ko!a !o t%a!s7o%m&%a d&!am& ka +ed!ad #a:3Q0 0 = (32)

L&!s$e & osta$& s -oka,a$& da se ,a-%em&!a %&+e !og ko%&ta !a d&o!& & tokamo e %a,mat%at& kao s ma d a d&+e$a: t, . -%&,mat& !e ,a-%em&!e &$& ode!ogt&+e$a &s-od +ed!e ,am&8$+e!e $&!&+e -o e!e -a%a$e$!o sa d!om %&+eke' &-&%am&da$!e ,a-%em&!e &$& ode!og t&+e$a &,me< te 5&mag&!a%!e $&!&+e6 &t%e! t!og od!og $& a 5s$&ka )6.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2(


27/50


Slika 7 Pod+e$a ,a-%em&!e %&+e !og ko%&ta -o L&!s$e

P&%am&da$!a ,a-%em&!a -o e3a a k -! ,a-%em&! tokom -o%asta &sma!+ +e +e tokom o-ada!+a odosta+a. Odat$e' ako se !a %ta d&+ag%am A:( 0) C ,a &s!ost &,$a,!og -%otoka & ,a-%em&!e ode -%omat%a!o+ d&o!& &'

-o+a &t& 3e se t, . -et$+a ko+a +e -os$+ed& a !esta &o!a%!og te e!+a ode !a-%omat%a!o+ d&o!& & 5s$&ka @6.

Slika C7 Po+a a 9-et$+e k%& $+& V 75 6 s$&+ed !esta &o!a%!og te e!+a

*#og toga' ,a -%o%a ! -&%am&da$!e ,a-%em&!e mo%a+ se %a,mat%at& & $a,!&/ & &,$a,!&A -%otok %&+e !e d&o!& e.

=-/ K%a5i1ta3ionarna 4etoda

Pro%aKaci0a dF %rirodnih vodotoka ili kanala

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2-


28/50


Slika D7 Ko!t%o$!& o$ me! -%&%od!og odotoka

Ako se +ed!ad #a ko!t&! &teta' &!teg%&%a ,a +ed! d&o!& %&+e !og toka' do#&+ese:

( ) ( )9

@@ =

+

dx x xt Q

dxt

xt # i4

5l

i4

5l

x

x

x

x (33)

( ) ( ) ( ) 9@ =+ t Qt Qdxt x #t 5l i4

x

x

i4

5l (3 )

I!teg%a$ +ed!ad #& (; -%edsta $+a ,a-%em&! %&+e !og ko%&ta(t) -a se +ed!ad #a ko!t&! &teta mo e !a-&sat& kao o#& !a d&7e%e! &+a$!a +ed!ad #a-% og %eda:

dt d0

QQ i4 5l = (3-)

*a %+e8a a!+e -o et!og -%o#$ema o-&sa!og +ed!ad #om (> -ot%e#!o +e ,adat&

-o et!& +et : 939 0 t 0 ==U o-3em s$ a+ ,a-%em&!a +e 7 !k &+a o#a -%otoka' $a,!og & &,$a,!og'

3@ i4 5l QQ0 0 = a$& se %ad& $ak8eg %a !a!+a od& -%et-osta ka 3i4 Q0 0 =

Ako se o a ,a &s!ost !a-%&+ed od%ed& ,a -%omat%a! d&o!& %&+e !og toka'-o et!& -%o#$em se mo e %+e8a at& -o &,$a,!om -%otok ' 8to +e & &$+ -%o%a !a.Ako se -%oto & !a $a,!om & &,$a,!om -%o7&$ -%omat%a+ s k es& !&m

%eme!sk&m &!te% a$&ma t te %ad& -%eg$ed!&+eg o,!a a a!+a ,a / Fl edeo,!aka / a ,a / i! ede o,!aka A +ed!ad #a se mo e -%edsta &t& o#$&k :

t 0 $Q = (34)

gd+e s Q & $ -%os+e !& -%oto & &!te% a$ t = t 0 t 0 1 a -%om+e!a,a-%em&!e %ete! &+e tom &!te% a$ :

222111 j j j j j j 0 0 $$QQ +=++ (3 )

U +ed!ad #& () -o,!ate s s e a%&+a#$e os&m A 0 & 0. O#,&%om !a &$+-%o%a !a' da se od%ed& -%o-ag&%a!& -%otokA 0 mo%a se est& dodat!a e,a&,me< -%otoka & ,a-%em&!e. S o#,&%om !a to da +eA 0 -%om+e!$+& a a%&+a#$a

ko+ t%a &mo' o &to +e da dodat!a +ed!ad #a mo%a #&t& o#$&ka3 j j 0 f $ = (39)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2


29/50

Hidrologija odabrana poglavlja_____________________________________________________ Jed!ad #a (@ se !e mo e d&%ekt!o %+e8a at& +e% sad% & d &+e !e-o,!ate

a%&+a#$eA 0 & 0 &+a +e me< so#!a ,a &s!ost !e$&!ea%!a.

Kada +e -&ta!+ -ot%e#a k a,&4sta &o!a%!e metode ,a -%o%a ! -%o-aga &+e-o-$a !og a$a k%o, ot o%e!e od!e toko e' ,a od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 26


30/50


-%omat%a!o+ d&o!& & ko%&8te!+em +ed!ad #e ko!t&! &teta $Qt

0 = . P%& tome

se !a g%a!& ama -%omat%a!e d&o!& e mo%a+ !a$a,&t& &d%omet%&+sk& -%o7&$& do#%o de7&!&%a!&m k%& $+ama -%otoka' tako da se $a,!& & &,$a,!& &d%og%am&ko+& odgo a%a+ +ed!om te &stom -o-$a !om a$ mog to !o de7&!&%at&. Kadase #&$a!s&%a!+em -o,!at& -o-$a !& a$o a !a $a,!o+ & &,$a,!o+ d&o!& &de7&!&%a ,a &s!ost &,$a,!og -%otoka & ,a-%em&!e %ete! &+e 30 f $ = do#& a se,a &s!ost o#$&ka -%&ka,a!og !a s$& & @. O a ,a &s!ost se ,am+e!+ +eos%ed!+e!om k%& $+om & da$+!+&m -%o%a !&ma ko%&st& +ed!o,!a !a,a &s!ost.

O#,&%om da +e metoda g%a7oa!a$&t& ka' ,a od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 9


31/50

Hidrologija odabrana poglavlja_____________________________________________________ 7 !k &o!a$!e ,a &s!ost& ,a-%em&!a 4 &,$a,!& -%otok' do$a,& se do ! me%& kog%+e8e!+a t%a!s7o%ma &+e -o-$a !& a$o a.

Po+ed!osta $+e!+e +e &, %8e!o !a !a &! da se d&!am& ko+ +ed!ad #&,a!ema%e!& &!e% &+a$!& $a! & $a! ko+& o# a3a t+e a+ -%om+e!e #%,&!ske

&s&!e ko+& s ,!at!o ma!+& od osta$& $a!o a. S$&+ed& da +e mode$ ,a -%o%a !-%o-aga &+e od!og a$a k%o, ak m $a &+ sasta $+e! od d&7e%e! &+a$!e

+ed!ad #e ko!t&! &teta 5d&7e%e! &+a$!& o#$&k +ed!ad #e #&$a! e ode6 &d&!am& ke +ed!ad #e ,am&+e!+e!e k%& $+om ,a-%em&!e ak m $a &+e.

U s$ a+ ak m $a &+a & %ete! &+a ko+e s s!a#d&+e a!e e ak a &+sk&mo#+ekt&ma &d -%e$+e a & teme$+!& &s- sta' -ogod!o +e +ed!ad #ko!t&! &teta 7o%m $&%at& -%eko kote %a,&!e' od!os!o %+e8a at& -o et!& -%o#$em:

( ) ( ) &i4 5l 3 & 3 6QQdt d3

3 # ==

( 1)

gd+e +e # 4 kota %a,&!e ode ak m $a &+&' > 4 -o %8&!a od!og $& aak m $a &+e' a # , 4 kota %a,&!e t%e! tk t , . *a -%o%a ! +e !eo- od!o-%et od!o od%ed&t& ,a &s!ost > = :(#).

Slika ,/7 Ko!t%o$!& o$ me! ak m $a &+e

*a-%em&!a ode ak m $a &+& +e tako(#) -o %8&!a od!og $& a ak m $a &+e ,a %a,&! ode # . Kod e$&k&ak m $a &+a mo e se -%et-osta &t& da +e:

3 #0 ( 2a)8to ,!a & da se &st& a!+e &, ak m $a &+e mo e &,%a,&t& 7 !k &+& ,a-%em&!eak m $a &+e' t+:

30 f Q i4 = ( 3)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1


32/50

Hidrologija odabrana poglavlja_____________________________________________________ Des!a st%a!a +ed!ad #e (1 -%edsta $+a 7 !k &+ %eme!a / Fl(t) +e ,ada!&

$a,!& &d%og%am ak m $a &+ ' a/ i! (t) +e &,$a,!& &d%og%am -%o7&$ #%a!e'ko+& se %a !a !a os!o !& og%ama ak m $a &+& & !a os!o t&-a &ka%akte%&st&ka e ak a &+sk& o#+ekata. =a -%&m+e%' ,a -%e$+e #e, sta e +e

3 2A1 3 f Q i4 = 5s$o#od!o -%e$&+e a!+e6' a ,a teme$+!& &s- st' 3 2A12 3 f Q i4 = .

U &d%o$og&+& se !a+ e83e ko%&st& t, . mod&7& &%a!a P $s metoda t%a!s7o%ma &-o-$a !& a$o a k%o, ak m $a &+e ko+a se sasto+& &te%at& !om %+e8a a!+

+ed!ad #e ko!t&! &teta , -osto+a!+e d &+e -%et-osta ke:o%&,o!ta$a! !& o ode ak m $a &+&' &

&s- 8ta!+e &, ak m $a &+e +e +ed!o,!a !a 7 !k &+a ,a-%em&!e.

*a -ot%e#e -%o%a !a !eo- od!o +e %as-o$agat& sa s$&+ede3&m ,a &s!ost&ma:,a-%em&!a 4 !& o ode ak m $a &+&' 3 3 f 0 =&,$a,!& -%otok 4 !& o ode ak m $a &+&' 3 3 f Q i4 =

K$as& !& &d%o$o8k& -%&ka, se sasto+& ko%&8te!+ +ed!ad #e ko!t&! &teta:

( )

++=

+ 222 111t

Q0 t

QQt

Q0 i4 j j5l

j5l

ji4

j j

( )

& ,a &s!ost& 3 3 f 0 = & 3 3 f Q i4 = !a os!o ko+& se od%e< +e d% ga -ot%e#!a,a &s!ost ,a -%o%a ! t%a!s7o%ma &+e od!og a$a: 30 f Q i4 =

Kao & kod -%&m+e!e o e metode ,a -%o%a ! t%a!s7o%ma &+e -o-$a !og a$ad %&+e !og ko%&ta' -o%ed ,a &s!ost& 30 f Q i4 = ,a od%e7 75*6 ,a ak m $a &+ 7o%m&%a! #%a!om !a ko+o+ se oda e ak &%a samo-omo3 s$o#od!og -%e$+e a & kada +e %a,!a ode ak m $a &+& * e3& &$& +ed!ak kot&k% !e -%e$+e a *-%

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 2


33/50


=-> &etoda &21kin 24

P%o%a ! -%o-aga &+e -o-$a !& a$o a d -%&%od!& odotoka & ka!a$a' -oo o+ metod& -o$a,& od -%et-osta ke da ,a-%em&!a ode !a %&+e !o+ d&o!& & !&+esamo 7 !k &o!a$!o e,a!a sa &,$a,!&m -%oto &ma' e3 ,a &s& & o d% g&m-a%ameta%&ma. =a -%&m+e%' s$ a+ da se -%otok !a $a,!om -%o7&$ d&o!& e-%om&+e!&' a !a &,$a,!om osta!e ko!sta!ta!' ,a-%em&!a ode !a d&o!& & sem&+e!+a' -a +e -%ema tome o!a 7 !k &+a o#a -%otoka. U tom s$ a+ se-o+a $+ +e -et$+a kod ,a &s!ost& &,me< odosta+a & -%otoka. Kada se -%oto &!a $a,!om & &,$a,!om -%o7&$ %&+e !e d&o!& e m&+e!+a+ %eme! ' ,a-%em&!a

ode !a sekto%a se mo e -od&+e$&t& !a -%&,mat& !& & k$&!ast& d&o' kako +e to-%&ka,a!o s$&kom . *a-%em&!a &s-od $&!&+e' ko+a +e -a%a$e$!a sa %&+e !&md!om' !a,& a se -%&,mat& !& d&o ,a-%em&!e' a ,a-%em&!a &,me< -a%a$e$!e$&!&+e & $&!&+e !& oa od!og og$eda$a !a,& a se k$&!ast& d&o ,a-%em&!e.

U tok -o%asta !& oa !a %&+e !o+ d&o!& & -o+a $+ + se -o,&t& !& k$&!ast& d&+e$o,a-%em&!e. Me< t&m' t%e! tk kada o-ada!+e $a,!og &d%og%ama -osta!e&!te!,& !&+e od o-ada!+a &,$a,!og &d%og%ama' -o+a $+ + se !egat& !& k$&!ast&d&+e$o & ,a-%em&!e 5s$&ka 1;6. Post -ak -%o%a !a -%o-aga &+e -o-$a !&

a$o a ,a t&+e a da se adek at!o sag$eda t+e a+ ,a-%em&!e' a -%&+e s egak$&!astog d&+e$a. To +e %a,$og 8to se -%o%a ! -%o-aga &+e mo%a+ &sto %eme!o

k$+ &t& -%oto & !a $a,!om & &,$a,!om -%o7&$ d&o!& e.

Slika @7 E$eme!t& ,a-%em&!e ode !a %&+e !o+ d&o!& & ,a %&+eme -%o$aska -o-$a !oga$a

Metoda ko%&st& $&!ea%! ,a &s!ost &,me< ,a-%em&!e ode & -%otoka/ !a

$a,!om' te -%otoka A !a &,$a,!om -%o7&$ %&+e !e d&o!& e' s d a -a%amet%a6 & . Po metod& M sk&!gam ,a-%em&!a ode se mo e &,%a,&t& kao te &!ska7 !k &+a s%ed!+& -%otoka !a g%a!& !&m -%o7&$&ma %&+e !e d&o!& e. O-3e!&to&,$a,!& -%otok +e 7 !k &+a ,a-%em&!e & $a,!og -%otoka &$& o#%! to C ,a-%em&!a

+e 7 !k &+a $a,!og & &,$a,!og -%otoka. P%et-osta &mo da +e k -!a ,a-%em&!a:$Q 0 x0 x0 += 31 ( 4)

&$& ,a-%em&!a +e te &!sk& %as-od&+e$+e!a 5-o!de% 1) -%eko ,a-%em&!e ko+ase od!os& !a $a, / & ,a-%em&!e ko+a se od!os& !a &,$a, A. Dak$e' te &!sk&koe7& &+e!t -oka, +e %e$at& !& t+e a+ $a,!og & &,$a,!og -%otoka !a,a-%em&! %ete! &+e.

Ako se &,$a,!& & $a,!& -%oto & &,%a,e kao eks-o!e! &+a$!a 7 !k &+a d #&!eode' 8to +e o-%a da!a -%et-osta ka &, Q e, +e e & Ma!!&!go e +ed!ad #e'

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


34/50

Hidrologija odabrana poglavlja_____________________________________________________ tada 3e ,a sta &o!a%!o +ed!o$&ko te e!+e ka!a$ $a,!& -%otok / ' &,$a,!&-%otok A & ,a-%em&!a %ete! &+e #&t& 7 !k &+a d #&!e ode ka!a$d :

n!

Q aQ

b0

= i n

!

$ a$

b0

= ( )

U %8ta a!+em +ed!ad #e ;) +ed!ad # ;? do#& a se:n!

n!

a$

b xaQ

xb0

+

= 31 ( 9)

Ako +e ,a-%em&!a samo 7 !k &+a &,$a,!og -%otoka' kao 8to +e to s$ a+ kodak m $a &+a' %&+ed!ost koe7& &+e!ta &,!os& ! $a' tako da +ed!ad #a 2@ &mao#$&k

n!

a

$b0

=

( ;)

Ako se -%et-osta & $&!ea%!& odgo o% ,a-%em&!e !a $a,!& & &,$a,!& -%otok 5m/!16' +ed!ad #a ;@ -o-%&ma o#$&k:

[ ]$ x xQ 7 $ab

xQab

x0 3131 +=+= (-,)

gd+e +e K #/a. Pa%ameta%6 +e -o,!at kao ko!sta!ta ,a-%em&!e' & -%$& !oodgo a%a %eme! - to a!+a od!og a$a od $a,!og do &,$a,!og -%o7&$a.

Jed!ad #a ;@ se mo e !a-&sat& & s$&+ede3em o#$&k :3 $Q 7x 7$0 += (-1)

gd+e d% g& $a! !a des!o+ st%a!& +ed!ad #e -%edsta $+a -&%am&da$! ,a-%em&!5ko+a +e 7 !k &+a %a,$&ke $a,a & &,$a,a6' dok se -% & $a! !a des!o+ st%a!&

+ed!ad #e od!os& !a -%&,mat& ! ,a-%em&! .

D% ga -ot%e#!a +ed!ad #a ,a -%&m+e! metode M sk&!gam +e +ed!ad #ako!t&! &teta' od!os!o

t 0 0 $$QQ j j j j j j

+=++ 111

22 (-2)

Kako +e 0 4 0 1 !a os!o +ed!ad #e >0:

( ) ( ) % j% j j j% j j $ x% xQ$ x% xQ 7 0 0 += (-3)

te se !+ego &m %8ta a!+em +ed!ad # >2 do#&+e

( ) ( ) +=

+

+ t

$ x% xQ$ x%Q 7

(

$$

(

QQ % j% j j j j% j j% j

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 4


35/50

Hidrologija odabrana poglavlja_____________________________________________________ (- )

8to !ako! s%e-, '$.enito

Ra &o!a$!o ko%&8te!+e oda & e7&kas!a ,a8t&ta k a$&tete oda s -od e$&k&mt+e a+em %e &ma ma$& oda %&+e !& toko a.

P%o#$em& -o+a e & t%a+a!+a ma$& oda kao & de7&!&%a!+e samog -o+ma ma$eode t&+es!o s -o e,a!& s 7e!ome!om s 8e' 8to +o8 e3o+ m+e%& !ag$a8a a

-ot%e# os&g %a!+a -%e%as-od+e$e od!oga %e &ma te se stoga & -o+a e ma$&oda !e mog &8e a!a$&,&%at& od o+e!o od k -!& -%o esa ot+e a!+a ! ta%&d%o$o8kog &k$ sa. %&+eme kad +e od &+e$e &d%o$og&+e g$a !om #&

do o$+!o -o,!a at& samo maks&ma$!e -%otoke kao os!o !og -oka,ate$+a-o+a a e$&k& oda ,a d&me!,&o!&%a!+e o#+ekata od od!+e' a m&!&ma$!e-%otoke kao os!o !og -oka,ate$+a ma$& oda ,a d&me!,&o!&%a!+e o#+ekata ,ako%&8te!+e oda' kao $&m&t&%a+ 3& &d%o$o8k& % #!& +eta' oda !o +e -%o8Isto tako se !&t& s sta & ,a ko%&8te!+e oda !e mog -%omat%at& od o+e!o ods o+ega ok% e!+a' a kao ,!a a+a! &d ko%&8te!+a oda t%e#a t%et&%at& & te e!+e

ode -%&%od!&m toko &ma & , to e,a!e -%o ese. *a +e$o &to %a, m&+e a!+e

7e!ome!a s 8e' od!os!o -o+a a ma$& oda ko!tekst %a,$& &t& &do ako%&8te!+a od!& %e,e% &' ! !o +e' , -o,!a a!+e &d%o$o8k& ,ako!&tost& &metodo$o8kog -%&st -a ,a !+& o a!a$&, ' & -o,!a a!+e ok &%a ko+em se

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> %


36/50

Hidrologija odabrana poglavlja_____________________________________________________ -%o es& e,a!& , te -o+a e doga


37/50


Slika ,@7 T%e!d oda o#o%&!a ,a . 4 III. m+ese !a -osta+& A#%am& 51 ?(.4200(.6

Po,!a a!+e %e &ma & ka%akte%&st&ka ma$& oda %&+e !& toko a eoma +e a !o,a -%o+ekt&%a!+e' g%a>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> -


38/50

Hidrologija odabrana poglavlja_____________________________________________________ -od% +&ma ko+e g$a !om ka%akte%&,&%a &,!&m!a os+et$+& ost' a 8to o-et!ag$a8a a a !ost -%o ed#e &d%o$o8k& a!a$&,a ma$& oda &$+ de7&!&%a!+am+e%oda !e ma$e ode' ko+e s +ed!a od os!o !& -od$oga !a teme$+ ko+e seod%e< +e & -%&+em!a mo3 odotoka.

A!a$&,a ma$& oda +ed!ako +e a !a & ,a -%a &$!o d&me!,&o!&%a!+e %a,!&&d%ote !& k& o#+ekata & s sta a. P%& tome se' ko$&ko -osto+e -oda &&d%o$o8k& -%omat%a!+a' ,!a a+ke ma$& oda o#& !o -%o a a+ s !eko$&ko

t&-o a &d%o$o8k& a!a$&,a' -%& em a$+a !ag$as&t& da k%8k& od!& %es %s&-%a &$ ,a t&+e a+ s$o e!&+e -%&st -e ,#og ma!+eg st -!+a de7&!&%a!ost&

&d%o$o8k& od!osa ! ta% !+& o & s sta a. Ug$a !om se -%&m+e!+ + :4 a!a$&,e %eme!a !ast -a ma$& oda t&+ekom god&!e'4 a!a$&,e k%& $+a t%a+a!+a -%otoka' odosta+a &$& !ekog d% gog-oka,ate$+a od!og %e &ma'4 sto ast& ke a!a$&,e -o+a a m&!&ma$!& &$& ka%akte%&st& !& os%ed!+e!&ma$& oda t&+ekom %a,do#$+a oda#%a!& d $+&!a'

4 a!a$&,e odo a &d%o$o8k& %eme!sk& se%&+a 5t%e!do &' -e%&od& !ost&a!a$&,e -ok%et!&m -%os+e &ma' RAPS se%&+ama' a toko%e$og%am&ma'a%mo!&+skom & s-ekt%a$!om a!a$&,om6'

4 k%osko%e$a &+sk&m a!a$&,ama &,me< t+e a+!& !&,o a &d%o$o8k&-odataka'

4 a!a$&,om +e%o+at!ost& -o+a e ka%akte%&st& !& &d%o$o8k& -odataka'4 a!a$&,e -omo3 sta!da%d!& %e es&+sk& k%& $+a -%a3e!+a %e,e% &-od,em!& oda'4 a!a$&,e -omo3 ke%!e$o & 7 !k &+a 57 !k &+a +ed&!& !og &m- $s!og

od,& a6'4 osta$e a!a$&,e -%&m+e!om %a,$& &t& d% g& metoda & -ost -aka.

Sasta !& d&o tak & a!a$&,a s & %a,$& &te %eg&o!a$&,a &+e ko+&ma +e ,adatak &to kast& -odataka a!a$&,e ma$& oda s -o+ed&!& &d%o$o8k& -odataka do#&t&8&%e ,ako!&tost& 4 #&$o da se %ad& o +ed!od&me!,&o!a$!&m %eg&o!a$!&m-od$ogama 5 t %< + se ,ako!&tost& ,d a!a$&,&%a!og odotoka6' &$& -ak o-%osto%!&m %eg&o!a$!&m -od$ogama gd+e se t %< + ,ako!&tost& -o+a amama$& oda -o s$& !&m -od% +&ma.

4.3 Stati1ti6ka anali5a 4alih %oda

Stat&st& ka a!a$&,a ma$& oda ,a t+e a se%&+e m&!&ma$!& god&8!+& -%otokat%a+a!+a t 1' 10' 20' (0....da!a. Stat&st& ke se%&+e se 7o%m&%a+ !a !a &! da se!a os!o -odataka d gogod&8!+& -%omat%a!+a d!e !og ot+e a!+a &,d o+e-%os+e !e %&+ed!ost& !a+ma!+& -%otoka t%a+a!+a 1' 10' 20' (0.... ,asto-!&da!a. O!& se ,o +ed!&m &me!om -%oto & -e%&oda ma$& oda. =&,o & -%otokamo%a+ ,ado o$+&t& os!o !e stat&st& ke k%&te%&+e kako #& se mog$& -od %g! t&o#%ad&. $a!o & !&,a mo%a+ #&t& s$ a+!e e$& &!e' a meteo%o$o8ke & &d%o$o8k

e$& &!e mo e se smat%at& s$ a+!&ma ,#og %$o e$&ka #%o+a %a,$& &t& t+e ao ko+&ma o!e o &se. Tako


39/50

Hidrologija odabrana poglavlja_____________________________________________________ Ako se ,a +eda! !&, / min !e mo e !a-%&+ed t %d&t& da ,ado o$+a a k%&te%&+s$ a+!ost& -ot%e#!o +e test&%at& !e,a &s!ost e$eme!ata %as-o$o & og ,o%ka.

=&, mo%a #&t& omoge!. omoge!ost &$& &sto %s!ost -odataka +e -ot%e#!o&s-&tat&. Is-&t& a!+a omoge!ost& -%o ode se %a,$& &t&m testo &ma' !a-%.N&$ oWo!o &m testom' Ko$mogo%o $+e &m testom & s$.' a !e omoge!ost !&,-odataka se tako-=-,&etoda odi0n!ih ek1tre4a

P%& stat&st& ko+ a!a$&,& ekst%ema %&+ed!ost& &d%o$o8k& e$& &!a 5 k$+m&!&ma$!e god&8!+e -%otoke6 !a+ e83e se ko%&st& metoda god&8!+& ekst%ema.O a metoda +e ,as!o a!a !a a!a$&,& ekst%em!o o-a e!& e$& &!a s ako+god&!& 5+eda! -odatak god&8!+e6 t&+ekom &8egod&8!+eg -e%&oda -%omat%a!+a.O#%adom -odataka do#& a se stat&st& k& !&, m&!&ma$!& god&8!+& -%otoka 4stat&st& k& ,o%ak & to kao:

! N

!i

!i

!i

!! QQQQQQ @...@@@@...@@ 1121 + ! N !i!i!i!! QQQQQQ + ...... 1121 (4,)

Q&$+ a!a$&,e +est da se do#&+e +e%o+at!ost -o+a e' od!os!o 7 !k &+a %as-od+e$e+e%o+at!ost& m&!&ma$!& god&8!+& -%otoka. To se -ost& e !a$a e!+em 7 !k &+e

%as-od+e$e +e%o+at!ost&:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 6


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!QQ P Q 8 =32 od!os!o !QQ P Q =32 (41)

+e% +e 7 !k &+a %as-od+e$e +e%o+at!ost&+(/) ' od!os!o 3Q ' -ot- !aka%akte%&st&ka %as-od+e$e. To ,!a & da se s & %e, $tat& o &s!& o s$ a+!o+

a%&+a#$&/ mog do#&t& &, 7 !k &+e %as-od+e$e +e%o+at!ost&+(/) ' od!os!o3Q . %&+ed!ost m&!&ma$!& god&8!+& -%otoka od%e


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>-=-=Anali5a $erioda 4alih %oda

Kod a!a$&,e -e%&oda ma$& oda -%o od& se a!a$&,a -%os+e !& %&+ed!ost&-%otoka !ekom' !a-%&+ed oda#%a!om' %eme!skom -e%&od ! ta% s 8!og-e%&oda god&!e. Se%&+e m&!&ma$!og -%otoka se 7o%m&%a+ !a !a &! da se !aos!o -odataka d gogod&8!+& -%omat%a!+a &,d a+a+ -%os+e !e m&!&ma$!egod&8!+e %&+ed!ost& -%otoka t%a+a!+a (' )' 10' 1;'... ,asto-!& da!a' ko+&-%edsta $+a+ m&!&ma$!e -%otoke -e%&oda ma$& oda.

Slika , 7 &-otetsk& god&8!+& &d%og%am %&+eke sa -%&m+e%om )4d!e !og -e%&oda ma$&oda & m&!&ma$!og god&8!+eg )4d!e !og -%otoka

Kod -e%&oda ma$& oda ko$& &!e ode odotok s !a+ma!+e' a sam&m t&me &mog 3!ost& %a,%+e


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Slika ,C7 B !k &+a %as-od+e$e +e%o+at!ost& -o+a e m&!&ma$!& god&8!+& -%otokat%a+a!+aXt 10' 20' (0' ?0 & 0 da!a

Slika ,D7 B !k &+a %as-od+e$e +e%o+at!ost& -o+a e m&!&ma$!& god&8!+& -%otokat%a+a!+a

Xt 10' 20' (0' ?0 & 0 da!a

>-> Re ionalna anali5a 4alih %oda

Metoda %eg&o!a$!& a!a$&,a %a, &+e!a +e ,a -ot%e#e od%e>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 42


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Hidrologija odabrana poglavlja_____________________________________________________ ka%akte%&st&ka s$& a' k$+ + 3& & geo$o8ke ka%akte%&st&ke. Mode$& &8est%%eg%es&+e ko%&ste se ,a o-&s& a!+e !eke od ka%akte%&st&ka ma$& oda kao7 !k &+ 7&,& ko4geog%a7sk& & k$&matsk& 7akto%a. K a$&teta %eg%es&+sk& mo &s& o ko$& &!& & k a$&tet& -odataka ko%&8te!& 7o%m $a &+& mode$a. U -%

-o%a#a %eg%es&+sk& mode$a +e esto og%a!& e!a !edo o$+!&m &$&!eadek at!&m -oda &ma o a%&+a#$ama k$+ e!&m mode$' kao !a -%&m+e%!eko%ekt!o o +e!+e!& to-og%a7sk& -a%amet%&' 8to do od& do !e,ado o$+a a+ 3&%e, $tata.Iako s o +e!e ka%akte%&st&ka ma$& oda odotoka !a os!o ka%akte%&st&kas$& !e -o %8&!e eoma g% #e' -ot%e#a ,a tom %stom -%o%a !a &mao-%a da!+a s$ a+ tamo gd+e s +et& ,a to -ogod!&.Metodom &8est% ke %eg%es&+e od%e< +e se +ed!a od ka%akte%&st&ka ma$& oda

odotoka kao 7 !k &+a 7&,& ko4geog%a7sk& & k$&matsk& ka%akte%&st&ka !+ego es$& !e -o %8&!e matemat& k&m mode$om o#$&ka:

nbn

bbb x x x xa y = ...21 21 (43)

gd+e +e 7 4 !eka od ka%akte%&st&ka ma$& oda 1 2 3 ... n 4 7&,& ko4geog%a7ske & k$&matske ka%akte%&st&ke s$& aa b1 b2 b3 ...bn 4 -a%amet%& %eg%es& !og mode$a

Ka%akte%&st&ka ma$& oda 7 ' de7&!&%a!a -%eko 7 !k &+e %as-od+e$e +e%o+at!ost&m&!&ma$!& god&8!+& -%otoka' &,%a a a se !a d a !a &!a:- kao -%oto & ko+& odgo a%a+ od%e


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Slika / 7 =a &! od%e


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Hidrologija odabrana poglavlja_____________________________________________________ Kod e7$ e!t!& odotoka' -o -%esta!k -o %8&!skog ot+e a!+a' do$a,& do-od,em!og ot+e a!+a ode ko+e se -oste-e!o sma!+ +e' & ko+e se o &s!o oka%akte%&st&kama s$& a' mo e ,ad% at& d & &$& k%a3& %eme!sk& -e%&od. Oso#&s$& a da ,ad% & od -od,em$+ &ma e$&k& t+e a+ !a %e &m ot+e a!+a ode'od!os!o !a o-ada+ 3 g%a! &d%og%ama ot+e a!+a. Ut %


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Hidrologija odabrana poglavlja_____________________________________________________ U s$ a+ ako se ,ako! &s %-$+e!+a -od,em!& oda !e m&+e!+a &, god&!e god&! !a os!o go%!+e +ed!ad #e mo e se -%$& !o od%ed&t& o$ me!-od,em!& %e,e% & t%e! tkt , ' -o$a,e3& od -%otoka / 0 ko+& odgo a%at , G

9

1Q0

=

(44)gd+e +e:

4 -%o +e!a ka-a &teta ,ad% a a!+a -od,em!& oda s$&

Ako +e/ , ,et m ( /s' a t da!&ma o!da +e +ed!ak

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 4(


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Slika //7 K%& $+e -%a!+e!+a &, o%a G%ado$e ,a %a,do#$+e od ). do @>. da!a 1 ;. god&!e

O-a e!& -%oto & a!a$&,&%a!og %a,do#$+a &ma$e & !eke ma!+e &,%a e!e os &$a &+e.Ra,$og toga s -%om+e!e m&k%o%e &m &st+e a!+a s$&+ed -a$& o#o%&!a

t&+ekom %a,do#$+a %e es&+e' kao & -%om+e!e %e &m %-$+e!+a. =o' kako o!e!&s #&t!&+e t+e a$e !a o-3& t&+ek %e &ma -%a !+e!+a -od,em!& %e,e% & tog&, o%a' & tak a se %a,do#$+a mog ko%&st&t& ,a -%o ed# %ege%es&+sk& a!a$&,a.

Reta%da &+ska k%& $+a &d%og%ama ot+e a!+a mo e se' , od%e


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Slika /=7 B !k &+a %as-od+e$e +e%o+at!ost& d &!e #esk&8!& -e%&oda

(. Pod -%et-osta kom da +e -o %at!& -e%&od +a $+a!+a ma$& odaT +ed!ak-o %at!om -e%&od d &!e #esk&8!& -e%&odad T m&!&ma$!& -%otok -o %at!og-e%&odaT 5god&!a6 od%e< +e se &, +ed!ad #e ?> %8ta a!+em(t t , ) = d T .

>- Anali5a kri%2l!e tra!an!a $rotoka

Oda#%a!e to ke !a do!+em k%a+ k%& $+e t%a+a!+a -%otoka mog se ko%&st&t&kao m+e%a ,a ma$e ode -%omat%a!og toka. P%&m+e%& e e$&ko+ "%&ta!&+& seko%&ste s$+ede3a d a &!deksa:1. P%otok t%a+a!+a > %eme!a 5/ ;-N 62. Postotak %eme!a t%a+a!+a -%otoka

4Q ' gd+e +e Q -%os+e !& &8egod&8!+&

-%otok

Slika />7 P%&ka, -%otoka t%a+a!+a > %eme!a !a k%& $+& t%a+a!+a -%otoka

U k%o!o$o8kom !&, d!e !& -%otoka' #%o+ ,asto-!& da!a tokom ko+eg !emam&!&ma$!og -%otoka !a,& a -e%&od ma$& oda. P%&m+e%& e ako -%otok/ ;-N !&+e,a#&$+e e! tok n da!a' tada se %ad& o -e%&od ma$& oda t%a+a!+an da!a.

=a os!o -odataka d gogod&8!+& -%omat%a!+a d!e !& -%otoka' t+. ' $&!&+a

t%a+a!+a ,a s ak god&! -%omat%a!+a' mog se &,d o+&t& t%a+a!+a -e%&oda saka%akte%&st&kom da +e/ / ;-N ' & !a #a,& o ako 7o%m&%a!e stat&st& ke se%&+e'&, %8&t& a!a$&,a +e%o+at!ost& -e%&oda ma$& oda.

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 4


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4.7 Vodo$ri%redni a1$ekt 4alih %oda

Pod od!&m %e &mom se -od%a, m&+e a &ta a d&!am&ka sta$!& -%om+e!ak a!t&tat& !& & k a$&tat& !& oso#&!a ode' kao & d&!am&ka od!osa ode soko$&!om ko+a +e ok% +e. od!& %e &m& mog #&t& -%&%od!& ko+& se te8ko !&kako !e mog -%a $+at& & !a,& a+ se !e -%a $+& & & -%a $+a!& od!& %e &mOs!o !& &$+ odo-%& %ed!& d+e$at!ost& +e da se &, s7e%e !e -%a $+a!& od!&%e &ma -%e


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Hidrologija odabrana poglavlja_____________________________________________________ -a%amet%e odoto &ma. "&o$o8k& m&!&m m !e mo%a #&t& +ed!ak -o+ed&!&mm+ese &ma &$& se,o!ama. U do!o8e!+ od$ ke o !+ego o+ e$& &!& t%e#a$& #&s d+e$o at& st% !+a & %a,$& &t& s-e &+a$!ost&: &d%o$o,&' &d%a $& a%&eko$o,&' & t&o$o,&' kem& a%&' %#a!&st& & s-e &+a$&st& osta$& ,a&!te%es&st% ka.

@ LITERATURA1. %e$+a' s!o 5200)6: Inenjerska hidrologija ' U!& e%,&tet Sa%a+e CG%a. Y ga+' Ra!ko: Uvodno o velikim vodama 9 &!te%!a sk%&-ta

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72531631 Analiza Velikih i Malih Voda