{"id":11891,"date":"2021-04-19T09:55:48","date_gmt":"2021-04-19T08:55:48","guid":{"rendered":"https:\/\/www.vtei.cz\/?p=11891"},"modified":"2024-07-17T11:50:07","modified_gmt":"2024-07-17T10:50:07","slug":"sensitivity-analysis-of-selected-input-parameters-of-the-numerical-model-hec-ras-in-and-floodplain-flow-calculations","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2021\/04\/sensitivity-analysis-of-selected-input-parameters-of-the-numerical-model-hec-ras-in-and-floodplain-flow-calculations\/","title":{"rendered":"Sensitivity analysis of selected input parameters of the numerical model HEC-RAS in and floodplain flow calculations"},"content":{"rendered":"

<\/i> This article is available in Czech only. For translation or more information on this topic, please contact author.<\/h4>\n

 <\/p>\n

Souhrn<\/h2>\n

Hydraulick\u00e9 v\u00fdpo\u010dty proud\u011bn\u00ed vody v korytech vodn\u00edch tok\u016f a z\u00e1plavov\u00fdch \u00fazem\u00edch se v sou\u010dasn\u00e9 in\u017een\u00fdrsk\u00e9 praxi prov\u00e1d\u011bj\u00ed prim\u00e1rn\u011b s pou\u017eit\u00edm 1D, 2D a sp\u0159a\u017een\u00fdch 1D\/2D numerick\u00fdch model\u016f. Matematick\u00fd model je v p\u0159\u00edpad\u011b zmi\u0148ovan\u00e9 2D schematizace obvykle zalo\u017een na tzv. rovnic\u00edch proud\u011bn\u00ed v m\u011blk\u00e9m proudu (shallow water equations), p\u0159i\u010dem\u017e k matematick\u00e9mu popisu turbulentn\u00edho proud\u011bn\u00ed se zde vyu\u017e\u00edvaj\u00ed tzv. turbulentn\u00ed modely s r\u016fzn\u00fdm pojet\u00edm modelov\u00e1n\u00ed turbulence. V na\u0161ich podm\u00ednk\u00e1ch je pro \u00fa\u010dely hydraulick\u00fdch v\u00fdpo\u010dt\u016f pom\u011brn\u011b roz\u0161\u00ed\u0159en\u00e9 programov\u00e9 vybaven\u00ed HEC-RAS, kter\u00e9 vyu\u017e\u00edv\u00e1 turbulentn\u00edho modelu zalo\u017een\u00e9ho na Boussinesqov\u011b aproximaci. C\u00edlem p\u0159\u00edsp\u011bvku je prezentace postup\u016f a z\u00e1v\u011br\u016f citlivostn\u00ed anal\u00fdzy, je\u017e zohled\u0148uje vliv vstupn\u00edch parametr\u016f uveden\u00e9ho turbulentn\u00edho modelu na v\u00fdsledky hydraulick\u00fdch v\u00fdpo\u010dt\u016f v p\u0159\u00edpad\u011b pou\u017eit\u00ed 2D, respektive sp\u0159a\u017een\u00e9ho 1D\/2D modelu. Sou\u010d\u00e1st\u00ed anal\u00fdz je rovn\u011b\u017e ov\u011b\u0159en\u00ed mo\u017en\u00e9ho ovlivn\u011bn\u00ed v\u00fdsledk\u016f zm\u011bnami dal\u0161\u00edch parametr\u016f v\u00fdpo\u010dtu, mezi kter\u00e9 pat\u0159\u00ed nap\u0159. zaveden\u00ed zjednodu\u0161en\u00e9ho \u0159e\u0161en\u00ed rovnic proud\u011bn\u00ed v m\u011blk\u00e9m proudu aproximac\u00ed difuzn\u00ed vlnou nebo zp\u016fsob prostorov\u00e9 diskretizace \u0159e\u0161en\u00e9 n\u00e1hradn\u00ed oblasti. K ov\u011b\u0159ovac\u00edm v\u00fdpo\u010dt\u016fm byl vybr\u00e1n jednak fiktivn\u00ed \u00fasek prizmatick\u00e9ho koryta lichob\u011b\u017en\u00edkov\u00e9ho pr\u016f\u0159ezu a d\u00e1le re\u00e1ln\u00fd \u00fasek koryta toku Svratka na \u00fazem\u00ed m\u011bsta Brna v d\u00e9lce cca 2,6 km. \u00da\u010delem p\u0159edkl\u00e1dan\u00e9ho p\u0159\u00edsp\u011bvku je p\u0159edev\u0161\u00edm poskytnout potenci\u00e1ln\u00edm u\u017eivatel\u016fm 2D numerick\u00fdch model\u016f, zalo\u017een\u00fdch na rovnic\u00edch m\u011blk\u00e9ho proudu, z\u00e1kladn\u00ed p\u0159edstavu o nejistot\u00e1ch ve v\u00fdsledc\u00edch hydraulick\u00fdch v\u00fdpo\u010dt\u016f, vypl\u00fdvaj\u00edc\u00edch z volby vybran\u00fdch vstupn\u00edch parametr\u016f.<\/p>\n

\u00davod<\/h2>\n

Pro \u00fa\u010dely hydraulick\u00fdch v\u00fdpo\u010dt\u016f proud\u011bn\u00ed vody v korytech tok\u016f a z\u00e1plavov\u00fdch \u00fazem\u00edch se v sou\u010dasnosti v in\u017een\u00fdrsk\u00e9 praxi vyu\u017e\u00edvaj\u00ed prim\u00e1rn\u011b 1D, 2D a sp\u0159a\u017een\u00e9 1D\/2D numerick\u00e9 modely. Uveden\u00fd typ hydraulick\u00fdch v\u00fdpo\u010dt\u016f zpravidla p\u0159edstavuje \u010dasov\u011b \u2013 a tedy i finan\u010dn\u011b \u2013 n\u00e1ro\u010dnou proceduru, kter\u00e1 je zat\u00ed\u017eena \u0159adou nejistot. Jako jeden z podstatn\u00fdch zdroj\u016f nejistot lze ozna\u010dit volbu vhodn\u00e9ho hydrodynamick\u00e9ho modelu k proveden\u00ed hydraulick\u00fdch v\u00fdpo\u010dt\u016f a s t\u00edm souvisej\u00edc\u00ed zp\u016fsob schematizace \u0159e\u0161en\u00e9 oblasti. Volba dimenze modelu spolu s dal\u0161\u00edmi vstupn\u00edmi parametry m\u016f\u017ee m\u00edt podstatn\u00fd vliv na v\u00fdsledky v\u00fdpo\u010dt\u016f. Zat\u00edmco 2D modely vych\u00e1zej\u00ed z p\u0159edpokladu dvourozm\u011brn\u00e9ho (2D) proud\u011bn\u00ed vody na cel\u00e9 \u0159e\u0161en\u00e9 n\u00e1hradn\u00ed oblasti, sp\u0159a\u017een\u00e9 1D\/2D modely uva\u017euj\u00ed v d\u00edl\u010d\u00edch \u010d\u00e1stech \u0159e\u0161en\u00e9 oblasti s jednorozm\u011brn\u00fdm (1D) p\u0159\u00edstupem [2\u20139]. Obvykl\u00e1 je schematizace samotn\u00e9ho vodn\u00edho toku v rozsahu b\u0159ehov\u00fdch hran pomoc\u00ed 1D modelu a p\u0159ilehl\u00e9ho z\u00e1plavov\u00e9ho \u00fazem\u00ed 2D modelem. Hlavn\u00edm p\u0159\u00ednosem pou\u017eit\u00ed sp\u0159a\u017een\u00fdch 1D\/2D model\u016f je zejm\u00e9na snadn\u011bj\u0161\u00ed hydraulick\u00e9 \u0159e\u0161en\u00ed objekt\u016f v z\u00e1jmov\u00e9 oblasti (nap\u0159. mosty, propustky, jezy) a d\u00e1le men\u0161\u00ed n\u00e1roky na podklady zachycuj\u00edc\u00ed morfologii koryta \u0159e\u0161en\u00fdch vodn\u00edch tok\u016f. V p\u0159\u00edpad\u011b 1D modelu lze koryto toku schematizovat soustavou p\u0159\u00ed\u010dn\u00fdch \u0159ez\u016f, zat\u00edmco pro 2D model je nezbytn\u00e9 zajistit kompletn\u00ed digit\u00e1ln\u00ed model reli\u00e9fu koryta toku. Nev\u00fdhodou pou\u017eit\u00ed sp\u0159a\u017een\u00fdch 1D\/2D model\u016f oproti 2D model\u016fm mohou b\u00fdt nap\u0159. p\u0159ijat\u00e1 zjednodu\u0161en\u00ed hydraulick\u00fdch jev\u016f v m\u00edstech propojen\u00ed mezi 1D a 2D oblastmi a mo\u017en\u00e1 v\u011bt\u0161\u00ed \u010dasov\u00e1 n\u00e1ro\u010dnost prov\u00e1d\u011bn\u00fdch v\u00fdpo\u010dt\u016f. Obecn\u011b je problematice srovn\u00e1n\u00ed 1D, 2D a 1D\/2D hydrodynamick\u00fdch model\u016f v\u011bnov\u00e1na \u0159ada publikac\u00ed, viz nap\u0159. [10\u201317].<\/p>\n

Zmi\u0148ovan\u00e9 2D numerick\u00e9 modely jsou obvykle zalo\u017eeny na matematick\u00e9m modelu zahrnuj\u00edc\u00edm tzv. rovnice proud\u011bn\u00ed v m\u011blk\u00e9m proudu (shallow water equations) [18], je\u017e v r\u016fzn\u00e9 m\u00ed\u0159e umo\u017e\u0148uj\u00ed rovn\u011b\u017e zohledn\u011bn\u00ed turbulence. K matematick\u00e9mu popisu turbulentn\u00edho proud\u011bn\u00ed se vyu\u017e\u00edvaj\u00ed tzv. turbulentn\u00ed modely s r\u016fzn\u00fdm pojet\u00edm modelov\u00e1n\u00ed turbulence [1]. V na\u0161ich podm\u00ednk\u00e1ch je pro \u00fa\u010dely hydraulick\u00fdch v\u00fdpo\u010dt\u016f pom\u011brn\u011b roz\u0161\u00ed\u0159en\u00e9 programov\u00e9 vybaven\u00ed HEC-RAS, kter\u00e9 v r\u00e1mci 2D schematizace vyu\u017e\u00edv\u00e1 turbulentn\u00edho modelu zalo\u017een\u00e9ho na Boussinesqov\u011b aproximaci [18]. Jeho podstatou je zaveden\u00ed tzv. turbulentn\u00ed viskozity. Pro jej\u00ed v\u00fdpo\u010det je v\u0161ak nezbytn\u00e1 specifikace bezrozm\u011brn\u00e9ho koeficientu, jen\u017e je z\u00e1visl\u00fd na charakteru proud\u011bn\u00ed a m\u016f\u017ee nab\u00fdvat hodnot v pom\u011brn\u011b \u0161irok\u00e9m rozp\u011bt\u00ed [18\u201320].<\/p>\n

C\u00edlem p\u0159\u00edsp\u011bvku je prezentace v\u00fdsledk\u016f citlivostn\u00ed anal\u00fdzy zohled\u0148uj\u00edc\u00ed vliv uveden\u00e9ho vstupn\u00edho parametru turbulentn\u00edho modelu na v\u00fdsledky hydraulick\u00fdch v\u00fdpo\u010dt\u016f v p\u0159\u00edpad\u011b pou\u017eit\u00ed 2D schematizace, respektive p\u0159i pou\u017eit\u00ed sp\u0159a\u017een\u00e9ho 1D\/2D modelu. Sou\u010d\u00e1st\u00ed anal\u00fdz je rovn\u011b\u017e ov\u011b\u0159en\u00ed mo\u017en\u00e9ho ovlivn\u011bn\u00ed v\u00fdsledk\u016f zm\u011bnami dal\u0161\u00edch parametr\u016f v\u00fdpo\u010dtu, mezi n\u011b\u017e pat\u0159\u00ed nap\u0159. zaveden\u00ed zjednodu\u0161en\u00e9ho \u0159e\u0161en\u00ed rovnic proud\u011bn\u00ed v m\u011blk\u00e9m proudu aproximac\u00ed difuzn\u00ed vlnou nebo zp\u016fsob prostorov\u00e9 diskretizace \u0159e\u0161en\u00e9 n\u00e1hradn\u00ed oblasti. K ov\u011b\u0159ovac\u00edm v\u00fdpo\u010dt\u016fm byl vybr\u00e1n jednak fiktivn\u00ed \u00fasek prizmatick\u00e9ho koryta lichob\u011b\u017en\u00edkov\u00e9ho pr\u016f\u0159ezu a d\u00e1le re\u00e1ln\u00fd \u00fasek koryta toku Svratka na \u00fazem\u00ed m\u011bsta Brna v d\u00e9lce cca 2,6 km. P\u0159edkl\u00e1dan\u00fd p\u0159\u00edsp\u011bvek si neklade za c\u00edl detailn\u00ed teoretick\u00fd rozbor dan\u00e9ho probl\u00e9mu. Jeho \u00fa\u010delem je p\u0159edev\u0161\u00edm poskytnout u\u017eivatel\u016fm 2D numerick\u00fdch model\u016f, zalo\u017een\u00fdch na rovnic\u00edch m\u011blk\u00e9ho proudu, z\u00e1kladn\u00ed p\u0159edstavu o nejistot\u00e1ch ve v\u00fdsledc\u00edch hydraulick\u00fdch v\u00fdpo\u010dt\u016f vypl\u00fdvaj\u00edc\u00edch z volby vybran\u00fdch vstupn\u00edch parametr\u016f.<\/p>\n

Metoda citlivostn\u00ed anal\u00fdzy<\/h2>\n

Citlivostn\u00ed anal\u00fdza vlivu bezrozm\u011brn\u00e9ho koeficientu pro v\u00fdpo\u010det turbulentn\u00ed viskozity na v\u00fdsledky hydraulick\u00fdch v\u00fdpo\u010dt\u016f proud\u011bn\u00ed vody v korytech tok\u016f a z\u00e1plavov\u00fdch \u00fazem\u00edch spo\u010d\u00edv\u00e1 v realizaci a n\u00e1sledn\u00e9 anal\u00fdze \u0159ady variantn\u00edch v\u00fdpo\u010dt\u016f s pou\u017eit\u00edm 2D, respektive sp\u0159a\u017een\u00e9ho 1D\/2D numerick\u00e9ho modelu. Pro tyto \u00fa\u010dely bylo zvoleno pom\u011brn\u011b roz\u0161\u00ed\u0159en\u00e9 programov\u00e9 vybaven\u00ed HEC-RAS, kter\u00e9 je zalo\u017eeno na matematick\u00e9m modelu dvourozm\u011brn\u00e9ho (2D) proud\u011bn\u00ed kapaliny o mal\u00e9 hloubce s volnou hladinou, tj. na tzv. rovnic\u00edch proud\u011bn\u00ed v m\u011blk\u00e9m proudu (FM). Matematick\u00fd model d\u00e1le umo\u017e\u0148uje v\u00fdpo\u010dty s pou\u017eit\u00edm zjednodu\u0161en\u00e9 formy rovnic m\u011blk\u00e9ho proudu bez pou\u017eit\u00ed turbulentn\u00edho modelu, ozna\u010dovan\u00e9 jako aproximace difuzn\u00ed vlnou (DW). Pro srovn\u00e1n\u00ed byl rovn\u011b\u017e vyu\u017eit matematick\u00fd model s jednorozm\u011brnou (1D) schematizac\u00ed. Podrobn\u00fd teoretick\u00fd popis zmi\u0148ovan\u00fdch matematick\u00fdch model\u016f lze nal\u00e9zt nap\u0159. v literatu\u0159e [18]. Konkr\u00e9tn\u00ed u\u017eivatelsk\u00e9 nastaven\u00ed parametr\u016f v programu HEC-RAS lze prov\u00e9st s pou\u017eit\u00edm p\u0159\u00edru\u010dky [22] (viz kl\u00ed\u010dov\u00e1 slova \u201eEddy Viscosity Transverse Mixing Coefficient\u201c, \u201eFull Momentum Equation\u201c a \u201eDiffusion Wave\u201c).<\/p>\n

Jednotliv\u00e9 \u0159e\u0161en\u00e9 varianty se v r\u00e1mci citlivostn\u00ed anal\u00fdzy li\u0161ily pou\u017eit\u00edm r\u016fzn\u00fdch hodnot bezrozm\u011brn\u00e9ho koeficientu D, nezbytn\u00e9ho pro v\u00fdpo\u010det turbulentn\u00ed viskozity, kter\u00e1 je podstatou turbulentn\u00edho modelu vyu\u017e\u00edvaj\u00edc\u00edho Boussinesqovu aproximaci. Sledovanou veli\u010dinou byla ve v\u0161ech p\u0159\u00edpadech vypo\u010dten\u00e1 \u00farove\u0148 hladiny v ose \u0159e\u0161en\u00fdch koryt tok\u016f. Zmi\u0148ovanou turbulentn\u00ed (tzv. \u201eeddy\u201c) viskozitu vt, vstupuj\u00edc\u00ed do \u0159e\u0161en\u00ed rovnic proud\u011bn\u00ed v m\u011blk\u00e9m proudu (FM), lze vyj\u00e1d\u0159it vztahem [18]:<\/p>\n\"\"<\/a>\n

kde D je bezrozm\u011brn\u00fd koeficient pro v\u00fdpo\u010det turbulentn\u00ed viskozity a smykov\u00e1 rychlost definovan\u00e1 jako:<\/p>\n\"\"<\/a>\n

kde R je hydraulick\u00fd polom\u011br, g t\u00edhov\u00e9 zrychlen\u00ed, S sklon \u010d\u00e1ry energie, C Ch\u00e9zyho rychlostn\u00ed sou\u010dinitel, |V| st\u0159edn\u00ed svislicov\u00e1 rychlost a n Manning\u016fv drsnostn\u00ed sou\u010dinitel. Pro hydraulick\u00e9 v\u00fdpo\u010dty v programu HEC-RAS ud\u00e1v\u00e1 Brunner [18] orienta\u010dn\u00ed rozsahy hodnot bezrozm\u011brn\u00e9ho koeficientu D pro v\u00fdpo\u010det turbulentn\u00ed viskozity uveden\u00e9 v tab. 1.<\/p>\n

Tab. 1. Hodnoty bezrozm\u011brn\u00e9ho koeficientu D pro v\u00fdpo\u010det turbulentn\u00ed viskozity dle [18]
\nTab. 1. Values of eddie viscosity transverse mixing coefficient D [18]<\/h5>\n\"\"<\/a>\n

Citlivostn\u00ed anal\u00fdza byla provedena na dvou typech model\u016f, kter\u00e9 jsou v dal\u0161\u00edm textu ozna\u010deny p\u00edsmeny A, B. Model A byl koncipov\u00e1n s ohledem na eliminaci dal\u0161\u00edch mo\u017en\u00fdch vliv\u016f na v\u00fdsledky v\u00fdpo\u010dt\u016f (nerovnom\u011brnost rychlostn\u00edho pole, n\u00e1hl\u00e9 kontrakce p\u0159i zm\u011bn\u00e1ch tvaru p\u0159\u00ed\u010dn\u00fdch profil\u016f apod.). Z tohoto d\u016fvodu bylo pro citlivostn\u00ed anal\u00fdzu zvoleno prizmatick\u00e9 koryto lichob\u011b\u017en\u00edkov\u00e9ho pr\u016f\u0159ezu, jeho\u017e hlavn\u00ed parametry jsou patrn\u00e9 z obr. 1 a tab. 2. Pro \u00fa\u010dely simulace odleh\u010dov\u00e1n\u00ed \u010d\u00e1sti pr\u016ftoku do inunda\u010dn\u00edho \u00fazem\u00ed bylo do modelu A za\u010dlen\u011bno rovn\u011b\u017e pravob\u0159e\u017en\u00ed lok\u00e1ln\u00ed sn\u00ed\u017een\u00ed b\u0159ehov\u00e9 hrany o 0,3 m v d\u00e9lce 100 m, nach\u00e1zej\u00edc\u00ed se uprost\u0159ed d\u00e9lky \u0159e\u0161en\u00e9ho \u00faseku koryta (viz obr. 1 a 6). Za takto vytvo\u0159enou p\u0159elivnou hranou byl zaveden p\u0159edpoklad voln\u00e9ho odtoku vody.<\/p>\n

Tab. 2. Model A \u2013 z\u00e1kladn\u00ed parametry koryta
\nTab. 2. Model A \u2013 river reach basic parameters<\/h5>\n\"\"<\/a>\n

Pro v\u00fd\u0161e popsan\u00fd model A byla n\u00e1sledn\u011b provedena citlivostn\u00ed anal\u00fdza spo\u010d\u00edvaj\u00edc\u00ed ve variantn\u00edch v\u00fdpo\u010dtech A.1 a\u017e A.4. Nastaven\u00ed jednotliv\u00fdch variant (viz tab. 3) bylo voleno tak, aby byl v\u017edy jeden z testovan\u00fdch vstupn\u00edch parametr\u016f modelu zad\u00e1n jako konstantn\u00ed a druh\u00fd s prom\u011bnliv\u00fdmi hodnotami (viz sloupce v\u00fdpo\u010detn\u00ed s\u00ed\u0165 a koeficient turbulence D v tab. 3). Z\u00e1rove\u0148 ve v\u0161ech \u0159e\u0161en\u00fdch va-\u2028riant\u00e1ch prob\u011bhlo ov\u011b\u0159en\u00ed vlivu pou\u017eit\u00e9ho matematick\u00e9ho modelu (viz sloupec model).<\/p>\n

Tab. 3. Model A \u2013 z\u00e1kladn\u00ed parametry \u0159e\u0161en\u00fdch variant v\u00fdpo\u010dt\u016f
\nTab. 3. Model A \u2013 basic parameters of solved calculation variants<\/h5>\n\"\"<\/a>\n

V\u00fdsledky 1D modelu byly ur\u010deny pouze k orienta\u010dn\u00edmu srovn\u00e1n\u00ed s 2D modely a nebyly p\u0159edm\u011btem citlivostn\u00ed anal\u00fdzy. Zvolen\u00e1 velikost element\u016f v\u00fdpo\u010detn\u00ed s\u00edt\u011b odpov\u00eddala rozm\u011br\u016fm koryta v p\u0159\u00ed\u010dn\u00e9m profilu dle obr. 1. Rozm\u011br element\u016f 18 m postihoval celou \u0161\u00ed\u0159ku koryta, rozm\u011br 6 m odpov\u00eddal d\u011blen\u00ed profilu na svahy a dno, rozm\u011bry element\u016f 1 m, 0,5 m a 0,25 m slou\u017eily k ov\u011b\u0159en\u00ed vlivu jemn\u011bj\u0161\u00edho d\u011blen\u00ed oblasti. Model B zachycuje re\u00e1ln\u00fd \u00fasek vodn\u00edho toku Svratky (viz obr. 2) cca mezi km 50,2 (jez Kamenn\u00fd ml\u00fdn) a\u017e km 52,8 (jez Kom\u00edn).<\/p>\n\"\"<\/a>\n

Obr. 1. Model A \u2013 p\u0159\u00ed\u010dn\u00fd profil koryta toku (p\u0159eliv je ve funkci pouze u varianty A.4 dle tab. 3)
\nFig. 1. Model A \u2013 river reach cross section (the overflow is functional only for variant A.4 according to tab. 3)<\/h6>\n\"\"<\/a>\n
Obr. 2. Situace modelu \u0159eky Svratky v \u00faseku km 50,2 a\u017e km 52,8
\nFig. 2. Situation of the Svratka river model in the section of km 50.2 to km 52.8<\/h6>\n

Pro \u0159e\u0161enou lokalitu byl p\u0159ipraven digit\u00e1ln\u00ed model ter\u00e9nu sestaven\u00fd na z\u00e1klad\u011b dat z digit\u00e1ln\u00edho modelu reli\u00e9fu 5. generace (DMR 5G) [21] a ze sonarov\u00e9ho zam\u011b\u0159en\u00ed dna koryta toku Svratka. D\u00e1le bylo provedeno d\u00edl\u010d\u00ed geodetick\u00e9 zam\u011b\u0159en\u00ed vybran\u00fdch ter\u00e9nn\u00edch hran metodou GPS \u2013 RTK (nap\u0159. b\u0159ehov\u00e9 hrany, zemn\u00ed t\u011blesa komunikac\u00ed apod.). Rozlo\u017een\u00ed drsnost\u00ed povrchu v z\u00e1jmov\u00e9m \u00fazem\u00ed bylo stanoveno odborn\u00fdm odhadem na z\u00e1klad\u011b m\u00edstn\u00edch \u0161et\u0159en\u00ed a mapov\u00fdch podklad\u016f ZABAGED [21]. Konkr\u00e9tn\u00ed pou\u017eit\u00e9 hodnoty sou\u010dinitel\u016f drsnost\u00ed n dle Manninga jsou uvedeny v tab. 4.<\/p>\n

Tab. 4. Sou\u010dinitel\u00e9 drsnosti povrchu n dle Manninga pro model B
\nTab. 4. Manning roughness coefficients n for model B<\/h5>\n\"\"<\/a>\n

Samotn\u00e9 sestaven\u00ed modelu v programu HEC-RAS prob\u011bhlo s pou\u017eit\u00edm aplikace RAS Mapper. Do modelu proud\u011bn\u00ed byl p\u0159ipojen digit\u00e1ln\u00ed model ter\u00e9nu a vrstva drsnost\u00ed povrchu. Pro zadanou oblast modelu proud\u011bn\u00ed byly dopln\u011bny v\u00fdznamn\u00e9 linie (b\u0159ehov\u00e9 linie, ter\u00e9nn\u00ed zlomy, p\u0159\u00ed\u010dn\u00e9 objekty v koryt\u011b). V\u00fdpo\u010detn\u00ed s\u00ed\u0165 \u0159e\u0161en\u00e9 n\u00e1hradn\u00ed oblasti byla tvo\u0159ena elementy ve tvaru hexagonu s rozm\u011bry cca 8 \u00d7 8 m a s lok\u00e1ln\u00edm zjemn\u011bn\u00edm v okol\u00ed v\u00fdznamn\u00fdch lini\u00ed. Hexagon\u00e1ln\u00ed elementy umo\u017e\u0148uj\u00ed, oproti \u010dtvercov\u00fdm element\u016fm pou\u017eit\u00fdm v p\u0159\u00edpad\u011b modelu A, snadn\u011bj\u0161\u00ed tvorbu v\u00fdpo\u010dtov\u00fdch s\u00edt\u00ed s nepravideln\u00fdmi hranicemi n\u00e1hradn\u00edch oblast\u00ed, pop\u0159. s po\u017eadavky lok\u00e1ln\u00ed zm\u011bny velikost\u00ed element\u016f. V\u00fdpo\u010detn\u00ed s\u00ed\u0165 sest\u00e1vala z celkov\u00e9ho po\u010dtu 80 200 element\u016f. Doln\u00ed okrajov\u00e1 podm\u00ednka byla zad\u00e1na m\u011brnou k\u0159ivkou jezu Kamenn\u00fd ml\u00fdn ve stani\u010den\u00ed km 50,2, horn\u00ed okrajov\u00e1 podm\u00ednka byla zad\u00e1na hodnotou pr\u016ftoku (viz tab. 5). Vytvo\u0159en\u00fd 2D model byl n\u00e1sledn\u011b upraven dle jednotliv\u00fdch \u0159e\u0161en\u00fdch variant v\u00fdpo\u010dtu (viz tab. 5),\u2028tj. byly zad\u00e1v\u00e1ny r\u016fzn\u00e9 hodnoty bezrozm\u011brn\u00e9ho koeficientu D pro v\u00fdpo\u010det turbulentn\u00ed viskozity, pou\u017eita aproximace difuzn\u00ed vlnou apod.<\/p>\n

Za \u00fa\u010delem srovn\u00e1n\u00ed v\u00fdsledk\u016f v\u00fdpo\u010dt\u016f byl vytvo\u0159en rovn\u011b\u017e 1D numerick\u00fd model koryta toku Svratka v z\u00e1jmov\u00e9m \u00faseku tak, aby s maxim\u00e1ln\u00ed m\u00edrou respektoval parametry 2D modelu. V p\u0159\u00edpad\u011b 1D modelu byla provedena schematizace geometrie koryta toku zad\u00e1n\u00edm osy a p\u0159\u00ed\u010dn\u00fdch \u0159ez\u016f ve vzd\u00e1lenostech 10 m.<\/p>\n

Citlivostn\u00ed anal\u00fdza byla provedena nad v\u00fdsledky v\u00fdpo\u010dt\u016f ve variant\u00e1ch B.1 a B.2 s parametry uveden\u00fdmi v tab. 5. Ve variant\u011b B.1 byla zvolena hodnota kulmina\u010dn\u00edho pr\u016ftoku Q5, kter\u00fd p\u0159ibli\u017en\u011b odpov\u00eddal kapacit\u011b \u0159e\u0161en\u00e9ho \u00faseku koryta. P\u0159i pr\u016ftoku Q20, pou\u017eit\u00e9m ve variant\u011b B.2, ji\u017e doch\u00e1zelo v mal\u00e9m rozsahu k rozliv\u016fm do p\u0159ilehl\u00e9ho \u00fazem\u00ed. Takto vznikl\u00e1 inunda\u010dn\u00ed \u00fazem\u00ed v\u0161ak nebyla pr\u016fto\u010dn\u00e1 a p\u0159\u00edpadn\u00e9 zm\u011bny pr\u016ftoku pod\u00e9l z\u00e1jmov\u00e9ho \u00faseku toku lze pova\u017eovat za zanedbateln\u00e9.<\/p>\n

Tab. 5. Model B \u2013 z\u00e1kladn\u00ed parametry \u0159e\u0161en\u00fdch variant v\u00fdpo\u010dt\u016f
\nTab. 5. Model B \u2013 basic parameters of solved calculation variants<\/h5>\n\"\"<\/a>\n

V\u00fdsledky citlivostn\u00ed anal\u00fdzy<\/h2>\n

V\u00fdsledky \u0159e\u0161en\u00fdch variant A.1 a\u017e A.4 pro model A, prizmatick\u00e9ho lichob\u011b\u017en\u00edkov\u00e9ho koryta, jsou patrn\u00e9 z obr. 3 a\u017e 6. V p\u0159\u00edpad\u011b citlivostn\u00ed anal\u00fdzy vlivu prostorov\u00e9 diskretizace bez zohledn\u011bn\u00ed turbulence (viz varianta A.1 na obr. 3) je patrn\u00e9, \u017ee za p\u0159edpokladu shodn\u00e9 velikosti element\u016f v\u00fdpo\u010detn\u00ed s\u00edt\u011b jsou rozd\u00edly mezi modely 2D (FM) a 2D (DW) minim\u00e1ln\u00ed. V porovn\u00e1n\u00ed s 1D modelem nar\u016fstaj\u00ed rozd\u00edly ve vypo\u010dten\u00fdch hloubk\u00e1ch vody se zmen\u0161uj\u00edc\u00ed se velikost\u00ed v\u00fdpo\u010dtov\u00fdch element\u016f. Jako hrani\u010dn\u00ed je mo\u017en\u00e9 ozna\u010dit rozm\u011br elementu cca 1 m, od kter\u00e9ho m\u00e1 ji\u017e dal\u0161\u00ed zjem\u0148ov\u00e1n\u00ed v\u00fdpo\u010detn\u00ed s\u00edt\u011b nepatrn\u00fd vliv.<\/p>\n\"\"<\/a>\n

Obr. 3. Varianta A.1 \u2013 v\u00fdsledky citlivostn\u00ed anal\u00fdzy vlivu prostorov\u00e9 diskretizace bez zohledn\u011bn\u00ed turbulence (model 2D DW nebo 2D FM s D = 0)
\nFig. 3. Variant A.1 \u2013 results of sensitivity analysis of the influence of spatial discretization without taking into account turbulence (model 2D DW or 2D FM with D = 0)<\/h6>\n\"\"<\/a>\n
Obr. 4. Varianta A.2 \u2013 v\u00fdsledky citlivostn\u00ed anal\u00fdzy vlivu parametr\u016f turbulentn\u00edho modelu (konstantn\u00ed velikost element\u016f 1 m)
\nFig. 4. Variant A.2 \u2013 results of sensitivity analysis of the influence of turbulence model parameters (constant size of elements 1 m)<\/h6>\n\"\"<\/a>\n
Obr. 5. Varianta A.3 \u2013 v\u00fdsledky citlivostn\u00ed anal\u00fdzy vlivu volby prostorov\u00e9 diskretizace p\u0159i konstantn\u00edch parametrech turbulentn\u00edho modelu (D = 0,3)
\nFig. 5. Variant A.3 \u2013 results of sensitivity analysis of the influence of the choice of spatial discretization at constant parameters of the turbulence model (D = 0,3)<\/h6>\n\"\"<\/a>\n
Obr. 6. Varianta A.4 \u2013 v\u00fdsledky citlivostn\u00ed anal\u00fdzy vlivu parametr\u016f turbulentn\u00edho modelu p\u0159i bo\u010dn\u00edm odleh\u010den\u00ed pr\u016ftok\u016f z koryta (konstantn\u00ed velikost element\u016f 1 m)
\nFig. 6. Variant A.4 \u2013 results of sensitivity analysis of the influence of turbulence model parameters during lateral overflow from the river reach (constant size of elements 1 m)<\/h6>\n

Z v\u00fdsledk\u016f citlivostn\u00ed anal\u00fdzy vlivu parametru turbulence p\u0159i konstantn\u00edch rozm\u011brech v\u00fdpo\u010dtov\u00e9 s\u00edt\u011b s velikost\u00ed elementu 1 m (viz varianta A.2 na obr. 4) je patrn\u00e9, \u017ee v\u00fdsledk\u016fm 1D modelu se nejv\u00edce bl\u00ed\u017e\u00ed hloubky vody vypo\u010dten\u00e9 pomoc\u00ed modelu 2D (FM) s koeficientem D = 0,30. Zji\u0161t\u011bn\u00e1 hodnota D = 0,30 je na hranici doporu\u010dovan\u00e9ho rozp\u011bt\u00ed hodnot dle tab. 1 pro zvolen\u00fd typ p\u0159\u00edm\u00e9ho prizmatick\u00e9ho koryta. Z obr. 4 je rovn\u011b\u017e jasn\u011b patrn\u00fd logick\u00fd trend zvy\u0161ov\u00e1n\u00ed \u00farovn\u011b hladiny, resp. hloubek vody v souvislosti s n\u00e1r\u016fstem hodnoty koeficientu D. Doln\u00ed ob\u00e1lku zji\u0161t\u011bn\u00fdch hloubek vody naopak p\u0159edstavuj\u00ed v\u00fdsledky model\u016f 2D (FM) s D = 0 a 2D (DW), tj. bez zohledn\u011bn\u00ed vlivu turbulence.<\/p>\n

Citlivostn\u00ed anal\u00fdza vlivu zvolen\u00e9 prostorov\u00e9 diskretizace p\u0159i uva\u017eov\u00e1n\u00ed konstantn\u00edho koeficientu D = 0,30 (viz varianta A.3 na obr. 5) prok\u00e1zala, \u017ee zvolen\u00e1 velikost element\u016f v\u00fdpo\u010detn\u00ed s\u00edt\u011b m\u00e1 p\u0159i konstantn\u00ed hodnot\u011b koeficient D = 0,30 vliv na vypo\u010dten\u00e9 \u00farovn\u011b hladin. Odchylky v tomto p\u0159\u00edpad\u011b nar\u016fstaj\u00ed se zv\u011bt\u0161uj\u00edc\u00ed se velikost\u00ed elementu. Jako hrani\u010dn\u00ed lze, obdobn\u011b jako ve variant\u011b A.1, ozna\u010dit velikost elementu cca 1 m. V\u00fdsledky ve variant\u011b A.4 na obr. 6 s pravob\u0159e\u017en\u00edm odleh\u010den\u00edm pr\u016ftoku potvrzuj\u00ed skute\u010dnosti zji\u0161t\u011bn\u00e9 v p\u0159edchoz\u00edch variant\u00e1ch A.1 a\u017e A.3. Oproti variant\u00e1m bez odleh\u010den\u00ed je zde patrn\u00e9 ovlivn\u011bn\u00ed \u00farovn\u00ed hladin v \u00faseku nad p\u0159elivem.<\/p>\n

V\u00fdsledky ve variant\u00e1ch B.1 a B.2, proveden\u00e9 na re\u00e1ln\u00e9m \u00faseku koryta, v z\u00e1sad\u011b potvrzuj\u00ed z\u00e1kladn\u00ed skute\u010dnosti zji\u0161t\u011bn\u00e9 ve variant\u00e1ch A.1 a\u017e A.4 pro fiktivn\u00ed prizmatick\u00e9 koryto. Z obr. 7 a 8 je patrn\u00fd nezanedbateln\u00fd vliv bezrozm\u011brn\u00e9ho koeficientu D na \u00farove\u0148 hladiny p\u0159i v\u00fdpo\u010dtech s pou\u017eit\u00edm modelu 2D (FM), tj. n\u00e1r\u016fst \u00farovn\u011b hladiny v souvislosti se zvy\u0161ov\u00e1n\u00edm hodnoty koeficientu D. P\u0159i vz\u00e1jemn\u00e9m srovn\u00e1n\u00ed v\u00fdsledk\u016f 2D (FM) a 1D modelu jsou oproti prizmatick\u00e9mu korytu (viz model A) patrn\u00e9 v\u00fdrazn\u011b vy\u0161\u0161\u00ed \u00farovn\u011b vypo\u010dten\u00fdch hladin, a to i v p\u0159\u00edpad\u011b doporu\u010den\u00e9ho rozmez\u00ed hodnot koeficientu D dle tab. 1. V\u00fdsledky modelu 2D (DW) vykazuj\u00ed naopak \u00farovn\u011b hladin podstatn\u011b ni\u017e\u0161\u00ed, ne\u017e je tomu u 1D modelu. U modelu B se ve srovn\u00e1n\u00ed s prizmatick\u00fdm korytem v modelu A d\u00e1le neprok\u00e1zala shoda ve v\u00fdsledc\u00edch v\u00fdpo\u010dt\u016f pomoc\u00ed model\u016f 2D (FM) s D = 0 a 2D (DW), tj. bez uva\u017eov\u00e1n\u00ed vlivu turbulence.<\/p>\n\"\"<\/a>\n

Obr. 7. Varianta B.1 \u2013 v\u00fdsledky citlivostn\u00ed anal\u00fdzy vlivu bezrozm\u011brn\u00e9ho koeficientu D na \u00farove\u0148 hladiny p\u0159i pr\u016ftoku Q5
\nFig. 7. Variant B.1 \u2013 results of sensitivity analysis of the influence of dimensionless\u2028coefficient D on the water level at discharge Q5<\/h6>\n\"\"<\/a>\n
Obr. 8. Varianta B.2 \u2013 v\u00fdsledky citlivostn\u00ed anal\u00fdzy vlivu bezrozm\u011brn\u00e9ho koeficientu D na \u00farove\u0148 hladiny p\u0159i pr\u016ftoku Q20
\nFig. 8. Variant B.2 \u2013 results of sensitivity analysis of the influence of dimensionless\u2028coefficient D on the water level at discharge Q20<\/h6>\n

Z\u00e1v\u011br a diskuze v\u00fdsledk\u016f<\/h2>\n

Zohledn\u011bn\u00ed vlivu turbulence p\u0159i hydraulick\u00fdch v\u00fdpo\u010dtech s pou\u017eit\u00edm 2D, resp. sp\u0159a\u017een\u00fdch 1D\/2D numerick\u00fdch model\u016f s sebou v\u011bt\u0161inou p\u0159in\u00e1\u0161\u00ed zv\u00fd\u0161enou \u010dasovou n\u00e1ro\u010dnost v\u00fdpo\u010dt\u016f, a to jak z hlediska podstatn\u00e9ho prodlou\u017een\u00ed v\u00fdpo\u010detn\u00edho \u010dasu, tak po str\u00e1nce vy\u0161\u0161\u00edch n\u00e1rok\u016f na kalibraci modelu. Provedenou citlivostn\u00ed anal\u00fdzou byla na modelov\u00fdch p\u0159\u00edpadech ov\u011b\u0159ena z\u00e1vislost vypo\u010dten\u00fdch \u00farovn\u00ed hladin na bezrozm\u011brn\u00e9m koeficientu D pro v\u00fdpo\u010det turbulentn\u00ed viskozity a souvisej\u00edc\u00ed prostorov\u00e9 diskretizaci \u0159e\u0161en\u00e9 n\u00e1hradn\u00ed oblasti. S ohledem na rozsah proveden\u00fdch anal\u00fdz a celkovou teoretickou n\u00e1ro\u010dnost \u0159e\u0161en\u00e9 problematiky lze p\u0159edkl\u00e1dan\u00fd p\u0159\u00edsp\u011bvek ch\u00e1pat jako \u00favod do dan\u00e9ho t\u00e9matu. Dosa\u017een\u00e9 v\u00fdsledky poskytuj\u00ed potenci\u00e1ln\u00edm u\u017eivatel\u016fm orienta\u010dn\u00ed p\u0159edstavu o m\u00ed\u0159e nejistot vypl\u00fdvaj\u00edc\u00edch z p\u0159\u00edpadn\u00e9ho zohledn\u011bn\u00ed, resp. zanedb\u00e1n\u00ed vlivu turbulence. Za stavu, kdy jsou v praxi obvykle zna\u010dn\u011b omezen\u00e9 zdroje odpov\u00eddaj\u00edc\u00edch kalibra\u010dn\u00edch \u00fadaj\u016f, p\u0159edstavuje nazna\u010den\u00fd postup citlivostn\u00ed anal\u00fdzy vhodn\u00fd zp\u016fsob pro z\u00edsk\u00e1n\u00ed z\u00e1kladn\u00ed p\u0159edstavy o m\u00ed\u0159e nejistot, kterou jsou zat\u00ed\u017eeny v\u00fdsledky v\u00fdpo\u010dt\u016f. Zji\u0161t\u011bn\u00e9 skute\u010dnosti rovn\u011b\u017e nab\u00edzej\u00ed mo\u017enosti dal\u0161\u00edho podrobn\u011bj\u0161\u00edho v\u00fdzkumu v dan\u00e9 oblasti. V t\u00e9to souvislosti lze zm\u00ednit nap\u0159. ot\u00e1zku nejistot souvisej\u00edc\u00edch s hydraulick\u00fdm \u0159e\u0161en\u00edm oblast\u00ed, kde doch\u00e1z\u00ed k vyb\u0159e\u017eov\u00e1n\u00ed vody z koryta toku do p\u0159ilehl\u00e9ho z\u00e1plavov\u00e9ho \u00fazem\u00ed, resp. k jej\u00edmu zp\u011btn\u00e9mu n\u00e1toku nap\u0159. v d\u016fsledku p\u0159el\u00e9v\u00e1n\u00ed ochrann\u00fdch hr\u00e1z\u00ed nebo p\u0159ekro\u010den\u00ed kapacity koryta.<\/p>\n

Pod\u011bkov\u00e1n\u00ed<\/h2>\n

P\u0159\u00edsp\u011bvek vznikl za podpory projektu FAST-S-20-6305 \u201eNejistoty v hydraulick\u00e9m posouzen\u00ed transforma\u010dn\u00edho \u00fa\u010dinku \u00fadoln\u00ed nivy s pou\u017eit\u00edm 2D a sp\u0159a\u017een\u00fdch 1D\/2D numerick\u00fdch model\u016f\u201c.<\/em><\/p>\n

P\u0159\u00edsp\u011bvek pro\u0161el lektorsk\u00fdm \u0159\u00edzen\u00edm.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

This article is available in Czech only. For translation or more information on this topic, please contact author.   Souhrn Hydraulick\u00e9 v\u00fdpo\u010dty proud\u011bn\u00ed vody v korytech vodn\u00edch tok\u016f a z\u00e1plavov\u00fdch \u00fazem\u00edch se v sou\u010dasn\u00e9 in\u017een\u00fdrsk\u00e9 praxi prov\u00e1d\u011bj\u00ed prim\u00e1rn\u011b s pou\u017eit\u00edm 1D, 2D a sp\u0159a\u017een\u00fdch 1D\/2D numerick\u00fdch model\u016f. Matematick\u00fd model je v p\u0159\u00edpad\u011b zmi\u0148ovan\u00e9 2D schematizace… Read more »<\/a><\/p>\n","protected":false},"author":8,"featured_media":11748,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2,86],"tags":[2455,2453,2434,2454,1099,2452],"coauthors":[2442,2443,2444,2445],"class_list":["post-11891","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-from-the-world-of-water-management","category-hydraulics-hydrology-and-hydrogeology","tag-2d-numerical-model","tag-floodplain","tag-hec-ras","tag-hydraulic-calculation","tag-sensitivity-analysis","tag-turbulence-model"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/11891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/comments?post=11891"}],"version-history":[{"count":2,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/11891\/revisions"}],"predecessor-version":[{"id":30623,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/11891\/revisions\/30623"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/11748"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=11891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=11891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=11891"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=11891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}