{"id":3897,"date":"2017-10-10T08:21:59","date_gmt":"2017-10-10T08:21:59","guid":{"rendered":"http:\/\/www.vtei.cz\/?p=3897"},"modified":"2024-07-16T12:26:24","modified_gmt":"2024-07-16T11:26:24","slug":"possibilities-of-extrapolation-of-digital-terrain-model-raster-dmr-5g","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2017\/10\/possibilities-of-extrapolation-of-digital-terrain-model-raster-dmr-5g\/","title":{"rendered":"Possibilities of extrapolation of digital terrain model raster DMR 5G"},"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

Nad \u00fazem\u00edm cel\u00e9 \u010cesk\u00e9 republiky bylo provedeno leteck\u00e9 laserov\u00e9 sn\u00edmkov\u00e1n\u00ed\u00a0(LiDAR), d\u00edky n\u011bmu\u017e je mo\u017en\u00e9 vytv\u00e1\u0159et rastry digit\u00e1ln\u00edho modelu ter\u00e9nu. Tyto podklady maj\u00ed \u0161irok\u00e9 uplatn\u011bn\u00ed v r\u016fzn\u00fdch odv\u011btv\u00edch. Z hlediska pot\u0159eb hydrologie je v\u0161ak nedostatkem pou\u017eit\u00e9 technologie nep\u0159esn\u00e9, resp. ne\u00fapln\u00e9, vykreslen\u00ed tvaru koryt, nebo\u0165 laserov\u00e9 paprsky bl\u00edzk\u00e9ho infra\u010derven\u00e9ho z\u00e1\u0159en\u00ed jsou absorbov\u00e1ny vodou. Z\u00a0toho d\u016fvodu je pot\u0159ebn\u00e9 data korigovat nahrazen\u00edm jejich \u010d\u00e1sti nap\u0159\u00edklad v\u00fdstupy z jin\u00fdch m\u011b\u0159en\u00ed, nap\u0159. teodolitem \u010di sonarem. Existuj\u00ed v\u0161ak postupy, pomoc\u00ed kter\u00fdch je mo\u017en\u00e9 geometrii koryt extrapolovat p\u0159\u00edmo z p\u016fvodn\u00edch rastr\u016f, a to na z\u00e1klad\u011b sklon\u016f b\u0159eh\u016f v r\u00e1mci p\u0159\u00ed\u010dn\u00fdch profil\u016f. V r\u00e1mci t\u00e9to pr\u00e1ce se vych\u00e1z\u00ed z postupu linear and double-linear estimation method podle Mersela a kol. [1].<\/p>\n\"ilustracni-3_edit\"<\/a>\n

P\u0159edlo\u017een\u00e1 pr\u00e1ce p\u0159edstavuje \u00favodn\u00ed krok sm\u011brem k vyu\u017eit\u00ed podobn\u00fdch extrapola\u010dn\u00edch postup\u016f. Celkem 82 profil\u016f bylo geodeticky zam\u011b\u0159eno a\u00a0n\u00e1sledn\u011b byly extrahov\u00e1ny p\u0159\u00ed\u010dn\u00e9 profily z rastru DMR 5G, na nich\u017e byla prov\u00e1d\u011bna extrapolace. Na dosavadn\u00edm souboru p\u0159\u00ed\u010dn\u00fdch profil\u016f se uk\u00e1zalo, \u017ee extrapola\u010dn\u00ed metoda vede k m\u00edrn\u00e9mu nadhodnocov\u00e1n\u00ed minim\u00e1ln\u00ed \u00farovn\u011b dna koryt oproti skute\u010dn\u011b zam\u011b\u0159en\u00fdm hodnot\u00e1m. Z toho d\u016fvodu bylo tak\u00e9 zji\u0161\u0165ov\u00e1no, nakolik je pot\u0159eba \u00fahly sklon\u016f b\u0159eh\u016f zv\u00fd\u0161it, aby bylo dosa\u017eeno dobr\u00e9 shody se skute\u010dn\u011b nam\u011b\u0159en\u00fdmi daty. Podstatn\u00e9 v\u0161ak je, \u017ee srovn\u00e1v\u00e1n\u00ed bylo prozat\u00edm prov\u00e1d\u011bno \u010dist\u011b na z\u00e1klad\u011b shody nejni\u017e\u0161\u00ed \u00farovn\u011b dna v p\u0159\u00ed\u010dn\u00e9m profilu, nikoli z hlediska vlivu na v\u00fdsledky hydrodynamick\u00e9ho modelov\u00e1n\u00ed.<\/p>\n

\u00davod<\/h2>\n

Modelov\u00e1n\u00ed v\u00a0hydrologii je krom\u011b dobr\u00e9 znalosti a simulace fyzik\u00e1ln\u00edch proces\u016f ovliv\u0148ov\u00e1no v\u00fdznamn\u011b i nep\u0159esnostmi vstupn\u00edch dat. Nejistotami v\u00a0hydrologick\u00e9m modelov\u00e1n\u00ed se zab\u00fdvala \u0159ada prac\u00ed [2\u20134]. Zdroje nep\u0159esnost\u00ed mohou plynout nap\u0159\u00edklad z\u00a0hodnot pr\u016ftok\u016f odvozen\u00fdch prost\u0159ednictv\u00edm hydrologick\u00e9ho modelu, v\u00a0n\u011bm\u017e ji\u017e vstupn\u00ed data (nap\u0159. sr\u00e1\u017ekov\u00e9 \u00fahrny \u010di vlhkost p\u016fdy) vykazuj\u00ed ur\u010dit\u00e9 nep\u0159esnosti [5]. Pokud je pr\u016ftok odvozov\u00e1n z\u00a0m\u011b\u0159en\u00ed vodn\u00edch stav\u016f, je p\u0159esnost ovlivn\u011bna kvalitou vztahu vodn\u00ed stav\/pr\u016ftok [2, 6]. Problematick\u00fdm faktorem p\u0159i modelov\u00e1n\u00ed povod\u0148ov\u00fdch rozliv\u016f je tak\u00e9 nastaven\u00ed hodnoty sou\u010dinitele drsnosti [7\u20139] a geometrick\u00fd popis koryta a \u0159\u00ed\u010dn\u00ed nivy (nap\u0159. [10\u201316]).<\/p>\n\"Caletka-1\"<\/a>\n

Obr. 1. Uk\u00e1zka m\u011b\u0159en\u00e9ho p\u0159\u00ed\u010dn\u00e9ho profilu na \u00faseku Hus\u00edho potoka ve Vlkovic\u00edch u\u00a0Fulneku
\nFig. 1. An example of a measured cross-section profile on the Hus\u00ed brook in Vlkovice near Fulnek<\/h6>\n

Problematice p\u0159\u00edpravy kvalitn\u00edho digit\u00e1ln\u00edho modelu ter\u00e9nu (DMT) je v hydrologii v\u011bnov\u00e1no zna\u010dn\u00e9 \u00fasil\u00ed. Zp\u0159es\u0148ov\u00e1n\u00ed DMT je mo\u017en\u00e9 prov\u00e1d\u011bt pomoc\u00ed r\u016fzn\u00fdch p\u0159\u00edstup\u016f, p\u0159edev\u0161\u00edm interpolac\u00ed geodeticky zam\u011b\u0159en\u00fdch p\u0159\u00ed\u010dn\u00fdch profil\u016f koryta \u010di interpolac\u00ed samostatn\u011b zam\u011b\u0159en\u00fdch bod\u016f batygrafie a jejich integrac\u00ed s\u00a0okoln\u00edm ter\u00e9nem [2]. Zna\u010dn\u00e9ho pokroku v\u00a0r\u00e1mci modelov\u00e1n\u00ed obecn\u011b bylo dosa\u017eeno zaveden\u00edm technologie leteck\u00e9ho laserov\u00e9ho sn\u00edmkov\u00e1n\u00ed ter\u00e9nu (z\u00a0angl. Light Detection and Ranging \u2013 akronym LiDAR). Jedn\u00e1 se o technologii,\u00a0kter\u00e1 umo\u017e\u0148uje m\u011b\u0159it zejm\u00e9na nadmo\u0159skou v\u00fd\u0161ku povrchu (tzv. topo LiDAR system) [17, 18]. M\u011b\u0159en\u00e1 data jsou ukl\u00e1d\u00e1na ve form\u011b mra\u010dna bod\u016f [19]. I p\u0159es zna\u010dn\u00e9 zlep\u0161en\u00ed m\u016f\u017ee b\u00fdt p\u0159esnost m\u011b\u0159en\u00fdch dat omezena. Laserov\u00fd paprsek nemus\u00ed v\u017edy proniknout a\u017e k\u00a0zemsk\u00e9mu povrchu v\u00a0p\u0159\u00edpad\u011b hust\u00e9 vegetace \u010di z\u00e1stavby. Nav\u00edc m\u016f\u017ee doch\u00e1zet k\u00a0pohlcov\u00e1n\u00ed laserov\u00e9ho paprsku vodou [20]. Absence topografie vodou vypln\u011bn\u00fdch \u010d\u00e1st\u00ed vodn\u00edch \u00fatvar\u016f p\u0159itom p\u0159edstavuje v\u00fdznamn\u00fd probl\u00e9m z\u00a0hlediska modelov\u00e1n\u00ed hydrauliky proud\u011bn\u00ed [11, 13, 14]. Z\u00a0toho d\u016fvodu byl krom\u011b technologi\u00ed, jako je sonar [21], digit\u00e1ln\u00ed fotogrammetrie [22] \u010di satelitn\u00ed m\u011b\u0159en\u00ed [23], vyvinut typ LiDARu umo\u017e\u0148uj\u00edc\u00ed i m\u011b\u0159en\u00ed batygrafie (bathymetric LiDAR system). Na rozd\u00edl od tradi\u010dn\u00edho LiDARu, vyu\u017e\u00edvaj\u00edc\u00edho bl\u00edzk\u00e9 infra\u010derven\u00e9 z\u00e1\u0159en\u00ed, pou\u017e\u00edv\u00e1 vlnov\u00e9 d\u00e9lky zelen\u00e9 \u010d\u00e1sti spektra, kter\u00e9 pronikaj\u00ed vodou [24].<\/p>\n

Pro eliminov\u00e1n\u00ed chyb spojen\u00fdch s\u00a0vyu\u017e\u00edv\u00e1n\u00edm konven\u010dn\u00edch m\u011b\u0159en\u00ed LiDARem (v\u00fdstupem takov\u00e9ho m\u011b\u0159en\u00ed je i sada DMR 4G a DMR 5G) vznikla \u0159ada extrapola\u010dn\u00edch metod pro ur\u010den\u00ed topografie \u010d\u00e1sti koryt, resp. p\u0159\u00ed\u010dn\u00fdch profil\u016f koryt, vypln\u011bn\u00fdch vodou. Z\u00e1kladn\u00ed a nejjednodu\u0161\u0161\u00ed metodou je tzv. linear a double-linear method [1, 25], spo\u010d\u00edvaj\u00edc\u00ed v\u00a0extrapolaci sklonu b\u0159eh\u016f sm\u011brem do koryta toku. Hlavn\u00edm c\u00edlem tohoto \u010dl\u00e1nku je: 1. prov\u00e9st prvotn\u00ed srovn\u00e1n\u00ed v\u00fdstup\u016f obou zm\u00edn\u011bn\u00fdch extrapola\u010dn\u00edch metod s\u00a0geodeticky zam\u011b\u0159en\u00fdmi p\u0159\u00ed\u010dn\u00fdmi profily koryt z\u00a0hlediska dosa\u017een\u00ed minim\u00e1ln\u00ed \u00farovn\u011b dna, 2. nal\u00e9zt pro ka\u017ed\u00fd p\u0159\u00ed\u010dn\u00fd profil vhodn\u00fd n\u00e1sobek sklonu b\u0159eh\u016f takov\u00fd, aby analogickou aplikac\u00ed uveden\u00e9 metody bylo dosa\u017eeno co nejlep\u0161\u00ed shody s\u00a0m\u011b\u0159en\u00fdmi profily.<\/p>\n\"Caletka-2\"<\/a>\n

Obr. 2. Srovn\u00e1n\u00ed p\u0159\u00ed\u010dn\u00e9ho profilu koryta Hus\u00edho potoka ve Vlkovic\u00edch zam\u011b\u0159en\u00e9ho teodolitem a extrahovan\u00e9ho z DMT DMR 5G
\nFig. 2. Comparison of cross-section profiles on the Hus\u00ed brook in Vlkovice measured by theodolite and extracted from the DMT DMR 5G<\/h6>\n

Vstupn\u00ed data a metodika<\/h2>\n

S\u00a0vyu\u017eit\u00edm celkem 82 p\u0159\u00ed\u010dn\u00fdch profil\u016f men\u0161\u00edch vodn\u00edch tok\u016f byla analyzov\u00e1na p\u0159esnost dosa\u017een\u00ed minim\u00e1ln\u00ed \u00farovn\u011b dna koryt (obr. 1<\/em>). Jejich skute\u010dn\u00fd (referen\u010dn\u00ed) tvar byl zam\u011b\u0159en pomoc\u00ed teodolitu a GPS stanice v\u00a0r\u00e1mci projektu NAKI\u00a0[26] a\u00a0KUS. Sou\u0159adnice v\u0161ech takto zam\u011b\u0159en\u00fdch bod\u016f byly importov\u00e1ny do prost\u0159ed\u00ed ESRI ArcGIS 10.3.1, kde byly na jejich z\u00e1klad\u011b vykresleny linie v\u0161ech p\u0159\u00ed\u010dn\u00fdch profil\u016f. Digit\u00e1ln\u00ed model ter\u00e9nu (DMT) byl vytvo\u0159en z\u00a0datov\u00e9 sady \u010c\u00daZK DMR 5G vznikl\u00e9 leteck\u00fdm laserov\u00fdm sn\u00edmkov\u00e1n\u00edm povrchu v\u00a0letech 2009 a\u017e 2013 [27]. Z\u00a0mra\u010dna diskr\u00e9tn\u00edch bod\u016f rozm\u00edst\u011bn\u00fdch v\u00a0nepravideln\u00e9 troj\u00faheln\u00edkov\u00e9 s\u00edti (angl. triangulated irregular network \u2013 TIN) o sou\u0159adnic\u00edch X, Y, H, kde H\u00a0je nadmo\u0159sk\u00e1 v\u00fd\u0161ka ve v\u00fd\u0161kov\u00e9m referen\u010dn\u00edm syst\u00e9mu Balt po vyrovn\u00e1n\u00ed (Bpv).<\/p>\n

Tabulka 1. Charakteristiky p\u0159esnosti DMR\u00a05G na r\u016fzn\u00e9m povrchu a p\u016fdn\u00edm krytu (p\u0159evzato z\u00a0Technick\u00e9 zpr\u00e1vy k\u00a0Digit\u00e1ln\u00edmu modelu 5. generace, \u010c\u00daZK, 2016)
\nTable 1. Accuracy characteristics of the of the DMR 5G dataset for various types of surfaces (according to the Technical report of the digital model of relief 5th<\/sup>\u00a0generation)<\/h5>\n\"Caletka-tabulka1\"<\/a>\n

Chyby v\u00fd\u0161ky pro r\u016fzn\u00e9 typy povrchu v\u00a0r\u00e1mci datov\u00e9 sady DMR\u00a05G jsou p\u0159ehledn\u011b uvedeny v\u00a0tabulce 1<\/em>. Krom\u011b deklarovan\u00fdch nep\u0159esnost\u00ed je negativn\u00ed vlastnost\u00ed DMT vytvo\u0159en\u00e9ho z\u00a0t\u00e9to datov\u00e9 sady rovn\u011b\u017e nep\u0159esn\u00e1, resp. ne\u00fapln\u00e1, topografie koryt vodn\u00edch tok\u016f. To je zap\u0159\u00ed\u010din\u011bno nepropustnost\u00ed vody pro laserov\u00fd paprsek dan\u00e9 vlnov\u00e9 d\u00e9lky. Ter\u00e9n vodn\u00edch ploch je proto interpolov\u00e1n z\u00a0bod\u016f bezprost\u0159edn\u011b p\u0159il\u00e9haj\u00edc\u00edch k\u00a0vodn\u00edmu \u00fatvaru.<\/p>\n\"Caletka-3\"<\/a>\n

Obr. 3. Sch\u00e9matick\u00e9 zn\u00e1zorn\u011bn\u00ed extrapolace metodou linear a double-linear (podle Mersela a kol. [1])
\nFig. 3. Schematic representation of linear and double-linear estimation method (according to Mersel et al. [1])<\/h6>\n

Prvn\u00edm krokem k\u00a0vytvo\u0159en\u00ed spojit\u00e9ho DMT v\u00a0prost\u0159ed\u00ed ESRI ArcGIS z\u00a0bodov\u00e9 vrstvy byla konstrukce TIN pomoc\u00ed n\u00e1stroje Create TIN bez omezen\u00ed Delaunayho triangulace. Tento TIN byl n\u00e1sledn\u011b pomoc\u00ed n\u00e1stroje TIN to Raster p\u0159eveden na rastr s\u00a0velmi jemn\u00fdm rozli\u0161en\u00edm 0,10\u00a0m. \u00dadaje o nadmo\u0159sk\u00e9 v\u00fd\u0161ce byly p\u0159eneseny z\u00a0podkladov\u00e9ho rastru DMT do borov\u00e9 vrstvy p\u0159\u00ed\u010dn\u00e9ho profilu pomoc\u00ed n\u00e1stroje Extract Values to Points (obr. 2<\/em>).<\/p>\n

Extrapolace koryta<\/h2>\n

Metody line\u00e1rn\u00edho odhadu<\/h3>\n

Nejjednodu\u0161\u0161\u00edmi zp\u016fsoby odstran\u011bn\u00ed zm\u00edn\u011bn\u00fdch nedostatk\u016f jsou metody line\u00e1rn\u00edho a dvojit\u00e9ho line\u00e1rn\u00edho odhadu (linear and double-linear estimate method) [1]. Tyto metody jsou zalo\u017eeny na line\u00e1rn\u00ed extrapolaci linie ter\u00e9nu na obou stran\u00e1ch p\u0159\u00ed\u010dn\u00e9ho profilu. Nejni\u017e\u0161\u00ed bod koryta je d\u00e1n pr\u016fse\u010d\u00edkem obou extrapolovan\u00fdch lini\u00ed (obr. 3<\/em>). Je z\u0159ejm\u00e9, \u017ee takto extrapolovan\u00e1 hloubka je z\u00e1visl\u00e1 na \u0161\u00ed\u0159ce koryta a na \u00fahlech sklonu\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>\u00a0obou b\u0159eh\u016f. Velikost \u00fahl\u016f\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>\u00a0je vypo\u010d\u00edt\u00e1na na z\u00e1klad\u011b vymezen\u00ed b\u0159eh\u016f (lev\u00fd b\u0159eh \u2013 body A, B; prav\u00fd b\u0159eh \u2013 body\u00a0C,\u00a0D). V\u00a0r\u00e1mci studie bylo vyu\u017eito obou v\u00fd\u0161e uveden\u00fdch metod. P\u0159i metod\u011b line\u00e1rn\u00edho odhadu jsou velikosti \u00fahl\u016f\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>\u00a0zachov\u00e1ny a nejni\u017e\u0161\u00edm bodem p\u0159\u00ed\u010dn\u00e9ho profilu je bod E. Metoda dvojit\u00e9ho line\u00e1rn\u00edho odhadu spo\u010d\u00edv\u00e1 ve sn\u00ed\u017een\u00ed \u00fahl\u016f\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>\u00a0na polovinu p\u016fvodn\u00ed velikosti. Nejni\u017e\u0161\u00ed bod je ozna\u010den E\u2018. Pr\u016fse\u010d\u00edk vodorovn\u00e9 p\u0159\u00edmky se sm\u011brov\u00fdm vektorem\u00a0h<\/em>\u00a0\u20d7, proch\u00e1zej\u00edc\u00ed bodem B, s\u00a0p\u0159\u00edmkou\u00a0p<\/em>\u00a0je bod F.<\/p>\n

V\u00fdpo\u010det pr\u016fse\u010d\u00edk\u016f E, E\u2018 se skl\u00e1d\u00e1 z\u00a0n\u011bkolika krok\u016f:<\/h3>\n

1. P\u0159evod sou\u0159adnic bod\u016f z\u00a0kartografick\u00fdch na relativn\u00ed<\/h4>\n

Sou\u0159adnice syst\u00e9mu S-JTSK K\u0159ov\u00e1k East North byly nahrazeny vzd\u00e1lenostmi dan\u00e9ho bodu od po\u010d\u00e1tku p\u0159\u00ed\u010dn\u00e9ho profilu.<\/p>\n

2. Sestaven\u00ed obecn\u00fdch rovnic p\u0159\u00edmek obou b\u0159eh\u016f<\/h4>\n

Ze sou\u0159adnic bod\u016f A, B, C, D byly odvozeny vektory\u00a0u<\/em>\u00a0\u20d7\u00a0a\u00a0v<\/em>\u00a0\u20d7, co\u017e jsou sm\u011brov\u00e9 vektory p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>.<\/p>\n\"Caletka-vzorec1\"<\/a>\n\"Caletka-vzorec2\"<\/a>\n

Obecn\u00e9 rovnice p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>\u00a0maj\u00ed tvar:<\/p>\n\"Caletka-vzorec3\"<\/a>\n\"Caletka-vzorec4\"<\/a>\n

3. V\u00fdpo\u010det pr\u016fse\u010d\u00edku p\u0159\u00edmek obou b\u0159eh\u016f<\/h4>\n

\u0158e\u0161en\u00edm soustavy rovnic (3) a (4) jsou sou\u0159adnice bodu E [XE<\/sub>; YE<\/sub>]. Sou\u0159adnice YE<\/sub>\u00a0ur\u010duje nadmo\u0159skou v\u00fd\u0161ku pr\u016fse\u010d\u00edku p\u0159i pou\u017eit\u00ed metody line\u00e1rn\u00edho odhadu.<\/p>\n

4. V\u00fdpo\u010det \u00fahl\u016f sklon\u016f obou b\u0159eh\u016f<\/h4>\n

Zji\u0161t\u011bn\u00ed \u00fahl\u016f\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>\u00a0vych\u00e1z\u00ed ze vztahu pro kosinus \u00fahlu dvou nenulov\u00fdch vektor\u016f. P\u0159i znalosti sm\u011brov\u00fdch vektor\u016f\u00a0u<\/em>\u00a0\u20d7\u00a0a\u00a0v<\/em>\u00a0\u20d7\u00a0p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>\u00a0posta\u010d\u00ed zvolit libovoln\u00fd vektor\u00a0h<\/em>\u20d7\u00a0v\u00a0horizont\u00e1ln\u00edm sm\u011bru (nap\u0159.\u00a0h<\/em>\u20d7\u00a0\u00a0= (1; 0)). Pak pro \u00fahel\u00a0\u03b1<\/em>\u00a0plat\u00ed, \u017ee:<\/p>\n\"Caletka-vzorec5\"<\/a>\n

a pro \u00fahel\u00a0\u03b2<\/em>:<\/p>\n\"Caletka-vzorec6\"<\/a>\n

5. V\u00fdpo\u010det pr\u016fse\u010d\u00edku p\u0159i polovi\u010dn\u00edch \u00fahlech<\/h4>\n

Bod E\u2018 [E\u20181<\/sub>; E\u20182<\/sub>] je pr\u016fse\u010d\u00edkem p\u0159\u00edmek, kter\u00e9 sv\u00edraj\u00ed s\u00a0vektorem\u00a0h<\/em>\u00a0\u20d7\u00a0\u00fahly\u00a0\u03b1\/2<\/em>,\u00a0\u03b2\/2<\/em>. P\u0159i v\u00fdpo\u010dtu sou\u0159adnic bodu je mo\u017en\u00e9 vych\u00e1zet ze sm\u011brnicov\u00fdch rovnic p\u0159\u00edmek\u00a0l<\/em>\u00a0a\u00a0p<\/em>, kter\u00e9 maj\u00ed tvar:<\/p>\n\"Caletka-vzorec7\"<\/a>\n\"Caletka-vzorec8\"<\/a>\n

Kde \u010d\u00edsla\u00a0k<\/em>l<\/sub>,\u00a0k<\/em>p<\/sub>\u00a0jsou sm\u011brnice p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>. Obecn\u011b plat\u00ed, \u017ee sm\u011brnice\u00a0k<\/em>\u00a0dan\u00e9 p\u0159\u00edmky je rovna tangent\u011b \u00fahlu, kter\u00fd tato p\u0159\u00edmka sv\u00edr\u00e1 s\u00a0kladnou poloosou\u00a0x<\/em>. Z\u00a0toho plyne, \u017ee ze vztah\u016f (7), (8) je mo\u017en\u00e9 sestavit rovnici:<\/p>\n\"Caletka-vzorec9\"<\/a>\n

z n\u00ed\u017e je mo\u017en\u00e9 vypo\u010d\u00edtat v\u00fdsledn\u00e9 sou\u0159adnice. Pro uveden\u00fd vztah v\u0161ak mus\u00ed b\u00fdt sou\u010dasn\u011b spln\u011bny tyto podm\u00ednky, kter\u00e9 jsou z\u0159ejm\u00e9 z\u00a0obr. 3<\/em>:<\/p>\n\"Caletka-vzorec10\"<\/a>\n\"Caletka-vzorec11\"<\/a>\n

6. V\u00fdpo\u010det odchylek od zam\u011b\u0159en\u00e9 nejni\u017e\u0161\u00ed \u00farovn\u011b dna<\/h4>\n

Pro ob\u011b extrapola\u010dn\u00ed metody jsou nakonec vypo\u010d\u00edt\u00e1ny odchylky \u00farovn\u011b pr\u016fse\u010d\u00edk\u016f p\u0159\u00edmek obou b\u0159eh\u016f od\u00a0Z<\/em>min<\/sub>.<\/p>\n

Metoda n-n\u00e1sobku \u00fahl\u016f<\/h4>\n

Metoda n-n\u00e1sobku \u00fahl\u016f je zalo\u017eena na hled\u00e1n\u00ed \u010d\u00edsla\u00a0n<\/em>\u00a0takov\u00e9ho, aby jeho sou\u010din s\u00a0\u00fahly\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>\u00a0ur\u010doval optim\u00e1ln\u00ed \u00fahly sm\u011brov\u00fdch vektor\u016f p\u0159\u00edmek v\u016f\u010di\u00a0h<\/em>\u00a0\u20d7. Pr\u016fse\u010d\u00edkem t\u011bchto p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>\u00a0by m\u011bl b\u00fdt bod Z [Z1<\/sub>; Z2<\/sub>], jeho\u017e sou\u0159adnice Z2<\/sub>\u00a0se bude svou hodnotou bl\u00ed\u017eit\u00a0Z<\/em>min<\/sub>\u00a0p\u0159\u00edslu\u0161n\u00e9ho p\u0159\u00ed\u010dn\u00e9ho profilu (obr. 4<\/em>).<\/p>\n\"Caletka-4\"<\/a>\n

Obr. 4. Sch\u00e9matick\u00e9 zn\u00e1zorn\u011bn\u00ed metody n-n\u00e1sobk\u016f \u00fahl\u016f\u00a0\u03b1, \u03b2
\n<\/em>Fig. 4. Schematic representation of the method of multiplier n<\/h6>\n

P\u0159i odvozen\u00ed vztahu pro v\u00fdpo\u010det \u010d\u00edsla\u00a0n<\/em>\u00a0je nutn\u00e9 vych\u00e1zet ze sm\u011brnicov\u00fdch rovnic p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>\u00a0(7), (8). \u010c\u00edsla\u00a0k<\/em>l<\/sub>,\u00a0k<\/em>p<\/sub>\u00a0jsou sm\u011brnice p\u0159\u00edmek\u00a0l<\/em>,\u00a0p<\/em>. Obecn\u011b plat\u00ed, \u017ee sm\u011brnice\u00a0k<\/em>\u00a0p\u0159\u00edmky je rovna tangent\u011b \u00fahlu, kter\u00fd sv\u00edr\u00e1 p\u0159\u00edmka s\u00a0kladnou poloosou\u00a0x<\/em>. Z\u00a0toho plyne, \u017ee ze vztah\u016f (7) a (8) je mo\u017en\u00e9 sestavit rovnici:<\/p>\n\"Caletka-vzorec12\"<\/a>\n

I zde mus\u00ed sou\u010dasn\u011b platit podm\u00ednky:<\/p>\n\"Caletka-vzorec13\"<\/a>\n\"Caletka-vzorec14\"<\/a>\n

Je-li zn\u00e1mo, \u017ee ot\u00e1\u010dej\u00edc\u00ed se p\u0159\u00edmka\u00a0l<\/em>\u00a0proch\u00e1z\u00ed bodem B a p\u0159\u00edmka\u00a0p<\/em>\u00a0bodem C, umo\u017e\u0148uje vztah (12) pro ka\u017ed\u00fd p\u0159\u00ed\u010dn\u00fd profil naj\u00edt optim\u00e1ln\u00ed hodnotu \u010d\u00edsla\u00a0n<\/em>, a t\u00edm p\u0159ibl\u00ed\u017een\u00ed k\u00a0Z<\/em>min<\/sub>\u00a0dan\u00e9ho p\u0159\u00ed\u010dn\u00e9ho profilu.<\/p>\n\"Caletka-5\"<\/a>\n

Obr. 5. P\u0159\u00edklad p\u0159\u00ed\u010dn\u00e9ho profilu s dobrou shodou (naho\u0159e), neshodou minim\u00e1ln\u00ed \u00farovn\u011b koryta extrapolovan\u00e9ho pomoc\u00ed metody linear estimation (dole) [1]
\nFig. 5. An example of a cross-section showin good match (above), discrepancy of the minimal level of channel bottom extrapolated by the linear estimation method (down) [1]<\/h6>\n

Uveden\u00fd probl\u00e9m je mo\u017en\u00e9 \u0159e\u0161it v\u00edce zp\u016fsoby. V\u00a0r\u00e1mci t\u00e9to studie bylo vyu\u017eito programovac\u00edho jazyka Python. Z\u00e1kladem sestaven\u00e9ho k\u00f3du je rovnice (9), do n\u00ed\u017e vstupuj\u00ed n\u00e1sobky p\u016fvodn\u00edch \u00fahl\u016f\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>. Obecn\u011b je tedy v\u00fdpo\u010det zalo\u017een na zvy\u0161ov\u00e1n\u00ed\u00a0n<\/em>\u00a0od minima, plynouc\u00edho z\u00a0podm\u00ednek (13) a (14), o velmi mal\u00fd krok (nap\u0159.\u00a010-5<\/sup>). P\u0159itom je nutn\u00e9 zajistit opakovan\u00e9 p\u0159epo\u010d\u00edt\u00e1v\u00e1n\u00ed hodnot\u00a0n\u03b1<\/em>,\u00a0n\u03b2<\/em>,\u00a0q<\/em>l<\/sub>,\u00a0q<\/em>p<\/sub>\u00a0a sou\u0159adnice Z2<\/sub>, kter\u00e1 ur\u010duje nadmo\u0159skou v\u00fd\u0161ku pr\u016fse\u010d\u00edku. V\u00a0okam\u017eiku, kdy je poprv\u00e9 zaznamen\u00e1na hodnota Z2<\/sub>\u00a0ni\u017e\u0161\u00ed ne\u017e\u00a0Z<\/em>min<\/sub>, v\u00fdpo\u010det se zastav\u00ed a\u00a0hodnota\u00a0n<\/em>\u00a0se sn\u00ed\u017e\u00ed o hodnotu jednoho kroku, pro kter\u00fd je rovn\u011b\u017e zji\u0161t\u011bna hodnota\u00a0Z2<\/sub>. Nakonec je vybr\u00e1na ta hodnota\u00a0n<\/em>, p\u0159i n\u00ed\u017e je absolutn\u00ed hodnota rozd\u00edlu v\u016f\u010di\u00a0Z<\/em>min<\/sub>\u00a0men\u0161\u00ed.<\/p>\n

V\u00fdsledky<\/h2>\n

Anal\u00fdza zpracovan\u00fdch p\u0159\u00ed\u010dn\u00fdch profil\u016f uk\u00e1zala, \u017ee p\u0159i vyu\u017eit\u00ed line\u00e1rn\u00ed extrapola\u010dn\u00ed metody podle Mersela a kol. [1] je mo\u017en\u00e9 dos\u00e1hnout pom\u011brn\u011b re\u00e1ln\u00e9ho \u00fadaje minim\u00e1ln\u00ed \u00farovn\u011b dna\u00a0Z<\/em>min<\/sub>. Mezi jednotliv\u00fdmi profily v\u0161ak byla zaznamen\u00e1na zna\u010dn\u00e1 variabilita (obr. 5<\/em>). Dokl\u00e1daj\u00ed to \u00fadaje uveden\u00e9 v\u00a0tabulce<\/em>\u00a02<\/em>. Pr\u016fm\u011brn\u00e1 odchylka minima \u010din\u00ed +0,16\u00a0m, hodnota medi\u00e1nu +0,71\u00a0m a sm\u011brodatn\u00e1 odchylka +0,77\u00a0m. Z\u00a0toho vypl\u00fdv\u00e1, \u017ee tato extrapola\u010dn\u00ed metoda z\u00a0hlediska pr\u016fm\u011bru \u00farove\u0148 dna sp\u00ed\u0161e nadhodnocuje. Je tedy z\u0159ejm\u00e9, \u017ee sn\u00ed\u017een\u00edm sklonu\u00a0b\u0159eh\u016f na polovinu p\u016fvodn\u00ed hodnoty \u017e\u00e1dn\u00e9ho zlep\u0161en\u00ed dos\u00e1hnout nelze. Pro \u00faplnost jsou v\u0161ak i pro tuto extrapolaci hodnoty z\u00e1kladn\u00edch popisn\u00fdch statistik uvedeny. Pro p\u0159ehlednost jsou na\u00a0obr. 6<\/em>\u00a0vyobrazeny krabicov\u00e9 grafy odchylek extrapolovan\u00e9 minim\u00e1ln\u00ed \u00farovn\u011b dna od minima zam\u011b\u0159en\u00e9ho v\u00a0ter\u00e9nu p\u0159i aplikaci obou uveden\u00fdch metod.<\/p>\n

Tabulka 2. Popisn\u00e9 statistiky odchylek nejni\u017e\u0161\u00ed \u00farovn\u011b extrapolovan\u00e9ho dna v\u016f\u010di Zmin<\/sub>\u00a0p\u0159i pou\u017eit\u00ed metody linear, double-linear a n\u00e1sobku n sklon\u016f b\u0159eh\u016f p\u0159\u00ed\u010dn\u00fdch profil\u016f
\nTable 2. Descriptive statistics\u2018 overview \u2013 deviations of the lowest level in the extrapolated cross sections using the linear, double-linear estimation method [1] and multiplier n method from the in situ geodetic measurements<\/h5>\n\"Caletka-tabulka2\"<\/a>\n

D\u00e1le se uk\u00e1zalo, \u017ee v\u00fdsledn\u00e1 odchylka dosa\u017een\u00e9 minim\u00e1ln\u00ed \u00farovn\u011b p\u0159\u00ed\u010dn\u00fdch profil\u016f v\u016f\u010di \u00farovni\u00a0Z<\/em>min<\/sub>\u00a0vykazuje ur\u010ditou z\u00e1vislost na sou\u010dtu \u00fahl\u016f b\u0159eh\u016f\u00a0\u03b1<\/em>\u00a0+<\/em>\u00a0\u03b2<\/em>. Obecn\u011b se d\u00e1 tvrdit, \u017ee pro n\u00edzk\u00e9 hodnoty sou\u010dt\u016f sklon\u016f b\u0159eh\u016f doch\u00e1z\u00ed p\u0159ev\u00e1\u017en\u011b k\u00a0nadhodnocen\u00ed minim\u00e1ln\u00ed \u00farovn\u011b dna extrapolovan\u00e9ho koryta a naopak (obr. 7<\/em>). Hodnota korela\u010dn\u00edho koeficientu \u010din\u00ed 0,64 (tj.\u00a0st\u0159edn\u00ed z\u00e1vislost). Nejv\u011bt\u0161\u00ed shody je dosahov\u00e1no nej\u010dast\u011bji v\u00a0rozmez\u00ed hodnot sou\u010dtu\u00a0\u03b1<\/em>\u00a0+<\/em>\u00a0\u03b2<\/em>\u00a0p\u0159ibli\u017en\u011b 0,8 a\u017e 1,0\u00a0rad (tj. p\u0159ibli\u017en\u011b 45\u00b0 a\u017e 57\u00b0). Nicm\u00e9n\u011b, pro jednozna\u010dn\u011bj\u0161\u00ed v\u00fdsledky by bylo pot\u0159ebn\u00e9 shrom\u00e1\u017edit v\u011bt\u0161\u00ed soubor p\u0159\u00ed\u010dn\u00fdch profil\u016f.<\/p>\n\"Caletka-6\"<\/a>\n

Obr. 6. Krabicov\u00fd graf odchylek nejni\u017e\u0161\u00edho bodu extrapolovan\u00e9ho dna v\u016f\u010di Zmin<\/sub>\u00a0zam\u011b\u0159en\u00e9 geodeticky
\nFig. 6. Boxplot of the deviations of the lowest level in the extrapolated cross sections using the linear and double-linear estimation method [1] from the in situ geodetic measurements<\/h6>\n

Snahou bylo tak\u00e9 nal\u00e9zt optim\u00e1ln\u00ed hodnotu n\u00e1sobku\u00a0n<\/em>\u00a0\u00fahl\u016f\u00a0\u03b1, \u03b2<\/em>. Postupem bl\u00ed\u017ee popsan\u00fdm v\u00fd\u0161e bylo zji\u0161t\u011bno, \u017ee pr\u016fm\u011brn\u00e1 hodnota n\u00e1sobku\u00a0n<\/em>\u00a0\u010din\u00ed pro soubor osmdes\u00e1ti dvou profil\u016f 1,30, hodnota medi\u00e1nu je 0,71. Krabicov\u00fd graf charakterizuj\u00edc\u00ed rozlo\u017een\u00ed hodnot n je uveden na\u00a0obr. 8<\/em>. Z\u00e1vislost rozlo\u017een\u00ed t\u011bchto hodnot na pom\u011bru sklon\u016f obou b\u0159eh\u016f\u00a0\u03b1<\/em>,\u00a0\u03b2<\/em>, jejich sou\u010dtu ani pom\u011bru se neprok\u00e1zala.<\/p>\n\"Caletka-7\"<\/a>\n

Obr. 7. Vztah odchylky nejni\u017e\u0161\u00ed \u00farovn\u011b dna koryt extrapolovan\u00fdch metodou linear a\u00a0sou\u010dtu sklon\u016f b\u0159eh\u016f \u03b1 + \u03b2 p\u0159\u00ed\u010dn\u00fdch profil\u016f
\nFig. 7. Relationship of the deviations of the lowest level in the extrapolated cross sections using the linear and double-linear estimation method [1] from the in situ geodetic measurements and sums of banks\u2018 slopes for each cross sectio<\/h6>\n

Z\u00e1v\u011br<\/h2>\n

Aplikace metody line\u00e1rn\u00edch extrapolac\u00ed b\u0159eh\u016f koryt z\u00a0DMT vytvo\u0159en\u00e9ho z\u00a0datov\u00e9 sady DMR\u00a05G za \u00fa\u010delem nalezen\u00ed minim\u00e1ln\u00ed \u00farovn\u011b koryta uk\u00e1zala, \u017ee tato metoda v p\u0159ev\u00e1\u017en\u00e9 \u010d\u00e1sti p\u0159\u00edpad\u016f vede k\u00a0m\u00edrn\u00e9mu nadhodnocov\u00e1n\u00ed minim\u00e1ln\u00ed \u00farovn\u011b dna (pr\u016fm\u011brn\u011b o +0,16 m). Z\u00a0toho plyne, \u017ee vhodn\u00fdm krokem vedouc\u00edm ke zp\u0159esn\u011bn\u00ed by bylo zv\u00fd\u0161en\u00ed sklon\u016f b\u0159eh\u016f o jist\u00fd n\u00e1sobek\u00a0n<\/em>\u00a0(pro konkr\u00e9tn\u00ed analyzovan\u00fd soubor profil\u016f je to pr\u016fm\u011brn\u011b 1,30). Do \u00favahy je v\u0161ak nutn\u00e9 br\u00e1t skute\u010dnost, \u017ee \u00fasp\u011b\u0161nost interpolace zde nen\u00ed hodnocena vzhledem k\u00a0v\u00fdstup\u016fm hydrodynamick\u00e9ho modelov\u00e1n\u00ed, ale \u010dist\u011b vzhledem k\u00a0nejni\u017e\u0161\u00ed \u00farovni koryt vodn\u00edch tok\u016f. V\u00a0tomto duchu je pot\u0159eba k\u00a0t\u00e9to studii a jej\u00edm v\u00fdsledk\u016fm p\u0159istupovat.<\/p>\n\"Caletka-8\"<\/a>\n

Obr. 8. Krabicov\u00fd graf optim\u00e1ln\u00edch n\u00e1sobk\u016f\u00a0n<\/em>\u00a0sklon\u016f b\u0159eh\u016f\u00a0\u03b1, \u03b2
\n<\/em>Fig. 8. Boxplot of optimal values of multiplier\u00a0n<\/em><\/h6>\n

Problematick\u00fdm aspektem extrapola\u010dn\u00ed metody je krom\u011b ji\u017e zm\u00edn\u011bn\u00fdch chyb datov\u00e9 sady DMR\u00a05G (\u00fapln\u00e1 st\u0159edn\u00ed chyba, maxim\u00e1ln\u00ed chyba) tak\u00e9 subjektivita vymezen\u00ed b\u0159eh\u016f koryt, resp. jejich po\u010d\u00e1te\u010dn\u00edch a koncov\u00fdch bod\u016f. Vymezen\u00ed m\u016f\u017ee b\u00fdt v\u00a0jednotliv\u00fdch p\u0159\u00edpadech nejednozna\u010dn\u00e9 s\u00a0ohledem na prom\u011bnlivost sklon\u016f. Dal\u0161\u00ed limituj\u00edc\u00ed skute\u010dnost\u00ed je zat\u00edm pom\u011brn\u011b omezen\u00fd vzorek p\u0159\u00ed\u010dn\u00fdch koryt a \u00fasek\u016f tok\u016f, pro kter\u00e9 byla anal\u00fdza provedena. K\u00a0podrobn\u011bj\u0161\u00edmu hodnocen\u00ed metody by bylo \u017e\u00e1douc\u00ed soubor p\u0159\u00ed\u010dn\u00fdch profil\u016f v\u00fdznamn\u011b roz\u0161\u00ed\u0159it a zohlednit p\u0159i tom i variabilitu koryt z\u00a0hlediska jejich geometrie a z\u00a0n\u00ed vypl\u00fdvaj\u00edc\u00ed nep\u0159esnosti digit\u00e1ln\u00edho modelu ter\u00e9nu v\u00a0\u00farovni koryta (byst\u0159iny, zarostl\u00e1 koryta, koryta s\u00a0podemlet\u00fdmi b\u0159ehy, koryta se svisl\u00fdmi b\u0159ehov\u00fdmi zdmi, lichob\u011b\u017en\u00edkov\u00e1 koryta aj.). To by umo\u017enilo detailn\u011b analyzovat vz\u00e1jemn\u00e9 vztahy mezi v\u00fdsledky extrapola\u010dn\u00edch metod a l\u00e9pe identifikovat parametry p\u0159\u00ed\u010dn\u00fdch profil\u016f a jejich kombinace ovliv\u0148uj\u00edc\u00ed \u00fasp\u011b\u0161nost extrapolace koryta. D\u00edky tomu bude mo\u017en\u00e9 vyvinout robustn\u00ed metody extrapolace koryt\u00a0definovan\u00fdch parametr\u016f z\u00a0podklad\u016f, kde \u00fapln\u00e1 topografie koryt vodn\u00edch tok\u016f nen\u00ed vykreslena.<\/p>\n","protected":false},"excerpt":{"rendered":"

Airborne laser imaging (LiDAR) has been carried out throughout the Czech Republic, enabling the creation of raster of digital model of terrain. This material is widely used in various fields. From the point of view of hydrology demands, however, the shortcoming of this technology resides in the absence of accurate\/complete channel topography due to the absorption of the near-infrared laser beams by water.<\/p>\n","protected":false},"author":8,"featured_media":3827,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[88],"tags":[931,928,929,930,279],"coauthors":[181],"class_list":["post-3897","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-informatics-cartography-in-water-management","tag-channel-geometry","tag-digital-model-of-relief-5th-generation","tag-digital-model-of-terrain","tag-extrapolation","tag-gis"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3897","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=3897"}],"version-history":[{"count":2,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3897\/revisions"}],"predecessor-version":[{"id":30416,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3897\/revisions\/30416"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/3827"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=3897"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=3897"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=3897"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=3897"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}