{"id":6522,"date":"2019-06-14T08:15:26","date_gmt":"2019-06-14T07:15:26","guid":{"rendered":"https:\/\/www.vtei.cz\/?p=6522"},"modified":"2024-07-16T15:48:04","modified_gmt":"2024-07-16T14:48:04","slug":"matematicke-stanoveni-batymetrie-vodniho-toku-software-bathy_supp","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2019\/06\/matematicke-stanoveni-batymetrie-vodniho-toku-software-bathy_supp\/","title":{"rendered":"Mathematical estimation of watercourse bathymetry \u2013 Bathy_supp software"},"content":{"rendered":"

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

Topografick\u00e9 \u00fadaje hraj\u00ed kl\u00ed\u010dovou roli v\u00a0ot\u00e1zce p\u0159esn\u00e9ho hydrodynamick\u00e9ho modelov\u00e1n\u00ed povod\u0148ov\u00fdch ud\u00e1lost\u00ed. \u010casto je vy\u017eadov\u00e1n p\u0159esn\u00fd digit\u00e1ln\u00ed model ter\u00e9nu (DMT), kter\u00fd obsahuje popis \u0159\u00ed\u010dn\u00ed batymetrie. DMT m\u016f\u017ee b\u00fdt z\u00edsk\u00e1n z\u00a0r\u016fzn\u00fdch zdroj\u016f dat, jako jsou pozemn\u00ed m\u011b\u0159en\u00ed nebo metody d\u00e1lkov\u00e9ho pr\u016fzkumu zem\u011b. Po\u0159\u00edzen\u00ed pozemn\u00edch, zejm\u00e9na geodetick\u00fdch, dat b\u00fdv\u00e1 \u010dasto finan\u010dn\u011b n\u00e1kladn\u00e9 a\u00a0\u010dasov\u011b n\u00e1ro\u010dn\u00e9. Dal\u0161\u00ed alternativou z\u00edsk\u00e1n\u00ed dat DMT jsou satelitn\u00ed zdroje, ty v\u0161ak zpravidla nedosahuj\u00ed p\u0159esnost\u00ed, kter\u00e9 jsou vhodn\u00e9 pro korektn\u00ed hydrodynamick\u00e9 modelov\u00e1n\u00ed. Jako nejv\u00edce vhodn\u00e1 se proto jev\u00ed data po\u0159\u00edzen\u00e1 technologi\u00ed leteck\u00e9ho laserov\u00e9ho skenov\u00e1n\u00ed (LLS).<\/p>\n\"\"<\/a>\n

Pro sb\u011br dat LLS se v\u00a0\u010cR vyu\u017e\u00edv\u00e1 sn\u00edm\u00e1n\u00ed infra\u010derven\u00fdm laserov\u00fdm paprskem. Omezen\u00edm ve vyu\u017eit\u00ed t\u00e9to technologie pro hydrodynamick\u00e9 modelov\u00e1n\u00ed je fakt, \u017ee infra\u010derven\u00fd laserov\u00fd paprsek je pohlcov\u00e1n vodn\u00ed hladinou. V\u00a0praxi to znamen\u00e1, \u017ee nelze z\u00edskat v\u00fd\u0161kopisnou informaci o\u00a0morfologii ter\u00e9nu pod vodn\u00ed hladinou. P\u0159i tvorb\u011b DMT z\u00a0dat LLS tak doch\u00e1z\u00ed k\u00a0vytvo\u0159en\u00ed modelu, kter\u00fd zanedb\u00e1v\u00e1 pr\u016fto\u010dnou plochu zam\u011b\u0159ovan\u00e9ho koryta vodn\u00edho toku.<\/p>\n

V\u00a0tomto p\u0159\u00edsp\u011bvku jsou prezentov\u00e1ny v\u00fdsledky z\u00a0vyv\u00edjen\u00e9ho softwaru Bathy_supp, kter\u00fd stanovuje batymetrii p\u0159irozen\u00e9ho \u0159\u00ed\u010dn\u00edho koryta. Batymetrie je stanovena pomoc\u00ed analytick\u00fdch k\u0159ivek, kter\u00e9 popisuj\u00ed pr\u016fb\u011bh p\u0159\u00ed\u010dn\u00fdch profil\u016f. N\u00e1sledn\u011b je provedena prostorov\u00e1 interpolace mezi odhadnut\u00fdmi profily, jej\u00edm\u017e v\u00fdsledkem je batymetrick\u00e1 bodov\u00e1 s\u00ed\u0165. Vytvo\u0159enou batymetrickou bodovou s\u00ed\u0165 lze spojit nap\u0159. s\u00a0daty LLS a\u00a0vytvo\u0159it tak DMT vhodn\u00fd pro hydrodynamick\u00e9 modelov\u00e1n\u00ed. V\u00a0p\u0159\u00edsp\u011bvku je prezentov\u00e1n praktick\u00fd p\u0159\u00edklad testov\u00e1n\u00ed softwaru na pilotn\u00ed lokalit\u011b. Dosa\u017een\u00e9 v\u00fdsledky ukazuj\u00ed, \u017ee v\u00fdsledky softwaru Bathy_supp v\u00fdrazn\u011b zlep\u0161uj\u00ed model ter\u00e9nu vytvo\u0159en\u00fd z\u00a0dat LLS.<\/p>\n

\u00davod<\/h2>\n

Kl\u00ed\u010dovou znalost\u00ed pro hydrodynamick\u00e9 modelov\u00e1n\u00ed povodn\u00ed je morfologie ter\u00e9nu. P\u0159esnost a\u00a0vyu\u017eitelnost hydrodynamick\u00fdch model\u016f z\u00e1vis\u00ed na charakteru, dostupnosti a\u00a0p\u0159esnosti zdrojov\u00fdch topografick\u00fdch dat, ze kter\u00fdch je generov\u00e1n v\u00fdsledn\u00fd DMT [1].<\/p>\n

Relevantn\u00ed v\u00fd\u0161kopisn\u00e9 \u00fadaje o\u00a0morfologii koryt vodn\u00edch tok\u016f a\u00a0p\u0159ilehl\u00e9ho inunda\u010dn\u00edho \u00fazem\u00ed je mo\u017en\u00e9 z\u00edskat r\u016fzn\u00fdmi, navz\u00e1jem \u010dasto kombinovateln\u00fdmi metodami. Jednou z\u00a0metod z\u00edsk\u00e1n\u00ed zdrojov\u00fdch dat pro DMT je m\u011b\u0159en\u00ed pomoc\u00ed dru\u017eicov\u00fdch polohov\u00fdch syst\u00e9m\u016f. Tato data v\u0161ak nejsou, d\u00edky sv\u00e9mu rozli\u0161en\u00ed, pro hydrodynamick\u00e9 modelov\u00e1n\u00ed dostate\u010dn\u011b p\u0159esn\u00e1. Naopak velmi p\u0159esnou metodou z\u00edsk\u00e1n\u00ed dat pro DMT je pozemn\u00ed geodetick\u00e9 m\u011b\u0159en\u00ed, tato metoda je nicm\u00e9n\u011b \u010dasov\u011b i\u00a0finan\u010dn\u011b velmi n\u00e1ro\u010dn\u00e1. T\u0159et\u00ed, nejmodern\u011bj\u0161\u00ed, metoda spo\u010d\u00edv\u00e1 ve vyu\u017eit\u00ed technologie LLS, kter\u00e1 m\u00e1 \u0161irok\u00e9 uplatn\u011bn\u00ed v\u00a0cel\u00e9 \u0159ad\u011b obor\u016f. B\u011b\u017en\u011b se vyu\u017e\u00edv\u00e1 p\u0159i po\u0159izov\u00e1n\u00ed prostorov\u00fdch geografick\u00fdch dat pro pot\u0159eby v\u00a0geod\u00e9zii, ve stavebnictv\u00ed, v\u00a0lesnictv\u00ed, v\u00a0archeologii atp. V\u00fdznamnou mo\u017enost\u00ed vyu\u017eit\u00ed LLS je i\u00a0oblast vodn\u00edho hospod\u00e1\u0159stv\u00ed, p\u0159\u00edkladem je zp\u0159es\u0148ov\u00e1n\u00ed polohy os vodn\u00edch tok\u016f a\u00a0vodn\u00edch ploch [2] nebo tvorba map povod\u0148ov\u00fdch rizik [3].<\/p>\n

Metoda LLS [4] vyu\u017e\u00edv\u00e1 technologii LiDARu (Light Detection and Ranging). Princip t\u00e9to technologie spo\u010d\u00edv\u00e1 v\u00a0m\u011b\u0159en\u00ed doby n\u00e1vratu vyza\u0159ovan\u00e9ho laserov\u00e9ho paprsku. Anal\u00fdzou t\u00e9to doby je pak ur\u010dena vzd\u00e1lenost m\u011b\u0159ic\u00ed jednotky (na palub\u011b letadla) od sn\u00edman\u00e9ho objektu (povrchu Zem\u011b), resp. nadmo\u0159sk\u00e1 v\u00fd\u0161ka mapovan\u00e9ho zemsk\u00e9ho povrchu. V\u00fdhodou LLS je jednak rychlost z\u00edsk\u00e1n\u00ed dat, d\u00e1le vysok\u00e1 p\u0159esnost a\u00a0vysok\u00e9 prostorov\u00e9 rozli\u0161en\u00ed vznikaj\u00edc\u00edho DMT. Skenery pou\u017e\u00edvan\u00e9 k\u00a0celoplo\u0161n\u00e9mu mapov\u00e1n\u00ed vyu\u017e\u00edvaj\u00ed laser o\u00a0vlnov\u00e9 d\u00e9lce bl\u00edzk\u00e9 infra\u010derven\u00e9mu spektru, p\u0159i\u010dem\u017e voda toto z\u00e1\u0159en\u00ed zcela pohlcuje [5]. To sice umo\u017e\u0148uje p\u0159esnou identifikaci hranice vodn\u00edch ploch, nicm\u00e9n\u011b informaci o\u00a0batymetrii dna nepod\u00e1v\u00e1. Proto byla vyvinuta du\u00e1ln\u00ed forma LiDARu (DiAL\u00a0\u2013 Differential Absorption Lidar), kter\u00e1 kombinuje dva laserov\u00e9 paprsky vyza\u0159ovan\u00e9 v\u00a0r\u016fzn\u00fdch vlnov\u00fdch d\u00e9lk\u00e1ch, v\u00a0infra\u010derven\u00e9m spektru (1\u00a0064 nm) pro mapov\u00e1n\u00ed topografie ter\u00e9nu a\u00a0v\u00a0zelen\u00e9m (zeleno-modr\u00e9m) spektru (532 nm), kter\u00e9 pronik\u00e1 pod vodn\u00ed hladinu [6, 7]. Tento specifick\u00fd typ LLS, zn\u00e1m\u00fd rovn\u011b\u017e pod ozna\u010den\u00edm leteck\u00e9 batymetrick\u00e9 laserov\u00e9 skenov\u00e1n\u00ed (LBLS) nebo v\u00a0anglick\u00e9m origin\u00e1le Airborne Lidar Bathymetry (ALB), se pou\u017e\u00edv\u00e1 p\u0159edev\u0161\u00edm v\u00a0m\u011blk\u00fdch p\u0159\u00edb\u0159e\u017en\u00edch mo\u0159sk\u00fdch vod\u00e1ch [8].<\/p>\n

St\u00e1le v\u0161ak p\u0159etrv\u00e1vaj\u00ed jist\u00e1 omezen\u00ed, m\u00edra proniknut\u00ed zelen\u00e9ho paprsku vodn\u00edm sloupcem z\u00e1vis\u00ed na pr\u016fhlednosti, resp. z\u00e1kalu a\u00a0proud\u011bn\u00ed vody [9, 10]. N\u011bkte\u0159\u00ed auto\u0159i [6\u20138] deklaruj\u00ed, v\u00a0z\u00e1vislosti na vn\u011bj\u0161\u00edch podm\u00ednk\u00e1ch (pr\u016fhlednost vody, z\u00e1kal,\u2026), \u017ee re\u00e1ln\u00e1 batymetrick\u00e1 data lze z\u00edsk\u00e1vat a\u017e do hloubky 50 m pod vodn\u00ed hladinu s\u00a0horizont\u00e1ln\u00ed p\u0159esnost\u00ed \u00b12,5 m a\u00a0s\u00a0vertik\u00e1ln\u00ed p\u0159esnost\u00ed \u00b10,25 m [7]. Guenther a\u00a0kol. [8] nav\u00edc doporu\u010duje v\u011bnovat maxim\u00e1ln\u00ed pozornost spr\u00e1vn\u00e9mu na\u010dasov\u00e1n\u00ed sn\u00edmkov\u00e1n\u00ed a\u00a0p\u0159\u00edpadn\u011b mapov\u00e1n\u00ed opakovat. V\u00a0podm\u00ednk\u00e1ch \u010cR byly, parametricky obdobn\u00fdm vybaven\u00edm, testov\u00e1ny vybran\u00e9 vodn\u00ed n\u00e1dr\u017ee a\u00a06 km dlouh\u00fd \u00fasek vodn\u00edho toku. Relevantn\u00ed v\u00fdsledky byly ov\u0161em dosa\u017eeny pouze do hloubky 1,5\u20132 m pod vodn\u00ed hladinou v\u00a0p\u0159\u00edpad\u011b vodn\u00ed n\u00e1dr\u017ee a\u00a0do hloubky 0,8\u00a0m v\u00a0p\u0159\u00edpad\u011b vodn\u00edho toku [11].<\/p>\n

D\u016fsledkem nejistoty z\u00edsk\u00e1n\u00ed relevantn\u00edch v\u00fdsledk\u016f LBLS mohou b\u00fdt nespolehliv\u00e1 zdrojov\u00e1 data. Konkr\u00e9tn\u011b m\u016f\u017ee doj\u00edt k\u00a0zanedb\u00e1n\u00ed hloubky a\u00a0tvaru koryta, co\u017e je z\u00e1sadn\u00ed probl\u00e9m pro hydrodynamick\u00e9 modelov\u00e1n\u00ed \u0159\u00ed\u010dn\u00edch tok\u016f a\u00a0spr\u00e1vn\u00e9 posouzen\u00ed ekologick\u00fdch a\u00a0geomorfologick\u00fdch vlastnost\u00ed vodn\u00edch tok\u016f [12].<\/p>\n

Dal\u0161\u00ed mo\u017enost\u00ed tvorby vysoce p\u0159esn\u00e9ho a\u00a0batymetricky korektn\u00edho DMT je kombinace dat LLS s\u00a0daty pozemn\u00edho m\u011b\u0159en\u00ed charakterizuj\u00edc\u00ed tvar koryta vodn\u00edch tok\u016f. Dodate\u010dn\u00fdm zdrojem batymetrick\u00fdch dat m\u016f\u017ee b\u00fdt geodetick\u00e9 zam\u011b\u0159en\u00ed vodn\u00edho toku nebo zam\u011b\u0159en\u00ed s\u00a0vyu\u017eit\u00edm SONARu (SOund Navigation And Ranging), tedy za\u0159\u00edzen\u00edm vyu\u017e\u00edvaj\u00edc\u00ed akustick\u00fdch vln jednak k\u00a0navigaci a\u00a0zam\u011b\u0159ov\u00e1n\u00ed objekt\u016f pod vodou, ale tak\u00e9 k\u00a0m\u011b\u0159en\u00ed hloubek [13]. Specifick\u00fdm p\u0159\u00edstrojem pro z\u00edsk\u00e1n\u00ed batymetrick\u00fdch dat je p\u0159\u00edstroj ADCP (Acoustic Dopler Current Profiler) vyu\u017e\u00edvaj\u00edc\u00ed Dopplerova jevu. Prim\u00e1rn\u011b je ur\u010den pro m\u011b\u0159en\u00ed pr\u016ftoku v\u00a0otev\u0159en\u00fdch korytech \u0159ek, jeho sekund\u00e1rn\u00edm vyu\u017eit\u00edm je pak batymetrick\u00e9 mapov\u00e1n\u00ed [13]. V\u0161echny tyto metody jsou v\u0161ak \u010dasov\u011b i\u00a0finan\u010dn\u011b n\u00e1ro\u010dn\u00e9.<\/p>\n

Nab\u00edz\u00ed se ot\u00e1zka alternativn\u00edho zji\u0161t\u011bn\u00ed tvaru p\u0159\u00ed\u010dn\u00e9ho profilu vodn\u00edho toku, resp. velikosti pr\u016fto\u010dn\u00e9 plochy, tedy hlavn\u00edch vstupn\u00edch dat pro hydrodynamick\u00e9 modely. Existuj\u00ed r\u016fzn\u00e9 metody dopln\u011bn\u00ed chyb\u011bj\u00edc\u00edch dat charakterizuj\u00edc\u00ed tvar koryt vodn\u00edch tok\u016f v\u00a0jejich p\u0159irozen\u00e9m tvaru.<\/p>\n

Caletka [14] popisuje metodu line\u00e1rn\u00ed extrapolace chyb\u011bj\u00edc\u00edch dat z\u00a0p\u016fvodn\u00edch rastr\u016f na z\u00e1klad\u011b sklonu b\u0159eh\u016f v\u00a0r\u00e1mci p\u0159\u00ed\u010dn\u00fdch profil\u016f, kde je schematizace prov\u00e1d\u011bna na z\u00e1klad\u011b volby vhodn\u00e9ho geometrick\u00e9ho obrazce, kter\u00fd by ide\u00e1ln\u011b vystihoval \u0159e\u0161en\u00fd p\u0159\u00ed\u010dn\u00fd profil. V\u00fdsledky vyu\u017eit\u00ed t\u00e9to metody zat\u00edm ukazuj\u00ed m\u00edrn\u00e9 nadhodnocov\u00e1n\u00ed minim\u00e1ln\u00ed \u00farovn\u011b dna koryta vodn\u00edho toku.<\/p>\n

Dal\u0161\u00ed mo\u017enost\u00ed vyu\u017eit\u00ed softwarov\u00fdch metod pro dopln\u011bn\u00ed chyb\u011bj\u00edc\u00edch batymetrick\u00fdch dat je software CroSolver [15, 16]. Ten nahrazuje \u0159\u00ed\u010dn\u00ed batymetrii korytem lichob\u011b\u017en\u00edkov\u00e9ho nebo obd\u00e9ln\u00edkov\u00e9ho pr\u016f\u0159ezu. Model koryta vodn\u00edho toku je n\u00e1sledn\u011b spojen s\u00a0daty LLS a\u00a0vznik\u00e1 tak zp\u0159esn\u011bn\u00fd DMT.<\/p>\n

Inovativn\u00edm p\u0159\u00edstupem ke stanoven\u00ed re\u00e1ln\u00e9 profilace vodn\u00edho toku je v\u00fdvoj softwarov\u00e9ho prost\u0159edku Bathy_supp. Software vyu\u017e\u00edv\u00e1 matematick\u00e9ho stanoven\u00ed tvaru p\u0159\u00ed\u010dn\u00fdch profil\u016f na z\u00e1klad\u011b jejich rozm\u00edst\u011bn\u00ed v\u00a0modelovan\u00e9 oblasti. N\u00e1sledn\u011b dopo\u010d\u00edt\u00e1v\u00e1 kompletn\u00ed batymetrii modelovan\u00e9ho \u00faseku vodn\u00edho toku. Takto z\u00edskan\u00e1 batymetrick\u00e1 data jsou posl\u00e9ze spolu se vstupn\u00edmi topografick\u00fdmi daty (TOPO) vyu\u017eita pro tvorbu celistv\u00e9ho DMT.<\/p>\n

Program Bathy_supp<\/h2>\n

Program Bathy_supp je vytvo\u0159en jako samostatn\u011b spustiteln\u00fd program v\u00a0programovac\u00edm jazyku C++ a\u00a0je ur\u010den pro stanoven\u00ed batymetrie vodn\u00edho toku. Koryto vodn\u00edho toku m\u016f\u017ee b\u00fdt ur\u010deno v\u00a0programu na z\u00e1klad\u011b zobrazen\u00ed dat TOPO, nebo jako seznam sou\u0159adnic p\u0159\u00ed\u010dn\u00fdch profil\u016f, definuj\u00edc\u00edch geometrii budouc\u00edho koryta vodn\u00edho toku. V\u00fdstupem je seznam sou\u0159adnic definuj\u00edc\u00edch (v\u00fd\u0161kov\u011b i\u00a0polohov\u011b) novou batymetrii koryta v\u00a0textov\u00e9m form\u00e1tu. Tento v\u00fdstup m\u016f\u017ee b\u00fdt nad\u00e1le pou\u017eit v\u00a0geografick\u00fdch informa\u010dn\u00edch syst\u00e9mech (GIS) k\u00a0samotn\u00e9 synt\u00e9ze dat z\u00a0programu Bathy_supp a\u00a0dat TOPO pro tvorbu celistv\u00fdch DMT.<\/p>\n\"\"<\/a>\n

Obr. 1. P\u0159\u00edklady prohnut\u00ed analytick\u00e9 k\u0159ivky
\nFig. 1. Examples of deflection of the analytical curve<\/h6>\n

Vstupn\u00ed data<\/h3>\n

Jak ji\u017e bylo \u0159e\u010deno, z\u00e1kladn\u00edmi vstupn\u00edmi \u00fadaji jsou data TOPO, v\u00a0na\u0161em p\u0159\u00edpad\u011b z\u00edskan\u00e1 metodou LLS. Tento vstup je ve form\u011b seznamu diskr\u00e9tn\u00edch bod\u016f o\u00a0sou\u0159adnic\u00edch XYZ. Tato data mus\u00ed b\u00fdt v\u00a0textov\u00e9m form\u00e1tu s\u00a0koncovkou \u201e*.txt\u201c nebo \u201e*.xyz\u201c, shodn\u011b \u0159azen\u00fdmi v\u00a0po\u0159ad\u00ed XYZ. Dal\u0161\u00edmi vstupn\u00edmi daty jsou informace o\u00a0pr\u016ftoku v\u00a0\u0159\u00ed\u010dn\u00edm koryt\u011b v\u00a0dob\u011b po\u0159\u00edzen\u00ed dat TOPO a\u00a0drsnostn\u00ed charakteristika koryta.<\/p>\n

Popis programu<\/h3>\n

Batymetrick\u00fd v\u00fdpo\u010det je proveden na z\u00e1klad\u011b virtu\u00e1ln\u00edch p\u0159\u00ed\u010dn\u00fdch profil\u016f, jejich\u017e rozm\u00edst\u011bn\u00ed definuje u\u017eivatel v\u00a0r\u00e1mci modelovan\u00e9ho \u00faseku \u0159eky. V\u00a0t\u011bchto profilech je z\u00a0dat TOPO ur\u010dena nadmo\u0159sk\u00e1 v\u00fd\u0161ka hladiny vody, na jej\u00edm\u017e z\u00e1klad\u011b jsou n\u00e1sledn\u011b odvozeny jednotliv\u00e9 profily, definovan\u00e9 sou\u0159adnicemi XYZ. Podle zvolen\u00e9 schematizace jsou pak mezi profily interpolov\u00e1ny sou\u0159adnice nov\u00fdch batymetrick\u00fdch bod\u016f. T\u00edmto postupem vznik\u00e1 bodov\u00e1 s\u00ed\u0165, ze kter\u00e9 je mo\u017en\u00e9 za pou\u017eit\u00ed b\u011b\u017en\u00fdch interpola\u010dn\u00edch technik vytvo\u0159it 3D batymetrick\u00fd model koryta vodn\u00edho toku.<\/p>\n

Geometrie vodn\u00edho toku<\/h4>\n

Prvn\u00edm krokem po spu\u0161t\u011bn\u00ed programu je nahr\u00e1n\u00ed dat TOPO. Na z\u00e1klad\u011b zobrazen\u00ed dat TOPO je mo\u017en\u00e9 v\u00a0grafick\u00e9m okn\u011b programu zvolit um\u00edst\u011bn\u00ed modelovan\u00fdch p\u0159\u00ed\u010dn\u00fdch profil\u016f. Poloha t\u011bchto profil\u016f definuje geometrii modelovan\u00e9 \u010d\u00e1sti vodn\u00edho toku, proto je nutn\u00e9 pe\u010dliv\u011b zva\u017eovat jejich rozm\u00edst\u011bn\u00ed v\u00a0modelovan\u00e9m prostoru. Profily mus\u00ed b\u00fdt definov\u00e1ny v\u00a0po sob\u011b jdouc\u00edm po\u0159ad\u00ed, a\u00a0to od nejv\u00fd\u0161e um\u00edst\u011bn\u00e9ho profilu. D\u00e9lka profil\u016f definuje \u0161\u00ed\u0159ku koryta, pro n\u00ed\u017e bude batymetrick\u00fd v\u00fdpo\u010det proveden. Rozestup profil\u016f mus\u00ed b\u00fdt volen s\u00a0ohledem na v\u00fdb\u011br schematiza\u010dn\u00edho algoritmu (viz kap. Meziprofilov\u00e1 interpolace). Po\u010det zad\u00e1van\u00fdch profil\u016f je volen u\u017eivatelem. Alternativou je mo\u017enost nahr\u00e1t um\u00edst\u011bn\u00ed profil\u016f formou seznamu jejich defini\u010dn\u00edch bod\u016f.<\/p>\n

Zahlouben\u00ed modelovan\u00fdch p\u0159\u00ed\u010dn\u00fdch profil\u016f<\/h4>\n

Pro modelovan\u00e9 p\u0159\u00ed\u010dn\u00e9 profily je ode\u010dtena z\u00a0dat TOPO nadmo\u0159sk\u00e1 v\u00fd\u0161ka hladiny v\u00a0m\u00edst\u011b profilu. Toho je doc\u00edleno tak, \u017ee v\u00a0okol\u00ed koncov\u00fdch bod\u016f ka\u017ed\u00e9ho profilu je programem vyhled\u00e1n bod s\u00a0nejni\u017e\u0161\u00ed nadmo\u0159skou v\u00fd\u0161kou. Tato nadmo\u0159sk\u00e1 v\u00fd\u0161ka je vybr\u00e1na jako v\u00fd\u0161ka hladiny vody v\u00a0dob\u011b po\u0159\u00edzen\u00ed dat TOPO. Po ur\u010den\u00ed nadmo\u0159sk\u00e9 v\u00fd\u0161ky hladin v\u00a0profilech program automaticky zkontroluje celkov\u00fd pod\u00e9ln\u00fd profil hladiny toku, p\u0159\u00edpadn\u011b nadmo\u0159sk\u00e9 v\u00fd\u0161ky hladin v\u00a0profilech automaticky uprav\u00ed.<\/p>\n

Zahlouben\u00ed koryta je provedeno na z\u00e1klad\u011b analytick\u00e9 k\u0159ivky. Jedn\u00e1 se o\u00a0dvou-parametrickou k\u0159ivku, jej\u00ed\u017e prohnut\u00ed (schopnost popsat pr\u016fb\u011bh p\u0159\u00ed\u010dn\u00e9ho profilu) z\u00e1le\u017e\u00ed na velikosti jej\u00edch parametr\u016f (obr. 1<\/em>). Parametry jsou ur\u010deny regresn\u00ed rovnic\u00ed na z\u00e1klad\u011b n\u00e1klonu profil\u016f a\u00a0b\u0159ehov\u00fdch vzd\u00e1lenost\u00ed po sob\u011b jdouc\u00edch modelovan\u00fdch p\u0159\u00ed\u010dn\u00fdch profil\u016f. Parametry regresn\u00ed rovnice je mo\u017en\u00e9 v\u00a0programu upravovat a\u00a0t\u00edm pr\u016fb\u011bh p\u0159\u00ed\u010dn\u00e9ho profilu ovliv\u0148ovat. Program tak\u00e9 umo\u017e\u0148uje manu\u00e1ln\u00ed korekci regresn\u00edch parametr\u016f na z\u00e1klad\u011b u\u017eivatelem vlo\u017een\u00e9ho re\u00e1ln\u00e9ho vzorov\u00e9ho profilu. Zahlouben\u00ed je provedeno tak, aby bylo dosa\u017eeno ekvivalentn\u00ed pr\u016fto\u010dn\u00e9 plochy v\u00a0modelovan\u00e9m profilu. Ekvivalentn\u00ed pr\u016fto\u010dn\u00e1 plocha je ur\u010dena v\u00fdpo\u010dtem za vyu\u017eit\u00ed Ch\u00e9zyho rovnice. Pro tento v\u00fdpo\u010det u\u017eivatel zad\u00e1v\u00e1 pr\u016ftok v\u00a0modelovan\u00e9m \u0159\u00ed\u010dn\u00edm \u00faseku a\u00a0Manning\u016fv sou\u010dinitel drsnosti ze dne po\u0159\u00edzen\u00ed dat TOPO. Pod\u00e9ln\u00fd sklon je automaticky ur\u010dov\u00e1n ze vzd\u00e1lenosti a\u00a0rozd\u00edl\u016f nadmo\u0159sk\u00fdch v\u00fd\u0161ek hladin v\u00a0po sob\u011b jdouc\u00edch profilech. Po\u010det bod\u016f, z\u00a0nich\u017e se budou modelovan\u00e9 profily skl\u00e1dat, definuje u\u017eivatel.<\/p>\n

Meziprofilov\u00e1 interpolace<\/h4>\n

Pro vytvo\u0159en\u00ed batymetrie vodn\u00edho toku je nutn\u00e9 prov\u00e9st prostorovou interpolaci mezi modelovan\u00fdmi p\u0159\u00ed\u010dn\u00fdmi profily. Celkov\u00e1 batymetrie vodn\u00edho toku je v\u00a0programu schematizov\u00e1na bodovou 3D s\u00edt\u00ed. Hustota t\u00e9to s\u00edt\u011b z\u00e1vis\u00ed na po\u010dtu bod\u016f v\u00a0modelovan\u00fdch p\u0159\u00ed\u010dn\u00fdch profilech a\u00a0po\u010dtu bod\u016f mezi profily. Oba parametry ur\u010duje u\u017eivatel. Pro vytvo\u0159en\u00ed 3D s\u00edt\u011b z\u00a03D modelovan\u00fdch profil\u016f lze vyu\u017e\u00edt celkem t\u0159i algoritmy pro tvorbu s\u00edt\u00ed (obr. 2<\/em>).<\/p>\n\"\"<\/a>\n

Obr. 2. Interpolace mezi profily
\nFig. 2. Interpolation between cross-sections<\/h6>\n
Tabulka 1. Povod\u0148ov\u00e9 ud\u00e1losti ve studovan\u00e9m \u00faseku
\nTable 1. Flood events in study river reach<\/h5>\n\"\"<\/a>\n

Prvn\u00ed algoritmus (SA1) [17] pou\u017e\u00edv\u00e1 pro pod\u00e9lnou (prostorovou) interpolaci mezi profily line\u00e1rn\u00ed interpola\u010dn\u00ed algoritmus. Ten prov\u00e1d\u00ed interpolaci mezi odpov\u00eddaj\u00edc\u00edmi si body v\u00a0po sob\u011b jdouc\u00edch profilech. To znamen\u00e1, \u017ee nov\u011b vznikl\u00e9 body le\u017e\u00ed na p\u0159\u00edmce mezi v\u00fdchoz\u00edmi body. Pro interpolaci nadmo\u0159sk\u00fdch v\u00fd\u0161ek je pou\u017eita tak\u00e9 line\u00e1rn\u00ed interpolace.<\/p>\n

Druh\u00fd algoritmus (SA2) [18] modelovan\u00fd profil nejd\u0159\u00edve p\u0159evzorkuje. Touto \u00fapravou dojde ke zm\u011bn\u011b rozestupu bod\u016f tak, aby na ob\u011b strany od nejhlub\u0161\u00edho m\u00edsta v\u00a0profilu le\u017eel stejn\u00fd po\u010det bod\u016f. P\u016fvodn\u00ed tvar profilu v\u0161ak z\u016fst\u00e1v\u00e1 zachov\u00e1n. D\u00edky p\u0159evzorkov\u00e1n\u00ed je respektov\u00e1na spojnice m\u00edst s\u00a0nejni\u017e\u0161\u00ed hloubkou v\u00a0profilech. To m\u00e1 za n\u00e1sledek re\u00e1ln\u011bj\u0161\u00ed schematizaci pr\u016fb\u011bhu hloubek mezi profily. Pot\u00e9 je op\u011bt vyu\u017eito line\u00e1rn\u00ed interpolace pro dopo\u010det bod\u016f mezi profily a\u00a0jejich nadmo\u0159sk\u00fdch v\u00fd\u0161ek.<\/p>\n

T\u0159et\u00ed algoritmus (SA3) [19] vyu\u017e\u00edv\u00e1 tak\u00e9 p\u0159evzorkov\u00e1n\u00ed modelovan\u00e9ho profilu a\u00a0nav\u00edc pro prostorov\u00e9 rozm\u00edst\u011bn\u00ed nov\u00fdch bod\u016f mezi profily vyu\u017e\u00edv\u00e1 kubick\u00e9 hermitovsk\u00e9 interpolace (CHS). Nov\u00e9 body tak nevznikaj\u00ed na p\u0159\u00edmkov\u00e9 spojnici, ale jsou interpolov\u00e1ny po obloukov\u00e9 k\u0159ivce. To zaji\u0161\u0165uje v\u011brohodn\u011bj\u0161\u00ed popis koryta mezi modelovan\u00fdmi profily zejm\u00e9na v\u00a0\u0159\u00ed\u010dn\u00edch oblouc\u00edch. Pro interpolaci nadmo\u0159sk\u00fdch v\u00fd\u0161ek je op\u011bt pou\u017eita line\u00e1rn\u00ed interpolace.<\/p>\n

Aplikace softwaru Bathy_supp<\/h2>\n

Pilotn\u00ed \u00fazem\u00ed<\/h3>\n

Jako pilotn\u00ed \u00fazem\u00ed byl vybr\u00e1n \u00fasek \u0159eky Otavy v\u00a0P\u00edsku (obr. 3<\/em>), p\u0159edev\u0161\u00edm z\u00a0d\u016fvodu dostupnosti topografick\u00fdch a\u00a0hydrologick\u00fdch dat (ve studovan\u00e9m \u00faseku se nach\u00e1z\u00ed m\u011brn\u00fd profil \u010d. 127). Vybran\u00fd \u00fasek je 1,65 km dlouh\u00fd a\u00a0je lokalizov\u00e1n v\u00a0\u00faseku mezi 22,83\u201324,48 \u0159\u00ed\u010dn\u00edho kilometru (\u0159. km). \u0160\u00ed\u0159ka toku ve studovan\u00e9m \u00fazem\u00ed se pohybuje mezi 25\u201335 m. Pr\u016fm\u011brn\u00e1 hloubka toku je 0,94\u00a0m. Pr\u016fm\u011brn\u00fd ro\u010dn\u00ed pr\u016ftok je 23,4 m3<\/sup>.s-1<\/sup>. Pr\u016fm\u011brn\u00e1 nadmo\u0159sk\u00e1 v\u00fd\u0161ka hladiny se pohybuje okolo 354,84 m n. m. P\u0159ehled povod\u0148ov\u00fdch ud\u00e1lost\u00ed v\u00a0tomto \u0159\u00ed\u010dn\u00edm \u00faseku je uveden v\u00a0tabulce 1<\/em>. N\u00e1vrhov\u00e9 pr\u016ftoky (QN<\/sub>) pro tento \u00fasek jsou uvedeny v\u00a0tabulce 2<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 3. Z\u00e1jmov\u00e9 \u00fazem\u00ed
\nFig. 3. The area of interest<\/h6>\n
Tabulka 2. N\u00e1vrhov\u00e9 pr\u016ftoky QN
\n<\/sub>Table 2. N-year flow discharges<\/h5>\n

 <\/p>\n\"\"<\/a>\n

Vstupn\u00ed data<\/h3>\n

Data TOPO poch\u00e1z\u00ed z\u00a0digit\u00e1ln\u00edho modelu reli\u00e9fu 5. generace (DMR 5G), kter\u00fd p\u0159edstavuje zobrazen\u00ed p\u0159irozen\u00e9ho nebo lidskou \u010dinnost\u00ed upraven\u00e9ho zemsk\u00e9ho povrchu [20]. Data DMR 5G jsou standardn\u011b dod\u00e1v\u00e1na v\u00a0po\u017eadovan\u00e9m form\u00e1tu s\u00a0koncovkou \u201e*.xyz\u201c. Data byla po\u0159\u00edzena dne 18. 4. 2011 ve 13:00 hod. Pr\u016ftok v\u00a0\u0159ece Otav\u011b v\u00a0tuto dobu byl 36,8 m3<\/sup>.s-1<\/sup>. Hodnota Manningova drsnostn\u00edho sou\u010dinitele (0,025 s.m-1\/3<\/sup>) byla zji\u0161t\u011bna kalibrac\u00ed hydrodynamick\u00e9ho modelu se zam\u011b\u0159enou topografi\u00ed.<\/p>\n

Tvorba DMT pro hydrodynamick\u00e9 modelov\u00e1n\u00ed<\/h3>\n

Na z\u00e1klad\u011b vstupn\u00edch dat byl programem Bathy_supp proveden v\u00fdpo\u010det t\u0159\u00ed batymetrick\u00fdch s\u00edt\u00ed (SA1\u2013SA3), kter\u00e9 byly v\u00a0prost\u0159ed\u00ed ArcGIS spojeny s\u00a0daty DMR\u00a05G. N\u00e1sledn\u011b byly vytvo\u0159eny celistv\u00e9 modely ter\u00e9nu, kde batymetrick\u00e9 s\u00edt\u011b popisuj\u00ed prostor v\u00a0koryt\u011b \u0159eky a\u00a0DMR 5G definuje jej\u00ed \u0161irok\u00e9 okol\u00ed. Celkov\u011b bylo vytvo\u0159eno p\u011bt model\u016f ter\u00e9nu (viz obr. 4<\/em>). Model ADCP, kter\u00fd byl vytvo\u0159en synt\u00e9zou re\u00e1ln\u00e9ho zam\u011b\u0159en\u00ed koryta toku pomoc\u00ed p\u0159\u00edstroje RiverSurveyor M9 a\u00a0dat DMR 5G, byl s\u00a0ohledem na svou p\u0159esnost zvolen jako referen\u010dn\u00ed. Model 5G byl vytvo\u0159en pouze na z\u00e1klad\u011b dat DMR 5G a\u00a0neobsahoval \u017e\u00e1dn\u00e9 dodate\u010dn\u00e9 informace o\u00a0batymetrii koryta. Modely S1, S2 a\u00a0S3 byly vytvo\u0159eny na z\u00e1klad\u011b synt\u00e9zy p\u0159\u00edslu\u0161n\u00e9 batymetrick\u00e9 s\u00edt\u011b (SA1, SA2 a\u00a0SA3) s\u00a0daty DMR 5G. Odhad p\u0159\u00ed\u010dn\u00fdch profil\u016f pro tvorbu batymetrick\u00fdch s\u00edt\u00ed SA1\u2013SA3 byl toto\u017en\u00fd.<\/p>\n\"\"<\/a>\n

Obr. 4. P\u0159\u00ed\u010dn\u00e9 \u0159ezy ter\u00e9nem; \u010d\u00e1st A\u00a0\u2013 \u0159ez v\u00a0rovn\u00e9m \u00faseku \u0159eky; \u010d\u00e1st B\u00a0\u2013 \u0159ez v\u00a0\u0159\u00ed\u010dn\u00edm oblouku
\nFig. 4. Cross-sectional cuts; part A, cut in the straight section of the river; part B, cut in the river arc<\/h6>\n

Hydrodynamick\u00e9 modelov\u00e1n\u00ed<\/h3>\n

Pro hodnocen\u00ed DMT z\u00a0hlediska hydrodynamick\u00e9ho modelov\u00e1n\u00ed byl pou\u017eit 1D model HEC-RAS, kter\u00fd byl pou\u017eit v\u00a0mnoha studi\u00edch hodnot\u00edc\u00edch vliv r\u016fzn\u00fdch zdroj\u016f topografick\u00fdch dat na stanoven\u00ed inunda\u010dn\u00edch \u00fazem\u00ed [5, 21\u201324].<\/p>\n

Hydrodynamick\u00e9 simulace proveden\u00e9 v\u00a0t\u00e9to studii se li\u0161\u00ed pouze topografick\u00fdm zdrojem dat (5G, S1, S2, S3). Na sestaven\u00ed \u0159\u00ed\u010dn\u00ed geometrie model\u016f bylo pou\u017eito 24 p\u0159\u00ed\u010dn\u00fdch profil\u016f. Manning\u016fv koeficient pro koryto \u0159eky byl nastaven na 0,025 s.m-1\/3<\/sup>. Zvolen\u00e9 hodnoty Manningova koeficientu byly zji\u0161t\u011bny kalibrac\u00ed modelu na pr\u016ftok bl\u00edzk\u00fd hodnot\u011b Q100<\/sub>. Jednalo se o\u00a0pr\u016ftok z\u00a09. 7. 1954, jeho\u017e hodnota byla 800 m3<\/sup>.s-1 <\/sup>(tabulka 1<\/em>). N-let\u00e9 n\u00e1vrhov\u00e9 pr\u016ftoky (Q5<\/sub>, Q50<\/sub> a\u00a0Q100<\/sub>) byly pou\u017eity jako horn\u00ed okrajov\u00e9 podm\u00ednky. Kritick\u00e1 hloubka byla pou\u017eita jako doln\u00ed okrajov\u00e1 podm\u00ednka. V\u00a0t\u00e9to studii byly v\u0161echny simulace vypo\u010dteny v\u00a0re\u017eimu ust\u00e1len\u00e9ho nerovnom\u011brn\u00e9ho proud\u011bn\u00ed [25, 26].<\/p>\n

V\u00fdsledky vypo\u010dten\u00e9 hydrodynamick\u00fdm modelem byly n\u00e1sledn\u011b zpracov\u00e1ny v\u00a0programu ArcGIS za pomoc\u00ed extenze HEC-GeoRAS, odkud byly exportov\u00e1ny hodnoty pro porovn\u00e1n\u00ed polohy hladiny (viz kap. Porovn\u00e1n\u00ed polohy hladiny) a\u00a0velikosti inunda\u010dn\u00ed oblasti (viz kap. Porovn\u00e1n\u00ed velikosti inunda\u010dn\u00ed oblasti) [27].<\/p>\n

Vyhodnocen\u00ed kvality DMT<\/h3>\n

Kvalita v\u00fdsledn\u00fdch DMT byla hodnocena formou detekce vertik\u00e1ln\u00edch rozd\u00edl\u016f mezi testovan\u00fdmi a\u00a0referen\u010dn\u00edm DMT. Jako referen\u010dn\u00ed DMT byl zvolen ADCP z\u00a0d\u016fvodu garance p\u0159esnosti jeho zdrojov\u00fdch dat. Pro hodnocen\u00ed byly pou\u017eity dv\u011b metody v\u00fdsledn\u00fdch DMT, jednou z\u00a0nich bylo porovn\u00e1n\u00ed p\u0159\u00ed\u010dn\u00fdch pr\u016f\u0159ez\u016f, druhou pak porovn\u00e1n\u00ed pod\u00e9ln\u00e9ho profilu dna v\u00a0ose toku. Pro porovn\u00e1n\u00ed p\u0159\u00ed\u010dn\u00fdch pr\u016f\u0159ez\u016f bylo zvoleno 29 srovn\u00e1vac\u00edch \u0159ez\u016f, kter\u00e9 byly n\u00e1hodn\u011b rozm\u00edst\u011bny v\u00a0modelovan\u00e9 oblasti. Um\u00edst\u011bn\u00ed t\u011bchto \u0159ez\u016f bylo identick\u00e9 pro v\u0161echny hodnocen\u00e9 DMT. St\u0159edn\u00ed kvadratick\u00e1 chyba (RMSE) a\u00a0st\u0159edn\u00ed absolutn\u00ed chyba (MAE) byly pou\u017eity p\u0159i hodnocen\u00ed kvality DMT. Rovnice pro tato krit\u00e9ria hodnocen\u00ed jsou n\u00e1sleduj\u00edc\u00ed:\u00a0\u00a0 \"\"<\/a> \"\"<\/a><\/p>\n\n\n\n\n\n
kde<\/td>\nElevDMT<\/sub><\/td>\nje<\/td>\nhodnota nadmo\u0159sk\u00e9 v\u00fd\u0161ky (m) odvozen\u00e1 z\u00a0model\u016f 5G, S1, S2 a\u00a0S3,<\/td>\n<\/tr>\n
<\/td>\nElevREF<\/sub><\/td>\n<\/td>\nodpov\u00eddaj\u00edc\u00ed referen\u010dn\u00ed hodnota odvozen\u00e1 z\u00a0modelu ADCP,<\/td>\n<\/tr>\n
<\/td>\nN<\/td>\n<\/td>\npo\u010det bod\u016f definuj\u00edc\u00edch dan\u00fd pr\u016f\u0159ez nebo osu toku.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Vyhodnocen\u00ed vlivu vstupn\u00edch dat DMT p\u0159i hydrodynamick\u00e9m modelov\u00e1n\u00ed<\/h3>\n

Za \u00fa\u010delem vyhodnocen\u00ed vlivu dat DMT byla zkoum\u00e1na rozloha inunda\u010dn\u00ed oblasti (IA) a\u00a0nadmo\u0159sk\u00e9 v\u00fd\u0161ky hladin (WSE).<\/p>\n

Pou\u017eit\u00e9 hodnot\u00edc\u00ed krit\u00e9rium rozsahu inunda\u010dn\u00ed oblasti (IA):<\/p>\n

 <\/p>\n\"\"<\/a>\n

 <\/p>\n\n\n\n\n\n
kde<\/td>\nIAdif<\/sub><\/td>\nje<\/td>\nrozd\u00edl v\u00a0rozsahu inunda\u010dn\u00edch ploch v\u00a0procentech,<\/td>\n<\/tr>\n
<\/td>\nIADEM<\/sub><\/td>\n<\/td>\ninunda\u010dn\u00ed plocha (km2<\/sup>) produkovan\u00e1 v\u00fdstupn\u00edmi DMT,<\/td>\n<\/tr>\n
<\/td>\nIAREF<\/sub><\/td>\n<\/td>\nreferen\u010dn\u00ed (ADCP) inunda\u010dn\u00ed plocha (km2<\/sup>).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

IA a\u00a0WSE byly hodnoceny pro N-let\u00e9 pr\u016ftoky Q5<\/sub>, Q50<\/sub> a\u00a0Q100<\/sub>. Pro toto hodnocen\u00ed byl pou\u017eit stejn\u00fd p\u0159\u00edstup, jako je pops\u00e1n v\u00a0kapitole Hydrodynamick\u00e9 modelov\u00e1n\u00ed. Model ADCP byl op\u011bt zvolen jako zdroj referen\u010dn\u00edch \u00fadaj\u016f. Chyba WSE byla hodnocena pomoc\u00ed rovnic 1 a\u00a02.<\/p>\n

V\u00fdsledky<\/h2>\n

Program Bathy_supp na z\u00e1klad\u011b u\u017eivatelem definovan\u00e9 geometrie vodn\u00edho toku nejprve odhaduje p\u0159\u00ed\u010dn\u00e9 profily a\u00a0z\u00a0nich je n\u00e1sledn\u011b tvo\u0159ena batymetrick\u00e1 s\u00ed\u0165. Ta je n\u00e1sledn\u011b spojena s\u00a0daty TOPO a\u00a0je vytvo\u0159en v\u00fdsledn\u00fd DMT.<\/p>\n

Shoda v\u00a0p\u0159\u00ed\u010dn\u00fdch profilech<\/h3>\n

Vizu\u00e1ln\u00ed porovn\u00e1n\u00ed pr\u016f\u0159ez\u016f odvozen\u00fdch z\u00a0hodnocen\u00fdch DMT je uvedeno na obr. 4<\/em>. \u010c\u00e1st A\u00a0ukazuje p\u0159\u00ed\u010dn\u00fd \u0159ez ter\u00e9nem v\u00a0rovn\u00e9m \u00faseku \u0159eky. Modely S1\u2013S3 zde vykazuj\u00ed podobn\u00e9 v\u00fdsledky bl\u00edzk\u00e9 referen\u010dn\u00edmu modelu ADCP. Model 5G vykazuje z\u00e1sadn\u00ed odch\u00fdlen\u00ed. V\u00a0\u010d\u00e1sti B je vyobrazen p\u0159\u00ed\u010dn\u00fd \u0159ez \u0159\u00ed\u010dn\u00edm obloukem. Modely S1\u2013S3 vykazuj\u00ed tvarovou podobnost, ale modely S1 a\u00a0S2 jsou vych\u00fdleny mimo osu toku. Model 5G op\u011bt vykazuje zanedb\u00e1n\u00ed velk\u00e9 \u010d\u00e1sti koryta toku.<\/p>\n

Obr\u00e1zek 5<\/em> popisuje rozptyl v\u00a0hodnot\u00e1ch RMSE a\u00a0MAE dosa\u017een\u00fdch pro v\u0161echny srovn\u00e1vac\u00ed pr\u016f\u0159ezy. Z\u00a0v\u00fdsledk\u016f vypl\u00fdv\u00e1, \u017ee chyby model\u016f S1, S2 a\u00a0S3 jsou srovnateln\u00e9. Model 5G se od ostatn\u00edch model\u016f op\u011bt v\u00fdrazn\u011b li\u0161\u00ed. Jak je patrn\u00e9 z\u00a0tabulky 3<\/em>, celkov\u00e1 hodnota RMSE modelu 5G byla 0,96 m. Pro S1, S2 a\u00a0S3 to bylo 0,44 m, 0,43 m a\u00a00,34 m. Celkov\u00e1 hodnota MAE modelu 5G byla 0,68 m, zat\u00edmco hodnoty S1, S2 a\u00a0S3 byly 0,25 m, 0,25 m a\u00a00,2 m. Z\u00a0v\u00fdsledk\u016f je patrn\u00e9, \u017ee nejmen\u0161\u00edch chyb dosahoval model S3.<\/p>\n\"\"<\/a>\n

Obr. 5. Rozptyl hodnot st\u0159edn\u00ed kvadratick\u00e9 chyby (RMSE) a\u00a0st\u0159edn\u00ed absolutn\u00ed chyby (MAE) p\u0159i porovn\u00e1v\u00e1n\u00ed pr\u016f\u0159ez\u016f
\nFig. 5. Variance of root mean square error (RMSE) and mean absolute error (MAE) values when comparing cross-sections<\/h6>\n

Hloubka dna v\u00a0ose koryta<\/h3>\n

Vizu\u00e1ln\u00ed srovn\u00e1n\u00ed \u0159ez\u016f veden\u00fdch osou vodn\u00edho toku (pod\u00e9ln\u00fd profil) je zn\u00e1zorn\u011bno na obr. 6<\/em> a\u00a0posouzen\u00ed shody je uvedeno v\u00a0tabulce 4<\/em>. Hodnota RMSE pro model 5G byla 1,50 m. Hodnoty RMSE pro modelovan\u00e9 s\u00edt\u011b S1, S2 a\u00a0S3 byly 0,44\u00a0m, 0,45 m a\u00a00,44 m. Hodnota MAE pro model 5G byla 1,47 m a\u00a0pro modelovan\u00e9 s\u00edt\u011b S1, S2 a\u00a0S3 0,34 m, 0,34 m a\u00a00,35 m. Z\u00a0v\u00fdsledk\u016f je patrn\u00e9, \u017ee modely S1, S2 a\u00a0S3 vykazovaly srovnateln\u00e9 chyby, kter\u00e9 v\u0161ak byly v\u00fdrazn\u011b ni\u017e\u0161\u00ed ne\u017e chyby modelu 5G.<\/p>\n\"\"<\/a>\n

Obr. 6. Srovn\u00e1n\u00ed \u0159ez\u016f v\u00a0ose koryta
\nFig. 6. Comparison of cuts in the channel axis<\/h6>\n

Porovn\u00e1n\u00ed polohy hladiny<\/h3>\n

Obr\u00e1zek 7<\/em> popisuje odchylky v\u00a0rozd\u00edlech WSE mezi srovn\u00e1van\u00fdmi DMT (5G, S1, S2, S3) a\u00a0referen\u010dn\u00edmi DMT. V\u00fdsledky ukazuj\u00ed, \u017ee nejhor\u0161\u00edho v\u00fdsledku bylo dosa\u017eeno modelem 5G a\u00a0\u017ee variabilita v\u00a0rozd\u00edlech WSE se u\u00a0tohoto modelu s\u00a0rostouc\u00edm pr\u016ftokem zvy\u0161uje. Nejlep\u0161\u00ed medi\u00e1nov\u00e1 hodnota a\u00a0nejni\u017e\u0161\u00ed variabilita u\u00a0WSE byla poskytnuta modelem S3, kter\u00fd dosahuje nejlep\u0161\u00edch v\u00fdsledk\u016f bez ohledu na modelovan\u00fd pr\u016ftok. Posouzen\u00ed velikosti chyb z\u00a0porovn\u00e1n\u00ed vypo\u010dten\u00e9 v\u00fd\u0161ky hladiny je uvedeno v\u00a0tabulce 5<\/em>.<\/p>\n\"\"<\/a>\n

Obr. 7. Porovn\u00e1n\u00ed WSE v\u00a0ose koryta
\nFig. 7. Comparison of WSE in the channel axis<\/h6>\n

Porovn\u00e1n\u00ed velikosti inunda\u010dn\u00ed oblasti<\/h3>\n

V\u00fdsledky porovn\u00e1n\u00ed IA jsou uvedeny v\u00a0tabulce 6<\/em>. Ve v\u0161ech p\u0159\u00edpadech model v\u00fdznamn\u011b nadhodnocuje rozsah IA. Pro pr\u016ftoky Q50<\/sub> bylo toto nadhodnocen\u00ed a\u017e o\u00a0t\u00e9m\u011b\u0159 15 %. Zbyl\u00e9 modely v\u00fdsledky m\u00edrn\u011b podhodnocovaly. Srovnateln\u00fdch v\u00fdsledk\u016f dos\u00e1hly modely S1 a\u00a0S2, kter\u00e9 podhodnocovaly s\u00a0chybou men\u0161\u00ed ne\u017e 5 %. Nejlep\u0161\u00edch v\u00fdsledk\u016f dos\u00e1hl model S3, jeho\u017e maxim\u00e1ln\u00ed chyba byla men\u0161\u00ed ne\u017e 2 %.<\/p>\n

Diskuse<\/h2>\n

Prezentovan\u00fd postup pro matematick\u00fd odhad \u0159\u00ed\u010dn\u00ed batymetrie vy\u017eaduje posouzen\u00ed nejistot spojen\u00fdch s\u00a0dan\u00fdmi p\u0159\u00edstupy. Podobn\u00e9 posouzen\u00ed vy\u017eaduje i\u00a0n\u00e1sledn\u00e1 synt\u00e9za vypo\u010dten\u00e9 \u0159\u00ed\u010dn\u00ed batymetrie s\u00a0daty TOPO a\u00a0celkov\u00e1 tvorba v\u00fdsledn\u00e9ho DMT ur\u010den\u00e9ho pro hydrodynamick\u00e9 modelov\u00e1n\u00ed.<\/p>\n

V\u00fdsledn\u00e1 p\u0159esnost p\u0159i ur\u010den\u00ed batymetrie je prim\u00e1rn\u011b z\u00e1visl\u00e1 na p\u0159esnosti vstupn\u00edch dat TOPO, kter\u00e1 definuj\u00ed v\u00fd\u0161kovou p\u0159esnost p\u0159ilehl\u00fdch inunda\u010dn\u00edch \u00fazem\u00ed. Na \u00fazem\u00ed \u010cR jsou v\u00a0sou\u010dasnosti standardn\u011b dostupn\u00e1 data TOPO z\u00edskan\u00e1 metodou LLS ve form\u011b DMR 5G. Deklarovan\u00e1 \u00fapln\u00e1 st\u0159edn\u00ed chyba t\u011bchto dat je 0,18 m pro vertik\u00e1ln\u00ed p\u0159esnost v\u00a0otev\u0159en\u00e9m ter\u00e9nu a\u00a00,30 m v\u00a0zalesn\u011bn\u00e9m ter\u00e9nu [29]. Poloha hladiny ur\u010den\u00e1 pro zahlouben\u00ed koryta toku zat\u00ed\u017eena touto chybou zan\u00e1\u0161\u00ed stejnou nejistotu i\u00a0do p\u0159esnosti ur\u010den\u00ed dna v\u00a0koryt\u011b toku. P\u0159i pou\u017eit\u00ed jin\u00fdch zdroj\u016f vstupn\u00edch dat, jako jsou nap\u0159\u00edklad dru\u017eicov\u00e1 data, se m\u016f\u017ee tato nejistota li\u0161it v\u00a0z\u00e1vislosti na pou\u017eit\u00e9 technologii sn\u00edm\u00e1n\u00ed zemsk\u00e9ho povrchu. Lze ale p\u0159edpokl\u00e1dat, \u017ee s\u00a0technologick\u00fdm pokrokem bude doch\u00e1zet\u00a0ke zp\u0159es\u0148ov\u00e1n\u00ed metod pro sn\u00edm\u00e1n\u00ed zemsk\u00e9ho povrchu a\u00a0t\u00edm i\u00a0k\u00a0postupn\u00e9mu sni\u017eov\u00e1n\u00ed t\u00e9to nejistoty. Nicm\u00e9n\u011b data TOPO z\u00edskan\u00e1 metodou LLS jsou v\u00a0sou\u010dasn\u00e9 dob\u011b hojn\u011b vyu\u017e\u00edv\u00e1na jako velmi p\u0159esn\u00fd zdroj topografick\u00fdch dat pro hydrodynamick\u00e9 modelov\u00e1n\u00ed [16\u201319, 26].<\/p>\n

Tabulka 3. Hodnoty st\u0159edn\u00edch kvadratick\u00fdch chyb (RMSE) a\u00a0st\u0159edn\u00edch absolutn\u00edch chyb (MAE) pro porovn\u00e1van\u00e9 modely DMT (srovn\u00e1n\u00ed pr\u016f\u0159ez\u016f)
\nTable 3. Root mean square error (RMSE) and mean absolute error (MAE) values for the compared DEMs (cross-sectional comparison)<\/h5>\n\"\"<\/a>\n

Na obr. 6<\/em> jsou vid\u011bt ve stani\u010den\u00ed cca 600 a\u00a0cca 1 600 dv\u011b m\u00edsta s\u00a0v\u00fdrazn\u00fdm odch\u00fdlen\u00edm dna od re\u00e1ln\u00e9ho pr\u016fb\u011bhu. Tyto odchylky mohou b\u00fdt zp\u016fsobeny pr\u00e1v\u011b ur\u010den\u00edm sklonu hladiny, kter\u00fd je vypo\u010d\u00edt\u00e1v\u00e1n z\u00a0pou\u017eit\u00fdch dat TOPO. Ur\u010den\u00ed \u0161patn\u00e9ho sklonu \u010d\u00e1ry energie m\u00e1 za n\u00e1sledek nespr\u00e1vn\u00fd v\u00fdpo\u010det pr\u016fto\u010dn\u00e9 plochy dan\u00e9ho profilu Ch\u00e9zyho rovnic\u00ed, tj. ust\u00e1len\u00fdm rovnom\u011brn\u00fdm proud\u011bn\u00edm. Software pak nadm\u011brn\u011b, nebo naopak nedostate\u010dn\u011b zahloub\u00ed modelovan\u00e9 koryto.<\/p>\n

Koeficienty regresn\u00ed rovnice jsou \u00fazce spjaty s\u00a0charakterem modelovan\u00e9ho toku. Pro u\u017eivatele jsou tyto koeficienty nezn\u00e1m\u00e9, a\u00a0proto je nutn\u00e9 je odhadovat na z\u00e1klad\u011b podobnosti tok\u016f. Pro n\u011bkolik r\u016fzn\u00fdch typ\u016f tok\u016f jsou v\u00a0softwaru tyto regresn\u00ed koeficienty i\u00a0s\u00a0fotodokumentac\u00ed uvedeny. Nejistota v\u00a0ur\u010den\u00ed regresn\u00edch koeficient\u016f je p\u0159edm\u011btem navazuj\u00edc\u00edho v\u00fdzkumu.<\/p>\n

Tabulka 4. Hodnoty st\u0159edn\u00edch kvadratick\u00fdch chyb (RMSE) a\u00a0st\u0159edn\u00edch absolutn\u00edch chyb (MAE) pro porovn\u00e1van\u00e9 DMT (srovn\u00e1n\u00ed \u0159ez\u016f v\u00a0ose toku)
\nTable 4. Root mean square error (RMSE) and mean absolute error (MAE) values for the compared DEMs (channel axis comparison)<\/h5>\n\"\"<\/a>\n

Zji\u0161t\u011bn\u00ed pr\u016ftok\u016f pot\u0159ebn\u00fdch pro v\u00fdpo\u010det batymetrick\u00e9 s\u00edt\u011b zaji\u0161\u0165uje p\u0159edev\u0161\u00edm s\u00ed\u0165 hydrografick\u00fdch stanic na v\u00fdznamn\u00fdch vodn\u00edch toc\u00edch. Pro ur\u010den\u00ed pr\u016ftok\u016f u\u00a0nepozorovan\u00fdch vodn\u00edch tok\u016f m\u016f\u017ee b\u00fdt vyu\u017eito metody hydrologick\u00e9 analogie. Je ot\u00e1zkou, zda nep\u0159esnosti t\u00e9to metody u\u00a0st\u0159edn\u00ed velikosti tok\u016f mohou v\u00fdrazn\u011b ovlivnit v\u00fdsledky hydrodynamick\u00e9ho modelov\u00e1n\u00ed, p\u0159i kter\u00e9m jsou modelovan\u00e9 pr\u016ftoky zpravidla vy\u0161\u0161\u00ed i\u00a0o\u00a0n\u011bkolik \u0159\u00e1d\u016f. Pou\u017eit\u00ed hydrologick\u00e9 analogie u\u00a0mal\u00fdch vodn\u00edch tok\u016f m\u016f\u017ee zan\u00e1\u0161et ji\u017e zna\u010dnou chybu.<\/p>\n

Tabulka 5. Chyby ve v\u00fd\u0161ce hladin (WSE) p\u0159i pou\u017eit\u00ed vybran\u00fdch digit\u00e1ln\u00edch model\u016f ter\u00e9nu (DMT) v\u00a0porovn\u00e1n\u00ed s\u00a0referen\u010dn\u00edm DMT pro vybran\u00e9 N-let\u00e9 pr\u016ftoky
\nTable 5. Water surface elevation (WSE) errors when usings elected digital elevation models (DEMs) compared to the reference DEM for the chosen N\u2013year flow rates<\/h5>\n\"\"<\/a>\n

Volba metody schematizace \u0159\u00ed\u010dn\u00edho koryta m\u016f\u017ee zna\u010dn\u011b ovliv\u0148ovat celkovou kvalitu v\u00fdsledk\u016f. P\u0159i nevhodn\u00e9m rozm\u00edst\u011bn\u00ed virtu\u00e1ln\u00edch p\u0159\u00ed\u010dn\u00fdch profil\u016f m\u016f\u017ee doch\u00e1zet k\u00a0tomu, \u017ee modelovan\u00e9 koryto m\u016f\u017ee b\u00fdt, zejm\u00e9na v\u00a0\u0159\u00ed\u010dn\u00edch oblouc\u00edch, vedeno p\u0159\u00edb\u0159e\u017en\u00ed z\u00f3nou nam\u00edsto v\u00a0prostoru re\u00e1ln\u00e9ho koryta. Tento p\u0159\u00edpad je zn\u00e1zorn\u011bn na obr. 4, \u010d\u00e1st B<\/em>. Jedn\u00e1 se o\u00a0jev typick\u00fd pro s\u00edt\u011b SA1 a\u00a0SA2 (obr. 2<\/em>), co\u017e je d\u00e1no vyu\u017eit\u00edm line\u00e1rn\u00ed interpolace mezi jednotliv\u00fdmi profily. Tato zkreslen\u00ed lze eliminovat zejm\u00e9na vhodn\u00fdm rozm\u00edst\u011bn\u00edm profil\u016f a\u00a0redukc\u00ed jejich vzd\u00e1lenost\u00ed.<\/p>\n

Tabulka 6. Plochy inunda\u010dn\u00edch oblast\u00ed a\u00a0jejich rozd\u00edly od referen\u010dn\u00ed hodnoty vypo\u010dten\u00e9 hydrodynamick\u00fdm modelem pro vybran\u00e9 N-let\u00e9 pr\u016ftoky
\nTable 6. Inundation areas and their differences from the reference value calculated by the hydrodynamic model for selected N-year flows<\/h5>\n\"\"<\/a>\n

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

C\u00edlem p\u0159\u00edsp\u011bvku je p\u0159edstaven\u00ed nov\u00fdch mo\u017enost\u00ed matematick\u00e9 schematizace re\u00e1ln\u00e9ho tvaru koryta vodn\u00edho toku. Metoda je zalo\u017eena na matematick\u00e9m odhadu re\u00e1ln\u00e9ho vzhledu p\u0159\u00ed\u010dn\u00fdch profil\u016f a\u00a0n\u00e1sledn\u00e9m vytvo\u0159en\u00ed batymetrick\u00e9 s\u00edt\u011b cel\u00e9ho \u0159\u00ed\u010dn\u00edho \u00faseku. Metoda vyu\u017e\u00edv\u00e1 p\u0159i tvorb\u011b celistv\u00e9ho DMT synt\u00e9zy dat TOPO s\u00a0hydrologick\u00fdmi daty (pr\u016ftok a\u00a0drsnost koryta v\u00a0dob\u011b sn\u00edmkov\u00e1n\u00ed dat LLS).<\/p>\n

Prezentovan\u00e9 v\u00fdsledky ukazuj\u00ed, \u017ee tvorba batymetrie koryta vodn\u00edho toku pomoc\u00ed softwaru Bathy_supp p\u0159in\u00e1\u0161\u00ed nov\u00e9 mo\u017enosti a\u00a0v\u00fdrazn\u00e9 zjednodu\u0161en\u00ed procesu p\u0159\u00edpravy DMT pro navazuj\u00edc\u00ed hydrodynamick\u00e9 modelov\u00e1n\u00ed.<\/p>\n

Pro hodnocen\u00ed nejistoty vstupn\u00edch veli\u010din softwaru Bathy_supp byly zpracov\u00e1ny citlivostn\u00ed anal\u00fdzy vlivu jednotliv\u00fdch parametr\u016f na spolehlivost ur\u010den\u00ed tvaru a\u00a0pr\u016fto\u010dn\u00e9 plochy modelovan\u00fdch p\u0159\u00ed\u010dn\u00fdch profil\u016f. V\u00fdsledky t\u011bchto anal\u00fdz ukazuj\u00ed, \u017ee p\u0159edlo\u017een\u00fd p\u0159\u00edstup p\u0159in\u00e1\u0161\u00ed v\u00fdrazn\u00e9 zp\u0159esn\u011bn\u00ed v\u00fdsledn\u00e9ho modelu ter\u00e9nu pou\u017eit\u00e9ho pro samotn\u00e9 hydrodynamick\u00e9 modelov\u00e1n\u00ed povod\u0148ov\u00fdch sc\u00e9n\u00e1\u0159\u016f. Zpracov\u00e1n\u00ed rozs\u00e1hl\u00e9 citlivostn\u00ed anal\u00fdzy bude p\u0159edm\u011btem navazuj\u00edc\u00ed publika\u010dn\u00ed \u010dinnosti.<\/p>\n

V\u00fdhodou dan\u00e9ho p\u0159\u00edstupu je jeho celosv\u011btov\u00e1 aplikovatelnost. P\u0159\u00edstup nen\u00ed omezen pouze na vyu\u017eit\u00ed dat LLS jako vstupu, ale i\u00a0ostatn\u00edch dat d\u00e1lkov\u00e9ho sn\u00edm\u00e1n\u00ed zem\u011b. D\u00edky tomu m\u016f\u017ee b\u00fdt vyu\u017eit i\u00a0v\u00a0m\u00edstech, kde prob\u00edh\u00e1 pouze satelitn\u00ed sn\u00edm\u00e1n\u00ed povrchu. Jedinou podm\u00ednkou je dostate\u010dn\u00e1 hustota topografick\u00fdch bodov\u00fdch dat pro model Bathy_supp.<\/p>\n

Auto\u0159i si uv\u011bdomuj\u00ed, \u017ee p\u0159esnost popsan\u00e9ho zp\u016fsobu tvorby \u0159\u00ed\u010dn\u00ed batymetrie m\u00e1 sv\u00e1 omezen\u00ed. Hlavn\u00edm omezen\u00edm je nejistota v\u00a0ur\u010den\u00ed v\u00fd\u0161ky hladiny a\u00a0jej\u00edho sklonu ve virtu\u00e1ln\u00edch p\u0159\u00ed\u010dn\u00fdch profilech. Ta je z\u00e1visl\u00e1 na deklarovan\u00e9 p\u0159esnosti dat LLS. Stejnou nejistotou je zat\u00ed\u017een i\u00a0parametr sklonu pro Ch\u00e9zyho rovnici. Lze ale p\u0159edpokl\u00e1dat, \u017ee s\u00a0technologick\u00fdm rozvojem metod pro sn\u00edm\u00e1n\u00ed zemsk\u00e9ho povrchu bude doch\u00e1zet ke sni\u017eov\u00e1n\u00ed t\u00e9to chyby.<\/p>\n

Pod\u011bkov\u00e1n\u00ed<\/h3>\n

Tento p\u0159\u00edsp\u011bvek vznikl za podpory Technologick\u00e9 agentury \u010cR, projektu \u010d\u00edslo TJ01000132 Pokro\u010dil\u00e9 zpracov\u00e1n\u00ed dat leteck\u00e9ho laserov\u00e9ho skenov\u00e1n\u00ed za \u00fa\u010delem schematizace vodn\u00edch tok\u016f pro pot\u0159eby matematick\u00e9ho modelov\u00e1n\u00ed.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Topografick\u00e9 \u00fadaje hraj\u00ed kl\u00ed\u010dovou roli v ot\u00e1zce p\u0159esn\u00e9ho hydrodynamick\u00e9ho modelov\u00e1n\u00ed povod\u0148ov\u00fdch ud\u00e1lost\u00ed. \u010casto je vy\u017eadov\u00e1n p\u0159esn\u00fd digit\u00e1ln\u00ed model ter\u00e9nu (DMT), kter\u00fd obsahuje popis \u0159\u00ed\u010dn\u00ed batymetrie. DMT m\u016f\u017ee b\u00fdt z\u00edsk\u00e1n z r\u016fzn\u00fdch zdroj\u016f dat, jako jsou pozemn\u00ed m\u011b\u0159en\u00ed nebo metody d\u00e1lkov\u00e9ho pr\u016fzkumu zem\u011b. <\/p>\n","protected":false},"author":8,"featured_media":6471,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86,88],"tags":[1594,906,1593,1592,513,839],"coauthors":[1578,1579,1580,1409,1581,1414],"class_list":["post-6522","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydraulics-hydrology-and-hydrogeology","category-informatics-cartography-in-water-management","tag-batymetrie","tag-digitalni-model-terenu","tag-hydrodynamicky-model","tag-letecke-laserove-skenovani","tag-povodne","tag-vodni-tok"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/6522","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=6522"}],"version-history":[{"count":4,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/6522\/revisions"}],"predecessor-version":[{"id":30521,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/6522\/revisions\/30521"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/6471"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=6522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=6522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=6522"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=6522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}