{"id":4663,"date":"2018-04-11T10:16:29","date_gmt":"2018-04-11T09:16:29","guid":{"rendered":"https:\/\/www.vtei.cz\/?p=4663"},"modified":"2024-07-16T14:19:29","modified_gmt":"2024-07-16T13:19:29","slug":"information-about-oram","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2018\/04\/information-about-oram\/","title":{"rendered":"Information about ORAM"},"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

Odra River Alarm Modul (ORAM) bude sou\u010d\u00e1st\u00ed projektu NAVAROSO. V\u00a0posledn\u00edch dvaceti letech nejsou k\u00a0dispozici \u017e\u00e1dn\u00e9 v\u00fdsledky ze stopovac\u00edch pokus\u016f \u010desk\u00e9 \u010d\u00e1sti \u0159eky Odry. Z\u00a0toho d\u016fvodu byly pro anal\u00fdzu pou\u017eity v\u00fdsledky ze stopovac\u00edch pokus\u016f na \u0159ece Svitav\u011b. Tento \u010dl\u00e1nek je specificky zam\u011b\u0159en na anal\u00fdzu p\u011bti pr\u016fnikov\u00fdch k\u0159ivek. Nejlep\u0161\u00ed aproximace pr\u016fnikov\u00e9 k\u0159ivky ve v\u0161ech p\u011bti p\u0159\u00edpadech byla d\u00e1na rovnic\u00ed (5) \u2013 Pearsonov\u00fdm rozd\u011blen\u00edm III. typu. Po\u010d\u00edt\u00e1 se s\u00a0t\u00edm, \u017ee v\u00fdsledky anal\u00fdzy budou pou\u017eity p\u0159i tvorb\u011b ORAM.<\/p>\n\"\"<\/a>\n

\u00davod<\/h2>\n

Pro modelov\u00e1n\u00ed \u0161\u00ed\u0159en\u00ed havarijn\u00edho zne\u010di\u0161t\u011bn\u00ed v\u00a0toc\u00edch se obvykle pou\u017e\u00edvaj\u00ed 1D\u00a0modely. Jako p\u0159\u00edklady mo\u017eno uv\u00e9st Rhine Alarm Model (RAM), Danube Basin Alarm Model (DBAM), Poplachov\u00fd model Labe (ALAMO), v\u00a0USA je to nap\u0159\u00edklad model RiverSpill, v\u00a0Rusku je mo\u017eno jmenovat nap\u0159\u00edklad model \u0159eky Tura. N\u00e1\u0161 v\u00fdzkumn\u00fd \u00fastav pracuje na projektu NAVAROSO. Jedn\u00e1 se o\u00a0v\u00fdvoj expertn\u00edho informa\u010dn\u00edho syst\u00e9mu, jeho\u017e c\u00edlem je vytvo\u0159en\u00ed a\u00a0napln\u011bn\u00ed specializovan\u00e9ho datab\u00e1zov\u00e9ho softwaru, umo\u017e\u0148uj\u00edc\u00edho rychl\u00e9 poskytov\u00e1n\u00ed k\u0159\u00ed\u017eov\u011b prov\u00e1zan\u00fdch \u00fadaj\u016f o\u00a0toc\u00edch, potenci\u00e1ln\u00edch zne\u010di\u0161\u0165ovatel\u00edch a\u00a0l\u00e1tk\u00e1ch, kter\u00e9 mohou zne\u010di\u0161t\u011bn\u00ed tok\u016f zp\u016fsobit a\u00a0tvorba verz\u00ed pro stacion\u00e1rn\u00ed i\u00a0mobiln\u00ed za\u0159\u00edzen\u00ed (pro opera\u010dn\u00ed syst\u00e9my Android, iOS a\u00a0Windows Phone). Tato datab\u00e1ze bude dopln\u011bna modulem umo\u017e\u0148uj\u00edc\u00edm hrub\u00fd odhad \u0161\u00ed\u0159en\u00ed havarijn\u00edho zne\u010di\u0161t\u011bn\u00ed vodn\u00edm tokem. Modul bude testov\u00e1n na \u0159ece Od\u0159e nad st\u00e1tn\u00ed hranic\u00ed s\u00a0Polskem pod n\u00e1zvem ORAM (Odra River Alarm Modul) a\u00a0zam\u011b\u0159\u00ed se jmenovit\u011b na toky Odra, Ol\u0161e, Ostravice, Opava a\u00a0Lu\u010dina. C\u00edlem tohoto \u010dl\u00e1nku je sezn\u00e1mit \u010dten\u00e1\u0159e s\u00a0n\u011bkter\u00fdmi poznatky, kter\u00e9 byly z\u00edsk\u00e1ny b\u011bhem p\u0159\u00edpravy tohoto modulu.<\/p>\n

Metodika<\/h2>\n

P\u0159ipravuje se modul umo\u017e\u0148uj\u00edc\u00ed odhady \u0161\u00ed\u0159en\u00ed havarijn\u00edho zne\u010di\u0161t\u011bn\u00ed v\u00a0toku. V\u00a0sou\u010dasn\u00e9 dob\u011b je nedostatek podrobn\u00fdch \u00fadaj\u016f o\u00a0vodn\u00edch toc\u00edch, pro kter\u00e9 m\u00e1 modul slou\u017eit, proto se v\u00a0prvn\u00ed f\u00e1zi modul omez\u00ed na metodu p\u0159edb\u011b\u017en\u00fdch odhad\u016f. C\u00edlem je poskytovat spr\u00e1vci toku, vodohospod\u00e1\u0159sk\u00e9mu org\u00e1nu, hasi\u010dsk\u00e9mu z\u00e1chrann\u00e9mu sboru a\u00a0dal\u0161\u00edm zainteresovan\u00fdm slo\u017ek\u00e1m p\u0159i \u0159e\u0161en\u00ed havarijn\u00edch situac\u00ed orienta\u010dn\u00ed informace o\u00a0dob\u00e1ch dob\u011bhu \u010dela mraku zne\u010di\u0161t\u011bn\u00ed do jednotliv\u00fdch profil\u016f na toku. V\u00a0p\u0159\u00edpadech, kdy bude k\u00a0dispozici odhad mno\u017estv\u00ed unikl\u00e9 zne\u010di\u0161\u0165uj\u00edc\u00ed l\u00e1tky p\u0159i okam\u017eit\u00e9m vnosu, umo\u017en\u00ed modul tak\u00e9 odhad maxim\u00e1ln\u00ed koncentrace, kter\u00e1 pravd\u011bpodobn\u011b bude dosa\u017eena ve zvolen\u00e9m z\u00e1jmov\u00e9m profilu na toku. K\u00a0p\u0159edb\u011b\u017en\u00fdm odhad\u016fm dotokov\u00fdch dob budou pou\u017eity empirick\u00e9 rovnice, kter\u00e9 jsou v\u00fdsledkem statistick\u00e9 anal\u00fdzy velk\u00e9ho mno\u017estv\u00ed stopovac\u00edch pokus\u016f uveden\u00e9 v\u00a0[1]. V\u00a0budoucnu se po\u010d\u00edt\u00e1 se zdokonalen\u00edm tohoto modulu. To v\u0161ak p\u0159edpokl\u00e1d\u00e1 daleko vy\u0161\u0161\u00ed n\u00e1roky na p\u0159\u00edpravu vstupn\u00edch dat t\u00fdkaj\u00edc\u00edch se vodn\u00edch tok\u016f (geometrie, hydrodynamika, \u2026), dat pro modelov\u00e1n\u00ed transportu l\u00e1tek (disperzn\u00ed sou\u010dinitele, konstanty kinetiky), apod. Rozsah podklad\u016f pot\u0159ebn\u00fd pro takov\u00fd model je uveden nap\u0159\u00edklad v\u00a0[2]. Sou\u010dasn\u00e1 p\u0159\u00edprava modulu se zam\u011b\u0159uje na t\u0159i na sebe navazuj\u00edc\u00ed kroky. Prvn\u00edm krokem je predikce dotokov\u00fdch dob, druh\u00fdm predikce maxim\u00e1ln\u00ed koncentrace v\u00a0z\u00e1jmov\u00e9m profilu a\u00a0t\u0159et\u00edm krokem predikce rozd\u011blen\u00ed koncentrac\u00ed b\u011bhem pr\u016fchodu zne\u010di\u0161t\u011bn\u00ed z\u00e1jmov\u00fdm profilem, jin\u00fdmi slovy predikce pr\u016fnikov\u00e9 k\u0159ivky v\u00a0z\u00e1jmov\u00e9m profilu. Dotokov\u00e9 doby m\u016f\u017eeme z\u00edskat bu\u010f p\u0159\u00edmo m\u011b\u0159en\u00edm p\u0159i stopovac\u00edch pokusech, nebo pomoc\u00ed v\u00fdpo\u010dt\u016f. V\u00fdpo\u010dty mohou b\u00fdt bu\u010f hydrotechnick\u00e9, nebo empirick\u00e9. Empirick\u00e9 vzorce op\u00edraj\u00edc\u00ed se o\u00a0hydrologick\u00e9 \u00fadaje a\u00a0\u00fadaje ze stopovac\u00edch pokus\u016f uv\u00e1d\u00ed nap\u0159\u00edklad Jobson [1]. Na doln\u00edm toku \u0159eky Ostravice a\u00a0v\u00a0\u00faseku Odry mezi \u00fast\u00edm Ostravice a\u00a0st\u00e1tn\u00ed hranic\u00ed s\u00a0Polskem lze dotokov\u00e9 doby odvodit z\u00a0kontinu\u00e1ln\u00edho m\u011b\u0159en\u00ed konduktivity a\u00a0pr\u016ftok\u016f ve stanic\u00edch Slezsk\u00e1 Ostrava a\u00a0Bohum\u00edn a\u00a0\u00fadaj\u016f o\u00a0vypou\u0161t\u011bn\u00ed slan\u00fdch d\u016fln\u00edch vod. Problematika dotokov\u00fdch dob je pom\u011brn\u011b rozs\u00e1hl\u00e1 a\u00a0nen\u00ed p\u0159edm\u011btem tohoto \u010dl\u00e1nku. Nejd\u016fle\u017eit\u011bj\u0161\u00ed dotokov\u00e9 doby jsou zn\u00e1zorn\u011bny na obr. 1<\/em>. Dotokov\u00e1 doba je rozd\u00edl mezi dv\u011bma \u010dasy, kde t0<\/sub><\/em> je \u010das okam\u017eit\u00e9ho vnosu, tB<\/sub><\/em> je \u010das, ve kter\u00e9m zne\u010di\u0161t\u011bn\u00ed doraz\u00ed do z\u00e1jmov\u00e9ho profilu, tL<\/sub><\/em> je \u010das, ve kter\u00e9m zne\u010di\u0161t\u011bn\u00ed dos\u00e1hne 10\u00a0% maxim\u00e1ln\u00ed koncentrace v\u00a0z\u00e1jmov\u00e9m profilu, tP<\/sub><\/em> je \u010das, ve kter\u00e9m zne\u010di\u0161t\u011bn\u00ed dos\u00e1hne maxim\u00e1ln\u00ed koncentrace v\u00a0z\u00e1jmov\u00e9m profilu, tT<\/sub><\/em> je \u010das, ve kter\u00e9m zne\u010di\u0161t\u011bn\u00ed poklesne 10\u00a0% maxim\u00e1ln\u00ed koncentrace v\u00a0z\u00e1jmov\u00e9m profilu, tE<\/sub><\/em> je \u010das ve kter\u00e9m zne\u010di\u0161t\u011bn\u00ed opust\u00ed z\u00e1jmov\u00fd profil a\u00a0Cp<\/sub><\/em> je maxim\u00e1ln\u00ed koncentrace zne\u010di\u0161\u0165uj\u00edc\u00ed l\u00e1tky dosa\u017een\u00e1 b\u011bhem pr\u016fchodu z\u00e1jmov\u00fdm profilem ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu. Z\u00e1jmov\u00fd profil je profil, ve kter\u00e9m chceme zn\u00e1t maxim\u00e1ln\u00ed koncentraci. Proto\u017ee \u010dasy tB<\/sub><\/em> a\u00a0tE<\/sub><\/em> je velice obt\u00ed\u017en\u00e9 ur\u010dit, pou\u017e\u00edvaj\u00ed se v\u00a0praxi p\u0159i anal\u00fdze v\u00fdsledk\u016f stopovac\u00edch pokus\u016f \u010dasy, ve kter\u00fdch koncentrace dos\u00e1hne 10\u00a0% z\u00a0maxim\u00e1ln\u00ed koncentrace, tyto \u010dasy jsou ozna\u010deny tL<\/sub><\/em> a\u00a0tT<\/sub><\/em>.<\/p>\n\"\"<\/a>\n

Obr. 1. D\u016fle\u017eit\u00e9 dotokov\u00e9 doby
\nFig. 1. Important travel times<\/h6>\n

Pro predikci maxim\u00e1ln\u00ed koncentrace v\u00a0p\u0159\u00edpad\u011b okam\u017eit\u00e9ho vnosu je mo\u017eno pou\u017e\u00edt vzorec (1) uveden\u00fd v\u00a0DBAM [3]:<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n\n\n\n\n
kde<\/td>\n\u00a0Cp<\/sub><\/em><\/td>\nje<\/td>\nmaxim\u00e1ln\u00ed koncentrace odpov\u00eddaj\u00edc\u00ed vrcholu pr\u016fnikov\u00e9 k\u0159ivky ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [g\/m3<\/sup>],<\/td>\n<\/tr>\n
<\/td>\nM<\/em><\/td>\n<\/td>\nhmotnost vnesen\u00e9 l\u00e1tky [g],<\/td>\n<\/tr>\n
<\/td>\nQ<\/em><\/td>\n<\/td>\npr\u016ftok ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [m3<\/sup>\/s],<\/td>\n<\/tr>\n
<\/td>\nU<\/em><\/td>\n<\/td>\npr\u016f\u0159ezov\u00e1 rychlost [m\/s],<\/td>\n<\/tr>\n
<\/td>\nD\u00a0<\/em><\/td>\n<\/td>\nkoeficient pod\u00e9ln\u00e9 disperze [m2<\/sup>\/s],<\/td>\n<\/tr>\n
<\/td>\nk<\/em><\/td>\n<\/td>\nrychlostn\u00ed konstanta 1. \u0159\u00e1du charakterizuj\u00edc\u00ed objemov\u00e9 zm\u011bny sledovan\u00e9 l\u00e1tky [1\/s],<\/td>\n<\/tr>\n
<\/td>\n t\u00a0\u00a0<\/em><\/td>\n<\/td>\n\u010das [s],<\/td>\n<\/tr>\n
<\/td>\nx\u00a0\u00a0<\/em><\/td>\n<\/td>\nvzd\u00e1lenost z\u00e1jmov\u00e9ho od m\u00edsta vnosu [m].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Dal\u0161\u00ed mo\u017enost\u00ed je pou\u017eit\u00ed empirick\u00e9ho vzorce (2). Vych\u00e1z\u00ed ze vzorce, kter\u00fd uv\u00e1d\u00ed Jobson [1] a\u00a0je upraven pro nekonzervativn\u00ed l\u00e1tku.<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n\n
kde<\/td>\nCp<\/sub><\/em><\/td>\nje<\/td>\nmaxim\u00e1ln\u00ed koncentrace odpov\u00eddaj\u00edc\u00ed vrcholu pr\u016fnikov\u00e9 k\u0159ivky ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [g\/m3<\/sup>],<\/td>\n<\/tr>\n
<\/td>\nM<\/em><\/td>\n<\/td>\nhmotnost injektovan\u00e9ho stopova\u010de [g],<\/td>\n<\/tr>\n
<\/td>\nQ<\/em><\/td>\n<\/td>\npr\u016ftok ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [m3<\/sup>\/s],<\/td>\n<\/tr>\n
<\/td>\nCup<\/sub><\/em><\/td>\n<\/td>\nmaxim\u00e1ln\u00ed jednotkov\u00e1 koncentrace ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [1\/s],<\/td>\n<\/tr>\n
<\/td>\n k<\/em><\/td>\n<\/td>\nrychlostn\u00ed konstanta 1. \u0159\u00e1du charakterizuj\u00edc\u00ed objemov\u00e9 zm\u011bny sledovan\u00e9 l\u00e1tky [1\/hod].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Jednotkov\u00e1 maxim\u00e1ln\u00ed koncentrace je definov\u00e1na jako 106<\/sup> n\u00e1sobek maxim\u00e1ln\u00ed koncentrace p\u0159i jednotkov\u00e9m pr\u016ftoku a\u00a0jednotkov\u00e9 hmotnosti l\u00e1tky vnesen\u00e9 do toku [1]. Jej\u00ed z\u00e1vislost na dotokov\u00e9 dob\u011b TP<\/sub> = tP<\/sub><\/em> – t0<\/sub><\/em> m\u016f\u017ee b\u00fdt vyj\u00e1d\u0159ena empirickou rovnic\u00ed (3) uvedenou v\u00a0[1]:<\/p>\n\"\"<\/a>\n

nebo rovnic\u00ed (4) rovn\u011b\u017e uvedenou v\u00a0[1]:<\/p>\n\"\"<\/a>\n\n\n\n\n\n
kde<\/td>\nTp<\/sub> = t<\/em>P<\/sub> – t<\/em>0<\/sub><\/td>\nje<\/td>\ndotokov\u00e1 doba odpov\u00eddaj\u00edc\u00ed vrcholu pr\u016fnikov\u00e9 k\u0159ivky ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [hod],<\/td>\n<\/tr>\n
<\/td>\nQ<\/em><\/td>\n<\/td>\npr\u016ftok ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [m3<\/sup>\/s],<\/td>\n<\/tr>\n
<\/td>\nQ<\/em>a<\/sub><\/td>\n<\/td>\ndlouhodob\u00fd pr\u016fm\u011brn\u00fd pr\u016ftok ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu [m3<\/sup>\/s].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

V\u00a0empirick\u00fdch rovnic\u00edch (2), (3) a\u00a0(4) se uv\u00e1d\u011bj\u00ed dotokov\u00e9 doby v\u00a0hodin\u00e1ch, proto rychlostn\u00ed konstanta 1. \u0159\u00e1du charakterizuj\u00edc\u00ed objemov\u00e9 zm\u011bny mus\u00ed m\u00edt v\u00a0rovnici (2) rozm\u011br 1\/hod.<\/p>\n

V\u00a0p\u0159\u00edpad\u011b odhadu maxim\u00e1ln\u00ed koncentrace pro konzervativn\u00ed l\u00e1tku je rychlostn\u00ed konstanta 1. \u0159\u00e1du charakterizuj\u00edc\u00ed objemov\u00e9 zm\u011bny sledovan\u00e9 l\u00e1tky rovna nule. Pro bezpe\u010dn\u00fd odhad maxim\u00e1ln\u00ed koncentrace p\u0159i havarijn\u00edm \u00faniku nekonzervativn\u00ed l\u00e1tky je nutno zv\u00e1\u017eit, zda nen\u00ed vhodn\u00e9 polo\u017eit rychlostn\u00ed konstantu 1.\u00a0\u0159\u00e1du charakterizuj\u00edc\u00ed objemov\u00e9 zm\u011bny rovn\u011b\u017e rovnu nule.<\/p>\n

M\u00e1me-li stanovenu maxim\u00e1ln\u00ed koncentraci Cp<\/sub> <\/em>v\u00a0z\u00e1jmov\u00e9m profilu ve vzd\u00e1lenosti x<\/em> od m\u00edsta vnosu, je mo\u017eno p\u0159istoupit k\u00a0t\u0159et\u00edmu kroku, a\u00a0t\u00edm je predikce rozd\u011blen\u00ed koncentrac\u00ed b\u011bhem pr\u016fchodu havarijn\u00edho zne\u010di\u0161t\u011bn\u00ed z\u00e1jmov\u00fdm profilem. V\u00a0r\u00e1mci p\u0159\u00edpravy modulu bylo hled\u00e1no takov\u00e9 rozd\u011blen\u00ed, kter\u00e9 co nejv\u00edce odpov\u00edd\u00e1 skute\u010dn\u00fdm hodnot\u00e1m nam\u011b\u0159en\u00fdm v\u00a0toku. Byla k\u00a0tomu pou\u017eita konkr\u00e9tn\u00ed data ze stopovac\u00edch pokus\u016f na \u0159ece Svitav\u011b [4].<\/p>\n

V\u00fdsledky a\u00a0diskuse<\/h2>\n

K\u00a0predikci maxim\u00e1ln\u00ed koncentrace, kterou lze o\u010dek\u00e1vat b\u011bhem pr\u016fchodu havarijn\u00edho zne\u010di\u0161t\u011bn\u00ed z\u00e1jmov\u00fdm profilem, lze pou\u017e\u00edt rovnici (1) nebo rovnici (2). Ob\u011b rovnice maj\u00ed ur\u010dit\u00e9 nev\u00fdhody. Nev\u00fdhodou rovnice (1) je obt\u00ed\u017enost spr\u00e1vn\u00e9ho odhadu koeficientu pod\u00e9ln\u00e9 disperze. V\u00a0odborn\u00e9 literatu\u0159e je toti\u017e doporu\u010deno mnoho r\u016fzn\u00fdch postup\u016f k\u00a0ur\u010den\u00ed tohoto koeficientu a\u00a0v\u00fdsledky jsou v\u00a0n\u011bkter\u00fdch p\u0159\u00edpadech zna\u010dn\u011b rozd\u00edln\u00e9. Na nev\u00fdhody rovnice (2) upozor\u0148uje ve sv\u00e9 diplomov\u00e9 pr\u00e1ci K\u016frkov\u00e1 [5]. Proto\u017ee v\u00a0rovnici (2) nen\u00ed zahrnuta pod\u00e9ln\u00e1 disperzivita, mohou se v\u00a0grafech projevit jej\u00ed zm\u011bny, p\u0159edev\u0161\u00edm pokud byly zkou\u0161ky prov\u00e1d\u011bny na r\u016fzn\u00fdch m\u00edstech a\u00a0p\u0159i r\u016fzn\u00fdch pr\u016ftoc\u00edch.<\/p>\n\"\"<\/a>\n

Obr. 2. Pr\u016fnikov\u00e1 k\u0159ivka \u2013 Svitava PF1 \u2013 \u010derven 2000
\nFig. 2. Breakthroughcurve \u2013 Svitava PF1 \u2013 June 2000<\/h6>\n

M\u00e1me-li stanovenu maxim\u00e1ln\u00ed koncentraci Cp<\/sub><\/em>, v\u00a0z\u00e1jmov\u00e9m profilu je mo\u017eno p\u0159istoupit k\u00a0t\u0159et\u00edmu kroku, a\u00a0t\u00edm je predikce rozd\u011blen\u00ed koncentrac\u00ed b\u011bhem pr\u016fchodu havarijn\u00edho zne\u010di\u0161t\u011bn\u00ed z\u00e1jmov\u00fdm profilem. V\u00a0povod\u00ed Odry nejsou v\u00a0posledn\u00ed dob\u011b k\u00a0dispozici \u017e\u00e1dn\u00e9 v\u00fdsledky ze stopovac\u00edch pokus\u016f, proto nezbylo, ne\u017e se p\u0159i p\u0159\u00edprav\u011b modelu omezit na data z\u00edsk\u00e1na odjinud. R\u016fzn\u00e9 varianty kroku t\u0159i byly ov\u011b\u0159ov\u00e1ny na konkr\u00e9tn\u00edch datech z\u00edskan\u00fdch stopovac\u00edmi pokusy na \u0159ece Svitav\u011b [4]. V\u00a0pr\u00e1ci [4] a\u00a0v\u00a0navazuj\u00edc\u00edch studi\u00edch byly pr\u016fnikov\u00e9 k\u0159ivky stopova\u010de modelov\u011b aproximov\u00e1ny analytick\u00fdm \u0159e\u0161en\u00edm, resp. za vyu\u017eit\u00ed numerick\u00e9ho modelu (MIKE11). V\u00a0r\u00e1mci p\u0159\u00edpravn\u00fdch studi\u00ed projektu NAVAROSO byl proveden pokus prov\u00e9st aproximaci pr\u016fnikov\u00e9 k\u0159ivky stopova\u010de pomoc\u00ed Pearsonova rozd\u011blen\u00ed III. typu, kter\u00e9 lze pro \u010dasy t <\/em>> tB<\/sub><\/em> vyj\u00e1d\u0159it pomoc\u00ed rovnice (5).<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n\n\n\n
kde<\/td>\nC<\/em><\/td>\nje<\/td>\nkoncentrace v\u00a0\u010dase t<\/em> [mg\/m3<\/sup>],<\/td>\n<\/tr>\n
<\/td>\nCp<\/sub>\u00a0\u00a0<\/em><\/td>\n<\/td>\nkoncentrace odpov\u00eddaj\u00edc\u00ed vrcholu pr\u016fnikov\u00e9 k\u0159ivky [mg\/m3<\/sup>],<\/td>\n<\/tr>\n
<\/td>\nt\u00a0\u00a0<\/em><\/td>\n<\/td>\n\u010das [s],<\/td>\n<\/tr>\n
<\/td>\n t<\/em>P<\/sub><\/td>\n<\/td>\n\u010das, ve kter\u00e9m zne\u010di\u0161t\u011bn\u00ed dos\u00e1hne maxim\u00e1ln\u00ed koncentrace v\u00a0z\u00e1jmov\u00e9m profilu [s],<\/td>\n<\/tr>\n
<\/td>\nb\u00a0<\/em><\/td>\n<\/td>\nkonstanta odpov\u00eddaj\u00edc\u00ed dob\u011b mezi tP<\/sub> <\/em>a\u00a0\u010dasem dosa\u017een\u00ed t\u011b\u017ei\u0161t\u011b plochy pod pr\u016fnikovou k\u0159ivkou [s],<\/td>\n<\/tr>\n
<\/td>\n a<\/em><\/td>\n<\/td>\nkonstanta odpov\u00eddaj\u00edc\u00ed dob\u011b mezi tB<\/sub><\/em> a\u00a0tP<\/sub><\/em> [s],<\/td>\n<\/tr>\n
<\/td>\ntB\u00a0\u00a0<\/sub><\/em><\/td>\n<\/td>\n\u010das p\u0159\u00edchodu nejrychlej\u0161\u00edch \u010d\u00e1stic zne\u010di\u0161t\u011bn\u00ed do z\u00e1jmov\u00e9ho profilu [s].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

V\u00a0\u010dasech t<\/em> rovn\u00fdch nebo men\u0161\u00edch ne\u017e tB<\/sub><\/em> p\u0159edpokl\u00e1d\u00e1me, \u017ee profil nebude havarijn\u00edm zne\u010di\u0161t\u011bn\u00edm ovlivn\u011bn. V\u00a0p\u0159\u00edpad\u011b, \u017ee se zne\u010di\u0161\u0165uj\u00edc\u00ed l\u00e1tka vyskytuje v\u00a0toku b\u011b\u017en\u011b i\u00a0p\u0159ed hav\u00e1ri\u00ed bude nutno rovnici (5) je\u0161t\u011b upravit i\u00a0pro tuto variantu. V\u00a0p\u0159\u00edpad\u011b, \u017ee zne\u010di\u0161\u0165uj\u00edc\u00ed l\u00e1tka, kter\u00e1 unikla p\u0159i hav\u00e1rii je nekonzervativn\u00ed, lze do rovnice (5) zav\u00e9st je\u0161t\u011b rychlostn\u00ed konstantu objemov\u00fdch zm\u011bn nebo rovnici zachovat v\u00a0p\u016fvodn\u00edm stavu ve prosp\u011bch bezpe\u010dnosti odhadu. Pro jednotliv\u00e9 profily na \u0159ece Svitav\u011b je na obr. 2<\/em> a\u017e 6<\/em> provedeno porovn\u00e1n\u00ed nam\u011b\u0159en\u00fdch hodnot s\u00a0modelem vyu\u017e\u00edvaj\u00edc\u00edm Pearsonovo rozd\u011blen\u00ed III. typu. Vyvst\u00e1v\u00e1 zde ot\u00e1zka, pro\u010d hledat zvl\u00e1\u0161tn\u00ed funkci pro aproximaci pr\u016fnikov\u00fdch k\u0159ivek (Pearson III), kdy\u017e funk\u010dn\u00ed z\u00e1vislost za dan\u00fdch, v\u00fd\u0161e uveden\u00fdch p\u0159edpoklad\u016f ud\u00e1v\u00e1 rovnice pr\u00e1ce (1). Jedn\u00e1 se o\u00a0snahu vyhnout se obt\u00ed\u017en\u00e9mu stanovov\u00e1n\u00ed koeficientu pod\u00e9ln\u00e9 disperze na z\u00e1klad\u011b prom\u011bnliv\u00fdch parametr\u016f \u0159\u00ed\u010dn\u00edho koryta. Podobnou snahu m\u016f\u017eeme vid\u011bt nap\u0159\u00edklad i\u00a0u\u00a0tv\u016frc\u016f modelu Riverspiell\u00a0[6], kdy\u017e zavedli novou metodu vyu\u017e\u00edvaj\u00edc\u00ed implicitn\u00ed korelaci mezi koeficientem pod\u00e9ln\u00e9 disperze a\u00a0dotokovou dobou. Snaha vyhnout se p\u0159\u00edm\u00e9 z\u00e1vislosti na prom\u011bnliv\u00fdch parametrech koryta toku (pr\u016fto\u010dn\u00e1 plocha, \u0161\u00ed\u0159ka, hloubka) je patrn\u00e1 i\u00a0u\u00a0rovnice (1).<\/p>\n\"\"<\/a>\n

Obr. 3. Pr\u016fnikov\u00e1 k\u0159ivka \u2013 Svitava PF2 \u2013 \u010derven 2000
\nFig. 3. Breakthroughcurve \u2013 Svitava PF2 \u2013 June 2000<\/h6>\n\"\"<\/a>\n
Obr. 4. Pr\u016fnikov\u00e1 k\u0159ivka \u2013 Svitava PF1 \u2013 srpen 2000
\nFig. 4. Breakthroughcurve \u2013 Svitava PF1 \u2013 August 2000<\/h6>\n

V\u00fdsledky jsou shrnuty v\u00a0tabulce 1.<\/em> Koeficienty a<\/em>\u00a0a\u00a0b<\/em> v\u00a0rovnici (5) byly z\u00edsk\u00e1ny metodou pokus omyl. Young a\u00a0kol. [7] doporu\u010dili pro posuzov\u00e1n\u00ed t\u011bsnosti mezi predikovan\u00fdmi a\u00a0m\u011b\u0159en\u00fdmi hodnotami vzorec pro v\u00fdpo\u010det koeficientu determinace. Pro na\u0161e pot\u0159eby byl pou\u017eit ve form\u011b rovnice (6).<\/p>\n\"\"<\/a>\n\n\n\n\n\n\n
kde<\/td>\nR<\/em>t<\/sub><\/td>\nje<\/td>\nkoeficient determinace [\u2013],<\/td>\n<\/tr>\n
<\/td>\nC<\/em>i<\/sub><\/td>\n<\/td>\ni-t\u00e1 hodnota m\u011b\u0159en\u00e9 koncentrace [mg\/m3<\/sup>],<\/td>\n<\/tr>\n
<\/td>\nC<\/em>Mi\u00a0<\/sub><\/td>\n<\/td>\ni-t\u00e1 hodnota koncentrace modelu [mg\/m3<\/sup>],<\/td>\n<\/tr>\n
<\/td>\n p<\/em><\/td>\n<\/td>\npo\u010det m\u011b\u0159en\u00ed v\u00a0\u010dasech t > t<\/em>B <\/sub>[\u2013].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Autor \u0160ajer [8] zjistil, \u017ee u\u00a0v\u0161ech p\u011bti analyzovan\u00fdch pr\u016fnikov\u00fdch k\u0159ivek lze vzestupnou \u010d\u00e1st pr\u016fnikov\u00e9 k\u0159ivky vyj\u00e1d\u0159it pomoc\u00ed rovnice (7).<\/p>\n\"\"<\/a>\n\n\n\n
kde<\/td>\nt<\/em><\/td>\nje<\/td>\n\u010das [s].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

V\u00a0praxi se p\u0159i vyhodnocov\u00e1n\u00ed stopovac\u00edch pokus\u016f zji\u0161\u0165uje \u010das tL<\/sub><\/em>, pro kter\u00fd lze rovnici (7) upravit na rovnici (8).<\/p>\n\"\"<\/a>\n

Vezmeme-li v\u00a0\u00favahu data, kter\u00e1 uv\u00e1d\u00ed Jobson v\u00a0p\u0159\u00edloze [1], pak pom\u011br mezi dobou pot\u0159ebnou pro dosa\u017een\u00ed maxim\u00e1ln\u00ed koncentrace Cp<\/sub><\/em> v\u00a0z\u00e1jmov\u00e9m profilu, tj. (tP<\/sub> – t0<\/sub>),<\/em> a\u00a0dobou od vnosu po p\u0159\u00edchod do z\u00e1jmov\u00e9ho profilu, p\u0159i kter\u00e9m je dosa\u017eena koncentrace jedna desetina maxim\u00e1ln\u00ed koncentrace Cp<\/sub><\/em> v\u00a0z\u00e1jmov\u00e9m profilu, tj. (tL<\/sub> – t0<\/sub>)<\/em>, b\u00fdv\u00e1 bl\u00edzko pod m\u00edstem injekt\u00e1\u017ee vy\u0161\u0161\u00ed, s\u00a0rostouc\u00ed vzd\u00e1lenost\u00ed se v\u0161ak v\u011bt\u0161inou ust\u00e1l\u00ed zhruba v\u00a0rozmez\u00ed 1,1 : 1 a\u017e 1,3 : 1. Vyskytuj\u00ed-li se v\u00a0toku v\u00fdznamn\u00e9 oblasti s\u00a0pomal\u00fdm proud\u011bn\u00edm (tzv. mrtv\u00e9 z\u00f3ny), pak je nutno po\u010d\u00edtat s\u00a0vy\u0161\u0161\u00edmi hodnotami. Jako p\u0159\u00edklad je mo\u017eno uv\u00e9st pom\u011br 1,68 : 1, kter\u00fd byl zji\u0161t\u011bn u\u00a0\u0159eky Punkvy [9]. Uveden\u00e9 pom\u011bry se t\u00fdkaj\u00ed okam\u017eit\u00e9ho vnosu konzervativn\u00ed l\u00e1tky do toku.<\/p>\n\"\"<\/a>\n

Obr. 5. Pr\u016fnikov\u00e1 k\u0159ivka \u2013 Svitava PF2 \u2013 srpen 2000
\nFig. 5. Breakthroughcurve \u2013 Svitava PF2 \u2013 August 2000<\/h6>\n\"\"<\/a>\n
Obr. 6. Pr\u016fnikov\u00e1 k\u0159ivka \u2013 Svitava PF21 \u2013 srpen 2000
\nFig. 6. Breakthroughcurve \u2013 Svitava PF21 \u2013 August 2000<\/h6>\n

Na z\u00e1klad\u011b uveden\u00fdch v\u00fdsledk\u016f budou do p\u0159ipravovan\u00e9ho modelu v\u00a0povod\u00ed \u0159eky Odry vlo\u017eeny vstupn\u00ed hodnoty tzv. defaulty, kter\u00e9 bude mo\u017eno na z\u00e1klad\u011b dal\u0161\u00edch zku\u0161enost\u00ed pro jednotliv\u00e9 toky postupn\u011b upravovat.<\/p>\n

Rovnice (1) a\u017e (5) je mo\u017eno pou\u017e\u00edt pouze v\u00a0p\u0159\u00edpad\u011b okam\u017eit\u00e9ho vnosu zne\u010di\u0161\u0165uj\u00edc\u00ed l\u00e1tky do toku. V\u00a0praxi se \u010dasto vyskytuje p\u0159i hav\u00e1ri\u00edch kontinu\u00e1ln\u00ed vnos s\u00a0omezenou dobou trv\u00e1n\u00ed. V\u00a0tom p\u0159\u00edpad\u011b lze p\u0159i modelov\u00e1n\u00ed koncentrace v\u00a0z\u00e1jmov\u00e9m profilu vych\u00e1zet z\u00a0rozd\u011blen\u00ed pro okam\u017eit\u00fd vnos (nap\u0159\u00edklad z\u00a0rovnice\u00a0(5)) a\u00a0n\u00e1sledn\u011b pou\u017e\u00edt metodu superpozice.<\/p>\n

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

Proto\u017ee v\u00a0posledn\u00ed dob\u011b nejsou v\u00a0povod\u00ed Odry k\u00a0dispozici \u017e\u00e1dn\u00e1 data ze stopovac\u00edch pokus\u016f, byla pro p\u0159\u00edpravu modelu \u0161\u00ed\u0159en\u00ed zne\u010di\u0161t\u011bn\u00ed v\u00a0tomto povod\u00ed vyu\u017eita data ze stopovac\u00edch pokus\u016f, kter\u00e9 byly realizov\u00e1ny na Svitav\u011b v\u00a0roce 2000. V\u00fdsledn\u00e9 pr\u016fnikov\u00e9 k\u0159ivky se nejl\u00e9pe poda\u0159ilo popsat pomoc\u00ed Pearsonova rozd\u011blen\u00ed 3. typu. Vych\u00e1z\u00ed se z\u00a0anal\u00fdzy pouze p\u011bti pr\u016fnikov\u00fdch k\u0159ivek, pro zobecn\u011bn\u00ed by bylo vhodn\u00e9 toto ov\u011b\u0159it na dal\u0161\u00edch v\u00fdsledc\u00edch z\u00a0jin\u00fdch stopovac\u00edch pokus\u016f. Do p\u0159ipravovan\u00e9ho modulu v\u00a0povod\u00ed Odry budou vlo\u017eeny defaulty vych\u00e1zej\u00edc\u00ed z\u00a0v\u00fd\u0161e uveden\u00fdch poznatk\u016f, kter\u00e9 bude mo\u017eno na z\u00e1klad\u011b dal\u0161\u00edch zku\u0161enost\u00ed pro jednotliv\u00e9 toky postupn\u011b upravovat.<\/p>\n

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

Tento p\u0159\u00edsp\u011bvek vznikl d\u00edky podpo\u0159e projektu \u010d. TH02030142 NAVAROSO, pro kter\u00fd je poskytovatelem podpory Technologick\u00e1 agentura \u010cesk\u00e9 republiky.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Odra River Alarm Modul (ORAM) will be part of the NAVAROSO project. There are no results of tracer studies of the Czech part of the Odra River in the last twenty years. That\u00b4s the reason, why tracer experiment data of the Svitava River were used for analysis. <\/p>\n","protected":false},"author":8,"featured_media":4583,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86,87],"tags":[1187,1185,1186,1188,301],"coauthors":[241],"class_list":["post-4663","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydraulics-hydrology-and-hydrogeology","category-hydrochemistry-radioecology-microbiology","tag-1d-modelling","tag-accidental-pollution","tag-instantaneous-spill","tag-pearson-distribution-type-3","tag-water-quality"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/4663","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=4663"}],"version-history":[{"count":2,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/4663\/revisions"}],"predecessor-version":[{"id":30452,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/4663\/revisions\/30452"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/4583"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=4663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=4663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=4663"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=4663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}