{"id":3900,"date":"2017-10-10T08:22:06","date_gmt":"2017-10-10T08:22:06","guid":{"rendered":"http:\/\/www.vtei.cz\/?p=3900"},"modified":"2024-07-16T12:27:35","modified_gmt":"2024-07-16T11:27:35","slug":"long-term-fluctuations-of-vltava-river-flows-in-prague","status":"publish","type":"post","link":"https:\/\/www.vtei.cz\/en\/2017\/10\/long-term-fluctuations-of-vltava-river-flows-in-prague\/","title":{"rendered":"Long-term fluctuations of Vltava River flows in Prague"},"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

Prvn\u00ed \u010d\u00e1st studie obsahuje doporu\u010den\u00ed pro v\u00fdb\u011br reprezentativn\u00edho obdob\u00ed pozorov\u00e1n\u00ed pro v\u00fdpo\u010det charakteristik pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f. Je to v\u00fdsledek anal\u00fdzy \u010dasov\u00e9 \u0159ady pr\u016ftok\u016f Vltavy v\u00a0Praze s\u00a0po\u010d\u00e1tkem v\u00a0roce 1801. V\u00a0dal\u0161\u00ed \u010d\u00e1sti jsou zkoum\u00e1ny mo\u017enosti predikce 10let\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f pr\u016ftoku vyu\u017e\u00edvaj\u00edc\u00ed autoregresn\u00ed model. Je prok\u00e1z\u00e1no, \u017ee 7let\u00e9 nebo 10let\u00e9 klouzav\u00e9 pr\u016fm\u011bry pr\u016ftok\u016f maj\u00ed pr\u016fb\u011bh podobn\u00fd jako geomagnetick\u00fd 22let\u00fd cyklus Slunce. Z\u00a0korelace mezi pr\u016fm\u011brn\u00fdmi ro\u010dn\u00edmi pr\u016ftoky a\u00a0maxim\u00e1ln\u00edmi kulmina\u010dn\u00edmi pr\u016ftoky vypl\u00fdv\u00e1, \u017ee kol\u00eds\u00e1n\u00ed v\u00edcelet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f z\u00a0podstatn\u00e9 \u010d\u00e1sti odpov\u00edd\u00e1 i\u00a0v\u00fdskytu a\u00a0velikosti povodn\u00ed.<\/p>\n\"ilustracni-4_edit\"<\/a>\n

\u00davod<\/h2>\n

Charakteristiky pr\u016ftok\u016f jsou z\u00e1kladem pro vodohospod\u00e1\u0159sk\u00e1 \u0159e\u0161en\u00ed z\u00e1sobov\u00e1n\u00ed vodou, ochranu mno\u017estv\u00ed i\u00a0kvality vod, stavebn\u00ed projekty na toc\u00edch i\u00a0jejich okol\u00ed a\u00a0\u0159adu dal\u0161\u00edch oblast\u00ed hospod\u00e1\u0159sk\u00fdch aktivit. P\u0159i jejich zpracov\u00e1n\u00ed se \u010dasto p\u0159edpokl\u00e1d\u00e1, \u017ee proces, kter\u00fd popisuj\u00ed, je stacion\u00e1rn\u00ed, tak\u017ee charakteristiky popisuj\u00edc\u00ed minul\u00fd stav jsou nejlep\u0161\u00edm odhadem stavu budouc\u00edho. Ve skute\u010dnosti v\u011bt\u0161inou pot\u0159ebujeme poskytnout charakteristiky popisuj\u00edc\u00ed pom\u011bry v\u00a0konkr\u00e9tn\u00edm budouc\u00edm obdob\u00ed o\u00a0d\u00e9lce n\u011bkolika desetilet\u00ed, tedy dlouhodobou p\u0159edpov\u011b\u010f. V\u00a0prvn\u00ed kapitole studie je obsa\u017eeno doporu\u010den\u00ed pro volbu reprezentativn\u00edho obdob\u00ed, ze\u00a0kter\u00e9ho se charakteristiky pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f odvozuj\u00ed. V\u00a0dal\u0161\u00ed \u010d\u00e1sti jsou zkoum\u00e1ny mo\u017enosti p\u0159edpov\u011bdi trendu zm\u011bn pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f v\u00a0m\u011b\u0159\u00edtku v\u00edcelet\u00fdch obdob\u00ed. V\u00a0sou\u010dasn\u00e9 dob\u011b, kdy se klimatick\u00e9 pom\u011bry dosti rychle m\u011bn\u00ed, je t\u0159eba v\u011bnovat pozornost periodick\u00fdm vlastnostem hydrologick\u00fdch proces\u016f. Bez jejich uv\u00e1\u017een\u00ed se zv\u011bt\u0161uje pravd\u011bpodobnost, \u017ee prob\u00edhaj\u00edc\u00edm zm\u011bn\u00e1m p\u0159isoud\u00edme neodpov\u00eddaj\u00edc\u00ed vysv\u011btlen\u00ed.<\/p>\n\"Kasparek-Ladislav-1\"<\/a>\n

Obr. 1. Pr\u016fm\u011bry absolutn\u00edch hodnot chyb p\u0159edpov\u00eddan\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f pro obdob\u00ed d\u00e9lky NP let z\u00edskan\u00e9 z\u00a0pozorov\u00e1n\u00ed d\u00e9lky N let
\nFig. 1. Average absolute deviation of the predicted average flow for the period length NP years derived from observation of length N years<\/h6>\n

V\u00fdzkum volby obdob\u00ed pou\u017eit\u00e9ho pro zpracov\u00e1n\u00ed charakteristik pr\u016ftok\u016f<\/h2>\n

Ve V\u00fdzkumn\u00e9m \u00fastavu vodohospod\u00e1\u0159sk\u00e9m byl \u0159e\u0161en \u00fakol Metody v\u00fdpo\u010dtu hydrologick\u00fdch dat v\u00a0m\u011bn\u00edc\u00edch se podm\u00ednk\u00e1ch. Jedn\u00edm z\u00a0jeho v\u00fdstup\u016f byla v\u00fdzkumn\u00e1 zpr\u00e1va [1] a\u00a0refer\u00e1t [2]. V\u00fdzkum byl zam\u011b\u0159en na problematiku volby n\u00e1vrhov\u00e9ho obdob\u00ed, pou\u017e\u00edvan\u00e9ho pro odvozen\u00ed charakteristik pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f. Ot\u00e1zkou bylo, zda p\u0159i nar\u016fstaj\u00edc\u00ed d\u00e9lce pozorovan\u00fdch \u0159ad m\u00e1 b\u00fdt reprezentativn\u00ed obdob\u00ed pou\u017eit\u00e9 v\u00a0minulosti prodlu\u017eov\u00e1no, nebo je vhodn\u011bj\u0161\u00ed pou\u017e\u00edvat obdob\u00ed o\u00a0d\u00e9lce n\u011bkolika des\u00edtek let kon\u010d\u00edc\u00ed kr\u00e1tce p\u0159ed zpracov\u00e1n\u00edm charakteristik.<\/p>\n

P\u0159i volb\u011b reprezentativn\u00edch obdob\u00ed p\u0159ed rokem 1980 byla snaha vyu\u017e\u00edvat co nejdel\u0161\u00ed v\u00fdchoz\u00ed obdob\u00ed pozorov\u00e1n\u00ed. P\u0159i v\u00fdb\u011bru obdob\u00ed pro zpracov\u00e1n\u00ed hydrologick\u00fdch charakteristik bylo v\u017edy posouzeno, zda charakteristiky pou\u017eit\u00e9ho obdob\u00ed jsou dostate\u010dn\u011b bl\u00edzk\u00e9 charakteristik\u00e1m vypo\u010dten\u00fdm z\u00a0nejdel\u0161\u00edch dostupn\u00fdch \u0159ad. Tato shoda byla pou\u017e\u00edv\u00e1na jako argument pro opr\u00e1vn\u011bnost volby u\u017eit\u00e9ho obdob\u00ed. Tento p\u0159\u00edstup p\u0159edpokl\u00e1d\u00e1, \u017ee \u0159ady jsou stacion\u00e1rn\u00ed, tak\u017ee odhad charakteristik z\u00a0minul\u00fdch \u0159ad za co nejdel\u0161\u00ed obdob\u00ed je tak\u00e9 nejvhodn\u011bj\u0161\u00edm odhadem pro budoucnost.<\/p>\n

Zkoum\u00e1n\u00ed \u010dasov\u00fdch meteorologick\u00fdch a\u00a0hydrologick\u00fdch \u0159ad i\u00a0jev\u016f, kter\u00e9 mohou tyto \u0159ady ovlivnit, ukazuje, \u017ee krom\u011b kr\u00e1tkodob\u00fdch kol\u00eds\u00e1n\u00ed (v\u00a0m\u011b\u0159\u00edtku men\u0161\u00edm ne\u017e 3\u20135\u00a0let) existuj\u00ed i\u00a0dlouhodob\u00e9 zm\u011bny s\u00a0\u010dasov\u00fdm m\u011b\u0159\u00edtkem des\u00edtky i\u00a0stovky let. Jen v\u00a0omezen\u00e9 m\u00ed\u0159e jsme schopni je identifikovat a\u00a0matematicky popsat a\u00a0je\u0161t\u011b m\u00e9n\u011b je um\u00edme vysv\u011btlit. Je velmi pravd\u011bpodobn\u00e9, \u017ee v\u011bt\u0161ina takov\u00fdch kol\u00eds\u00e1n\u00ed m\u00e1 charakter, ovlivn\u011bn\u00fd periodick\u00fdmi i\u00a0n\u00e1hodn\u00fdmi vlivy. Odhad hydrologick\u00fdch charakteristik ze zvolen\u00e9ho obdob\u00ed m\u016f\u017ee pak b\u00fdt citliv\u00fd na pom\u011br d\u00e9lky i\u00a0um\u00edst\u011bn\u00ed reprezentativn\u00edho obdob\u00ed vzhledem k\u00a0periodick\u00e9 slo\u017ece pr\u016ftokov\u00fdch \u0159ad.<\/p>\n\"Kasparek-Ladislav-2\"<\/a>\n

Obr. 2. Autokorela\u010dn\u00ed funkce \u0159ady pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f \u0159ady 1801\u20131996
\nFig. 2. Autocorrelation function of annual mean flow series for the period 1801\u20131996<\/h6>\n

Pro posouzen\u00ed, jak d\u00e9lka reprezentativn\u00edho obdob\u00ed ovliv\u0148uje chyby p\u0159edpov\u011bdi pr\u016fm\u011brn\u00e9ho pr\u016ftoku na dobu 20\u00a0let, byla ve studii [1] pou\u017eita \u0159ada pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f Vltavy v\u00a0Praze z\u00a0obdob\u00ed 1801\u20131996. V\u00a0pou\u017eit\u00e9m postupu simuluj\u00edc\u00edm extrapolace pr\u016ftok\u016f v\u00a0ka\u017ed\u00e9m roce se p\u0159edpokl\u00e1d\u00e1, \u017ee pr\u016fm\u011brn\u00fd pr\u016ftok z\u00a0p\u0159edchoz\u00edch N let pozorov\u00e1n\u00ed bude stejn\u00fd i\u00a0v\u00a0n\u00e1sleduj\u00edc\u00edch NP letech. D\u00e9lka v\u00fdchoz\u00ed \u0159ady N byla zvolena 20, 30, 40, 50, 60 a\u00a070\u00a0let, d\u00e9lka p\u0159edpov\u011bdn\u00edho obdob\u00ed NP byla zvolena 10, 20 a\u00a030\u00a0let. Podle pr\u016fm\u011bru absolutn\u00edch hodnot odchylek takto extrapolovan\u00e9ho pr\u016fm\u011brn\u00e9ho pr\u016ftoku od pozorovan\u00e9 hodnoty byla vyhled\u00e1v\u00e1na optim\u00e1ln\u00ed d\u00e9lka n\u00e1vrhov\u00e9ho obdob\u00ed.<\/p>\n

Na\u00a0obr. 1<\/em>\u00a0je vynesen pr\u016fm\u011br absolutn\u00edch hodnot chyb p\u0159edpov\u011bd\u00ed pro uveden\u00e9 d\u00e9lky NP v\u00a0z\u00e1vislosti na d\u00e9lce v\u00fdchoz\u00edho obdob\u00ed N. U\u00a0d\u00e9lky p\u0159edpov\u011bdn\u00edho obdob\u00ed NP = 10\u00a0let o\u010dividn\u011b p\u0159eva\u017euje vliv kol\u00eds\u00e1n\u00ed desetilet\u00fdch pr\u016fm\u011br\u016f nad vlivem d\u00e9lky v\u00fdchoz\u00edho obdob\u00ed, nejmen\u0161\u00ed pr\u016fm\u011br absolutn\u00edch hodnot je u\u00a0trv\u00e1n\u00ed v\u00fdchoz\u00edho obdob\u00ed N = 40\u00a0let. Pr\u016fm\u011br absolutn\u00edch hodnot chyb p\u0159edpov\u011bd\u00ed je u\u00a0trv\u00e1n\u00ed p\u0159edpov\u011bdn\u00edho obdob\u00ed NP = 20 a\u00a030\u00a0let podstatn\u011b men\u0161\u00ed, pro d\u00e9lky v\u00fdchoz\u00edho obdob\u00ed 30\u00a0let m\u00e1 minimum bl\u00ed\u017e\u00edc\u00ed se 8\u00a0%. Ze zobrazen\u00fdch v\u00fdsledk\u016f byl vyvozen z\u00e1v\u011br: z\u00a0hlediska soustavn\u00e9ho vych\u00fdlen\u00ed se jev\u00ed jako vhodn\u011bj\u0161\u00ed v\u00fdchoz\u00ed obdob\u00ed pro v\u00fdpo\u010det s\u00a0krat\u0161\u00edmi d\u00e9lkami, p\u0159ech\u00e1zej\u00edc\u00ed dob\u011b zpracov\u00e1n\u00ed, podle pr\u016fm\u011bru absolutn\u00edch chyb o\u00a0d\u00e9lce 30 a\u017e 40\u00a0let. Pro aktu\u00e1ln\u00ed zpracov\u00e1n\u00ed pr\u016fm\u011brn\u00fdch a\u00a0m-denn\u00edch pr\u016ftok\u016f v\u00a0\u010cHM\u00da bylo v\u00a0souladu s\u00a0t\u00edmto doporu\u010den\u00edm zvoleno obdob\u00ed 1981\u20132010, viz [3].<\/p>\n

Periodick\u00e9 slo\u017eky dlouhodob\u00e9ho kol\u00eds\u00e1n\u00ed pr\u016ftok\u016f<\/h2>\n

Sou\u010d\u00e1st\u00ed studie [1] byl tak\u00e9 pokus ov\u011b\u0159it, zda pro odhad pr\u016fm\u011brn\u00e9ho pr\u016ftoku za v\u00edcelet\u00e1 obdob\u00ed lze s\u00a0p\u0159ijatelnou spolehlivost\u00ed pou\u017e\u00edt extrapolaci vyu\u017e\u00edvaj\u00edc\u00ed autokorela\u010dn\u00ed vazby mezi ro\u010dn\u00edmi pr\u016fm\u011brn\u00fdmi pr\u016ftoky.<\/p>\n

V\u00a0pr\u016fb\u011bhu klouzav\u00fdch pr\u016fm\u011br\u016f \u0159ad ro\u010dn\u00edch pr\u016ftok\u016f a\u00a0sr\u00e1\u017eek se objevuj\u00ed prvky periodick\u00fdch kol\u00eds\u00e1n\u00ed. Ta m\u016f\u017eeme popsat autokorela\u010dn\u00edm, resp. autoregresn\u00edm modelem, pokud takov\u00fd model uva\u017euje i\u00a0vzd\u00e1len\u011bj\u0161\u00ed autokorela\u010dn\u00ed vazby mezi \u010dleny \u0159ady. Pro posouzen\u00ed mo\u017enost\u00ed aplikace t\u00e9to metody pro odhad v\u00fdvoje dlouhodob\u00fdch zm\u011bn pr\u016ftok\u016f na zvolen\u00e9 obdob\u00ed jsme vyu\u017eili program [3].<\/p>\n

Autokorela\u010dn\u00ed funkce \u0159ady pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f na\u00a0obr. 2<\/em>\u00a0sv\u011bd\u010d\u00ed pouze o\u00a0p\u0159enosu z\u00e1sob vody z\u00a0p\u0159edch\u00e1zej\u00edc\u00edho do n\u00e1sleduj\u00edc\u00edho roku, \u017e\u00e1dn\u00e9 vzd\u00e1len\u011bj\u0161\u00ed vazby neukazuje. Z\u00a0autokorela\u010dn\u00ed funkce pr\u016ftok\u016f za v\u00edcelet\u00e1 obdob\u00ed, nap\u0159. ze\u00a0sedmilet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f, lze na periodick\u00e9 slo\u017eky v\u00a0pr\u016ftokov\u00fdch \u0159ad\u00e1ch usuzovat, viz\u00a0obr. 3<\/em>.<\/p>\n\"Kasparek-Ladislav-3\"<\/a>\n

Obr. 3. Autokorela\u010dn\u00ed funkce \u0159ady 10let\u00fdch klouzav\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f 1801\u20131996
\nFig. 3. Autocorrelation function of 10-year moving averages of the annual mean flow series for the period 1801\u20131996<\/h6>\n

Pro \u0159ady klouzav\u00fdch pr\u016fm\u011br\u016f ro\u010dn\u00edch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f s\u00a0intervalem pr\u016fm\u011brov\u00e1n\u00ed 2 a\u017e 15\u00a0let byly vypo\u010dteny spektr\u00e1ln\u00ed hustoty. Pro ka\u017ed\u00fd interval pr\u016fm\u011brov\u00e1n\u00ed byla vyhled\u00e1na d\u00e9lka periody s\u00a0maxim\u00e1ln\u00ed hodnotou spektr\u00e1ln\u00ed hustoty. V\u00fdsledky shrnuje\u00a0tabulka 1<\/em>. Nejv\u00fdzna\u010dn\u011bj\u0161\u00ed periody se p\u0159i d\u00e9lk\u00e1ch pr\u016fm\u011brov\u00e1n\u00ed m\u00e9n\u011b ne\u017e 10\u00a0let pohybuj\u00ed v\u00a0rozmez\u00ed 16 a\u017e 19\u00a0let, p\u0159i pr\u016fm\u011brov\u00e1n\u00ed 10 a\u017e 14\u00a0let d\u00e9lka periody soustavn\u011b stoup\u00e1 od 19 do 25\u00a0let. P\u0159\u00edklad pr\u016fb\u011bhu spektr\u00e1ln\u00ed hustoty pro sedmilet\u00e9 pr\u016fm\u011bry ro\u010dn\u00edch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f je na\u00a0obr. 4<\/em>. Podle tohoto grafu pro \u0159adu obsahuj\u00edc\u00ed i\u00a0pozorov\u00e1n\u00ed z\u00a019. stolet\u00ed je nejv\u011bt\u0161\u00ed hodnota spektr\u00e1ln\u00ed hustoty u\u00a0d\u00e9lky periody 19\u00a0let, pro \u0159adu od roku 1920 do 2015, kde je periodick\u00e9 kol\u00eds\u00e1n\u00ed z\u0159eteln\u011bj\u0161\u00ed, 22\u00a0let.<\/p>\n

Program [4] poskytuje i\u00a0d\u00e9lku obdob\u00ed, na kter\u00e9 je opodstatn\u011bn\u00e9 p\u0159edpov\u00eddat (dosah p\u0159edpov\u011bdi). Prom\u011bna t\u00e9to veli\u010diny s\u00a0d\u00e9lkou pr\u016fm\u011brov\u00e1n\u00ed je patrn\u00e1 z\u00a0tabulky 1<\/em>. Pro intervaly pr\u016fm\u011brov\u00e1n\u00ed od 9 do 14\u00a0let a\u00a0tak\u00e9 pro interval pr\u016fm\u011brov\u00e1n\u00ed 7\u00a0let je dosah p\u0159edpov\u011bdi podstatn\u011b v\u011bt\u0161\u00ed, ne\u017e pro intervaly pr\u016fm\u011brov\u00e1n\u00ed krat\u0161\u00ed nebo del\u0161\u00ed.<\/p>\n

Tabulka 1. D\u00e9lka v\u00fdznamn\u00fdch period a\u00a0optim\u00e1ln\u00ed stupe\u0148 autoregresn\u00edho modelu pro r\u016fzn\u00e9 d\u00e9lky pr\u016fm\u011brov\u00e1n\u00ed \u0159ady pr\u016ftok\u016f
\nTable 1. Significant period length and optimal degree of the autoregressive model for different averaging lengths of flow series<\/h5>\n\"Kasparek-Ladislav-tabulka1\"<\/a>\n

Pro \u0159ady klouzav\u00fdch pr\u016fm\u011br\u016f s\u00a0intervalem pr\u016fm\u011brov\u00e1n\u00ed 2 a\u017e 15\u00a0let byly v\u00a0roce 1996 vypo\u010dteny p\u0159edpov\u011bdi autoregresn\u00edm modelem, popsan\u00fdm nap\u0159\u00edklad ve\u00a0skriptech \u010cVUT [5]. P\u0159i v\u00fdpo\u010dtech byl stupe\u0148 regrese zvolen 15, na d\u00e9lce pr\u016fm\u011brov\u00e1n\u00ed z\u0159ejm\u011b systematicky nez\u00e1vis\u00ed, viz\u00a0tabulka 1<\/em>.<\/p>\n\"Kasparek-Ladislav-4\"<\/a>\n

Obr. 4. Spektr\u00e1ln\u00ed hustota 7let\u00fdch klouzav\u00fdch pr\u016ftok\u016f vypo\u010d\u00edtan\u00fdch z\u00a0\u0159ad 1801\u20131995 a\u00a01920\u20132015
\nFig. 4. Spectral density of 7-year moving average flow calculated from the 1801\u20131995 and 1920\u20132015 series<\/h6>\n

P\u0159edpov\u011bdi pro pr\u016fm\u011bry z\u00a0obdob\u00ed o\u00a0d\u00e9lce K\u00a0= 7, 8, 9, 10 a\u00a011\u00a0let jsou na\u00a0obr. 5<\/em>. Uk\u00e1zalo se, \u017ee r\u00e1mcov\u011b indikovaly dlouhodob\u00e9 kol\u00eds\u00e1n\u00ed pr\u016ftok\u016f s\u00a0koncem vodn\u00e9ho obdob\u00ed v\u00a0letech 2003\u20132004 a\u00a0s\u00a0n\u00e1sleduj\u00edc\u00edm obdob\u00edm s\u00a0men\u0161\u00edmi pr\u016ftoky a\u017e do let 2011\u20132014. V\u00fdpo\u010dty ukazuj\u00ed, \u017ee p\u0159edpov\u011b\u010f nen\u00ed z\u00e1sadn\u00edm zp\u016fsobem ovlivn\u011bna t\u00edm, jak\u00fd interval pr\u016fm\u011brov\u00e1n\u00ed pou\u017eijeme, pokud bude z\u00a0pou\u017eit\u00e9ho rozmez\u00ed.<\/p>\n\"Kasparek-Ladislav-5\"<\/a>\n

Obr. 5. P\u0159edpov\u011bdi K-let\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f vypo\u010d\u00edtan\u00e9 autoregresn\u00edmi modely
\nFig. 5. Predictions of K-year moving average flows calculated by autoregression models<\/h6>\n

V\u00a0dal\u0161\u00ed etap\u011b v\u00fdzkumu jsme posoudili, zda p\u0159i pou\u017eit\u00ed autoregresn\u00edch p\u0159edpov\u011bd\u00ed klouzav\u00fdch pr\u016fm\u011br\u016f (zvolili jsme d\u00e9lku pr\u016fm\u011brov\u00e1n\u00ed 10\u00a0let) pro p\u0159edpov\u011b\u010f na 10\u00a0let z\u00edsk\u00e1me p\u0159edpov\u011bdi \u00fasp\u011b\u0161n\u011bj\u0161\u00ed, ne\u017e p\u0159i p\u0159edpov\u011bdi p\u0159i extrapolaci p\u0159edch\u00e1zej\u00edc\u00edho pr\u016fm\u011brn\u00e9ho pr\u016ftoku. Autoregresn\u00ed model se m\u016f\u017ee li\u0161it \u0159\u00e1dem, ale tak\u00e9 volbou obdob\u00ed, podle kter\u00e9ho jsou odvozov\u00e1ny autoregresn\u00ed koeficienty. D\u00e1le uveden\u00e9 v\u00fdsledky jsou p\u0159edpov\u011bdi desetilet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f podle autokorela\u010dn\u00edch koeficient\u016f odvozen\u00fdch z\u00a0cel\u00e9 \u0159ady 1801\u20131995. \u0158\u00e1d regrese byl zvolen 11\u00a0let. Numerick\u00fd pokus simuloval p\u0159edpov\u011b\u010f zpracovanou v\u00a0ka\u017ed\u00e9m roce od dvan\u00e1ct\u00e9ho roku \u0159ady. V\u00fdstupem programu jsou p\u0159edpov\u011bdi desetilet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f na NP n\u00e1sleduj\u00edc\u00edch let. Pro posouzen\u00ed, zda pou\u017eit\u00ed regresn\u00edch p\u0159edpov\u011bd\u00ed vede k\u00a0lep\u0161\u00edm odhad\u016fm, ne\u017e p\u0159edpov\u011b\u010f podle pr\u016fm\u011bru p\u0159edch\u00e1zej\u00edc\u00edho obdob\u00ed nebo ne\u017e u\u017eit\u00ed konstantn\u00edho dlouhodob\u00e9ho pr\u016fm\u011bru, byl vypo\u010dten pro ka\u017edou p\u0159edpov\u011b\u010f pr\u016fm\u011br absolutn\u00edch hodnot odchylek p\u0159edpov\u011bd\u00ed od pozorovan\u00fdch hodnot za p\u0159edpov\u00eddan\u00e9 obdob\u00ed. Tyto charakteristiky chyb byly pro ka\u017ed\u00fd rok porovn\u00e1ny s\u00a0analogicky vypo\u010dten\u00fdmi ukazateli \u201esetrval\u00fdch\u201c p\u0159edpov\u011bd\u00ed podle p\u0159edch\u00e1zej\u00edc\u00edho pr\u016fm\u011brn\u00e9ho pr\u016ftoku za 10\u00a0let a\u00a0s\u00a0analogicky vypo\u010dten\u00fdmi ukazateli odchylek pozorovan\u00fdch pr\u016ftok\u016f od dlouhodob\u00e9ho pr\u016fm\u011bru. Extr\u00e9my pr\u016fm\u011br\u016f odchylek jsou u\u00a0regresn\u00edch p\u0159edpov\u011bd\u00ed znateln\u011b men\u0161\u00ed, ne\u017e u\u00a0odchylek od dlouhodob\u00e9ho pr\u016fm\u011bru, tot\u00e9\u017e plat\u00ed (i\u00a0kdy\u017e m\u00e9n\u011b v\u00fdrazn\u011b) pro porovn\u00e1n\u00ed s\u00a0pr\u016fm\u011bry odchylek p\u0159edpov\u011bd\u00ed podle p\u0159edch\u00e1zej\u00edc\u00edho pr\u016fm\u011bru. Pro v\u00fdsledn\u00e9 porovn\u00e1n\u00ed byly vypo\u010dteny pr\u016fm\u011bry z\u00a0pr\u016fm\u011brn\u00fdch absolutn\u00edch hodnot odchylek ze v\u0161ech p\u0159edpov\u011bd\u00ed v\u00a0jednotliv\u00fdch letech pro pou\u017eit\u00e9 p\u0159edpov\u011bdn\u00ed postupy. Jsou uvedeny v\u00a0tabulce 2<\/em>\u00a0a\u00a0ukazuj\u00ed, \u017ee regresn\u00ed p\u0159edpov\u011bdi v\u00a0pr\u016fm\u011bru vedou k\u00a0men\u0161\u00edm odchylk\u00e1m.<\/p>\n

Tabulka 2. Porovn\u00e1n\u00ed pr\u016fm\u011br\u016f absolutn\u00edch hodnot chyb p\u0159edpov\u011bdi podle r\u016fzn\u00fdch postup\u016f v\u00fdpo\u010dtu
\nTable 2. Comparison of averages absolute forecast errors according to different calculation procedures<\/h5>\n\"Kasparek-Ladislav-tabulka2\"<\/a>\n

V\u00a0sou\u010dasn\u00e9 dob\u011b uplynulo od zpracov\u00e1n\u00ed v\u00fd\u0161e popsan\u00fdch v\u00fdpo\u010dt\u016f p\u0159edpov\u011bd\u00ed 18\u00a0let, tak\u017ee m\u016f\u017eeme posoudit, zda p\u0159edpov\u011bdi podle autoregresn\u00edho modelu mohly poskytnout alespo\u0148 \u010d\u00e1ste\u010dn\u011b pou\u017eiteln\u00e9 informace o\u00a0v\u00fdvoji pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f Vltavy v\u00a0Praze. Na\u00a0obr. 6<\/em>\u00a0jsou zobrazeny pr\u016fb\u011bhy p\u0159edpov\u011bzen\u00e9 a\u00a0pr\u016fb\u011bhy vypo\u010d\u00edtan\u00e9 podle pozorov\u00e1n\u00ed, pro d\u00e9lky pr\u016fm\u011brov\u00e1n\u00ed K\u00a0= 7 a\u00a010\u00a0let. Z\u00a0obr\u00e1zku je patrn\u00e9, \u017ee do roku 2004 vystihly u\u00a0obou d\u00e9lek pr\u016fm\u011brov\u00e1n\u00ed postupn\u00fd n\u00e1r\u016fst pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f. P\u0159edpov\u011b\u010f pro K\u00a0= 7 se nijak z\u00e1sadn\u011b neodchyluje od pozorovan\u00e9ho pr\u016fb\u011bhu. V\u00a0pokra\u010duj\u00edc\u00edm \u00faseku \u0159ady po roce 2005 p\u0159edpov\u011bdi sice indikuj\u00ed postupn\u00fd r\u00e1mcov\u00fd pokles pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f a\u017e do roku 2015, v\u00a0absolutn\u00edch velikostech pr\u016ftoku jsou v\u0161ak realit\u011b zna\u010dn\u011b vzd\u00e1len\u00e9. Z\u00a0t\u011bchto v\u00fdsledk\u016f m\u016f\u017eeme usuzovat, \u017ee p\u0159edpov\u011bdi autoregresn\u00edm modelem mohou poskytnout pou\u017eiteln\u00e9 informace jen s\u00a0p\u0159edstihem n\u011bkolika let.<\/p>\n\"Kasparek-Ladislav-6\"<\/a>\n

Obr. 6. P\u0159edpov\u011bdi klouzav\u00fdch pr\u016ftok\u016f K-rok\u016f vypo\u010dten\u00fdch v\u00a0roce 1996 autoregresn\u00edmi modely ve srovn\u00e1n\u00ed s\u00a0pozorovan\u00fdmi hodnotami
\nFig. 6. Predictions of K-years moving average flows calculated in 1996 by autoregressive models compared with observed values<\/h6>\n

Podle tohoto poznatku jsme vypo\u010d\u00edtali simulaci p\u0159edpov\u011bd\u00ed sedmilet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f autoregresn\u00edm modelem v\u00a0dvoulet\u00e9m intervalu po\u010d\u00ednaje rokem 2002, v\u017edy na n\u00e1sleduj\u00edc\u00edch 5\u00a0let. Takto vypo\u010d\u00edtan\u00e9 pr\u016fb\u011bhy spolu s\u00a0pr\u016fb\u011bhem sedmilet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f podle pozorov\u00e1n\u00ed jsou na\u00a0obr. 7<\/em>. P\u0159edpov\u011bdi by v\u00a0posuzovan\u00e9m obdob\u00ed p\u0159ijateln\u011b indikovaly dlouhodob\u00e9 tendence zm\u011bn pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f.<\/p>\n

Mo\u017enostmi dlouhodob\u00fdch p\u0159edpov\u011bd\u00ed pomoc\u00ed harmonick\u00e9ho modelu PYTHIA a\u00a0autoregresn\u00edho modelu klouzav\u00fdch pr\u016ftok\u016f se zab\u00fdvala Pek\u00e1rov\u00e1 [6]. Podle v\u00fdsledk\u016f z\u00a0modelu PYTHIA m\u00e1 b\u00fdt v\u00edcelet\u00e9 such\u00e9 obdob\u00ed 2013\u20132020. V\u00fdrazn\u011b pr\u016ftokov\u011b podpr\u016fm\u011brn\u00e9 roky v\u00a0obdob\u00ed po roce 2015 p\u0159edpov\u00eddal i\u00a0sezonn\u00ed autoregresn\u00ed model (SARIMA) [6].<\/p>\n\"Kasparek-Ladislav-7\"<\/a>\n

Obr. 7. Simulace postupn\u00fdch p\u0159edpov\u011bd\u00ed pr\u016fm\u011brn\u00fdch sedmilet\u00fdch pr\u016ftok\u016f vypo\u010d\u00edtan\u00e9 po dvou letech, s\u00a0p\u0159edstihem 1 a\u017e 5\u00a0let
\nFig. 7. Simulation of\u00a0successive predictions of 7-year moving average flow calculated every two years with forecast horizon 1 to 5 years<\/h6>\n

Souvislosti dlouhodob\u00e9ho kol\u00eds\u00e1n\u00ed pr\u016ftok\u016f s\u00a0geomagnetick\u00fdm slune\u010dn\u00edm cyklem<\/h2>\n

P\u0159ed rokem 1965 zpracoval Bratr\u00e1nek [7] p\u0159edpov\u011b\u010f v\u00fdskytu maxim a\u00a0minim pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f Vltavy v\u00a0Praze podle postupu, v\u00a0kter\u00e9m se pou\u017e\u00edvaly \u010dasov\u00e9 vazby mezi pr\u016fb\u011bhem po\u010dtu slune\u010dn\u00edch skvrn a\u00a0v\u00fdskytem extr\u00e9m\u016f ro\u010dn\u00edch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f.\u00a0Obr\u00e1zek 8<\/em>\u00a0ukazuje, \u017ee jeho p\u0159edpov\u011b\u010f byla \u00fasp\u011b\u0161n\u00e1. P\u0159i pokusech o\u00a0dal\u0161\u00ed aplikace j\u00edm navr\u017een\u00e9ho postupu jsme shledali, \u017ee p\u0159edpokl\u00e1dan\u00e9 \u010dasov\u00e9 relace se dlouhodob\u011b nezachov\u00e1vaj\u00ed.<\/p>\n\"Kasparek-Ladislav-8\"<\/a>\n

Obr. 8. Pr\u016fb\u011bh pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f Vltavy v\u00a0Praze a\u00a0predikce vypo\u010d\u00edtan\u00e9 Bratr\u00e1nkem [7]
\nFig. 8. Average annual flow of the Vltava River in Prague and the prediction calculated by Bratr\u00e1nek [7]<\/h6>\n

Podle\u00a0obr. 4<\/em>\u00a0je pro sedmilet\u00e9 klouzav\u00e9 pr\u016fm\u011bry pro \u0159adu pr\u016ftok\u016f Vltavy v\u00a0Praze s\u00a0po\u010d\u00e1tkem v\u00a0roce 1801 charakteristick\u00e1 perioda s\u00a0d\u00e9lkou 19\u00a0let, v\u00a0pozd\u011bj\u0161\u00edm obdob\u00ed 22\u00a0let, u\u00a0\u0159ad pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch sr\u00e1\u017eek podle [1] tak\u00e9 22\u00a0let, co\u017e je dvojn\u00e1sobek st\u0159edn\u00ed d\u00e9lky jeden\u00e1ctilet\u00e9 periody kol\u00eds\u00e1n\u00ed po\u010dtu slune\u010dn\u00edch skvrn. D\u00e9lku periody 22\u00a0let m\u00e1 Hale\u016fv cyklus magnetick\u00e9ho pole Slunce, kter\u00fd vypl\u00fdv\u00e1 z\u00a0toho, \u017ee v\u017edy za 11\u00a0let se magnetick\u00e9 pole Slunce p\u0159ep\u00f3luje a\u00a0za dal\u0161\u00edch 11\u00a0let se p\u0159ep\u00f3luje zp\u011bt, viz [8]. Pro posouzen\u00ed zda dlouhodob\u00e9 kol\u00eds\u00e1n\u00ed pr\u016ftok\u016f Vltavy m\u016f\u017ee souviset s\u00a0Haleov\u00fdm cyklem, jsme \u0159adu po\u010dtu slune\u010dn\u00edch skvrn transformovali tak, \u017ee po\u010dty ka\u017ed\u00e9ho druh\u00e9ho cyklu jsme vyn\u00e1sobili \u010d\u00edslem -1. Takto z\u00edskan\u00fd pr\u016fb\u011bh je na\u00a0obr. 9<\/em>\u00a0zobrazen spole\u010dn\u011b s\u00a0pr\u016fb\u011bhem sedmilet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f ro\u010dn\u00edch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f, ob\u011b veli\u010diny jsou transformovan\u00e9 na sm\u011brodatn\u00e9 prom\u011bnn\u00e9. Ze sedmi cykl\u016f z\u00a0obdob\u00ed 1851\u20132015 lze v\u00a0p\u011bti shledat p\u0159\u00edznaky podobnosti. Koeficient korelace mezi po\u0159adnicemi magnetick\u00e9ho cyklu a\u00a0klouzav\u00fdmi pr\u016fm\u011brn\u00fdmi sedmilet\u00fdmi pr\u016ftoky je 0,61. M\u016f\u017eeme tedy usuzovat, \u017ee kol\u00eds\u00e1n\u00ed pr\u016ftok\u016f v\u00a0pou\u017eit\u00e9m m\u011b\u0159\u00edtku n\u011bjak\u00fdm zp\u016fsobem, kter\u00fd nezn\u00e1me, souvis\u00ed s\u00a0geomagnetick\u00fdm Haleov\u00fdm cyklem Slunce.<\/p>\n\"Kasparek-Ladislav-9\"<\/a>\n

Obr. 9. \u010casov\u00fd pr\u016fb\u011bh sm\u011brodatn\u00fdch prom\u011bnn\u00fdch magnetick\u00e9ho cyklu Slunce a\u00a0sedmilet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f pr\u016ftok\u016f Vltavy
\nFig. 9. Time series of the standardized variables of the magnetic cycle of the Sun and seven-year moving averages flow in the Vltava River<\/h6>\n

Pozn\u00e1mka<\/h4>\n

Pro v\u00fd\u0161e uveden\u00e9 posouzen\u00ed jsme pou\u017eili \u0159adu pr\u016ftok\u016f Vltavy s\u00a0po\u010d\u00e1tkem v\u00a0roce 1851. D\u016fvodem je p\u0159\u00edli\u0161n\u00e1 nejistota, kterou je zat\u00ed\u017eena p\u0159edch\u00e1zej\u00edc\u00ed \u010d\u00e1st \u0159ady, na kterou upozornila studie viz [7]. Ke\u00a0stejn\u00e9mu z\u00e1v\u011bru vedly i\u00a0v\u00fdsledky modelov\u00e1n\u00ed hydrologick\u00e9 bilance, proveden\u00e9 v\u00a0r\u00e1mci sou\u010dasn\u00fdch prac\u00ed.<\/p>\n

Vztah mezi dlouhodob\u00fdm kol\u00eds\u00e1n\u00edm pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f a\u00a0kulmina\u010dn\u00edch pr\u016ftok\u016f povodn\u00ed<\/h2>\n

Kol\u00eds\u00e1n\u00ed v\u00edcelet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f za sedmilet\u00e9 nebo desetilet\u00e9 obdob\u00ed je z\u00e1visl\u00e9 p\u0159edev\u0161\u00edm na v\u00fdskytech mimo\u0159\u00e1dn\u011b velk\u00e9 hodnoty jednoho nebo i\u00a0n\u011bkolika ro\u010dn\u00edch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f. Pr\u016fb\u011bh sm\u011brodatn\u00fdch prom\u011bnn\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f za\u00a0desetilet\u00e1 obdob\u00ed, vypo\u010d\u00edtan\u00fdch z\u00a0pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f a\u00a0z\u00a0maxim pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f na\u00a0obr. 10<\/em>\u00a0jsou podobn\u00e9.<\/p>\n\"Kasparek-Ladislav-10\"<\/a>\n

Obr. 10. Standardizovan\u00e9 prom\u011bnn\u00e9 vypo\u010dten\u00e9 z 10let\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f a z maxim\u00e1ln\u00edch ro\u010dn\u00edch pr\u016ftok\u016f v desetilet\u00fdch obdob\u00edch
\nFig. 10. Standardized variables calculated from 10-year moving average annual flow and from 10-year running maxima of the annual flow<\/h6>\n

Podstatnou \u010d\u00e1st variability ro\u010dn\u00edch pr\u016ftok\u016f lze vysv\u011btlit maxim\u00e1ln\u00edmi kulmina\u010dn\u00edmi pr\u016ftoky jako ukazateli v\u00fdskytu povodn\u00ed. Sv\u011bd\u010d\u00ed o\u00a0tom regresn\u00ed vztah mezi pr\u016fm\u011brn\u00fdmi ro\u010dn\u00edmi pr\u016ftoky a\u00a0maxim\u00e1ln\u00edmi kulmina\u010dn\u00edmi pr\u016ftoky v\u00a0roce na\u00a0obr. 11<\/em>, kter\u00fd je charakterizov\u00e1n koeficientem korelace 0,687. Tak\u00e9 koeficient korelace vztahu mezi desetilet\u00fdmi klouzav\u00fdmi pr\u016fm\u011brn\u00fdmi pr\u016ftoky\u00a0a\u00a0desetilet\u00fdmi klouzav\u00fdmi pr\u016fm\u011bry kulmina\u010dn\u00edch pr\u016ftok\u016f m\u00e1 hodnotu 0,599. I\u00a0kol\u00eds\u00e1n\u00ed desetilet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f je tedy podstatn\u011b ur\u010dov\u00e1no v\u00fdskytem a\u00a0velikost\u00ed povodn\u00ed. Ukazuje se to tak\u00e9 na\u00a0obr. 12<\/em>, kde jsou pr\u016fb\u011bhy klouzav\u00fdch pr\u016fm\u011br\u016f sm\u011brodatn\u00fdch prom\u011bnn\u00fdch pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f a\u00a0maxim\u00e1ln\u00edch kulmina\u010dn\u00edch pr\u016ftok\u016f.<\/p>\n\"Kasparek-Ladislav-11\"<\/a>\n

Obr. 11. Korela\u010dn\u00ed vztah mezi pr\u016fm\u011brn\u00fdmi ro\u010dn\u00edmi pr\u016ftoky a\u00a0maxim\u00e1ln\u00edmi kulmina\u010dn\u00edmi pr\u016ftoky
\nFig. 11. Correlation between the average annual flow and the maximum flood peak flows<\/h6>\n\"Kasparek-Ladislav-12\"<\/a>\n
Obr. 12. Pr\u016fb\u011bh desetilet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f sm\u011brodatn\u00fdch prom\u011bnn\u00fdch pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f a\u00a0maxim\u00e1ln\u00edch kulmina\u010dn\u00edch pr\u016ftok\u016f
\nFig. 12. Moving average of the standardised average annual flow and maximum flood peak flows<\/h6>\n

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

P\u0159i volb\u011b reprezentativn\u00edho obdob\u00ed se jev\u00ed jako vhodn\u011bj\u0161\u00ed vyu\u017e\u00edvat obdob\u00ed o\u00a0d\u00e9lce 30 a\u017e 40\u00a0let p\u0159ech\u00e1zej\u00edc\u00ed dob\u011b zpracov\u00e1n\u00ed, ne\u017e prodlu\u017eovat d\u0159\u00edve pou\u017e\u00edvan\u00e1 obdob\u00ed (nap\u0159\u00edklad 1931\u20131980) do sou\u010dasnosti.<\/p>\n

V\u00a0\u0159ad\u011b pr\u016ftok\u016f Vltavy v\u00a0Praze se p\u0159i pou\u017eit\u00ed v\u00edcelet\u00fdch klouzav\u00fdch pr\u016fm\u011br\u016f projevuj\u00ed periodick\u00e9 slo\u017eky kol\u00eds\u00e1n\u00ed. Autoregresn\u00edm modelem lze na tomto z\u00e1klad\u011b p\u0159edpov\u00eddat budouc\u00ed v\u00fdvoj vodnosti, s\u00a0p\u0159edstihem nap\u0159\u00edklad 5\u00a0let. P\u0159edpov\u00eddat lze jen n\u011bkolikalet\u00e9 pr\u016fm\u011bry, nikoliv jednotliv\u00e9 ro\u010dn\u00ed pr\u016fm\u011bry.<\/p>\n

Periodick\u00e9 kol\u00eds\u00e1n\u00ed v\u00edcelet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f je dosti podobn\u00e9 a\u00a0v\u011bt\u0161inou synchronn\u00ed s\u00a0pr\u016fb\u011bhem 22let\u00e9ho geomagnetick\u00e9ho cyklu Slunce.<\/p>\n

Velikost pr\u016fm\u011brn\u00fdch ro\u010dn\u00edch pr\u016ftok\u016f i\u00a0v\u00edcelet\u00fdch pr\u016fm\u011brn\u00fdch pr\u016ftok\u016f je podstatn\u011b z\u00e1visl\u00e1 na v\u00fdskytu a\u00a0velikosti povodn\u00ed, tak\u017ee kol\u00eds\u00e1n\u00ed pr\u016ftok\u016f v\u00a0m\u011b\u0159\u00edtku v\u00edcelet\u00fdch obdob\u00ed je projevem kol\u00eds\u00e1n\u00ed re\u017eimu povodn\u00ed. Tato vazba je patrn\u00e1, i\u00a0kdy\u017e povodn\u011b popisujeme jen kulmina\u010dn\u00edm pr\u016ftokem.<\/p>\n","protected":false},"excerpt":{"rendered":"

The first part the present study contains recommendations for the selection of representative observation period used for the calculation of average flow characteristics. This is the result of calculations based on time series of flows of the Vltava River in Prague with beginning in 1801.<\/p>\n","protected":false},"author":8,"featured_media":3849,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86],"tags":[932,934,933,935],"coauthors":[35],"class_list":["post-3900","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydraulics-hydrology-and-hydrogeology","tag-mean-flow","tag-periodicity-of-flows","tag-representative-observation-period","tag-the-geomagnetic-cycle-of-the-sun"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3900","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=3900"}],"version-history":[{"count":2,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3900\/revisions"}],"predecessor-version":[{"id":30418,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/posts\/3900\/revisions\/30418"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media\/3849"}],"wp:attachment":[{"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/media?parent=3900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/categories?post=3900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/tags?post=3900"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.vtei.cz\/en\/wp-json\/wp\/v2\/coauthors?post=3900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}