Hidrológiai Közlöny 1961 (41. évfolyam)

4. szám - Szigyártó Zoltán: Az éghajlati valószínűségi függvény és a valószínűség

Szigyártó Z.: Az éghajlati valószínűségi függvény Hidrológiai Közlöny 1961. 4. sz. 289 •5. Németh E. : Hidrológia ós hidrometria. Tankönyv­kiadó. Budapest, 1954. 6. Szepessy A. : Mértékadó vízhozamok meghatározása a belvízvédelem tervezéséhez. Beszámoló a Víz­Gazdálkodási Tudományos Kutató Intézet 1954. évi munkásságáról. 171—184. o. Műszaki Kiadó, Buda­pest, 1955. 7. Szigyártó Z. : Statisztikus törvényszerűségek a csa­padék évi járásában. Kandidátusi disszertáció, Buda­pest, 1956. 8. Szigyártó Z. : Hidrológiai események visszatérési ideje. Hidrológiai Közlöny, Budapest, 1957. 4. sz. 325—329. o. KJ1HMATHMECKA51 OyHKUHfl BEPOflTHOCTM H BEPOílTHOCTb JJp. 3. Cudapmo KaHfl. 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He HMeeT CB5I3U c BepoHTHOCTbio. YMHTbiBayi ee xapaKTep­Hbie cBoiícTBa öojiee Bcero MOWHO HasbiBaTb ee epedned </>yHKtfueü. HaKOHeu CTaTbH 3aHHMaeTca c TOJiKOBaHHeM He3a­BHCHMoro nepeMeHHOro flaHHon (JiyHKHHH, T. e. c TOJIKO­BaHHeM npoflOJDKHTenbHOCTH T. Ha cpue. 1. yKa3bma­ETCH Ha TO, MTO ,,NPO,NOJI>KHTEJIBHOCTB ocaflKa" MOWCT 6biTb ycTaHOBJieHa TOJibKO np0ii3B0JibHbiM nyTeM, a Ha 0ue. 2. HarjijiflHO BHAHO, MTO TaK KaK npoflOJDKHTeJib­HocTb oca^Ka HBJIHCTCH HenpepuBHo pacnpeflejiHioiueucH nepeMeHHOíi BCPOHTHOCTH — T3KHM 0öpa30M Ka>KFLAH npoflOJi>KHTejibHocTb oca^Ka HMeeT pa3H0ií AJiHiejib­HOCTH —, nojiojKeHiie (j)yHKHHH MAKCHMYMA B Sojibnioü Mepe 33BHCHT OT BejlHMHHbl UCHbl flejieHHJI, BbIŐp3HH0H npu pa3pa6oTKe AaHHbix. YMiiTbiBaa Bee BbiineonucaHHbie, B CTaTbe yKa3bi­BAETCH Ha TO, MTO (FIYHKUMI MaKCHMyMa ocaflKa MOJKCT ÖblTb HOCTpOeHa 0AH03H3MH0 TOJibKO Tor«a, Kor«a He3a­BHCHMbiM nepeMeHHbiM (JjyHKHHH BbiönpaeTca „npofloji­>KHTCJIbHOCTb, CMHT33 C H3M3Jia BbinS/jeHMH OCa^KOB", HJIH „np0H3B0JlbH0 Bbl6p3HH3JI np0«0JI>KHTejIbH0CTb", pa3Meuuuomaaoi He3aBiicHM0 OT CBH33HHOCTH. PaccMaTpuBan TOJiKOBaHne He33BiicnMoro nepe­MeHHoro cpeflHeH (JjyHKHHH OCAFLKOB B CTaTbe aBTop npn­xoflHT K n0fl06H0My pe3yjibTaTy c flonojiHeHHeM, MTO ecjin OCHOBOH ripOpaÖOTKH HBJlíieTCJI , ,npOH3BOJIbHO BblÖpaH­H3H npOflOJI>KHTejIbHOCTb", TO Hy>KHO IipHAep>KHB3TbCÍI K TpeSoBaHino, MTOöbi npu cocTaBjieHHH flaHHbix no OCa^KaM O^HHaKOBbie npOflOJl>KIITCJIbHOCTII, HO c pa3HbIM KOJiHMecTBOM ocaflKOB He MOTJIH noi<pbiTb flpyr-flpyra (0UZ. 3.). Qnejiaji npai<THMecKHe BbiBOflbi, aBTopoM ycTaHaB­jiHBaeTCH, MTO (JjyHKmiH MaKCHMyMa ocaflKOB ii cpeflHue (JjyHKHHH uejiecoű6pa3H0 onpeAejniTb TaKHM 06pa30M, MTOÖbl npOMOKyTOK BpeMeHH, npHHÍITblií 3a He3aBIICH­MblM nepeMeHHbiM 6bIJI TaKOIÍ ,,IipOH3BOJIbHO BIiIÖpaHHOií np0fl0ji>KHTejibH0CTbK)", HaMajio KOTopoíí He3aBiicejio OT HaMajia Bbinaflenna oca^KOB. The Climatic Funetion and l'rohability By Dr. Z. Szigyártó Candidate of Teehnical Sciences In solving practical problems of hydraulic engin­eering especially such related to the removal of excess surface waters, as well as to municipal canaliz­ation, functions of the form h = h (T) are commonly used, where the likely maximum pre­cipitation during a time interval (T) is given as the funetion of the same. These relationships are eonstructed by establishing for an observation period of N years the highest pre­cipitation values pertaining to various time intervals T, and by correlating the points thus obtained by graphic­al methods. However, other relationships h = h (T) are alsó applied, which are obtained by correlating, rather than the maximum precipitation values observed in various intervals during N years, the second, third, . . ., i-th subsequent highest value. The functions of these two types are referred to in Hungárián hydraulic engineering practice as „cli­matic probability functions". The relation of these functions to mathematical probability is investigated in the present paper, and eriteria are established for constructing the functions. Referring to an earlier paper [7] it is pointed out, that the functions belonging to the first group, which are used for estimating the highest precipitation values, are a kind of maximum functions according to the terminology used in mathematical statistics. Therefore, this type should rather be termed as precipitation maxi­mum funetion. It can be shown, that the only relation bet­ween these functions and probability in the true mathematical sense of the word is, that with increasing number of observations the peak precipitation values observed converge stochastically to the corresponding value of the theoretical maximum funetion. The other group of functions is established, instead of the peak, generally on the basis of the i-th value pertaining to various time intervals T. For deseribing these functions, the ratio i/N, or N/i is used in practice. As pointed out in the paper, the ratio i/N indi­cates the average number of values equalto, or exceeding the corresponding value of the funetion during a year and for any arbitrary interval. On the other hand, the ratio N/i is identical with

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