Vízügyi Közlemények, 2001 (83. évfolyam)

2. füzet - Reimann J.-Fehér J.-Gáspár J.: A mértékadó vízhozam hossz-szelvény meghatározása

.4 mértékadó vízállás/vízhozam hossz-szelvény meghatározása 263 IRODALOM Jordán K.: Fejezetek a klasszikus valószínüségszámításból. Akadémiai Kiadó, Budapest, 1956. Poincaré, H:. Calcul des Probabilités 2. Edition, Paris 1912. Reimann J—Fehér J.—Gáspár J.: Véletlen folyamatokra vonatkozó események együttes valószínűségeire alapozott mértékadó vízállás/vízhozam hossz-szelvény meghatározása. Kézirat, VITUKI Consult Rt. Budapest, 1997. * * * Determination of the longitudinal profiles of design water stage/flow by Dr. József REIMANN mathematician. Doctor of Science, János FEHER and Judit GASPAR civil engineers The behaviour of the process X

t, the continuous curve derived from the daily time series of water level (or flow), was investigated along a selected longitudinal profile (Figure /.). At the gauging stations t\,t2...t„ intervals А\,Аг, ..;A„ were arbitrarily selected, the probabilities of which are P(A\

), (A2),.

. ..P(A„). In Figure 2., each realisation X

t corresponds to a point and the set A

1 is the set of all those elemental events (realisations) "e", which realisations go through the interval A

1. If this number is divided by the total number of points, then one obtains the probability P(0). For the calculation of probability P(

m) the probabilities of all those elemental events (point) should be summed, which fall into the common part of exactly m number of event A

1. Applying the general probability law (which is the generalisation of the binominal distribution of Bernoulli) the probability of simultaneous occurrence of exactly к number of events A

1, Аг,..-Ап was determined. The probabilities of simultaneous occurrence shall be estimated on the basis of observation records, on the basis of relative frequencies, using the possible longest record. Let intervals A\, A2, A3 of the sampling sites t\, ti, ti of a longitudinal profile be the 10% lower quantiles, that is let P(A\)=P(AÏ)=P(Ai)=0.\ (.Figure 3). The validity of theoretical results was proven by using the data of the 10% low water stage of 8 gauging stations of the Danube reach between Komárom and Mohács (details of the data processing are given in Tables I. and II.). The simultaneous occurrence of events was only 6.35% compared to the individual estimate of 10%. This method can be widely used in hydrology, since the behaviour of a river can only be characterised through its statistical features (combined and conditional probabilities), which were obtained, for the simultaneous occurrences of water level and flow along the longitudinal profile, using the data of all gauging stations. * * * Ermittlung des maßgeblichen Längsschnittes von Wasserstand/Abfluß von Dr.-Math. József REIMANN DSc.. Dipl.-lng. János FEHÉR und Dipl.-Ing. Judit GÁSPÁR Es wurde das längschnittsmäßige Verhalten der Realisationen der - als kontinuierliche Kurven der täglichen Wasserstände (oder Abflüsse) dargestellten - ProzesseX, untersucht (Bild