Vízügyi Közlemények, 1983 (65. évfolyam)
3. füzet - Kovács György: Az árvizek előfordulási valószínűsége számításánek kérdései
344 Kovács György dates) obtained by resolving the year must be determined for each particular river system separately in conformity with the actual flow regime. Independence. The problem is one of ensuring physical, rather than statistical independence of the data. For physical independence the local maxima should be selected as peaks from periods that are long enough to make the probability of interference between the successive flood waves very low. The investigations have shown, however, the variations in the length of the memory defined in this way to affect but insignificantly the results of the analysis. For this reason, as long as no more accurate criteria can be derived for ensuring independence from further investigations, on small streams local maxima are believed acceptable which represent higher flows than those recorded during two-day periods preceding and following it. On the strength of the foregoing considerations the method of Todorovic-Zelenhasic (1970) is believed most suited to performing the statistical analyses. The probability of flows surpassing the threshold value relative to the population number is thus found from Eq. (1), while the annual probability from Eq. (5). For estimating the probable number of exceedances the approximation by a Poisson-type distribution is considered acceptable, provided that the analysis is performed by subdividing the year into several groups of months, Eq. (3), following the suggestion of Reimann (1975). There are, however, two steps where changes are considered necessary in the interest of closer approximation and hydrologically consistent method of treatment: Fitting distribution functions. Regardless whether we intend to fit a distribution function to the data surpassing the threshold value, or to all local maxima in the interest of determining the exceedance level-the streamflow data should be transformed according to Eq. (9). The exponent n involved here is adopted between the theoretical limits 0.4 and 0.667 depending on the character of the head-discharge curve, or it is entered with the average value of л = 0.5 into the calculations. Choice of the exceedance level. In order to regard this level a hydrological parameter relevant to the entire river system, its determination is derived from the population including all local maxima. All peak values should therefore be noted-reducing their number only by taking into account the memory period of the system to increase the probability of independence-and the three parameters Q 0 , к and X of the gamma function fitting to the sample obtained should be determined. Evidently, in order to eliminate structural inhomogeneity, this operation, too, should be performed by subdividing the year into month-groups. In the knowledge of the above three parameters the exceedance level is found from Eq. (12). This threshold level has three advantageous properties: - it has a uniform hydrological interpetation in all cross sections, - it can be demonstrated that an exponential distribution can be fitted to the data surpassing it (when using streamflow data, these should here again be transformed according to Eq. (9)) and - the number of the flood waves surpassing it is in general still sufficient for performing the statistical analysis (30 to 60 per cent of all local maxima are higher than the threshold, depending on the skewness of the entire population). As described in the foregoing, the statistical methods serving to estimate the floods of different probabilities can be refined by taking into consideration also the relationships derived from the inherent physical nature of the data as well. I expect that the discussion on the problems raised, further analytical checks and the inclusion of additional ideas into the system will eventually contribute to the development of a generally applicable procedure of calculation. * * * Berechnung der Hochwasserwahrscheinlichkeit von Dr. György KOVÁCS Zweck der Untersuchungen war, die bei der Ermittlung von Hochwasserdurchflüssen verschiedener Wahrscheinlichkeiten verwendeten mathematisch-statistischen Methoden in ein System zusammenzufassen, welches auch den physikalischen Informationsgehalt der Daten nutzbar macht. Im Interesse dessen wurde versucht, die drei grundlegenden Voraussetzungen der statistischen Verfahren physikalisch zu interpretieren:
