Vízügyi Közlemények, 2001 (83. évfolyam)

2. füzet - Reimann József: Az árvizek tetőzésének és tartósságának valószínűség-számítása

Árvízi tetőzések és tartósságok valószínűségének számítása 245 A ténylegesen tapasztalt várható érték 1489,37. Figyelembe véve a nagy szórást az elméleti és a tapasztalati érték összhangban van egymással. IRODALOM Reimann J:. Mathematical statistics with application in flood hydrology. Akadémia Kiadó, Budapest, 1989. Reimann J. : Positively Quadrant Dependent Bivariate Distributions with Given Marginals. Periodica Polytechnica Ser. Civil Eng., Vol. 36. No 4. 1992. Reimann J:. Investigation of positively quadrant dependent bivariate distributions. Periodica Polytechnica, Vol. 32. Nos 1-2. 1988. Rényi A.: Probability Theory. Tankönyvkiadó. Budapest. 1970. Yevjevich, V:. Stochastic Processes in Hydrology. Water Res. Publ. Fort Collins, 1972. Zelenhasic, E:. Theoretical Probability Distribution for Flood Peaks. Colorado State Univ., Fort Collins, 1970. * * * Calculating the probability of flood peak and duration by Dr. József REIMANN, mathematician, Doctor of Science Statistical features of flood behaviour can be better obtained from the full statistical sample of the flood records, than from the records of annual highest water stages. A large part of the highest water stages (about 40-50% in the case of the River Tisza) will not be considered in the currently used method, if there are also 2—3 higher floods, of which latter only the highest is taken into account. If X\ denotes the peak flood water stage and Xi the annual highest water stage, then probability variable X\ is stochastically higher than X% This means that for example for the River Tisza the expectable value of X\ and its quantiles (e.g. the 99% one) are nearly by 1.00 metre higher, than the respective parameters of Хг. Therefore the recalculation of the design flood water levels with the method presented in this study seems to be a must. This method considers the water level time series a stochastic process, to which characteristic variables shall be coupled. These variables are: X— the magnitude (m) of exceedances above a chosen (sufficiently high) level с ; Y — the duration of the flood in days; the intensity of the flood; the maximum rate of flow of the flood hydrograph considered, etc. Adding level с to the value X of the exceedance above level с (generally the level of stage 1 preparedness) one obtains the peak stage T(Figure /.). The primary concern of this study is the distribution of exceedances X, of duration Y, the stochastic relationship between variables Xand Fand their combined distribution (Equations 1-3). The exponential character of the distribution of exceedance X (Figures 2-^4) enables the reliable estimation (Equation 4) of the design flood water levels (as the respective quantiles of the exponential distribution). This may form the basis of calculating the return period (Tables I—II) of floods of given levels (Equations 10-15). The practical application of this method is shown in Tables V-VI. The comparison of this method with the currently used one is given in Figures 5 and 6. It may happen that the expectable value of the exponential distribution of exceedance X changes from time to time, due to the changes of the environment, due for example to technical measures. This means that the parameter proper is also a random variable. In this case the resultant Bayes distribution is the Pareto II. distribution function (Equations 21—23).