Vízügyi Közlemények, 2002 (84. évfolyam)
4. füzet - Klemeš, Vit: A simuló eloszlásfüggvények és az L-momentumok fetisizálása a hidrológiában
648 Vit Klemes Fetishizing the fitting probability distribution functions and the L-moments in hydrology by Professor Vit KLEMES, C. Eng. The paper is based on a lecture of the Author, first delivered in 1998 when receiving the Ven Te Chow Award and then repeated in 2002 in the Hungarian Hydrological Society. The paper demonstrates that the duration curve of any hydrological variable, compiled from the elements, arranged in order of magnitude, of the statistical sample related to that variable — which can also be called empirical distribution function and has generally been used in the practice of hydrology and hydrotechnics for a long time—, no matter if plotted either in a linear, or logarithmic system or one of the numerous available probabilistic papers (Fig. /), can be extrapolated in the domain of very rare events (e.g., floods) by adopting various mathematical methods (so-called "distribution models") with the same reliability as when making the extrapolation "by eye", as it had been done, at the first time, in 1914, by the American engineer Allan Hazen. The basic contradiction of the theory of frequency analysis is that it assumes, on one hand, a mutual independence between the observed values, but is using, on the other, methods, by whose adoption there is quite a strong dependency between the the greatest extremes and the smallest events. A further contradiction consists in the fact, that while the probabilities of the random sample elements themselves represent a random sample from a uniform distribution, in the practice of hydrological statistics the elements are always being plotted in regularly distributed (equidistant) positions (Fig. 2). To the elements of the random sample deriving from an uknown distribution, no preferred plotting positions must be attributed. The inherent uncertainty of this procedure is well visualized b Fig 4 , showing ten different "equally likely" realizations of samples of various sizes, as well as by Fig. 5 showing the uncertainty zone based on 500 "equally likely" realizations of the distribution curve of Fig. lb; this uncertainty zone obviously does not indicate any "distribution model". The Author judges that the adoption of the method of linear moments (L-moments), having become wide-spread in the last decade and still being recommended for the estimation of fitting distribution functions (Hosking & Wallis 1997) is particularly dangerous, partly due to its arbitrarily defined weighting functions (Eq. (8) and Fig 6), and particularly because its insensivity against the "outlying" values of the statistical sample, thus because it strongly reduces the safety of designing structures. In fact, what is being praised by the authors of the L-moment method is essentially its inability to make use of the all-important additional information provided by the actually recorded rare extreme events. As a summary, in can be stated that the increased mathematization of hydrological frequency analysis over the past 50 years has not increased at all the validity of estimates of the frequencies of high extremes and thus has not improved our possibility to assess the safety of structures whose design characteristics arc based on them. The distribution models used nowadays, thogh disguised in rigorous mathematical garb, are no more, and quite likely less, valid for estimating the probabilities of rare events than were the extensions "by eye" of duration curves employed 50 years ago. This is because the "modem" methods rely more heavily on those parts of observation records which either may provide misleading information about the high extremes or are largerly irrelevant because they can equally be fitted with almost any model. As a result, the bulk of the theory of frequency analysis, with all its exalted rigour and polish, is spurious, not to say dangerous. It creates an illusion of knowledge which does not exist; and this illusion of knowledge can do more harm than awareness of ignorance.
