TITLE:
On Return Periodof the Largest Historical Flood
AUTHORS:
Witold G. Strupczewski, Krzysztof Kochanek, Ewa Bogdanowicz
KEYWORDS:
Flood Frequency Analysis, Historical Information, Error Analysis, Maximum Likelihood, Monte Carlo Simulations
JOURNAL NAME:
Journal of Geoscience and Environment Protection,
Vol.2 No.3,
June
13,
2014
ABSTRACT:
The use of nonsystematic flood data for
statistical purposes depends on reliability of assessment both flood magnitudes
and their return period. The earliest known extreme flood year is usually the
beginning of the historical record. Even though the magnitudes of historic
floods are properly assessed, a problem of their retun periods remains
unsolved. Only largest flood (XM) is known during whole historical period and
its occurrence carves the mark of the beginning of the historical period and
defines its length (L). So, it is a common practice of using the earliest known
flood year as the beginning of the record. It means that the L value selected
is an empirical estimate of the lower bound on the effective historical length
M. The estimation of the return period of XM based on its occurrence, i.e.
, gives the severe upward bias. Problem is to estimate the
time period (M) representative of the largest observed flood XM. From the discrete
uniform distribution with support of the probability of the L position of XM
one gets
which has been taken
as the return period of XM and as the effective historical record length. The
efficiency of using the largest historical flood (XM) for large quantile
estimation (i.e. one with return period T = 100 years) has been assessed using
maximum likelihood (ML) method with various length of systematic record (N) and
various estimates of historical period length
com- paring accuracy
with the case when only systematic records alone (N) are used. The i-th simula-
tion procedure incorporates systematic record and one largest historic flood
(XMi) in the period M which appeared in the Li year backward from the end of
historical period. The simulation result for selected distributions, values of
their parameters, different N and M values are presented in terms of bias (B)
and root mean square error (RMSE) of the quantile of interest and widely
discussed.