Methodology - Response of Flood Events to Land Use and Climate Change - page 85

by insufficient data sets or missing data. Therefore, in many cases the discharge
data series is no longer than 30-50 years. Consequently, estimation of floods with
return periods above 100 years is an uncertain level.
He also mentioned that the 1D or 1D-2D hydrodynamic models approaches
associated with certain discharge values can include the effects of dyke breaches.
However, since the T-year discharge for certain river sections is taken from flood
frequency analysis, the effects of upstream dyke breaches do not propagate and do
not affect the flood frequency analysis at downstream gages [ 84 ].
Except for the return period calculation, another aim of flood frequency analysis
in this research was to investigate how flood frequency distributions were influ-
enced by dyke breaches. Therefore, with the assumption of dyke breaches, the flow
propagation and flood behavior was also estimated. In return period analysis, it is
supposed that an extreme event is defined to have occurred if a random variable
X is greater than or equal to some level x T . The recurring interval t is the
time between occurrences of X C x T [ 94 ]. For each observation, there are two
possible outcomes: either ''success'' X C x T (probability p) or ''failure'' X \ x T
(probability 1-p). Since the observations are independent, the probability of a
recurrence interval of duration T is the product of the probabilities of t - 1 failures
followed by one success, that is, (1- p) t -1 p. Assuming that the series of data is
infinite, the E(T) can be expressed as:

E ðÞ¼ X

1

Þ t 1 : p ð 1 p ð 3 : 34 Þ

t ¼ 1

Developing this expression in terms and after some algebra is shown in the fol-
lowing equation:

E ðÞ¼ T ¼ 1
p

ð 3 : 35 Þ

So the probability of occurrence of an event in any observation is the inverse of its
return period.

Þ 1
T

PX xT

ð ð 3 : 36 Þ

3.11.2 Gumbel Extreme Value Distribution

The objective of these distributions is to build the relation between the probability
of the occurrence of a certain event, period, and its magnitude. For this purpose,
first, the maximum discharge values were ranked values from low to high. So the
first value was assigned to the lowest data value and the last one was assigned to
the highest data value.