Environmental Engineering Reference
In-Depth Information
Box 22.2
Approaches for dealing with the calculation of flood frequency
The general statistical expression for the calculation of the frequency of occurrence of an event is:
NoEvents
ð
Frequency
i
¼
n
þ
1
Þ
where:
i
¼
point in space for which the probability is calculated;
NoEvents
¼
total number of events in the period of analysis (n).
In terms ofmodelling, two approaches to calculating the probability of occurrence of an event can be
identified, as follows:
Approach I
F
event
¼ W
½
Frequency
ð
Input
Þ
Approach II
F
event
¼
Frequency
Wð
Input
Þ
½
where:
F
event
¼
frequency of an event, e.g. the occurrence of groundwater-induced surface flooding, expressed
as the number of times over a period that water is above the ground surface;
Input represents the driving hydrometeorological phenomenon, e.g. a flowhydrograph or a time series
of rainfall, and
W
represents the response function of the physical system to the hydrometeorological driver.
The first approach is usually emloyed in the representation of fluvial flooding, where the above
expression translates into the following steps:
1 Statistical analysis of annual series of flowmaxima to derive a time series (flow-time; rainfall-time)
with different frequency of occurrence [frequency(input)].
2 Execution of a mathematical model (i.e. a 1-D river flowmodel) using the above inputs to estimate
the response of the system in the form of predicted water levels along a river and its floodplain
[
W
(frequency(input))].
3 Calculation of the flood extent associated with the water levels for each return period (yielding the
FPM).
The second approach is most suitable for the representation of the occurrence of distributed events
and is appropriate for groundwater-induced flooding processes. In this case, the approach normally
consists of the following steps:
1 Execution of a mathematical model (i.e. a hydrological rainfall-runoff model coupled to a 3-D
groundwater flow model) using time series of rainfall and evapotranspiration (input) to estimate the
groundwater level for every simulated time step over the period of calculation (n). This results in the
calculation of [
(input)]:
2 Calculation of the number of occurrences of a flood event, performing a calculation of a flood/no
flood situation for every time step by comparing the groundwater level fromthemodel with the level of
the ground surface.
3 Calculation of the flooding frequency as [frequency(
W
W
(input))].
