SME
Hydrology
Flood frequency
Use this for “A house is built in the 100-year floodplain. What is the chance of at least one 100-year flood during a 30-year mortgage?”
Chart
R(30) ≈ 26.03
This is an example. Type your own values to start a new problem.
R
%
=
100
×
(1
−
(1
−
%
÷
100)
)
T
Return period
example · yr
Formulas
p
=
100
T
1
=
100
100
R
=
100
×
(1
−
(1 −
p
100
)
N
)
26.03
=
100
×
(1
−
(1 −
1
100
)
30
)
Assumptions
•
Each year is independent of the others: a flood this year doesn’t make one next year more or less likely.
•
The “100-year flood” has a 1 % chance every year; it is not a flood that comes once a century.
•
The record is long enough that the return period T describes the river today.
Step-by-step
WE KNOW
T = 100 yr, N = 30 yr
FIND
yearly chance (p), risk of one or more (R)
Step 1 · Find yearly chance (p)
Use p = 100 ÷ T
A
flood
reached
on
average
once
in
T
years
has
a
chance
of
1
in
T
each
year.
p
=
100
100
p
=
1%
Step 2 · Find risk of one or more (R)
Use R = 100 × (1 − (1 − p ÷ 100)ᴺ)
The
chance
of
no
flood
in
one
year,
raised
to
N
,
is
the
chance
of
none
in
N
years;
the
rest
is
the
risk.
R
=
100
×
(1
−
(1 −
1
100
)
30
)
1
−
1
100
=
0.99
0.99
30
=
0.7397
100 × (1 − 0.7397) = 26.03
R
=
26.03%
Check
Put the numbers back in. Both sides should match.
1
=
100
100
✓
26.03
=
100
×
(1
−
(1 −
1
100
)
30
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Return period from a flood’s rank
Use this for “A gauge has 49 years of yearly peak flows. What are the return period and yearly chance of the largest one?”
The 100-year flood by Gumbel’s method
Use this for “Yearly peak flows average 500 m³/s with a standard deviation of 150 m³/s. Estimate the 100-year flood by Gumbel’s method.”