SME
Hydrology · Problem type
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?”
Table
Rank (m)
Return period (T)
(yr)
This is an example. Type your own values to start a new problem.
T (yr)
=
(
n
+
1)
÷
m
p
Yearly chance
calculated · %
Formulas
T
=
n
+ 1
m
50
=
49 + 1
1
p
=
100
T
2
=
100
50
Assumptions
•
Each year gives one peak, its largest flow; rank them with the largest as rank 1.
•
The Weibull formula T = (n + 1) ÷ m is the average gap between floods at least that big.
•
A short record can’t rate rare floods: the largest of 49 years plots at only 50 years.
Step-by-step
WE KNOW
m = 1, n = 49 yr
FIND
return period (T), yearly chance (p)
Step 1 · Find return period (T)
Use T = (n + 1) ÷ m
Rank
m
means
m
floods
at
least
this
big
in
n
years;
adding
1
to
n
keeps
the
largest
from
reading
as
certain.
T
=
49 + 1
1
T
=
50
yr
Step 2 · 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
50
p
=
2%
Check
Put the numbers back in. Both sides should match.
50
=
49 + 1
1
✓
2
=
100
50
✓
Topic check
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