Geoscience Reference
In-Depth Information
13.6
What is the probability that a 100 y flood will be exceeded after exactly 100 y? What is the
probability that it will be exceeded some time in the coming 100 y?
13.7
Multiple choice. Indicate which of the following statements are correct. When a flood of a certain
magnitude is called the 50 y event, it means that:
(a)
the probability that it will be exceeded in any given year is 98%;
(b)
the probability that it will be exceeded once in any 3 y period is 5.8%;
(c)
after it has been exceeded, it will take on the average 50 y before it will be exceeded again.
(d)
it is the largest event that will occur during any period of record of 50 y;
(e)
the probability that it will be exceeded during the course ofa1yperiod is approximately
20%.
13.8
Multiple choice. Indicate which of the following statements are correct. Among the disadvantages
of using
P
m
=
m
/
n
(where
m
=
1 is the smallest and
m
=
n
is the largest) to obtain the frequency
of annual floods one has the following:
(a)
the return period of the smallest event is 1 y;
(b)
the return period of the largest event is equal to twice the period of record;
(c)
the probability of the smallest event is equivalent to the assumption of certainty of a larger
event;
(d)
the probability of the largest event is equivalent to the assumption that a larger event cannot
happen;
(e)
it can be applied only to small samples.
13.9
Multiple choice. Indicate which of the following statements are correct. The Weibull plotting
position
m
/
(
n
+
1) (in which
m
is the order number for the items ranked in increasing magnitude,
and
n
is the sample size):
(a)
is the mean of the probability (“that the event will be smaller than or equal to . . .”) of the
m
th event of the sample;
(b)
is exactly the probability that in any occurrence the magnitude of an event will be smaller
than or equal to the
m
th event of the sample;
(c)
is the probability of the mean of the
m
th event of the sample;
(d)
can be used as an estimate of the probability that the
m
th event will not be exceeded;
(e)
is applicable in the analysis only of the largest values but not of the smallest.
13.10
From a long-term rainfall record for a given location, we know that in summer on average 3 weeks
out of 12 are without rain. What is the probability of having 6 weeks out of 12 without rain this
coming summer? Assume, as a first approximation, that the likelihood of rainfall in summer is
independent from one week to the next.
13.11
Multiple choice. Indicate which of the following statements are correct. For yearly events, the
return period or recurrence interval
T
r
:
(a)
in the case of floods, corresponds to the inverse of the probability that the event will be
smaller than a given magnitude;
(b)
signifies that, once the
T
r
year event has occurred, we are safe from any event exceeding it
for the next
T
r
years;
(c)
can be calculated from the probability that an event be smaller than, or equal to, a given
magnitude;
