Geoscience Reference
In-Depth Information
13.16
Select a river gaging station in your region of interest, preferably with a period of record in
excess of 50 y. Tabulate the annual peak discharges for each water year on record. Calculate
the first three moments of these discharges and of their logarithms. Then, carry out several or
all of the following. (a) Determine for the generalized log-Pearson Type III distribution, the
quantiles for the selected probabilities listed in Table 13.2 with these moments of the logarithms.
(b) Repeat (a) with skew assumed to be zero. (c) Calculate the parameters
α
n
and
u
n
of the first
asymptotic distribution for the largest values. (d) Calculate the parameters,
a
,
b
, and
c
,ofthe
generalized extreme value distribution. (e) Plot the data and these four theoretical curves on log-
normal probability paper. (f) Plot the data and these four theoretical curves on probability paper
based on the first asymptote (see Figure 13.3). (In the United States, data records can be found on
the web at http://waterdata.usgs.gov/usa/nwis/sw)
13.17
In the design of a bridge opening (i.e. clearance), it is necessary to determine the 40 y flood. Give
the estimates according to the distributions determined in parts (a), (b), (c) and (d) of Problem
13.16.
13.18
Multiple choice. Indicate which of the following statements are correct. As defined in
Equation (13.3), the theoretical distribution functions
F
(
x
) that are used to describe the occurrence
of hydrologic events:
(a)
have a magnitude, which ranges in general between
−∞
and
+∞
;
(b)
have parameters that can be determined from observed data by the method of moments;
(c)
can never assume a value smaller than zero;
(d)
are symmetrical about the mean;
(e)
yield unity [i.e.
F
(
x
)
=
1] when future events cannot be smaller than
x
.
