FLOOD00764

• County: Statewide
• Community: Nationwide
• Title: Use of Extreme Value Theory in Estimating Flood Peaks from Mixed Populations
• Date: 2/1/1980
• Prepared By: Utah State University Water Research Laboratory
• Floodplain - Doc Type: Educational/Technical/Reference Information

Table 5. Selected stations exhibiting nonhomogeneity in source.
Drainage Years
No. Station Country River Location Area, Record Missing Years of
Km2 Record
1 hE1833 Canada Saguenay Isle-Maligne 73,000 1913-1970 58
2 aB36 Mali Niger Dire 340,000 1924-1968 43
3 aB72 Mali Niger Koulikoro 120,000 1907-1968 62
4 aESS USA Penobscot W. Enfield 17 , 090 1902-1967 1913,1928,1944 60
1951,1960,1964
5 CG60 Finland Kymijoki Pernoo 36.535 1900-1968 69
6 eG8! Finland Vuoksi Imatra 61,280 1847-1968 122
7 BF42 Po land Oder Gozdowice 109,365 1901-1968 1945 67
8 CF28 Sweden Vanerngota Vanesborg 46,830 1807-1968 162
9 DF09 USSR Neva Novosaratovka 281,000 1859-1969 1942 90
10 jE9955 Canada Assiniboine Brandon 92,000 1902-1970 65
11 JE791 Canada Red Emerson 104,000 1913-1970 58
17

Substituting
solving for 61

f or a 2
gives

19 and

in Equation

o "
1

C~l

2"2)
WrY!

01) ( n
W.ELiY. E
1 1 1==1

( n
- ,
1:1

02) ( n "('''2\ !r n
WiELfYi 1:1 WiY! )/\i:l

2
u1+aZ)
WiY!

( n 201) ( n
. L: Wi Yi . E
1=1 1'=1

202)
WiY! .

(23)

The result of Equation 23 is substituted into
Equation 22 to yield equations for both 81
and 82 which involve the parameters (11
and a2 as the only unknowns. These equat ions
are substituted for 81 and 82 io EquatIons
20 and 21 giving two equations in two un-
knowns ... al and a2. This system of
equations can be solved numerIcally using the
1MSL (1977) library subroutine ZSYS!M. Given
this solution as a., the estimate 8 of 8 is
computed from Equations 21 and 23:- Initial
values of al and a2 are required in ZSYSTM.
These are obtained as the slopes of the lInes
observed in the graph (e.g. see Figures 19
through 28). Appendix C contains FORTRAN
programs for these estimates.

A Burroughs 6700 computer was used to
solve for a. Since the Burroughs or any
other computer system is finite, a scaling
factor was found to be a computational
necessity, i.e., Equation 17 becomes

"

n { "1 (yi)OI
1:1 VW;Z ELi + (sf) 81 Sf ~

"2 (Yi)"2 )'
+ (sf) 82 ~ ~ .

(24)

For convenience 81 and 82 are
so that Equation 24 may be written

I' ede fined

'I

n { (y.)"1
1:1 ~ ELi + 8 t s~

(Y1)"2 ~.}2
sf i

~ + e*
1 2

(25)

*
where 8.
1

O.
1
(sf) 8i, i '" 1.2.

For 8
study, an
difference
flood and
smallest of

of the 11 data sets used in this
adequate scale factor was the
between the specified maximum
the first order statistic or
the maximum yearly floods:

sf=b-h(l)

(26)

The other three data sets required manipula-
t ion of the scale factor to insure that no
numbers got too large or too close to zero
for the computer to handle. Of course,
larger and more powerful computer facilitIes
would lessen the importance of the scale
factor.

The rivers for which data were obtained
are shown in Table 5. Estimates of the
parameters for each river are shown in Tables
6 and 7. It was found that the value of ~ in
Equation 25 was very insensitive to b for
large values of b. Therefore in order to
conserve computer tIme, b was est imated by
using a few passes to arrive at an 11approxi_
mateH estimate. This procedure could be
automated so that no hand preparation is
necessary and slightly better estimates could
be obtained. However, very little improve-
ment is expected.

Goodness-at-fit Nonhomogeneous Data

The same goodness-of-fit statistics as
described previously and used by Bobee and
Robitaille were used for these data. Since
the data (empirical) values of river flows
for the selected return periods were not
available for these rivers in Bobee and
Robitaille1s (1977) work, they are shown here
in Tables 8, 9, and 10.