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

INTRODUCTION

The central relationship for flood
control and floodplain management planning is
that between peak flow and return period.
The relal ionship is established by select ing
an appropriate distribution to represent the
populat ion of peak flows, one from each year
of record (the annual flood series), and
estimating parameters for that dIstribution
that best fit the recorded data.

The primary criterion used to select an
appropr iate d istr ibul ion has been goodness-
of-fiL as measured empirIcally. Accordingly,
the parameterg of several distributions are
estimated from the same data set. Some
goodness-oE-fit criterion is then used to
choose the best-fitting distribution (e.g.,
Bobee and Robitaille 1977). The log Pearson
type III distributIon was selected for
general use on federal water resources
studies (U.S. Water Resources Council 1976,
Appendix 14) on this basis.

The Monte Carlo experiment described in
the next sectIon Illustrates that serious
estimatIng errors may arise if the distri-
bution is selected solely on the basis of
goodness of fit. The magnitudes of these
errors clearly demonstrate that empirical fit

alone does not provide an adequate basis for
select iog a d istr ibut ion. Theory provides
supplemental informat ion. The annual flood
event is the maximum or extreme value of all
the events occurrIng during the year;
therefore, extreme value theory would seem to
provide a reasonable theoret ical base Lo
explore and is examined here. Although
extreme value distributions have been used in
hydrology, no systemat ic examinat ion of
the theory to determine the most appropriate
form is reported in the literature.

The first section of this report pre-
sents the problem encountered when empirical
f It alone is used to select a "best" distri-
but ion. The second sect ion deals with
application of extreme value theory to stream
flows which have homogeneous sources. The
results clearly demonstrate the usefulness of
extreme value theory. The third section
extends extreme value theory to the case in
which the events in the annual series are
random variables from two different popula-
t Ions (e.g., thunderstorm and cyclonic
events). The fourth sect ion descr ibes how
one goes about the mechanics of applying
these results in flood frequency analysis.

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