PROOF COPY [HE/2001/022449] 002305QHE
PROOF COPY [HE/2001/022449] 002305QHE
Nonparametric Approach for Estimating Return Periods
of Droughts in Arid Regions
Tae-Woong Kim
1
; Juan B. Valde
´
s
2
; and Chulsang Yoo
3
Abstract: Droughts cause severe damage in terms of both natural environments and human lives, and hydrologists and water resources
managers are concerned with estimating the relative frequencies of these events. Univariate parametric methods for frequency analysis
may not reveal significant relationships among drought characteristics. Alternatively, nonparametric methods provide local estimates of
the univariate and multivariate density function by using weighted moving averages of the data in a small neighborhood around the point
of estimation and opposed to parametric methods. A methodology for estimating the return period of droughts using a nonparametric
kernel estimator is presented in order to examine the univariate as well as the bivariate behavior of droughts. After evaluating and
validating a nonparametric kernel estimator, a drought frequency analysis is conducted to estimate the return periods of droughts for the
Conchos River Basin in Mexico. The results show that, for the univariate analysis, the return periods of the severe drought occurring in
the 1990s are 100 years or higher. For the bivariate analysis, the return periods are approximately 50 years for joint distributions and more
than 120 years for the conditional distributions of severity and duration.
DOI: 10.1061/ASCE1084-069920038:51
CE Database subject headings: Droughts; Arid lands; Frequency; Estimation.
Introduction
Hydrologic systems are impacted by extreme events such as
floods and droughts, which cause severe damage to natural envi-
ronments and human lives. For example, the 1987–1989 drought,
which lasted 3 years and covered 36% of the United States,
caused approximately $39 billion in losses of energy, water, the
ecosystem, and agriculture National 2000. These extreme events
are usually expressed by return periods in hydrology and water
resources engineering. When the concept of the return period is
applied to drought-related variables, the return period will be the
average time between events with a certain magnitude or less
Haan 1977. In general, a drought is defined as a sustained period
of significantly lower soil moisture levels and water supply rela-
tive to normal levels. During droughts, water supplies are inad-
equate to meet the water demand of management systems, and
lack of rainfall adversely affects the environment and human so-
ciety Dracup et al. 1980.
A significant number of studies on droughts deal with the defi-
nition of droughts, low-flow frequency analysis, and climatic im-
pacts of droughts Smakhtin 2001. Lee et al. 1986 developed a
practical approach for the frequency analysis of multiyear drought
durations of annual streamflow series. A technique that smooths
the frequency-curve irregularity of drought durations was used to
reduce the statistical uncertainties associated with sample-size
limitations. Nathan and McMahon 1990 evaluated the applica-
tion of the Weibull distribution to low-flow frequency analysis.
They investigated the differences between low-flow frequency es-
timates based on calendar and hydrologic years, and they made
recommendations for the selection of an appropriate subset of the
data.
In recent years, several papers were published addressing the
methodology for estimating drought return periods Ferna
´
ndez
and Salas 1999a,b; Chung and Salas 2000. Ferna
´
ndez and Salas
1999a,b summarized the definitions of the return period and
estimated the risk of failure of hydraulic structures, especially
applied to drought events. They estimated the return periods and
the associated risks of failure of hydrologic events related to me-
teorological droughts, low flows, annual maximum floods, and
hydrological droughts, which are either dependent or indepen-
dent. Chung and Salas 2000 dealt with drought occurrence prob-
abilities, return periods, and risks of drought events for dependent
hydrologic processes. Rather than using Markovian models,
which traditionally have been used for modeling hydrologic pro-
cesses, low-order discrete autoregressive moving average
ARMA models were used for modeling wet and dry years, since
they are adequate for processes exhibiting longer time depen-
dence. They concluded that low order ARMA models are useful
for representing the occurrence of wet and dry periods and, con-
sequently, are capable of modeling and simulating drought condi-
tions that are observed historically.
A general approach used in drought-related frequency analyses
is to derive the distributions of drought durations and severities
separately Sen 1976; Mathier et al. 1992; Stedinger et al. 1992.
A drought event, however, is a multivariate event characterized
by its duration, magnitude, and intensity Salas 1992, which are
1
Graduate Research Assistant, Dept. of Civil Engineering and Engi-
neering Mechanics, and Center for Sustainability of Semi-Arid Hydrol-
ogy and Riparian Areas SAHRA, The Univ. of Arizona, Tucson, AZ
85721-0072. E-mail: taek@email.arizona.edu
2
Professor and Head, Dept. of Civil Engineering and Engineering Me-
chanics, and Center for Sustainability of Semi-Arid Hydrology and Ri-
parian Areas SAHRA, The Univ. of Arizona, Tucson, AZ 85721-0072.
E-mail: jvaldes@u.arizona.edu
3
Associate Professor, Dept. of Civil and Environmental Engineering,
Korea Univ., Seoul, Korea 136-701. E-mail: cyoo@korea.ac.kr
Note. Discussion open until February 1, 2004. Separate discussions
must be submitted for individual papers. To extend the closing date by
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and pos-
sible publication on October 18, 2001; approved on January 21, 2003.
This paper is part of the Journal of Hydrologic Engineering, Vol. 8, No.
5, September 1, 2003. ©ASCE, ISSN 1084-0699/2003/5-1–10/$18.00.
JOURNAL OF HYDROLOGIC ENGINEERING © ASCE / SEPTEMER/OCTOBER 2003 / 1
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