Water Resources Management 8:183-201, 1994. 183
© 1994 KluwerAcademic Publishers. Printed in the Netherlands.
Frequency Analysis of Upper Cauvery Flood Data
by L-Moments
A. RAMACHANDRA RAO and KHALED H. HAMED
School of Civil Engineering, Purdue University, WestLafayette, IN 47907, U.S.A.
(Received: 12 November 1993)
Abstract. The objectives of the present study are to investigate the hydrological homogeneity of
Upper Cauvery annual maximum flow data and to select a suitable distribution for the frequency
analysis. The L-moments method is used in this analysis. The Upper Cauvery river basin is shown
to be hydrologically heterogeneous. The 3 parameter log normal and the generalized extreme value
distributions are recommended for the frequency analysisof data in this region.
Key words: hydrological homogeneity, flood data, L-moments methods
1. Introduction
The concept of probability weighted moments (PWM) was introduced by Green-
wood et aI. (1979). Since then it has received considerable attention from Landwehr
et al. (1979a, b), Hosking et al. (1985), Hosking (1986), Hosking and Wallis (1987)
and others. PWM estimates are robust in the presence of outliers. Parameter esti-
mates from small samples computed by using the PWM method are sometimes
more accurate than even the maximum likelihood (ML) estimates. The PWM
method is less complicated than the ML method. With some distributions, such
as the symmetrical Lambda and Weibull distributions, explicit expressions for the
parameters are obtained by the PWM method, which cannot be done with either
the ML or the method of moments (MOM).
Hosking (1986, 1990) has defined the L-moments which are analogous to the
conventional moments and are estimated by linear combinations of order statistics.
They can also be expressed by linear combinations of PWM. Thus, procedure~
based on PWM and L-moments are equivalent. However, L-moments are more
convenient because they are directly interpretable as measures of the scale and
of the shape of probability distributions. Hosking (1990) has used L-moment
ratio diagrams to identify underlying parent distributions and L-moment ratios for
testing hypotheses about forms of probability distributions. Hosking and Wallis
(1991) extended the use of L-moments and developed statistics that can be used
in regional frequency analysis to measure discordancy, regional homogeneity and
goodness-of-fit.
The objective of the present work is to analyze the annual maximum flow data
from the Cauvery River basin in south India by using the L-moment method. Both
regional and at-site parameter and quantile estimates are used and the differences