Keywords: regional flood frequency analysis, L-moments, homogenous regions, regional frequency distribution, discordance measure, heterogeneity measure, goodness-of-fit measure.

Flood frequency analyses are often carried out to estimate flood quantities QT, at a project location for a return period T. The analyses primarily use annual maximum flood data observed at a desired project location or streamgaging station to estimate flood quantiles. When a station contains a long record, analyses can be based on the available record alone. Yet, it is often the case that available record lengths at gaging sites are less than the return period of interest. Thus estimating the frequencies of extreme events is difficult because extreme events are, by definition, rare and the relevant data record is often short. As a result, quantile estimates obtained using such observations tend to be very unreliable. Regional frequency analyses can resolve this problem by trading space for time, that is, by using data from several sites, which are judged to have frequency distributions similar to the site of interest, in estimating event frequencies at that site.

Most regional flood frequency analysis methods are based on the use of annual maximum flood peaks while a few are based on peaks over a threshold. At present, the direct regression method and the index-flood method are the most frequently used regional flood frequency procedures. Regional flood frequency analysis typically involves four stages: (a) screening of the data; (b) identification of homogeneous regions; (c) choice of a regional frequency distribution; and (d) estimation of the regional frequency distribution[1,2,3].

Three different statistical measures are useful in regional flood frequency analyses: (a) a discordance measure, for identifying unusual sites in a region; (b) a heterogeneity measure, for assessing whether a proposed region is homogeneous; and (c) a goodness-of-fit measure, for assessing whether a particular regional distribution provides an adequate fit to the data[4,5,6].

The application of regional flood frequency analyses using L-moments is demonstrated in the case of Gediz, Buyuk Menderes and Bakircay river basins along the Aegean coast of Turkey. Annual maximum streamflow data are analysed at 17 gaging stations in Gediz; 26 gaging stations in Buyuk Menderes and 14 gaging stations in the Bakircay river basin. At-site and average L-CV, L-skewness, and L- kurtosis values computed are not particularly high, indicating that frequency distributions are not necessarily highly skewed. For the Gediz basin, the highest discordancy measure has been found to be 2.97 (that is less than 3.0), suggesting that no site is discordant. The highest discordancy measures have been calculated as 3.38 and 3.18 for Buyuk Menderes and Bakircay regions, indicating that such stations are discordant. The heterogeneity measures (H1) were calculated from observed and 500 sets of simulated data as 3.21, 10.51, and 5.35 respectively for Gediz, Buyuk Menderes and Bakircay basins. These results indicate that the three sets of data are definitely heterogeneous. Therefore a redefinition of these three regions was considered by subdividing the basins into smaller regions. Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Extreme Value (GEV), Pearson Type III (PE III), Generalized Normal (GNO), and Lognormal (LN3) were fitted to these redefined regions. Using the above best fit distributions, standardized quantiles have been computed at selected return periods of 5, 10, 20, 50, 100, and 1000 years and plotted against these return periods. The following conclusions have been drawn:

• Gauging sites of study basins have been found to be homogeneous after redefinition of regions;
• GLO and PE3 distributions, GLO distribution, and PE3 distribution were determined as appropriate distribution functions to analyse flood flow frequency in Gediz, Buyuk Menderes and Bakircay river basins, respectively.

1

K.W. Potter, "Research on flood frequency analysis: 1983-1986", Rev. Geophys., 25(2), 113-118, 1987. doi:10.1029/RG025i002p00113

2

W.Kirby, M. Moss, "Summary of flood frequency analysis in the United States", J. Hydrol., 96, 5-14, 1987. doi:10.1016/0022-1694(87)90139-9

3

J-L. Daviau, K. Adamowski, and G.G. Patry, "Regional flood frequency analysis using GIS, L-moment and geostatistical methods", Hydrol. Process., 14, 2731-2753, 2000. doi:10.1002/1099-1085(20001030)14:15<2731::AID-HYP89>3.0.CO;2-U

4

J.R.M. Hosking, "L-moments: Analysis and estimation of distributions using linear combinations of order statistics", J. R. Statist. Soc., Ser. B, 52(1), 105- 124, 1990.

5

Q.J. Wang, "LH moments for statistical analysis of extreme events", Water Resour. Res., 33(12), 2841-2848, 1997. doi:10.1029/97WR02134

6

A.J. Robson, and D. Jakob, "L-moments for flood frequency analysis, in Flood Estimation Handbook, vol. 3, chapter 14, Institute of Hydrology, Wallingford, UK, 1999.

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