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Examination of homogeneity of selected Irish pooling groups
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Abstract. In regional flood frequency estimation, a homogeneous pooling group of sites leads to a reduction in the error of quantile estimators which is the main aim of a regional flood frequency analysis. Examination of the homogeneity of regions/pooling groups is usually based on a statistic that relates to the formulation of a frequency distribution model, e.g. the coefficient of variation (Wiltshire, 1986; Fill and Stedinger, 1995) and/or skew coefficient, their L-moment equivalents (Chowdhury et al., 1991; Hosking and Wallis, 1997) or of dimensionless quantiles such as the 10-yr event (Dalrymple, 1960; Lu and Stedinger, 1992). Hosking andWallis (1993, 1997) proposed homogeneity tests based on L-moment ratios such as L-CV alone (H1) and L-CV & L-skewness jointly (H2) which were also recently investigated by Viglione et al. (2007). In this paper a study, based on annual maximum series obtained from 85 Irish gauging stations, examines how successful a common method of identifying pooling group membership is in selecting groups that actually are homogeneous. Each station has its own unique pooling group selected by use of a Euclidean distance measure in catchment descriptor space, commonly denoted dij and with a minimum of 500 station years of data in the pooling group, which satisfies the 5T rule (FEH, 1999, 3, p. 169) for the 100 yr quantile. It was found that dij could be effectively defined in terms of catchment area, mean rainfall and baseflow index. The sampling distribution of L-CV (t2) in each pooling group and the 95% confidence limits about the pooled estimate of t2 are obtained by simulation. The t2 values of the selected group members are compared with these confidence limits both graphically and numerically. Of the 85 stations, only 1 station's pooling group members have all their t2 values within the confidence limits, while 7, 33 and 44 of them have 1, 2 or 3 or more, t2 values outside the confidence limits. The outcomes are also compared with the heterogeneity measures H1 and H2. The H1 values show an upward trend with the ranges of t2 values in the pooling group whereas the H2 values do not show any such dependency. A selection of 27 pooling groups, found to be heterogeneous, were further examined with the help of box-plots of catchment descriptor values and one particular case is considered in detail. Overall the results show that even with a carefully considered selection procedure, it is not certain that perfectly homogeneous pooling groups are identified. As a compromise it is recommended that a group containing more than 2 values of t2 outside the confidence limits should not be considered homogeneous.
Title: Examination of homogeneity of selected Irish pooling groups
Description:
Abstract.
In regional flood frequency estimation, a homogeneous pooling group of sites leads to a reduction in the error of quantile estimators which is the main aim of a regional flood frequency analysis.
Examination of the homogeneity of regions/pooling groups is usually based on a statistic that relates to the formulation of a frequency distribution model, e.
g.
the coefficient of variation (Wiltshire, 1986; Fill and Stedinger, 1995) and/or skew coefficient, their L-moment equivalents (Chowdhury et al.
, 1991; Hosking and Wallis, 1997) or of dimensionless quantiles such as the 10-yr event (Dalrymple, 1960; Lu and Stedinger, 1992).
Hosking andWallis (1993, 1997) proposed homogeneity tests based on L-moment ratios such as L-CV alone (H1) and L-CV & L-skewness jointly (H2) which were also recently investigated by Viglione et al.
(2007).
In this paper a study, based on annual maximum series obtained from 85 Irish gauging stations, examines how successful a common method of identifying pooling group membership is in selecting groups that actually are homogeneous.
Each station has its own unique pooling group selected by use of a Euclidean distance measure in catchment descriptor space, commonly denoted dij and with a minimum of 500 station years of data in the pooling group, which satisfies the 5T rule (FEH, 1999, 3, p.
169) for the 100 yr quantile.
It was found that dij could be effectively defined in terms of catchment area, mean rainfall and baseflow index.
The sampling distribution of L-CV (t2) in each pooling group and the 95% confidence limits about the pooled estimate of t2 are obtained by simulation.
The t2 values of the selected group members are compared with these confidence limits both graphically and numerically.
Of the 85 stations, only 1 station's pooling group members have all their t2 values within the confidence limits, while 7, 33 and 44 of them have 1, 2 or 3 or more, t2 values outside the confidence limits.
The outcomes are also compared with the heterogeneity measures H1 and H2.
The H1 values show an upward trend with the ranges of t2 values in the pooling group whereas the H2 values do not show any such dependency.
A selection of 27 pooling groups, found to be heterogeneous, were further examined with the help of box-plots of catchment descriptor values and one particular case is considered in detail.
Overall the results show that even with a carefully considered selection procedure, it is not certain that perfectly homogeneous pooling groups are identified.
As a compromise it is recommended that a group containing more than 2 values of t2 outside the confidence limits should not be considered homogeneous.
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