Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. I. A re-visit to regional homogeneity

As part I of a sequence of two papers, previously developed L-moments by Hosking (J R Stat Soc Ser B Methodol 52(2):105-124, 1990), and the LH-moments by Wang (Water Resour Res 33(12):2841-2848, 1997) are re-visited. New relationships are developed for regional homogeneity analysis by the LH-moments, and further establishment of regional homogeneity is investigated. Previous works of Hosking (J R Stat Soc Ser B Methodol 52(2):105-124, 1990) and Wang (Water Resour Res 33(12):2841-2848, 1997) on L-moments and LH-moments for the generalized extreme value (GEV) distribution are extended to the generalized Pareto (GPA) and the generalized logistic (GLO) distributions. The Karkhe watershed, located in western Iran is used as a case study area. Regional homogeneity was investigated by first assuming the entire study area as one regional cluster. Then the entire study area was designated "homogeneous" by the L-moments (L); and was designated "heterogeneous" by all four levels of the LH-moments (L-1 to L-4). The k-means method was used to investigate the case of two regional clusters. All levels of the L- and LH-moments designated the upper watershed (region A), "homogeneous", and the lower watershed (region B) "possibly-homogeneous". The L-3 level of the GPA and the L-4 level of the GLO were selected for regions A and B, respectively. Wang (Water Resour Res 33(12):2841-2848, 1997) identified a reversing trend in improved performance of the GEV distribution at the LH-moments level of L-3 (during the goodness-of-fit test). Similar results were also obtained in this research for the GEV distribution. However, for the case of the GPA distribution the reversing trend started at L-4 for region A; and at L-2 for region B. As for the case of the GLO, an improved performance was observed for all levels (moving from L to L-4); for both regions.