TL-Moment-Based Regional Frequency Analysis of Extreme Rainfall Using Ward's Clustering and Kappa-Type Distributions

Muhammad Nura¹ and Zahratul Amani Binti Zakaria^2,

¹Department of Statistics, Kano State Polytechnic, Kano, Nigeria

²Faculty of Computing and Informatics, Universiti Sultan Zainal Abidin, Kampus Besut, 22200 Besut, Terengganu, Malaysia

Cite this paper:
Muhammad Nura and Zahratul Amani Binti Zakaria. TL-Moment-Based Regional Frequency Analysis of Extreme Rainfall Using Ward's Clustering and Kappa-Type Distributions. American Journal of Water Resources. 2026; 14(2):46-54. doi: 10.12691/ajwr-14-2-3

Abstract

Peninsular Malaysia is highly flood-prone. Conventional L-moment regional frequency analysis (RFA) is sensitive to post-2013 extreme monsoon outliers at multiple stations across the peninsula. This study presents the first parallel TL-moment and L-moment RFA for the comprehensive 179-station DID network (1971–2023), simultaneously evaluating GEV, GLO, GPA, and K3D-II distributions across three climatologically distinct regions. Ward's minimum-variance hierarchical clustering was applied to TL-moment site characteristics, optimized by the average silhouette width (ASW) criterion. Discordancy, heterogeneity, goodness-of-fit (Z-test), and quantile estimation were executed in strict parallel under both estimation frameworks. Parametric bootstrap (B = 1,000 replicates) was applied to derive 90% confidence intervals for all regional quantiles. Three acceptably homogeneous regions were delineated: R1 (N = 55; west coast, mean = 115.0 mm), R2 (N = 94; interior, mean = 117.7 mm), and R3 (N = 30; east coast interior, mean = 200.9 mm). Under L-moments, GLO was best for R1 and R2; GPA was the sole passing distribution for R3. Under TL-moments, K3D-II was best for R2, GPA for R3. No standard distribution passed for R1 under TL-moments. TL-moment quantiles were 7–44% lower than L-moment estimates at T ≥ 10 years. Bootstrap 90% CI widths for T = 100 years were 0.076 (R1), 0.037 (R2), and 0.066 (R3) growth-factor units. L-moment and TL-moment quantiles should be used jointly as upper and lower design-rainfall bounds. For life-safety-critical structures, the L-moment estimate is the conservative upper bound.

Keywords:
regional frequency analysis TL-moments Ward's clustering design rainfall bootstrap confidence intervals monsoon extremes

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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