A standardized rainfall extremity index for equitable flash-flood warning in South Korea

Abstract. Conventional Intensity–Duration–Frequency (IDF) curves quantify rainfall depth at fixed durations. We develop their event-based dual—the Modified Inter-Amount Time (M-IAT), the duration for cumulative precipitation within an event to reach a critical depth—and derive a Standardized Torrential Rainfall Index (STRI) by mapping M-IAT to a normal-quantile scale through extreme-value theory. Hourly precipitation from 65 Automated Synoptic Observing System (ASOS) stations in South Korea (1990–2024) is analysed under stationary and non-stationary Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) models, with temporal dependence removed by a Ferro–Segers-verified cluster-minimum construction. Both shape parameters concentrate in the bounded reverse-Weibull domain (ξ^ˆ < 0); with the GEV shape Winsorized at the regularity boundary ξ^ˆ = −1, the GEV and GPD shapes agree closely (median |Δξ^ˆ| = 0.18). The magnitude of M-IAT extremes is largely stationary—trends survive at only 3.1 % (GEV) and 5.6 % (GPD) of combinations, and only one GEV combination after multiplicity correction—whereas exceedance frequency trends positive at all nine critical values. This signal is not significant in the 35-year record but becomes significant across all critical values when extended to 1975–2024: intensification here manifests as more frequent, not larger, fast-accumulation events. Against precipitation-independent impact records from the national disaster yearbook, the event-level peak STRI is significantly rank-correlated with casualties (Spearman ρ = 0.56) and property losses (ρ = 0.46) over 27 events. STRI is proposed not as a hindsight competitor to precipitation totals but as a station-standardised diagnostic: its normal-quantile scale renders one threshold comparable across differing climatologies, and M-IAT is monitorable prospectively as rainfall accumulates. Equity here denotes between-station consistency of detection, not social or demographic fairness: a warning rule is equitable if, at a fixed alarm budget, its probability of capturing a damage day is independent of station wetness. At a matched damage-capture rate (recall = 0.60), recall under an absolute-depth threshold rises with wetness (Spearman ρ = +0.32, p = 0.009; the national advisory depth was met on only 53.9 % of damage station–days); under a fixed STRI threshold the dependence vanishes (ρ = 0.00, p = 0.99) and the between-station spread of recall narrows from 0.18 to 0.13. Operational use requires local threshold calibration and a prospective, nowcasting-based demonstration of skill.