Global Applicability of the Kappa Distribution for Rainfall Frequency Analysis

Abstract

Extreme rainfall events have profound implications across various sectors, necessitating accurate modeling to assess risks and devise effective adaptation strategies. The common practice of employing three-parameter probability distributions, such as the Generalized Extreme Value (GEV) and Pearson Type III distributions, in rainfall frequency analysis often encounters limitations in capturing rare, heavy-tailed events with a lack of consensus as to which distribution is the most applicable. In this study, we explore the applicability of the four-parameter Kappa distribution (K4D) for modeling extreme daily rainfalls using annual maxima from the Global Historical Climatology Network-Daily database. Quality checks and thresholds were used to remove erroneous and poor-quality data, retaining 20,500 stations with 50 or more years of data. The variation in the second shape parameter ($h$) was examined across regime characteristics, geospatial regions, and climate regional groupings to identify where the K4D is best able to model extreme rainfalls. Consistent with theoretical expectations, $h$ converges toward zero (i.e., toward the limiting GEV distribution) as the average number of rainfall events per year increases (here approximated by rain days). However, in arid regions with a limited number of annual storm events, we observe average values of $h$ greater than zero, with a strong regional and climatic coherence in $h$. Our results suggest that there is merit in using the K4D for modeling heavy tail behavior, particularly in regions with a small number of events per year. These findings will contribute to advancing statistical modeling techniques for extreme rainfall, benefiting hydrological modeling and risk assessments.