Using the 4-parameter Kappa distribution to model extreme rainfall

Rainfall frequency analysis is routinely required for hydrological applications such as in the derivation of intensity-duration-frequency (IDF) curves for engineering design and planning. Commonly the Generalized Extreme Value (GEV) is used for rainfall frequency analysis, but it encounters limitations in capturing rare events which have heavy tailed distributions. An alternative is to use the four-parameter Kappa distribution which is a generalization of commonly used three-parameter extreme value distributions. Here, the applicability of the four‐parameter Kappa distribution for modelling extreme daily rainfalls using a global data set of annual rainfall maxima is presented.

The second shape parameter (h) of the four‐parameter Kappa distribution was found to vary regionally. Consistent with theoretical expectations, the second shape parameter converged toward zero (i.e., toward the limiting GEV distribution) as the average number of rain days events per year increased. However, in arid regions h was greater than zero suggesting there is merit in using the four‐parameter Kappa distribution for modelling heavy tail behaviour, particularly in regions which experience a small number of rainfall events per year. Information on the uncertainty in h as a function of the number of wet days per year is provided to facilitate Bayesian inference for at-site analyses.

As the four‐parameter Kappa distribution can be difficult to estimate, parameter estimation can be improved by using a two-step fitting approach based on maximum likelihood estimation which separately models storm intensity and the arrival frequency. Leveraging additional information from a peak-over-threshold series in the fitting improves quantile estimation and reduces uncertainty compared to fitting using annual maxima. These results demonstrate that the four‐parameter Kappa distribution is suitable for both at-site and regional rainfall frequency analyses.