Which theoretical distribution function best fits measured within day rainfall distributions across Australia?

Abstract

Rainfall data at high temporal resolutions is required to accurately model the dynamics of surface runoff processes, in particular sediment entrainment. These processes respond to rainfall intensity variations over short intervals, yet measurement of rainfall intensity at sufficient resolution is available only at a limited number of locations across Australia. On the other hand there is good coverage of rainfall data registered at a daily time step, thus it is desirable to establish a means to estimate within-day distributions of rainfall intensity given the daily rainfall depth and other readily available hydrometeorological data (e.g. temperature, pressure). As a first step towards such a method, an investigation was conducted into the shape of the temporal distribution of high-resolution (6 minute) rainfall intensity within the wet part of rainy days (total rainfall depth > 10mm). This paper quantifies the skill of nine different theoretical distribution functions (TDFs) in fitting characteristics of measured rainfall that are most likely to drive sediment entrainment and transport on hillslopes. Skill is reported by two goodness-of-fit statistics: the Root Mean Square Error (RMSE) between the fitted and observed within-day distribution; and the efficiency of prediction of the 30 minutes of highest rainfall intensity (average intensity of the 5 highest intensity intervals). Four TDFs provided relatively poor fits to higher intensity rainfall (two and three parameter lognormal, two parameter Generalized Pareto and Gumbel), and also showed higher RMSE values. The remaining five TDFs performed equally well for both goodness-of-fit measures. Two of these TDFs are extreme value distributions (Generalized Extreme Value and Weibull) and in a strict statistical sense should not be applied to within-day rainfall intensity data. On this basis, the remaining three TDFs (gamma, exponential and the three parameter Generalized Pareto) were selected as suitable candidates to represent within-day rainfall distributions in Australia, in particular for hydrological models seeking to estimate runoff and erosion.